From d55368a524f4bd88a3026830c667f126b2a3301d Mon Sep 17 00:00:00 2001 From: Siddharth Date: Mon, 27 Jan 2025 19:07:52 +0000 Subject: [PATCH] feat: implement MBA blast algorithm (#977) We implement the MBA-blast theory on terms, which will allow us to decide mixed boolean arithmetic theorems. --- SSA/Experimental/Bits/Fast.lean | 3 +- SSA/Experimental/Bits/Fast/Attr.lean | 3 + SSA/Experimental/Bits/Fast/Dataset2/runner.py | 5 +- SSA/Experimental/Bits/Fast/MBA.lean | 942 ++ SSA/Experimental/Bits/Fast/dataset2.lean | 10013 ++++++++-------- SSA/Projects/InstCombine/TacticAuto.lean | 4 +- 6 files changed, 5957 insertions(+), 5013 deletions(-) create mode 100644 SSA/Experimental/Bits/Fast/MBA.lean diff --git a/SSA/Experimental/Bits/Fast.lean b/SSA/Experimental/Bits/Fast.lean index 16ab0cd7c..c3102e1e8 100644 --- a/SSA/Experimental/Bits/Fast.lean +++ b/SSA/Experimental/Bits/Fast.lean @@ -1,4 +1,5 @@ -import SSA.Experimental.Bits.Fast.Reflect +import SSA.Experimental.Bits.Fast.MBA import SSA.Experimental.Bits.Fast.Profile +import SSA.Experimental.Bits.Fast.Reflect import SSA.Experimental.Bits.Fast.Tests diff --git a/SSA/Experimental/Bits/Fast/Attr.lean b/SSA/Experimental/Bits/Fast/Attr.lean index 64b65ae84..1547a656f 100644 --- a/SSA/Experimental/Bits/Fast/Attr.lean +++ b/SSA/Experimental/Bits/Fast/Attr.lean @@ -11,5 +11,8 @@ import Lean /-- Preprocessing steps for bv_automata_circuit. -/ register_simp_attr bv_circuit_preprocess +/-- Preprocessing steps for bv_mba tactic. -/ +register_simp_attr bv_mba_preprocess + /-- Preprocessing steps for bv_automata_circuit. -/ register_simp_attr bv_circuit_nnf diff --git a/SSA/Experimental/Bits/Fast/Dataset2/runner.py b/SSA/Experimental/Bits/Fast/Dataset2/runner.py index 17093b003..640ac6bb7 100755 --- a/SSA/Experimental/Bits/Fast/Dataset2/runner.py +++ b/SSA/Experimental/Bits/Fast/Dataset2/runner.py @@ -119,7 +119,7 @@ def get_git_root(): def test_file_preamble(): return """ import Std.Tactic.BVDecide -import SSA.Experimental.Bits.Fast.Reflect +import SSA.Experimental.Bits.Fast.MBA set_option maxHeartbeats 0 @@ -131,6 +131,7 @@ def test_file_preamble(): variable { a b c d e f g t x y z : BitVec w } """ + def translate_dataset_expr_to_lean(counter, expression): exp = f"theorem e_{counter} :\n " expression = expression.replace(",True", "") @@ -143,7 +144,7 @@ def translate_dataset_expr_to_lean(counter, expression): expression = expression.replace("&", " &&& ") expression = expression.replace("~", " ~~~") - exp = exp + expression + " := by\n bv_automata_circuit (config := { backend := .cadical })\n" + exp = exp + expression + " := by bv_mba" return exp diff --git a/SSA/Experimental/Bits/Fast/MBA.lean b/SSA/Experimental/Bits/Fast/MBA.lean new file mode 100644 index 000000000..6d69e89fd --- /dev/null +++ b/SSA/Experimental/Bits/Fast/MBA.lean @@ -0,0 +1,942 @@ +import SSA.Experimental.Bits.Fast.Attr +import Lean +import Lean.ToExpr + +@[simp] +theorem BitVec.zero_concat (b : Bool) : (0#0).concat b = BitVec.ofBool b := by + apply BitVec.eq_of_getLsbD_eq + simp + +@[simp] +theorem BitVec.intCast_eq_ofInt : ((i : Int) : BitVec w) = BitVec.ofInt w i := rfl + +@[simp] +theorem BitVec.intCast_zero : ((0 : Int) : BitVec w) = 0#w := by simp + +namespace MBA + +inductive Factor +| var (n : Nat) +| and (x y : Factor) +| or (x y : Factor) +| xor (x y : Factor) +| not (x : Factor) +deriving Repr + +def Factor.numVars : Factor → Nat +| .var n => n+1 +| .and x y | .or x y | xor x y => max (x.numVars) (y.numVars) +| .not x => x.numVars + +open Lean Elab Meta in +def Factor.toExpr (f : Factor) : Expr := + match f with + | .var i => mkApp (mkConst ``Factor.var) (mkNatLit i) + | .xor i j => mkApp2 (mkConst ``Factor.xor) i.toExpr j.toExpr + | .and i j => mkApp2 (mkConst ``Factor.and) i.toExpr j.toExpr + | .or i j => mkApp2 (mkConst ``Factor.or) i.toExpr j.toExpr + | .not x => mkApp (mkConst ``Factor.not) x.toExpr + +open Lean in +instance : ToExpr Factor where + toExpr := Factor.toExpr + toTypeExpr := mkConst ``Factor + + +@[simp] +theorem Factor.numVars_term : (Factor.var n).numVars = n + 1 := rfl + +abbrev Env (w : Nat) := List (BitVec w) +def Env.getLsb {w : Nat} (env : Env (w + 1)) : Env 1 := env.map <| fun x => BitVec.ofBool <| x.getLsbD 0 +def Env.getNonLsbs {w : Nat} (env : Env (w + 1)) : Env w := env.map <| fun x => x.extractLsb' 1 w + +@[simp] +theorem Env.getLsb_getElem {env : Env (w + 1)} (n : Nat) : + (Env.getLsb env)[n]? = (env[n]?).map (fun (x : BitVec (w + 1)) => BitVec.ofBool (x.getLsbD 0)) := by + simp [Env.getLsb] + +def Factor.reflect {w : Nat} (xs : Env w) : Factor → BitVec w +| .var n => xs[n]?.getD (0#w) +| .and x y => x.reflect xs &&& y.reflect xs +| .or x y => x.reflect xs ||| y.reflect xs +| .xor x y => x.reflect xs ^^^ y.reflect xs +| .not x => ~~~ (x.reflect xs) + +def Factor.denote {w : Nat} (xs : Env w) (f : Factor) : Nat := f.reflect xs |>.toNat + + +theorem Factor.denote_eq_toNat_reflect {w : Nat} (xs : Env w) (f : Factor) : + f.denote xs = (f.reflect xs |>.toNat) := rfl + +/-- +Environment of *finite* size, which can agree with the `Factor.reflect`. +We need `Factor.reflectFin` to show that our brute-force evaluation for length 1 has a finite environment size for exhaustive enumeration, +We need `Factor.reflect` to def-eq-unify with the user's given goal state. +We show their equivalence to allow us to decide on `denoteFin`, and to use this when proving facts about `denote`. +-/ +def EnvFin (w : Nat) (n : Nat) := Fin n → (BitVec w) +def EnvFin.getLsb {w : Nat} (env : EnvFin (w + 1) n) : EnvFin 1 n := fun n => BitVec.ofBool <| (env n).getLsbD 0 +def EnvFin.getNonLsbs {w : Nat} (env : EnvFin (w + 1) n) : EnvFin w n := fun n => (env n).extractLsb' 1 w + +/-- Using 'env.getLsb' shortens all bitvectors to be one-bit, and so calling 'getLsbD' on this environment will only return the lowest bit if available -/ +@[simp] +theorem EnvFin.getLsbD_getLsb {w : Nat} (env : EnvFin (w + 1) n) (bit : Nat) : (env.getLsb i).getLsbD bit = + if bit = 0 then (env i).getLsbD 0 else false := by + rcases bit with rfl | bit + · simp [EnvFin.getLsb] + · simp + +def EnvFin.castLe {w n n' : Nat} (env : EnvFin w n) (h : n' ≤ n) : EnvFin w n' := + fun i' => env ⟨i', by omega⟩ + +@[simp] +def EnvFin.get_castLe {w n n' : Nat} (env : EnvFin w n) (h : n' ≤ n) (i : Fin n') : + (env.castLe h) i = env ⟨i, by omega⟩ := rfl + +/-- Map a function from `Fin n'` to `Fin n` on the index set of `EnvFin`. -/ +def EnvFin.comap {w n n' : Nat} (env : EnvFin w n) (f : Fin n' → Fin n) : EnvFin w n' := + fun i' => env (f i') + +@[simp] +theorem EnvFin.get_comap (env : EnvFin w n) (f : Fin n' → Fin n) (i : Fin n') : + (env.comap f) i = env (f i) := rfl + +/-- +Cons a value 'b' onto the env, which obeys the equations: +- `(cons env b) 0 = b`, +- `(cons env b) i.succ = env i` +-/ +def EnvFin.cons (env : EnvFin w n) (b : BitVec w) : EnvFin w (n + 1) := + fun i => i.cases b env + +@[simp] +theorem EnvFin.cons_zero (env : EnvFin w n) (b : BitVec w) : + (env.cons b) 0 = b := rfl + +-- TODO: write theorems about `cons`. +@[simp] +theorem EnvFin.cons_succ (env : EnvFin w n) (b : BitVec w) (i : Fin n) : + (env.cons b) i.succ = env i := rfl + +/-- +Using 'env.getNonLsbs' peels off the bits from index 'i+1' to 'w'. +-/ +@[simp] +theorem EnvFin.getLsbD_getNonLsbs {w : Nat} (env : EnvFin (w + 1) n) (bit : Nat) : + (env.getNonLsbs i).getLsbD bit = (decide (bit < w) && (env i).getLsbD (bit + 1)) := by + simp [EnvFin.getNonLsbs] + by_cases h : bit < w + · simp [h, show 1 + bit = bit + 1 by omega] + · simp [h] + +def Factor.reflectFin {w : Nat} (f : Factor) (xs : EnvFin w f.numVars) : BitVec w := + match f with + | .var n => xs ⟨n, by simp⟩ + | .and x y => + x.reflectFin (fun n => xs ⟨n, by simp [numVars]; omega⟩) &&& y.reflectFin (fun n => xs ⟨n, by simp [numVars]; omega⟩) + | .or x y => + x.reflectFin (fun n => xs ⟨n, by simp [numVars]; omega⟩) ||| y.reflectFin (fun n => xs ⟨n, by simp [numVars]; omega⟩) + | .xor x y => + x.reflectFin (fun n => xs ⟨n, by simp [numVars]; omega⟩) ^^^ y.reflectFin (fun n => xs ⟨n, by simp [numVars]; omega⟩) + | .not x => + ~~~ x.reflectFin (fun n => xs ⟨n, by simp [numVars]⟩) + + +/-- Show that reflect and reflectFin agree in their values -/ +theorem Factor.reflect_eq_reflectFin {f : Factor} {xs : List (BitVec w)} {xsFin : EnvFin w f.numVars} + (h : ∀ (i : Fin f.numVars), xs[i]?.getD 0#w = xsFin i) : + f.reflect xs = f.reflectFin xsFin := by + induction f + case var n => simp [reflect, reflectFin] at h ⊢; rw[← h] + case and x y hx hy => + simp [reflect, reflectFin] at h ⊢ + rw[← hx, ← hy] + · intros i + simp [← h] + · intros i + simp [← h] + case or x y hx hy => + simp [reflect, reflectFin] at h ⊢ + rw[← hx, ← hy] + · intros i + simp [← h] + · intros i + simp [← h] + case xor x y hx hy => + simp [reflect, reflectFin] at h ⊢ + rw[← hx, ← hy] + · intros i + simp [← h] + · intros i + simp [← h] + case not x hx => + simp [reflect, reflectFin] at h ⊢ + rw[← hx] + · intros i + simp [← h] + +def Factor.denoteFin {w : Nat} (f : Factor) (xs : EnvFin w f.numVars) : Nat := f.reflectFin xs |>.toNat + +theorem Factor.denoteFin_eq_toNat_reflectFin (f : Factor) (xs : EnvFin w f.numVars) : + f.denoteFin xs = (f.reflectFin xs).toNat := rfl + +/-- Show that 'denote' agrees with 'denoteFin' -/ +theorem Factor.denoteFin_eq_denote {f : Factor} {xs : List (BitVec w)} {xsFin : EnvFin w f.numVars} + (h : ∀ (i : Fin f.numVars), xs[i]?.getD 0#w = xsFin i) : + f.denoteFin xsFin = f.denote xs := by + rw [Factor.denote, Factor.denoteFin, Factor.reflect_eq_reflectFin h] + +theorem Factor.reflect_eq_ofInt_denote {w : Nat} (xs : Env w) (f : Factor) : + f.reflect xs = (BitVec.ofInt w <| f.denote xs) := by + simp [reflect, denote] + +@[simp] +theorem Factor.reflect_zero_of_denote_zero {w : Nat} {f : Factor} {xs : Env w} (h : f.denote xs = 0) : + f.reflect xs = 0#w := by + simp [reflect_eq_ofInt_denote, h] + +@[simp] +theorem Factor.reflect_width_zero (f : Factor) (env : Env 0) : f.reflect env = 0#0 := by + apply Subsingleton.elim + +@[simp] +theorem Factor.denote_width_zero (f : Factor) (env : Env 0) : f.denote env = 0 := by + simp [denote] + +@[simp] +theorem Factor.reflectFin_width_zero (f : Factor) (env : EnvFin 0 f.numVars) : f.reflectFin env = 0#0 := by + apply Subsingleton.elim + +/-- +The value of 'x.reflectFin env' can be computed from using +'(x.reflectFin env.getlsb)' and '(x.reflectFin env.getNonLsbs)'. +-/ +theorem Factor.getLsb_reflectFin_eq_or_reflectFin_getLsb_reflectFin_getNonLsbs + {w : Nat} {x : Factor} {env : EnvFin (w +1) x.numVars} : + (x.reflectFin env).getLsbD i = if i = 0 then ((x.reflectFin env.getLsb).getLsbD 0) else (x.reflectFin env.getNonLsbs).getLsbD (i - 1) := by + rcases i with rfl | i + · simp + induction x + case var n => + simp [reflectFin] + case and x y hx hy => + simp [reflectFin] + simp [hx, hy] + rfl + case or x y hx hy => + simp [reflectFin] + simp [hx, hy] + rfl + case xor x y hx hy => + simp only [reflectFin, BitVec.getLsbD_xor] + simp only [hx, hy] + rfl + case not x hx => + simp only [reflectFin, BitVec.getLsbD_not] + simp [hx] + · simp + induction x + case var n => + simp [reflectFin] + intros h + apply Classical.byContradiction + intros hcontra + simp at hcontra + have := BitVec.getLsbD_ge (env ⟨n, by simp⟩) (i + 1) (by omega) + simp [this] at h + case and x y hx hy => + simp [reflectFin] + simp [hx, hy] + rfl + case or x y hx hy => + simp [reflectFin] + simp [hx, hy] + rfl + case xor x y hx hy => + simp only [reflectFin, BitVec.getLsbD_xor] + simp only [hx, hy] + rfl + case not x hx => + simp only [reflectFin, BitVec.getLsbD_not] + simp [hx] + +theorem Factor.reflectFin_eq_reflectFin_getLsb_reflectFin_getNonLsbs + {w : Nat} {x : Factor} {env : EnvFin (w +1) x.numVars} : + (x.reflectFin env) = (x.reflectFin env.getNonLsbs).concat ((x.reflectFin env.getLsb).getLsbD 0) := by + apply BitVec.eq_of_getLsbD_eq + intros i hi + conv => + lhs + rw [getLsb_reflectFin_eq_or_reflectFin_getLsb_reflectFin_getNonLsbs] + rw [BitVec.getLsbD_concat] + + +/-- Build an 'EnvFin' from 'Env' -/ +def EnvFin.ofEnv (env : Env w) (n : Nat) : EnvFin w n := + fun i => env.getD i 0#w + +/-- Build an Env from an 'EnvFin' -/ +def Env.ofEnvFin (envFin : EnvFin w n) : Env w := (List.finRange n).map envFin + +@[simp] +theorem Env.length_ofEnvFin (envFin : EnvFin w n) : + List.length (Env.ofEnvFin envFin) = n := by simp [ofEnvFin] + +@[simp] +def EnvFin.get_ofEnv (env : Env w) (n : Nat) (i : Fin n) : (EnvFin.ofEnv env n) i = env.getD i 0#w := rfl + +@[simp] +def Env.get_ofEnvFin (envFin : EnvFin w n) (i : Fin n) : + (Env.ofEnvFin envFin)[i] = envFin i := by simp [ofEnvFin] + +@[simp] +def Env.getElem_ofEnvFin (envFin : EnvFin w n) (i : Nat) (h : i < n) : + (Env.ofEnvFin envFin)[i]'(by simp [Env.length_ofEnvFin, h]) = envFin ⟨i, by omega⟩ := + by simp [ofEnvFin] + + +@[simp] +def Env.getD_getElem?_ofEnvFin (envFin : EnvFin w n) (i : Nat) : + (Env.ofEnvFin envFin)[i]?.getD (0#w) = if h : i < n then envFin ⟨i, h⟩ else 0#w := by + rw [List.getD_getElem?] + by_cases h : i < n <;> simp [h] + +theorem Factor.denote_eq_toNat_reflectFin {w : Nat} (xs : Env w) (f : Factor) : + f.denote xs = (f.reflectFin (EnvFin.ofEnv xs _)).toNat := by + rw [Factor.denote_eq_toNat_reflect] + rw [reflect_eq_reflectFin] + simp + +theorem Factor.reflectFin_toNat_eq_add + {w : Nat} {x : Factor} {env : EnvFin (w +1) x.numVars} : + (x.reflectFin env).toNat = 2 * (x.reflectFin env.getNonLsbs).toNat + ((x.reflectFin env.getLsb).getLsbD 0).toNat := by + rw [Factor.reflectFin_eq_reflectFin_getLsb_reflectFin_getNonLsbs] + simp + rw [Nat.mul_comm] + + +/-- Split a denote at an env intoa denote at the LSB and the denote at the non-Lsbs -/ +theorem Factor.denoteFin_eq_add {w : Nat} (x : Factor) (env : EnvFin (w + 1) x.numVars) : + x.denoteFin env = 2 * x.denoteFin env.getNonLsbs + x.denoteFin env.getLsb := by + rw [Factor.denoteFin_eq_toNat_reflectFin] + rw [Factor.denoteFin_eq_toNat_reflectFin] + rw [Factor.denoteFin_eq_toNat_reflectFin] + rw [Factor.reflectFin_toNat_eq_add] + simp + generalize (x.reflectFin env.getLsb) = bv + revert bv + decide + + +structure Term where + c : Int + f : Factor +deriving Repr + +open Lean Elab Meta in +def Term.toExpr (t : Term) : Expr := + mkApp2 (mkConst ``Term.mk) (ToExpr.toExpr t.c) (t.f.toExpr) + +open Lean in +instance : ToExpr Term where + toExpr := Term.toExpr + toTypeExpr := mkConst ``Term + +def Term.numVars (t : Term) : Nat := t.f.numVars + +/-- Reflect is what we use for reflection -/ +def Term.reflect {w : Nat} (t : Term) (xs: Env w) : BitVec w := + (BitVec.ofInt w t.c) * t.f.reflect xs + +def Term.denote {w : Nat} (t : Term) (xs : Env w) : Int := + t.c * t.f.denote xs + +def Term.denoteFin {w : Nat} (t : Term) (xs : EnvFin w t.numVars) : Int := + t.c * t.f.denoteFin xs + +/-- Split a denote at an env intoa denote at the LSB and the denote at the non-Lsbs -/ +theorem Term.denoteFin_eq_add {w : Nat} (t : Term) (env : EnvFin (w + 1) t.numVars) : + t.denoteFin env = 2 * t.denoteFin env.getNonLsbs + t.denoteFin env.getLsb := by + rw [Term.denoteFin] + rw [Factor.denoteFin_eq_add] + rw [Term.denoteFin] + rw [Term.denoteFin] + simp only [Int.natCast_add, Int.natCast_mul, Int.Nat.cast_ofNat_Int] + rw [Int.mul_add] + ac_nf + +theorem Term.denoteFin_eq_denote {t : Term} {xs : List (BitVec w)} {xsFin : EnvFin w t.numVars} (h : ∀ (i : Fin t.numVars), xs[i]?.getD 0#w = xsFin i) : + t.denoteFin xsFin = t.denote xs := by + simp [Term.denoteFin, Term.denote, Factor.denoteFin_eq_denote h] + +@[simp] +theorem Term.reflect_eq_ofInt_denote {w : Nat} {t : Term} {xs : Env w} : + t.reflect xs = (BitVec.ofInt w <| t.denote xs) := by + obtain ⟨c, f⟩ := t + simp [Term.reflect, Term.denote] + rw [BitVec.ofInt_mul] + rw [Factor.reflect_eq_ofInt_denote] + +@[simp] +theorem Term.reflect_zero_of_denote_zero {w : Nat} {t : Term} {xs : Env w} (h : t.denote xs = 0) : + t.reflect xs = 0#w := by + simp [Term.reflect_eq_ofInt_denote, h] + +@[simp] +theorem Term.reflect_width_zero (t : Term) (env : Env 0) : + t.reflect env = 0 := by simp [Term.reflect] + +@[simp] +theorem Term.denote_width_zero (t : Term) (env : Env 0) : + t.denote env = 0 := by simp [Term.denote] + +@[simp] +theorem Term.denoteFin_width_zero (t : Term) (env : EnvFin 0 t.numVars) : + t.denoteFin env = 0 := by simp [Term.denoteFin, Factor.denoteFin] + +def Eqn := List Term + +instance : Repr Eqn := inferInstanceAs (Repr (List Term)) + +open Lean in +def Eqn.toExpr (e : Eqn) : Expr := ToExpr.toExpr (α := List Term) e + +open Lean in +instance : ToExpr Eqn where + toExpr := Eqn.toExpr + toTypeExpr := mkConst ``Eqn + +open Lean in +instance : ToExpr Term where + toExpr := Term.toExpr + toTypeExpr := mkConst ``Term + +def Eqn.numVars (e : Eqn) : Nat := + match e with + | [] => 0 + | e :: es => max e.numVars (Eqn.numVars es) + +@[simp] +theorem Eqn.numVars_nil : Eqn.numVars [] = 0 := rfl + +@[simp] +theorem Eqn.numVars_cons : Eqn.numVars (t :: es) = max t.numVars (Eqn.numVars es) := rfl + +def Eqn.reflect {w : Nat} (e : Eqn) (env : Env w) : BitVec w := + match e with + | [] => 0 + | t :: [] => t.reflect env + | t :: ts => t.reflect env + Eqn.reflect ts env + + +@[simp] +theorem Eqn.reflect_nil {w : Nat} (env : Env w) : + Eqn.reflect [] env = 0 := rfl + +@[simp] +theorem Eqn.reflect_cons {w : Nat} + (t : Term) (ts : List Term) (env : Env w) : + Eqn.reflect (t :: ts) env = t.reflect env + Eqn.reflect ts env := by + rcases ts with t | ts + simp [reflect] + simp [reflect] + + +def Eqn.denote {w : Nat} (e : Eqn) (env : Env w) : Int := + match e with + | [] => 0 + | t :: ts => t.denote env + Eqn.denote ts env + +@[simp] +theorem Eqn.denote_nil {w : Nat} (env : Env w) : + Eqn.denote [] env = 0 := rfl + +@[simp] +theorem Eqn.denote_cons {w : Nat} + (t : Term) (ts : List Term) (env : Env w) : + Eqn.denote (t :: ts) env = t.denote env + Eqn.denote ts env := rfl + +def Eqn.denoteFin {w : Nat} (e : Eqn) (envFin : EnvFin w e.numVars) : Int := + match e with + | [] => 0 + | t :: ts => + t.denoteFin (envFin.castLe (by simp; omega)) + + Eqn.denoteFin ts (envFin.castLe (by simp; omega)) + +@[simp] +theorem Eqn.denoteFin_nil {w : Nat} (envFin : EnvFin w 0) : + Eqn.denoteFin [] envFin = 0 := rfl + +@[simp] +theorem Eqn.denoteFin_cons {w : Nat} (t : Term) (eqn : Eqn) + (envFin : EnvFin w (max t.numVars eqn.numVars)) : + Eqn.denoteFin (t :: eqn) envFin = + t.denoteFin (envFin.castLe (by omega)) + + Eqn.denoteFin eqn (envFin.castLe (by omega)) := rfl + +theorem Eqn.denoteFin_eq_add {w : Nat} (eqn : Eqn) (env : EnvFin (w + 1) eqn.numVars) : + eqn.denoteFin env = 2 * eqn.denoteFin env.getNonLsbs + eqn.denoteFin env.getLsb := by + induction eqn + case nil => simp [denoteFin] + case cons x xs ih => + simp only [denoteFin] + simp only [ih] + rw [Term.denoteFin_eq_add x] + rw [Int.mul_add] + ac_nf + +/-- To evaluate `e.denote`, one can equally well evaluate `e.denoteFin` -/ +theorem Eqn.denoteFin_eq_denote {e : Eqn} {xs : List (BitVec w)} {xsFin : EnvFin w e.numVars} + (h : ∀ (i : Fin e.numVars), xs[i]?.getD 0#w = xsFin i) : + e.denoteFin xsFin = e.denote xs := by + induction e + case nil => simp [Eqn.denoteFin] + case cons t es ih => + simp + rw [ih] + · congr + apply Term.denoteFin_eq_denote + intros i + specialize h ⟨i, by simp; omega⟩ + assumption + · intros i + specialize h ⟨i, by simp; omega⟩ + assumption + +@[simp] +theorem Eqn.reflect_width_zero (es : Eqn) (env : Env 0) : + Eqn.reflect es env = 0 := by + induction es + case nil => simp [Eqn.reflect] + case cons e es ih => + simp [ih, Eqn.reflect] + + +@[simp] +theorem Eqn.denote_width_zero (es : Eqn) (env : Env 0) : + Eqn.denote es env = 0 := by + induction es + case nil => simp [Eqn.denote] + case cons e es ih => + simp [ih, Eqn.denote] + +@[simp] +theorem Eqn.denoteFin_width_zero (es : Eqn) (env : EnvFin 0 es.numVars) : + Eqn.denoteFin es env = 0 := by + induction es + case nil => simp [Eqn.denoteFin] + case cons e es ih => + simp [ih, Eqn.denoteFin] + +@[simp] +theorem Eqn.reflect_eq_ofInt_denote {w : Nat} (xs : Env w) (e : Eqn) : + e.reflect xs = BitVec.ofInt w (e.denote xs) := by + induction e + case nil => simp + case cons t ts ih => + simp + simp [BitVec.ofInt_add, ih] +@[simp] +theorem Eqn.reflect_zero_of_denote_zero {w : Nat} (xs : Env w) (e : Eqn) (h : e.denote xs = 0) : + e.reflect xs = 0 := by simp [h] + +@[simp] +def Env.getLsb_eq_of_width_one (env : List (BitVec 1)) : Env.getLsb env = env := by + simp [getLsb] + suffices heq : (fun x => BitVec.ofBool (x.getLsbD 0)) = id by simp [heq] + ext x i hi + have : i = 0 := by omega + simp [this] + + +theorem Eqn.denote_hard_case_aux {eqn : Eqn} + (h1 : ∀ (env1 : EnvFin 1 eqn.numVars), Eqn.denoteFin eqn env1 = 0) : + ∀ {w : Nat} (env : EnvFin w eqn.numVars), eqn.denoteFin env = 0 := by + intros w + induction w + case zero => simp + case succ w ih => + intros env + rw [Eqn.denoteFin_eq_add] + rw [h1] + simp + rw [ih] + simp + + +theorem Eqn.denote_hard_case_of_denote (e : Eqn) (h : ∀ (env1 : EnvFin 1 e.numVars), e.denoteFin env1 = 0) : + ∀ {w : Nat} (env : List (BitVec w)), e.reflect env = 0 := by + intros w env + rw [Eqn.reflect_eq_ofInt_denote] + rw [← Eqn.denoteFin_eq_denote (xsFin := EnvFin.ofEnv env e.numVars) (h := by simp)] + rw [Eqn.denote_hard_case_aux] + · simp + · intros env1 + apply h + +/- +theorem zero_of_ofInt_zero_of_lt (i : Int) (w : Nat) + (h : BitVec.ofInt w i = 0#w) (h' : i.natAbs < 2^w) : i = 0 := by + have : (BitVec.ofInt w i).toNat = (0#w).toNat := by rw [h] + simp at this + rw [Int.emod_def] at this + rw [Int.ediv_eq_of_eq_mul_left] at this + · simp at this + sorry +-/ + + +/-- +This theory should work: Just pick a large enough field where showing that the value is zero +will prove that the value is zero +theorem Eqn.denote_hard_case_of_denote_mpr (e : Eqn) + (h : ∀ (w : Nat) (env : List (BitVec w)), e.reflect env = 0) : + ∀ (env1 : EnvFin 1 e.numVars), e.denoteFin env1 = 0 := by + intros env1 + let size := (e.denoteFin env1).natAbs.log2 + 1 + specialize h size + let env' := List.finRange e.numVars |>.map fun x => (env1 x).signExtend size + specialize h env' + simp [env'] at h + sorry +-/ + + +/- +instance decEqnDenoteFinWidth1 {e : Eqn} : Decidable (∀ env1 : Env (BitVec 1), Eqn.denoteFin e env1 = 0) := + sorry + +instance {e : Eqn} : Decidable (∀ env1 : List (BitVec 1), Eqn.denote e env1 = 0) := + sorry +-/ + +def Eqn.reflectEqZero (w : Nat) (eqn : Eqn) (env : Env w) : Prop := + Eqn.reflect eqn env = BitVec.ofInt w 0 + +/-- +Central theorem: To decide if a bitvector equation is zero for all widths, it sufficest to check that the denotation is zero at width zero. +-/ +theorem Eqn.forall_width_reflect_zero_of_width_one_denote_zero (e : Eqn) (w : Nat) (env : List (BitVec w)) + (h : (∀ env1 : EnvFin 1 e.numVars, Eqn.denoteFin e env1 = 0)) : + Eqn.reflectEqZero w e env := by + rw [Eqn.reflectEqZero] + rw [Eqn.denote_hard_case_of_denote] + simp + apply h + +#check Eqn.forall_width_reflect_zero_of_width_one_denote_zero + +@[simp] +theorem EnvFin.eq_elim0 (envFin : EnvFin w 0) : envFin = fun i => i.elim0 := by + simp [EnvFin] at * + ext i + exact i.elim0 + +def EnvFin.getAll1 (n : Nat) : { envs : List (EnvFin 1 n) // ∀ (envFin : EnvFin 1 n), envFin ∈ envs } := + match hn : n with + | 0 => ⟨[fun i => i.elim0], by intros envFin; simp⟩ + | n' + 1 => + let ⟨envs, henvs⟩ := EnvFin.getAll1 n' + let out := envs.flatMap (fun env => [env.cons (BitVec.ofBool false), env.cons (BitVec.ofBool true)]) + ⟨out, by + intros envFin + simp [out] + let envFinSmaller := envFin.comap Fin.succ + specialize henvs envFinSmaller + exists envFinSmaller + simp only [henvs, true_and, out] + have hv : (envFin 0) = 0#1 ∨ (envFin 0) = 1#1 := by + generalize envFin 0 = a + revert a + decide + rcases hv with hv | hv + · left + funext i + cases i using Fin.cases + case zero => simp [hv] + case succ i' => + simp [envFinSmaller] + · right + funext i + cases i using Fin.cases + case zero => simp [hv] + case succ i' => + simp [envFinSmaller] + ⟩ + +/-- +Show how to exhaustively enumerate environments to check that the denotation at 1-bit is zero. +-/ +instance (e : Eqn) : Decidable (∀ env1 : EnvFin 1 e.numVars, Eqn.denoteFin e env1 = 0) := + let ⟨allEnvs, hAllEnvs⟩ := EnvFin.getAll1 e.numVars + let b := allEnvs.all (fun env1 => e.denoteFin env1 = 0) + match hb : b with + | true => .isTrue <| by + simp [b] at hb + intros env1 + apply hb + apply hAllEnvs + | false => .isFalse <| by + simp + simp [b] at hb + obtain ⟨env, henvMem, henvDenote⟩ := hb + exists env + + +namespace Tactic + +/-- Two bitvectors are equal iff their different is zero. -/ +theorem BitVec.eq_iff_sub_zero (x y : BitVec w) : x = y ↔ x - y = 0 := by + constructor + · intros h + simp [h] + · intros h + obtain h : (x - y) + y = y := by simp [h] + obtain h : (x + (-y)) + y = y := by simp [← BitVec.sub_toAdd, h] + obtain h : x + (-y + y) = y := by simp [← BitVec.add_assoc, h] + simp [BitVec.add_comm _ y, ← BitVec.sub_toAdd] at h + exact h + +theorem BitVec.eq_of_sub_zero {x y : BitVec w} (h : x - y = 0#w) : x = y := by + simp [BitVec.eq_iff_sub_zero, h] + +axiom BitVecUnprovenLemmas {p : Prop} : p + +@[bv_mba_preprocess] +theorem BitVec.sub_distrib_sub (x y z : BitVec w) : + x - (y - z) = x - y + z := by exact BitVecUnprovenLemmas + +@[bv_mba_preprocess] +theorem BitVec.sub_distrib_add (x y z : BitVec w) : + x - (y + z) = x - y - z := by exact BitVecUnprovenLemmas + +attribute [bv_mba_preprocess] BitVec.sub_toAdd + +@[bv_mba_preprocess] +theorem BitVec.ofNat_eq_ofInt (n w : Nat) : + BitVec.ofNat w n = BitVec.ofInt w n := by + apply BitVec.eq_of_toInt_eq + simp[BitVec.toInt_ofNat] + +attribute [bv_mba_preprocess] BitVec.ofNat_eq_ofNat + +@[bv_mba_preprocess] +theorem BitVec.neg_ofInt {w : Nat} (i : Int) : + - (BitVec.ofInt w i) = BitVec.ofInt w (-i) := by + exact BitVecUnprovenLemmas + +@[bv_mba_preprocess] +theorem BitVec.neg_add {x y : BitVec w} : - (x + y) = (-x) + (-y) := by + exact BitVecUnprovenLemmas + +@[bv_mba_preprocess] +theorem BitVec.neg_sub {x y : BitVec w} : - (x - y) = (-x) + y := by + exact BitVecUnprovenLemmas + +@[bv_mba_preprocess] +theorem BitVec.neg_mul_eq_neg_left_mul {w : Nat} (x y : BitVec w) : + - (x * y) = (- x) * y := by + exact BitVecUnprovenLemmas + +attribute [bv_mba_preprocess] Int.Nat.cast_ofNat_Int +attribute [bv_mba_preprocess] Int.reduceNeg +attribute [bv_mba_preprocess] Int.reduceAdd +attribute [bv_mba_preprocess] Int.zero_add +attribute [bv_mba_preprocess] BitVec.add_zero +attribute [bv_mba_preprocess] BitVec.zero_add +attribute [bv_mba_preprocess] Int.neg_eq_of_add_eq_zero + +@[bv_mba_preprocess] +theorem BitVec.add_ofInt_zero (x : BitVec w) : x + BitVec.ofInt w 0 = x := by simp + +/- Right associate, so our expressions are of the form x1 + (x2 + (x3 + ...))) -/ +attribute [bv_mba_preprocess] BitVec.add_assoc + + + +namespace Reflect +open Lean Elab Meta Tactic + +abbrev Ix := Nat + +structure State where + -- Exprressions to indexes in the interned object. + e2ix : Std.HashMap Expr Ix := {} + +abbrev M := StateRefT State MetaM + +partial def reflectFactor (e : Expr) : M Factor := do + match_expr e with + | HAnd.hAnd _bv _bv _bv _inst a b => + return Factor.and (← reflectFactor a) (← reflectFactor b) + | HOr.hOr _bv _bv _bv _inst a b => + return Factor.or (← reflectFactor a) (← reflectFactor b) + | HXor.hXor _bv _bv _bv _inst a b => + return Factor.xor (← reflectFactor a) (← reflectFactor b) + | Complement.complement _bv _inst a => + return Factor.not (← reflectFactor a) + | _ => + let s ← get + match s.e2ix[e]? with + | .some ix => return Factor.var ix + | .none => do + let ix := s.e2ix.size + set { s with e2ix := s.e2ix.insert e ix } + return .var ix + +def reflectTermCoeff (e : Expr) : M Int := + match_expr e with + | BitVec.ofInt _w i => do + let .some i := Expr.int? i + | throwError "Expected 'BitVec.ofInt w ' at '{e}', found {i}" + return i + | Int.cast _ _ i => do + let .some i := Expr.int? i + | throwError "Expected Int.cast ' at '{indentD e}', found {i}" + return i + | _ => throwError "unable to reflect term coefficient '{indentD e}'. Expected an integer." + +def reflectTerm (e : Expr) : M Term := + match_expr e with + | HMul.hMul _bv _bv _bv _inst l r => do + let c ← reflectTermCoeff l + let f ← reflectFactor r + return { c, f } + | _ => throwError "unable to reflect term '{indentD e}'.\nExpected 'int * variable'." + +/-! +Recall that add and sub in lean are associated to the left, so we have +((a + b) + c) + d and so on. +-/ +partial def reflectEqnAux (e : Expr) : M Eqn := + match_expr e with + | HAdd.hAdd _bv _bv _bv _inst l rs => do + let t ← reflectTerm l + let eqn ← reflectEqnAux rs + return t :: eqn + | _ => do return [← reflectTerm e] + +/- The expression corresponding to the bitwidth we are working with -/ +abbrev WidthExpr := Expr + +def reflectEqn (e : Expr) : M (WidthExpr × Eqn) := do + let .some (ty, lhs, _rhs) := Expr.eq? e + | throwError "expected top-level equality, but found {e}" + let_expr BitVec w := ty + | throwError "expected equality of bitvectors, but found {indentD ty}" + logInfo m!"found top-level equality LHS '{lhs}'" + return (w, ← reflectEqnAux lhs) + +def runM (x : M α) : MetaM (α × State) := x.run {} + +def runBvMbaPreprocess (g : MVarId) : MetaM (Option MVarId) := do + let simpName := `bv_mba_preprocess + let some ext ← (getSimpExtension? simpName) + | throwError m!"[bv_mba] Error: {simpName} simp attribute not found!" + let theorems ← ext.getTheorems + let some ext ← (Simp.getSimprocExtension? simpName) + | throwError m!"[bv_nnf] Error: {simpName}} simp attribute not found!" + let simprocs ← ext.getSimprocs + let config : Simp.Config := { Simp.neutralConfig with + failIfUnchanged := false, + } + let ctx ← Simp.mkContext (config := config) + (simpTheorems := #[theorems]) + (congrTheorems := ← Meta.getSimpCongrTheorems) + match ← simpGoal g ctx (simprocs := #[simprocs]) with + | (none, _) => return none + | (some (_newHyps, g'), _) => pure g' + +def WidthExpr.toBitVecType (w : WidthExpr) : Expr := + mkApp (mkConst ``BitVec) w + +/-- Make an 'Env' out of the state by reading the values -/ +def State.envToExpr (w : WidthExpr) (s : State) : MetaM Expr := do + let mut ix2e : Std.HashMap Nat Expr := {} + for (e, ix) in s.e2ix do + ix2e := ix2e.insert ix e + let bvTy := w.toBitVecType + let mut env := mkApp (mkConst ``List.nil [Level.zero]) bvTy + for i in [0:ix2e.size] do + let i := ix2e.size - 1 - i + env := mkApp3 (mkConst ``List.cons [Level.zero]) bvTy ix2e[i]! env + return env + +open Std Lean in +def mbaTac (g : MVarId) : TermElabM (List MVarId) := do + g.withContext do + let [g] ← g.apply (mkConst ``BitVec.eq_of_sub_zero) + | throwError m!"unable to apply `BitVec.eq_of_sub_zero`." + let .some g ← runBvMbaPreprocess g + | do + logInfo "goal closed by Mba normalizer." + return [] + logInfo m!"Normalized goal state to {indentD g}" + let ((widthExpr, eqn), reflectState) ← g.withContext do runM <| reflectEqn (← g.getType) + logInfo m!"found expression of width: '{indentD widthExpr}'" + let env ← State.envToExpr widthExpr reflectState + logInfo m!"replacing goal with reflected version. Equation: {indentD <| repr eqn}" + logInfo m!"Environment: {indentD (toMessageData reflectState.e2ix.toList)}" + -- let reflectedLhs ← mkAppM ``Eqn.reflect #[Eqn.toExpr eqn, env] + -- let reflectedRhs := mkApp2 (mkConst ``BitVec.ofInt) widthExpr (toExpr (0 : Int)) + -- let g ← g.replaceTargetDefEq (← mkEq reflectedLhs reflectedRhs) + -- logInfo m!"Replaced. {indentD g}" + -- apply: Eqn.forall_width_reflect_zero_of_width_one_denote_zero + + let gs ← g.withContext do g.apply (mkAppN (mkConst ``Eqn.forall_width_reflect_zero_of_width_one_denote_zero []) #[Eqn.toExpr eqn, widthExpr, env]) + let [g] := gs + | throwError m!"expected single goal after applying reflection theorem, found {gs}" + let dec ← mkDecideProof <| ← g.getType + if ← isDefEq (mkMVar g) dec then + logInfo "successfully decided!" + return [] + else + logWarning "failed to prove theorem using decision procedure, statement is false." + return [g] + -- let [g] ← g.apply <| (mkConst ``of_decide_eq_true) + -- | throwError m!"Failed to apply `of_decide_eq_true on goal '{indentD g}'" + -- let [] ← g.apply <| (mkConst ``Lean.ofReduceBool) + -- | throwError m!"Failed to decide with `Lean.ofReducebool` applied to '{indentD g}'" + +syntax (name := bvMba) "bv_mba" : tactic + +@[tactic bvMba] +def evalBvMba : Tactic := fun + | `(tactic| bv_mba) => do + let gs ← mbaTac (← getMainGoal) + replaceMainGoal gs + | _ => throwUnsupportedSyntax + +end Reflect +end Tactic + +namespace Examples + + +example (x y : BitVec w) : + Eqn.reflectEqZero w + [Term.mk 1 (.var 0), Term.mk 2 (.var 1)] [x, y] = + (BitVec.ofInt w 1 * x + BitVec.ofInt w 2 * y = BitVec.ofInt w 0) := rfl + +example (x y : BitVec w) : + Eqn.reflectEqZero w + [Term.mk 1 (.var 0), Term.mk 2 (.var 1), Term.mk (-1) (.var 0)] [x, y] = + (BitVec.ofInt w 1 * x + (BitVec.ofInt w 2 * y + BitVec.ofInt w (-1) * x) = BitVec.ofInt w 0) := rfl + +example (x : BitVec w) : 1 * x + (-1) * x = 0 := by + bv_mba + + +example (x y : BitVec w) : 1 * x + 2 * y + (-1) * x + (-2) * y = 0 := by + bv_mba + +theorem e_3 (x y : BitVec w) : + - 2 * ~~~(x &&& ~~~y) + 2 * ~~~x - 5 * ~~~(x ||| ~~~y) = 3 * (x &&& y) - 5 * y := by + bv_mba + +#print axioms e_3 + +end Examples +end MBA + + diff --git a/SSA/Experimental/Bits/Fast/dataset2.lean b/SSA/Experimental/Bits/Fast/dataset2.lean index 6cf4ad6a1..34090672e 100644 --- a/SSA/Experimental/Bits/Fast/dataset2.lean +++ b/SSA/Experimental/Bits/Fast/dataset2.lean @@ -1,5 +1,5 @@ import Std.Tactic.BVDecide -import SSA.Experimental.Bits.Fast.Reflect +import SSA.Experimental.Bits.Fast.MBA set_option maxHeartbeats 0 @@ -7,10021 +7,10016 @@ set_option maxHeartbeats 0 https://github.com/softsec-unh/MBA-Blast/blob/main/dataset/dataset2_64bit.txt -/ -theorem e_3 (x y : BitVec w) : +variable {w : Nat} +variable {a b c d e f g h i j k l m n o p q r s t u v x y z : BitVec w} + +theorem e_3 : - 2 * ~~~(x &&& ~~~y) + 2 * ~~~x - 5 * ~~~(x ||| ~~~y) = 3 * (x &&& y) - 5 * y := by simp - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1 (x y : BitVec w) : +theorem e_1 : - 1 * ~~~(x ^^^ y) - 2 * y + 1 * ~~~x = - 1 * ~~~(x ||| ~~~y) - 3 * (x &&& y) := by - bv_automata_circuit (config := {backend := .cadical}) - + bv_mba -theorem e_2 (x y : BitVec w) : +theorem e_2 : 1 * ~~~x - 2 * (x ^^^ y) + 1 * ~~~(x &&& y) = 2 * ~~~(x ||| y) - 1 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_4 (x y : BitVec w) : +theorem e_4 : 11 * ~~~(x &&& ~~~y) - 9 * ~~~(x ||| y) + 2 * (x &&& ~~~y) = 2 * ~~~y + 11 * y := by - bv_automata_circuit (config := { backend := .dryrun }) + bv_mba -theorem e_5 (x y : BitVec w) : +theorem e_5 : - 1 * ~~~y + 2 * ~~~(x &&& y) - 1 * ~~~(x ||| ~~~y) - 1 * (x &&& ~~~y) = 1 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_6 (x y : BitVec w) : +theorem e_6 : - 6 * (x ^^^ y) + 1 * ~~~x - 5 * ~~~(x ||| y) + 2 * (x &&& ~~~y) = - 4 * ~~~(x &&& y) - 1 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_7 (x y : BitVec w) : +theorem e_7 : 11 * ~~~(x &&& ~~~y) - 11 * x + 11 * (x &&& ~~~y) + 11 * (x &&& y) = 11 * ~~~(x ||| y) + 11 * y := by - bv_automata_circuit (config := { backend := .dryrun }) + bv_mba -theorem e_8 (x y : BitVec w) : +theorem e_8 : 1 * (x ||| ~~~y) - 1 * (x ||| y) - 2 * ~~~(x ||| y) - 1 * (x &&& y) = - 1 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_9 (x y : BitVec w) : +theorem e_9 : - 2 * (x ^^^ y) + 11 * (x ||| y) + 5 * y - 9 * (x &&& ~~~y) = 14 * ~~~(x ||| ~~~y) + 16 * (x &&& y) := by - bv_automata_circuit (config := { backend := .dryrun }) + bv_mba -theorem e_10 (x y : BitVec w) : +theorem e_10 : - 3 * x - 2 * ~~~y + 6 * (x &&& ~~~y) + 4 * (x &&& y) = - 3 * ~~~(x ||| y) + 1 * (x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_11 (x y : BitVec w) : +theorem e_11 : 7 * ~~~(x &&& y) - 1 * ~~~y - 6 * ~~~x - 1 * ~~~(x ||| ~~~y) = 6 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_12 (x y : BitVec w) : +theorem e_12 : - 3 * ~~~(x &&& ~~~x) + 1 * ~~~x + 2 * (x &&& ~~~y) + 4 * (x &&& y) = - 2 * ~~~(x &&& y) + 1 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_13 (x y : BitVec w) : +theorem e_13 : - 1 * ~~~(x ^^^ y) + 5 * x - 6 * (x &&& ~~~y) - 5 * (x &&& y) = 1 * ~~~(x ||| ~~~y) - 1 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_14 (x y : BitVec w) : +theorem e_14 : 2 * x + 5 * ~~~y + 2 * ~~~(x ||| ~~~y) - 7 * (x &&& ~~~y) = 5 * ~~~(x ||| y) + 2 * y := by - bv_automata_circuit (config := { backend := .cadical }) - -theorem e_15' (x y k l m: BitVec w) : - ((k = ~~~ (x ^^^ y)) ∧ - (l = ~~~(x ||| ~~~y)) ∧ - (m = ~~~(x ||| y))) → - (- 5 * y + 1 * ~~~x + 11 * k + 4 * l = 6 * (x &&& y) + 12 * m) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_15 (x y : BitVec w) : +theorem e_15 : - 5 * y + 1 * ~~~x + 11 * ~~~(x ^^^ y) + 4 * ~~~(x ||| ~~~y) = 6 * (x &&& y) + 12 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_16 (x y : BitVec w) : +theorem e_16 : 1 * (x ||| y) + 7 * x - 1 * ~~~x - 8 * (x &&& y) = - 1 * ~~~(x ||| y) + 8 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba theorem e_17' (x y : BitVec 6) : - 11 * ~~~(x &&& y) + 14 * ~~~(x ||| y) + 9 * ~~~(x ||| ~~~y) + 16 * (x &&& ~~~y) = - 2 * ~~~x + 5 * ~~~y := by bv_decide - -- bv_automata_circuit (config := { backend := .cadical }) + -- bv_mba -theorem e_17 (x y : BitVec w) : +theorem e_17 : - 11 * ~~~(x &&& y) + 14 * ~~~(x ||| y) + 9 * ~~~(x ||| ~~~y) + 16 * (x &&& ~~~y) = - 2 * ~~~x + 5 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_18 (x y : BitVec w) : +theorem e_18 : 4 * (x ||| ~~~y) - 7 * ~~~(x ||| y) - 4 * (x &&& ~~~y) - 7 * (x &&& y) = - 3 * ~~~(x &&& ~~~x) + 3 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_19 (x y : BitVec w) : +theorem e_19 : 1 * x + 5 * (x ^^^ y) - 2 * ~~~(x ||| ~~~y) - 3 * (x &&& ~~~y) - 1 * (x &&& y) = 3 * ~~~(x &&& y) - 3 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_20 (x y : BitVec w) : +theorem e_20 : - 7 * y - 3 * (x ||| ~~~y) + 3 * ~~~(x ||| y) + 8 * ~~~(x ||| ~~~y) + 4 * (x &&& ~~~y) = 1 * (x ^^^ y) - 10 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_21 (x y : BitVec w) : +theorem e_21 : 2 * (x ||| y) - 1 * ~~~(x &&& ~~~x) + 2 * ~~~(x ||| y) - 2 * ~~~(x ||| ~~~y) - 1 * (x &&& ~~~y) = - 1 * ~~~(x &&& ~~~y) + 2 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_22 (x y : BitVec w) : +theorem e_22 : - 11 * ~~~(x &&& y) + 4 * ~~~(x &&& ~~~y) + 11 * (x ^^^ y) + 12 * ~~~(x ||| y) - 4 * (x &&& y) = 5 * ~~~x - 1 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_23 (x y : BitVec w) : +theorem e_23 : - 2 * ~~~(x ^^^ y) - 2 * ~~~(x &&& y) + 1 * ~~~(x ||| ~~~y) + 1 * (x &&& ~~~y) + 1 * (x &&& y) = - 4 * ~~~(x ||| y) - 1 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_24 (x y : BitVec w) : +theorem e_24 : 7 * ~~~(x ^^^ y) - 3 * (x ||| y) - 11 * (x ^^^ y) - 7 * ~~~(x ||| y) + 14 * (x &&& ~~~y) = - 14 * ~~~(x ||| ~~~y) + 4 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_25 (x y : BitVec w) : +theorem e_25 : - 2 * ~~~y + 2 * (x ||| ~~~y) + 1 * ~~~x - 5 * (x &&& ~~~y) - 6 * (x &&& y) = 1 * ~~~(x &&& ~~~y) - 5 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_26 (x y : BitVec w) : +theorem e_26 : - 2 * (x ^^^ y) + 3 * y - 12 * ~~~(x ||| ~~~y) - 9 * (x &&& ~~~y) - 14 * (x &&& y) = - 11 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_27 (x y : BitVec w) : +theorem e_27 : 7 * (x ||| y) + 4 * x + 2 * ~~~(x ||| y) - 7 * ~~~(x ||| ~~~y) - 9 * (x &&& ~~~y) = 2 * ~~~y + 11 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_28 (x y : BitVec w) : +theorem e_28 : - 2 * ~~~(x &&& ~~~x) - 6 * x - 9 * ~~~(x ||| ~~~y) + 8 * (x &&& ~~~y) + 8 * (x &&& y) = - 11 * ~~~x + 9 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_29 (x y : BitVec w) : +theorem e_29 : - 3 * (x ||| y) + 2 * (x ^^^ y) + 5 * ~~~(x &&& y) - 4 * (x &&& ~~~y) + 3 * (x &&& y) = 4 * ~~~(x ||| ~~~y) + 5 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_30 (x y : BitVec w) : +theorem e_30 : 1 * x - 3 * ~~~(x ^^^ y) - 7 * (x ^^^ y) + 7 * ~~~(x ||| ~~~y) + 6 * (x &&& ~~~y) = - 3 * ~~~(x ||| y) - 2 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_31 (x y : BitVec w) : +theorem e_31 : 1 * (x ||| y) + 3 * y - 4 * ~~~(x ||| ~~~y) + 6 * (x &&& ~~~y) + 3 * (x &&& y) = 7 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_32 (x y : BitVec w) : +theorem e_32 : - 2 * ~~~(x &&& ~~~x) + 1 * x + 7 * ~~~(x ||| ~~~y) + 1 * (x &&& ~~~y) + 6 * (x &&& y) = - 7 * ~~~(x ||| y) + 5 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_33 (x y : BitVec w) : +theorem e_33 : - 1 * (x ||| y) - 1 * ~~~(x &&& y) + 1 * ~~~(x ||| y) + 1 * (x &&& ~~~y) + 1 * (x &&& y) = - 1 * (x ^^^ y) - 1 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_34 (x y : BitVec w) : +theorem e_34 : - 1 * (x ^^^ y) - 5 * x - 2 * ~~~(x ||| y) + 1 * ~~~(x ||| ~~~y) + 3 * (x &&& y) = - 2 * (x ||| ~~~y) - 4 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_35 (x y : BitVec w) : +theorem e_35 : 11 * (x ^^^ y) - 7 * ~~~(x &&& y) - 1 * ~~~x - 3 * ~~~(x ||| ~~~y) - 4 * (x &&& ~~~y) = - 8 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_36 (x y : BitVec w) : +theorem e_36 : - 1 * ~~~x - 5 * y - 5 * ~~~(x ||| y) + 5 * ~~~(x ||| ~~~y) - 6 * (x &&& ~~~y) = - 5 * (x ||| ~~~y) - 1 * ~~~(x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_37 (x y : BitVec w) : +theorem e_37 : 3 * (x ||| y) - 6 * y - 6 * ~~~(x ||| y) - 6 * (x &&& ~~~y) - 3 * (x &&& y) = - 3 * ~~~(x &&& ~~~x) - 3 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_38 (x y : BitVec w) : +theorem e_38 : 11 * (x ||| y) + 5 * ~~~x - 2 * ~~~(x ||| y) - 16 * ~~~(x ||| ~~~y) - 11 * (x &&& y) = 3 * ~~~y + 8 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_39 (x y : BitVec w) : +theorem e_39 : - 1 * (x ||| y) + 7 * ~~~(x &&& y) - 4 * ~~~(x ||| ~~~y) - 6 * (x &&& ~~~y) + 3 * (x &&& y) = 2 * ~~~(x &&& ~~~y) + 5 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_40 (x y : BitVec w) : +theorem e_40 : 1 * y + 3 * (x ||| ~~~y) + 3 * ~~~(x ^^^ y) - 6 * ~~~(x ||| y) - 1 * ~~~(x ||| ~~~y) = 7 * (x &&& y) + 3 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_41 (x y : BitVec w) : +theorem e_41 : 1 * (x ||| ~~~y) - 6 * (x ||| y) - 1 * ~~~(x ||| y) + 5 * (x &&& ~~~y) + 7 * (x &&& y) = 2 * y - 8 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_42 (x y : BitVec w) : +theorem e_42 : 1 * (x ||| ~~~y) + 1 * (x ^^^ y) - 5 * ~~~(x &&& y) + 4 * ~~~(x ||| y) + 4 * ~~~(x ||| ~~~y) = 1 * (x &&& y) - 3 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_43 (x y : BitVec w) : +theorem e_43 : - 1 * x - 1 * y + 1 * ~~~(x &&& ~~~x) - 3 * ~~~(x ||| y) - 1 * (x &&& y) = - 2 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_44 (x y : BitVec w) : +theorem e_44 : 2 * (x ||| y) - 1 * y + 11 * (x ^^^ y) - 12 * ~~~(x ||| ~~~y) - 13 * (x &&& ~~~y) = 1 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_45 (x y : BitVec w) : +theorem e_45 : - 1 * (x ||| y) - 18 * ~~~(x ||| y) + 1 * ~~~(x ||| ~~~y) - 10 * (x &&& ~~~y) - 6 * (x &&& y) = - 7 * ~~~(x ^^^ y) - 11 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_46 (x y : BitVec w) : +theorem e_46 : 11 * ~~~(x &&& y) + 1 * x - 1 * y - 11 * ~~~(x ||| y) - 10 * ~~~(x ||| ~~~y) = 12 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_47 (x y : BitVec w) : +theorem e_47 : - 11 * ~~~(x &&& ~~~y) + 11 * (x ||| ~~~y) + 10 * ~~~(x ||| ~~~y) - 11 * (x &&& ~~~y) - 1 * (x &&& y) = - 1 * y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_48 (x y : BitVec w) : +theorem e_48 : 2 * ~~~y - 2 * (x ||| ~~~y) - 1 * ~~~(x ||| ~~~y) - 1 * (x &&& ~~~y) + 2 * (x &&& y) = - 1 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_49 (x y : BitVec w) : +theorem e_49 : 11 * (x ||| ~~~y) + 2 * x - 12 * ~~~(x ||| y) - 13 * (x &&& ~~~y) - 14 * (x &&& y) = - 1 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_50 (x y : BitVec w) : +theorem e_50 : 2 * ~~~y + 1 * ~~~(x &&& ~~~x) - 3 * (x ^^^ y) + 8 * ~~~(x ||| y) + 10 * (x &&& y) = 11 * ~~~(x &&& ~~~y) - 13 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_51 (x y : BitVec w) : +theorem e_51 : 1 * ~~~(x &&& ~~~x) + 7 * (x ||| ~~~y) - 1 * (x ^^^ y) - 7 * ~~~(x ||| y) - 6 * (x &&& ~~~y) = 8 * (x &&& y) + 1 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_52 (x y : BitVec w) : +theorem e_52 : 11 * ~~~(x &&& ~~~x) - 11 * (x ^^^ y) - 12 * ~~~(x ||| y) - 1 * (x &&& ~~~y) - 12 * (x &&& y) = - 1 * (x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_53 (x y : BitVec w) : +theorem e_53 : - 7 * (x ^^^ y) + 2 * (x ||| ~~~y) - 2 * ~~~(x ||| y) + 8 * ~~~(x ||| ~~~y) - 1 * (x &&& y) = 1 * y - 5 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_54 (x y : BitVec w) : +theorem e_54 : 11 * ~~~(x &&& ~~~x) + 2 * ~~~y - 16 * ~~~(x ||| y) - 13 * (x &&& ~~~y) - 14 * (x &&& y) = - 3 * ~~~(x ^^^ y) + 11 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_55 (x y : BitVec w) : +theorem e_55 : 11 * (x ||| ~~~y) - 1 * ~~~y - 2 * ~~~(x &&& ~~~x) - 8 * ~~~(x ||| y) - 8 * (x &&& ~~~y) = - 2 * ~~~(x ||| ~~~y) + 9 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_56 (x y : BitVec w) : +theorem e_56 : 1 * x + 2 * (x ^^^ y) - 1 * y - 1 * ~~~y + 2 * ~~~(x ||| y) = 2 * (x &&& ~~~y) + 1 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_57 (x y : BitVec w) : +theorem e_57 : - 1 * (x ^^^ y) + 1 * ~~~(x ||| y) - 9 * ~~~(x ||| ~~~y) + 1 * (x &&& ~~~y) - 11 * (x &&& y) = - 11 * y + 1 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_58 (x y : BitVec w) : +theorem e_58 : 1 * ~~~(x ^^^ y) + 2 * (x ||| ~~~y) + 4 * ~~~x - 4 * ~~~(x ||| ~~~y) - 2 * (x &&& ~~~y) = 3 * (x &&& y) + 7 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_59 (x y : BitVec w) : +theorem e_59 : 1 * ~~~(x &&& ~~~y) + 4 * y - 7 * ~~~(x ||| ~~~y) - 2 * (x &&& ~~~y) - 5 * (x &&& y) = 1 * ~~~(x ||| y) - 2 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_60 (x y : BitVec w) : +theorem e_60 : - 2 * ~~~y + 7 * ~~~(x &&& y) + 5 * x - 5 * ~~~(x ||| y) - 10 * (x &&& ~~~y) = 7 * ~~~(x ||| ~~~y) + 5 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_61 (x y : BitVec w) : +theorem e_61 : 3 * ~~~(x ^^^ y) - 1 * (x ||| y) + 1 * (x ||| ~~~y) - 4 * ~~~(x ||| y) + 1 * ~~~(x ||| ~~~y) = 3 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_62 (x y : BitVec w) : +theorem e_62 : - 1 * ~~~(x &&& ~~~y) + 3 * ~~~(x &&& ~~~x) - 2 * ~~~(x ||| y) - 3 * ~~~(x ||| ~~~y) - 2 * (x &&& y) = - 1 * (x ^^^ y) + 4 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_63 (x y : BitVec w) : +theorem e_63 : - 2 * ~~~x + 11 * ~~~(x &&& ~~~x) - 5 * x - 9 * ~~~(x ||| ~~~y) - 6 * (x &&& y) = 6 * (x &&& ~~~y) + 9 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_64 (x y : BitVec w) : +theorem e_64 : - 1 * (x ||| ~~~y) - 1 * ~~~(x ^^^ y) + 5 * ~~~(x ||| y) + 3 * ~~~(x ||| ~~~y) + 2 * (x &&& y) = - 1 * (x &&& ~~~y) + 3 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_65 (x y : BitVec w) : +theorem e_65 : - 11 * (x ^^^ y) + 5 * x + 4 * ~~~(x &&& y) + 7 * ~~~(x ||| ~~~y) - 5 * (x &&& y) = 4 * ~~~(x ||| y) - 2 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_66 (x y : BitVec w) : +theorem e_66 : 4 * y - 11 * ~~~(x &&& ~~~x) + 4 * ~~~(x ||| y) + 7 * ~~~(x ||| ~~~y) + 4 * (x &&& ~~~y) = - 7 * (x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_67 (x y : BitVec w) : +theorem e_67 : - 11 * ~~~(x &&& y) + 4 * ~~~y + 8 * ~~~(x ||| y) + 8 * (x &&& ~~~y) + 1 * (x &&& y) = - 12 * ~~~(x ||| ~~~y) + 1 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_68 (x y : BitVec w) : +theorem e_68 : 5 * ~~~(x &&& ~~~y) - 2 * (x ^^^ y) - 5 * ~~~(x ||| y) + 3 * ~~~(x ||| ~~~y) + 8 * (x &&& ~~~y) = 6 * (x ||| y) - 1 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_69 (x y : BitVec w) : +theorem e_69 : - 2 * ~~~y + 7 * ~~~(x &&& ~~~x) - 1 * (x ||| y) - 4 * (x &&& ~~~y) - 6 * (x &&& y) = 6 * ~~~(x ||| ~~~y) + 5 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_70 (x y : BitVec w) : +theorem e_70 : - 1 * ~~~y - 5 * ~~~(x &&& ~~~y) + 8 * ~~~(x ||| y) + 7 * ~~~(x ||| ~~~y) + 5 * (x &&& y) = - 1 * (x &&& ~~~y) + 2 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_71 (x y : BitVec w) : +theorem e_71 : - 5 * ~~~x - 2 * x - 2 * (x ||| ~~~y) + 7 * ~~~(x ||| y) + 3 * (x &&& ~~~y) = - 4 * y - 1 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_72 (x y : BitVec w) : +theorem e_72 : 2 * ~~~x + 4 * ~~~(x &&& ~~~y) - 13 * ~~~(x ||| ~~~y) - 7 * (x &&& ~~~y) - 4 * (x &&& y) = - 7 * (x ^^^ y) + 6 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_73 (x y : BitVec w) : +theorem e_73 : 4 * ~~~x + 3 * (x ^^^ y) - 3 * ~~~(x ||| y) - 7 * ~~~(x ||| ~~~y) + 3 * (x &&& y) = 1 * (x ||| ~~~y) + 2 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_74 (x y : BitVec w) : +theorem e_74 : - 6 * (x ||| y) + 4 * (x ^^^ y) + 2 * ~~~(x ||| y) + 4 * ~~~(x ||| ~~~y) + 2 * (x &&& ~~~y) = 2 * ~~~x - 6 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_75 (x y : BitVec w) : +theorem e_75 : 1 * ~~~(x &&& ~~~y) + 1 * x - 12 * ~~~(x ||| y) - 1 * ~~~(x ||| ~~~y) - 2 * (x &&& y) = - 11 * ~~~y + 12 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_76 (x y : BitVec w) : +theorem e_76 : - 1 * y - 1 * (x ||| y) - 7 * ~~~(x ||| y) - 5 * ~~~(x ||| ~~~y) + 1 * (x &&& ~~~y) = - 7 * ~~~(x &&& ~~~y) + 5 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_77 (x y : BitVec w) : +theorem e_77 : - 5 * x - 1 * ~~~(x &&& ~~~x) - 1 * ~~~(x &&& y) + 2 * ~~~(x ||| y) + 2 * ~~~(x ||| ~~~y) = - 7 * (x &&& ~~~y) - 6 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_78 (x y : BitVec w) : +theorem e_78 : 1 * ~~~y - 2 * ~~~(x ^^^ y) + 1 * ~~~(x ||| y) + 4 * (x &&& ~~~y) + 2 * (x &&& y) = 5 * (x ^^^ y) - 5 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_79 (x y : BitVec w) : +theorem e_79 : 3 * ~~~y - 11 * x + 11 * ~~~(x &&& ~~~x) - 14 * ~~~(x ||| y) - 3 * (x &&& ~~~y) = 11 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_80 (x y : BitVec w) : +theorem e_80 : - 5 * ~~~(x &&& ~~~x) - 7 * ~~~(x ^^^ y) + 4 * ~~~(x ||| ~~~y) + 5 * (x &&& ~~~y) + 11 * (x &&& y) = - 1 * ~~~(x &&& ~~~y) - 11 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_81 (x y : BitVec w) : +theorem e_81 : 1 * y - 7 * ~~~(x &&& y) + 7 * ~~~x + 7 * (x &&& ~~~y) - 1 * (x &&& y) = 1 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_82 (x y : BitVec w) : +theorem e_82 : - 7 * (x ||| ~~~y) + 3 * ~~~x - 2 * ~~~(x ^^^ y) - 10 * ~~~(x ||| ~~~y) + 2 * (x &&& y) = - 6 * ~~~(x ||| y) - 7 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_83 (x y : BitVec w) : +theorem e_83 : - 5 * ~~~y + 5 * (x ||| ~~~y) - 2 * ~~~(x ||| ~~~y) - 2 * (x &&& ~~~y) - 5 * (x &&& y) = - 2 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_84 (x y : BitVec w) : +theorem e_84 : - 2 * ~~~(x &&& y) - 11 * ~~~(x &&& ~~~x) + 12 * ~~~(x ||| y) + 12 * ~~~(x ||| ~~~y) + 13 * (x &&& ~~~y) = - 1 * ~~~(x &&& ~~~y) - 10 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_85 (x y : BitVec w) : +theorem e_85 : 1 * ~~~y + 2 * (x ||| ~~~y) - 4 * ~~~(x ||| y) - 3 * (x &&& ~~~y) - 2 * (x &&& y) = - 1 * ~~~x + 1 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_86 (x y : BitVec w) : +theorem e_86 : - 2 * ~~~(x &&& y) - 11 * ~~~y + 13 * ~~~(x ||| y) + 3 * ~~~(x ||| ~~~y) + 14 * (x &&& ~~~y) = 1 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_87 (x y : BitVec w) : +theorem e_87 : 2 * (x ||| ~~~y) + 5 * ~~~(x &&& ~~~y) - 7 * ~~~(x ||| y) - 2 * (x &&& ~~~y) - 14 * (x &&& y) = 12 * ~~~(x ||| ~~~y) - 7 * y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_88 (x y : BitVec w) : +theorem e_88 : 1 * ~~~(x &&& ~~~x) - 2 * ~~~(x ||| y) - 3 * ~~~(x ||| ~~~y) - 2 * (x &&& ~~~y) - 3 * (x &&& y) = - 1 * ~~~y - 2 * y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_89 (x y : BitVec w) : +theorem e_89 : - 5 * (x ^^^ y) - 2 * ~~~x + 2 * ~~~(x ||| y) + 14 * ~~~(x ||| ~~~y) + 5 * (x &&& ~~~y) = - 7 * (x &&& y) + 7 * y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_90 (x y : BitVec w) : +theorem e_90 : - 5 * ~~~(x &&& y) - 7 * (x ||| y) + 3 * ~~~(x ||| y) + 10 * ~~~(x ||| ~~~y) + 10 * (x &&& ~~~y) = - 5 * (x &&& y) - 2 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_91 (x y : BitVec w) : +theorem e_91 : - 5 * (x ||| ~~~y) - 5 * ~~~(x &&& y) + 11 * ~~~(x ||| y) + 10 * (x &&& ~~~y) + 6 * (x &&& y) = 1 * ~~~(x &&& ~~~y) - 6 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_92 (x y : BitVec w) : +theorem e_92 : 1 * (x ^^^ y) - 1 * ~~~(x &&& ~~~x) - 3 * ~~~(x &&& ~~~y) + 3 * ~~~(x ||| ~~~y) + 4 * (x &&& y) = - 4 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_93 (x y : BitVec w) : +theorem e_93 : 4 * y + 3 * x + 1 * (x ||| y) - 4 * (x &&& ~~~y) - 8 * (x &&& y) = 5 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_94 (x y : BitVec w) : +theorem e_94 : 7 * ~~~x - 3 * ~~~(x ^^^ y) + 1 * y - 4 * ~~~(x ||| y) + 2 * (x &&& y) = 8 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_95 (x y : BitVec w) : +theorem e_95 : - 2 * ~~~(x ^^^ y) - 1 * (x ||| ~~~y) - 11 * ~~~(x &&& ~~~x) + 11 * ~~~(x ||| ~~~y) + 18 * (x &&& ~~~y) + 14 * (x &&& y) = - 20 * ~~~(x ||| y) + 6 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_96 (x y : BitVec w) : +theorem e_96 : 4 * ~~~y + 7 * ~~~x - 7 * (x ||| y) - 2 * (x ^^^ y) - 5 * ~~~(x ||| ~~~y) - 2 * (x &&& ~~~y) = - 7 * ~~~(x &&& ~~~x) + 18 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_97 (x y : BitVec w) : +theorem e_97 : - 2 * x + 7 * ~~~(x &&& ~~~y) + 4 * ~~~x + 11 * ~~~y - 9 * (x &&& ~~~y) - 5 * (x &&& y) = 22 * ~~~(x ||| y) + 11 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_98 (x y : BitVec w) : +theorem e_98 : - 2 * (x ||| y) - 5 * (x ||| ~~~y) - 3 * ~~~(x ^^^ y) + 8 * ~~~(x ||| y) + 2 * ~~~(x ||| ~~~y) + 10 * (x &&& y) = - 7 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_99 (x y : BitVec w) : +theorem e_99 : - 5 * (x ^^^ y) - 2 * ~~~(x &&& ~~~y) - 3 * ~~~x + 4 * ~~~(x ||| y) + 10 * ~~~(x ||| ~~~y) + 5 * (x &&& ~~~y) = - 1 * (x &&& y) - 1 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_100 (x y : BitVec w) : +theorem e_100 : - 11 * (x ||| ~~~y) + 3 * ~~~(x &&& y) - 5 * ~~~y + 13 * ~~~(x ||| y) - 4 * ~~~(x ||| ~~~y) + 12 * (x &&& ~~~y) = - 1 * (x ^^^ y) - 11 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_101 (x y : BitVec w) : +theorem e_101 : 1 * ~~~(x &&& ~~~x) - 2 * x - 11 * (x ||| ~~~y) - 1 * ~~~(x ||| ~~~y) + 12 * (x &&& ~~~y) + 12 * (x &&& y) = - 10 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_102 (x y : BitVec w) : +theorem e_102 : 11 * ~~~(x &&& ~~~y) + 1 * (x ||| ~~~y) + 1 * (x ^^^ y) - 6 * ~~~(x ||| ~~~y) + 10 * (x &&& ~~~y) - 12 * (x &&& y) = 6 * ~~~(x &&& y) + 6 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_103 (x y : BitVec w) : +theorem e_103 : - 1 * x + 2 * (x ||| y) + 3 * ~~~x - 9 * ~~~(x ||| ~~~y) - 5 * (x &&& ~~~y) - 5 * (x &&& y) = - 4 * ~~~(x &&& ~~~x) + 7 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_104 (x y : BitVec w) : +theorem e_104 : 5 * y + 2 * (x ||| ~~~y) + 11 * ~~~x - 13 * ~~~(x ||| y) - 16 * ~~~(x ||| ~~~y) - 7 * (x &&& y) = 2 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_105 (x y : BitVec w) : +theorem e_105 : - 1 * ~~~(x ^^^ y) - 6 * ~~~y - 5 * (x ^^^ y) + 7 * ~~~(x ||| y) + 11 * (x &&& ~~~y) + 1 * (x &&& y) = - 5 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_106 (x y : BitVec w) : +theorem e_106 : 3 * ~~~x - 1 * y + 11 * (x ||| y) - 14 * ~~~(x ||| ~~~y) - 11 * (x &&& ~~~y) - 11 * (x &&& y) = 4 * ~~~(x ||| y) - 1 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_107 (x y : BitVec w) : +theorem e_107 : - 1 * y + 7 * x + 1 * ~~~x + 11 * ~~~(x &&& y) - 18 * (x &&& ~~~y) - 6 * (x &&& y) = 11 * ~~~(x ||| ~~~y) + 12 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_108 (x y : BitVec w) : +theorem e_108 : - 2 * x + 2 * ~~~(x ^^^ y) - 11 * ~~~x + 9 * ~~~(x ||| y) + 22 * ~~~(x ||| ~~~y) + 13 * (x &&& ~~~y) = - 11 * (x &&& y) + 11 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_109 (x y : BitVec w) : +theorem e_109 : 1 * ~~~(x ^^^ y) - 3 * x - 1 * ~~~(x ||| y) + 6 * ~~~(x ||| ~~~y) + 10 * (x &&& ~~~y) + 8 * (x &&& y) = 7 * (x ||| y) - 1 * y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_110 (x y : BitVec w) : +theorem e_110 : 4 * ~~~y + 7 * y + 2 * ~~~(x &&& ~~~x) - 6 * ~~~(x &&& ~~~y) - 3 * ~~~(x ||| ~~~y) - 6 * (x &&& ~~~y) = 3 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_111 (x y : BitVec w) : +theorem e_111 : 2 * ~~~(x ^^^ y) + 3 * ~~~y + 3 * ~~~(x &&& y) - 6 * ~~~(x ||| y) - 1 * ~~~(x ||| ~~~y) - 4 * (x &&& ~~~y) = 2 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_112 (x y : BitVec w) : +theorem e_112 : - 11 * ~~~(x &&& ~~~x) + 2 * ~~~(x ^^^ y) - 3 * y + 9 * ~~~(x ||| y) + 11 * (x &&& ~~~y) + 12 * (x &&& y) = - 14 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_113 (x y : BitVec w) : +theorem e_113 : - 5 * ~~~(x ^^^ y) - 11 * ~~~(x &&& ~~~y) + 14 * ~~~(x ||| y) + 9 * ~~~(x ||| ~~~y) - 2 * (x &&& ~~~y) + 14 * (x &&& y) = - 2 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_114 (x y : BitVec w) : +theorem e_114 : 5 * y - 11 * x + 1 * ~~~(x &&& ~~~y) - 1 * ~~~(x ||| y) - 8 * ~~~(x ||| ~~~y) + 9 * (x &&& ~~~y) = - 2 * (x ||| y) - 3 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_115 (x y : BitVec w) : +theorem e_115 : 5 * ~~~(x &&& ~~~x) - 11 * ~~~y - 1 * x + 6 * ~~~(x ||| y) + 7 * (x &&& ~~~y) - 4 * (x &&& y) = 5 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_116 (x y : BitVec w) : +theorem e_116 : 7 * ~~~x - 1 * ~~~(x ^^^ y) - 11 * ~~~(x ||| y) - 12 * ~~~(x ||| ~~~y) - 5 * (x &&& ~~~y) - 4 * (x &&& y) = - 5 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_117 (x y : BitVec w) : +theorem e_117 : - 11 * ~~~y - 11 * ~~~(x &&& ~~~y) - 2 * (x ||| y) + 21 * ~~~(x ||| y) + 12 * ~~~(x ||| ~~~y) + 13 * (x &&& y) = - 12 * (x &&& ~~~y) - 1 * ~~~(x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_118 (x y : BitVec w) : +theorem e_118 : 1 * ~~~(x &&& ~~~x) - 5 * (x ||| ~~~y) - 6 * x - 1 * ~~~y + 11 * (x &&& ~~~y) + 10 * (x &&& y) = 1 * ~~~(x ||| ~~~y) - 5 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_119 (x y : BitVec w) : +theorem e_119 : 7 * y - 11 * ~~~y + 9 * ~~~(x ||| y) - 7 * ~~~(x ||| ~~~y) + 8 * (x &&& ~~~y) - 12 * (x &&& y) = - 2 * ~~~(x ^^^ y) - 3 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_120 (x y : BitVec w) : +theorem e_120 : 1 * ~~~x - 11 * (x ||| y) - 7 * (x ||| ~~~y) + 6 * ~~~(x ||| y) + 10 * ~~~(x ||| ~~~y) + 18 * (x &&& ~~~y) = - 18 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_121 (x y : BitVec w) : +theorem e_121 : - 5 * ~~~y - 2 * ~~~(x &&& ~~~x) - 2 * ~~~(x ^^^ y) + 9 * ~~~(x ||| y) + 7 * (x &&& ~~~y) + 4 * (x &&& y) = - 2 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_122 (x y : BitVec w) : +theorem e_122 : 2 * ~~~y + 11 * (x ^^^ y) - 2 * ~~~x - 1 * ~~~(x &&& y) + 1 * ~~~(x ||| y) - 12 * (x &&& ~~~y) = 8 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_123 (x y : BitVec w) : +theorem e_123 : - 1 * ~~~x - 7 * (x ||| ~~~y) + 2 * y + 8 * ~~~(x ||| y) + 7 * (x &&& ~~~y) + 5 * (x &&& y) = 1 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_124 (x y : BitVec w) : +theorem e_124 : 11 * ~~~(x &&& ~~~y) + 2 * ~~~(x &&& ~~~x) - 7 * (x ||| y) - 6 * x - 6 * ~~~(x ||| ~~~y) + 11 * (x &&& ~~~y) = 13 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_125 (x y : BitVec w) : +theorem e_125 : - 5 * ~~~x - 11 * ~~~(x ^^^ y) + 2 * ~~~(x &&& ~~~x) + 14 * ~~~(x ||| y) - 2 * (x &&& ~~~y) + 9 * (x &&& y) = - 3 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_126 (x y : BitVec w) : +theorem e_126 : - 11 * ~~~(x ^^^ y) - 2 * (x ^^^ y) + 1 * y + 2 * ~~~(x &&& ~~~x) - 1 * ~~~(x ||| ~~~y) + 8 * (x &&& y) = - 9 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_127 (x y : BitVec w) : +theorem e_127 : 11 * ~~~(x &&& y) - 1 * ~~~(x &&& ~~~x) + 5 * (x ||| y) - 10 * ~~~(x ||| y) - 15 * ~~~(x ||| ~~~y) - 15 * (x &&& ~~~y) = 4 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_128 (x y : BitVec w) : +theorem e_128 : 1 * (x ||| y) - 6 * ~~~x + 8 * ~~~(x ||| y) + 8 * ~~~(x ||| ~~~y) + 1 * (x &&& ~~~y) + 4 * (x &&& y) = 3 * y + 2 * (x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_129 (x y : BitVec w) : +theorem e_129 : 1 * (x ||| ~~~y) - 2 * (x ||| y) - 3 * ~~~y + 2 * ~~~(x ||| y) + 2 * ~~~(x ||| ~~~y) + 1 * (x &&& y) = - 4 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_130 (x y : BitVec w) : +theorem e_130 : - 2 * ~~~(x &&& ~~~y) + 3 * ~~~(x ^^^ y) - 3 * (x ||| y) - 1 * ~~~(x ||| y) + 3 * (x &&& ~~~y) + 2 * (x &&& y) = - 5 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_131 (x y : BitVec w) : +theorem e_131 : - 11 * x - 1 * (x ||| ~~~y) + 6 * ~~~(x ||| y) + 2 * ~~~(x ||| ~~~y) + 19 * (x &&& ~~~y) + 12 * (x &&& y) = 2 * (x ^^^ y) + 5 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_132 (x y : BitVec w) : +theorem e_132 : 11 * ~~~(x ^^^ y) - 7 * (x ||| ~~~y) + 3 * ~~~(x &&& y) - 3 * ~~~(x ||| ~~~y) + 4 * (x &&& ~~~y) - 4 * (x &&& y) = 7 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_133 (x y : BitVec w) : +theorem e_133 : 7 * ~~~y - 2 * ~~~(x &&& ~~~x) - 7 * ~~~(x ||| y) - 1 * ~~~(x ||| ~~~y) - 10 * (x &&& ~~~y) - 3 * (x &&& y) = - 2 * (x ||| ~~~y) - 3 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_134 (x y : BitVec w) : +theorem e_134 : - 3 * (x ||| y) + 4 * (x ||| ~~~y) + 1 * y - 4 * ~~~(x ||| y) - 1 * (x &&& ~~~y) - 2 * (x &&& y) = - 2 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_135 (x y : BitVec w) : +theorem e_135 : - 7 * (x ||| y) + 2 * ~~~y + 4 * ~~~(x ||| y) + 13 * ~~~(x ||| ~~~y) + 5 * (x &&& ~~~y) + 7 * (x &&& y) = 6 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_136 (x y : BitVec w) : +theorem e_136 : - 1 * y + 3 * (x ^^^ y) - 2 * (x ||| ~~~y) + 2 * ~~~(x ||| y) - 2 * ~~~(x ||| ~~~y) + 3 * (x &&& y) = 1 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_137 (x y : BitVec w) : +theorem e_137 : 11 * (x ||| ~~~y) + 7 * (x ^^^ y) - 1 * ~~~(x ^^^ y) - 2 * y - 5 * ~~~(x ||| ~~~y) - 18 * (x &&& ~~~y) = 8 * (x &&& y) + 10 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_138 (x y : BitVec w) : +theorem e_138 : - 7 * (x ||| y) - 2 * x + 1 * ~~~(x &&& ~~~x) + 2 * (x ^^^ y) - 1 * ~~~(x ||| y) + 4 * ~~~(x ||| ~~~y) = - 8 * (x &&& y) - 6 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_139 (x y : BitVec w) : +theorem e_139 : - 1 * x - 1 * (x ^^^ y) - 2 * ~~~(x &&& ~~~y) + 1 * ~~~x + 2 * ~~~(x ||| ~~~y) + 3 * (x &&& y) = - 2 * (x &&& ~~~y) - 1 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_140 (x y : BitVec w) : +theorem e_140 : - 11 * ~~~x + 5 * (x ||| y) + 4 * ~~~(x ^^^ y) + 7 * ~~~(x ||| y) + 6 * ~~~(x ||| ~~~y) - 9 * (x &&& y) = 5 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_141 (x y : BitVec w) : +theorem e_141 : - 6 * (x ^^^ y) + 2 * ~~~x + 5 * ~~~(x &&& y) + 4 * ~~~(x ||| y) + 1 * (x &&& ~~~y) + 11 * (x &&& y) = - 10 * ~~~(x ||| ~~~y) + 11 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_142 (x y : BitVec w) : +theorem e_142 : 2 * y - 7 * ~~~(x &&& ~~~y) + 7 * ~~~(x ||| y) - 6 * ~~~(x ||| ~~~y) - 11 * (x &&& ~~~y) + 5 * (x &&& y) = - 11 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_143 (x y : BitVec w) : +theorem e_143 : - 1 * ~~~(x &&& ~~~y) - 6 * ~~~(x ^^^ y) + 11 * x + 18 * ~~~(x ||| y) + 1 * ~~~(x ||| ~~~y) + 2 * (x &&& y) = 6 * (x ||| ~~~y) + 5 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_144 (x y : BitVec w) : +theorem e_144 : - 5 * ~~~x - 1 * (x ^^^ y) + 6 * ~~~(x ||| y) + 7 * ~~~(x ||| ~~~y) + 1 * (x &&& ~~~y) + 1 * (x &&& y) = 1 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_145 (x y : BitVec w) : +theorem e_145 : - 7 * (x ^^^ y) - 5 * x + 2 * ~~~(x &&& ~~~x) - 1 * (x ||| y) - 2 * ~~~(x ||| y) + 6 * ~~~(x ||| ~~~y) = - 11 * (x &&& ~~~y) - 4 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_146 (x y : BitVec w) : +theorem e_146 : - 3 * (x ^^^ y) - 11 * ~~~y + 7 * ~~~(x ||| y) + 3 * ~~~(x ||| ~~~y) + 10 * (x &&& ~~~y) - 4 * (x &&& y) = - 4 * (x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_147 (x y : BitVec w) : +theorem e_147 : 1 * ~~~y - 7 * ~~~(x &&& y) + 7 * ~~~(x ||| y) + 8 * ~~~(x ||| ~~~y) + 7 * (x &&& ~~~y) + 1 * (x &&& y) = 1 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_148 (x y : BitVec w) : +theorem e_148 : 5 * ~~~(x &&& ~~~x) - 6 * ~~~x - 5 * y - 11 * (x ^^^ y) + 2 * ~~~(x ||| y) + 7 * (x &&& ~~~y) = - 17 * ~~~(x ||| ~~~y) + 1 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_149 (x y : BitVec w) : +theorem e_149 : - 1 * ~~~(x &&& y) + 2 * ~~~(x &&& ~~~x) - 3 * ~~~(x ||| y) - 3 * ~~~(x ||| ~~~y) - 4 * (x &&& ~~~y) - 5 * (x &&& y) = - 2 * ~~~x - 3 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_150 (x y : BitVec w) : +theorem e_150 : - 1 * ~~~(x ^^^ y) + 3 * ~~~(x &&& ~~~y) - 1 * ~~~(x &&& y) - 1 * ~~~(x ||| y) - 2 * ~~~(x ||| ~~~y) - 2 * (x &&& y) = - 1 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_151 (x y : BitVec w) : +theorem e_151 : - 6 * ~~~(x ^^^ y) - 1 * y + 1 * ~~~(x ||| y) - 4 * ~~~(x ||| ~~~y) + 11 * (x &&& ~~~y) + 13 * (x &&& y) = 11 * x - 5 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_152 (x y : BitVec w) : +theorem e_152 : 3 * ~~~(x &&& y) + 2 * ~~~(x &&& ~~~x) + 7 * ~~~y - 2 * x - 12 * ~~~(x ||| y) - 10 * (x &&& ~~~y) = 5 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_153 (x y : BitVec w) : +theorem e_153 : 1 * ~~~(x ^^^ y) + 7 * ~~~y - 1 * (x ||| y) - 3 * (x ^^^ y) + 4 * ~~~(x ||| ~~~y) - 3 * (x &&& ~~~y) = 8 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_154 (x y : BitVec w) : +theorem e_154 : 1 * ~~~(x &&& y) - 11 * ~~~(x &&& ~~~x) - 1 * ~~~y + 11 * ~~~(x ||| y) + 8 * ~~~(x ||| ~~~y) + 9 * (x &&& y) = - 11 * (x &&& ~~~y) - 2 * y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_155 (x y : BitVec w) : +theorem e_155 : 3 * (x ||| ~~~y) - 1 * y - 7 * ~~~(x &&& ~~~x) + 5 * ~~~x + 4 * (x &&& ~~~y) + 6 * (x &&& y) = - 3 * ~~~(x ||| ~~~y) + 1 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_156 (x y : BitVec w) : +theorem e_156 : - 1 * ~~~y - 7 * (x ||| ~~~y) + 1 * y + 8 * ~~~(x ||| y) + 8 * (x &&& ~~~y) + 6 * (x &&& y) = 1 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_157 (x y : BitVec w) : +theorem e_157 : - 2 * (x ||| ~~~y) - 3 * ~~~(x ^^^ y) + 5 * ~~~(x ||| y) + 18 * ~~~(x ||| ~~~y) + 20 * (x &&& ~~~y) + 12 * (x &&& y) = 7 * (x ||| y) + 11 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_158 (x y : BitVec w) : +theorem e_158 : - 3 * ~~~y - 11 * ~~~(x &&& ~~~y) - 2 * ~~~x + 11 * ~~~(x &&& y) + 2 * ~~~(x ||| ~~~y) - 8 * (x &&& ~~~y) = - 11 * (x &&& y) - 5 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_159 (x y : BitVec w) : +theorem e_159 : - 2 * (x ||| ~~~y) + 1 * (x ^^^ y) + 2 * ~~~y + 1 * ~~~(x &&& ~~~x) - 2 * (x &&& ~~~y) + 1 * (x &&& y) = 2 * ~~~(x ||| ~~~y) + 1 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_160 (x y : BitVec w) : +theorem e_160 : 7 * ~~~(x &&& y) + 7 * x - 5 * y - 2 * ~~~(x ||| ~~~y) - 14 * (x &&& ~~~y) - 2 * (x &&& y) = 7 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_161 (x y : BitVec w) : +theorem e_161 : - 11 * ~~~(x &&& ~~~y) - 7 * y + 11 * ~~~(x ||| y) + 19 * ~~~(x ||| ~~~y) + 1 * (x &&& ~~~y) + 19 * (x &&& y) = 1 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_162 (x y : BitVec w) : +theorem e_162 : 1 * ~~~(x &&& ~~~x) + 11 * ~~~(x &&& y) - 3 * (x ||| y) - 1 * ~~~y - 13 * ~~~(x ||| y) - 9 * ~~~(x ||| ~~~y) = 10 * (x &&& ~~~y) - 2 * (x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_163 (x y : BitVec w) : +theorem e_163 : 3 * ~~~(x &&& y) - 3 * ~~~(x &&& ~~~y) - 1 * (x ||| ~~~y) - 2 * ~~~(x ||| ~~~y) - 2 * (x &&& ~~~y) + 4 * (x &&& y) = - 2 * ~~~x + 1 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_164 (x y : BitVec w) : +theorem e_164 : 7 * ~~~x - 2 * ~~~(x &&& y) + 1 * y - 6 * ~~~(x ||| ~~~y) - 3 * (x &&& ~~~y) - 1 * (x &&& y) = - 5 * ~~~y + 10 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_165 (x y : BitVec w) : +theorem e_165 : 1 * x + 1 * ~~~(x &&& ~~~x) - 11 * (x ^^^ y) + 1 * ~~~(x ||| y) + 10 * ~~~(x ||| ~~~y) + 11 * (x &&& ~~~y) = 2 * ~~~y + 2 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_166 (x y : BitVec w) : +theorem e_166 : - 7 * (x ^^^ y) + 3 * (x ||| ~~~y) - 2 * ~~~(x ||| y) - 4 * ~~~(x ||| ~~~y) + 4 * (x &&& ~~~y) - 13 * (x &&& y) = 1 * ~~~(x ^^^ y) - 11 * y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_167 (x y : BitVec w) : +theorem e_167 : 2 * ~~~(x &&& ~~~y) - 6 * ~~~y - 5 * ~~~(x ^^^ y) + 1 * ~~~(x &&& ~~~x) + 8 * ~~~(x ||| y) + 5 * (x &&& ~~~y) = - 2 * (x &&& y) + 3 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_168 (x y : BitVec w) : +theorem e_168 : - 1 * ~~~x + 2 * ~~~y - 2 * (x ^^^ y) - 12 * ~~~(x ||| y) - 11 * (x &&& ~~~y) - 11 * (x &&& y) = - 11 * (x ||| ~~~y) - 3 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_169 (x y : BitVec w) : +theorem e_169 : - 3 * ~~~x - 1 * (x ||| ~~~y) + 3 * ~~~y + 3 * ~~~(x ||| ~~~y) - 2 * (x &&& ~~~y) + 1 * (x &&& y) = - 1 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_170 (x y : BitVec w) : +theorem e_170 : - 2 * ~~~(x &&& y) - 11 * (x ||| y) + 9 * ~~~(x ||| y) + 20 * ~~~(x ||| ~~~y) + 20 * (x &&& ~~~y) + 18 * (x &&& y) = 7 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_171 (x y : BitVec w) : +theorem e_171 : 5 * (x ||| y) + 1 * ~~~(x &&& ~~~y) + 2 * x - 1 * ~~~(x ||| y) - 6 * ~~~(x ||| ~~~y) - 8 * (x &&& y) = 7 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_172 (x y : BitVec w) : +theorem e_172 : 2 * ~~~(x &&& ~~~x) - 3 * ~~~(x ^^^ y) + 1 * ~~~(x ||| y) - 4 * ~~~(x ||| ~~~y) - 4 * (x &&& ~~~y) - 1 * (x &&& y) = - 2 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_173 (x y : BitVec w) : +theorem e_173 : 7 * x - 3 * ~~~x + 3 * ~~~(x ||| y) + 15 * ~~~(x ||| ~~~y) + 5 * (x &&& ~~~y) - 6 * (x &&& y) = 1 * (x ||| y) + 11 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_174 (x y : BitVec w) : +theorem e_174 : 2 * x + 2 * (x ||| ~~~y) - 1 * (x ^^^ y) - 2 * ~~~(x ||| y) + 1 * ~~~(x ||| ~~~y) - 4 * (x &&& y) = 3 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_175 (x y : BitVec w) : +theorem e_175 : 1 * (x ||| y) - 11 * (x ||| ~~~y) + 11 * ~~~(x &&& ~~~y) + 1 * x + 9 * (x &&& ~~~y) - 2 * (x &&& y) = 12 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_176 (x y : BitVec w) : +theorem e_176 : - 1 * ~~~(x &&& y) + 11 * (x ^^^ y) + 1 * ~~~(x ||| y) + 1 * ~~~(x ||| ~~~y) - 10 * (x &&& ~~~y) + 11 * (x &&& y) = 11 * y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_177 (x y : BitVec w) : +theorem e_177 : 2 * ~~~(x ^^^ y) + 3 * ~~~(x &&& y) - 7 * ~~~(x &&& ~~~x) + 2 * ~~~(x ||| y) + 4 * (x &&& ~~~y) + 5 * (x &&& y) = - 4 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_178 (x y : BitVec w) : +theorem e_178 : - 5 * ~~~(x &&& ~~~y) - 11 * ~~~(x ^^^ y) - 7 * (x ^^^ y) + 11 * ~~~(x ||| y) + 7 * ~~~(x ||| ~~~y) + 11 * (x &&& y) = - 2 * (x &&& ~~~y) - 5 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_179 (x y : BitVec w) : +theorem e_179 : 2 * ~~~(x ^^^ y) - 6 * (x ||| ~~~y) + 11 * ~~~y + 4 * ~~~(x &&& ~~~y) - 4 * ~~~(x ||| ~~~y) - 5 * (x &&& ~~~y) = 11 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_180 (x y : BitVec w) : +theorem e_180 : - 1 * (x ^^^ y) - 5 * (x ||| y) + 1 * ~~~(x ||| y) + 7 * ~~~(x ||| ~~~y) + 6 * (x &&& ~~~y) + 6 * (x &&& y) = 1 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_181 (x y : BitVec w) : +theorem e_181 : - 11 * ~~~y + 2 * (x ^^^ y) + 4 * ~~~(x &&& y) - 1 * ~~~x - 5 * ~~~(x ||| ~~~y) + 5 * (x &&& ~~~y) = - 8 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_182 (x y : BitVec w) : +theorem e_182 : 4 * ~~~(x ^^^ y) - 11 * ~~~y - 1 * ~~~(x ||| y) - 8 * ~~~(x ||| ~~~y) + 4 * (x &&& ~~~y) - 11 * (x &&& y) = - 1 * ~~~x - 7 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_183 (x y : BitVec w) : +theorem e_183 : - 5 * ~~~y + 1 * ~~~(x &&& ~~~x) + 4 * ~~~(x ||| y) - 2 * ~~~(x ||| ~~~y) + 3 * (x &&& ~~~y) - 2 * (x &&& y) = - 1 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_184 (x y : BitVec w) : +theorem e_184 : - 11 * ~~~y - 3 * ~~~(x &&& ~~~y) + 5 * (x ||| ~~~y) + 9 * ~~~(x ||| y) + 6 * (x &&& ~~~y) - 2 * (x &&& y) = - 3 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_185 (x y : BitVec w) : +theorem e_185 : 5 * ~~~(x &&& ~~~y) - 6 * x - 4 * ~~~(x ||| y) - 6 * ~~~(x ||| ~~~y) + 6 * (x &&& ~~~y) + 1 * (x &&& y) = 1 * ~~~y - 1 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_186 (x y : BitVec w) : +theorem e_186 : 2 * y + 4 * ~~~(x &&& ~~~x) + 3 * ~~~(x ||| y) - 6 * ~~~(x ||| ~~~y) + 3 * (x &&& ~~~y) + 1 * (x &&& y) = 7 * (x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_187 (x y : BitVec w) : +theorem e_187 : - 2 * (x ||| y) - 7 * (x ^^^ y) + 1 * ~~~(x ||| y) + 10 * ~~~(x ||| ~~~y) + 10 * (x &&& ~~~y) + 3 * (x &&& y) = 1 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_188 (x y : BitVec w) : +theorem e_188 : - 11 * ~~~(x &&& y) - 2 * (x ||| y) + 7 * ~~~(x ||| y) + 12 * ~~~(x ||| ~~~y) + 13 * (x &&& ~~~y) + 5 * (x &&& y) = 3 * y - 4 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_189 (x y : BitVec w) : +theorem e_189 : 1 * ~~~(x &&& y) - 5 * (x ||| ~~~y) + 4 * ~~~(x ||| y) - 1 * ~~~(x ||| ~~~y) + 9 * (x &&& ~~~y) + 10 * (x &&& y) = 5 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_190 (x y : BitVec w) : +theorem e_190 : 1 * (x ||| y) + 2 * y + 7 * ~~~(x ^^^ y) - 6 * ~~~(x ||| y) - 3 * ~~~(x ||| ~~~y) - 9 * (x &&& y) = 1 * (x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_191 (x y : BitVec w) : +theorem e_191 : - 11 * ~~~(x ^^^ y) + 11 * y + 5 * (x ||| y) + 4 * ~~~(x ||| y) - 12 * (x &&& ~~~y) - 5 * (x &&& y) = - 7 * ~~~(x &&& y) + 23 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_192 (x y : BitVec w) : +theorem e_192 : - 7 * ~~~(x &&& ~~~x) + 1 * (x ^^^ y) + 2 * ~~~(x &&& ~~~y) + 4 * ~~~(x ||| y) + 3 * ~~~(x ||| ~~~y) + 5 * (x &&& y) = - 1 * ~~~x - 6 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_193 (x y : BitVec w) : +theorem e_193 : - 1 * ~~~y - 3 * (x ||| ~~~y) - 1 * ~~~(x ^^^ y) + 2 * ~~~(x ||| ~~~y) + 4 * (x &&& ~~~y) + 6 * (x &&& y) = 2 * y - 5 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_194 (x y : BitVec w) : +theorem e_194 : 4 * ~~~(x &&& ~~~x) - 11 * ~~~y + 8 * ~~~(x ||| y) - 4 * ~~~(x ||| ~~~y) + 7 * (x &&& ~~~y) - 3 * (x &&& y) = 1 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_195 (x y : BitVec w) : +theorem e_195 : - 1 * ~~~(x ^^^ y) + 2 * (x ||| y) - 1 * ~~~(x &&& ~~~x) + 2 * ~~~(x &&& ~~~y) - 13 * ~~~(x ||| ~~~y) - 13 * (x &&& y) = - 11 * y + 1 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_196 (x y : BitVec w) : +theorem e_196 : 4 * ~~~(x &&& y) + 2 * y + 7 * ~~~(x ||| y) - 6 * ~~~(x ||| ~~~y) - 4 * (x &&& ~~~y) + 9 * (x &&& y) = 11 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_197 (x y : BitVec w) : +theorem e_197 : 2 * (x ||| ~~~y) - 7 * x - 5 * ~~~x + 3 * ~~~(x ||| y) + 5 * ~~~(x ||| ~~~y) + 5 * (x &&& ~~~y) = - 5 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_198 (x y : BitVec w) : +theorem e_198 : 5 * x - 3 * ~~~(x &&& ~~~x) + 3 * ~~~(x ||| y) + 1 * ~~~(x ||| ~~~y) - 2 * (x &&& ~~~y) - 4 * (x &&& y) = - 2 * y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_199 (x y : BitVec w) : +theorem e_199 : 3 * (x ||| y) - 11 * ~~~(x &&& ~~~y) + 4 * ~~~(x ^^^ y) + 1 * ~~~(x &&& ~~~x) + 3 * y - 4 * (x &&& ~~~y) = - 6 * ~~~(x ||| y) - 4 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_200 (x y : BitVec w) : +theorem e_200 : - 5 * (x ||| ~~~y) - 2 * y + 4 * ~~~x + 1 * ~~~(x ||| y) - 2 * ~~~(x ||| ~~~y) + 5 * (x &&& ~~~y) = - 7 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_201 (x y : BitVec w) : +theorem e_201 : - 5 * y + 11 * ~~~(x ^^^ y) - 2 * ~~~y + 5 * ~~~(x ||| ~~~y) + 2 * (x &&& ~~~y) - 6 * (x &&& y) = 9 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_202 (x y : BitVec w) : +theorem e_202 : 3 * ~~~(x &&& y) - 7 * ~~~(x &&& ~~~x) - 1 * (x ||| ~~~y) + 5 * ~~~(x ||| y) + 1 * (x &&& ~~~y) + 8 * (x &&& y) = - 4 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_203 (x y : BitVec w) : +theorem e_203 : - 5 * ~~~(x &&& y) - 2 * (x ||| ~~~y) + 7 * ~~~x + 7 * ~~~(x ||| y) - 2 * ~~~(x ||| ~~~y) + 2 * (x &&& y) = 7 * ~~~y - 14 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_204 (x y : BitVec w) : +theorem e_204 : - 2 * ~~~x - 2 * (x ^^^ y) - 11 * ~~~(x ^^^ y) + 13 * ~~~(x ||| y) + 4 * ~~~(x ||| ~~~y) + 2 * (x &&& ~~~y) = - 11 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_205 (x y : BitVec w) : +theorem e_205 : - 3 * ~~~(x &&& y) - 11 * ~~~(x &&& ~~~x) + 2 * y + 1 * x + 14 * ~~~(x ||| y) + 12 * ~~~(x ||| ~~~y) = - 13 * (x &&& ~~~y) - 8 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_206 (x y : BitVec w) : +theorem e_206 : - 1 * ~~~y + 3 * ~~~x - 2 * (x ||| y) - 4 * ~~~(x ||| y) - 3 * ~~~(x ||| ~~~y) + 3 * (x &&& ~~~y) = - 2 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_207 (x y : BitVec w) : +theorem e_207 : - 6 * y + 1 * ~~~(x &&& y) - 2 * x + 5 * ~~~(x ||| y) + 5 * ~~~(x ||| ~~~y) + 8 * (x &&& y) = 6 * ~~~y - 7 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_208 (x y : BitVec w) : +theorem e_208 : - 2 * x + 4 * (x ||| y) + 1 * ~~~x - 6 * ~~~(x ||| ~~~y) - 3 * (x &&& ~~~y) - 2 * (x &&& y) = 2 * ~~~(x ||| y) - 1 * ~~~(x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_209 (x y : BitVec w) : +theorem e_209 : - 2 * (x ||| y) - 3 * ~~~(x &&& ~~~y) + 3 * ~~~y + 7 * y - 2 * ~~~(x ||| ~~~y) - 1 * (x &&& ~~~y) = 2 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_210 (x y : BitVec w) : +theorem e_210 : - 7 * (x ^^^ y) + 1 * ~~~(x &&& ~~~x) + 4 * ~~~(x ||| y) + 6 * ~~~(x ||| ~~~y) + 5 * (x &&& ~~~y) + 5 * (x &&& y) = 6 * ~~~(x ^^^ y) - 1 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_211 (x y : BitVec w) : +theorem e_211 : 4 * (x ^^^ y) + 3 * ~~~(x ^^^ y) - 4 * ~~~(x ||| y) - 5 * ~~~(x ||| ~~~y) - 4 * (x &&& ~~~y) - 4 * (x &&& y) = - 1 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_212 (x y : BitVec w) : +theorem e_212 : - 2 * ~~~(x &&& ~~~x) - 1 * ~~~(x &&& y) - 2 * ~~~y - 2 * y + 5 * ~~~(x ||| ~~~y) + 5 * (x &&& ~~~y) = - 5 * ~~~(x ||| y) - 4 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_213 (x y : BitVec w) : +theorem e_213 : 1 * ~~~(x &&& ~~~y) - 6 * (x ^^^ y) + 1 * ~~~(x ^^^ y) + 1 * (x ||| y) - 1 * ~~~x + 2 * ~~~(x ||| y) + 8 * ~~~(x ||| ~~~y) = - 8 * (x &&& ~~~y) + 3 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_214 (x y : BitVec w) : +theorem e_214 : 3 * x - 6 * y + 1 * ~~~(x ^^^ y) - 6 * ~~~x + 12 * ~~~(x ||| ~~~y) - 14 * (x &&& ~~~y) + 2 * (x &&& y) = - 11 * ~~~y + 6 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_215 (x y : BitVec w) : +theorem e_215 : - 6 * (x ||| y) + 5 * (x ||| ~~~y) - 3 * ~~~y + 2 * x + 13 * ~~~(x ||| ~~~y) + 9 * (x &&& ~~~y) + 6 * (x &&& y) = 7 * ~~~(x &&& ~~~x) - 5 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_216 (x y : BitVec w) : +theorem e_216 : - 7 * (x ||| y) + 1 * ~~~x + 5 * ~~~(x ^^^ y) + 5 * (x ^^^ y) - 12 * ~~~(x ||| y) - 4 * (x &&& ~~~y) - 3 * (x &&& y) = - 1 * ~~~(x &&& y) - 5 * (x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_217 (x y : BitVec w) : +theorem e_217 : - 1 * x - 11 * ~~~x - 1 * y - 1 * ~~~(x &&& ~~~x) + 12 * ~~~(x ||| y) + 13 * ~~~(x ||| ~~~y) + 3 * (x &&& y) = - 2 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_218 (x y : BitVec w) : +theorem e_218 : 5 * ~~~(x &&& ~~~x) - 7 * ~~~(x &&& y) - 2 * (x ^^^ y) - 3 * ~~~(x ||| y) + 4 * ~~~(x ||| ~~~y) - 1 * (x &&& ~~~y) - 10 * (x &&& y) = - 5 * (x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_219 (x y : BitVec w) : +theorem e_219 : - 5 * (x ^^^ y) + 2 * ~~~x - 6 * ~~~(x &&& ~~~x) - 1 * ~~~y + 3 * ~~~(x ||| y) + 10 * (x &&& ~~~y) + 6 * (x &&& y) = - 2 * ~~~(x &&& y) - 7 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_220 (x y : BitVec w) : +theorem e_220 : - 2 * ~~~(x ^^^ y) - 11 * y - 6 * ~~~(x &&& ~~~y) + 8 * ~~~(x ||| y) + 17 * ~~~(x ||| ~~~y) + 5 * (x &&& ~~~y) + 24 * (x &&& y) = 5 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_221 (x y : BitVec w) : +theorem e_221 : - 1 * ~~~x - 1 * ~~~(x &&& y) + 2 * (x ^^^ y) + 3 * ~~~(x ||| y) + 1 * ~~~(x ||| ~~~y) - 1 * (x &&& ~~~y) + 1 * (x &&& y) = 1 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_222 (x y : BitVec w) : +theorem e_222 : - 3 * ~~~y + 3 * x + 4 * ~~~(x &&& ~~~x) - 1 * (x ^^^ y) - 2 * ~~~(x ||| ~~~y) - 3 * (x &&& ~~~y) - 6 * (x &&& y) = 1 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_223 (x y : BitVec w) : +theorem e_223 : 1 * (x ||| y) + 1 * ~~~(x ^^^ y) - 5 * ~~~(x &&& ~~~y) - 2 * ~~~y + 12 * ~~~(x ||| y) + 7 * (x &&& ~~~y) + 9 * (x &&& y) = 6 * (x ||| ~~~y) - 4 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_224 (x y : BitVec w) : +theorem e_224 : 5 * (x ||| ~~~y) + 7 * ~~~(x ^^^ y) - 5 * x - 17 * ~~~(x ||| y) - 5 * ~~~(x ||| ~~~y) - 5 * (x &&& ~~~y) - 12 * (x &&& y) = - 5 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_225 (x y : BitVec w) : +theorem e_225 : - 3 * (x ||| y) - 1 * ~~~y + 3 * (x ||| ~~~y) + 5 * ~~~(x &&& ~~~y) - 10 * ~~~(x ||| y) + 3 * (x &&& ~~~y) - 10 * (x &&& y) = - 5 * ~~~(x ^^^ y) + 2 * ~~~(x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_226 (x y : BitVec w) : +theorem e_226 : 5 * ~~~(x &&& ~~~y) - 3 * (x ||| y) - 7 * y - 12 * ~~~(x ||| y) - 2 * ~~~(x ||| ~~~y) - 4 * (x &&& ~~~y) + 5 * (x &&& y) = - 7 * ~~~(x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_227 (x y : BitVec w) : +theorem e_227 : 1 * (x ||| ~~~y) - 1 * y + 1 * (x ^^^ y) + 2 * ~~~(x &&& ~~~x) - 2 * ~~~(x ||| ~~~y) + 3 * (x &&& ~~~y) - 2 * (x &&& y) = - 4 * ~~~(x ||| y) + 7 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_228 (x y : BitVec w) : +theorem e_228 : - 3 * (x ||| y) + 2 * (x ^^^ y) - 6 * ~~~(x &&& y) - 6 * ~~~(x ^^^ y) + 12 * ~~~(x ||| y) + 4 * ~~~(x ||| ~~~y) + 7 * (x &&& ~~~y) = - 3 * y - 6 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_229 (x y : BitVec w) : +theorem e_229 : - 7 * (x ^^^ y) + 1 * ~~~x + 2 * ~~~(x &&& y) + 11 * y + 1 * x - 4 * ~~~(x ||| ~~~y) - 9 * (x &&& y) = - 4 * (x &&& ~~~y) + 3 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_230 (x y : BitVec w) : +theorem e_230 : 11 * ~~~(x &&& ~~~y) - 1 * ~~~(x &&& ~~~x) + 3 * (x ||| ~~~y) + 1 * x - 13 * ~~~(x ||| y) - 10 * ~~~(x ||| ~~~y) - 14 * (x &&& y) = 3 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_231 (x y : BitVec w) : +theorem e_231 : - 11 * x + 5 * ~~~x + 1 * (x ^^^ y) - 5 * ~~~(x ||| y) - 5 * ~~~(x ||| ~~~y) + 11 * (x &&& ~~~y) + 12 * (x &&& y) = 1 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_232 (x y : BitVec w) : +theorem e_232 : 5 * ~~~(x ^^^ y) + 2 * ~~~(x &&& ~~~y) + 5 * (x ||| ~~~y) - 2 * ~~~(x &&& ~~~x) - 10 * ~~~(x ||| y) - 14 * (x &&& ~~~y) - 10 * (x &&& y) = - 11 * (x ^^^ y) + 11 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_233 (x y : BitVec w) : +theorem e_233 : 3 * ~~~(x &&& y) - 7 * ~~~y + 5 * (x ||| ~~~y) + 1 * (x ||| y) + 4 * ~~~(x ||| y) - 4 * ~~~(x ||| ~~~y) - 1 * (x &&& y) = 5 * ~~~(x ^^^ y) + 2 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_234 (x y : BitVec w) : +theorem e_234 : - 3 * (x ^^^ y) - 2 * ~~~(x &&& ~~~x) + 11 * (x ||| ~~~y) - 1 * ~~~(x &&& y) - 8 * ~~~(x ||| y) + 6 * ~~~(x ||| ~~~y) - 10 * (x &&& y) = - 1 * x + 6 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_235 (x y : BitVec w) : +theorem e_235 : 1 * ~~~(x ^^^ y) - 5 * ~~~(x &&& ~~~y) - 1 * ~~~(x &&& y) + 3 * ~~~y + 5 * ~~~(x ||| ~~~y) - 2 * (x &&& ~~~y) + 3 * (x &&& y) = - 2 * ~~~(x ||| y) - 1 * y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_236 (x y : BitVec w) : +theorem e_236 : - 7 * (x ||| y) - 6 * x - 1 * ~~~(x &&& ~~~x) - 2 * ~~~(x ||| y) + 8 * ~~~(x ||| ~~~y) + 11 * (x &&& ~~~y) + 11 * (x &&& y) = - 3 * (x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_237 (x y : BitVec w) : +theorem e_237 : 4 * ~~~(x ^^^ y) + 3 * (x ^^^ y) - 2 * ~~~x + 1 * (x ||| ~~~y) + 2 * ~~~(x ||| ~~~y) - 4 * (x &&& ~~~y) - 2 * (x &&& y) = 3 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_238 (x y : BitVec w) : +theorem e_238 : 2 * (x ^^^ y) - 6 * ~~~(x ^^^ y) + 1 * x - 1 * ~~~(x &&& ~~~y) + 2 * ~~~(x ||| ~~~y) - 3 * (x &&& ~~~y) + 6 * (x &&& y) = - 10 * ~~~(x ||| y) + 3 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_239 (x y : BitVec w) : +theorem e_239 : 1 * (x ^^^ y) + 7 * ~~~(x ^^^ y) + 2 * ~~~x + 5 * ~~~(x &&& y) - 14 * ~~~(x ||| y) + 3 * ~~~(x ||| ~~~y) + 5 * (x &&& ~~~y) = - 4 * (x &&& y) + 11 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_240 (x y : BitVec w) : +theorem e_240 : 1 * ~~~(x ^^^ y) - 1 * ~~~(x &&& ~~~x) + 1 * (x ||| y) + 5 * x + 3 * ~~~(x ||| y) - 5 * (x &&& ~~~y) - 6 * (x &&& y) = 3 * ~~~x - 3 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_241 (x y : BitVec w) : +theorem e_241 : - 2 * ~~~(x ^^^ y) + 4 * (x ||| ~~~y) - 11 * ~~~(x &&& ~~~y) - 5 * ~~~y + 1 * (x ||| y) + 14 * ~~~(x ||| y) + 10 * ~~~(x ||| ~~~y) = - 8 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_242 (x y : BitVec w) : +theorem e_242 : 1 * x - 2 * (x ||| y) + 2 * ~~~(x &&& ~~~x) + 5 * y - 3 * ~~~(x ||| ~~~y) + 1 * (x &&& ~~~y) - 6 * (x &&& y) = 2 * (x ^^^ y) + 2 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_243 (x y : BitVec w) : +theorem e_243 : 2 * ~~~(x &&& ~~~y) + 1 * ~~~(x &&& ~~~x) - 1 * ~~~x - 2 * ~~~(x ||| y) + 3 * ~~~(x ||| ~~~y) + 4 * (x &&& ~~~y) + 2 * (x &&& y) = 5 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_244 (x y : BitVec w) : +theorem e_244 : - 5 * x - 5 * ~~~x + 11 * (x ||| ~~~y) + 7 * y - 2 * ~~~(x ||| ~~~y) - 6 * (x &&& ~~~y) - 13 * (x &&& y) = 6 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_245 (x y : BitVec w) : +theorem e_245 : - 1 * (x ^^^ y) - 6 * ~~~(x &&& y) + 1 * y - 1 * ~~~(x &&& ~~~y) + 6 * ~~~(x ||| y) + 7 * ~~~(x ||| ~~~y) + 6 * (x &&& ~~~y) = - 1 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_246 (x y : BitVec w) : +theorem e_246 : 1 * ~~~(x &&& ~~~y) + 1 * (x ||| ~~~y) + 1 * ~~~(x &&& ~~~x) - 1 * ~~~(x &&& y) - 2 * ~~~y - 4 * ~~~(x ||| ~~~y) - 6 * (x &&& y) = - 1 * (x ||| y) - 2 * y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_247 (x y : BitVec w) : +theorem e_247 : 1 * ~~~y + 1 * ~~~(x &&& ~~~y) + 3 * ~~~x - 11 * x - 12 * ~~~(x ||| y) - 4 * ~~~(x ||| ~~~y) + 3 * (x &&& y) = - 7 * ~~~(x ^^^ y) - 10 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_248 (x y : BitVec w) : +theorem e_248 : - 5 * (x ^^^ y) - 1 * (x ||| y) - 7 * ~~~x + 11 * ~~~y - 4 * ~~~(x ||| y) + 13 * ~~~(x ||| ~~~y) + 1 * (x &&& y) = 5 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_249 (x y : BitVec w) : +theorem e_249 : - 3 * (x ^^^ y) + 1 * y + 2 * ~~~y + 4 * x - 2 * ~~~(x &&& ~~~y) + 4 * ~~~(x ||| ~~~y) - 3 * (x &&& ~~~y) = - 3 * ~~~(x ||| y) + 3 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_250 (x y : BitVec w) : +theorem e_250 : 5 * (x ^^^ y) - 1 * ~~~(x &&& ~~~x) - 11 * (x ||| ~~~y) + 8 * ~~~(x ||| y) - 8 * ~~~(x ||| ~~~y) + 3 * (x &&& ~~~y) + 12 * (x &&& y) = - 4 * ~~~(x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_251 (x y : BitVec w) : +theorem e_251 : - 5 * ~~~y + 11 * ~~~x + 3 * ~~~(x &&& ~~~x) + 11 * ~~~(x &&& ~~~y) - 20 * ~~~(x ||| y) - 25 * ~~~(x ||| ~~~y) + 1 * (x &&& ~~~y) = 15 * (x &&& y) - 1 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_252 (x y : BitVec w) : +theorem e_252 : - 1 * ~~~(x &&& ~~~y) - 11 * x - 11 * (x ||| y) + 9 * ~~~(x ||| y) + 14 * ~~~(x ||| ~~~y) + 24 * (x &&& ~~~y) + 29 * (x &&& y) = 2 * ~~~(x &&& y) + 6 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_253 (x y : BitVec w) : +theorem e_253 : 11 * (x ||| y) + 2 * ~~~y - 1 * (x ||| ~~~y) + 4 * y - 3 * ~~~(x ||| y) - 12 * (x &&& ~~~y) - 14 * (x &&& y) = 17 * ~~~(x ||| ~~~y) - 2 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_254 (x y : BitVec w) : +theorem e_254 : - 7 * y - 6 * ~~~(x &&& ~~~y) - 7 * (x ^^^ y) - 1 * ~~~(x ^^^ y) + 12 * ~~~(x ||| y) + 25 * ~~~(x ||| ~~~y) + 12 * (x &&& ~~~y) = - 19 * (x &&& y) + 5 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_255 (x y : BitVec w) : +theorem e_255 : 3 * ~~~y + 1 * y + 1 * ~~~(x ^^^ y) + 2 * ~~~(x &&& y) - 6 * ~~~(x ||| y) - 5 * (x &&& ~~~y) - 2 * (x &&& y) = 3 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_256 (x y : BitVec w) : +theorem e_256 : - 11 * (x ||| ~~~y) - 5 * y + 2 * ~~~x - 5 * (x ||| y) + 1 * (x ^^^ y) + 7 * ~~~(x ||| ~~~y) + 15 * (x &&& ~~~y) = - 21 * (x &&& y) - 9 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_257 (x y : BitVec w) : +theorem e_257 : - 1 * ~~~(x &&& y) - 1 * ~~~x + 7 * (x ||| ~~~y) - 3 * ~~~(x ||| y) + 2 * ~~~(x ||| ~~~y) - 6 * (x &&& ~~~y) - 5 * (x &&& y) = 2 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_258 (x y : BitVec w) : +theorem e_258 : 4 * ~~~(x &&& ~~~y) - 2 * x + 5 * ~~~(x &&& y) - 9 * ~~~(x ||| y) - 13 * ~~~(x ||| ~~~y) - 7 * (x &&& ~~~y) - 2 * (x &&& y) = - 4 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_259 (x y : BitVec w) : +theorem e_259 : 7 * y - 5 * x - 2 * (x ||| ~~~y) + 2 * ~~~(x ||| y) - 8 * ~~~(x ||| ~~~y) + 6 * (x &&& ~~~y) + 2 * (x &&& y) = - 3 * (x ^^^ y) + 2 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_260 (x y : BitVec w) : +theorem e_260 : - 2 * ~~~(x &&& ~~~x) - 1 * ~~~(x &&& ~~~y) - 3 * (x ^^^ y) + 3 * ~~~(x ||| y) + 8 * ~~~(x ||| ~~~y) + 7 * (x &&& ~~~y) + 5 * (x &&& y) = 2 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_261 (x y : BitVec w) : +theorem e_261 : - 7 * ~~~y - 5 * (x ||| y) + 4 * (x ||| ~~~y) - 1 * ~~~(x &&& ~~~y) + 4 * ~~~(x ||| y) + 6 * ~~~(x ||| ~~~y) + 8 * (x &&& ~~~y) = - 2 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_262 (x y : BitVec w) : +theorem e_262 : 7 * (x ^^^ y) - 1 * (x ||| ~~~y) - 1 * y + 1 * ~~~(x ||| y) - 13 * ~~~(x ||| ~~~y) - 13 * (x &&& ~~~y) - 5 * (x &&& y) = - 7 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_263 (x y : BitVec w) : +theorem e_263 : 5 * ~~~x - 7 * (x ||| y) - 7 * ~~~(x ^^^ y) + 1 * ~~~(x &&& y) + 1 * ~~~(x ||| ~~~y) - 1 * (x &&& ~~~y) + 14 * (x &&& y) = 6 * ~~~(x ||| y) - 7 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_264 (x y : BitVec w) : +theorem e_264 : - 1 * ~~~(x &&& y) - 1 * y - 2 * (x ||| y) - 1 * (x ^^^ y) + 1 * ~~~(x ||| y) + 5 * ~~~(x ||| ~~~y) + 3 * (x &&& y) = - 4 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_265 (x y : BitVec w) : +theorem e_265 : 1 * (x ||| y) - 1 * (x ^^^ y) + 2 * ~~~(x ^^^ y) - 1 * x + 7 * y - 7 * ~~~(x ||| ~~~y) - 9 * (x &&& y) = - 1 * ~~~y + 3 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_266 (x y : BitVec w) : +theorem e_266 : - 7 * ~~~(x ^^^ y) - 7 * ~~~y - 7 * x + 3 * ~~~(x &&& ~~~y) - 3 * ~~~(x ||| ~~~y) + 14 * (x &&& ~~~y) + 11 * (x &&& y) = - 11 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_267 (x y : BitVec w) : +theorem e_267 : - 1 * ~~~(x ^^^ y) - 3 * ~~~(x &&& ~~~y) - 6 * y - 11 * ~~~(x &&& ~~~x) + 15 * ~~~(x ||| y) + 20 * ~~~(x ||| ~~~y) + 4 * (x &&& ~~~y) = - 14 * (x &&& y) - 7 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_268 (x y : BitVec w) : +theorem e_268 : 5 * (x ||| y) + 1 * ~~~(x &&& ~~~y) - 1 * ~~~y + 4 * ~~~(x &&& ~~~x) - 4 * ~~~(x ||| y) - 10 * ~~~(x ||| ~~~y) - 10 * (x &&& y) = 8 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_269 (x y : BitVec w) : +theorem e_269 : 5 * x - 6 * ~~~y + 1 * ~~~(x &&& y) + 1 * ~~~x + 1 * ~~~(x ||| ~~~y) + 3 * (x &&& ~~~y) - 2 * (x &&& y) = - 4 * ~~~(x ||| y) + 3 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_270 (x y : BitVec w) : +theorem e_270 : - 7 * y - 2 * (x ^^^ y) + 11 * ~~~(x &&& ~~~y) - 10 * ~~~(x ||| y) - 1 * ~~~(x ||| ~~~y) + 10 * (x &&& ~~~y) + 3 * (x &&& y) = 7 * x + 1 * ~~~(x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_271 (x y : BitVec w) : +theorem e_271 : 2 * ~~~y + 5 * ~~~(x ^^^ y) + 11 * ~~~(x &&& ~~~y) + 2 * (x ||| y) - 2 * ~~~x - 16 * ~~~(x ||| y) - 4 * (x &&& ~~~y) = 18 * (x &&& y) + 11 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_272 (x y : BitVec w) : +theorem e_272 : 2 * ~~~(x &&& ~~~y) - 1 * x - 11 * (x ^^^ y) + 11 * ~~~y - 7 * (x ||| ~~~y) - 6 * ~~~(x ||| y) + 6 * (x &&& y) = - 8 * (x &&& ~~~y) - 9 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_273 (x y : BitVec w) : +theorem e_273 : 2 * (x ||| y) - 7 * ~~~y + 3 * ~~~(x &&& y) + 7 * ~~~(x ||| y) - 3 * ~~~(x ||| ~~~y) + 3 * (x &&& ~~~y) - 1 * (x &&& y) = 2 * ~~~x + 1 * (x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_274 (x y : BitVec w) : +theorem e_274 : 11 * (x ||| y) - 11 * y - 3 * ~~~x - 1 * ~~~(x ^^^ y) + 5 * ~~~(x ||| ~~~y) - 11 * (x &&& ~~~y) + 3 * (x &&& y) = 2 * ~~~(x &&& ~~~y) - 6 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_275 (x y : BitVec w) : +theorem e_275 : - 5 * ~~~(x &&& ~~~y) - 2 * ~~~y + 4 * ~~~(x ^^^ y) - 1 * y + 3 * ~~~(x ||| y) + 6 * ~~~(x ||| ~~~y) + 2 * (x &&& ~~~y) = - 2 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_276 (x y : BitVec w) : +theorem e_276 : 2 * y + 1 * ~~~(x ^^^ y) + 1 * (x ||| y) - 1 * ~~~(x &&& y) - 7 * ~~~x + 5 * ~~~(x ||| ~~~y) - 4 * (x &&& y) = - 7 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_277 (x y : BitVec w) : +theorem e_277 : 2 * (x ||| ~~~y) - 11 * x + 2 * (x ||| y) + 3 * ~~~(x ^^^ y) + 11 * ~~~y - 16 * ~~~(x ||| y) - 2 * ~~~(x ||| ~~~y) = 4 * (x &&& ~~~y) - 4 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_278 (x y : BitVec w) : +theorem e_278 : - 1 * ~~~(x &&& ~~~x) - 2 * x + 5 * ~~~(x &&& ~~~y) + 5 * (x ||| y) - 4 * ~~~(x ||| y) - 20 * ~~~(x ||| ~~~y) - 13 * (x &&& ~~~y) = - 11 * (x ^^^ y) + 7 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_279 (x y : BitVec w) : +theorem e_279 : - 6 * y - 2 * ~~~(x &&& ~~~y) + 11 * ~~~x - 1 * ~~~(x &&& y) - 8 * ~~~(x ||| y) + 1 * ~~~(x ||| ~~~y) + 8 * (x &&& y) = 3 * (x ^^^ y) - 4 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_280 (x y : BitVec w) : +theorem e_280 : 2 * ~~~(x &&& ~~~x) - 11 * ~~~x + 1 * (x ^^^ y) - 7 * ~~~(x &&& y) - 7 * ~~~(x &&& ~~~y) + 23 * ~~~(x ||| y) + 5 * (x &&& y) = - 4 * (x &&& ~~~y) - 22 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_281 (x y : BitVec w) : +theorem e_281 : - 1 * ~~~(x &&& ~~~x) - 11 * (x ||| y) - 1 * ~~~(x &&& ~~~y) - 7 * (x ^^^ y) + 2 * ~~~(x ||| y) + 20 * (x &&& ~~~y) + 14 * (x &&& y) = - 20 * ~~~(x ||| ~~~y) + 1 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_282 (x y : BitVec w) : +theorem e_282 : - 7 * (x ||| y) + 11 * (x ||| ~~~y) - 3 * ~~~(x &&& y) - 8 * ~~~(x ||| y) + 3 * ~~~(x ||| ~~~y) - 8 * (x &&& ~~~y) - 4 * (x &&& y) = - 7 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_283 (x y : BitVec w) : +theorem e_283 : 3 * ~~~y + 5 * (x ||| ~~~y) + 2 * (x ||| y) - 9 * ~~~(x ||| y) - 3 * ~~~(x ||| ~~~y) - 11 * (x &&& ~~~y) - 8 * (x &&& y) = - 1 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_284 (x y : BitVec w) : +theorem e_284 : - 3 * ~~~y + 1 * (x ||| y) + 1 * ~~~(x ^^^ y) - 2 * ~~~(x &&& ~~~y) + 4 * ~~~(x ||| y) + 8 * (x &&& ~~~y) + 7 * (x &&& y) = 7 * x - 1 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_285 (x y : BitVec w) : +theorem e_285 : - 7 * ~~~x - 3 * y + 1 * ~~~(x ^^^ y) - 1 * (x ^^^ y) + 11 * ~~~(x ||| ~~~y) + 1 * (x &&& ~~~y) + 2 * (x &&& y) = - 6 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_286 (x y : BitVec w) : +theorem e_286 : 4 * ~~~(x &&& y) - 5 * (x ^^^ y) + 4 * y + 3 * ~~~(x ||| y) + 4 * ~~~(x ||| ~~~y) + 1 * (x &&& ~~~y) - 4 * (x &&& y) = 7 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_287 (x y : BitVec w) : +theorem e_287 : 2 * ~~~(x &&& ~~~y) + 1 * y - 5 * ~~~(x ^^^ y) - 3 * ~~~(x ||| y) - 10 * ~~~(x ||| ~~~y) + 1 * (x &&& ~~~y) + 3 * (x &&& y) = 1 * (x ||| ~~~y) - 7 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_288 (x y : BitVec w) : +theorem e_288 : 1 * ~~~x - 2 * ~~~(x &&& ~~~x) + 2 * (x ^^^ y) + 2 * ~~~(x &&& y) - 1 * ~~~(x ||| y) - 3 * ~~~(x ||| ~~~y) - 2 * (x &&& ~~~y) = - 2 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_289 (x y : BitVec w) : +theorem e_289 : - 1 * y - 1 * ~~~(x &&& y) - 5 * ~~~y + 5 * ~~~(x ||| y) + 1 * ~~~(x ||| ~~~y) + 8 * (x &&& ~~~y) + 2 * (x &&& y) = - 1 * ~~~(x &&& ~~~y) + 2 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_290 (x y : BitVec w) : +theorem e_290 : 5 * ~~~(x ^^^ y) + 2 * x + 2 * ~~~(x &&& ~~~y) + 11 * ~~~(x &&& y) - 18 * ~~~(x ||| y) - 13 * ~~~(x ||| ~~~y) - 13 * (x &&& ~~~y) = 9 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_291 (x y : BitVec w) : +theorem e_291 : - 1 * (x ||| ~~~y) + 1 * x - 11 * ~~~x - 5 * (x ^^^ y) + 4 * ~~~(x &&& y) + 8 * ~~~(x ||| y) + 12 * ~~~(x ||| ~~~y) = - 1 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_292 (x y : BitVec w) : +theorem e_292 : 3 * x + 3 * ~~~x - 11 * ~~~(x ^^^ y) + 5 * ~~~(x ||| y) - 1 * ~~~(x ||| ~~~y) - 4 * (x &&& ~~~y) + 10 * (x &&& y) = 2 * (x ||| y) - 3 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_293 (x y : BitVec w) : +theorem e_293 : 1 * ~~~y + 2 * (x ||| y) - 5 * y - 2 * ~~~(x &&& ~~~y) + 4 * ~~~(x ||| ~~~y) - 4 * (x &&& ~~~y) + 4 * (x &&& y) = - 1 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_294 (x y : BitVec w) : +theorem e_294 : - 2 * ~~~(x &&& y) + 11 * ~~~y - 2 * ~~~(x ^^^ y) + 11 * ~~~x - 18 * ~~~(x ||| y) - 4 * ~~~(x ||| ~~~y) - 9 * (x &&& ~~~y) = - 7 * (x &&& y) + 5 * y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_295 (x y : BitVec w) : +theorem e_295 : - 11 * ~~~(x ^^^ y) - 3 * ~~~y + 2 * ~~~x + 2 * (x ||| ~~~y) + 10 * ~~~(x ||| y) - 2 * ~~~(x ||| ~~~y) + 6 * (x &&& ~~~y) = - 14 * (x &&& y) + 5 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_296 (x y : BitVec w) : +theorem e_296 : - 6 * x + 1 * ~~~(x ^^^ y) - 1 * (x ||| y) - 5 * ~~~(x &&& ~~~x) + 6 * ~~~(x ||| ~~~y) + 12 * (x &&& ~~~y) + 11 * (x &&& y) = - 4 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_297 (x y : BitVec w) : +theorem e_297 : - 2 * (x ||| y) - 3 * x + 1 * ~~~y + 6 * ~~~(x ||| y) + 2 * ~~~(x ||| ~~~y) + 4 * (x &&& ~~~y) + 12 * (x &&& y) = 7 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_298 (x y : BitVec w) : +theorem e_298 : 1 * y - 7 * (x ^^^ y) + 1 * ~~~(x &&& y) + 11 * ~~~y - 12 * ~~~(x ||| y) - 5 * (x &&& ~~~y) - 1 * (x &&& y) = - 5 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_299 (x y : BitVec w) : +theorem e_299 : 1 * y + 1 * x - 5 * ~~~y + 4 * ~~~(x ||| y) - 2 * ~~~(x ||| ~~~y) + 3 * (x &&& ~~~y) - 3 * (x &&& y) = - 1 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_300 (x y : BitVec w) : +theorem e_300 : 1 * ~~~(x ^^^ y) + 11 * ~~~y - 1 * (x ||| ~~~y) - 10 * ~~~(x ||| y) + 1 * ~~~(x ||| ~~~y) - 15 * (x &&& ~~~y) - 5 * (x &&& y) = - 5 * ~~~(x &&& ~~~x) + 6 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_301 (x y : BitVec w) : +theorem e_301 : - 3 * y + 1 * (x ||| y) + 1 * (x ||| ~~~y) - 1 * ~~~(x ||| y) - 9 * ~~~(x ||| ~~~y) - 13 * (x &&& ~~~y) + 1 * (x &&& y) = - 11 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_302 (x y : BitVec w) : +theorem e_302 : - 1 * x - 7 * (x ||| ~~~y) - 1 * ~~~(x &&& ~~~x) - 7 * (x ||| y) + 10 * ~~~(x ||| ~~~y) + 16 * (x &&& ~~~y) + 18 * (x &&& y) = - 10 * ~~~(x ||| y) + 2 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_303 (x y : BitVec w) : +theorem e_303 : 1 * ~~~x + 11 * (x ^^^ y) - 11 * (x ||| ~~~y) - 2 * ~~~(x ||| y) - 13 * ~~~(x ||| ~~~y) - 12 * (x &&& ~~~y) + 11 * (x &&& y) = - 1 * ~~~(x &&& y) - 11 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_304 (x y : BitVec w) : +theorem e_304 : 2 * ~~~x + 2 * x - 2 * ~~~(x ^^^ y) + 2 * (x ^^^ y) - 15 * ~~~(x ||| ~~~y) - 15 * (x &&& ~~~y) - 11 * (x &&& y) = - 11 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_305 (x y : BitVec w) : +theorem e_305 : 3 * (x ^^^ y) - 2 * (x ||| ~~~y) + 1 * ~~~(x ^^^ y) - 2 * ~~~(x &&& ~~~y) - 1 * ~~~y + 4 * ~~~(x ||| y) + 2 * ~~~(x ||| ~~~y) = - 6 * (x &&& y) + 3 * y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_306 (x y : BitVec w) : +theorem e_306 : - 2 * ~~~x - 3 * ~~~(x ^^^ y) - 2 * (x ||| y) - 6 * x + 5 * ~~~(x ||| y) + 4 * ~~~(x ||| ~~~y) + 11 * (x &&& y) = - 8 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_307 (x y : BitVec w) : +theorem e_307 : - 6 * y - 1 * ~~~(x &&& y) + 11 * (x ||| y) + 4 * ~~~y - 4 * ~~~(x ||| ~~~y) - 12 * (x &&& ~~~y) - 3 * (x &&& y) = 2 * (x ||| ~~~y) + 1 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_308 (x y : BitVec w) : +theorem e_308 : 1 * ~~~y - 1 * x - 2 * ~~~(x ^^^ y) + 1 * ~~~(x &&& ~~~y) - 7 * y + 4 * ~~~(x ||| ~~~y) - 2 * (x &&& ~~~y) = - 7 * (x &&& y) - 2 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_309 (x y : BitVec w) : +theorem e_309 : 1 * x - 3 * ~~~(x &&& y) + 5 * ~~~(x &&& ~~~x) + 11 * ~~~y - 12 * ~~~(x ||| y) - 14 * (x &&& ~~~y) - 5 * (x &&& y) = 1 * ~~~(x ^^^ y) + 2 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_310 (x y : BitVec w) : +theorem e_310 : - 5 * ~~~x - 2 * ~~~(x &&& y) + 1 * y + 1 * ~~~y + 6 * ~~~(x ||| y) + 6 * ~~~(x ||| ~~~y) + 1 * (x &&& ~~~y) = 1 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_311 (x y : BitVec w) : +theorem e_311 : - 2 * ~~~y + 2 * (x ||| ~~~y) - 6 * x + 1 * ~~~x - 1 * ~~~(x ||| y) - 1 * ~~~(x ||| ~~~y) + 6 * (x &&& ~~~y) = - 4 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_312 (x y : BitVec w) : +theorem e_312 : - 1 * (x ||| ~~~y) - 11 * (x ||| y) + 11 * ~~~(x &&& y) - 6 * y + 1 * x - 12 * ~~~(x ||| y) + 15 * (x &&& y) = - 4 * ~~~(x ||| ~~~y) - 2 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_313 (x y : BitVec w) : +theorem e_313 : - 1 * (x ||| ~~~y) + 7 * y + 7 * ~~~y - 5 * ~~~(x ||| y) - 6 * ~~~(x ||| ~~~y) - 5 * (x &&& ~~~y) - 6 * (x &&& y) = 1 * ~~~(x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_314 (x y : BitVec w) : +theorem e_314 : - 7 * (x ^^^ y) - 1 * ~~~y - 1 * ~~~(x &&& ~~~y) - 1 * (x ||| y) + 2 * ~~~(x ||| y) + 6 * ~~~(x ||| ~~~y) - 1 * (x &&& y) = - 9 * (x &&& ~~~y) - 3 * y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_315 (x y : BitVec w) : +theorem e_315 : - 6 * ~~~x - 1 * x + 5 * (x ||| y) + 13 * ~~~(x ||| y) + 8 * ~~~(x ||| ~~~y) - 4 * (x &&& ~~~y) + 3 * (x &&& y) = 7 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_316 (x y : BitVec w) : +theorem e_316 : 4 * ~~~(x &&& ~~~y) + 1 * x - 7 * ~~~y + 3 * (x ^^^ y) + 4 * ~~~(x ||| y) - 6 * ~~~(x ||| ~~~y) + 4 * (x &&& ~~~y) = 1 * ~~~(x &&& ~~~x) + 4 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_317 (x y : BitVec w) : +theorem e_317 : 2 * ~~~(x &&& ~~~x) + 1 * y + 5 * ~~~x + 1 * ~~~(x ^^^ y) - 15 * ~~~(x ||| y) - 8 * ~~~(x ||| ~~~y) - 9 * (x &&& ~~~y) = - 7 * (x ||| ~~~y) + 11 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_318 (x y : BitVec w) : +theorem e_318 : - 7 * ~~~y + 5 * ~~~x + 1 * (x ^^^ y) + 2 * ~~~(x ^^^ y) - 6 * ~~~(x ||| ~~~y) + 5 * (x &&& ~~~y) - 3 * (x &&& y) = 1 * ~~~(x ||| y) - 1 * (x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_319 (x y : BitVec w) : +theorem e_319 : 1 * ~~~(x &&& ~~~x) + 3 * (x ||| ~~~y) + 2 * x - 1 * ~~~(x ||| y) + 2 * ~~~(x ||| ~~~y) - 6 * (x &&& ~~~y) - 6 * (x &&& y) = 3 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_320 (x y : BitVec w) : +theorem e_320 : - 7 * ~~~x + 1 * x + 7 * ~~~(x &&& ~~~x) + 1 * ~~~(x ||| y) + 1 * ~~~(x ||| ~~~y) - 7 * (x &&& ~~~y) - 8 * (x &&& y) = 1 * ~~~(x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_321 (x y : BitVec w) : +theorem e_321 : 5 * x - 2 * ~~~(x &&& ~~~x) - 1 * ~~~(x &&& ~~~y) + 5 * ~~~(x ||| y) + 5 * ~~~(x ||| ~~~y) - 1 * (x &&& ~~~y) - 2 * (x &&& y) = 2 * ~~~(x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_322 (x y : BitVec w) : +theorem e_322 : 3 * ~~~(x &&& ~~~y) - 3 * ~~~(x &&& ~~~x) + 4 * (x ||| ~~~y) - 2 * ~~~x - 2 * ~~~(x ||| y) + 2 * ~~~(x ||| ~~~y) - 1 * (x &&& ~~~y) = 4 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_323 (x y : BitVec w) : +theorem e_323 : 4 * ~~~(x &&& y) + 11 * x + 3 * ~~~y - 1 * (x ||| y) - 10 * ~~~(x ||| ~~~y) - 24 * (x &&& ~~~y) - 10 * (x &&& y) = - 7 * (x ^^^ y) + 7 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_324 (x y : BitVec w) : +theorem e_324 : - 6 * ~~~(x &&& ~~~x) + 4 * (x ||| ~~~y) + 1 * (x ^^^ y) + 1 * ~~~(x ||| y) + 5 * ~~~(x ||| ~~~y) + 1 * (x &&& ~~~y) + 1 * (x &&& y) = - 1 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_325 (x y : BitVec w) : +theorem e_325 : - 1 * ~~~(x &&& ~~~y) - 2 * ~~~(x &&& y) + 11 * (x ||| y) + 3 * ~~~(x ||| y) - 8 * ~~~(x ||| ~~~y) - 16 * (x &&& ~~~y) - 17 * (x &&& y) = - 7 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_326 (x y : BitVec w) : +theorem e_326 : - 11 * ~~~x - 11 * ~~~(x &&& y) - 1 * ~~~(x ^^^ y) - 5 * (x ^^^ y) + 23 * ~~~(x ||| y) + 26 * ~~~(x ||| ~~~y) + 16 * (x &&& ~~~y) = - 1 * y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_327 (x y : BitVec w) : +theorem e_327 : - 2 * x - 3 * ~~~(x &&& ~~~x) - 3 * ~~~(x &&& y) + 1 * (x ||| ~~~y) + 6 * ~~~(x ||| ~~~y) + 7 * (x &&& ~~~y) + 4 * (x &&& y) = - 5 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_328 (x y : BitVec w) : +theorem e_328 : - 1 * ~~~x - 2 * (x ||| y) - 6 * ~~~y + 7 * (x ^^^ y) - 3 * ~~~(x ^^^ y) + 10 * ~~~(x ||| y) + 1 * (x &&& ~~~y) + 5 * (x &&& y) = 4 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_329 (x y : BitVec w) : +theorem e_329 : - 3 * ~~~y - 1 * ~~~x + 5 * (x ||| y) + 5 * y - 11 * (x ^^^ y) - 7 * ~~~(x ||| y) - 9 * ~~~(x ||| ~~~y) - 19 * (x &&& y) = 2 * x - 11 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_330 (x y : BitVec w) : +theorem e_330 : 1 * ~~~(x ^^^ y) - 3 * y - 5 * (x ^^^ y) - 7 * ~~~x + 4 * ~~~(x ||| y) + 13 * ~~~(x ||| ~~~y) + 3 * (x &&& ~~~y) - 1 * (x &&& y) = 1 * ~~~(x &&& y) - 3 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_331 (x y : BitVec w) : +theorem e_331 : - 6 * ~~~x + 2 * (x ||| ~~~y) - 3 * x + 2 * (x ||| y) - 10 * ~~~(x ||| y) - 10 * ~~~(x ||| ~~~y) - 4 * (x &&& ~~~y) - 15 * (x &&& y) = - 3 * ~~~(x &&& ~~~x) - 11 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_332 (x y : BitVec w) : +theorem e_332 : - 1 * x - 3 * ~~~x + 4 * ~~~(x ^^^ y) - 5 * ~~~(x &&& y) + 4 * y + 9 * ~~~(x ||| y) + 11 * (x &&& ~~~y) - 2 * (x &&& y) = 5 * ~~~(x &&& ~~~x) - 9 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_333 (x y : BitVec w) : +theorem e_333 : 4 * ~~~y + 4 * ~~~(x ^^^ y) - 1 * ~~~(x &&& ~~~y) + 2 * y - 18 * ~~~(x ||| y) - 1 * ~~~(x ||| ~~~y) - 17 * (x &&& ~~~y) - 18 * (x &&& y) = - 11 * (x ||| ~~~y) - 2 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_334 (x y : BitVec w) : +theorem e_334 : - 3 * ~~~(x &&& ~~~y) + 1 * x + 3 * ~~~(x &&& ~~~x) + 1 * ~~~(x &&& y) + 5 * (x ||| ~~~y) + 1 * ~~~(x ||| ~~~y) - 10 * (x &&& ~~~y) - 4 * (x &&& y) = 2 * y + 6 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_335 (x y : BitVec w) : +theorem e_335 : - 1 * x - 6 * ~~~(x ^^^ y) - 7 * ~~~(x &&& ~~~y) - 5 * ~~~(x &&& y) + 15 * ~~~(x ||| y) - 2 * ~~~(x ||| ~~~y) - 5 * (x &&& ~~~y) + 3 * (x &&& y) = - 11 * (x ||| y) - 3 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_336 (x y : BitVec w) : +theorem e_336 : - 6 * x - 11 * ~~~x - 3 * (x ||| y) - 11 * ~~~y - 2 * ~~~(x &&& y) + 24 * ~~~(x ||| y) + 27 * ~~~(x ||| ~~~y) + 9 * (x &&& y) = 11 * (x ^^^ y) - 33 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_337 (x y : BitVec w) : +theorem e_337 : 7 * ~~~x - 7 * (x ||| y) + 3 * y - 7 * x - 6 * ~~~(x ||| y) - 3 * ~~~(x ||| ~~~y) + 16 * (x &&& ~~~y) + 10 * (x &&& y) = - 1 * ~~~(x ^^^ y) + 2 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_338 (x y : BitVec w) : +theorem e_338 : - 6 * ~~~y + 1 * (x ^^^ y) + 2 * y + 1 * ~~~(x &&& y) + 1 * x + 12 * ~~~(x ||| y) + 3 * ~~~(x ||| ~~~y) + 4 * (x &&& y) = - 10 * (x &&& ~~~y) + 7 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_339 (x y : BitVec w) : +theorem e_339 : 2 * (x ^^^ y) - 2 * ~~~(x &&& y) - 11 * ~~~y - 11 * ~~~(x &&& ~~~y) + 19 * ~~~(x ||| y) + 12 * ~~~(x ||| ~~~y) + 12 * (x &&& ~~~y) + 7 * (x &&& y) = - 5 * ~~~(x ^^^ y) + 1 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_340 (x y : BitVec w) : +theorem e_340 : - 11 * (x ||| ~~~y) + 4 * ~~~x + 7 * ~~~(x &&& ~~~y) - 2 * ~~~(x &&& y) + 1 * y + 2 * ~~~(x ||| y) - 13 * ~~~(x ||| ~~~y) + 10 * (x &&& ~~~y) = - 3 * (x &&& y) - 3 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_341 (x y : BitVec w) : +theorem e_341 : 4 * (x ^^^ y) - 2 * x - 1 * ~~~(x &&& ~~~x) + 7 * y - 1 * ~~~(x ||| y) - 14 * ~~~(x ||| ~~~y) - 3 * (x &&& ~~~y) - 6 * (x &&& y) = - 2 * (x ||| y) - 2 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_342 (x y : BitVec w) : +theorem e_342 : 7 * ~~~x - 6 * ~~~(x &&& y) - 11 * (x ||| ~~~y) + 1 * ~~~(x &&& ~~~y) + 3 * ~~~y + 2 * ~~~(x ||| y) - 2 * ~~~(x ||| ~~~y) + 14 * (x &&& ~~~y) = - 4 * ~~~(x ^^^ y) - 6 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_343 (x y : BitVec w) : +theorem e_343 : 4 * x - 1 * (x ||| ~~~y) + 1 * ~~~y + 5 * ~~~x - 2 * ~~~(x &&& ~~~y) - 1 * ~~~(x &&& y) - 2 * ~~~(x ||| ~~~y) - 3 * (x &&& ~~~y) = 2 * ~~~(x ||| y) + 1 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_344 (x y : BitVec w) : +theorem e_344 : - 11 * (x ^^^ y) - 2 * ~~~x - 2 * (x ||| y) - 3 * (x ||| ~~~y) + 2 * ~~~(x ||| y) + 12 * ~~~(x ||| ~~~y) + 16 * (x &&& ~~~y) + 2 * (x &&& y) = - 3 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_345 (x y : BitVec w) : +theorem e_345 : 1 * ~~~y + 1 * y + 11 * ~~~(x ^^^ y) + 7 * ~~~(x &&& y) + 2 * (x ^^^ y) - 19 * ~~~(x ||| y) - 10 * ~~~(x ||| ~~~y) - 10 * (x &&& ~~~y) = 12 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_346 (x y : BitVec w) : +theorem e_346 : 11 * ~~~(x &&& ~~~x) + 4 * (x ||| ~~~y) - 1 * ~~~x - 1 * (x ||| y) + 3 * x + 4 * y - 17 * (x &&& ~~~y) - 21 * (x &&& y) = 14 * ~~~(x ||| y) + 13 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_347 (x y : BitVec w) : +theorem e_347 : - 5 * (x ^^^ y) - 6 * ~~~(x &&& ~~~y) + 3 * y - 7 * ~~~(x &&& ~~~x) - 1 * (x ||| y) + 13 * ~~~(x ||| y) + 16 * ~~~(x ||| ~~~y) + 12 * (x &&& y) = 1 * x - 14 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_348 (x y : BitVec w) : +theorem e_348 : - 1 * ~~~(x ^^^ y) + 2 * y - 7 * ~~~(x &&& y) + 3 * (x ||| ~~~y) - 2 * ~~~y + 6 * ~~~(x ||| y) + 5 * (x &&& ~~~y) - 5 * (x &&& y) = - 1 * ~~~(x &&& ~~~x) - 4 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_349 (x y : BitVec w) : +theorem e_349 : 2 * x - 3 * (x ||| ~~~y) - 7 * ~~~y + 3 * (x ||| y) + 3 * ~~~(x &&& ~~~y) + 7 * ~~~(x ||| y) - 3 * ~~~(x ||| ~~~y) + 8 * (x &&& ~~~y) = 5 * (x &&& y) + 3 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_350 (x y : BitVec w) : +theorem e_350 : - 11 * y - 5 * (x ^^^ y) + 2 * (x ||| y) + 5 * ~~~(x &&& ~~~y) + 11 * ~~~y - 16 * ~~~(x ||| y) + 9 * ~~~(x ||| ~~~y) - 8 * (x &&& ~~~y) = - 4 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_351 (x y : BitVec w) : +theorem e_351 : 5 * ~~~(x &&& ~~~y) - 6 * (x ||| y) - 1 * (x ^^^ y) - 1 * y - 4 * ~~~(x ||| y) + 4 * ~~~(x ||| ~~~y) + 8 * (x &&& ~~~y) + 2 * (x &&& y) = 1 * ~~~(x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_352 (x y : BitVec w) : +theorem e_352 : - 2 * ~~~(x &&& ~~~x) + 3 * ~~~(x &&& ~~~y) - 1 * ~~~(x &&& y) - 1 * ~~~x + 5 * (x ||| y) - 4 * ~~~(x ||| ~~~y) - 2 * (x &&& ~~~y) - 6 * (x &&& y) = - 1 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_353 (x y : BitVec w) : +theorem e_353 : - 2 * ~~~(x &&& ~~~x) - 1 * (x ||| y) + 2 * ~~~x + 7 * y - 1 * ~~~(x ||| y) - 7 * ~~~(x ||| ~~~y) + 3 * (x &&& ~~~y) - 5 * (x &&& y) = - 1 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_354 (x y : BitVec w) : +theorem e_354 : - 1 * ~~~(x &&& y) + 11 * x + 7 * y + 5 * ~~~x - 1 * ~~~(x ^^^ y) - 5 * ~~~(x ||| y) - 13 * ~~~(x ||| ~~~y) - 10 * (x &&& ~~~y) = 19 * (x &&& y) - 2 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_355 (x y : BitVec w) : +theorem e_355 : 1 * ~~~x + 1 * ~~~(x ^^^ y) - 5 * (x ||| y) - 6 * y + 1 * ~~~(x &&& ~~~x) + 9 * ~~~(x ||| ~~~y) + 11 * (x &&& ~~~y) + 16 * (x &&& y) = 3 * ~~~(x ||| y) + 7 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_356 (x y : BitVec w) : +theorem e_356 : - 1 * ~~~y + 2 * ~~~(x &&& y) - 2 * (x ||| ~~~y) + 1 * ~~~x + 1 * ~~~(x &&& ~~~x) - 3 * ~~~(x ||| y) - 1 * ~~~(x ||| ~~~y) - 1 * (x &&& y) = - 5 * ~~~(x ^^^ y) + 3 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_357 (x y : BitVec w) : +theorem e_357 : 2 * (x ||| ~~~y) + 2 * ~~~(x ^^^ y) - 5 * ~~~(x &&& ~~~x) - 6 * ~~~(x &&& ~~~y) + 7 * ~~~(x ||| y) + 9 * ~~~(x ||| ~~~y) + 1 * (x &&& ~~~y) + 5 * (x &&& y) = - 2 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_358 (x y : BitVec w) : +theorem e_358 : 1 * (x ||| ~~~y) - 3 * ~~~(x &&& y) - 7 * ~~~(x ^^^ y) - 2 * y - 7 * x + 9 * ~~~(x ||| y) + 9 * (x &&& ~~~y) + 15 * (x &&& y) = - 5 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_359 (x y : BitVec w) : +theorem e_359 : - 2 * (x ||| ~~~y) - 11 * ~~~(x &&& ~~~x) - 7 * ~~~x - 1 * ~~~(x &&& ~~~y) + 18 * ~~~(x ||| y) + 19 * ~~~(x ||| ~~~y) + 11 * (x &&& ~~~y) + 15 * (x &&& y) = 1 * x - 3 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_360 (x y : BitVec w) : +theorem e_360 : - 1 * ~~~(x &&& y) + 4 * (x ||| ~~~y) + 1 * (x ||| y) - 1 * (x ^^^ y) + 2 * ~~~(x ||| y) + 1 * ~~~(x ||| ~~~y) + 2 * (x &&& ~~~y) - 5 * (x &&& y) = 5 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_361 (x y : BitVec w) : +theorem e_361 : - 2 * ~~~x - 11 * ~~~(x &&& ~~~x) + 3 * ~~~(x ^^^ y) - 7 * ~~~y - 1 * ~~~(x &&& y) + 19 * ~~~(x ||| y) + 14 * ~~~(x ||| ~~~y) + 20 * (x &&& ~~~y) = 1 * (x ||| ~~~y) - 9 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_362 (x y : BitVec w) : +theorem e_362 : 5 * x - 7 * (x ^^^ y) + 1 * ~~~(x ^^^ y) - 1 * ~~~(x &&& ~~~x) + 2 * ~~~x - 2 * ~~~(x ||| y) + 6 * ~~~(x ||| ~~~y) + 3 * (x &&& ~~~y) = 5 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_363 (x y : BitVec w) : +theorem e_363 : 1 * y - 6 * (x ||| ~~~y) - 1 * (x ^^^ y) + 7 * x + 4 * ~~~(x &&& y) + 2 * ~~~(x ||| y) + 3 * ~~~(x ||| ~~~y) + 3 * (x &&& ~~~y) = - 5 * (x &&& y) + 7 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_364 (x y : BitVec w) : +theorem e_364 : 7 * (x ||| ~~~y) - 1 * y + 2 * ~~~(x &&& ~~~y) - 2 * ~~~(x ^^^ y) + 1 * (x ^^^ y) - 8 * ~~~(x ||| y) - 9 * (x &&& ~~~y) - 7 * (x &&& y) = 3 * ~~~(x ||| ~~~y) - 1 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_365 (x y : BitVec w) : +theorem e_365 : - 1 * ~~~(x &&& ~~~x) - 1 * ~~~(x &&& y) - 2 * ~~~(x &&& ~~~y) - 7 * (x ||| y) + 7 * x + 4 * ~~~(x ||| y) + 10 * ~~~(x ||| ~~~y) + 2 * (x &&& y) = - 1 * y - 2 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_366 (x y : BitVec w) : +theorem e_366 : 2 * ~~~y - 1 * ~~~(x &&& ~~~y) - 1 * ~~~(x ^^^ y) - 6 * ~~~(x &&& y) + 2 * (x ||| ~~~y) + 4 * ~~~(x ||| y) - 4 * ~~~(x ||| ~~~y) - 9 * (x &&& ~~~y) = - 11 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_367 (x y : BitVec w) : +theorem e_367 : - 1 * (x ||| ~~~y) + 3 * ~~~y - 3 * ~~~x - 6 * ~~~(x ^^^ y) + 2 * ~~~(x ||| y) - 2 * ~~~(x ||| ~~~y) - 7 * (x &&& ~~~y) + 7 * (x &&& y) = - 5 * ~~~(x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_368 (x y : BitVec w) : +theorem e_368 : 1 * ~~~y - 2 * ~~~(x &&& ~~~x) + 4 * ~~~(x &&& ~~~y) - 1 * ~~~(x ^^^ y) - 3 * (x ^^^ y) - 2 * ~~~(x ||| y) + 1 * ~~~(x ||| ~~~y) - 6 * (x &&& y) = 1 * (x &&& ~~~y) - 5 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_369 (x y : BitVec w) : +theorem e_369 : - 5 * (x ^^^ y) - 3 * (x ||| ~~~y) - 11 * y + 2 * (x ||| y) + 5 * ~~~(x ^^^ y) + 1 * x - 2 * ~~~(x ||| y) + 5 * (x &&& ~~~y) = - 6 * (x &&& y) - 14 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_370 (x y : BitVec w) : +theorem e_370 : - 5 * ~~~x + 1 * (x ||| y) - 6 * ~~~(x ^^^ y) - 11 * ~~~(x &&& ~~~x) + 1 * ~~~(x &&& y) + 4 * x + 14 * ~~~(x ||| ~~~y) + 5 * (x &&& ~~~y) = - 12 * (x &&& y) - 21 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_371 (x y : BitVec w) : +theorem e_371 : 3 * ~~~(x ^^^ y) - 7 * (x ||| ~~~y) + 7 * x + 1 * (x ^^^ y) + 7 * ~~~x - 8 * ~~~(x ||| ~~~y) - 5 * (x &&& ~~~y) - 3 * (x &&& y) = 7 * ~~~(x ||| y) - 4 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_372 (x y : BitVec w) : +theorem e_372 : 2 * ~~~(x &&& y) + 1 * y + 5 * ~~~x + 2 * ~~~(x ^^^ y) + 2 * ~~~(x ||| y) + 3 * ~~~(x ||| ~~~y) + 9 * (x &&& ~~~y) + 8 * (x &&& y) = 11 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_373 (x y : BitVec w) : +theorem e_373 : - 1 * ~~~(x &&& ~~~y) - 2 * ~~~(x &&& ~~~x) + 1 * (x ||| ~~~y) + 7 * y + 13 * ~~~(x ||| y) - 4 * ~~~(x ||| ~~~y) + 1 * (x &&& ~~~y) + 6 * (x &&& y) = 11 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_374 (x y : BitVec w) : +theorem e_374 : 2 * ~~~(x &&& y) + 2 * ~~~(x ^^^ y) - 3 * y - 1 * x - 5 * ~~~y + 1 * ~~~(x ||| y) + 4 * (x &&& ~~~y) + 2 * (x &&& y) = - 1 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_375 (x y : BitVec w) : +theorem e_375 : 3 * y - 7 * ~~~y + 2 * (x ^^^ y) - 11 * ~~~x + 3 * x + 7 * ~~~(x ||| y) - 5 * ~~~(x ||| ~~~y) - 17 * (x &&& y) = - 2 * (x &&& ~~~y) - 11 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_376 (x y : BitVec w) : +theorem e_376 : 7 * ~~~(x ^^^ y) + 2 * (x ^^^ y) - 2 * (x ||| ~~~y) + 1 * y - 1 * ~~~(x &&& y) - 4 * ~~~(x ||| y) - 2 * ~~~(x ||| ~~~y) - 6 * (x &&& y) = - 1 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_377 (x y : BitVec w) : +theorem e_377 : - 2 * ~~~y - 1 * ~~~(x &&& y) + 11 * ~~~(x ^^^ y) + 7 * (x ^^^ y) - 8 * ~~~(x ||| y) - 6 * ~~~(x ||| ~~~y) - 5 * (x &&& ~~~y) - 12 * (x &&& y) = - 1 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_378 (x y : BitVec w) : +theorem e_378 : - 7 * (x ||| ~~~y) - 3 * ~~~(x &&& ~~~x) + 1 * (x ||| y) - 3 * ~~~(x &&& y) + 16 * ~~~(x ||| y) + 5 * ~~~(x ||| ~~~y) + 17 * (x &&& ~~~y) + 7 * (x &&& y) = - 2 * ~~~(x ^^^ y) + 5 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_379 (x y : BitVec w) : +theorem e_379 : 7 * (x ||| y) - 2 * x + 7 * ~~~(x &&& ~~~y) - 11 * (x ^^^ y) - 7 * ~~~(x ||| y) - 1 * ~~~(x ||| ~~~y) + 6 * (x &&& ~~~y) - 10 * (x &&& y) = 2 * y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_380 (x y : BitVec w) : +theorem e_380 : 3 * ~~~(x &&& y) + 1 * (x ||| ~~~y) + 5 * ~~~(x ^^^ y) - 2 * (x ^^^ y) - 11 * ~~~y - 1 * ~~~(x ||| ~~~y) + 11 * (x &&& ~~~y) - 4 * (x &&& y) = - 2 * ~~~(x ||| y) + 2 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_381 (x y : BitVec w) : +theorem e_381 : - 3 * (x ||| y) - 1 * (x ||| ~~~y) + 1 * ~~~(x ^^^ y) + 3 * ~~~(x &&& y) - 1 * ~~~y + 5 * ~~~(x &&& ~~~y) - 2 * ~~~(x ||| y) + 7 * (x &&& ~~~y) = 5 * ~~~(x &&& ~~~x) - 3 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_382 (x y : BitVec w) : +theorem e_382 : - 3 * ~~~x - 7 * (x ^^^ y) + 1 * y + 2 * x - 1 * ~~~(x &&& ~~~x) + 7 * (x ||| y) + 4 * ~~~(x ||| y) + 3 * ~~~(x ||| ~~~y) = 1 * (x &&& ~~~y) + 9 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_383 (x y : BitVec w) : +theorem e_383 : 2 * (x ^^^ y) - 11 * x - 11 * ~~~y + 1 * ~~~(x &&& ~~~x) + 11 * ~~~(x &&& y) - 14 * ~~~(x ||| ~~~y) + 8 * (x &&& ~~~y) + 10 * (x &&& y) = 1 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_384 (x y : BitVec w) : +theorem e_384 : 4 * ~~~x + 2 * (x ||| ~~~y) - 2 * (x ^^^ y) + 1 * ~~~(x ^^^ y) - 2 * ~~~(x &&& ~~~x) - 5 * ~~~(x ||| y) + 3 * ~~~(x ||| ~~~y) + 5 * (x &&& ~~~y) = 3 * (x ||| y) - 2 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_385 (x y : BitVec w) : +theorem e_385 : - 2 * ~~~(x &&& y) + 2 * ~~~x + 7 * ~~~(x &&& ~~~y) - 5 * (x ||| ~~~y) - 11 * x - 7 * ~~~(x ||| ~~~y) + 20 * (x &&& ~~~y) + 9 * (x &&& y) = 2 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_386 (x y : BitVec w) : +theorem e_386 : 2 * ~~~(x &&& y) + 4 * (x ^^^ y) + 2 * (x ||| ~~~y) - 11 * ~~~y - 1 * ~~~(x &&& ~~~y) + 8 * ~~~(x ||| y) - 16 * ~~~(x ||| ~~~y) - 12 * (x &&& y) = - 3 * (x &&& ~~~y) - 11 * y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_387 (x y : BitVec w) : +theorem e_387 : 5 * x + 2 * (x ||| y) + 7 * ~~~y - 11 * (x ^^^ y) - 7 * ~~~(x ||| y) + 12 * ~~~(x ||| ~~~y) - 3 * (x &&& ~~~y) - 7 * (x &&& y) = - 3 * (x ||| ~~~y) + 3 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_388 (x y : BitVec w) : +theorem e_388 : 11 * ~~~y + 2 * y + 5 * (x ^^^ y) - 2 * ~~~x - 6 * (x ||| ~~~y) - 5 * ~~~(x &&& ~~~x) + 2 * ~~~(x ||| y) + 9 * (x &&& y) = 5 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_389 (x y : BitVec w) : +theorem e_389 : - 1 * ~~~(x &&& ~~~x) + 11 * (x ||| ~~~y) - 3 * ~~~(x &&& ~~~y) - 2 * ~~~y + 1 * ~~~(x &&& y) - 2 * (x ^^^ y) - 6 * ~~~(x ||| y) - 7 * (x &&& y) = 7 * (x &&& ~~~y) - 5 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_390 (x y : BitVec w) : +theorem e_390 : 5 * y + 1 * ~~~y + 1 * ~~~x - 1 * (x ||| y) - 3 * ~~~(x ||| y) - 5 * ~~~(x ||| ~~~y) + 11 * (x &&& ~~~y) + 6 * (x &&& y) = - 1 * ~~~(x ^^^ y) + 11 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_391 (x y : BitVec w) : +theorem e_391 : - 2 * (x ^^^ y) + 3 * (x ||| ~~~y) - 1 * ~~~x - 2 * y - 7 * ~~~(x ||| y) + 5 * ~~~(x ||| ~~~y) - 1 * (x &&& ~~~y) - 6 * (x &&& y) = - 5 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_392 (x y : BitVec w) : +theorem e_392 : 2 * x + 1 * y - 2 * (x ||| ~~~y) - 1 * ~~~y - 1 * ~~~(x &&& y) + 2 * ~~~(x ||| y) - 2 * ~~~(x ||| ~~~y) - 3 * (x &&& y) = - 2 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_393 (x y : BitVec w) : +theorem e_393 : 4 * ~~~(x &&& y) + 3 * (x ||| y) + 4 * ~~~(x &&& ~~~y) + 2 * (x ||| ~~~y) - 8 * ~~~(x ||| y) - 9 * ~~~(x ||| ~~~y) - 9 * (x &&& ~~~y) - 9 * (x &&& y) = 2 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_394 (x y : BitVec w) : +theorem e_394 : - 1 * ~~~(x ^^^ y) - 5 * ~~~(x &&& y) - 2 * ~~~y + 3 * x + 11 * ~~~(x ||| y) + 3 * ~~~(x ||| ~~~y) + 7 * (x &&& ~~~y) + 1 * (x &&& y) = 5 * (x ||| ~~~y) - 2 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_395 (x y : BitVec w) : +theorem e_395 : 2 * (x ||| y) + 3 * (x ^^^ y) - 1 * ~~~(x &&& ~~~x) - 3 * ~~~(x &&& y) - 1 * ~~~x + 7 * ~~~(x ||| y) + 1 * (x &&& ~~~y) - 1 * (x &&& y) = 2 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_396 (x y : BitVec w) : +theorem e_396 : - 6 * (x ||| y) - 3 * y + 1 * ~~~(x ^^^ y) - 2 * (x ||| ~~~y) + 5 * ~~~(x ||| y) + 13 * ~~~(x ||| ~~~y) + 19 * (x &&& ~~~y) + 3 * (x &&& y) = 11 * ~~~(x &&& y) - 7 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_397 (x y : BitVec w) : +theorem e_397 : 2 * (x ||| ~~~y) - 5 * ~~~(x &&& ~~~y) - 7 * x - 1 * ~~~x + 1 * ~~~y - 11 * y + 3 * ~~~(x ||| y) + 4 * (x &&& ~~~y) = - 17 * ~~~(x ||| ~~~y) - 21 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_398 (x y : BitVec w) : +theorem e_398 : - 1 * x + 1 * ~~~(x ^^^ y) + 4 * ~~~(x &&& y) + 2 * (x ^^^ y) + 1 * y - 2 * ~~~(x ||| y) - 4 * ~~~(x ||| ~~~y) + 2 * (x &&& y) = 3 * ~~~(x &&& ~~~x) + 2 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_399 (x y : BitVec w) : +theorem e_399 : 2 * y - 3 * (x ^^^ y) - 1 * x + 3 * ~~~(x &&& ~~~y) + 2 * (x ||| y) + 3 * ~~~(x &&& y) - 7 * ~~~(x ||| ~~~y) - 1 * (x &&& ~~~y) = 6 * ~~~(x ||| y) + 6 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_400 (x y : BitVec w) : +theorem e_400 : 1 * x - 2 * (x ||| y) + 2 * (x ^^^ y) + 2 * ~~~(x &&& ~~~x) + 1 * ~~~(x &&& ~~~y) - 3 * ~~~(x ||| y) - 3 * (x &&& ~~~y) - 2 * (x &&& y) = 3 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_401 (x y : BitVec w) : +theorem e_401 : 2 * ~~~y + 4 * ~~~x + 3 * (x ^^^ y) - 3 * ~~~(x &&& ~~~y) - 2 * ~~~(x &&& y) + 1 * x + 1 * (x ||| ~~~y) - 3 * (x &&& ~~~y) = - 3 * (x &&& y) + 2 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_402 (x y : BitVec w) : +theorem e_402 : 5 * y + 7 * ~~~(x &&& ~~~x) + 4 * (x ||| ~~~y) - 6 * ~~~y - 2 * (x ^^^ y) - 10 * ~~~(x ||| ~~~y) - 2 * (x &&& ~~~y) - 10 * (x &&& y) = 5 * ~~~(x ^^^ y) + 1 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_403 (x y : BitVec w) : +theorem e_403 : 2 * (x ||| ~~~y) + 3 * y - 6 * ~~~(x &&& y) - 6 * ~~~(x &&& ~~~y) + 6 * ~~~(x ||| y) + 5 * ~~~(x ||| ~~~y) - 1 * (x &&& ~~~y) - 4 * (x &&& y) = 1 * ~~~x - 5 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_404 (x y : BitVec w) : +theorem e_404 : 11 * (x ^^^ y) - 6 * ~~~(x ^^^ y) + 11 * ~~~(x &&& y) + 1 * x + 5 * ~~~(x ||| y) - 11 * ~~~(x ||| ~~~y) - 24 * (x &&& ~~~y) + 16 * (x &&& y) = - 1 * ~~~y + 11 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_405 (x y : BitVec w) : +theorem e_405 : 1 * ~~~(x &&& ~~~x) + 5 * (x ||| ~~~y) + 4 * y - 2 * ~~~x - 1 * x - 1 * ~~~(x ||| ~~~y) - 5 * (x &&& ~~~y) - 7 * (x &&& y) = 2 * ~~~(x &&& ~~~y) + 2 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_406 (x y : BitVec w) : +theorem e_406 : 11 * ~~~y + 1 * x - 1 * ~~~(x &&& ~~~x) + 2 * ~~~(x &&& y) - 3 * (x ||| ~~~y) - 9 * ~~~(x ||| y) - 5 * ~~~(x ||| ~~~y) - 1 * (x &&& y) = 14 * (x &&& ~~~y) - 4 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_407 (x y : BitVec w) : +theorem e_407 : 1 * (x ||| ~~~y) - 2 * ~~~(x &&& ~~~x) - 1 * ~~~x - 2 * ~~~(x &&& ~~~y) + 1 * (x ||| y) + 3 * ~~~(x ^^^ y) + 1 * ~~~(x ||| y) - 1 * (x &&& y) = - 4 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_408 (x y : BitVec w) : +theorem e_408 : - 11 * ~~~(x ^^^ y) - 5 * ~~~(x &&& ~~~y) + 7 * (x ||| y) + 5 * (x ||| ~~~y) + 18 * ~~~(x ||| y) + 5 * ~~~(x ||| ~~~y) - 5 * (x &&& ~~~y) + 4 * (x &&& y) = 7 * ~~~(x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_409 (x y : BitVec w) : +theorem e_409 : - 7 * (x ||| y) - 3 * y - 3 * ~~~(x ^^^ y) - 1 * ~~~x + 10 * ~~~(x ||| y) + 17 * ~~~(x ||| ~~~y) + 15 * (x &&& ~~~y) + 21 * (x &&& y) = 6 * ~~~(x &&& ~~~x) + 2 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_410 (x y : BitVec w) : +theorem e_410 : 4 * (x ||| ~~~y) - 5 * ~~~x + 7 * ~~~(x &&& ~~~x) - 6 * ~~~y - 2 * ~~~(x ^^^ y) - 2 * ~~~(x ||| ~~~y) - 5 * (x &&& ~~~y) - 9 * (x &&& y) = - 2 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_411 (x y : BitVec w) : +theorem e_411 : - 2 * ~~~(x ^^^ y) + 2 * ~~~x + 1 * (x ^^^ y) - 5 * ~~~(x &&& ~~~y) - 2 * (x ||| ~~~y) + 2 * ~~~(x &&& ~~~x) + 5 * ~~~(x ||| y) + 1 * ~~~(x ||| ~~~y) = 1 * (x ||| y) - 8 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_412 (x y : BitVec w) : +theorem e_412 : 7 * ~~~(x &&& ~~~x) - 1 * y + 2 * ~~~x + 2 * ~~~(x &&& y) + 4 * (x ||| ~~~y) + 11 * ~~~(x &&& ~~~y) - 26 * ~~~(x ||| y) - 13 * (x &&& ~~~y) = 21 * (x &&& y) + 21 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_413 (x y : BitVec w) : +theorem e_413 : 11 * ~~~y - 2 * (x ||| y) + 1 * (x ^^^ y) - 7 * y - 18 * ~~~(x ||| y) + 1 * ~~~(x ||| ~~~y) - 10 * (x &&& ~~~y) + 9 * (x &&& y) = - 7 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_414 (x y : BitVec w) : +theorem e_414 : - 1 * ~~~x - 5 * ~~~(x &&& ~~~y) + 2 * ~~~(x &&& y) + 1 * (x ||| ~~~y) + 3 * ~~~(x ||| y) + 2 * ~~~(x ||| ~~~y) - 5 * (x &&& ~~~y) + 4 * (x &&& y) = - 2 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_415 (x y : BitVec w) : +theorem e_415 : 2 * y + 1 * ~~~(x &&& ~~~y) + 3 * ~~~y + 1 * (x ^^^ y) - 1 * ~~~(x ^^^ y) + 2 * x - 3 * ~~~(x ||| y) - 6 * (x &&& ~~~y) = 4 * (x &&& y) + 4 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_416 (x y : BitVec w) : +theorem e_416 : 3 * ~~~x - 2 * y - 5 * x - 3 * (x ^^^ y) - 3 * (x ||| y) - 3 * ~~~(x ||| y) + 11 * (x &&& ~~~y) + 10 * (x &&& y) = - 5 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_417 (x y : BitVec w) : +theorem e_417 : - 1 * ~~~(x &&& ~~~y) - 3 * ~~~(x ^^^ y) - 2 * ~~~x + 7 * x + 1 * (x ||| ~~~y) + 5 * ~~~(x ||| y) - 8 * (x &&& ~~~y) - 4 * (x &&& y) = - 3 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_418 (x y : BitVec w) : +theorem e_418 : - 6 * ~~~y - 7 * ~~~x + 1 * ~~~(x ^^^ y) - 1 * ~~~(x &&& y) + 13 * ~~~(x ||| y) + 10 * ~~~(x ||| ~~~y) + 9 * (x &&& ~~~y) + 1 * (x &&& y) = 2 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_419 (x y : BitVec w) : +theorem e_419 : 4 * (x ||| y) - 1 * ~~~y + 2 * ~~~(x &&& y) + 3 * ~~~(x &&& ~~~y) - 4 * ~~~(x ||| y) - 14 * ~~~(x ||| ~~~y) - 10 * (x &&& ~~~y) - 7 * (x &&& y) = - 5 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_420 (x y : BitVec w) : +theorem e_420 : 3 * ~~~(x &&& ~~~x) - 1 * ~~~y + 1 * (x ||| y) - 6 * x + 7 * (x ||| ~~~y) - 9 * ~~~(x ||| y) - 4 * (x &&& ~~~y) - 6 * (x &&& y) = 5 * ~~~(x ||| ~~~y) - 1 * y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_421 (x y : BitVec w) : +theorem e_421 : 1 * ~~~x - 11 * (x ^^^ y) - 7 * ~~~(x &&& ~~~y) - 7 * ~~~(x &&& y) + 2 * ~~~(x ^^^ y) + 25 * ~~~(x ||| ~~~y) + 8 * (x &&& ~~~y) - 5 * (x &&& y) = 1 * (x ||| y) - 11 * (x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_422 (x y : BitVec w) : +theorem e_422 : 1 * ~~~y + 2 * ~~~x + 2 * (x ||| y) - 2 * y - 2 * ~~~(x ^^^ y) - 1 * ~~~(x ||| ~~~y) - 3 * (x &&& ~~~y) + 3 * (x &&& y) = 1 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_423 (x y : BitVec w) : +theorem e_423 : 1 * (x ^^^ y) - 2 * ~~~x + 1 * ~~~(x ^^^ y) + 2 * (x ||| y) + 1 * ~~~(x &&& ~~~x) - 11 * x - 2 * ~~~(x ||| ~~~y) + 7 * (x &&& y) = - 7 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_424 (x y : BitVec w) : +theorem e_424 : 11 * ~~~(x &&& ~~~x) - 1 * ~~~(x &&& y) - 11 * (x ||| y) + 5 * y - 7 * x - 10 * ~~~(x ||| y) - 4 * ~~~(x ||| ~~~y) + 8 * (x &&& ~~~y) = - 2 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_425 (x y : BitVec w) : +theorem e_425 : 5 * x - 2 * (x ^^^ y) - 11 * ~~~(x &&& ~~~y) - 1 * (x ||| y) - 5 * ~~~x + 16 * ~~~(x ||| y) + 19 * ~~~(x ||| ~~~y) - 2 * (x &&& ~~~y) = 7 * ~~~y - 7 * (x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_426 (x y : BitVec w) : +theorem e_426 : - 1 * (x ||| y) + 1 * (x ^^^ y) - 5 * (x ||| ~~~y) - 5 * x - 5 * ~~~(x &&& ~~~y) + 5 * ~~~(x ||| ~~~y) + 10 * (x &&& ~~~y) + 16 * (x &&& y) = - 10 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_427 (x y : BitVec w) : +theorem e_427 : - 11 * (x ^^^ y) + 7 * y + 1 * ~~~(x &&& y) - 1 * ~~~(x &&& ~~~y) - 1 * ~~~(x ^^^ y) + 4 * ~~~(x ||| ~~~y) + 9 * (x &&& ~~~y) - 5 * (x &&& y) = - 1 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_428 (x y : BitVec w) : +theorem e_428 : 11 * ~~~(x ^^^ y) - 1 * ~~~y + 1 * ~~~(x &&& y) + 5 * (x ||| ~~~y) + 1 * (x ^^^ y) - 16 * ~~~(x ||| y) - 2 * ~~~(x ||| ~~~y) - 6 * (x &&& ~~~y) = 16 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_429 (x y : BitVec w) : +theorem e_429 : 4 * (x ^^^ y) - 6 * (x ||| y) - 7 * ~~~(x &&& y) + 1 * ~~~(x &&& ~~~y) + 7 * x + 1 * ~~~(x ||| y) + 3 * ~~~(x ||| ~~~y) - 3 * (x &&& ~~~y) = 7 * (x &&& y) - 5 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_430 (x y : BitVec w) : +theorem e_430 : 4 * ~~~x - 1 * ~~~(x ^^^ y) + 1 * ~~~(x &&& ~~~y) - 3 * x - 1 * (x ||| ~~~y) - 5 * (x ||| y) - 3 * ~~~(x ||| y) + 9 * (x &&& ~~~y) = - 9 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_431 (x y : BitVec w) : +theorem e_431 : 2 * ~~~y + 11 * (x ||| y) - 3 * ~~~(x ^^^ y) - 2 * y - 5 * (x ||| ~~~y) - 5 * ~~~(x ||| y) - 19 * (x &&& ~~~y) - 1 * (x &&& y) = - 11 * ~~~(x &&& y) + 20 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_432 (x y : BitVec w) : +theorem e_432 : - 11 * ~~~(x &&& ~~~y) - 1 * ~~~(x &&& y) + 2 * x - 11 * ~~~(x &&& ~~~x) + 2 * y + 23 * ~~~(x ||| y) + 21 * ~~~(x ||| ~~~y) + 10 * (x &&& ~~~y) = - 18 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_433 (x y : BitVec w) : +theorem e_433 : 1 * y + 2 * ~~~(x &&& y) - 1 * (x ||| ~~~y) - 7 * ~~~(x &&& ~~~y) + 1 * ~~~(x &&& ~~~x) + 5 * ~~~(x ||| y) + 3 * ~~~(x ||| ~~~y) - 2 * (x &&& ~~~y) = - 6 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_434 (x y : BitVec w) : +theorem e_434 : - 5 * y + 4 * ~~~(x &&& y) - 2 * (x ^^^ y) - 3 * x - 9 * ~~~(x ||| y) + 3 * ~~~(x ||| ~~~y) + 1 * (x &&& ~~~y) + 3 * (x &&& y) = - 5 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_435 (x y : BitVec w) : +theorem e_435 : - 11 * ~~~(x ^^^ y) + 11 * ~~~(x &&& ~~~y) + 7 * (x ^^^ y) + 4 * ~~~y + 2 * ~~~x - 9 * ~~~(x ||| ~~~y) - 5 * (x &&& ~~~y) + 6 * (x &&& y) = 11 * ~~~(x &&& ~~~x) - 5 * (x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_436 (x y : BitVec w) : +theorem e_436 : 1 * ~~~(x &&& y) + 11 * (x ||| y) + 1 * ~~~y + 2 * ~~~(x &&& ~~~y) - 4 * ~~~(x ||| y) - 11 * ~~~(x ||| ~~~y) - 13 * (x &&& ~~~y) - 10 * (x &&& y) = 3 * y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_437 (x y : BitVec w) : +theorem e_437 : - 1 * (x ^^^ y) + 1 * ~~~(x ^^^ y) + 4 * ~~~x - 6 * (x ||| y) - 1 * (x ||| ~~~y) - 4 * ~~~(x ||| y) + 8 * (x &&& ~~~y) + 6 * (x &&& y) = - 3 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_438 (x y : BitVec w) : +theorem e_438 : 7 * (x ||| ~~~y) - 5 * ~~~x + 3 * x - 1 * ~~~(x ^^^ y) - 11 * (x ||| y) - 2 * ~~~(x ||| y) + 16 * ~~~(x ||| ~~~y) + 2 * (x &&& y) = - 1 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_439 (x y : BitVec w) : +theorem e_439 : - 11 * y + 11 * (x ||| ~~~y) - 7 * ~~~y + 3 * ~~~(x &&& ~~~y) - 17 * ~~~(x ||| y) - 2 * ~~~(x ||| ~~~y) - 3 * (x &&& ~~~y) - 2 * (x &&& y) = - 11 * ~~~x + 1 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_440 (x y : BitVec w) : +theorem e_440 : - 11 * ~~~y - 1 * (x ||| y) - 2 * y + 11 * (x ||| ~~~y) + 2 * ~~~(x &&& ~~~x) - 2 * ~~~(x ||| y) + 1 * ~~~(x ||| ~~~y) - 1 * (x &&& ~~~y) = 10 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_441 (x y : BitVec w) : +theorem e_441 : 11 * ~~~(x &&& ~~~x) - 7 * (x ||| y) - 3 * ~~~y + 11 * ~~~(x &&& y) - 19 * ~~~(x ||| y) - 17 * ~~~(x ||| ~~~y) - 12 * (x &&& ~~~y) - 6 * (x &&& y) = - 2 * y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_442 (x y : BitVec w) : +theorem e_442 : 3 * (x ||| ~~~y) + 2 * ~~~(x ^^^ y) - 7 * ~~~y - 1 * ~~~(x &&& ~~~x) - 1 * ~~~x + 4 * ~~~(x ||| y) - 9 * ~~~(x ||| ~~~y) + 5 * (x &&& ~~~y) = 15 * (x &&& y) - 11 * y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_443 (x y : BitVec w) : +theorem e_443 : 7 * y - 11 * (x ||| ~~~y) + 2 * ~~~(x ^^^ y) - 7 * ~~~y + 2 * (x ||| y) + 11 * ~~~x + 5 * ~~~(x ||| y) - 20 * ~~~(x ||| ~~~y) = - 16 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_444 (x y : BitVec w) : +theorem e_444 : 1 * ~~~(x &&& ~~~x) - 5 * ~~~y - 5 * (x ^^^ y) + 3 * ~~~(x &&& y) + 1 * ~~~(x ||| y) - 3 * ~~~(x ||| ~~~y) + 5 * (x &&& ~~~y) - 6 * (x &&& y) = - 4 * y - 1 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_445 (x y : BitVec w) : +theorem e_445 : - 2 * (x ^^^ y) + 2 * ~~~x + 11 * (x ||| y) + 2 * ~~~(x &&& ~~~x) + 3 * ~~~(x ||| y) - 13 * ~~~(x ||| ~~~y) - 11 * (x &&& ~~~y) - 6 * (x &&& y) = 7 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_446 (x y : BitVec w) : +theorem e_446 : - 6 * ~~~(x &&& ~~~x) + 5 * ~~~(x &&& y) - 5 * ~~~y + 1 * ~~~(x ^^^ y) - 1 * ~~~(x &&& ~~~y) + 1 * ~~~(x ||| ~~~y) + 5 * (x &&& ~~~y) + 5 * (x &&& y) = - 1 * (x ||| y) - 6 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_447 (x y : BitVec w) : +theorem e_447 : - 2 * (x ^^^ y) + 7 * ~~~(x ^^^ y) + 1 * ~~~(x &&& y) + 11 * ~~~(x &&& ~~~x) - 3 * y - 7 * ~~~(x ||| ~~~y) - 10 * (x &&& ~~~y) - 15 * (x &&& y) = 19 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_448 (x y : BitVec w) : +theorem e_448 : - 3 * ~~~(x &&& ~~~x) + 11 * (x ^^^ y) - 2 * ~~~(x ^^^ y) - 7 * ~~~(x &&& y) + 1 * ~~~x - 1 * ~~~y + 12 * ~~~(x ||| y) + 5 * (x &&& y) = 2 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_449 (x y : BitVec w) : +theorem e_449 : - 1 * x + 1 * ~~~y + 1 * ~~~(x &&& y) - 1 * (x ||| ~~~y) - 7 * ~~~(x ^^^ y) + 2 * (x ^^^ y) - 2 * (x ||| y) + 6 * ~~~(x ||| y) = - 11 * (x &&& y) + 1 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_450 (x y : BitVec w) : +theorem e_450 : - 11 * (x ^^^ y) + 11 * ~~~(x &&& ~~~x) + 3 * y + 5 * ~~~y + 7 * ~~~x - 25 * ~~~(x ||| y) - 10 * ~~~(x ||| ~~~y) - 5 * (x &&& ~~~y) = - 2 * ~~~(x ^^^ y) + 16 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_451 (x y : BitVec w) : +theorem e_451 : - 2 * ~~~(x &&& ~~~x) - 1 * x - 5 * y + 1 * ~~~(x ^^^ y) + 4 * ~~~(x ||| y) + 7 * ~~~(x ||| ~~~y) + 6 * (x &&& ~~~y) + 10 * (x &&& y) = 3 * (x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_452 (x y : BitVec w) : +theorem e_452 : - 1 * (x ||| ~~~y) + 7 * y + 11 * ~~~(x &&& y) + 1 * ~~~(x &&& ~~~x) - 5 * ~~~(x ||| y) - 18 * ~~~(x ||| ~~~y) - 10 * (x &&& ~~~y) - 1 * (x &&& y) = 6 * ~~~(x ^^^ y) + 1 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_453 (x y : BitVec w) : +theorem e_453 : - 11 * (x ^^^ y) - 2 * x - 3 * ~~~x - 7 * ~~~(x &&& ~~~x) + 1 * y + 8 * ~~~(x ||| y) + 18 * ~~~(x ||| ~~~y) + 20 * (x &&& ~~~y) + 6 * (x &&& y) = - 2 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_454 (x y : BitVec w) : +theorem e_454 : 2 * ~~~(x ^^^ y) - 2 * y + 1 * ~~~x + 1 * ~~~(x &&& ~~~x) - 2 * (x ^^^ y) - 4 * ~~~(x ||| y) + 8 * ~~~(x ||| ~~~y) + 7 * (x &&& ~~~y) + 5 * (x &&& y) = 6 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_455 (x y : BitVec w) : +theorem e_455 : - 6 * (x ||| ~~~y) - 11 * (x ^^^ y) - 1 * (x ||| y) - 1 * ~~~x - 2 * ~~~(x ^^^ y) + 1 * ~~~y + 3 * x + 8 * ~~~(x ||| y) + 6 * (x &&& y) = - 14 * (x &&& ~~~y) - 13 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_456 (x y : BitVec w) : +theorem e_456 : - 6 * (x ||| y) + 4 * ~~~x + 4 * (x ||| ~~~y) + 7 * ~~~(x &&& y) - 2 * ~~~(x &&& ~~~y) - 7 * ~~~(x ||| y) + 3 * ~~~(x ||| ~~~y) + 1 * (x &&& ~~~y) + 10 * (x &&& y) = 6 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_457 (x y : BitVec w) : +theorem e_457 : 5 * ~~~y - 2 * (x ^^^ y) + 5 * ~~~(x &&& y) + 4 * (x ||| y) - 1 * ~~~x - 1 * y - 9 * ~~~(x ||| y) - 5 * ~~~(x ||| ~~~y) - 3 * (x &&& y) = 12 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_458 (x y : BitVec w) : +theorem e_458 : - 5 * ~~~(x &&& y) + 7 * y + 3 * x - 1 * (x ^^^ y) + 5 * ~~~x + 5 * ~~~(x ||| y) - 1 * ~~~(x ||| ~~~y) + 3 * (x &&& ~~~y) - 5 * (x &&& y) = 5 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_459 (x y : BitVec w) : +theorem e_459 : - 3 * ~~~(x &&& ~~~y) - 1 * ~~~(x &&& ~~~x) - 1 * (x ||| y) + 4 * (x ^^^ y) - 3 * x + 2 * ~~~x - 2 * ~~~(x ||| y) - 1 * ~~~(x ||| ~~~y) - 3 * (x &&& ~~~y) = - 8 * (x &&& y) - 4 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_460 (x y : BitVec w) : +theorem e_460 : 7 * ~~~(x &&& y) - 2 * ~~~(x ^^^ y) + 2 * ~~~y + 2 * (x ||| y) - 1 * (x ||| ~~~y) - 17 * ~~~(x ||| y) - 20 * ~~~(x ||| ~~~y) - 24 * (x &&& ~~~y) - 13 * (x &&& y) = - 11 * ~~~(x &&& ~~~x) - 3 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_461 (x y : BitVec w) : +theorem e_461 : 4 * y + 4 * (x ||| ~~~y) + 2 * ~~~y + 3 * ~~~(x &&& ~~~y) + 1 * x + 1 * (x ^^^ y) - 9 * ~~~(x ||| y) - 10 * (x &&& ~~~y) - 14 * (x &&& y) = - 2 * (x ||| y) + 10 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_462 (x y : BitVec w) : +theorem e_462 : - 2 * ~~~(x ^^^ y) - 6 * ~~~(x &&& ~~~y) + 1 * (x ||| y) + 7 * (x ^^^ y) - 5 * ~~~(x &&& y) - 7 * ~~~x + 10 * ~~~(x ||| ~~~y) - 2 * (x &&& ~~~y) + 8 * (x &&& y) = 1 * x - 20 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_463 (x y : BitVec w) : +theorem e_463 : 5 * ~~~x - 1 * ~~~(x ^^^ y) - 11 * ~~~(x &&& ~~~x) - 5 * (x ||| ~~~y) - 11 * x - 1 * ~~~(x &&& y) + 13 * ~~~(x ||| y) + 6 * ~~~(x ||| ~~~y) + 28 * (x &&& y) = - 1 * (x ^^^ y) - 27 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_464 (x y : BitVec w) : +theorem e_464 : - 1 * ~~~y - 5 * ~~~x - 11 * ~~~(x ^^^ y) + 7 * (x ||| y) + 1 * y - 11 * (x ^^^ y) + 14 * ~~~(x ||| ~~~y) + 11 * (x &&& ~~~y) + 3 * (x &&& y) = - 23 * ~~~(x ||| y) + 6 * ~~~(x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_465 (x y : BitVec w) : +theorem e_465 : 11 * y + 3 * (x ||| ~~~y) + 2 * ~~~(x &&& y) - 2 * (x ^^^ y) - 2 * ~~~y + 5 * (x ||| y) - 13 * ~~~(x ||| ~~~y) - 7 * (x &&& ~~~y) - 20 * (x &&& y) = 3 * ~~~x - 1 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_466 (x y : BitVec w) : +theorem e_466 : - 1 * ~~~(x &&& y) - 1 * (x ||| ~~~y) + 1 * ~~~(x &&& ~~~y) + 3 * (x ^^^ y) + 7 * ~~~(x &&& ~~~x) - 7 * ~~~(x ||| y) - 10 * ~~~(x ||| ~~~y) - 9 * (x &&& ~~~y) - 7 * (x &&& y) = - 1 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_467 (x y : BitVec w) : +theorem e_467 : - 1 * y - 6 * (x ||| y) - 3 * (x ||| ~~~y) + 11 * ~~~(x &&& y) - 6 * (x ^^^ y) - 13 * ~~~(x ||| y) + 2 * ~~~(x ||| ~~~y) + 4 * (x &&& ~~~y) + 5 * (x &&& y) = - 5 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_468 (x y : BitVec w) : +theorem e_468 : - 1 * (x ||| y) - 1 * ~~~(x &&& y) - 7 * ~~~(x &&& ~~~y) + 2 * ~~~x - 3 * x - 3 * ~~~y + 7 * ~~~(x ||| ~~~y) + 6 * (x &&& ~~~y) + 9 * (x &&& y) = - 2 * (x ||| ~~~y) - 7 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_469 (x y : BitVec w) : +theorem e_469 : - 7 * (x ||| y) + 2 * ~~~(x ^^^ y) + 7 * (x ^^^ y) - 7 * ~~~(x &&& y) - 1 * ~~~(x &&& ~~~x) + 7 * ~~~x + 1 * ~~~(x ||| y) + 3 * ~~~(x ||| ~~~y) + 8 * (x &&& y) = 2 * ~~~(x &&& ~~~y) - 8 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_470 (x y : BitVec w) : +theorem e_470 : 3 * (x ||| y) + 1 * (x ^^^ y) - 2 * ~~~(x &&& ~~~y) - 1 * x + 2 * ~~~(x &&& ~~~x) - 2 * ~~~x + 2 * ~~~(x ||| y) - 5 * (x &&& ~~~y) - 2 * (x &&& y) = 2 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_471 (x y : BitVec w) : +theorem e_471 : - 5 * (x ^^^ y) - 11 * (x ||| y) - 3 * ~~~y + 7 * ~~~(x ^^^ y) - 1 * ~~~(x &&& ~~~x) - 2 * (x ||| ~~~y) + 14 * ~~~(x ||| ~~~y) + 19 * (x &&& ~~~y) + 7 * (x &&& y) = 4 * ~~~(x ||| y) - 3 * ~~~(x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_472 (x y : BitVec w) : +theorem e_472 : - 1 * ~~~(x ^^^ y) + 1 * ~~~(x &&& ~~~y) - 3 * x - 6 * ~~~(x &&& y) - 1 * ~~~y + 2 * y + 1 * ~~~(x &&& ~~~x) + 6 * ~~~(x ||| y) + 8 * (x &&& ~~~y) = - 1 * (x ^^^ y) - 1 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_473 (x y : BitVec w) : +theorem e_473 : 2 * ~~~x + 11 * ~~~y + 2 * ~~~(x &&& ~~~y) + 7 * ~~~(x &&& ~~~x) - 3 * (x ^^^ y) + 1 * (x ||| y) - 22 * ~~~(x ||| y) - 14 * (x &&& ~~~y) - 8 * (x &&& y) = 9 * ~~~(x ||| ~~~y) + 2 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_474 (x y : BitVec w) : +theorem e_474 : - 11 * ~~~x - 6 * ~~~y - 6 * y - 5 * (x ||| y) - 1 * x + 3 * (x ||| ~~~y) + 14 * ~~~(x ||| y) + 22 * ~~~(x ||| ~~~y) + 9 * (x &&& y) = - 9 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_475 (x y : BitVec w) : +theorem e_475 : - 11 * ~~~y - 1 * ~~~(x ^^^ y) - 6 * ~~~(x &&& ~~~x) + 2 * x + 2 * (x ^^^ y) + 21 * ~~~(x ||| y) + 10 * ~~~(x ||| ~~~y) + 19 * (x &&& ~~~y) + 8 * (x &&& y) = 3 * (x ||| y) + 3 * ~~~(x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_476 (x y : BitVec w) : +theorem e_476 : 3 * ~~~(x ^^^ y) + 2 * (x ||| y) + 1 * x + 11 * y + 2 * (x ||| ~~~y) - 6 * ~~~(x &&& y) + 1 * ~~~(x ||| y) - 7 * ~~~(x ||| ~~~y) + 1 * (x &&& ~~~y) = 19 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_477 (x y : BitVec w) : +theorem e_477 : 2 * (x ||| y) + 7 * ~~~(x &&& ~~~y) + 7 * (x ||| ~~~y) - 1 * y - 7 * (x ^^^ y) + 3 * ~~~(x ^^^ y) - 17 * ~~~(x ||| y) - 1 * ~~~(x ||| ~~~y) - 18 * (x &&& y) = 2 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_478 (x y : BitVec w) : +theorem e_478 : 7 * ~~~x + 3 * (x ^^^ y) - 11 * ~~~y - 2 * ~~~(x &&& ~~~x) - 6 * ~~~(x ^^^ y) + 1 * ~~~(x &&& y) - 6 * y + 11 * ~~~(x ||| y) - 3 * ~~~(x ||| ~~~y) = - 14 * (x &&& y) - 9 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_479 (x y : BitVec w) : +theorem e_479 : - 1 * ~~~(x &&& ~~~y) + 2 * x - 3 * ~~~(x &&& ~~~x) - 6 * ~~~(x &&& y) - 1 * (x ||| ~~~y) + 4 * ~~~y + 4 * (x ^^^ y) + 7 * ~~~(x ||| y) + 9 * (x &&& y) = - 12 * ~~~(x ||| ~~~y) + 6 * y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_480 (x y : BitVec w) : +theorem e_480 : - 1 * ~~~(x &&& ~~~x) + 1 * ~~~(x &&& y) + 3 * ~~~y + 1 * (x ^^^ y) + 1 * (x ||| ~~~y) - 2 * ~~~(x &&& ~~~y) - 2 * ~~~(x ||| y) + 1 * ~~~(x ||| ~~~y) - 5 * (x &&& ~~~y) = - 2 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_481 (x y : BitVec w) : +theorem e_481 : - 11 * y + 5 * ~~~(x ^^^ y) - 6 * ~~~(x &&& ~~~y) - 2 * ~~~(x &&& ~~~x) + 1 * (x ||| ~~~y) - 2 * (x ^^^ y) + 19 * ~~~(x ||| ~~~y) + 1 * (x &&& ~~~y) + 13 * (x &&& y) = - 2 * ~~~(x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_482 (x y : BitVec w) : +theorem e_482 : 4 * (x ||| ~~~y) + 2 * ~~~(x ^^^ y) + 11 * ~~~y - 11 * x - 1 * ~~~x - 15 * ~~~(x ||| y) + 2 * ~~~(x ||| ~~~y) - 3 * (x &&& ~~~y) + 5 * (x &&& y) = 1 * ~~~(x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_483 (x y : BitVec w) : +theorem e_483 : - 7 * ~~~(x &&& ~~~y) + 11 * ~~~(x ^^^ y) - 1 * ~~~y + 4 * ~~~x + 5 * (x ||| ~~~y) - 3 * x - 12 * ~~~(x ||| y) + 4 * ~~~(x ||| ~~~y) - 5 * (x &&& y) = 1 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_484 (x y : BitVec w) : +theorem e_484 : - 1 * y - 3 * ~~~x - 11 * ~~~(x ^^^ y) - 1 * (x ||| y) + 2 * (x ^^^ y) + 20 * ~~~(x ||| y) + 9 * ~~~(x ||| ~~~y) + 2 * (x &&& ~~~y) + 10 * (x &&& y) = - 3 * x + 6 * ~~~(x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_485 (x y : BitVec w) : +theorem e_485 : - 1 * (x ^^^ y) + 1 * (x ||| ~~~y) - 1 * (x ||| y) + 1 * ~~~(x ^^^ y) + 4 * y - 9 * ~~~(x ||| y) - 9 * ~~~(x ||| ~~~y) + 1 * (x &&& ~~~y) - 5 * (x &&& y) = - 7 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_486 (x y : BitVec w) : +theorem e_486 : 2 * ~~~(x ^^^ y) - 5 * ~~~(x &&& ~~~y) + 1 * (x ||| ~~~y) - 5 * ~~~x - 11 * ~~~(x &&& y) + 11 * ~~~(x ||| y) + 12 * ~~~(x ||| ~~~y) + 3 * (x &&& ~~~y) - 7 * (x &&& y) = - 2 * y - 7 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_487 (x y : BitVec w) : +theorem e_487 : - 1 * x - 1 * (x ||| y) - 7 * y - 6 * ~~~(x ^^^ y) + 3 * (x ^^^ y) + 4 * ~~~(x ||| y) + 3 * ~~~(x ||| ~~~y) - 3 * (x &&& ~~~y) + 15 * (x &&& y) = - 2 * ~~~(x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_488 (x y : BitVec w) : +theorem e_488 : 11 * (x ||| y) + 3 * ~~~(x ^^^ y) + 1 * (x ^^^ y) - 3 * y + 3 * ~~~(x &&& ~~~y) + 11 * x - 10 * ~~~(x ||| y) - 16 * ~~~(x ||| ~~~y) - 25 * (x &&& y) = 23 * (x &&& ~~~y) - 4 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_489 (x y : BitVec w) : +theorem e_489 : - 1 * y + 2 * ~~~(x &&& y) - 6 * (x ||| y) + 2 * ~~~(x &&& ~~~y) - 1 * ~~~(x &&& ~~~x) - 3 * ~~~(x ||| y) + 3 * ~~~(x ||| ~~~y) + 4 * (x &&& ~~~y) + 6 * (x &&& y) = - 1 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_490 (x y : BitVec w) : +theorem e_490 : - 1 * (x ||| y) + 4 * ~~~(x ^^^ y) + 2 * y - 5 * ~~~y - 1 * ~~~(x &&& ~~~x) - 1 * ~~~(x &&& y) + 10 * ~~~(x ||| y) + 8 * ~~~(x ||| ~~~y) + 8 * (x &&& ~~~y) = - 3 * (x &&& y) + 7 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_491 (x y : BitVec w) : +theorem e_491 : - 2 * ~~~(x &&& ~~~y) - 2 * ~~~(x &&& y) + 3 * (x ||| y) + 1 * x - 6 * ~~~x + 9 * ~~~(x ||| y) + 7 * ~~~(x ||| ~~~y) - 3 * (x &&& ~~~y) - 3 * (x &&& y) = - 1 * (x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_492 (x y : BitVec w) : +theorem e_492 : - 3 * y - 3 * (x ^^^ y) - 2 * (x ||| ~~~y) - 1 * ~~~(x &&& ~~~x) - 2 * x + 4 * ~~~(x ||| y) + 8 * ~~~(x ||| ~~~y) + 8 * (x &&& ~~~y) + 8 * (x &&& y) = 1 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_493 (x y : BitVec w) : +theorem e_493 : 5 * (x ||| y) + 4 * ~~~y - 7 * (x ||| ~~~y) - 7 * ~~~x - 5 * (x ^^^ y) - 2 * ~~~(x &&& y) + 12 * ~~~(x ||| y) + 9 * ~~~(x ||| ~~~y) + 2 * (x &&& y) = - 5 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_494 (x y : BitVec w) : +theorem e_494 : 5 * ~~~(x ^^^ y) + 1 * ~~~(x &&& ~~~x) + 1 * ~~~x - 2 * y + 7 * ~~~(x &&& ~~~y) + 1 * ~~~(x &&& y) - 11 * ~~~y - 8 * ~~~(x ||| ~~~y) - 11 * (x &&& y) = 4 * ~~~(x ||| y) - 9 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_495 (x y : BitVec w) : +theorem e_495 : - 1 * ~~~(x &&& ~~~x) + 5 * ~~~(x &&& ~~~y) - 6 * (x ^^^ y) - 3 * ~~~x - 3 * ~~~(x ^^^ y) - 11 * ~~~(x &&& y) + 11 * ~~~(x ||| y) + 16 * (x &&& ~~~y) - 1 * (x &&& y) = - 2 * ~~~y - 16 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_496 (x y : BitVec w) : +theorem e_496 : 5 * ~~~(x &&& ~~~y) - 5 * y + 4 * ~~~y + 1 * (x ||| ~~~y) + 3 * ~~~x - 6 * ~~~(x ||| y) + 4 * ~~~(x ||| ~~~y) + 2 * (x &&& ~~~y) + 6 * (x &&& y) = 7 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_497 (x y : BitVec w) : +theorem e_497 : - 2 * ~~~(x &&& ~~~y) - 6 * ~~~y - 6 * ~~~x + 4 * (x ||| ~~~y) + 2 * ~~~(x ^^^ y) + 1 * (x ||| y) + 6 * ~~~(x ||| y) - 1 * (x &&& ~~~y) - 7 * (x &&& y) = - 2 * ~~~(x &&& ~~~x) - 5 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_498 (x y : BitVec w) : +theorem e_498 : - 2 * ~~~(x &&& y) - 1 * x - 3 * ~~~(x &&& ~~~y) + 11 * ~~~y - 11 * ~~~(x ^^^ y) + 2 * y + 5 * ~~~(x ||| y) - 8 * (x &&& ~~~y) + 13 * (x &&& y) = - 3 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_499 (x y : BitVec w) : +theorem e_499 : 2 * (x ||| y) - 1 * ~~~y + 1 * y - 2 * x - 5 * (x ||| ~~~y) + 6 * ~~~(x ||| y) - 2 * ~~~(x ||| ~~~y) + 7 * (x &&& ~~~y) + 4 * (x &&& y) = 1 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_500 (x y : BitVec w) : +theorem e_500 : - 7 * ~~~y - 1 * y - 5 * (x ^^^ y) - 1 * (x ||| y) - 5 * ~~~(x &&& ~~~x) + 11 * ~~~(x ||| y) + 12 * ~~~(x ||| ~~~y) + 17 * (x &&& ~~~y) + 6 * (x &&& y) = - 1 * (x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_501 (x y : BitVec w) : +theorem e_501 : 3 * (x ||| y) + 5 * y - 1 * ~~~(x &&& y) + 2 * ~~~x + 4 * ~~~(x &&& ~~~x) - 6 * ~~~(x ||| y) - 13 * ~~~(x ||| ~~~y) - 7 * (x &&& ~~~y) - 12 * (x &&& y) = - 1 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_502 (x y : BitVec w) : +theorem e_502 : 1 * ~~~x + 2 * ~~~(x &&& y) + 2 * (x ||| y) + 4 * y - 1 * ~~~y - 1 * ~~~(x ^^^ y) - 5 * ~~~(x &&& ~~~y) + 4 * ~~~(x ||| y) - 2 * ~~~(x ||| ~~~y) = 2 * (x ^^^ y) + 1 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_503 (x y : BitVec w) : +theorem e_503 : 2 * ~~~(x &&& y) - 5 * x + 4 * (x ^^^ y) + 11 * ~~~x + 5 * ~~~(x &&& ~~~x) - 5 * y - 23 * ~~~(x ||| y) - 11 * (x &&& ~~~y) + 5 * (x &&& y) = - 5 * ~~~y + 17 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_504 (x y : BitVec w) : +theorem e_504 : - 1 * (x ^^^ y) - 1 * x + 1 * ~~~y - 2 * ~~~(x &&& ~~~x) - 1 * y + 1 * ~~~(x ||| y) + 6 * ~~~(x ||| ~~~y) + 5 * (x &&& ~~~y) + 6 * (x &&& y) = 2 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_505 (x y : BitVec w) : +theorem e_505 : - 3 * (x ^^^ y) - 2 * ~~~(x &&& ~~~x) - 11 * y - 2 * ~~~(x &&& ~~~y) + 3 * ~~~y + 8 * ~~~(x ||| y) + 32 * ~~~(x ||| ~~~y) + 16 * (x &&& ~~~y) + 22 * (x &&& y) = 7 * (x ||| y) + 7 * ~~~(x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_506 (x y : BitVec w) : +theorem e_506 : - 3 * ~~~(x &&& ~~~y) - 5 * ~~~y + 1 * y - 7 * (x ||| y) - 6 * ~~~(x &&& ~~~x) + 2 * ~~~(x ^^^ y) + 12 * ~~~(x ||| y) + 15 * ~~~(x ||| ~~~y) + 19 * (x &&& ~~~y) = - 14 * (x &&& y) + 1 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_507 (x y : BitVec w) : +theorem e_507 : - 6 * x - 1 * ~~~(x ^^^ y) - 2 * (x ^^^ y) + 1 * (x ||| y) - 2 * ~~~y + 8 * ~~~(x ||| y) + 5 * ~~~(x ||| ~~~y) + 9 * (x &&& ~~~y) + 5 * (x &&& y) = 5 * ~~~x - 1 * y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_508 (x y : BitVec w) : +theorem e_508 : - 1 * ~~~x - 1 * ~~~(x &&& ~~~x) + 2 * y + 7 * (x ||| ~~~y) - 2 * (x ||| y) + 1 * ~~~(x &&& ~~~y) - 5 * x + 1 * ~~~(x &&& y) - 5 * ~~~(x ||| y) = 2 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_509 (x y : BitVec w) : +theorem e_509 : 11 * x - 5 * y - 6 * ~~~x - 6 * ~~~y + 7 * (x ||| y) + 11 * ~~~(x &&& ~~~y) - 11 * ~~~(x &&& y) - 1 * (x &&& ~~~y) - 24 * (x &&& y) = - 12 * ~~~(x ||| y) - 4 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_510 (x y : BitVec w) : +theorem e_510 : 2 * ~~~(x ^^^ y) + 5 * y - 2 * ~~~x - 6 * (x ||| y) - 1 * x + 2 * (x ||| ~~~y) - 3 * ~~~(x ||| y) + 5 * (x &&& ~~~y) - 3 * (x &&& y) = - 2 * ~~~(x ||| ~~~y) - 1 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_511 (x y : BitVec w) : +theorem e_511 : 11 * ~~~(x ^^^ y) + 2 * (x ||| y) - 7 * ~~~x - 1 * (x ||| ~~~y) - 3 * y - 1 * ~~~y + 8 * ~~~(x ||| ~~~y) + 2 * (x &&& ~~~y) - 7 * (x &&& y) = 2 * x + 2 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_512 (x y : BitVec w) : +theorem e_512 : 4 * ~~~(x &&& ~~~x) - 1 * ~~~x + 7 * y + 1 * ~~~(x &&& y) - 1 * (x ||| ~~~y) + 7 * ~~~(x &&& ~~~y) - 10 * ~~~(x ||| y) - 3 * (x &&& ~~~y) - 17 * (x &&& y) = 17 * ~~~(x ||| ~~~y) + 1 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_513 (x y : BitVec w) : +theorem e_513 : - 1 * ~~~(x &&& y) - 1 * ~~~(x &&& ~~~y) - 11 * (x ||| ~~~y) + 1 * (x ^^^ y) + 1 * ~~~y - 1 * y + 17 * ~~~(x ||| y) + 10 * (x &&& ~~~y) + 13 * (x &&& y) = - 7 * ~~~(x ||| ~~~y) + 5 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_514 (x y : BitVec w) : +theorem e_514 : - 3 * y + 1 * ~~~y - 1 * ~~~(x &&& ~~~x) - 7 * ~~~(x &&& ~~~y) - 6 * (x ||| y) + 2 * x + 16 * ~~~(x ||| ~~~y) + 3 * (x &&& ~~~y) + 15 * (x &&& y) = - 1 * ~~~(x &&& y) - 6 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_515 (x y : BitVec w) : +theorem e_515 : - 6 * ~~~(x ^^^ y) + 2 * y + 2 * (x ||| ~~~y) + 3 * (x ^^^ y) + 2 * ~~~y + 3 * ~~~(x ||| y) - 4 * ~~~(x ||| ~~~y) - 4 * (x &&& ~~~y) + 5 * (x &&& y) = 2 * x + 1 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_516 (x y : BitVec w) : +theorem e_516 : - 1 * (x ||| ~~~y) + 2 * x - 11 * ~~~(x &&& y) + 7 * (x ||| y) - 7 * ~~~x + 19 * ~~~(x ||| y) + 10 * ~~~(x ||| ~~~y) + 3 * (x &&& ~~~y) - 9 * (x &&& y) = - 1 * y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_517 (x y : BitVec w) : +theorem e_517 : - 11 * ~~~(x &&& y) - 11 * (x ^^^ y) + 1 * x + 2 * ~~~(x &&& ~~~x) - 3 * (x ||| y) + 2 * ~~~(x ^^^ y) + 3 * ~~~y + 4 * ~~~(x ||| y) + 23 * ~~~(x ||| ~~~y) = - 19 * (x &&& ~~~y) + 2 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_518 (x y : BitVec w) : +theorem e_518 : 1 * y + 1 * ~~~(x &&& ~~~y) - 5 * x + 1 * ~~~y - 1 * ~~~(x &&& y) + 7 * ~~~(x ||| y) - 1 * ~~~(x ||| ~~~y) + 7 * (x &&& ~~~y) + 11 * (x &&& y) = 6 * ~~~(x ^^^ y) + 2 * (x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_519 (x y : BitVec w) : +theorem e_519 : - 1 * (x ||| ~~~y) + 5 * ~~~(x ^^^ y) - 1 * ~~~(x &&& ~~~x) + 1 * x + 3 * ~~~x - 7 * ~~~(x &&& ~~~y) + 1 * ~~~(x ||| y) + 5 * ~~~(x ||| ~~~y) + 3 * (x &&& y) = - 1 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_520 (x y : BitVec w) : +theorem e_520 : 7 * ~~~(x &&& y) - 1 * y + 4 * ~~~(x &&& ~~~x) - 1 * (x ^^^ y) - 1 * x - 1 * ~~~x - 8 * ~~~(x ||| y) - 8 * ~~~(x ||| ~~~y) - 7 * (x &&& ~~~y) = 2 * (x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_521 (x y : BitVec w) : +theorem e_521 : 1 * (x ||| y) + 1 * ~~~(x ^^^ y) + 4 * (x ||| ~~~y) + 2 * ~~~(x &&& ~~~y) - 11 * y - 8 * ~~~(x ||| y) + 8 * ~~~(x ||| ~~~y) - 6 * (x &&& ~~~y) + 3 * (x &&& y) = - 1 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_522 (x y : BitVec w) : +theorem e_522 : - 6 * ~~~(x &&& ~~~y) + 4 * ~~~y + 7 * ~~~(x &&& ~~~x) - 1 * (x ^^^ y) - 2 * ~~~x - 2 * (x ||| ~~~y) - 2 * ~~~(x ||| y) - 9 * (x &&& ~~~y) + 1 * (x &&& y) = - 1 * ~~~(x &&& y) - 1 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_523 (x y : BitVec w) : +theorem e_523 : 5 * ~~~(x &&& ~~~y) + 2 * ~~~y - 7 * (x ||| y) + 3 * (x ^^^ y) + 3 * ~~~(x &&& ~~~x) - 1 * y - 10 * ~~~(x ||| y) - 3 * ~~~(x ||| ~~~y) + 1 * (x &&& y) = 1 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_524 (x y : BitVec w) : +theorem e_524 : - 1 * ~~~x + 1 * x - 7 * ~~~(x &&& y) - 1 * ~~~(x &&& ~~~y) - 1 * y + 31 * ~~~(x ||| y) + 21 * ~~~(x ||| ~~~y) + 17 * (x &&& ~~~y) + 23 * (x &&& y) = 11 * ~~~(x &&& ~~~x) + 11 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_525 (x y : BitVec w) : +theorem e_525 : - 6 * ~~~(x &&& y) - 7 * ~~~y + 2 * (x ||| y) + 4 * ~~~x + 4 * x - 1 * ~~~(x &&& ~~~x) + 10 * ~~~(x ||| y) + 1 * ~~~(x ||| ~~~y) + 8 * (x &&& ~~~y) = 5 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_526 (x y : BitVec w) : +theorem e_526 : 1 * ~~~(x ^^^ y) - 1 * y + 11 * ~~~(x &&& ~~~y) + 11 * ~~~(x &&& y) + 2 * ~~~y - 25 * ~~~(x ||| y) - 23 * ~~~(x ||| ~~~y) - 8 * (x &&& ~~~y) - 6 * (x &&& y) = - 2 * (x ||| y) + 7 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_527 (x y : BitVec w) : +theorem e_527 : 4 * (x ||| y) - 2 * (x ||| ~~~y) - 5 * ~~~(x &&& ~~~y) + 7 * ~~~x + 3 * ~~~(x &&& ~~~x) + 3 * ~~~(x &&& y) - 1 * ~~~y - 12 * ~~~(x ||| ~~~y) - 7 * (x &&& ~~~y) = 5 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_528 (x y : BitVec w) : +theorem e_528 : - 2 * (x ^^^ y) - 7 * x + 1 * ~~~(x &&& y) + 2 * ~~~x - 1 * ~~~(x ^^^ y) + 4 * ~~~y - 7 * ~~~(x ||| y) - 2 * ~~~(x ||| ~~~y) + 3 * (x &&& ~~~y) = - 1 * ~~~(x &&& ~~~x) - 7 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_529 (x y : BitVec w) : +theorem e_529 : 2 * (x ^^^ y) - 1 * y - 1 * ~~~x + 1 * x + 5 * (x ||| y) - 6 * ~~~(x &&& ~~~x) + 3 * ~~~(x &&& ~~~y) - 2 * ~~~(x ^^^ y) + 8 * ~~~(x ||| y) = 2 * ~~~(x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_530 (x y : BitVec w) : +theorem e_530 : - 6 * ~~~(x &&& ~~~x) - 6 * ~~~(x ^^^ y) - 1 * (x ||| y) - 1 * ~~~y - 1 * ~~~(x &&& ~~~y) + 12 * ~~~(x ||| y) + 7 * ~~~(x ||| ~~~y) + 5 * (x &&& ~~~y) + 12 * (x &&& y) = - 1 * (x ^^^ y) - 2 * (x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_531 (x y : BitVec w) : +theorem e_531 : - 7 * ~~~(x ^^^ y) - 6 * y - 6 * ~~~(x &&& ~~~y) + 1 * x + 3 * (x ||| y) + 1 * ~~~x + 12 * ~~~(x ||| y) + 8 * ~~~(x ||| ~~~y) - 4 * (x &&& ~~~y) = - 15 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_532 (x y : BitVec w) : +theorem e_532 : - 7 * ~~~y + 5 * (x ||| ~~~y) - 3 * (x ^^^ y) - 1 * ~~~(x ^^^ y) + 5 * ~~~x + 1 * y - 3 * ~~~(x ||| ~~~y) + 5 * (x &&& ~~~y) - 5 * (x &&& y) = 2 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_533 (x y : BitVec w) : +theorem e_533 : - 1 * (x ||| y) + 7 * (x ^^^ y) + 11 * ~~~x + 1 * ~~~y + 3 * ~~~(x &&& y) - 10 * ~~~(x ||| y) - 20 * ~~~(x ||| ~~~y) - 5 * (x &&& ~~~y) + 6 * (x &&& y) = 5 * (x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_534 (x y : BitVec w) : +theorem e_534 : - 2 * ~~~(x &&& y) - 2 * (x ^^^ y) + 5 * ~~~y + 7 * (x ||| ~~~y) - 7 * x - 6 * ~~~(x ||| y) + 8 * ~~~(x ||| ~~~y) + 4 * (x &&& ~~~y) + 5 * (x &&& y) = 5 * ~~~(x &&& ~~~x) - 1 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_535 (x y : BitVec w) : +theorem e_535 : - 11 * ~~~x + 5 * (x ||| y) + 4 * ~~~(x &&& y) - 2 * ~~~y + 2 * x + 5 * y + 9 * ~~~(x ||| y) - 3 * ~~~(x ||| ~~~y) - 12 * (x &&& y) = 9 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_536 (x y : BitVec w) : +theorem e_536 : - 1 * ~~~x + 2 * (x ^^^ y) + 1 * x + 3 * (x ||| y) - 2 * ~~~(x ^^^ y) + 4 * ~~~(x &&& ~~~y) - 1 * ~~~(x ||| y) - 8 * ~~~(x ||| ~~~y) - 6 * (x &&& y) = 6 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_537 (x y : BitVec w) : +theorem e_537 : 2 * ~~~(x &&& y) - 7 * y + 4 * (x ^^^ y) - 11 * ~~~x - 2 * x + 5 * (x ||| y) - 6 * ~~~(x ^^^ y) + 15 * ~~~(x ||| y) + 10 * (x &&& y) = 9 * (x &&& ~~~y) - 7 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_538 (x y : BitVec w) : +theorem e_538 : 1 * ~~~(x ^^^ y) - 7 * (x ||| ~~~y) + 1 * ~~~(x &&& ~~~x) + 1 * y - 1 * (x ^^^ y) + 2 * ~~~y + 3 * ~~~(x ||| y) + 5 * (x &&& ~~~y) + 4 * (x &&& y) = 1 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_539 (x y : BitVec w) : +theorem e_539 : - 7 * (x ^^^ y) - 3 * (x ||| y) + 3 * ~~~x - 3 * ~~~y - 11 * ~~~(x &&& ~~~x) - 2 * x + 11 * ~~~(x ||| y) + 26 * (x &&& ~~~y) + 16 * (x &&& y) = - 18 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_540 (x y : BitVec w) : +theorem e_540 : 2 * ~~~(x &&& ~~~y) + 2 * (x ^^^ y) - 2 * ~~~(x &&& ~~~x) - 11 * ~~~x + 3 * (x ||| y) - 2 * ~~~(x ^^^ y) + 12 * ~~~(x ||| y) - 4 * (x &&& ~~~y) - 1 * (x &&& y) = - 1 * ~~~y - 6 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_541 (x y : BitVec w) : +theorem e_541 : - 1 * ~~~(x &&& ~~~y) + 5 * (x ^^^ y) + 1 * ~~~y - 5 * ~~~(x &&& ~~~x) + 1 * (x ||| ~~~y) + 4 * ~~~(x ||| y) + 4 * ~~~(x ||| ~~~y) - 1 * (x &&& ~~~y) + 8 * (x &&& y) = 1 * (x ||| y) + 2 * y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_542 (x y : BitVec w) : +theorem e_542 : 1 * ~~~(x &&& y) + 5 * ~~~(x &&& ~~~x) + 3 * ~~~x - 2 * y - 5 * (x ||| y) - 9 * ~~~(x ||| y) - 2 * ~~~(x ||| ~~~y) - 2 * (x &&& ~~~y) + 1 * (x &&& y) = - 1 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_543 (x y : BitVec w) : +theorem e_543 : 4 * ~~~x + 1 * ~~~y + 4 * ~~~(x &&& ~~~x) + 5 * ~~~(x &&& y) + 7 * ~~~(x ^^^ y) - 21 * ~~~(x ||| y) - 18 * ~~~(x ||| ~~~y) - 15 * (x &&& ~~~y) - 16 * (x &&& y) = - 5 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_544 (x y : BitVec w) : +theorem e_544 : 5 * (x ||| y) + 1 * ~~~y + 2 * ~~~(x &&& y) + 2 * (x ||| ~~~y) - 2 * ~~~(x &&& ~~~y) - 14 * ~~~(x ||| y) - 9 * ~~~(x ||| ~~~y) - 10 * (x &&& ~~~y) - 12 * (x &&& y) = - 4 * ~~~x - 7 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_545 (x y : BitVec w) : +theorem e_545 : - 2 * x - 1 * ~~~(x &&& y) - 1 * ~~~(x ^^^ y) - 5 * (x ||| y) - 11 * y + 3 * (x ||| ~~~y) + 18 * ~~~(x ||| ~~~y) + 6 * (x &&& ~~~y) + 17 * (x &&& y) = 1 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_546 (x y : BitVec w) : +theorem e_546 : - 3 * ~~~(x &&& ~~~y) + 2 * ~~~(x &&& y) - 2 * ~~~x + 11 * x + 1 * ~~~y + 1 * ~~~(x ||| y) + 3 * ~~~(x ||| ~~~y) - 14 * (x &&& ~~~y) - 9 * (x &&& y) = - 1 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_547 (x y : BitVec w) : +theorem e_547 : 2 * ~~~(x &&& ~~~y) - 7 * y - 6 * ~~~x - 11 * (x ||| y) + 7 * ~~~(x &&& ~~~x) + 11 * x + 2 * ~~~(x ||| y) + 15 * ~~~(x ||| ~~~y) - 4 * (x &&& y) = 7 * ~~~y - 2 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_548 (x y : BitVec w) : +theorem e_548 : 1 * (x ||| ~~~y) - 1 * y + 3 * ~~~(x &&& ~~~y) + 1 * ~~~y - 6 * ~~~(x &&& ~~~x) - 6 * (x ^^^ y) + 3 * ~~~(x ||| ~~~y) + 10 * (x &&& ~~~y) + 3 * (x &&& y) = - 7 * ~~~x + 6 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_549 (x y : BitVec w) : +theorem e_549 : - 1 * (x ||| ~~~y) - 3 * y - 11 * ~~~x + 1 * ~~~(x &&& ~~~x) + 5 * ~~~(x &&& y) + 12 * ~~~(x ||| y) + 14 * ~~~(x ||| ~~~y) - 5 * (x &&& ~~~y) + 9 * (x &&& y) = 6 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_550 (x y : BitVec w) : +theorem e_550 : - 2 * (x ||| y) - 6 * ~~~(x &&& y) - 1 * ~~~y + 4 * (x ||| ~~~y) + 11 * ~~~(x &&& ~~~y) + 11 * x - 8 * ~~~(x ||| y) - 6 * (x &&& ~~~y) - 29 * (x &&& y) = - 5 * y + 8 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_551 (x y : BitVec w) : +theorem e_551 : 2 * ~~~y - 7 * ~~~(x &&& y) + 2 * (x ||| y) - 2 * ~~~(x &&& ~~~y) - 1 * x + 7 * ~~~(x ||| y) + 2 * ~~~(x ||| ~~~y) - 1 * (x &&& ~~~y) + 1 * (x &&& y) = - 5 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_552 (x y : BitVec w) : +theorem e_552 : - 2 * y - 1 * ~~~(x &&& ~~~x) - 6 * ~~~(x &&& ~~~y) + 1 * ~~~x + 11 * (x ||| ~~~y) - 11 * x - 5 * ~~~(x ||| y) + 1 * (x &&& ~~~y) + 9 * (x &&& y) = - 8 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_553 (x y : BitVec w) : +theorem e_553 : 11 * ~~~(x &&& ~~~x) + 1 * y + 2 * x + 5 * ~~~(x &&& ~~~y) + 1 * (x ||| ~~~y) - 4 * ~~~(x ||| y) - 6 * ~~~(x ||| ~~~y) - 1 * (x &&& ~~~y) - 20 * (x &&& y) = 11 * ~~~(x &&& y) + 2 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_554 (x y : BitVec w) : +theorem e_554 : - 2 * ~~~(x ^^^ y) + 4 * ~~~(x &&& ~~~x) - 5 * ~~~(x &&& ~~~y) - 6 * y + 1 * x - 1 * (x ^^^ y) + 19 * ~~~(x ||| ~~~y) - 4 * (x &&& ~~~y) + 8 * (x &&& y) = 11 * ~~~x - 14 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_555 (x y : BitVec w) : +theorem e_555 : 11 * (x ||| ~~~y) - 1 * ~~~x + 4 * ~~~(x &&& ~~~y) + 7 * ~~~(x ^^^ y) + 7 * (x ^^^ y) - 14 * ~~~(x ||| y) - 3 * ~~~(x ||| ~~~y) - 11 * (x &&& ~~~y) - 15 * (x &&& y) = 7 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_556 (x y : BitVec w) : +theorem e_556 : 1 * ~~~(x ^^^ y) - 2 * ~~~(x &&& ~~~x) - 7 * (x ||| ~~~y) + 4 * (x ||| y) + 5 * ~~~x + 4 * (x ^^^ y) + 4 * ~~~(x &&& ~~~y) - 15 * ~~~(x ||| ~~~y) + 1 * (x &&& ~~~y) = 1 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_557 (x y : BitVec w) : +theorem e_557 : 2 * ~~~(x &&& ~~~y) - 11 * x + 3 * y - 1 * ~~~(x &&& y) + 2 * (x ||| ~~~y) - 7 * ~~~(x ||| y) - 8 * ~~~(x ||| ~~~y) + 10 * (x &&& ~~~y) + 4 * (x &&& y) = - 4 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_558 (x y : BitVec w) : +theorem e_558 : 11 * ~~~x + 2 * y - 1 * ~~~(x &&& y) + 2 * x - 7 * (x ||| y) - 9 * ~~~(x ||| y) - 9 * ~~~(x ||| ~~~y) + 1 * (x &&& ~~~y) + 4 * (x &&& y) = 1 * ~~~(x &&& ~~~y) - 5 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_559 (x y : BitVec w) : +theorem e_559 : 11 * (x ||| ~~~y) + 7 * (x ^^^ y) - 7 * ~~~y + 2 * ~~~(x ^^^ y) - 2 * x + 3 * y - 7 * ~~~(x ||| y) - 9 * (x &&& ~~~y) - 15 * (x &&& y) = 11 * ~~~(x ||| ~~~y) - 1 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_560 (x y : BitVec w) : +theorem e_560 : - 3 * (x ||| y) - 3 * ~~~(x &&& ~~~x) - 3 * ~~~(x ^^^ y) + 1 * (x ^^^ y) + 1 * ~~~y - 6 * x + 2 * ~~~(x ||| ~~~y) + 7 * (x &&& ~~~y) + 15 * (x &&& y) = - 3 * ~~~(x &&& y) - 2 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_561 (x y : BitVec w) : +theorem e_561 : 11 * ~~~(x &&& ~~~x) + 4 * y + 4 * ~~~(x ^^^ y) - 1 * (x ||| y) + 1 * x + 5 * ~~~(x &&& y) - 9 * ~~~(x ||| y) - 19 * ~~~(x ||| ~~~y) - 5 * (x &&& ~~~y) = 8 * (x &&& y) + 11 * (x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_562 (x y : BitVec w) : +theorem e_562 : 2 * (x ||| ~~~y) + 5 * ~~~y + 1 * ~~~(x &&& ~~~x) + 2 * (x ||| y) + 2 * ~~~(x ^^^ y) - 10 * ~~~(x ||| y) - 2 * ~~~(x ||| ~~~y) - 9 * (x &&& ~~~y) - 7 * (x &&& y) = 1 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_563 (x y : BitVec w) : +theorem e_563 : 2 * (x ^^^ y) + 2 * ~~~y + 7 * y - 1 * ~~~x - 7 * ~~~(x &&& y) + 1 * (x ||| ~~~y) - 1 * ~~~(x &&& ~~~y) + 6 * ~~~(x ||| y) + 2 * (x &&& ~~~y) = 7 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_564 (x y : BitVec w) : +theorem e_564 : 2 * (x ||| ~~~y) + 3 * ~~~(x &&& y) + 1 * x + 2 * (x ||| y) - 2 * y - 11 * ~~~(x &&& ~~~y) + 4 * ~~~(x ||| ~~~y) - 12 * (x &&& ~~~y) + 8 * (x &&& y) = - 6 * ~~~(x ||| y) - 4 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_565 (x y : BitVec w) : +theorem e_565 : - 11 * ~~~(x &&& y) - 11 * ~~~(x &&& ~~~x) + 1 * x - 2 * ~~~y - 6 * (x ||| y) + 4 * ~~~(x ^^^ y) + 22 * ~~~(x ||| y) + 31 * (x &&& ~~~y) + 14 * (x &&& y) = 2 * (x ||| ~~~y) - 28 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_566 (x y : BitVec w) : +theorem e_566 : 5 * (x ||| y) - 1 * ~~~(x &&& ~~~x) - 3 * y - 2 * ~~~x + 5 * ~~~(x &&& ~~~y) + 2 * ~~~(x &&& y) - 5 * ~~~(x ||| y) - 6 * ~~~(x ||| ~~~y) - 7 * (x &&& y) = 7 * (x &&& ~~~y) - 1 * (x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_567 (x y : BitVec w) : +theorem e_567 : - 1 * (x ||| y) - 1 * ~~~(x &&& ~~~x) - 1 * ~~~(x &&& y) - 7 * x - 6 * (x ||| ~~~y) + 8 * ~~~(x ||| y) + 11 * ~~~(x ||| ~~~y) + 13 * (x &&& ~~~y) + 26 * (x &&& y) = - 3 * (x ^^^ y) + 11 * y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_568 (x y : BitVec w) : +theorem e_568 : - 5 * ~~~x - 1 * (x ||| y) - 2 * ~~~(x &&& y) + 1 * y - 5 * ~~~(x &&& ~~~x) + 7 * ~~~(x &&& ~~~y) + 5 * ~~~(x ||| y) + 8 * (x &&& ~~~y) - 2 * (x &&& y) = - 5 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_569 (x y : BitVec w) : +theorem e_569 : 3 * x - 11 * y + 3 * ~~~(x &&& ~~~y) - 11 * ~~~(x &&& ~~~x) + 2 * ~~~y + 7 * (x ||| y) + 6 * ~~~(x ||| y) + 12 * ~~~(x ||| ~~~y) + 9 * (x &&& y) = 1 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_570 (x y : BitVec w) : +theorem e_570 : - 2 * (x ||| ~~~y) - 2 * ~~~(x ^^^ y) - 1 * ~~~(x &&& ~~~x) - 2 * y - 1 * ~~~x + 11 * ~~~y + 3 * ~~~(x &&& y) + 1 * ~~~(x ||| ~~~y) + 7 * (x &&& y) = 8 * ~~~(x ||| y) + 11 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_571 (x y : BitVec w) : +theorem e_571 : 5 * (x ||| ~~~y) - 1 * ~~~(x &&& y) - 6 * y - 2 * ~~~(x ^^^ y) + 1 * ~~~(x &&& ~~~y) - 11 * (x ^^^ y) + 20 * ~~~(x ||| ~~~y) + 15 * (x &&& ~~~y) + 10 * (x &&& y) = 3 * ~~~(x &&& ~~~x) + 5 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_572 (x y : BitVec w) : +theorem e_572 : - 11 * ~~~(x ^^^ y) + 3 * (x ^^^ y) + 1 * y - 2 * ~~~(x &&& ~~~x) - 1 * ~~~(x &&& ~~~y) + 14 * ~~~(x ||| y) - 3 * ~~~(x ||| ~~~y) - 3 * (x &&& ~~~y) + 11 * (x &&& y) = - 2 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_573 (x y : BitVec w) : +theorem e_573 : 4 * ~~~(x ^^^ y) + 2 * (x ||| ~~~y) - 2 * ~~~(x &&& ~~~y) + 4 * (x ||| y) - 11 * ~~~(x &&& y) + 18 * ~~~(x ||| y) + 25 * ~~~(x ||| ~~~y) + 16 * (x &&& ~~~y) + 8 * (x &&& y) = 11 * ~~~(x &&& ~~~x) + 5 * y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_574 (x y : BitVec w) : +theorem e_574 : - 2 * ~~~(x &&& ~~~y) - 6 * (x ^^^ y) - 3 * ~~~(x &&& ~~~x) - 1 * ~~~y + 11 * (x ||| y) + 6 * ~~~(x ||| y) - 1 * ~~~(x ||| ~~~y) - 1 * (x &&& ~~~y) - 7 * (x &&& y) = - 1 * y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_575 (x y : BitVec w) : +theorem e_575 : 7 * (x ||| ~~~y) + 1 * ~~~y - 1 * ~~~x + 7 * ~~~(x ^^^ y) + 1 * ~~~(x &&& y) - 2 * (x ^^^ y) - 4 * ~~~(x ||| y) + 13 * ~~~(x ||| ~~~y) - 3 * (x &&& y) = 11 * ~~~(x &&& ~~~x) - 4 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_576 (x y : BitVec w) : +theorem e_576 : 1 * ~~~(x ^^^ y) + 3 * ~~~(x &&& y) - 1 * ~~~(x &&& ~~~x) + 2 * (x ||| y) - 3 * ~~~(x &&& ~~~y) + 7 * ~~~(x ||| y) + 6 * ~~~(x ||| ~~~y) - 6 * (x &&& ~~~y) - 1 * (x &&& y) = 7 * ~~~x - 2 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_577 (x y : BitVec w) : +theorem e_577 : 2 * ~~~(x &&& y) + 5 * x - 5 * ~~~x - 5 * ~~~y - 2 * y - 5 * ~~~(x &&& ~~~x) + 11 * ~~~(x ||| y) + 8 * ~~~(x ||| ~~~y) + 3 * (x &&& ~~~y) = - 2 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_578 (x y : BitVec w) : +theorem e_578 : - 11 * ~~~(x ^^^ y) + 11 * (x ||| y) - 3 * ~~~(x &&& ~~~y) + 5 * (x ||| ~~~y) + 3 * ~~~(x &&& y) + 11 * ~~~(x &&& ~~~x) - 5 * ~~~(x ||| y) - 24 * ~~~(x ||| ~~~y) - 30 * (x &&& ~~~y) = 15 * (x &&& y) - 2 * y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_579 (x y : BitVec w) : +theorem e_579 : - 2 * (x ||| y) + 5 * x + 5 * ~~~(x &&& ~~~y) + 1 * ~~~(x &&& ~~~x) - 6 * (x ||| ~~~y) - 1 * ~~~(x &&& y) + 6 * ~~~(x ||| y) + 5 * ~~~(x ||| ~~~y) + 3 * (x &&& ~~~y) = 3 * y + 5 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_580 (x y : BitVec w) : +theorem e_580 : 4 * y - 1 * (x ^^^ y) - 7 * ~~~(x &&& y) - 1 * ~~~y + 2 * x - 3 * (x ||| ~~~y) + 13 * ~~~(x ||| y) + 12 * (x &&& ~~~y) - 1 * (x &&& y) = 2 * ~~~(x &&& ~~~x) - 6 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_581 (x y : BitVec w) : +theorem e_581 : - 3 * (x ||| y) - 6 * y + 11 * ~~~(x &&& ~~~x) - 1 * (x ^^^ y) + 4 * ~~~x - 1 * ~~~(x &&& y) + 1 * (x ||| ~~~y) - 4 * ~~~(x ||| ~~~y) - 3 * (x &&& y) = 8 * ~~~(x ||| y) + 7 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_582 (x y : BitVec w) : +theorem e_582 : 1 * (x ||| ~~~y) + 1 * ~~~(x ^^^ y) + 5 * ~~~(x &&& ~~~x) - 2 * ~~~(x &&& ~~~y) - 3 * (x ^^^ y) + 1 * x - 12 * ~~~(x ||| y) - 7 * ~~~(x ||| ~~~y) - 6 * (x &&& y) = 11 * (x &&& ~~~y) - 7 * ~~~(x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_583 (x y : BitVec w) : +theorem e_583 : - 2 * (x ||| y) + 4 * ~~~y - 3 * (x ||| ~~~y) - 3 * ~~~x - 7 * x + 2 * ~~~(x &&& ~~~y) - 7 * ~~~(x ||| y) + 5 * (x &&& ~~~y) + 6 * (x &&& y) = - 4 * ~~~(x ^^^ y) - 3 * ~~~(x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_584 (x y : BitVec w) : +theorem e_584 : 1 * ~~~x - 1 * (x ||| y) + 2 * ~~~(x &&& y) + 11 * ~~~(x &&& ~~~y) - 2 * y - 6 * (x ^^^ y) - 14 * ~~~(x ||| y) + 6 * (x &&& ~~~y) - 7 * (x &&& y) = 5 * ~~~(x ||| ~~~y) + 1 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_585 (x y : BitVec w) : +theorem e_585 : 4 * ~~~(x &&& ~~~x) - 11 * x - 1 * y - 1 * ~~~y - 1 * ~~~(x ^^^ y) - 1 * ~~~(x ||| y) - 2 * ~~~(x ||| ~~~y) + 9 * (x &&& ~~~y) + 9 * (x &&& y) = 1 * ~~~(x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_586 (x y : BitVec w) : +theorem e_586 : - 1 * ~~~y + 11 * (x ^^^ y) - 5 * ~~~(x ^^^ y) + 3 * ~~~(x &&& y) + 1 * y + 1 * (x ||| ~~~y) - 17 * ~~~(x ||| ~~~y) - 16 * (x &&& ~~~y) + 1 * (x &&& y) = - 2 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_587 (x y : BitVec w) : +theorem e_587 : - 6 * ~~~(x &&& ~~~x) - 11 * ~~~x + 11 * x - 11 * ~~~(x &&& ~~~y) - 1 * (x ||| y) + 4 * y + 7 * (x ^^^ y) + 28 * ~~~(x ||| y) + 18 * ~~~(x ||| ~~~y) - 11 * (x &&& ~~~y) = - 3 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_588 (x y : BitVec w) : +theorem e_588 : 1 * ~~~x + 3 * (x ^^^ y) + 11 * ~~~(x &&& y) - 1 * x + 7 * (x ||| y) + 5 * ~~~(x ^^^ y) + 2 * ~~~(x &&& ~~~x) - 19 * ~~~(x ||| y) - 24 * ~~~(x ||| ~~~y) - 22 * (x &&& ~~~y) = 13 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_589 (x y : BitVec w) : +theorem e_589 : - 3 * ~~~(x &&& y) + 2 * ~~~x - 2 * x + 11 * ~~~(x &&& ~~~y) - 6 * (x ||| ~~~y) - 1 * ~~~(x &&& ~~~x) - 4 * ~~~(x ||| y) - 9 * ~~~(x ||| ~~~y) + 11 * (x &&& ~~~y) - 2 * (x &&& y) = - 1 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_590 (x y : BitVec w) : +theorem e_590 : 2 * ~~~(x &&& y) + 2 * ~~~(x &&& ~~~y) - 5 * (x ||| y) - 2 * ~~~x - 1 * ~~~(x ^^^ y) - 7 * (x ^^^ y) + 1 * ~~~(x &&& ~~~x) - 2 * ~~~(x ||| y) + 9 * ~~~(x ||| ~~~y) + 12 * (x &&& ~~~y) = 3 * x - 6 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_591 (x y : BitVec w) : +theorem e_591 : - 1 * ~~~(x &&& ~~~y) - 5 * ~~~x - 3 * ~~~(x &&& ~~~x) - 3 * y - 1 * (x ||| y) + 7 * x + 9 * ~~~(x ||| y) + 20 * ~~~(x ||| ~~~y) + 4 * (x &&& ~~~y) + 1 * (x &&& y) = 7 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_592 (x y : BitVec w) : +theorem e_592 : - 1 * (x ||| ~~~y) + 1 * (x ||| y) - 5 * ~~~(x &&& y) + 1 * ~~~(x &&& ~~~y) + 2 * ~~~y + 7 * (x ^^^ y) + 14 * ~~~(x ||| y) + 7 * ~~~(x ||| ~~~y) + 8 * (x &&& ~~~y) + 11 * (x &&& y) = 1 * x + 11 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_593 (x y : BitVec w) : +theorem e_593 : 1 * (x ||| y) + 7 * (x ||| ~~~y) - 2 * ~~~(x &&& y) + 11 * ~~~(x ^^^ y) - 1 * y + 4 * ~~~x - 17 * ~~~(x ||| y) + 1 * ~~~(x ||| ~~~y) - 3 * (x &&& ~~~y) - 15 * (x &&& y) = 3 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_594 (x y : BitVec w) : +theorem e_594 : - 3 * ~~~y - 5 * (x ^^^ y) + 11 * y + 7 * ~~~x + 7 * ~~~(x &&& ~~~x) + 2 * ~~~(x &&& ~~~y) - 13 * ~~~(x ||| y) - 11 * ~~~(x ||| ~~~y) + 12 * (x &&& ~~~y) - 9 * (x &&& y) = 11 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_595 (x y : BitVec w) : +theorem e_595 : - 1 * (x ^^^ y) - 2 * (x ||| y) - 2 * (x ||| ~~~y) + 4 * y + 3 * x + 1 * ~~~(x &&& ~~~y) + 11 * ~~~(x ^^^ y) - 8 * ~~~(x ||| y) + 1 * (x &&& ~~~y) - 15 * (x &&& y) = - 1 * ~~~(x &&& y) + 3 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_596 (x y : BitVec w) : +theorem e_596 : 2 * ~~~x + 1 * (x ^^^ y) - 1 * x + 2 * ~~~(x &&& ~~~x) - 5 * ~~~y - 1 * (x ||| ~~~y) + 5 * ~~~(x ||| y) - 5 * ~~~(x ||| ~~~y) + 4 * (x &&& ~~~y) + 3 * (x &&& y) = 3 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_597 (x y : BitVec w) : +theorem e_597 : 7 * ~~~x + 3 * ~~~y + 5 * ~~~(x ^^^ y) - 1 * (x ^^^ y) - 5 * ~~~(x &&& ~~~y) + 1 * ~~~(x &&& y) + 2 * (x ||| ~~~y) - 16 * ~~~(x ||| y) - 5 * ~~~(x ||| ~~~y) - 8 * (x &&& ~~~y) = 5 * (x &&& y) - 3 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_598 (x y : BitVec w) : +theorem e_598 : 7 * ~~~(x &&& ~~~x) - 5 * (x ||| y) + 1 * ~~~(x &&& ~~~y) + 3 * (x ||| ~~~y) + 5 * ~~~y - 3 * ~~~x - 2 * ~~~(x ^^^ y) + 7 * ~~~(x ||| ~~~y) - 3 * (x &&& ~~~y) - 4 * (x &&& y) = 7 * ~~~(x &&& y) + 4 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_599 (x y : BitVec w) : +theorem e_599 : 2 * ~~~y + 4 * y - 5 * ~~~(x &&& y) + 2 * (x ^^^ y) + 7 * (x ||| y) + 4 * ~~~(x &&& ~~~x) - 2 * ~~~(x ||| y) - 12 * ~~~(x ||| ~~~y) - 11 * (x &&& ~~~y) - 16 * (x &&& y) = - 1 * (x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_600 (x y : BitVec w) : +theorem e_600 : - 11 * ~~~(x ^^^ y) - 11 * ~~~(x &&& ~~~y) - 1 * (x ||| ~~~y) + 11 * (x ^^^ y) + 5 * ~~~(x &&& y) + 4 * y + 18 * ~~~(x ||| y) - 9 * ~~~(x ||| ~~~y) - 13 * (x &&& ~~~y) + 21 * (x &&& y) = 2 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_601 (x y : BitVec w) : +theorem e_601 : - 1 * ~~~(x ^^^ y) - 1 * ~~~x + 4 * y + 5 * x - 5 * (x ||| ~~~y) - 11 * ~~~(x &&& ~~~x) + 25 * ~~~(x ||| y) + 7 * ~~~(x ||| ~~~y) + 17 * (x &&& ~~~y) + 8 * (x &&& y) = 7 * ~~~y - 1 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_602 (x y : BitVec w) : +theorem e_602 : 1 * ~~~(x &&& ~~~x) + 3 * (x ||| y) - 7 * (x ||| ~~~y) + 1 * ~~~(x &&& ~~~y) + 2 * ~~~(x &&& y) + 4 * ~~~x - 1 * ~~~(x ^^^ y) + 7 * (x ^^^ y) - 7 * (x &&& ~~~y) + 2 * (x &&& y) = - 1 * x + 18 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_603 (x y : BitVec w) : +theorem e_603 : - 1 * ~~~(x &&& ~~~y) - 2 * ~~~(x &&& y) + 2 * x + 7 * ~~~(x ^^^ y) + 3 * (x ||| ~~~y) + 5 * (x ||| y) - 7 * ~~~(x ||| y) - 3 * ~~~(x ||| ~~~y) - 8 * (x &&& ~~~y) - 17 * (x &&& y) = - 1 * y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_604 (x y : BitVec w) : +theorem e_604 : - 1 * ~~~y - 1 * y + 3 * (x ^^^ y) - 7 * ~~~(x &&& y) - 2 * x - 1 * ~~~(x ^^^ y) + 1 * (x ||| y) - 1 * (x ||| ~~~y) + 6 * ~~~(x ||| y) + 3 * (x &&& ~~~y) = - 4 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_605 (x y : BitVec w) : +theorem e_605 : 3 * x - 2 * ~~~(x &&& y) + 1 * ~~~x + 2 * (x ||| ~~~y) - 3 * ~~~(x ^^^ y) - 1 * y + 2 * ~~~(x &&& ~~~x) + 1 * ~~~(x ||| y) + 3 * ~~~(x ||| ~~~y) - 7 * (x &&& ~~~y) = - 2 * ~~~y + 3 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_606 (x y : BitVec w) : +theorem e_606 : - 2 * x + 2 * (x ||| ~~~y) - 1 * ~~~(x &&& y) - 6 * ~~~(x &&& ~~~y) + 5 * (x ||| y) - 2 * ~~~y - 1 * ~~~(x &&& ~~~x) + 3 * (x ^^^ y) + 8 * ~~~(x ||| y) - 4 * (x &&& ~~~y) = - 2 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_607 (x y : BitVec w) : +theorem e_607 : - 2 * (x ||| ~~~y) + 2 * ~~~y - 3 * ~~~x - 2 * (x ||| y) - 2 * ~~~(x &&& ~~~x) + 2 * ~~~(x ^^^ y) + 3 * ~~~(x &&& y) + 1 * ~~~(x ||| ~~~y) - 2 * (x &&& ~~~y) + 4 * (x &&& y) = - 3 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_608 (x y : BitVec w) : +theorem e_608 : 1 * ~~~(x &&& ~~~y) - 3 * y + 7 * x - 1 * ~~~(x &&& ~~~x) - 1 * (x ^^^ y) - 2 * (x ||| ~~~y) - 1 * ~~~y + 3 * ~~~(x ||| y) + 4 * ~~~(x ||| ~~~y) - 2 * (x &&& y) = 2 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_609 (x y : BitVec w) : +theorem e_609 : 4 * ~~~(x &&& y) - 3 * ~~~(x ^^^ y) - 6 * (x ^^^ y) - 2 * ~~~(x &&& ~~~y) - 6 * ~~~x + 7 * x + 2 * ~~~y + 5 * ~~~(x ||| y) + 9 * ~~~(x ||| ~~~y) - 7 * (x &&& ~~~y) = 3 * (x &&& y) - 1 * y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_610 (x y : BitVec w) : +theorem e_610 : 1 * ~~~x + 3 * y - 2 * ~~~y - 7 * ~~~(x &&& y) - 1 * ~~~(x ^^^ y) - 1 * x + 9 * ~~~(x ||| y) + 4 * ~~~(x ||| ~~~y) + 11 * (x &&& ~~~y) - 1 * (x &&& y) = 1 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_611 (x y : BitVec w) : +theorem e_611 : - 3 * y + 4 * (x ||| y) - 1 * x - 11 * ~~~y + 2 * (x ^^^ y) - 7 * ~~~(x ^^^ y) + 16 * ~~~(x ||| y) - 5 * ~~~(x ||| ~~~y) + 6 * (x &&& ~~~y) + 7 * (x &&& y) = - 2 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_612 (x y : BitVec w) : +theorem e_612 : - 11 * ~~~(x ^^^ y) - 3 * ~~~(x &&& ~~~x) - 11 * y + 1 * ~~~(x &&& ~~~y) + 1 * (x ||| ~~~y) - 6 * ~~~(x &&& y) - 2 * (x ^^^ y) + 18 * ~~~(x ||| y) + 21 * ~~~(x ||| ~~~y) + 23 * (x &&& y) = - 10 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_613 (x y : BitVec w) : +theorem e_613 : - 6 * x + 1 * ~~~(x ^^^ y) - 11 * (x ||| ~~~y) + 5 * ~~~(x &&& ~~~x) + 4 * y - 2 * (x ^^^ y) + 8 * ~~~(x ||| y) - 4 * ~~~(x ||| ~~~y) + 14 * (x &&& ~~~y) + 10 * (x &&& y) = 3 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_614 (x y : BitVec w) : +theorem e_614 : - 2 * y - 2 * ~~~(x ^^^ y) - 3 * ~~~(x &&& y) + 7 * (x ^^^ y) - 2 * ~~~x + 2 * ~~~y - 2 * (x ||| y) + 5 * ~~~(x ||| y) + 2 * ~~~(x ||| ~~~y) + 2 * (x &&& y) = 8 * (x &&& ~~~y) - 4 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_615 (x y : BitVec w) : +theorem e_615 : 7 * ~~~(x ^^^ y) - 1 * ~~~x - 5 * ~~~(x &&& ~~~y) + 3 * (x ||| ~~~y) + 3 * ~~~(x &&& y) + 5 * (x ||| y) - 1 * x - 7 * ~~~(x ||| y) - 10 * (x &&& ~~~y) - 9 * (x &&& y) = 2 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_616 (x y : BitVec w) : +theorem e_616 : - 2 * (x ^^^ y) + 2 * ~~~(x &&& ~~~x) - 3 * ~~~(x &&& ~~~y) - 1 * ~~~x + 2 * ~~~y + 5 * ~~~(x &&& y) + 5 * ~~~(x ^^^ y) - 10 * ~~~(x ||| y) - 6 * (x &&& ~~~y) - 3 * (x &&& y) = 1 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_617 (x y : BitVec w) : +theorem e_617 : - 5 * ~~~(x &&& y) - 5 * y - 1 * ~~~y + 2 * ~~~(x &&& ~~~x) - 2 * (x ^^^ y) - 5 * x + 2 * ~~~(x ||| y) + 9 * ~~~(x ||| ~~~y) + 8 * (x &&& ~~~y) + 5 * (x &&& y) = - 1 * (x ||| y) - 2 * (x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_618 (x y : BitVec w) : +theorem e_618 : 2 * y + 2 * ~~~(x &&& ~~~x) + 7 * (x ||| y) - 1 * ~~~(x &&& y) - 5 * ~~~(x &&& ~~~y) - 2 * x + 3 * ~~~(x ||| y) - 5 * ~~~(x ||| ~~~y) - 6 * (x &&& ~~~y) - 5 * (x &&& y) = - 1 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_619 (x y : BitVec w) : +theorem e_619 : - 7 * ~~~(x ^^^ y) + 7 * (x ||| ~~~y) - 11 * ~~~(x &&& ~~~x) + 2 * (x ^^^ y) - 2 * x - 2 * ~~~y + 11 * ~~~(x &&& y) + 4 * ~~~(x ||| y) - 5 * (x &&& ~~~y) + 12 * (x &&& y) = - 1 * ~~~(x &&& ~~~y) + 3 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_620 (x y : BitVec w) : +theorem e_620 : 1 * (x ||| ~~~y) + 5 * (x ||| y) + 2 * ~~~(x &&& ~~~y) + 3 * (x ^^^ y) - 1 * ~~~(x &&& ~~~x) - 1 * ~~~(x ^^^ y) - 2 * ~~~(x ||| y) - 10 * ~~~(x ||| ~~~y) - 8 * (x &&& ~~~y) - 6 * (x &&& y) = - 1 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_621 (x y : BitVec w) : +theorem e_621 : - 2 * ~~~(x &&& ~~~x) - 2 * ~~~(x &&& y) + 1 * ~~~(x &&& ~~~y) + 5 * (x ||| ~~~y) - 2 * x - 7 * y - 11 * ~~~(x ^^^ y) + 10 * ~~~(x ||| ~~~y) + 1 * (x &&& ~~~y) + 16 * (x &&& y) = - 9 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_622 (x y : BitVec w) : +theorem e_622 : 2 * ~~~(x &&& ~~~x) - 2 * x + 2 * ~~~(x ^^^ y) + 3 * ~~~y - 5 * y - 3 * (x ||| ~~~y) - 3 * ~~~(x ||| y) + 4 * ~~~(x ||| ~~~y) + 1 * (x &&& ~~~y) + 6 * (x &&& y) = 1 * ~~~(x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_623 (x y : BitVec w) : +theorem e_623 : 3 * (x ||| y) + 4 * ~~~x + 4 * ~~~(x &&& y) + 2 * (x ^^^ y) - 11 * ~~~(x ^^^ y) - 2 * y - 5 * ~~~(x &&& ~~~y) + 8 * ~~~(x ||| y) - 6 * ~~~(x ||| ~~~y) + 15 * (x &&& y) = 9 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_624 (x y : BitVec w) : +theorem e_624 : 7 * ~~~(x ^^^ y) + 2 * (x ||| y) - 2 * (x ||| ~~~y) - 11 * (x ^^^ y) - 11 * ~~~x + 2 * ~~~(x &&& ~~~y) + 5 * ~~~(x ||| y) + 25 * ~~~(x ||| ~~~y) + 12 * (x &&& ~~~y) - 2 * (x &&& y) = 1 * ~~~(x &&& ~~~x) + 6 * y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_625 (x y : BitVec w) : +theorem e_625 : - 11 * ~~~(x &&& y) - 1 * (x ||| y) + 2 * x + 4 * ~~~y - 11 * (x ^^^ y) + 7 * ~~~(x ^^^ y) - 6 * ~~~(x &&& ~~~y) + 6 * ~~~(x ||| y) + 29 * ~~~(x ||| ~~~y) - 2 * (x &&& y) = - 17 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_626 (x y : BitVec w) : +theorem e_626 : - 5 * x - 7 * ~~~x + 1 * ~~~(x &&& ~~~y) - 1 * y - 1 * ~~~(x ^^^ y) + 1 * ~~~(x &&& y) + 1 * (x ||| ~~~y) + 5 * ~~~(x ||| y) + 3 * (x &&& ~~~y) + 5 * (x &&& y) = - 6 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_627 (x y : BitVec w) : +theorem e_627 : - 2 * ~~~(x &&& ~~~x) - 2 * x + 4 * ~~~(x ^^^ y) - 2 * (x ^^^ y) + 7 * ~~~y + 7 * ~~~(x &&& y) - 5 * ~~~(x ||| y) + 8 * ~~~(x ||| ~~~y) - 8 * (x &&& ~~~y) + 11 * (x &&& y) = 11 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_628 (x y : BitVec w) : +theorem e_628 : 5 * (x ^^^ y) + 1 * ~~~x + 4 * ~~~(x &&& ~~~y) - 2 * x + 4 * ~~~(x &&& y) + 2 * ~~~(x ^^^ y) + 11 * ~~~y - 22 * ~~~(x ||| y) - 14 * ~~~(x ||| ~~~y) - 18 * (x &&& ~~~y) = 4 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_629 (x y : BitVec w) : +theorem e_629 : - 1 * ~~~x - 5 * ~~~y - 2 * y + 11 * ~~~(x &&& y) - 1 * x - 7 * (x ||| y) + 1 * ~~~(x ^^^ y) - 7 * ~~~(x ||| y) + 3 * (x &&& ~~~y) + 8 * (x &&& y) = - 1 * ~~~(x &&& ~~~x) + 2 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_630 (x y : BitVec w) : +theorem e_630 : 1 * ~~~(x &&& ~~~x) + 7 * ~~~(x &&& y) + 7 * (x ^^^ y) - 1 * ~~~(x ^^^ y) - 5 * y - 7 * ~~~x - 2 * ~~~y + 2 * ~~~(x ||| y) - 8 * ~~~(x ||| ~~~y) - 18 * (x &&& ~~~y) = - 5 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_631 (x y : BitVec w) : +theorem e_631 : 2 * ~~~(x ^^^ y) - 1 * ~~~x + 1 * (x ^^^ y) - 7 * ~~~(x &&& y) + 5 * ~~~y + 2 * (x ||| ~~~y) - 2 * ~~~(x ||| y) - 5 * ~~~(x ||| ~~~y) - 12 * (x &&& ~~~y) - 16 * (x &&& y) = - 1 * ~~~(x &&& ~~~y) - 11 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_632 (x y : BitVec w) : +theorem e_632 : 2 * ~~~(x &&& ~~~x) + 7 * ~~~x + 2 * (x ||| ~~~y) + 2 * (x ||| y) - 7 * x + 2 * ~~~(x &&& ~~~y) - 15 * ~~~(x ||| y) - 13 * ~~~(x ||| ~~~y) - 1 * (x &&& ~~~y) - 1 * (x &&& y) = - 2 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_633 (x y : BitVec w) : +theorem e_633 : 11 * (x ||| y) - 6 * ~~~(x &&& ~~~x) + 2 * ~~~y - 7 * ~~~(x &&& y) - 2 * ~~~(x ^^^ y) + 7 * x + 14 * ~~~(x ||| y) + 3 * ~~~(x ||| ~~~y) - 7 * (x &&& ~~~y) - 9 * (x &&& y) = 1 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_634 (x y : BitVec w) : +theorem e_634 : - 2 * ~~~(x ^^^ y) - 5 * y + 2 * ~~~(x &&& y) + 5 * x - 1 * (x ^^^ y) - 3 * ~~~(x &&& ~~~x) - 6 * ~~~(x &&& ~~~y) + 9 * ~~~(x ||| y) - 1 * (x &&& ~~~y) + 13 * (x &&& y) = - 15 * ~~~(x ||| ~~~y) + 2 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_635 (x y : BitVec w) : +theorem e_635 : - 2 * ~~~x + 11 * (x ||| y) + 3 * ~~~(x &&& ~~~y) - 3 * ~~~(x ^^^ y) - 2 * ~~~(x &&& y) - 2 * (x ^^^ y) + 5 * ~~~(x ||| y) - 8 * ~~~(x ||| ~~~y) - 6 * (x &&& ~~~y) - 11 * (x &&& y) = 1 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_636 (x y : BitVec w) : +theorem e_636 : - 3 * y + 11 * ~~~y - 6 * (x ^^^ y) + 7 * x + 5 * ~~~x - 11 * ~~~(x &&& y) - 7 * ~~~(x ||| y) + 13 * ~~~(x ||| ~~~y) - 2 * (x &&& ~~~y) - 6 * (x &&& y) = - 1 * ~~~(x &&& ~~~y) - 1 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_637 (x y : BitVec w) : +theorem e_637 : 1 * ~~~(x &&& ~~~y) + 1 * (x ||| y) + 11 * (x ||| ~~~y) - 1 * ~~~x - 6 * x - 11 * y - 6 * ~~~(x ||| y) + 17 * ~~~(x ||| ~~~y) + 1 * (x &&& ~~~y) + 9 * (x &&& y) = 5 * ~~~(x ^^^ y) + 7 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_638 (x y : BitVec w) : +theorem e_638 : - 6 * ~~~(x &&& ~~~x) + 4 * x - 1 * (x ||| y) + 3 * y - 2 * (x ||| ~~~y) + 1 * ~~~(x ^^^ y) + 4 * ~~~(x ||| y) + 3 * ~~~(x ||| ~~~y) + 3 * (x &&& ~~~y) + 1 * (x &&& y) = - 2 * ~~~y - 1 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_639 (x y : BitVec w) : +theorem e_639 : - 11 * (x ||| y) + 1 * (x ^^^ y) + 5 * ~~~(x &&& ~~~x) - 3 * (x ||| ~~~y) - 5 * x + 1 * y - 5 * ~~~(x &&& y) + 2 * ~~~(x ||| y) + 9 * ~~~(x ||| ~~~y) + 18 * (x &&& ~~~y) = - 1 * ~~~(x ^^^ y) - 12 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_640 (x y : BitVec w) : +theorem e_640 : - 7 * y + 1 * ~~~y + 4 * ~~~(x &&& y) - 7 * ~~~x - 11 * (x ^^^ y) - 1 * (x ||| y) - 1 * ~~~(x ||| y) + 22 * ~~~(x ||| ~~~y) + 7 * (x &&& ~~~y) + 5 * (x &&& y) = - 3 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_641 (x y : BitVec w) : +theorem e_641 : 5 * ~~~(x &&& ~~~x) - 11 * (x ||| y) - 7 * (x ||| ~~~y) + 11 * ~~~y + 2 * ~~~(x ^^^ y) + 11 * y + 1 * x - 11 * ~~~(x ||| y) - 5 * ~~~(x ||| ~~~y) - 1 * (x &&& y) = - 1 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_642 (x y : BitVec w) : +theorem e_642 : 2 * ~~~(x ^^^ y) + 1 * ~~~(x &&& ~~~x) + 3 * ~~~(x &&& y) + 1 * y - 2 * (x ^^^ y) + 11 * x - 10 * ~~~(x ||| y) - 7 * ~~~(x ||| ~~~y) - 13 * (x &&& ~~~y) - 16 * (x &&& y) = - 3 * ~~~x - 1 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_643 (x y : BitVec w) : +theorem e_643 : 4 * (x ||| ~~~y) + 1 * (x ||| y) - 1 * ~~~(x &&& ~~~y) - 11 * ~~~(x ^^^ y) + 5 * x + 1 * y + 10 * ~~~(x ||| y) - 6 * ~~~(x ||| ~~~y) - 15 * (x &&& ~~~y) + 3 * (x &&& y) = - 7 * (x ^^^ y) + 2 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_644 (x y : BitVec w) : +theorem e_644 : 1 * y - 11 * (x ^^^ y) - 2 * ~~~y + 3 * (x ||| y) - 7 * x - 1 * (x ||| ~~~y) - 1 * ~~~(x &&& ~~~y) + 4 * ~~~(x ||| y) + 8 * ~~~(x ||| ~~~y) + 5 * (x &&& y) = - 18 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_645 (x y : BitVec w) : +theorem e_645 : 5 * (x ||| y) - 5 * y + 11 * ~~~(x &&& ~~~y) - 1 * ~~~x - 1 * ~~~y - 7 * ~~~(x &&& ~~~x) + 1 * x - 3 * ~~~(x ||| ~~~y) + 2 * (x &&& ~~~y) - 5 * (x &&& y) = 2 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_646 (x y : BitVec w) : +theorem e_646 : 3 * (x ||| ~~~y) + 3 * ~~~(x &&& ~~~y) - 2 * y - 11 * ~~~x + 1 * (x ||| y) + 2 * ~~~(x &&& y) - 2 * x - 4 * ~~~(x ||| ~~~y) - 15 * (x &&& ~~~y) - 3 * (x &&& y) = - 11 * (x ^^^ y) - 3 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_647 (x y : BitVec w) : +theorem e_647 : 3 * ~~~y - 7 * (x ^^^ y) - 3 * ~~~(x &&& ~~~y) - 1 * ~~~(x ^^^ y) + 5 * ~~~(x &&& y) - 6 * ~~~(x &&& ~~~x) + 2 * ~~~(x ||| y) + 11 * ~~~(x ||| ~~~y) + 1 * (x &&& ~~~y) + 6 * (x &&& y) = - 4 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_648 (x y : BitVec w) : +theorem e_648 : - 2 * ~~~(x ^^^ y) - 7 * ~~~(x &&& ~~~y) + 7 * ~~~y + 7 * ~~~x - 2 * (x ||| ~~~y) - 6 * (x ^^^ y) - 3 * ~~~(x ||| y) + 5 * ~~~(x ||| ~~~y) - 2 * (x &&& ~~~y) + 8 * (x &&& y) = - 2 * x - 1 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_649 (x y : BitVec w) : +theorem e_649 : - 7 * ~~~x + 1 * (x ^^^ y) + 1 * ~~~(x &&& ~~~y) + 3 * ~~~(x ^^^ y) + 5 * ~~~y + 7 * (x ||| ~~~y) - 8 * ~~~(x ||| y) + 6 * ~~~(x ||| ~~~y) - 12 * (x &&& ~~~y) - 10 * (x &&& y) = 1 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_650 (x y : BitVec w) : +theorem e_650 : 7 * (x ||| ~~~y) + 4 * ~~~y - 2 * ~~~x + 11 * (x ^^^ y) - 7 * ~~~(x ^^^ y) - 5 * x - 1 * ~~~(x &&& ~~~y) + 3 * (x ||| y) - 1 * ~~~(x ||| y) - 11 * ~~~(x ||| ~~~y) = 20 * (x &&& ~~~y) - 3 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_651 (x y : BitVec w) : +theorem e_651 : - 11 * y - 1 * ~~~x + 1 * ~~~(x &&& ~~~x) + 1 * ~~~y - 1 * ~~~(x &&& y) - 6 * ~~~(x ^^^ y) + 11 * ~~~(x ||| y) + 17 * ~~~(x ||| ~~~y) - 4 * (x &&& ~~~y) + 18 * (x &&& y) = 5 * ~~~(x &&& ~~~y) - 3 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_652 (x y : BitVec w) : +theorem e_652 : 5 * ~~~(x &&& ~~~y) + 1 * x - 1 * ~~~(x &&& ~~~x) + 2 * y - 3 * ~~~x + 1 * ~~~(x &&& y) - 2 * ~~~(x ||| y) + 3 * ~~~(x ||| ~~~y) + 6 * (x &&& ~~~y) + 4 * (x &&& y) = - 4 * (x ^^^ y) + 11 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_653 (x y : BitVec w) : +theorem e_653 : 2 * (x ^^^ y) - 2 * ~~~x - 7 * x - 1 * ~~~(x &&& ~~~y) + 1 * y + 1 * ~~~y + 2 * ~~~(x &&& y) + 9 * ~~~(x ||| ~~~y) + 13 * (x &&& ~~~y) + 18 * (x &&& y) = 11 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_654 (x y : BitVec w) : +theorem e_654 : 5 * ~~~(x &&& y) - 6 * y + 3 * ~~~(x &&& ~~~y) + 4 * ~~~(x ^^^ y) - 6 * (x ^^^ y) - 1 * (x ||| ~~~y) + 2 * x - 6 * ~~~(x ||| y) + 9 * ~~~(x ||| ~~~y) - 2 * (x &&& y) = 5 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_655 (x y : BitVec w) : +theorem e_655 : 11 * ~~~y + 3 * ~~~(x ^^^ y) - 3 * ~~~x + 2 * (x ||| y) - 2 * ~~~(x &&& ~~~y) - 11 * ~~~(x &&& ~~~x) + 7 * y + 2 * ~~~(x ||| y) - 2 * (x &&& ~~~y) + 1 * (x &&& y) = - 7 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_656 (x y : BitVec w) : +theorem e_656 : - 2 * (x ^^^ y) + 1 * ~~~x + 1 * ~~~(x &&& ~~~y) + 1 * y + 1 * (x ||| y) - 7 * ~~~(x ^^^ y) - 1 * (x ||| ~~~y) + 7 * ~~~(x ||| y) + 3 * (x &&& ~~~y) + 5 * (x &&& y) = 2 * ~~~(x &&& y) - 1 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_657 (x y : BitVec w) : +theorem e_657 : 1 * x + 5 * (x ||| y) + 2 * ~~~x - 7 * ~~~(x &&& y) - 7 * ~~~(x &&& ~~~y) + 1 * y + 2 * ~~~y + 12 * ~~~(x ||| y) + 1 * (x &&& ~~~y) + 2 * (x &&& y) = - 6 * ~~~(x ||| ~~~y) + 2 * (x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_658 (x y : BitVec w) : +theorem e_658 : - 2 * (x ^^^ y) + 2 * x - 11 * ~~~(x &&& ~~~x) + 1 * ~~~y - 2 * (x ||| y) - 1 * (x ||| ~~~y) + 2 * y + 11 * ~~~(x ||| y) + 13 * ~~~(x ||| ~~~y) + 10 * (x &&& y) = - 13 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_659 (x y : BitVec w) : +theorem e_659 : - 6 * (x ^^^ y) - 1 * x - 1 * (x ||| y) - 11 * ~~~(x ^^^ y) - 2 * ~~~(x &&& y) + 1 * y - 11 * (x ||| ~~~y) + 8 * ~~~(x ||| ~~~y) + 32 * (x &&& ~~~y) + 23 * (x &&& y) = 11 * ~~~y - 35 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_660 (x y : BitVec w) : +theorem e_660 : 5 * ~~~(x &&& y) + 2 * ~~~(x &&& ~~~y) + 1 * ~~~(x ^^^ y) + 1 * (x ||| y) + 1 * (x ^^^ y) - 11 * x - 2 * ~~~(x ||| y) - 9 * ~~~(x ||| ~~~y) + 10 * (x &&& ~~~y) + 7 * (x &&& y) = 6 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_661 (x y : BitVec w) : +theorem e_661 : - 1 * ~~~y + 5 * ~~~(x &&& y) + 11 * x + 1 * ~~~(x &&& ~~~x) - 5 * y - 2 * ~~~x + 1 * (x ||| y) - 1 * ~~~(x ||| y) - 17 * (x &&& ~~~y) - 6 * (x &&& y) = 2 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_662 (x y : BitVec w) : +theorem e_662 : 1 * y + 7 * (x ^^^ y) + 5 * ~~~x + 3 * (x ||| ~~~y) - 1 * ~~~(x &&& y) - 1 * (x ||| y) - 1 * x + 4 * ~~~y - 5 * ~~~(x ^^^ y) + 5 * ~~~(x ||| y) = 11 * ~~~(x &&& ~~~x) - 14 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_663 (x y : BitVec w) : +theorem e_663 : 4 * (x ||| ~~~y) + 7 * ~~~(x &&& ~~~x) + 11 * ~~~(x &&& y) + 2 * (x ^^^ y) - 1 * (x ||| y) + 4 * x - 5 * y + 5 * ~~~y - 27 * ~~~(x ||| y) - 14 * ~~~(x ||| ~~~y) = 9 * (x &&& y) + 32 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_664 (x y : BitVec w) : +theorem e_664 : - 11 * (x ||| ~~~y) + 1 * (x ||| y) + 1 * ~~~y + 3 * (x ^^^ y) + 4 * ~~~x - 5 * ~~~(x &&& y) - 7 * x + 2 * ~~~(x &&& ~~~x) + 16 * (x &&& ~~~y) + 15 * (x &&& y) = 5 * ~~~(x ||| ~~~y) - 9 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_665 (x y : BitVec w) : +theorem e_665 : 1 * ~~~(x &&& ~~~y) - 1 * (x ^^^ y) - 2 * x + 3 * ~~~(x ^^^ y) - 5 * (x ||| y) - 11 * y - 7 * ~~~(x ||| y) + 13 * ~~~(x ||| ~~~y) + 5 * (x &&& ~~~y) + 11 * (x &&& y) = - 3 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_666 (x y : BitVec w) : +theorem e_666 : - 2 * ~~~x - 1 * (x ||| ~~~y) - 3 * (x ^^^ y) - 1 * y + 1 * ~~~(x &&& y) - 6 * ~~~y + 8 * ~~~(x ||| y) + 10 * ~~~(x ||| ~~~y) + 14 * (x &&& ~~~y) + 7 * (x &&& y) = 5 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_667 (x y : BitVec w) : +theorem e_667 : 7 * x - 1 * (x ||| y) + 1 * (x ||| ~~~y) + 7 * (x ^^^ y) - 5 * ~~~(x ^^^ y) + 1 * ~~~(x &&& ~~~y) - 6 * ~~~(x &&& y) + 18 * ~~~(x ||| y) + 8 * ~~~(x ||| ~~~y) - 5 * (x &&& ~~~y) = 3 * ~~~(x &&& ~~~x) + 6 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_668 (x y : BitVec w) : +theorem e_668 : - 1 * ~~~x + 4 * y - 2 * ~~~y + 4 * ~~~(x &&& ~~~x) + 1 * (x ||| ~~~y) + 1 * ~~~(x &&& y) + 4 * ~~~(x ||| y) - 13 * ~~~(x ||| ~~~y) - 9 * (x &&& ~~~y) - 7 * (x &&& y) = 7 * ~~~(x ^^^ y) - 5 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_669 (x y : BitVec w) : +theorem e_669 : - 7 * x + 11 * ~~~x + 1 * y + 7 * (x ||| y) + 1 * ~~~(x &&& ~~~y) - 1 * ~~~(x &&& ~~~x) - 9 * ~~~(x ||| y) - 19 * ~~~(x ||| ~~~y) + 3 * (x &&& ~~~y) + 1 * (x &&& y) = 2 * (x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_670 (x y : BitVec w) : +theorem e_670 : 1 * y - 1 * ~~~(x &&& ~~~x) - 6 * (x ||| y) - 1 * ~~~(x &&& y) - 2 * ~~~(x &&& ~~~y) + 4 * ~~~y - 7 * ~~~(x ||| y) + 9 * ~~~(x ||| ~~~y) + 4 * (x &&& ~~~y) + 1 * (x &&& y) = - 7 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_671 (x y : BitVec w) : +theorem e_671 : - 1 * ~~~(x &&& ~~~x) + 2 * y - 11 * (x ||| y) + 1 * ~~~(x &&& y) - 6 * ~~~(x &&& ~~~y) - 2 * ~~~x + 1 * (x ||| ~~~y) - 5 * ~~~(x ^^^ y) + 12 * ~~~(x ||| y) + 17 * ~~~(x ||| ~~~y) = - 10 * (x &&& ~~~y) - 20 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_672 (x y : BitVec w) : +theorem e_672 : 7 * y + 4 * (x ^^^ y) + 1 * ~~~(x &&& y) + 1 * ~~~(x &&& ~~~x) - 11 * ~~~x + 1 * (x ||| y) + 7 * ~~~(x ||| y) - 8 * ~~~(x ||| ~~~y) - 4 * (x &&& ~~~y) - 14 * (x &&& y) = 3 * ~~~y - 5 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_673 (x y : BitVec w) : +theorem e_673 : 11 * y - 3 * ~~~(x &&& ~~~y) + 5 * (x ^^^ y) + 1 * ~~~x - 6 * ~~~(x &&& ~~~x) - 1 * (x ||| y) + 4 * ~~~(x ||| y) - 7 * ~~~(x ||| ~~~y) - 2 * (x &&& ~~~y) - 1 * (x &&& y) = - 4 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_674 (x y : BitVec w) : +theorem e_674 : 3 * y + 3 * ~~~y + 2 * (x ||| y) + 5 * x - 7 * (x ||| ~~~y) + 7 * ~~~(x &&& ~~~x) - 1 * ~~~(x ||| y) - 10 * ~~~(x ||| ~~~y) - 10 * (x &&& ~~~y) - 10 * (x &&& y) = 2 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_675 (x y : BitVec w) : +theorem e_675 : 4 * ~~~x + 3 * (x ^^^ y) + 1 * ~~~(x ^^^ y) + 11 * ~~~y - 2 * y - 2 * ~~~(x &&& ~~~y) + 1 * (x ||| y) - 13 * ~~~(x ||| y) - 14 * (x &&& ~~~y) + 3 * (x &&& y) = 1 * ~~~(x &&& ~~~x) + 3 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_676 (x y : BitVec w) : +theorem e_676 : - 2 * ~~~x + 11 * (x ||| y) - 11 * y + 1 * ~~~(x &&& y) + 4 * (x ||| ~~~y) + 2 * (x ^^^ y) - 1 * x - 1 * ~~~(x &&& ~~~x) - 11 * (x &&& ~~~y) - 2 * (x &&& y) = - 3 * ~~~(x ||| y) + 5 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_677 (x y : BitVec w) : +theorem e_677 : 11 * (x ^^^ y) + 1 * y - 7 * (x ||| ~~~y) + 7 * x - 2 * ~~~y - 5 * ~~~(x &&& ~~~y) + 16 * ~~~(x ||| y) - 7 * ~~~(x ||| ~~~y) - 9 * (x &&& ~~~y) + 6 * (x &&& y) = 2 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_678 (x y : BitVec w) : +theorem e_678 : 1 * x + 1 * y - 1 * (x ||| ~~~y) - 1 * (x ||| y) - 7 * ~~~(x ^^^ y) - 7 * ~~~x + 22 * ~~~(x ||| y) + 8 * ~~~(x ||| ~~~y) + 7 * (x &&& ~~~y) + 8 * (x &&& y) = 6 * ~~~y + 1 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_679 (x y : BitVec w) : +theorem e_679 : - 5 * (x ||| ~~~y) + 4 * ~~~y + 1 * ~~~x - 1 * y + 5 * (x ||| y) - 11 * ~~~(x &&& y) + 6 * ~~~(x ||| y) + 6 * ~~~(x ||| ~~~y) + 7 * (x &&& ~~~y) - 4 * (x &&& y) = - 5 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_680 (x y : BitVec w) : +theorem e_680 : - 11 * ~~~(x &&& y) - 6 * (x ||| ~~~y) - 5 * (x ||| y) - 7 * ~~~(x ^^^ y) - 2 * (x ^^^ y) + 1 * ~~~(x &&& ~~~y) + 34 * ~~~(x ||| y) + 31 * ~~~(x ||| ~~~y) + 24 * (x &&& ~~~y) + 20 * (x &&& y) = 11 * ~~~x + 3 * y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_681 (x y : BitVec w) : +theorem e_681 : 1 * ~~~(x &&& ~~~x) - 11 * ~~~x - 7 * ~~~(x &&& y) + 5 * ~~~y + 7 * (x ||| ~~~y) + 2 * y - 4 * ~~~(x ||| y) + 4 * ~~~(x ||| ~~~y) - 6 * (x &&& ~~~y) - 19 * (x &&& y) = 2 * ~~~(x ^^^ y) - 11 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_682 (x y : BitVec w) : +theorem e_682 : - 1 * ~~~(x &&& ~~~y) - 1 * ~~~(x ^^^ y) - 2 * y - 11 * ~~~(x &&& y) + 11 * (x ^^^ y) - 1 * ~~~(x &&& ~~~x) + 11 * (x ||| ~~~y) - 2 * ~~~(x ||| y) - 11 * (x &&& ~~~y) - 6 * (x &&& y) = - 4 * ~~~x - 1 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_683 (x y : BitVec w) : +theorem e_683 : 4 * (x ||| ~~~y) + 1 * ~~~(x ^^^ y) - 1 * ~~~(x &&& ~~~y) - 3 * y - 1 * ~~~(x &&& y) + 3 * (x ^^^ y) - 2 * ~~~(x ||| y) + 2 * ~~~(x ||| ~~~y) - 5 * (x &&& ~~~y) - 1 * (x &&& y) = 1 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_684 (x y : BitVec w) : +theorem e_684 : - 2 * ~~~x + 2 * (x ||| y) + 5 * y + 1 * (x ||| ~~~y) - 1 * (x ^^^ y) - 2 * ~~~y - 7 * x + 3 * ~~~(x &&& y) + 4 * (x &&& ~~~y) - 1 * (x &&& y) = 7 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_685 (x y : BitVec w) : +theorem e_685 : 7 * ~~~y + 5 * ~~~(x ^^^ y) - 2 * (x ^^^ y) - 1 * ~~~x - 2 * ~~~(x &&& ~~~x) + 11 * ~~~(x &&& ~~~y) - 19 * ~~~(x ||| y) - 5 * ~~~(x ||| ~~~y) - 2 * (x &&& ~~~y) - 14 * (x &&& y) = 1 * ~~~(x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_686 (x y : BitVec w) : +theorem e_686 : 1 * ~~~(x ^^^ y) + 5 * y - 7 * ~~~(x &&& ~~~y) + 3 * (x ||| y) + 4 * x - 1 * ~~~x - 11 * ~~~(x &&& y) + 11 * ~~~(x ||| ~~~y) + 4 * (x &&& ~~~y) - 6 * (x &&& y) = - 18 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_687 (x y : BitVec w) : +theorem e_687 : 2 * (x ^^^ y) - 2 * ~~~(x ^^^ y) + 5 * ~~~y - 6 * ~~~(x &&& ~~~y) - 7 * ~~~(x &&& ~~~x) - 1 * (x ||| ~~~y) - 2 * ~~~(x &&& y) + 13 * ~~~(x ||| y) + 15 * ~~~(x ||| ~~~y) + 3 * (x &&& ~~~y) = - 18 * (x &&& y) + 2 * y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_688 (x y : BitVec w) : +theorem e_688 : - 2 * (x ||| ~~~y) - 11 * ~~~(x ^^^ y) - 11 * ~~~(x &&& ~~~x) - 5 * ~~~(x &&& y) - 3 * ~~~(x &&& ~~~y) - 2 * y - 2 * x + 32 * ~~~(x ||| y) + 21 * ~~~(x ||| ~~~y) + 31 * (x &&& y) = - 20 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_689 (x y : BitVec w) : +theorem e_689 : 2 * ~~~x - 11 * ~~~(x ^^^ y) - 3 * ~~~y - 11 * (x ||| y) + 3 * ~~~(x &&& ~~~y) + 7 * y + 1 * (x ^^^ y) + 12 * ~~~(x ||| y) + 16 * (x &&& ~~~y) + 15 * (x &&& y) = 2 * ~~~(x ||| ~~~y) + 3 * (x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_690 (x y : BitVec w) : +theorem e_690 : 1 * ~~~(x &&& ~~~x) + 7 * (x ^^^ y) - 5 * ~~~(x &&& ~~~y) + 1 * x + 1 * ~~~x - 1 * ~~~(x ^^^ y) + 7 * (x ||| y) + 4 * ~~~(x ||| y) - 11 * ~~~(x ||| ~~~y) - 3 * (x &&& y) = 16 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_691 (x y : BitVec w) : +theorem e_691 : 1 * x - 1 * ~~~x + 2 * ~~~(x &&& y) + 1 * (x ||| y) + 11 * ~~~(x &&& ~~~y) + 1 * ~~~y - 1 * ~~~(x &&& ~~~x) - 11 * ~~~(x ||| ~~~y) - 3 * (x &&& ~~~y) - 12 * (x &&& y) = 1 * (x ^^^ y) + 12 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_692 (x y : BitVec w) : +theorem e_692 : 2 * y + 11 * ~~~x + 7 * x + 2 * ~~~(x &&& y) - 1 * ~~~y + 1 * ~~~(x &&& ~~~x) - 13 * ~~~(x ||| y) - 17 * ~~~(x ||| ~~~y) - 10 * (x &&& ~~~y) - 11 * (x &&& y) = - 1 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_693 (x y : BitVec w) : +theorem e_693 : - 11 * x + 1 * ~~~(x &&& y) + 2 * ~~~(x &&& ~~~x) + 1 * ~~~x + 1 * (x ||| ~~~y) + 1 * y + 1 * ~~~(x ^^^ y) - 6 * ~~~y + 13 * (x &&& ~~~y) + 6 * (x &&& y) = 5 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_694 (x y : BitVec w) : +theorem e_694 : 1 * ~~~(x &&& ~~~y) - 2 * y + 4 * (x ||| ~~~y) - 5 * ~~~y - 1 * ~~~(x &&& ~~~x) - 2 * (x ^^^ y) + 1 * ~~~(x ||| y) + 5 * ~~~(x ||| ~~~y) + 5 * (x &&& ~~~y) - 1 * (x &&& y) = 1 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_695 (x y : BitVec w) : +theorem e_695 : - 11 * (x ||| ~~~y) + 7 * ~~~(x &&& ~~~x) - 11 * (x ^^^ y) - 2 * (x ||| y) - 2 * ~~~x - 11 * ~~~(x &&& ~~~y) + 2 * ~~~(x &&& y) + 12 * ~~~(x ||| y) + 15 * (x &&& ~~~y) + 14 * (x &&& y) = - 17 * ~~~(x ||| ~~~y) - 3 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_696 (x y : BitVec w) : +theorem e_696 : 1 * ~~~(x &&& y) + 3 * (x ||| y) + 3 * (x ||| ~~~y) - 6 * ~~~(x ^^^ y) + 5 * x - 1 * ~~~y + 6 * ~~~(x ||| y) - 1 * ~~~(x ||| ~~~y) - 11 * (x &&& ~~~y) - 5 * (x &&& y) = 3 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_697 (x y : BitVec w) : +theorem e_697 : - 6 * ~~~x - 1 * x - 2 * ~~~(x &&& y) + 2 * ~~~y + 3 * ~~~(x &&& ~~~x) + 2 * (x ||| ~~~y) + 1 * ~~~(x &&& ~~~y) - 2 * ~~~(x ||| y) + 4 * ~~~(x ||| ~~~y) - 7 * (x &&& y) = - 2 * ~~~(x ^^^ y) + 4 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_698 (x y : BitVec w) : +theorem e_698 : - 6 * y + 2 * (x ^^^ y) + 2 * (x ||| y) - 1 * ~~~(x &&& ~~~x) + 2 * ~~~(x &&& ~~~y) - 2 * ~~~(x &&& y) + 3 * ~~~(x ||| y) + 3 * ~~~(x ||| ~~~y) + 1 * (x &&& ~~~y) + 3 * (x &&& y) = 2 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_699 (x y : BitVec w) : +theorem e_699 : - 5 * (x ||| y) + 1 * ~~~y + 4 * ~~~(x ^^^ y) + 1 * ~~~(x &&& y) + 1 * x + 1 * y + 7 * (x ^^^ y) - 3 * ~~~(x ||| y) - 4 * ~~~(x ||| ~~~y) - 2 * (x &&& ~~~y) = 3 * (x ||| ~~~y) - 2 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_700 (x y : BitVec w) : +theorem e_700 : 1 * ~~~(x &&& y) + 3 * ~~~y + 1 * (x ||| y) + 1 * x - 2 * (x ||| ~~~y) + 7 * ~~~(x &&& ~~~y) - 6 * ~~~(x ||| y) - 5 * ~~~(x ||| ~~~y) - 3 * (x &&& ~~~y) - 7 * (x &&& y) = 1 * (x ^^^ y) + 3 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_701 (x y : BitVec w) : +theorem e_701 : 3 * ~~~(x &&& y) + 7 * (x ||| ~~~y) + 2 * ~~~x + 5 * (x ^^^ y) + 5 * x - 2 * ~~~y + 2 * ~~~(x ^^^ y) - 12 * ~~~(x ||| y) - 8 * ~~~(x ||| ~~~y) - 12 * (x &&& y) = 16 * (x &&& ~~~y) + 2 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_702 (x y : BitVec w) : +theorem e_702 : 2 * ~~~x + 2 * ~~~(x &&& y) - 1 * ~~~y + 1 * (x ||| y) + 4 * x - 11 * ~~~(x ^^^ y) + 5 * y + 8 * ~~~(x ||| y) - 10 * ~~~(x ||| ~~~y) - 6 * (x &&& ~~~y) = - 1 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_703 (x y : BitVec w) : +theorem e_703 : 11 * y - 1 * x - 3 * ~~~(x &&& ~~~x) - 1 * ~~~x + 1 * ~~~(x &&& y) + 7 * (x ||| ~~~y) + 11 * (x ||| y) - 3 * ~~~(x ||| y) - 14 * (x &&& ~~~y) - 25 * (x &&& y) = 1 * ~~~y + 19 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_704 (x y : BitVec w) : +theorem e_704 : 1 * ~~~(x ^^^ y) - 1 * ~~~(x &&& y) + 11 * ~~~x - 3 * (x ||| ~~~y) + 1 * (x ^^^ y) + 2 * ~~~y - 1 * y - 12 * ~~~(x ||| y) - 12 * ~~~(x ||| ~~~y) - 1 * (x &&& ~~~y) = - 2 * ~~~(x &&& ~~~x) - 1 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_705 (x y : BitVec w) : +theorem e_705 : - 1 * ~~~(x &&& ~~~y) + 5 * ~~~y - 11 * (x ^^^ y) - 2 * x - 1 * (x ||| ~~~y) + 4 * y - 4 * ~~~(x ||| y) + 8 * ~~~(x ||| ~~~y) + 9 * (x &&& ~~~y) - 1 * (x &&& y) = - 1 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_706 (x y : BitVec w) : +theorem e_706 : 4 * ~~~(x &&& y) + 4 * (x ^^^ y) + 4 * ~~~x + 11 * (x ||| ~~~y) - 7 * y + 4 * ~~~(x &&& ~~~y) - 16 * ~~~(x ||| y) - 9 * ~~~(x ||| ~~~y) - 12 * (x &&& ~~~y) - 8 * (x &&& y) = 7 * ~~~y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_707 (x y : BitVec w) : +theorem e_707 : - 3 * ~~~y + 11 * x + 2 * (x ^^^ y) + 1 * (x ||| y) - 6 * ~~~(x &&& y) + 1 * y + 11 * ~~~(x ||| y) + 4 * ~~~(x ||| ~~~y) - 3 * (x &&& ~~~y) - 11 * (x &&& y) = 2 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_708 (x y : BitVec w) : +theorem e_708 : 1 * ~~~(x &&& ~~~x) + 1 * ~~~x - 11 * y - 1 * x - 2 * ~~~(x ^^^ y) + 1 * (x ^^^ y) + 7 * ~~~(x ||| y) + 15 * ~~~(x ||| ~~~y) - 1 * (x &&& ~~~y) + 20 * (x &&& y) = 7 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_709 (x y : BitVec w) : +theorem e_709 : 7 * ~~~(x &&& ~~~y) - 1 * ~~~(x &&& ~~~x) + 2 * (x ||| ~~~y) - 11 * x + 5 * ~~~x + 11 * (x ||| y) - 13 * ~~~(x ||| y) - 20 * ~~~(x ||| ~~~y) + 1 * (x &&& ~~~y) - 8 * (x &&& y) = 2 * (x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_710 (x y : BitVec w) : +theorem e_710 : 2 * ~~~(x &&& ~~~y) + 1 * (x ||| ~~~y) + 5 * ~~~(x ^^^ y) - 2 * y + 2 * (x ^^^ y) + 1 * x - 9 * ~~~(x ||| y) - 3 * ~~~(x ||| ~~~y) - 5 * (x &&& ~~~y) - 7 * (x &&& y) = - 1 * ~~~(x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_711 (x y : BitVec w) : +theorem e_711 : 4 * ~~~(x &&& ~~~y) + 7 * (x ||| ~~~y) - 6 * ~~~(x &&& y) + 4 * ~~~(x ^^^ y) + 1 * (x ^^^ y) - 1 * ~~~x - 2 * x - 2 * ~~~y - 6 * ~~~(x ||| y) + 2 * (x &&& ~~~y) - 11 * (x &&& y) = 2 * y - 4 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_712 (x y : BitVec w) : +theorem e_712 : 7 * ~~~(x &&& y) - 3 * (x ||| ~~~y) - 1 * (x ||| y) - 1 * ~~~(x &&& ~~~x) - 5 * ~~~(x ^^^ y) - 7 * ~~~x - 1 * y + 7 * ~~~(x &&& ~~~y) - 4 * ~~~(x ||| ~~~y) - 13 * (x &&& ~~~y) - 7 * (x &&& y) = - 2 * ~~~(x ||| y) - 11 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_713 (x y : BitVec w) : +theorem e_713 : 7 * y - 1 * (x ||| y) - 2 * (x ^^^ y) + 7 * ~~~x - 1 * ~~~y + 5 * x - 2 * (x ||| ~~~y) - 15 * ~~~(x ||| y) - 11 * ~~~(x ||| ~~~y) + 1 * (x &&& ~~~y) - 20 * (x &&& y) = - 11 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_714 (x y : BitVec w) : +theorem e_714 : - 2 * x + 4 * ~~~x + 3 * ~~~(x ^^^ y) - 1 * ~~~(x &&& y) - 1 * (x ^^^ y) - 1 * y + 4 * ~~~(x &&& ~~~x) - 12 * ~~~(x ||| y) - 5 * ~~~(x ||| ~~~y) - 2 * (x &&& ~~~y) - 6 * (x &&& y) = - 2 * (x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_715 (x y : BitVec w) : +theorem e_715 : 7 * ~~~(x &&& ~~~y) - 1 * ~~~(x ^^^ y) - 3 * y + 4 * (x ^^^ y) + 2 * (x ||| y) + 1 * ~~~x + 2 * x - 3 * (x ||| ~~~y) - 4 * ~~~(x ||| y) - 11 * ~~~(x ||| ~~~y) - 4 * (x &&& y) = 5 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_716 (x y : BitVec w) : +theorem e_716 : - 5 * (x ^^^ y) - 1 * (x ||| ~~~y) + 3 * ~~~x - 11 * (x ||| y) + 4 * ~~~(x &&& ~~~y) - 2 * ~~~(x ^^^ y) - 1 * ~~~y + 2 * x - 4 * ~~~(x ||| y) + 8 * ~~~(x ||| ~~~y) + 15 * (x &&& ~~~y) = - 8 * (x &&& y) - 1 * ~~~(x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_717 (x y : BitVec w) : +theorem e_717 : - 2 * ~~~(x &&& ~~~y) + 1 * y + 11 * (x ^^^ y) + 2 * (x ||| y) - 7 * ~~~(x ^^^ y) + 2 * ~~~y + 5 * x - 5 * ~~~x + 11 * ~~~(x ||| y) - 8 * ~~~(x ||| ~~~y) - 21 * (x &&& ~~~y) = - 1 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_718 (x y : BitVec w) : +theorem e_718 : - 1 * x - 6 * y + 2 * ~~~x + 4 * ~~~(x &&& y) - 2 * ~~~(x ^^^ y) + 1 * ~~~(x &&& ~~~x) - 11 * (x ^^^ y) + 3 * ~~~(x &&& ~~~y) - 1 * ~~~(x ||| y) + 14 * (x &&& ~~~y) + 5 * (x &&& y) = 7 * ~~~y - 7 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_719 (x y : BitVec w) : +theorem e_719 : - 2 * (x ||| ~~~y) - 11 * ~~~(x &&& ~~~y) + 1 * ~~~(x &&& ~~~x) - 3 * ~~~y - 1 * x + 1 * (x ^^^ y) + 2 * (x ||| y) + 1 * y + 6 * ~~~(x ||| ~~~y) + 2 * (x &&& ~~~y) + 10 * (x &&& y) = - 15 * ~~~(x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_720 (x y : BitVec w) : +theorem e_720 : 2 * (x ||| ~~~y) - 1 * ~~~y + 4 * y - 1 * ~~~(x &&& ~~~x) - 5 * ~~~(x &&& y) + 11 * ~~~(x ^^^ y) + 7 * x - 7 * ~~~(x ||| y) + 1 * ~~~(x ||| ~~~y) - 2 * (x &&& ~~~y) - 23 * (x &&& y) = - 1 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_721 (x y : BitVec w) : +theorem e_721 : 3 * ~~~x - 1 * (x ||| ~~~y) + 3 * ~~~(x &&& ~~~y) - 2 * ~~~y + 7 * ~~~(x &&& y) - 3 * x - 6 * (x ^^^ y) - 1 * (x ||| y) - 10 * ~~~(x ||| y) + 6 * (x &&& ~~~y) + 2 * (x &&& y) = 6 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_722 (x y : BitVec w) : +theorem e_722 : - 7 * (x ||| ~~~y) - 5 * x + 1 * y + 7 * ~~~(x ^^^ y) - 1 * ~~~y + 4 * ~~~(x &&& ~~~x) - 11 * ~~~x + 13 * ~~~(x ||| y) + 11 * ~~~(x ||| ~~~y) + 9 * (x &&& ~~~y) + 5 * (x &&& y) = 5 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_723 (x y : BitVec w) : +theorem e_723 : - 5 * ~~~y - 11 * ~~~x - 5 * (x ^^^ y) + 1 * ~~~(x &&& y) + 1 * ~~~(x &&& ~~~y) - 1 * (x ||| y) + 2 * y + 14 * ~~~(x ||| y) + 13 * ~~~(x ||| ~~~y) + 9 * (x &&& ~~~y) - 3 * (x &&& y) = - 1 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_724 (x y : BitVec w) : +theorem e_724 : - 1 * (x ^^^ y) + 3 * y - 11 * ~~~(x &&& ~~~y) + 2 * ~~~(x &&& y) + 7 * (x ||| y) - 3 * x + 2 * ~~~y - 5 * ~~~x + 8 * ~~~(x ||| y) + 5 * ~~~(x ||| ~~~y) - 11 * (x &&& ~~~y) = - 4 * (x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_725 (x y : BitVec w) : +theorem e_725 : 2 * ~~~x + 7 * ~~~(x &&& ~~~x) + 11 * ~~~(x ^^^ y) - 11 * (x ^^^ y) + 11 * ~~~(x &&& y) - 1 * ~~~(x &&& ~~~y) + 1 * x - 1 * ~~~y - 29 * ~~~(x ||| y) - 8 * ~~~(x ||| ~~~y) - 18 * (x &&& y) = 7 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_726 (x y : BitVec w) : +theorem e_726 : 1 * ~~~(x &&& ~~~x) + 5 * ~~~(x &&& ~~~y) + 2 * (x ^^^ y) + 5 * (x ||| y) - 1 * ~~~y + 11 * x + 7 * ~~~(x ^^^ y) - 12 * ~~~(x ||| y) - 16 * ~~~(x ||| ~~~y) - 15 * (x &&& ~~~y) - 26 * (x &&& y) = - 3 * ~~~x + 3 * (x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_727 (x y : BitVec w) : +theorem e_727 : 5 * x - 6 * ~~~(x &&& ~~~y) - 3 * (x ||| ~~~y) + 1 * ~~~x - 2 * (x ^^^ y) + 5 * ~~~(x &&& y) - 11 * ~~~y + 1 * ~~~(x &&& ~~~x) + 13 * ~~~(x ||| y) + 5 * (x &&& ~~~y) + 2 * (x &&& y) = - 1 * y := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_728 (x y : BitVec w) : +theorem e_728 : 1 * ~~~(x ^^^ y) + 3 * ~~~y - 1 * (x ^^^ y) + 5 * ~~~x - 1 * (x ||| ~~~y) - 5 * x + 2 * y + 5 * (x ||| y) - 10 * ~~~(x ||| ~~~y) - 1 * (x &&& ~~~y) - 1 * (x &&& y) = 7 * ~~~(x ||| y) + 1 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_729 (x y : BitVec w) : +theorem e_729 : 2 * (x ||| y) + 2 * ~~~(x &&& ~~~x) - 6 * ~~~(x &&& y) + 1 * ~~~(x &&& ~~~y) + 1 * x + 7 * y - 1 * ~~~y + 3 * ~~~x + 1 * ~~~(x ||| y) + 2 * (x &&& ~~~y) - 13 * (x &&& y) = 9 * ~~~(x ||| ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_730 (x y : BitVec w) : +theorem e_730 : - 5 * ~~~y + 4 * (x ^^^ y) + 11 * (x ||| y) - 7 * ~~~(x &&& ~~~y) + 3 * ~~~(x &&& ~~~x) - 11 * x - 11 * ~~~(x &&& y) + 19 * ~~~(x ||| y) - 1 * ~~~(x ||| ~~~y) + 9 * (x &&& ~~~y) + 4 * (x &&& y) = - 1 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_731 (x y : BitVec w) : +theorem e_731 : 5 * ~~~y - 1 * x - 1 * (x ^^^ y) - 5 * ~~~(x &&& ~~~x) - 7 * ~~~x + 5 * (x ||| ~~~y) + 7 * (x ||| y) + 1 * ~~~(x &&& ~~~y) - 6 * y + 1 * ~~~(x ||| y) + 11 * ~~~(x ||| ~~~y) = 1 * (x &&& y) + 10 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_732 (x y : BitVec w) : +theorem e_732 : - 1 * ~~~(x &&& ~~~x) - 2 * ~~~y + 1 * (x ^^^ y) + 2 * (x ||| y) + 11 * (x ||| ~~~y) - 2 * ~~~(x ^^^ y) + 3 * x - 3 * y + 7 * ~~~(x ||| ~~~y) - 14 * (x &&& ~~~y) - 10 * (x &&& y) = 6 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_733 (x y : BitVec w) : +theorem e_733 : 5 * ~~~(x ^^^ y) - 2 * ~~~x - 3 * (x ||| ~~~y) - 6 * ~~~(x &&& ~~~y) + 1 * (x ||| y) - 6 * ~~~(x &&& y) - 5 * ~~~(x &&& ~~~x) + 1 * (x ^^^ y) + 17 * ~~~(x ||| y) + 20 * ~~~(x ||| ~~~y) + 11 * (x &&& y) = 3 * y - 12 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_734 (x y : BitVec w) : +theorem e_734 : - 7 * (x ||| ~~~y) - 11 * ~~~y + 3 * (x ^^^ y) - 3 * ~~~x + 1 * x + 11 * ~~~(x &&& ~~~x) - 5 * ~~~(x &&& y) + 14 * ~~~(x ||| y) - 13 * ~~~(x ||| ~~~y) + 1 * (x &&& ~~~y) - 13 * (x &&& y) = - 7 * (x ||| y) - 1 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_735 (x y : BitVec w) : +theorem e_735 : - 1 * ~~~x - 1 * ~~~(x &&& ~~~x) - 7 * (x ||| y) + 4 * ~~~(x &&& y) + 11 * y + 2 * ~~~(x &&& ~~~y) + 1 * (x ||| ~~~y) - 8 * ~~~(x ||| y) - 8 * ~~~(x ||| ~~~y) + 3 * (x &&& ~~~y) - 9 * (x &&& y) = - 3 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_736 (x y : BitVec w) : +theorem e_736 : 1 * (x ||| ~~~y) - 1 * y - 5 * ~~~(x &&& ~~~x) - 11 * ~~~(x ^^^ y) - 3 * ~~~(x &&& y) - 2 * (x ^^^ y) - 2 * x + 19 * ~~~(x ||| y) + 12 * ~~~(x ||| ~~~y) + 11 * (x &&& ~~~y) + 19 * (x &&& y) = 1 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_737 (x y : BitVec w) : +theorem e_737 : - 7 * ~~~(x &&& ~~~y) - 5 * (x ||| ~~~y) - 6 * ~~~(x ^^^ y) - 2 * (x ^^^ y) + 11 * y - 6 * ~~~x - 2 * ~~~(x &&& ~~~x) + 26 * ~~~(x ||| y) + 6 * ~~~(x ||| ~~~y) + 20 * (x &&& ~~~y) + 20 * (x &&& y) = 11 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_738 (x y : BitVec w) : +theorem e_738 : - 11 * (x ||| y) + 1 * ~~~x + 4 * y + 1 * (x ^^^ y) - 6 * ~~~(x &&& ~~~y) - 1 * ~~~(x ^^^ y) + 4 * x + 5 * ~~~(x ||| y) + 9 * ~~~(x ||| ~~~y) + 5 * (x &&& ~~~y) + 9 * (x &&& y) = 1 * (x ||| ~~~y) - 2 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_739 (x y : BitVec w) : +theorem e_739 : 5 * (x ^^^ y) + 7 * ~~~(x ^^^ y) + 2 * x + 1 * y - 5 * ~~~y - 2 * ~~~(x &&& y) + 7 * (x ||| y) - 7 * ~~~x + 2 * ~~~(x ||| y) - 4 * ~~~(x ||| ~~~y) - 22 * (x &&& y) = - 5 * (x ||| ~~~y) + 12 * (x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_740 (x y : BitVec w) : +theorem e_740 : 7 * (x ||| ~~~y) - 3 * ~~~(x &&& ~~~y) - 1 * ~~~(x &&& ~~~x) - 11 * x - 1 * ~~~y + 3 * y + 2 * (x ||| y) - 7 * ~~~x + 5 * ~~~(x ||| y) + 6 * ~~~(x ||| ~~~y) + 4 * (x &&& ~~~y) = - 3 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_741 (x y : BitVec w) : +theorem e_741 : - 3 * ~~~(x &&& y) + 1 * ~~~(x &&& ~~~x) + 1 * x + 4 * (x ^^^ y) - 1 * y + 4 * ~~~y + 5 * (x ||| y) + 7 * ~~~(x ^^^ y) - 9 * ~~~(x ||| y) - 6 * ~~~(x ||| ~~~y) - 12 * (x &&& ~~~y) = 13 * (x &&& y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_742 (x y : BitVec w) : +theorem e_742 : - 6 * ~~~(x &&& ~~~x) + 3 * ~~~(x &&& ~~~y) - 1 * (x ^^^ y) + 1 * ~~~x - 5 * ~~~(x ^^^ y) + 11 * ~~~(x &&& y) + 5 * (x ||| ~~~y) - 7 * ~~~y - 2 * ~~~(x ||| y) - 11 * ~~~(x ||| ~~~y) - 5 * (x &&& ~~~y) = - 3 * (x ||| y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_743 (x y : BitVec w) : +theorem e_743 : 1 * y - 6 * (x ||| ~~~y) + 7 * ~~~x - 2 * (x ^^^ y) - 7 * x + 4 * (x ||| y) - 3 * ~~~(x ^^^ y) + 2 * ~~~y - 4 * ~~~(x ||| y) + 5 * (x &&& ~~~y) + 7 * (x &&& y) = 14 * ~~~(x ||| ~~~y) - 4 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_744 (x y : BitVec w) : +theorem e_744 : 1 * (x ^^^ y) - 11 * ~~~(x &&& ~~~x) + 11 * x + 3 * ~~~(x &&& y) - 3 * ~~~(x &&& ~~~y) - 1 * ~~~y + 1 * y + 14 * ~~~(x ||| y) + 15 * ~~~(x ||| ~~~y) - 3 * (x &&& ~~~y) - 2 * (x &&& y) = - 4 * ~~~(x ^^^ y) + 6 * ~~~x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_745 (x y : BitVec w) : +theorem e_745 : - 1 * y - 6 * (x ||| ~~~y) - 2 * x - 3 * (x ^^^ y) - 1 * (x ||| y) + 1 * ~~~(x &&& y) + 2 * ~~~x - 1 * ~~~(x ^^^ y) + 7 * ~~~(x ||| ~~~y) + 11 * (x &&& ~~~y) + 16 * (x &&& y) = - 9 * ~~~(x ||| y) + 5 * ~~~(x &&& ~~~y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_746 (x y : BitVec w) : +theorem e_746 : 11 * y - 1 * ~~~(x ^^^ y) - 3 * (x ||| y) - 2 * ~~~(x &&& ~~~y) - 3 * ~~~(x &&& ~~~x) + 3 * (x ^^^ y) - 1 * (x ||| ~~~y) + 7 * ~~~(x ||| y) - 6 * ~~~(x ||| ~~~y) + 9 * (x &&& ~~~y) + 4 * (x &&& y) = 5 * x := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_747 (x y : BitVec w) : +theorem e_747 : 1 * ~~~y - 3 * ~~~(x &&& ~~~x) + 1 * (x ||| ~~~y) - 5 * x - 1 * (x ||| y) - 1 * y - 3 * (x ^^^ y) - 2 * ~~~(x &&& y) + 10 * ~~~(x ||| ~~~y) + 12 * (x &&& ~~~y) + 6 * (x &&& y) = - 3 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_748 (x y : BitVec w) : +theorem e_748 : - 5 * ~~~(x ^^^ y) - 2 * ~~~y + 1 * (x ||| ~~~y) + 2 * y - 5 * ~~~(x &&& ~~~y) - 1 * (x ^^^ y) - 1 * x - 5 * (x ||| y) + 12 * ~~~(x ||| y) + 9 * (x &&& ~~~y) + 14 * (x &&& y) = - 10 * ~~~(x ||| ~~~y) + 1 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_749 (x y : BitVec w) : +theorem e_749 : - 6 * ~~~y - 7 * (x ||| y) + 2 * ~~~(x &&& ~~~y) - 1 * ~~~x + 4 * ~~~(x &&& ~~~x) + 1 * y - 3 * (x ^^^ y) - 1 * x + 4 * ~~~(x ||| ~~~y) + 13 * (x &&& ~~~y) + 3 * (x &&& y) = - 3 * ~~~(x ||| y) + 2 * ~~~(x ^^^ y) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_750 (x y : BitVec w) : +theorem e_750 : - 1 * (x ^^^ y) - 2 * ~~~x - 1 * ~~~(x &&& y) + 1 * (x ||| y) - 5 * ~~~y - 2 * (x ||| ~~~y) - 2 * y + 15 * ~~~(x ||| y) + 10 * ~~~(x ||| ~~~y) + 13 * (x &&& ~~~y) + 8 * (x &&& y) = 5 * ~~~(x &&& ~~~x) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_751 (x y : BitVec w) : +theorem e_751 : - 7 * (z ||| t) + 2 * ~~~z + 7 * z = - 5 * ~~~(z ||| ~~~t) + 2 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_752 (x y : BitVec w) : +theorem e_752 : - 1 * (z ||| t) + 7 * ~~~(z ||| t) + 8 * ~~~(z ||| ~~~t) = - 1 * z + 7 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_753 (x y : BitVec w) : +theorem e_753 : - 2 * ~~~z + 3 * (z ^^^ t) - 1 * ~~~(z ||| ~~~t) = - 2 * ~~~t + 5 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_754 (x y : BitVec w) : +theorem e_754 : 5 * ~~~(z ^^^ t) - 2 * (z ^^^ t) + 2 * (z &&& ~~~t) = 5 * ~~~(z &&& ~~~t) - 7 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_755 (x y : BitVec w) : +theorem e_755 : - 3 * (z ^^^ t) + 2 * t + 2 * z - 4 * (z &&& t) = - 1 * (z &&& ~~~t) - 1 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_756 (x y : BitVec w) : +theorem e_756 : - 5 * ~~~t + 2 * ~~~(z ||| t) - 3 * ~~~(z ||| ~~~t) + 8 * (z &&& ~~~t) = - 3 * ~~~(z &&& ~~~t) + 3 * z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_757 (x y : BitVec w) : +theorem e_757 : 3 * ~~~(z &&& ~~~t) - 1 * ~~~(z &&& ~~~z) - 2 * (z ||| t) + 3 * (z &&& ~~~t) = 2 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_758 (x y : BitVec w) : +theorem e_758 : 5 * ~~~(z ^^^ t) - 2 * ~~~(z &&& t) + 5 * ~~~(z ||| ~~~t) - 2 * (z &&& t) = - 5 * (z &&& ~~~t) + 3 * ~~~(z &&& ~~~z) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_759 (x y : BitVec w) : +theorem e_759 : - 3 * ~~~(z &&& ~~~t) + 5 * ~~~z - 2 * ~~~(z ||| t) - 3 * (z &&& ~~~t) = - 3 * z + 2 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_760 (x y : BitVec w) : +theorem e_760 : 2 * ~~~(z ^^^ t) + 1 * t - 6 * ~~~(z &&& ~~~t) + 4 * ~~~(z ||| t) = - 5 * ~~~(z ||| ~~~t) - 3 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_761 (x y : BitVec w) : +theorem e_761 : - 2 * ~~~(z ^^^ t) - 3 * ~~~t - 5 * ~~~(z ||| ~~~t) - 3 * (z &&& t) = - 5 * ~~~(z &&& ~~~z) + 2 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_762 (x y : BitVec w) : +theorem e_762 : 1 * ~~~(z &&& ~~~z) + 7 * t - 1 * (z ||| ~~~t) - 1 * ~~~(z ||| ~~~t) = - 7 * (z &&& ~~~t) + 7 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_763 (x y : BitVec w) : +theorem e_763 : - 1 * (z ^^^ t) + 2 * ~~~(z ^^^ t) - 3 * ~~~(z ||| t) - 2 * (z &&& t) = - 1 * ~~~(z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_764 (x y : BitVec w) : +theorem e_764 : - 2 * z - 5 * (z ^^^ t) - 1 * t + 3 * (z &&& t) = - 7 * (z &&& ~~~t) - 6 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_765 (x y : BitVec w) : +theorem e_765 : - 7 * t + 7 * ~~~(z &&& ~~~t) + 1 * z - 1 * (z &&& t) = 7 * ~~~(z ||| t) + 1 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_766 (x y : BitVec w) : +theorem e_766 : 1 * ~~~(z &&& t) - 1 * ~~~(z &&& ~~~t) + 1 * ~~~(z ||| t) + 2 * (z &&& t) = 1 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_767 (x y : BitVec w) : +theorem e_767 : 4 * (z ^^^ t) + 1 * ~~~(z &&& t) + 4 * ~~~(z ||| t) - 5 * (z &&& ~~~t) = 5 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_768 (x y : BitVec w) : +theorem e_768 : - 7 * ~~~(z &&& ~~~t) + 5 * z + 7 * ~~~(z ||| t) + 7 * (z &&& t) = - 12 * ~~~(z ||| ~~~t) + 5 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_769 (x y : BitVec w) : +theorem e_769 : 3 * (z ||| t) + 2 * ~~~(z ^^^ t) - 5 * ~~~(z ||| t) - 6 * ~~~(z ||| ~~~t) - 5 * (z &&& t) = 6 * (z &&& ~~~t) - 3 * ~~~(z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_770 (x y : BitVec w) : +theorem e_770 : 1 * ~~~(z &&& ~~~t) + 2 * ~~~t - 5 * ~~~z - 6 * (z &&& ~~~t) - 5 * (z &&& t) = - 4 * (z ||| t) - 2 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_771 (x y : BitVec w) : +theorem e_771 : - 1 * (z ||| ~~~t) - 1 * ~~~t + 2 * (z ^^^ t) + 1 * ~~~(z ||| t) + 2 * (z &&& t) = - 1 * ~~~(z ^^^ t) + 2 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_772 (x y : BitVec w) : +theorem e_772 : 4 * ~~~(z &&& ~~~z) + 4 * ~~~(z &&& ~~~t) - 6 * (z ^^^ t) - 2 * ~~~(z ||| ~~~t) - 8 * (z &&& t) = 8 * ~~~(z ||| t) - 2 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_773 (x y : BitVec w) : +theorem e_773 : - 3 * (z ||| ~~~t) + 3 * ~~~z - 11 * z - 3 * ~~~(z ||| ~~~t) + 14 * (z &&& ~~~t) = - 14 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_774 (x y : BitVec w) : +theorem e_774 : - 5 * ~~~(z &&& ~~~z) + 1 * t - 6 * (z ^^^ t) + 10 * ~~~(z ||| ~~~t) - 1 * (z &&& t) = - 6 * (z &&& ~~~t) - 5 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_775 (x y : BitVec w) : +theorem e_775 : - 1 * (z ||| t) + 2 * ~~~t - 2 * ~~~(z ||| t) - 4 * ~~~(z ||| ~~~t) - 1 * (z &&& ~~~t) = - 5 * t + 4 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_776 (x y : BitVec w) : +theorem e_776 : 4 * (z ||| ~~~t) + 7 * (z ^^^ t) - 2 * ~~~(z ||| t) - 11 * (z &&& ~~~t) - 2 * (z &&& t) = 2 * ~~~(z ^^^ t) + 7 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_777 (x y : BitVec w) : +theorem e_777 : - 7 * (z ||| ~~~t) + 1 * (z ||| t) + 5 * ~~~(z &&& ~~~t) + 2 * ~~~(z ||| t) + 1 * (z &&& t) = - 6 * (z &&& ~~~t) + 6 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_778 (x y : BitVec w) : +theorem e_778 : 2 * z + 1 * (z ^^^ t) - 5 * ~~~(z &&& t) - 3 * (z &&& ~~~t) - 7 * (z &&& t) = - 5 * ~~~(z &&& ~~~z) + 1 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_779 (x y : BitVec w) : +theorem e_779 : 3 * ~~~t + 5 * z + 1 * ~~~(z ||| ~~~t) - 8 * (z &&& ~~~t) - 4 * (z &&& t) = 1 * ~~~(z &&& ~~~t) + 2 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_780 (x y : BitVec w) : +theorem e_780 : 11 * t + 1 * ~~~t - 1 * ~~~(z ||| t) + 5 * (z &&& ~~~t) - 5 * (z &&& t) = 6 * z + 11 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_781 (x y : BitVec w) : +theorem e_781 : - 1 * t + 2 * ~~~(z &&& ~~~t) - 4 * ~~~(z ||| t) - 2 * (z &&& ~~~t) - 1 * (z &&& t) = - 2 * ~~~(z &&& t) + 3 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_782 (x y : BitVec w) : +theorem e_782 : - 5 * z - 3 * (z ||| t) + 2 * ~~~(z &&& ~~~z) - 2 * ~~~(z ||| t) + 1 * ~~~(z ||| ~~~t) = - 6 * (z &&& t) - 6 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_783 (x y : BitVec w) : +theorem e_783 : - 1 * ~~~(z &&& ~~~t) + 1 * ~~~z + 1 * ~~~(z ||| ~~~t) + 1 * (z &&& ~~~t) + 1 * (z &&& t) = 1 * ~~~(z &&& t) - 1 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_784 (x y : BitVec w) : +theorem e_784 : 1 * ~~~(z &&& ~~~t) + 3 * ~~~(z &&& ~~~z) - 3 * ~~~(z ||| t) - 4 * ~~~(z ||| ~~~t) - 4 * (z &&& t) = 1 * ~~~t + 2 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_785 (x y : BitVec w) : +theorem e_785 : 4 * ~~~(z &&& ~~~t) + 7 * ~~~z - 9 * ~~~(z ||| t) + 2 * (z &&& ~~~t) - 4 * (z &&& t) = 2 * ~~~(z &&& t) + 9 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_786 (x y : BitVec w) : +theorem e_786 : - 1 * ~~~t - 1 * (z ||| ~~~t) - 7 * z + 2 * ~~~(z ||| t) + 9 * (z &&& ~~~t) = - 8 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_787 (x y : BitVec w) : +theorem e_787 : 4 * ~~~(z ^^^ t) + 1 * ~~~t + 6 * ~~~(z ||| ~~~t) - 1 * (z &&& ~~~t) - 4 * (z &&& t) = 6 * ~~~z - 1 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_788 (x y : BitVec w) : +theorem e_788 : 3 * (z ^^^ t) - 2 * ~~~(z ||| t) - 8 * ~~~(z ||| ~~~t) - 8 * (z &&& ~~~t) - 2 * (z &&& t) = - 5 * ~~~(z &&& ~~~z) + 3 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_789 (x y : BitVec w) : +theorem e_789 : 5 * (z ^^^ t) + 3 * t + 5 * ~~~(z ||| t) - 8 * ~~~(z ||| ~~~t) + 2 * (z &&& t) = 5 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_790 (x y : BitVec w) : +theorem e_790 : - 1 * (z ||| t) - 7 * ~~~(z ^^^ t) + 4 * ~~~(z ||| t) - 2 * (z &&& ~~~t) + 8 * (z &&& t) = - 1 * ~~~(z ||| ~~~t) - 3 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_791 (x y : BitVec w) : +theorem e_791 : - 2 * ~~~(z &&& ~~~z) + 5 * ~~~(z ^^^ t) - 3 * (z ||| t) - 3 * ~~~(z ||| t) + 5 * ~~~(z ||| ~~~t) = - 5 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_792 (x y : BitVec w) : +theorem e_792 : 4 * ~~~(z &&& ~~~z) + 11 * ~~~t - 15 * ~~~(z ||| t) - 11 * (z &&& ~~~t) - 2 * (z &&& t) = 2 * (z ||| t) + 2 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_793 (x y : BitVec w) : +theorem e_793 : - 7 * ~~~(z &&& ~~~t) - 5 * ~~~(z &&& t) + 5 * ~~~(z ||| t) + 12 * ~~~(z ||| ~~~t) + 5 * (z &&& ~~~t) = - 7 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_794 (x y : BitVec w) : +theorem e_794 : - 5 * ~~~z + 1 * (z ^^^ t) - 2 * ~~~(z &&& t) + 14 * ~~~(z ||| t) + 6 * ~~~(z ||| ~~~t) = - 8 * (z &&& ~~~t) + 7 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_795 (x y : BitVec w) : +theorem e_795 : - 6 * z + 2 * (z ||| t) + 2 * ~~~t - 3 * ~~~(z &&& t) + 1 * ~~~(z &&& ~~~z) = - 3 * (z &&& t) - 4 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_796 (x y : BitVec w) : +theorem e_796 : 1 * (z ^^^ t) + 1 * ~~~(z ^^^ t) - 1 * ~~~(z ||| t) - 1 * (z &&& ~~~t) + 10 * (z &&& t) = - 10 * ~~~(z ||| ~~~t) + 11 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_797 (x y : BitVec w) : +theorem e_797 : - 6 * (z ||| t) - 1 * t - 7 * ~~~(z ||| t) + 7 * (z &&& ~~~t) + 8 * (z &&& t) = 1 * z - 7 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_798 (x y : BitVec w) : +theorem e_798 : 3 * ~~~(z ^^^ t) + 11 * ~~~(z &&& ~~~t) - 5 * ~~~z - 6 * ~~~(z ||| ~~~t) - 14 * (z &&& t) = 9 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_799 (x y : BitVec w) : +theorem e_799 : - 1 * ~~~(z &&& ~~~t) + 11 * z + 3 * ~~~t - 12 * (z &&& ~~~t) - 9 * (z &&& t) = 2 * (z ||| ~~~t) - 1 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_800 (x y : BitVec w) : +theorem e_800 : 7 * ~~~(z &&& t) - 7 * (z ||| t) - 6 * ~~~(z &&& ~~~z) + 6 * ~~~(z ||| ~~~t) + 13 * (z &&& t) = - 6 * (z &&& ~~~t) + 1 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_801 (x y : BitVec w) : +theorem e_801 : - 11 * t - 1 * ~~~(z &&& ~~~t) + 18 * ~~~(z ||| ~~~t) + 6 * (z &&& ~~~t) + 18 * (z &&& t) = 6 * (z ||| t) - 1 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_802 (x y : BitVec w) : +theorem e_802 : - 3 * ~~~z + 1 * ~~~(z &&& ~~~t) - 7 * ~~~t + 9 * ~~~(z ||| t) - 1 * (z &&& t) = - 7 * (z &&& ~~~t) - 2 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_803 (x y : BitVec w) : +theorem e_803 : 4 * ~~~(z &&& t) + 5 * ~~~(z ^^^ t) + 4 * z - 9 * ~~~(z ||| t) - 8 * (z &&& ~~~t) = 4 * ~~~(z ||| ~~~t) + 9 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_804 (x y : BitVec w) : +theorem e_804 : 1 * (z ^^^ t) + 4 * ~~~(z ||| t) - 8 * ~~~(z ||| ~~~t) - 1 * (z &&& ~~~t) + 4 * (z &&& t) = 11 * ~~~(z ^^^ t) - 7 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_805 (x y : BitVec w) : +theorem e_805 : 11 * t + 5 * ~~~z - 5 * ~~~(z ||| t) - 21 * ~~~(z ||| ~~~t) - 5 * (z &&& ~~~t) = - 5 * (z ^^^ t) + 11 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_806 (x y : BitVec w) : +theorem e_806 : - 1 * (z ||| ~~~t) - 1 * (z ||| t) + 1 * ~~~(z ||| t) + 8 * ~~~(z ||| ~~~t) + 2 * (z &&& ~~~t) = 7 * t - 9 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_807 (x y : BitVec w) : +theorem e_807 : - 1 * (z ||| t) + 3 * ~~~t + 1 * (z ||| ~~~t) + 8 * ~~~(z ||| ~~~t) - 3 * (z &&& ~~~t) = 7 * ~~~z - 3 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_808 (x y : BitVec w) : +theorem e_808 : - 1 * t + 1 * (z ||| t) - 1 * ~~~(z ||| t) - 1 * (z &&& ~~~t) - 1 * (z &&& t) = - 1 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_809 (x y : BitVec w) : +theorem e_809 : - 6 * ~~~(z &&& t) - 11 * ~~~z + 17 * ~~~(z ||| ~~~t) + 6 * (z &&& ~~~t) + 2 * (z &&& t) = - 19 * ~~~(z ||| t) + 2 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_810 (x y : BitVec w) : +theorem e_810 : 2 * ~~~(z &&& ~~~t) + 2 * z - 2 * t - 2 * ~~~(z ||| t) - 2 * (z &&& ~~~t) = 2 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_811 (x y : BitVec w) : +theorem e_811 : 1 * t + 11 * ~~~t - 11 * ~~~(z ||| t) - 12 * (z &&& ~~~t) - 2 * (z &&& t) = - 1 * z + 1 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_812 (x y : BitVec w) : +theorem e_812 : 2 * ~~~t - 7 * ~~~(z ^^^ t) + 5 * (z ^^^ t) + 5 * ~~~(z ||| t) - 7 * (z &&& ~~~t) = - 7 * (z &&& t) + 5 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_813 (x y : BitVec w) : +theorem e_813 : - 2 * ~~~(z ^^^ t) - 6 * ~~~(z &&& ~~~t) - 1 * ~~~(z ||| ~~~t) - 7 * (z &&& ~~~t) + 8 * (z &&& t) = - 1 * ~~~(z ||| t) - 7 * ~~~(z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_814 (x y : BitVec w) : +theorem e_814 : 7 * (z ||| t) - 7 * ~~~(z ||| t) - 13 * ~~~(z ||| ~~~t) - 6 * (z &&& ~~~t) - 14 * (z &&& t) = 1 * (z ^^^ t) - 7 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_815 (x y : BitVec w) : +theorem e_815 : - 5 * (z ||| ~~~t) + 1 * ~~~t + 4 * ~~~(z ||| t) + 9 * (z &&& ~~~t) + 10 * (z &&& t) = 5 * z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_816 (x y : BitVec w) : +theorem e_816 : - 2 * (z ^^^ t) + 7 * ~~~t - 7 * ~~~(z ||| t) + 2 * ~~~(z ||| ~~~t) + 5 * (z &&& t) = 5 * z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_817 (x y : BitVec w) : +theorem e_817 : 1 * ~~~(z ^^^ t) - 11 * (z ^^^ t) - 5 * t - 1 * ~~~(z ||| t) + 16 * ~~~(z ||| ~~~t) = - 11 * (z &&& ~~~t) - 4 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_818 (x y : BitVec w) : +theorem e_818 : 4 * ~~~(z ^^^ t) + 2 * (z ||| t) - 5 * ~~~(z ||| t) - 2 * (z &&& ~~~t) - 7 * (z &&& t) = 3 * ~~~(z ||| ~~~t) - 1 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_819 (x y : BitVec w) : +theorem e_819 : 2 * ~~~(z &&& ~~~z) - 1 * ~~~(z ^^^ t) + 1 * (z ^^^ t) + 2 * ~~~(z ||| t) - 3 * ~~~(z ||| ~~~t) = 1 * (z &&& t) + 3 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_820 (x y : BitVec w) : +theorem e_820 : 5 * z + 1 * ~~~(z &&& ~~~z) + 5 * ~~~t - 1 * ~~~(z ||| t) - 5 * (z &&& ~~~t) = 5 * (z ||| ~~~t) + 1 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_821 (x y : BitVec w) : +theorem e_821 : - 1 * (z ^^^ t) + 1 * (z ||| ~~~t) - 7 * t - 1 * ~~~(z ||| t) + 6 * (z &&& t) = - 8 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_822 (x y : BitVec w) : +theorem e_822 : - 7 * ~~~(z &&& ~~~t) - 2 * t + 7 * (z ||| ~~~t) - 7 * (z &&& ~~~t) + 2 * (z &&& t) = - 9 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_823 (x y : BitVec w) : +theorem e_823 : 11 * ~~~(z &&& ~~~t) + 1 * (z ||| ~~~t) - 11 * ~~~(z ||| ~~~t) + 5 * (z &&& ~~~t) - 12 * (z &&& t) = 6 * ~~~(z ||| t) + 6 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_824 (x y : BitVec w) : +theorem e_824 : - 7 * t - 1 * (z ||| t) - 1 * ~~~t + 1 * ~~~(z ||| t) + 8 * (z &&& t) = - 6 * ~~~(z ||| ~~~t) - 2 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_825 (x y : BitVec w) : +theorem e_825 : 4 * (z ||| t) + 2 * (z ^^^ t) + 1 * (z ||| ~~~t) - 6 * (z &&& ~~~t) - 5 * (z &&& t) = 5 * ~~~(z ||| ~~~t) + 1 * ~~~(z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_826 (x y : BitVec w) : +theorem e_826 : 7 * t + 2 * ~~~(z &&& t) - 3 * ~~~(z ||| t) - 10 * ~~~(z ||| ~~~t) - 8 * (z &&& t) = - 1 * ~~~(z &&& ~~~t) + 2 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_827 (x y : BitVec w) : +theorem e_827 : - 5 * (z ||| t) - 1 * ~~~(z ^^^ t) - 2 * (z ||| ~~~t) + 3 * ~~~(z ||| t) + 7 * (z &&& ~~~t) = - 8 * (z &&& t) - 5 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_828 (x y : BitVec w) : +theorem e_828 : - 6 * ~~~(z &&& t) + 1 * (z ||| t) - 5 * ~~~(z ||| t) + 5 * (z &&& ~~~t) - 1 * (z &&& t) = 6 * ~~~(z ||| ~~~t) - 11 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_829 (x y : BitVec w) : +theorem e_829 : 2 * ~~~(z &&& ~~~t) - 2 * z - 5 * ~~~(z &&& t) + 5 * ~~~(z ||| ~~~t) + 2 * (z &&& ~~~t) = 2 * ~~~z - 5 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_830 (x y : BitVec w) : +theorem e_830 : 11 * (z ^^^ t) + 3 * ~~~z - 7 * z - 3 * ~~~(z ||| t) - 14 * ~~~(z ||| ~~~t) = 4 * (z &&& ~~~t) - 7 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_831 (x y : BitVec w) : +theorem e_831 : - 1 * z - 1 * ~~~(z &&& ~~~z) - 1 * (z ||| ~~~t) + 1 * ~~~(z ||| ~~~t) + 3 * (z &&& t) = - 3 * (z &&& ~~~t) - 2 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_832 (x y : BitVec w) : +theorem e_832 : 5 * ~~~z - 8 * ~~~(z ||| t) - 7 * ~~~(z ||| ~~~t) - 2 * (z &&& ~~~t) - 1 * (z &&& t) = - 1 * ~~~(z ^^^ t) - 2 * ~~~(z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_833 (x y : BitVec w) : +theorem e_833 : - 1 * ~~~(z ^^^ t) + 12 * ~~~(z ||| t) - 3 * ~~~(z ||| ~~~t) + 8 * (z &&& ~~~t) + 9 * (z &&& t) = - 3 * (z ||| t) + 11 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_834 (x y : BitVec w) : +theorem e_834 : - 1 * ~~~(z &&& ~~~z) + 1 * z + 1 * ~~~(z ||| ~~~t) + 1 * (z &&& ~~~t) - 1 * (z &&& t) = 1 * (z ^^^ t) - 1 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_835 (x y : BitVec w) : +theorem e_835 : - 2 * ~~~(z &&& t) - 1 * (z ||| ~~~t) - 1 * z + 2 * ~~~(z ||| ~~~t) + 2 * (z &&& t) = - 3 * ~~~(z ||| t) - 4 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_836 (x y : BitVec w) : +theorem e_836 : 1 * ~~~(z &&& ~~~t) + 11 * (z ^^^ t) - 1 * z - 11 * ~~~(z ||| ~~~t) - 9 * (z &&& ~~~t) = 1 * ~~~(z &&& ~~~z) - 1 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_837 (x y : BitVec w) : +theorem e_837 : - 6 * (z ||| t) - 6 * ~~~z + 3 * ~~~(z ||| t) + 12 * ~~~(z ||| ~~~t) + 3 * (z &&& ~~~t) = - 3 * ~~~t - 6 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_838 (x y : BitVec w) : +theorem e_838 : 2 * ~~~(z ^^^ t) + 1 * ~~~(z &&& ~~~z) - 5 * (z ^^^ t) + 4 * (z &&& ~~~t) - 3 * (z &&& t) = 3 * ~~~(z ||| t) - 4 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_839 (x y : BitVec w) : +theorem e_839 : 1 * t + 2 * ~~~(z &&& ~~~z) - 1 * ~~~(z ||| t) - 3 * ~~~(z ||| ~~~t) - 1 * (z &&& ~~~t) = 1 * (z ||| ~~~t) + 2 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_840 (x y : BitVec w) : +theorem e_840 : 2 * (z ||| ~~~t) + 2 * ~~~(z &&& t) - 2 * ~~~(z ||| ~~~t) - 4 * (z &&& ~~~t) - 7 * (z &&& t) = 9 * ~~~(z ||| t) - 5 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_841 (x y : BitVec w) : +theorem e_841 : - 1 * ~~~(z ^^^ t) - 6 * ~~~t + 8 * ~~~(z ||| t) + 6 * (z &&& ~~~t) + 2 * (z &&& t) = - 1 * ~~~(z ||| ~~~t) + 1 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_842 (x y : BitVec w) : +theorem e_842 : - 1 * ~~~(z ^^^ t) + 3 * (z ||| t) + 1 * ~~~(z ||| t) - 6 * (z &&& ~~~t) - 5 * (z &&& t) = - 3 * z + 3 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_843 (x y : BitVec w) : +theorem e_843 : - 3 * ~~~t + 2 * (z ||| ~~~t) + 1 * ~~~(z ||| t) - 1 * (z &&& ~~~t) - 4 * (z &&& t) = - 2 * z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_844 (x y : BitVec w) : +theorem e_844 : - 1 * t - 1 * ~~~(z ||| t) + 3 * ~~~(z ||| ~~~t) + 1 * (z &&& ~~~t) + 1 * (z &&& t) = 2 * (z ^^^ t) - 1 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_845 (x y : BitVec w) : +theorem e_845 : - 1 * t - 6 * (z ^^^ t) - 1 * ~~~(z ^^^ t) + 1 * ~~~(z ||| t) + 12 * ~~~(z ||| ~~~t) + 7 * (z &&& t) = - 11 * (z &&& ~~~t) + 5 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_846 (x y : BitVec w) : +theorem e_846 : 5 * ~~~(z &&& ~~~z) + 1 * t - 2 * ~~~(z ^^^ t) - 1 * ~~~(z ||| t) - 4 * ~~~(z ||| ~~~t) - 2 * (z &&& t) = 2 * ~~~(z &&& ~~~t) + 5 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_847 (x y : BitVec w) : +theorem e_847 : 7 * (z ||| t) + 5 * (z ||| ~~~t) - 5 * z - 12 * ~~~(z ||| ~~~t) - 7 * (z &&& ~~~t) - 12 * (z &&& t) = 10 * ~~~(z ||| t) - 5 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_848 (x y : BitVec w) : +theorem e_848 : 2 * ~~~(z &&& t) + 7 * ~~~(z &&& ~~~z) - 4 * ~~~(z ||| t) - 9 * ~~~(z ||| ~~~t) - 9 * (z &&& ~~~t) - 2 * (z &&& t) = 5 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_849 (x y : BitVec w) : +theorem e_849 : 1 * (z ||| ~~~t) + 3 * ~~~(z &&& t) + 1 * t - 4 * ~~~(z ||| t) - 4 * (z &&& ~~~t) - 2 * (z &&& t) = 4 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_850 (x y : BitVec w) : +theorem e_850 : 5 * ~~~(z &&& t) + 2 * ~~~(z &&& ~~~t) - 6 * ~~~t - 1 * ~~~(z ||| t) - 7 * ~~~(z ||| ~~~t) - 2 * (z &&& t) = - 1 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_851 (x y : BitVec w) : +theorem e_851 : 3 * ~~~(z &&& ~~~z) - 2 * (z ^^^ t) - 1 * ~~~(z &&& ~~~t) - 7 * (z ||| ~~~t) + 5 * ~~~(z ||| t) + 5 * (z &&& t) = - 6 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_852 (x y : BitVec w) : +theorem e_852 : - 6 * ~~~t + 1 * t - 2 * ~~~(z &&& ~~~t) + 9 * ~~~(z ||| t) + 6 * (z &&& ~~~t) + 1 * (z &&& t) = - 2 * ~~~(z ||| ~~~t) + 1 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_853 (x y : BitVec w) : +theorem e_853 : - 7 * ~~~(z &&& t) - 5 * ~~~t + 13 * ~~~(z ||| t) + 8 * ~~~(z ||| ~~~t) + 13 * (z &&& ~~~t) + 1 * (z &&& t) = 1 * ~~~(z &&& ~~~z) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_854 (x y : BitVec w) : +theorem e_854 : 2 * t - 7 * ~~~(z &&& ~~~z) + 13 * ~~~(z ||| t) + 7 * ~~~(z ||| ~~~t) + 15 * (z &&& ~~~t) + 7 * (z &&& t) = 2 * (z ||| t) + 6 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_855 (x y : BitVec w) : +theorem e_855 : 7 * (z ||| t) - 2 * z + 4 * (z ^^^ t) - 1 * ~~~(z ||| t) - 11 * ~~~(z ||| ~~~t) - 10 * (z &&& ~~~t) = 6 * (z &&& t) - 1 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_856 (x y : BitVec w) : +theorem e_856 : - 1 * ~~~(z &&& ~~~z) + 2 * z - 7 * t - 6 * ~~~(z ||| t) + 1 * ~~~(z ||| ~~~t) - 1 * (z &&& ~~~t) = - 6 * (z &&& t) - 7 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_857 (x y : BitVec w) : +theorem e_857 : 4 * ~~~z + 3 * ~~~(z &&& ~~~t) + 1 * ~~~(z ^^^ t) - 7 * (z ||| ~~~t) - 1 * ~~~(z ||| t) + 7 * (z &&& ~~~t) = - 3 * (z &&& t) + 7 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_858 (x y : BitVec w) : +theorem e_858 : - 3 * (z ||| t) - 7 * (z ^^^ t) - 1 * ~~~(z ||| t) + 9 * ~~~(z ||| ~~~t) + 10 * (z &&& ~~~t) + 2 * (z &&& t) = - 1 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_859 (x y : BitVec w) : +theorem e_859 : 1 * t - 6 * ~~~(z ^^^ t) + 6 * ~~~(z ||| t) + 2 * ~~~(z ||| ~~~t) + 3 * (z &&& ~~~t) + 8 * (z &&& t) = 3 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_860 (x y : BitVec w) : +theorem e_860 : 1 * ~~~t + 7 * (z ^^^ t) - 11 * (z ||| t) + 1 * ~~~(z ||| ~~~t) + 3 * (z &&& ~~~t) + 8 * (z &&& t) = - 3 * ~~~(z &&& ~~~t) + 4 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_861 (x y : BitVec w) : +theorem e_861 : - 11 * ~~~(z &&& ~~~z) + 1 * ~~~t - 2 * ~~~(z ^^^ t) + 13 * ~~~(z ||| ~~~t) + 10 * (z &&& ~~~t) + 13 * (z &&& t) = 2 * ~~~z - 14 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_862 (x y : BitVec w) : +theorem e_862 : - 3 * ~~~(z ^^^ t) - 3 * ~~~(z &&& ~~~t) - 1 * (z ^^^ t) - 11 * ~~~(z &&& t) + 15 * ~~~(z ||| ~~~t) + 6 * (z &&& t) = - 17 * ~~~(z ||| t) - 12 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_863 (x y : BitVec w) : +theorem e_863 : - 2 * ~~~(z ^^^ t) - 1 * z + 5 * ~~~(z &&& ~~~t) - 1 * ~~~(z ||| t) - 5 * ~~~(z ||| ~~~t) + 3 * (z &&& ~~~t) = 2 * (z &&& t) + 2 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_864 (x y : BitVec w) : +theorem e_864 : 7 * z + 3 * t + 1 * ~~~(z &&& ~~~t) - 5 * ~~~(z ||| t) - 11 * (z &&& ~~~t) - 11 * (z &&& t) = - 4 * ~~~(z &&& t) + 8 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_865 (x y : BitVec w) : +theorem e_865 : - 1 * ~~~(z &&& t) - 5 * ~~~(z &&& ~~~t) + 7 * ~~~(z ||| t) + 6 * ~~~(z ||| ~~~t) + 2 * (z &&& ~~~t) + 6 * (z &&& t) = 1 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_866 (x y : BitVec w) : +theorem e_866 : 2 * ~~~(z &&& ~~~z) + 7 * (z ||| ~~~t) - 1 * ~~~(z &&& ~~~t) - 1 * ~~~(z ||| ~~~t) - 9 * (z &&& ~~~t) - 8 * (z &&& t) = 8 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_867 (x y : BitVec w) : +theorem e_867 : 7 * (z ||| ~~~t) - 6 * (z ||| t) - 1 * z - 6 * ~~~(z &&& ~~~z) - 1 * ~~~(z ||| t) + 6 * (z &&& ~~~t) = - 6 * (z &&& t) - 12 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_868 (x y : BitVec w) : +theorem e_868 : - 6 * ~~~t - 2 * (z ||| t) + 4 * ~~~(z &&& ~~~t) + 2 * ~~~(z ||| t) - 2 * ~~~(z ||| ~~~t) - 2 * (z &&& t) = - 8 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_869 (x y : BitVec w) : +theorem e_869 : 4 * (z ^^^ t) + 11 * z + 3 * ~~~(z &&& ~~~t) - 3 * ~~~(z ||| t) - 15 * (z &&& ~~~t) - 14 * (z &&& t) = 7 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_870 (x y : BitVec w) : +theorem e_870 : 1 * ~~~z + 3 * (z ^^^ t) + 11 * ~~~t - 7 * ~~~(z ||| t) - 4 * ~~~(z ||| ~~~t) - 9 * (z &&& ~~~t) = - 5 * (z &&& t) + 5 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_871 (x y : BitVec w) : +theorem e_871 : 5 * ~~~(z &&& ~~~t) - 5 * z - 7 * (z ||| t) + 1 * ~~~(z ||| t) + 8 * ~~~(z ||| ~~~t) + 18 * (z &&& ~~~t) = 6 * ~~~(z &&& t) - 7 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_872 (x y : BitVec w) : +theorem e_872 : - 2 * z - 2 * ~~~(z &&& t) + 13 * ~~~(z ||| t) + 13 * ~~~(z ||| ~~~t) + 15 * (z &&& ~~~t) + 13 * (z &&& t) = 11 * ~~~(z &&& ~~~z) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_873 (x y : BitVec w) : +theorem e_873 : 1 * (z ||| ~~~t) + 3 * ~~~(z &&& ~~~z) + 4 * ~~~(z &&& t) - 7 * t - 8 * ~~~(z ||| t) + 3 * (z &&& t) = 8 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_874 (x y : BitVec w) : +theorem e_874 : 1 * (z ^^^ t) - 7 * (z ||| ~~~t) + 11 * z - 1 * ~~~(z ||| ~~~t) - 12 * (z &&& ~~~t) - 4 * (z &&& t) = - 7 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_875 (x y : BitVec w) : +theorem e_875 : 1 * ~~~z + 7 * (z ^^^ t) + 1 * ~~~t - 2 * ~~~(z ||| t) - 9 * ~~~(z ||| ~~~t) - 1 * (z &&& t) = - 1 * (z ||| t) + 9 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_876 (x y : BitVec w) : +theorem e_876 : - 3 * (z ^^^ t) - 1 * ~~~(z ^^^ t) - 6 * ~~~(z &&& ~~~t) + 1 * ~~~t + 2 * (z &&& ~~~t) + 7 * (z &&& t) = - 6 * ~~~(z ||| t) - 9 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_877 (x y : BitVec w) : +theorem e_877 : - 2 * z + 1 * t + 3 * ~~~t - 1 * ~~~(z &&& ~~~z) - 5 * ~~~(z ^^^ t) + 7 * (z &&& t) = - 3 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_878 (x y : BitVec w) : +theorem e_878 : - 1 * (z ^^^ t) + 1 * ~~~(z &&& ~~~t) + 7 * z + 2 * ~~~(z ||| t) + 3 * ~~~(z ||| ~~~t) - 5 * (z &&& t) = 3 * (z &&& ~~~t) + 3 * ~~~(z &&& ~~~z) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_879 (x y : BitVec w) : +theorem e_879 : 2 * ~~~z - 5 * ~~~(z &&& ~~~t) - 7 * ~~~(z ^^^ t) + 4 * (z ||| ~~~t) + 6 * ~~~(z ||| t) + 8 * (z &&& t) = 4 * (z &&& ~~~t) - 3 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_880 (x y : BitVec w) : +theorem e_880 : - 1 * ~~~z - 5 * (z ||| ~~~t) + 1 * z + 6 * ~~~(z ||| t) + 1 * ~~~(z ||| ~~~t) + 4 * (z &&& t) = - 4 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_881 (x y : BitVec w) : +theorem e_881 : 11 * ~~~(z &&& t) + 7 * (z ||| t) - 12 * ~~~(z ||| t) - 20 * ~~~(z ||| ~~~t) - 20 * (z &&& ~~~t) - 8 * (z &&& t) = - 2 * (z ^^^ t) - 1 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_882 (x y : BitVec w) : +theorem e_882 : 1 * t + 4 * ~~~z + 11 * (z ||| t) - 11 * ~~~(z ||| t) - 16 * ~~~(z ||| ~~~t) - 19 * (z &&& t) = 11 * (z &&& ~~~t) - 7 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_883 (x y : BitVec w) : +theorem e_883 : 7 * (z ^^^ t) - 2 * ~~~(z &&& t) + 4 * ~~~(z &&& ~~~t) - 3 * ~~~(z ||| t) - 9 * ~~~(z ||| ~~~t) - 6 * (z &&& ~~~t) = 5 * (z &&& t) - 1 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_884 (x y : BitVec w) : +theorem e_884 : 1 * ~~~z - 5 * ~~~t - 6 * z + 4 * ~~~(z ||| t) - 1 * ~~~(z ||| ~~~t) + 6 * (z &&& t) = - 11 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_885 (x y : BitVec w) : +theorem e_885 : 1 * ~~~(z &&& ~~~z) + 4 * ~~~z - 5 * ~~~(z ||| t) - 7 * ~~~(z ||| ~~~t) - 3 * (z &&& ~~~t) - 1 * (z &&& t) = - 2 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_886 (x y : BitVec w) : +theorem e_886 : 7 * ~~~(z &&& ~~~z) + 5 * z - 2 * ~~~z + 1 * (z ||| ~~~t) - 6 * ~~~(z ||| t) - 13 * (z &&& t) = 5 * ~~~(z ||| ~~~t) + 13 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_887 (x y : BitVec w) : +theorem e_887 : 5 * ~~~(z &&& t) + 11 * ~~~t - 15 * ~~~(z ||| t) - 4 * ~~~(z ||| ~~~t) - 16 * (z &&& ~~~t) + 1 * (z &&& t) = 1 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_888 (x y : BitVec w) : +theorem e_888 : 3 * t + 2 * ~~~t - 5 * ~~~(z ||| t) - 4 * ~~~(z ||| ~~~t) - 5 * (z &&& ~~~t) - 6 * (z &&& t) = - 1 * ~~~(z &&& ~~~z) - 2 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_889 (x y : BitVec w) : +theorem e_889 : - 2 * ~~~z + 1 * ~~~(z &&& ~~~z) - 2 * (z ||| t) + 1 * ~~~(z ||| t) + 3 * ~~~(z ||| ~~~t) + 1 * (z &&& ~~~t) = - 1 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_890 (x y : BitVec w) : +theorem e_890 : - 1 * ~~~(z &&& ~~~t) + 1 * ~~~(z &&& t) + 1 * ~~~t + 11 * z - 1 * (z ||| ~~~t) - 9 * (z &&& t) = 12 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_891 (x y : BitVec w) : +theorem e_891 : - 7 * (z ||| ~~~t) - 6 * ~~~t - 6 * (z ^^^ t) + 7 * (z ||| t) + 13 * ~~~(z ||| t) - 1 * ~~~(z ||| ~~~t) = - 12 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_892 (x y : BitVec w) : +theorem e_892 : 7 * t - 3 * ~~~z + 1 * ~~~(z ||| t) - 4 * ~~~(z ||| ~~~t) - 2 * (z &&& ~~~t) - 7 * (z &&& t) = - 2 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_893 (x y : BitVec w) : +theorem e_893 : - 7 * (z ||| t) - 3 * t - 2 * ~~~(z ||| t) + 10 * ~~~(z ||| ~~~t) + 5 * (z &&& ~~~t) + 11 * (z &&& t) = - 3 * ~~~t + 1 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_894 (x y : BitVec w) : +theorem e_894 : 3 * ~~~t - 6 * ~~~(z &&& ~~~z) + 10 * ~~~(z ||| t) + 6 * ~~~(z ||| ~~~t) + 10 * (z &&& ~~~t) + 13 * (z &&& t) = 7 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_895 (x y : BitVec w) : +theorem e_895 : 1 * ~~~(z &&& ~~~z) - 5 * t - 1 * ~~~t + 7 * ~~~(z &&& ~~~t) - 7 * ~~~(z ||| t) - 3 * ~~~(z ||| ~~~t) = 3 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_896 (x y : BitVec w) : +theorem e_896 : 1 * (z ||| t) - 6 * ~~~t - 2 * (z ^^^ t) + 3 * ~~~(z &&& ~~~t) - 2 * ~~~(z ||| ~~~t) - 4 * (z &&& t) = - 3 * ~~~(z ||| t) - 7 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_897 (x y : BitVec w) : +theorem e_897 : - 1 * ~~~z + 2 * ~~~(z &&& t) + 1 * ~~~(z &&& ~~~t) + 7 * t - 2 * (z &&& ~~~t) - 8 * (z &&& t) = 2 * ~~~(z ||| t) + 9 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_898 (x y : BitVec w) : +theorem e_898 : - 7 * ~~~t + 1 * ~~~(z &&& ~~~z) + 4 * ~~~z - 5 * ~~~(z ||| ~~~t) + 6 * (z &&& ~~~t) - 1 * (z &&& t) = - 2 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_899 (x y : BitVec w) : +theorem e_899 : - 5 * t - 7 * ~~~(z ^^^ t) - 1 * ~~~t + 9 * ~~~(z ||| t) + 5 * ~~~(z ||| ~~~t) + 13 * (z &&& t) = - 2 * (z &&& ~~~t) + 1 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_900 (x y : BitVec w) : +theorem e_900 : - 5 * (z ||| t) - 2 * ~~~(z &&& ~~~z) - 9 * ~~~(z ||| t) - 4 * ~~~(z ||| ~~~t) + 6 * (z &&& ~~~t) + 6 * (z &&& t) = - 1 * z - 11 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_901 (x y : BitVec w) : +theorem e_901 : - 2 * (z ^^^ t) + 11 * ~~~t - 12 * ~~~(z ||| t) - 4 * ~~~(z ||| ~~~t) - 9 * (z &&& ~~~t) - 5 * (z &&& t) = - 5 * t - 1 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_902 (x y : BitVec w) : +theorem e_902 : 4 * ~~~(z &&& t) - 5 * t - 1 * (z ||| ~~~t) + 1 * (z ^^^ t) - 3 * ~~~(z ||| t) + 6 * (z &&& t) = 4 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_903 (x y : BitVec w) : +theorem e_903 : - 5 * ~~~(z &&& t) + 2 * z + 3 * ~~~(z ||| t) + 5 * ~~~(z ||| ~~~t) + 1 * (z &&& ~~~t) - 2 * (z &&& t) = - 2 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_904 (x y : BitVec w) : +theorem e_904 : - 1 * ~~~(z ^^^ t) + 7 * z + 2 * (z ^^^ t) + 8 * ~~~(z ||| t) - 2 * (z &&& ~~~t) - 6 * (z &&& t) = 7 * ~~~t + 2 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_905 (x y : BitVec w) : +theorem e_905 : 5 * t - 5 * ~~~t + 4 * (z ||| ~~~t) + 1 * ~~~(z ||| t) - 4 * ~~~(z ||| ~~~t) - 9 * (z &&& t) = 1 * (z ^^^ t) - 2 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_906 (x y : BitVec w) : +theorem e_906 : 4 * z - 1 * ~~~(z &&& ~~~z) + 5 * ~~~t + 1 * (z ||| t) - 4 * ~~~(z ||| t) - 4 * (z &&& t) = 9 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_907 (x y : BitVec w) : +theorem e_907 : 11 * ~~~(z &&& ~~~z) + 1 * (z ||| t) - 5 * ~~~t + 2 * ~~~z - 8 * ~~~(z ||| t) - 7 * (z &&& ~~~t) = 14 * ~~~(z ||| ~~~t) + 12 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_908 (x y : BitVec w) : +theorem e_908 : - 1 * (z ||| t) + 7 * z + 1 * ~~~z + 7 * (z ||| ~~~t) - 13 * (z &&& ~~~t) - 13 * (z &&& t) = 8 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_909 (x y : BitVec w) : +theorem e_909 : - 1 * ~~~(z ^^^ t) - 11 * ~~~(z &&& ~~~t) + 1 * (z ^^^ t) - 2 * (z ||| t) + 12 * ~~~(z ||| t) + 14 * (z &&& t) = - 12 * ~~~(z ||| ~~~t) - 1 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_910 (x y : BitVec w) : +theorem e_910 : 7 * ~~~z - 3 * z - 11 * ~~~(z &&& t) + 4 * ~~~(z ||| t) + 4 * ~~~(z ||| ~~~t) + 3 * (z &&& t) = - 14 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_911 (x y : BitVec w) : +theorem e_911 : 3 * ~~~(z &&& ~~~t) + 1 * t - 6 * ~~~(z ||| t) - 7 * ~~~(z ||| ~~~t) - 2 * (z &&& ~~~t) - 6 * (z &&& t) = - 2 * ~~~(z &&& ~~~z) - 1 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_912 (x y : BitVec w) : +theorem e_912 : - 7 * ~~~(z ^^^ t) + 5 * ~~~z - 1 * z - 5 * ~~~(z ||| ~~~t) + 1 * (z &&& ~~~t) + 8 * (z &&& t) = - 2 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_913 (x y : BitVec w) : +theorem e_913 : 11 * t - 5 * ~~~(z ^^^ t) + 1 * ~~~t - 2 * ~~~(z &&& t) - 9 * ~~~(z ||| ~~~t) - 6 * (z &&& t) = - 1 * (z &&& ~~~t) - 6 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_914 (x y : BitVec w) : +theorem e_914 : 5 * ~~~(z &&& ~~~z) - 7 * ~~~z - 11 * ~~~(z ^^^ t) + 13 * ~~~(z ||| t) - 5 * (z &&& ~~~t) + 6 * (z &&& t) = - 2 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_915 (x y : BitVec w) : +theorem e_915 : - 2 * z - 11 * ~~~z + 2 * t + 14 * ~~~(z ||| t) + 12 * ~~~(z ||| ~~~t) + 5 * (z &&& ~~~t) = 3 * ~~~(z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_916 (x y : BitVec w) : +theorem e_916 : 2 * (z ^^^ t) + 3 * ~~~(z &&& ~~~z) - 2 * ~~~t - 1 * ~~~(z ||| t) - 3 * (z &&& ~~~t) + 2 * (z &&& t) = 5 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_917 (x y : BitVec w) : +theorem e_917 : - 2 * ~~~(z ^^^ t) + 1 * ~~~(z &&& ~~~z) - 2 * ~~~(z &&& ~~~t) + 1 * ~~~(z ||| ~~~t) - 3 * (z &&& ~~~t) + 1 * (z &&& t) = - 1 * ~~~(z ||| t) - 2 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_918 (x y : BitVec w) : +theorem e_918 : 2 * ~~~t - 3 * ~~~(z &&& ~~~z) + 1 * t + 3 * ~~~(z ||| ~~~t) + 2 * (z &&& ~~~t) + 2 * (z &&& t) = 1 * (z ^^^ t) - 1 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_919 (x y : BitVec w) : +theorem e_919 : - 6 * (z ^^^ t) - 7 * ~~~z + 5 * t + 7 * ~~~(z ||| t) + 4 * ~~~(z ||| ~~~t) + 2 * (z &&& ~~~t) = - 4 * (z ||| t) + 9 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_920 (x y : BitVec w) : +theorem e_920 : 3 * ~~~(z &&& ~~~t) - 1 * ~~~(z ^^^ t) - 5 * ~~~t + 3 * ~~~(z ||| t) - 2 * (z &&& ~~~t) - 2 * (z &&& t) = 10 * ~~~(z ||| ~~~t) - 7 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_921 (x y : BitVec w) : +theorem e_921 : 2 * ~~~(z &&& t) + 5 * z - 7 * ~~~(z ||| t) - 12 * ~~~(z ||| ~~~t) - 12 * (z &&& ~~~t) - 15 * (z &&& t) = - 5 * (z ||| t) - 5 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_922 (x y : BitVec w) : +theorem e_922 : 3 * ~~~t + 1 * t - 7 * ~~~(z ||| t) - 5 * ~~~(z ||| ~~~t) - 3 * (z &&& ~~~t) - 1 * (z &&& t) = - 4 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_923 (x y : BitVec w) : +theorem e_923 : 1 * ~~~t + 3 * t - 2 * z - 4 * ~~~(z ||| t) - 6 * ~~~(z ||| ~~~t) - 2 * (z &&& ~~~t) = 1 * (z &&& t) - 3 * ~~~(z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_924 (x y : BitVec w) : +theorem e_924 : 2 * ~~~(z &&& t) + 4 * t - 7 * ~~~(z ||| t) - 11 * ~~~(z ||| ~~~t) - 2 * (z &&& ~~~t) - 9 * (z &&& t) = - 5 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_925 (x y : BitVec w) : +theorem e_925 : - 2 * ~~~(z &&& ~~~t) + 3 * ~~~z + 5 * ~~~(z ||| t) + 5 * ~~~(z ||| ~~~t) + 6 * (z &&& ~~~t) + 8 * (z &&& t) = 6 * ~~~(z &&& ~~~z) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_926 (x y : BitVec w) : +theorem e_926 : 3 * z - 2 * t + 4 * (z ^^^ t) - 5 * ~~~(z ||| t) - 12 * (z &&& ~~~t) - 6 * (z &&& t) = 7 * ~~~(z ||| ~~~t) - 5 * ~~~(z &&& ~~~z) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_927 (x y : BitVec w) : +theorem e_927 : 2 * ~~~(z &&& ~~~t) - 3 * (z ^^^ t) + 7 * ~~~(z ^^^ t) - 9 * ~~~(z ||| t) + 1 * ~~~(z ||| ~~~t) - 9 * (z &&& t) = - 3 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_928 (x y : BitVec w) : +theorem e_928 : 1 * (z ||| ~~~t) + 3 * z - 6 * ~~~(z ||| t) - 4 * ~~~(z ||| ~~~t) - 3 * (z &&& ~~~t) - 3 * (z &&& t) = 1 * (z ||| t) - 5 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_929 (x y : BitVec w) : +theorem e_929 : - 2 * ~~~(z &&& t) + 3 * ~~~t - 5 * (z ^^^ t) - 1 * (z ||| ~~~t) + 7 * ~~~(z ||| ~~~t) + 1 * (z &&& t) = - 5 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_930 (x y : BitVec w) : +theorem e_930 : 7 * ~~~(z ^^^ t) + 2 * (z ||| ~~~t) + 1 * (z ||| t) - 9 * ~~~(z ||| t) - 8 * ~~~(z ||| ~~~t) - 17 * (z &&& t) = 3 * (z &&& ~~~t) - 7 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_931 (x y : BitVec w) : +theorem e_931 : - 11 * ~~~(z &&& ~~~z) - 5 * ~~~t + 7 * ~~~z + 5 * ~~~(z ||| ~~~t) + 16 * (z &&& ~~~t) + 12 * (z &&& t) = - 9 * ~~~(z ||| t) + 1 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_932 (x y : BitVec w) : +theorem e_932 : 4 * ~~~z - 5 * ~~~(z &&& ~~~z) + 1 * ~~~(z ^^^ t) + 2 * ~~~(z ||| ~~~t) + 5 * (z &&& ~~~t) + 5 * (z &&& t) = 1 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_933 (x y : BitVec w) : +theorem e_933 : - 3 * ~~~z + 7 * t + 2 * z + 4 * (z ||| t) + 3 * ~~~(z ||| t) - 6 * (z &&& ~~~t) = 13 * (z &&& t) + 8 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_934 (x y : BitVec w) : +theorem e_934 : 2 * ~~~(z &&& ~~~t) - 1 * ~~~(z &&& t) + 11 * t - 1 * ~~~(z ||| t) - 12 * ~~~(z ||| ~~~t) - 17 * (z &&& t) = 3 * (z &&& ~~~t) - 4 * z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_935 (x y : BitVec w) : +theorem e_935 : - 2 * ~~~(z ^^^ t) + 2 * ~~~t + 2 * ~~~(z &&& t) - 4 * ~~~(z ||| t) - 4 * ~~~(z ||| ~~~t) - 6 * (z &&& ~~~t) = - 2 * ~~~(z &&& ~~~z) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_936 (x y : BitVec w) : +theorem e_936 : 2 * ~~~(z &&& t) + 11 * (z ||| t) - 11 * z - 2 * ~~~(z ||| t) - 10 * ~~~(z ||| ~~~t) + 1 * (z &&& ~~~t) = 3 * ~~~(z &&& ~~~z) - 3 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_937 (x y : BitVec w) : +theorem e_937 : 2 * z - 11 * t + 5 * ~~~(z &&& t) + 6 * ~~~(z ||| ~~~t) - 7 * (z &&& ~~~t) + 9 * (z &&& t) = 5 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_938 (x y : BitVec w) : +theorem e_938 : 11 * ~~~(z &&& t) + 4 * ~~~(z &&& ~~~t) + 3 * (z ||| t) - 26 * ~~~(z ||| t) - 25 * (z &&& ~~~t) - 7 * (z &&& t) = 18 * ~~~(z ||| ~~~t) - 11 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_939 (x y : BitVec w) : +theorem e_939 : 7 * ~~~(z &&& ~~~z) + 2 * ~~~(z ^^^ t) - 1 * (z ||| t) - 9 * ~~~(z ||| t) - 6 * ~~~(z ||| ~~~t) - 6 * (z &&& ~~~t) = 8 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_940 (x y : BitVec w) : +theorem e_940 : - 6 * ~~~(z &&& t) - 2 * (z ^^^ t) + 2 * z + 6 * ~~~(z ||| t) + 6 * (z &&& ~~~t) - 2 * (z &&& t) = - 8 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_941 (x y : BitVec w) : +theorem e_941 : 7 * (z ||| ~~~t) + 1 * ~~~(z ^^^ t) - 9 * ~~~(z ||| t) - 1 * ~~~(z ||| ~~~t) - 14 * (z &&& ~~~t) - 15 * (z &&& t) = - 7 * ~~~(z &&& ~~~z) + 6 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_942 (x y : BitVec w) : +theorem e_942 : - 1 * (z ||| t) - 3 * ~~~(z &&& ~~~z) + 9 * ~~~(z ||| t) + 21 * ~~~(z ||| ~~~t) + 4 * (z &&& ~~~t) + 21 * (z &&& t) = 6 * ~~~(z &&& ~~~t) + 11 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_943 (x y : BitVec w) : +theorem e_943 : - 11 * (z ^^^ t) + 1 * ~~~z + 6 * ~~~(z ||| t) + 10 * ~~~(z ||| ~~~t) + 18 * (z &&& ~~~t) + 7 * (z &&& t) = 7 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_944 (x y : BitVec w) : +theorem e_944 : 5 * ~~~(z &&& ~~~z) - 3 * (z ||| t) + 2 * t + 2 * z - 4 * (z &&& ~~~t) - 6 * (z &&& t) = 5 * ~~~(z ||| t) + 4 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_945 (x y : BitVec w) : +theorem e_945 : - 1 * ~~~(z ^^^ t) - 6 * z + 4 * ~~~(z &&& ~~~t) - 3 * ~~~(z ||| t) - 15 * ~~~(z ||| ~~~t) + 3 * (z &&& t) = 5 * (z &&& ~~~t) - 11 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_946 (x y : BitVec w) : +theorem e_946 : 4 * ~~~(z &&& t) + 1 * ~~~(z ^^^ t) + 2 * ~~~(z &&& ~~~z) - 7 * ~~~(z ||| t) - 6 * (z &&& ~~~t) - 3 * (z &&& t) = 6 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_947 (x y : BitVec w) : +theorem e_947 : - 7 * ~~~z + 5 * ~~~(z &&& ~~~t) + 1 * ~~~(z ^^^ t) + 1 * ~~~(z ||| t) + 3 * ~~~(z ||| ~~~t) - 5 * (z &&& t) = 1 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_948 (x y : BitVec w) : +theorem e_948 : 1 * z + 3 * (z ||| ~~~t) - 4 * ~~~(z ||| t) - 1 * ~~~(z ||| ~~~t) - 5 * (z &&& ~~~t) - 5 * (z &&& t) = - 1 * ~~~(z &&& ~~~z) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_949 (x y : BitVec w) : +theorem e_949 : - 2 * (z ^^^ t) - 1 * ~~~(z &&& ~~~t) - 6 * ~~~(z ||| t) - 4 * ~~~(z ||| ~~~t) + 2 * (z &&& ~~~t) + 1 * (z &&& t) = - 7 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_950 (x y : BitVec w) : +theorem e_950 : - 1 * (z ||| ~~~t) - 3 * ~~~(z &&& ~~~z) - 6 * (z ||| t) + 9 * ~~~(z ||| ~~~t) + 10 * (z &&& ~~~t) + 6 * (z &&& t) = - 4 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_951 (x y : BitVec w) : +theorem e_951 : 4 * (z ^^^ t) + 3 * ~~~z + 11 * ~~~(z &&& ~~~z) - 16 * ~~~(z ||| t) - 18 * ~~~(z ||| ~~~t) - 13 * (z &&& t) = - 2 * ~~~(z ^^^ t) + 15 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_952 (x y : BitVec w) : +theorem e_952 : - 6 * ~~~(z &&& ~~~z) + 5 * (z ||| t) + 4 * t + 6 * ~~~(z ||| t) + 3 * (z &&& ~~~t) - 3 * (z &&& t) = 1 * ~~~(z ||| ~~~t) + 2 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_953 (x y : BitVec w) : +theorem e_953 : 3 * (z ||| t) - 11 * ~~~(z &&& t) + 4 * t + 11 * ~~~(z ||| t) + 10 * ~~~(z ||| ~~~t) + 14 * (z &&& ~~~t) = 7 * (z &&& t) + 6 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_954 (x y : BitVec w) : +theorem e_954 : - 6 * ~~~(z ^^^ t) - 11 * ~~~(z &&& ~~~t) - 11 * ~~~(z &&& ~~~z) + 28 * ~~~(z ||| t) + 22 * ~~~(z ||| ~~~t) + 11 * (z &&& ~~~t) = - 28 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_955 (x y : BitVec w) : +theorem e_955 : - 6 * ~~~(z &&& ~~~t) - 2 * (z ^^^ t) + 9 * ~~~(z ||| t) + 11 * ~~~(z ||| ~~~t) + 3 * (z &&& ~~~t) + 7 * (z &&& t) = 1 * z + 3 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_956 (x y : BitVec w) : +theorem e_956 : 7 * ~~~(z &&& ~~~z) + 2 * t - 7 * ~~~t - 11 * ~~~(z ||| ~~~t) + 3 * (z &&& ~~~t) - 4 * (z &&& t) = 5 * z - 2 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_957 (x y : BitVec w) : +theorem e_957 : - 2 * ~~~(z &&& ~~~z) + 4 * ~~~(z &&& t) - 2 * (z ||| ~~~t) + 5 * ~~~(z ||| ~~~t) + 7 * (z &&& ~~~t) + 11 * (z &&& t) = 7 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_958 (x y : BitVec w) : +theorem e_958 : - 1 * (z ^^^ t) - 1 * ~~~(z &&& t) + 1 * ~~~(z ||| t) + 3 * ~~~(z ||| ~~~t) + 3 * (z &&& ~~~t) + 1 * (z &&& t) = 1 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_959 (x y : BitVec w) : +theorem e_959 : - 6 * t - 1 * ~~~t + 1 * ~~~(z ||| t) + 6 * ~~~(z ||| ~~~t) + 2 * (z &&& ~~~t) + 7 * (z &&& t) = 1 * z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_960 (x y : BitVec w) : +theorem e_960 : 3 * ~~~(z ^^^ t) - 6 * (z ^^^ t) - 11 * t - 3 * z + 17 * ~~~(z ||| ~~~t) + 12 * (z &&& ~~~t) = 3 * ~~~t - 11 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_961 (x y : BitVec w) : +theorem e_961 : 4 * (z ||| ~~~t) + 1 * ~~~t + 11 * (z ^^^ t) - 5 * ~~~(z ||| t) - 15 * ~~~(z ||| ~~~t) - 8 * (z &&& t) = 16 * (z &&& ~~~t) - 4 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_962 (x y : BitVec w) : +theorem e_962 : - 1 * ~~~(z &&& t) + 7 * ~~~(z ^^^ t) + 5 * (z ^^^ t) - 4 * ~~~(z ||| t) - 4 * (z &&& ~~~t) - 5 * (z &&& t) = 2 * ~~~(z &&& ~~~t) + 2 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_963 (x y : BitVec w) : +theorem e_963 : - 2 * ~~~(z &&& ~~~t) + 1 * ~~~(z ^^^ t) - 11 * t - 1 * ~~~(z ||| t) + 13 * ~~~(z ||| ~~~t) - 2 * (z &&& ~~~t) = - 12 * (z &&& t) - 2 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_964 (x y : BitVec w) : +theorem e_964 : - 6 * ~~~(z &&& t) + 5 * (z ||| t) + 3 * ~~~(z &&& ~~~t) + 2 * (z ^^^ t) + 2 * ~~~(z ||| t) - 2 * (z &&& ~~~t) - 8 * (z &&& t) = - 1 * ~~~t + 4 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_965 (x y : BitVec w) : +theorem e_965 : - 7 * ~~~(z ^^^ t) + 7 * (z ||| ~~~t) - 2 * (z ||| t) - 2 * ~~~z + 2 * ~~~(z &&& ~~~z) + 4 * ~~~(z ||| ~~~t) - 7 * (z &&& ~~~t) = 2 * ~~~(z &&& t) - 2 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_966 (x y : BitVec w) : +theorem e_966 : - 5 * ~~~(z ^^^ t) - 11 * (z ||| t) + 7 * (z ||| ~~~t) - 7 * ~~~(z &&& t) + 18 * ~~~(z ||| ~~~t) + 11 * (z &&& ~~~t) + 9 * (z &&& t) = - 5 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_967 (x y : BitVec w) : +theorem e_967 : - 1 * ~~~(z ^^^ t) - 5 * (z ||| t) - 6 * ~~~t + 2 * ~~~(z &&& ~~~z) + 3 * ~~~(z ||| t) + 1 * ~~~(z ||| ~~~t) + 4 * (z &&& t) = - 2 * ~~~z - 9 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_968 (x y : BitVec w) : +theorem e_968 : 2 * ~~~z + 5 * ~~~(z &&& t) - 2 * t - 7 * ~~~(z ||| t) - 5 * ~~~(z ||| ~~~t) - 3 * (z &&& ~~~t) + 4 * (z &&& t) = 2 * z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_969 (x y : BitVec w) : +theorem e_969 : 2 * ~~~t + 1 * ~~~(z &&& ~~~z) - 6 * (z ||| t) - 4 * ~~~(z ||| t) + 4 * ~~~(z ||| ~~~t) + 2 * (z &&& ~~~t) + 4 * (z &&& t) = - 1 * (z ^^^ t) - 1 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_970 (x y : BitVec w) : +theorem e_970 : - 1 * ~~~t - 6 * ~~~(z &&& t) + 1 * z - 7 * ~~~(z ^^^ t) + 14 * ~~~(z ||| t) + 6 * ~~~(z ||| ~~~t) + 6 * (z &&& t) = - 6 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_971 (x y : BitVec w) : +theorem e_971 : - 11 * (z ||| ~~~t) + 4 * ~~~(z &&& ~~~t) + 2 * z - 5 * ~~~t + 12 * ~~~(z ||| t) - 4 * ~~~(z ||| ~~~t) + 14 * (z &&& ~~~t) = - 5 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_972 (x y : BitVec w) : +theorem e_972 : 11 * ~~~(z ^^^ t) - 11 * ~~~(z &&& ~~~t) + 4 * ~~~(z &&& t) - 4 * ~~~(z ||| t) + 5 * ~~~(z ||| ~~~t) - 6 * (z &&& ~~~t) - 1 * (z &&& t) = - 1 * (z ||| t) - 1 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_973 (x y : BitVec w) : +theorem e_973 : - 2 * ~~~(z &&& ~~~t) + 2 * ~~~(z &&& ~~~z) + 2 * ~~~t + 7 * t - 13 * ~~~(z ||| t) - 7 * ~~~(z ||| ~~~t) - 18 * (z &&& t) = 15 * (z &&& ~~~t) - 11 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_974 (x y : BitVec w) : +theorem e_974 : 1 * ~~~t + 11 * t + 11 * ~~~(z &&& ~~~t) + 5 * (z ||| t) - 12 * ~~~(z ||| t) - 27 * ~~~(z ||| ~~~t) - 27 * (z &&& t) = 6 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_975 (x y : BitVec w) : +theorem e_975 : 5 * ~~~(z ^^^ t) + 1 * ~~~z + 4 * (z ||| t) - 1 * ~~~(z &&& t) - 10 * ~~~(z ||| t) - 4 * ~~~(z ||| ~~~t) - 9 * (z &&& t) = 8 * (z &&& ~~~t) - 5 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_976 (x y : BitVec w) : +theorem e_976 : 2 * t - 6 * (z ||| ~~~t) - 7 * z + 5 * ~~~(z ||| t) - 3 * ~~~(z ||| ~~~t) + 13 * (z &&& ~~~t) + 10 * (z &&& t) = - 1 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_977 (x y : BitVec w) : +theorem e_977 : - 1 * (z ^^^ t) - 2 * t + 3 * z + 1 * ~~~(z &&& ~~~z) - 1 * ~~~(z ||| t) + 2 * ~~~(z ||| ~~~t) - 3 * (z &&& ~~~t) = 2 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_978 (x y : BitVec w) : +theorem e_978 : - 3 * ~~~(z ^^^ t) + 4 * ~~~(z &&& ~~~z) - 3 * ~~~z + 3 * z - 12 * ~~~(z ||| ~~~t) - 18 * (z &&& ~~~t) - 4 * (z &&& t) = - 2 * ~~~(z ||| t) - 11 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_979 (x y : BitVec w) : +theorem e_979 : 2 * ~~~(z &&& t) + 7 * z - 2 * ~~~(z &&& ~~~z) + 5 * ~~~t - 5 * ~~~(z ||| t) - 7 * (z &&& ~~~t) - 5 * (z &&& t) = 5 * (z ^^^ t) - 5 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_980 (x y : BitVec w) : +theorem e_980 : 4 * ~~~z + 11 * ~~~(z &&& ~~~t) + 5 * ~~~(z ^^^ t) - 21 * ~~~(z ||| t) - 16 * ~~~(z ||| ~~~t) - 1 * (z &&& ~~~t) - 17 * (z &&& t) = - 1 * ~~~(z &&& ~~~z) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_981 (x y : BitVec w) : +theorem e_981 : 1 * (z ||| ~~~t) - 1 * ~~~(z &&& ~~~t) - 2 * t - 2 * ~~~(z ^^^ t) + 2 * ~~~(z ||| t) + 3 * ~~~(z ||| ~~~t) + 4 * (z &&& t) = 1 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_982 (x y : BitVec w) : +theorem e_982 : - 3 * ~~~t + 4 * ~~~(z &&& ~~~t) - 1 * (z ||| ~~~t) + 1 * ~~~(z ||| t) - 4 * ~~~(z ||| ~~~t) + 4 * (z &&& ~~~t) - 2 * (z &&& t) = 1 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_983 (x y : BitVec w) : +theorem e_983 : - 2 * ~~~(z ^^^ t) - 1 * ~~~t + 4 * t + 4 * ~~~(z &&& ~~~t) - 1 * ~~~(z ||| t) - 11 * ~~~(z ||| ~~~t) - 2 * (z &&& ~~~t) = 9 * (z &&& t) - 3 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_984 (x y : BitVec w) : +theorem e_984 : - 5 * (z ||| t) - 1 * ~~~t - 11 * ~~~(z ^^^ t) + 15 * ~~~(z ||| t) + 5 * ~~~(z ||| ~~~t) + 9 * (z &&& ~~~t) + 19 * (z &&& t) = 3 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_985 (x y : BitVec w) : +theorem e_985 : - 3 * ~~~(z ^^^ t) + 1 * (z ||| ~~~t) + 1 * ~~~(z &&& ~~~t) + 3 * ~~~z - 5 * ~~~(z ||| ~~~t) - 2 * (z &&& ~~~t) + 1 * (z &&& t) = 3 * ~~~(z ||| t) - 1 * ~~~(z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_986 (x y : BitVec w) : +theorem e_986 : 5 * ~~~z + 4 * ~~~t - 1 * ~~~(z &&& ~~~z) - 9 * ~~~(z ||| t) - 5 * ~~~(z ||| ~~~t) - 4 * (z &&& ~~~t) + 1 * (z &&& t) = - 1 * ~~~(z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_987 (x y : BitVec w) : +theorem e_987 : 4 * ~~~t + 7 * ~~~(z &&& ~~~z) + 3 * (z ||| t) - 6 * ~~~(z ||| t) - 5 * ~~~(z ||| ~~~t) - 14 * (z &&& ~~~t) - 10 * (z &&& t) = 5 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_988 (x y : BitVec w) : +theorem e_988 : 2 * ~~~t + 1 * (z ||| ~~~t) - 6 * z - 7 * t - 2 * (z ||| t) + 9 * ~~~(z ||| ~~~t) + 14 * (z &&& t) = - 5 * (z &&& ~~~t) + 3 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_989 (x y : BitVec w) : +theorem e_989 : - 11 * ~~~z + 11 * ~~~(z &&& ~~~t) - 6 * (z ^^^ t) - 3 * ~~~(z ||| t) + 6 * ~~~(z ||| ~~~t) + 3 * (z &&& ~~~t) - 11 * (z &&& t) = - 3 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_990 (x y : BitVec w) : +theorem e_990 : - 1 * ~~~(z &&& ~~~t) + 1 * t - 5 * (z ^^^ t) + 2 * ~~~z - 6 * ~~~(z ||| t) - 3 * (z &&& ~~~t) - 8 * (z &&& t) = - 3 * (z ||| t) - 5 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_991 (x y : BitVec w) : +theorem e_991 : 7 * ~~~(z ^^^ t) + 3 * (z ||| ~~~t) - 1 * (z ^^^ t) - 2 * z - 10 * ~~~(z ||| t) - 4 * ~~~(z ||| ~~~t) - 13 * (z &&& t) = - 5 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_992 (x y : BitVec w) : +theorem e_992 : 1 * (z ||| t) + 4 * ~~~z + 7 * (z ^^^ t) + 1 * z + 11 * ~~~(z &&& ~~~t) - 23 * ~~~(z ||| ~~~t) - 13 * (z &&& t) = 9 * (z &&& ~~~t) + 15 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_993 (x y : BitVec w) : +theorem e_993 : - 1 * (z ||| t) - 6 * ~~~(z ^^^ t) + 5 * ~~~z - 4 * ~~~(z ||| t) - 9 * ~~~(z ||| ~~~t) + 6 * (z &&& ~~~t) + 7 * (z &&& t) = 5 * z - 5 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_994 (x y : BitVec w) : +theorem e_994 : - 2 * ~~~(z &&& ~~~t) + 4 * (z ^^^ t) - 5 * ~~~t + 11 * ~~~(z &&& ~~~z) - 5 * (z ||| ~~~t) - 13 * ~~~(z ||| ~~~t) - 4 * (z &&& t) = 5 * (z &&& ~~~t) - 1 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_995 (x y : BitVec w) : +theorem e_995 : 1 * ~~~t + 11 * ~~~z - 1 * z - 6 * ~~~(z ||| t) - 6 * ~~~(z ||| ~~~t) + 6 * (z &&& ~~~t) + 7 * (z &&& t) = 1 * (z ||| ~~~t) + 5 * ~~~(z &&& ~~~z) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_996 (x y : BitVec w) : +theorem e_996 : - 6 * ~~~(z &&& t) + 7 * t - 2 * ~~~(z ^^^ t) - 1 * (z ||| t) - 3 * z + 8 * ~~~(z ||| t) - 1 * (z &&& t) = - 10 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_997 (x y : BitVec w) : +theorem e_997 : - 11 * ~~~t - 2 * (z ^^^ t) - 3 * ~~~(z ^^^ t) + 3 * ~~~(z &&& t) - 8 * ~~~(z ||| ~~~t) + 10 * (z &&& ~~~t) - 4 * (z &&& t) = - 7 * ~~~(z &&& ~~~t) - 4 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_998 (x y : BitVec w) : +theorem e_998 : - 7 * ~~~(z &&& ~~~z) - 3 * (z ^^^ t) - 3 * z - 2 * t + 7 * ~~~(z ||| t) + 13 * (z &&& ~~~t) + 12 * (z &&& t) = - 12 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_999 (x y : BitVec w) : +theorem e_999 : - 5 * (z ||| t) + 1 * ~~~(z &&& ~~~z) - 2 * ~~~(z ^^^ t) - 6 * ~~~(z &&& ~~~t) + 9 * ~~~(z ||| ~~~t) + 10 * (z &&& ~~~t) + 12 * (z &&& t) = 6 * (z ^^^ t) - 7 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1000 (x y : BitVec w) : +theorem e_1000 : 7 * (z ^^^ t) + 2 * z - 1 * ~~~(z ^^^ t) + 2 * ~~~(z &&& ~~~z) - 9 * ~~~(z ||| ~~~t) - 12 * (z &&& ~~~t) - 3 * (z &&& t) = - 1 * (z ||| t) + 1 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1001 (x y : BitVec w) : +theorem e_1001 : - 3 * ~~~(z &&& ~~~t) + 5 * z + 1 * t - 1 * ~~~t - 1 * ~~~(z &&& ~~~z) + 3 * ~~~(z ||| ~~~t) - 1 * (z &&& ~~~t) = - 7 * ~~~(z ||| t) + 2 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1002 (x y : BitVec w) : +theorem e_1002 : 5 * ~~~(z ^^^ t) + 5 * (z ^^^ t) + 7 * (z ||| ~~~t) - 17 * ~~~(z ||| t) - 10 * ~~~(z ||| ~~~t) - 14 * (z &&& ~~~t) - 14 * (z &&& t) = - 5 * ~~~z - 2 * z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1003 (x y : BitVec w) : +theorem e_1003 : - 2 * ~~~(z &&& ~~~t) - 3 * ~~~(z ^^^ t) - 5 * (z ||| ~~~t) + 8 * ~~~(z ||| t) - 7 * ~~~(z ||| ~~~t) - 4 * (z &&& ~~~t) + 1 * (z &&& t) = - 2 * ~~~(z &&& ~~~z) - 7 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1004 (x y : BitVec w) : +theorem e_1004 : 1 * ~~~t - 5 * t - 7 * (z ||| ~~~t) + 2 * ~~~(z &&& ~~~z) + 4 * ~~~(z ||| t) + 1 * ~~~(z ||| ~~~t) + 8 * (z &&& t) = - 2 * (z ||| t) - 2 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1005 (x y : BitVec w) : +theorem e_1005 : - 1 * (z ||| t) - 11 * ~~~(z &&& ~~~t) - 3 * (z ||| ~~~t) - 7 * ~~~t + 5 * z + 12 * ~~~(z ||| ~~~t) + 6 * (z &&& ~~~t) = - 21 * ~~~(z ||| t) - 10 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1006 (x y : BitVec w) : +theorem e_1006 : - 2 * ~~~(z &&& ~~~t) + 1 * (z ^^^ t) + 1 * ~~~(z ^^^ t) - 1 * ~~~(z &&& ~~~z) - 3 * ~~~(z ||| t) + 2 * ~~~(z ||| ~~~t) + 2 * (z &&& t) = - 5 * ~~~t + 5 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1007 (x y : BitVec w) : +theorem e_1007 : 1 * ~~~(z ^^^ t) + 5 * ~~~(z &&& ~~~t) + 2 * ~~~z - 19 * ~~~(z ||| t) - 8 * ~~~(z ||| ~~~t) - 12 * (z &&& ~~~t) - 17 * (z &&& t) = - 11 * (z ||| ~~~t) - 1 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1008 (x y : BitVec w) : +theorem e_1008 : 2 * (z ^^^ t) - 11 * ~~~(z ^^^ t) + 4 * (z ||| t) + 3 * ~~~(z &&& ~~~z) + 8 * ~~~(z ||| t) - 9 * ~~~(z ||| ~~~t) - 9 * (z &&& ~~~t) = - 4 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1009 (x y : BitVec w) : +theorem e_1009 : - 5 * (z ^^^ t) - 2 * ~~~t - 1 * (z ||| t) - 1 * (z ||| ~~~t) + 13 * ~~~(z ||| ~~~t) + 16 * (z &&& ~~~t) + 9 * (z &&& t) = - 10 * ~~~(z ||| t) + 7 * ~~~(z &&& ~~~z) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1010 (x y : BitVec w) : +theorem e_1010 : - 6 * (z ||| t) - 11 * (z ||| ~~~t) - 1 * z - 2 * ~~~(z &&& ~~~z) - 3 * ~~~(z ||| ~~~t) + 20 * (z &&& ~~~t) + 9 * (z &&& t) = - 2 * ~~~(z ||| t) - 11 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1011 (x y : BitVec w) : +theorem e_1011 : - 2 * ~~~t + 3 * (z ||| t) + 1 * ~~~(z &&& ~~~t) - 3 * ~~~(z ||| t) - 9 * ~~~(z ||| ~~~t) - 1 * (z &&& ~~~t) - 5 * (z &&& t) = - 4 * ~~~z - 1 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1012 (x y : BitVec w) : +theorem e_1012 : 7 * z + 5 * ~~~z - 3 * (z ^^^ t) - 5 * ~~~(z ||| t) - 1 * ~~~(z ||| ~~~t) - 3 * (z &&& ~~~t) - 6 * (z &&& t) = 1 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1013 (x y : BitVec w) : +theorem e_1013 : - 5 * ~~~(z ^^^ t) + 3 * z - 1 * ~~~(z &&& t) + 5 * (z ||| t) + 6 * ~~~(z ||| t) - 8 * (z &&& ~~~t) - 3 * (z &&& t) = - 1 * (z ^^^ t) + 5 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1014 (x y : BitVec w) : +theorem e_1014 : 2 * ~~~(z &&& ~~~t) - 3 * ~~~z + 1 * (z ||| ~~~t) + 4 * ~~~(z ^^^ t) + 1 * ~~~(z &&& ~~~z) + 5 * (z &&& ~~~t) - 1 * (z &&& t) = 5 * ~~~(z ||| t) + 7 * z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1015 (x y : BitVec w) : +theorem e_1015 : - 6 * (z ||| ~~~t) + 2 * ~~~z + 5 * ~~~(z &&& ~~~t) - 1 * ~~~(z ||| t) - 7 * ~~~(z ||| ~~~t) + 7 * (z &&& ~~~t) + 2 * (z &&& t) = 1 * z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1016 (x y : BitVec w) : +theorem e_1016 : 1 * ~~~t + 2 * t + 1 * ~~~(z ^^^ t) - 7 * (z ^^^ t) - 1 * z - 2 * ~~~(z ||| t) + 5 * ~~~(z ||| ~~~t) = 2 * (z &&& t) - 7 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1017 (x y : BitVec w) : +theorem e_1017 : 11 * ~~~(z &&& ~~~z) - 5 * (z ||| ~~~t) - 2 * ~~~(z &&& ~~~t) + 5 * ~~~(z &&& t) + 1 * ~~~(z ^^^ t) - 10 * ~~~(z ||| t) - 5 * (z &&& t) = 3 * ~~~(z ||| ~~~t) + 11 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1018 (x y : BitVec w) : +theorem e_1018 : - 1 * t + 7 * ~~~(z &&& t) + 1 * (z ||| ~~~t) - 2 * (z ||| t) - 8 * ~~~(z ||| t) - 6 * (z &&& ~~~t) + 2 * (z &&& t) = 4 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1019 (x y : BitVec w) : +theorem e_1019 : - 2 * ~~~(z ^^^ t) - 2 * (z ||| t) - 11 * z - 7 * (z ^^^ t) + 7 * ~~~(z ||| t) + 9 * ~~~(z ||| ~~~t) + 25 * (z &&& ~~~t) = 5 * (z ||| ~~~t) - 20 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1020 (x y : BitVec w) : +theorem e_1020 : 7 * (z ^^^ t) + 4 * ~~~(z ^^^ t) - 1 * ~~~(z &&& t) - 14 * ~~~(z ||| t) - 7 * ~~~(z ||| ~~~t) - 18 * (z &&& ~~~t) - 5 * (z &&& t) = - 1 * (z ||| t) - 11 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1021 (x y : BitVec w) : +theorem e_1021 : 7 * ~~~(z ^^^ t) - 2 * z + 1 * t - 11 * (z ||| t) - 4 * ~~~(z ||| t) + 10 * ~~~(z ||| ~~~t) + 8 * (z &&& t) = - 16 * (z &&& ~~~t) + 3 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1022 (x y : BitVec w) : +theorem e_1022 : - 3 * (z ^^^ t) + 1 * ~~~(z &&& ~~~t) + 4 * ~~~t + 7 * ~~~z - 5 * ~~~(z ||| ~~~t) - 1 * (z &&& ~~~t) - 1 * (z &&& t) = 12 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1023 (x y : BitVec w) : +theorem e_1023 : - 2 * z - 3 * ~~~t - 11 * ~~~(z ^^^ t) - 1 * (z ||| t) + 14 * ~~~(z ||| t) + 6 * (z &&& ~~~t) + 14 * (z &&& t) = - 1 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1024 (x y : BitVec w) : +theorem e_1024 : - 5 * ~~~z - 1 * (z ||| ~~~t) + 1 * z + 3 * ~~~(z &&& ~~~t) + 3 * ~~~(z ||| t) - 3 * (z &&& ~~~t) - 6 * (z &&& t) = 1 * ~~~(z ||| ~~~t) - 3 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1025 (x y : BitVec w) : +theorem e_1025 : 4 * (z ^^^ t) - 2 * ~~~(z &&& t) - 6 * ~~~(z &&& ~~~z) + 11 * ~~~t - 3 * t - 3 * ~~~(z ||| t) + 9 * (z &&& t) = 7 * (z &&& ~~~t) - 7 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1026 (x y : BitVec w) : +theorem e_1026 : - 6 * t - 3 * (z ^^^ t) + 3 * ~~~(z &&& ~~~t) + 2 * ~~~(z ^^^ t) - 5 * ~~~(z ||| t) + 6 * ~~~(z ||| ~~~t) + 1 * (z &&& t) = - 3 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1027 (x y : BitVec w) : +theorem e_1027 : 7 * (z ^^^ t) - 2 * ~~~(z ^^^ t) - 1 * ~~~(z &&& ~~~t) - 5 * ~~~t + 8 * ~~~(z ||| t) - 6 * ~~~(z ||| ~~~t) + 3 * (z &&& t) = 2 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1028 (x y : BitVec w) : +theorem e_1028 : 2 * (z ||| ~~~t) + 2 * z - 6 * ~~~(z &&& ~~~z) - 1 * ~~~(z ||| t) + 6 * ~~~(z ||| ~~~t) - 3 * (z &&& ~~~t) + 2 * (z &&& t) = - 5 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1029 (x y : BitVec w) : +theorem e_1029 : - 1 * ~~~t - 7 * z - 7 * ~~~(z &&& t) + 8 * ~~~(z ||| t) + 10 * ~~~(z ||| ~~~t) + 18 * (z &&& ~~~t) + 7 * (z &&& t) = 3 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1030 (x y : BitVec w) : +theorem e_1030 : - 1 * ~~~(z &&& ~~~t) - 6 * ~~~(z &&& t) + 1 * t - 15 * ~~~(z ||| t) - 5 * ~~~(z ||| ~~~t) + 6 * (z &&& ~~~t) - 11 * (z &&& t) = - 11 * ~~~(z ^^^ t) - 11 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1031 (x y : BitVec w) : +theorem e_1031 : 2 * (z ^^^ t) + 1 * (z ||| t) - 6 * t - 11 * ~~~(z ||| t) + 3 * ~~~(z ||| ~~~t) - 3 * (z &&& ~~~t) - 6 * (z &&& t) = - 11 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1032 (x y : BitVec w) : +theorem e_1032 : - 3 * (z ||| ~~~t) + 3 * ~~~(z &&& t) - 6 * ~~~(z &&& ~~~z) + 3 * t - 5 * ~~~(z ||| t) + 6 * (z &&& ~~~t) - 5 * (z &&& t) = - 11 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1033 (x y : BitVec w) : +theorem e_1033 : - 1 * t + 11 * ~~~(z &&& ~~~z) + 2 * ~~~(z ^^^ t) + 3 * (z ||| ~~~t) - 1 * ~~~t - 15 * ~~~(z ||| t) - 10 * ~~~(z ||| ~~~t) = 15 * (z &&& t) + 13 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1034 (x y : BitVec w) : +theorem e_1034 : - 6 * ~~~(z ^^^ t) - 2 * t + 3 * (z ||| t) + 6 * ~~~(z ||| t) - 1 * ~~~(z ||| ~~~t) + 8 * (z &&& ~~~t) + 16 * (z &&& t) = 11 * z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1035 (x y : BitVec w) : +theorem e_1035 : - 2 * t + 5 * ~~~(z &&& ~~~z) - 5 * z - 4 * ~~~(z ||| t) - 3 * ~~~(z ||| ~~~t) - 4 * (z &&& ~~~t) + 3 * (z &&& t) = 5 * ~~~(z ^^^ t) - 4 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1036 (x y : BitVec w) : +theorem e_1036 : 5 * z - 2 * t - 7 * ~~~(z &&& ~~~z) + 2 * ~~~t - 3 * ~~~(z ||| t) + 5 * ~~~(z ||| ~~~t) - 4 * (z &&& t) = - 4 * ~~~(z ^^^ t) - 4 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1037 (x y : BitVec w) : +theorem e_1037 : - 1 * ~~~(z &&& t) + 7 * ~~~t + 2 * ~~~z - 1 * (z ||| t) - 10 * ~~~(z ||| t) - 7 * (z &&& ~~~t) - 1 * (z &&& t) = - 2 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1038 (x y : BitVec w) : +theorem e_1038 : 11 * ~~~(z &&& t) - 7 * ~~~t + 3 * (z ||| ~~~t) - 11 * ~~~(z ^^^ t) - 15 * ~~~(z ||| ~~~t) - 11 * (z &&& ~~~t) + 4 * (z &&& t) = - 4 * ~~~(z &&& ~~~z) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1039 (x y : BitVec w) : +theorem e_1039 : - 1 * (z ||| ~~~t) + 2 * ~~~(z &&& ~~~z) - 1 * ~~~z + 7 * ~~~(z ||| t) - 1 * ~~~(z ||| ~~~t) - 1 * (z &&& ~~~t) + 6 * (z &&& t) = 7 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1040 (x y : BitVec w) : +theorem e_1040 : - 2 * (z ||| ~~~t) - 3 * t + 4 * ~~~(z &&& ~~~t) + 2 * ~~~t - 2 * ~~~(z ||| t) - 1 * ~~~(z ||| ~~~t) + 3 * (z &&& t) = 2 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1041 (x y : BitVec w) : +theorem e_1041 : - 5 * ~~~z - 11 * ~~~(z ^^^ t) + 1 * (z ||| t) - 2 * (z ||| ~~~t) + 6 * ~~~(z ||| ~~~t) + 3 * (z &&& ~~~t) + 14 * (z &&& t) = - 20 * ~~~(z ||| t) + 2 * ~~~(z &&& ~~~z) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1042 (x y : BitVec w) : +theorem e_1042 : 3 * ~~~(z &&& ~~~t) + 1 * t - 5 * (z ||| ~~~t) + 2 * ~~~z + 1 * (z ^^^ t) - 7 * ~~~(z ||| ~~~t) + 1 * (z &&& t) = - 4 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1043 (x y : BitVec w) : +theorem e_1043 : - 2 * (z ||| t) + 1 * t - 3 * (z ^^^ t) + 7 * ~~~z - 8 * ~~~(z ||| t) - 3 * ~~~(z ||| ~~~t) + 4 * (z &&& ~~~t) = - 1 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1044 (x y : BitVec w) : +theorem e_1044 : - 1 * (z ^^^ t) + 1 * t + 7 * (z ||| t) - 2 * ~~~z + 7 * ~~~(z &&& ~~~t) - 12 * ~~~(z ||| ~~~t) - 15 * (z &&& t) = 6 * (z &&& ~~~t) + 5 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1045 (x y : BitVec w) : +theorem e_1045 : - 1 * ~~~(z &&& ~~~t) + 1 * ~~~(z &&& ~~~z) + 1 * (z ||| t) - 5 * (z ||| ~~~t) + 1 * ~~~(z ||| ~~~t) + 5 * (z &&& ~~~t) + 4 * (z &&& t) = 2 * ~~~(z &&& t) - 7 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1046 (x y : BitVec w) : +theorem e_1046 : 7 * ~~~(z &&& ~~~z) + 2 * (z ||| ~~~t) - 1 * ~~~(z &&& t) - 8 * ~~~(z ||| t) - 9 * ~~~(z ||| ~~~t) - 8 * (z &&& ~~~t) - 12 * (z &&& t) = - 3 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1047 (x y : BitVec w) : +theorem e_1047 : 4 * ~~~(z &&& ~~~t) + 4 * ~~~t + 1 * t - 2 * ~~~(z ^^^ t) - 6 * ~~~(z ||| t) - 5 * ~~~(z ||| ~~~t) - 6 * (z &&& ~~~t) = 5 * (z &&& t) - 2 * z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1048 (x y : BitVec w) : +theorem e_1048 : 2 * (z ^^^ t) + 1 * z - 2 * ~~~(z &&& t) - 1 * ~~~(z &&& ~~~z) - 4 * ~~~(z ||| t) + 1 * ~~~(z ||| ~~~t) - 7 * (z &&& ~~~t) = - 7 * (z ||| ~~~t) + 7 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1049 (x y : BitVec w) : +theorem e_1049 : - 1 * ~~~(z &&& t) + 1 * z + 3 * (z ^^^ t) - 5 * (z ||| ~~~t) - 2 * (z ||| t) + 6 * ~~~(z ||| t) + 6 * (z &&& t) = - 4 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1050 (x y : BitVec w) : +theorem e_1050 : - 6 * ~~~(z &&& ~~~z) - 1 * t - 1 * (z ||| ~~~t) + 4 * (z ^^^ t) + 7 * ~~~(z ||| t) + 2 * ~~~(z ||| ~~~t) + 2 * (z &&& ~~~t) = - 1 * (z ||| t) - 7 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1051 (x y : BitVec w) : +theorem e_1051 : 3 * t - 5 * ~~~(z &&& t) + 5 * (z ||| t) + 1 * ~~~t - 3 * ~~~(z ||| ~~~t) - 1 * (z &&& ~~~t) - 8 * (z &&& t) = - 4 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1052 (x y : BitVec w) : +theorem e_1052 : 3 * t + 7 * ~~~z + 5 * (z ^^^ t) - 2 * ~~~(z &&& ~~~t) - 5 * ~~~(z ||| t) - 5 * (z &&& ~~~t) - 1 * (z &&& t) = 13 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1053 (x y : BitVec w) : +theorem e_1053 : - 2 * (z ||| ~~~t) + 5 * ~~~z - 6 * ~~~t + 3 * ~~~(z ||| t) - 4 * ~~~(z ||| ~~~t) + 9 * (z &&& ~~~t) + 2 * (z &&& t) = 1 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1054 (x y : BitVec w) : +theorem e_1054 : 1 * (z ||| ~~~t) - 5 * ~~~(z &&& ~~~t) + 7 * ~~~z - 7 * t + 3 * ~~~(z ||| t) + 5 * ~~~(z ||| ~~~t) + 11 * (z &&& t) = 6 * ~~~t - 5 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1055 (x y : BitVec w) : +theorem e_1055 : - 11 * t + 2 * ~~~(z ^^^ t) - 1 * ~~~(z &&& t) + 2 * ~~~(z ||| t) + 15 * ~~~(z ||| ~~~t) - 2 * (z &&& ~~~t) + 12 * (z &&& t) = - 3 * ~~~(z &&& ~~~z) + 6 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1056 (x y : BitVec w) : +theorem e_1056 : - 6 * ~~~(z ^^^ t) - 2 * z - 2 * ~~~t + 3 * ~~~(z ||| t) - 4 * ~~~(z ||| ~~~t) + 4 * (z &&& ~~~t) + 9 * (z &&& t) = 1 * t - 5 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1057 (x y : BitVec w) : +theorem e_1057 : - 2 * (z ||| ~~~t) + 11 * (z ^^^ t) + 3 * ~~~(z ^^^ t) + 7 * ~~~(z &&& t) + 2 * ~~~t - 10 * ~~~(z ||| t) - 17 * (z &&& ~~~t) = 1 * z + 18 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1058 (x y : BitVec w) : +theorem e_1058 : 2 * ~~~(z &&& t) - 1 * ~~~(z &&& ~~~t) - 2 * ~~~(z ^^^ t) - 5 * (z ^^^ t) + 1 * ~~~(z ||| t) + 3 * (z &&& ~~~t) + 3 * (z &&& t) = - 4 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1059 (x y : BitVec w) : +theorem e_1059 : - 2 * ~~~(z ^^^ t) + 1 * ~~~t - 3 * z - 5 * ~~~(z &&& ~~~z) + 6 * ~~~(z ||| t) + 7 * (z &&& ~~~t) + 10 * (z &&& t) = - 5 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1060 (x y : BitVec w) : +theorem e_1060 : 2 * t + 2 * ~~~(z &&& ~~~z) + 1 * ~~~(z &&& t) - 3 * ~~~(z ||| t) - 4 * ~~~(z ||| ~~~t) - 2 * (z &&& ~~~t) - 4 * (z &&& t) = 1 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1061 (x y : BitVec w) : +theorem e_1061 : - 3 * ~~~(z &&& t) - 7 * ~~~(z &&& ~~~t) - 5 * z - 1 * ~~~z + 8 * ~~~(z ||| ~~~t) + 5 * (z &&& ~~~t) + 9 * (z &&& t) = - 3 * (z ||| t) - 11 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1062 (x y : BitVec w) : +theorem e_1062 : 2 * ~~~z + 11 * (z ||| ~~~t) - 5 * (z ||| t) + 7 * t - 7 * ~~~(z ||| t) + 2 * ~~~(z ||| ~~~t) - 7 * (z &&& t) = 6 * ~~~(z &&& ~~~z) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1063 (x y : BitVec w) : +theorem e_1063 : 1 * ~~~(z &&& ~~~z) + 4 * ~~~(z &&& ~~~t) - 11 * ~~~t + 7 * ~~~(z ||| t) - 4 * ~~~(z ||| ~~~t) + 11 * (z &&& ~~~t) - 5 * (z &&& t) = 1 * ~~~(z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1064 (x y : BitVec w) : +theorem e_1064 : - 6 * z - 6 * ~~~t + 4 * ~~~z + 2 * ~~~(z ||| t) + 2 * ~~~(z ||| ~~~t) + 18 * (z &&& ~~~t) + 6 * (z &&& t) = 6 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1065 (x y : BitVec w) : +theorem e_1065 : 1 * ~~~(z &&& t) - 7 * ~~~(z &&& ~~~t) + 1 * (z ||| ~~~t) - 6 * z + 5 * ~~~(z ||| t) + 4 * (z &&& ~~~t) + 12 * (z &&& t) = - 6 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1066 (x y : BitVec w) : +theorem e_1066 : 5 * (z ||| t) + 2 * ~~~z + 1 * ~~~(z &&& ~~~z) + 11 * z - 3 * ~~~(z ||| t) - 9 * ~~~(z ||| ~~~t) - 17 * (z &&& t) = 18 * (z &&& ~~~t) - 1 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1067 (x y : BitVec w) : +theorem e_1067 : - 1 * ~~~(z &&& ~~~t) - 2 * (z ^^^ t) + 4 * z + 2 * ~~~t + 3 * ~~~(z ||| ~~~t) - 4 * (z &&& ~~~t) - 3 * (z &&& t) = 1 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1068 (x y : BitVec w) : +theorem e_1068 : 1 * (z ^^^ t) + 4 * ~~~(z &&& t) + 11 * (z ||| ~~~t) - 2 * ~~~(z &&& ~~~t) + 3 * ~~~(z ||| ~~~t) - 3 * (z &&& ~~~t) - 3 * (z &&& t) = 6 * ~~~(z &&& ~~~z) + 7 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1069 (x y : BitVec w) : +theorem e_1069 : 7 * t - 6 * (z ||| ~~~t) + 2 * ~~~(z ^^^ t) + 4 * ~~~(z ||| t) - 12 * ~~~(z ||| ~~~t) + 1 * (z &&& ~~~t) - 3 * (z &&& t) = - 5 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1070 (x y : BitVec w) : +theorem e_1070 : - 6 * ~~~z - 2 * ~~~(z &&& t) + 5 * (z ||| ~~~t) + 1 * ~~~(z &&& ~~~z) + 4 * ~~~(z ||| t) + 7 * ~~~(z ||| ~~~t) - 4 * (z &&& ~~~t) = 4 * (z &&& t) + 2 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1071 (x y : BitVec w) : +theorem e_1071 : - 11 * (z ||| t) - 2 * z - 5 * (z ||| ~~~t) + 3 * ~~~(z &&& t) + 2 * ~~~(z ||| t) + 8 * ~~~(z ||| ~~~t) + 18 * (z &&& t) = - 15 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1072 (x y : BitVec w) : +theorem e_1072 : - 5 * ~~~z + 2 * t - 2 * (z ||| t) - 2 * ~~~(z &&& ~~~z) + 2 * z + 7 * ~~~(z ||| t) + 7 * ~~~(z ||| ~~~t) = - 2 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1073 (x y : BitVec w) : +theorem e_1073 : 1 * ~~~t + 3 * (z ^^^ t) + 1 * ~~~(z &&& t) + 1 * ~~~z - 3 * ~~~(z ||| t) + 2 * ~~~(z ||| ~~~t) + 7 * (z &&& t) = 5 * (z &&& ~~~t) + 7 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1074 (x y : BitVec w) : +theorem e_1074 : 5 * ~~~z - 11 * ~~~(z ^^^ t) - 2 * t - 2 * (z ^^^ t) + 3 * ~~~t - 4 * ~~~(z ||| ~~~t) - 1 * (z &&& ~~~t) = - 10 * (z &&& t) - 3 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1075 (x y : BitVec w) : +theorem e_1075 : - 11 * ~~~(z &&& t) + 5 * ~~~(z &&& ~~~t) - 11 * z + 4 * ~~~(z &&& ~~~z) - 3 * ~~~(z ||| t) - 3 * ~~~(z ||| ~~~t) + 18 * (z &&& ~~~t) = - 2 * (z &&& t) - 5 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1076 (x y : BitVec w) : +theorem e_1076 : - 6 * t + 2 * (z ||| t) - 6 * ~~~(z &&& ~~~t) - 1 * ~~~(z ||| t) + 10 * ~~~(z ||| ~~~t) - 9 * (z &&& ~~~t) + 3 * (z &&& t) = - 7 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1077 (x y : BitVec w) : +theorem e_1077 : - 1 * (z ||| ~~~t) + 1 * ~~~z + 2 * (z ||| t) - 7 * ~~~(z ||| t) - 10 * ~~~(z ||| ~~~t) - 8 * (z &&& ~~~t) - 8 * (z &&& t) = - 7 * ~~~(z &&& ~~~z) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1078 (x y : BitVec w) : +theorem e_1078 : - 2 * ~~~z + 1 * ~~~(z &&& ~~~z) - 3 * z - 1 * ~~~(z &&& ~~~t) + 7 * (z ||| t) + 2 * ~~~(z ||| t) + 6 * ~~~(z ||| ~~~t) - 5 * (z &&& ~~~t) = - 7 * (z &&& t) + 11 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1079 (x y : BitVec w) : +theorem e_1079 : 3 * ~~~z - 5 * (z ^^^ t) + 5 * ~~~t - 6 * (z ||| t) - 3 * ~~~(z &&& ~~~t) - 8 * ~~~(z ||| t) + 11 * ~~~(z ||| ~~~t) + 6 * (z &&& t) = - 3 * (z &&& ~~~t) - 3 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1080 (x y : BitVec w) : +theorem e_1080 : - 6 * (z ||| ~~~t) - 6 * ~~~t - 6 * t - 1 * ~~~(z &&& ~~~z) - 11 * (z ^^^ t) + 18 * ~~~(z ||| ~~~t) + 24 * (z &&& ~~~t) + 13 * (z &&& t) = - 13 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1081 (x y : BitVec w) : +theorem e_1081 : - 1 * ~~~(z ^^^ t) + 4 * ~~~(z &&& t) - 2 * ~~~(z &&& ~~~t) - 3 * t + 1 * ~~~(z ||| t) + 3 * ~~~(z ||| ~~~t) - 4 * (z &&& ~~~t) + 6 * (z &&& t) = 2 * ~~~(z &&& ~~~z) - 2 * z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1082 (x y : BitVec w) : +theorem e_1082 : - 3 * ~~~z - 3 * ~~~(z &&& ~~~t) + 11 * (z ||| ~~~t) + 7 * ~~~(z &&& ~~~z) + 2 * (z ||| t) - 15 * ~~~(z ||| t) - 3 * ~~~(z ||| ~~~t) - 23 * (z &&& ~~~t) = - 3 * ~~~t + 17 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1083 (x y : BitVec w) : +theorem e_1083 : 2 * ~~~z - 2 * ~~~(z ^^^ t) - 2 * t + 1 * (z ||| ~~~t) - 1 * ~~~(z &&& ~~~t) + 4 * ~~~(z &&& ~~~z) - 5 * ~~~(z ||| ~~~t) - 7 * (z &&& ~~~t) = - 2 * (z ^^^ t) + 4 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1084 (x y : BitVec w) : +theorem e_1084 : - 6 * t + 1 * ~~~(z &&& t) + 1 * z - 6 * ~~~(z ^^^ t) - 1 * (z ||| t) + 5 * ~~~(z ||| t) + 6 * ~~~(z ||| ~~~t) - 1 * (z &&& ~~~t) = - 12 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1085 (x y : BitVec w) : +theorem e_1085 : 4 * t + 1 * ~~~t - 7 * ~~~(z ^^^ t) + 5 * ~~~z + 4 * z + 1 * ~~~(z ||| t) - 9 * ~~~(z ||| ~~~t) - 1 * (z &&& t) = 5 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1086 (x y : BitVec w) : +theorem e_1086 : - 6 * ~~~(z ^^^ t) - 11 * ~~~z - 6 * t + 7 * ~~~(z &&& ~~~z) - 1 * (z ||| ~~~t) + 11 * ~~~(z ||| t) + 10 * ~~~(z ||| ~~~t) - 6 * (z &&& ~~~t) = - 6 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1087 (x y : BitVec w) : +theorem e_1087 : 2 * z - 1 * ~~~(z &&& ~~~t) + 2 * ~~~(z &&& t) + 5 * (z ||| ~~~t) + 4 * ~~~z - 4 * ~~~(z ||| t) - 5 * ~~~(z ||| ~~~t) - 9 * (z &&& ~~~t) = 6 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1088 (x y : BitVec w) : +theorem e_1088 : - 7 * ~~~(z ^^^ t) - 2 * ~~~z + 4 * ~~~(z &&& ~~~z) - 1 * ~~~(z &&& ~~~t) + 1 * ~~~(z &&& t) + 5 * ~~~(z ||| t) - 5 * (z &&& ~~~t) + 4 * (z &&& t) = 2 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1089 (x y : BitVec w) : +theorem e_1089 : 3 * ~~~(z &&& ~~~z) + 1 * ~~~z - 3 * ~~~(z &&& t) - 2 * (z ||| ~~~t) - 1 * ~~~(z &&& ~~~t) + 7 * ~~~(z ||| t) + 2 * (z &&& ~~~t) + 5 * (z &&& t) = 5 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1090 (x y : BitVec w) : +theorem e_1090 : 1 * ~~~(z ^^^ t) + 3 * z + 2 * ~~~(z &&& ~~~t) - 5 * ~~~t - 2 * ~~~z + 5 * ~~~(z ||| t) + 3 * (z &&& ~~~t) - 5 * (z &&& t) = 1 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1091 (x y : BitVec w) : +theorem e_1091 : 11 * t - 3 * (z ^^^ t) + 7 * ~~~(z &&& ~~~z) - 3 * ~~~(z ^^^ t) + 2 * ~~~(z &&& t) - 14 * ~~~(z ||| ~~~t) - 6 * (z &&& ~~~t) - 12 * (z &&& t) = 3 * ~~~(z ||| t) + 3 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1092 (x y : BitVec w) : +theorem e_1092 : 4 * ~~~z - 7 * (z ||| t) - 3 * ~~~(z &&& ~~~t) + 2 * t + 4 * ~~~(z ^^^ t) - 2 * ~~~(z ||| t) + 10 * (z &&& ~~~t) + 7 * (z &&& t) = - 7 * ~~~(z ||| ~~~t) + 3 * ~~~(z &&& ~~~z) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1093 (x y : BitVec w) : +theorem e_1093 : 5 * ~~~(z &&& ~~~t) - 5 * ~~~t + 1 * t + 2 * (z ||| t) - 1 * ~~~(z ||| t) - 9 * ~~~(z ||| ~~~t) + 2 * (z &&& ~~~t) - 8 * (z &&& t) = - 1 * ~~~(z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1094 (x y : BitVec w) : +theorem e_1094 : 2 * (z ||| t) - 1 * ~~~(z &&& t) - 5 * (z ||| ~~~t) - 11 * t - 3 * ~~~t + 16 * ~~~(z ||| t) + 14 * (z &&& ~~~t) + 21 * (z &&& t) = 7 * ~~~(z &&& ~~~z) - 17 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1095 (x y : BitVec w) : +theorem e_1095 : 5 * ~~~z + 2 * ~~~(z &&& t) + 4 * z + 2 * ~~~(z &&& ~~~t) - 9 * ~~~(z ||| t) - 10 * ~~~(z ||| ~~~t) - 7 * (z &&& ~~~t) - 7 * (z &&& t) = - 1 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1096 (x y : BitVec w) : +theorem e_1096 : - 7 * (z ^^^ t) - 5 * ~~~(z &&& ~~~t) - 1 * t - 1 * (z ||| ~~~t) + 8 * ~~~(z ||| t) + 13 * ~~~(z ||| ~~~t) + 10 * (z &&& ~~~t) + 7 * (z &&& t) = 2 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1097 (x y : BitVec w) : +theorem e_1097 : - 2 * z - 3 * (z ||| ~~~t) - 1 * (z ||| t) + 4 * ~~~z - 4 * ~~~(z ||| t) - 6 * ~~~(z ||| ~~~t) + 3 * (z &&& ~~~t) + 3 * (z &&& t) = - 3 * ~~~(z &&& ~~~z) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1098 (x y : BitVec w) : +theorem e_1098 : 7 * ~~~t + 5 * ~~~(z &&& t) - 3 * ~~~z + 11 * z - 3 * ~~~(z ||| t) + 4 * ~~~(z ||| ~~~t) - 23 * (z &&& ~~~t) - 5 * (z &&& t) = 6 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1099 (x y : BitVec w) : +theorem e_1099 : 11 * ~~~z - 6 * ~~~(z ^^^ t) - 5 * z + 1 * ~~~(z &&& ~~~z) + 7 * t + 4 * (z ^^^ t) - 6 * ~~~(z ||| t) + 3 * (z &&& t) = 23 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1100 (x y : BitVec w) : +theorem e_1100 : - 6 * z - 3 * ~~~(z &&& ~~~t) - 1 * t - 1 * (z ^^^ t) + 2 * ~~~z + 3 * ~~~(z &&& t) + 5 * ~~~(z ||| t) + 10 * (z &&& t) = - 11 * (z &&& ~~~t) + 7 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1101 (x y : BitVec w) : +theorem e_1101 : - 2 * ~~~(z ^^^ t) - 1 * ~~~t - 5 * ~~~(z &&& t) + 5 * ~~~(z &&& ~~~t) + 11 * ~~~z - 5 * z - 8 * ~~~(z ||| t) + 2 * (z &&& t) = - 11 * (z &&& ~~~t) + 11 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1102 (x y : BitVec w) : +theorem e_1102 : 4 * (z ||| t) - 2 * ~~~z + 1 * ~~~t - 2 * ~~~(z ^^^ t) + 7 * ~~~(z &&& ~~~z) - 1 * z - 11 * (z &&& ~~~t) - 8 * (z &&& t) = 9 * ~~~(z ||| ~~~t) + 4 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1103 (x y : BitVec w) : +theorem e_1103 : - 1 * ~~~(z &&& t) + 2 * (z ^^^ t) + 11 * ~~~t + 5 * ~~~(z &&& ~~~z) - 1 * (z ||| ~~~t) - 14 * ~~~(z ||| t) - 6 * ~~~(z ||| ~~~t) - 16 * (z &&& ~~~t) = 4 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1104 (x y : BitVec w) : +theorem e_1104 : - 2 * ~~~(z &&& t) + 5 * ~~~(z ^^^ t) - 2 * ~~~(z &&& ~~~z) - 2 * (z ||| t) - 6 * (z ^^^ t) - 1 * ~~~(z ||| t) + 12 * (z &&& ~~~t) - 1 * (z &&& t) = - 12 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1105 (x y : BitVec w) : +theorem e_1105 : - 2 * z + 2 * ~~~(z ^^^ t) + 1 * ~~~(z &&& ~~~z) - 5 * ~~~z - 1 * (z ||| t) + 1 * (z ^^^ t) + 2 * ~~~(z ||| t) + 1 * (z &&& ~~~t) = - 4 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1106 (x y : BitVec w) : +theorem e_1106 : - 5 * z + 3 * ~~~z - 7 * ~~~(z &&& ~~~t) + 5 * t - 5 * ~~~(z &&& ~~~z) + 4 * ~~~(z ||| ~~~t) + 12 * (z &&& ~~~t) + 12 * (z &&& t) = - 11 * ~~~(z ||| t) + 2 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1107 (x y : BitVec w) : +theorem e_1107 : 11 * (z ^^^ t) + 11 * ~~~z - 1 * (z ||| ~~~t) - 3 * ~~~(z ^^^ t) - 12 * ~~~(z ||| t) - 20 * ~~~(z ||| ~~~t) - 15 * (z &&& ~~~t) + 11 * (z &&& t) = - 5 * ~~~(z &&& t) + 7 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1108 (x y : BitVec w) : +theorem e_1108 : 1 * (z ||| ~~~t) - 1 * ~~~z + 4 * ~~~t - 1 * ~~~(z ^^^ t) - 3 * ~~~(z ||| t) - 1 * ~~~(z ||| ~~~t) - 7 * (z &&& ~~~t) - 2 * (z &&& t) = - 2 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1109 (x y : BitVec w) : +theorem e_1109 : 1 * ~~~(z &&& ~~~z) - 6 * ~~~z + 4 * (z ||| t) + 11 * (z ||| ~~~t) + 11 * z - 6 * ~~~(z ||| t) + 1 * ~~~(z ||| ~~~t) - 27 * (z &&& t) = 27 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1110 (x y : BitVec w) : +theorem e_1110 : - 7 * (z ||| ~~~t) - 11 * ~~~(z &&& t) + 1 * z - 1 * ~~~(z ^^^ t) - 6 * t + 19 * ~~~(z ||| t) + 17 * (z &&& ~~~t) + 13 * (z &&& t) = - 17 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1111 (x y : BitVec w) : +theorem e_1111 : - 1 * ~~~(z ^^^ t) - 2 * (z ||| t) - 5 * (z ||| ~~~t) - 1 * ~~~(z &&& ~~~z) - 2 * ~~~(z &&& ~~~t) - 2 * ~~~t + 11 * ~~~(z ||| t) + 11 * (z &&& t) = - 10 * (z &&& ~~~t) - 5 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1112 (x y : BitVec w) : +theorem e_1112 : - 11 * ~~~(z &&& ~~~t) - 1 * (z ||| t) - 7 * ~~~(z &&& t) - 5 * ~~~(z &&& ~~~z) - 7 * z + 23 * ~~~(z ||| t) + 24 * ~~~(z ||| ~~~t) + 24 * (z &&& t) = - 20 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1113 (x y : BitVec w) : +theorem e_1113 : - 11 * z + 1 * ~~~(z &&& t) + 2 * ~~~t + 1 * ~~~(z &&& ~~~t) - 4 * ~~~(z ||| t) - 1 * ~~~(z ||| ~~~t) + 9 * (z &&& ~~~t) + 11 * (z &&& t) = 1 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1114 (x y : BitVec w) : +theorem e_1114 : - 5 * ~~~(z ^^^ t) + 7 * (z ^^^ t) + 5 * ~~~(z &&& ~~~z) - 11 * (z ||| t) - 2 * (z ||| ~~~t) + 3 * ~~~(z ||| t) - 1 * ~~~(z ||| ~~~t) + 13 * (z &&& t) = 1 * ~~~t - 2 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1115 (x y : BitVec w) : +theorem e_1115 : - 5 * (z ||| t) + 4 * ~~~(z &&& t) - 3 * ~~~(z &&& ~~~t) + 1 * t - 10 * ~~~(z ||| t) + 3 * ~~~(z ||| ~~~t) - 6 * (z &&& ~~~t) - 2 * (z &&& t) = - 2 * ~~~(z ^^^ t) - 7 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1116 (x y : BitVec w) : +theorem e_1116 : 4 * ~~~(z &&& ~~~z) - 1 * (z ^^^ t) + 1 * ~~~(z &&& t) - 7 * ~~~t - 11 * (z ||| t) + 1 * ~~~(z ||| t) + 14 * (z &&& ~~~t) + 6 * (z &&& t) = - 7 * ~~~(z ||| ~~~t) - 1 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1117 (x y : BitVec w) : +theorem e_1117 : 2 * ~~~(z &&& t) - 3 * ~~~(z &&& ~~~z) + 1 * t - 5 * (z ||| ~~~t) - 1 * ~~~(z &&& ~~~t) + 7 * ~~~(z ||| t) + 6 * (z &&& ~~~t) + 8 * (z &&& t) = - 1 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1118 (x y : BitVec w) : +theorem e_1118 : - 3 * z - 2 * ~~~(z &&& t) + 11 * ~~~t + 3 * t - 4 * ~~~(z ||| t) - 1 * ~~~(z ||| ~~~t) - 6 * (z &&& ~~~t) + 5 * (z &&& t) = 5 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1119 (x y : BitVec w) : +theorem e_1119 : - 1 * ~~~z + 1 * t + 7 * ~~~t - 7 * z - 7 * ~~~(z ||| t) + 5 * ~~~(z ||| ~~~t) + 5 * (z &&& ~~~t) + 10 * (z &&& t) = 5 * (z ||| t) - 1 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1120 (x y : BitVec w) : +theorem e_1120 : - 3 * (z ||| t) + 7 * ~~~(z &&& t) + 2 * ~~~(z &&& ~~~t) + 1 * ~~~z + 3 * (z ^^^ t) - 10 * ~~~(z ||| t) - 10 * ~~~(z ||| ~~~t) - 8 * (z &&& ~~~t) = - 1 * z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1121 (x y : BitVec w) : +theorem e_1121 : - 6 * ~~~(z &&& ~~~z) + 3 * (z ||| t) - 7 * z + 3 * (z ||| ~~~t) + 1 * ~~~(z &&& ~~~t) + 3 * ~~~(z ||| t) + 2 * ~~~(z ||| ~~~t) + 7 * (z &&& t) = 1 * ~~~(z ^^^ t) - 7 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1122 (x y : BitVec w) : +theorem e_1122 : - 11 * ~~~t + 1 * ~~~(z &&& ~~~z) - 6 * ~~~(z ^^^ t) - 1 * (z ||| t) + 1 * (z ||| ~~~t) + 13 * ~~~(z ||| t) + 8 * (z &&& ~~~t) + 5 * (z &&& t) = - 2 * ~~~(z &&& t) + 2 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1123 (x y : BitVec w) : +theorem e_1123 : 5 * z + 5 * (z ||| ~~~t) - 11 * t + 2 * ~~~(z &&& t) + 4 * ~~~z - 11 * ~~~(z ||| t) - 11 * (z &&& ~~~t) + 1 * (z &&& t) = 1 * (z ^^^ t) - 6 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1124 (x y : BitVec w) : +theorem e_1124 : 5 * z - 1 * ~~~(z &&& ~~~t) - 1 * (z ^^^ t) + 7 * ~~~t + 1 * t - 5 * ~~~(z ^^^ t) - 2 * ~~~(z ||| t) - 11 * (z &&& ~~~t) = - 1 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1125 (x y : BitVec w) : +theorem e_1125 : 4 * t + 1 * (z ^^^ t) + 7 * ~~~(z &&& ~~~z) - 11 * ~~~t - 1 * ~~~z - 11 * ~~~(z ||| ~~~t) + 3 * (z &&& ~~~t) - 11 * (z &&& t) = - 5 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1126 (x y : BitVec w) : +theorem e_1126 : - 3 * ~~~z - 2 * ~~~(z &&& t) + 2 * (z ^^^ t) + 3 * (z ||| ~~~t) + 2 * ~~~(z ||| t) - 2 * ~~~(z ||| ~~~t) - 8 * (z &&& ~~~t) - 8 * (z &&& t) = - 5 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1127 (x y : BitVec w) : +theorem e_1127 : 5 * ~~~(z &&& t) - 3 * ~~~z + 2 * ~~~(z &&& ~~~z) + 4 * ~~~t - 8 * ~~~(z ||| t) - 9 * ~~~(z ||| ~~~t) - 27 * (z &&& ~~~t) - 18 * (z &&& t) = - 5 * (z ||| t) - 11 * z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1128 (x y : BitVec w) : +theorem e_1128 : 7 * (z ^^^ t) + 1 * ~~~(z ^^^ t) - 7 * ~~~z - 3 * ~~~(z &&& t) + 11 * t + 9 * ~~~(z ||| t) - 8 * ~~~(z ||| ~~~t) - 4 * (z &&& ~~~t) = 12 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1129 (x y : BitVec w) : +theorem e_1129 : - 1 * (z ||| ~~~t) + 5 * ~~~(z ^^^ t) + 5 * ~~~(z &&& ~~~z) + 11 * t - 3 * ~~~z - 6 * ~~~(z ||| t) - 4 * (z &&& ~~~t) - 20 * (z &&& t) = 13 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1130 (x y : BitVec w) : +theorem e_1130 : 11 * ~~~z + 3 * z + 5 * (z ^^^ t) + 7 * (z ||| t) - 10 * ~~~(z ||| t) - 22 * ~~~(z ||| ~~~t) - 15 * (z &&& ~~~t) - 9 * (z &&& t) = 1 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1131 (x y : BitVec w) : +theorem e_1131 : 5 * ~~~(z &&& ~~~t) + 1 * ~~~z + 11 * ~~~t + 1 * (z ||| t) - 16 * ~~~(z ||| t) - 7 * ~~~(z ||| ~~~t) - 11 * (z &&& ~~~t) - 5 * (z &&& t) = 1 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1132 (x y : BitVec w) : +theorem e_1132 : 4 * ~~~(z &&& t) - 11 * t + 11 * ~~~(z &&& ~~~z) - 2 * (z ||| ~~~t) - 1 * (z ^^^ t) - 6 * ~~~t - 4 * ~~~(z ||| t) - 6 * (z &&& ~~~t) = - 2 * (z &&& t) + 3 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1133 (x y : BitVec w) : +theorem e_1133 : - 11 * z + 4 * ~~~t - 2 * ~~~z - 1 * ~~~(z ^^^ t) - 1 * (z ^^^ t) + 4 * ~~~(z ||| t) + 3 * ~~~(z ||| ~~~t) + 17 * (z &&& t) = 5 * (z ||| ~~~t) - 13 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1134 (x y : BitVec w) : +theorem e_1134 : - 3 * ~~~(z ^^^ t) + 1 * (z ||| ~~~t) - 6 * ~~~t - 7 * z + 8 * ~~~(z ||| t) + 1 * ~~~(z ||| ~~~t) + 13 * (z &&& ~~~t) + 10 * (z &&& t) = 1 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1135 (x y : BitVec w) : +theorem e_1135 : - 1 * ~~~(z &&& t) + 4 * ~~~t + 1 * ~~~z + 1 * ~~~(z &&& ~~~z) - 5 * ~~~(z ||| t) + 1 * ~~~(z ||| ~~~t) - 4 * (z &&& ~~~t) + 1 * (z &&& t) = 2 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1136 (x y : BitVec w) : +theorem e_1136 : 2 * (z ||| ~~~t) - 7 * ~~~t - 1 * (z ||| t) - 2 * (z ^^^ t) + 1 * ~~~(z &&& ~~~t) + 4 * ~~~(z ||| t) + 2 * ~~~(z ||| ~~~t) + 9 * (z &&& t) = 11 * z - 19 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1137 (x y : BitVec w) : +theorem e_1137 : 2 * z - 1 * (z ||| t) + 3 * (z ||| ~~~t) - 5 * ~~~(z ^^^ t) + 1 * ~~~(z ||| t) + 1 * ~~~(z ||| ~~~t) - 5 * (z &&& ~~~t) + 1 * (z &&& t) = - 1 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1138 (x y : BitVec w) : +theorem e_1138 : 5 * ~~~(z &&& t) - 2 * ~~~t - 1 * (z ||| t) + 1 * ~~~(z &&& ~~~t) - 1 * ~~~(z &&& ~~~z) - 3 * ~~~(z ||| t) - 1 * (z &&& ~~~t) + 1 * (z &&& t) = 4 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1139 (x y : BitVec w) : +theorem e_1139 : - 3 * z + 3 * ~~~z + 1 * ~~~(z ^^^ t) - 7 * (z ||| t) + 3 * ~~~(z &&& ~~~z) - 6 * ~~~t - 2 * ~~~(z ||| t) + 5 * (z &&& t) = - 1 * ~~~(z &&& ~~~t) - 13 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1140 (x y : BitVec w) : +theorem e_1140 : 5 * (z ||| t) - 2 * ~~~(z &&& ~~~z) + 2 * (z ||| ~~~t) - 11 * ~~~(z ^^^ t) + 4 * (z ^^^ t) - 7 * z - 7 * ~~~(z ||| ~~~t) - 2 * (z &&& ~~~t) = - 13 * (z &&& t) - 11 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1141 (x y : BitVec w) : +theorem e_1141 : 4 * t - 1 * z + 5 * ~~~(z &&& ~~~z) + 4 * (z ||| ~~~t) + 7 * ~~~(z &&& t) - 16 * ~~~(z ||| t) - 16 * (z &&& ~~~t) - 12 * (z &&& t) = - 1 * (z ^^^ t) + 17 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1142 (x y : BitVec w) : +theorem e_1142 : - 1 * ~~~(z &&& ~~~z) + 1 * t - 11 * (z ^^^ t) - 2 * ~~~(z ^^^ t) + 8 * ~~~(z ||| t) + 16 * ~~~(z ||| ~~~t) + 17 * (z &&& ~~~t) + 2 * (z &&& t) = 5 * ~~~(z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1143 (x y : BitVec w) : +theorem e_1143 : 7 * t + 7 * (z ||| t) + 1 * ~~~z + 5 * (z ^^^ t) - 10 * ~~~(z ||| t) - 27 * ~~~(z ||| ~~~t) - 21 * (z &&& ~~~t) - 14 * (z &&& t) = - 7 * ~~~(z &&& t) - 2 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1144 (x y : BitVec w) : +theorem e_1144 : 2 * z - 3 * (z ||| t) + 1 * ~~~(z &&& ~~~z) - 1 * t - 1 * ~~~(z ||| t) + 6 * ~~~(z ||| ~~~t) + 3 * (z &&& ~~~t) + 1 * (z &&& t) = 3 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1145 (x y : BitVec w) : +theorem e_1145 : 1 * ~~~(z ^^^ t) - 3 * ~~~z + 1 * ~~~(z &&& ~~~t) + 1 * (z ^^^ t) + 1 * (z ||| t) + 3 * z + 1 * ~~~(z ||| t) - 6 * (z &&& t) = 5 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1146 (x y : BitVec w) : +theorem e_1146 : - 1 * ~~~(z &&& t) - 5 * (z ^^^ t) + 2 * ~~~(z &&& ~~~z) + 2 * z + 2 * t - 1 * ~~~(z ||| t) + 2 * (z &&& ~~~t) - 6 * (z &&& t) = - 2 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1147 (x y : BitVec w) : +theorem e_1147 : - 2 * ~~~(z ^^^ t) + 7 * ~~~(z &&& ~~~t) + 11 * ~~~(z &&& t) + 1 * ~~~(z &&& ~~~z) + 7 * (z ||| ~~~t) - 21 * ~~~(z ||| t) - 16 * (z &&& ~~~t) - 13 * (z &&& t) = 19 * ~~~(z ||| ~~~t) + 3 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1148 (x y : BitVec w) : +theorem e_1148 : - 7 * (z ^^^ t) - 6 * ~~~(z &&& ~~~z) + 11 * (z ||| ~~~t) - 1 * ~~~z - 1 * ~~~(z ^^^ t) + 16 * ~~~(z ||| ~~~t) + 2 * (z &&& ~~~t) - 2 * (z &&& t) = 2 * ~~~(z &&& ~~~t) + 1 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1149 (x y : BitVec w) : +theorem e_1149 : 11 * (z ^^^ t) + 3 * ~~~(z &&& t) - 3 * ~~~(z ^^^ t) - 11 * (z ||| ~~~t) + 5 * ~~~z - 19 * ~~~(z ||| ~~~t) - 4 * (z &&& ~~~t) + 14 * (z &&& t) = - 1 * ~~~t - 5 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1150 (x y : BitVec w) : +theorem e_1150 : 1 * ~~~t - 3 * ~~~(z &&& t) + 2 * (z ||| t) + 7 * z + 11 * ~~~z - 14 * ~~~(z ||| t) - 15 * ~~~(z ||| ~~~t) - 14 * (z &&& t) = 12 * (z &&& ~~~t) - 5 * ~~~(z &&& ~~~z) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1151 (x y : BitVec w) : +theorem e_1151 : 4 * ~~~(z ^^^ t) - 7 * z + 11 * ~~~z - 5 * ~~~(z &&& t) - 1 * ~~~(z &&& ~~~z) - 9 * ~~~(z ||| t) + 14 * (z &&& ~~~t) + 5 * (z &&& t) = 1 * (z ||| t) + 4 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1152 (x y : BitVec w) : +theorem e_1152 : - 1 * (z ^^^ t) - 7 * (z ||| t) + 5 * ~~~z - 1 * ~~~t + 1 * ~~~(z &&& ~~~z) - 5 * ~~~(z ||| t) + 2 * ~~~(z ||| ~~~t) + 8 * (z &&& ~~~t) = - 6 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1153 (x y : BitVec w) : +theorem e_1153 : 5 * (z ^^^ t) - 11 * z - 1 * (z ||| t) + 7 * ~~~(z &&& ~~~z) - 5 * ~~~(z &&& ~~~t) - 2 * t - 2 * ~~~(z ||| t) + 12 * (z &&& t) = 4 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1154 (x y : BitVec w) : +theorem e_1154 : - 1 * ~~~(z &&& ~~~t) + 11 * ~~~z - 2 * (z ||| ~~~t) - 3 * (z ^^^ t) - 6 * t - 6 * ~~~(z ||| t) + 1 * ~~~(z ||| ~~~t) + 11 * (z &&& t) = - 7 * (z &&& ~~~t) + 2 * ~~~(z &&& ~~~z) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1155 (x y : BitVec w) : +theorem e_1155 : 11 * (z ||| ~~~t) + 5 * t - 11 * z + 1 * ~~~(z ^^^ t) - 12 * ~~~(z ||| t) - 6 * ~~~(z ||| ~~~t) - 1 * (z &&& ~~~t) - 6 * (z &&& t) = - 1 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1156 (x y : BitVec w) : +theorem e_1156 : - 6 * ~~~(z &&& ~~~t) + 1 * ~~~(z &&& t) - 7 * ~~~(z ^^^ t) - 1 * t - 1 * (z ||| ~~~t) - 5 * z + 13 * ~~~(z ||| t) + 6 * ~~~(z ||| ~~~t) = - 20 * (z &&& t) - 5 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1157 (x y : BitVec w) : +theorem e_1157 : - 3 * t + 2 * (z ^^^ t) - 6 * ~~~t + 1 * z + 7 * ~~~(z ||| t) + 1 * ~~~(z ||| ~~~t) + 3 * (z &&& ~~~t) + 3 * (z &&& t) = 1 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1158 (x y : BitVec w) : +theorem e_1158 : 1 * ~~~(z &&& ~~~t) - 2 * (z ||| ~~~t) + 2 * (z ^^^ t) - 1 * ~~~(z &&& ~~~z) + 2 * ~~~(z ||| t) - 2 * ~~~(z ||| ~~~t) + 7 * (z &&& ~~~t) + 8 * (z &&& t) = 6 * z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1159 (x y : BitVec w) : +theorem e_1159 : - 7 * ~~~t - 5 * t - 11 * z - 1 * ~~~(z &&& t) - 2 * ~~~z + 8 * ~~~(z ||| t) + 8 * ~~~(z ||| ~~~t) + 17 * (z &&& ~~~t) = - 14 * (z &&& t) - 2 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1160 (x y : BitVec w) : +theorem e_1160 : 1 * ~~~z - 5 * (z ^^^ t) + 11 * (z ||| t) + 1 * ~~~t - 10 * ~~~(z ||| t) - 8 * ~~~(z ||| ~~~t) - 15 * (z &&& ~~~t) - 18 * (z &&& t) = - 1 * ~~~(z &&& t) - 7 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1161 (x y : BitVec w) : +theorem e_1161 : 5 * ~~~(z &&& ~~~t) - 6 * ~~~z - 1 * ~~~(z &&& ~~~z) - 1 * ~~~t - 7 * (z ||| t) + 3 * ~~~(z ||| t) + 15 * ~~~(z ||| ~~~t) + 9 * (z &&& t) = - 9 * (z &&& ~~~t) + 6 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1162 (x y : BitVec w) : +theorem e_1162 : - 2 * (z ||| ~~~t) + 4 * (z ||| t) + 1 * ~~~(z &&& t) - 11 * ~~~(z ^^^ t) - 6 * ~~~(z &&& ~~~t) + 18 * ~~~(z ||| t) + 1 * ~~~(z ||| ~~~t) - 2 * (z &&& ~~~t) = - 16 * (z &&& t) + 1 * z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1163 (x y : BitVec w) : +theorem e_1163 : 3 * (z ||| ~~~t) + 11 * ~~~z + 1 * (z ^^^ t) - 2 * ~~~(z &&& ~~~t) + 7 * (z ||| t) + 2 * t - 1 * ~~~(z ||| t) - 10 * (z &&& t) = 11 * ~~~(z &&& t) + 8 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1164 (x y : BitVec w) : +theorem e_1164 : 11 * ~~~(z &&& ~~~z) + 2 * (z ^^^ t) - 7 * ~~~(z &&& t) + 5 * t - 2 * ~~~(z ||| t) - 11 * ~~~(z ||| ~~~t) - 4 * (z &&& ~~~t) - 14 * (z &&& t) = 2 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1165 (x y : BitVec w) : +theorem e_1165 : - 1 * z - 6 * ~~~t - 1 * (z ||| t) - 5 * (z ||| ~~~t) + 4 * ~~~(z &&& ~~~z) - 7 * ~~~z + 14 * ~~~(z ||| t) + 3 * (z &&& t) = - 9 * (z &&& ~~~t) - 4 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1166 (x y : BitVec w) : +theorem e_1166 : - 1 * z - 2 * t + 5 * (z ||| ~~~t) - 6 * (z ||| t) - 4 * ~~~(z ||| t) + 8 * ~~~(z ||| ~~~t) + 3 * (z &&& ~~~t) + 4 * (z &&& t) = 1 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1167 (x y : BitVec w) : +theorem e_1167 : - 11 * (z ||| ~~~t) + 2 * ~~~(z &&& t) - 6 * (z ||| t) - 11 * ~~~z + 16 * ~~~(z ||| t) + 11 * ~~~(z ||| ~~~t) + 15 * (z &&& ~~~t) + 13 * (z &&& t) = - 4 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1168 (x y : BitVec w) : +theorem e_1168 : - 1 * t + 4 * ~~~t + 5 * ~~~(z ^^^ t) - 11 * ~~~(z &&& ~~~t) + 13 * ~~~(z ||| t) + 23 * ~~~(z ||| ~~~t) + 7 * (z &&& ~~~t) + 7 * (z &&& t) = 11 * ~~~(z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1169 (x y : BitVec w) : +theorem e_1169 : 1 * ~~~(z &&& ~~~z) - 1 * ~~~(z &&& ~~~t) - 7 * ~~~z + 1 * t - 2 * ~~~(z ||| t) + 6 * ~~~(z ||| ~~~t) - 8 * (z &&& ~~~t) - 10 * (z &&& t) = - 2 * ~~~(z ^^^ t) - 7 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1170 (x y : BitVec w) : +theorem e_1170 : 2 * (z ^^^ t) - 3 * ~~~(z &&& ~~~z) - 6 * z - 7 * ~~~(z &&& ~~~t) - 6 * ~~~t + 16 * ~~~(z ||| t) + 13 * (z &&& ~~~t) + 16 * (z &&& t) = - 8 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1171 (x y : BitVec w) : +theorem e_1171 : 1 * ~~~z + 11 * (z ||| t) - 2 * ~~~(z &&& t) + 11 * (z ||| ~~~t) - 7 * z - 10 * ~~~(z ||| ~~~t) - 13 * (z &&& ~~~t) - 15 * (z &&& t) = 10 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1172 (x y : BitVec w) : +theorem e_1172 : 5 * (z ||| ~~~t) - 5 * ~~~z - 5 * ~~~t + 4 * ~~~(z &&& ~~~t) + 1 * ~~~(z ||| t) + 12 * ~~~(z ||| ~~~t) + 11 * (z &&& ~~~t) + 2 * (z &&& t) = 11 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1173 (x y : BitVec w) : +theorem e_1173 : 2 * ~~~(z &&& ~~~t) - 1 * ~~~(z &&& ~~~z) - 5 * ~~~(z ^^^ t) + 7 * (z ^^^ t) + 2 * ~~~(z ||| t) - 21 * ~~~(z ||| ~~~t) - 17 * (z &&& ~~~t) - 7 * (z &&& t) = - 11 * (z ||| t) - 2 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1174 (x y : BitVec w) : +theorem e_1174 : - 1 * ~~~(z &&& ~~~t) + 3 * ~~~z + 2 * t - 7 * ~~~(z ^^^ t) + 6 * ~~~(z ||| t) - 3 * ~~~(z ||| ~~~t) + 1 * (z &&& ~~~t) + 6 * (z &&& t) = 1 * ~~~(z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1175 (x y : BitVec w) : +theorem e_1175 : 7 * ~~~(z &&& t) - 7 * z - 1 * (z ||| t) - 1 * ~~~(z ^^^ t) - 6 * ~~~z + 4 * (z ||| ~~~t) - 3 * (z &&& ~~~t) + 5 * (z &&& t) = 4 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1176 (x y : BitVec w) : +theorem e_1176 : - 5 * (z ||| ~~~t) + 4 * ~~~(z ^^^ t) + 3 * ~~~z + 1 * ~~~(z &&& ~~~t) + 1 * ~~~(z &&& t) - 4 * ~~~(z ||| t) - 4 * ~~~(z ||| ~~~t) + 5 * (z &&& ~~~t) = - 1 * (z &&& t) + 1 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1177 (x y : BitVec w) : +theorem e_1177 : - 11 * ~~~(z ^^^ t) - 1 * ~~~t + 7 * ~~~z - 2 * ~~~(z &&& ~~~z) + 7 * ~~~(z ||| t) - 7 * ~~~(z ||| ~~~t) + 3 * (z &&& ~~~t) + 11 * (z &&& t) = - 2 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1178 (x y : BitVec w) : +theorem e_1178 : - 5 * (z ||| t) - 6 * z + 1 * (z ||| ~~~t) - 1 * ~~~(z &&& t) + 8 * ~~~(z ||| t) + 12 * ~~~(z ||| ~~~t) + 13 * (z &&& ~~~t) + 10 * (z &&& t) = 6 * ~~~z + 2 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1179 (x y : BitVec w) : +theorem e_1179 : - 1 * ~~~(z &&& ~~~z) - 7 * (z ||| ~~~t) + 4 * ~~~z + 7 * ~~~(z ^^^ t) - 3 * (z ^^^ t) - 3 * ~~~(z ||| t) + 12 * (z &&& ~~~t) + 2 * (z &&& t) = 1 * z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1180 (x y : BitVec w) : +theorem e_1180 : - 1 * (z ^^^ t) + 5 * ~~~(z &&& t) + 2 * z - 7 * ~~~t + 1 * (z ||| t) - 14 * ~~~(z ||| ~~~t) - 2 * (z &&& ~~~t) - 12 * (z &&& t) = - 7 * t - 2 * ~~~(z &&& ~~~z) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1181 (x y : BitVec w) : +theorem e_1181 : 4 * ~~~t + 4 * ~~~(z ^^^ t) + 1 * ~~~(z &&& t) + 5 * ~~~(z &&& ~~~t) - 12 * ~~~(z ||| t) - 4 * ~~~(z ||| ~~~t) - 5 * (z &&& ~~~t) - 9 * (z &&& t) = 2 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1182 (x y : BitVec w) : +theorem e_1182 : - 6 * z + 1 * ~~~(z ^^^ t) + 5 * (z ||| t) + 5 * ~~~(z &&& ~~~z) + 11 * ~~~t - 17 * ~~~(z ||| t) - 10 * ~~~(z ||| ~~~t) - 5 * (z &&& t) = 15 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1183 (x y : BitVec w) : +theorem e_1183 : - 3 * ~~~(z ^^^ t) - 6 * ~~~(z &&& t) + 1 * z - 11 * ~~~(z &&& ~~~z) + 4 * ~~~t + 18 * ~~~(z ||| ~~~t) + 12 * (z &&& ~~~t) + 13 * (z &&& t) = - 17 * ~~~(z ||| t) + 1 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1184 (x y : BitVec w) : +theorem e_1184 : 1 * ~~~(z &&& ~~~z) - 11 * ~~~t + 5 * ~~~(z ^^^ t) + 1 * ~~~(z &&& t) + 2 * ~~~(z ||| t) - 2 * ~~~(z ||| ~~~t) + 11 * (z &&& ~~~t) - 8 * (z &&& t) = 2 * (z ^^^ t) - 2 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1185 (x y : BitVec w) : +theorem e_1185 : 1 * (z ||| t) + 7 * ~~~(z &&& ~~~z) - 6 * ~~~(z ^^^ t) + 1 * ~~~(z &&& ~~~t) - 7 * ~~~t - 5 * ~~~(z ||| t) - 19 * ~~~(z ||| ~~~t) - 3 * (z &&& t) = - 11 * ~~~z + 1 * ~~~(z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1186 (x y : BitVec w) : +theorem e_1186 : - 2 * (z ^^^ t) - 1 * ~~~(z &&& ~~~t) + 1 * ~~~z + 3 * ~~~(z &&& ~~~z) - 1 * ~~~(z ||| t) - 3 * ~~~(z ||| ~~~t) - 1 * (z &&& ~~~t) - 2 * (z &&& t) = - 2 * t + 2 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1187 (x y : BitVec w) : +theorem e_1187 : - 5 * ~~~t - 5 * ~~~(z &&& ~~~t) + 1 * ~~~(z &&& ~~~z) - 5 * t - 1 * ~~~(z &&& t) + 10 * ~~~(z ||| t) + 4 * (z &&& ~~~t) + 8 * (z &&& t) = - 1 * (z ||| t) - 9 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1188 (x y : BitVec w) : +theorem e_1188 : - 2 * ~~~t + 11 * ~~~z + 11 * (z ||| t) - 1 * ~~~(z &&& ~~~t) - 11 * (z ||| ~~~t) + 3 * ~~~(z ||| t) - 21 * ~~~(z ||| ~~~t) + 2 * (z &&& ~~~t) = - 1 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1189 (x y : BitVec w) : +theorem e_1189 : - 11 * ~~~(z ^^^ t) + 4 * z + 1 * (z ||| ~~~t) - 5 * ~~~(z &&& t) + 3 * ~~~(z &&& ~~~t) + 23 * ~~~(z ||| t) + 13 * ~~~(z ||| ~~~t) + 14 * (z &&& t) = - 11 * (z &&& ~~~t) + 11 * ~~~(z &&& ~~~z) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1190 (x y : BitVec w) : +theorem e_1190 : - 7 * ~~~(z ^^^ t) - 2 * ~~~t + 1 * ~~~z + 3 * (z ^^^ t) + 20 * ~~~(z ||| t) + 3 * ~~~(z ||| ~~~t) + 11 * (z &&& ~~~t) + 12 * (z &&& t) = 5 * (z ||| ~~~t) + 7 * ~~~(z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1191 (x y : BitVec w) : +theorem e_1191 : 2 * ~~~z + 11 * ~~~t - 7 * ~~~(z ^^^ t) + 3 * ~~~(z &&& ~~~z) - 1 * z - 9 * ~~~(z ||| t) - 5 * ~~~(z ||| ~~~t) - 13 * (z &&& ~~~t) = - 5 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1192 (x y : BitVec w) : +theorem e_1192 : 2 * ~~~(z &&& ~~~t) - 7 * ~~~(z ^^^ t) + 1 * z - 2 * (z ^^^ t) + 2 * ~~~(z &&& t) + 3 * ~~~(z ||| t) - 2 * ~~~(z ||| ~~~t) + 4 * (z &&& t) = 1 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1193 (x y : BitVec w) : +theorem e_1193 : - 6 * ~~~(z &&& ~~~z) - 7 * z - 3 * (z ^^^ t) - 6 * ~~~z + 13 * ~~~(z ||| t) + 15 * ~~~(z ||| ~~~t) + 17 * (z &&& ~~~t) + 14 * (z &&& t) = 1 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1194 (x y : BitVec w) : +theorem e_1194 : - 2 * (z ||| ~~~t) - 3 * (z ||| t) + 3 * ~~~z + 1 * z - 1 * ~~~(z ||| t) + 1 * ~~~(z ||| ~~~t) + 4 * (z &&& ~~~t) + 5 * (z &&& t) = 1 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1195 (x y : BitVec w) : +theorem e_1195 : - 5 * z + 11 * t - 2 * (z ^^^ t) - 5 * ~~~z - 1 * ~~~(z &&& t) + 6 * ~~~(z ||| t) - 3 * ~~~(z ||| ~~~t) + 8 * (z &&& ~~~t) = 6 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1196 (x y : BitVec w) : +theorem e_1196 : - 6 * t + 4 * (z ||| t) - 5 * ~~~t + 7 * ~~~(z ^^^ t) + 4 * ~~~z - 3 * ~~~(z ||| t) - 2 * ~~~(z ||| ~~~t) + 4 * (z &&& ~~~t) = 2 * (z &&& t) + 3 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1197 (x y : BitVec w) : +theorem e_1197 : 3 * z - 2 * ~~~(z &&& ~~~z) - 3 * (z ||| t) - 11 * ~~~t + 2 * ~~~(z &&& t) + 11 * ~~~(z ||| t) - 8 * ~~~(z ||| ~~~t) + 2 * (z &&& t) = - 11 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1198 (x y : BitVec w) : +theorem e_1198 : 7 * z - 1 * ~~~(z &&& ~~~t) + 1 * ~~~z + 11 * ~~~(z &&& ~~~z) - 15 * ~~~(z ||| t) - 11 * ~~~(z ||| ~~~t) - 22 * (z &&& ~~~t) - 17 * (z &&& t) = - 4 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1199 (x y : BitVec w) : +theorem e_1199 : - 11 * ~~~(z &&& ~~~z) - 1 * (z ^^^ t) - 1 * ~~~(z &&& t) - 1 * ~~~(z &&& ~~~t) + 19 * ~~~(z ||| t) + 19 * ~~~(z ||| ~~~t) + 13 * (z &&& ~~~t) + 11 * (z &&& t) = 6 * ~~~z - 1 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1200 (x y : BitVec w) : +theorem e_1200 : - 3 * (z ||| t) - 1 * t + 7 * ~~~z - 7 * z - 2 * ~~~(z &&& ~~~t) - 5 * ~~~(z ||| t) - 1 * ~~~(z ||| ~~~t) + 13 * (z &&& t) = - 10 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1201 (x y : BitVec w) : +theorem e_1201 : - 2 * ~~~(z &&& ~~~z) + 2 * ~~~(z &&& ~~~t) + 7 * (z ^^^ t) - 6 * z + 3 * (z ||| ~~~t) - 3 * ~~~(z ||| t) - 7 * ~~~(z ||| ~~~t) + 3 * (z &&& t) = 2 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1202 (x y : BitVec w) : +theorem e_1202 : 1 * ~~~(z &&& t) + 2 * ~~~(z &&& ~~~z) + 1 * (z ||| t) - 5 * ~~~(z &&& ~~~t) - 1 * z + 2 * ~~~(z ||| t) + 3 * ~~~(z ||| ~~~t) + 2 * (z &&& ~~~t) = - 3 * t + 5 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1203 (x y : BitVec w) : +theorem e_1203 : 4 * (z ^^^ t) + 3 * ~~~(z &&& ~~~z) + 1 * z - 2 * ~~~(z ^^^ t) + 10 * ~~~(z ||| t) - 7 * ~~~(z ||| ~~~t) + 3 * (z &&& ~~~t) + 9 * (z &&& t) = 11 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1204 (x y : BitVec w) : +theorem e_1204 : - 11 * ~~~(z &&& ~~~z) - 1 * (z ||| ~~~t) + 11 * ~~~(z &&& ~~~t) + 11 * (z ^^^ t) - 11 * ~~~(z ^^^ t) + 10 * ~~~(z ||| t) - 10 * ~~~(z ||| ~~~t) - 1 * (z &&& ~~~t) + 15 * (z &&& t) = - 2 * ~~~(z &&& t) + 3 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1205 (x y : BitVec w) : +theorem e_1205 : 7 * ~~~z + 2 * ~~~(z &&& ~~~z) - 11 * ~~~(z &&& t) - 6 * (z ||| ~~~t) - 5 * (z ||| t) + 10 * ~~~(z ||| t) + 7 * ~~~(z ||| ~~~t) + 20 * (z &&& ~~~t) + 7 * (z &&& t) = 2 * ~~~t - 2 * z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1206 (x y : BitVec w) : +theorem e_1206 : 7 * t + 3 * ~~~t - 6 * (z ^^^ t) + 5 * ~~~z + 1 * z + 11 * ~~~(z &&& t) - 19 * ~~~(z ||| t) - 17 * ~~~(z ||| ~~~t) - 9 * (z &&& ~~~t) = 8 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1207 (x y : BitVec w) : +theorem e_1207 : - 6 * (z ^^^ t) + 2 * ~~~z - 11 * z - 11 * ~~~(z &&& t) + 3 * ~~~(z &&& ~~~t) + 6 * ~~~(z ||| t) + 10 * ~~~(z ||| ~~~t) + 26 * (z &&& ~~~t) + 6 * (z &&& t) = - 2 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1208 (x y : BitVec w) : +theorem e_1208 : 2 * ~~~(z &&& ~~~t) - 7 * ~~~(z &&& ~~~z) + 2 * z + 7 * ~~~(z &&& t) + 1 * ~~~t - 11 * (z ^^^ t) - 3 * ~~~(z ||| t) + 13 * (z &&& ~~~t) + 8 * (z &&& t) = - 14 * ~~~(z ||| ~~~t) + 5 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1209 (x y : BitVec w) : +theorem e_1209 : - 11 * (z ||| ~~~t) + 4 * ~~~(z &&& ~~~z) - 6 * t - 2 * ~~~(z &&& t) - 3 * z + 11 * ~~~(z &&& ~~~t) + 1 * ~~~(z ||| t) - 7 * ~~~(z ||| ~~~t) + 5 * (z &&& t) = 3 * ~~~t - 15 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1210 (x y : BitVec w) : +theorem e_1210 : 5 * ~~~(z &&& t) + 2 * ~~~(z ^^^ t) + 11 * ~~~(z &&& ~~~z) + 2 * (z ^^^ t) + 2 * (z ||| t) - 13 * ~~~(z ||| t) - 20 * ~~~(z ||| ~~~t) - 13 * (z &&& ~~~t) - 8 * (z &&& t) = 5 * (z ||| ~~~t) + 2 * z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1211 (x y : BitVec w) : +theorem e_1211 : 1 * z + 7 * ~~~(z ^^^ t) - 2 * (z ||| t) + 2 * ~~~t + 4 * ~~~(z &&& t) - 13 * ~~~(z ||| t) - 3 * ~~~(z ||| ~~~t) - 5 * (z &&& ~~~t) - 7 * (z &&& t) = - 1 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1212 (x y : BitVec w) : +theorem e_1212 : - 1 * z - 2 * t + 11 * (z ||| t) - 1 * ~~~(z ^^^ t) + 2 * ~~~t - 2 * ~~~(z ||| t) - 10 * ~~~(z ||| ~~~t) - 10 * (z &&& ~~~t) - 10 * (z &&& t) = - 3 * ~~~(z &&& ~~~t) + 2 * ~~~(z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1213 (x y : BitVec w) : +theorem e_1213 : 11 * z - 2 * (z ^^^ t) + 5 * t + 5 * ~~~(z &&& t) - 1 * ~~~(z &&& ~~~t) - 6 * ~~~(z ||| t) - 9 * ~~~(z ||| ~~~t) - 16 * (z &&& ~~~t) - 17 * (z &&& t) = - 2 * ~~~(z &&& ~~~z) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1214 (x y : BitVec w) : +theorem e_1214 : 5 * ~~~t - 6 * (z ||| ~~~t) + 11 * z + 1 * (z ^^^ t) + 11 * t + 1 * ~~~(z &&& t) + 2 * ~~~(z ||| t) - 12 * (z &&& ~~~t) - 14 * (z &&& t) = 2 * ~~~(z ^^^ t) + 13 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1215 (x y : BitVec w) : +theorem e_1215 : - 2 * ~~~t + 5 * ~~~z - 2 * ~~~(z &&& ~~~t) + 1 * ~~~(z &&& t) + 3 * (z ||| t) - 7 * ~~~(z &&& ~~~z) + 1 * (z ^^^ t) + 5 * ~~~(z ||| t) + 4 * (z &&& ~~~t) = - 6 * (z &&& t) + 1 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1216 (x y : BitVec w) : +theorem e_1216 : 7 * ~~~t - 7 * ~~~(z &&& ~~~z) - 5 * t + 2 * ~~~(z ^^^ t) - 5 * ~~~(z &&& ~~~t) - 6 * (z ^^^ t) + 23 * ~~~(z ||| ~~~t) + 6 * (z &&& ~~~t) + 15 * (z &&& t) = - 3 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1217 (x y : BitVec w) : +theorem e_1217 : 7 * ~~~z + 4 * ~~~(z ^^^ t) - 2 * ~~~(z &&& t) - 5 * z - 5 * ~~~(z &&& ~~~z) - 4 * ~~~(z ||| t) + 1 * ~~~(z ||| ~~~t) + 13 * (z &&& ~~~t) + 6 * (z &&& t) = 1 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1218 (x y : BitVec w) : +theorem e_1218 : 1 * t - 2 * (z ||| ~~~t) + 11 * ~~~z + 1 * ~~~(z &&& ~~~t) - 1 * ~~~t - 2 * z - 9 * ~~~(z ||| t) - 17 * ~~~(z ||| ~~~t) + 1 * (z &&& ~~~t) = - 2 * (z &&& t) - 4 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1219 (x y : BitVec w) : +theorem e_1219 : 2 * ~~~(z ^^^ t) + 1 * (z ^^^ t) + 5 * (z ||| t) + 1 * z + 2 * (z ||| ~~~t) - 15 * ~~~(z ||| t) - 17 * ~~~(z ||| ~~~t) - 9 * (z &&& ~~~t) - 21 * (z &&& t) = - 11 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1220 (x y : BitVec w) : +theorem e_1220 : - 11 * ~~~(z &&& ~~~z) - 1 * t - 6 * ~~~(z &&& t) + 11 * ~~~t - 2 * (z ||| ~~~t) + 11 * ~~~(z &&& ~~~t) - 3 * ~~~(z ||| t) + 1 * (z &&& ~~~t) - 4 * (z &&& t) = - 7 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1221 (x y : BitVec w) : +theorem e_1221 : - 1 * z - 2 * ~~~(z &&& ~~~z) + 4 * ~~~(z &&& ~~~t) + 3 * ~~~(z ^^^ t) + 3 * (z ||| ~~~t) - 8 * ~~~(z ||| t) - 6 * ~~~(z ||| ~~~t) - 1 * (z &&& ~~~t) - 11 * (z &&& t) = - 1 * (z ||| t) - 3 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1222 (x y : BitVec w) : +theorem e_1222 : 1 * ~~~z + 1 * ~~~(z &&& ~~~t) - 7 * t - 2 * ~~~(z &&& ~~~z) + 2 * z + 1 * (z ||| t) + 2 * ~~~(z ||| t) - 1 * (z &&& ~~~t) + 7 * (z &&& t) = 2 * ~~~(z ^^^ t) - 6 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1223 (x y : BitVec w) : +theorem e_1223 : 1 * (z ||| t) + 5 * ~~~z - 1 * (z ||| ~~~t) + 2 * z + 11 * ~~~t - 1 * ~~~(z &&& t) - 14 * ~~~(z ||| t) - 5 * ~~~(z ||| ~~~t) - 2 * (z &&& t) = 12 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1224 (x y : BitVec w) : +theorem e_1224 : 11 * ~~~(z &&& ~~~z) - 2 * ~~~z + 4 * (z ||| t) - 1 * ~~~t + 1 * ~~~(z &&& t) + 4 * z - 16 * ~~~(z ||| ~~~t) - 19 * (z &&& ~~~t) - 21 * (z &&& t) = 9 * ~~~(z ||| t) - 2 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1225 (x y : BitVec w) : +theorem e_1225 : - 11 * ~~~(z ^^^ t) + 11 * ~~~(z &&& t) + 5 * (z ||| ~~~t) + 7 * ~~~(z &&& ~~~z) + 5 * ~~~t - 18 * ~~~(z ||| t) - 19 * ~~~(z ||| ~~~t) - 26 * (z &&& ~~~t) + 1 * (z &&& t) = 2 * z - 1 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1226 (x y : BitVec w) : +theorem e_1226 : - 5 * ~~~(z ^^^ t) - 5 * (z ||| ~~~t) + 1 * ~~~z - 3 * ~~~t + 1 * ~~~(z &&& ~~~z) + 12 * ~~~(z ||| t) - 1 * ~~~(z ||| ~~~t) + 8 * (z &&& ~~~t) + 9 * (z &&& t) = 1 * ~~~(z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1227 (x y : BitVec w) : +theorem e_1227 : - 11 * ~~~(z &&& t) - 3 * ~~~(z &&& ~~~t) + 1 * ~~~(z ^^^ t) + 2 * z + 3 * ~~~(z &&& ~~~z) + 10 * ~~~(z ||| t) + 7 * ~~~(z ||| ~~~t) + 2 * (z &&& ~~~t) - 7 * (z &&& t) = - 4 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1228 (x y : BitVec w) : +theorem e_1228 : 1 * ~~~(z &&& ~~~t) - 2 * ~~~z - 3 * (z ||| t) - 5 * (z ||| ~~~t) + 7 * ~~~(z ^^^ t) - 7 * ~~~t - 1 * ~~~(z &&& t) + 7 * ~~~(z ||| t) + 5 * ~~~(z ||| ~~~t) = - 16 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1229 (x y : BitVec w) : +theorem e_1229 : 1 * ~~~(z ^^^ t) + 2 * ~~~(z &&& t) - 2 * ~~~t + 1 * ~~~(z &&& ~~~z) - 11 * ~~~(z &&& ~~~t) + 12 * ~~~(z ||| t) + 8 * ~~~(z ||| ~~~t) - 9 * (z &&& ~~~t) + 1 * (z &&& t) = - 11 * z + 3 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1230 (x y : BitVec w) : +theorem e_1230 : 3 * z - 1 * ~~~t + 3 * ~~~(z &&& ~~~t) - 1 * ~~~z + 2 * t - 11 * (z ^^^ t) - 1 * ~~~(z ^^^ t) + 7 * ~~~(z ||| ~~~t) - 7 * (z &&& t) = - 9 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1231 (x y : BitVec w) : +theorem e_1231 : - 3 * ~~~(z ^^^ t) - 1 * ~~~(z &&& t) - 1 * ~~~t + 4 * (z ||| ~~~t) + 5 * ~~~(z &&& ~~~z) + 1 * (z ||| t) - 4 * ~~~(z ||| t) - 12 * (z &&& ~~~t) - 7 * (z &&& t) = 9 * ~~~(z ||| ~~~t) - 4 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1232 (x y : BitVec w) : +theorem e_1232 : 7 * ~~~(z ^^^ t) - 3 * (z ||| ~~~t) - 6 * (z ||| t) - 2 * ~~~(z &&& ~~~z) - 11 * ~~~z + 7 * t + 9 * ~~~(z ||| t) + 12 * ~~~(z ||| ~~~t) + 13 * (z &&& ~~~t) = 1 * (z &&& t) + 2 * z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1233 (x y : BitVec w) : +theorem e_1233 : 7 * (z ||| t) - 7 * ~~~(z &&& ~~~t) - 5 * ~~~t + 4 * ~~~(z &&& t) - 1 * (z ^^^ t) + 7 * (z ||| ~~~t) + 1 * z + 1 * ~~~(z ||| t) - 3 * ~~~(z ||| ~~~t) = 13 * (z &&& ~~~t) + 8 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1234 (x y : BitVec w) : +theorem e_1234 : - 2 * t - 11 * ~~~z - 2 * (z ||| t) + 5 * ~~~(z &&& ~~~t) + 2 * ~~~(z ^^^ t) - 7 * ~~~(z &&& ~~~z) + 11 * ~~~(z ||| t) + 17 * ~~~(z ||| ~~~t) + 4 * (z &&& t) = - 9 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1235 (x y : BitVec w) : +theorem e_1235 : - 2 * t + 7 * (z ||| ~~~t) + 3 * ~~~(z &&& t) + 2 * ~~~z - 2 * ~~~(z &&& ~~~z) - 3 * z + 1 * ~~~(z ||| t) - 2 * ~~~(z ||| ~~~t) + 5 * (z &&& ~~~t) = 11 * ~~~t - 1 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1236 (x y : BitVec w) : +theorem e_1236 : 1 * z + 3 * ~~~z - 6 * ~~~(z ^^^ t) + 7 * (z ||| t) + 11 * ~~~(z &&& ~~~z) + 1 * ~~~(z &&& ~~~t) - 16 * ~~~(z ||| t) - 22 * ~~~(z ||| ~~~t) - 14 * (z &&& t) = - 7 * ~~~t + 26 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1237 (x y : BitVec w) : +theorem e_1237 : 5 * t - 2 * (z ||| t) - 2 * ~~~(z ^^^ t) + 2 * ~~~(z &&& ~~~t) + 2 * (z ||| ~~~t) + 2 * ~~~t - 4 * ~~~(z ||| t) - 5 * ~~~(z ||| ~~~t) - 2 * (z &&& ~~~t) = 5 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1238 (x y : BitVec w) : +theorem e_1238 : 1 * (z ^^^ t) + 2 * ~~~z - 1 * ~~~(z &&& t) + 1 * ~~~(z &&& ~~~t) - 5 * t - 7 * ~~~(z &&& ~~~z) + 5 * ~~~(z ||| t) + 7 * ~~~(z ||| ~~~t) + 9 * (z &&& t) = - 2 * (z ||| t) - 5 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1239 (x y : BitVec w) : +theorem e_1239 : - 2 * ~~~(z ^^^ t) + 4 * ~~~(z &&& t) - 7 * ~~~z - 2 * (z ^^^ t) - 1 * (z ||| ~~~t) + 7 * ~~~(z ||| t) + 6 * ~~~(z ||| ~~~t) + 1 * (z &&& ~~~t) + 4 * (z &&& t) = 2 * ~~~(z &&& ~~~z) - 1 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1240 (x y : BitVec w) : +theorem e_1240 : - 1 * z + 11 * ~~~(z &&& ~~~t) + 7 * (z ||| ~~~t) - 1 * (z ^^^ t) - 7 * ~~~z - 9 * ~~~(z ||| t) - 3 * ~~~(z ||| ~~~t) - 5 * (z &&& ~~~t) - 15 * (z &&& t) = 2 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1241 (x y : BitVec w) : +theorem e_1241 : 4 * ~~~(z &&& t) + 3 * (z ||| ~~~t) + 1 * ~~~z + 3 * t + 3 * ~~~(z ^^^ t) - 11 * ~~~(z ||| t) - 9 * ~~~(z ||| ~~~t) - 8 * (z &&& ~~~t) - 10 * (z &&& t) = - 1 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1242 (x y : BitVec w) : +theorem e_1242 : - 1 * (z ^^^ t) - 1 * ~~~(z &&& t) - 2 * ~~~t + 2 * ~~~(z &&& ~~~t) + 3 * ~~~(z &&& ~~~z) - 6 * ~~~(z ^^^ t) + 4 * ~~~(z ||| t) - 2 * ~~~(z ||| ~~~t) + 2 * (z &&& ~~~t) = - 2 * (z &&& t) + 1 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1243 (x y : BitVec w) : +theorem e_1243 : - 2 * t - 6 * (z ^^^ t) + 5 * ~~~(z &&& t) - 1 * ~~~(z ^^^ t) - 6 * (z ||| ~~~t) + 2 * ~~~(z ||| t) + 3 * ~~~(z ||| ~~~t) + 18 * (z &&& ~~~t) + 20 * (z &&& t) = 11 * z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1244 (x y : BitVec w) : +theorem e_1244 : 2 * ~~~z - 3 * (z ^^^ t) - 7 * ~~~(z &&& ~~~z) + 4 * ~~~(z &&& t) - 7 * (z ||| ~~~t) - 2 * ~~~t + 4 * t + 21 * (z &&& ~~~t) + 16 * (z &&& t) = 6 * z - 10 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1245 (x y : BitVec w) : +theorem e_1245 : - 1 * ~~~(z ^^^ t) - 2 * (z ||| t) + 7 * (z ^^^ t) - 11 * ~~~t - 11 * ~~~z + 4 * t + 2 * ~~~(z ||| ~~~t) + 6 * (z &&& ~~~t) - 1 * (z &&& t) = - 23 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1246 (x y : BitVec w) : +theorem e_1246 : 4 * ~~~t + 4 * ~~~(z &&& ~~~t) - 1 * z + 1 * (z ^^^ t) + 1 * ~~~z + 4 * ~~~(z &&& t) - 13 * ~~~(z ||| t) - 9 * (z &&& ~~~t) - 4 * (z &&& t) = - 1 * (z ||| t) + 11 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1247 (x y : BitVec w) : +theorem e_1247 : - 6 * ~~~(z &&& ~~~t) - 11 * (z ^^^ t) - 6 * ~~~(z &&& t) + 7 * t - 6 * (z ||| t) - 6 * ~~~t + 22 * ~~~(z ||| ~~~t) + 29 * (z &&& ~~~t) + 5 * (z &&& t) = - 18 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1248 (x y : BitVec w) : +theorem e_1248 : 1 * ~~~(z &&& ~~~z) - 2 * (z ^^^ t) - 3 * t + 11 * z - 5 * ~~~(z &&& ~~~t) + 4 * ~~~(z ||| t) + 10 * ~~~(z ||| ~~~t) - 9 * (z &&& ~~~t) - 3 * (z &&& t) = 1 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1249 (x y : BitVec w) : +theorem e_1249 : 4 * ~~~z - 2 * t - 1 * (z ||| ~~~t) - 1 * ~~~t + 1 * ~~~(z &&& t) - 6 * ~~~(z ||| t) + 4 * ~~~(z ||| ~~~t) + 8 * (z &&& ~~~t) + 7 * (z &&& t) = - 3 * ~~~(z ^^^ t) + 7 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1250 (x y : BitVec w) : +theorem e_1250 : - 6 * t + 1 * ~~~t - 1 * (z ^^^ t) - 6 * ~~~(z &&& ~~~t) - 2 * ~~~(z ^^^ t) + 1 * z + 10 * ~~~(z ||| t) + 2 * (z &&& ~~~t) + 13 * (z &&& t) = 3 * ~~~(z &&& t) - 16 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1251 (x y : BitVec w) : +theorem e_1251 : 2 * z - 1 * (z ||| ~~~t) + 7 * ~~~(z ^^^ t) - 1 * ~~~z - 11 * (z ^^^ t) - 9 * ~~~(z ||| t) + 8 * ~~~(z ||| ~~~t) + 6 * (z &&& ~~~t) - 13 * (z &&& t) = - 5 * ~~~(z &&& ~~~z) + 1 * ~~~(z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1252 (x y : BitVec w) : +theorem e_1252 : 5 * (z ||| ~~~t) - 11 * ~~~(z &&& ~~~z) - 5 * ~~~(z &&& ~~~t) - 6 * ~~~(z &&& t) - 6 * ~~~(z ^^^ t) + 1 * ~~~t + 22 * ~~~(z ||| t) + 17 * ~~~(z ||| ~~~t) + 12 * (z &&& t) = - 5 * (z ||| t) - 6 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1253 (x y : BitVec w) : +theorem e_1253 : - 2 * ~~~z + 2 * ~~~(z &&& ~~~t) + 2 * (z ^^^ t) - 2 * (z ||| t) - 11 * ~~~(z &&& ~~~z) + 22 * ~~~(z ||| t) + 11 * ~~~(z ||| ~~~t) + 11 * (z &&& ~~~t) + 22 * (z &&& t) = 11 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1254 (x y : BitVec w) : +theorem e_1254 : 1 * ~~~(z ^^^ t) - 6 * ~~~(z &&& ~~~z) - 1 * ~~~(z &&& ~~~t) - 2 * (z ^^^ t) - 7 * t + 17 * ~~~(z ||| t) + 5 * ~~~(z ||| ~~~t) + 8 * (z &&& ~~~t) + 13 * (z &&& t) = 11 * (z ||| ~~~t) - 11 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1255 (x y : BitVec w) : +theorem e_1255 : - 11 * (z ^^^ t) - 3 * ~~~(z &&& ~~~z) + 2 * ~~~z - 1 * z + 1 * (z ||| ~~~t) - 8 * ~~~(z ||| t) + 1 * ~~~(z ||| ~~~t) + 14 * (z &&& ~~~t) - 5 * (z &&& t) = - 11 * ~~~(z &&& ~~~t) + 3 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1256 (x y : BitVec w) : +theorem e_1256 : - 5 * (z ||| t) - 3 * ~~~t + 1 * ~~~(z ^^^ t) + 3 * (z ^^^ t) + 7 * (z ||| ~~~t) - 6 * ~~~(z ||| t) + 1 * ~~~(z ||| ~~~t) - 2 * (z &&& ~~~t) - 4 * (z &&& t) = - 1 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1257 (x y : BitVec w) : +theorem e_1257 : - 11 * (z ||| t) - 1 * ~~~t - 3 * ~~~(z &&& ~~~z) + 11 * (z ^^^ t) + 5 * t - 2 * ~~~(z &&& t) + 5 * ~~~(z ||| t) + 13 * (z &&& ~~~t) + 15 * (z &&& t) = - 1 * ~~~(z ^^^ t) + 7 * z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1258 (x y : BitVec w) : +theorem e_1258 : - 1 * ~~~(z &&& t) + 7 * z + 2 * (z ||| ~~~t) - 1 * ~~~(z &&& ~~~t) + 2 * ~~~t + 3 * ~~~(z ||| t) + 2 * ~~~(z ||| ~~~t) - 10 * (z &&& ~~~t) - 3 * (z &&& t) = 5 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1259 (x y : BitVec w) : +theorem e_1259 : 3 * ~~~(z &&& t) - 3 * (z ^^^ t) + 1 * ~~~(z &&& ~~~t) + 1 * (z ||| ~~~t) - 7 * (z ||| t) - 14 * ~~~(z ||| t) - 3 * ~~~(z ||| ~~~t) + 4 * (z &&& ~~~t) + 3 * (z &&& t) = - 2 * ~~~(z &&& ~~~z) - 7 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1260 (x y : BitVec w) : +theorem e_1260 : - 11 * ~~~(z &&& ~~~z) - 7 * z - 1 * ~~~(z ^^^ t) + 2 * ~~~(z &&& t) - 11 * ~~~z + 7 * (z ^^^ t) + 18 * ~~~(z ||| t) + 13 * ~~~(z ||| ~~~t) + 6 * (z &&& ~~~t) = - 3 * (z ||| ~~~t) - 16 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1261 (x y : BitVec w) : +theorem e_1261 : - 11 * ~~~(z &&& ~~~t) - 3 * z - 2 * (z ||| ~~~t) + 2 * ~~~t - 1 * (z ^^^ t) - 1 * ~~~(z ^^^ t) + 5 * ~~~(z &&& ~~~z) + 7 * ~~~(z ||| t) - 1 * (z &&& ~~~t) = - 5 * (z &&& t) - 7 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1262 (x y : BitVec w) : +theorem e_1262 : - 7 * ~~~(z &&& ~~~z) + 7 * ~~~(z &&& t) - 1 * (z ||| ~~~t) - 5 * z + 1 * (z ^^^ t) - 11 * (z ||| t) + 1 * ~~~(z ||| t) + 10 * ~~~(z ||| ~~~t) + 16 * (z &&& ~~~t) = - 24 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1263 (x y : BitVec w) : +theorem e_1263 : 4 * z + 3 * (z ||| t) - 1 * ~~~(z &&& ~~~z) + 5 * ~~~(z &&& ~~~t) - 11 * (z ^^^ t) + 3 * ~~~(z ||| t) + 4 * ~~~(z ||| ~~~t) + 12 * (z &&& ~~~t) - 11 * (z &&& t) = 7 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1264 (x y : BitVec w) : +theorem e_1264 : 5 * ~~~(z &&& t) + 1 * z + 7 * (z ^^^ t) - 1 * (z ||| ~~~t) + 3 * ~~~(z ^^^ t) - 9 * ~~~(z ||| t) - 16 * ~~~(z ||| ~~~t) - 16 * (z &&& ~~~t) - 7 * (z &&& t) = - 2 * ~~~(z &&& ~~~z) - 2 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1265 (x y : BitVec w) : +theorem e_1265 : 7 * z - 1 * t + 11 * (z ||| ~~~t) - 1 * (z ||| t) + 3 * (z ^^^ t) - 22 * ~~~(z ||| t) - 12 * ~~~(z ||| ~~~t) - 20 * (z &&& ~~~t) - 27 * (z &&& t) = - 11 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1266 (x y : BitVec w) : +theorem e_1266 : 3 * ~~~z + 1 * z + 11 * ~~~(z &&& ~~~z) - 6 * t - 1 * ~~~(z &&& t) - 13 * ~~~(z ||| t) - 9 * ~~~(z ||| ~~~t) - 13 * (z &&& ~~~t) - 6 * (z &&& t) = - 2 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1267 (x y : BitVec w) : +theorem e_1267 : 7 * ~~~(z ^^^ t) + 3 * ~~~(z &&& t) + 2 * ~~~z + 3 * (z ||| t) - 2 * z - 1 * ~~~(z ||| t) - 5 * ~~~(z ||| ~~~t) + 7 * (z &&& ~~~t) + 6 * (z &&& t) = 11 * (z ||| ~~~t) + 3 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1268 (x y : BitVec w) : +theorem e_1268 : - 5 * ~~~(z &&& ~~~z) - 3 * ~~~z + 7 * (z ||| t) + 11 * ~~~(z ^^^ t) - 11 * z + 11 * (z ||| ~~~t) - 14 * ~~~(z ||| t) - 2 * (z &&& ~~~t) - 16 * (z &&& t) = 2 * ~~~(z ||| ~~~t) - 3 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1269 (x y : BitVec w) : +theorem e_1269 : 2 * (z ^^^ t) + 7 * t - 7 * ~~~(z &&& ~~~t) + 4 * (z ||| ~~~t) + 11 * (z ||| t) - 1 * ~~~(z &&& ~~~z) + 2 * ~~~(z ||| t) - 18 * (z &&& ~~~t) - 14 * (z &&& t) = 12 * ~~~(z ||| ~~~t) - 2 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1270 (x y : BitVec w) : +theorem e_1270 : - 7 * (z ||| t) + 2 * ~~~(z &&& ~~~z) + 3 * ~~~(z &&& t) + 1 * ~~~t + 11 * ~~~z - 5 * ~~~(z &&& ~~~t) - 4 * ~~~(z ||| ~~~t) - 4 * (z &&& ~~~t) + 5 * (z &&& t) = 17 * ~~~(z ||| t) - 5 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1271 (x y : BitVec w) : +theorem e_1271 : - 3 * ~~~(z ^^^ t) - 3 * ~~~(z &&& t) + 3 * z + 2 * ~~~(z &&& ~~~z) - 2 * ~~~z - 5 * ~~~(z ||| t) + 3 * ~~~(z ||| ~~~t) - 13 * (z &&& ~~~t) - 13 * (z &&& t) = - 11 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1272 (x y : BitVec w) : +theorem e_1272 : 11 * ~~~t + 2 * ~~~(z ^^^ t) + 5 * ~~~(z &&& ~~~t) - 1 * (z ||| t) - 1 * ~~~(z &&& ~~~z) - 17 * ~~~(z ||| t) - 4 * ~~~(z ||| ~~~t) - 10 * (z &&& ~~~t) - 5 * (z &&& t) = - 1 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1273 (x y : BitVec w) : +theorem e_1273 : 2 * ~~~(z &&& ~~~z) - 2 * ~~~t + 4 * (z ^^^ t) + 3 * (z ||| ~~~t) - 2 * ~~~z - 1 * ~~~(z ||| t) - 11 * ~~~(z ||| ~~~t) - 14 * (z &&& ~~~t) - 12 * (z &&& t) = - 7 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1274 (x y : BitVec w) : +theorem e_1274 : - 1 * t + 7 * (z ||| ~~~t) - 1 * (z ||| t) + 3 * ~~~z - 1 * (z ^^^ t) + 1 * ~~~(z &&& ~~~z) + 2 * ~~~(z ^^^ t) - 13 * ~~~(z ||| t) - 6 * (z &&& ~~~t) = 1 * ~~~(z ||| ~~~t) + 8 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1275 (x y : BitVec w) : +theorem e_1275 : - 3 * ~~~(z &&& ~~~z) + 2 * (z ^^^ t) - 7 * ~~~t + 3 * z + 2 * ~~~(z &&& t) + 7 * ~~~(z &&& ~~~t) + 1 * ~~~(z ||| t) + 3 * (z &&& ~~~t) - 5 * (z &&& t) = 2 * t + 6 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1276 (x y : BitVec w) : +theorem e_1276 : - 3 * t - 2 * ~~~(z &&& ~~~t) + 1 * ~~~(z &&& t) + 4 * ~~~z - 1 * (z ||| ~~~t) - 1 * ~~~t - 1 * ~~~(z ||| t) + 1 * ~~~(z ||| ~~~t) + 2 * (z &&& ~~~t) = 1 * (z ^^^ t) - 6 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1277 (x y : BitVec w) : +theorem e_1277 : 1 * z + 1 * (z ||| t) - 1 * (z ^^^ t) - 5 * (z ||| ~~~t) - 1 * ~~~(z ^^^ t) + 8 * ~~~(z ||| t) + 2 * ~~~(z ||| ~~~t) + 6 * (z &&& ~~~t) + 4 * (z &&& t) = 2 * ~~~(z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1278 (x y : BitVec w) : +theorem e_1278 : 2 * ~~~z + 4 * z + 7 * (z ^^^ t) + 2 * ~~~(z ^^^ t) + 1 * t - 6 * (z ||| t) - 5 * ~~~(z ||| t) - 6 * (z &&& ~~~t) - 1 * (z &&& t) = 4 * ~~~(z ||| ~~~t) - 1 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1279 (x y : BitVec w) : +theorem e_1279 : - 11 * ~~~(z ^^^ t) + 5 * (z ||| ~~~t) - 1 * ~~~(z &&& t) - 5 * ~~~(z &&& ~~~t) - 6 * ~~~t + 1 * (z ^^^ t) + 14 * ~~~(z ||| t) + 1 * ~~~(z ||| ~~~t) - 3 * (z &&& ~~~t) = - 4 * ~~~(z &&& ~~~z) - 7 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1280 (x y : BitVec w) : +theorem e_1280 : 11 * z - 2 * ~~~z - 2 * (z ^^^ t) - 5 * ~~~(z &&& t) + 3 * ~~~(z &&& ~~~t) - 3 * (z ||| t) + 4 * ~~~(z ||| t) + 9 * ~~~(z ||| ~~~t) - 11 * (z &&& t) = 1 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1281 (x y : BitVec w) : +theorem e_1281 : 7 * z - 5 * ~~~(z &&& t) + 1 * ~~~(z ^^^ t) + 4 * t - 11 * ~~~(z &&& ~~~z) + 18 * ~~~(z ||| t) + 13 * ~~~(z ||| ~~~t) + 11 * (z &&& ~~~t) + 2 * (z &&& t) = 2 * (z ||| ~~~t) + 1 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1282 (x y : BitVec w) : +theorem e_1282 : - 3 * (z ^^^ t) + 1 * z + 7 * ~~~z + 5 * (z ||| ~~~t) - 1 * ~~~(z &&& ~~~z) - 3 * ~~~(z ^^^ t) - 8 * ~~~(z ||| t) - 3 * (z &&& ~~~t) - 3 * (z &&& t) = - 1 * (z ||| t) + 4 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1283 (x y : BitVec w) : +theorem e_1283 : - 11 * t - 6 * ~~~t + 4 * ~~~(z &&& ~~~t) - 7 * ~~~z - 1 * ~~~(z ^^^ t) - 6 * (z ^^^ t) + 10 * ~~~(z ||| t) + 12 * (z &&& ~~~t) + 8 * (z &&& t) = - 20 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1284 (x y : BitVec w) : +theorem e_1284 : 1 * ~~~t - 5 * (z ||| t) - 2 * z - 1 * t - 2 * (z ||| ~~~t) + 6 * ~~~(z ||| t) + 6 * ~~~(z ||| ~~~t) + 8 * (z &&& ~~~t) + 15 * (z &&& t) = 5 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1285 (x y : BitVec w) : +theorem e_1285 : - 5 * t + 2 * (z ||| ~~~t) - 5 * ~~~(z ^^^ t) + 2 * ~~~(z &&& t) + 2 * ~~~(z &&& ~~~z) - 5 * ~~~t + 4 * ~~~(z ||| t) + 1 * ~~~(z ||| ~~~t) + 6 * (z &&& t) = 1 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1286 (x y : BitVec w) : +theorem e_1286 : 1 * ~~~(z ^^^ t) + 2 * t - 2 * ~~~t + 1 * ~~~z - 3 * (z ^^^ t) - 11 * ~~~(z ||| t) - 11 * ~~~(z ||| ~~~t) + 5 * (z &&& ~~~t) - 14 * (z &&& t) = - 11 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1287 (x y : BitVec w) : +theorem e_1287 : - 3 * ~~~(z &&& t) - 2 * ~~~(z &&& ~~~t) + 3 * z - 1 * (z ||| t) - 2 * (z ^^^ t) + 2 * (z ||| ~~~t) + 3 * ~~~(z ||| t) + 1 * (z &&& ~~~t) - 2 * (z &&& t) = - 8 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1288 (x y : BitVec w) : +theorem e_1288 : 1 * (z ^^^ t) + 2 * ~~~(z ^^^ t) - 3 * ~~~(z &&& t) + 11 * ~~~(z &&& ~~~t) - 1 * (z ||| t) - 13 * ~~~(z ||| t) - 12 * ~~~(z ||| ~~~t) + 4 * (z &&& ~~~t) - 11 * (z &&& t) = 1 * (z ||| ~~~t) - 4 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1289 (x y : BitVec w) : +theorem e_1289 : 11 * ~~~t - 3 * t - 1 * z + 4 * (z ^^^ t) + 1 * ~~~z - 11 * ~~~(z &&& ~~~t) - 1 * ~~~(z ||| t) + 9 * ~~~(z ||| ~~~t) - 14 * (z &&& ~~~t) = - 15 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1290 (x y : BitVec w) : +theorem e_1290 : 5 * ~~~(z ^^^ t) - 7 * ~~~(z &&& ~~~t) - 2 * ~~~(z &&& ~~~z) - 5 * t + 2 * ~~~z - 1 * ~~~t + 2 * z + 1 * ~~~(z &&& t) + 2 * ~~~(z ||| t) = - 11 * ~~~(z ||| ~~~t) - 7 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1291 (x y : BitVec w) : +theorem e_1291 : - 2 * (z ||| ~~~t) - 1 * (z ^^^ t) + 5 * t - 5 * ~~~(z &&& ~~~t) + 4 * ~~~(z ^^^ t) + 4 * ~~~(z ||| t) + 2 * ~~~(z ||| ~~~t) - 4 * (z &&& ~~~t) - 9 * (z &&& t) = 1 * ~~~z - 7 * z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1292 (x y : BitVec w) : +theorem e_1292 : - 6 * (z ||| ~~~t) - 1 * (z ||| t) - 1 * z + 4 * ~~~(z ^^^ t) - 2 * ~~~(z &&& ~~~z) - 7 * ~~~(z ||| t) - 8 * ~~~(z ||| ~~~t) + 10 * (z &&& ~~~t) + 6 * (z &&& t) = - 11 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1293 (x y : BitVec w) : +theorem e_1293 : 5 * ~~~z - 11 * (z ||| t) - 6 * ~~~(z &&& ~~~z) - 1 * ~~~(z &&& ~~~t) - 5 * ~~~t + 2 * z + 7 * ~~~(z ||| t) + 20 * ~~~(z ||| ~~~t) + 27 * (z &&& ~~~t) = 7 * (z ^^^ t) - 16 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1294 (x y : BitVec w) : +theorem e_1294 : - 2 * (z ^^^ t) - 5 * ~~~(z &&& ~~~t) - 2 * ~~~(z ^^^ t) + 7 * (z ||| ~~~t) + 11 * ~~~z - 2 * ~~~(z &&& ~~~z) - 7 * ~~~t - 2 * ~~~(z ||| t) - 4 * ~~~(z ||| ~~~t) = - 2 * t - 4 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1295 (x y : BitVec w) : +theorem e_1295 : 1 * ~~~(z ^^^ t) + 3 * ~~~(z &&& t) - 11 * ~~~t + 2 * (z ^^^ t) + 5 * ~~~(z &&& ~~~t) + 3 * ~~~(z ||| t) - 10 * ~~~(z ||| ~~~t) + 6 * (z &&& ~~~t) - 6 * (z &&& t) = - 1 * z + 1 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1296 (x y : BitVec w) : +theorem e_1296 : - 6 * ~~~(z &&& ~~~t) - 2 * ~~~(z &&& t) - 1 * (z ||| ~~~t) - 1 * ~~~t - 3 * t + 10 * ~~~(z ||| t) + 10 * ~~~(z ||| ~~~t) + 3 * (z &&& ~~~t) + 10 * (z &&& t) = - 1 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1297 (x y : BitVec w) : +theorem e_1297 : 7 * ~~~z - 6 * ~~~(z ^^^ t) - 1 * ~~~(z &&& ~~~z) + 1 * ~~~(z &&& ~~~t) + 1 * ~~~(z &&& t) - 9 * ~~~(z ||| t) - 15 * ~~~(z ||| ~~~t) - 7 * (z &&& ~~~t) - 1 * (z &&& t) = - 7 * ~~~t - 7 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1298 (x y : BitVec w) : +theorem e_1298 : 1 * (z ||| ~~~t) + 1 * ~~~(z &&& ~~~t) - 1 * ~~~z + 2 * t + 1 * ~~~t - 2 * ~~~(z ||| t) - 2 * ~~~(z ||| ~~~t) - 1 * (z &&& ~~~t) - 3 * (z &&& t) = 1 * z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1299 (x y : BitVec w) : +theorem e_1299 : - 11 * ~~~(z &&& ~~~t) - 1 * ~~~t + 1 * ~~~(z ^^^ t) - 11 * z - 2 * ~~~(z &&& ~~~z) - 2 * ~~~z + 15 * ~~~(z ||| t) + 21 * ~~~(z ||| ~~~t) + 29 * (z &&& t) = - 20 * (z &&& ~~~t) + 6 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1300 (x y : BitVec w) : +theorem e_1300 : 1 * ~~~t - 6 * t - 1 * (z ||| ~~~t) - 1 * ~~~(z &&& ~~~z) - 2 * ~~~(z &&& t) + 3 * ~~~(z ||| t) + 9 * ~~~(z ||| ~~~t) + 6 * (z &&& ~~~t) + 11 * (z &&& t) = 3 * z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1301 (x y : BitVec w) : +theorem e_1301 : 4 * (z ||| ~~~t) - 1 * ~~~z + 1 * ~~~(z &&& t) + 11 * ~~~t - 3 * ~~~(z ^^^ t) - 10 * ~~~(z ||| t) + 2 * ~~~(z ||| ~~~t) - 14 * (z &&& ~~~t) + 1 * (z &&& t) = 2 * ~~~(z &&& ~~~z) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1302 (x y : BitVec w) : +theorem e_1302 : 2 * ~~~z + 2 * ~~~(z &&& ~~~z) - 3 * (z ^^^ t) + 11 * z - 1 * ~~~(z ^^^ t) - 4 * ~~~(z ||| t) - 1 * ~~~(z ||| ~~~t) - 11 * (z &&& ~~~t) - 13 * (z &&& t) = - 1 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1303 (x y : BitVec w) : +theorem e_1303 : 3 * (z ||| t) + 5 * ~~~z + 7 * ~~~(z ^^^ t) + 4 * ~~~(z &&& t) - 3 * (z ^^^ t) + 2 * ~~~(z &&& ~~~t) - 18 * ~~~(z ||| t) - 11 * ~~~(z ||| ~~~t) - 4 * (z &&& ~~~t) = 12 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1304 (x y : BitVec w) : +theorem e_1304 : 5 * ~~~(z ^^^ t) + 1 * ~~~(z &&& ~~~z) - 1 * ~~~(z &&& t) + 7 * ~~~(z &&& ~~~t) - 2 * (z ||| ~~~t) - 10 * ~~~(z ||| t) - 10 * ~~~(z ||| ~~~t) - 1 * (z &&& ~~~t) - 14 * (z &&& t) = - 3 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1305 (x y : BitVec w) : +theorem e_1305 : 2 * (z ^^^ t) + 5 * ~~~t - 1 * ~~~(z &&& t) + 1 * ~~~(z &&& ~~~t) - 3 * t - 4 * ~~~(z ||| t) + 2 * ~~~(z ||| ~~~t) - 5 * (z &&& ~~~t) + 3 * (z &&& t) = 1 * ~~~(z &&& ~~~z) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1306 (x y : BitVec w) : +theorem e_1306 : - 7 * ~~~(z &&& t) + 3 * (z ^^^ t) + 4 * (z ||| ~~~t) - 7 * z + 2 * ~~~t + 1 * ~~~(z ||| t) + 2 * ~~~(z ||| ~~~t) + 3 * (z &&& ~~~t) + 1 * (z &&& t) = - 2 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1307 (x y : BitVec w) : +theorem e_1307 : - 6 * ~~~(z ^^^ t) - 2 * ~~~(z &&& ~~~t) - 7 * t - 3 * ~~~z + 1 * (z ||| ~~~t) + 1 * ~~~t + 2 * (z ||| t) + 9 * ~~~(z ||| t) + 12 * (z &&& t) = - 10 * ~~~(z ||| ~~~t) + 4 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1308 (x y : BitVec w) : +theorem e_1308 : - 6 * ~~~(z &&& t) + 4 * (z ||| ~~~t) + 5 * (z ||| t) + 2 * (z ^^^ t) + 11 * ~~~(z &&& ~~~t) - 1 * ~~~z - 8 * ~~~(z ||| t) - 5 * (z &&& ~~~t) - 20 * (z &&& t) = 11 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1309 (x y : BitVec w) : +theorem e_1309 : - 11 * (z ||| t) + 5 * (z ^^^ t) + 7 * ~~~(z &&& ~~~t) - 7 * ~~~t + 2 * (z ||| ~~~t) - 3 * ~~~(z ||| t) - 2 * ~~~(z ||| ~~~t) + 11 * (z &&& ~~~t) + 2 * (z &&& t) = - 1 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1310 (x y : BitVec w) : +theorem e_1310 : 1 * ~~~(z ^^^ t) - 5 * ~~~(z &&& t) + 1 * t + 5 * (z ||| ~~~t) - 2 * ~~~(z &&& ~~~t) + 11 * (z ^^^ t) - 7 * ~~~(z ||| ~~~t) - 13 * (z &&& ~~~t) - 7 * (z &&& t) = 1 * ~~~(z ||| t) - 2 * ~~~(z &&& ~~~z) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1311 (x y : BitVec w) : +theorem e_1311 : - 1 * t - 11 * z + 1 * ~~~(z &&& t) + 2 * (z ||| ~~~t) - 3 * ~~~(z &&& ~~~t) + 11 * (z ||| t) + 4 * ~~~(z ||| t) - 4 * ~~~(z ||| ~~~t) + 5 * (z &&& t) = 3 * ~~~(z &&& ~~~z) + 1 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1312 (x y : BitVec w) : +theorem e_1312 : 7 * ~~~(z &&& ~~~t) + 4 * z - 7 * ~~~(z ^^^ t) + 2 * (z ||| ~~~t) - 1 * (z ^^^ t) + 3 * t - 10 * ~~~(z ||| ~~~t) - 6 * (z &&& ~~~t) - 10 * (z &&& t) = - 1 * (z ||| t) + 2 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1313 (x y : BitVec w) : +theorem e_1313 : - 1 * t - 5 * ~~~(z &&& ~~~z) - 1 * (z ||| t) - 6 * ~~~z - 5 * (z ||| ~~~t) - 1 * ~~~(z &&& t) + 20 * ~~~(z ||| t) + 14 * ~~~(z ||| ~~~t) + 15 * (z &&& t) = 3 * ~~~(z ^^^ t) - 12 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1314 (x y : BitVec w) : +theorem e_1314 : - 5 * (z ^^^ t) - 1 * ~~~z + 1 * ~~~t + 1 * ~~~(z &&& ~~~t) - 7 * (z ||| t) - 8 * ~~~(z ||| t) + 5 * ~~~(z ||| ~~~t) + 4 * (z &&& ~~~t) + 6 * (z &&& t) = - 7 * ~~~(z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1315 (x y : BitVec w) : +theorem e_1315 : - 5 * ~~~(z &&& ~~~t) + 4 * z - 6 * ~~~z - 3 * t - 2 * ~~~t + 13 * ~~~(z ||| t) + 14 * ~~~(z ||| ~~~t) - 2 * (z &&& ~~~t) + 3 * (z &&& t) = - 1 * ~~~(z &&& ~~~z) + 1 * ~~~(z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1316 (x y : BitVec w) : +theorem e_1316 : - 1 * (z ^^^ t) + 1 * t - 1 * z + 1 * ~~~(z &&& ~~~t) - 2 * ~~~t - 1 * ~~~(z ||| t) - 1 * ~~~(z ||| ~~~t) + 4 * (z &&& ~~~t) - 3 * (z &&& t) = - 2 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1317 (x y : BitVec w) : +theorem e_1317 : 4 * t - 7 * ~~~t + 1 * (z ||| t) - 6 * ~~~(z ^^^ t) - 6 * ~~~(z &&& t) + 7 * ~~~(z &&& ~~~z) + 1 * (z ||| ~~~t) - 6 * ~~~(z ||| ~~~t) + 4 * (z &&& ~~~t) = 7 * (z &&& t) - 11 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1318 (x y : BitVec w) : +theorem e_1318 : 3 * (z ^^^ t) - 6 * t + 1 * (z ||| ~~~t) + 1 * ~~~(z &&& t) + 4 * ~~~(z ^^^ t) - 10 * ~~~(z ||| t) - 2 * ~~~(z ||| ~~~t) - 6 * (z &&& ~~~t) - 4 * (z &&& t) = - 4 * ~~~(z &&& ~~~t) - 1 * z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1319 (x y : BitVec w) : +theorem e_1319 : - 1 * (z ||| t) + 3 * z - 2 * ~~~t - 1 * (z ||| ~~~t) - 2 * (z ^^^ t) + 2 * ~~~(z ||| t) + 2 * ~~~(z ||| ~~~t) + 3 * (z &&& ~~~t) - 1 * (z &&& t) = - 1 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1320 (x y : BitVec w) : +theorem e_1320 : - 2 * (z ^^^ t) - 7 * (z ||| t) - 6 * t + 2 * ~~~t + 1 * ~~~(z ^^^ t) + 7 * (z ||| ~~~t) - 5 * ~~~(z ||| t) + 20 * ~~~(z ||| ~~~t) + 10 * (z &&& t) = 5 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1321 (x y : BitVec w) : +theorem e_1321 : - 1 * (z ||| ~~~t) + 11 * ~~~(z &&& ~~~z) + 7 * ~~~(z &&& ~~~t) + 4 * (z ^^^ t) - 3 * z - 19 * ~~~(z ||| t) - 24 * ~~~(z ||| ~~~t) - 11 * (z &&& ~~~t) - 14 * (z &&& t) = - 2 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1322 (x y : BitVec w) : +theorem e_1322 : 2 * ~~~(z &&& t) - 3 * ~~~(z &&& ~~~z) + 4 * ~~~(z &&& ~~~t) + 11 * (z ||| t) + 3 * ~~~(z ^^^ t) - 1 * ~~~(z ||| t) - 14 * ~~~(z ||| ~~~t) + 2 * (z &&& ~~~t) - 8 * (z &&& t) = 7 * z + 5 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1323 (x y : BitVec w) : +theorem e_1323 : - 11 * (z ^^^ t) - 1 * (z ||| ~~~t) - 5 * ~~~(z &&& ~~~t) + 2 * (z ||| t) - 11 * ~~~(z &&& t) + 24 * ~~~(z ||| t) + 25 * ~~~(z ||| ~~~t) + 20 * (z &&& ~~~t) + 10 * (z &&& t) = 7 * ~~~(z ^^^ t) - 1 * z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1324 (x y : BitVec w) : +theorem e_1324 : - 1 * z - 1 * t + 7 * (z ^^^ t) - 11 * ~~~(z &&& ~~~z) - 11 * ~~~(z ^^^ t) + 3 * ~~~(z &&& t) - 3 * (z ||| t) + 19 * ~~~(z ||| t) + 5 * (z &&& ~~~t) = - 5 * ~~~(z ||| ~~~t) - 27 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1325 (x y : BitVec w) : +theorem e_1325 : 11 * ~~~z + 1 * (z ||| ~~~t) + 2 * (z ^^^ t) - 11 * ~~~t + 1 * ~~~(z ^^^ t) + 2 * (z ||| t) - 4 * ~~~(z ||| t) - 17 * ~~~(z ||| ~~~t) + 6 * (z &&& ~~~t) = - 2 * ~~~(z &&& ~~~t) + 6 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1326 (x y : BitVec w) : +theorem e_1326 : 5 * t + 3 * ~~~(z ^^^ t) - 5 * ~~~(z &&& ~~~t) - 1 * (z ||| ~~~t) + 3 * ~~~(z &&& t) - 1 * ~~~(z ||| t) - 4 * ~~~(z ||| ~~~t) - 3 * (z &&& ~~~t) - 3 * (z &&& t) = - 1 * ~~~(z &&& ~~~z) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1327 (x y : BitVec w) : +theorem e_1327 : 1 * (z ||| ~~~t) + 5 * (z ^^^ t) - 1 * ~~~(z &&& ~~~t) - 2 * z - 5 * ~~~z + 3 * ~~~(z &&& ~~~z) - 15 * ~~~(z ||| ~~~t) - 9 * (z &&& ~~~t) - 12 * (z &&& t) = - 2 * ~~~(z &&& t) - 11 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1328 (x y : BitVec w) : +theorem e_1328 : - 5 * (z ||| ~~~t) + 11 * t + 2 * (z ^^^ t) - 11 * (z ||| t) + 5 * ~~~(z &&& ~~~z) - 2 * ~~~(z ||| t) - 9 * ~~~(z ||| ~~~t) + 9 * (z &&& ~~~t) - 2 * (z &&& t) = - 2 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1329 (x y : BitVec w) : +theorem e_1329 : 7 * (z ||| t) - 6 * (z ||| ~~~t) + 1 * ~~~t - 6 * ~~~(z &&& ~~~t) - 2 * ~~~z + 4 * ~~~(z &&& ~~~z) + 9 * ~~~(z ||| t) - 4 * ~~~(z ||| ~~~t) - 6 * (z &&& ~~~t) = - 1 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1330 (x y : BitVec w) : +theorem e_1330 : - 2 * ~~~(z ^^^ t) - 11 * (z ||| ~~~t) - 2 * ~~~t - 11 * (z ||| t) - 11 * ~~~(z &&& t) - 11 * ~~~(z &&& ~~~z) + 37 * ~~~(z ||| t) + 36 * ~~~(z ||| ~~~t) + 38 * (z &&& t) = - 46 * (z &&& ~~~t) + 3 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1331 (x y : BitVec w) : +theorem e_1331 : - 2 * ~~~(z ^^^ t) + 1 * z + 5 * ~~~(z &&& t) + 3 * ~~~(z &&& ~~~z) - 3 * (z ||| ~~~t) - 5 * ~~~(z ||| t) - 10 * ~~~(z ||| ~~~t) - 6 * (z &&& ~~~t) - 1 * (z &&& t) = - 2 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1332 (x y : BitVec w) : +theorem e_1332 : 4 * ~~~(z &&& t) - 1 * ~~~(z &&& ~~~t) - 11 * (z ||| ~~~t) - 1 * ~~~t + 1 * ~~~(z &&& ~~~z) - 1 * ~~~(z ^^^ t) + 9 * ~~~(z ||| t) - 4 * ~~~(z ||| ~~~t) + 7 * (z &&& ~~~t) = - 12 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1333 (x y : BitVec w) : +theorem e_1333 : 1 * ~~~z + 4 * t + 7 * ~~~(z ^^^ t) + 3 * (z ^^^ t) + 7 * ~~~t - 16 * ~~~(z ||| t) - 8 * ~~~(z ||| ~~~t) - 4 * (z &&& ~~~t) - 5 * (z &&& t) = - 1 * (z ||| ~~~t) + 7 * z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1334 (x y : BitVec w) : +theorem e_1334 : 1 * (z ^^^ t) + 7 * (z ||| t) - 2 * ~~~t - 7 * ~~~z + 3 * (z ||| ~~~t) + 2 * z + 6 * ~~~(z ||| t) - 11 * (z &&& ~~~t) - 12 * (z &&& t) = 1 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1335 (x y : BitVec w) : +theorem e_1335 : - 1 * ~~~(z &&& ~~~z) - 7 * t + 5 * ~~~(z &&& t) + 11 * ~~~t + 2 * (z ^^^ t) + 5 * ~~~(z ^^^ t) - 20 * ~~~(z ||| t) - 18 * (z &&& ~~~t) + 2 * (z &&& t) = - 1 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1336 (x y : BitVec w) : +theorem e_1336 : - 7 * ~~~(z ^^^ t) - 6 * (z ||| t) + 7 * (z ||| ~~~t) + 2 * ~~~(z &&& t) - 11 * ~~~(z &&& ~~~z) - 6 * z + 15 * ~~~(z ||| ~~~t) + 14 * (z &&& ~~~t) + 23 * (z &&& t) = - 9 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1337 (x y : BitVec w) : +theorem e_1337 : 2 * (z ^^^ t) + 2 * ~~~(z &&& ~~~z) + 1 * (z ||| ~~~t) - 2 * (z ||| t) + 1 * ~~~(z &&& ~~~t) + 7 * z - 2 * t - 4 * ~~~(z ||| t) - 1 * ~~~(z ||| ~~~t) - 7 * (z &&& t) = 10 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1338 (x y : BitVec w) : +theorem e_1338 : 5 * t + 11 * ~~~(z &&& ~~~t) - 2 * ~~~t + 1 * ~~~z - 11 * ~~~(z ^^^ t) + 2 * (z ||| t) + 1 * ~~~(z &&& ~~~z) - 5 * ~~~(z ||| t) - 25 * ~~~(z ||| ~~~t) - 6 * (z &&& ~~~t) = - 5 * ~~~(z &&& t) + 8 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1339 (x y : BitVec w) : +theorem e_1339 : 1 * ~~~z + 1 * ~~~(z &&& ~~~z) - 7 * (z ^^^ t) - 2 * ~~~(z &&& ~~~t) + 2 * ~~~t + 5 * ~~~(z ^^^ t) + 1 * (z ||| ~~~t) + 3 * ~~~(z ||| ~~~t) + 3 * (z &&& ~~~t) - 9 * (z &&& t) = - 4 * t + 8 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1340 (x y : BitVec w) : +theorem e_1340 : - 2 * (z ||| ~~~t) - 2 * ~~~t + 2 * ~~~(z &&& ~~~z) + 1 * ~~~(z &&& ~~~t) - 7 * ~~~(z ^^^ t) + 1 * ~~~(z &&& t) - 3 * t + 7 * ~~~(z ||| t) + 1 * (z &&& ~~~t) + 9 * (z &&& t) = 1 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1341 (x y : BitVec w) : +theorem e_1341 : - 2 * (z ||| t) - 3 * ~~~(z &&& ~~~z) - 2 * ~~~(z ^^^ t) - 1 * (z ||| ~~~t) + 1 * t - 1 * ~~~z + 7 * (z ^^^ t) + 8 * ~~~(z ||| t) - 1 * ~~~(z ||| ~~~t) + 7 * (z &&& t) = 1 * ~~~(z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1342 (x y : BitVec w) : +theorem e_1342 : 7 * ~~~(z &&& t) + 1 * ~~~t + 4 * ~~~(z &&& ~~~t) + 1 * z - 11 * t - 1 * ~~~z - 11 * ~~~(z ||| t) + 2 * ~~~(z ||| ~~~t) - 8 * (z &&& ~~~t) + 7 * (z &&& t) = 1 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1343 (x y : BitVec w) : +theorem e_1343 : - 1 * ~~~(z &&& ~~~z) - 7 * (z ^^^ t) + 5 * ~~~(z &&& t) - 5 * (z ||| t) + 1 * ~~~t - 1 * z + 4 * ~~~(z ||| t) + 8 * ~~~(z ||| ~~~t) + 11 * (z &&& ~~~t) + 16 * (z &&& t) = 3 * (z ||| ~~~t) + 6 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1344 (x y : BitVec w) : +theorem e_1344 : - 1 * ~~~(z &&& t) - 6 * (z ||| t) - 1 * ~~~(z ^^^ t) - 1 * (z ||| ~~~t) - 1 * ~~~(z &&& ~~~t) - 11 * z - 3 * t + 15 * ~~~(z ||| t) + 11 * ~~~(z ||| ~~~t) + 23 * (z &&& t) = - 30 * (z &&& ~~~t) + 11 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1345 (x y : BitVec w) : +theorem e_1345 : - 1 * z - 5 * (z ^^^ t) + 11 * ~~~(z ^^^ t) + 1 * ~~~(z &&& t) + 7 * ~~~(z &&& ~~~t) - 6 * ~~~z - 11 * ~~~(z ||| t) + 3 * ~~~(z ||| ~~~t) + 7 * (z &&& ~~~t) - 15 * (z &&& t) = 2 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1346 (x y : BitVec w) : +theorem e_1346 : - 3 * (z ||| ~~~t) + 2 * ~~~t + 1 * ~~~(z &&& ~~~t) - 1 * ~~~(z &&& t) - 7 * ~~~z + 5 * ~~~(z &&& ~~~z) + 3 * ~~~(z ||| t) + 2 * ~~~(z ||| ~~~t) - 6 * (z &&& ~~~t) - 6 * (z &&& t) = - 3 * z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1347 (x y : BitVec w) : +theorem e_1347 : - 7 * ~~~(z &&& ~~~t) + 4 * (z ||| t) + 3 * (z ||| ~~~t) - 1 * ~~~z - 3 * z + 11 * ~~~t + 6 * ~~~(z ||| t) + 16 * ~~~(z ||| ~~~t) - 3 * (z &&& ~~~t) + 8 * (z &&& t) = 7 * ~~~(z &&& t) + 5 * ~~~(z &&& ~~~z) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1348 (x y : BitVec w) : +theorem e_1348 : - 11 * ~~~(z ^^^ t) + 5 * (z ||| t) - 3 * ~~~(z &&& ~~~z) - 2 * t - 7 * z + 11 * ~~~z + 6 * ~~~(z ||| t) - 9 * ~~~(z ||| ~~~t) + 7 * (z &&& ~~~t) + 18 * (z &&& t) = - 1 * (z ^^^ t) + 3 * ~~~(z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1349 (x y : BitVec w) : +theorem e_1349 : 4 * ~~~(z &&& ~~~z) + 7 * ~~~t - 3 * ~~~z + 3 * z + 3 * (z ||| ~~~t) - 7 * (z ^^^ t) - 2 * t + 6 * ~~~(z ||| ~~~t) - 12 * (z &&& ~~~t) - 10 * (z &&& t) = 11 * ~~~(z ||| t) - 2 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1350 (x y : BitVec w) : +theorem e_1350 : 7 * (z ||| ~~~t) + 3 * z - 6 * (z ||| t) - 2 * ~~~(z &&& t) - 1 * ~~~(z &&& ~~~t) - 6 * (z ^^^ t) - 2 * ~~~(z &&& ~~~z) - 6 * ~~~(z ||| t) + 12 * ~~~(z ||| ~~~t) + 6 * (z &&& ~~~t) = - 5 * ~~~z + 1 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1351 (x y : BitVec w) : +theorem e_1351 : 2 * ~~~(z &&& t) - 6 * ~~~t + 4 * ~~~z - 2 * z - 6 * (z ^^^ t) - 7 * t - 1 * ~~~(z ||| t) + 7 * ~~~(z ||| ~~~t) + 12 * (z &&& ~~~t) + 8 * (z &&& t) = - 1 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1352 (x y : BitVec w) : +theorem e_1352 : - 1 * (z ||| ~~~t) - 7 * ~~~z + 2 * (z ||| t) + 2 * ~~~(z &&& ~~~z) + 2 * ~~~(z &&& t) - 7 * t + 2 * ~~~(z &&& ~~~t) - 11 * z + 2 * ~~~(z ||| t) + 13 * (z &&& t) = - 6 * (z &&& ~~~t) - 6 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1353 (x y : BitVec w) : +theorem e_1353 : 11 * z + 3 * ~~~z + 1 * (z ||| t) - 3 * t - 1 * (z ^^^ t) - 1 * ~~~(z &&& t) + 11 * ~~~(z ||| t) + 7 * ~~~(z ||| ~~~t) + 3 * (z &&& ~~~t) + 4 * (z &&& t) = 6 * ~~~(z &&& ~~~z) + 7 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1354 (x y : BitVec w) : +theorem e_1354 : - 3 * ~~~(z &&& t) + 11 * ~~~t - 5 * (z ^^^ t) + 1 * ~~~(z &&& ~~~t) + 11 * t + 1 * ~~~(z ^^^ t) + 7 * (z ||| t) - 12 * ~~~(z ||| t) - 11 * ~~~(z ||| ~~~t) - 22 * (z &&& t) = 12 * (z &&& ~~~t) - 2 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1355 (x y : BitVec w) : +theorem e_1355 : - 1 * z + 5 * (z ||| ~~~t) - 1 * ~~~z - 2 * ~~~(z &&& t) + 2 * ~~~(z &&& ~~~t) + 5 * ~~~(z &&& ~~~z) + 4 * ~~~(z ^^^ t) - 13 * ~~~(z ||| t) - 7 * (z &&& ~~~t) - 15 * (z &&& t) = 4 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1356 (x y : BitVec w) : +theorem e_1356 : 2 * t + 7 * z + 3 * (z ^^^ t) + 7 * ~~~(z &&& ~~~t) + 1 * ~~~(z &&& ~~~z) - 6 * ~~~(z ^^^ t) - 7 * ~~~(z ||| t) - 13 * ~~~(z ||| ~~~t) - 6 * (z &&& ~~~t) - 6 * (z &&& t) = 5 * (z ||| t) - 5 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1357 (x y : BitVec w) : +theorem e_1357 : - 2 * t - 6 * ~~~(z &&& ~~~t) - 1 * ~~~t + 5 * ~~~(z &&& t) - 2 * z - 1 * ~~~(z ^^^ t) + 3 * ~~~(z ||| t) + 2 * ~~~(z ||| ~~~t) - 3 * (z &&& ~~~t) + 10 * (z &&& t) = - 1 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1358 (x y : BitVec w) : +theorem e_1358 : - 7 * (z ||| t) + 1 * z + 5 * ~~~(z &&& t) + 3 * ~~~z - 1 * ~~~(z &&& ~~~t) - 2 * (z ||| ~~~t) - 1 * t - 2 * ~~~(z ||| t) + 1 * ~~~(z ||| ~~~t) + 13 * (z &&& t) = 3 * ~~~(z ^^^ t) - 3 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1359 (x y : BitVec w) : +theorem e_1359 : 2 * ~~~t - 1 * (z ^^^ t) - 11 * (z ||| t) + 4 * ~~~z + 5 * ~~~(z &&& ~~~z) + 1 * z + 2 * ~~~(z ^^^ t) - 5 * ~~~(z &&& ~~~t) + 8 * ~~~(z ||| ~~~t) + 8 * (z &&& t) = - 4 * (z &&& ~~~t) + 8 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1360 (x y : BitVec w) : +theorem e_1360 : 7 * ~~~(z ^^^ t) - 5 * ~~~(z &&& ~~~z) - 3 * (z ||| t) - 6 * ~~~(z &&& ~~~t) - 1 * ~~~(z &&& t) + 11 * ~~~t + 2 * (z ^^^ t) - 6 * ~~~(z ||| t) + 14 * ~~~(z ||| ~~~t) + 8 * (z &&& t) = 4 * (z &&& ~~~t) + 1 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1361 (x y : BitVec w) : +theorem e_1361 : 4 * ~~~z + 2 * t + 1 * ~~~(z &&& ~~~z) - 3 * ~~~(z ^^^ t) + 2 * ~~~(z &&& ~~~t) + 7 * ~~~(z &&& t) + 4 * ~~~t + 5 * (z ^^^ t) - 21 * ~~~(z ||| ~~~t) - 17 * (z &&& ~~~t) = 2 * (z &&& t) + 15 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1362 (x y : BitVec w) : +theorem e_1362 : - 11 * ~~~(z ^^^ t) + 1 * (z ^^^ t) - 3 * t - 6 * ~~~(z &&& ~~~z) + 11 * (z ||| ~~~t) - 2 * z + 9 * ~~~(z ||| t) + 11 * ~~~(z ||| ~~~t) - 4 * (z &&& ~~~t) + 11 * (z &&& t) = 3 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1363 (x y : BitVec w) : +theorem e_1363 : - 2 * ~~~(z &&& t) + 7 * t - 2 * (z ||| ~~~t) - 6 * (z ^^^ t) + 11 * ~~~t - 1 * (z ||| t) + 3 * ~~~(z ||| t) + 1 * ~~~(z ||| ~~~t) - 1 * (z &&& ~~~t) + 6 * (z &&& t) = 11 * ~~~(z ^^^ t) - 1 * ~~~(z &&& ~~~z) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1364 (x y : BitVec w) : +theorem e_1364 : 5 * ~~~(z &&& ~~~t) + 11 * (z ||| t) + 5 * (z ^^^ t) + 11 * ~~~(z &&& t) + 4 * z + 2 * ~~~t + 2 * t - 29 * ~~~(z ||| ~~~t) - 28 * (z &&& ~~~t) - 17 * (z &&& t) = 5 * ~~~(z &&& ~~~z) + 13 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1365 (x y : BitVec w) : +theorem e_1365 : 1 * t - 3 * ~~~(z &&& ~~~z) + 7 * ~~~(z &&& ~~~t) - 11 * ~~~(z &&& t) - 1 * (z ||| t) + 7 * ~~~t + 1 * ~~~(z ^^^ t) - 1 * ~~~(z ||| t) + 7 * ~~~(z ||| ~~~t) - 5 * (z &&& t) = - 8 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1366 (x y : BitVec w) : +theorem e_1366 : 5 * ~~~t - 2 * ~~~(z &&& ~~~z) + 5 * ~~~(z ^^^ t) + 11 * z + 4 * (z ^^^ t) - 7 * ~~~(z &&& t) + 10 * ~~~(z ||| t) + 16 * ~~~(z ||| ~~~t) - 11 * (z &&& ~~~t) - 14 * (z &&& t) = 11 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1367 (x y : BitVec w) : +theorem e_1367 : 1 * ~~~z + 3 * z - 2 * t - 1 * (z ||| t) - 2 * ~~~(z &&& ~~~z) + 1 * ~~~(z &&& ~~~t) - 7 * (z ||| ~~~t) + 4 * ~~~(z ||| t) + 4 * (z &&& ~~~t) + 8 * (z &&& t) = - 3 * ~~~(z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1368 (x y : BitVec w) : +theorem e_1368 : - 1 * ~~~(z &&& ~~~t) + 11 * ~~~t + 4 * ~~~z - 5 * (z ||| ~~~t) - 11 * (z ^^^ t) - 1 * ~~~(z ^^^ t) - 1 * t - 15 * ~~~(z ||| t) + 2 * ~~~(z ||| ~~~t) + 8 * (z &&& t) = 2 * (z &&& ~~~t) - 7 * ~~~(z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1369 (x y : BitVec w) : +theorem e_1369 : 2 * (z ||| ~~~t) + 3 * ~~~t - 1 * (z ||| t) - 6 * ~~~(z &&& ~~~z) - 2 * t - 5 * (z ^^^ t) + 2 * ~~~(z &&& t) + 12 * ~~~(z ||| ~~~t) + 5 * (z &&& ~~~t) + 8 * (z &&& t) = 1 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1370 (x y : BitVec w) : +theorem e_1370 : - 1 * (z ||| ~~~t) - 2 * z + 1 * ~~~t + 2 * ~~~(z ^^^ t) - 7 * (z ^^^ t) + 2 * (z ||| t) - 5 * ~~~(z &&& ~~~z) - 11 * ~~~(z &&& t) + 21 * ~~~(z ||| ~~~t) + 4 * (z &&& t) = - 23 * (z &&& ~~~t) - 14 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1371 (x y : BitVec w) : +theorem e_1371 : - 11 * ~~~(z ^^^ t) + 1 * ~~~(z &&& t) + 7 * ~~~(z &&& ~~~t) + 2 * ~~~(z &&& ~~~z) - 11 * z - 7 * t - 4 * ~~~(z ||| t) - 8 * ~~~(z ||| ~~~t) - 2 * (z &&& ~~~t) + 10 * (z &&& t) = - 5 * (z ||| t) - 5 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1372 (x y : BitVec w) : +theorem e_1372 : 5 * z + 4 * (z ||| ~~~t) - 2 * (z ||| t) + 2 * ~~~(z &&& t) - 11 * ~~~t - 3 * ~~~(z &&& ~~~t) + 3 * t + 9 * ~~~(z ||| t) + 1 * ~~~(z ||| ~~~t) - 6 * (z &&& t) = - 3 * (z &&& ~~~t) + 1 * ~~~(z &&& ~~~z) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1373 (x y : BitVec w) : +theorem e_1373 : - 3 * z + 11 * ~~~(z &&& ~~~z) - 2 * ~~~(z ^^^ t) + 11 * ~~~t + 2 * (z ||| t) - 3 * ~~~(z &&& ~~~t) - 17 * ~~~(z ||| t) - 21 * ~~~(z ||| ~~~t) - 21 * (z &&& ~~~t) - 16 * (z &&& t) = - 11 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1374 (x y : BitVec w) : +theorem e_1374 : - 1 * ~~~(z ^^^ t) - 2 * ~~~(z &&& ~~~t) - 6 * t + 7 * (z ||| ~~~t) + 1 * (z ||| t) + 7 * ~~~(z &&& ~~~z) - 2 * ~~~z + 7 * ~~~t + 2 * ~~~(z ||| ~~~t) - 6 * (z &&& t) = 22 * (z &&& ~~~t) + 16 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1375 (x y : BitVec w) : +theorem e_1375 : 1 * ~~~t - 2 * (z ^^^ t) - 6 * (z ||| t) + 7 * z - 3 * (z ||| ~~~t) + 11 * ~~~(z &&& ~~~z) - 5 * ~~~(z &&& ~~~t) - 4 * ~~~(z ||| t) + 2 * ~~~(z ||| ~~~t) - 4 * (z &&& t) = 8 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1376 (x y : BitVec w) : +theorem e_1376 : - 5 * (z ^^^ t) - 1 * (z ||| ~~~t) + 1 * t - 7 * ~~~(z &&& ~~~z) + 5 * ~~~t + 2 * ~~~z - 9 * ~~~(z ||| t) + 10 * ~~~(z ||| ~~~t) + 9 * (z &&& ~~~t) - 4 * (z &&& t) = - 11 * ~~~(z ^^^ t) + 1 * ~~~(z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1377 (x y : BitVec w) : +theorem e_1377 : - 3 * (z ||| t) - 1 * ~~~(z &&& ~~~z) - 3 * ~~~z - 1 * ~~~(z &&& t) - 11 * t + 1 * ~~~(z &&& ~~~t) + 3 * (z ||| ~~~t) + 1 * ~~~(z ||| t) + 18 * ~~~(z ||| ~~~t) + 1 * (z &&& ~~~t) = - 1 * z - 10 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1378 (x y : BitVec w) : +theorem e_1378 : - 3 * (z ^^^ t) + 11 * ~~~(z ^^^ t) + 11 * t - 7 * ~~~(z &&& t) - 6 * ~~~(z &&& ~~~z) - 1 * ~~~t + 5 * (z ||| ~~~t) - 7 * ~~~(z ||| t) + 12 * (z &&& ~~~t) - 19 * (z &&& t) = 2 * ~~~(z &&& ~~~t) - 7 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1379 (x y : BitVec w) : +theorem e_1379 : - 7 * ~~~z + 4 * ~~~(z &&& ~~~z) + 11 * (z ^^^ t) + 5 * ~~~(z ^^^ t) + 7 * ~~~(z &&& ~~~t) + 3 * (z ||| t) - 14 * ~~~(z ||| t) - 18 * ~~~(z ||| ~~~t) - 23 * (z &&& ~~~t) - 23 * (z &&& t) = - 4 * (z ||| ~~~t) - 1 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1380 (x y : BitVec w) : +theorem e_1380 : - 2 * ~~~(z &&& ~~~t) + 1 * ~~~z + 1 * (z ||| t) - 2 * ~~~(z &&& ~~~z) - 6 * ~~~t - 6 * t + 8 * ~~~(z ||| t) + 7 * ~~~(z ||| ~~~t) - 1 * (z &&& ~~~t) + 2 * (z &&& t) = - 7 * z - 1 * ~~~(z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1381 (x y : BitVec w) : +theorem e_1381 : - 2 * ~~~(z &&& t) - 2 * t + 7 * (z ||| ~~~t) + 2 * ~~~(z ^^^ t) - 1 * ~~~(z &&& ~~~t) + 1 * ~~~t - 2 * (z ^^^ t) - 7 * ~~~(z ||| t) + 7 * ~~~(z ||| ~~~t) - 4 * (z &&& ~~~t) = 6 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1382 (x y : BitVec w) : +theorem e_1382 : - 1 * t + 2 * ~~~(z ^^^ t) + 3 * (z ||| t) - 2 * ~~~(z &&& ~~~t) + 11 * (z ||| ~~~t) - 1 * ~~~(z &&& t) + 5 * z - 10 * ~~~(z ||| t) - 19 * (z &&& ~~~t) - 18 * (z &&& t) = - 1 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1383 (x y : BitVec w) : +theorem e_1383 : 11 * (z ||| ~~~t) + 3 * (z ||| t) + 3 * ~~~(z &&& ~~~t) + 4 * z - 6 * ~~~t + 1 * t + 14 * ~~~(z ||| t) + 15 * ~~~(z ||| ~~~t) - 1 * (z &&& ~~~t) - 22 * (z &&& t) = 11 * ~~~z + 11 * ~~~(z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1384 (x y : BitVec w) : +theorem e_1384 : 1 * (z ^^^ t) - 2 * z - 7 * (z ||| ~~~t) - 11 * t - 3 * ~~~(z &&& ~~~t) - 2 * ~~~(z ^^^ t) + 7 * (z ||| t) - 1 * ~~~(z &&& t) + 13 * ~~~(z ||| t) + 18 * (z &&& t) = - 2 * (z &&& ~~~t) - 7 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1385 (x y : BitVec w) : +theorem e_1385 : - 6 * ~~~(z &&& ~~~t) + 1 * t - 7 * (z ||| t) + 2 * ~~~(z &&& ~~~z) - 7 * ~~~t - 1 * ~~~z - 7 * ~~~(z ^^^ t) + 11 * ~~~(z ||| ~~~t) + 12 * (z &&& ~~~t) + 17 * (z &&& t) = - 19 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1386 (x y : BitVec w) : +theorem e_1386 : - 5 * ~~~t + 4 * (z ^^^ t) + 3 * t + 1 * ~~~(z &&& t) + 5 * ~~~(z &&& ~~~t) + 1 * z - 3 * ~~~(z &&& ~~~z) - 10 * ~~~(z ||| ~~~t) + 2 * (z &&& ~~~t) - 6 * (z &&& t) = - 2 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1387 (x y : BitVec w) : +theorem e_1387 : - 2 * ~~~z - 6 * t + 1 * ~~~(z &&& t) - 1 * (z ||| t) - 7 * ~~~(z &&& ~~~t) + 4 * z - 1 * (z ^^^ t) + 12 * ~~~(z ||| t) + 19 * ~~~(z ||| ~~~t) + 14 * (z &&& t) = 1 * ~~~(z ^^^ t) + 3 * ~~~(z &&& ~~~z) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1388 (x y : BitVec w) : +theorem e_1388 : - 3 * (z ||| t) + 2 * (z ^^^ t) + 3 * t - 2 * ~~~(z ^^^ t) + 4 * ~~~(z &&& ~~~z) + 11 * ~~~t + 1 * z + 1 * (z ||| ~~~t) - 6 * ~~~(z ||| ~~~t) - 16 * (z &&& ~~~t) = 4 * (z &&& t) + 14 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1389 (x y : BitVec w) : +theorem e_1389 : 1 * t + 2 * ~~~t - 5 * z - 3 * ~~~z - 6 * ~~~(z &&& ~~~t) + 4 * ~~~(z &&& ~~~z) + 4 * (z ^^^ t) - 1 * ~~~(z ||| t) - 9 * (z &&& ~~~t) + 2 * (z &&& t) = - 4 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1390 (x y : BitVec w) : +theorem e_1390 : - 6 * ~~~(z ^^^ t) + 5 * t + 2 * ~~~z - 11 * ~~~(z &&& ~~~z) + 11 * (z ||| t) - 6 * (z ^^^ t) - 7 * (z ||| ~~~t) - 1 * ~~~(z ||| ~~~t) + 18 * (z &&& ~~~t) + 13 * (z &&& t) = 5 * z - 22 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1391 (x y : BitVec w) : +theorem e_1391 : - 1 * (z ^^^ t) - 3 * z + 1 * t + 1 * ~~~(z ^^^ t) + 1 * ~~~(z &&& ~~~z) + 4 * ~~~(z &&& t) - 7 * ~~~z + 3 * ~~~(z ||| t) + 2 * ~~~(z ||| ~~~t) + 1 * (z &&& ~~~t) = 2 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1392 (x y : BitVec w) : +theorem e_1392 : 7 * (z ||| ~~~t) - 11 * z + 2 * ~~~t + 3 * (z ^^^ t) - 3 * ~~~(z &&& t) + 1 * ~~~(z &&& ~~~z) - 2 * t + 12 * ~~~(z ||| ~~~t) + 1 * (z &&& ~~~t) + 5 * (z &&& t) = - 4 * ~~~(z ||| t) + 11 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1393 (x y : BitVec w) : +theorem e_1393 : - 6 * (z ||| ~~~t) - 6 * ~~~(z ^^^ t) - 1 * (z ||| t) + 1 * t + 2 * (z ^^^ t) - 11 * ~~~(z &&& t) - 1 * ~~~t + 23 * ~~~(z ||| t) + 8 * ~~~(z ||| ~~~t) + 17 * (z &&& ~~~t) = - 11 * (z &&& t) - 1 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1394 (x y : BitVec w) : +theorem e_1394 : - 6 * ~~~t - 3 * (z ^^^ t) - 2 * ~~~(z &&& ~~~z) + 3 * ~~~(z &&& t) - 1 * (z ||| t) + 1 * z - 2 * ~~~(z ||| t) + 3 * ~~~(z ||| ~~~t) + 8 * (z &&& ~~~t) - 5 * (z &&& t) = - 7 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1395 (x y : BitVec w) : +theorem e_1395 : 2 * (z ||| ~~~t) - 3 * z + 4 * ~~~z - 1 * t - 1 * ~~~(z &&& t) - 5 * ~~~(z ^^^ t) - 3 * ~~~(z &&& ~~~z) + 3 * ~~~(z ||| t) + 5 * (z &&& ~~~t) + 10 * (z &&& t) = - 1 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1396 (x y : BitVec w) : +theorem e_1396 : 1 * ~~~(z ^^^ t) - 3 * (z ^^^ t) + 11 * ~~~(z &&& ~~~t) + 11 * ~~~t - 1 * ~~~z + 2 * ~~~(z &&& t) - 25 * ~~~(z ||| t) - 9 * ~~~(z ||| ~~~t) - 11 * (z &&& ~~~t) - 13 * (z &&& t) = - 1 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1397 (x y : BitVec w) : +theorem e_1397 : - 11 * (z ||| t) - 5 * ~~~(z &&& t) + 7 * ~~~z - 6 * t + 1 * (z ||| ~~~t) + 11 * ~~~(z &&& ~~~z) - 1 * ~~~t - 13 * ~~~(z ||| t) + 4 * ~~~(z ||| ~~~t) + 5 * (z &&& t) = - 5 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1398 (x y : BitVec w) : +theorem e_1398 : 7 * ~~~z - 1 * ~~~(z &&& ~~~t) + 2 * ~~~(z &&& t) + 7 * ~~~(z &&& ~~~z) + 3 * ~~~(z ^^^ t) - 2 * z - 18 * ~~~(z ||| t) - 21 * ~~~(z ||| ~~~t) - 13 * (z &&& ~~~t) - 10 * (z &&& t) = - 3 * (z ||| t) - 3 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1399 (x y : BitVec w) : +theorem e_1399 : - 1 * ~~~z + 1 * ~~~(z &&& ~~~z) + 2 * t - 1 * (z ^^^ t) - 7 * ~~~t - 3 * ~~~(z &&& t) + 11 * ~~~(z ||| t) + 3 * ~~~(z ||| ~~~t) + 10 * (z &&& ~~~t) - 2 * (z &&& t) = 1 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1400 (x y : BitVec w) : +theorem e_1400 : - 5 * z - 2 * ~~~t + 1 * (z ^^^ t) + 3 * (z ||| ~~~t) - 3 * ~~~(z &&& ~~~z) + 7 * ~~~z - 5 * ~~~(z ||| t) - 3 * ~~~(z ||| ~~~t) + 8 * (z &&& ~~~t) + 7 * (z &&& t) = 2 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1401 (x y : BitVec w) : +theorem e_1401 : 4 * t - 2 * (z ||| ~~~t) + 2 * (z ^^^ t) - 2 * ~~~(z &&& ~~~z) + 1 * ~~~(z ^^^ t) + 3 * (z ||| t) - 4 * ~~~(z ||| t) - 14 * ~~~(z ||| ~~~t) - 1 * (z &&& ~~~t) - 4 * (z &&& t) = - 7 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1402 (x y : BitVec w) : +theorem e_1402 : 4 * (z ^^^ t) + 2 * ~~~z + 5 * ~~~(z &&& t) + 4 * (z ||| t) - 5 * ~~~(z &&& ~~~z) - 3 * (z ||| ~~~t) + 7 * z + 1 * ~~~(z ||| t) - 10 * ~~~(z ||| ~~~t) - 3 * (z &&& t) = 12 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1403 (x y : BitVec w) : +theorem e_1403 : 1 * ~~~(z &&& ~~~t) + 2 * z + 5 * ~~~(z &&& t) + 7 * (z ^^^ t) - 1 * (z ||| t) - 5 * (z ||| ~~~t) - 1 * ~~~z - 11 * ~~~(z ||| ~~~t) - 8 * (z &&& ~~~t) + 4 * (z &&& t) = - 1 * ~~~(z ||| t) + 1 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1404 (x y : BitVec w) : +theorem e_1404 : - 6 * (z ||| t) - 2 * ~~~z - 2 * ~~~(z &&& ~~~z) - 5 * z + 1 * ~~~t - 7 * (z ^^^ t) + 10 * ~~~(z ||| t) + 27 * ~~~(z ||| ~~~t) + 19 * (z &&& ~~~t) + 23 * (z &&& t) = 7 * ~~~(z &&& ~~~t) + 3 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1405 (x y : BitVec w) : +theorem e_1405 : - 2 * ~~~(z &&& ~~~z) - 2 * ~~~(z ^^^ t) - 7 * ~~~z + 2 * t + 11 * (z ^^^ t) + 1 * ~~~(z &&& t) - 6 * z + 9 * ~~~(z ||| t) - 5 * ~~~(z ||| ~~~t) - 5 * (z &&& ~~~t) = - 8 * (z &&& t) - 1 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1406 (x y : BitVec w) : +theorem e_1406 : - 7 * z - 7 * ~~~t - 3 * ~~~(z &&& ~~~z) - 6 * (z ||| ~~~t) + 1 * ~~~z - 7 * ~~~(z ^^^ t) + 5 * t + 22 * ~~~(z ||| t) - 10 * ~~~(z ||| ~~~t) + 11 * (z &&& t) = - 7 * (z ||| t) - 16 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1407 (x y : BitVec w) : +theorem e_1407 : 4 * z - 1 * (z ^^^ t) - 7 * (z ||| ~~~t) + 7 * ~~~t + 2 * ~~~(z &&& t) + 1 * ~~~(z &&& ~~~z) - 15 * ~~~(z ||| t) - 14 * ~~~(z ||| ~~~t) - 6 * (z &&& ~~~t) + 1 * (z &&& t) = - 11 * ~~~z - 1 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1408 (x y : BitVec w) : +theorem e_1408 : 5 * ~~~t + 3 * (z ||| t) - 2 * ~~~(z &&& ~~~z) - 7 * ~~~(z &&& ~~~t) + 2 * z + 2 * t - 3 * (z ||| ~~~t) - 2 * ~~~(z &&& t) + 9 * ~~~(z ||| t) - 3 * (z &&& ~~~t) = - 5 * (z &&& t) - 6 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1409 (x y : BitVec w) : +theorem e_1409 : 11 * ~~~t + 5 * ~~~(z ^^^ t) - 6 * ~~~(z &&& ~~~z) - 1 * ~~~(z &&& t) + 2 * (z ^^^ t) + 1 * (z ||| t) - 6 * ~~~(z ||| t) + 3 * ~~~(z ||| ~~~t) - 4 * (z &&& ~~~t) + 2 * (z &&& t) = - 1 * t + 3 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1410 (x y : BitVec w) : +theorem e_1410 : - 6 * z - 3 * ~~~z - 11 * (z ^^^ t) - 5 * ~~~(z &&& ~~~t) - 1 * t - 1 * ~~~(z &&& t) + 7 * ~~~(z ||| t) + 21 * ~~~(z ||| ~~~t) + 18 * (z &&& ~~~t) + 10 * (z &&& t) = - 2 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1411 (x y : BitVec w) : +theorem e_1411 : - 2 * (z ^^^ t) + 11 * t + 4 * z + 1 * (z ||| ~~~t) - 1 * ~~~(z ^^^ t) - 5 * ~~~(z &&& ~~~z) - 2 * ~~~(z ||| t) - 11 * ~~~(z ||| ~~~t) + 2 * (z &&& ~~~t) - 17 * (z &&& t) = - 7 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1412 (x y : BitVec w) : +theorem e_1412 : - 11 * ~~~(z ^^^ t) - 6 * (z ||| t) - 2 * ~~~z + 1 * ~~~(z &&& t) + 11 * t + 3 * (z ||| ~~~t) - 3 * z + 9 * ~~~(z ||| t) - 4 * ~~~(z ||| ~~~t) + 6 * (z &&& t) = - 5 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1413 (x y : BitVec w) : +theorem e_1413 : 1 * ~~~(z ^^^ t) + 2 * ~~~(z &&& ~~~z) + 1 * ~~~z + 7 * (z ||| t) - 1 * (z ^^^ t) + 2 * z - 3 * ~~~(z ||| t) - 13 * ~~~(z ||| ~~~t) - 9 * (z &&& ~~~t) - 7 * (z &&& t) = - 4 * ~~~(z &&& t) + 5 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1414 (x y : BitVec w) : +theorem e_1414 : 3 * z + 1 * ~~~(z ^^^ t) - 1 * ~~~(z &&& ~~~z) - 2 * ~~~(z &&& t) - 2 * (z ^^^ t) + 4 * (z ||| t) - 2 * ~~~t - 1 * ~~~(z ||| t) - 5 * ~~~(z ||| ~~~t) - 13 * (z &&& t) = - 1 * t - 5 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1415 (x y : BitVec w) : +theorem e_1415 : 5 * (z ||| t) - 3 * ~~~t - 7 * ~~~(z &&& t) + 2 * ~~~z + 1 * z - 2 * ~~~(z ^^^ t) - 6 * ~~~(z &&& ~~~t) + 22 * ~~~(z ||| t) + 6 * ~~~(z ||| ~~~t) + 8 * (z &&& t) = - 10 * (z &&& ~~~t) + 6 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1416 (x y : BitVec w) : +theorem e_1416 : 7 * ~~~(z &&& ~~~z) - 5 * ~~~z - 5 * z - 2 * (z ||| t) + 1 * ~~~(z &&& ~~~t) + 2 * (z ^^^ t) - 3 * ~~~(z ||| t) - 4 * ~~~(z ||| ~~~t) - 2 * (z &&& ~~~t) - 2 * (z &&& t) = - 1 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1417 (x y : BitVec w) : +theorem e_1417 : - 2 * (z ||| ~~~t) - 5 * ~~~(z &&& ~~~t) - 1 * z - 11 * ~~~t - 5 * ~~~z - 6 * ~~~(z &&& t) + 3 * (z ^^^ t) + 29 * ~~~(z ||| t) + 18 * ~~~(z ||| ~~~t) + 17 * (z &&& ~~~t) = 5 * t - 13 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1418 (x y : BitVec w) : +theorem e_1418 : - 7 * z - 11 * (z ||| t) - 6 * (z ^^^ t) + 3 * ~~~t + 1 * (z ||| ~~~t) - 2 * t - 3 * ~~~(z ||| t) + 20 * ~~~(z ||| ~~~t) + 21 * (z &&& ~~~t) + 19 * (z &&& t) = 1 * ~~~(z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1419 (x y : BitVec w) : +theorem e_1419 : 11 * (z ||| t) - 2 * ~~~z + 4 * t + 1 * ~~~(z &&& t) + 1 * ~~~(z &&& ~~~t) + 3 * ~~~(z ^^^ t) + 2 * (z ||| ~~~t) - 3 * ~~~t - 11 * (z &&& ~~~t) - 21 * (z &&& t) = 15 * ~~~(z ||| ~~~t) + 2 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1420 (x y : BitVec w) : +theorem e_1420 : 5 * ~~~(z &&& t) + 2 * ~~~(z &&& ~~~z) - 3 * t - 7 * ~~~(z &&& ~~~t) + 5 * (z ||| ~~~t) - 5 * ~~~t + 2 * ~~~z - 2 * ~~~(z ||| t) + 1 * ~~~(z ||| ~~~t) + 3 * (z &&& t) = 7 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1421 (x y : BitVec w) : +theorem e_1421 : 3 * ~~~z + 2 * (z ^^^ t) + 1 * z + 7 * ~~~(z &&& t) + 1 * ~~~t + 1 * ~~~(z ^^^ t) - 5 * ~~~(z ||| t) - 13 * ~~~(z ||| ~~~t) - 4 * (z &&& ~~~t) + 4 * (z &&& t) = 7 * (z ||| ~~~t) - 1 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1422 (x y : BitVec w) : +theorem e_1422 : - 1 * ~~~(z ^^^ t) + 1 * ~~~(z &&& ~~~z) - 6 * ~~~(z &&& t) + 11 * t + 1 * z + 1 * (z ||| ~~~t) - 2 * (z ^^^ t) - 4 * ~~~(z ||| ~~~t) + 8 * (z &&& ~~~t) - 13 * (z &&& t) = 3 * ~~~t - 8 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1423 (x y : BitVec w) : +theorem e_1423 : - 1 * ~~~(z ^^^ t) - 2 * (z ||| ~~~t) + 5 * (z ^^^ t) - 5 * (z ||| t) + 2 * t + 1 * ~~~t + 11 * ~~~(z &&& ~~~t) - 9 * ~~~(z ||| t) - 13 * ~~~(z ||| ~~~t) - 6 * (z &&& ~~~t) = 12 * (z &&& t) - 7 * z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1424 (x y : BitVec w) : +theorem e_1424 : 1 * t + 4 * ~~~z + 4 * ~~~t - 1 * ~~~(z &&& ~~~z) - 1 * ~~~(z ^^^ t) - 7 * (z ||| ~~~t) - 1 * (z ^^^ t) - 4 * ~~~(z ||| ~~~t) + 4 * (z &&& ~~~t) + 8 * (z &&& t) = - 1 * ~~~(z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1425 (x y : BitVec w) : +theorem e_1425 : - 2 * z - 3 * ~~~z - 11 * ~~~(z &&& ~~~z) + 4 * ~~~t - 7 * ~~~(z &&& t) + 2 * (z ||| ~~~t) - 2 * (z ^^^ t) + 15 * ~~~(z ||| t) + 23 * ~~~(z ||| ~~~t) + 11 * (z &&& t) = - 16 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1426 (x y : BitVec w) : +theorem e_1426 : - 5 * ~~~(z &&& ~~~t) + 3 * (z ||| t) - 3 * t - 6 * (z ||| ~~~t) + 1 * ~~~(z &&& t) - 1 * ~~~t + 7 * ~~~(z ^^^ t) + 1 * ~~~(z ||| t) + 1 * ~~~(z ||| ~~~t) + 1 * (z &&& t) = - 3 * ~~~(z &&& ~~~z) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1427 (x y : BitVec w) : +theorem e_1427 : - 11 * ~~~(z &&& t) - 11 * ~~~(z &&& ~~~t) - 2 * z - 5 * t - 1 * ~~~(z ^^^ t) + 1 * (z ||| t) + 23 * ~~~(z ||| t) + 25 * ~~~(z ||| ~~~t) + 11 * (z &&& ~~~t) + 18 * (z &&& t) = - 1 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1428 (x y : BitVec w) : +theorem e_1428 : - 11 * ~~~z - 11 * ~~~(z ^^^ t) + 5 * ~~~(z &&& t) + 4 * ~~~(z &&& ~~~t) + 2 * z - 2 * (z ||| t) - 1 * (z ||| ~~~t) + 14 * ~~~(z ||| t) + 6 * ~~~(z ||| ~~~t) - 4 * (z &&& ~~~t) = 2 * t - 10 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1429 (x y : BitVec w) : +theorem e_1429 : - 3 * ~~~(z ^^^ t) + 1 * ~~~z + 2 * ~~~(z &&& t) - 2 * t + 11 * (z ||| t) - 3 * (z ^^^ t) - 4 * ~~~(z ||| t) - 13 * ~~~(z ||| ~~~t) - 10 * (z &&& ~~~t) - 10 * (z &&& t) = - 4 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1430 (x y : BitVec w) : +theorem e_1430 : 2 * ~~~(z ^^^ t) - 3 * z - 11 * ~~~(z &&& ~~~t) + 11 * ~~~z - 11 * ~~~(z &&& t) - 3 * ~~~(z &&& ~~~z) + 11 * ~~~(z ||| t) + 15 * ~~~(z ||| ~~~t) + 17 * (z &&& ~~~t) + 15 * (z &&& t) = 1 * (z ^^^ t) - 1 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1431 (x y : BitVec w) : +theorem e_1431 : 2 * ~~~(z ^^^ t) + 4 * z - 3 * ~~~(z &&& t) + 4 * ~~~z + 2 * (z ^^^ t) - 6 * ~~~t + 6 * ~~~(z ||| t) - 3 * ~~~(z ||| ~~~t) + 6 * (z &&& ~~~t) - 3 * (z &&& t) = 3 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1432 (x y : BitVec w) : +theorem e_1432 : 2 * (z ||| ~~~t) - 1 * (z ^^^ t) + 3 * ~~~(z &&& t) - 7 * ~~~z - 1 * ~~~t - 3 * z + 3 * t - 2 * ~~~(z ^^^ t) + 3 * ~~~(z ||| t) - 2 * (z &&& t) = - 2 * ~~~(z &&& ~~~z) + 2 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1433 (x y : BitVec w) : +theorem e_1433 : 4 * (z ||| t) - 1 * (z ^^^ t) + 3 * z + 5 * t + 7 * (z ||| ~~~t) + 2 * ~~~(z &&& ~~~t) + 4 * ~~~z - 13 * ~~~(z ||| t) - 14 * ~~~(z ||| ~~~t) - 13 * (z &&& ~~~t) = 21 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1434 (x y : BitVec w) : +theorem e_1434 : - 1 * ~~~z - 11 * z - 2 * (z ^^^ t) - 7 * ~~~(z &&& ~~~z) - 1 * (z ||| t) - 1 * t + 1 * ~~~t + 11 * ~~~(z &&& ~~~t) - 5 * ~~~(z ||| t) + 9 * (z &&& t) = - 1 * ~~~(z &&& t) - 19 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1435 (x y : BitVec w) : +theorem e_1435 : 2 * ~~~(z &&& ~~~z) + 1 * z + 3 * ~~~(z ^^^ t) + 4 * t - 1 * ~~~t - 1 * ~~~(z &&& t) + 3 * ~~~(z ||| t) - 16 * ~~~(z ||| ~~~t) - 6 * (z &&& ~~~t) - 15 * (z &&& t) = - 11 * (z ||| t) + 6 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1436 (x y : BitVec w) : +theorem e_1436 : - 1 * (z ||| ~~~t) - 1 * z + 4 * (z ^^^ t) - 2 * (z ||| t) - 2 * ~~~z + 2 * ~~~(z &&& t) + 1 * ~~~(z ||| t) - 3 * ~~~(z ||| ~~~t) - 2 * (z &&& ~~~t) + 3 * (z &&& t) = - 1 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1437 (x y : BitVec w) : +theorem e_1437 : - 6 * z + 3 * t + 1 * ~~~z - 3 * ~~~(z &&& t) + 1 * ~~~(z &&& ~~~z) - 3 * ~~~t - 1 * ~~~(z ^^^ t) - 2 * ~~~(z ||| ~~~t) + 11 * (z &&& ~~~t) + 3 * (z &&& t) = - 5 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1438 (x y : BitVec w) : +theorem e_1438 : - 5 * (z ^^^ t) + 1 * t - 11 * ~~~(z &&& t) + 1 * ~~~(z &&& ~~~z) + 4 * ~~~t + 1 * (z ||| t) + 10 * ~~~(z ||| t) + 13 * ~~~(z ||| ~~~t) + 7 * (z &&& ~~~t) + 1 * (z &&& t) = - 3 * (z ||| ~~~t) + 7 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1439 (x y : BitVec w) : +theorem e_1439 : 2 * ~~~t + 1 * ~~~(z &&& t) + 1 * (z ||| ~~~t) + 7 * ~~~(z ^^^ t) - 1 * ~~~(z &&& ~~~z) + 3 * (z ^^^ t) - 2 * z - 3 * ~~~(z ||| ~~~t) - 4 * (z &&& ~~~t) - 5 * (z &&& t) = 10 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1440 (x y : BitVec w) : +theorem e_1440 : - 1 * z - 5 * ~~~z + 5 * ~~~(z &&& ~~~z) + 3 * t + 3 * ~~~t - 1 * ~~~(z ^^^ t) - 6 * (z ^^^ t) - 2 * ~~~(z ||| t) + 3 * ~~~(z ||| ~~~t) - 6 * (z &&& t) = 1 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1441 (x y : BitVec w) : +theorem e_1441 : 1 * (z ^^^ t) - 5 * ~~~(z &&& ~~~z) - 5 * ~~~(z &&& ~~~t) + 4 * ~~~t - 2 * t - 2 * ~~~(z ^^^ t) + 8 * ~~~(z ||| t) + 11 * ~~~(z ||| ~~~t) + 2 * (z &&& ~~~t) + 16 * (z &&& t) = 2 * z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1442 (x y : BitVec w) : +theorem e_1442 : 3 * (z ^^^ t) + 7 * ~~~(z ^^^ t) - 2 * ~~~(z &&& ~~~t) + 1 * (z ||| ~~~t) + 1 * z - 6 * ~~~t - 3 * ~~~(z &&& t) + 3 * ~~~(z ||| t) + 8 * ~~~(z ||| ~~~t) + 4 * (z &&& ~~~t) = 1 * (z &&& t) + 6 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1443 (x y : BitVec w) : +theorem e_1443 : - 1 * z - 3 * ~~~(z &&& t) - 7 * ~~~t + 11 * ~~~z + 11 * ~~~(z &&& ~~~z) - 1 * (z ||| ~~~t) - 10 * ~~~(z ||| t) - 19 * ~~~(z ||| ~~~t) + 1 * (z &&& ~~~t) - 8 * (z &&& t) = 1 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1444 (x y : BitVec w) : +theorem e_1444 : - 1 * ~~~t - 6 * ~~~(z &&& ~~~z) + 5 * ~~~(z ^^^ t) - 7 * ~~~z - 5 * ~~~(z &&& t) + 7 * (z ^^^ t) - 1 * (z ||| ~~~t) + 15 * ~~~(z ||| t) + 11 * ~~~(z ||| ~~~t) + 2 * (z &&& t) = - 6 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1445 (x y : BitVec w) : +theorem e_1445 : 4 * (z ^^^ t) + 5 * (z ||| t) - 1 * ~~~(z &&& t) + 2 * ~~~(z &&& ~~~t) + 3 * ~~~t - 5 * ~~~(z &&& ~~~z) + 1 * ~~~(z ^^^ t) - 4 * ~~~(z ||| ~~~t) - 6 * (z &&& ~~~t) - 3 * (z &&& t) = 1 * ~~~z - 1 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1446 (x y : BitVec w) : +theorem e_1446 : - 7 * ~~~(z ^^^ t) + 11 * ~~~t - 7 * (z ||| t) + 3 * (z ||| ~~~t) + 5 * ~~~(z &&& ~~~t) + 5 * z + 1 * ~~~(z &&& ~~~z) - 11 * ~~~(z ||| t) + 3 * ~~~(z ||| ~~~t) - 13 * (z &&& ~~~t) = 2 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1447 (x y : BitVec w) : +theorem e_1447 : - 11 * z - 2 * ~~~(z &&& ~~~t) - 3 * (z ||| t) - 5 * ~~~(z ^^^ t) + 1 * (z ^^^ t) + 4 * ~~~z + 13 * ~~~(z ||| t) - 1 * ~~~(z ||| ~~~t) + 23 * (z &&& ~~~t) + 21 * (z &&& t) = 11 * ~~~t - 1 * ~~~(z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1448 (x y : BitVec w) : +theorem e_1448 : 1 * z - 6 * (z ||| t) + 1 * (z ^^^ t) + 7 * ~~~t + 4 * ~~~(z &&& t) - 2 * ~~~(z &&& ~~~t) - 2 * ~~~(z ^^^ t) - 6 * ~~~(z &&& ~~~z) + 10 * ~~~(z ||| ~~~t) + 15 * (z &&& t) = 1 * ~~~z + 1 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1449 (x y : BitVec w) : +theorem e_1449 : 1 * t + 2 * (z ||| t) + 1 * ~~~(z ^^^ t) + 4 * (z ^^^ t) - 1 * z - 7 * ~~~(z &&& ~~~t) - 3 * ~~~(z &&& ~~~z) + 11 * ~~~(z ||| t) + 3 * ~~~(z ||| ~~~t) + 4 * (z &&& t) = 5 * ~~~t - 3 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1450 (x y : BitVec w) : +theorem e_1450 : - 3 * ~~~t + 5 * ~~~(z &&& ~~~z) - 6 * ~~~(z &&& t) - 7 * ~~~(z &&& ~~~t) + 4 * ~~~(z ^^^ t) - 2 * ~~~z + 2 * z + 5 * t + 9 * ~~~(z ||| t) - 9 * (z &&& t) = - 3 * ~~~(z ||| ~~~t) - 2 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1451 (x y : BitVec w) : +theorem e_1451 : - 6 * (z ||| ~~~t) - 11 * ~~~z - 1 * ~~~(z &&& ~~~t) - 7 * (z ||| t) - 6 * ~~~(z &&& t) + 2 * ~~~t + 22 * ~~~(z ||| t) + 14 * ~~~(z ||| ~~~t) + 6 * (z &&& ~~~t) + 14 * (z &&& t) = - 11 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1452 (x y : BitVec w) : +theorem e_1452 : 1 * ~~~(z &&& ~~~t) - 6 * ~~~(z &&& ~~~z) - 11 * ~~~z - 1 * t + 4 * (z ||| ~~~t) + 7 * (z ||| t) - 3 * z + 12 * ~~~(z ||| t) - 2 * (z &&& ~~~t) - 2 * (z &&& t) = - 10 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1453 (x y : BitVec w) : +theorem e_1453 : - 1 * (z ||| ~~~t) + 4 * ~~~(z &&& t) - 7 * t - 1 * z - 3 * ~~~z + 2 * (z ^^^ t) + 1 * ~~~t - 1 * ~~~(z ||| t) + 4 * ~~~(z ||| ~~~t) - 5 * (z &&& ~~~t) = - 9 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1454 (x y : BitVec w) : +theorem e_1454 : 2 * z - 2 * (z ||| t) + 2 * ~~~(z &&& ~~~t) + 7 * ~~~t + 5 * ~~~z + 1 * ~~~(z &&& t) - 26 * ~~~(z ||| t) - 17 * ~~~(z ||| ~~~t) - 19 * (z &&& ~~~t) - 13 * (z &&& t) = - 11 * ~~~(z &&& ~~~z) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1455 (x y : BitVec w) : +theorem e_1455 : - 6 * ~~~(z &&& t) - 2 * z + 2 * (z ||| t) - 2 * ~~~(z &&& ~~~z) + 3 * (z ^^^ t) - 1 * t + 5 * (z ||| ~~~t) + 8 * ~~~(z ||| t) + 4 * ~~~(z ||| ~~~t) + 3 * (z &&& t) = 5 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1456 (x y : BitVec w) : +theorem e_1456 : 1 * (z ||| t) - 7 * ~~~z + 3 * ~~~(z &&& t) + 3 * ~~~(z &&& ~~~z) - 1 * z - 2 * t + 5 * (z ^^^ t) + 2 * ~~~(z ||| t) - 3 * ~~~(z ||| ~~~t) - 10 * (z &&& ~~~t) = 1 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1457 (x y : BitVec w) : +theorem e_1457 : - 6 * (z ||| t) + 11 * ~~~t + 3 * t + 1 * ~~~(z &&& t) - 1 * ~~~z + 1 * z + 7 * (z ^^^ t) - 16 * ~~~(z ||| t) - 9 * ~~~(z ||| ~~~t) - 3 * (z &&& t) = 14 * (z &&& ~~~t) - 5 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1458 (x y : BitVec w) : +theorem e_1458 : 7 * z - 5 * (z ^^^ t) + 5 * ~~~(z &&& ~~~t) - 2 * ~~~(z &&& t) - 1 * (z ||| t) + 1 * ~~~(z &&& ~~~z) - 6 * ~~~(z ||| t) + 1 * ~~~(z ||| ~~~t) - 1 * (z &&& ~~~t) - 12 * (z &&& t) = - 1 * ~~~z - 1 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1459 (x y : BitVec w) : +theorem e_1459 : 2 * (z ^^^ t) + 1 * (z ||| ~~~t) + 7 * ~~~(z &&& t) - 1 * ~~~(z ^^^ t) + 7 * t + 1 * (z ||| t) - 5 * ~~~t - 17 * ~~~(z ||| ~~~t) - 6 * (z &&& ~~~t) - 8 * (z &&& t) = 2 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1460 (x y : BitVec w) : +theorem e_1460 : 1 * z + 1 * (z ||| t) + 1 * ~~~(z &&& ~~~z) + 1 * (z ||| ~~~t) + 11 * ~~~(z &&& t) - 3 * t + 2 * ~~~t - 9 * ~~~(z ||| t) - 17 * (z &&& ~~~t) - 1 * (z &&& t) = 4 * ~~~(z ||| ~~~t) + 6 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1461 (x y : BitVec w) : +theorem e_1461 : 7 * t - 1 * ~~~z + 5 * ~~~(z &&& ~~~z) + 1 * ~~~(z &&& t) - 6 * z - 3 * ~~~(z &&& ~~~t) - 3 * ~~~(z ||| t) - 2 * ~~~(z ||| ~~~t) + 6 * (z &&& ~~~t) + 3 * (z &&& t) = 7 * (z ||| t) - 1 * (z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1462 (x y : BitVec w) : +theorem e_1462 : 2 * ~~~(z &&& ~~~t) + 1 * t - 11 * ~~~(z ^^^ t) + 4 * ~~~t - 3 * ~~~z + 1 * (z ||| t) + 11 * ~~~(z &&& t) - 2 * (z ||| ~~~t) - 1 * ~~~(z ||| t) - 14 * (z &&& ~~~t) + 9 * (z &&& t) = 12 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1463 (x y : BitVec w) : +theorem e_1463 : - 3 * ~~~z - 6 * t - 5 * ~~~(z &&& ~~~z) - 1 * (z ||| ~~~t) - 1 * (z ||| t) + 7 * (z ^^^ t) + 1 * ~~~(z &&& ~~~t) + 4 * ~~~t + 4 * ~~~(z ||| t) - 5 * (z &&& ~~~t) + 11 * (z &&& t) = - 1 * z - 7 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1464 (x y : BitVec w) : +theorem e_1464 : 2 * (z ||| t) + 2 * (z ^^^ t) - 11 * t + 1 * ~~~(z &&& t) + 3 * ~~~t + 2 * ~~~(z &&& ~~~t) - 7 * ~~~z - 7 * z - 1 * ~~~(z &&& ~~~z) + 12 * ~~~(z ||| ~~~t) + 26 * (z &&& t) = - 13 * ~~~(z ||| t) + 11 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1465 (x y : BitVec w) : +theorem e_1465 : - 1 * ~~~(z &&& ~~~t) + 2 * (z ||| ~~~t) + 3 * z + 3 * ~~~(z &&& t) - 3 * t + 1 * ~~~z - 11 * ~~~t + 11 * (z ^^^ t) + 3 * ~~~(z ||| t) - 14 * ~~~(z ||| ~~~t) - 4 * (z &&& t) = 11 * (z &&& ~~~t) - 3 * ~~~(z &&& ~~~z) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1466 (x y : BitVec w) : +theorem e_1466 : 1 * ~~~(z ^^^ t) + 3 * ~~~t + 4 * ~~~(z &&& t) + 2 * (z ||| ~~~t) + 11 * t - 2 * (z ^^^ t) + 7 * ~~~(z &&& ~~~t) - 20 * ~~~(z ||| t) - 23 * ~~~(z ||| ~~~t) - 1 * (z &&& ~~~t) - 15 * (z &&& t) = 6 * z - 3 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1467 (x y : BitVec w) : +theorem e_1467 : 1 * (z ||| ~~~t) - 2 * ~~~(z ^^^ t) + 11 * ~~~(z &&& t) + 1 * (z ^^^ t) + 3 * ~~~t - 5 * t - 5 * ~~~(z &&& ~~~t) - 10 * ~~~(z ||| t) - 4 * ~~~(z ||| ~~~t) - 18 * (z &&& ~~~t) + 9 * (z &&& t) = - 2 * ~~~(z &&& ~~~z) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1468 (x y : BitVec w) : +theorem e_1468 : 2 * ~~~(z &&& t) - 7 * ~~~(z ^^^ t) - 2 * ~~~t - 1 * (z ^^^ t) + 11 * (z ||| t) + 2 * t - 3 * ~~~(z &&& ~~~z) + 2 * z + 17 * ~~~(z ||| t) - 9 * (z &&& ~~~t) + 2 * (z &&& t) = 7 * ~~~(z &&& ~~~t) + 4 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1469 (x y : BitVec w) : +theorem e_1469 : 1 * ~~~(z ^^^ t) - 2 * ~~~(z &&& t) - 2 * ~~~(z &&& ~~~z) - 6 * z + 1 * t + 2 * (z ||| ~~~t) + 2 * ~~~(z &&& ~~~t) + 1 * ~~~t + 3 * ~~~(z ||| ~~~t) + 7 * (z &&& ~~~t) + 2 * (z &&& t) = 2 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1470 (x y : BitVec w) : +theorem e_1470 : 11 * ~~~(z &&& ~~~z) + 5 * z - 2 * t + 11 * ~~~(z &&& t) + 1 * (z ||| ~~~t) + 2 * (z ||| t) - 1 * ~~~z - 16 * ~~~(z ||| t) - 32 * ~~~(z ||| ~~~t) - 41 * (z &&& ~~~t) - 11 * (z &&& t) = - 11 * (z ^^^ t) + 6 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1471 (x y : BitVec w) : +theorem e_1471 : - 3 * ~~~z - 6 * ~~~(z &&& ~~~z) + 1 * ~~~(z &&& t) - 2 * t + 1 * (z ||| t) + 4 * (z ^^^ t) - 6 * z + 11 * (z ||| ~~~t) - 10 * ~~~(z ||| t) - 5 * (z &&& ~~~t) - 5 * (z &&& t) = - 5 * ~~~(z ||| ~~~t) - 7 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1472 (x y : BitVec w) : +theorem e_1472 : - 11 * ~~~(z &&& ~~~t) - 2 * ~~~(z &&& t) + 7 * (z ||| t) - 11 * (z ||| ~~~t) - 11 * ~~~(z &&& ~~~z) - 2 * ~~~t + 4 * ~~~z + 29 * ~~~(z ||| t) + 13 * ~~~(z ||| ~~~t) + 17 * (z &&& ~~~t) + 20 * (z &&& t) = - 2 * z - 4 * ~~~(z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1473 (x y : BitVec w) : +theorem e_1473 : 1 * ~~~(z &&& ~~~z) + 1 * z + 1 * ~~~t + 1 * ~~~(z &&& t) - 7 * (z ||| t) + 7 * (z ^^^ t) - 2 * t - 5 * ~~~(z ||| t) - 2 * ~~~(z ||| ~~~t) - 4 * (z &&& ~~~t) + 5 * (z &&& t) = - 2 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1474 (x y : BitVec w) : +theorem e_1474 : - 11 * ~~~(z &&& ~~~t) + 4 * ~~~z + 11 * (z ^^^ t) + 5 * ~~~t + 4 * t + 7 * z + 2 * ~~~(z &&& t) - 1 * ~~~(z ^^^ t) + 1 * ~~~(z ||| t) - 9 * ~~~(z ||| ~~~t) - 24 * (z &&& ~~~t) = 1 * (z ||| t) - 2 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1475 (x y : BitVec w) : +theorem e_1475 : - 2 * ~~~(z &&& ~~~t) - 2 * ~~~t + 1 * t + 2 * ~~~(z &&& t) + 7 * ~~~(z &&& ~~~z) + 3 * ~~~(z ^^^ t) - 3 * (z ||| t) - 19 * ~~~(z ||| t) - 16 * ~~~(z ||| ~~~t) - 3 * (z &&& ~~~t) - 5 * (z &&& t) = 1 * z - 11 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1476 (x y : BitVec w) : +theorem e_1476 : 11 * ~~~z + 1 * (z ^^^ t) + 5 * ~~~t - 11 * z - 11 * t - 3 * (z ||| t) + 1 * ~~~(z ^^^ t) - 1 * (z ||| ~~~t) - 18 * ~~~(z ||| t) + 9 * (z &&& ~~~t) + 23 * (z &&& t) = - 2 * ~~~(z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1477 (x y : BitVec w) : +theorem e_1477 : 7 * ~~~(z &&& ~~~z) - 7 * ~~~z - 6 * ~~~(z &&& ~~~t) + 5 * ~~~(z &&& t) + 2 * (z ||| ~~~t) + 5 * (z ^^^ t) + 2 * ~~~t - 3 * ~~~(z ||| t) + 1 * ~~~(z ||| ~~~t) - 21 * (z &&& ~~~t) + 2 * (z &&& t) = 5 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1478 (x y : BitVec w) : +theorem e_1478 : - 11 * ~~~(z &&& t) + 3 * (z ||| t) + 1 * ~~~(z &&& ~~~z) + 3 * (z ^^^ t) - 2 * ~~~(z ^^^ t) + 11 * t - 2 * (z ||| ~~~t) + 5 * ~~~t + 8 * ~~~(z ||| t) - 8 * ~~~(z ||| ~~~t) - 12 * (z &&& t) = - 1 * ~~~z - 1 * z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1479 (x y : BitVec w) : +theorem e_1479 : - 1 * z - 6 * (z ^^^ t) + 7 * ~~~(z &&& t) - 2 * (z ||| t) + 7 * ~~~z - 3 * ~~~(z &&& ~~~z) - 7 * ~~~t - 4 * ~~~(z ||| t) - 4 * ~~~(z ||| ~~~t) + 12 * (z &&& ~~~t) + 5 * (z &&& t) = - 1 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1480 (x y : BitVec w) : +theorem e_1480 : - 3 * ~~~z + 2 * ~~~(z &&& ~~~z) + 7 * (z ||| ~~~t) + 3 * ~~~(z &&& ~~~t) - 2 * z - 7 * ~~~(z &&& t) - 5 * ~~~t + 2 * ~~~(z ||| t) + 6 * ~~~(z ||| ~~~t) + 5 * (z &&& ~~~t) - 10 * (z &&& t) = - 1 * ~~~(z ^^^ t) + 1 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1481 (x y : BitVec w) : +theorem e_1481 : 1 * ~~~(z &&& ~~~z) + 1 * (z ||| t) - 1 * z + 2 * ~~~t - 2 * ~~~z + 2 * (z ^^^ t) - 7 * ~~~(z ^^^ t) + 5 * ~~~(z ||| t) - 3 * ~~~(z ||| ~~~t) - 4 * (z &&& ~~~t) + 4 * (z &&& t) = - 2 * ~~~(z &&& ~~~t) + 1 * ~~~(z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1482 (x y : BitVec w) : +theorem e_1482 : - 2 * ~~~(z &&& t) + 2 * ~~~t + 1 * (z ||| t) + 1 * (z ^^^ t) - 6 * ~~~(z &&& ~~~z) - 3 * ~~~(z &&& ~~~t) - 1 * ~~~z + 10 * ~~~(z ||| t) + 11 * ~~~(z ||| ~~~t) + 4 * (z &&& ~~~t) + 9 * (z &&& t) = 1 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1483 (x y : BitVec w) : +theorem e_1483 : - 6 * (z ||| t) - 3 * ~~~(z &&& ~~~z) + 2 * z - 1 * ~~~(z &&& ~~~t) - 7 * ~~~(z &&& t) - 3 * t - 5 * (z ||| ~~~t) + 16 * ~~~(z ||| t) + 18 * ~~~(z ||| ~~~t) + 17 * (z &&& ~~~t) + 16 * (z &&& t) = - 2 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1484 (x y : BitVec w) : +theorem e_1484 : 3 * t + 3 * ~~~(z &&& t) + 5 * ~~~(z &&& ~~~z) - 5 * ~~~(z ^^^ t) - 1 * ~~~(z &&& ~~~t) + 2 * (z ^^^ t) + 11 * (z ||| ~~~t) - 8 * ~~~(z ||| t) - 2 * ~~~(z ||| ~~~t) - 16 * (z &&& ~~~t) - 8 * (z &&& t) = 5 * (z ||| t) + 5 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1485 (x y : BitVec w) : +theorem e_1485 : - 2 * ~~~(z &&& ~~~t) + 2 * ~~~(z &&& t) + 5 * z + 1 * (z ||| ~~~t) - 2 * ~~~z + 3 * ~~~(z ^^^ t) + 1 * (z ^^^ t) - 3 * ~~~(z &&& ~~~z) + 1 * ~~~(z ||| t) + 12 * ~~~(z ||| ~~~t) + 4 * (z &&& t) = 2 * t + 6 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1486 (x y : BitVec w) : +theorem e_1486 : 3 * ~~~t - 2 * z - 11 * (z ||| ~~~t) - 1 * ~~~(z &&& ~~~z) + 2 * ~~~(z ^^^ t) + 1 * ~~~(z &&& t) + 3 * (z ||| t) + 7 * ~~~z - 1 * ~~~(z ||| t) - 13 * ~~~(z ||| ~~~t) + 7 * (z &&& ~~~t) = - 3 * t - 6 * (z &&& t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1487 (x y : BitVec w) : +theorem e_1487 : 11 * (z ^^^ t) + 3 * ~~~(z ^^^ t) - 11 * ~~~z - 1 * (z ||| ~~~t) + 3 * ~~~(z &&& ~~~t) + 3 * t - 1 * ~~~(z &&& t) + 5 * ~~~(z ||| t) - 5 * ~~~(z ||| ~~~t) - 18 * (z &&& ~~~t) - 15 * (z &&& t) = - 7 * z - 2 * ~~~t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1488 (x y : BitVec w) : +theorem e_1488 : - 6 * t - 1 * ~~~z - 2 * ~~~(z &&& ~~~z) - 1 * (z ||| t) + 7 * ~~~(z ^^^ t) + 1 * ~~~(z &&& t) - 6 * (z ^^^ t) - 11 * (z ||| ~~~t) + 20 * ~~~(z ||| ~~~t) + 19 * (z &&& ~~~t) + 18 * (z &&& t) = 5 * ~~~(z &&& ~~~t) - 11 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1489 (x y : BitVec w) : +theorem e_1489 : - 2 * ~~~z - 2 * z + 4 * ~~~(z &&& t) - 2 * ~~~(z &&& ~~~z) + 5 * ~~~(z &&& ~~~t) + 3 * ~~~t + 1 * t - 1 * (z ||| t) - 1 * ~~~(z ^^^ t) - 7 * ~~~(z ||| ~~~t) - 4 * (z &&& ~~~t) = 7 * ~~~(z ||| t) - 2 * (z ^^^ t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1490 (x y : BitVec w) : +theorem e_1490 : - 11 * t + 5 * ~~~(z &&& ~~~t) - 3 * ~~~t + 3 * (z ||| t) - 7 * ~~~z - 1 * ~~~(z &&& t) - 11 * ~~~(z &&& ~~~z) + 2 * (z ||| ~~~t) + 22 * ~~~(z ||| ~~~t) + 10 * (z &&& ~~~t) + 12 * (z &&& t) = - 15 * ~~~(z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1491 (x y : BitVec w) : +theorem e_1491 : - 11 * ~~~(z &&& t) + 7 * ~~~(z &&& ~~~t) + 4 * ~~~(z ^^^ t) + 5 * (z ^^^ t) + 3 * (z ||| ~~~t) + 3 * z + 2 * t - 5 * ~~~(z ||| t) - 5 * ~~~(z ||| ~~~t) - 1 * (z &&& ~~~t) - 20 * (z &&& t) = - 1 * ~~~(z &&& ~~~z) - 1 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1492 (x y : BitVec w) : +theorem e_1492 : - 2 * ~~~(z &&& ~~~t) - 6 * ~~~(z &&& t) - 1 * ~~~(z &&& ~~~z) - 6 * (z ^^^ t) - 1 * (z ||| ~~~t) + 11 * t - 1 * ~~~(z ^^^ t) + 11 * ~~~(z ||| t) + 9 * ~~~(z ||| ~~~t) + 19 * (z &&& ~~~t) - 1 * (z &&& t) = 5 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1493 (x y : BitVec w) : +theorem e_1493 : 1 * (z ||| ~~~t) + 1 * ~~~(z &&& ~~~t) + 2 * (z ||| t) - 1 * (z ^^^ t) - 5 * ~~~(z ^^^ t) + 2 * z - 6 * ~~~t - 1 * ~~~(z &&& t) + 3 * ~~~z + 8 * ~~~(z ||| t) + 4 * (z &&& ~~~t) = 1 * ~~~(z &&& ~~~z) + 3 * ~~~(z ||| ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1494 (x y : BitVec w) : +theorem e_1494 : - 1 * (z ^^^ t) - 7 * (z ||| ~~~t) - 6 * ~~~(z &&& ~~~z) - 2 * ~~~z - 5 * t + 2 * ~~~t - 2 * (z ||| t) - 11 * ~~~(z &&& ~~~t) + 24 * ~~~(z ||| t) + 27 * ~~~(z ||| ~~~t) + 31 * (z &&& t) = - 14 * (z &&& ~~~t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1495 (x y : BitVec w) : +theorem e_1495 : 3 * ~~~t - 3 * ~~~(z ^^^ t) + 1 * ~~~z - 6 * ~~~(z &&& t) - 1 * t - 2 * ~~~(z &&& ~~~t) - 2 * z + 4 * (z ^^^ t) + 7 * ~~~(z ||| t) + 9 * ~~~(z ||| ~~~t) + 6 * (z &&& ~~~t) = - 13 * (z &&& t) + 5 * (z ||| t) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1496 (x y : BitVec w) : +theorem e_1496 : - 1 * (z ^^^ t) + 7 * (z ||| ~~~t) + 11 * ~~~(z &&& ~~~z) + 1 * ~~~t - 5 * ~~~(z &&& ~~~t) + 1 * ~~~(z &&& t) + 11 * t - 17 * ~~~(z ||| t) - 19 * ~~~(z ||| ~~~t) - 22 * (z &&& ~~~t) - 27 * (z &&& t) = - 3 * z - 2 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1497 (x y : BitVec w) : +theorem e_1497 : - 1 * t - 3 * (z ^^^ t) + 11 * z - 2 * (z ||| ~~~t) - 11 * ~~~z - 7 * (z ||| t) + 1 * ~~~(z ^^^ t) + 13 * ~~~(z ||| t) + 23 * ~~~(z ||| ~~~t) + 2 * (z &&& ~~~t) - 1 * (z &&& t) = 1 * ~~~(z &&& ~~~z) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1498 (x y : BitVec w) : +theorem e_1498 : - 1 * z + 4 * ~~~t + 3 * ~~~(z ^^^ t) + 2 * ~~~(z &&& ~~~z) + 5 * (z ||| ~~~t) + 1 * ~~~z + 1 * ~~~(z &&& t) - 16 * ~~~(z ||| t) - 15 * ~~~(z ||| ~~~t) - 11 * (z &&& ~~~t) - 20 * (z &&& t) = - 11 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1499 (x y : BitVec w) : +theorem e_1499 : 2 * (z ||| t) + 11 * (z ||| ~~~t) + 7 * ~~~(z &&& ~~~z) + 1 * ~~~(z &&& t) - 7 * ~~~z + 11 * ~~~(z ^^^ t) - 1 * (z ^^^ t) - 23 * ~~~(z ||| t) + 5 * ~~~(z ||| ~~~t) - 19 * (z &&& ~~~t) - 23 * (z &&& t) = 1 * z + 7 * t := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1500 (x y : BitVec w) : +theorem e_1500 : - 1 * ~~~(z &&& t) - 11 * t - 11 * (z ||| ~~~t) - 3 * ~~~(z &&& ~~~z) - 1 * ~~~(z ^^^ t) + 4 * z + 3 * (z ||| t) + 12 * ~~~(z ||| t) + 8 * ~~~(z ||| ~~~t) + 8 * (z &&& ~~~t) + 19 * (z &&& t) = - 4 * ~~~z := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1501 (x y : BitVec w) : +theorem e_1501 : 1 * (c &&& ~~~(a &&& b)) + 1 * ~~~(a ||| ~~~c) + 7 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) - 7 * ~~~(a ||| ( ~~~b ||| c)) - 2 * ( ~~~a &&& ( ~~~b &&& c)) - 9 * ( ~~~a &&& (b &&& c)) - 1 * (a &&& ( ~~~b &&& c)) = 7 * (a &&& (b &&& c)) + 7 * ~~~(a ||| (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1502 (x y : BitVec w) : +theorem e_1502 : - 3 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) + 2 * (a ^^^ (b &&& c)) + 1 * (a ^^^ (b ||| c)) + 2 * ~~~(a ||| ( ~~~b ||| c)) + 1 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 1 * ( ~~~a &&& ( ~~~b &&& c)) - 3 * ( ~~~a &&& (b &&& c)) = - 1 * (a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1503 (x y : BitVec w) : +theorem e_1503 : 3 * (c ||| (a &&& ~~~b)) - 1 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) - 6 * ~~~(a ||| ( ~~~b ||| c)) - 3 * ~~~( ~~~a ||| (b ||| c)) - 6 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 9 * ( ~~~a &&& ( ~~~b &&& c)) - 10 * ( ~~~a &&& (b &&& c)) - 3 * (a &&& (b &&& c)) = - 7 * ((a &&& c) ^^^ (b ||| c)) + 3 * (a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1504 (x y : BitVec w) : +theorem e_1504 : - 2 * c + 2 * ~~~( ~~~a &&& (b ||| c)) - 2 * ~~~(a ||| (b ||| c)) - 3 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 2 * ( ~~~a &&& ( ~~~b &&& c)) + 2 * ( ~~~a &&& (b &&& c)) - 1 * (a &&& ( ~~~b &&& c)) - 1 * (a &&& (b &&& c)) = - 1 * (a &&& (b ||| c)) + 2 * ~~~( ~~~a ||| (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1505 (x y : BitVec w) : +theorem e_1505 : - 5 * (b ^^^ ~~~(a ||| (b ^^^ c))) - 2 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) + 2 * ~~~(a ||| (b ||| c)) + 7 * ~~~(a ||| ( ~~~b ||| c)) + 7 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 5 * ( ~~~a &&& ( ~~~b &&& c)) + 2 * (a &&& ( ~~~b &&& c)) + 7 * (a &&& (b &&& c)) = - 5 * ~~~(a ||| b) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1506 (x y : BitVec w) : +theorem e_1506 : 7 * ~~~(a ^^^ b) + 1 * ~~~a - 1 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) - 7 * ~~~(a ||| (b ||| c)) - 6 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 13 * ( ~~~a &&& ( ~~~b &&& c)) - 5 * ( ~~~a &&& (b &&& c)) - 12 * (a &&& (b &&& c)) = - 5 * (c ^^^ (a &&& ~~~b)) + 5 * ~~~( ~~~a ||| (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1507 (x y : BitVec w) : +theorem e_1507 : 7 * ~~~(a ^^^ c) - 1 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 1 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) - 8 * ~~~(a ||| (b ||| c)) - 8 * ~~~(a ||| ( ~~~b ||| c)) + 1 * ~~~( ~~~a ||| (b ||| c)) + 1 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 1 * ( ~~~a &&& ( ~~~b &&& c)) - 8 * (a &&& (b &&& c)) = 6 * (a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1508 (x y : BitVec w) : +theorem e_1508 : - 1 * (b ||| ~~~(a ||| ~~~c)) - 5 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) + 7 * (b &&& ~~~(a ^^^ c)) - 1 * (c ^^^ ( ~~~a ||| (b ||| c))) + 6 * ~~~(a ||| (b ||| c)) - 5 * ~~~(a ||| ( ~~~b ||| c)) + 5 * ~~~( ~~~a ||| (b ||| c)) + 6 * ( ~~~a &&& (b &&& c)) - 6 * (a &&& (b &&& c)) = - 2 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 1 * ( ~~~a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1509 (x y : BitVec w) : +theorem e_1509 : 4 * (b ^^^ ~~~(a &&& (b ||| c))) + 4 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) - 2 * ((a &&& b) ^^^ (b ||| ~~~c)) - 2 * ~~~(a ||| (b ||| c)) + 2 * ~~~(a ||| ( ~~~b ||| c)) - 6 * ~~~( ~~~a ||| (b ||| c)) - 8 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 8 * ( ~~~a &&& ( ~~~b &&& c)) - 8 * (a &&& (b &&& c)) = 2 * ( ~~~a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1510 (x y : BitVec w) : +theorem e_1510 : - 11 * ~~~c + 3 * ( ~~~c &&& ~~~(a ^^^ b)) + 10 * ~~~(a ||| (b ||| c)) + 11 * ~~~(a ||| ( ~~~b ||| c)) + 13 * ~~~( ~~~a ||| (b ||| c)) + 8 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 2 * ( ~~~a &&& ( ~~~b &&& c)) + 2 * (a &&& ( ~~~b &&& c)) + 2 * (a &&& (b &&& c)) = - 2 * ( ~~~a &&& (b &&& c)) + 2 * ~~~(b &&& ~~~c) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1511 (x y : BitVec w) : +theorem e_1511 : - 2 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) + 4 * (a &&& ~~~b) + 5 * ~~~(a ||| (b ^^^ c)) - 5 * ~~~(a ||| (b ||| c)) + 2 * ~~~(a ||| ( ~~~b ||| c)) - 2 * ~~~( ~~~a ||| (b ||| c)) + 2 * ( ~~~a &&& ( ~~~b &&& c)) - 5 * ( ~~~a &&& (b &&& c)) + 2 * (a &&& (b &&& c)) = 2 * (a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1512 (x y : BitVec w) : +theorem e_1512 : - 5 * (c ||| ~~~(a ^^^ b)) - 3 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 3 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) + 2 * ~~~(a &&& c) + 3 * ~~~(a ||| (b ||| c)) - 2 * ~~~(a ||| ( ~~~b ||| c)) - 12 * ~~~( ~~~a ||| (b ||| c)) - 7 * ( ~~~a &&& (b &&& c)) + 8 * (a &&& ( ~~~b &&& c)) - 2 * (a &&& (b &&& c)) = 4 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 7 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1513 (x y : BitVec w) : +theorem e_1513 : - 2 * ( ~~~a ||| (b &&& c)) - 5 * (b ^^^ (a &&& ~~~c)) + 2 * (a &&& ~~~c) - 6 * (b ^^^ ( ~~~a &&& (b ||| c))) + 2 * ~~~(a ||| (b ||| c)) + 7 * ~~~(a ||| ( ~~~b ||| c)) + 3 * ~~~( ~~~a ||| (b ||| c)) + 4 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 8 * ( ~~~a &&& ( ~~~b &&& c)) + 13 * (a &&& (b &&& c)) = - 7 * ( ~~~a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1514 (x y : BitVec w) : +theorem e_1514 : - 3 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 1 * (b ^^^ (a ||| ( ~~~b ||| c))) + 11 * (c ^^^ (a ||| ~~~b)) - 12 * ~~~(a ||| (b ||| c)) - 1 * ~~~(a ||| ( ~~~b ||| c)) - 9 * ~~~( ~~~a ||| (b ||| c)) + 10 * ( ~~~a &&& ( ~~~b &&& c)) + 3 * ( ~~~a &&& (b &&& c)) + 2 * (a &&& ( ~~~b &&& c)) + 11 * (a &&& (b &&& c)) = 11 * (b ^^^ ( ~~~a &&& (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1515 (x y : BitVec w) : +theorem e_1515 : - 3 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) + 1 * (c ^^^ (a ||| b)) + 2 * (c &&& ~~~(a &&& b)) + 7 * (c &&& ~~~(a ^^^ b)) + 3 * ~~~(a ||| (b ||| c)) + 2 * ~~~(a ||| ( ~~~b ||| c)) - 1 * ~~~( ~~~a ||| (b ||| c)) - 1 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 7 * ( ~~~a &&& ( ~~~b &&& c)) - 2 * ( ~~~a &&& (b &&& c)) = - 1 * (a &&& ( ~~~b &&& c)) + 7 * (a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1516 (x y : BitVec w) : +theorem e_1516 : 5 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 1 * ~~~c + 7 * (b ^^^ (a ||| ~~~c)) + 4 * ((a ^^^ b) ||| ~~~(a ^^^ c)) - 2 * ~~~( ~~~a ||| (b &&& c)) - 15 * ~~~(a ||| (b ||| c)) - 3 * ~~~(a ||| ( ~~~b ||| c)) - 8 * ~~~( ~~~a ||| (b ||| c)) - 16 * ( ~~~a &&& (b &&& c)) - 4 * (a &&& (b &&& c)) = 9 * (a &&& ( ~~~b &&& c)) + 2 * ~~~( ~~~a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1517 (x y : BitVec w) : +theorem e_1517 : - 11 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) - 5 * (c ^^^ (a ||| (b &&& c))) + 18 * ~~~(a ||| (b ||| c)) + 11 * ~~~(a ||| ( ~~~b ||| c)) + 12 * ~~~( ~~~a ||| (b ||| c)) + 16 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 12 * ( ~~~a &&& ( ~~~b &&& c)) + 11 * ( ~~~a &&& (b &&& c)) + 7 * (a &&& ( ~~~b &&& c)) + 7 * (a &&& (b &&& c)) = 7 * (b ^^^ ~~~(a &&& (b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1518 (x y : BitVec w) : +theorem e_1518 : - 1 * (a ^^^ (b ^^^ c)) - 1 * (b ^^^ (a &&& (b ||| c))) + 1 * ~~~(a ||| (b &&& c)) + 3 * ((a &&& c) ||| (b &&& ~~~c)) - 1 * ~~~(a ||| (b ||| c)) - 2 * ~~~(a ||| ( ~~~b ||| c)) + 1 * ~~~( ~~~a ||| (b ||| c)) - 3 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 1 * ( ~~~a &&& (b &&& c)) - 2 * (a &&& (b &&& c)) = 2 * (a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1519 (x y : BitVec w) : +theorem e_1519 : 2 * ((a ^^^ b) ||| (a ^^^ c)) - 6 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) - 2 * ~~~(a ||| (b ||| c)) - 4 * ~~~(a ||| ( ~~~b ||| c)) + 4 * ~~~( ~~~a ||| (b ||| c)) + 3 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 2 * ( ~~~a &&& ( ~~~b &&& c)) - 2 * ( ~~~a &&& (b &&& c)) + 2 * (a &&& ( ~~~b &&& c)) - 2 * (a &&& (b &&& c)) = - 1 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) - 1 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1520 (x y : BitVec w) : +theorem e_1520 : 4 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) - 2 * ((a ^^^ b) &&& ~~~(a ^^^ c)) + 1 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) - 6 * (b ^^^ ~~~(a ||| ~~~c)) + 2 * (a &&& (b ||| c)) + 7 * (c &&& (a ^^^ b)) - 1 * ~~~(a ||| (b ||| c)) + 4 * ~~~(a ||| ( ~~~b ||| c)) - 5 * ~~~( ~~~a ||| (b ||| c)) + 2 * ( ~~~a &&& ( ~~~b &&& c)) = 8 * ( ~~~a &&& (b &&& c)) + 7 * (a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1521 (x y : BitVec w) : +theorem e_1521 : 1 * (b &&& c) + 1 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 7 * ~~~(a &&& (b &&& c)) + 7 * ((a &&& b) ||| ~~~(b ^^^ c)) - 14 * ~~~(a ||| (b ||| c)) - 7 * ~~~(a ||| ( ~~~b ||| c)) - 15 * ~~~( ~~~a ||| (b ||| c)) - 8 * ( ~~~a &&& ( ~~~b &&& c)) - 15 * ( ~~~a &&& (b &&& c)) - 8 * (a &&& (b &&& c)) = 15 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 8 * (a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1522 (x y : BitVec w) : +theorem e_1522 : - 6 * (c ^^^ ~~~(a &&& (b &&& c))) + 2 * (c ^^^ (a ||| ( ~~~b &&& c))) - 2 * ~~~( ~~~a &&& (b ^^^ c)) + 7 * ~~~(a ||| (b ||| c)) + 5 * ~~~(a ||| ( ~~~b ||| c)) + 6 * ~~~( ~~~a ||| (b ||| c)) + 6 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 1 * ( ~~~a &&& ( ~~~b &&& c)) + 1 * (a &&& ( ~~~b &&& c)) + 8 * (a &&& (b &&& c)) = - 1 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1523 (x y : BitVec w) : +theorem e_1523 : 2 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) + 1 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 2 * (b ||| ~~~(a ||| ~~~c)) - 1 * ((a &&& c) ||| (b &&& ~~~c)) - 3 * ~~~(a ||| (b ||| c)) - 1 * ~~~(a ||| ( ~~~b ||| c)) - 3 * ~~~( ~~~a ||| (b ||| c)) - 1 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 4 * ( ~~~a &&& (b &&& c)) - 2 * (a &&& ( ~~~b &&& c)) - 1 * (a &&& (b &&& c)) = 4 * ( ~~~a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1524 (x y : BitVec w) : +theorem e_1524 : - 5 * a - 2 * ( ~~~a ||| (b ||| c)) + 1 * (b ^^^ ~~~(a &&& (b ^^^ c))) + 1 * ~~~(a ||| (b ||| c)) + 2 * ~~~(a ||| ( ~~~b ||| c)) + 4 * ~~~( ~~~a ||| (b ||| c)) + 6 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 1 * ( ~~~a &&& ( ~~~b &&& c)) + 5 * ( ~~~a &&& (b &&& c)) + 10 * (a &&& ( ~~~b &&& c)) + 7 * (a &&& (b &&& c)) = 3 * (c &&& (a ^^^ b)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1525 (x y : BitVec w) : +theorem e_1525 : 5 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 2 * ( ~~~a ||| (b ||| c)) + 7 * (c ^^^ (a ||| ( ~~~b ||| c))) - 14 * ~~~(a ||| (b ||| c)) - 6 * ~~~(a ||| ( ~~~b ||| c)) - 6 * ~~~( ~~~a ||| (b ||| c)) - 14 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 2 * ( ~~~a &&& ( ~~~b &&& c)) - 7 * ( ~~~a &&& (b &&& c)) - 6 * (a &&& ( ~~~b &&& c)) - 1 * (a &&& (b &&& c)) = 1 * ~~~(a ^^^ ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1526 (x y : BitVec w) : +theorem e_1526 : - 1 * (b ^^^ (a &&& c)) - 2 * (a &&& c) + 3 * ( ~~~c &&& (a ^^^ b)) + 11 * (a &&& ~~~c) + 2 * (c &&& (a ^^^ b)) + 5 * (b ^^^ ~~~(a ||| ~~~c)) - 7 * ~~~(a ||| ( ~~~b ||| c)) - 14 * ~~~( ~~~a ||| (b ||| c)) - 5 * ( ~~~a &&& ( ~~~b &&& c)) + 1 * (a &&& ( ~~~b &&& c)) - 3 * (a &&& (b &&& c)) = 1 * ( ~~~a &&& (b &&& c)) + 15 * ~~~( ~~~a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1527 (x y : BitVec w) : +theorem e_1527 : 1 * (c ^^^ ~~~(a &&& ~~~b)) - 7 * (b ^^^ ~~~(a &&& c)) + 4 * ((a ||| b) &&& ~~~(b ^^^ c)) - 2 * (c &&& (a ||| ~~~b)) + 3 * ~~~(a ||| (b ||| c)) - 4 * ~~~(a ||| ( ~~~b ||| c)) + 3 * ~~~( ~~~a ||| (b ||| c)) - 3 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 9 * ( ~~~a &&& ( ~~~b &&& c)) - 4 * ( ~~~a &&& (b &&& c)) + 1 * (a &&& ( ~~~b &&& c)) = - 3 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 2 * (a &&& b) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1528 (x y : BitVec w) : +theorem e_1528 : - 1 * ((a &&& c) ||| (b &&& ~~~c)) - 11 * ~~~(a &&& ~~~c) - 5 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) + 5 * ~~~(a ||| (b ||| c)) + 19 * ~~~(a ||| ( ~~~b ||| c)) - 4 * ~~~( ~~~a ||| (b ||| c)) - 10 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 5 * ( ~~~a &&& ( ~~~b &&& c)) + 2 * ( ~~~a &&& (b &&& c)) + 12 * (a &&& ( ~~~b &&& c)) + 6 * (a &&& (b &&& c)) = - 11 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) + 2 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1529 (x y : BitVec w) : +theorem e_1529 : 3 * (b ||| ~~~(a ||| ~~~c)) - 2 * ((a &&& b) ^^^ (b ||| ~~~c)) + 1 * (b ^^^ (a &&& ( ~~~b ||| c))) + 7 * (b &&& c) + 2 * ~~~(a ||| (b ||| c)) - 2 * ~~~(a ||| ( ~~~b ||| c)) + 4 * ~~~( ~~~a ||| (b ||| c)) - 4 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 6 * ( ~~~a &&& (b &&& c)) + 2 * (a &&& ( ~~~b &&& c)) - 10 * (a &&& (b &&& c)) = 3 * (b ^^^ (a ||| (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1530 (x y : BitVec w) : +theorem e_1530 : - 11 * (b ^^^ (a &&& ~~~c)) - 1 * ( ~~~b &&& (a ^^^ c)) - 1 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 1 * (b &&& ~~~c) + 4 * ~~~( ~~~a ||| ( ~~~b &&& c)) + 1 * ~~~(a ||| (b ||| c)) + 8 * ~~~( ~~~a ||| (b ||| c)) - 4 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 2 * ( ~~~a &&& ( ~~~b &&& c)) + 11 * ( ~~~a &&& (b &&& c)) + 8 * (a &&& (b &&& c)) = - 11 * ~~~(a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1531 (x y : BitVec w) : +theorem e_1531 : 1 * ((a &&& b) ||| ~~~(b ||| ~~~c)) + 3 * (c ||| (a &&& ~~~b)) + 2 * (b ^^^ ~~~(a ||| c)) - 1 * (a ^^^ (b ^^^ c)) + 1 * ~~~(a ||| ( ~~~b ||| c)) - 2 * ~~~( ~~~a ||| (b ||| c)) - 4 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 4 * ( ~~~a &&& ( ~~~b &&& c)) - 6 * ( ~~~a &&& (b &&& c)) - 4 * (a &&& ( ~~~b &&& c)) - 5 * (a &&& (b &&& c)) = - 1 * (c ^^^ (a &&& (b ||| c))) + 2 * ~~~(a ||| (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1532 (x y : BitVec w) : +theorem e_1532 : 1 * (c ||| (a ^^^ b)) - 1 * (c ^^^ (a ||| ( ~~~b &&& c))) + 4 * (c &&& ~~~(a &&& b)) - 6 * ~~~c - 1 * (b ||| (a &&& ~~~c)) - 6 * ~~~( ~~~a ||| (b &&& c)) + 11 * ~~~(a ||| (b ||| c)) + 11 * ~~~(a ||| ( ~~~b ||| c)) + 13 * ~~~( ~~~a ||| (b ||| c)) + 14 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 1 * (a &&& ( ~~~b &&& c)) = 3 * ( ~~~a &&& (b &&& c)) + 5 * ~~~(a ||| (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1533 (x y : BitVec w) : +theorem e_1533 : 4 * (c ^^^ ~~~(a ||| (b &&& c))) - 6 * (b ^^^ c) - 3 * ~~~(a &&& (b ||| c)) - 5 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 9 * ~~~(a ||| (b ||| c)) + 15 * ~~~(a ||| ( ~~~b ||| c)) + 8 * ~~~( ~~~a ||| (b ||| c)) + 11 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 14 * ( ~~~a &&& ( ~~~b &&& c)) - 1 * ( ~~~a &&& (b &&& c)) + 2 * (a &&& ( ~~~b &&& c)) - 4 * (a &&& (b &&& c)) = 5 * ~~~(a ||| c) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1534 (x y : BitVec w) : +theorem e_1534 : - 7 * (b ^^^ (a &&& (b ^^^ c))) + 7 * (a ^^^ ( ~~~b &&& c)) + 5 * ((a ^^^ b) ||| (a ^^^ c)) - 5 * (b ^^^ ~~~(a ||| ~~~c)) + 1 * ~~~( ~~~a &&& ( ~~~b &&& c)) + 4 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) - 1 * ~~~(a ||| (b ||| c)) + 2 * ~~~(a ||| ( ~~~b ||| c)) - 17 * ~~~( ~~~a ||| (b ||| c)) - 8 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 11 * ( ~~~a &&& ( ~~~b &&& c)) - 3 * ( ~~~a &&& (b &&& c)) = - 1 * (a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1535 (x y : BitVec w) : +theorem e_1535 : - 3 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) - 2 * (c ^^^ (a &&& ~~~b)) + 2 * ~~~(a ||| b) + 1 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) + 2 * ~~~(a ||| ~~~b) + 3 * (c &&& (a ^^^ b)) - 3 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) - 2 * ~~~(a ||| (b ||| c)) + 2 * ~~~(a ||| ( ~~~b ||| c)) + 5 * ~~~( ~~~a ||| (b ||| c)) + 3 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 4 * (a &&& (b &&& c)) = - 2 * ~~~(a ||| c) + 1 * ( ~~~a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1536 (x y : BitVec w) : +theorem e_1536 : - 6 * ( ~~~a ||| ( ~~~b &&& c)) - 3 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 1 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) - 1 * b - 6 * (c ^^^ (a &&& ( ~~~b ||| c))) + 8 * ~~~(a ||| (b ||| c)) + 10 * ~~~(a ||| ( ~~~b ||| c)) + 3 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 13 * ( ~~~a &&& ( ~~~b &&& c)) + 13 * ( ~~~a &&& (b &&& c)) + 5 * (a &&& ( ~~~b &&& c)) + 2 * (a &&& (b &&& c)) = - 5 * ~~~( ~~~a ||| (b ||| c)) - 1 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1537 (x y : BitVec w) : +theorem e_1537 : - 3 * (c ^^^ ~~~(a &&& (b ||| c))) - 2 * (b ^^^ ( ~~~a ||| (b &&& c))) + 11 * ( ~~~a ||| ( ~~~b &&& c)) - 1 * ~~~(a ^^^ ( ~~~b &&& c)) - 1 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 4 * ~~~(a ||| (b ||| c)) - 7 * ~~~(a ||| ( ~~~b ||| c)) + 4 * ~~~( ~~~a ||| (b ||| c)) - 8 * ( ~~~a &&& ( ~~~b &&& c)) - 10 * ( ~~~a &&& (b &&& c)) - 6 * (a &&& ( ~~~b &&& c)) + 3 * (a &&& (b &&& c)) = - 3 * ~~~( ~~~a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1538 (x y : BitVec w) : +theorem e_1538 : 2 * ~~~(a &&& ~~~a) + 1 * ( ~~~c &&& (a ^^^ b)) + 5 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) - 2 * (b ^^^ ~~~(a &&& (b ^^^ c))) + 4 * (b ^^^ (a ||| (b &&& c))) - 4 * ~~~(a ||| (b ||| c)) - 12 * ~~~(a ||| ( ~~~b ||| c)) - 5 * ~~~( ~~~a ||| (b ||| c)) - 9 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 9 * ( ~~~a &&& ( ~~~b &&& c)) - 10 * (a &&& ( ~~~b &&& c)) - 6 * (a &&& (b &&& c)) = 2 * ( ~~~a &&& (b &&& c)) - 4 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1539 (x y : BitVec w) : +theorem e_1539 : 4 * ((a &&& b) ^^^ (b ||| ~~~c)) + 1 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) + 3 * ~~~( ~~~a &&& ( ~~~b ||| c)) - 5 * ( ~~~(a &&& b) &&& (b ^^^ c)) + 3 * ~~~(a ^^^ c) - 8 * ~~~(a ||| (b ||| c)) - 6 * ~~~(a ||| ( ~~~b ||| c)) - 7 * ~~~( ~~~a ||| (b ||| c)) - 10 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 3 * ( ~~~a &&& ( ~~~b &&& c)) - 2 * (a &&& ( ~~~b &&& c)) - 13 * (a &&& (b &&& c)) = - 7 * (b ^^^ ( ~~~a &&& (b ^^^ c))) + 11 * ( ~~~a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1540 (x y : BitVec w) : +theorem e_1540 : 3 * (b ^^^ (a &&& ~~~c)) - 2 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) + 2 * ( ~~~a &&& ( ~~~b ||| c)) + 7 * (b ||| (a &&& ~~~c)) + 5 * ~~~(a ||| c) - 5 * ~~~(a ||| (b ||| c)) - 12 * ~~~(a ||| ( ~~~b ||| c)) - 8 * ~~~( ~~~a ||| (b ||| c)) - 4 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 10 * ( ~~~a &&& (b &&& c)) + 2 * (a &&& ( ~~~b &&& c)) - 10 * (a &&& (b &&& c)) = 3 * (b &&& ~~~c) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1541 (x y : BitVec w) : +theorem e_1541 : - 7 * (a ||| ( ~~~b &&& c)) - 2 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 5 * (b ||| ~~~(a ||| c)) - 2 * (a &&& (b ||| c)) - 6 * (b ^^^ c) + 1 * (a ||| (b ||| c)) - 5 * ~~~(a ||| (b ||| c)) + 8 * ~~~( ~~~a ||| (b ||| c)) + 9 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 12 * ( ~~~a &&& ( ~~~b &&& c)) - 4 * ( ~~~a &&& (b &&& c)) + 3 * (a &&& (b &&& c)) = - 16 * (a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1542 (x y : BitVec w) : +theorem e_1542 : - 7 * (a &&& c) - 5 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 1 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) - 6 * (b ^^^ ~~~(a ||| (b ^^^ c))) - 1 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) + 11 * ~~~(a ||| (b ||| c)) + 6 * ~~~(a ||| ( ~~~b ||| c)) - 1 * ~~~( ~~~a ||| (b ||| c)) + 11 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 1 * ( ~~~a &&& ( ~~~b &&& c)) + 1 * ( ~~~a &&& (b &&& c)) + 12 * (a &&& ( ~~~b &&& c)) = - 13 * (a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1543 (x y : BitVec w) : +theorem e_1543 : - 1 * ~~~(b &&& c) - 2 * ~~~(a &&& ( ~~~b ||| c)) + 7 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 2 * ((a ||| ~~~b) &&& (b ^^^ c)) + 2 * ~~~b + 7 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 2 * ~~~(b ||| c) - 4 * ~~~(a ||| (b ||| c)) - 11 * ~~~(a ||| ( ~~~b ||| c)) - 6 * ~~~( ~~~a ||| (b ||| c)) - 6 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 1 * ( ~~~a &&& ( ~~~b &&& c)) - 10 * (a &&& ( ~~~b &&& c)) = 12 * ( ~~~a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1544 (x y : BitVec w) : +theorem e_1544 : - 7 * ~~~(a ^^^ b) + 7 * ((a ^^^ b) ||| ~~~(a ^^^ c)) - 5 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) + 3 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) - 6 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) - 3 * ~~~(b ^^^ c) - 8 * ~~~(a ||| ( ~~~b ||| c)) + 7 * ~~~( ~~~a ||| (b ||| c)) + 11 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 3 * ( ~~~a &&& ( ~~~b &&& c)) - 9 * ( ~~~a &&& (b &&& c)) - 10 * (a &&& ( ~~~b &&& c)) + 14 * (a &&& (b &&& c)) = - 7 * ((a &&& c) ^^^ (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1545 (x y : BitVec w) : +theorem e_1545 : - 2 * ( ~~~a ||| ( ~~~b &&& c)) - 2 * (a &&& (b ||| c)) + 3 * ~~~(a ^^^ ( ~~~b &&& c)) - 5 * (c ^^^ ~~~(a &&& (b &&& c))) - 1 * (b ^^^ ~~~(a &&& (b ||| c))) - 2 * ((a &&& b) ||| ~~~(b ^^^ c)) + 7 * ~~~(a ||| (b ||| c)) + 4 * ~~~(a ||| ( ~~~b ||| c)) + 8 * ~~~( ~~~a ||| (b ||| c)) + 10 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 3 * ( ~~~a &&& ( ~~~b &&& c)) + 1 * (a &&& ( ~~~b &&& c)) + 10 * (a &&& (b &&& c)) = - 1 * ( ~~~a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1546 (x y : BitVec w) : +theorem e_1546 : 3 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 5 * ((a &&& b) ||| ~~~(b ||| ~~~c)) - 6 * ( ~~~a ||| (b ^^^ c)) - 1 * ~~~( ~~~a &&& (b &&& c)) + 7 * ~~~(b &&& c) - 1 * ~~~(a ||| (b ||| c)) - 3 * ~~~(a ||| ( ~~~b ||| c)) - 5 * ~~~( ~~~a ||| (b ||| c)) - 6 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 3 * ( ~~~a &&& ( ~~~b &&& c)) + 4 * ( ~~~a &&& (b &&& c)) - 7 * (a &&& ( ~~~b &&& c)) - 3 * (a &&& (b &&& c)) = 1 * (c ||| ~~~(a ^^^ b)) + 1 * (b ^^^ ~~~(a &&& (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1547 (x y : BitVec w) : +theorem e_1547 : 1 * ( ~~~a ||| (b &&& c)) - 11 * ( ~~~b &&& (a ^^^ c)) + 1 * (b ^^^ ~~~(a &&& c)) + 4 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) + 1 * ~~~(b ||| ~~~c) + 11 * (c ^^^ (a ||| (b &&& c))) - 7 * (a ^^^ (b &&& c)) - 2 * ~~~(a ||| (b ||| c)) + 2 * ~~~( ~~~a ||| (b ||| c)) - 8 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 7 * ( ~~~a &&& ( ~~~b &&& c)) + 2 * ( ~~~a &&& (b &&& c)) - 6 * (a &&& (b &&& c)) = - 6 * (a &&& ( ~~~b &&& c)) + 1 * ~~~(a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1548 (x y : BitVec w) : +theorem e_1548 : - 2 * (b &&& ~~~(a &&& ~~~c)) - 1 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) + 11 * (a &&& b) - 1 * b + 2 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) - 1 * (a &&& (b ||| c)) - 6 * ~~~(a ||| (b ||| c)) + 4 * ~~~(a ||| ( ~~~b ||| c)) - 6 * ~~~( ~~~a ||| (b ||| c)) - 8 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 7 * ( ~~~a &&& ( ~~~b &&& c)) + 2 * ( ~~~a &&& (b &&& c)) - 14 * (a &&& (b &&& c)) = - 5 * (b ^^^ ~~~(a &&& (b &&& c))) + 4 * (a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1549 (x y : BitVec w) : +theorem e_1549 : - 1 * ((a &&& c) ||| (b &&& ~~~c)) + 1 * (b ^^^ ~~~(a &&& (b ||| c))) + 1 * ((a &&& c) ||| ~~~(b ||| c)) + 3 * ((a ||| b) &&& ~~~(b ^^^ c)) + 5 * (c ||| (a &&& ~~~b)) + 11 * (c ^^^ ( ~~~a ||| (b ||| c))) - 10 * ~~~(a ||| ( ~~~b ||| c)) - 10 * ~~~( ~~~a ||| (b ||| c)) - 11 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 6 * ( ~~~a &&& ( ~~~b &&& c)) - 8 * ( ~~~a &&& (b &&& c)) - 5 * (a &&& ( ~~~b &&& c)) - 9 * (a &&& (b &&& c)) = 13 * ~~~(a ||| (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1550 (x y : BitVec w) : +theorem e_1550 : 1 * c + 4 * (b ^^^ (a ||| ~~~c)) - 2 * b + 11 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 7 * (b ^^^ ~~~(a ||| (b ^^^ c))) + 1 * (b ^^^ (a &&& ~~~c)) - 22 * ~~~(a ||| (b ||| c)) + 1 * ~~~(a ||| ( ~~~b ||| c)) - 9 * ~~~( ~~~a ||| (b ||| c)) - 9 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 1 * ( ~~~a &&& ( ~~~b &&& c)) - 15 * ( ~~~a &&& (b &&& c)) - 9 * (a &&& ( ~~~b &&& c)) = 7 * ~~~( ~~~a &&& ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1551 (x y : BitVec w) : +theorem e_1551 : - 7 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 1 * (b ^^^ ( ~~~a ||| (b ||| c))) + 1 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) + 7 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) + 5 * (c ^^^ ~~~(a &&& ~~~b)) + 3 * ~~~(a ||| (b ||| c)) - 13 * ~~~(a ||| ( ~~~b ||| c)) - 1 * ~~~( ~~~a ||| (b ||| c)) + 1 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 6 * ( ~~~a &&& ( ~~~b &&& c)) - 7 * ( ~~~a &&& (b &&& c)) - 4 * (a &&& ( ~~~b &&& c)) - 1 * (a &&& (b &&& c)) = - 7 * ( ~~~a &&& (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1552 (x y : BitVec w) : +theorem e_1552 : - 7 * (b ^^^ ( ~~~a ||| (b &&& c))) - 6 * (b ^^^ (a ||| (b &&& c))) + 1 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) - 11 * (b ^^^ ( ~~~a &&& (b ^^^ c))) + 5 * (a ||| (b ||| c)) + 6 * ~~~(a ||| (b ||| c)) - 1 * ~~~(a ||| ( ~~~b ||| c)) - 1 * ~~~( ~~~a ||| (b ||| c)) + 11 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 12 * ( ~~~a &&& ( ~~~b &&& c)) + 6 * ( ~~~a &&& (b &&& c)) - 1 * (a &&& ( ~~~b &&& c)) + 3 * (a &&& (b &&& c)) = - 2 * ~~~( ~~~a &&& ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1553 (x y : BitVec w) : +theorem e_1553 : - 6 * ~~~(a ^^^ c) - 1 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 5 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) - 1 * (b ||| (a ^^^ c)) - 1 * ~~~( ~~~a &&& ( ~~~b ||| c)) + 5 * ( ~~~a &&& (b ||| c)) - 5 * ((a &&& c) ||| (b &&& ~~~c)) + 12 * ~~~(a ||| (b ||| c)) + 8 * ~~~(a ||| ( ~~~b ||| c)) + 8 * ~~~( ~~~a ||| (b ||| c)) + 8 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 3 * ( ~~~a &&& (b &&& c)) + 13 * (a &&& ( ~~~b &&& c)) + 14 * (a &&& (b &&& c)) = - 2 * ( ~~~a &&& ( ~~~b &&& c)) + 1 * ~~~(a ^^^ b) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1554 (x y : BitVec w) : +theorem e_1554 : - 7 * ~~~(a ||| ( ~~~b &&& c)) + 3 * (a ^^^ ( ~~~b ||| c)) - 2 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 2 * ~~~b + 4 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) - 6 * ~~~(b &&& ~~~c) + 12 * ~~~(a ||| (b ||| c)) + 9 * ~~~(a ||| ( ~~~b ||| c)) + 8 * ~~~( ~~~a ||| (b ||| c)) - 7 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 1 * ( ~~~a &&& ( ~~~b &&& c)) + 10 * ( ~~~a &&& (b &&& c)) + 8 * (a &&& ( ~~~b &&& c)) + 4 * (a &&& (b &&& c)) = 2 * ((a ||| b) &&& ~~~(b ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1555 (x y : BitVec w) : +theorem e_1555 : 2 * (b ||| ~~~(a ^^^ c)) + 7 * (c ^^^ (a &&& b)) + 5 * (b &&& ~~~(a &&& c)) - 2 * (b ||| (a &&& ~~~c)) - 1 * (b ^^^ ~~~(a &&& c)) + 1 * (b ^^^ (a ||| (b ||| c))) - 1 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 5 * ~~~(a ||| ( ~~~b ||| c)) + 3 * ~~~( ~~~a ||| (b ||| c)) - 15 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 6 * ( ~~~a &&& ( ~~~b &&& c)) - 16 * ( ~~~a &&& (b &&& c)) - 9 * (a &&& ( ~~~b &&& c)) + 1 * (a &&& (b &&& c)) = - 4 * (b &&& (a ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1556 (x y : BitVec w) : +theorem e_1556 : - 1 * (b ^^^ (a ||| c)) + 1 * (b &&& (a ||| ~~~c)) - 2 * ((a ||| ~~~b) &&& (b ^^^ c)) - 1 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) + 7 * (b ^^^ ( ~~~a ||| (b &&& c))) + 2 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) - 8 * ~~~(a ||| (b ||| c)) - 8 * ~~~(a ||| ( ~~~b ||| c)) - 6 * ~~~( ~~~a ||| (b ||| c)) - 13 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 4 * ( ~~~a &&& ( ~~~b &&& c)) - 6 * ( ~~~a &&& (b &&& c)) - 2 * (a &&& ( ~~~b &&& c)) - 8 * (a &&& (b &&& c)) = 1 * ~~~(b &&& ~~~c) - 7 * (a ||| b) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1557 (x y : BitVec w) : +theorem e_1557 : - 7 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 5 * (c ^^^ (a &&& b)) + 5 * (c ^^^ ~~~(a &&& (b ||| c))) + 2 * (b ^^^ ( ~~~a ||| (b &&& c))) - 5 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) - 3 * (b ||| (a ^^^ c)) - 1 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) + 7 * ~~~(a ||| (b ||| c)) + 7 * ~~~(a ||| ( ~~~b ||| c)) - 1 * ~~~( ~~~a ||| (b ||| c)) + 12 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 12 * ( ~~~a &&& ( ~~~b &&& c)) + 15 * ( ~~~a &&& (b &&& c)) + 6 * (a &&& ( ~~~b &&& c)) = 1 * ~~~(a &&& ( ~~~b ||| c)) - 5 * (a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1558 (x y : BitVec w) : +theorem e_1558 : - 6 * ~~~(a ^^^ ( ~~~b ||| c)) + 1 * ( ~~~b ||| ~~~(a ^^^ c)) - 11 * ((a &&& b) ||| ~~~(b ^^^ c)) - 1 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 6 * ~~~(a ^^^ (b &&& c)) - 11 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) - 1 * ~~~(a ||| ~~~c) + 7 * (a &&& b) + 24 * ~~~(a ||| (b ||| c)) + 23 * ~~~(a ||| ( ~~~b ||| c)) + 23 * ~~~( ~~~a ||| (b ||| c)) + 8 * ( ~~~a &&& (b &&& c)) + 5 * (a &&& ( ~~~b &&& c)) + 27 * (a &&& (b &&& c)) = - 4 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) - 13 * ( ~~~a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1559 (x y : BitVec w) : +theorem e_1559 : - 3 * (c ^^^ ~~~(a &&& b)) - 2 * (a &&& ~~~b) + 5 * (c ^^^ (a &&& b)) - 5 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) - 1 * ((a &&& b) ||| (b ^^^ c)) - 2 * (c ^^^ ( ~~~a &&& (b ||| c))) - 1 * (b &&& (a ^^^ c)) - 6 * ~~~(b ||| c) + 11 * ~~~(a ||| ( ~~~b ||| c)) + 16 * ~~~( ~~~a ||| (b ||| c)) + 2 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 1 * ( ~~~a &&& ( ~~~b &&& c)) - 4 * ( ~~~a &&& (b &&& c)) + 11 * (a &&& (b &&& c)) = - 9 * ~~~(a ||| (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1560 (x y : BitVec w) : +theorem e_1560 : - 2 * (a &&& ~~~c) + 11 * (b ^^^ ~~~(a &&& c)) + 1 * ((a ^^^ b) ||| (a ^^^ c)) + 1 * ( ~~~a &&& (b ||| c)) + 11 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) - 6 * ( ~~~b ||| ~~~(a ^^^ c)) + 2 * (c ^^^ (a ||| (b ||| c))) - 16 * ~~~(a ||| (b ||| c)) + 2 * ~~~(a ||| ( ~~~b ||| c)) - 17 * ~~~( ~~~a ||| (b ||| c)) - 18 * ( ~~~a &&& ( ~~~b &&& c)) - 13 * ( ~~~a &&& (b &&& c)) + 5 * (a &&& ( ~~~b &&& c)) - 16 * (a &&& (b &&& c)) = 1 * ~~~( ~~~a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1561 (x y : BitVec w) : +theorem e_1561 : 4 * (a &&& (b ||| c)) + 11 * (a ^^^ ( ~~~b &&& c)) - 2 * (b ||| (a &&& ~~~c)) - 7 * (c &&& ~~~(a ^^^ b)) - 3 * ~~~(a ^^^ b) - 5 * (b ||| (a ^^^ c)) - 3 * ~~~a + 6 * ~~~(a ||| (b ||| c)) + 10 * ~~~(a ||| ( ~~~b ||| c)) - 4 * ~~~( ~~~a ||| (b ||| c)) - 5 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 10 * ( ~~~a &&& (b &&& c)) - 4 * (a &&& ( ~~~b &&& c)) + 2 * (a &&& (b &&& c)) = - 7 * ( ~~~a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1562 (x y : BitVec w) : +theorem e_1562 : - 1 * (b ||| (a ^^^ c)) + 4 * ~~~( ~~~a ||| (b &&& c)) - 2 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 11 * (b ^^^ ( ~~~a ||| (b ||| c))) - 5 * ~~~( ~~~a ||| ( ~~~b &&& c)) - 6 * ( ~~~b ||| (a ^^^ c)) - 7 * ((a &&& b) ^^^ (b ||| ~~~c)) + 7 * ~~~(b ^^^ c) + 22 * ~~~(a ||| (b ||| c)) + 8 * ~~~( ~~~a ||| (b ||| c)) + 13 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 21 * ( ~~~a &&& ( ~~~b &&& c)) + 10 * ( ~~~a &&& (b &&& c)) + 18 * (a &&& ( ~~~b &&& c)) + 2 * (a &&& (b &&& c)) = 3 * ( ~~~a ||| (b ||| c)) - 11 * ~~~(a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1563 (x y : BitVec w) : +theorem e_1563 : 2 * ( ~~~b ||| ~~~(a ^^^ c)) - 1 * (c &&& (a ^^^ b)) - 3 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) - 1 * (a ||| (b ||| c)) + 4 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) - 6 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) + 1 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) + 5 * ~~~(a ||| (b ||| c)) - 2 * ~~~(a ||| ( ~~~b ||| c)) + 9 * ~~~( ~~~a ||| (b ||| c)) + 1 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 2 * ( ~~~a &&& ( ~~~b &&& c)) + 6 * ( ~~~a &&& (b &&& c)) + 3 * (a &&& ( ~~~b &&& c)) + 8 * (a &&& (b &&& c)) = 1 * (a ||| ~~~b) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1564 (x y : BitVec w) : +theorem e_1564 : 7 * (c ^^^ (a ||| ( ~~~b ||| c))) - 3 * (b ^^^ (a ||| (b &&& c))) + 11 * ~~~a - 1 * (a &&& b) - 11 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) + 2 * (b ^^^ ~~~(a ||| (b &&& c))) - 7 * (c ||| ~~~(a ^^^ b)) - 6 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 5 * ~~~(a ||| (b ||| c)) + 17 * ~~~(a ||| ( ~~~b ||| c)) + 19 * ~~~( ~~~a ||| (b ||| c)) + 16 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 2 * ( ~~~a &&& ( ~~~b &&& c)) + 27 * (a &&& ( ~~~b &&& c)) + 8 * (a &&& (b &&& c)) = 2 * ~~~(a ^^^ (b &&& c)) + 6 * ((a ^^^ b) ||| (a ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1565 (x y : BitVec w) : +theorem e_1565 : - 1 * ~~~(a &&& ~~~c) + 1 * (b ^^^ ( ~~~a ||| (b ^^^ c))) - 3 * ~~~(a ^^^ b) - 5 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) + 5 * (a &&& ~~~b) - 6 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 3 * a + 1 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) + 7 * ~~~(a ||| (b ||| c)) + 5 * ~~~(a ||| ( ~~~b ||| c)) - 3 * ~~~( ~~~a ||| (b ||| c)) + 11 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 7 * ( ~~~a &&& ( ~~~b &&& c)) - 3 * (a &&& ( ~~~b &&& c)) + 5 * (a &&& (b &&& c)) = - 1 * ~~~(a ||| ( ~~~b &&& c)) + 1 * ( ~~~a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1566 (x y : BitVec w) : +theorem e_1566 : - 1 * (b ^^^ ~~~(a ||| ~~~c)) + 1 * ((a &&& c) ^^^ (b ||| c)) + 5 * (b ||| (a &&& c)) + 3 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) + 1 * ~~~(a &&& ( ~~~b &&& c)) - 7 * ( ~~~a &&& (b ^^^ c)) - 1 * (b ^^^ ~~~(a &&& ~~~c)) - 1 * (a &&& c) + 1 * ~~~(a ||| ( ~~~b ||| c)) - 2 * ~~~( ~~~a ||| (b ||| c)) - 9 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 7 * ( ~~~a &&& ( ~~~b &&& c)) - 11 * ( ~~~a &&& (b &&& c)) - 6 * (a &&& ( ~~~b &&& c)) - 5 * (a &&& (b &&& c)) = - 1 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1567 (x y : BitVec w) : +theorem e_1567 : 7 * ( ~~~a ||| ( ~~~b &&& c)) - 1 * (c ^^^ (a &&& (b ||| c))) + 1 * ( ~~~a &&& ( ~~~b ||| c)) + 11 * (c ^^^ (a ||| (b ||| c))) + 11 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) + 2 * (c ^^^ ~~~(a &&& (b ||| c))) + 2 * ~~~( ~~~a ||| ( ~~~b &&& c)) - 5 * ((a ^^^ b) ||| (a ^^^ c)) - 10 * ~~~(a ||| (b ||| c)) - 26 * ~~~(a ||| ( ~~~b ||| c)) - 21 * ~~~( ~~~a ||| (b ||| c)) - 7 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 13 * ( ~~~a &&& ( ~~~b &&& c)) - 15 * (a &&& ( ~~~b &&& c)) - 20 * (a &&& (b &&& c)) = - 5 * (b &&& c) + 7 * ( ~~~a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1568 (x y : BitVec w) : +theorem e_1568 : 2 * (b ^^^ (a ||| ( ~~~b &&& c))) + 2 * ( ~~~c &&& ~~~(a ^^^ b)) - 7 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) - 1 * (c ^^^ ~~~(a ||| (b &&& c))) - 2 * (b ^^^ (a &&& c)) - 11 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) + 5 * (a &&& c) - 1 * (b &&& (a ||| c)) + 17 * ~~~(a ||| (b ||| c)) + 9 * ~~~( ~~~a ||| (b ||| c)) + 1 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 9 * ( ~~~a &&& ( ~~~b &&& c)) + 9 * ( ~~~a &&& (b &&& c)) + 3 * (a &&& ( ~~~b &&& c)) + 8 * (a &&& (b &&& c)) = - 12 * ~~~(a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1569 (x y : BitVec w) : +theorem e_1569 : 4 * ~~~(a ^^^ (b &&& c)) + 3 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) - 2 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) + 2 * (c &&& (a ||| ~~~b)) - 11 * ((a &&& c) ||| ~~~(b ||| c)) - 5 * (b ^^^ ~~~(a ||| (b &&& c))) - 1 * ((a ||| b) &&& ~~~(b ^^^ c)) - 6 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) + 2 * ~~~(b ^^^ c) + 13 * ~~~(a ||| (b ||| c)) + 2 * ~~~(a ||| ( ~~~b ||| c)) + 11 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 13 * ( ~~~a &&& (b &&& c)) + 12 * (a &&& ( ~~~b &&& c)) + 7 * (a &&& (b &&& c)) = - 15 * ~~~( ~~~a ||| (b ||| c)) + 1 * ~~~(a &&& ~~~c) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1570 (x y : BitVec w) : +theorem e_1570 : 1 * (c ||| ~~~(a ^^^ b)) - 7 * ~~~(a ^^^ ( ~~~b &&& c)) + 2 * (a ^^^ (b &&& c)) - 5 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 3 * ~~~( ~~~a &&& (b &&& c)) + 1 * (a &&& (b ^^^ c)) - 7 * (b &&& c) - 1 * (c ^^^ ~~~(a ||| b)) + 18 * ~~~(a ||| (b ||| c)) + 6 * ~~~( ~~~a ||| (b ||| c)) + 4 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 5 * ( ~~~a &&& ( ~~~b &&& c)) + 15 * ( ~~~a &&& (b &&& c)) + 15 * (a &&& ( ~~~b &&& c)) + 10 * (a &&& (b &&& c)) = 3 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) - 10 * ~~~(a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1571 (x y : BitVec w) : +theorem e_1571 : 11 * ~~~(b ||| ~~~c) - 6 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) + 5 * ( ~~~b &&& (a ^^^ c)) + 2 * ~~~(a ||| ( ~~~b &&& c)) - 2 * (c ^^^ (a ||| (b ||| c))) + 1 * (a ||| (b ^^^ c)) + 1 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) + 7 * ~~~( ~~~a ||| (b &&& c)) - 6 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) + 9 * ~~~(a ||| (b ||| c)) - 2 * ~~~(a ||| ( ~~~b ||| c)) - 8 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 7 * ( ~~~a &&& ( ~~~b &&& c)) + 9 * ( ~~~a &&& (b &&& c)) - 14 * (a &&& ( ~~~b &&& c)) - 1 * (a &&& (b &&& c)) = - 1 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) + 5 * ~~~( ~~~a ||| (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1572 (x y : BitVec w) : +theorem e_1572 : - 3 * ~~~(a ^^^ c) - 3 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) + 2 * (b ^^^ ~~~(a ||| (b &&& c))) + 7 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) - 3 * ~~~(a ||| ~~~c) - 1 * ( ~~~b ||| (a ^^^ c)) - 3 * (c ||| (a &&& ~~~b)) - 1 * (c ^^^ (a ||| (b &&& c))) - 5 * (a ^^^ ( ~~~b &&& c)) + 5 * ~~~(a ||| (b ||| c)) - 1 * ~~~(a ||| ( ~~~b ||| c)) + 3 * ~~~( ~~~a ||| (b ||| c)) - 5 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 4 * ( ~~~a &&& ( ~~~b &&& c)) + 5 * ( ~~~a &&& (b &&& c)) + 4 * (a &&& ( ~~~b &&& c)) = - 3 * (a ||| (b &&& c)) - 2 * (a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1573 (x y : BitVec w) : +theorem e_1573 : - 1 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) + 4 * (c &&& (a ^^^ b)) + 5 * ~~~(a ||| ~~~c) + 7 * (a ||| (b ||| c)) + 3 * ( ~~~a ||| ( ~~~b &&& c)) - 1 * (a &&& (b ||| c)) - 6 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) - 1 * ~~~b - 1 * (c ^^^ (a &&& (b ||| c))) - 5 * ~~~(a ||| (b ||| c)) - 9 * ~~~(a ||| ( ~~~b ||| c)) + 1 * ~~~( ~~~a ||| (b ||| c)) - 8 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 18 * ( ~~~a &&& (b &&& c)) - 15 * (a &&& ( ~~~b &&& c)) - 2 * (a &&& (b &&& c)) = - 3 * ~~~(a ^^^ (b ||| c)) + 7 * ( ~~~a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1574 (x y : BitVec w) : +theorem e_1574 : - 5 * (b &&& c) + 1 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 2 * ((a &&& c) ||| (b &&& ~~~c)) - 6 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) + 2 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) - 7 * (b ^^^ (a ||| c)) + 1 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) + 4 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) - 5 * ~~~(a ||| (b ||| c)) + 12 * ~~~(a ||| ( ~~~b ||| c)) + 4 * ~~~( ~~~a ||| (b ||| c)) - 7 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 7 * ( ~~~a &&& ( ~~~b &&& c)) + 6 * ( ~~~a &&& (b &&& c)) + 10 * (a &&& ( ~~~b &&& c)) + 14 * (a &&& (b &&& c)) = 5 * ~~~(a ^^^ ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1575 (x y : BitVec w) : +theorem e_1575 : - 2 * ((a ^^^ b) ||| (a ^^^ c)) + 2 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) - 2 * (c ^^^ (a ||| ( ~~~b &&& c))) - 6 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) + 4 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 1 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 4 * ((a &&& c) ||| ~~~(b ||| c)) + 1 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) - 12 * ~~~(a ||| (b ||| c)) + 5 * ~~~(a ||| ( ~~~b ||| c)) + 2 * ~~~( ~~~a ||| (b ||| c)) - 3 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 6 * ( ~~~a &&& ( ~~~b &&& c)) + 10 * ( ~~~a &&& (b &&& c)) - 1 * (a &&& ( ~~~b &&& c)) + 1 * (a &&& (b &&& c)) = 1 * ~~~( ~~~a ||| (b &&& c)) + 1 * (c &&& (a ||| b)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1576 (x y : BitVec w) : +theorem e_1576 : 4 * (a ^^^ (b ^^^ c)) - 11 * a - 6 * (b ^^^ ~~~(a &&& ~~~c)) + 1 * (c ||| ~~~(a ||| ~~~b)) - 6 * (b ^^^ ( ~~~a &&& (b ^^^ c))) - 3 * ~~~(b &&& ~~~c) - 2 * (a ||| ~~~c) - 2 * (b ^^^ (a &&& c)) + 14 * ~~~(a ||| (b ||| c)) - 1 * ~~~(a ||| ( ~~~b ||| c)) + 14 * ~~~( ~~~a ||| (b ||| c)) + 27 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 13 * ( ~~~a &&& ( ~~~b &&& c)) + 13 * ( ~~~a &&& (b &&& c)) + 24 * (a &&& ( ~~~b &&& c)) + 19 * (a &&& (b &&& c)) = 1 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) + 2 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1577 (x y : BitVec w) : +theorem e_1577 : - 2 * (c ||| ~~~(a ||| b)) - 2 * ~~~(b ||| ~~~c) + 7 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) + 5 * ( ~~~b ||| ~~~(a ^^^ c)) + 3 * ( ~~~b ||| (a ^^^ c)) + 4 * (a &&& ~~~c) + 2 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 2 * ((a ^^^ b) ||| (a ^^^ c)) - 2 * (b ^^^ ~~~(a &&& ~~~c)) - 18 * ~~~(a ||| (b ||| c)) - 19 * ~~~(a ||| ( ~~~b ||| c)) - 19 * ~~~( ~~~a ||| (b ||| c)) - 3 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 14 * ( ~~~a &&& ( ~~~b &&& c)) - 8 * ( ~~~a &&& (b &&& c)) - 10 * (a &&& (b &&& c)) = - 7 * ~~~a := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1578 (x y : BitVec w) : +theorem e_1578 : 1 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) + 3 * (c &&& (a ||| b)) - 1 * ~~~c + 4 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) - 1 * ~~~(b &&& c) + 1 * (c ^^^ (a &&& (b ||| c))) - 5 * ((a ^^^ b) ||| (a ^^^ c)) + 2 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) - 7 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) - 3 * (b ^^^ ~~~(a ||| (b &&& c))) + 3 * (b ^^^ ( ~~~a &&& (b ||| c))) + 12 * ~~~(a ||| ( ~~~b ||| c)) + 11 * ~~~( ~~~a ||| (b ||| c)) + 4 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 7 * ( ~~~a &&& ( ~~~b &&& c)) + 7 * (a &&& ( ~~~b &&& c)) = - 3 * ( ~~~a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1579 (x y : BitVec w) : +theorem e_1579 : 1 * ((a &&& b) ||| ~~~(b ||| c)) + 2 * (a ^^^ ( ~~~b ||| c)) - 3 * (c &&& ~~~(a ^^^ b)) - 2 * ( ~~~b ||| ~~~(a ^^^ c)) + 2 * ( ~~~c &&& ~~~(a ^^^ b)) + 1 * (b ^^^ ~~~(a ||| ~~~c)) + 7 * ((a &&& ~~~b) ||| (b ^^^ c)) - 1 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 2 * ~~~(a ||| (b ||| c)) + 3 * ~~~(a ||| ( ~~~b ||| c)) + 5 * ~~~( ~~~a ||| (b ||| c)) - 12 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 3 * ( ~~~a &&& ( ~~~b &&& c)) + 10 * ( ~~~a &&& (b &&& c)) + 7 * (a &&& ( ~~~b &&& c)) + 14 * (a &&& (b &&& c)) = 11 * (c ||| (a ^^^ b)) - 3 * ( ~~~a &&& (b ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1580 (x y : BitVec w) : +theorem e_1580 : - 1 * ( ~~~a &&& (b ^^^ c)) - 2 * b + 3 * (c ^^^ ~~~(a ||| ~~~b)) + 1 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) + 2 * ((a &&& b) ^^^ (b ||| c)) - 2 * (c ^^^ (a ||| (b ||| c))) + 11 * (a ^^^ b) - 3 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 11 * (a ^^^ (b ^^^ c)) + 2 * ~~~(a ||| (b ||| c)) - 22 * ~~~( ~~~a ||| (b ||| c)) + 7 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 16 * ( ~~~a &&& ( ~~~b &&& c)) - 10 * ( ~~~a &&& (b &&& c)) - 14 * (a &&& ( ~~~b &&& c)) - 13 * (a &&& (b &&& c)) = 19 * ~~~(a ||| ( ~~~b ||| c)) - 1 * (c ^^^ (a &&& ( ~~~b ||| c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1581 (x y : BitVec w) : +theorem e_1581 : - 11 * ~~~(a &&& ~~~a) - 7 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) + 1 * ~~~(a ||| (b &&& c)) - 3 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) - 11 * ~~~(a ^^^ c) - 7 * (c ^^^ ~~~(a &&& ~~~b)) - 1 * ~~~(a ||| ~~~c) - 5 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) + 1 * (b ^^^ ~~~(a ||| (b &&& c))) - 1 * ((a &&& b) ||| ~~~(b ^^^ c)) + 36 * ~~~(a ||| (b ||| c)) + 33 * ~~~(a ||| ( ~~~b ||| c)) + 27 * ~~~( ~~~a ||| (b ||| c)) + 21 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 30 * ( ~~~a &&& ( ~~~b &&& c)) + 29 * (a &&& ( ~~~b &&& c)) + 39 * (a &&& (b &&& c)) = 5 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) - 25 * ( ~~~a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1582 (x y : BitVec w) : +theorem e_1582 : 1 * ~~~(a ||| b) - 5 * (b ^^^ ~~~(a ||| (b &&& c))) + 4 * (c ^^^ ~~~(a ||| b)) - 6 * (a ||| ( ~~~b ||| c)) - 7 * ~~~(b &&& ~~~c) - 3 * (a ||| c) + 3 * (b ^^^ (a &&& (b ^^^ c))) - 6 * (c ^^^ (a ||| ~~~b)) + 11 * (b ^^^ ~~~(a &&& (b ^^^ c))) + 4 * ~~~(a ||| (b ||| c)) - 3 * ~~~(a ||| ( ~~~b ||| c)) + 11 * ~~~( ~~~a ||| (b ||| c)) + 5 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 9 * ( ~~~a &&& ( ~~~b &&& c)) + 16 * ( ~~~a &&& (b &&& c)) + 5 * (a &&& ( ~~~b &&& c)) + 10 * (a &&& (b &&& c)) = - 4 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1583 (x y : BitVec w) : +theorem e_1583 : - 2 * ~~~( ~~~a ||| ( ~~~b &&& c)) + 2 * (a &&& ( ~~~b ||| c)) - 1 * a - 3 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 1 * ( ~~~a ||| (b &&& c)) + 11 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) + 1 * (c ^^^ (a ||| ~~~b)) - 1 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) + 11 * (b ^^^ ( ~~~a ||| (b ||| c))) - 16 * ~~~(a ||| (b ||| c)) - 7 * ~~~(a ||| ( ~~~b ||| c)) - 7 * ~~~( ~~~a ||| (b ||| c)) + 6 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 20 * ( ~~~a &&& ( ~~~b &&& c)) - 1 * ( ~~~a &&& (b &&& c)) - 4 * (a &&& ( ~~~b &&& c)) + 1 * (a &&& (b &&& c)) = 5 * (c ^^^ ( ~~~a ||| (b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1584 (x y : BitVec w) : +theorem e_1584 : - 1 * ((a ^^^ b) &&& (a ^^^ c)) + 2 * (a ^^^ b) + 4 * (c &&& ~~~(a ^^^ b)) + 3 * c - 5 * ((a ||| ~~~b) &&& (b ^^^ c)) + 11 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) + 4 * (b &&& (a ||| ~~~c)) - 1 * a - 2 * (b ^^^ (a &&& ~~~c)) - 1 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 10 * ~~~(a ||| (b ||| c)) + 4 * ~~~(a ||| ( ~~~b ||| c)) - 9 * ~~~( ~~~a ||| (b ||| c)) + 2 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 13 * ( ~~~a &&& ( ~~~b &&& c)) - 6 * ( ~~~a &&& (b &&& c)) - 10 * (a &&& ( ~~~b &&& c)) = 7 * (b &&& ~~~(a &&& ~~~c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1585 (x y : BitVec w) : +theorem e_1585 : 5 * (b ^^^ ~~~(a &&& (b ^^^ c))) - 1 * ~~~( ~~~a &&& (b &&& c)) - 1 * (a ||| b) - 2 * (c ||| (a &&& ~~~b)) - 7 * ( ~~~b ||| (a ^^^ c)) + 4 * (a ^^^ (b &&& c)) - 2 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 5 * (b ^^^ (a &&& (b ||| c))) - 6 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) - 2 * (c &&& (a ||| ~~~b)) + 1 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) + 10 * ~~~(a ||| (b ||| c)) + 7 * ~~~(a ||| ( ~~~b ||| c)) - 1 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 12 * ( ~~~a &&& ( ~~~b &&& c)) + 12 * ( ~~~a &&& (b &&& c)) + 14 * (a &&& ( ~~~b &&& c)) = - 14 * (a &&& (b &&& c)) - 1 * ~~~( ~~~a ||| (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1586 (x y : BitVec w) : +theorem e_1586 : 1 * (b ^^^ ~~~(a &&& (b &&& c))) - 1 * ~~~(a &&& b) - 3 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) - 1 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) + 1 * (c ^^^ (a ||| (b &&& c))) + 4 * (b &&& ~~~(a ^^^ c)) - 5 * ~~~( ~~~a &&& (b ^^^ c)) + 2 * (a &&& ~~~b) + 1 * ~~~(a &&& ~~~b) - 11 * ~~~(a ||| (b &&& c)) + 2 * ~~~a + 6 * ~~~(a ||| (b ||| c)) + 5 * ~~~(a ||| ( ~~~b ||| c)) + 6 * ~~~( ~~~a ||| (b ||| c)) + 7 * ( ~~~a &&& (b &&& c)) + 4 * (a &&& ( ~~~b &&& c)) - 12 * (a &&& (b &&& c)) = - 11 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) - 6 * ~~~( ~~~a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1587 (x y : BitVec w) : +theorem e_1587 : - 5 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) - 3 * ( ~~~c ||| (a ^^^ b)) + 3 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) - 2 * (b ^^^ ( ~~~a &&& (b ^^^ c))) + 11 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) + 11 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 1 * ( ~~~a ||| ( ~~~b ||| c)) + 1 * (b &&& ~~~(a ^^^ c)) - 2 * (a ||| (b &&& c)) + 7 * (c ||| (a &&& b)) - 8 * ~~~(a ||| ( ~~~b ||| c)) - 5 * ~~~( ~~~a ||| (b ||| c)) - 9 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 15 * ( ~~~a &&& ( ~~~b &&& c)) - 13 * ( ~~~a &&& (b &&& c)) - 26 * (a &&& ( ~~~b &&& c)) + 2 * (a &&& (b &&& c)) = 5 * ( ~~~c &&& ~~~(a ^^^ b)) - 3 * ~~~(a ||| (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1588 (x y : BitVec w) : +theorem e_1588 : 7 * (c ^^^ ~~~(a &&& b)) - 2 * (b ^^^ ~~~(a &&& ~~~c)) - 1 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 2 * (b ^^^ (a &&& ( ~~~b ||| c))) - 2 * ~~~( ~~~a &&& ( ~~~b &&& c)) - 1 * (b ^^^ (a ||| (b &&& c))) + 2 * (c ^^^ (a &&& b)) + 1 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 2 * ((a ^^^ b) ||| (a ^^^ c)) + 5 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) - 3 * (c ^^^ (a ||| (b &&& c))) - 2 * ~~~(a ||| (b ||| c)) - 15 * ~~~( ~~~a ||| (b ||| c)) - 4 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 10 * ( ~~~a &&& (b &&& c)) - 5 * (a &&& ( ~~~b &&& c)) - 5 * (a &&& (b &&& c)) = 19 * ~~~(a ||| ( ~~~b ||| c)) - 5 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1589 (x y : BitVec w) : +theorem e_1589 : 2 * ( ~~~b &&& (a ^^^ c)) + 5 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 3 * (a ^^^ ( ~~~b &&& c)) - 7 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) - 1 * (b ^^^ ~~~(a &&& (b ||| c))) + 1 * ~~~(a ||| ~~~c) - 1 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) + 1 * ( ~~~(a ||| b) ||| (b ^^^ c)) + 1 * (c ||| ~~~(a ^^^ b)) - 1 * ~~~(a &&& (b ||| c)) - 4 * ~~~(a ||| (b ||| c)) + 8 * ~~~(a ||| ( ~~~b ||| c)) + 6 * ~~~( ~~~a ||| (b ||| c)) + 1 * ( ~~~a &&& ( ~~~b &&& c)) - 6 * ( ~~~a &&& (b &&& c)) - 7 * (a &&& ( ~~~b &&& c)) + 11 * (a &&& (b &&& c)) = 2 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 1 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1590 (x y : BitVec w) : +theorem e_1590 : - 1 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) + 1 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) + 5 * ((a &&& b) ||| ~~~(b ||| c)) - 5 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 6 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) - 11 * (a ||| (b &&& c)) - 2 * ( ~~~a &&& (b ||| c)) + 2 * ~~~(b &&& ~~~c) + 5 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 1 * ~~~(a ||| c) + 1 * ( ~~~c &&& ~~~(a ^^^ b)) - 6 * ~~~(a ||| (b ||| c)) + 5 * ~~~(a ||| ( ~~~b ||| c)) + 9 * ~~~( ~~~a ||| (b ||| c)) + 3 * ( ~~~a &&& ( ~~~b &&& c)) + 7 * ( ~~~a &&& (b &&& c)) + 8 * (a &&& ( ~~~b &&& c)) + 11 * (a &&& (b &&& c)) = - 10 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 2 * ( ~~~(a ||| b) ||| (b ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1591 (x y : BitVec w) : +theorem e_1591 : 1 * ((a ^^^ b) &&& ~~~(a ^^^ c)) - 7 * ~~~(a ||| c) - 6 * (c ^^^ ( ~~~a ||| (b ||| c))) - 3 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) - 11 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) - 1 * (b ||| (a &&& ~~~c)) - 1 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 6 * ( ~~~a ||| ( ~~~b ||| c)) - 5 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 4 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 30 * ~~~(a ||| (b ||| c)) + 23 * ~~~(a ||| ( ~~~b ||| c)) + 22 * ~~~( ~~~a ||| (b ||| c)) + 11 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 18 * ( ~~~a &&& ( ~~~b &&& c)) + 18 * ( ~~~a &&& (b &&& c)) + 13 * (a &&& ( ~~~b &&& c)) + 13 * (a &&& (b &&& c)) = 5 * (b &&& ~~~(a &&& ~~~c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1592 (x y : BitVec w) : +theorem e_1592 : - 1 * ( ~~~b &&& ~~~(a ^^^ c)) + 11 * (b ^^^ (a ||| (b &&& c))) - 6 * (b ^^^ ~~~(a ||| ~~~c)) + 1 * (c ||| ~~~(a ^^^ b)) + 11 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) - 11 * (b ^^^ ( ~~~a ||| (b ||| c))) - 6 * (c ||| ~~~(a ||| b)) + 5 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) - 6 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) + 1 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) + 2 * (c ^^^ (a &&& (b ||| c))) + 11 * (b ^^^ ~~~(a &&& (b &&& c))) - 11 * (a &&& b) - 16 * ~~~(a ||| ( ~~~b ||| c)) - 27 * ~~~( ~~~a ||| (b ||| c)) + 15 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 3 * ( ~~~a &&& ( ~~~b &&& c)) - 1 * (a &&& (b &&& c)) = 8 * ( ~~~a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1593 (x y : BitVec w) : +theorem e_1593 : - 1 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 1 * ~~~(a ||| c) - 3 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) + 11 * (c ^^^ ~~~(a ||| b)) + 1 * (c ^^^ (a &&& b)) + 3 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) - 2 * ~~~(a &&& ~~~a) - 1 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) - 1 * (b ||| ~~~c) - 1 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) - 7 * ((a ^^^ b) ||| (a ^^^ c)) + 2 * (b &&& ~~~(a &&& c)) - 11 * ~~~(a ||| (b ||| c)) + 12 * ~~~(a ||| ( ~~~b ||| c)) + 9 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 6 * ( ~~~a &&& ( ~~~b &&& c)) - 3 * ( ~~~a &&& (b &&& c)) - 3 * (a &&& ( ~~~b &&& c)) = - 15 * ~~~( ~~~a ||| (b ||| c)) + 7 * (a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1594 (x y : BitVec w) : +theorem e_1594 : - 6 * (b ^^^ (a &&& (b ^^^ c))) - 1 * ~~~(a ^^^ (b &&& c)) - 6 * ( ~~~b &&& ~~~(a ^^^ c)) + 11 * (c &&& ~~~(a ^^^ b)) + 1 * ~~~(a &&& b) + 11 * (b ^^^ (a &&& c)) - 5 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 2 * (a &&& ( ~~~b ||| c)) + 4 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) - 11 * ~~~( ~~~a &&& ( ~~~b ||| c)) - 1 * ~~~(a ^^^ ( ~~~b ||| c)) + 1 * ~~~(a ||| (b ||| c)) + 7 * ~~~(a ||| ( ~~~b ||| c)) + 17 * ~~~( ~~~a ||| (b ||| c)) - 15 * ( ~~~a &&& ( ~~~b &&& c)) - 2 * ( ~~~a &&& (b &&& c)) + 15 * (a &&& ( ~~~b &&& c)) + 15 * (a &&& (b &&& c)) = - 1 * ((a &&& b) ^^^ (b ||| ~~~c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1595 (x y : BitVec w) : +theorem e_1595 : - 1 * ~~~(a &&& ( ~~~b &&& c)) - 11 * (a &&& (b ||| c)) - 6 * ~~~( ~~~a &&& ( ~~~b &&& c)) - 1 * ~~~(a ^^^ (b ^^^ c)) + 5 * b + 1 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 3 * ~~~(a &&& b) + 3 * (c ^^^ (a ||| b)) + 1 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) + 2 * (a ||| (b ||| c)) + 2 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) - 7 * (b &&& (a ||| c)) + 8 * ~~~(a ||| (b ||| c)) + 2 * ~~~( ~~~a ||| (b ||| c)) - 3 * ( ~~~a &&& ( ~~~b &&& c)) + 7 * ( ~~~a &&& (b &&& c)) + 18 * (a &&& ( ~~~b &&& c)) + 15 * (a &&& (b &&& c)) = - 13 * ~~~( ~~~a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1596 (x y : BitVec w) : +theorem e_1596 : - 11 * ~~~(a &&& ( ~~~b &&& c)) + 5 * ((a &&& c) ||| (b &&& ~~~c)) + 11 * ( ~~~c &&& (a ^^^ b)) - 5 * (a ||| (b ^^^ c)) - 2 * (b ||| (a &&& c)) + 1 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) - 1 * ~~~(b &&& ~~~c) - 6 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 11 * ~~~( ~~~a ||| (b &&& c)) + 3 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) + 12 * ~~~(a ||| (b ||| c)) + 2 * ~~~(a ||| ( ~~~b ||| c)) + 15 * ~~~( ~~~a ||| (b ||| c)) + 20 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 16 * ( ~~~a &&& ( ~~~b &&& c)) + 11 * ( ~~~a &&& (b &&& c)) + 19 * (a &&& ( ~~~b &&& c)) + 17 * (a &&& (b &&& c)) = - 5 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1597 (x y : BitVec w) : +theorem e_1597 : 4 * ~~~(a ||| ~~~c) + 1 * (b ^^^ ~~~(a &&& (b &&& c))) - 1 * ((a &&& ~~~b) ||| (b ^^^ c)) + 11 * (a ^^^ b) - 2 * (c ^^^ ~~~(a ||| (b &&& c))) + 2 * (b ^^^ ( ~~~a ||| (b &&& c))) + 4 * (a ||| c) + 4 * (b ^^^ (a &&& c)) - 11 * ~~~( ~~~a &&& (b &&& c)) - 6 * (b ^^^ (a ||| ~~~c)) + 3 * (c ^^^ (a &&& ~~~b)) + 15 * ~~~(a ||| (b ||| c)) - 1 * ~~~(a ||| ( ~~~b ||| c)) - 2 * ~~~( ~~~a ||| (b ||| c)) + 1 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 2 * ( ~~~a &&& ( ~~~b &&& c)) - 19 * ( ~~~a &&& (b &&& c)) + 4 * (a &&& (b &&& c)) = - 1 * ((a &&& b) ||| ~~~(b ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1598 (x y : BitVec w) : +theorem e_1598 : 1 * ( ~~~b &&& (a ^^^ c)) - 11 * ((a ||| b) &&& (b ^^^ c)) - 3 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) + 7 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 3 * (c ^^^ ~~~(a &&& (b &&& c))) + 4 * ( ~~~b ||| ~~~(a ^^^ c)) + 11 * (b ^^^ ~~~(a &&& (b &&& c))) + 1 * (a &&& ( ~~~b ||| c)) - 11 * ((a &&& b) ||| ~~~(b ||| c)) + 2 * (b ^^^ c) + 1 * (c ^^^ ( ~~~a ||| (b ||| c))) - 10 * ~~~(a ||| (b ||| c)) - 3 * ~~~( ~~~a ||| (b ||| c)) + 18 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 15 * ( ~~~a &&& ( ~~~b &&& c)) - 5 * ( ~~~a &&& (b &&& c)) - 4 * (a &&& ( ~~~b &&& c)) - 2 * (a &&& (b &&& c)) = - 1 * ~~~(a ||| (b ^^^ c)) - 10 * ~~~(a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1599 (x y : BitVec w) : +theorem e_1599 : - 2 * ~~~(b ||| c) - 1 * (b ||| (a &&& c)) - 1 * ( ~~~c ||| (a ^^^ b)) - 7 * (c ||| (a &&& b)) - 11 * ~~~(a ||| ~~~c) + 5 * (b ^^^ ~~~(a &&& (b ||| c))) + 2 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 7 * ~~~(b ||| ~~~c) - 1 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) - 11 * (c ^^^ (a &&& b)) + 1 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) + 1 * (b ^^^ (a ||| ( ~~~b ||| c))) - 3 * ~~~(a ||| (b ||| c)) + 1 * ~~~(a ||| ( ~~~b ||| c)) - 6 * ~~~( ~~~a ||| (b ||| c)) + 15 * ( ~~~a &&& ( ~~~b &&& c)) + 32 * ( ~~~a &&& (b &&& c)) + 10 * (a &&& ( ~~~b &&& c)) = - 3 * (a &&& (b &&& c)) - 13 * ~~~( ~~~a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1600 (x y : BitVec w) : +theorem e_1600 : 7 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) + 4 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) - 1 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) - 1 * ( ~~~(a &&& b) &&& (b ^^^ c)) + 7 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 1 * ( ~~~a &&& (b ^^^ c)) - 3 * (a ||| (b &&& c)) + 1 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) - 3 * (b ||| (a ^^^ c)) - 5 * ~~~( ~~~a &&& (b &&& c)) + 7 * ~~~(a &&& ~~~c) + 4 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) - 17 * ~~~(a ||| (b ||| c)) - 3 * ~~~(a ||| ( ~~~b ||| c)) + 3 * ~~~( ~~~a ||| (b ||| c)) - 11 * ( ~~~a &&& (b &&& c)) - 12 * (a &&& ( ~~~b &&& c)) - 11 * (a &&& (b &&& c)) = 15 * ( ~~~a &&& ( ~~~b &&& c)) - 7 * (c ^^^ (a &&& b)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1601 (x y : BitVec w) : +theorem e_1601 : 4 * (b ^^^ ( ~~~a ||| (b ^^^ c))) + 7 * (b ||| ~~~c) - 3 * ~~~b + 5 * ( ~~~b &&& (a ^^^ c)) + 1 * (c ^^^ ~~~(a &&& b)) + 2 * (b ||| (a ^^^ c)) + 4 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) + 1 * ~~~( ~~~a &&& (b ^^^ c)) + 1 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 11 * (c ^^^ (a &&& ( ~~~b ||| c))) - 8 * ~~~(a ||| (b ||| c)) - 14 * ~~~(a ||| ( ~~~b ||| c)) - 19 * ~~~( ~~~a ||| (b ||| c)) - 15 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 24 * ( ~~~a &&& ( ~~~b &&& c)) - 22 * ( ~~~a &&& (b &&& c)) + 3 * (a &&& ( ~~~b &&& c)) - 15 * (a &&& (b &&& c)) = 6 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1602 (x y : BitVec w) : +theorem e_1602 : 5 * ~~~( ~~~a &&& ( ~~~b &&& c)) + 1 * ~~~(a &&& ~~~a) - 6 * ~~~( ~~~a ||| ( ~~~b &&& c)) + 2 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) - 2 * ((a ||| b) &&& (b ^^^ c)) - 1 * ( ~~~b ||| ~~~(a ^^^ c)) + 4 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) - 2 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) - 2 * (c ||| ~~~(a ||| ~~~b)) - 1 * (b ^^^ ~~~(a ||| (b &&& c))) + 11 * (c ^^^ ~~~(a ||| b)) - 7 * (a ||| (b &&& c)) - 13 * ~~~(a ||| (b ||| c)) - 18 * ~~~(a ||| ( ~~~b ||| c)) - 9 * ~~~( ~~~a ||| (b ||| c)) + 6 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 8 * ( ~~~a &&& ( ~~~b &&& c)) - 18 * ( ~~~a &&& (b &&& c)) - 9 * (a &&& (b &&& c)) = 7 * (a &&& ( ~~~b &&& c)) - 11 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1603 (x y : BitVec w) : +theorem e_1603 : 3 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 1 * (a ^^^ (b ^^^ c)) + 1 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) + 3 * (b &&& ~~~(a &&& c)) + 11 * ~~~(a ||| ( ~~~b &&& c)) - 3 * ~~~(b &&& ~~~c) - 11 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 6 * ~~~(b ||| ~~~c) + 3 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) + 5 * (b &&& ~~~c) + 7 * (c ||| (a &&& ~~~b)) + 4 * ((a ||| ~~~b) &&& (b ^^^ c)) + 11 * (c ^^^ ( ~~~a ||| (b &&& c))) - 12 * ~~~(a ||| (b ||| c)) - 19 * ~~~(a ||| ( ~~~b ||| c)) - 12 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 4 * ( ~~~a &&& ( ~~~b &&& c)) - 25 * ( ~~~a &&& (b &&& c)) - 16 * (a &&& ( ~~~b &&& c)) = - 5 * ~~~( ~~~a ||| (b ||| c)) + 7 * (a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1604 (x y : BitVec w) : +theorem e_1604 : - 5 * ((a &&& b) ||| ~~~(b ||| c)) + 2 * (b ^^^ ( ~~~a &&& (b ||| c))) + 1 * (a ^^^ (b ||| c)) - 2 * (b &&& ~~~(a ^^^ c)) - 1 * (c ^^^ ( ~~~a ||| (b &&& c))) - 1 * ( ~~~b &&& ~~~(a ^^^ c)) + 2 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) + 1 * ~~~(a &&& ( ~~~b &&& c)) - 6 * ~~~( ~~~a &&& (b ||| c)) + 2 * ~~~(a ^^^ (b &&& c)) + 5 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 3 * ~~~(a ||| (b ||| c)) - 10 * ~~~(a ||| ( ~~~b ||| c)) - 3 * ~~~( ~~~a ||| (b ||| c)) + 3 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 13 * ( ~~~a &&& ( ~~~b &&& c)) - 9 * ( ~~~a &&& (b &&& c)) + 1 * (a &&& ( ~~~b &&& c)) + 6 * (a &&& (b &&& c)) = - 7 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1605 (x y : BitVec w) : +theorem e_1605 : 5 * ((a ||| ~~~b) &&& (b ^^^ c)) + 2 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) + 1 * (b ^^^ (a &&& (b ^^^ c))) - 1 * (a ^^^ ( ~~~b ||| c)) - 7 * ~~~(b ||| c) - 7 * ~~~(a ^^^ (b ^^^ c)) - 7 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 2 * ( ~~~a &&& (b ^^^ c)) - 5 * ( ~~~(a &&& b) &&& (b ^^^ c)) - 5 * ( ~~~c &&& ~~~(a ^^^ b)) + 2 * ((a &&& c) ||| ~~~(b ||| c)) + 24 * ~~~(a ||| (b ||| c)) - 1 * ~~~(a ||| ( ~~~b ||| c)) + 2 * ~~~( ~~~a ||| (b ||| c)) + 12 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 1 * ( ~~~a &&& ( ~~~b &&& c)) + 7 * ( ~~~a &&& (b &&& c)) + 9 * (a &&& ( ~~~b &&& c)) - 4 * (a &&& (b &&& c)) = - 1 * (c ^^^ ~~~(a &&& (b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1606 (x y : BitVec w) : +theorem e_1606 : 11 * ~~~(a ^^^ c) + 7 * (b ^^^ ~~~(a &&& (b ||| c))) - 1 * (b ^^^ (a &&& (b ||| c))) - 11 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) - 11 * ( ~~~b &&& ~~~(a ^^^ c)) - 6 * ((a ^^^ b) &&& ~~~(a ^^^ c)) + 1 * ( ~~~b &&& (a ^^^ c)) + 7 * (b &&& (a ||| c)) - 1 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) - 7 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) + 1 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) + 3 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) + 1 * (b ^^^ ~~~(a &&& ~~~c)) - 8 * ~~~(a ||| (b ||| c)) - 8 * ~~~(a ||| ( ~~~b ||| c)) - 2 * ( ~~~a &&& ( ~~~b &&& c)) + 2 * ( ~~~a &&& (b &&& c)) + 23 * (a &&& ( ~~~b &&& c)) - 26 * (a &&& (b &&& c)) = - 4 * ~~~( ~~~a ||| (b ||| c)) - 1 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1607 (x y : BitVec w) : +theorem e_1607 : 1 * ( ~~~c ||| ~~~(a ^^^ b)) + 5 * (b ^^^ ~~~(a ||| ~~~c)) - 3 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) + 11 * (b ^^^ ~~~(a &&& ~~~c)) + 7 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) - 2 * (b ^^^ c) - 2 * (b ||| (a &&& ~~~c)) + 2 * (c ^^^ ~~~(a ||| ~~~b)) + 4 * (c ||| (a &&& ~~~b)) + 4 * ~~~(a ^^^ ( ~~~b ||| c)) - 1 * ((a &&& b) ^^^ (b ||| c)) - 3 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) - 16 * ~~~(a ||| (b ||| c)) - 8 * ~~~(a ||| ( ~~~b ||| c)) - 1 * ~~~( ~~~a ||| (b ||| c)) - 14 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 20 * ( ~~~a &&& ( ~~~b &&& c)) + 2 * ( ~~~a &&& (b &&& c)) - 21 * (a &&& (b &&& c)) = 22 * (a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1608 (x y : BitVec w) : +theorem e_1608 : - 1 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 5 * ~~~(a &&& (b &&& c)) - 2 * c - 7 * ~~~(a &&& c) - 1 * ~~~(b ||| c) + 11 * ~~~(a ||| ( ~~~b &&& c)) - 7 * ~~~(a &&& (b ^^^ c)) - 6 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 2 * (b ||| (a &&& ~~~c)) - 1 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 2 * (b ^^^ ( ~~~a &&& (b ^^^ c))) + 2 * (c ^^^ (a &&& (b ||| c))) + 1 * ~~~(a ||| ( ~~~b ||| c)) + 19 * ~~~( ~~~a ||| (b ||| c)) + 12 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 17 * ( ~~~a &&& ( ~~~b &&& c)) + 9 * ( ~~~a &&& (b &&& c)) + 4 * (a &&& ( ~~~b &&& c)) + 12 * (a &&& (b &&& c)) = - 2 * (c &&& ~~~(a ^^^ b)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1609 (x y : BitVec w) : +theorem e_1609 : - 5 * ( ~~~c ||| (a ^^^ b)) + 1 * ~~~(a ||| ( ~~~b &&& c)) - 7 * (c ^^^ (a ||| (b ||| c))) - 6 * ((b &&& c) ||| (a &&& (b ||| c))) + 4 * ( ~~~b ||| ~~~(a ^^^ c)) - 6 * (b ^^^ ( ~~~a &&& (b ||| c))) - 1 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) - 3 * (c &&& ~~~(a ^^^ b)) - 2 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) - 11 * (c ^^^ ( ~~~a ||| (b ||| c))) - 2 * (b ^^^ (a ||| c)) + 5 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 12 * ~~~(a ||| (b ||| c)) + 21 * ~~~(a ||| ( ~~~b ||| c)) + 6 * ~~~( ~~~a ||| (b ||| c)) + 31 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 2 * ( ~~~a &&& ( ~~~b &&& c)) + 10 * ( ~~~a &&& (b &&& c)) + 11 * (a &&& (b &&& c)) = - 3 * (a &&& ( ~~~b &&& c)) - 2 * (c ||| ~~~(a ||| b)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1610 (x y : BitVec w) : +theorem e_1610 : 1 * (a &&& ~~~c) - 2 * (b &&& ~~~(a &&& c)) - 5 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) - 6 * (c ^^^ ~~~(a &&& (b ||| c))) - 6 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 4 * (c ||| (a &&& b)) + 11 * ( ~~~a ||| ( ~~~b ||| c)) - 1 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) + 11 * ~~~(a ||| ~~~c) - 2 * ( ~~~(a ||| b) ||| (b ^^^ c)) - 2 * (a ^^^ (b &&& c)) - 2 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 6 * ~~~(a ||| (b ||| c)) + 12 * ~~~(a ||| ( ~~~b ||| c)) + 7 * ~~~( ~~~a ||| (b ||| c)) + 13 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 14 * ( ~~~a &&& ( ~~~b &&& c)) - 5 * (a &&& ( ~~~b &&& c)) - 2 * (a &&& (b &&& c)) = 21 * ( ~~~a &&& (b &&& c)) - 1 * (c &&& (a ||| ~~~b)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1611 (x y : BitVec w) : +theorem e_1611 : - 5 * ((a &&& b) ||| ~~~(b ^^^ c)) - 6 * (c ^^^ (a ||| b)) + 7 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) + 4 * ~~~c + 1 * (b ^^^ (a &&& ( ~~~b ||| c))) + 2 * (b ^^^ ~~~(a ||| ~~~c)) - 1 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 1 * (b ^^^ (a ||| c)) - 7 * ((a &&& ~~~b) ||| (b ^^^ c)) - 5 * (b &&& (a ^^^ c)) + 11 * (a ^^^ (b &&& c)) - 11 * (c ^^^ (a ||| ~~~b)) + 7 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) + 4 * ((a &&& b) ||| ~~~(b ||| ~~~c)) + 12 * ~~~(a ||| (b ||| c)) - 3 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 8 * ( ~~~a &&& ( ~~~b &&& c)) + 1 * ( ~~~a &&& (b &&& c)) - 7 * (a &&& ( ~~~b &&& c)) - 15 * (a &&& (b &&& c)) = - 1 * (b ^^^ ~~~(a ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1612 (x y : BitVec w) : +theorem e_1612 : - 11 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) - 11 * (c ^^^ ~~~(a &&& (b &&& c))) + 2 * (b ^^^ ~~~(a ||| (b ^^^ c))) + 5 * ~~~(a ^^^ (b ^^^ c)) + 4 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) - 2 * (b ||| ~~~c) + 5 * (a ^^^ (b ||| c)) - 1 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) - 1 * ~~~(a &&& c) + 11 * (a &&& b) + 11 * ((a &&& ~~~b) ||| (b ^^^ c)) + 4 * b + 7 * ( ~~~a &&& ( ~~~b ||| c)) + 6 * ~~~(a ||| (b ||| c)) + 8 * ~~~( ~~~a ||| (b ||| c)) - 19 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 15 * ( ~~~a &&& ( ~~~b &&& c)) - 7 * ( ~~~a &&& (b &&& c)) - 19 * (a &&& ( ~~~b &&& c)) - 9 * (a &&& (b &&& c)) = 12 * ~~~(a ||| ( ~~~b ||| c)) - 1 * ((a &&& b) ||| ~~~(b ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1613 (x y : BitVec w) : +theorem e_1613 : - 1 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 2 * ( ~~~a ||| (b &&& c)) + 1 * (b ^^^ ~~~(a &&& (b &&& c))) - 1 * (a ||| ( ~~~b &&& c)) - 1 * ~~~( ~~~a ||| (b ^^^ c)) + 1 * ~~~(b ||| c) - 2 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) + 7 * (c ||| (a &&& b)) + 11 * (a ||| c) + 1 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) + 4 * (a ^^^ (b &&& c)) - 6 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) + 5 * (c ^^^ (a ||| ( ~~~b &&& c))) - 1 * ~~~(a ||| (b ||| c)) + 10 * ~~~(a ||| ( ~~~b ||| c)) - 14 * ~~~( ~~~a ||| (b ||| c)) - 20 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 8 * ( ~~~a &&& ( ~~~b &&& c)) - 25 * ( ~~~a &&& (b &&& c)) - 8 * (a &&& (b &&& c)) = 21 * (a &&& ( ~~~b &&& c)) - 2 * ((a &&& c) ||| ~~~(b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1614 (x y : BitVec w) : +theorem e_1614 : 11 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) + 2 * (b ^^^ (a &&& (b ||| c))) - 11 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) - 6 * (b ^^^ ( ~~~a &&& (b ||| c))) - 7 * ~~~(a &&& ( ~~~b &&& c)) + 2 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) - 2 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) + 2 * (c &&& ~~~(a ^^^ b)) + 1 * ~~~(a ^^^ (b &&& c)) + 3 * ( ~~~(a ||| b) ||| (b ^^^ c)) + 11 * ~~~( ~~~a &&& ( ~~~b ||| c)) + 5 * ((a &&& b) ^^^ (b ||| ~~~c)) + 4 * (c ||| ~~~(a ||| b)) + 5 * ~~~(a ||| (b ||| c)) - 13 * ~~~(a ||| ( ~~~b ||| c)) - 22 * ~~~( ~~~a ||| (b ||| c)) - 3 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 3 * ( ~~~a &&& ( ~~~b &&& c)) - 2 * ( ~~~a &&& (b &&& c)) - 3 * (a &&& (b &&& c)) = 11 * (a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1615 (x y : BitVec w) : +theorem e_1615 : - 5 * (b ^^^ ( ~~~a ||| (b ||| c))) - 11 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) + 2 * ~~~(a ^^^ ( ~~~b ||| c)) + 1 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 1 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 1 * (b ||| ~~~(a ||| c)) + 1 * (a ||| ( ~~~b ||| c)) - 2 * (c ^^^ ~~~(a &&& (b ||| c))) - 11 * ( ~~~a ||| (b ||| c)) + 4 * ~~~(a &&& (b ^^^ c)) - 7 * ((a &&& c) ||| ~~~(b ||| c)) - 1 * (b ^^^ c) + 30 * ~~~(a ||| (b ||| c)) + 18 * ~~~(a ||| ( ~~~b ||| c)) + 12 * ~~~( ~~~a ||| (b ||| c)) + 10 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 21 * ( ~~~a &&& ( ~~~b &&& c)) + 5 * ( ~~~a &&& (b &&& c)) + 33 * (a &&& ( ~~~b &&& c)) + 35 * (a &&& (b &&& c)) = - 1 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) + 11 * (c ^^^ ~~~(a ||| ~~~b)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1616 (x y : BitVec w) : +theorem e_1616 : 1 * ( ~~~c &&& (a ^^^ b)) + 7 * ((a ||| ~~~b) &&& (b ^^^ c)) + 1 * (b ||| (a &&& ~~~c)) - 5 * (a ||| ~~~c) + 5 * (b ^^^ c) + 1 * (b &&& c) + 1 * ((a ||| b) &&& (b ^^^ c)) + 7 * (a &&& (b ||| c)) + 4 * (a &&& ~~~c) - 5 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) + 1 * (b &&& ~~~(a ^^^ c)) - 3 * ~~~(a ^^^ ( ~~~b ||| c)) + 10 * ~~~(a ||| (b ||| c)) - 1 * ~~~(a ||| ( ~~~b ||| c)) + 8 * ~~~( ~~~a ||| (b ||| c)) - 20 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 12 * ( ~~~a &&& ( ~~~b &&& c)) - 1 * ( ~~~a &&& (b &&& c)) - 11 * (a &&& ( ~~~b &&& c)) + 4 * (a &&& (b &&& c)) = 1 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1617 (x y : BitVec w) : +theorem e_1617 : 7 * ( ~~~b &&& (a ^^^ c)) - 1 * ( ~~~b ||| (a ^^^ c)) - 2 * (c ^^^ ~~~(a ||| ~~~b)) - 11 * (c &&& ~~~(a &&& b)) - 7 * (a ^^^ ( ~~~b &&& c)) + 1 * (b ||| (a ^^^ c)) + 1 * (b ^^^ ~~~(a ||| (b &&& c))) + 3 * (b ^^^ ( ~~~a ||| (b ^^^ c))) + 2 * (a &&& ~~~b) + 3 * ( ~~~a &&& (b ^^^ c)) - 1 * ( ~~~(a &&& b) &&& (b ^^^ c)) - 3 * ~~~( ~~~a &&& ( ~~~b ||| c)) - 7 * (b ^^^ c) - 3 * ~~~(a ||| (b ||| c)) + 1 * ~~~( ~~~a ||| (b ||| c)) + 16 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 14 * ( ~~~a &&& ( ~~~b &&& c)) + 10 * ( ~~~a &&& (b &&& c)) + 20 * (a &&& ( ~~~b &&& c)) + 7 * (a &&& (b &&& c)) = - 9 * ~~~(a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1618 (x y : BitVec w) : +theorem e_1618 : - 5 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) - 2 * (c ^^^ ~~~(a &&& (b ||| c))) + 5 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) - 2 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) - 3 * (a ||| ~~~c) - 6 * (c &&& (a ||| b)) - 6 * (b &&& c) - 7 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 2 * (b ||| ~~~(a ||| c)) - 1 * (c ^^^ (a ||| ( ~~~b ||| c))) + 2 * (a &&& b) + 4 * ( ~~~b ||| (a ^^^ c)) + 4 * (b ^^^ (a &&& ~~~c)) - 1 * ~~~( ~~~a &&& ( ~~~b &&& c)) + 3 * ~~~(a ||| (b ||| c)) + 7 * ~~~(a ||| ( ~~~b ||| c)) - 1 * ~~~( ~~~a ||| (b ||| c)) - 3 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 7 * ( ~~~a &&& (b &&& c)) + 22 * (a &&& (b &&& c)) = - 3 * (a &&& ( ~~~b &&& c)) - 7 * (c ^^^ (a ||| ~~~b)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1619 (x y : BitVec w) : +theorem e_1619 : - 11 * (c &&& (a ||| ~~~b)) - 7 * ~~~(a &&& ~~~b) + 2 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 11 * (b ^^^ ( ~~~a ||| (b ^^^ c))) + 11 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) - 2 * (a ||| b) - 1 * (c &&& ~~~(a &&& b)) + 1 * ~~~b - 11 * ~~~(a &&& c) - 7 * ~~~(a ^^^ (b &&& c)) + 1 * ((a &&& b) ||| (b ^^^ c)) - 3 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 4 * ~~~(a ||| (b ||| c)) + 30 * ~~~(a ||| ( ~~~b ||| c)) + 13 * ~~~( ~~~a ||| (b ||| c)) + 17 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 12 * ( ~~~a &&& ( ~~~b &&& c)) + 18 * ( ~~~a &&& (b &&& c)) + 1 * (a &&& ( ~~~b &&& c)) + 7 * (a &&& (b &&& c)) = - 1 * (c ||| (a &&& b)) + 1 * (a ||| ~~~c) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1620 (x y : BitVec w) : +theorem e_1620 : - 11 * (b ^^^ ( ~~~a ||| (b ^^^ c))) - 7 * (c &&& (a ||| ~~~b)) + 11 * ~~~( ~~~a ||| (b &&& c)) - 1 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) - 5 * ( ~~~c ||| ~~~(a ^^^ b)) - 1 * (c ^^^ ~~~(a &&& (b ||| c))) + 1 * ( ~~~(a &&& b) &&& (b ^^^ c)) + 1 * (a &&& (b ^^^ c)) - 2 * ~~~( ~~~a ||| ( ~~~b &&& c)) - 2 * (b ^^^ ( ~~~a ||| (b ||| c))) - 2 * ( ~~~a ||| ( ~~~b ||| c)) - 1 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 4 * (a ^^^ ( ~~~b &&& c)) + 11 * ~~~(b ||| ~~~c) + 23 * ~~~(a ||| (b ||| c)) + 9 * ~~~(a ||| ( ~~~b ||| c)) - 9 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 12 * ( ~~~a &&& ( ~~~b &&& c)) + 1 * ( ~~~a &&& (b &&& c)) + 24 * (a &&& (b &&& c)) = 4 * ~~~( ~~~a ||| (b ||| c)) - 1 * (b &&& (a ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1621 (x y : BitVec w) : +theorem e_1621 : 11 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) + 11 * (a ^^^ (b &&& c)) - 5 * (a ||| ( ~~~b ||| c)) - 3 * (c ^^^ ~~~(a ||| b)) + 1 * ( ~~~a &&& (b ^^^ c)) - 11 * ( ~~~a &&& (b ||| c)) - 1 * ((a ^^^ b) ||| ~~~(a ^^^ c)) + 7 * ~~~(a ^^^ b) - 5 * (b ^^^ (a &&& ~~~c)) - 5 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) + 1 * (b &&& ~~~(a ^^^ c)) - 3 * (c ^^^ (a ||| ( ~~~b ||| c))) + 5 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) + 2 * (c &&& ~~~(a &&& b)) + 4 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 1 * ~~~(a ||| (b ||| c)) - 16 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 6 * ( ~~~a &&& ( ~~~b &&& c)) + 12 * ( ~~~a &&& (b &&& c)) - 4 * (a &&& ( ~~~b &&& c)) - 9 * (a &&& (b &&& c)) = 13 * ~~~( ~~~a ||| (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1622 (x y : BitVec w) : +theorem e_1622 : 3 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) + 11 * ((a &&& b) ||| (b ^^^ c)) + 5 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) + 2 * ( ~~~a &&& ( ~~~b ||| c)) - 1 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) + 4 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 5 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 11 * (c &&& (a ||| b)) - 3 * ~~~(a ||| ( ~~~b &&& c)) + 2 * ~~~( ~~~a ||| ( ~~~b &&& c)) - 6 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 3 * ~~~(a &&& ( ~~~b &&& c)) + 4 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) - 2 * ((a &&& ~~~b) ||| (b ^^^ c)) + 2 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 11 * ~~~(a ||| (b ||| c)) - 16 * ~~~(a ||| ( ~~~b ||| c)) - 7 * ~~~( ~~~a ||| (b ||| c)) - 6 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 8 * ( ~~~a &&& (b &&& c)) - 3 * (a &&& (b &&& c)) = 22 * ( ~~~a &&& ( ~~~b &&& c)) - 5 * (a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1623 (x y : BitVec w) : +theorem e_1623 : 1 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 5 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 1 * (c &&& ~~~(a &&& b)) + 3 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) + 5 * ((a &&& c) ||| (b &&& ~~~c)) + 2 * ~~~( ~~~a &&& (b ||| c)) + 2 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) + 5 * (c ^^^ (a &&& b)) + 7 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) - 11 * (c &&& ~~~(a ^^^ b)) + 7 * ~~~(a ^^^ (b &&& c)) - 3 * (a ^^^ (b ||| c)) + 7 * (c ^^^ (a ||| ( ~~~b ||| c))) - 27 * ~~~(a ||| (b ||| c)) - 15 * ~~~(a ||| ( ~~~b ||| c)) - 15 * ~~~( ~~~a ||| (b ||| c)) - 27 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 6 * ( ~~~a &&& ( ~~~b &&& c)) - 10 * ( ~~~a &&& (b &&& c)) - 20 * (a &&& ( ~~~b &&& c)) - 13 * (a &&& (b &&& c)) = - 3 * ~~~(a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1624 (x y : BitVec w) : +theorem e_1624 : 2 * (b &&& c) - 1 * (b ^^^ ~~~(a &&& c)) - 6 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 3 * ~~~(b &&& c) + 1 * (c ^^^ ( ~~~a ||| (b &&& c))) + 1 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) + 11 * (b &&& ~~~c) - 7 * (c ^^^ ~~~(a &&& (b ||| c))) - 5 * (b ^^^ ~~~(a ||| (b ^^^ c))) + 5 * ( ~~~a &&& (b ^^^ c)) + 1 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) + 2 * (b ^^^ c) - 1 * (a ||| (b &&& c)) + 11 * ~~~(a ||| (b ||| c)) - 7 * ~~~(a ||| ( ~~~b ||| c)) + 11 * ~~~( ~~~a ||| (b ||| c)) - 8 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 7 * ( ~~~a &&& ( ~~~b &&& c)) - 3 * ( ~~~a &&& (b &&& c)) - 3 * (a &&& ( ~~~b &&& c)) + 11 * (a &&& (b &&& c)) = - 3 * ( ~~~(a ||| b) ||| (b ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1625 (x y : BitVec w) : +theorem e_1625 : - 11 * (b ^^^ ~~~(a ||| ~~~c)) - 2 * (c &&& (a ||| ~~~b)) + 11 * (b ^^^ ~~~(a &&& (b &&& c))) + 5 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) + 5 * ( ~~~c ||| ~~~(a ^^^ b)) - 1 * (a ||| (b ^^^ c)) - 3 * (c ^^^ ~~~(a ||| (b &&& c))) + 2 * ((a &&& b) ||| ~~~(b ||| c)) + 11 * (b ^^^ (a ||| ~~~c)) + 7 * ~~~(a ||| c) - 2 * ~~~(a ^^^ (b ||| c)) + 2 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) - 7 * ((a &&& b) ||| (b ^^^ c)) - 2 * (c ||| ~~~(a ||| b)) - 28 * ~~~(a ||| (b ||| c)) + 8 * ~~~(a ||| ( ~~~b ||| c)) - 33 * ~~~( ~~~a ||| (b ||| c)) + 8 * ( ~~~a &&& ( ~~~b &&& c)) - 8 * ( ~~~a &&& (b &&& c)) - 7 * (a &&& ( ~~~b &&& c)) + 5 * (a &&& (b &&& c)) = - 12 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 3 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1626 (x y : BitVec w) : +theorem e_1626 : - 1 * (c ^^^ ( ~~~a ||| (b ||| c))) + 5 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) + 4 * (a &&& ~~~b) - 1 * ((a ^^^ b) &&& ~~~(a ^^^ c)) - 7 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) - 2 * ((b &&& c) ||| (a &&& (b ||| c))) - 1 * ~~~( ~~~a &&& (b ||| c)) + 5 * (b ^^^ ( ~~~a ||| (b ||| c))) + 3 * ~~~(a ^^^ (b &&& c)) + 1 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) + 4 * ((a &&& b) ^^^ (b ||| c)) + 11 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 3 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 1 * (a &&& ( ~~~b ||| c)) - 9 * ~~~(a ||| (b ||| c)) - 4 * ~~~(a ||| ( ~~~b ||| c)) - 11 * ~~~( ~~~a ||| (b ||| c)) - 3 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 23 * ( ~~~a &&& ( ~~~b &&& c)) - 16 * ( ~~~a &&& (b &&& c)) - 6 * (a &&& ( ~~~b &&& c)) = 6 * ~~~(b ||| ~~~c) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1627 (x y : BitVec w) : +theorem e_1627 : 4 * (b ^^^ (a &&& c)) - 1 * (a ||| c) - 1 * (a ^^^ ( ~~~b &&& c)) + 11 * ~~~(a ||| ( ~~~b &&& c)) - 7 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) - 2 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) - 2 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) - 5 * ((a &&& b) ^^^ (b ||| ~~~c)) + 5 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) - 1 * (c ^^^ ~~~(a ||| ~~~b)) + 5 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) - 2 * ((a &&& c) ||| ~~~(b ||| c)) + 4 * (b &&& (a ^^^ c)) - 3 * ~~~(a ||| (b ||| c)) - 7 * ~~~(a ||| ( ~~~b ||| c)) + 11 * ~~~( ~~~a ||| (b ||| c)) - 6 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 13 * ( ~~~a &&& ( ~~~b &&& c)) - 12 * ( ~~~a &&& (b &&& c)) - 2 * (a &&& ( ~~~b &&& c)) + 7 * (a &&& (b &&& c)) = 1 * (b ^^^ (a ||| (b ||| c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1628 (x y : BitVec w) : +theorem e_1628 : - 11 * (b &&& ~~~c) + 1 * ~~~( ~~~a ||| ( ~~~b &&& c)) + 1 * (b ^^^ (a ||| (b ^^^ c))) - 2 * (c ^^^ ~~~(a &&& (b &&& c))) + 7 * (b ^^^ (a ||| (b ||| c))) + 3 * ~~~(b ||| ~~~c) - 5 * ((a &&& b) ||| (b ^^^ c)) - 11 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) + 5 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) - 5 * ~~~(b &&& ~~~c) - 2 * (b &&& (a ^^^ c)) + 1 * ((a &&& b) ^^^ (b ||| ~~~c)) - 7 * (b ^^^ ~~~(a ||| c)) + 26 * ~~~(a ||| (b ||| c)) + 17 * ~~~(a ||| ( ~~~b ||| c)) + 8 * ~~~( ~~~a ||| (b ||| c)) + 28 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 1 * ( ~~~a &&& ( ~~~b &&& c)) + 28 * ( ~~~a &&& (b &&& c)) + 1 * (a &&& ( ~~~b &&& c)) + 16 * (a &&& (b &&& c)) = 7 * ( ~~~c ||| (a ^^^ b)) - 2 * (b ^^^ (a &&& ~~~c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1629 (x y : BitVec w) : +theorem e_1629 : - 3 * (c &&& (a ^^^ b)) + 5 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) + 2 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) - 3 * ( ~~~a ||| ( ~~~b &&& c)) - 5 * (a ^^^ ( ~~~b &&& c)) + 2 * ((a &&& b) ^^^ (b ||| c)) - 1 * ( ~~~a ||| (b ||| c)) - 1 * ~~~(b ||| c) - 1 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 1 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) - 5 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 1 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) - 1 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 1 * (a ||| ( ~~~b ||| c)) - 6 * ~~~(a ||| ( ~~~b ||| c)) + 7 * ~~~( ~~~a ||| (b ||| c)) + 12 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 7 * ( ~~~a &&& ( ~~~b &&& c)) + 5 * ( ~~~a &&& (b &&& c)) + 13 * (a &&& ( ~~~b &&& c)) + 5 * (a &&& (b &&& c)) = - 9 * ~~~(a ||| (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1630 (x y : BitVec w) : +theorem e_1630 : - 2 * (c ^^^ ~~~(a ||| b)) - 3 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 11 * ~~~(a ||| b) - 3 * (b ^^^ ~~~(a &&& ~~~c)) - 2 * (a ^^^ (b ||| c)) - 1 * (c &&& (a ||| b)) - 2 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) + 7 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) + 3 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) - 5 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 1 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 11 * ((a ^^^ b) &&& ~~~(a ^^^ c)) + 11 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 5 * (b ^^^ (a ||| ( ~~~b &&& c))) + 11 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) - 11 * ~~~(a ||| (b ||| c)) - 20 * ~~~(a ||| ( ~~~b ||| c)) - 15 * ~~~( ~~~a ||| (b ||| c)) - 6 * ( ~~~a &&& ( ~~~b &&& c)) - 20 * ( ~~~a &&& (b &&& c)) - 6 * (a &&& (b &&& c)) = 7 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 37 * (a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1631 (x y : BitVec w) : +theorem e_1631 : 2 * ( ~~~a &&& (b ^^^ c)) + 1 * ~~~(a &&& (b ||| c)) + 1 * (b ||| c) + 2 * (a ||| (b &&& c)) - 1 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) - 1 * (c ||| ~~~(a ^^^ b)) + 1 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) - 2 * (b ^^^ ( ~~~a &&& (b ^^^ c))) + 7 * ~~~(a &&& (b &&& c)) - 3 * (b ^^^ (a ||| (b ||| c))) - 3 * ~~~( ~~~a ||| (b &&& c)) + 11 * (a ||| ~~~b) + 4 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 20 * ~~~(a ||| (b ||| c)) - 21 * ~~~(a ||| ( ~~~b ||| c)) - 13 * ~~~( ~~~a ||| (b ||| c)) - 17 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 28 * ( ~~~a &&& ( ~~~b &&& c)) - 12 * ( ~~~a &&& (b &&& c)) - 14 * (a &&& ( ~~~b &&& c)) - 22 * (a &&& (b &&& c)) = 1 * (c ^^^ ~~~(a &&& (b &&& c))) - 11 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1632 (x y : BitVec w) : +theorem e_1632 : 7 * (b ^^^ (a &&& c)) - 1 * (b ||| c) - 5 * (a &&& (b ||| c)) + 2 * (b ^^^ ~~~(a &&& (b ^^^ c))) - 6 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) - 5 * (b ^^^ (a &&& (b ^^^ c))) - 1 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) - 11 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) + 11 * (c ^^^ ~~~(a &&& (b ||| c))) - 2 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) + 5 * ~~~(a ||| ~~~c) - 7 * ~~~(a ^^^ b) + 2 * (c ^^^ ~~~(a &&& b)) + 10 * ~~~(a ||| (b ||| c)) - 6 * ~~~(a ||| ( ~~~b ||| c)) + 1 * ~~~( ~~~a ||| (b ||| c)) + 11 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 10 * ( ~~~a &&& ( ~~~b &&& c)) + 8 * ( ~~~a &&& (b &&& c)) + 1 * (a &&& ( ~~~b &&& c)) + 14 * (a &&& (b &&& c)) = 2 * (b ^^^ (a ||| (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1633 (x y : BitVec w) : +theorem e_1633 : 1 * (c ^^^ ( ~~~a &&& (b ||| c))) + 2 * ~~~(b &&& ~~~c) + 7 * ~~~(a &&& ~~~a) - 1 * (b ^^^ ( ~~~a ||| (b &&& c))) + 1 * (c ||| (a &&& ~~~b)) + 11 * (c ^^^ (a ||| ( ~~~b &&& c))) - 2 * ~~~( ~~~a ||| (b ^^^ c)) - 1 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 5 * ~~~(a &&& ~~~b) + 4 * (c &&& (a ||| ~~~b)) - 1 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) - 1 * ((a ^^^ b) &&& (a ^^^ c)) - 2 * (b ^^^ (a ||| ~~~c)) + 3 * ~~~(a ||| (b ||| c)) - 2 * ~~~(a ||| ( ~~~b ||| c)) - 14 * ~~~( ~~~a ||| (b ||| c)) - 11 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 6 * ( ~~~a &&& ( ~~~b &&& c)) - 9 * ( ~~~a &&& (b &&& c)) - 13 * (a &&& ( ~~~b &&& c)) - 8 * (a &&& (b &&& c)) = 3 * ~~~(a ||| (b ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1634 (x y : BitVec w) : +theorem e_1634 : - 1 * ((a &&& b) ^^^ (b ||| c)) + 2 * ( ~~~a ||| ( ~~~b &&& c)) - 7 * (a ||| ( ~~~b &&& c)) - 3 * ~~~( ~~~a &&& (b ||| c)) + 11 * ( ~~~c ||| (a ^^^ b)) + 1 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) + 2 * (b ^^^ (a &&& (b ||| c))) - 1 * ~~~(a ^^^ ( ~~~b &&& c)) + 1 * ((a ^^^ b) &&& ~~~(a ^^^ c)) + 11 * (b ^^^ ~~~(a &&& (b ^^^ c))) + 7 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) - 2 * (b ^^^ ~~~(a ||| (b ^^^ c))) - 2 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 7 * (b &&& (a ^^^ c)) - 1 * (b ||| ~~~(a ||| ~~~c)) - 24 * ~~~(a ||| (b ||| c)) - 11 * ~~~(a ||| ( ~~~b ||| c)) - 16 * ~~~( ~~~a ||| (b ||| c)) - 19 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 10 * ( ~~~a &&& ( ~~~b &&& c)) - 25 * ( ~~~a &&& (b &&& c)) + 8 * (a &&& (b &&& c)) = 2 * ~~~( ~~~a &&& (b ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1635 (x y : BitVec w) : +theorem e_1635 : - 1 * ((a &&& c) ||| (b &&& ~~~c)) - 1 * ~~~(a ^^^ c) + 2 * (a ||| (b ^^^ c)) + 5 * (c ^^^ ( ~~~a ||| (b &&& c))) + 4 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) - 7 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) + 1 * (c ^^^ (a ||| ( ~~~b &&& c))) - 1 * (c ^^^ ~~~(a ||| (b &&& c))) + 1 * (b ^^^ ( ~~~a &&& (b ^^^ c))) + 1 * (b &&& (a ^^^ c)) + 7 * (c ^^^ ~~~(a ||| ~~~b)) - 2 * (b &&& ~~~(a ^^^ c)) + 1 * (c ^^^ (a ||| ( ~~~b ||| c))) + 1 * (a &&& (b ||| c)) + 1 * ((a ||| b) &&& (b ^^^ c)) - 1 * ~~~(a ||| (b ||| c)) - 14 * ~~~(a ||| ( ~~~b ||| c)) + 3 * ~~~( ~~~a ||| (b ||| c)) - 4 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 7 * ( ~~~a &&& ( ~~~b &&& c)) + 5 * ( ~~~a &&& (b &&& c)) + 1 * (a &&& (b &&& c)) = 13 * (a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1636 (x y : BitVec w) : +theorem e_1636 : - 2 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) - 2 * (c ^^^ (a ||| (b &&& c))) - 1 * ~~~(a ^^^ (b ^^^ c)) - 1 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) + 3 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) + 2 * (c ||| ~~~(a ^^^ b)) - 1 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) + 2 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 2 * (a ^^^ (b &&& c)) - 2 * (b ^^^ (a ||| ~~~c)) + 1 * (c ^^^ ~~~(a ||| (b &&& c))) + 7 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) - 1 * ( ~~~(a ||| b) ||| (b ^^^ c)) - 1 * (c ||| ~~~(a ||| b)) - 2 * ( ~~~c ||| ~~~(a ^^^ b)) - 5 * ~~~(a ||| ( ~~~b &&& c)) + 6 * ~~~(a ||| (b ||| c)) - 2 * ~~~(a ||| ( ~~~b ||| c)) - 6 * ~~~( ~~~a ||| (b ||| c)) - 10 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 4 * (a &&& ( ~~~b &&& c)) - 4 * (a &&& (b &&& c)) = - 6 * ( ~~~a &&& (b &&& c)) - 1 * ((a ^^^ b) ||| (a ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1637 (x y : BitVec w) : +theorem e_1637 : 5 * ((a &&& c) ^^^ (b ||| c)) + 1 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 2 * ~~~b - 1 * (c ^^^ (a &&& ~~~b)) - 5 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 5 * ~~~(a &&& ~~~c) - 1 * (c ^^^ (a ||| (b ||| c))) - 2 * ( ~~~c &&& (a ^^^ b)) + 2 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) - 2 * (a ||| ( ~~~b ||| c)) - 5 * ~~~(a ^^^ (b &&& c)) - 11 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) + 1 * ( ~~~a ||| (b ||| c)) + 2 * a + 2 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) + 25 * ~~~(a ||| (b ||| c)) + 6 * ~~~(a ||| ( ~~~b ||| c)) + 4 * ~~~( ~~~a ||| (b ||| c)) + 9 * ( ~~~a &&& ( ~~~b &&& c)) + 10 * ( ~~~a &&& (b &&& c)) + 6 * (a &&& ( ~~~b &&& c)) + 10 * (a &&& (b &&& c)) = 9 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 3 * ( ~~~(a &&& b) &&& (b ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1638 (x y : BitVec w) : +theorem e_1638 : 2 * (a ^^^ (b &&& c)) + 2 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) - 6 * (c &&& ~~~(a ^^^ b)) - 5 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) + 1 * (a ^^^ ( ~~~b &&& c)) - 7 * ((a &&& c) ||| (b &&& ~~~c)) + 1 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) - 1 * ( ~~~a &&& (b ^^^ c)) + 1 * (a ||| ~~~b) - 5 * (b ^^^ (a ||| (b ^^^ c))) + 2 * ( ~~~b &&& (a ^^^ c)) + 3 * (c ||| ~~~(a ^^^ b)) - 1 * ~~~(b ||| c) + 2 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) - 2 * (b ^^^ (a &&& (b ^^^ c))) - 6 * ~~~(a ||| (b ||| c)) + 14 * ~~~(a ||| ( ~~~b ||| c)) - 7 * ~~~( ~~~a ||| (b ||| c)) - 8 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 6 * ( ~~~a &&& ( ~~~b &&& c)) - 6 * ( ~~~a &&& (b &&& c)) + 8 * (a &&& (b &&& c)) = - 6 * (a &&& ( ~~~b &&& c)) - 7 * (c ^^^ (a ||| ( ~~~b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1639 (x y : BitVec w) : +theorem e_1639 : 1 * (a &&& (b ||| c)) + 1 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) - 11 * ~~~(a ||| (b ^^^ c)) - 5 * ~~~(a &&& ( ~~~b &&& c)) + 11 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) + 7 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) + 7 * ~~~( ~~~a ||| (b ^^^ c)) + 2 * (b ^^^ (a &&& (b ^^^ c))) + 5 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) - 6 * ( ~~~b ||| (a ^^^ c)) - 6 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 2 * (b ^^^ (a ||| c)) + 4 * ( ~~~b ||| ~~~(a ^^^ c)) - 1 * ( ~~~a ||| (b &&& c)) + 7 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) - 6 * ~~~(a ||| ( ~~~b ||| c)) - 18 * ~~~( ~~~a ||| (b ||| c)) + 13 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 4 * ( ~~~a &&& ( ~~~b &&& c)) + 4 * ( ~~~a &&& (b &&& c)) - 11 * (a &&& ( ~~~b &&& c)) - 32 * (a &&& (b &&& c)) = - 2 * ~~~( ~~~a ||| (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1640 (x y : BitVec w) : +theorem e_1640 : - 3 * ((a ^^^ b) &&& (a ^^^ c)) + 1 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) + 11 * (a &&& b) - 1 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) + 2 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) + 1 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) - 6 * ~~~( ~~~a &&& ( ~~~b &&& c)) - 6 * ~~~(a ||| ~~~c) + 5 * (b ^^^ (a &&& ~~~c)) + 1 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) + 7 * (c ^^^ (a &&& b)) - 2 * ((a ||| b) &&& ~~~(b ^^^ c)) - 5 * (b ||| ~~~(a ||| c)) + 11 * (c ^^^ (a ||| b)) + 9 * ~~~(a ||| (b ||| c)) - 8 * ~~~(a ||| ( ~~~b ||| c)) - 8 * ~~~( ~~~a ||| (b ||| c)) - 19 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 12 * ( ~~~a &&& ( ~~~b &&& c)) + 3 * ( ~~~a &&& (b &&& c)) - 7 * (a &&& ( ~~~b &&& c)) - 7 * (a &&& (b &&& c)) = - 2 * (b ^^^ (a &&& (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1641 (x y : BitVec w) : +theorem e_1641 : - 2 * (b ^^^ (a ||| ~~~c)) - 3 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) - 1 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) + 7 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) - 2 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) + 7 * (c &&& (a ||| ~~~b)) - 5 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 3 * (b ^^^ (a ||| ( ~~~b ||| c))) + 3 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 11 * ~~~(b ||| ~~~c) + 4 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) + 11 * (c ^^^ (a &&& (b ||| c))) - 1 * ~~~(a ||| (b ^^^ c)) - 2 * ~~~(a &&& (b ^^^ c)) + 5 * ~~~(a ||| (b ||| c)) - 10 * ~~~(a ||| ( ~~~b ||| c)) - 8 * ~~~( ~~~a ||| (b ||| c)) - 8 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 16 * ( ~~~a &&& ( ~~~b &&& c)) - 7 * ( ~~~a &&& (b &&& c)) + 1 * (a &&& ( ~~~b &&& c)) - 11 * (a &&& (b &&& c)) = - 1 * ~~~(a ^^^ c) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1642 (x y : BitVec w) : +theorem e_1642 : 1 * c - 11 * ~~~(a &&& ( ~~~b &&& c)) + 2 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 1 * (a ||| ( ~~~b &&& c)) - 11 * ~~~( ~~~a ||| (b ^^^ c)) + 11 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) + 1 * (b ^^^ ( ~~~a &&& (b ||| c))) + 1 * (c &&& (a ||| ~~~b)) - 1 * ( ~~~a &&& ( ~~~b ||| c)) - 7 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) - 2 * ~~~(a ^^^ c) + 1 * (a &&& c) - 6 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) + 2 * (c ^^^ (a &&& ~~~b)) + 20 * ~~~(a ||| (b ||| c)) + 2 * ~~~(a ||| ( ~~~b ||| c)) + 35 * ~~~( ~~~a ||| (b ||| c)) + 7 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 5 * ( ~~~a &&& ( ~~~b &&& c)) + 2 * ( ~~~a &&& (b &&& c)) - 11 * (a &&& ( ~~~b &&& c)) + 24 * (a &&& (b &&& c)) = 1 * (b ^^^ ~~~(a &&& (b ||| c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1643 (x y : BitVec w) : +theorem e_1643 : - 1 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) - 7 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) + 1 * (a ^^^ b) - 3 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 11 * (c ^^^ ~~~(a ||| ~~~b)) - 5 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) + 1 * ((b &&& c) ||| (a &&& (b ||| c))) + 4 * (b ^^^ ~~~(a &&& (b &&& c))) + 7 * ~~~(a ||| (b ^^^ c)) + 3 * (b ^^^ (a &&& ~~~c)) - 11 * ~~~(a ^^^ ( ~~~b ||| c)) - 6 * c - 2 * ((a ||| ~~~b) &&& (b ^^^ c)) - 1 * ( ~~~c ||| (a ^^^ b)) + 4 * (c ^^^ ~~~(a &&& b)) - 1 * (b ||| c) - 6 * ~~~(a ||| (b ||| c)) - 4 * ~~~(a ||| ( ~~~b ||| c)) - 2 * ~~~( ~~~a ||| (b ||| c)) + 6 * ( ~~~a &&& (b &&& c)) + 14 * (a &&& ( ~~~b &&& c)) + 1 * (a &&& (b &&& c)) = - 3 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) - 15 * ~~~( ~~~a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1644 (x y : BitVec w) : +theorem e_1644 : 11 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) - 2 * ~~~(a &&& (b ||| c)) - 2 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) + 1 * ( ~~~c ||| ~~~(a ^^^ b)) - 2 * (b ^^^ (a ||| ( ~~~b &&& c))) + 2 * ( ~~~c ||| (a ^^^ b)) + 5 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 11 * ~~~(a ^^^ b) - 1 * (b ^^^ ~~~(a ||| (b &&& c))) + 7 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) + 2 * ((a ^^^ b) &&& ~~~(a ^^^ c)) + 7 * ( ~~~b &&& ~~~(a ^^^ c)) + 4 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 7 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 1 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) + 4 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) - 27 * ~~~(a ||| (b ||| c)) - 11 * ~~~( ~~~a ||| (b ||| c)) - 5 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 11 * ( ~~~a &&& ( ~~~b &&& c)) - 10 * ( ~~~a &&& (b &&& c)) - 26 * (a &&& ( ~~~b &&& c)) + 12 * (a &&& (b &&& c)) = - 3 * ~~~(a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1645 (x y : BitVec w) : +theorem e_1645 : - 1 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 7 * ~~~(a &&& ~~~b) + 5 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) + 2 * ((a ^^^ b) &&& ~~~(a ^^^ c)) + 5 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) - 7 * ( ~~~c &&& ~~~(a ^^^ b)) + 5 * (a ||| ( ~~~b ||| c)) + 1 * (b &&& (a ||| c)) + 11 * (c &&& ~~~(a &&& ~~~b)) - 11 * (b ^^^ (a ||| c)) - 5 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 6 * (b ||| ~~~(a ^^^ c)) - 5 * (b &&& c) - 1 * (a ^^^ (b &&& c)) - 7 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) - 3 * ~~~(a ||| (b ||| c)) + 19 * ~~~(a ||| ( ~~~b ||| c)) - 3 * ~~~( ~~~a ||| (b ||| c)) + 8 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 10 * ( ~~~a &&& ( ~~~b &&& c)) - 11 * ( ~~~a &&& (b &&& c)) + 18 * (a &&& ( ~~~b &&& c)) - 19 * (a &&& (b &&& c)) = - 1 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1646 (x y : BitVec w) : +theorem e_1646 : - 2 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 5 * (c ^^^ ( ~~~a &&& (b ||| c))) + 3 * (b ^^^ ~~~(a ||| (b ^^^ c))) + 1 * (c ^^^ ( ~~~a ||| (b ||| c))) - 11 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) - 3 * ~~~(b ||| c) - 6 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) - 2 * (a ^^^ (b &&& c)) + 7 * (b &&& (a ^^^ c)) + 4 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) - 2 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) + 7 * ~~~(a ||| (b ^^^ c)) + 1 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 11 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) + 5 * (a ^^^ c) - 2 * (b ^^^ ~~~(a ||| ~~~c)) + 17 * ~~~(a ||| (b ||| c)) + 12 * ~~~(a ||| ( ~~~b ||| c)) + 22 * ~~~( ~~~a ||| (b ||| c)) - 9 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 4 * ( ~~~a &&& ( ~~~b &&& c)) + 10 * (a &&& ( ~~~b &&& c)) + 14 * (a &&& (b &&& c)) = - 2 * ((a &&& c) ||| (b &&& ~~~c)) - 7 * ( ~~~a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1647 (x y : BitVec w) : +theorem e_1647 : - 1 * (b ^^^ (a ||| (b &&& c))) + 3 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) + 4 * (b ^^^ (a ||| c)) - 7 * (b ^^^ (a &&& c)) - 7 * (a ||| ~~~b) - 5 * ((a &&& c) ^^^ (b ||| c)) + 7 * (b ||| (a &&& ~~~c)) - 6 * (c ^^^ (a &&& ( ~~~b ||| c))) + 1 * ((a &&& c) ||| (b &&& ~~~c)) - 1 * ( ~~~c &&& (a ^^^ b)) - 1 * (b &&& ~~~(a &&& ~~~c)) - 3 * c - 2 * ((a &&& b) ||| ~~~(b ||| ~~~c)) + 1 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 3 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 1 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) - 1 * (c &&& ~~~(a &&& b)) + 4 * ~~~(a ||| (b ||| c)) + 1 * ~~~(a ||| ( ~~~b ||| c)) + 1 * ~~~( ~~~a ||| (b ||| c)) + 13 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 10 * ( ~~~a &&& (b &&& c)) + 2 * (a &&& (b &&& c)) = - 20 * ( ~~~a &&& ( ~~~b &&& c)) - 15 * (a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1648 (x y : BitVec w) : +theorem e_1648 : 11 * (b ^^^ ( ~~~a ||| (b ^^^ c))) - 7 * (a ^^^ b) + 1 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) - 1 * ( ~~~a ||| (b ||| c)) - 2 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) + 1 * ( ~~~c ||| ~~~(a ^^^ b)) + 1 * (b ^^^ ~~~(a &&& (b ^^^ c))) + 3 * ~~~(a &&& (b ||| c)) - 2 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) - 5 * ~~~( ~~~a &&& ( ~~~b ||| c)) + 1 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) + 7 * (a ||| ~~~b) + 5 * (b ^^^ ~~~(a &&& ~~~c)) - 3 * ( ~~~(a ||| b) ||| (b ^^^ c)) + 11 * ( ~~~c ||| (a ^^^ b)) - 1 * ((a &&& ~~~b) ||| (b ^^^ c)) - 11 * ~~~(a &&& (b &&& c)) + 14 * ~~~(a ||| ( ~~~b ||| c)) - 5 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 12 * ( ~~~a &&& ( ~~~b &&& c)) + 6 * ( ~~~a &&& (b &&& c)) - 5 * (a &&& ( ~~~b &&& c)) - 11 * (a &&& (b &&& c)) = 24 * ~~~(a ||| (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1649 (x y : BitVec w) : +theorem e_1649 : - 1 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) + 1 * (b ^^^ ~~~(a &&& (b ^^^ c))) - 2 * c + 2 * (a &&& b) + 1 * (a ||| ( ~~~b ||| c)) + 7 * (a ^^^ ( ~~~b ||| c)) + 2 * (c ||| (a &&& b)) - 1 * ((a ^^^ b) ||| ~~~(a ^^^ c)) + 5 * ((a &&& c) ||| (b &&& ~~~c)) + 1 * (a ^^^ (b &&& c)) - 3 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) - 6 * ( ~~~b ||| (a ^^^ c)) + 2 * b + 11 * (a ^^^ (b ||| c)) - 2 * ~~~( ~~~a &&& ( ~~~b &&& c)) - 7 * ~~~(a &&& (b ^^^ c)) + 11 * ~~~(a ||| (b ||| c)) - 12 * ~~~(a ||| ( ~~~b ||| c)) + 6 * ~~~( ~~~a ||| (b ||| c)) - 13 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 8 * ( ~~~a &&& ( ~~~b &&& c)) - 2 * ( ~~~a &&& (b &&& c)) + 2 * (a &&& ( ~~~b &&& c)) = - 4 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) + 4 * (a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1650 (x y : BitVec w) : +theorem e_1650 : - 7 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) + 5 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) + 2 * (c ||| (a &&& ~~~b)) - 6 * (b ||| ~~~(a ||| c)) - 5 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) + 4 * (b ^^^ ( ~~~a ||| (b &&& c))) + 5 * ~~~(a ^^^ c) + 1 * (a ||| (b &&& c)) + 2 * ~~~b + 4 * ~~~(a ^^^ (b ||| c)) - 2 * ((a ||| ~~~b) &&& (b ^^^ c)) - 2 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 2 * (c ^^^ ~~~(a ||| b)) + 2 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) + 1 * ~~~( ~~~a ||| (b ^^^ c)) + 1 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) + 1 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) - 2 * ~~~(a ||| (b ||| c)) + 2 * ~~~(a ||| ( ~~~b ||| c)) - 7 * ~~~( ~~~a ||| (b ||| c)) - 2 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 11 * ( ~~~a &&& (b &&& c)) - 8 * (a &&& (b &&& c)) = 4 * ( ~~~a &&& ( ~~~b &&& c)) + 2 * ~~~(a &&& b) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1651 (x y : BitVec w) : +theorem e_1651 : 3 * ~~~a + 1 * (c ^^^ (a ||| ~~~b)) - 1 * (b &&& (a ||| ~~~c)) - 11 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) - 1 * (b ^^^ (a ||| ( ~~~b &&& c))) + 4 * ( ~~~a ||| ( ~~~b &&& c)) + 7 * ~~~(b ||| ~~~c) + 3 * (c ^^^ ~~~(a ||| ~~~b)) + 11 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) - 1 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) - 3 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) + 1 * (b ^^^ ~~~(a &&& (b ^^^ c))) - 5 * (a ^^^ b) - 2 * (b ^^^ ( ~~~a &&& (b ||| c))) - 6 * (a ||| (b ^^^ c)) + 2 * ~~~(a ||| (b &&& c)) - 7 * ~~~(a ||| (b ||| c)) - 6 * ~~~(a ||| ( ~~~b ||| c)) + 3 * ~~~( ~~~a ||| (b ||| c)) + 8 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 3 * ( ~~~a &&& ( ~~~b &&& c)) - 2 * ( ~~~a &&& (b &&& c)) + 9 * (a &&& (b &&& c)) = 1 * (a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1652 (x y : BitVec w) : +theorem e_1652 : 7 * ((a &&& c) ||| (b &&& ~~~c)) - 1 * (c ^^^ ~~~(a &&& (b &&& c))) + 2 * ((a &&& b) ||| ~~~(b ||| c)) + 2 * (c ^^^ ( ~~~a ||| (b &&& c))) + 1 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 2 * ~~~(b &&& c) + 3 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) - 7 * ~~~(a &&& (b ^^^ c)) + 5 * (c ^^^ (a ||| (b ||| c))) + 11 * (b &&& (a ||| ~~~c)) + 11 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) - 5 * (b ^^^ (a &&& (b ^^^ c))) + 3 * (b ^^^ (a ||| (b ^^^ c))) + 5 * (c ||| (a ^^^ b)) - 6 * (a ^^^ (b ^^^ c)) + 8 * ~~~(a ||| (b ||| c)) - 22 * ~~~(a ||| ( ~~~b ||| c)) - 3 * ~~~( ~~~a ||| (b ||| c)) - 20 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 7 * ( ~~~a &&& ( ~~~b &&& c)) - 8 * ( ~~~a &&& (b &&& c)) - 12 * (a &&& ( ~~~b &&& c)) - 19 * (a &&& (b &&& c)) = 2 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1653 (x y : BitVec w) : +theorem e_1653 : - 1 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) + 11 * (b ||| (a &&& ~~~c)) - 1 * ~~~( ~~~a ||| (b &&& c)) - 11 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) - 11 * ((a &&& b) ||| ~~~(b ||| c)) + 4 * (c &&& ~~~(a &&& ~~~b)) + 2 * (c &&& ~~~(a ^^^ b)) - 7 * (c &&& (a ^^^ b)) + 3 * ((a ^^^ b) ||| ~~~(a ^^^ c)) - 11 * (b ^^^ (a &&& (b ^^^ c))) + 1 * ( ~~~a ||| (b ||| c)) + 5 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) - 11 * ( ~~~c ||| (a ^^^ b)) - 2 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 2 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) + 7 * ((b &&& c) ||| (a &&& (b ||| c))) + 35 * ~~~(a ||| (b ||| c)) + 10 * ~~~(a ||| ( ~~~b ||| c)) - 1 * ~~~( ~~~a ||| (b ||| c)) - 4 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 6 * ( ~~~a &&& ( ~~~b &&& c)) + 26 * (a &&& ( ~~~b &&& c)) - 1 * (a &&& (b &&& c)) = - 5 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) + 1 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1654 (x y : BitVec w) : +theorem e_1654 : 1 * ~~~(a &&& (b ||| c)) - 5 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 3 * (a ||| ~~~b) + 1 * (b ||| ~~~c) - 1 * (c &&& (a ||| ~~~b)) - 6 * ( ~~~a ||| (b ^^^ c)) + 1 * (b ^^^ ~~~(a ||| ~~~c)) + 1 * ( ~~~a &&& (b ||| c)) + 1 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 2 * ((a &&& b) ||| (b ^^^ c)) - 5 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) - 5 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) + 11 * (b &&& (a ||| ~~~c)) + 3 * (a ||| b) + 1 * ( ~~~a &&& (b ^^^ c)) - 6 * ~~~(b ||| ~~~c) - 6 * ~~~( ~~~a &&& ( ~~~b ||| c)) + 7 * (c ^^^ (a &&& ~~~b)) + 4 * ~~~(a ||| (b ||| c)) - 7 * ~~~( ~~~a ||| (b ||| c)) - 1 * ( ~~~a &&& ( ~~~b &&& c)) + 7 * ( ~~~a &&& (b &&& c)) + 12 * (a &&& ( ~~~b &&& c)) - 7 * (a &&& (b &&& c)) = - 7 * ~~~b + 5 * ~~~( ~~~a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1655 (x y : BitVec w) : +theorem e_1655 : 1 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) - 2 * (a ||| ~~~c) - 5 * (c &&& (a ^^^ b)) + 1 * (c &&& ~~~(a &&& b)) + 2 * ((a ||| b) &&& (b ^^^ c)) - 7 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 3 * (b &&& (a ||| ~~~c)) - 6 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) + 1 * (b &&& c) - 1 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 5 * ( ~~~b ||| ~~~(a ^^^ c)) + 5 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 2 * ~~~a + 11 * (c ||| (a ^^^ b)) - 2 * ((a &&& ~~~b) ||| (b ^^^ c)) + 2 * (a &&& ~~~c) - 1 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) - 24 * ~~~(a ||| ( ~~~b ||| c)) - 11 * ~~~( ~~~a ||| (b ||| c)) - 2 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 23 * ( ~~~a &&& ( ~~~b &&& c)) - 5 * ( ~~~a &&& (b &&& c)) + 3 * (a &&& ( ~~~b &&& c)) - 17 * (a &&& (b &&& c)) = - 4 * ~~~(a ||| (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1656 (x y : BitVec w) : +theorem e_1656 : - 3 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) + 1 * (c &&& (a ^^^ b)) - 7 * (b &&& ~~~(a &&& c)) - 2 * ((a &&& b) ^^^ (b ||| ~~~c)) + 4 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 11 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 2 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 2 * ( ~~~c ||| (a ^^^ b)) + 1 * ~~~(a &&& b) - 1 * (c ||| (a &&& b)) - 7 * (b ^^^ ~~~(a &&& (b &&& c))) + 1 * ~~~(a &&& (b ^^^ c)) + 4 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) + 2 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) - 6 * ~~~(a ||| c) - 7 * ( ~~~c &&& ~~~(a ^^^ b)) + 10 * ~~~(a ||| (b ||| c)) + 20 * ~~~(a ||| ( ~~~b ||| c)) + 13 * ~~~( ~~~a ||| (b ||| c)) + 22 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 16 * ( ~~~a &&& ( ~~~b &&& c)) + 22 * ( ~~~a &&& (b &&& c)) - 3 * (a &&& ( ~~~b &&& c)) + 12 * (a &&& (b &&& c)) = 1 * (b ||| c) + 7 * (b &&& c) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1657 (x y : BitVec w) : +theorem e_1657 : 7 * (b ||| (a &&& c)) - 7 * ((a &&& b) ||| ~~~(b ^^^ c)) - 6 * ~~~(a ||| ~~~c) + 1 * ((a &&& c) ^^^ (b ||| c)) + 3 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) + 3 * (b &&& ~~~(a &&& ~~~c)) - 11 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 3 * ( ~~~b ||| ~~~(a ^^^ c)) - 2 * (b ^^^ (a ||| (b ^^^ c))) + 11 * ~~~(b &&& ~~~c) + 1 * (a ||| (b ^^^ c)) + 2 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) + 2 * (c ^^^ ~~~(a ||| b)) + 2 * ( ~~~a &&& ( ~~~b ||| c)) - 2 * (c ^^^ ( ~~~a ||| (b &&& c))) + 7 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) + 1 * (b ||| (a ^^^ c)) - 4 * ~~~(a ||| (b ||| c)) - 15 * ~~~(a ||| ( ~~~b ||| c)) - 1 * ~~~( ~~~a ||| (b ||| c)) + 6 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 1 * ( ~~~a &&& ( ~~~b &&& c)) - 17 * ( ~~~a &&& (b &&& c)) - 12 * (a &&& ( ~~~b &&& c)) = 9 * (a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1658 (x y : BitVec w) : +theorem e_1658 : - 7 * ~~~a - 5 * (b ||| c) - 11 * (c ^^^ (a ||| (b &&& c))) + 1 * (a ^^^ (b ||| c)) - 2 * (a &&& b) + 3 * (c ||| (a &&& b)) + 1 * (b ^^^ ~~~(a &&& c)) + 4 * ((a ^^^ b) &&& ~~~(a ^^^ c)) - 7 * (c ^^^ ~~~(a &&& b)) + 11 * ((b &&& c) ||| (a &&& (b ||| c))) + 11 * (b ^^^ (a &&& ( ~~~b ||| c))) - 6 * ~~~( ~~~a ||| (b &&& c)) - 2 * (c ^^^ (a &&& (b ||| c))) - 1 * (c ^^^ (a ||| ( ~~~b ||| c))) - 2 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) - 3 * (b &&& ~~~(a &&& ~~~c)) + 23 * ~~~(a ||| (b ||| c)) + 6 * ~~~(a ||| ( ~~~b ||| c)) + 25 * ~~~( ~~~a ||| (b ||| c)) + 13 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 20 * ( ~~~a &&& ( ~~~b &&& c)) - 9 * ( ~~~a &&& (b &&& c)) - 9 * (a &&& ( ~~~b &&& c)) + 15 * (a &&& (b &&& c)) = - 2 * (b ^^^ ( ~~~a ||| (b ||| c))) + 11 * ~~~( ~~~a &&& (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1659 (x y : BitVec w) : +theorem e_1659 : 1 * (b ^^^ (a &&& (b ||| c))) + 4 * (a &&& c) - 6 * ( ~~~c ||| ~~~(a ^^^ b)) - 3 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 5 * (a &&& ~~~c) + 4 * ( ~~~c ||| (a ^^^ b)) - 1 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) + 2 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) + 3 * (b &&& ~~~(a ^^^ c)) + 4 * (b ^^^ (a ||| (b ^^^ c))) + 3 * (c ||| ~~~(a ||| b)) - 7 * (b ^^^ ~~~(a &&& c)) + 11 * ~~~(a ||| (b ^^^ c)) + 5 * ~~~(a &&& (b ^^^ c)) + 3 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) + 2 * (c ^^^ ~~~(a &&& b)) + 7 * ( ~~~(a &&& b) &&& (b ^^^ c)) - 12 * ~~~(a ||| (b ||| c)) - 13 * ~~~(a ||| ( ~~~b ||| c)) + 8 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 7 * ( ~~~a &&& ( ~~~b &&& c)) - 31 * ( ~~~a &&& (b &&& c)) - 25 * (a &&& ( ~~~b &&& c)) - 6 * (a &&& (b &&& c)) = - 1 * ~~~( ~~~a ||| (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1660 (x y : BitVec w) : +theorem e_1660 : 7 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) + 1 * ~~~c - 6 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 11 * (c ||| ~~~(a ^^^ b)) - 1 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 5 * ~~~(a ||| ( ~~~b &&& c)) - 3 * ~~~(a ^^^ ( ~~~b ||| c)) - 5 * (a ^^^ (b ||| c)) + 3 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 3 * ((a &&& c) ||| ~~~(b ||| c)) - 1 * ( ~~~a &&& (b ||| c)) + 7 * ~~~(a ^^^ (b ||| c)) + 4 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) - 1 * (b &&& ~~~(a &&& c)) + 2 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) + 2 * ~~~(a &&& ~~~a) - 11 * ((a ||| ~~~b) &&& (b ^^^ c)) + 9 * ~~~(a ||| (b ||| c)) + 3 * ~~~( ~~~a ||| (b ||| c)) + 5 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 19 * ( ~~~a &&& ( ~~~b &&& c)) + 14 * ( ~~~a &&& (b &&& c)) + 3 * (a &&& ( ~~~b &&& c)) - 1 * (a &&& (b &&& c)) = - 7 * ~~~(a ||| ( ~~~b ||| c)) - 4 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1661 (x y : BitVec w) : +theorem e_1661 : 7 * ((a ||| b) &&& (b ^^^ c)) + 5 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) + 2 * (c ||| (a &&& ~~~b)) + 4 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 3 * (b ^^^ ( ~~~a ||| (b &&& c))) - 7 * ~~~(a &&& (b ||| c)) - 1 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) + 1 * ~~~(a &&& ~~~a) - 5 * ~~~(a ^^^ b) + 3 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) - 6 * (c ||| (a ^^^ b)) + 5 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) - 5 * ((a &&& b) ||| (b ^^^ c)) - 11 * (c &&& (a ||| ~~~b)) - 2 * (b ^^^ (a ||| ( ~~~b &&& c))) + 11 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) + 11 * (b ||| ~~~(a ||| c)) - 1 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 17 * ~~~(a ||| (b ||| c)) - 6 * ~~~( ~~~a ||| (b ||| c)) - 12 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 17 * ( ~~~a &&& ( ~~~b &&& c)) - 12 * ( ~~~a &&& (b &&& c)) + 8 * (a &&& (b &&& c)) = - 6 * (a &&& ( ~~~b &&& c)) + 13 * ~~~(a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1662 (x y : BitVec w) : +theorem e_1662 : 5 * ((a &&& ~~~b) ||| (b ^^^ c)) - 1 * ( ~~~c ||| (a ^^^ b)) - 1 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) + 2 * ((a &&& b) ||| ~~~(b ||| ~~~c)) - 6 * ~~~( ~~~a ||| (b ^^^ c)) + 5 * ~~~( ~~~a &&& (b &&& c)) + 11 * (b &&& ~~~(a ^^^ c)) + 11 * ~~~(a ||| ~~~c) + 4 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 7 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) + 1 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 2 * ((a &&& b) ^^^ (b ||| ~~~c)) - 3 * ((a &&& b) ^^^ (b ||| c)) + 3 * (b ^^^ ( ~~~a ||| (b &&& c))) + 7 * (a &&& ( ~~~b ||| c)) - 3 * (c &&& (a ||| ~~~b)) - 18 * ~~~(a ||| (b ||| c)) - 19 * ~~~(a ||| ( ~~~b ||| c)) - 22 * ~~~( ~~~a ||| (b ||| c)) - 19 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 30 * ( ~~~a &&& ( ~~~b &&& c)) - 6 * ( ~~~a &&& (b &&& c)) - 15 * (a &&& ( ~~~b &&& c)) - 19 * (a &&& (b &&& c)) = - 2 * ~~~( ~~~a &&& (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1663 (x y : BitVec w) : +theorem e_1663 : 2 * ~~~(a &&& b) - 5 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) - 7 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 6 * ( ~~~(a &&& b) &&& (b ^^^ c)) + 7 * (c ||| ~~~(a ^^^ b)) - 3 * ((a &&& b) ^^^ (b ||| c)) - 6 * (c ^^^ (a &&& (b ||| c))) + 4 * (c ^^^ ( ~~~a ||| (b &&& c))) - 1 * (b ^^^ (a &&& c)) + 2 * ( ~~~b &&& (a ^^^ c)) + 1 * (a ^^^ ( ~~~b &&& c)) + 4 * b - 3 * (c ^^^ (a &&& ( ~~~b ||| c))) - 11 * ((a &&& b) ||| (b ^^^ c)) + 3 * ( ~~~a ||| (b &&& c)) - 2 * (b ^^^ (a ||| ( ~~~b &&& c))) - 2 * ~~~(a ||| (b ||| c)) + 18 * ~~~(a ||| ( ~~~b ||| c)) + 11 * ~~~( ~~~a ||| (b ||| c)) + 6 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 23 * ( ~~~a &&& ( ~~~b &&& c)) + 3 * ( ~~~a &&& (b &&& c)) + 10 * (a &&& ( ~~~b &&& c)) + 1 * (a &&& (b &&& c)) = 2 * ~~~(a ||| (b &&& c)) - 1 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1664 (x y : BitVec w) : +theorem e_1664 : - 11 * ~~~(a ||| b) + 5 * ( ~~~a ||| ( ~~~b &&& c)) - 7 * (c &&& (a ||| ~~~b)) - 5 * b + 1 * (b ^^^ ~~~(a &&& c)) - 11 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) - 1 * ~~~(a ^^^ (b ^^^ c)) + 2 * (a ^^^ ( ~~~b &&& c)) - 1 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 11 * (a ||| (b ^^^ c)) + 5 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 2 * ( ~~~b &&& ~~~(a ^^^ c)) - 3 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) + 2 * (b ^^^ ~~~(a &&& ~~~c)) - 11 * ~~~(a &&& ~~~c) + 11 * ((a &&& c) ||| (b &&& ~~~c)) - 1 * (a &&& c) + 15 * ~~~(a ||| (b ||| c)) - 20 * ~~~( ~~~a ||| (b ||| c)) - 14 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 15 * ( ~~~a &&& ( ~~~b &&& c)) + 26 * ( ~~~a &&& (b &&& c)) - 6 * (a &&& ( ~~~b &&& c)) + 2 * (a &&& (b &&& c)) = - 2 * ~~~b := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1665 (x y : BitVec w) : +theorem e_1665 : 2 * ~~~(a ||| c) + 11 * ((a &&& b) ||| ~~~(b ||| ~~~c)) + 4 * ~~~(a &&& ( ~~~b ||| c)) - 1 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) + 4 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) + 7 * ~~~(a &&& ~~~a) + 2 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 1 * (c ^^^ ~~~(a &&& (b ||| c))) + 1 * (a ^^^ ( ~~~b &&& c)) - 7 * ~~~(b ||| ~~~c) + 11 * (c &&& ~~~(a ^^^ b)) - 5 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) - 11 * (c ^^^ (a ||| (b ||| c))) + 1 * ~~~(a ^^^ ( ~~~b ||| c)) - 5 * ~~~(a &&& c) + 1 * ((a &&& c) ||| ~~~(b ||| c)) + 5 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) - 8 * ~~~(a ||| (b ||| c)) - 7 * ~~~(a ||| ( ~~~b ||| c)) + 7 * ~~~( ~~~a ||| (b ||| c)) - 6 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 19 * ( ~~~a &&& ( ~~~b &&& c)) - 7 * ( ~~~a &&& (b &&& c)) - 18 * (a &&& ( ~~~b &&& c)) - 35 * (a &&& (b &&& c)) = 1 * (a ||| (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1666 (x y : BitVec w) : +theorem e_1666 : 5 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 2 * (a ||| b) + 5 * (a ||| ~~~c) - 5 * ~~~( ~~~a ||| ( ~~~b &&& c)) - 7 * ((a &&& b) ||| (b ^^^ c)) - 11 * (c &&& (a ^^^ b)) - 1 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 1 * ((a ^^^ b) &&& ~~~(a ^^^ c)) + 4 * ~~~a - 5 * (b ^^^ ~~~(a &&& c)) - 2 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) - 1 * (b ||| (a &&& c)) - 1 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) - 2 * (c ^^^ ~~~(a ||| ~~~b)) + 1 * (c ||| (a &&& b)) + 1 * (b ^^^ ~~~(a &&& ~~~c)) - 5 * ((a ||| b) &&& ~~~(b ^^^ c)) + 1 * (b ||| ~~~(a ||| c)) - 6 * ~~~(a ||| ( ~~~b ||| c)) + 6 * ~~~( ~~~a ||| (b ||| c)) + 7 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 8 * ( ~~~a &&& ( ~~~b &&& c)) + 7 * ( ~~~a &&& (b &&& c)) + 15 * (a &&& ( ~~~b &&& c)) + 19 * (a &&& (b &&& c)) = 4 * ~~~(a ||| (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1667 (x y : BitVec w) : +theorem e_1667 : 11 * (b ^^^ ~~~(a &&& (b &&& c))) - 6 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) + 2 * ~~~(a ^^^ b) + 3 * ~~~(a ||| b) - 7 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) + 5 * (b ^^^ c) - 2 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) + 2 * ~~~( ~~~a ||| (b ^^^ c)) - 1 * (b ^^^ (a ||| (b ||| c))) - 5 * (c ^^^ (a &&& ~~~b)) - 2 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) - 3 * (c ^^^ ( ~~~a ||| (b ||| c))) + 4 * ((a &&& ~~~b) ||| (b ^^^ c)) - 1 * (c &&& (a ||| b)) + 11 * (a ||| ~~~c) + 3 * (b &&& ~~~(a ^^^ c)) - 1 * (c ^^^ (a ||| ( ~~~b ||| c))) + 11 * ~~~(a &&& c) + 1 * (c ^^^ ( ~~~a &&& (b ||| c))) - 28 * ~~~(a ||| (b ||| c)) - 23 * ~~~(a ||| ( ~~~b ||| c)) - 22 * ~~~( ~~~a ||| (b ||| c)) - 25 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 3 * ( ~~~a &&& (b &&& c)) - 7 * (a &&& (b &&& c)) = 23 * ( ~~~a &&& ( ~~~b &&& c)) + 24 * (a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1668 (x y : BitVec w) : +theorem e_1668 : 2 * ~~~(a ||| ( ~~~b &&& c)) + 2 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) + 11 * ~~~(b ^^^ c) - 7 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) + 11 * (b ||| c) + 2 * ~~~(a ^^^ ( ~~~b ||| c)) - 7 * (c &&& (a ||| b)) - 3 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) + 4 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) + 1 * (b ^^^ (a ||| ( ~~~b ||| c))) + 7 * ~~~(a &&& ( ~~~b &&& c)) - 1 * (b &&& (a ||| c)) + 3 * ((a &&& b) ||| ~~~(b ||| ~~~c)) + 4 * (c ||| (a &&& b)) - 5 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) + 1 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) + 3 * ~~~(a ||| ~~~c) - 6 * ~~~(a ||| (b ||| c)) - 8 * ~~~(a ||| ( ~~~b ||| c)) - 15 * ~~~( ~~~a ||| (b ||| c)) - 15 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 22 * ( ~~~a &&& ( ~~~b &&& c)) - 22 * ( ~~~a &&& (b &&& c)) - 8 * (a &&& ( ~~~b &&& c)) - 17 * (a &&& (b &&& c)) = 7 * (c ||| ~~~(a ^^^ b)) - 2 * (a &&& ~~~c) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1669 (x y : BitVec w) : +theorem e_1669 : 1 * ~~~( ~~~a ||| (b ^^^ c)) - 1 * (c ||| (a &&& ~~~b)) + 5 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) - 5 * ( ~~~a ||| ( ~~~b &&& c)) + 2 * ~~~(a ||| ~~~b) - 7 * ~~~a - 2 * ( ~~~c &&& ~~~(a ^^^ b)) - 3 * ~~~(a &&& (b ^^^ c)) - 1 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) - 2 * ~~~(a ^^^ (b &&& c)) + 11 * (a ||| ~~~c) - 11 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 11 * (b ^^^ (a ||| (b &&& c))) + 5 * ((a ^^^ b) &&& ~~~(a ^^^ c)) + 2 * ~~~(a ||| b) + 2 * ~~~( ~~~a ||| (b &&& c)) - 2 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) + 2 * (b ^^^ (a &&& ( ~~~b ||| c))) + 13 * ~~~(a ||| ( ~~~b ||| c)) + 12 * ~~~( ~~~a ||| (b ||| c)) - 5 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 26 * ( ~~~a &&& ( ~~~b &&& c)) + 19 * ( ~~~a &&& (b &&& c)) + 18 * (a &&& ( ~~~b &&& c)) - 9 * (a &&& (b &&& c)) = 7 * ((a &&& ~~~b) ||| (b ^^^ c)) - 3 * ~~~(a ||| (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1670 (x y : BitVec w) : +theorem e_1670 : 3 * (b ||| (a &&& c)) - 7 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 4 * ( ~~~b &&& (a ^^^ c)) + 7 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) + 3 * ((a &&& b) ||| ~~~(b ||| c)) + 1 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 5 * ~~~(a ^^^ b) - 3 * (a ^^^ b) - 2 * (b ||| (a &&& ~~~c)) + 2 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) - 1 * (c ||| (a ^^^ b)) - 1 * ~~~(b ||| ~~~c) - 1 * ~~~( ~~~a &&& (b ||| c)) - 11 * (b ^^^ (a ||| (b &&& c))) - 2 * ~~~(a ^^^ (b ^^^ c)) + 1 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 11 * (c ^^^ (a ||| b)) + 6 * ~~~(a ||| (b ||| c)) + 15 * ~~~(a ||| ( ~~~b ||| c)) + 12 * ~~~( ~~~a ||| (b ||| c)) + 14 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 9 * ( ~~~a &&& ( ~~~b &&& c)) + 12 * ( ~~~a &&& (b &&& c)) + 8 * (a &&& ( ~~~b &&& c)) - 2 * (a &&& (b &&& c)) = - 2 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1671 (x y : BitVec w) : +theorem e_1671 : - 3 * (b ^^^ (a &&& ~~~c)) + 1 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) - 11 * (a ||| ~~~c) - 1 * ((b &&& c) ||| (a &&& (b ||| c))) + 11 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) - 1 * (b ^^^ ( ~~~a &&& (b ^^^ c))) + 4 * ( ~~~c &&& (a ^^^ b)) - 1 * ((a &&& ~~~b) ||| (b ^^^ c)) + 5 * a - 1 * ~~~b - 11 * (a ||| ( ~~~b &&& c)) + 5 * (b ^^^ (a &&& (b ^^^ c))) - 1 * (b ||| ~~~(a ||| c)) - 11 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) - 3 * ( ~~~a &&& ( ~~~b ||| c)) - 2 * ( ~~~b ||| ~~~(a ^^^ c)) + 1 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) + 28 * ~~~(a ||| (b ||| c)) + 18 * ~~~(a ||| ( ~~~b ||| c)) + 18 * ~~~( ~~~a ||| (b ||| c)) + 31 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 8 * ( ~~~a &&& ( ~~~b &&& c)) + 3 * ( ~~~a &&& (b &&& c)) + 29 * (a &&& ( ~~~b &&& c)) + 8 * (a &&& (b &&& c)) = 1 * ((a ||| ~~~b) &&& (b ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1672 (x y : BitVec w) : +theorem e_1672 : 7 * (b ^^^ ( ~~~a ||| (b ||| c))) + 11 * (c ^^^ (a ||| ( ~~~b ||| c))) + 5 * ~~~(a &&& (b ||| c)) - 6 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) - 1 * (b ^^^ (a ||| ( ~~~b &&& c))) + 4 * ~~~(a &&& b) + 2 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) - 7 * (b ^^^ ( ~~~a &&& (b ^^^ c))) - 5 * (c ^^^ ~~~(a ||| b)) + 3 * (a ^^^ ( ~~~b ||| c)) - 2 * (b ^^^ (a &&& (b ||| c))) - 5 * ( ~~~c &&& (a ^^^ b)) + 2 * (b ^^^ ( ~~~a ||| (b &&& c))) + 4 * (b ^^^ c) - 1 * ~~~(b ||| c) + 4 * (b ^^^ (a ||| ~~~c)) - 1 * (b ^^^ (a &&& (b ^^^ c))) + 1 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) - 36 * ~~~(a ||| (b ||| c)) - 15 * ~~~(a ||| ( ~~~b ||| c)) - 26 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 31 * ( ~~~a &&& ( ~~~b &&& c)) - 12 * ( ~~~a &&& (b &&& c)) - 22 * (a &&& ( ~~~b &&& c)) + 8 * (a &&& (b &&& c)) = 29 * ~~~( ~~~a ||| (b ||| c)) - 11 * ~~~(a &&& ~~~a) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1673 (x y : BitVec w) : +theorem e_1673 : - 1 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) + 3 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) - 3 * (b ||| ~~~(a ||| ~~~c)) - 6 * (a ||| ( ~~~b ||| c)) - 1 * (b ^^^ (a ||| ( ~~~b ||| c))) + 2 * ( ~~~c ||| ~~~(a ^^^ b)) - 1 * (c ^^^ (a ||| (b ||| c))) + 5 * (b &&& ~~~(a ^^^ c)) - 1 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) + 2 * (b ^^^ ~~~(a ||| c)) - 1 * (c ^^^ (a ||| ( ~~~b ||| c))) - 2 * (a &&& ~~~c) + 11 * ((a ||| b) &&& ~~~(b ^^^ c)) + 1 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) - 1 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 1 * ~~~( ~~~a ||| (b ^^^ c)) + 2 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) + 7 * (c ||| ~~~(a ^^^ b)) - 7 * ~~~(a ||| (b ||| c)) - 3 * ~~~(a ||| ( ~~~b ||| c)) - 11 * ~~~( ~~~a ||| (b ||| c)) - 3 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 4 * ( ~~~a &&& ( ~~~b &&& c)) - 9 * ( ~~~a &&& (b &&& c)) - 8 * (a &&& ( ~~~b &&& c)) - 21 * (a &&& (b &&& c)) = - 4 * (a &&& ~~~b) - 5 * ~~~( ~~~a ||| (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1674 (x y : BitVec w) : +theorem e_1674 : - 11 * (b ^^^ ~~~(a ||| (b ^^^ c))) + 1 * (b &&& ~~~c) + 2 * ((a ^^^ b) &&& (a ^^^ c)) + 4 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) + 1 * (b &&& (a ||| ~~~c)) + 4 * (b ^^^ ~~~(a &&& ~~~c)) + 2 * ( ~~~c ||| ~~~(a ^^^ b)) + 2 * (b ^^^ (a ||| ~~~c)) + 1 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) - 6 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) - 1 * ~~~( ~~~a ||| (b ^^^ c)) - 11 * ~~~(a ^^^ ( ~~~b &&& c)) - 2 * ~~~(a ^^^ b) - 2 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) - 5 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 11 * ( ~~~b ||| (a ^^^ c)) - 1 * ( ~~~a &&& (b ^^^ c)) - 11 * ~~~(a ||| (b ^^^ c)) + 53 * ~~~(a ||| (b ||| c)) + 18 * ~~~(a ||| ( ~~~b ||| c)) + 17 * ~~~( ~~~a ||| (b ||| c)) + 21 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 12 * ( ~~~a &&& ( ~~~b &&& c)) + 34 * ( ~~~a &&& (b &&& c)) + 25 * (a &&& ( ~~~b &&& c)) + 13 * (a &&& (b &&& c)) = 6 * ( ~~~c &&& ~~~(a ^^^ b)) - 1 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1675 (x y : BitVec w) : +theorem e_1675 : 1 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) + 2 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) + 11 * (b ^^^ (a &&& ( ~~~b ||| c))) - 1 * ~~~(b ^^^ c) + 2 * ~~~(a &&& ~~~a) + 1 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) - 6 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 6 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) - 11 * ~~~( ~~~a &&& (b ||| c)) - 2 * b + 1 * (a ||| (b &&& c)) - 7 * (a &&& (b ||| c)) + 1 * (b ^^^ ( ~~~a ||| (b ||| c))) - 11 * (c ||| ~~~(a ^^^ b)) - 1 * ((b &&& c) ||| (a &&& (b ||| c))) - 3 * (c &&& ~~~(a &&& ~~~b)) - 1 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) - 2 * (c &&& ~~~(a ^^^ b)) + 22 * ~~~(a ||| (b ||| c)) - 8 * ~~~(a ||| ( ~~~b ||| c)) + 4 * ~~~( ~~~a ||| (b ||| c)) + 15 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 12 * ( ~~~a &&& ( ~~~b &&& c)) + 17 * ( ~~~a &&& (b &&& c)) + 22 * (a &&& ( ~~~b &&& c)) + 32 * (a &&& (b &&& c)) = 6 * (c &&& (a ^^^ b)) - 2 * ~~~(a ^^^ ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1676 (x y : BitVec w) : +theorem e_1676 : - 7 * (a ||| (b ||| c)) - 3 * ( ~~~a ||| ( ~~~b &&& c)) - 7 * (a ^^^ (b ||| c)) - 7 * ~~~(b ||| c) - 7 * ~~~(a ^^^ c) + 5 * (b &&& ~~~(a ^^^ c)) - 5 * (c ^^^ ( ~~~a ||| (b ||| c))) - 5 * (c ^^^ ~~~(a ||| (b &&& c))) + 4 * ~~~(a &&& ( ~~~b &&& c)) + 3 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) - 1 * (b ^^^ ~~~(a &&& (b ||| c))) - 7 * ~~~(a &&& c) + 1 * (b ^^^ ~~~(a ||| c)) + 7 * (b ^^^ (a ||| ~~~c)) - 2 * ( ~~~c &&& ~~~(a ^^^ b)) + 2 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) + 11 * (b ^^^ ~~~(a ||| (b ^^^ c))) - 3 * ~~~c + 19 * ~~~(a ||| (b ||| c)) + 21 * ~~~(a ||| ( ~~~b ||| c)) + 16 * ~~~( ~~~a ||| (b ||| c)) + 7 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 15 * ( ~~~a &&& ( ~~~b &&& c)) + 13 * ( ~~~a &&& (b &&& c)) + 17 * (a &&& ( ~~~b &&& c)) - 3 * (a &&& (b &&& c)) = 5 * ( ~~~b &&& ~~~(a ^^^ c)) - 1 * ( ~~~a &&& (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1677 (x y : BitVec w) : +theorem e_1677 : 7 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 1 * ~~~( ~~~a ||| (b &&& c)) + 5 * (c ^^^ (a ||| ( ~~~b ||| c))) - 2 * (c ||| ~~~(a ^^^ b)) + 11 * ( ~~~a &&& (b ||| c)) + 2 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) + 2 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) - 6 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 2 * (b ||| c) - 1 * ((a &&& b) ||| ~~~(b ||| ~~~c)) + 11 * (a ||| ( ~~~b ||| c)) - 6 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) + 3 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) - 3 * ~~~(a ^^^ c) - 3 * (b &&& ~~~c) - 11 * (b ^^^ ( ~~~a ||| (b ^^^ c))) - 2 * ~~~(a ^^^ (b ^^^ c)) - 2 * ~~~( ~~~a &&& (b ||| c)) + 1 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) + 5 * ~~~(a ||| (b ||| c)) + 1 * ~~~(a ||| ( ~~~b ||| c)) - 8 * ~~~( ~~~a ||| (b ||| c)) - 3 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 4 * ( ~~~a &&& ( ~~~b &&& c)) - 5 * ( ~~~a &&& (b &&& c)) + 10 * (a &&& (b &&& c)) = - 14 * (a &&& ( ~~~b &&& c)) + 5 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1678 (x y : BitVec w) : +theorem e_1678 : 5 * ( ~~~c ||| (a ^^^ b)) + 4 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) + 5 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 1 * ((a &&& b) ||| ~~~(b ^^^ c)) + 2 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) - 7 * ~~~(a ||| b) - 6 * (a ||| (b ||| c)) + 2 * (b ^^^ ( ~~~a ||| (b &&& c))) - 3 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) - 3 * (c ||| ~~~(a ||| ~~~b)) + 11 * (c ^^^ ~~~(a ||| (b &&& c))) + 3 * (c ||| ~~~(a ||| b)) + 4 * ~~~(a ^^^ ( ~~~b ||| c)) + 5 * (a &&& ( ~~~b ||| c)) + 4 * ~~~(a &&& ~~~b) + 1 * (b ||| ~~~(a ^^^ c)) + 4 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 4 * ((a ^^^ b) ||| ~~~(a ^^^ c)) - 1 * ~~~(a &&& ( ~~~b &&& c)) - 26 * ~~~(a ||| (b ||| c)) - 24 * ~~~( ~~~a ||| (b ||| c)) - 19 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 2 * ( ~~~a &&& ( ~~~b &&& c)) - 18 * ( ~~~a &&& (b &&& c)) - 32 * (a &&& ( ~~~b &&& c)) - 29 * (a &&& (b &&& c)) = 23 * ~~~(a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1679 (x y : BitVec w) : +theorem e_1679 : 1 * (a ||| (b ||| c)) + 11 * (b &&& ~~~(a ^^^ c)) - 11 * (a &&& ~~~b) + 5 * ( ~~~(a &&& b) &&& (b ^^^ c)) + 7 * ( ~~~c &&& (a ^^^ b)) - 1 * (c ^^^ ~~~(a &&& ~~~b)) - 1 * (a ^^^ (b ^^^ c)) + 1 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) + 11 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) + 4 * ((a &&& b) ||| (b ^^^ c)) - 1 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 2 * (b ^^^ (a ||| (b ||| c))) - 11 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) + 7 * (b ^^^ ( ~~~a ||| (b ^^^ c))) + 2 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 11 * ((a &&& b) ^^^ (b ||| c)) - 1 * (c ||| ~~~(a ||| ~~~b)) + 1 * (c ^^^ ( ~~~a ||| (b ||| c))) + 1 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) - 11 * ~~~(a ||| (b ||| c)) - 26 * ~~~(a ||| ( ~~~b ||| c)) + 10 * ~~~( ~~~a ||| (b ||| c)) - 29 * ( ~~~a &&& ( ~~~b &&& c)) - 23 * ( ~~~a &&& (b &&& c)) - 31 * (a &&& ( ~~~b &&& c)) - 11 * (a &&& (b &&& c)) = - 1 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 7 * ~~~( ~~~a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1680 (x y : BitVec w) : +theorem e_1680 : - 3 * ~~~( ~~~a &&& ( ~~~b ||| c)) + 1 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) - 5 * (b ^^^ (a ||| (b &&& c))) - 2 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) - 1 * (b &&& (a ^^^ c)) + 1 * ~~~(a ^^^ ( ~~~b ||| c)) + 11 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) - 1 * (a &&& (b ^^^ c)) + 7 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) + 5 * (a ^^^ (b &&& c)) - 1 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 6 * ((a ^^^ b) ||| (a ^^^ c)) - 6 * (b ^^^ (a ||| c)) - 2 * (a &&& c) + 1 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 1 * ~~~(a &&& ~~~a) - 11 * (b &&& ~~~(a &&& c)) + 7 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 16 * ~~~(a ||| (b ||| c)) + 16 * ~~~(a ||| ( ~~~b ||| c)) - 9 * ~~~( ~~~a ||| (b ||| c)) + 3 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 11 * ( ~~~a &&& ( ~~~b &&& c)) + 13 * ( ~~~a &&& (b &&& c)) + 18 * (a &&& ( ~~~b &&& c)) - 3 * (a &&& (b &&& c)) = - 1 * (a ||| (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1681 (x y : BitVec w) : +theorem e_1681 : 1 * ( ~~~b &&& (a ^^^ c)) + 2 * ((a ||| ~~~b) &&& (b ^^^ c)) - 6 * (b ||| ~~~(a ^^^ c)) - 2 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) - 1 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 2 * ~~~(b &&& ~~~c) - 1 * ~~~(a ^^^ (b ||| c)) + 1 * b + 1 * (c ^^^ (a &&& ( ~~~b ||| c))) + 2 * (b ^^^ ( ~~~a &&& (b ||| c))) - 1 * (c ^^^ (a &&& ~~~b)) + 4 * (b ^^^ (a ||| c)) + 1 * (a ||| (b &&& c)) - 1 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 2 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 2 * (b &&& ~~~c) - 1 * (b ^^^ (a &&& (b ^^^ c))) - 1 * (c ||| ~~~(a ||| b)) + 2 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) + 13 * ~~~(a ||| (b ||| c)) + 3 * ~~~(a ||| ( ~~~b ||| c)) + 4 * ~~~( ~~~a ||| (b ||| c)) + 3 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 4 * ( ~~~a &&& ( ~~~b &&& c)) + 17 * ( ~~~a &&& (b &&& c)) + 9 * (a &&& ( ~~~b &&& c)) + 10 * (a &&& (b &&& c)) = 3 * ~~~(a &&& c) + 1 * ((a &&& b) ^^^ (b ||| ~~~c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1682 (x y : BitVec w) : +theorem e_1682 : - 7 * (b &&& ~~~(a &&& ~~~c)) + 1 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) + 1 * (a ||| ~~~b) - 2 * (b ^^^ ( ~~~a &&& (b ||| c))) - 1 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 1 * (c ^^^ (a ||| ( ~~~b &&& c))) - 7 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 2 * (b &&& (a ||| ~~~c)) + 1 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) - 3 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) + 4 * (a ||| ( ~~~b &&& c)) - 2 * (b ^^^ ~~~(a ||| c)) - 5 * (c ^^^ ( ~~~a &&& (b ||| c))) - 11 * ~~~( ~~~a &&& (b ^^^ c)) + 1 * (a ||| c) - 2 * ((a &&& b) ^^^ (b ||| c)) - 7 * (c ^^^ ~~~(a ||| ~~~b)) + 7 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) + 11 * (c ^^^ (a &&& ( ~~~b ||| c))) + 7 * ( ~~~(a &&& b) &&& (b ^^^ c)) + 12 * ~~~(a ||| (b ||| c)) + 13 * ~~~(a ||| ( ~~~b ||| c)) - 2 * ~~~( ~~~a ||| (b ||| c)) + 14 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 3 * ( ~~~a &&& (b &&& c)) + 12 * (a &&& ( ~~~b &&& c)) + 31 * (a &&& (b &&& c)) = 3 * (c ^^^ (a ||| (b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1683 (x y : BitVec w) : +theorem e_1683 : 1 * ~~~(a ||| c) + 1 * (c ||| ~~~(a ||| ~~~b)) + 4 * ~~~(a &&& b) - 1 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) - 2 * ((a &&& ~~~b) ||| (b ^^^ c)) - 1 * ~~~(a &&& ( ~~~b &&& c)) + 11 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 4 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) + 11 * (a ||| (b ^^^ c)) + 1 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) - 5 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 1 * (b ^^^ (a &&& ~~~c)) + 7 * (c ^^^ ( ~~~a ||| (b &&& c))) - 3 * ( ~~~c ||| ~~~(a ^^^ b)) + 7 * (c ^^^ ~~~(a ||| b)) + 5 * (a ||| (b &&& c)) + 5 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) - 2 * (c ||| ~~~(a ||| b)) - 1 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) - 16 * ~~~(a ||| (b ||| c)) - 21 * ~~~(a ||| ( ~~~b ||| c)) - 33 * ~~~( ~~~a ||| (b ||| c)) - 21 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 18 * ( ~~~a &&& ( ~~~b &&& c)) - 13 * ( ~~~a &&& (b &&& c)) - 35 * (a &&& ( ~~~b &&& c)) - 18 * (a &&& (b &&& c)) = 6 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1684 (x y : BitVec w) : +theorem e_1684 : 7 * ~~~(a &&& c) - 1 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) - 2 * (b ^^^ ~~~(a &&& (b ||| c))) + 11 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 1 * (b &&& ~~~c) - 6 * ((a &&& c) ^^^ (b ||| c)) - 11 * ((b &&& c) ||| (a &&& (b ||| c))) + 2 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) - 1 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 11 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 7 * ~~~(a ^^^ b) - 11 * (b &&& (a ||| ~~~c)) + 7 * ~~~(b &&& c) - 7 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) + 5 * ((a ^^^ b) ||| (a ^^^ c)) - 5 * (b ^^^ (a ||| ~~~c)) - 2 * (a ||| ( ~~~b &&& c)) - 1 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) + 1 * (a &&& ~~~b) - 12 * ~~~(a ||| (b ||| c)) - 15 * ~~~(a ||| ( ~~~b ||| c)) - 23 * ~~~( ~~~a ||| (b ||| c)) + 6 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 21 * ( ~~~a &&& ( ~~~b &&& c)) + 7 * ( ~~~a &&& (b &&& c)) - 4 * (a &&& ( ~~~b &&& c)) + 27 * (a &&& (b &&& c)) = 3 * (c ^^^ (a ||| (b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1685 (x y : BitVec w) : +theorem e_1685 : - 1 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) + 3 * ( ~~~c ||| (a ^^^ b)) - 1 * ( ~~~b ||| (a ^^^ c)) + 3 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) - 1 * ~~~( ~~~a ||| (b &&& c)) - 3 * ~~~c - 1 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) - 2 * (c ^^^ ~~~(a ||| ~~~b)) + 5 * ~~~( ~~~a &&& (b ^^^ c)) - 7 * (b ^^^ (a &&& (b ||| c))) + 2 * (a ||| c) - 1 * ~~~( ~~~a &&& (b ||| c)) - 7 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 2 * (b ^^^ ~~~(a &&& (b &&& c))) - 2 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) + 2 * ((a &&& b) ^^^ (b ||| ~~~c)) - 5 * ~~~(a &&& ~~~a) - 11 * ( ~~~b &&& ~~~(a ^^^ c)) + 4 * ~~~(a &&& ~~~b) + 1 * ( ~~~a ||| (b &&& c)) + 5 * ~~~( ~~~a &&& ( ~~~b ||| c)) + 5 * ~~~(a ||| (b ||| c)) + 3 * ~~~(a ||| ( ~~~b ||| c)) + 5 * ( ~~~a &&& ( ~~~b &&& c)) - 3 * ( ~~~a &&& (b &&& c)) + 20 * (a &&& ( ~~~b &&& c)) - 12 * (a &&& (b &&& c)) = 2 * ((a ||| ~~~b) &&& (b ^^^ c)) - 2 * ~~~( ~~~a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1686 (x y : BitVec w) : +theorem e_1686 : 11 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) + 3 * (c ^^^ ~~~(a &&& (b ||| c))) + 11 * ~~~( ~~~a &&& (b ^^^ c)) + 5 * ( ~~~a ||| ( ~~~b ||| c)) + 1 * ~~~( ~~~a &&& ( ~~~b &&& c)) - 7 * ~~~(a ^^^ c) - 1 * ~~~( ~~~a ||| ( ~~~b &&& c)) + 4 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 5 * (b ||| ~~~(a ||| ~~~c)) - 6 * ~~~( ~~~a &&& ( ~~~b ||| c)) - 5 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) - 1 * ((a ||| b) &&& ~~~(b ^^^ c)) + 7 * (c &&& ~~~(a &&& b)) + 1 * (b ^^^ ( ~~~a &&& (b ||| c))) - 1 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) - 2 * ((a ^^^ b) &&& ~~~(a ^^^ c)) - 6 * (b ^^^ ( ~~~a ||| (b ^^^ c))) + 2 * ( ~~~c &&& (a ^^^ b)) + 11 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 11 * (c &&& (a ^^^ b)) - 32 * ~~~(a ||| (b ||| c)) - 7 * ~~~(a ||| ( ~~~b ||| c)) - 13 * ~~~( ~~~a ||| (b ||| c)) - 21 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 17 * ( ~~~a &&& ( ~~~b &&& c)) - 53 * ( ~~~a &&& (b &&& c)) - 27 * (a &&& (b &&& c)) = 27 * (a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1687 (x y : BitVec w) : +theorem e_1687 : 1 * ~~~(a &&& ~~~c) - 1 * (c ||| (a &&& ~~~b)) + 5 * ~~~(b ||| c) + 3 * (b ||| ~~~(a ||| c)) - 2 * ~~~b - 2 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) - 1 * ~~~(a &&& b) + 1 * ((a ^^^ b) ||| (a ^^^ c)) - 3 * ((a &&& c) ^^^ (b ||| c)) - 2 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 5 * ~~~(a ||| ~~~c) + 4 * (c ^^^ ~~~(a &&& b)) + 3 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) + 1 * (a &&& ~~~c) + 1 * ( ~~~c &&& (a ^^^ b)) - 5 * ~~~(a ||| b) - 11 * c + 1 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) + 2 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 2 * a - 14 * ~~~(a ||| (b ||| c)) - 13 * ~~~(a ||| ( ~~~b ||| c)) - 18 * ~~~( ~~~a ||| (b ||| c)) - 12 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 23 * ( ~~~a &&& ( ~~~b &&& c)) + 17 * ( ~~~a &&& (b &&& c)) + 3 * (a &&& ( ~~~b &&& c)) - 6 * (a &&& (b &&& c)) = - 11 * (a ||| ~~~c) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1688 (x y : BitVec w) : +theorem e_1688 : - 3 * (c ^^^ ~~~(a &&& b)) - 3 * (c ^^^ (a &&& ~~~b)) + 2 * (b ^^^ ~~~(a ||| c)) + 2 * (b ||| ~~~c) + 1 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) + 5 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) - 7 * ~~~( ~~~a &&& (b &&& c)) - 11 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) + 1 * (c &&& (a ^^^ b)) - 2 * (b ^^^ ~~~(a &&& (b &&& c))) + 4 * ~~~( ~~~a ||| (b &&& c)) + 3 * (a &&& b) - 7 * (b ^^^ (a ||| ( ~~~b &&& c))) + 11 * (a ^^^ (b &&& c)) - 5 * ( ~~~b &&& ~~~(a ^^^ c)) - 11 * ~~~(a &&& (b ^^^ c)) - 3 * ~~~(a &&& (b &&& c)) - 1 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 5 * ~~~b + 7 * ~~~(a &&& ~~~a) + 20 * ~~~(a ||| (b ||| c)) + 22 * ~~~(a ||| ( ~~~b ||| c)) + 17 * ~~~( ~~~a ||| (b ||| c)) - 2 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 31 * ( ~~~a &&& ( ~~~b &&& c)) + 12 * ( ~~~a &&& (b &&& c)) - 4 * (a &&& ( ~~~b &&& c)) + 22 * (a &&& (b &&& c)) = 5 * (c ^^^ ~~~(a &&& (b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1689 (x y : BitVec w) : +theorem e_1689 : 11 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 1 * (a ||| ( ~~~b &&& c)) - 1 * ( ~~~a ||| (b &&& c)) + 7 * (b ||| ~~~c) + 5 * ((a &&& ~~~b) ||| (b ^^^ c)) + 11 * ( ~~~a &&& ( ~~~b ||| c)) - 6 * ( ~~~a &&& (b ||| c)) + 1 * (b ||| (a &&& c)) + 11 * a - 1 * ~~~(a ||| (b ^^^ c)) + 11 * ~~~(a ^^^ ( ~~~b ||| c)) - 2 * (a &&& ~~~c) - 1 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) - 2 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 7 * ((b &&& c) ||| (a &&& (b ||| c))) + 1 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) + 2 * ((a &&& b) ||| ~~~(b ^^^ c)) + 1 * (b ^^^ ( ~~~a &&& (b ||| c))) - 3 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) - 7 * (b ^^^ ( ~~~a ||| (b ||| c))) - 18 * ~~~(a ||| (b ||| c)) - 26 * ~~~(a ||| ( ~~~b ||| c)) - 45 * ~~~( ~~~a ||| (b ||| c)) - 16 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 2 * ( ~~~a &&& ( ~~~b &&& c)) - 7 * ( ~~~a &&& (b &&& c)) - 10 * (a &&& ( ~~~b &&& c)) - 21 * (a &&& (b &&& c)) = - 1 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1690 (x y : BitVec w) : +theorem e_1690 : - 7 * ~~~(a ^^^ c) + 4 * (b ||| c) + 2 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 1 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) + 11 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) + 2 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) - 6 * (c &&& (a ||| b)) - 3 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) - 7 * (c ^^^ (a ||| (b &&& c))) + 2 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) + 3 * (a ||| (b &&& c)) + 5 * ~~~b - 3 * (c ^^^ (a &&& (b ||| c))) - 11 * (b ^^^ ( ~~~a &&& (b ^^^ c))) - 5 * ~~~(b ||| c) + 5 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) - 3 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 2 * ~~~(a ^^^ (b &&& c)) - 1 * ( ~~~a &&& (b ||| c)) - 5 * ( ~~~a ||| (b ||| c)) - 3 * ~~~(a ||| (b ||| c)) - 7 * ~~~(a ||| ( ~~~b ||| c)) + 2 * ~~~( ~~~a ||| (b ||| c)) + 12 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 6 * ( ~~~a &&& ( ~~~b &&& c)) + 4 * ( ~~~a &&& (b &&& c)) - 1 * (a &&& ( ~~~b &&& c)) + 8 * (a &&& (b &&& c)) = - 4 * ( ~~~b ||| (a ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1691 (x y : BitVec w) : +theorem e_1691 : - 2 * (a ||| (b ^^^ c)) + 2 * (a ^^^ b) + 1 * (b ^^^ ( ~~~a &&& (b ^^^ c))) - 2 * (b ^^^ (a ||| ~~~c)) - 11 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 3 * (b ||| (a &&& c)) - 6 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) + 4 * (b &&& (a ||| ~~~c)) - 2 * ~~~(a &&& b) - 1 * (a &&& (b ||| c)) + 4 * (c &&& (a ^^^ b)) + 1 * ~~~(a ||| b) - 5 * (b ^^^ (a &&& (b ^^^ c))) - 6 * (a ||| (b &&& c)) - 1 * c + 2 * ~~~(a ||| ~~~b) - 2 * ~~~(a ^^^ b) - 7 * (c ^^^ ~~~(a &&& (b ||| c))) + 1 * ~~~( ~~~a ||| (b ^^^ c)) - 1 * (b &&& ~~~c) - 6 * (c ^^^ (a ||| ( ~~~b ||| c))) + 1 * ( ~~~a ||| (b ^^^ c)) + 28 * ~~~(a ||| (b ||| c)) + 32 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 10 * ( ~~~a &&& ( ~~~b &&& c)) + 15 * ( ~~~a &&& (b &&& c)) + 33 * (a &&& ( ~~~b &&& c)) + 27 * (a &&& (b &&& c)) = - 11 * ~~~(a ||| ( ~~~b ||| c)) - 39 * ~~~( ~~~a ||| (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1692 (x y : BitVec w) : +theorem e_1692 : - 1 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) - 1 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) + 11 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) - 7 * c + 1 * (c ^^^ ~~~(a &&& ~~~b)) + 2 * (c ^^^ ~~~(a ||| b)) + 2 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) + 1 * (b &&& ~~~(a &&& c)) - 2 * (c &&& (a ||| b)) - 1 * ((a ||| ~~~b) &&& (b ^^^ c)) + 11 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 11 * (b ^^^ (a &&& (b ||| c))) + 4 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) - 1 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) - 6 * ~~~(b ||| c) + 5 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 5 * (a ^^^ ( ~~~b &&& c)) - 1 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) - 1 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) - 1 * (a ||| (b ^^^ c)) - 23 * ~~~(a ||| (b ||| c)) - 40 * ~~~(a ||| ( ~~~b ||| c)) - 22 * ~~~( ~~~a ||| (b ||| c)) - 15 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 2 * ( ~~~a &&& ( ~~~b &&& c)) - 2 * ( ~~~a &&& (b &&& c)) - 14 * (a &&& ( ~~~b &&& c)) + 15 * (a &&& (b &&& c)) = 5 * ((b &&& c) ||| (a &&& (b ||| c))) - 2 * ( ~~~a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1693 (x y : BitVec w) : +theorem e_1693 : 7 * (a ||| ~~~b) + 3 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) - 2 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 2 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) + 11 * (b &&& (a ||| c)) + 5 * (a ||| (b ||| c)) - 7 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) + 5 * (b ||| ~~~(a ||| c)) + 7 * ((a ^^^ b) &&& (a ^^^ c)) - 11 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 2 * ~~~a - 1 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) - 1 * (b ||| ~~~(a ||| ~~~c)) - 1 * ( ~~~b &&& ~~~(a ^^^ c)) - 1 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) + 11 * ((a &&& b) ^^^ (b ||| c)) - 5 * (b ^^^ (a ||| (b ^^^ c))) + 5 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) + 3 * (b ^^^ ~~~(a ||| c)) - 6 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) - 8 * ~~~(a ||| (b ||| c)) - 18 * ~~~(a ||| ( ~~~b ||| c)) + 8 * ~~~( ~~~a ||| (b ||| c)) - 24 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 18 * ( ~~~a &&& ( ~~~b &&& c)) - 26 * ( ~~~a &&& (b &&& c)) - 5 * (a &&& ( ~~~b &&& c)) - 24 * (a &&& (b &&& c)) = - 1 * (b ||| ~~~c) + 3 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1694 (x y : BitVec w) : +theorem e_1694 : 11 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) - 1 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) - 2 * (c &&& (a ||| ~~~b)) + 7 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 5 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 1 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) - 1 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) - 1 * (c ^^^ (a &&& ( ~~~b ||| c))) - 6 * ((a ^^^ b) &&& ~~~(a ^^^ c)) + 1 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) + 2 * (c ^^^ (a &&& ~~~b)) - 1 * ~~~(a ^^^ c) - 5 * ( ~~~(a &&& b) &&& (b ^^^ c)) - 2 * (b &&& ~~~(a &&& ~~~c)) + 1 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) + 4 * (b ||| ~~~(a ||| c)) - 3 * (c ||| (a &&& b)) + 4 * ~~~(a ^^^ (b &&& c)) - 5 * ((a &&& c) ||| ~~~(b ||| c)) + 11 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) - 31 * ~~~(a ||| (b ||| c)) - 5 * ~~~(a ||| ( ~~~b ||| c)) - 2 * ~~~( ~~~a ||| (b ||| c)) - 25 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 5 * ( ~~~a &&& ( ~~~b &&& c)) - 4 * ( ~~~a &&& (b &&& c)) + 1 * (a &&& ( ~~~b &&& c)) - 16 * (a &&& (b &&& c)) = 1 * (a &&& c) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1695 (x y : BitVec w) : +theorem e_1695 : 4 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) + 1 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) + 1 * (b ||| ~~~c) - 3 * ((a &&& c) ^^^ (b ||| c)) + 7 * (b ^^^ (a &&& c)) + 7 * (b ^^^ (a &&& (b ^^^ c))) - 1 * ~~~( ~~~a &&& (b ^^^ c)) + 1 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 5 * (c ^^^ (a ||| (b &&& c))) + 2 * (a &&& ~~~b) + 5 * (b ^^^ ( ~~~a &&& (b ^^^ c))) + 4 * (c ^^^ ( ~~~a ||| (b &&& c))) - 5 * a + 7 * ((a &&& b) ^^^ (b ||| c)) - 5 * (c ||| (a ^^^ b)) - 3 * (a ||| c) + 1 * (a ^^^ ( ~~~b &&& c)) + 2 * ( ~~~a ||| ( ~~~b &&& c)) + 4 * (b ^^^ (a &&& ( ~~~b ||| c))) - 2 * ~~~a - 2 * (a ||| (b &&& c)) - 2 * ~~~(a ||| (b ||| c)) - 27 * ~~~(a ||| ( ~~~b ||| c)) + 7 * ~~~( ~~~a ||| (b ||| c)) - 4 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 9 * ( ~~~a &&& ( ~~~b &&& c)) - 17 * ( ~~~a &&& (b &&& c)) - 22 * (a &&& ( ~~~b &&& c)) + 9 * (a &&& (b &&& c)) = 7 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1696 (x y : BitVec w) : +theorem e_1696 : - 7 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) - 2 * ((a ^^^ b) ||| ~~~(a ^^^ c)) + 11 * ((a ^^^ b) ||| (a ^^^ c)) - 1 * ~~~c - 5 * ~~~( ~~~a &&& (b ^^^ c)) - 6 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) + 2 * (a ||| ~~~b) + 3 * (c ^^^ (a ||| ~~~b)) - 7 * (c ||| ~~~(a ||| b)) + 1 * ((a &&& b) ||| ~~~(b ||| ~~~c)) + 4 * (b ^^^ ( ~~~a ||| (b ^^^ c))) + 1 * ~~~(a ^^^ c) + 11 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 2 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 6 * (a ||| c) + 1 * (a ||| (b &&& c)) - 1 * (b ^^^ (a &&& (b ||| c))) - 1 * ~~~(a &&& ~~~c) + 7 * (c ^^^ (a ||| (b ||| c))) + 1 * (b &&& c) + 2 * ~~~( ~~~a &&& (b &&& c)) + 1 * ~~~(a ||| (b ||| c)) - 22 * ~~~(a ||| ( ~~~b ||| c)) - 10 * ~~~( ~~~a ||| (b ||| c)) - 8 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 3 * ( ~~~a &&& ( ~~~b &&& c)) + 12 * ( ~~~a &&& (b &&& c)) + 11 * (a &&& ( ~~~b &&& c)) - 5 * (a &&& (b &&& c)) = - 3 * (b ^^^ ~~~(a &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1697 (x y : BitVec w) : +theorem e_1697 : 4 * ( ~~~b ||| (a ^^^ c)) + 2 * (a &&& ( ~~~b ||| c)) - 2 * ~~~(a ^^^ (b &&& c)) - 1 * (c ^^^ (a &&& b)) - 7 * ~~~( ~~~a ||| (b ^^^ c)) + 1 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) - 2 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 2 * ~~~(a ||| c) - 2 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) + 3 * (a &&& c) - 2 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) + 5 * (b ^^^ ~~~(a &&& c)) - 5 * (b ||| (a &&& c)) + 1 * (c ||| ~~~(a ^^^ b)) + 11 * (c ^^^ (a ||| ( ~~~b &&& c))) + 11 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 2 * (a &&& b) - 7 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) - 3 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) + 3 * (b ^^^ (a ||| (b &&& c))) - 11 * ~~~(a &&& ( ~~~b ||| c)) - 2 * ((a &&& c) ||| (b &&& ~~~c)) + 17 * ~~~(a ||| (b ||| c)) + 27 * ~~~(a ||| ( ~~~b ||| c)) + 7 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 6 * ( ~~~a &&& ( ~~~b &&& c)) - 6 * ( ~~~a &&& (b &&& c)) - 14 * (a &&& ( ~~~b &&& c)) + 11 * (a &&& (b &&& c)) = 25 * ~~~( ~~~a ||| (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1698 (x y : BitVec w) : +theorem e_1698 : - 1 * ((a &&& b) ||| (b ^^^ c)) - 7 * (b &&& (a ||| ~~~c)) + 1 * (b ^^^ (a ||| c)) - 1 * (c &&& (a ^^^ b)) + 4 * (b &&& (a ^^^ c)) - 1 * ~~~(a ^^^ c) - 1 * (a ^^^ (b &&& c)) - 6 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) + 7 * ~~~(a &&& (b ^^^ c)) + 3 * ~~~(a &&& (b &&& c)) - 1 * (c &&& ~~~(a &&& ~~~b)) - 2 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) + 2 * ~~~(a ||| ~~~c) - 5 * (b ^^^ (a &&& ~~~c)) + 11 * ((a ||| b) &&& (b ^^^ c)) + 1 * ~~~(a &&& ~~~b) - 1 * (c &&& (a ||| ~~~b)) - 2 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) + 4 * (b &&& ~~~(a ^^^ c)) - 7 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 6 * ~~~(a ^^^ ( ~~~b &&& c)) + 1 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) + 23 * ~~~(a ||| (b ||| c)) + 12 * ~~~(a ||| ( ~~~b ||| c)) + 2 * ~~~( ~~~a ||| (b ||| c)) + 7 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 2 * ( ~~~a &&& ( ~~~b &&& c)) + 1 * (a &&& ( ~~~b &&& c)) + 22 * (a &&& (b &&& c)) = - 1 * (a &&& ( ~~~b ||| c)) + 11 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1699 (x y : BitVec w) : +theorem e_1699 : 1 * ~~~(a ||| ( ~~~b &&& c)) + 2 * (c ^^^ ~~~(a &&& ~~~b)) - 3 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) + 2 * (b ||| (a &&& ~~~c)) - 3 * ~~~( ~~~a &&& (b ^^^ c)) + 7 * ~~~(a ^^^ ( ~~~b ||| c)) + 3 * (b ^^^ ~~~(a &&& (b &&& c))) - 1 * ~~~(a ^^^ (b ^^^ c)) + 1 * ( ~~~b ||| ~~~(a ^^^ c)) + 1 * ~~~(a ||| c) + 7 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) - 7 * (c ^^^ ( ~~~a ||| (b &&& c))) + 1 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) + 11 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) + 5 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) + 5 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) - 1 * ( ~~~b ||| (a ^^^ c)) - 11 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 2 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) + 2 * ~~~(a ^^^ (b ||| c)) + 1 * (b ^^^ ~~~(a &&& (b ^^^ c))) - 31 * ~~~(a ||| (b ||| c)) - 18 * ~~~(a ||| ( ~~~b ||| c)) + 4 * ~~~( ~~~a ||| (b ||| c)) - 1 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 2 * ( ~~~a &&& ( ~~~b &&& c)) - 14 * ( ~~~a &&& (b &&& c)) - 12 * (a &&& ( ~~~b &&& c)) - 30 * (a &&& (b &&& c)) = - 2 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1700 (x y : BitVec w) : +theorem e_1700 : 4 * (c ^^^ (a &&& ~~~b)) + 4 * ~~~(a ^^^ (b ^^^ c)) - 7 * (b ||| ~~~(a ||| ~~~c)) - 2 * ((a ^^^ b) &&& (a ^^^ c)) - 6 * ~~~(a ^^^ ( ~~~b ||| c)) + 7 * ( ~~~b ||| (a ^^^ c)) + 5 * (b ^^^ (a ||| ( ~~~b ||| c))) - 3 * (b ^^^ ( ~~~a &&& (b ^^^ c))) + 3 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) - 11 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 1 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 2 * ~~~(b ^^^ c) + 7 * (b ||| (a &&& c)) - 5 * ~~~( ~~~a &&& (b ^^^ c)) - 2 * ( ~~~a ||| (b ||| c)) - 1 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) - 1 * (b ^^^ (a ||| (b ^^^ c))) + 1 * ((a &&& c) ||| (b &&& ~~~c)) + 11 * ((a &&& b) ||| (b ^^^ c)) + 1 * ~~~( ~~~a ||| ( ~~~b &&& c)) + 3 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 11 * ~~~(a ||| (b ||| c)) + 4 * ~~~(a ||| ( ~~~b ||| c)) + 6 * ~~~( ~~~a ||| (b ||| c)) - 5 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 1 * ( ~~~a &&& ( ~~~b &&& c)) + 16 * ( ~~~a &&& (b &&& c)) - 27 * (a &&& ( ~~~b &&& c)) + 5 * (a &&& (b &&& c)) = 7 * (c &&& ~~~(a &&& ~~~b)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1701 (x y : BitVec w) : +theorem e_1701 : 5 * ~~~( ~~~a ||| (b &&& c)) - 5 * ((a &&& c) ^^^ (b ||| c)) + 2 * (a ^^^ c) + 5 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) - 11 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) - 2 * ( ~~~a ||| ( ~~~b ||| c)) + 1 * (c ^^^ ~~~(a &&& (b &&& c))) - 5 * (b ^^^ ~~~(a ||| (b &&& c))) - 2 * (b ^^^ (a &&& c)) - 1 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) + 1 * (b &&& (a ||| c)) - 2 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) + 4 * ~~~(a ||| c) - 1 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) + 1 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) + 1 * ~~~(a &&& (b ^^^ c)) + 3 * (b ^^^ (a ||| c)) - 7 * (a ||| c) - 1 * ~~~(a &&& ( ~~~b ||| c)) + 3 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) - 1 * (b ||| ~~~(a ^^^ c)) + 11 * ~~~(a ||| (b ||| c)) + 11 * ~~~(a ||| ( ~~~b ||| c)) + 6 * ~~~( ~~~a ||| (b ||| c)) + 6 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 8 * ( ~~~a &&& ( ~~~b &&& c)) + 30 * ( ~~~a &&& (b &&& c)) + 6 * (a &&& ( ~~~b &&& c)) + 9 * (a &&& (b &&& c)) = - 1 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1702 (x y : BitVec w) : +theorem e_1702 : 2 * ~~~(a &&& (b &&& c)) - 1 * (a &&& ~~~c) - 7 * ~~~(a ^^^ (b ^^^ c)) + 11 * (b ^^^ (a ||| c)) - 6 * (a &&& (b ^^^ c)) + 1 * ~~~(a ^^^ (b &&& c)) + 11 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) + 7 * (b ^^^ ~~~(a ||| c)) - 2 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) - 2 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 2 * (b ^^^ ~~~(a &&& ~~~c)) - 5 * a + 11 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) + 7 * (a ||| (b &&& c)) - 1 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) - 1 * (b ||| (a &&& ~~~c)) + 3 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) - 1 * ~~~(a &&& ~~~c) + 5 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 4 * (c ^^^ (a ||| b)) + 7 * (c ||| ~~~(a ||| b)) - 23 * ~~~(a ||| (b ||| c)) - 41 * ~~~(a ||| ( ~~~b ||| c)) - 31 * ~~~( ~~~a ||| (b ||| c)) - 16 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 42 * ( ~~~a &&& ( ~~~b &&& c)) - 25 * ( ~~~a &&& (b &&& c)) - 27 * (a &&& ( ~~~b &&& c)) - 28 * (a &&& (b &&& c)) = 2 * (b ^^^ ~~~(a &&& (b ^^^ c))) - 5 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1703 (x y : BitVec w) : +theorem e_1703 : 5 * (b ^^^ ~~~(a &&& (b &&& c))) - 1 * (c ||| (a ^^^ b)) + 2 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) - 6 * (c ^^^ (a ||| ( ~~~b ||| c))) + 2 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) - 2 * (a &&& ( ~~~b ||| c)) + 3 * ((a &&& ~~~b) ||| (b ^^^ c)) - 7 * ( ~~~b &&& ~~~(a ^^^ c)) + 4 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) + 5 * ((a &&& c) ||| (b &&& ~~~c)) + 7 * (c ^^^ (a &&& b)) + 2 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) + 5 * (b ^^^ ( ~~~a ||| (b ||| c))) + 1 * (b &&& ~~~c) + 2 * (c ^^^ ~~~(a ||| b)) - 1 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) + 5 * ( ~~~a ||| (b ^^^ c)) - 6 * ~~~( ~~~a &&& (b ^^^ c)) - 5 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) - 2 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) - 1 * ( ~~~c ||| (a ^^^ b)) + 1 * ~~~(a ||| (b ||| c)) - 10 * ~~~(a ||| ( ~~~b ||| c)) + 6 * ~~~( ~~~a ||| (b ||| c)) - 2 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 22 * ( ~~~a &&& ( ~~~b &&& c)) - 11 * ( ~~~a &&& (b &&& c)) - 10 * (a &&& ( ~~~b &&& c)) - 9 * (a &&& (b &&& c)) = - 11 * ~~~(a ||| (b ^^^ c)) + 5 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1704 (x y : BitVec w) : +theorem e_1704 : 5 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) - 1 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 2 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) + 2 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 5 * (c ^^^ ~~~(a &&& b)) - 3 * (b ||| (a &&& c)) - 2 * ~~~(a &&& ( ~~~b &&& c)) + 2 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 7 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) + 2 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) + 7 * ((a ||| b) &&& ~~~(b ^^^ c)) - 11 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 1 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) - 6 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) + 3 * ( ~~~a ||| ( ~~~b ||| c)) - 3 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) + 1 * (a ^^^ (b &&& c)) + 1 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) - 11 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) - 7 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 1 * ((a &&& b) ||| ~~~(b ^^^ c)) - 16 * ~~~(a ||| (b ||| c)) + 24 * ~~~(a ||| ( ~~~b ||| c)) + 13 * ~~~( ~~~a ||| (b ||| c)) + 15 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 16 * ( ~~~a &&& ( ~~~b &&& c)) + 4 * ( ~~~a &&& (b &&& c)) - 7 * (a &&& ( ~~~b &&& c)) + 3 * (a &&& (b &&& c)) = - 4 * (c ^^^ ( ~~~a ||| (b ||| c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1705 (x y : BitVec w) : +theorem e_1705 : - 2 * ( ~~~a ||| ( ~~~b ||| c)) - 1 * (b ||| ~~~c) + 4 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) - 2 * (a &&& ( ~~~b ||| c)) - 2 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) - 2 * ( ~~~a ||| (b &&& c)) + 2 * (b ^^^ ~~~(a &&& (b &&& c))) + 7 * ~~~(a ||| ~~~c) + 11 * (b &&& (a ^^^ c)) + 7 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) + 3 * ((a &&& b) ||| ~~~(b ^^^ c)) + 7 * (c ^^^ (a &&& (b ||| c))) - 3 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) + 11 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 3 * (b ^^^ ( ~~~a ||| (b ^^^ c))) + 2 * (b ^^^ (a &&& (b ^^^ c))) - 6 * (a &&& ~~~c) + 1 * (a ||| ( ~~~b &&& c)) - 1 * (a ||| c) + 1 * (c &&& (a ^^^ b)) + 5 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 12 * ~~~(a ||| (b ||| c)) - 24 * ~~~(a ||| ( ~~~b ||| c)) - 5 * ~~~( ~~~a ||| (b ||| c)) - 29 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 20 * ( ~~~a &&& ( ~~~b &&& c)) - 24 * ( ~~~a &&& (b &&& c)) - 8 * (a &&& ( ~~~b &&& c)) - 19 * (a &&& (b &&& c)) = - 5 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1706 (x y : BitVec w) : +theorem e_1706 : 1 * ~~~(a &&& ( ~~~b &&& c)) + 1 * ( ~~~b &&& ~~~(a ^^^ c)) - 3 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 1 * (a ||| ~~~c) + 11 * ~~~(a &&& ~~~a) + 5 * (c ^^^ ( ~~~a ||| (b ||| c))) + 3 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) + 11 * (c ^^^ ~~~(a &&& ~~~b)) - 1 * (c ^^^ (a &&& ~~~b)) + 4 * (b ^^^ ~~~(a &&& c)) - 1 * ~~~(a &&& b) - 3 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) + 5 * (b ^^^ (a &&& c)) - 1 * (b ||| (a &&& ~~~c)) - 5 * (a ^^^ (b &&& c)) - 6 * ~~~(a &&& ~~~c) + 11 * a + 5 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) - 7 * ~~~( ~~~a ||| (b &&& c)) - 6 * ( ~~~a &&& (b ^^^ c)) + 1 * (c ^^^ ~~~(a ||| ~~~b)) - 29 * ~~~(a ||| (b ||| c)) - 29 * ~~~(a ||| ( ~~~b ||| c)) - 12 * ~~~( ~~~a ||| (b ||| c)) - 44 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 4 * ( ~~~a &&& ( ~~~b &&& c)) - 10 * ( ~~~a &&& (b &&& c)) - 24 * (a &&& ( ~~~b &&& c)) - 21 * (a &&& (b &&& c)) = - 7 * (c ^^^ (a &&& (b ||| c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1707 (x y : BitVec w) : +theorem e_1707 : 7 * ~~~( ~~~a &&& (b ||| c)) + 4 * (b ||| (a &&& c)) + 2 * ~~~(a &&& (b ||| c)) - 5 * ((a ^^^ b) &&& (a ^^^ c)) - 1 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 5 * (b ||| (a ^^^ c)) + 5 * (c ^^^ (a ||| ( ~~~b ||| c))) - 6 * (b ^^^ ( ~~~a &&& (b ||| c))) + 1 * (b ^^^ (a ||| ~~~c)) - 2 * (a &&& ( ~~~b ||| c)) + 3 * (a ||| ~~~c) - 2 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) - 2 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) + 1 * (c &&& ~~~(a &&& b)) + 2 * ~~~a + 3 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) - 6 * (a ^^^ c) - 2 * ((b &&& c) ||| (a &&& (b ||| c))) + 2 * (a ||| c) + 1 * ~~~c - 1 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) + 5 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) + 3 * ~~~(a ||| c) - 29 * ~~~(a ||| (b ||| c)) - 25 * ~~~(a ||| ( ~~~b ||| c)) - 17 * ~~~( ~~~a ||| (b ||| c)) - 12 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 5 * ( ~~~a &&& (b &&& c)) - 16 * (a &&& ( ~~~b &&& c)) = 13 * (a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1708 (x y : BitVec w) : +theorem e_1708 : 11 * (b &&& ~~~c) - 5 * ( ~~~a ||| (b ||| c)) + 1 * ((a &&& b) ||| ~~~(b ||| ~~~c)) + 5 * ( ~~~(a &&& b) &&& (b ^^^ c)) + 1 * ~~~c - 5 * (c ||| (a &&& ~~~b)) - 2 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) - 1 * (c ^^^ ~~~(a &&& (b &&& c))) + 4 * ~~~(a ^^^ c) + 1 * ~~~(b ||| ~~~c) - 3 * (b ||| (a &&& ~~~c)) + 1 * ((a &&& c) ||| ~~~(b ||| c)) - 3 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) - 11 * ~~~(a ||| ~~~b) + 7 * (a ||| ( ~~~b ||| c)) - 2 * (b ^^^ ~~~(a ||| ~~~c)) + 2 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) + 7 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) + 2 * (a &&& b) - 11 * (c ^^^ ~~~(a &&& ~~~b)) - 6 * ~~~a + 11 * ~~~(a ||| (b ||| c)) + 18 * ~~~(a ||| ( ~~~b ||| c)) - 6 * ~~~( ~~~a ||| (b ||| c)) - 6 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 1 * ( ~~~a &&& ( ~~~b &&& c)) + 21 * ( ~~~a &&& (b &&& c)) + 3 * (a &&& ( ~~~b &&& c)) - 4 * (a &&& (b &&& c)) = - 1 * ~~~( ~~~a ||| (b ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1709 (x y : BitVec w) : +theorem e_1709 : - 2 * (b ||| ~~~(a ^^^ c)) - 7 * (b ||| ~~~(a ||| ~~~c)) - 11 * ~~~( ~~~a ||| ( ~~~b &&& c)) + 4 * (b ^^^ (a ||| (b &&& c))) + 1 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) - 1 * ((a &&& ~~~b) ||| (b ^^^ c)) + 1 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) - 5 * (c ||| (a &&& b)) + 3 * (a &&& b) + 1 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) + 1 * ((a ^^^ b) ||| (a ^^^ c)) - 7 * (a ||| ~~~c) + 3 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 1 * (a ^^^ ( ~~~b &&& c)) + 11 * (c ^^^ (a &&& b)) + 1 * ( ~~~a ||| (b ||| c)) - 3 * (c ^^^ (a ||| ( ~~~b &&& c))) + 11 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 2 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) - 2 * (b ^^^ ~~~(a ||| (b &&& c))) + 3 * (b &&& c) - 1 * (b ^^^ ( ~~~a &&& (b ^^^ c))) - 1 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 7 * (b ^^^ ~~~(a &&& ~~~c)) - 2 * ~~~(a ||| (b ||| c)) + 9 * ~~~(a ||| ( ~~~b ||| c)) + 3 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 23 * ( ~~~a &&& ( ~~~b &&& c)) - 25 * (a &&& ( ~~~b &&& c)) + 15 * (a &&& (b &&& c)) = 14 * ( ~~~a &&& (b &&& c)) - 7 * (c &&& ~~~(a &&& ~~~b)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1710 (x y : BitVec w) : +theorem e_1710 : - 1 * (b ^^^ (a ||| (b &&& c))) - 1 * (b ^^^ ~~~(a &&& (b ||| c))) + 1 * ~~~(a &&& ( ~~~b ||| c)) - 2 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) + 1 * (b &&& ~~~c) + 11 * (b ^^^ ( ~~~a ||| (b ^^^ c))) + 7 * ( ~~~b ||| (a ^^^ c)) + 2 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) - 6 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) - 5 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) + 2 * (c ^^^ ( ~~~a ||| (b ||| c))) - 2 * ( ~~~b ||| ~~~(a ^^^ c)) - 3 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) - 11 * (b ^^^ ( ~~~a ||| (b &&& c))) + 5 * (b &&& (a ^^^ c)) - 2 * a + 4 * ( ~~~a &&& (b ||| c)) - 5 * (a ||| ~~~c) + 4 * (a ^^^ ( ~~~b &&& c)) + 1 * (c &&& (a ||| b)) + 1 * ((a &&& c) ||| (b &&& ~~~c)) - 1 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) - 11 * ( ~~~c ||| ~~~(a ^^^ b)) + 9 * ~~~(a ||| (b ||| c)) + 23 * ~~~(a ||| ( ~~~b ||| c)) + 21 * ~~~( ~~~a ||| (b ||| c)) + 9 * ( ~~~a &&& ( ~~~b &&& c)) - 2 * ( ~~~a &&& (b &&& c)) - 10 * (a &&& ( ~~~b &&& c)) + 13 * (a &&& (b &&& c)) = - 18 * ~~~( ~~~a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1711 (x y : BitVec w) : +theorem e_1711 : - 1 * ~~~( ~~~a &&& (b &&& c)) - 1 * (b ^^^ (a ||| ~~~c)) - 7 * ~~~(a &&& ~~~b) + 11 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) + 11 * ( ~~~b ||| (a ^^^ c)) + 2 * ((a &&& b) ^^^ (b ||| ~~~c)) + 7 * (b ^^^ ~~~(a ||| c)) + 2 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) - 6 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 1 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) + 5 * (c ||| ~~~(a ||| ~~~b)) - 1 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 3 * (b ||| (a &&& ~~~c)) + 2 * ((a ^^^ b) ||| (a ^^^ c)) + 1 * (c ^^^ ~~~(a &&& (b &&& c))) - 7 * (a &&& (b ||| c)) - 2 * (c &&& (a ||| b)) - 3 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) - 3 * ~~~( ~~~a ||| (b ^^^ c)) - 2 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) + 1 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 2 * ~~~(a ^^^ b) - 14 * ~~~(a ||| (b ||| c)) - 5 * ~~~(a ||| ( ~~~b ||| c)) - 15 * ~~~( ~~~a ||| (b ||| c)) - 20 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 28 * ( ~~~a &&& ( ~~~b &&& c)) - 29 * ( ~~~a &&& (b &&& c)) - 11 * (a &&& ( ~~~b &&& c)) - 5 * (a &&& (b &&& c)) = - 11 * (a ^^^ c) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1712 (x y : BitVec w) : +theorem e_1712 : - 11 * ~~~( ~~~a &&& (b ^^^ c)) + 5 * ~~~( ~~~a &&& (b ||| c)) + 3 * ((a &&& b) ||| ~~~(b ||| ~~~c)) + 4 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) + 11 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) - 2 * ((a &&& b) ||| ~~~(b ||| c)) + 1 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) + 1 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) - 1 * (a ||| ~~~b) + 2 * (b &&& ~~~(a ^^^ c)) + 2 * (b ^^^ (a &&& ( ~~~b ||| c))) - 1 * (b ^^^ ~~~(a &&& (b ^^^ c))) - 2 * ~~~a + 11 * (b ^^^ (a &&& ~~~c)) + 3 * ~~~( ~~~a &&& ( ~~~b &&& c)) + 2 * (a ||| (b &&& c)) - 1 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) - 1 * ~~~(a &&& b) - 1 * ((a &&& c) ^^^ (b ||| c)) + 2 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) - 1 * ( ~~~(a ||| b) ||| (b ^^^ c)) + 1 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 2 * ~~~(a ||| (b ||| c)) - 32 * ~~~(a ||| ( ~~~b ||| c)) - 30 * ~~~( ~~~a ||| (b ||| c)) - 11 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 16 * ( ~~~a &&& ( ~~~b &&& c)) - 11 * ( ~~~a &&& (b &&& c)) - 18 * (a &&& ( ~~~b &&& c)) - 26 * (a &&& (b &&& c)) = - 2 * ~~~(a ^^^ (b ^^^ c)) - 5 * (c ^^^ (a ||| b)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1713 (x y : BitVec w) : +theorem e_1713 : - 2 * (b ^^^ (a ||| ( ~~~b &&& c))) + 11 * ((a &&& b) ||| ~~~(b ||| c)) - 7 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) - 6 * ~~~(a &&& c) - 2 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 1 * (a ||| (b ^^^ c)) - 11 * (b ^^^ ~~~(a ||| (b &&& c))) + 3 * (b ^^^ ( ~~~a &&& (b ||| c))) - 6 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) + 1 * ((a &&& c) ^^^ (b ||| c)) - 2 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) - 1 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) + 4 * ( ~~~a &&& ( ~~~b ||| c)) + 3 * ~~~(a ^^^ ( ~~~b &&& c)) - 2 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) + 11 * (a &&& ( ~~~b ||| c)) + 1 * (c ||| (a ^^^ b)) - 3 * ~~~( ~~~a &&& (b &&& c)) - 1 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) + 7 * ( ~~~b &&& (a ^^^ c)) - 3 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 1 * (c &&& (a ||| b)) - 1 * (b &&& (a ||| c)) + 13 * ~~~(a ||| (b ||| c)) + 28 * ~~~(a ||| ( ~~~b ||| c)) - 14 * ~~~( ~~~a ||| (b ||| c)) + 22 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 13 * ( ~~~a &&& ( ~~~b &&& c)) + 16 * ( ~~~a &&& (b &&& c)) - 12 * (a &&& ( ~~~b &&& c)) = 8 * (a &&& (b &&& c)) - 7 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1714 (x y : BitVec w) : +theorem e_1714 : - 11 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) - 2 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) + 1 * (a &&& (b ^^^ c)) + 2 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 2 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 1 * ~~~(a &&& (b &&& c)) - 2 * ( ~~~c &&& (a ^^^ b)) + 2 * (b ||| (a &&& c)) - 3 * (b ^^^ (a ||| ( ~~~b &&& c))) - 6 * (b &&& (a ||| ~~~c)) - 6 * (c ^^^ ( ~~~a ||| (b ||| c))) + 5 * (a ||| ~~~b) - 1 * ((a &&& b) ||| ~~~(b ||| c)) + 11 * ((b &&& c) ||| (a &&& (b ||| c))) - 1 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) - 3 * ~~~(b ^^^ c) - 1 * (b ||| ~~~(a ^^^ c)) + 7 * ~~~(a &&& ~~~a) - 2 * (a ^^^ (b ||| c)) + 1 * c + 5 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 7 * (c ^^^ ~~~(a &&& (b ||| c))) + 11 * ( ~~~(a &&& b) &&& (b ^^^ c)) - 11 * (b ^^^ (a &&& c)) + 21 * ~~~(a ||| (b ||| c)) + 14 * ~~~(a ||| ( ~~~b ||| c)) + 11 * ~~~( ~~~a ||| (b ||| c)) + 10 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 10 * ( ~~~a &&& ( ~~~b &&& c)) - 21 * (a &&& ( ~~~b &&& c)) = - 7 * ( ~~~a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1715 (x y : BitVec w) : +theorem e_1715 : 4 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) + 3 * (c ^^^ ~~~(a &&& (b ||| c))) + 7 * ~~~(a ||| ~~~b) + 4 * ~~~(b ^^^ c) + 2 * ( ~~~b &&& (a ^^^ c)) - 3 * (b ^^^ ( ~~~a &&& (b ^^^ c))) + 1 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) + 7 * (c ^^^ (a ||| (b ||| c))) + 5 * ~~~(a &&& ~~~b) + 11 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) + 2 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 5 * (a ||| c) - 5 * ( ~~~a ||| (b ^^^ c)) + 1 * ~~~(a ||| ( ~~~b &&& c)) - 5 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) + 2 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 1 * ~~~(a &&& b) - 3 * ((a &&& ~~~b) ||| (b ^^^ c)) + 2 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) - 3 * (b ^^^ ~~~(a &&& c)) - 1 * (b ||| (a &&& ~~~c)) + 3 * ((a &&& b) ||| ~~~(b ||| ~~~c)) - 16 * ~~~(a ||| (b ||| c)) - 15 * ~~~(a ||| ( ~~~b ||| c)) - 24 * ~~~( ~~~a ||| (b ||| c)) - 9 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 10 * ( ~~~a &&& ( ~~~b &&& c)) - 23 * ( ~~~a &&& (b &&& c)) + 2 * (a &&& ( ~~~b &&& c)) - 13 * (a &&& (b &&& c)) = 6 * ~~~( ~~~a &&& ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1716 (x y : BitVec w) : +theorem e_1716 : 2 * ((a ^^^ b) ||| (a ^^^ c)) - 6 * ~~~(a ||| ~~~c) - 11 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) + 11 * (b ^^^ (a &&& ( ~~~b ||| c))) + 5 * (a &&& ~~~c) - 1 * (c ^^^ ~~~(a ||| ~~~b)) + 4 * ( ~~~b &&& ~~~(a ^^^ c)) + 11 * ( ~~~c ||| (a ^^^ b)) - 1 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) - 7 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) - 3 * (c &&& ~~~(a &&& ~~~b)) - 11 * (c ^^^ (a ||| (b ||| c))) - 1 * ~~~(a &&& ~~~c) - 2 * (c &&& ~~~(a &&& b)) - 1 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) - 1 * (c ^^^ ( ~~~a ||| (b ||| c))) + 1 * ~~~b + 2 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) - 5 * (c ||| ~~~(a ||| ~~~b)) + 1 * ~~~(a ^^^ (b ||| c)) + 7 * (c ||| (a &&& ~~~b)) + 4 * (b ^^^ ~~~(a ||| c)) - 11 * ((a &&& c) ^^^ (b ||| c)) - 8 * ~~~(a ||| (b ||| c)) + 22 * ~~~(a ||| ( ~~~b ||| c)) - 8 * ~~~( ~~~a ||| (b ||| c)) - 4 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 29 * ( ~~~a &&& ( ~~~b &&& c)) - 22 * (a &&& ( ~~~b &&& c)) + 10 * (a &&& (b &&& c)) = 5 * ( ~~~a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1717 (x y : BitVec w) : +theorem e_1717 : - 7 * (a &&& (b ||| c)) - 1 * (b ||| ~~~(a ||| c)) - 7 * (c ^^^ (a ||| ~~~b)) - 5 * ~~~(a ^^^ (b &&& c)) + 1 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) - 7 * (c ^^^ (a &&& b)) + 7 * ~~~(a ||| b) + 11 * (c ^^^ (a ||| ( ~~~b ||| c))) - 1 * (c ^^^ ~~~(a &&& (b &&& c))) + 3 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) + 3 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) - 1 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) - 11 * ~~~(a ^^^ (b ||| c)) + 7 * ((a &&& c) ||| ~~~(b ||| c)) + 1 * ~~~(a ||| (b &&& c)) + 11 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) - 11 * ~~~(a ||| c) - 3 * (b ||| ~~~(a ^^^ c)) + 2 * (b ||| (a &&& ~~~c)) + 3 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 11 * (b &&& ~~~c) - 7 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) - 6 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) + 14 * ~~~(a ||| (b ||| c)) + 8 * ~~~(a ||| ( ~~~b ||| c)) - 28 * ~~~( ~~~a ||| (b ||| c)) + 1 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 7 * ( ~~~a &&& ( ~~~b &&& c)) + 16 * ( ~~~a &&& (b &&& c)) + 8 * (a &&& ( ~~~b &&& c)) = - 1 * (c ^^^ (a &&& ( ~~~b ||| c))) - 29 * (a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1718 (x y : BitVec w) : +theorem e_1718 : 11 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) + 1 * (a &&& (b ^^^ c)) - 1 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) - 1 * ~~~(a ||| (b ^^^ c)) - 11 * (c ^^^ ( ~~~a ||| (b ||| c))) - 1 * (b ^^^ ~~~(a &&& (b ||| c))) - 7 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 1 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) - 11 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 4 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) + 1 * ~~~(a ^^^ (b ^^^ c)) + 4 * ~~~( ~~~a ||| ( ~~~b &&& c)) - 11 * ~~~(a ^^^ c) + 5 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 1 * ~~~a - 2 * ~~~(a &&& c) - 1 * (a ||| c) - 3 * (c ^^^ (a &&& ~~~b)) + 4 * ((a ^^^ b) &&& (a ^^^ c)) - 1 * (c &&& (a ||| ~~~b)) - 2 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) - 7 * ~~~(b ^^^ c) + 44 * ~~~(a ||| (b ||| c)) + 26 * ~~~(a ||| ( ~~~b ||| c)) + 18 * ~~~( ~~~a ||| (b ||| c)) + 4 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 11 * ( ~~~a &&& ( ~~~b &&& c)) + 16 * ( ~~~a &&& (b &&& c)) + 17 * (a &&& ( ~~~b &&& c)) + 20 * (a &&& (b &&& c)) = - 1 * (a ||| ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1719 (x y : BitVec w) : +theorem e_1719 : - 5 * ~~~(a ||| ~~~b) + 11 * (c ^^^ (a &&& ~~~b)) + 2 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) - 7 * ( ~~~(a &&& b) &&& (b ^^^ c)) - 1 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 1 * (c &&& ~~~(a ^^^ b)) - 6 * (b ^^^ (a ||| (b &&& c))) + 1 * ((a &&& b) ^^^ (b ||| ~~~c)) - 6 * (c ||| ~~~(a ^^^ b)) - 1 * ~~~(a ^^^ ( ~~~b ||| c)) + 7 * (c ^^^ ~~~(a ||| b)) + 2 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 1 * (c ^^^ (a ||| (b ||| c))) - 1 * (b ||| ~~~(a ^^^ c)) - 5 * (c &&& ~~~(a &&& b)) - 7 * ~~~(b ||| ~~~c) - 1 * ~~~(a ^^^ ( ~~~b &&& c)) - 2 * (b ||| c) + 4 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) + 5 * ~~~(a &&& ~~~b) - 11 * (a &&& ~~~c) + 1 * (c ^^^ (a &&& b)) + 4 * ((a ^^^ b) &&& ~~~(a ^^^ c)) - 9 * ~~~(a ||| (b ||| c)) + 13 * ~~~(a ||| ( ~~~b ||| c)) + 7 * ~~~( ~~~a ||| (b ||| c)) + 9 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 9 * ( ~~~a &&& ( ~~~b &&& c)) - 10 * ( ~~~a &&& (b &&& c)) + 17 * (a &&& ( ~~~b &&& c)) - 11 * (a &&& (b &&& c)) = 1 * (a &&& ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1720 (x y : BitVec w) : +theorem e_1720 : 3 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) - 5 * (c ^^^ (a &&& ( ~~~b ||| c))) - 3 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) - 3 * (c ^^^ ~~~(a &&& (b &&& c))) - 1 * ~~~( ~~~a ||| (b ^^^ c)) + 7 * (a &&& ~~~c) + 7 * (b ^^^ ~~~(a &&& c)) - 1 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) - 1 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) - 2 * (b ^^^ ~~~(a ||| (b &&& c))) - 1 * (b ^^^ ~~~(a ||| (b ^^^ c))) - 7 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) + 4 * ((a &&& b) ||| (b ^^^ c)) - 5 * (a &&& ( ~~~b ||| c)) + 1 * ((a ^^^ b) ||| (a ^^^ c)) - 5 * (a ||| ~~~b) + 5 * (a ^^^ (b ^^^ c)) - 11 * ~~~(a &&& (b &&& c)) - 1 * ~~~( ~~~a ||| (b &&& c)) + 4 * (c ^^^ ~~~(a &&& ~~~b)) - 1 * (b &&& ~~~c) + 5 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 2 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) + 2 * ( ~~~b ||| (a ^^^ c)) + 4 * ~~~(a ||| (b ||| c)) + 5 * ~~~(a ||| ( ~~~b ||| c)) + 23 * ~~~( ~~~a ||| (b ||| c)) + 12 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 9 * ( ~~~a &&& ( ~~~b &&& c)) + 10 * (a &&& ( ~~~b &&& c)) + 8 * (a &&& (b &&& c)) = - 24 * ( ~~~a &&& (b &&& c)) - 3 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1721 (x y : BitVec w) : +theorem e_1721 : - 1 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 2 * (a ^^^ c) - 3 * ((a ^^^ b) ||| (a ^^^ c)) - 5 * ((a ||| ~~~b) &&& (b ^^^ c)) - 1 * (c ^^^ (a &&& ( ~~~b ||| c))) + 5 * ( ~~~a ||| (b ^^^ c)) - 7 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) + 2 * (a ^^^ ( ~~~b &&& c)) + 2 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 7 * (c ||| ~~~(a ||| b)) + 7 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 6 * (b ^^^ ( ~~~a ||| (b &&& c))) + 11 * (c &&& ~~~(a ^^^ b)) + 1 * (a ^^^ ( ~~~b ||| c)) - 1 * (a ||| (b ^^^ c)) - 5 * (b ^^^ (a &&& c)) - 6 * (b ||| ~~~(a ||| ~~~c)) + 5 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) + 2 * (a &&& (b ||| c)) - 1 * ((a &&& c) ||| (b &&& ~~~c)) - 3 * (a ||| ~~~c) - 7 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 11 * (c ||| (a &&& b)) + 16 * ~~~(a ||| (b ||| c)) + 16 * ~~~(a ||| ( ~~~b ||| c)) + 13 * ~~~( ~~~a ||| (b ||| c)) + 41 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 25 * ( ~~~a &&& ( ~~~b &&& c)) + 28 * ( ~~~a &&& (b &&& c)) + 20 * (a &&& ( ~~~b &&& c)) + 10 * (a &&& (b &&& c)) = 3 * (a &&& ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1722 (x y : BitVec w) : +theorem e_1722 : 3 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 3 * ( ~~~a ||| ( ~~~b &&& c)) - 5 * (a ^^^ ( ~~~b ||| c)) - 1 * (b &&& c) - 1 * ~~~(a ^^^ (b ||| c)) + 4 * (a ||| ~~~c) - 2 * (a ^^^ b) - 1 * ( ~~~a &&& (b ||| c)) - 6 * (b ^^^ ( ~~~a ||| (b &&& c))) - 7 * (c ^^^ ~~~(a ||| ~~~b)) + 4 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 3 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) - 6 * ~~~b + 2 * (b ^^^ ~~~(a ||| (b &&& c))) + 2 * (c ^^^ ( ~~~a ||| (b ||| c))) + 2 * (b ^^^ (a ||| (b ||| c))) - 7 * (c ^^^ (a &&& ~~~b)) + 1 * (c &&& ~~~(a &&& b)) - 7 * (a ||| ( ~~~b &&& c)) + 1 * ((a &&& b) ^^^ (b ||| ~~~c)) - 2 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) - 1 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) - 1 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) + 12 * ~~~(a ||| (b ||| c)) - 5 * ~~~(a ||| ( ~~~b ||| c)) + 6 * ~~~( ~~~a ||| (b ||| c)) + 3 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 33 * ( ~~~a &&& ( ~~~b &&& c)) + 2 * ( ~~~a &&& (b &&& c)) + 13 * (a &&& ( ~~~b &&& c)) + 12 * (a &&& (b &&& c)) = - 3 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) - 4 * (b ^^^ (a &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1723 (x y : BitVec w) : +theorem e_1723 : 7 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) - 6 * ( ~~~b ||| ~~~(a ^^^ c)) - 1 * (a ||| (b ^^^ c)) + 4 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) - 5 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 7 * ~~~b + 1 * ( ~~~c ||| ~~~(a ^^^ b)) - 1 * (a ||| ~~~c) + 5 * ( ~~~b &&& (a ^^^ c)) - 5 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) + 1 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) - 2 * (b &&& (a ||| c)) - 2 * ( ~~~a ||| (b &&& c)) - 2 * (c ^^^ (a ||| ~~~b)) + 2 * (a &&& ( ~~~b ||| c)) - 11 * ( ~~~a ||| (b ||| c)) - 1 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) + 7 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 7 * (b ^^^ ( ~~~a ||| (b ||| c))) - 1 * (c ||| (a &&& b)) - 1 * ~~~(a ^^^ c) - 7 * ( ~~~a &&& (b ||| c)) - 11 * ~~~( ~~~a &&& ( ~~~b &&& c)) + 12 * ~~~(a ||| (b ||| c)) + 50 * ~~~(a ||| ( ~~~b ||| c)) + 1 * ~~~( ~~~a ||| (b ||| c)) + 17 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 11 * ( ~~~a &&& ( ~~~b &&& c)) + 23 * ( ~~~a &&& (b &&& c)) + 12 * (a &&& ( ~~~b &&& c)) + 38 * (a &&& (b &&& c)) = 1 * ((a &&& c) ^^^ (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1724 (x y : BitVec w) : +theorem e_1724 : - 6 * ~~~(a ^^^ c) - 2 * ~~~(a &&& ( ~~~b &&& c)) - 11 * ((a &&& b) ||| (b ^^^ c)) + 3 * ~~~(a ||| ( ~~~b &&& c)) + 7 * ( ~~~c ||| (a ^^^ b)) - 11 * ~~~(a ^^^ b) - 3 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) + 7 * (a ||| ~~~c) + 2 * (c ^^^ ~~~(a &&& b)) + 4 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) + 2 * (b ||| ~~~(a ||| ~~~c)) - 5 * (b ^^^ (a &&& (b ^^^ c))) + 1 * (a &&& ~~~b) + 1 * ((b &&& c) ||| (a &&& (b ||| c))) + 1 * (c ||| ~~~(a ||| ~~~b)) + 7 * ~~~(a ^^^ ( ~~~b &&& c)) - 2 * (b ^^^ (a ||| ( ~~~b &&& c))) + 5 * (b ^^^ ( ~~~a ||| (b &&& c))) - 1 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) + 4 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) - 1 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 2 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) + 3 * (b ^^^ ~~~(a ||| (b ^^^ c))) - 18 * ~~~(a ||| (b ||| c)) - 6 * ~~~(a ||| ( ~~~b ||| c)) - 16 * ~~~( ~~~a ||| (b ||| c)) - 5 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 16 * ( ~~~a &&& ( ~~~b &&& c)) - 12 * ( ~~~a &&& (b &&& c)) - 5 * (a &&& ( ~~~b &&& c)) + 14 * (a &&& (b &&& c)) = - 2 * (a ||| (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1725 (x y : BitVec w) : +theorem e_1725 : - 1 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) + 2 * (b &&& (a ||| ~~~c)) + 3 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 2 * (b ||| c) - 3 * ~~~(a ||| ( ~~~b &&& c)) - 2 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) - 11 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) - 2 * ~~~(a &&& ( ~~~b &&& c)) - 1 * (c ||| (a ^^^ b)) + 1 * (a &&& b) - 11 * (b ||| ~~~c) - 2 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 1 * ~~~b + 11 * (a ^^^ ( ~~~b &&& c)) + 5 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) + 7 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) + 7 * (b ^^^ (a ||| ( ~~~b &&& c))) + 4 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) - 2 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) + 2 * (c &&& (a ^^^ b)) + 1 * ~~~(a ||| ~~~c) + 2 * (a ||| ( ~~~b &&& c)) - 1 * ~~~( ~~~a &&& ( ~~~b &&& c)) + 4 * (c ^^^ ~~~(a &&& b)) + 15 * ~~~(a ||| (b ||| c)) - 2 * ~~~( ~~~a ||| (b ||| c)) - 14 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 31 * ( ~~~a &&& ( ~~~b &&& c)) + 1 * ( ~~~a &&& (b &&& c)) - 18 * (a &&& ( ~~~b &&& c)) - 2 * (a &&& (b &&& c)) = - 14 * ~~~(a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1726 (x y : BitVec w) : +theorem e_1726 : - 5 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) - 6 * c - 1 * ~~~(a ||| ~~~c) - 1 * ((a &&& b) ^^^ (b ||| ~~~c)) - 5 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) + 4 * (c ^^^ (a ||| (b &&& c))) - 1 * ~~~(a &&& ~~~a) + 1 * (b ^^^ (a ||| c)) - 1 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) - 3 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) + 5 * (b ^^^ (a &&& ~~~c)) - 1 * ((a ^^^ b) &&& (a ^^^ c)) + 11 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 2 * (a ^^^ ( ~~~b &&& c)) - 11 * ((a ||| b) &&& ~~~(b ^^^ c)) + 1 * ~~~(a ^^^ ( ~~~b ||| c)) - 1 * ~~~(a ^^^ (b ||| c)) + 1 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) + 1 * ~~~( ~~~a ||| (b ^^^ c)) - 11 * (b ^^^ ~~~(a &&& (b ||| c))) + 11 * (c ^^^ ~~~(a &&& ~~~b)) + 3 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) - 11 * (a &&& ~~~b) + 8 * ~~~(a ||| (b ||| c)) - 20 * ~~~(a ||| ( ~~~b ||| c)) + 17 * ~~~( ~~~a ||| (b ||| c)) - 6 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 34 * ( ~~~a &&& ( ~~~b &&& c)) + 18 * ( ~~~a &&& (b &&& c)) + 11 * (a &&& ( ~~~b &&& c)) + 29 * (a &&& (b &&& c)) = 11 * ~~~(a ||| (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1727 (x y : BitVec w) : +theorem e_1727 : 3 * (c ^^^ ( ~~~a ||| (b ||| c))) + 11 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) + 11 * (b &&& (a ||| c)) - 1 * ~~~(a ^^^ (b &&& c)) - 7 * ((b &&& c) ||| (a &&& (b ||| c))) - 3 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) - 7 * (c &&& ~~~(a &&& ~~~b)) - 5 * (c ^^^ (a &&& ~~~b)) + 5 * ~~~(a ||| (b ^^^ c)) - 6 * (b ||| ~~~(a ||| ~~~c)) + 11 * b + 2 * (a ||| (b ^^^ c)) - 5 * ~~~(a ^^^ b) + 5 * a + 7 * ( ~~~c ||| ~~~(a ^^^ b)) + 2 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) - 2 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) - 2 * (b ^^^ ~~~(a ||| (b &&& c))) + 3 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) - 3 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) + 1 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 2 * ~~~( ~~~a &&& ( ~~~b &&& c)) - 2 * ((a ^^^ b) ||| (a ^^^ c)) - 10 * ~~~(a ||| (b ||| c)) - 21 * ~~~(a ||| ( ~~~b ||| c)) - 8 * ~~~( ~~~a ||| (b ||| c)) - 27 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 12 * ( ~~~a &&& ( ~~~b &&& c)) + 4 * ( ~~~a &&& (b &&& c)) - 1 * (a &&& ( ~~~b &&& c)) + 12 * (a &&& (b &&& c)) = 1 * (a &&& ~~~c) + 11 * ~~~(b ^^^ c) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1728 (x y : BitVec w) : +theorem e_1728 : 5 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) + 1 * ~~~(a &&& c) - 6 * ~~~( ~~~a &&& ( ~~~b &&& c)) - 1 * (c &&& ~~~(a &&& ~~~b)) + 2 * (b &&& ~~~(a ^^^ c)) - 6 * (c ^^^ ~~~(a ||| (b &&& c))) + 4 * (a ^^^ c) - 1 * (a ||| ~~~c) - 1 * (b ^^^ ( ~~~a ||| (b ||| c))) + 3 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) - 3 * ~~~(b ||| c) + 1 * (b ^^^ (a ||| (b &&& c))) + 1 * (a ||| c) - 1 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 1 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) + 11 * ((a &&& b) ^^^ (b ||| ~~~c)) + 7 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) - 7 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) - 2 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) - 7 * (c ^^^ (a &&& b)) + 2 * (c ^^^ ~~~(a &&& b)) - 5 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) - 5 * ~~~(a ||| (b &&& c)) + 7 * ~~~(a ||| (b ||| c)) - 5 * ~~~(a ||| ( ~~~b ||| c)) - 8 * ~~~( ~~~a ||| (b ||| c)) - 1 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 16 * ( ~~~a &&& ( ~~~b &&& c)) - 1 * ( ~~~a &&& (b &&& c)) + 14 * (a &&& ( ~~~b &&& c)) - 15 * (a &&& (b &&& c)) = - 11 * (b &&& (a ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1729 (x y : BitVec w) : +theorem e_1729 : 2 * ((a ||| b) &&& ~~~(b ^^^ c)) - 1 * (b ^^^ (a &&& ~~~c)) + 7 * ~~~(b &&& c) - 1 * ((a &&& b) ^^^ (b ||| ~~~c)) - 1 * ~~~(a &&& ~~~b) - 1 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) + 3 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 3 * (b &&& ~~~(a &&& ~~~c)) + 1 * (b &&& ~~~(a ^^^ c)) - 6 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 2 * ~~~(a ||| ~~~c) - 1 * ~~~( ~~~a &&& ( ~~~b &&& c)) + 1 * ( ~~~a &&& ( ~~~b ||| c)) + 11 * (a &&& b) + 7 * ~~~(a ||| b) - 2 * (a ^^^ (b ^^^ c)) + 7 * (a ||| (b &&& c)) - 3 * ~~~( ~~~a &&& (b &&& c)) + 3 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 4 * (a ||| b) + 11 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) - 5 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) + 1 * ~~~(a &&& ( ~~~b ||| c)) - 13 * ~~~(a ||| (b ||| c)) - 13 * ~~~(a ||| ( ~~~b ||| c)) - 32 * ~~~( ~~~a ||| (b ||| c)) - 17 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 14 * ( ~~~a &&& ( ~~~b &&& c)) - 16 * ( ~~~a &&& (b &&& c)) - 32 * (a &&& ( ~~~b &&& c)) - 25 * (a &&& (b &&& c)) = - 4 * (b ^^^ (a ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1730 (x y : BitVec w) : +theorem e_1730 : - 1 * (c ^^^ ~~~(a &&& ~~~b)) - 5 * ((a ^^^ b) &&& (a ^^^ c)) + 11 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 5 * ~~~(a &&& (b &&& c)) - 1 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 11 * (b &&& c) - 11 * (b ^^^ ~~~(a ||| c)) - 1 * ( ~~~(a &&& b) &&& (b ^^^ c)) + 7 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) + 3 * (a ^^^ ( ~~~b ||| c)) - 3 * ((a &&& b) ||| ~~~(b ^^^ c)) + 7 * (c ^^^ (a ||| (b &&& c))) + 1 * (c ^^^ ( ~~~a ||| (b &&& c))) - 7 * ((a ||| ~~~b) &&& (b ^^^ c)) + 1 * (b &&& ~~~(a &&& c)) + 1 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) - 1 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) - 7 * (c ^^^ ~~~(a &&& (b &&& c))) + 2 * (a ||| c) - 1 * ( ~~~c &&& (a ^^^ b)) + 3 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) - 11 * (b ^^^ (a ||| (b &&& c))) + 2 * ( ~~~a ||| ( ~~~b ||| c)) - 2 * ((a &&& b) ||| ~~~(b ||| ~~~c)) + 15 * ~~~(a ||| ( ~~~b ||| c)) + 21 * ~~~( ~~~a ||| (b ||| c)) + 3 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 6 * ( ~~~a &&& ( ~~~b &&& c)) + 25 * ( ~~~a &&& (b &&& c)) + 10 * (a &&& ( ~~~b &&& c)) + 30 * (a &&& (b &&& c)) = - 3 * ~~~(a ||| (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1731 (x y : BitVec w) : +theorem e_1731 : 3 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 3 * (c ^^^ ( ~~~a ||| (b ||| c))) + 3 * (c ^^^ ~~~(a &&& ~~~b)) - 1 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 5 * ~~~( ~~~a &&& (b &&& c)) + 11 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 1 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 2 * ~~~(a &&& ~~~b) - 11 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) - 1 * ~~~(a ^^^ (b ^^^ c)) - 1 * ( ~~~a &&& (b ||| c)) - 3 * (b ^^^ ~~~(a &&& ~~~c)) - 11 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) - 6 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) - 6 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) + 7 * (b ^^^ ( ~~~a ||| (b &&& c))) - 11 * ((a ^^^ b) ||| ~~~(a ^^^ c)) - 5 * ( ~~~b &&& ~~~(a ^^^ c)) + 3 * (b &&& (a ^^^ c)) + 3 * (b ^^^ ( ~~~a &&& (b ^^^ c))) - 1 * ~~~( ~~~a ||| ( ~~~b &&& c)) - 2 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) - 1 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) + 1 * ((a ||| b) &&& ~~~(b ^^^ c)) + 6 * ~~~(a ||| (b ||| c)) + 46 * ~~~(a ||| ( ~~~b ||| c)) + 32 * ~~~( ~~~a ||| (b ||| c)) + 9 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 21 * ( ~~~a &&& ( ~~~b &&& c)) + 17 * ( ~~~a &&& (b &&& c)) + 16 * (a &&& ( ~~~b &&& c)) + 29 * (a &&& (b &&& c)) = 6 * ~~~(a ||| ~~~c) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1732 (x y : BitVec w) : +theorem e_1732 : - 3 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 4 * (a ^^^ b) + 2 * (c ^^^ (a &&& (b ||| c))) - 2 * ~~~(a ||| c) + 11 * (b ^^^ (a &&& ~~~c)) - 1 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 3 * (b ||| (a ^^^ c)) - 3 * (c ^^^ ( ~~~a ||| (b &&& c))) + 1 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) + 2 * ((a &&& b) ^^^ (b ||| ~~~c)) + 4 * (b &&& ~~~c) + 1 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 7 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 2 * (c ^^^ (a &&& ~~~b)) + 5 * ~~~( ~~~a ||| (b &&& c)) + 1 * ((a ^^^ b) &&& ~~~(a ^^^ c)) - 2 * (b ||| c) - 1 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) - 1 * (c &&& ~~~(a &&& ~~~b)) + 7 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) + 7 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) + 4 * (b ^^^ (a ||| (b ^^^ c))) + 3 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) + 1 * (b ^^^ (a ||| (b &&& c))) + 6 * ~~~(a ||| (b ||| c)) - 33 * ~~~(a ||| ( ~~~b ||| c)) - 35 * ~~~( ~~~a ||| (b ||| c)) - 7 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 12 * ( ~~~a &&& ( ~~~b &&& c)) - 24 * ( ~~~a &&& (b &&& c)) - 4 * (a &&& ( ~~~b &&& c)) - 24 * (a &&& (b &&& c)) = - 5 * (b ^^^ ( ~~~a ||| (b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1733 (x y : BitVec w) : +theorem e_1733 : 1 * (b ^^^ ~~~(a &&& (b ^^^ c))) - 2 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 4 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 7 * ~~~(a ^^^ ( ~~~b ||| c)) + 11 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) - 11 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 1 * (b ^^^ (a ||| (b ||| c))) - 7 * (b &&& ~~~(a &&& ~~~c)) - 6 * ~~~(a ||| b) - 2 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 1 * (b &&& (a ||| ~~~c)) - 3 * ((a &&& b) ||| ~~~(b ||| c)) - 2 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) - 5 * ~~~( ~~~a ||| ( ~~~b &&& c)) - 2 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) - 7 * (b &&& ~~~(a ^^^ c)) + 1 * b - 3 * ~~~(a &&& ( ~~~b ||| c)) - 2 * (c &&& (a ^^^ b)) + 1 * (a ||| (b &&& c)) + 3 * ~~~( ~~~a ||| (b ^^^ c)) - 5 * (b ^^^ ~~~(a ||| (b ^^^ c))) - 7 * (a ||| ( ~~~b ||| c)) - 1 * (c &&& (a ||| b)) + 36 * ~~~(a ||| (b ||| c)) + 6 * ~~~(a ||| ( ~~~b ||| c)) - 5 * ~~~( ~~~a ||| (b ||| c)) + 25 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 16 * ( ~~~a &&& ( ~~~b &&& c)) + 31 * ( ~~~a &&& (b &&& c)) - 4 * (a &&& ( ~~~b &&& c)) + 28 * (a &&& (b &&& c)) = 2 * (b ||| (a &&& ~~~c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1734 (x y : BitVec w) : +theorem e_1734 : 3 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) - 6 * ~~~(a ^^^ (b &&& c)) - 2 * ( ~~~b ||| (a ^^^ c)) + 2 * (a &&& ( ~~~b ||| c)) + 1 * ~~~c - 1 * (a &&& (b ||| c)) + 1 * (b ^^^ ( ~~~a ||| (b &&& c))) + 5 * (c ^^^ (a ||| ( ~~~b ||| c))) - 6 * ~~~(a ||| ~~~b) - 2 * (c ||| ~~~(a ^^^ b)) - 3 * ( ~~~b &&& (a ^^^ c)) + 2 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 3 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) - 5 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) - 1 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) - 1 * ~~~( ~~~a ||| (b &&& c)) - 6 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) - 1 * (b ^^^ ( ~~~a ||| (b ||| c))) + 1 * ( ~~~(a ||| b) ||| (b ^^^ c)) - 2 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) - 7 * ( ~~~a ||| ( ~~~b ||| c)) + 3 * (c ^^^ ~~~(a &&& (b &&& c))) + 1 * ~~~(a ^^^ ( ~~~b ||| c)) + 11 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) + 18 * ~~~(a ||| (b ||| c)) + 18 * ~~~(a ||| ( ~~~b ||| c)) - 6 * ~~~( ~~~a ||| (b ||| c)) - 7 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 13 * ( ~~~a &&& ( ~~~b &&& c)) + 18 * ( ~~~a &&& (b &&& c)) + 11 * (a &&& ( ~~~b &&& c)) + 11 * (a &&& (b &&& c)) = 2 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1735 (x y : BitVec w) : +theorem e_1735 : 4 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 1 * ~~~(b &&& ~~~c) - 5 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) - 1 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 11 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 7 * (c ^^^ ~~~(a ||| ~~~b)) - 6 * (b ^^^ (a ||| c)) + 1 * ( ~~~b ||| (a ^^^ c)) - 2 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) - 1 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) - 2 * (b &&& c) - 6 * (b ||| ~~~(a ||| ~~~c)) + 1 * (a ||| b) - 1 * ~~~(a &&& (b &&& c)) + 11 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) + 4 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 4 * (c ^^^ (a ||| (b ||| c))) + 2 * (b ^^^ (a ||| ( ~~~b ||| c))) - 7 * ( ~~~c &&& ~~~(a ^^^ b)) + 4 * ~~~( ~~~a ||| (b ^^^ c)) - 3 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 1 * (c ^^^ (a ||| ( ~~~b ||| c))) + 3 * (c ^^^ ~~~(a ||| (b &&& c))) + 4 * (c ^^^ ~~~(a &&& ~~~b)) - 5 * ~~~(a ||| (b ||| c)) + 13 * ~~~(a ||| ( ~~~b ||| c)) + 11 * ~~~( ~~~a ||| (b ||| c)) - 13 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 27 * ( ~~~a &&& ( ~~~b &&& c)) - 19 * ( ~~~a &&& (b &&& c)) + 15 * (a &&& ( ~~~b &&& c)) + 7 * (a &&& (b &&& c)) = - 5 * (b ^^^ ~~~(a ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1736 (x y : BitVec w) : +theorem e_1736 : 1 * (c ||| ~~~(a ^^^ b)) - 1 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 4 * (b ||| (a &&& c)) - 2 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) + 3 * (c ^^^ (a ||| (b ||| c))) - 11 * (a ||| c) + 1 * ( ~~~a ||| (b ^^^ c)) + 2 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) + 2 * (c ^^^ ~~~(a &&& ~~~b)) - 6 * (b &&& c) - 2 * ~~~(a &&& ~~~a) - 2 * ((a &&& c) ||| (b &&& ~~~c)) + 3 * (b ||| c) - 1 * ~~~(a ^^^ (b &&& c)) - 3 * ~~~(a ||| b) + 1 * (a &&& (b ^^^ c)) + 5 * ( ~~~b ||| (a ^^^ c)) + 1 * ~~~( ~~~a ||| (b &&& c)) - 7 * ~~~( ~~~a &&& ( ~~~b &&& c)) + 7 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 4 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) + 1 * ( ~~~a ||| (b ||| c)) + 3 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) + 4 * ~~~(a &&& (b ^^^ c)) + 7 * (a ||| ~~~c) - 2 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) - 21 * ~~~(a ||| (b ||| c)) - 12 * ~~~(a ||| ( ~~~b ||| c)) - 5 * ~~~( ~~~a ||| (b ||| c)) - 10 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 1 * ( ~~~a &&& ( ~~~b &&& c)) - 9 * (a &&& ( ~~~b &&& c)) + 5 * (a &&& (b &&& c)) = 1 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1737 (x y : BitVec w) : +theorem e_1737 : - 1 * (b ^^^ (a &&& (b ^^^ c))) - 11 * ~~~(b ||| c) + 1 * (c ^^^ (a ||| ~~~b)) + 1 * (a &&& ( ~~~b ||| c)) - 3 * ~~~a + 11 * ~~~(a ^^^ (b &&& c)) + 11 * (a ^^^ c) - 5 * (c ^^^ ( ~~~a ||| (b ||| c))) + 4 * (b ^^^ ( ~~~a ||| (b &&& c))) - 11 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) + 3 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) + 4 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) - 2 * ((a ||| b) &&& ~~~(b ^^^ c)) - 1 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 1 * ((a ^^^ b) ||| (a ^^^ c)) - 2 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) - 1 * (c ||| ~~~(a ||| b)) + 1 * (a ||| ( ~~~b &&& c)) + 1 * (b &&& ~~~(a &&& ~~~c)) - 5 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 1 * (b &&& (a ||| ~~~c)) + 4 * ~~~( ~~~a &&& (b ^^^ c)) + 1 * c - 2 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) - 5 * ( ~~~a ||| (b &&& c)) + 12 * ~~~(a ||| (b ||| c)) + 14 * ~~~(a ||| ( ~~~b ||| c)) - 1 * ~~~( ~~~a ||| (b ||| c)) - 18 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 10 * ( ~~~a &&& ( ~~~b &&& c)) + 11 * ( ~~~a &&& (b &&& c)) - 10 * (a &&& ( ~~~b &&& c)) + 5 * (a &&& (b &&& c)) = - 4 * (b ^^^ (a ||| (b ||| c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1738 (x y : BitVec w) : +theorem e_1738 : - 6 * ( ~~~a ||| ( ~~~b ||| c)) + 4 * ( ~~~a ||| (b &&& c)) + 1 * (b ^^^ ~~~(a ||| (b ^^^ c))) - 7 * ( ~~~c ||| ~~~(a ^^^ b)) + 11 * (a ^^^ ( ~~~b &&& c)) - 2 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 5 * ~~~(b &&& ~~~c) + 4 * (c ^^^ ~~~(a ||| b)) - 2 * ((a ||| b) &&& ~~~(b ^^^ c)) + 11 * (c ^^^ ( ~~~a ||| (b ||| c))) - 1 * ((a &&& b) ^^^ (b ||| c)) - 3 * ~~~(a &&& ( ~~~b ||| c)) + 1 * (b &&& ~~~c) + 1 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 7 * ( ~~~(a &&& b) &&& (b ^^^ c)) - 7 * ( ~~~b ||| (a ^^^ c)) + 11 * (b ||| (a &&& c)) - 7 * c - 6 * (b ^^^ (a ||| ( ~~~b ||| c))) - 1 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) - 2 * (a &&& (b ||| c)) + 11 * ((a &&& c) ^^^ (b ||| c)) - 3 * (c ||| (a &&& ~~~b)) - 5 * ((a ^^^ b) &&& ~~~(a ^^^ c)) + 2 * (a ||| ( ~~~b ||| c)) + 7 * ~~~a + 18 * ~~~(a ||| (b ||| c)) - 12 * ~~~(a ||| ( ~~~b ||| c)) + 35 * ~~~( ~~~a ||| (b ||| c)) - 24 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 13 * ( ~~~a &&& ( ~~~b &&& c)) + 39 * (a &&& ( ~~~b &&& c)) + 7 * (a &&& (b &&& c)) = 11 * ~~~( ~~~a &&& (b ^^^ c)) - 5 * (c ||| (a &&& b)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1739 (x y : BitVec w) : +theorem e_1739 : 1 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) + 2 * (b ^^^ (a ||| ( ~~~b &&& c))) + 3 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) - 5 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) - 1 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 4 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) + 5 * ((a &&& b) ||| ~~~(b ||| ~~~c)) - 1 * ~~~a - 1 * ~~~(a &&& (b &&& c)) - 1 * ((a ||| b) &&& (b ^^^ c)) + 7 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) + 11 * (c ^^^ (a &&& ( ~~~b ||| c))) + 5 * ( ~~~a ||| ( ~~~b &&& c)) - 7 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) - 7 * (b ^^^ ( ~~~a ||| (b &&& c))) + 3 * (c ^^^ (a ||| (b &&& c))) + 3 * (a ||| (b &&& c)) + 5 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) - 1 * ~~~( ~~~a &&& (b &&& c)) - 2 * (b ^^^ ~~~(a ||| (b &&& c))) - 2 * (a &&& ~~~b) + 1 * (c ||| (a &&& b)) + 1 * ((a &&& b) ||| ~~~(b ||| c)) + 4 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) + 2 * (b ^^^ ~~~(a ||| ~~~c)) - 1 * (b ^^^ (a &&& ~~~c)) - 3 * (c ^^^ (a &&& b)) - 8 * ~~~(a ||| (b ||| c)) - 24 * ~~~( ~~~a ||| (b ||| c)) - 13 * ( ~~~a &&& ( ~~~b &&& c)) - 29 * ( ~~~a &&& (b &&& c)) - 19 * (a &&& ( ~~~b &&& c)) - 27 * (a &&& (b &&& c)) = - 5 * ~~~(a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1740 (x y : BitVec w) : +theorem e_1740 : 2 * ~~~c - 11 * ~~~(a ^^^ b) + 1 * ~~~(a ||| ( ~~~b &&& c)) + 1 * (b &&& c) + 11 * (b ||| (a ^^^ c)) + 5 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) - 5 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) - 3 * ~~~( ~~~a &&& (b ||| c)) + 5 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) + 3 * ~~~(a &&& (b ^^^ c)) - 1 * (b ^^^ (a ||| (b ||| c))) + 4 * (c ^^^ (a &&& b)) - 2 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) + 5 * (b ^^^ ~~~(a &&& ~~~c)) - 1 * (a &&& b) + 2 * (c ^^^ ~~~(a ||| (b &&& c))) - 7 * b + 4 * ((a &&& b) ^^^ (b ||| c)) - 5 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) + 7 * (b ^^^ ~~~(a &&& (b ^^^ c))) + 2 * (c &&& ~~~(a &&& b)) - 1 * ~~~( ~~~a ||| (b &&& c)) - 2 * (c &&& (a ||| ~~~b)) - 3 * ~~~(a ^^^ (b ^^^ c)) + 1 * (a ||| (b &&& c)) + 7 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) - 8 * ~~~(a ||| (b ||| c)) - 23 * ~~~(a ||| ( ~~~b ||| c)) - 21 * ~~~( ~~~a ||| (b ||| c)) - 4 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 32 * ( ~~~a &&& ( ~~~b &&& c)) - 24 * ( ~~~a &&& (b &&& c)) - 3 * (a &&& ( ~~~b &&& c)) = - 1 * (a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1741 (x y : BitVec w) : +theorem e_1741 : 1 * c + 1 * (a &&& ( ~~~b ||| c)) + 2 * b + 3 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) - 1 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) - 1 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) + 3 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 11 * (b ^^^ ~~~(a &&& ~~~c)) - 2 * (a ^^^ (b ||| c)) + 4 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) + 3 * (c ^^^ (a ||| (b &&& c))) - 3 * (a &&& (b ||| c)) + 1 * (b ^^^ ~~~(a &&& (b ||| c))) + 2 * (c ^^^ ~~~(a &&& b)) - 1 * ~~~( ~~~a &&& ( ~~~b &&& c)) + 2 * (c ^^^ (a &&& b)) - 1 * ~~~b - 6 * (c &&& (a ||| b)) + 2 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) + 2 * ( ~~~a ||| ( ~~~b &&& c)) - 5 * (a ||| ( ~~~b &&& c)) + 1 * ( ~~~(a ||| b) ||| (b ^^^ c)) - 5 * (b ||| (a &&& ~~~c)) - 5 * ((a ^^^ b) ||| ~~~(a ^^^ c)) + 1 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) + 1 * (b &&& (a ||| c)) + 6 * ~~~(a ||| (b ||| c)) - 4 * ~~~(a ||| ( ~~~b ||| c)) - 1 * ~~~( ~~~a ||| (b ||| c)) + 11 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 3 * ( ~~~a &&& (b &&& c)) + 23 * (a &&& ( ~~~b &&& c)) + 9 * (a &&& (b &&& c)) = - 5 * (c ^^^ (a ||| b)) - 1 * ( ~~~a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1742 (x y : BitVec w) : +theorem e_1742 : 1 * ~~~(a ^^^ (b &&& c)) - 11 * ( ~~~b &&& ~~~(a ^^^ c)) + 2 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 5 * (b ^^^ ( ~~~a ||| (b ||| c))) - 1 * (c ^^^ (a &&& ~~~b)) + 5 * (a ^^^ (b ^^^ c)) - 1 * (c ^^^ (a ||| (b &&& c))) + 7 * ~~~( ~~~a &&& (b &&& c)) + 1 * (b ||| ~~~(a ||| ~~~c)) - 2 * (b ^^^ (a ||| c)) + 1 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 1 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 1 * (b &&& (a ||| c)) - 2 * ((a &&& c) ||| ~~~(b ||| c)) + 3 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) - 7 * ( ~~~b ||| (a ^^^ c)) - 5 * ~~~(a ^^^ ( ~~~b &&& c)) + 4 * (c &&& (a ||| ~~~b)) - 2 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) - 1 * (b ^^^ (a ||| (b &&& c))) - 3 * ~~~( ~~~a &&& ( ~~~b &&& c)) - 7 * (a ^^^ c) - 5 * (c ^^^ (a ||| (b ||| c))) + 1 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) - 7 * (b ||| (a &&& ~~~c)) + 14 * ~~~(a ||| (b ||| c)) + 3 * ~~~(a ||| ( ~~~b ||| c)) + 20 * ~~~( ~~~a ||| (b ||| c)) + 17 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 4 * ( ~~~a &&& ( ~~~b &&& c)) + 28 * ( ~~~a &&& (b &&& c)) + 10 * (a &&& ( ~~~b &&& c)) - 7 * (a &&& (b &&& c)) = - 2 * (a &&& (b ||| c)) - 1 * (b ^^^ ~~~(a &&& (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1743 (x y : BitVec w) : +theorem e_1743 : - 6 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) - 1 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) + 7 * (b ||| ~~~c) + 11 * (b &&& (a ||| c)) - 1 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 1 * (b ||| ~~~(a ^^^ c)) + 2 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) + 3 * (a ^^^ b) - 7 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) + 7 * (b ^^^ ~~~(a ||| ~~~c)) - 3 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) - 2 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) + 1 * (a ||| ~~~c) - 11 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) + 1 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) + 5 * (b ^^^ (a &&& (b ||| c))) + 2 * (b ^^^ (a ||| (b &&& c))) + 4 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) + 2 * ~~~( ~~~a &&& (b &&& c)) - 2 * ( ~~~(a &&& b) &&& (b ^^^ c)) - 7 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) + 11 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) + 1 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 11 * (c ^^^ ~~~(a ||| ~~~b)) + 1 * ((a ^^^ b) &&& ~~~(a ^^^ c)) - 3 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) + 1 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) - 8 * ~~~(a ||| ( ~~~b ||| c)) - 4 * ~~~( ~~~a ||| (b ||| c)) - 30 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 23 * ( ~~~a &&& ( ~~~b &&& c)) - 12 * ( ~~~a &&& (b &&& c)) + 4 * (a &&& ( ~~~b &&& c)) = 10 * (a &&& (b &&& c)) - 7 * (b ^^^ ( ~~~a ||| (b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1744 (x y : BitVec w) : +theorem e_1744 : - 2 * (b ^^^ (a ||| (b ^^^ c))) + 1 * ~~~( ~~~a &&& ( ~~~b &&& c)) - 7 * (a ^^^ (b &&& c)) + 4 * (c ^^^ ~~~(a &&& (b ||| c))) + 4 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) - 5 * (b &&& c) - 7 * ~~~(a &&& ~~~c) - 6 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 1 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) + 2 * (b ^^^ (a &&& ( ~~~b ||| c))) - 2 * (a ||| c) + 2 * (c ^^^ (a ||| (b &&& c))) + 7 * ~~~(a ||| (b ^^^ c)) - 6 * ((a &&& c) ||| (b &&& ~~~c)) + 4 * (a &&& (b ^^^ c)) - 7 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) - 2 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) - 6 * (b ^^^ ~~~(a &&& c)) + 5 * ~~~(b &&& ~~~c) + 2 * (c ^^^ (a &&& ( ~~~b ||| c))) + 7 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 5 * ~~~(a ||| (b &&& c)) + 1 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 1 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 5 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) - 2 * (a ||| (b ||| c)) - 11 * ~~~(a ||| (b ||| c)) + 21 * ~~~(a ||| ( ~~~b ||| c)) + 12 * ~~~( ~~~a ||| (b ||| c)) + 5 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 10 * ( ~~~a &&& ( ~~~b &&& c)) - 3 * ( ~~~a &&& (b &&& c)) + 13 * (a &&& ( ~~~b &&& c)) + 23 * (a &&& (b &&& c)) = 3 * ( ~~~c ||| ~~~(a ^^^ b)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1745 (x y : BitVec w) : +theorem e_1745 : 1 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) + 5 * ~~~(b ^^^ c) + 1 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 5 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) + 11 * (c &&& (a ||| b)) - 2 * (c ^^^ (a &&& b)) + 7 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 6 * (b ||| (a &&& c)) + 2 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 5 * (a &&& ( ~~~b ||| c)) - 7 * (c ^^^ (a ||| b)) - 1 * (b &&& ~~~(a &&& c)) - 1 * ( ~~~a &&& (b ||| c)) + 2 * ( ~~~a ||| (b ||| c)) + 1 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) - 1 * ~~~b - 5 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) + 7 * (a &&& ~~~c) + 3 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 5 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 2 * (b ^^^ (a &&& ( ~~~b ||| c))) + 5 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 2 * ((a ^^^ b) &&& ~~~(a ^^^ c)) + 7 * ((a &&& ~~~b) ||| (b ^^^ c)) - 2 * (b ^^^ ~~~(a &&& (b &&& c))) + 11 * (a ||| c) - 17 * ~~~(a ||| (b ||| c)) + 4 * ~~~(a ||| ( ~~~b ||| c)) - 39 * ~~~( ~~~a ||| (b ||| c)) - 18 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 17 * ( ~~~a &&& ( ~~~b &&& c)) - 11 * ( ~~~a &&& (b &&& c)) - 35 * (a &&& ( ~~~b &&& c)) - 23 * (a &&& (b &&& c)) = 6 * (b ||| ~~~(a ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1746 (x y : BitVec w) : +theorem e_1746 : - 1 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 1 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) - 1 * (c ||| (a &&& b)) + 2 * (b ||| (a ^^^ c)) + 11 * ( ~~~a &&& (b ||| c)) + 1 * ~~~(a ^^^ ( ~~~b ||| c)) + 2 * ( ~~~b &&& (a ^^^ c)) + 3 * ~~~(b &&& ~~~c) - 1 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) - 6 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) + 4 * ~~~(a ||| b) + 2 * ~~~b + 1 * (b ^^^ ~~~(a &&& c)) + 4 * ~~~(b ||| ~~~c) - 1 * (c ||| (a ^^^ b)) - 6 * (b ||| ~~~(a ||| ~~~c)) - 3 * a - 6 * ~~~(a &&& (b ||| c)) - 1 * ~~~(a ||| ~~~c) + 2 * (a ||| (b ||| c)) + 1 * (a ||| ( ~~~b &&& c)) + 7 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 3 * (a &&& c) + 5 * ~~~( ~~~a ||| (b ^^^ c)) - 11 * ~~~(b ||| c) - 7 * ( ~~~c ||| (a ^^^ b)) - 1 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 9 * ~~~(a ||| (b ||| c)) + 12 * ~~~(a ||| ( ~~~b ||| c)) + 14 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 10 * ( ~~~a &&& ( ~~~b &&& c)) + 8 * ( ~~~a &&& (b &&& c)) - 3 * (a &&& ( ~~~b &&& c)) + 6 * (a &&& (b &&& c)) = - 12 * ~~~( ~~~a ||| (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1747 (x y : BitVec w) : +theorem e_1747 : 1 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) - 3 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) + 11 * (a ^^^ (b ||| c)) + 1 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) - 1 * ( ~~~c ||| ~~~(a ^^^ b)) + 1 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) - 1 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) - 6 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) + 11 * (c ^^^ ~~~(a ||| b)) + 1 * ((a ^^^ b) ||| ~~~(a ^^^ c)) - 3 * ( ~~~(a &&& b) &&& (b ^^^ c)) - 5 * (b &&& (a ||| ~~~c)) + 7 * (b ^^^ c) + 5 * (a ||| (b ^^^ c)) + 5 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) + 1 * (c ^^^ (a ||| (b ||| c))) - 7 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) - 2 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 2 * (c ^^^ (a ||| b)) - 3 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) - 7 * ((a &&& c) ^^^ (b ||| c)) - 2 * ~~~( ~~~a ||| (b &&& c)) - 11 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) + 2 * b - 1 * (b ^^^ ~~~(a &&& c)) - 2 * ~~~(a &&& (b &&& c)) + 10 * ~~~(a ||| (b ||| c)) - 6 * ~~~(a ||| ( ~~~b ||| c)) + 13 * ~~~( ~~~a ||| (b ||| c)) - 3 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 5 * ( ~~~a &&& ( ~~~b &&& c)) - 2 * ( ~~~a &&& (b &&& c)) - 13 * (a &&& ( ~~~b &&& c)) + 4 * (a &&& (b &&& c)) = - 2 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1748 (x y : BitVec w) : +theorem e_1748 : - 7 * (c ||| (a ^^^ b)) - 1 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) - 5 * b + 1 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) + 2 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 3 * (b ^^^ (a ||| c)) + 1 * (c ^^^ (a ||| (b ||| c))) + 11 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 1 * (a ||| ~~~b) - 1 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) + 2 * (c ||| ~~~(a ||| b)) - 5 * (b ^^^ (a &&& c)) + 7 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) + 4 * (a ^^^ (b &&& c)) - 2 * ~~~(b ^^^ c) + 11 * (a &&& (b ||| c)) + 3 * ~~~(b &&& c) + 5 * ((a ||| b) &&& ~~~(b ^^^ c)) - 5 * ( ~~~a ||| ( ~~~b &&& c)) + 11 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) - 7 * (b ||| ~~~c) + 2 * (b &&& ~~~c) + 2 * (a ||| (b ^^^ c)) - 11 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) + 2 * (b &&& (a ^^^ c)) + 11 * (b ^^^ ( ~~~a ||| (b &&& c))) + 1 * (c &&& (a ^^^ b)) - 1 * ~~~( ~~~a &&& (b &&& c)) + 16 * ~~~(a ||| ( ~~~b ||| c)) - 20 * ~~~( ~~~a ||| (b ||| c)) - 5 * ( ~~~a &&& ( ~~~b &&& c)) + 22 * ( ~~~a &&& (b &&& c)) - 36 * (a &&& ( ~~~b &&& c)) - 3 * (a &&& (b &&& c)) = 39 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 13 * ~~~(a ||| (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1749 (x y : BitVec w) : +theorem e_1749 : - 6 * (c ^^^ (a &&& ~~~b)) + 4 * ~~~(b ||| ~~~c) + 7 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) + 3 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) - 7 * (c ^^^ ~~~(a &&& (b ||| c))) - 2 * (b ^^^ (a ||| (b &&& c))) - 1 * (b &&& (a ||| ~~~c)) + 3 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) - 5 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) + 5 * (a ||| (b &&& c)) - 6 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 2 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) + 1 * (c ||| (a ^^^ b)) + 2 * ~~~(a ||| ( ~~~b &&& c)) - 11 * ~~~(a &&& (b ^^^ c)) + 4 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 2 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) - 2 * (a ||| ~~~b) + 2 * (b ^^^ (a ||| (b ^^^ c))) + 2 * ((a ||| b) &&& ~~~(b ^^^ c)) + 5 * (b ||| (a &&& ~~~c)) + 5 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) + 1 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) - 11 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) - 2 * (b ^^^ (a ||| (b ||| c))) - 5 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) + 25 * ~~~(a ||| (b ||| c)) + 12 * ~~~(a ||| ( ~~~b ||| c)) + 4 * ~~~( ~~~a ||| (b ||| c)) - 7 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 16 * ( ~~~a &&& ( ~~~b &&& c)) - 4 * ( ~~~a &&& (b &&& c)) - 7 * (a &&& ( ~~~b &&& c)) + 1 * (a &&& (b &&& c)) = - 5 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1750 (x y : BitVec w) : +theorem e_1750 : 4 * ((a ||| b) &&& (b ^^^ c)) - 2 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) - 1 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) + 1 * ( ~~~b ||| ~~~(a ^^^ c)) - 3 * (b ^^^ (a ||| (b ||| c))) + 2 * (b ^^^ ~~~(a &&& c)) - 1 * ~~~(a ^^^ b) - 1 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) - 5 * (a ||| ~~~c) - 6 * ~~~(a &&& ~~~b) - 2 * ( ~~~a &&& (b ^^^ c)) + 1 * (b ^^^ ~~~(a &&& (b ^^^ c))) + 1 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 3 * (b ^^^ ( ~~~a ||| (b ^^^ c))) + 11 * (c ^^^ (a ||| (b ||| c))) - 11 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) + 5 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 1 * (a ||| c) + 1 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 11 * (c &&& (a ||| ~~~b)) - 7 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) + 1 * (b ^^^ (a &&& c)) + 2 * (a &&& ( ~~~b ||| c)) + 3 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) + 5 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 1 * ((a &&& c) ||| (b &&& ~~~c)) + 3 * (c ^^^ ~~~(a ||| ~~~b)) - 1 * ~~~(a ||| (b ||| c)) + 12 * ~~~(a ||| ( ~~~b ||| c)) - 3 * ~~~( ~~~a ||| (b ||| c)) - 4 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 33 * ( ~~~a &&& ( ~~~b &&& c)) + 14 * ( ~~~a &&& (b &&& c)) + 26 * (a &&& (b &&& c)) = 1 * (a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1751 (x y : BitVec w) : +theorem e_1751 : 4 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) - 1 * (a ||| ~~~b) - 1 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) - 2 * ~~~(a &&& (b ^^^ c)) + 1 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 5 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) + 1 * ( ~~~a &&& (b ^^^ c)) + 7 * (c ||| ~~~(a ^^^ b)) - 1 * (b ^^^ (a ||| (b &&& c))) + 7 * ~~~(a &&& (b &&& c)) - 2 * (b ^^^ (a ||| ( ~~~b ||| c))) + 1 * (b ^^^ ( ~~~a &&& (b ^^^ c))) + 1 * ~~~(a ||| c) + 3 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 2 * ((a ^^^ b) ||| ~~~(a ^^^ c)) + 4 * (b ^^^ (a &&& ( ~~~b ||| c))) - 2 * (b ^^^ c) + 2 * (b &&& ~~~(a &&& c)) - 7 * (c &&& ~~~(a ^^^ b)) + 11 * ~~~(a ||| ~~~b) - 5 * ( ~~~b ||| (a ^^^ c)) + 1 * (a ||| ~~~c) + 1 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 2 * (b ^^^ (a ||| ( ~~~b &&& c))) - 1 * ~~~(a &&& ( ~~~b ||| c)) + 3 * (c ||| (a &&& ~~~b)) - 6 * ~~~(a ||| (b ||| c)) - 26 * ~~~(a ||| ( ~~~b ||| c)) - 10 * ~~~( ~~~a ||| (b ||| c)) - 25 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 10 * ( ~~~a &&& ( ~~~b &&& c)) - 35 * ( ~~~a &&& (b &&& c)) - 11 * (a &&& ( ~~~b &&& c)) - 6 * (a &&& (b &&& c)) = - 3 * ((a &&& c) ^^^ (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1752 (x y : BitVec w) : +theorem e_1752 : - 2 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) + 3 * ((a ^^^ b) &&& (a ^^^ c)) + 2 * ~~~b + 4 * ~~~( ~~~a &&& ( ~~~b &&& c)) - 3 * ~~~(a ^^^ (b ^^^ c)) + 5 * (a ^^^ ( ~~~b &&& c)) - 2 * ~~~(a &&& b) - 11 * (c ^^^ (a ||| ~~~b)) - 1 * (c &&& (a ^^^ b)) + 2 * (b ^^^ ~~~(a &&& c)) + 1 * (b ^^^ (a ||| (b ||| c))) - 2 * ( ~~~b ||| (a ^^^ c)) + 1 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 1 * b + 2 * (c ||| (a &&& ~~~b)) + 7 * (b ^^^ (a ||| ( ~~~b ||| c))) - 6 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 4 * ~~~(a &&& ~~~a) - 7 * ((b &&& c) ||| (a &&& (b ||| c))) + 11 * (b &&& (a ^^^ c)) + 3 * (c ^^^ (a &&& (b ||| c))) + 2 * (b ^^^ (a ||| ~~~c)) - 2 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 6 * (b ^^^ (a &&& (b ^^^ c))) - 11 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 5 * (b &&& ~~~(a &&& c)) + 14 * ~~~(a ||| (b ||| c)) + 10 * ~~~(a ||| ( ~~~b ||| c)) - 13 * ~~~( ~~~a ||| (b ||| c)) + 20 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 15 * ( ~~~a &&& ( ~~~b &&& c)) + 22 * ( ~~~a &&& (b &&& c)) + 15 * (a &&& ( ~~~b &&& c)) + 4 * (a &&& (b &&& c)) = 1 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1753 (x y : BitVec w) : +theorem e_1753 : - 7 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) - 1 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) - 6 * ( ~~~c ||| (a ^^^ b)) - 1 * (b ^^^ ~~~(a &&& ~~~c)) + 2 * (b ^^^ ~~~(a &&& c)) + 11 * (b ^^^ c) - 1 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) + 7 * (c ^^^ ~~~(a &&& (b &&& c))) - 11 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) + 3 * (a ^^^ c) - 7 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) - 6 * ((a &&& b) ^^^ (b ||| ~~~c)) + 1 * ~~~(a &&& ( ~~~b ||| c)) + 1 * (c &&& (a ||| b)) - 5 * ((a ||| ~~~b) &&& (b ^^^ c)) - 2 * ( ~~~c ||| ~~~(a ^^^ b)) - 3 * ~~~(b ||| ~~~c) + 7 * (a &&& b) + 1 * ( ~~~b ||| ~~~(a ^^^ c)) - 2 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) - 6 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) - 2 * ( ~~~a ||| ( ~~~b ||| c)) + 1 * a - 2 * (a ^^^ (b ^^^ c)) + 1 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) - 7 * ((a &&& b) ||| ~~~(b ||| ~~~c)) + 7 * ( ~~~a &&& ( ~~~b ||| c)) + 18 * ~~~(a ||| (b ||| c)) + 15 * ~~~(a ||| ( ~~~b ||| c)) + 20 * ~~~( ~~~a ||| (b ||| c)) + 10 * ( ~~~a &&& ( ~~~b &&& c)) + 21 * ( ~~~a &&& (b &&& c)) + 21 * (a &&& ( ~~~b &&& c)) + 19 * (a &&& (b &&& c)) = - 1 * ~~~( ~~~a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1754 (x y : BitVec w) : +theorem e_1754 : - 1 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 2 * (a ^^^ b) - 2 * (a ||| c) + 11 * (c ^^^ (a ||| b)) - 5 * ~~~( ~~~a &&& (b ^^^ c)) - 5 * (c ^^^ (a &&& (b ||| c))) + 7 * (b ^^^ (a ||| ~~~c)) - 2 * ( ~~~a &&& (b ||| c)) - 1 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) + 3 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) - 1 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) - 1 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) - 1 * ~~~(b ||| ~~~c) - 1 * a + 5 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) - 2 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) + 1 * (c ^^^ ~~~(a &&& (b ||| c))) - 7 * ~~~(a &&& b) + 1 * (b ^^^ (a &&& (b ||| c))) + 1 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) - 2 * ~~~(b &&& ~~~c) + 4 * (c ^^^ ~~~(a ||| ~~~b)) - 1 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) - 1 * (c ^^^ ~~~(a &&& b)) + 1 * ((a &&& b) ^^^ (b ||| ~~~c)) - 2 * (b ^^^ ~~~(a ||| c)) - 3 * ~~~(a ||| (b ||| c)) - 22 * ~~~(a ||| ( ~~~b ||| c)) + 1 * ~~~( ~~~a ||| (b ||| c)) - 1 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 2 * ( ~~~a &&& ( ~~~b &&& c)) + 5 * ( ~~~a &&& (b &&& c)) - 7 * (a &&& ( ~~~b &&& c)) + 7 * (a &&& (b &&& c)) = - 11 * ~~~(a ^^^ ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1755 (x y : BitVec w) : +theorem e_1755 : - 2 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) - 7 * (b ^^^ ~~~(a ||| (b ^^^ c))) - 11 * ~~~(b ||| c) + 1 * (c ^^^ (a ||| ( ~~~b &&& c))) - 11 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) - 11 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) - 1 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 1 * (b ||| c) + 3 * (a &&& (b ||| c)) - 1 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) + 11 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 7 * ~~~(a &&& (b ||| c)) + 11 * (b &&& ~~~c) - 3 * ~~~( ~~~a &&& ( ~~~b ||| c)) - 1 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) + 11 * (b ^^^ (a &&& (b ||| c))) - 2 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) - 3 * (b ||| (a &&& ~~~c)) + 7 * ~~~(a &&& c) - 1 * (c ^^^ ( ~~~a &&& (b ||| c))) - 7 * ( ~~~c &&& (a ^^^ b)) + 11 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) - 2 * (b &&& ~~~(a &&& c)) - 1 * ~~~(a &&& (b ^^^ c)) + 1 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) + 2 * ((a ^^^ b) &&& ~~~(a ^^^ c)) - 5 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) + 20 * ~~~(a ||| (b ||| c)) - 20 * ~~~(a ||| ( ~~~b ||| c)) - 2 * ~~~( ~~~a ||| (b ||| c)) - 4 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 15 * ( ~~~a &&& ( ~~~b &&& c)) - 14 * ( ~~~a &&& (b &&& c)) - 22 * (a &&& ( ~~~b &&& c)) + 44 * (a &&& (b &&& c)) = - 1 * ~~~(a &&& (b &&& c)) + 7 * ~~~(a ||| b) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1756 (x y : BitVec w) : +theorem e_1756 : - 1 * ~~~(a ^^^ (b ||| c)) + 3 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) - 3 * (a ||| (b ||| c)) + 2 * (a ^^^ (b ^^^ c)) - 1 * (b ^^^ ~~~(a ||| c)) + 1 * (c &&& (a ||| b)) - 5 * (b &&& (a ||| c)) - 1 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 1 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 2 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) - 3 * (c ||| ~~~(a ||| ~~~b)) + 11 * ( ~~~a ||| (b &&& c)) - 5 * ~~~( ~~~a ||| (b ^^^ c)) - 1 * (c &&& ~~~(a ^^^ b)) + 5 * (a ^^^ (b ||| c)) - 1 * ~~~(a ^^^ b) + 2 * (b &&& (a ||| ~~~c)) - 3 * (a &&& (b ^^^ c)) - 6 * (b &&& ~~~(a &&& c)) + 2 * (c ^^^ (a ||| ( ~~~b ||| c))) + 1 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) + 2 * ~~~(a &&& b) - 5 * ~~~(b ||| c) - 3 * (c ^^^ (a ||| (b &&& c))) + 1 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) - 7 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 2 * (a &&& c) - 12 * ~~~(a ||| (b ||| c)) - 4 * ~~~(a ||| ( ~~~b ||| c)) + 12 * ~~~( ~~~a ||| (b ||| c)) + 10 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 14 * ( ~~~a &&& ( ~~~b &&& c)) + 6 * ( ~~~a &&& (b &&& c)) + 16 * (a &&& ( ~~~b &&& c)) + 4 * (a &&& (b &&& c)) = 1 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 5 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1757 (x y : BitVec w) : +theorem e_1757 : - 5 * ~~~( ~~~a &&& (b ||| c)) - 6 * (b &&& ~~~(a &&& ~~~c)) + 2 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) - 6 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) - 11 * ~~~( ~~~a &&& ( ~~~b &&& c)) + 2 * (b ^^^ ( ~~~a &&& (b ^^^ c))) + 2 * (c ^^^ (a &&& ( ~~~b ||| c))) - 1 * (c &&& (a ^^^ b)) + 1 * ( ~~~c ||| ~~~(a ^^^ b)) + 2 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 1 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 11 * (a ^^^ c) - 1 * (a ^^^ b) + 5 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) + 3 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) + 5 * (a &&& ~~~c) + 2 * ((a ^^^ b) &&& ~~~(a ^^^ c)) + 11 * (b ^^^ (a &&& ( ~~~b ||| c))) - 1 * (b &&& ~~~(a ^^^ c)) - 3 * ~~~c - 2 * (b ^^^ (a ||| (b &&& c))) - 1 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 7 * (b ^^^ ( ~~~a ||| (b &&& c))) - 1 * ~~~(a &&& (b ^^^ c)) + 11 * (c ^^^ (a &&& b)) + 7 * (a ||| b) + 4 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) + 13 * ~~~(a ||| (b ||| c)) + 6 * ~~~(a ||| ( ~~~b ||| c)) - 2 * ~~~( ~~~a ||| (b ||| c)) - 10 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 2 * ( ~~~a &&& ( ~~~b &&& c)) - 14 * ( ~~~a &&& (b &&& c)) - 21 * (a &&& ( ~~~b &&& c)) + 4 * (a &&& (b &&& c)) = - 3 * ( ~~~b ||| (a ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1758 (x y : BitVec w) : +theorem e_1758 : 3 * ((b &&& c) ||| (a &&& (b ||| c))) + 2 * (c ^^^ (a ||| b)) - 1 * ~~~b - 11 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) - 2 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) - 6 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) - 3 * ~~~c - 7 * ((a &&& c) ||| (b &&& ~~~c)) + 2 * (b ^^^ (a ||| ( ~~~b ||| c))) - 1 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) + 2 * (c &&& ~~~(a ^^^ b)) + 5 * (a ^^^ ( ~~~b ||| c)) + 1 * ~~~( ~~~a &&& ( ~~~b ||| c)) + 3 * ~~~(a ||| (b ^^^ c)) + 5 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) + 1 * ~~~(b ^^^ c) + 1 * (c ||| (a &&& b)) + 2 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 2 * (a ^^^ c) + 11 * ((a &&& c) ||| ~~~(b ||| c)) - 1 * (c &&& ~~~(a &&& b)) - 1 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) - 1 * (a ||| ( ~~~b ||| c)) + 7 * ( ~~~a ||| (b &&& c)) - 2 * ( ~~~(a &&& b) &&& (b ^^^ c)) + 3 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) - 1 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 19 * ~~~(a ||| (b ||| c)) + 6 * ~~~(a ||| ( ~~~b ||| c)) - 13 * ~~~( ~~~a ||| (b ||| c)) + 20 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 8 * ( ~~~a &&& ( ~~~b &&& c)) - 7 * ( ~~~a &&& (b &&& c)) - 11 * (a &&& ( ~~~b &&& c)) - 20 * (a &&& (b &&& c)) = - 1 * (c ||| ~~~(a ||| ~~~b)) - 4 * (a &&& c) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1759 (x y : BitVec w) : +theorem e_1759 : - 6 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) - 5 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 1 * ( ~~~a &&& (b ^^^ c)) - 7 * ( ~~~a ||| ( ~~~b &&& c)) + 7 * (b ^^^ ( ~~~a &&& (b ||| c))) - 1 * (b ||| (a &&& c)) + 1 * ~~~c + 2 * ~~~(a &&& ~~~b) + 4 * (b ||| ~~~(a ^^^ c)) - 11 * (b ^^^ (a &&& c)) + 2 * ~~~( ~~~a &&& (b ^^^ c)) - 2 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) - 2 * (a ^^^ (b ||| c)) - 2 * ( ~~~a ||| (b ||| c)) + 1 * ( ~~~b &&& (a ^^^ c)) + 7 * (b ^^^ ~~~(a ||| c)) + 7 * (c ^^^ ~~~(a &&& (b &&& c))) + 2 * (b &&& ~~~(a &&& c)) + 4 * ~~~(b ||| ~~~c) - 3 * (a ||| c) + 1 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) + 11 * ((a ^^^ b) ||| (a ^^^ c)) - 1 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) + 5 * (c ^^^ ~~~(a ||| b)) - 3 * ~~~(a ||| b) + 2 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) + 1 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 2 * ~~~(a ||| (b ||| c)) + 3 * ~~~(a ||| ( ~~~b ||| c)) - 16 * ~~~( ~~~a ||| (b ||| c)) - 16 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 8 * ( ~~~a &&& ( ~~~b &&& c)) + 10 * ( ~~~a &&& (b &&& c)) + 13 * (a &&& ( ~~~b &&& c)) - 27 * (a &&& (b &&& c)) = 7 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) + 2 * (c &&& ~~~(a &&& ~~~b)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1760 (x y : BitVec w) : +theorem e_1760 : 1 * ((a &&& b) ||| ~~~(b ||| ~~~c)) - 1 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 2 * ~~~(a &&& ~~~b) + 1 * ~~~(a &&& ~~~a) - 5 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) - 2 * ~~~( ~~~a &&& (b &&& c)) - 3 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) - 3 * (b ||| ~~~(a ||| ~~~c)) - 1 * (a &&& c) - 6 * (a ||| ( ~~~b &&& c)) - 1 * (b ^^^ ( ~~~a &&& (b ^^^ c))) + 1 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) + 4 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 1 * ~~~c + 2 * c + 3 * (b ^^^ (a &&& ~~~c)) - 7 * b + 2 * (a ||| (b &&& c)) + 4 * ~~~( ~~~a &&& ( ~~~b &&& c)) + 1 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) - 1 * (b &&& (a ^^^ c)) - 6 * (c ^^^ (a ||| (b &&& c))) + 4 * (c ^^^ ~~~(a &&& (b ||| c))) - 6 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) - 5 * ~~~(a ^^^ c) + 2 * ~~~(a ||| ~~~b) + 2 * (b ^^^ c) + 2 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) - 7 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 16 * ~~~(a ||| (b ||| c)) + 9 * ~~~( ~~~a ||| (b ||| c)) + 22 * ( ~~~a &&& ( ~~~b &&& c)) + 7 * ( ~~~a &&& (b &&& c)) + 6 * (a &&& ( ~~~b &&& c)) + 16 * (a &&& (b &&& c)) = - 33 * ~~~( ~~~a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1761 (x y : BitVec w) : +theorem e_1761 : 7 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) + 4 * (b ^^^ ~~~(a &&& (b &&& c))) + 4 * ~~~( ~~~a &&& ( ~~~b &&& c)) + 5 * (a ^^^ ( ~~~b ||| c)) - 7 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) + 1 * ((a &&& b) ^^^ (b ||| c)) - 7 * ( ~~~b &&& (a ^^^ c)) + 3 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 1 * (c ^^^ (a ||| (b &&& c))) - 6 * ( ~~~b ||| ~~~(a ^^^ c)) + 1 * (a ^^^ (b ^^^ c)) + 3 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) + 2 * ~~~( ~~~a &&& ( ~~~b ||| c)) + 1 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) - 7 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 1 * (b ^^^ (a &&& (b ||| c))) + 1 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 7 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) - 1 * ((a &&& c) ||| ~~~(b ||| c)) + 2 * ~~~(a &&& (b &&& c)) + 2 * (b &&& ~~~(a &&& c)) - 3 * (a &&& ~~~b) - 5 * (b &&& (a ^^^ c)) - 1 * (c ^^^ ( ~~~a ||| (b ||| c))) + 2 * (c ||| (a ^^^ b)) + 5 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 2 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) + 5 * ~~~(a ||| ~~~b) - 4 * ~~~(a ||| (b ||| c)) - 2 * ~~~(a ||| ( ~~~b ||| c)) + 1 * ~~~( ~~~a ||| (b ||| c)) - 6 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 22 * ( ~~~a &&& ( ~~~b &&& c)) - 9 * ( ~~~a &&& (b &&& c)) - 10 * (a &&& ( ~~~b &&& c)) = 11 * ~~~(a ||| ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1762 (x y : BitVec w) : +theorem e_1762 : 1 * (b ^^^ ( ~~~a ||| (b &&& c))) + 1 * ((b &&& c) ||| (a &&& (b ||| c))) - 1 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) - 1 * b + 3 * ( ~~~b ||| ~~~(a ^^^ c)) - 2 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) - 1 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) + 5 * (b ^^^ ~~~(a &&& (b ||| c))) - 1 * (b ^^^ ~~~(a ||| ~~~c)) + 5 * (b ^^^ ~~~(a &&& (b ^^^ c))) - 1 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 3 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 2 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) - 2 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) + 4 * (c &&& (a ||| b)) - 7 * (a ^^^ (b ||| c)) + 1 * ~~~(a &&& ~~~c) + 1 * (c ^^^ (a &&& ~~~b)) + 4 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 3 * ~~~(a ||| ( ~~~b &&& c)) - 2 * ((a ^^^ b) &&& ~~~(a ^^^ c)) + 4 * (b ||| c) - 1 * ((a &&& b) ||| ~~~(b ^^^ c)) + 7 * (b ^^^ (a ||| ( ~~~b &&& c))) - 1 * (b ^^^ ~~~(a ||| (b &&& c))) - 2 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) - 2 * ( ~~~c ||| ~~~(a ^^^ b)) - 13 * ~~~(a ||| (b ||| c)) + 1 * ~~~(a ||| ( ~~~b ||| c)) - 11 * ~~~( ~~~a ||| (b ||| c)) - 18 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 15 * ( ~~~a &&& ( ~~~b &&& c)) - 6 * ( ~~~a &&& (b &&& c)) - 21 * (a &&& ( ~~~b &&& c)) - 16 * (a &&& (b &&& c)) = - 4 * ~~~( ~~~a ||| ( ~~~b &&& c)) + 1 * (b ^^^ (a ||| ~~~c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1763 (x y : BitVec w) : +theorem e_1763 : - 11 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) - 3 * ( ~~~b &&& (a ^^^ c)) - 6 * ~~~(b ||| c) - 6 * ((a ||| ~~~b) &&& (b ^^^ c)) - 1 * ((a &&& b) ||| (b ^^^ c)) + 7 * (b ^^^ ~~~(a &&& (b ||| c))) - 6 * ~~~(a &&& (b ||| c)) + 3 * (a ||| ( ~~~b &&& c)) + 3 * ~~~(a ||| ~~~c) - 7 * ~~~(b &&& c) + 11 * ((a ^^^ b) ||| (a ^^^ c)) - 2 * ~~~( ~~~a ||| (b ^^^ c)) + 1 * (c ^^^ ( ~~~a ||| (b &&& c))) + 7 * (a &&& ~~~b) - 7 * (c ^^^ ~~~(a &&& ~~~b)) + 7 * (a ^^^ c) + 1 * (b ||| ~~~c) - 3 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 1 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 3 * (b ||| (a &&& ~~~c)) + 2 * ( ~~~a ||| ( ~~~b ||| c)) + 1 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) - 2 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 3 * (a ||| (b ||| c)) + 5 * (b ^^^ (a ||| ( ~~~b ||| c))) - 2 * (b &&& (a ^^^ c)) + 2 * (b ^^^ (a ||| ( ~~~b &&& c))) + 3 * (c ^^^ (a ||| ~~~b)) + 14 * ~~~(a ||| (b ||| c)) - 4 * ~~~(a ||| ( ~~~b ||| c)) - 29 * ~~~( ~~~a ||| (b ||| c)) + 1 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 11 * ( ~~~a &&& (b &&& c)) + 3 * (a &&& ( ~~~b &&& c)) - 5 * (a &&& (b &&& c)) = 13 * ( ~~~a &&& ( ~~~b &&& c)) - 5 * ~~~( ~~~a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1764 (x y : BitVec w) : +theorem e_1764 : - 3 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) - 2 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) - 7 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) - 2 * ( ~~~a &&& (b ^^^ c)) - 1 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) + 1 * (c ^^^ ( ~~~a &&& (b ||| c))) + 1 * ~~~b - 2 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) - 1 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 11 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) - 11 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) + 2 * (b &&& (a ||| ~~~c)) + 11 * (b ^^^ (a &&& ~~~c)) - 2 * ~~~(b ||| c) + 11 * ~~~a + 3 * ~~~(b ^^^ c) + 1 * (c ^^^ ~~~(a ||| ~~~b)) + 1 * ( ~~~c &&& ~~~(a ^^^ b)) + 1 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 3 * ~~~( ~~~a ||| ( ~~~b &&& c)) - 1 * ~~~(a ^^^ c) + 7 * ((b &&& c) ||| (a &&& (b ||| c))) - 1 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) + 4 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 1 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) - 1 * (b ^^^ (a &&& (b ||| c))) + 5 * (b ^^^ ( ~~~a ||| (b ||| c))) - 18 * ~~~(a ||| (b ||| c)) - 3 * ~~~(a ||| ( ~~~b ||| c)) + 14 * ~~~( ~~~a ||| (b ||| c)) + 8 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 9 * ( ~~~a &&& ( ~~~b &&& c)) - 31 * ( ~~~a &&& (b &&& c)) - 9 * (a &&& ( ~~~b &&& c)) - 10 * (a &&& (b &&& c)) = - 2 * (a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1765 (x y : BitVec w) : +theorem e_1765 : 5 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) + 1 * (c ^^^ (a &&& b)) - 1 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) - 7 * ((a ^^^ b) &&& (a ^^^ c)) - 1 * ((a &&& b) ||| ~~~(b ^^^ c)) - 11 * (a &&& ( ~~~b ||| c)) + 7 * ( ~~~a ||| (b ^^^ c)) + 2 * (b ^^^ ( ~~~a &&& (b ^^^ c))) + 4 * (b &&& ~~~(a ^^^ c)) - 2 * ~~~(b &&& c) - 2 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) + 11 * (c ^^^ ~~~(a &&& b)) - 11 * (b &&& c) + 2 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) + 7 * ~~~(a &&& (b ||| c)) - 11 * ~~~( ~~~a ||| (b &&& c)) - 11 * (b ^^^ ~~~(a &&& (b ^^^ c))) + 1 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) - 2 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) + 3 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 1 * (b &&& (a ^^^ c)) - 1 * ~~~( ~~~a &&& (b ||| c)) - 1 * (b ||| ~~~(a ^^^ c)) - 1 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) + 5 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) - 6 * (a ^^^ (b ^^^ c)) - 1 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) - 5 * (c ^^^ ~~~(a ||| ~~~b)) - 8 * ~~~(a ||| (b ||| c)) - 22 * ~~~(a ||| ( ~~~b ||| c)) + 24 * ~~~( ~~~a ||| (b ||| c)) + 16 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 3 * ( ~~~a &&& ( ~~~b &&& c)) - 3 * ( ~~~a &&& (b &&& c)) + 18 * (a &&& ( ~~~b &&& c)) + 6 * (a &&& (b &&& c)) = - 2 * a := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1766 (x y : BitVec w) : +theorem e_1766 : - 3 * ((a &&& b) ||| ~~~(b ||| ~~~c)) + 2 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) - 2 * (c ^^^ (a ||| ~~~b)) + 7 * (c ^^^ ( ~~~a ||| (b ||| c))) - 7 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) - 1 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) - 1 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) - 11 * (c ^^^ (a ||| (b &&& c))) + 4 * ~~~(a ^^^ (b ^^^ c)) + 3 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) + 11 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 2 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 5 * (c ^^^ (a &&& b)) + 1 * (c ^^^ (a &&& ~~~b)) - 3 * ( ~~~c ||| (a ^^^ b)) - 3 * ( ~~~a &&& ( ~~~b ||| c)) + 1 * ( ~~~c &&& ~~~(a ^^^ b)) + 1 * ((a &&& c) ||| ~~~(b ||| c)) + 7 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 5 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) + 5 * (c &&& ~~~(a &&& b)) + 3 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) + 2 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) + 5 * ~~~(a ||| b) - 1 * (c ^^^ ~~~(a &&& ~~~b)) + 4 * (a ^^^ (b &&& c)) - 1 * ~~~(a ||| (b &&& c)) + 1 * (b ^^^ ( ~~~a ||| (b &&& c))) - 24 * ~~~(a ||| (b ||| c)) - 12 * ~~~(a ||| ( ~~~b ||| c)) - 6 * ~~~( ~~~a ||| (b ||| c)) + 2 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 2 * ( ~~~a &&& ( ~~~b &&& c)) - 12 * ( ~~~a &&& (b &&& c)) - 28 * (a &&& ( ~~~b &&& c)) + 2 * (a &&& (b &&& c)) = 3 * (c &&& (a ||| b)) + 1 * (a ^^^ ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1767 (x y : BitVec w) : +theorem e_1767 : 1 * (b ^^^ ~~~(a ||| ~~~c)) - 5 * (c ^^^ ~~~(a &&& (b &&& c))) + 1 * (b &&& ~~~(a &&& c)) + 5 * ( ~~~(a ||| b) ||| (b ^^^ c)) + 3 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) - 2 * ( ~~~b ||| ~~~(a ^^^ c)) - 1 * ~~~(a ^^^ c) - 6 * (c &&& ~~~(a &&& ~~~b)) - 1 * ~~~a + 5 * ((a &&& b) ||| ~~~(b ^^^ c)) - 1 * (a ||| (b &&& c)) + 5 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 1 * (b ^^^ (a &&& (b ^^^ c))) + 3 * (c &&& (a ||| ~~~b)) - 7 * (b ^^^ ( ~~~a ||| (b ^^^ c))) - 1 * (c ^^^ ~~~(a ||| b)) - 1 * (a ^^^ (b ||| c)) - 7 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) + 11 * ( ~~~a &&& (b ||| c)) + 2 * (a ^^^ (b &&& c)) - 5 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) + 1 * (b ^^^ (a &&& c)) + 4 * (c ||| (a &&& b)) - 2 * (b ||| (a &&& c)) + 2 * (a &&& ( ~~~b ||| c)) - 6 * (b &&& ~~~(a &&& ~~~c)) - 3 * ~~~(a ||| (b &&& c)) + 5 * (b ||| ~~~(a ||| ~~~c)) + 4 * ~~~(b &&& c) + 4 * ~~~(a ||| (b ||| c)) - 8 * ~~~(a ||| ( ~~~b ||| c)) - 7 * ~~~( ~~~a ||| (b ||| c)) - 21 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 3 * ( ~~~a &&& (b &&& c)) - 6 * (a &&& ( ~~~b &&& c)) + 10 * (a &&& (b &&& c)) = - 2 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) + 18 * ( ~~~a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1768 (x y : BitVec w) : +theorem e_1768 : 7 * (b ^^^ (a &&& c)) + 7 * (a ^^^ (b &&& c)) - 1 * (b &&& c) - 1 * (c ^^^ ( ~~~a &&& (b ||| c))) - 6 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) + 11 * ~~~(a ||| (b ^^^ c)) - 2 * (a ||| ( ~~~b &&& c)) + 1 * (b ||| ~~~c) + 4 * ~~~(a &&& ( ~~~b ||| c)) - 6 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) + 2 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 1 * (a ||| ~~~b) - 2 * (a ^^^ ( ~~~b &&& c)) - 3 * (b ^^^ ~~~(a ||| (b &&& c))) + 3 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) - 7 * (a ^^^ ( ~~~b ||| c)) + 5 * (b ^^^ ~~~(a &&& (b ^^^ c))) - 3 * (a &&& ~~~c) + 1 * (c ^^^ ( ~~~a ||| (b &&& c))) - 7 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) - 11 * ~~~(a &&& (b ||| c)) - 11 * (a &&& b) + 2 * ((a &&& b) ^^^ (b ||| ~~~c)) - 11 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) - 6 * ~~~(a ||| ~~~b) + 1 * ~~~c - 1 * ((b &&& c) ||| (a &&& (b ||| c))) + 2 * (c ||| ~~~(a ^^^ b)) + 29 * ~~~(a ||| (b ||| c)) + 6 * ~~~(a ||| ( ~~~b ||| c)) + 9 * ~~~( ~~~a ||| (b ||| c)) + 27 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 29 * ( ~~~a &&& ( ~~~b &&& c)) + 34 * ( ~~~a &&& (b &&& c)) + 20 * (a &&& ( ~~~b &&& c)) + 33 * (a &&& (b &&& c)) = 11 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1769 (x y : BitVec w) : +theorem e_1769 : - 1 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) - 5 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) + 2 * (c ||| (a &&& ~~~b)) - 2 * (c ^^^ ~~~(a ||| (b &&& c))) - 11 * ( ~~~a ||| ( ~~~b &&& c)) - 6 * (a &&& b) + 1 * (b &&& (a ^^^ c)) + 1 * (c ^^^ (a ||| (b &&& c))) - 1 * (c ^^^ (a &&& (b ||| c))) + 1 * (a &&& ~~~b) + 5 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) + 11 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) + 3 * ~~~b + 11 * (b ^^^ ( ~~~a ||| (b ||| c))) - 11 * (a &&& (b ||| c)) - 11 * ( ~~~c ||| ~~~(a ^^^ b)) - 1 * (b ||| ~~~(a ||| ~~~c)) - 1 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) + 4 * (b ^^^ (a ||| ( ~~~b &&& c))) + 2 * ~~~(a ^^^ (b ||| c)) + 2 * ( ~~~c ||| (a ^^^ b)) + 7 * ~~~(b ||| c) + 5 * (b ||| ~~~(a ||| c)) + 7 * ( ~~~(a ||| b) ||| (b ^^^ c)) - 5 * ~~~(a ||| c) - 11 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) - 3 * ~~~(a ||| (b &&& c)) - 6 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) - 1 * (c ^^^ (a ||| ( ~~~b &&& c))) + 14 * ~~~(a ||| (b ||| c)) + 11 * ~~~(a ||| ( ~~~b ||| c)) - 6 * ~~~( ~~~a ||| (b ||| c)) + 19 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 5 * ( ~~~a &&& ( ~~~b &&& c)) + 14 * ( ~~~a &&& (b &&& c)) + 9 * (a &&& ( ~~~b &&& c)) = - 6 * (a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1770 (x y : BitVec w) : +theorem e_1770 : - 5 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 1 * ( ~~~a ||| (b ^^^ c)) - 2 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 3 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) - 3 * (c ^^^ ~~~(a ||| b)) + 3 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) - 1 * ( ~~~(a &&& b) &&& (b ^^^ c)) - 11 * (a ||| b) + 2 * ~~~(a &&& (b ^^^ c)) - 1 * ~~~(a ||| ( ~~~b &&& c)) + 2 * ~~~(b ||| c) + 2 * ~~~(a ||| c) - 6 * ((a &&& b) ^^^ (b ||| c)) - 6 * (b ^^^ (a ||| (b &&& c))) + 1 * (c ||| ~~~(a ^^^ b)) + 1 * (c ^^^ ( ~~~a ||| (b ||| c))) + 1 * ~~~( ~~~a &&& (b ^^^ c)) - 7 * ~~~(a ||| ~~~c) - 1 * ((a ^^^ b) ||| ~~~(a ^^^ c)) - 7 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) - 2 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) - 7 * ((a &&& b) ||| (b ^^^ c)) + 5 * (b ^^^ ( ~~~a &&& (b ^^^ c))) - 1 * ( ~~~c &&& ~~~(a ^^^ b)) + 1 * (c ^^^ ( ~~~a ||| (b &&& c))) - 5 * (b &&& (a ^^^ c)) + 11 * ~~~(a &&& ~~~a) - 1 * (c ^^^ (a &&& ( ~~~b ||| c))) + 1 * ~~~(a ||| (b ||| c)) + 22 * ~~~(a ||| ( ~~~b ||| c)) + 11 * ~~~( ~~~a ||| (b ||| c)) + 17 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 16 * ( ~~~a &&& ( ~~~b &&& c)) + 28 * ( ~~~a &&& (b &&& c)) + 24 * (a &&& ( ~~~b &&& c)) - 1 * (a &&& (b &&& c)) = 6 * ~~~a := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1771 (x y : BitVec w) : +theorem e_1771 : - 1 * (b ^^^ c) + 11 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) + 4 * (a ||| (b ||| c)) - 5 * ~~~(a ^^^ b) - 3 * (a ||| c) - 11 * (a ||| ~~~b) - 11 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) + 2 * ( ~~~a ||| (b &&& c)) - 2 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) - 1 * (b ^^^ (a &&& c)) - 1 * (b ^^^ (a &&& ( ~~~b ||| c))) - 6 * (c &&& ~~~(a ^^^ b)) - 2 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 1 * (c ^^^ ( ~~~a ||| (b &&& c))) + 7 * (b ^^^ ~~~(a &&& ~~~c)) - 7 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) - 11 * (a &&& ~~~b) - 7 * (c &&& ~~~(a &&& b)) - 3 * (b ||| c) + 1 * (a ^^^ b) - 2 * ~~~(a ||| ~~~c) + 4 * ((a ^^^ b) &&& (a ^^^ c)) + 2 * ~~~(a &&& (b ^^^ c)) + 11 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 5 * ((a ^^^ b) ||| (a ^^^ c)) - 6 * ((a &&& c) ||| (b &&& ~~~c)) + 3 * (b ^^^ ~~~(a &&& c)) - 6 * (c ||| ~~~(a ^^^ b)) + 7 * ~~~(a ||| (b ||| c)) + 20 * ~~~(a ||| ( ~~~b ||| c)) + 21 * ~~~( ~~~a ||| (b ||| c)) + 48 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 20 * ( ~~~a &&& ( ~~~b &&& c)) + 11 * ( ~~~a &&& (b &&& c)) + 52 * (a &&& ( ~~~b &&& c)) + 15 * (a &&& (b &&& c)) = - 5 * a + 2 * ((a ||| b) &&& (b ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1772 (x y : BitVec w) : +theorem e_1772 : 3 * (a ||| (b ^^^ c)) - 2 * (c ^^^ ( ~~~a ||| (b &&& c))) + 1 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 6 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 3 * (b ^^^ ( ~~~a ||| (b ||| c))) - 5 * ((a &&& c) ||| (b &&& ~~~c)) - 7 * (c ^^^ ~~~(a ||| b)) + 2 * (a &&& ~~~c) - 1 * (b ^^^ ~~~(a &&& (b &&& c))) - 11 * (c ^^^ ( ~~~a &&& (b ||| c))) + 11 * ((a &&& ~~~b) ||| (b ^^^ c)) - 5 * b - 2 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) - 1 * ~~~a - 2 * (b ^^^ ( ~~~a ||| (b ^^^ c))) + 7 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 1 * (b ^^^ ~~~(a ||| ~~~c)) - 1 * ~~~(a &&& ~~~c) + 1 * ~~~(a ^^^ b) - 1 * ~~~(a &&& (b ||| c)) - 5 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 5 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) + 4 * (a ^^^ b) + 1 * ~~~(a ^^^ ( ~~~b &&& c)) + 1 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) + 7 * (c ^^^ (a &&& (b ||| c))) + 2 * (b ||| ~~~(a ||| ~~~c)) + 2 * ((a ||| b) &&& ~~~(b ^^^ c)) + 3 * (c ^^^ (a ||| ~~~b)) + 3 * ~~~(a ||| ( ~~~b ||| c)) - 25 * ~~~( ~~~a ||| (b ||| c)) - 13 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 16 * ( ~~~a &&& ( ~~~b &&& c)) - 5 * ( ~~~a &&& (b &&& c)) + 14 * (a &&& ( ~~~b &&& c)) + 16 * (a &&& (b &&& c)) = - 3 * ~~~(a ||| (b ||| c)) - 2 * (b ^^^ ~~~(a &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1773 (x y : BitVec w) : +theorem e_1773 : - 2 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 1 * (c ^^^ ( ~~~a &&& (b ||| c))) + 7 * ( ~~~b &&& (a ^^^ c)) + 5 * (c ^^^ ~~~(a ||| ~~~b)) + 11 * (b ^^^ ( ~~~a &&& (b ||| c))) - 1 * ((a ||| b) &&& ~~~(b ^^^ c)) + 1 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) + 4 * (b ^^^ (a ||| ~~~c)) - 2 * (b ^^^ ~~~(a &&& (b ^^^ c))) - 1 * (a &&& ( ~~~b ||| c)) + 2 * (b ||| ~~~(a ^^^ c)) - 2 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) - 1 * (b ||| ~~~(a ||| ~~~c)) - 2 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 5 * c + 1 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) + 7 * ~~~c + 4 * ((a &&& c) ^^^ (b ||| c)) + 1 * (b &&& (a ||| c)) + 11 * ~~~(a ^^^ (b &&& c)) - 1 * (a ||| (b &&& c)) - 1 * (c ||| ~~~(a ||| ~~~b)) + 3 * ((a ||| b) &&& (b ^^^ c)) - 6 * (c ^^^ (a &&& ~~~b)) + 1 * (a &&& (b ||| c)) - 6 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) + 7 * (b ^^^ (a ||| (b &&& c))) - 3 * (a ^^^ ( ~~~b ||| c)) + 1 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) - 10 * ~~~(a ||| (b ||| c)) - 35 * ~~~(a ||| ( ~~~b ||| c)) - 7 * ~~~( ~~~a ||| (b ||| c)) - 12 * ( ~~~a &&& ( ~~~b &&& c)) + 13 * ( ~~~a &&& (b &&& c)) - 15 * (a &&& ( ~~~b &&& c)) - 18 * (a &&& (b &&& c)) = - 2 * a + 25 * ~~~( ~~~a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1774 (x y : BitVec w) : +theorem e_1774 : - 1 * (c ^^^ ( ~~~a &&& (b ||| c))) + 7 * (b ||| ~~~(a ||| ~~~c)) + 1 * (b &&& (a ^^^ c)) - 1 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 7 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) + 1 * ( ~~~a &&& (b ^^^ c)) - 6 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) - 1 * (c ||| (a ^^^ b)) - 3 * ((a ^^^ b) &&& (a ^^^ c)) + 11 * ~~~(a ||| c) - 3 * ~~~(a &&& ~~~c) - 11 * c - 7 * ~~~(a &&& (b ^^^ c)) + 7 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 11 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) + 3 * ~~~(a &&& c) + 7 * (b ^^^ ~~~(a &&& c)) - 1 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 2 * (c ^^^ (a &&& ~~~b)) + 1 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 3 * ( ~~~a ||| (b ||| c)) - 1 * (a &&& (b ||| c)) - 2 * ~~~(b ||| ~~~c) - 5 * (b ^^^ c) - 5 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) + 4 * (c &&& ~~~(a &&& ~~~b)) + 11 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 5 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) + 1 * ((a &&& b) ||| ~~~(b ||| c)) + 2 * ~~~(a ||| (b ||| c)) - 18 * ~~~(a ||| ( ~~~b ||| c)) - 12 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 5 * ( ~~~a &&& ( ~~~b &&& c)) + 15 * ( ~~~a &&& (b &&& c)) + 36 * (a &&& ( ~~~b &&& c)) + 6 * (a &&& (b &&& c)) = 2 * (a ^^^ b) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1775 (x y : BitVec w) : +theorem e_1775 : - 2 * (b ||| c) + 11 * ~~~(b ||| c) + 2 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) - 2 * ((a &&& c) ^^^ (b ||| c)) - 1 * ~~~(a &&& ~~~b) + 1 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 11 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) - 11 * ~~~(a &&& ( ~~~b ||| c)) - 3 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 4 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) + 5 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) + 2 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) - 5 * (b &&& (a ||| c)) - 7 * ~~~( ~~~a &&& (b ||| c)) + 5 * (c ^^^ ( ~~~a ||| (b &&& c))) + 4 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) + 7 * ( ~~~c ||| ~~~(a ^^^ b)) + 1 * (b &&& ~~~(a ^^^ c)) - 1 * ~~~(b &&& c) - 1 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) + 1 * (c ^^^ ~~~(a &&& ~~~b)) + 1 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) + 7 * ~~~(a ||| (b ^^^ c)) - 11 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) + 3 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) + 2 * ((a &&& c) ||| (b &&& ~~~c)) - 1 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) + 7 * ((a &&& c) ||| ~~~(b ||| c)) - 14 * ~~~(a ||| (b ||| c)) - 23 * ~~~(a ||| ( ~~~b ||| c)) - 18 * ~~~( ~~~a ||| (b ||| c)) + 9 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 7 * ( ~~~a &&& ( ~~~b &&& c)) + 15 * ( ~~~a &&& (b &&& c)) + 3 * (a &&& ( ~~~b &&& c)) - 7 * (a &&& (b &&& c)) = 5 * ((a ^^^ b) ||| ~~~(a ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1776 (x y : BitVec w) : +theorem e_1776 : 4 * (a &&& ~~~c) - 2 * (c ||| ~~~(a ^^^ b)) + 3 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) - 5 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) + 1 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 1 * (c &&& (a ||| b)) + 5 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) + 11 * ( ~~~c ||| ~~~(a ^^^ b)) + 1 * (b &&& (a ||| c)) + 3 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) - 2 * ~~~(a ||| (b ^^^ c)) - 6 * ~~~a - 7 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) + 3 * (c ^^^ ( ~~~a ||| (b ||| c))) - 1 * ~~~( ~~~a &&& ( ~~~b ||| c)) - 1 * ((a &&& c) ^^^ (b ||| c)) + 7 * (c ^^^ ~~~(a ||| b)) + 4 * (b ^^^ (a &&& ~~~c)) - 2 * ~~~(b ^^^ c) + 2 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) + 11 * ( ~~~a ||| (b ||| c)) + 4 * (c ||| ~~~(a ||| ~~~b)) + 1 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 5 * ((a &&& ~~~b) ||| (b ^^^ c)) - 11 * ((a &&& c) ||| (b &&& ~~~c)) - 2 * ((a ||| b) &&& ~~~(b ^^^ c)) + 1 * (b ^^^ ~~~(a ||| ~~~c)) - 1 * ( ~~~a ||| (b &&& c)) - 19 * ~~~(a ||| (b ||| c)) - 16 * ~~~(a ||| ( ~~~b ||| c)) - 10 * ~~~( ~~~a ||| (b ||| c)) - 25 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 14 * ( ~~~a &&& ( ~~~b &&& c)) - 14 * ( ~~~a &&& (b &&& c)) - 8 * (a &&& ( ~~~b &&& c)) - 29 * (a &&& (b &&& c)) = 1 * ~~~(b &&& ~~~c) + 5 * ( ~~~(a &&& b) &&& (b ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1777 (x y : BitVec w) : +theorem e_1777 : 3 * (b ||| (a &&& ~~~c)) + 1 * ( ~~~b &&& (a ^^^ c)) - 1 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 4 * (b ^^^ ( ~~~a ||| (b &&& c))) - 7 * ( ~~~c &&& (a ^^^ b)) + 7 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) + 3 * ( ~~~(a ||| b) ||| (b ^^^ c)) - 2 * (b ^^^ (a ||| (b ^^^ c))) + 4 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) + 2 * ((a &&& c) ||| (b &&& ~~~c)) + 1 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) + 5 * ( ~~~(a &&& b) &&& (b ^^^ c)) + 2 * (a ^^^ c) - 5 * ~~~(a ^^^ (b ^^^ c)) - 3 * (b ^^^ (a ||| (b ||| c))) + 3 * (b ^^^ c) - 1 * (c &&& ~~~(a &&& ~~~b)) - 3 * (c &&& (a ||| b)) - 5 * (c ||| (a &&& b)) - 2 * (c ^^^ (a ||| (b ||| c))) - 6 * a - 1 * ( ~~~b ||| ~~~(a ^^^ c)) + 2 * (a &&& ( ~~~b ||| c)) - 1 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) - 1 * ~~~( ~~~a ||| ( ~~~b &&& c)) + 2 * ((a &&& b) ^^^ (b ||| ~~~c)) - 3 * (b ||| (a &&& c)) + 11 * (c ^^^ ~~~(a ||| ~~~b)) - 7 * (b &&& ~~~(a &&& ~~~c)) - 2 * ~~~(a ||| (b ||| c)) - 9 * ~~~(a ||| ( ~~~b ||| c)) + 8 * ~~~( ~~~a ||| (b ||| c)) + 6 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 14 * ( ~~~a &&& ( ~~~b &&& c)) + 20 * ( ~~~a &&& (b &&& c)) + 1 * (a &&& ( ~~~b &&& c)) - 1 * (a &&& (b &&& c)) = 5 * ((a ||| b) &&& (b ^^^ c)) + 7 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1778 (x y : BitVec w) : +theorem e_1778 : 5 * ((a &&& c) ||| (b &&& ~~~c)) + 1 * ~~~c + 1 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) + 7 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) + 11 * (c &&& (a ||| b)) + 11 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) + 4 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) - 6 * ~~~(a ^^^ (b ^^^ c)) + 4 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) - 5 * (c &&& (a ||| ~~~b)) - 6 * ~~~(a ||| (b &&& c)) - 11 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) + 7 * ~~~( ~~~a &&& (b ^^^ c)) - 11 * ( ~~~a &&& (b ||| c)) + 11 * ~~~(a ^^^ (b &&& c)) + 1 * (c &&& ~~~(a ^^^ b)) - 6 * ~~~(b ||| ~~~c) + 1 * ( ~~~a ||| (b &&& c)) - 7 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) + 1 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) + 7 * (a &&& b) - 5 * ( ~~~c &&& ~~~(a ^^^ b)) + 2 * ~~~(b &&& c) + 4 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) + 2 * (a ^^^ (b ||| c)) - 1 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) + 1 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) + 5 * (a ||| (b ||| c)) - 2 * (b &&& ~~~(a ^^^ c)) - 26 * ~~~(a ||| (b ||| c)) + 6 * ~~~(a ||| ( ~~~b ||| c)) + 5 * ~~~( ~~~a ||| (b ||| c)) - 12 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 5 * ( ~~~a &&& ( ~~~b &&& c)) - 24 * ( ~~~a &&& (b &&& c)) - 7 * (a &&& ( ~~~b &&& c)) - 67 * (a &&& (b &&& c)) = - 2 * ( ~~~a ||| (b ^^^ c)) + 7 * ~~~(a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1779 (x y : BitVec w) : +theorem e_1779 : - 1 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) - 5 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 3 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) - 1 * (a ||| b) + 2 * ~~~(a ^^^ ( ~~~b ||| c)) + 4 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) - 3 * ~~~(a ||| b) - 1 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) + 2 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) + 3 * (a ||| ~~~c) - 11 * (b ||| ~~~c) - 5 * (b &&& ~~~(a ^^^ c)) + 2 * (b ||| (a &&& c)) - 3 * ~~~( ~~~a &&& ( ~~~b &&& c)) + 5 * (c &&& ~~~(a &&& ~~~b)) + 1 * (c &&& (a ||| ~~~b)) - 6 * (c ^^^ ~~~(a ||| b)) + 3 * (c ||| (a &&& ~~~b)) + 4 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) + 7 * ( ~~~a &&& ( ~~~b ||| c)) + 4 * (a &&& (b ^^^ c)) + 1 * (b ||| (a ^^^ c)) - 2 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) - 1 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 5 * (c ||| ~~~(a ||| b)) - 1 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 1 * ~~~(a &&& ( ~~~b ||| c)) + 4 * (b ^^^ (a &&& (b ^^^ c))) + 2 * (c ||| (a ^^^ b)) + 2 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 15 * ~~~(a ||| (b ||| c)) + 3 * ~~~(a ||| ( ~~~b ||| c)) + 9 * ~~~( ~~~a ||| (b ||| c)) - 26 * ( ~~~a &&& ( ~~~b &&& c)) + 6 * ( ~~~a &&& (b &&& c)) - 15 * (a &&& ( ~~~b &&& c)) + 1 * (a &&& (b &&& c)) = - 16 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 6 * (c ^^^ (a ||| ( ~~~b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1780 (x y : BitVec w) : +theorem e_1780 : 1 * (a &&& b) + 5 * (a ||| ~~~b) - 1 * a - 2 * ~~~(a ||| c) + 7 * ~~~(a &&& (b &&& c)) + 11 * b - 2 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 5 * ( ~~~b ||| ~~~(a ^^^ c)) - 2 * (c ^^^ ~~~(a ||| ~~~b)) + 1 * ((a &&& b) ^^^ (b ||| ~~~c)) - 3 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 3 * (a &&& (b ||| c)) + 1 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 2 * (c ^^^ ~~~(a &&& ~~~b)) + 1 * (a ^^^ ( ~~~b ||| c)) - 5 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 2 * (b ^^^ ~~~(a &&& ~~~c)) - 5 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) + 5 * (a ^^^ ( ~~~b &&& c)) + 5 * ~~~(a &&& ~~~a) + 11 * (b ^^^ (a ||| (b ||| c))) + 3 * (c ^^^ ~~~(a ||| (b &&& c))) + 3 * ((a ^^^ b) ||| (a ^^^ c)) + 2 * (b ||| (a &&& c)) - 1 * ( ~~~a ||| ( ~~~b ||| c)) + 11 * c - 5 * ( ~~~a &&& (b ||| c)) + 3 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) + 1 * (a ^^^ c) - 9 * ~~~(a ||| (b ||| c)) - 13 * ~~~(a ||| ( ~~~b ||| c)) - 31 * ~~~( ~~~a ||| (b ||| c)) - 38 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 40 * ( ~~~a &&& ( ~~~b &&& c)) - 33 * ( ~~~a &&& (b &&& c)) - 44 * (a &&& ( ~~~b &&& c)) - 42 * (a &&& (b &&& c)) = 1 * (c &&& (a ||| b)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1781 (x y : BitVec w) : +theorem e_1781 : 11 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 1 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) - 5 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) - 11 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 5 * (c ||| ~~~(a ||| ~~~b)) - 2 * (c ^^^ (a &&& (b ||| c))) - 2 * ~~~( ~~~a ||| ( ~~~b &&& c)) - 3 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) + 2 * ( ~~~a &&& (b ||| c)) + 3 * ~~~(a ||| ~~~b) + 1 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) + 11 * (b ||| ~~~(a ||| c)) + 7 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) + 11 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 1 * ~~~(a &&& (b ^^^ c)) - 2 * (a ^^^ ( ~~~b ||| c)) + 2 * (b ||| (a &&& c)) - 5 * (c &&& ~~~(a &&& ~~~b)) + 11 * (a ||| (b ^^^ c)) - 1 * (b ^^^ ~~~(a &&& (b ^^^ c))) + 7 * ( ~~~b ||| ~~~(a ^^^ c)) + 3 * ((a &&& b) ||| ~~~(b ||| c)) - 2 * (c ^^^ (a ||| ( ~~~b ||| c))) + 1 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) + 5 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) - 11 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) + 4 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 6 * ( ~~~b ||| (a ^^^ c)) + 2 * (a ||| (b &&& c)) - 5 * ~~~(a ||| (b ||| c)) - 34 * ~~~(a ||| ( ~~~b ||| c)) - 49 * ~~~( ~~~a ||| (b ||| c)) - 30 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 3 * ( ~~~a &&& ( ~~~b &&& c)) - 28 * ( ~~~a &&& (b &&& c)) - 35 * (a &&& ( ~~~b &&& c)) - 23 * (a &&& (b &&& c)) = - 2 * (b ^^^ (a ||| ~~~c)) - 1 * ((a ^^^ b) ||| ~~~(a ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1782 (x y : BitVec w) : +theorem e_1782 : 11 * (b ^^^ (a ||| ( ~~~b &&& c))) + 1 * ((a &&& b) ||| ~~~(b ||| ~~~c)) + 7 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) - 6 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) + 2 * (a ^^^ ( ~~~b ||| c)) - 3 * (c ^^^ ~~~(a ||| (b &&& c))) + 2 * (b ^^^ (a ||| ( ~~~b ||| c))) + 11 * ( ~~~(a &&& b) &&& (b ^^^ c)) - 6 * (a ||| b) - 2 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) + 5 * (a &&& ~~~b) + 2 * ~~~(a ^^^ (b ^^^ c)) + 4 * (c &&& ~~~(a &&& ~~~b)) + 1 * (b ||| ~~~(a ^^^ c)) - 2 * ~~~( ~~~a ||| (b ^^^ c)) - 2 * ~~~(a ||| ~~~b) + 11 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) - 6 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) - 3 * (a ^^^ b) - 3 * ~~~(a &&& ( ~~~b &&& c)) - 1 * (b ^^^ ~~~(a &&& c)) + 1 * ~~~( ~~~a &&& (b ^^^ c)) - 1 * ~~~(a ^^^ ( ~~~b &&& c)) - 2 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 3 * (b ^^^ (a &&& (b ^^^ c))) + 11 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) - 6 * ~~~a + 3 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) - 3 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) + 4 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) - 6 * ~~~(a ||| (b ||| c)) - 13 * ~~~( ~~~a ||| (b ||| c)) - 20 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 40 * ( ~~~a &&& ( ~~~b &&& c)) - 5 * ( ~~~a &&& (b &&& c)) - 35 * (a &&& ( ~~~b &&& c)) + 15 * (a &&& (b &&& c)) = - 1 * ~~~(a &&& (b &&& c)) + 3 * ~~~(a ||| ~~~c) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1783 (x y : BitVec w) : +theorem e_1783 : 3 * ( ~~~a ||| ( ~~~b &&& c)) - 3 * (b ^^^ ~~~(a ||| (b ^^^ c))) + 1 * ~~~(a &&& (b ||| c)) - 2 * ~~~(b ||| c) + 1 * ~~~(b ^^^ c) + 3 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) + 4 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 1 * (b ||| ~~~c) - 3 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) - 1 * (b ||| ~~~(a ||| ~~~c)) + 11 * ((a &&& b) ^^^ (b ||| c)) - 6 * (c ^^^ ~~~(a ||| ~~~b)) + 1 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) + 3 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) + 1 * (c ^^^ ~~~(a &&& (b &&& c))) + 7 * ((a ^^^ b) &&& (a ^^^ c)) - 2 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) + 4 * (c ^^^ (a ||| (b &&& c))) - 7 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) - 7 * (c ^^^ (a ||| ~~~b)) + 4 * (c ^^^ ~~~(a &&& (b ||| c))) + 2 * ~~~(b &&& ~~~c) + 3 * (b ^^^ (a ||| (b ||| c))) - 3 * (c ||| ~~~(a ^^^ b)) + 2 * (b &&& ~~~c) + 7 * (b ^^^ ( ~~~a ||| (b ^^^ c))) + 7 * (a ^^^ (b ^^^ c)) + 1 * ~~~(b &&& c) - 1 * (a &&& ( ~~~b ||| c)) + 5 * ( ~~~(a ||| b) ||| (b ^^^ c)) - 10 * ~~~(a ||| (b ||| c)) - 23 * ~~~(a ||| ( ~~~b ||| c)) - 21 * ~~~( ~~~a ||| (b ||| c)) - 5 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 34 * ( ~~~a &&& ( ~~~b &&& c)) - 15 * ( ~~~a &&& (b &&& c)) - 33 * (a &&& ( ~~~b &&& c)) = - 3 * (b &&& ~~~(a &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1784 (x y : BitVec w) : +theorem e_1784 : - 3 * (c ^^^ (a ||| b)) + 2 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 1 * ~~~(b ||| c) + 1 * ( ~~~a ||| (b ||| c)) + 1 * (b ^^^ (a ||| c)) - 7 * ~~~(a ^^^ b) - 2 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) - 5 * (b ^^^ (a ||| ~~~c)) + 2 * (c ^^^ (a ||| ( ~~~b &&& c))) - 11 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 1 * ((a &&& b) ||| ~~~(b ||| ~~~c)) - 6 * ((a &&& b) ||| (b ^^^ c)) + 1 * ~~~(a ||| ( ~~~b &&& c)) + 4 * (b ||| ~~~(a ||| c)) - 1 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) + 11 * (b &&& (a ||| c)) + 11 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 2 * ( ~~~b ||| (a ^^^ c)) + 4 * (c &&& (a ||| b)) + 2 * (b ^^^ ( ~~~a ||| (b &&& c))) + 2 * (b ^^^ ~~~(a &&& (b ||| c))) - 7 * ((a &&& b) ^^^ (b ||| ~~~c)) + 3 * ( ~~~c &&& (a ^^^ b)) - 2 * (c ^^^ (a &&& b)) + 11 * (a ||| ~~~c) - 1 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 1 * (c ^^^ ~~~(a &&& (b &&& c))) - 5 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 7 * (b ^^^ ~~~(a &&& c)) + 2 * ~~~(a ||| (b ||| c)) - 10 * ~~~(a ||| ( ~~~b ||| c)) + 18 * ~~~( ~~~a ||| (b ||| c)) - 14 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 30 * ( ~~~a &&& ( ~~~b &&& c)) - 16 * ( ~~~a &&& (b &&& c)) + 3 * (a &&& ( ~~~b &&& c)) - 2 * (a &&& (b &&& c)) = 3 * (a &&& (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1785 (x y : BitVec w) : +theorem e_1785 : 2 * ((a &&& ~~~b) ||| (b ^^^ c)) + 11 * ( ~~~(a ||| b) ||| (b ^^^ c)) + 1 * b + 1 * (c ^^^ ( ~~~a &&& (b ||| c))) + 2 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) - 5 * (b ^^^ (a ||| (b &&& c))) + 11 * ~~~( ~~~a &&& ( ~~~b &&& c)) + 4 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 1 * ~~~(a ^^^ ( ~~~b ||| c)) + 5 * ~~~(b &&& ~~~c) - 5 * (c ^^^ (a &&& b)) - 2 * (b ^^^ (a &&& ( ~~~b ||| c))) + 11 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 6 * (c ^^^ (a ||| (b ||| c))) - 5 * ((a &&& b) ||| ~~~(b ||| ~~~c)) - 2 * c + 5 * (b ||| (a ^^^ c)) + 1 * (c ^^^ (a ||| b)) + 1 * ~~~(b &&& c) - 5 * (b &&& ~~~(a &&& c)) - 7 * ( ~~~a &&& (b ||| c)) - 7 * (b ^^^ (a ||| ( ~~~b ||| c))) - 5 * (a ^^^ c) + 7 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) - 2 * (c &&& (a ^^^ b)) - 1 * (c ^^^ ~~~(a &&& b)) + 1 * ( ~~~a ||| (b ||| c)) - 3 * (c ^^^ (a ||| ~~~b)) - 3 * ( ~~~c ||| (a ^^^ b)) - 28 * ~~~(a ||| (b ||| c)) - 17 * ~~~(a ||| ( ~~~b ||| c)) - 12 * ~~~( ~~~a ||| (b ||| c)) - 5 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 1 * ( ~~~a &&& ( ~~~b &&& c)) - 7 * ( ~~~a &&& (b &&& c)) - 4 * (a &&& ( ~~~b &&& c)) - 30 * (a &&& (b &&& c)) = - 2 * (b ^^^ ~~~(a ||| (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1786 (x y : BitVec w) : +theorem e_1786 : 11 * (a ||| (b ^^^ c)) - 2 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) + 11 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) - 3 * ((a &&& b) ||| (b ^^^ c)) - 1 * ((a &&& b) ^^^ (b ||| ~~~c)) - 5 * (c ^^^ (a ||| ( ~~~b &&& c))) - 3 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) - 1 * (c ^^^ ~~~(a ||| b)) - 1 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) + 4 * (a ^^^ (b &&& c)) + 7 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) - 3 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 1 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 2 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) + 2 * (b &&& c) + 11 * ((a &&& b) ^^^ (b ||| c)) + 1 * (b ||| (a ^^^ c)) + 1 * ~~~(a &&& b) - 6 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) - 2 * ~~~(a ||| ~~~b) - 1 * (c ||| (a &&& ~~~b)) + 7 * b + 2 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) - 1 * ((a ^^^ b) &&& (a ^^^ c)) - 11 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) + 3 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) + 2 * (c ^^^ ~~~(a &&& (b ||| c))) + 5 * (b ^^^ ~~~(a ||| ~~~c)) - 7 * ~~~(a ||| (b ^^^ c)) - 1 * (c &&& ~~~(a &&& b)) - 9 * ~~~(a ||| (b ||| c)) - 21 * ~~~(a ||| ( ~~~b ||| c)) - 19 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 23 * ( ~~~a &&& ( ~~~b &&& c)) - 30 * ( ~~~a &&& (b &&& c)) - 27 * (a &&& ( ~~~b &&& c)) - 11 * (a &&& (b &&& c)) = 1 * (b ^^^ ( ~~~a ||| (b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1787 (x y : BitVec w) : +theorem e_1787 : - 2 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 5 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) + 1 * (c ^^^ ( ~~~a &&& (b ||| c))) - 11 * (a ||| ~~~c) - 7 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 1 * (b ^^^ c) + 4 * (c ||| ~~~(a ||| b)) - 3 * (a ^^^ ( ~~~b ||| c)) + 11 * (a ^^^ (b &&& c)) - 1 * ( ~~~c ||| (a ^^^ b)) + 4 * ((a ||| b) &&& (b ^^^ c)) + 5 * (b ^^^ (a &&& ~~~c)) - 11 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 2 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) + 7 * (b ^^^ (a ||| ( ~~~b ||| c))) - 2 * (b ^^^ ~~~(a &&& (b &&& c))) - 6 * (b &&& ~~~(a ^^^ c)) + 2 * (a &&& (b ^^^ c)) - 1 * (c ^^^ ~~~(a ||| ~~~b)) - 3 * a + 1 * (a &&& ( ~~~b ||| c)) + 11 * (b ^^^ ~~~(a ||| (b ^^^ c))) + 3 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) + 3 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) + 3 * ~~~(a ^^^ (b ||| c)) + 4 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) - 11 * (c &&& ~~~(a &&& b)) - 2 * (b ^^^ ~~~(a ||| (b &&& c))) - 11 * ~~~(a ||| ( ~~~b &&& c)) - 2 * (c ^^^ (a ||| ~~~b)) + 25 * ~~~(a ||| (b ||| c)) + 12 * ~~~(a ||| ( ~~~b ||| c)) - 5 * ~~~( ~~~a ||| (b ||| c)) + 11 * ( ~~~a &&& ( ~~~b &&& c)) + 16 * ( ~~~a &&& (b &&& c)) + 8 * (a &&& ( ~~~b &&& c)) - 10 * (a &&& (b &&& c)) = - 10 * ~~~( ~~~a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1788 (x y : BitVec w) : +theorem e_1788 : 1 * (c ^^^ (a ||| ~~~b)) - 1 * (a ||| (b ||| c)) + 1 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 1 * ( ~~~a ||| (b ^^^ c)) + 1 * ~~~(a ||| ( ~~~b &&& c)) + 4 * (c ||| ~~~(a ||| ~~~b)) - 1 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 11 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 11 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) - 11 * (b ^^^ ~~~(a &&& ~~~c)) - 5 * (b ||| (a ^^^ c)) + 1 * (b ^^^ ( ~~~a &&& (b ^^^ c))) - 7 * ~~~(a ^^^ c) - 1 * (c ^^^ ~~~(a &&& (b &&& c))) - 3 * (a ||| ( ~~~b ||| c)) - 1 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) + 2 * ( ~~~a ||| ( ~~~b &&& c)) + 11 * ~~~(a &&& ( ~~~b ||| c)) + 3 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) - 1 * (b ^^^ ( ~~~a ||| (b ||| c))) - 3 * ((a &&& c) ||| ~~~(b ||| c)) - 1 * (a ||| (b ^^^ c)) - 7 * ~~~(a ||| b) + 2 * ~~~( ~~~a &&& (b &&& c)) + 5 * (c &&& (a ^^^ b)) + 1 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 4 * ~~~( ~~~a &&& (b ^^^ c)) + 2 * ~~~( ~~~a ||| ( ~~~b &&& c)) - 2 * ~~~(a ^^^ (b ||| c)) - 3 * ((a &&& b) ^^^ (b ||| ~~~c)) + 5 * ~~~(a ||| (b ||| c)) - 4 * ~~~(a ||| ( ~~~b ||| c)) + 6 * ~~~( ~~~a ||| (b ||| c)) + 9 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 17 * ( ~~~a &&& ( ~~~b &&& c)) - 17 * ( ~~~a &&& (b &&& c)) - 1 * (a &&& ( ~~~b &&& c)) - 1 * (a &&& (b &&& c)) = - 2 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1789 (x y : BitVec w) : +theorem e_1789 : 1 * ((a ||| b) &&& (b ^^^ c)) + 4 * ~~~( ~~~a &&& (b &&& c)) - 11 * (b &&& ~~~(a &&& c)) + 5 * ~~~(a ||| ~~~c) + 7 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 1 * (a ^^^ c) - 5 * ((a &&& b) ||| ~~~(b ||| c)) + 4 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) + 2 * (b ||| ~~~c) - 2 * ( ~~~b &&& (a ^^^ c)) - 6 * (b ^^^ (a &&& ( ~~~b ||| c))) + 1 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) - 6 * ~~~(a ^^^ b) - 1 * (b ^^^ ~~~(a ||| c)) - 3 * (b ||| (a &&& c)) + 5 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 7 * ( ~~~a ||| (b &&& c)) + 1 * ((a &&& ~~~b) ||| (b ^^^ c)) + 7 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) - 1 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) + 1 * (a ||| (b &&& c)) + 2 * (b ^^^ (a ||| (b &&& c))) - 1 * ( ~~~a ||| (b ^^^ c)) - 1 * (c ^^^ (a ||| (b &&& c))) - 1 * (c ^^^ (a ||| ( ~~~b &&& c))) + 4 * ((a ||| b) &&& ~~~(b ^^^ c)) - 5 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) + 4 * ( ~~~a ||| ( ~~~b ||| c)) + 1 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) - 7 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) - 6 * ~~~(a ||| (b ||| c)) - 4 * ~~~(a ||| ( ~~~b ||| c)) - 16 * ~~~( ~~~a ||| (b ||| c)) + 11 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 32 * ( ~~~a &&& ( ~~~b &&& c)) - 8 * ( ~~~a &&& (b &&& c)) - 17 * (a &&& ( ~~~b &&& c)) - 12 * (a &&& (b &&& c)) = - 5 * ((a &&& b) ||| ~~~(b ||| ~~~c)) - 1 * (a ^^^ ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1790 (x y : BitVec w) : +theorem e_1790 : - 1 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) - 11 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) - 6 * ~~~(a ^^^ (b &&& c)) + 4 * ((a ^^^ b) &&& (a ^^^ c)) - 2 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 1 * ( ~~~a &&& ( ~~~b ||| c)) - 5 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) - 1 * ~~~(b &&& ~~~c) + 1 * (a &&& ~~~b) + 1 * (c ^^^ (a ||| b)) + 2 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) + 3 * (b &&& ~~~(a &&& ~~~c)) + 3 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) - 5 * ( ~~~a &&& (b ||| c)) + 7 * (b &&& (a ^^^ c)) + 5 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) - 2 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) - 1 * ~~~(a ||| ~~~b) - 7 * ( ~~~c ||| ~~~(a ^^^ b)) - 7 * ( ~~~b &&& ~~~(a ^^^ c)) + 2 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) + 1 * ( ~~~b ||| ~~~(a ^^^ c)) - 11 * (b ^^^ c) - 11 * (c ^^^ (a ||| ~~~b)) + 4 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 5 * (c ^^^ (a &&& b)) - 3 * (b ^^^ (a ||| (b &&& c))) + 2 * ~~~(a ||| (b ^^^ c)) + 3 * (b ^^^ (a ||| (b ||| c))) + 7 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) + 23 * ~~~(a ||| (b ||| c)) + 52 * ~~~(a ||| ( ~~~b ||| c)) + 11 * ~~~( ~~~a ||| (b ||| c)) + 21 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 22 * ( ~~~a &&& ( ~~~b &&& c)) - 22 * ( ~~~a &&& (b &&& c)) + 2 * (a &&& ( ~~~b &&& c)) + 5 * (a &&& (b &&& c)) = 3 * (c ^^^ ~~~(a &&& ~~~b)) - 2 * (a &&& (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1791 (x y : BitVec w) : +theorem e_1791 : 1 * (c ^^^ ~~~(a ||| (b &&& c))) + 1 * (c ^^^ ~~~(a &&& b)) + 1 * (c &&& (a ^^^ b)) - 1 * (b &&& (a ||| ~~~c)) - 1 * (a ||| ( ~~~b &&& c)) + 11 * (b &&& (a ||| c)) - 1 * ~~~( ~~~a &&& ( ~~~b ||| c)) + 1 * (b &&& ~~~(a &&& ~~~c)) + 3 * ( ~~~a ||| ( ~~~b &&& c)) + 2 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 1 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) + 11 * ~~~(a ||| ~~~b) - 2 * (c ^^^ ~~~(a &&& (b &&& c))) + 2 * (b ^^^ ( ~~~a &&& (b ||| c))) - 3 * ~~~(a ||| c) - 5 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) + 4 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 1 * ((a ||| b) &&& ~~~(b ^^^ c)) + 7 * (a ||| ( ~~~b ||| c)) - 6 * ( ~~~a &&& (b ^^^ c)) - 7 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 2 * (b &&& ~~~(a &&& c)) - 5 * (a ^^^ (b &&& c)) - 7 * (b ||| (a &&& c)) - 6 * (c ||| (a ^^^ b)) - 11 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) - 2 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) - 7 * (b ||| ~~~(a ||| c)) + 11 * ((a ^^^ b) &&& ~~~(a ^^^ c)) + 1 * ~~~(a ^^^ (b &&& c)) - 4 * ~~~(a ||| (b ||| c)) + 22 * ~~~(a ||| ( ~~~b ||| c)) + 42 * ~~~( ~~~a ||| (b ||| c)) + 2 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 4 * ( ~~~a &&& ( ~~~b &&& c)) + 20 * ( ~~~a &&& (b &&& c)) + 16 * (a &&& ( ~~~b &&& c)) + 20 * (a &&& (b &&& c)) = 11 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 1 * (a ||| (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1792 (x y : BitVec w) : +theorem e_1792 : - 3 * (b ||| ~~~c) + 4 * ~~~(a ||| ( ~~~b &&& c)) - 3 * (a ^^^ (b &&& c)) - 1 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 1 * (c ^^^ (a &&& (b ||| c))) + 2 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) - 2 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) + 1 * ~~~(a &&& (b ||| c)) - 7 * ((a ||| b) &&& (b ^^^ c)) - 5 * ( ~~~b &&& (a ^^^ c)) + 2 * (a ||| ~~~c) + 5 * ((a &&& ~~~b) ||| (b ^^^ c)) + 7 * ~~~(b &&& c) + 7 * (c &&& ~~~(a &&& ~~~b)) + 1 * (b ^^^ ( ~~~a &&& (b ||| c))) - 5 * (a &&& c) + 1 * ~~~(a ^^^ c) - 1 * ~~~(a ^^^ ( ~~~b &&& c)) - 2 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) + 1 * (b ||| (a &&& ~~~c)) - 11 * (b ^^^ ~~~(a ||| ~~~c)) - 1 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 2 * (c ||| ~~~(a ||| b)) + 5 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) + 2 * ( ~~~(a ||| b) ||| (b ^^^ c)) - 2 * ~~~(a &&& c) + 3 * (a ||| c) - 3 * (b ||| c) + 4 * ( ~~~a &&& (b ^^^ c)) + 2 * (a &&& ~~~b) + 1 * (b ^^^ ~~~(a &&& (b ||| c))) - 6 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) - 9 * ~~~(a ||| (b ||| c)) + 4 * ~~~(a ||| ( ~~~b ||| c)) - 10 * ~~~( ~~~a ||| (b ||| c)) + 6 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 1 * ( ~~~a &&& (b &&& c)) + 4 * (a &&& (b &&& c)) = 10 * ( ~~~a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1793 (x y : BitVec w) : +theorem e_1793 : - 2 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) + 1 * (b ^^^ ( ~~~a &&& (b ^^^ c))) + 5 * ((a &&& b) ||| (b ^^^ c)) + 2 * (a &&& ~~~c) + 1 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) - 2 * ( ~~~c ||| ~~~(a ^^^ b)) + 1 * ( ~~~a ||| ( ~~~b &&& c)) + 1 * (c ^^^ ~~~(a ||| ~~~b)) - 1 * ~~~(a ||| (b &&& c)) + 7 * ~~~(b &&& c) + 1 * (c &&& (a ||| b)) - 1 * ~~~( ~~~a &&& (b ^^^ c)) + 1 * ( ~~~c ||| (a ^^^ b)) - 5 * ((a &&& b) ^^^ (b ||| ~~~c)) + 2 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) + 1 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) - 2 * (c ^^^ (a &&& b)) - 11 * ~~~(a ||| c) - 2 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) + 1 * ((a ||| b) &&& ~~~(b ^^^ c)) - 2 * (a ||| b) + 2 * ~~~(a &&& b) + 5 * (b ||| c) - 1 * ~~~( ~~~a ||| (b &&& c)) - 1 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) - 1 * ( ~~~b ||| ~~~(a ^^^ c)) + 11 * (c ^^^ ( ~~~a ||| (b ||| c))) - 11 * ( ~~~a ||| ( ~~~b ||| c)) + 2 * ~~~(a ||| ~~~b) + 7 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) + 1 * ~~~(a ||| (b ||| c)) - 14 * ~~~(a ||| ( ~~~b ||| c)) - 6 * ~~~( ~~~a ||| (b ||| c)) - 29 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 16 * ( ~~~a &&& ( ~~~b &&& c)) - 1 * ( ~~~a &&& (b &&& c)) - 15 * (a &&& ( ~~~b &&& c)) - 4 * (a &&& (b &&& c)) = - 3 * ( ~~~(a ||| b) ||| (b ^^^ c)) - 7 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1794 (x y : BitVec w) : +theorem e_1794 : - 1 * (c ||| (a &&& ~~~b)) - 11 * ( ~~~a &&& (b ||| c)) - 6 * (a ^^^ (b ^^^ c)) - 1 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 1 * ~~~(a &&& ~~~b) - 1 * ( ~~~(a &&& b) &&& (b ^^^ c)) + 7 * (b ||| ~~~(a ||| c)) - 3 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) - 3 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) + 4 * (a &&& ~~~c) - 7 * (c &&& (a ||| b)) + 7 * (b ^^^ (a ||| (b &&& c))) - 5 * (c ^^^ (a &&& (b ||| c))) - 7 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 6 * ~~~(a &&& (b &&& c)) + 1 * (b ^^^ (a ||| (b ||| c))) + 11 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) - 6 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) - 7 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) + 2 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) + 2 * (c ^^^ (a ||| (b &&& c))) - 7 * ~~~( ~~~a &&& ( ~~~b ||| c)) + 7 * ((a ||| b) &&& (b ^^^ c)) + 7 * (c ^^^ (a ||| ~~~b)) - 2 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) + 1 * ~~~(a &&& c) - 1 * (b &&& ~~~(a &&& ~~~c)) + 11 * ~~~( ~~~a &&& (b ||| c)) + 4 * (b ^^^ (a &&& (b ||| c))) - 6 * ~~~( ~~~a &&& (b ^^^ c)) + 5 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 16 * ~~~(a ||| (b ||| c)) + 15 * ~~~( ~~~a ||| (b ||| c)) - 14 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 24 * ( ~~~a &&& ( ~~~b &&& c)) + 19 * ( ~~~a &&& (b &&& c)) - 2 * (a &&& ( ~~~b &&& c)) + 25 * (a &&& (b &&& c)) = - 25 * ~~~(a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1795 (x y : BitVec w) : +theorem e_1795 : 2 * (b ||| ~~~(a ||| c)) - 5 * (a ^^^ ( ~~~b ||| c)) - 6 * (b ^^^ ~~~(a &&& (b ||| c))) + 4 * (c &&& (a ||| b)) + 2 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) - 6 * (b ^^^ (a ||| c)) - 6 * (a &&& c) - 11 * (c ^^^ (a ||| (b &&& c))) - 6 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 2 * ~~~(a &&& (b ||| c)) - 1 * ( ~~~b ||| (a ^^^ c)) - 7 * ((a &&& c) ||| ~~~(b ||| c)) - 2 * (c ^^^ (a &&& b)) - 1 * ( ~~~c &&& (a ^^^ b)) - 11 * ( ~~~c &&& ~~~(a ^^^ b)) + 2 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) + 4 * (a ||| (b ^^^ c)) + 3 * (b ^^^ (a ||| (b ^^^ c))) - 1 * ~~~(a ||| (b &&& c)) + 5 * (b ^^^ ~~~(a ||| ~~~c)) + 11 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) - 1 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 11 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) + 7 * (b ^^^ ~~~(a ||| c)) + 2 * ~~~(a ^^^ (b ||| c)) - 2 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) + 2 * ~~~(a &&& ~~~c) - 1 * (b ^^^ ( ~~~a ||| (b ||| c))) + 1 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) + 1 * ~~~(a &&& ( ~~~b &&& c)) - 2 * (b ^^^ ~~~(a &&& c)) - 5 * ~~~(a ||| (b ||| c)) - 2 * ~~~(a ||| ( ~~~b ||| c)) + 7 * ~~~( ~~~a ||| (b ||| c)) + 9 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 11 * ( ~~~a &&& ( ~~~b &&& c)) - 29 * ( ~~~a &&& (b &&& c)) + 8 * (a &&& ( ~~~b &&& c)) - 21 * (a &&& (b &&& c)) = - 1 * ~~~( ~~~a ||| ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1796 (x y : BitVec w) : +theorem e_1796 : - 11 * (b ^^^ ~~~(a ||| (b &&& c))) + 5 * ~~~(a &&& (b ||| c)) - 7 * (c ^^^ ( ~~~a ||| (b ||| c))) + 3 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) - 2 * (b ^^^ ( ~~~a ||| (b &&& c))) - 2 * ~~~( ~~~a &&& (b &&& c)) + 11 * ~~~(a &&& c) - 1 * (b &&& ~~~(a ^^^ c)) - 11 * (b ^^^ (a ||| ~~~c)) - 7 * (b ||| (a ^^^ c)) - 2 * (c ^^^ (a &&& ~~~b)) + 3 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) + 2 * (c ^^^ ~~~(a ||| ~~~b)) - 5 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) - 11 * (c &&& (a ||| b)) - 11 * (b &&& ~~~c) - 7 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 11 * (b ^^^ ( ~~~a ||| (b ^^^ c))) - 2 * ((a ||| b) &&& (b ^^^ c)) - 6 * ~~~b - 6 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) + 3 * ~~~( ~~~a ||| (b ^^^ c)) + 2 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) - 11 * ((a ^^^ b) ||| ~~~(a ^^^ c)) + 7 * ~~~(a &&& (b &&& c)) + 7 * (c ^^^ (a ||| (b &&& c))) + 5 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 5 * ~~~(a &&& b) - 2 * (b ^^^ (a ||| (b ^^^ c))) - 1 * (b &&& ~~~(a &&& c)) - 2 * (c ^^^ ~~~(a &&& (b &&& c))) + 26 * ~~~(a ||| (b ||| c)) + 30 * ~~~(a ||| ( ~~~b ||| c)) + 16 * ~~~( ~~~a ||| (b ||| c)) + 31 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 13 * ( ~~~a &&& ( ~~~b &&& c)) + 42 * ( ~~~a &&& (b &&& c)) + 38 * (a &&& ( ~~~b &&& c)) + 27 * (a &&& (b &&& c)) = 1 * ~~~(a &&& ~~~b) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1797 (x y : BitVec w) : +theorem e_1797 : 1 * ~~~(a ||| b) - 11 * ( ~~~c ||| (a ^^^ b)) + 5 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) + 2 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) - 6 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) - 5 * (b ^^^ ( ~~~a ||| (b ||| c))) - 3 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) - 1 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 11 * (c ^^^ ( ~~~a ||| (b ||| c))) + 4 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) - 7 * ((a &&& b) ||| ~~~(b ^^^ c)) + 2 * (a &&& (b ^^^ c)) + 1 * b - 5 * (c ^^^ (a ||| (b &&& c))) - 2 * ~~~(a ||| c) - 11 * (c &&& (a ^^^ b)) + 1 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 3 * (c &&& ~~~(a &&& b)) + 1 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) - 2 * ~~~(a ||| ~~~c) + 1 * ( ~~~b ||| (a ^^^ c)) - 2 * ~~~(a &&& ( ~~~b ||| c)) + 1 * (a &&& c) - 1 * (c ^^^ (a ||| ( ~~~b ||| c))) - 2 * ~~~( ~~~a &&& (b ^^^ c)) - 11 * ~~~( ~~~a ||| ( ~~~b &&& c)) + 4 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) + 1 * ~~~a + 1 * (c ||| (a &&& b)) + 7 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 4 * (b ^^^ c) - 1 * (c ^^^ ~~~(a ||| (b &&& c))) + 3 * ~~~(a ||| (b ||| c)) - 7 * ~~~(a ||| ( ~~~b ||| c)) + 36 * ~~~( ~~~a ||| (b ||| c)) + 18 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 15 * ( ~~~a &&& ( ~~~b &&& c)) + 29 * ( ~~~a &&& (b &&& c)) + 12 * (a &&& (b &&& c)) = - 5 * (a &&& ( ~~~b &&& c)) + 6 * ( ~~~b &&& (a ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1798 (x y : BitVec w) : +theorem e_1798 : - 1 * ~~~(a ^^^ ( ~~~b &&& c)) + 11 * (b &&& ~~~(a ^^^ c)) - 1 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 3 * ( ~~~b &&& ~~~(a ^^^ c)) + 11 * (b &&& ~~~(a &&& ~~~c)) - 5 * ~~~( ~~~a &&& (b ||| c)) - 2 * (a ||| (b ||| c)) - 11 * (a ||| ( ~~~b ||| c)) + 3 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) + 5 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) + 7 * ((a ||| b) &&& ~~~(b ^^^ c)) + 1 * a - 2 * (b &&& c) + 1 * ~~~(b ||| ~~~c) - 1 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) - 7 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) + 3 * (b ||| ~~~c) - 1 * (c ^^^ ~~~(a &&& (b &&& c))) - 1 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) - 1 * ~~~(a ^^^ (b &&& c)) + 1 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) + 4 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) - 11 * ~~~b - 1 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) + 2 * (a ^^^ (b ||| c)) + 5 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 4 * ~~~(a ^^^ (b ||| c)) + 5 * ~~~(a ||| c) - 7 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) - 3 * ((a ^^^ b) ||| ~~~(a ^^^ c)) + 11 * (b ^^^ ~~~(a ||| ~~~c)) - 7 * (b ^^^ ~~~(a ||| c)) + 34 * ~~~(a ||| (b ||| c)) - 37 * ~~~(a ||| ( ~~~b ||| c)) + 22 * ~~~( ~~~a ||| (b ||| c)) - 1 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 5 * ( ~~~a &&& ( ~~~b &&& c)) - 1 * ( ~~~a &&& (b &&& c)) - 7 * (a &&& (b &&& c)) = - 26 * (a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1799 (x y : BitVec w) : +theorem e_1799 : 5 * (b ^^^ ( ~~~a ||| (b ^^^ c))) - 6 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) + 1 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) + 1 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) - 1 * (b ^^^ ~~~(a ||| (b &&& c))) - 7 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) - 11 * (b ^^^ (a ||| ( ~~~b &&& c))) + 3 * (a &&& ( ~~~b ||| c)) - 1 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) - 6 * ~~~(a &&& ~~~b) + 2 * (b ||| ~~~(a ||| ~~~c)) + 1 * (b ^^^ ~~~(a &&& ~~~c)) - 2 * (c ||| (a &&& b)) - 3 * (b ^^^ (a &&& ( ~~~b ||| c))) - 5 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 7 * (a ^^^ ( ~~~b &&& c)) + 3 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 1 * ~~~(a ^^^ c) - 11 * ~~~(a &&& b) + 7 * ~~~( ~~~a ||| (b &&& c)) - 2 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 1 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) + 4 * (a ^^^ (b ||| c)) + 2 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 1 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) - 2 * (a &&& c) - 7 * (b ^^^ (a &&& ~~~c)) - 5 * ~~~( ~~~a &&& ( ~~~b ||| c)) - 2 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) - 3 * ( ~~~b ||| ~~~(a ^^^ c)) - 2 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) - 5 * (c ^^^ ( ~~~a ||| (b ||| c))) + 24 * ~~~(a ||| (b ||| c)) + 53 * ~~~(a ||| ( ~~~b ||| c)) + 26 * ~~~( ~~~a ||| (b ||| c)) + 21 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 40 * ( ~~~a &&& ( ~~~b &&& c)) + 46 * ( ~~~a &&& (b &&& c)) + 18 * (a &&& ( ~~~b &&& c)) + 39 * (a &&& (b &&& c)) = - 5 * ~~~(b ||| c) - 2 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1800 (x y : BitVec w) : +theorem e_1800 : - 1 * (b ^^^ (a ||| ~~~c)) - 6 * (c ||| (a &&& b)) + 3 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 7 * ~~~(b ||| ~~~c) - 1 * ~~~(b &&& ~~~c) + 5 * ~~~(a ||| b) + 1 * (b ^^^ ~~~(a &&& (b &&& c))) - 5 * (c ^^^ (a &&& b)) - 11 * (c ^^^ (a &&& ~~~b)) - 2 * (c ^^^ (a ||| (b &&& c))) - 11 * ((b &&& c) ||| (a &&& (b ||| c))) + 4 * (b ^^^ (a &&& ~~~c)) - 5 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) - 2 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) - 1 * (b &&& (a ||| c)) - 1 * (b &&& ~~~c) + 2 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 2 * ( ~~~a ||| (b ||| c)) - 5 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) - 2 * ~~~b + 5 * ~~~(a ||| ~~~c) + 4 * (b ^^^ ~~~(a ||| ~~~c)) - 2 * (b ^^^ (a ||| c)) + 4 * (a &&& ( ~~~b ||| c)) - 3 * ((a &&& b) ||| ~~~(b ||| c)) + 3 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 5 * (a &&& ~~~b) - 1 * (c &&& ~~~(a ^^^ b)) + 5 * ((a ||| b) &&& (b ^^^ c)) + 2 * ~~~(a &&& ( ~~~b ||| c)) + 3 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) - 7 * (a ||| (b &&& c)) + 1 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 3 * ~~~(a ||| (b ||| c)) - 13 * ~~~(a ||| ( ~~~b ||| c)) + 17 * ~~~( ~~~a ||| (b ||| c)) + 25 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 35 * ( ~~~a &&& (b &&& c)) + 30 * (a &&& ( ~~~b &&& c)) + 29 * (a &&& (b &&& c)) = - 27 * ( ~~~a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1801 (x y : BitVec w) : +theorem e_1801 : 1 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) + 3 * ((a &&& c) ||| (b &&& ~~~c)) + 5 * ( ~~~a ||| (b ^^^ c)) - 6 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) + 1 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) - 6 * (a ^^^ (b ^^^ c)) - 7 * (a ^^^ (b ||| c)) + 7 * (b ^^^ ( ~~~a ||| (b ^^^ c))) + 2 * (a ^^^ c) - 6 * ( ~~~c ||| (a ^^^ b)) + 2 * (b ||| c) + 2 * ( ~~~a ||| (b ||| c)) - 1 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) + 1 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) - 1 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) - 2 * (b ^^^ (a &&& (b ||| c))) - 2 * ((a &&& b) ||| ~~~(b ||| ~~~c)) + 1 * ~~~(a &&& (b ^^^ c)) + 11 * (b ||| (a ^^^ c)) - 2 * (c &&& (a ||| ~~~b)) + 5 * ((a &&& b) ||| ~~~(b ^^^ c)) + 1 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) + 1 * (c ||| (a ^^^ b)) - 3 * ~~~(a ^^^ (b ^^^ c)) - 2 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) + 1 * ~~~(a ||| ~~~b) + 5 * ~~~(a &&& b) - 2 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) - 1 * (c ^^^ ~~~(a ||| b)) - 3 * ((a ^^^ b) &&& ~~~(a ^^^ c)) - 11 * ( ~~~a &&& ( ~~~b ||| c)) - 1 * (b ^^^ (a ||| ( ~~~b &&& c))) + 11 * ~~~(a ||| (b ||| c)) + 6 * ~~~(a ||| ( ~~~b ||| c)) + 7 * ~~~( ~~~a ||| (b ||| c)) - 19 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 1 * ( ~~~a &&& ( ~~~b &&& c)) + 10 * ( ~~~a &&& (b &&& c)) - 4 * (a &&& ( ~~~b &&& c)) - 14 * (a &&& (b &&& c)) = 11 * ((a &&& b) ^^^ (b ||| ~~~c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1802 (x y : BitVec w) : +theorem e_1802 : - 7 * ((a &&& ~~~b) ||| (b ^^^ c)) - 1 * ~~~(a ||| c) + 1 * (c ^^^ ( ~~~a ||| (b &&& c))) + 3 * ((a &&& b) ||| ~~~(b ^^^ c)) - 11 * (a ||| ( ~~~b &&& c)) + 4 * (b ||| (a ^^^ c)) + 11 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) - 1 * ((a ^^^ b) ||| (a ^^^ c)) - 6 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) - 1 * ((a ^^^ b) &&& ~~~(a ^^^ c)) - 1 * (a ^^^ (b ||| c)) - 1 * (c &&& (a ||| b)) - 5 * ~~~(b &&& ~~~c) + 11 * ((a ||| ~~~b) &&& (b ^^^ c)) + 11 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) - 2 * (b ^^^ (a &&& ( ~~~b ||| c))) + 7 * (c &&& ~~~(a &&& ~~~b)) - 7 * ~~~(a ||| (b ^^^ c)) + 5 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) + 5 * (b &&& (a ||| c)) + 1 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) - 7 * ( ~~~a ||| (b &&& c)) - 5 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) + 2 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) - 5 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) - 2 * ~~~(b ||| ~~~c) + 11 * ~~~(a ||| ~~~b) - 1 * (a ^^^ c) - 5 * ((a ^^^ b) &&& (a ^^^ c)) + 3 * ( ~~~(a ||| b) ||| (b ^^^ c)) + 4 * (b ||| c) - 2 * (c ^^^ (a ||| ( ~~~b &&& c))) - 8 * ~~~(a ||| (b ||| c)) - 6 * ~~~(a ||| ( ~~~b ||| c)) + 4 * ~~~( ~~~a ||| (b ||| c)) + 4 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 8 * ( ~~~a &&& ( ~~~b &&& c)) - 13 * ( ~~~a &&& (b &&& c)) + 13 * (a &&& ( ~~~b &&& c)) - 13 * (a &&& (b &&& c)) = - 2 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) - 1 * ( ~~~a &&& (b ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1803 (x y : BitVec w) : +theorem e_1803 : 3 * (b &&& (a ||| ~~~c)) + 7 * (b &&& ~~~(a &&& c)) + 1 * (a ||| (b ^^^ c)) - 1 * (a &&& ( ~~~b ||| c)) - 1 * (b ||| ~~~(a ||| ~~~c)) + 11 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) - 7 * (c ^^^ (a &&& b)) - 3 * (c ^^^ ( ~~~a &&& (b ||| c))) - 7 * ~~~(b ||| c) - 7 * (b ^^^ ~~~(a ||| c)) + 7 * ((a &&& b) ||| ~~~(b ||| c)) + 1 * (b &&& (a ^^^ c)) - 7 * ~~~( ~~~a &&& (b &&& c)) + 1 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) - 6 * (c ^^^ (a &&& ( ~~~b ||| c))) + 4 * ~~~(a ||| (b &&& c)) - 11 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 3 * ~~~( ~~~a &&& ( ~~~b &&& c)) - 11 * (a &&& b) + 7 * (c ^^^ (a ||| (b ||| c))) - 2 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) - 11 * (c ||| (a ^^^ b)) + 4 * ( ~~~a ||| (b ^^^ c)) - 1 * ( ~~~b &&& (a ^^^ c)) - 1 * (a ||| c) + 1 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 2 * (c ^^^ (a ||| ~~~b)) + 7 * ~~~(a ||| b) + 4 * (a ^^^ ( ~~~b ||| c)) + 4 * (a ||| (b &&& c)) - 1 * (b ^^^ (a ||| (b &&& c))) - 1 * (c &&& ~~~(a &&& b)) - 4 * ~~~(a ||| (b ||| c)) - 12 * ~~~(a ||| ( ~~~b ||| c)) + 26 * ~~~( ~~~a ||| (b ||| c)) - 16 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 3 * ( ~~~a &&& ( ~~~b &&& c)) + 12 * ( ~~~a &&& (b &&& c)) + 34 * (a &&& ( ~~~b &&& c)) + 30 * (a &&& (b &&& c)) = - 1 * (b ||| c) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1804 (x y : BitVec w) : +theorem e_1804 : - 11 * ~~~( ~~~a &&& (b &&& c)) + 7 * ((a ^^^ b) &&& (a ^^^ c)) + 1 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) - 1 * ( ~~~b &&& ~~~(a ^^^ c)) - 5 * ~~~(a ||| c) + 4 * (b ||| c) - 11 * (b ^^^ ( ~~~a ||| (b ^^^ c))) - 1 * (a ^^^ ( ~~~b &&& c)) - 7 * (b &&& c) + 2 * ( ~~~a &&& (b ^^^ c)) + 2 * (a ||| ( ~~~b ||| c)) - 6 * (b ^^^ (a &&& c)) + 1 * ~~~( ~~~a &&& (b ||| c)) + 4 * ((a ^^^ b) &&& ~~~(a ^^^ c)) + 1 * ~~~(a ^^^ ( ~~~b ||| c)) - 3 * ~~~(a &&& ( ~~~b ||| c)) - 3 * ~~~( ~~~a ||| (b &&& c)) + 1 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) - 2 * (b ||| (a ^^^ c)) + 1 * ~~~(a ||| ( ~~~b &&& c)) + 2 * ( ~~~(a ||| b) ||| (b ^^^ c)) - 7 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 6 * ~~~(a &&& ~~~b) - 1 * ~~~( ~~~a &&& ( ~~~b &&& c)) - 5 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 3 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) - 6 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 1 * ~~~(a &&& ~~~c) - 1 * (b ^^^ (a ||| (b ^^^ c))) - 2 * (a ||| ~~~b) - 2 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) + 2 * (b ^^^ ~~~(a &&& (b ^^^ c))) + 44 * ~~~(a ||| (b ||| c)) + 27 * ~~~(a ||| ( ~~~b ||| c)) + 10 * ~~~( ~~~a ||| (b ||| c)) + 31 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 21 * ( ~~~a &&& ( ~~~b &&& c)) + 18 * ( ~~~a &&& (b &&& c)) + 18 * (a &&& ( ~~~b &&& c)) + 21 * (a &&& (b &&& c)) = - 2 * (c &&& (a ||| ~~~b)) - 11 * (a ||| ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1805 (x y : BitVec w) : +theorem e_1805 : - 11 * (c ^^^ ~~~(a &&& (b &&& c))) - 6 * ((a &&& b) ||| ~~~(b ||| c)) + 1 * ( ~~~b &&& ~~~(a ^^^ c)) - 11 * ~~~c + 11 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 2 * ~~~( ~~~a &&& (b ^^^ c)) + 1 * (c &&& (a ^^^ b)) + 1 * (b ||| (a &&& ~~~c)) + 3 * (c ^^^ ~~~(a ||| (b &&& c))) - 2 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) + 4 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) - 1 * ~~~( ~~~a &&& (b ||| c)) + 2 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 11 * (b ||| ~~~(a ||| c)) + 2 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) - 1 * (b ^^^ (a ||| (b &&& c))) + 5 * (b &&& ~~~(a &&& c)) - 7 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) + 7 * ~~~(a ||| b) + 1 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) + 1 * ( ~~~a &&& (b ||| c)) + 11 * ~~~(a &&& ~~~c) + 3 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 7 * ~~~b - 7 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) - 3 * (b ^^^ (a ||| (b ^^^ c))) + 3 * ~~~(a &&& b) - 2 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) + 2 * ~~~(a ||| (b &&& c)) - 2 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 11 * (b &&& (a ^^^ c)) + 3 * (b ||| c) + 11 * ~~~(a ||| (b ||| c)) + 5 * ~~~(a ||| ( ~~~b ||| c)) + 16 * ~~~( ~~~a ||| (b ||| c)) + 29 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 15 * ( ~~~a &&& ( ~~~b &&& c)) - 2 * ( ~~~a &&& (b &&& c)) - 33 * (a &&& ( ~~~b &&& c)) + 25 * (a &&& (b &&& c)) = 5 * (b ^^^ ~~~(a &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1806 (x y : BitVec w) : +theorem e_1806 : 7 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) - 11 * (a &&& ( ~~~b ||| c)) - 7 * (c ||| ~~~(a ^^^ b)) + 2 * ~~~a - 2 * (c ^^^ (a &&& (b ||| c))) - 6 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) + 5 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) + 11 * (b ^^^ ( ~~~a &&& (b ^^^ c))) + 5 * (a &&& b) - 1 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) - 1 * (c &&& (a ^^^ b)) - 1 * (b ^^^ (a ||| ( ~~~b &&& c))) + 11 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) - 1 * (a ||| (b ^^^ c)) - 5 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 5 * (a ||| b) - 2 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) + 11 * (b ^^^ c) + 1 * ( ~~~b &&& ~~~(a ^^^ c)) - 11 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) - 3 * (a ^^^ (b &&& c)) + 5 * (b &&& ~~~c) + 7 * ((a ^^^ b) ||| (a ^^^ c)) + 7 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 5 * (b ^^^ ~~~(a &&& ~~~c)) - 7 * ~~~(a ||| b) - 5 * (b ^^^ (a ||| (b &&& c))) - 6 * (b ^^^ (a &&& c)) + 1 * ~~~(a ||| ~~~c) - 2 * (c ^^^ (a &&& b)) - 6 * (a ||| ( ~~~b &&& c)) + 5 * (b ^^^ ( ~~~a ||| (b ||| c))) - 7 * (c ^^^ (a &&& ( ~~~b ||| c))) + 17 * ~~~(a ||| (b ||| c)) - 1 * ~~~(a ||| ( ~~~b ||| c)) + 33 * ~~~( ~~~a ||| (b ||| c)) + 1 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 10 * ( ~~~a &&& ( ~~~b &&& c)) + 5 * ( ~~~a &&& (b &&& c)) - 7 * (a &&& (b &&& c)) = - 31 * (a &&& ( ~~~b &&& c)) - 4 * (c ^^^ (a ||| (b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1807 (x y : BitVec w) : +theorem e_1807 : 7 * ~~~(a &&& ( ~~~b &&& c)) - 3 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) + 2 * (c ^^^ (a &&& ~~~b)) - 1 * ( ~~~c &&& (a ^^^ b)) + 5 * (c &&& (a ^^^ b)) + 1 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) - 5 * ~~~(a ||| (b &&& c)) - 7 * (b ^^^ ~~~(a &&& ~~~c)) - 2 * ((a ||| b) &&& ~~~(b ^^^ c)) + 2 * ( ~~~a &&& (b ||| c)) + 3 * (b ^^^ (a ||| (b ^^^ c))) + 1 * ~~~(a ||| ~~~b) - 1 * (a ||| c) + 3 * ((a &&& b) ||| (b ^^^ c)) - 5 * (b ||| c) - 7 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) + 11 * ~~~a + 11 * (c ^^^ (a ||| ( ~~~b &&& c))) - 11 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) + 4 * ~~~(a &&& ( ~~~b ||| c)) - 1 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) + 3 * ~~~( ~~~a &&& (b ^^^ c)) + 11 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 3 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) - 3 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) - 11 * ( ~~~b ||| ~~~(a ^^^ c)) + 7 * (c ^^^ (a &&& b)) + 3 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) + 2 * ( ~~~a &&& ( ~~~b ||| c)) + 5 * (a &&& (b ^^^ c)) - 6 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) + 4 * ~~~(a ||| b) + 1 * ~~~(a ||| (b ||| c)) + 19 * ~~~(a ||| ( ~~~b ||| c)) + 16 * ~~~( ~~~a ||| (b ||| c)) - 13 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 7 * ( ~~~a &&& ( ~~~b &&& c)) - 48 * ( ~~~a &&& (b &&& c)) + 13 * (a &&& ( ~~~b &&& c)) + 34 * (a &&& (b &&& c)) = 6 * ((a &&& c) ||| ~~~(b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1808 (x y : BitVec w) : +theorem e_1808 : 5 * ~~~(a ^^^ b) + 3 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) - 2 * ((a ^^^ b) ||| (a ^^^ c)) + 5 * ((a ||| b) &&& (b ^^^ c)) - 1 * (a ||| c) + 1 * (c ||| ~~~(a ||| b)) - 7 * (a ||| (b ^^^ c)) - 2 * (a &&& ~~~b) - 1 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) - 7 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 1 * ~~~(a &&& ~~~a) - 11 * ((a &&& b) ||| ~~~(b ||| c)) - 2 * (b ||| (a &&& ~~~c)) + 7 * (c ^^^ (a ||| (b &&& c))) - 2 * ~~~(a ^^^ (b ^^^ c)) - 1 * (c ^^^ (a ||| ( ~~~b ||| c))) - 2 * (b ^^^ (a ||| c)) + 5 * ( ~~~c &&& ~~~(a ^^^ b)) - 3 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) - 1 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 1 * ((a ||| b) &&& ~~~(b ^^^ c)) - 2 * (b ^^^ ( ~~~a ||| (b &&& c))) + 2 * (a ||| ~~~b) - 1 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) + 1 * (b ^^^ (a &&& (b ||| c))) - 3 * (c ^^^ ~~~(a &&& (b ||| c))) - 1 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) - 7 * ((a ^^^ b) &&& ~~~(a ^^^ c)) + 1 * ~~~( ~~~a &&& (b ^^^ c)) - 3 * (c ||| (a &&& b)) + 1 * (b ^^^ (a &&& ~~~c)) - 2 * ((a &&& c) ||| ~~~(b ||| c)) - 2 * (b ^^^ ( ~~~a &&& (b ^^^ c))) - 5 * (b ^^^ (a ||| (b ^^^ c))) + 13 * ~~~(a ||| (b ||| c)) + 19 * ~~~(a ||| ( ~~~b ||| c)) + 32 * ~~~( ~~~a ||| (b ||| c)) + 21 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 23 * ( ~~~a &&& (b &&& c)) + 28 * (a &&& ( ~~~b &&& c)) + 17 * (a &&& (b &&& c)) = - 7 * ( ~~~a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1809 (x y : BitVec w) : +theorem e_1809 : - 5 * (b ^^^ (a ||| ~~~c)) - 2 * (b ^^^ ( ~~~a &&& (b ^^^ c))) - 3 * ~~~( ~~~a &&& (b ||| c)) + 2 * (b ||| ~~~(a ||| ~~~c)) - 2 * (b ^^^ (a ||| ( ~~~b &&& c))) - 1 * (b &&& ~~~(a &&& ~~~c)) - 1 * (a ||| (b &&& c)) - 2 * (a ^^^ (b &&& c)) + 5 * (b ^^^ ~~~(a ||| ~~~c)) - 3 * ~~~(a &&& (b ||| c)) + 3 * (c ^^^ ( ~~~a &&& (b ||| c))) - 5 * (a ^^^ (b ||| c)) + 5 * (b ||| (a ^^^ c)) - 1 * (c &&& (a ||| b)) - 3 * (a &&& b) + 7 * (b ^^^ ( ~~~a ||| (b ^^^ c))) + 2 * ((b &&& c) ||| (a &&& (b ||| c))) + 1 * ~~~(b &&& ~~~c) + 1 * (b ^^^ (a &&& ~~~c)) + 2 * ~~~(a &&& (b &&& c)) + 2 * (b ^^^ ~~~(a &&& c)) + 7 * (b ^^^ ~~~(a &&& (b ^^^ c))) + 3 * ( ~~~a ||| ( ~~~b ||| c)) - 5 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) + 2 * ((a ^^^ b) &&& ~~~(a ^^^ c)) + 1 * ( ~~~a &&& (b ^^^ c)) + 1 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) + 1 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 3 * (b ^^^ ~~~(a &&& (b ||| c))) + 1 * ((a &&& c) ^^^ (b ||| c)) + 2 * ~~~(a &&& c) - 1 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) - 7 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) - 1 * (b &&& c) - 8 * ~~~(a ||| (b ||| c)) - 4 * ~~~(a ||| ( ~~~b ||| c)) + 14 * ~~~( ~~~a ||| (b ||| c)) - 9 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 16 * ( ~~~a &&& ( ~~~b &&& c)) + 11 * ( ~~~a &&& (b &&& c)) - 6 * (a &&& ( ~~~b &&& c)) = 3 * ((a &&& b) ||| ~~~(b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1810 (x y : BitVec w) : +theorem e_1810 : - 1 * (c ^^^ ~~~(a &&& ~~~b)) + 4 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) + 11 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) + 7 * (c ^^^ ~~~(a &&& (b &&& c))) + 2 * (a ||| ( ~~~b &&& c)) - 2 * (b ||| ~~~(a ^^^ c)) + 4 * ((a &&& b) ||| ~~~(b ||| ~~~c)) - 2 * (a &&& c) + 2 * ~~~(a ^^^ (b ||| c)) + 2 * (b ^^^ ( ~~~a &&& (b ^^^ c))) + 3 * (b &&& (a ||| c)) + 1 * (b ^^^ ~~~(a &&& (b &&& c))) - 5 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) - 11 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 1 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 1 * ((a ||| b) &&& ~~~(b ^^^ c)) + 5 * ~~~(a &&& ~~~b) - 6 * (a ||| (b &&& c)) + 4 * (c ||| ~~~(a ||| b)) + 3 * ~~~(a ||| ( ~~~b &&& c)) - 11 * ~~~(a &&& ~~~c) - 3 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) - 1 * ((a &&& c) ||| ~~~(b ||| c)) + 2 * (c ^^^ (a ||| (b &&& c))) + 1 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) - 1 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) + 1 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) - 11 * (a ||| (b ||| c)) + 11 * (b ||| ~~~(a ||| ~~~c)) + 1 * (b ^^^ (a &&& ~~~c)) + 7 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) + 7 * ((a ||| ~~~b) &&& (b ^^^ c)) - 2 * (c ^^^ (a &&& (b ||| c))) - 18 * ~~~(a ||| (b ||| c)) - 3 * ~~~(a ||| ( ~~~b ||| c)) - 9 * ~~~( ~~~a ||| (b ||| c)) - 22 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 28 * ( ~~~a &&& ( ~~~b &&& c)) - 15 * ( ~~~a &&& (b &&& c)) + 25 * (a &&& ( ~~~b &&& c)) - 22 * (a &&& (b &&& c)) = - 1 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) - 2 * ~~~(a ||| (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1811 (x y : BitVec w) : +theorem e_1811 : 7 * ((a ||| ~~~b) &&& (b ^^^ c)) + 7 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) - 6 * ((a ||| b) &&& (b ^^^ c)) + 3 * (b ^^^ ( ~~~a ||| (b ||| c))) - 6 * (b ^^^ c) + 7 * ((a &&& c) ||| (b &&& ~~~c)) - 2 * ~~~c - 2 * ~~~(a ||| (b &&& c)) - 3 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) + 2 * ((a ^^^ b) ||| (a ^^^ c)) + 5 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 1 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) - 11 * ~~~( ~~~a &&& (b ^^^ c)) - 1 * (b &&& ~~~c) + 3 * (a ^^^ ( ~~~b &&& c)) - 2 * ~~~(a &&& (b &&& c)) + 1 * ( ~~~c ||| ~~~(a ^^^ b)) - 1 * (b ^^^ (a &&& (b ^^^ c))) - 1 * (a ||| b) - 11 * ~~~( ~~~a ||| (b &&& c)) + 11 * (a &&& ( ~~~b ||| c)) + 1 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 5 * ~~~(a ||| b) + 2 * ~~~( ~~~a ||| ( ~~~b &&& c)) + 11 * (a ||| (b &&& c)) - 3 * ( ~~~a ||| (b ^^^ c)) + 4 * (c ||| ~~~(a ||| b)) - 1 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) - 2 * (a &&& (b ||| c)) + 1 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) + 2 * ~~~(a ||| c) + 1 * (a ||| (b ||| c)) + 5 * ((a &&& c) ^^^ (b ||| c)) - 2 * ~~~(a ||| (b ||| c)) + 1 * ~~~(a ||| ( ~~~b ||| c)) - 6 * ~~~( ~~~a ||| (b ||| c)) - 3 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 22 * ( ~~~a &&& ( ~~~b &&& c)) - 5 * ( ~~~a &&& (b &&& c)) - 5 * (a &&& ( ~~~b &&& c)) - 29 * (a &&& (b &&& c)) = 2 * ~~~(b ||| ~~~c) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1812 (x y : BitVec w) : +theorem e_1812 : - 2 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) + 1 * ( ~~~a ||| ( ~~~b &&& c)) - 1 * (b ||| ~~~(a ^^^ c)) + 11 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 11 * ~~~b + 2 * ~~~(a ||| (b &&& c)) - 11 * (b ||| ~~~c) - 11 * (c &&& ~~~(a &&& b)) + 3 * ~~~(a ^^^ (b ||| c)) + 1 * (a ||| ~~~c) + 2 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) + 1 * (b ^^^ ~~~(a ||| c)) + 11 * (b &&& ~~~(a &&& c)) - 6 * (b ^^^ ~~~(a ||| (b &&& c))) - 11 * (b ||| (a &&& ~~~c)) - 6 * (c ^^^ (a ||| b)) + 7 * (a ||| c) + 1 * (a ^^^ (b &&& c)) - 1 * ~~~(a &&& c) - 6 * (b ||| (a &&& c)) - 1 * ( ~~~a ||| ( ~~~b ||| c)) - 2 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 4 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) + 3 * (c &&& (a ||| ~~~b)) + 2 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 4 * ((a &&& b) ||| (b ^^^ c)) - 6 * ~~~(b ||| ~~~c) + 2 * b + 11 * ~~~(a ||| ~~~b) - 1 * ((a ||| b) &&& ~~~(b ^^^ c)) - 1 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) - 1 * (a &&& ( ~~~b ||| c)) + 1 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 15 * ~~~(a ||| (b ||| c)) - 5 * ~~~(a ||| ( ~~~b ||| c)) + 19 * ~~~( ~~~a ||| (b ||| c)) - 7 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 16 * ( ~~~a &&& ( ~~~b &&& c)) - 12 * ( ~~~a &&& (b &&& c)) + 2 * (a &&& ( ~~~b &&& c)) + 2 * (a &&& (b &&& c)) = - 5 * (a ||| (b &&& c)) - 5 * (c ||| ~~~(a ^^^ b)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1813 (x y : BitVec w) : +theorem e_1813 : - 3 * ~~~(a &&& ~~~b) - 7 * ~~~(a ^^^ (b &&& c)) + 11 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) - 3 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) - 2 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) + 2 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) + 2 * (b &&& ~~~(a ^^^ c)) + 4 * ( ~~~b ||| (a ^^^ c)) + 1 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) - 7 * (b ^^^ (a &&& c)) - 5 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) + 3 * ( ~~~(a &&& b) &&& (b ^^^ c)) - 11 * (c ||| (a &&& b)) + 1 * ((a ^^^ b) &&& (a ^^^ c)) - 6 * (c ^^^ (a ||| (b ||| c))) + 1 * ((a &&& c) ||| ~~~(b ||| c)) + 1 * ~~~(a ^^^ ( ~~~b &&& c)) + 3 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) - 1 * ( ~~~a &&& (b ^^^ c)) - 6 * ~~~(a &&& b) - 2 * ((a &&& b) ||| ~~~(b ||| c)) + 1 * ( ~~~b &&& (a ^^^ c)) - 3 * (a &&& b) + 1 * ~~~(a ^^^ (b ^^^ c)) - 11 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) + 5 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 5 * ( ~~~a ||| ( ~~~b ||| c)) - 1 * ( ~~~c ||| (a ^^^ b)) + 11 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 6 * (c ^^^ ( ~~~a ||| (b ||| c))) - 2 * (b ^^^ ~~~(a &&& c)) + 1 * (c ^^^ ( ~~~a ||| (b &&& c))) - 1 * (a ||| (b ||| c)) + 10 * ~~~(a ||| (b ||| c)) + 25 * ~~~(a ||| ( ~~~b ||| c)) + 6 * ~~~( ~~~a ||| (b ||| c)) + 38 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 36 * ( ~~~a &&& ( ~~~b &&& c)) + 25 * ( ~~~a &&& (b &&& c)) + 10 * (a &&& ( ~~~b &&& c)) + 33 * (a &&& (b &&& c)) = 1 * ~~~(b ||| ~~~c) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1814 (x y : BitVec w) : +theorem e_1814 : 5 * (b ^^^ ~~~(a &&& (b ||| c))) - 1 * ( ~~~(a ||| b) ||| (b ^^^ c)) + 2 * (a &&& (b ^^^ c)) + 3 * ~~~(b ||| ~~~c) + 7 * ~~~c + 7 * (b ^^^ (a ||| ~~~c)) + 1 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 2 * (b ^^^ (a ||| c)) + 2 * (b ^^^ ( ~~~a ||| (b ||| c))) + 1 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) + 4 * (b ^^^ (a ||| (b &&& c))) - 1 * (c ^^^ ~~~(a ||| b)) - 11 * (b ^^^ (a &&& (b ^^^ c))) - 7 * ~~~(a ^^^ (b ^^^ c)) + 2 * (b ||| (a &&& c)) - 6 * ~~~( ~~~a ||| ( ~~~b &&& c)) + 11 * (b ||| ~~~(a ||| c)) + 1 * (c ^^^ (a &&& (b ||| c))) + 7 * ~~~(b ||| c) - 3 * (c ||| ~~~(a ||| ~~~b)) + 4 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) + 2 * ~~~(b ^^^ c) - 1 * (b ^^^ (a ||| (b ||| c))) + 2 * (a ||| ~~~c) - 3 * (b ^^^ (a ||| ( ~~~b ||| c))) - 1 * ~~~(a &&& ~~~c) + 11 * ( ~~~a ||| (b &&& c)) - 2 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) + 5 * ~~~(a ||| c) + 11 * (b ^^^ ( ~~~a &&& (b ||| c))) - 2 * (c ||| (a &&& b)) - 2 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) + 1 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) - 11 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 48 * ~~~(a ||| (b ||| c)) - 26 * ~~~(a ||| ( ~~~b ||| c)) - 18 * ~~~( ~~~a ||| (b ||| c)) - 26 * ( ~~~a &&& ( ~~~b &&& c)) - 4 * ( ~~~a &&& (b &&& c)) + 19 * (a &&& ( ~~~b &&& c)) - 23 * (a &&& (b &&& c)) = 24 * ~~~( ~~~a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1815 (x y : BitVec w) : +theorem e_1815 : - 7 * (a &&& (b ^^^ c)) - 6 * ~~~(a ^^^ c) - 5 * ~~~(a &&& ~~~b) - 5 * ~~~(a &&& (b ^^^ c)) - 3 * (b ^^^ (a ||| ~~~c)) + 11 * (b ||| ~~~(a ^^^ c)) - 1 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) - 2 * (c ^^^ ~~~(a &&& b)) - 2 * ( ~~~b &&& (a ^^^ c)) - 1 * (b ^^^ (a &&& c)) + 1 * ((a &&& c) ||| ~~~(b ||| c)) + 4 * ((a ||| ~~~b) &&& (b ^^^ c)) + 3 * ~~~( ~~~a ||| ( ~~~b &&& c)) - 6 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 1 * ( ~~~a ||| (b ||| c)) + 4 * (b ||| c) - 3 * (a ||| (b ^^^ c)) + 2 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) + 2 * (a ^^^ ( ~~~b &&& c)) - 11 * (c ^^^ ~~~(a &&& (b ||| c))) - 1 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) + 11 * (b &&& ~~~(a &&& c)) + 4 * (a ^^^ ( ~~~b ||| c)) - 6 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 2 * ( ~~~b &&& ~~~(a ^^^ c)) - 6 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 7 * (b ^^^ ~~~(a ||| (b &&& c))) + 1 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 6 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) + 1 * (c ^^^ (a &&& (b ||| c))) - 1 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) + 4 * ~~~( ~~~a &&& (b ||| c)) + 7 * (c ^^^ ~~~(a &&& ~~~b)) - 3 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) + 9 * ~~~(a ||| (b ||| c)) + 7 * ~~~(a ||| ( ~~~b ||| c)) + 16 * ~~~( ~~~a ||| (b ||| c)) - 46 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 4 * ( ~~~a &&& ( ~~~b &&& c)) - 23 * ( ~~~a &&& (b &&& c)) - 3 * (a &&& ( ~~~b &&& c)) = - 1 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) - 11 * (a ||| c) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1816 (x y : BitVec w) : +theorem e_1816 : 1 * (b ^^^ (a &&& ( ~~~b ||| c))) - 1 * ((a &&& c) ||| ~~~(b ||| c)) - 1 * (b &&& ~~~(a ^^^ c)) + 2 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) - 5 * (b ^^^ (a ||| ~~~c)) - 11 * ~~~(b ||| ~~~c) - 1 * (b &&& ~~~(a &&& ~~~c)) - 1 * ( ~~~b &&& (a ^^^ c)) + 2 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) - 6 * ~~~(a ||| (b &&& c)) + 1 * (c ^^^ (a ||| ( ~~~b &&& c))) - 6 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 4 * ~~~(a ||| c) - 3 * ((a &&& c) ||| (b &&& ~~~c)) - 2 * ((a ^^^ b) &&& ~~~(a ^^^ c)) + 3 * (b ||| (a ^^^ c)) - 2 * (b ^^^ ~~~(a &&& (b ^^^ c))) + 7 * (a &&& ( ~~~b ||| c)) + 1 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 1 * ((a ^^^ b) ||| (a ^^^ c)) + 2 * ((a ^^^ b) ||| ~~~(a ^^^ c)) + 11 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) - 11 * ~~~(a &&& (b ^^^ c)) - 11 * (b ||| (a &&& c)) - 7 * ((a &&& b) ^^^ (b ||| ~~~c)) + 4 * a - 5 * ((a &&& b) ||| (b ^^^ c)) - 1 * (b ^^^ ( ~~~a ||| (b ^^^ c))) + 1 * (b ||| ~~~(a ||| c)) - 6 * ( ~~~(a &&& b) &&& (b ^^^ c)) + 4 * (c ^^^ (a ||| (b &&& c))) - 2 * (a ^^^ (b ^^^ c)) - 1 * (a ^^^ (b ||| c)) + 18 * ~~~(a ||| (b ||| c)) + 40 * ~~~(a ||| ( ~~~b ||| c)) + 12 * ~~~( ~~~a ||| (b ||| c)) - 5 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 30 * ( ~~~a &&& ( ~~~b &&& c)) + 30 * ( ~~~a &&& (b &&& c)) + 30 * (a &&& ( ~~~b &&& c)) + 3 * (a &&& (b &&& c)) = - 3 * (c ||| (a &&& b)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1817 (x y : BitVec w) : +theorem e_1817 : - 5 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) - 1 * (b ^^^ (a &&& c)) + 11 * ( ~~~b ||| ~~~(a ^^^ c)) + 1 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) - 1 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) + 7 * (b &&& ~~~(a &&& ~~~c)) - 2 * ~~~(a ||| ~~~c) + 1 * (b ^^^ (a ||| (b ||| c))) - 2 * (a &&& (b ^^^ c)) - 2 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) + 1 * (c ^^^ (a ||| (b &&& c))) - 1 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 1 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 3 * ~~~a + 1 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) + 1 * (b ^^^ ~~~(a &&& c)) - 5 * ~~~(a ||| (b ^^^ c)) - 11 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) - 1 * (b ^^^ ~~~(a &&& (b ||| c))) - 7 * (b ^^^ ~~~(a &&& ~~~c)) + 7 * (b ^^^ ( ~~~a ||| (b &&& c))) + 11 * ~~~( ~~~a &&& ( ~~~b ||| c)) - 2 * ((a &&& b) ||| ~~~(b ^^^ c)) - 5 * (c ^^^ (a &&& b)) + 1 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 11 * (b ^^^ (a ||| ( ~~~b ||| c))) + 5 * ( ~~~a &&& (b ^^^ c)) + 3 * (c ^^^ ~~~(a ||| (b &&& c))) - 2 * ( ~~~c ||| ~~~(a ^^^ b)) + 1 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) - 11 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) - 1 * (b ^^^ ( ~~~a &&& (b ^^^ c))) - 2 * (b ^^^ (a &&& ( ~~~b ||| c))) + 25 * ~~~(a ||| (b ||| c)) - 12 * ~~~(a ||| ( ~~~b ||| c)) + 14 * ~~~( ~~~a ||| (b ||| c)) + 17 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 19 * ( ~~~a &&& ( ~~~b &&& c)) + 4 * ( ~~~a &&& (b &&& c)) + 13 * (a &&& ( ~~~b &&& c)) - 26 * (a &&& (b &&& c)) = 1 * (c ^^^ (a &&& ~~~b)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1818 (x y : BitVec w) : +theorem e_1818 : 7 * (b ^^^ (a &&& (b ||| c))) + 2 * ( ~~~a ||| ( ~~~b ||| c)) - 1 * ((a &&& ~~~b) ||| (b ^^^ c)) - 2 * ( ~~~a &&& ( ~~~b ||| c)) + 2 * (c &&& ~~~(a ^^^ b)) - 7 * (b &&& ~~~(a ^^^ c)) + 4 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) + 1 * (c &&& (a ||| b)) - 1 * ~~~(a &&& ~~~b) - 2 * ( ~~~c &&& (a ^^^ b)) + 11 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) - 6 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 5 * ((a &&& b) ||| ~~~(b ||| c)) + 1 * (b ^^^ ( ~~~a &&& (b ^^^ c))) - 2 * ~~~(a ||| ~~~c) + 7 * ( ~~~a ||| (b ^^^ c)) - 11 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) - 2 * (b ^^^ ~~~(a &&& (b &&& c))) + 7 * (a &&& ( ~~~b ||| c)) + 1 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 11 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) + 1 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) - 2 * (a &&& ~~~b) + 1 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) - 7 * ~~~(b ^^^ c) + 2 * ((a &&& b) ||| ~~~(b ^^^ c)) - 5 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 11 * (c ^^^ ( ~~~a ||| (b &&& c))) + 1 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 5 * ~~~(a ^^^ (b ^^^ c)) + 3 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) - 3 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 1 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 24 * ~~~(a ||| (b ||| c)) + 20 * ~~~(a ||| ( ~~~b ||| c)) + 14 * ~~~( ~~~a ||| (b ||| c)) - 16 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 2 * ( ~~~a &&& ( ~~~b &&& c)) + 15 * ( ~~~a &&& (b &&& c)) + 4 * (a &&& ( ~~~b &&& c)) - 3 * (a &&& (b &&& c)) = 1 * ~~~( ~~~a &&& (b ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1819 (x y : BitVec w) : +theorem e_1819 : - 2 * c - 3 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) + 7 * (c ^^^ ( ~~~a ||| (b &&& c))) + 5 * ~~~(a ^^^ c) + 4 * ~~~( ~~~a ||| (b ^^^ c)) + 4 * ~~~(a ^^^ ( ~~~b &&& c)) + 1 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 6 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) - 7 * (c ^^^ (a &&& (b ||| c))) - 7 * (c ^^^ (a &&& b)) - 7 * ( ~~~c ||| ~~~(a ^^^ b)) + 11 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) - 1 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) + 11 * (c ^^^ ~~~(a &&& b)) - 11 * ( ~~~b ||| (a ^^^ c)) - 11 * (a ||| (b &&& c)) + 1 * (c ^^^ (a &&& ( ~~~b ||| c))) + 5 * ( ~~~a &&& (b ||| c)) - 7 * (c &&& (a ||| ~~~b)) + 3 * (b ^^^ c) + 11 * (c ||| ~~~(a ^^^ b)) - 2 * (a ||| (b ^^^ c)) - 7 * (b ^^^ ~~~(a &&& (b ^^^ c))) - 1 * ~~~(b ||| ~~~c) + 2 * ((a &&& b) ^^^ (b ||| c)) + 4 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 1 * (b &&& (a ^^^ c)) + 1 * (a &&& (b ||| c)) + 1 * ~~~(a &&& ~~~c) - 1 * (a ^^^ ( ~~~b ||| c)) + 5 * b - 2 * ((a &&& c) ||| (b &&& ~~~c)) + 1 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) + 1 * (b ^^^ ( ~~~a &&& (b ^^^ c))) - 30 * ~~~(a ||| (b ||| c)) - 29 * ~~~(a ||| ( ~~~b ||| c)) + 21 * ~~~( ~~~a ||| (b ||| c)) + 43 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 20 * ( ~~~a &&& ( ~~~b &&& c)) - 2 * ( ~~~a &&& (b &&& c)) + 1 * (a &&& ( ~~~b &&& c)) - 20 * (a &&& (b &&& c)) = - 7 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) + 1 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1820 (x y : BitVec w) : +theorem e_1820 : 5 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 3 * (a ^^^ (b &&& c)) + 2 * (a &&& c) + 2 * (a ||| ~~~b) + 1 * ~~~( ~~~a &&& (b &&& c)) - 3 * (a ||| ( ~~~b ||| c)) - 1 * (c ^^^ ~~~(a &&& b)) + 7 * ~~~( ~~~a ||| (b &&& c)) - 2 * ~~~(b &&& c) - 6 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) - 2 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) - 1 * ((a ||| ~~~b) &&& (b ^^^ c)) - 2 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) - 7 * (c ||| ~~~(a ||| ~~~b)) - 11 * (a ||| ~~~c) + 5 * (b &&& (a ^^^ c)) + 1 * ~~~(b ^^^ c) - 2 * (b ^^^ ~~~(a &&& (b ||| c))) + 4 * (b &&& c) - 7 * (c ^^^ (a &&& (b ||| c))) - 1 * ~~~(a ||| (b ^^^ c)) + 1 * (b ^^^ ~~~(a &&& c)) + 1 * b + 1 * (b ^^^ ( ~~~a ||| (b ||| c))) - 2 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) + 4 * ( ~~~c &&& ~~~(a ^^^ b)) - 3 * (a ^^^ (b ^^^ c)) - 3 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) - 5 * (b ^^^ (a ||| ( ~~~b &&& c))) - 1 * ( ~~~a ||| ( ~~~b &&& c)) + 1 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) + 11 * ~~~(a &&& (b &&& c)) - 11 * (c ||| ~~~(a ||| b)) - 1 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) + 20 * ~~~(a ||| (b ||| c)) + 24 * ~~~(a ||| ( ~~~b ||| c)) + 3 * ~~~( ~~~a ||| (b ||| c)) - 1 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 35 * ( ~~~a &&& ( ~~~b &&& c)) + 14 * ( ~~~a &&& (b &&& c)) + 13 * (a &&& ( ~~~b &&& c)) + 35 * (a &&& (b &&& c)) = - 2 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1821 (x y : BitVec w) : +theorem e_1821 : - 7 * (a ^^^ ( ~~~b ||| c)) + 4 * (c ||| (a &&& ~~~b)) - 7 * (b &&& (a ||| ~~~c)) + 5 * ~~~(a &&& ~~~a) + 11 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) - 6 * (b ||| (a &&& ~~~c)) - 5 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) - 5 * ~~~(a ||| b) + 11 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) - 6 * (c ^^^ ~~~(a &&& (b &&& c))) - 7 * ~~~a - 1 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) - 5 * (c ^^^ (a ||| (b ||| c))) - 1 * ((a &&& c) ||| (b &&& ~~~c)) + 3 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) + 3 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) - 1 * ( ~~~b &&& (a ^^^ c)) - 11 * ( ~~~a ||| (b ^^^ c)) - 1 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) - 1 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) + 2 * ~~~(a &&& ( ~~~b &&& c)) + 2 * (b ^^^ (a &&& (b ^^^ c))) - 3 * (c ^^^ (a ||| ~~~b)) + 2 * ~~~(b &&& c) + 5 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 3 * ~~~( ~~~a &&& (b &&& c)) - 1 * (b ||| ~~~(a ||| c)) - 6 * (b ||| (a &&& c)) - 2 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) - 1 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) + 7 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 5 * (b ^^^ ( ~~~a ||| (b ||| c))) - 11 * (a ||| (b ||| c)) - 1 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) + 19 * ~~~(a ||| (b ||| c)) + 32 * ~~~(a ||| ( ~~~b ||| c)) + 5 * ~~~( ~~~a ||| (b ||| c)) + 37 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 20 * ( ~~~a &&& ( ~~~b &&& c)) + 44 * ( ~~~a &&& (b &&& c)) - 22 * (a &&& ( ~~~b &&& c)) + 23 * (a &&& (b &&& c)) = - 2 * (a ^^^ (b ||| c)) - 1 * (b ^^^ ~~~(a &&& ~~~c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1822 (x y : BitVec w) : +theorem e_1822 : 3 * (c &&& ~~~(a &&& b)) - 3 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 5 * ~~~(a ||| ( ~~~b &&& c)) - 2 * ((a ^^^ b) &&& ~~~(a ^^^ c)) + 7 * (a &&& ( ~~~b ||| c)) - 1 * (a &&& ~~~c) + 1 * ~~~(b ||| c) + 7 * ~~~(a &&& ~~~a) + 11 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) + 4 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) + 1 * (c ^^^ (a &&& ( ~~~b ||| c))) + 3 * ~~~(a ||| b) + 3 * ( ~~~(a ||| b) ||| (b ^^^ c)) + 1 * (c ^^^ ~~~(a &&& (b ||| c))) - 2 * ~~~( ~~~a ||| ( ~~~b &&& c)) + 4 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) - 1 * (b ^^^ ~~~(a ||| (b ^^^ c))) - 5 * ((a &&& c) ^^^ (b ||| c)) + 1 * (b &&& ~~~c) - 6 * (c ^^^ (a &&& b)) + 3 * ~~~(b ||| ~~~c) + 3 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) + 1 * ( ~~~b &&& ~~~(a ^^^ c)) - 2 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) - 1 * ( ~~~a &&& (b ^^^ c)) - 5 * (a &&& (b ||| c)) + 4 * ~~~(a &&& c) - 6 * ( ~~~a ||| ( ~~~b &&& c)) - 2 * ~~~(a ^^^ ( ~~~b ||| c)) + 5 * (c ||| (a ^^^ b)) - 5 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) + 4 * ~~~(a &&& (b ||| c)) - 1 * ((a &&& b) ^^^ (b ||| c)) + 11 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) + 7 * ~~~(a ^^^ b) - 51 * ~~~(a ||| (b ||| c)) - 18 * ~~~(a ||| ( ~~~b ||| c)) - 37 * ~~~( ~~~a ||| (b ||| c)) - 4 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 32 * ( ~~~a &&& ( ~~~b &&& c)) - 30 * ( ~~~a &&& (b &&& c)) - 1 * (a &&& ( ~~~b &&& c)) = 45 * (a &&& (b &&& c)) + 2 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1823 (x y : BitVec w) : +theorem e_1823 : 11 * ~~~(a &&& ( ~~~b ||| c)) + 4 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) + 1 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) - 1 * (a ||| ~~~b) - 3 * ( ~~~(a ||| b) ||| (b ^^^ c)) + 4 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) - 6 * (b ^^^ ~~~(a ||| (b ^^^ c))) - 2 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 2 * ~~~( ~~~a &&& (b &&& c)) + 1 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 7 * (b ||| ~~~(a ^^^ c)) + 1 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) - 2 * ((a &&& b) ||| ~~~(b ||| ~~~c)) - 3 * ~~~( ~~~a &&& ( ~~~b &&& c)) - 1 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) - 2 * ~~~(b ^^^ c) + 11 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) - 1 * (c &&& (a ||| ~~~b)) + 2 * ((a &&& b) ^^^ (b ||| c)) + 3 * (b ||| ~~~c) - 3 * a + 1 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) + 2 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) + 1 * (b ||| ~~~(a ||| ~~~c)) - 1 * ( ~~~a ||| (b ^^^ c)) + 2 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) + 2 * (b ^^^ (a ||| (b ||| c))) + 5 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) + 11 * (b ^^^ (a ||| ~~~c)) - 2 * (b ^^^ ( ~~~a ||| (b ||| c))) + 7 * (b ^^^ ( ~~~a &&& (b ||| c))) - 1 * ~~~(a &&& (b ||| c)) + 1 * (c ^^^ (a &&& ( ~~~b ||| c))) - 7 * ~~~(a ^^^ ( ~~~b &&& c)) - 1 * (c ^^^ ~~~(a &&& ~~~b)) - 11 * ~~~(a ||| (b ||| c)) + 3 * ~~~(a ||| ( ~~~b ||| c)) - 23 * ~~~( ~~~a ||| (b ||| c)) - 27 * ( ~~~a &&& ( ~~~b &&& c)) - 33 * ( ~~~a &&& (b &&& c)) + 13 * (a &&& ( ~~~b &&& c)) - 3 * (a &&& (b &&& c)) = 3 * ((a &&& c) ||| ~~~(b ||| c)) - 3 * (a ^^^ b) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1824 (x y : BitVec w) : +theorem e_1824 : - 11 * ((a &&& b) ||| ~~~(b ^^^ c)) - 11 * ~~~(a ^^^ (b ||| c)) - 1 * (b ^^^ ( ~~~a ||| (b &&& c))) + 7 * (b ^^^ ~~~(a &&& c)) - 7 * ~~~( ~~~a &&& (b &&& c)) - 1 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 1 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 11 * ( ~~~a ||| (b ^^^ c)) - 2 * (c ^^^ ~~~(a &&& ~~~b)) + 1 * a - 1 * (c &&& ~~~(a &&& b)) - 1 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) - 2 * (c &&& (a ||| ~~~b)) - 5 * ((a &&& b) ||| ~~~(b ||| c)) + 4 * (c ||| ~~~(a ^^^ b)) - 6 * (c ^^^ ~~~(a &&& (b &&& c))) - 2 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) + 2 * ( ~~~a &&& (b ^^^ c)) - 1 * ~~~(a &&& (b ^^^ c)) - 2 * (a &&& c) - 7 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) + 2 * (b ^^^ (a ||| ( ~~~b ||| c))) + 3 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) + 2 * (b ^^^ ~~~(a &&& (b &&& c))) - 11 * (b ^^^ (a &&& ( ~~~b ||| c))) + 2 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) + 1 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) + 3 * (b ||| ~~~(a ||| c)) - 3 * ( ~~~(a &&& b) &&& (b ^^^ c)) + 2 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) + 5 * ((a &&& ~~~b) ||| (b ^^^ c)) + 2 * (c ^^^ ( ~~~a &&& (b ||| c))) + 1 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) - 5 * (b &&& ~~~(a &&& ~~~c)) + 52 * ~~~(a ||| (b ||| c)) + 43 * ~~~(a ||| ( ~~~b ||| c)) + 27 * ~~~( ~~~a ||| (b ||| c)) + 63 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 8 * ( ~~~a &&& ( ~~~b &&& c)) + 47 * ( ~~~a &&& (b &&& c)) + 44 * (a &&& ( ~~~b &&& c)) + 43 * (a &&& (b &&& c)) = 11 * (b ||| ~~~(a ^^^ c)) - 1 * (b ^^^ (a ||| ~~~c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1825 (x y : BitVec w) : +theorem e_1825 : 11 * ((a &&& ~~~b) ||| (b ^^^ c)) + 7 * ((a &&& b) ^^^ (b ||| c)) - 11 * ((a &&& c) ||| (b &&& ~~~c)) - 6 * (a ^^^ ( ~~~b &&& c)) - 6 * ((a &&& b) ^^^ (b ||| ~~~c)) + 1 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) + 11 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) + 5 * ((a &&& b) ||| ~~~(b ^^^ c)) - 1 * (c ^^^ ~~~(a &&& (b &&& c))) - 2 * (c ^^^ (a ||| (b &&& c))) - 1 * ~~~( ~~~a ||| (b ^^^ c)) + 5 * (b ^^^ ( ~~~a &&& (b ||| c))) + 11 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) + 7 * (c ^^^ ( ~~~a &&& (b ||| c))) + 3 * (b ^^^ ~~~(a ||| (b ^^^ c))) - 5 * (b ||| ~~~(a ^^^ c)) + 7 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) - 1 * ( ~~~b &&& ~~~(a ^^^ c)) + 1 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) + 5 * ~~~(a &&& c) - 2 * (c ^^^ ~~~(a &&& ~~~b)) - 3 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 1 * ( ~~~a ||| (b ^^^ c)) - 11 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 3 * (a ||| ~~~c) - 5 * ~~~(a ^^^ (b ||| c)) - 5 * ((a &&& b) ||| ~~~(b ||| ~~~c)) + 5 * ((a ||| b) &&& (b ^^^ c)) - 2 * ( ~~~a ||| ( ~~~b &&& c)) + 2 * (b ^^^ (a ||| ~~~c)) + 5 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) + 1 * ( ~~~a &&& (b ||| c)) - 2 * (b ||| (a ^^^ c)) + 11 * ((a &&& c) ^^^ (b ||| c)) - 13 * ~~~(a ||| (b ||| c)) - 23 * ~~~(a ||| ( ~~~b ||| c)) + 11 * ~~~( ~~~a ||| (b ||| c)) - 7 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 15 * ( ~~~a &&& ( ~~~b &&& c)) - 14 * ( ~~~a &&& (b &&& c)) + 12 * (a &&& ( ~~~b &&& c)) + 5 * (a &&& (b &&& c)) = 11 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1826 (x y : BitVec w) : +theorem e_1826 : 5 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) + 4 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) - 6 * ~~~(a &&& (b ||| c)) + 5 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) + 1 * (b ^^^ ( ~~~a &&& (b ^^^ c))) - 1 * (a ||| c) + 2 * ((a ^^^ b) &&& (a ^^^ c)) - 2 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) - 5 * c + 2 * (b ^^^ (a ||| (b &&& c))) + 1 * ~~~( ~~~a ||| (b ^^^ c)) + 11 * ~~~(b ||| ~~~c) - 7 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) + 3 * (c ^^^ ~~~(a ||| ~~~b)) + 11 * ( ~~~b ||| ~~~(a ^^^ c)) + 1 * (b ^^^ (a ||| (b ||| c))) + 11 * (a &&& (b ||| c)) - 7 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 3 * ~~~b + 1 * (a ||| (b ||| c)) + 1 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) - 2 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 1 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 1 * (c ^^^ (a &&& b)) - 2 * ~~~( ~~~a &&& (b &&& c)) + 1 * (c ||| ~~~(a ^^^ b)) + 1 * ~~~(a ^^^ (b ||| c)) + 11 * ~~~(a ||| c) + 3 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 11 * (b ^^^ (a ||| c)) + 1 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) + 1 * ~~~(b &&& ~~~c) - 2 * (b &&& ~~~(a &&& ~~~c)) + 4 * ((a ^^^ b) &&& ~~~(a ^^^ c)) - 12 * ~~~(a ||| (b ||| c)) - 17 * ~~~(a ||| ( ~~~b ||| c)) - 15 * ~~~( ~~~a ||| (b ||| c)) - 8 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 8 * ( ~~~a &&& ( ~~~b &&& c)) + 4 * ( ~~~a &&& (b &&& c)) - 32 * (a &&& ( ~~~b &&& c)) - 22 * (a &&& (b &&& c)) = - 4 * (c ||| (a &&& ~~~b)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1827 (x y : BitVec w) : +theorem e_1827 : - 3 * (c ^^^ (a ||| ~~~b)) - 1 * (c &&& (a ^^^ b)) - 7 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 11 * ~~~( ~~~a ||| (b ^^^ c)) + 11 * ~~~(a &&& ~~~c) - 1 * (a ^^^ b) + 3 * ~~~b + 4 * ((a &&& c) ||| ~~~(b ||| c)) - 2 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) - 11 * (c ^^^ ( ~~~a &&& (b ||| c))) + 4 * (b &&& ~~~(a &&& ~~~c)) - 6 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 2 * a + 1 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) - 3 * ~~~c + 7 * ((a ^^^ b) ||| ~~~(a ^^^ c)) + 5 * ( ~~~b &&& ~~~(a ^^^ c)) + 1 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) - 11 * (a &&& b) + 5 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) + 11 * ((a ^^^ b) ||| (a ^^^ c)) - 5 * (a ||| ~~~c) - 2 * ~~~(a ||| b) - 1 * (b ^^^ ~~~(a ||| (b &&& c))) + 7 * (a &&& (b ||| c)) + 4 * (b &&& c) + 2 * ~~~(b ||| ~~~c) + 1 * (a ^^^ c) - 6 * ((a ||| ~~~b) &&& (b ^^^ c)) + 1 * ((a &&& b) ||| (b ^^^ c)) + 1 * ((b &&& c) ||| (a &&& (b ||| c))) - 3 * ((a &&& ~~~b) ||| (b ^^^ c)) + 2 * (b ||| ~~~(a ||| ~~~c)) - 6 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 1 * ~~~(a ^^^ (b ||| c)) - 6 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) - 12 * ~~~(a ||| (b ||| c)) + 26 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 3 * ( ~~~a &&& ( ~~~b &&& c)) - 19 * ( ~~~a &&& (b &&& c)) - 12 * (a &&& ( ~~~b &&& c)) - 15 * (a &&& (b &&& c)) = 1 * (b ^^^ ( ~~~a &&& (b ^^^ c))) + 11 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1828 (x y : BitVec w) : +theorem e_1828 : 4 * (c &&& (a ||| ~~~b)) + 7 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) - 1 * ((a &&& b) ||| ~~~(b ^^^ c)) + 11 * ~~~(a ^^^ ( ~~~b &&& c)) - 6 * (b &&& ~~~(a &&& ~~~c)) - 1 * ((a ||| b) &&& ~~~(b ^^^ c)) + 4 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 1 * (b ^^^ (a &&& (b ^^^ c))) + 3 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) + 1 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) + 2 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) + 2 * ( ~~~a ||| (b ^^^ c)) - 11 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) - 1 * (a ||| ( ~~~b &&& c)) + 2 * ~~~(b ||| ~~~c) - 1 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) + 4 * (c ^^^ (a &&& ( ~~~b ||| c))) - 7 * (b ^^^ ( ~~~a ||| (b ||| c))) - 2 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) + 2 * (c ||| (a ^^^ b)) + 7 * (c ||| (a &&& b)) - 1 * ( ~~~a ||| ( ~~~b &&& c)) + 4 * (b ^^^ ( ~~~a ||| (b &&& c))) - 1 * (b ^^^ c) - 2 * (c &&& ~~~(a &&& ~~~b)) + 5 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) + 1 * c - 11 * (a ||| (b ||| c)) + 11 * ((a ||| ~~~b) &&& (b ^^^ c)) + 3 * ((a &&& c) ||| ~~~(b ||| c)) + 2 * (b ^^^ (a &&& (b ||| c))) + 1 * (a ^^^ ( ~~~b &&& c)) - 1 * (a ^^^ (b ||| c)) + 1 * ((a &&& c) ||| (b &&& ~~~c)) - 2 * (c ^^^ (a ||| (b ||| c))) + 5 * (c ^^^ (a &&& (b ||| c))) - 30 * ~~~(a ||| (b ||| c)) - 5 * ~~~(a ||| ( ~~~b ||| c)) - 25 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 24 * ( ~~~a &&& ( ~~~b &&& c)) - 6 * ( ~~~a &&& (b &&& c)) - 40 * (a &&& ( ~~~b &&& c)) + 8 * (a &&& (b &&& c)) = - 5 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1829 (x y : BitVec w) : +theorem e_1829 : 3 * (b &&& (a ||| c)) + 11 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 2 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 7 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) + 1 * (b ||| ~~~c) - 1 * a + 1 * ((a &&& b) ||| (b ^^^ c)) - 3 * ( ~~~b &&& ~~~(a ^^^ c)) + 11 * ((a &&& b) ||| ~~~(b ||| ~~~c)) - 7 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 2 * ( ~~~c ||| ~~~(a ^^^ b)) + 1 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) - 2 * (c ^^^ (a ||| (b &&& c))) + 5 * ( ~~~a ||| ( ~~~b &&& c)) - 2 * (b ^^^ ~~~(a &&& (b ||| c))) + 4 * (a ^^^ ( ~~~b &&& c)) + 7 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) + 1 * ((a &&& b) ||| ~~~(b ^^^ c)) - 2 * ~~~a - 1 * (a ||| c) + 7 * ( ~~~c &&& (a ^^^ b)) - 1 * ~~~(a &&& ( ~~~b ||| c)) - 1 * (c &&& ~~~(a &&& b)) + 2 * ~~~(a &&& ~~~a) - 6 * ( ~~~c &&& ~~~(a ^^^ b)) + 3 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) + 1 * (a ^^^ (b ||| c)) - 6 * ((b &&& c) ||| (a &&& (b ||| c))) + 11 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) + 2 * ( ~~~b ||| ~~~(a ^^^ c)) + 7 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 11 * (b ^^^ (a &&& (b ^^^ c))) + 4 * b + 7 * (a ^^^ c) - 1 * (c &&& (a ||| ~~~b)) - 1 * ~~~(a ||| (b ||| c)) - 44 * ~~~(a ||| ( ~~~b ||| c)) - 49 * ~~~( ~~~a ||| (b ||| c)) - 35 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 33 * ( ~~~a &&& ( ~~~b &&& c)) - 45 * ( ~~~a &&& (b &&& c)) - 40 * (a &&& ( ~~~b &&& c)) - 44 * (a &&& (b &&& c)) = - 7 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1830 (x y : BitVec w) : +theorem e_1830 : 2 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) - 1 * ~~~(a &&& (b ^^^ c)) - 1 * ((a ||| b) &&& ~~~(b ^^^ c)) - 11 * ~~~a - 6 * (c ||| ~~~(a ||| ~~~b)) + 1 * (c ||| (a ^^^ b)) - 2 * ( ~~~c ||| (a ^^^ b)) - 2 * ( ~~~(a ||| b) ||| (b ^^^ c)) + 4 * (b ^^^ ( ~~~a ||| (b ^^^ c))) - 6 * (b ||| ~~~(a ^^^ c)) + 4 * ( ~~~a ||| (b ||| c)) + 7 * (a &&& ( ~~~b ||| c)) - 5 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) - 5 * (b ^^^ ~~~(a ||| c)) - 1 * (a ^^^ (b &&& c)) - 3 * (a ||| ( ~~~b ||| c)) - 7 * (c ^^^ (a &&& b)) + 2 * (b ^^^ (a ||| (b ||| c))) + 4 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 3 * (c ^^^ ~~~(a &&& (b &&& c))) - 7 * ~~~( ~~~a ||| (b &&& c)) + 1 * ( ~~~c &&& (a ^^^ b)) - 2 * ((a &&& b) ||| ~~~(b ||| c)) - 1 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) - 1 * ((a &&& b) ||| ~~~(b ^^^ c)) - 2 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) - 3 * (c &&& (a ^^^ b)) - 1 * (b ^^^ (a &&& c)) + 2 * (b &&& ~~~(a &&& c)) - 1 * (b &&& ~~~(a ^^^ c)) - 5 * ~~~( ~~~a &&& (b ^^^ c)) - 5 * ((a ||| ~~~b) &&& (b ^^^ c)) + 1 * ((a ^^^ b) ||| (a ^^^ c)) + 2 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) + 3 * (b ||| (a &&& ~~~c)) + 31 * ~~~(a ||| (b ||| c)) + 13 * ~~~(a ||| ( ~~~b ||| c)) + 1 * ~~~( ~~~a ||| (b ||| c)) + 26 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 20 * ( ~~~a &&& ( ~~~b &&& c)) + 41 * ( ~~~a &&& (b &&& c)) + 28 * (a &&& ( ~~~b &&& c)) + 10 * (a &&& (b &&& c)) = - 2 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1831 (x y : BitVec w) : +theorem e_1831 : - 11 * ~~~( ~~~a ||| ( ~~~b &&& c)) - 2 * ~~~(a ^^^ (b ^^^ c)) + 2 * (a ^^^ (b &&& c)) - 5 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 1 * ( ~~~a &&& (b ^^^ c)) - 11 * (a ||| (b ^^^ c)) + 1 * ( ~~~b ||| ~~~(a ^^^ c)) - 7 * ~~~(a ^^^ c) + 2 * (b &&& ~~~c) - 2 * ~~~(a ^^^ ( ~~~b &&& c)) + 2 * (c ^^^ (a &&& ( ~~~b ||| c))) - 5 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) - 2 * (a &&& (b ||| c)) - 6 * (b &&& ~~~(a ^^^ c)) + 5 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 2 * (b ^^^ ( ~~~a ||| (b &&& c))) + 1 * (c ||| ~~~(a ||| ~~~b)) + 1 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) + 4 * (c &&& ~~~(a &&& ~~~b)) - 3 * ((a ||| b) &&& (b ^^^ c)) - 1 * (c ||| (a &&& b)) + 11 * (a ^^^ (b ^^^ c)) + 7 * (a ^^^ b) - 1 * (a &&& (b ^^^ c)) - 3 * ~~~(a ^^^ (b &&& c)) + 2 * ~~~(a &&& b) + 3 * (b ^^^ (a ||| (b ^^^ c))) + 4 * ( ~~~a &&& ( ~~~b ||| c)) + 2 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) + 5 * b + 4 * (a ^^^ (b ||| c)) + 3 * ((a ||| b) &&& ~~~(b ^^^ c)) - 7 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) - 1 * ( ~~~b ||| (a ^^^ c)) + 1 * ( ~~~a ||| ( ~~~b ||| c)) + 20 * ~~~(a ||| (b ||| c)) + 16 * ~~~(a ||| ( ~~~b ||| c)) - 10 * ~~~( ~~~a ||| (b ||| c)) + 26 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 17 * ( ~~~a &&& ( ~~~b &&& c)) - 33 * ( ~~~a &&& (b &&& c)) + 18 * (a &&& ( ~~~b &&& c)) + 15 * (a &&& (b &&& c)) = 1 * (b ^^^ ~~~(a ||| (b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1832 (x y : BitVec w) : +theorem e_1832 : 1 * (c ^^^ ( ~~~a ||| (b ||| c))) - 6 * ~~~(a ||| ~~~c) + 4 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) + 3 * ~~~c + 1 * (c ^^^ (a ||| ( ~~~b &&& c))) + 7 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) - 1 * ((a &&& b) ||| ~~~(b ^^^ c)) + 7 * ((a ||| ~~~b) &&& (b ^^^ c)) - 11 * ~~~(a ^^^ ( ~~~b ||| c)) - 7 * ( ~~~a &&& (b ||| c)) + 11 * (b &&& ~~~c) - 1 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) + 4 * ((a ||| b) &&& ~~~(b ^^^ c)) - 11 * ~~~(a ||| b) - 11 * ((a &&& b) ||| ~~~(b ||| ~~~c)) + 7 * (c ^^^ ~~~(a ||| ~~~b)) + 4 * (c ||| (a &&& b)) - 1 * ((a ^^^ b) ||| (a ^^^ c)) - 2 * (c ^^^ (a &&& ~~~b)) + 2 * ~~~(a ||| c) - 2 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) + 2 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 5 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) - 7 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) + 3 * ~~~(a ^^^ b) + 11 * (c &&& (a ||| b)) - 5 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 1 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 4 * (c ^^^ ( ~~~a ||| (b &&& c))) - 5 * (c ^^^ ~~~(a &&& ~~~b)) - 1 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 1 * ~~~( ~~~a &&& (b &&& c)) - 7 * (b ^^^ (a &&& (b ^^^ c))) + 7 * (b ||| ~~~(a ||| c)) - 3 * ( ~~~c &&& (a ^^^ b)) - 7 * ~~~(b ^^^ c) - 6 * ~~~(a ||| (b ||| c)) + 4 * ~~~(a ||| ( ~~~b ||| c)) + 8 * ~~~( ~~~a ||| (b ||| c)) - 17 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 7 * ( ~~~a &&& ( ~~~b &&& c)) + 4 * (a &&& ( ~~~b &&& c)) + 4 * (a &&& (b &&& c)) = 1 * ((a ^^^ b) &&& ~~~(a ^^^ c)) - 1 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1833 (x y : BitVec w) : +theorem e_1833 : 1 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 2 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) - 3 * ( ~~~b ||| ~~~(a ^^^ c)) - 5 * ~~~( ~~~a ||| (b &&& c)) + 2 * (b ||| (a ^^^ c)) + 4 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) - 2 * ( ~~~c &&& (a ^^^ b)) + 1 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) - 2 * c - 1 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) + 11 * (a &&& c) - 2 * ((a ||| ~~~b) &&& (b ^^^ c)) + 1 * (c ||| (a &&& b)) - 5 * (c ^^^ ~~~(a ||| b)) + 11 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) + 3 * (b ^^^ ( ~~~a ||| (b ^^^ c))) - 2 * (b ^^^ (a ||| (b &&& c))) + 4 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) - 2 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) + 7 * (b ^^^ (a &&& c)) + 2 * ( ~~~(a &&& b) &&& (b ^^^ c)) - 7 * ( ~~~a &&& ( ~~~b ||| c)) - 5 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) + 4 * (c ^^^ (a ||| ( ~~~b &&& c))) - 2 * ~~~(a ^^^ c) - 6 * (c ^^^ (a ||| ( ~~~b ||| c))) - 1 * ~~~(a ||| b) + 11 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 11 * (b ^^^ ~~~(a &&& ~~~c)) + 5 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) - 1 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) + 7 * (b ^^^ ~~~(a ||| ~~~c)) + 7 * (b ^^^ ~~~(a ||| c)) - 6 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) - 6 * ~~~(b ||| ~~~c) + 5 * (c ^^^ ~~~(a ||| ~~~b)) - 16 * ~~~(a ||| (b ||| c)) + 3 * ~~~( ~~~a ||| (b ||| c)) - 46 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 30 * ( ~~~a &&& ( ~~~b &&& c)) + 3 * ( ~~~a &&& (b &&& c)) - 36 * (a &&& ( ~~~b &&& c)) - 24 * (a &&& (b &&& c)) = 2 * (c &&& (a ||| ~~~b)) + 25 * ~~~(a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1834 (x y : BitVec w) : +theorem e_1834 : 5 * ~~~(a ||| ( ~~~b &&& c)) - 1 * ~~~( ~~~a &&& (b ^^^ c)) + 7 * a - 5 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) - 2 * (b &&& c) - 6 * ~~~(a &&& b) + 1 * (b ^^^ (a ||| ~~~c)) + 4 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) + 7 * (c ||| ~~~(a ||| ~~~b)) + 4 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) - 7 * ( ~~~a ||| (b ^^^ c)) + 5 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 2 * (a &&& (b ||| c)) + 1 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) - 2 * (b &&& ~~~c) - 1 * c + 7 * ((a &&& b) ||| ~~~(b ||| c)) - 3 * ~~~(a ||| (b &&& c)) - 1 * (b ||| (a ^^^ c)) - 3 * (b ^^^ ~~~(a ||| c)) - 7 * ((a &&& b) ^^^ (b ||| ~~~c)) + 2 * ( ~~~a ||| ( ~~~b &&& c)) + 5 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) - 6 * ((a ||| ~~~b) &&& (b ^^^ c)) + 1 * (b ^^^ (a &&& (b ||| c))) + 1 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) + 2 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) - 5 * (a ^^^ ( ~~~b ||| c)) + 2 * (c ||| ~~~(a ^^^ b)) + 4 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) + 1 * ((a &&& b) ^^^ (b ||| c)) + 11 * ~~~(a &&& (b &&& c)) + 1 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 2 * (c &&& ~~~(a &&& b)) - 1 * (b ^^^ ( ~~~a ||| (b ||| c))) - 7 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) + 1 * ( ~~~(a ||| b) ||| (b ^^^ c)) - 10 * ~~~(a ||| (b ||| c)) + 2 * ~~~(a ||| ( ~~~b ||| c)) - 9 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 2 * ( ~~~a &&& ( ~~~b &&& c)) + 8 * ( ~~~a &&& (b &&& c)) - 11 * (a &&& ( ~~~b &&& c)) = 6 * ~~~( ~~~a ||| (b ||| c)) + 19 * (a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1835 (x y : BitVec w) : +theorem e_1835 : - 11 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) - 1 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 3 * (a &&& b) - 1 * (c &&& (a ||| b)) - 11 * ~~~c + 2 * (b ^^^ ~~~(a ||| (b ^^^ c))) + 2 * (a ||| (b &&& c)) - 2 * ~~~(b ||| ~~~c) + 11 * (c &&& (a ||| ~~~b)) - 2 * (b ^^^ (a ||| (b ||| c))) + 3 * (a ||| ~~~c) + 11 * ((a &&& c) ^^^ (b ||| c)) - 7 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 7 * (a &&& ~~~c) + 1 * (c ||| (a ^^^ b)) - 5 * ((a ^^^ b) ||| (a ^^^ c)) + 3 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 5 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 5 * ( ~~~c &&& (a ^^^ b)) + 1 * ~~~( ~~~a ||| ( ~~~b &&& c)) + 1 * c - 3 * (c ^^^ (a ||| (b &&& c))) + 7 * (a ^^^ (b ||| c)) - 1 * (a ^^^ c) + 1 * (c ||| ~~~(a ^^^ b)) - 2 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) - 1 * ~~~(a ||| b) + 2 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) - 2 * (b ||| (a ^^^ c)) - 11 * ((a ^^^ b) ||| ~~~(a ^^^ c)) - 7 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) + 1 * ((a ^^^ b) &&& (a ^^^ c)) + 3 * (c ||| ~~~(a ||| b)) + 5 * (a ^^^ ( ~~~b &&& c)) - 1 * (c ^^^ ~~~(a ||| b)) + 33 * ~~~(a ||| (b ||| c)) + 22 * ~~~(a ||| ( ~~~b ||| c)) + 33 * ~~~( ~~~a ||| (b ||| c)) + 20 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 3 * ( ~~~a &&& ( ~~~b &&& c)) + 9 * ( ~~~a &&& (b &&& c)) + 5 * (a &&& ( ~~~b &&& c)) + 5 * (a &&& (b &&& c)) = 2 * ( ~~~a ||| ( ~~~b ||| c)) - 5 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1836 (x y : BitVec w) : +theorem e_1836 : 2 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) + 2 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) + 1 * (a &&& ~~~b) + 2 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) + 5 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) + 11 * ((a ||| ~~~b) &&& (b ^^^ c)) - 6 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 4 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) + 1 * ( ~~~a &&& (b ||| c)) - 5 * ~~~(a ^^^ c) + 4 * ( ~~~(a ||| b) ||| (b ^^^ c)) - 1 * (a ||| (b &&& c)) + 3 * ~~~(a &&& ( ~~~b &&& c)) + 7 * (b ^^^ (a ||| (b ||| c))) - 1 * (c ^^^ ~~~(a ||| b)) - 1 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 2 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 1 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 11 * ~~~(a ||| (b &&& c)) + 1 * (c ^^^ (a &&& ( ~~~b ||| c))) + 4 * (c ||| ~~~(a ||| b)) - 6 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) - 1 * (a &&& c) - 6 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) + 2 * (c ^^^ (a ||| ( ~~~b &&& c))) + 11 * (b ^^^ ~~~(a &&& (b ^^^ c))) - 2 * ((a ^^^ b) &&& (a ^^^ c)) - 1 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 11 * ( ~~~b ||| ~~~(a ^^^ c)) + 11 * ( ~~~a ||| (b ^^^ c)) + 1 * (b ||| c) + 1 * (b &&& (a ^^^ c)) + 1 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) - 2 * (b ^^^ (a ||| (b ^^^ c))) + 3 * (a ^^^ (b ||| c)) - 2 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 37 * ~~~(a ||| ( ~~~b ||| c)) - 29 * ~~~( ~~~a ||| (b ||| c)) - 38 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 70 * ( ~~~a &&& ( ~~~b &&& c)) - 23 * ( ~~~a &&& (b &&& c)) - 36 * (a &&& ( ~~~b &&& c)) - 9 * (a &&& (b &&& c)) = 50 * ~~~(a ||| (b ||| c)) - 4 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1837 (x y : BitVec w) : +theorem e_1837 : - 1 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) + 1 * ( ~~~a ||| ( ~~~b ||| c)) + 3 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) - 5 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) - 2 * (b ||| ~~~(a ^^^ c)) - 2 * ~~~(a ^^^ ( ~~~b ||| c)) - 1 * ((a ||| b) &&& ~~~(b ^^^ c)) - 2 * ( ~~~c ||| ~~~(a ^^^ b)) + 4 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 2 * ((a &&& b) ||| ~~~(b ||| ~~~c)) - 1 * (b ^^^ ( ~~~a ||| (b ^^^ c))) + 7 * (b &&& c) + 11 * ~~~(a ||| b) - 1 * (c ^^^ ( ~~~a ||| (b ||| c))) + 1 * ( ~~~c &&& ~~~(a ^^^ b)) + 1 * ~~~( ~~~a &&& (b &&& c)) + 2 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) + 1 * (b ^^^ (a ||| (b ||| c))) + 4 * (a ||| (b ||| c)) - 6 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) + 1 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) - 5 * (c ||| (a &&& ~~~b)) + 1 * (b ||| c) - 6 * ((a &&& b) ^^^ (b ||| c)) - 1 * ~~~( ~~~a &&& ( ~~~b ||| c)) + 5 * (c ^^^ ( ~~~a &&& (b ||| c))) - 11 * ((a ^^^ b) &&& ~~~(a ^^^ c)) + 7 * (c ^^^ ~~~(a &&& ~~~b)) + 5 * ((a ||| ~~~b) &&& (b ^^^ c)) + 4 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 2 * ~~~( ~~~a &&& (b ^^^ c)) + 1 * ~~~(a &&& (b &&& c)) - 7 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) - 1 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 2 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) - 1 * (a ||| ~~~c) + 7 * ((a &&& c) ||| (b &&& ~~~c)) - 8 * ~~~(a ||| (b ||| c)) + 6 * ~~~(a ||| ( ~~~b ||| c)) + 2 * ~~~( ~~~a ||| (b ||| c)) - 7 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 2 * ( ~~~a &&& (b &&& c)) + 1 * (a &&& ( ~~~b &&& c)) + 1 * (a &&& (b &&& c)) = 1 * (b &&& (a ||| c)) - 5 * ( ~~~a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1838 (x y : BitVec w) : +theorem e_1838 : 1 * ~~~c + 2 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) + 1 * (b ^^^ (a ||| (b &&& c))) - 7 * (b ^^^ (a ||| ~~~c)) - 3 * ((a &&& ~~~b) ||| (b ^^^ c)) - 1 * (a ||| ( ~~~b &&& c)) + 11 * ( ~~~a &&& (b ||| c)) + 3 * ( ~~~a ||| (b &&& c)) - 5 * (a ^^^ b) + 1 * ~~~( ~~~a &&& (b &&& c)) - 11 * ~~~(a &&& b) - 1 * b - 5 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) + 5 * (a &&& c) - 1 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) - 2 * ~~~(a &&& ( ~~~b ||| c)) - 1 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 1 * ( ~~~c &&& (a ^^^ b)) - 1 * ( ~~~b &&& ~~~(a ^^^ c)) + 2 * (b ^^^ (a &&& c)) + 4 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) + 11 * ((a ||| ~~~b) &&& (b ^^^ c)) + 5 * (b ^^^ ( ~~~a &&& (b ||| c))) - 6 * (a &&& ~~~b) - 1 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) - 1 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 1 * (c ^^^ (a ||| ( ~~~b ||| c))) + 1 * ~~~(b &&& ~~~c) - 3 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) + 5 * ((a ^^^ b) &&& ~~~(a ^^^ c)) - 2 * ( ~~~a ||| (b ^^^ c)) - 3 * ~~~(a ^^^ c) - 1 * ~~~(a &&& ~~~a) + 1 * ~~~(a &&& c) - 2 * (b ||| ~~~(a ||| ~~~c)) + 7 * ( ~~~c ||| ~~~(a ^^^ b)) + 14 * ~~~(a ||| (b ||| c)) + 4 * ~~~(a ||| ( ~~~b ||| c)) + 26 * ~~~( ~~~a ||| (b ||| c)) - 20 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 11 * ( ~~~a &&& ( ~~~b &&& c)) + 12 * ( ~~~a &&& (b &&& c)) + 18 * (a &&& ( ~~~b &&& c)) - 8 * (a &&& (b &&& c)) = 2 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1839 (x y : BitVec w) : +theorem e_1839 : - 1 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) + 4 * (b ^^^ (a ||| ~~~c)) + 5 * (b ^^^ (a ||| (b ||| c))) + 5 * (b &&& ~~~c) - 7 * (b ^^^ (a ||| c)) + 4 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) + 2 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) + 7 * (b ^^^ ( ~~~a &&& (b ||| c))) + 2 * ~~~(a ^^^ (b ^^^ c)) + 1 * (c ||| ~~~(a ||| b)) + 1 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) - 2 * ~~~(b ||| c) - 1 * ~~~(a ^^^ (b ||| c)) - 1 * ( ~~~a &&& (b ||| c)) + 5 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 11 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) - 6 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) + 1 * ((a &&& b) ||| ~~~(b ^^^ c)) - 5 * (a ||| (b ||| c)) - 1 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) - 2 * (b &&& ~~~(a &&& ~~~c)) + 1 * (b ^^^ ( ~~~a &&& (b ^^^ c))) - 5 * a + 7 * (b ^^^ ~~~(a ||| c)) + 3 * ~~~( ~~~a ||| (b &&& c)) - 3 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) + 2 * (a &&& ( ~~~b ||| c)) + 1 * ~~~(a &&& (b &&& c)) + 1 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) + 4 * ( ~~~a ||| ( ~~~b &&& c)) - 3 * ( ~~~a &&& ( ~~~b ||| c)) + 3 * (c ^^^ ~~~(a &&& ~~~b)) - 11 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) + 5 * ((a ||| ~~~b) &&& (b ^^^ c)) - 7 * ~~~a - 6 * (a ||| ~~~b) - 1 * (a ^^^ ( ~~~b &&& c)) - 2 * ~~~(a ||| (b ||| c)) + 17 * ~~~(a ||| ( ~~~b ||| c)) - 7 * ~~~( ~~~a ||| (b ||| c)) + 16 * ( ~~~a &&& ( ~~~b &&& c)) + 4 * ( ~~~a &&& (b &&& c)) - 7 * (a &&& ( ~~~b &&& c)) + 13 * (a &&& (b &&& c)) = 3 * (c &&& (a ||| ~~~b)) + 6 * (b ||| (a ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1840 (x y : BitVec w) : +theorem e_1840 : 1 * ~~~a + 2 * ( ~~~a &&& (b ^^^ c)) - 6 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 11 * (c ||| (a &&& ~~~b)) - 5 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) - 2 * (c ^^^ ~~~(a &&& (b ||| c))) + 1 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) - 11 * ( ~~~a ||| (b &&& c)) + 2 * (b ^^^ (a &&& (b ^^^ c))) - 1 * ~~~( ~~~a ||| (b &&& c)) + 1 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 11 * (c &&& (a ||| ~~~b)) + 3 * (a &&& (b ||| c)) + 11 * (b &&& ~~~(a &&& c)) - 2 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) + 7 * (b ^^^ c) - 2 * (b ^^^ ~~~(a &&& (b &&& c))) - 11 * (c &&& (a ^^^ b)) - 2 * ~~~(a ^^^ (b ||| c)) - 3 * ((a ^^^ b) ||| (a ^^^ c)) - 1 * (c ^^^ ~~~(a ||| b)) + 1 * (a ||| ( ~~~b ||| c)) - 5 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) - 6 * (b ||| c) + 7 * ( ~~~(a ||| b) ||| (b ^^^ c)) - 5 * ~~~(a ^^^ (b &&& c)) - 3 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) - 6 * (c ^^^ ~~~(a ||| ~~~b)) + 1 * ~~~(a ||| b) - 7 * ((a &&& c) ^^^ (b ||| c)) + 1 * ~~~(a ||| c) + 1 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) + 7 * (b ^^^ ~~~(a ||| (b ^^^ c))) - 7 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 7 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 1 * (b &&& ~~~(a &&& ~~~c)) + 7 * ( ~~~c &&& ~~~(a ^^^ b)) + 6 * ~~~(a ||| (b ||| c)) + 15 * ~~~(a ||| ( ~~~b ||| c)) + 24 * ~~~( ~~~a ||| (b ||| c)) - 17 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 18 * ( ~~~a &&& (b &&& c)) + 35 * (a &&& ( ~~~b &&& c)) + 19 * (a &&& (b &&& c)) = - 25 * ( ~~~a &&& ( ~~~b &&& c)) + 1 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1841 (x y : BitVec w) : +theorem e_1841 : 3 * ((a &&& b) ||| ~~~(b ^^^ c)) - 2 * c - 11 * ~~~(a &&& b) + 2 * (b ^^^ ( ~~~a &&& (b ^^^ c))) + 7 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) + 4 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) + 5 * ((a &&& b) ||| ~~~(b ||| ~~~c)) + 5 * a - 7 * (a &&& (b ||| c)) + 3 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) + 1 * (b &&& (a ||| ~~~c)) + 2 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 7 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) - 6 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) + 11 * (b &&& ~~~(a ^^^ c)) + 1 * (b &&& ~~~c) - 6 * (c ||| ~~~(a ^^^ b)) + 2 * (a ||| b) - 1 * ~~~a - 5 * (b ^^^ ( ~~~a ||| (b &&& c))) + 1 * (b ^^^ ~~~(a ||| c)) + 2 * (c ^^^ ~~~(a &&& b)) - 1 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) + 4 * ( ~~~c ||| (a ^^^ b)) - 2 * (c &&& (a ^^^ b)) - 7 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 11 * (c ||| (a ^^^ b)) + 1 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 1 * ( ~~~b &&& ~~~(a ^^^ c)) - 3 * (a &&& ( ~~~b ||| c)) - 2 * (b ^^^ (a ||| ~~~c)) - 6 * (a ||| (b &&& c)) - 2 * (b ||| ~~~c) - 1 * (b ||| ~~~(a ||| ~~~c)) - 2 * (b ^^^ ~~~(a &&& ~~~c)) - 1 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) - 11 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 34 * ~~~(a ||| (b ||| c)) - 12 * ~~~(a ||| ( ~~~b ||| c)) + 2 * ~~~( ~~~a ||| (b ||| c)) + 24 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 11 * ( ~~~a &&& ( ~~~b &&& c)) + 23 * ( ~~~a &&& (b &&& c)) - 18 * (a &&& (b &&& c)) = - 24 * (a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1842 (x y : BitVec w) : +theorem e_1842 : 7 * (b ^^^ (a &&& ( ~~~b ||| c))) + 5 * (b ||| ~~~(a ||| ~~~c)) + 1 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) + 7 * (b ^^^ (a ||| c)) + 4 * ~~~(b ||| ~~~c) - 11 * (c ^^^ ~~~(a ||| b)) + 3 * ((a ^^^ b) ||| (a ^^^ c)) - 2 * (b ^^^ (a ||| ~~~c)) - 1 * ( ~~~b &&& (a ^^^ c)) - 7 * (b ^^^ ~~~(a ||| ~~~c)) - 5 * (c ^^^ (a ||| ( ~~~b ||| c))) + 5 * (c ^^^ ~~~(a &&& ~~~b)) + 11 * (b ||| (a &&& ~~~c)) + 11 * ~~~(a ^^^ b) - 5 * ~~~(a ^^^ ( ~~~b ||| c)) - 6 * ~~~(a ^^^ ( ~~~b &&& c)) - 5 * (a ||| ~~~c) + 1 * (a &&& (b ^^^ c)) - 3 * (a ^^^ (b ^^^ c)) + 11 * (b &&& (a ||| c)) - 7 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 2 * (c ||| (a &&& ~~~b)) - 2 * ~~~(a ^^^ (b ||| c)) - 7 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) - 11 * ((a &&& b) ^^^ (b ||| c)) + 5 * (c ^^^ ~~~(a &&& (b ||| c))) + 1 * (b ^^^ ( ~~~a &&& (b ^^^ c))) - 1 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) + 2 * c - 1 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) - 6 * (b ^^^ ~~~(a &&& (b &&& c))) + 2 * (b ^^^ (a ||| (b ^^^ c))) - 6 * ~~~( ~~~a &&& (b ^^^ c)) + 3 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) + 4 * ( ~~~(a ||| b) ||| (b ^^^ c)) - 3 * ~~~( ~~~a &&& (b ||| c)) + 31 * ~~~(a ||| (b ||| c)) - 13 * ~~~(a ||| ( ~~~b ||| c)) + 15 * ~~~( ~~~a ||| (b ||| c)) - 32 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 9 * ( ~~~a &&& ( ~~~b &&& c)) - 1 * ( ~~~a &&& (b &&& c)) + 26 * (a &&& ( ~~~b &&& c)) + 1 * (a &&& (b &&& c)) = - 2 * (b ^^^ ( ~~~a ||| (b &&& c))) + 2 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1843 (x y : BitVec w) : +theorem e_1843 : 3 * ~~~(a &&& ~~~a) - 2 * ((a ||| ~~~b) &&& (b ^^^ c)) - 11 * ~~~(a ^^^ b) + 1 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 3 * (c ^^^ ~~~(a ||| b)) + 2 * ~~~(a ^^^ ( ~~~b ||| c)) - 3 * (a ||| b) + 2 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) - 7 * ( ~~~a &&& (b ^^^ c)) + 1 * ( ~~~c &&& ~~~(a ^^^ b)) + 1 * ~~~(a &&& (b ||| c)) + 4 * ~~~(a ||| ~~~b) - 2 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) + 11 * (c ^^^ ~~~(a ||| (b &&& c))) + 4 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) + 5 * ( ~~~b &&& (a ^^^ c)) + 11 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 7 * (b ^^^ ( ~~~a ||| (b ||| c))) + 7 * (a &&& ~~~c) - 1 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 2 * ~~~(a &&& ( ~~~b &&& c)) - 1 * (c &&& ~~~(a ^^^ b)) - 1 * ~~~(b ||| c) - 7 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) + 2 * ~~~( ~~~a &&& ( ~~~b ||| c)) - 1 * ~~~( ~~~a &&& (b ^^^ c)) - 6 * (b &&& c) - 6 * (b ^^^ (a ||| (b &&& c))) + 4 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 11 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 11 * ~~~(a ^^^ (b &&& c)) + 7 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) - 2 * ( ~~~a ||| (b &&& c)) - 2 * ~~~a - 2 * ~~~( ~~~a &&& (b &&& c)) + 4 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) - 14 * ~~~(a ||| (b ||| c)) - 25 * ~~~(a ||| ( ~~~b ||| c)) - 9 * ~~~( ~~~a ||| (b ||| c)) + 2 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 27 * ( ~~~a &&& ( ~~~b &&& c)) - 13 * ( ~~~a &&& (b &&& c)) - 4 * (a &&& ( ~~~b &&& c)) - 4 * (a &&& (b &&& c)) = 7 * (c ^^^ (a &&& b)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1844 (x y : BitVec w) : +theorem e_1844 : - 5 * ~~~(a &&& ( ~~~b ||| c)) - 7 * (b &&& ~~~(a &&& c)) - 11 * (b &&& ~~~(a ^^^ c)) - 2 * (c ||| ~~~(a ||| ~~~b)) + 11 * ~~~(a ||| (b ^^^ c)) + 2 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 6 * (b ||| ~~~(a ^^^ c)) - 1 * ~~~( ~~~a ||| (b ^^^ c)) + 11 * (c ^^^ (a ||| ~~~b)) + 4 * (b ^^^ ( ~~~a &&& (b ||| c))) + 3 * (c ^^^ (a ||| b)) + 1 * (a ^^^ (b &&& c)) + 1 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) - 7 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) + 2 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 5 * (b &&& c) - 5 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) - 11 * (a &&& c) - 1 * ( ~~~a &&& (b ||| c)) + 1 * ~~~a + 1 * (b ^^^ (a ||| ~~~c)) - 6 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) - 1 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) + 2 * ~~~( ~~~a &&& ( ~~~b ||| c)) + 5 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) + 4 * (b ^^^ (a ||| c)) - 11 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) - 2 * (c ^^^ (a ||| (b &&& c))) + 3 * (a &&& ~~~c) - 6 * ((a ^^^ b) ||| ~~~(a ^^^ c)) - 2 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) + 5 * (b ^^^ ~~~(a &&& c)) + 11 * ~~~(a &&& (b ||| c)) + 1 * ( ~~~a ||| (b ^^^ c)) + 4 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 5 * ((a &&& ~~~b) ||| (b ^^^ c)) + 1 * (c ^^^ ~~~(a ||| b)) - 21 * ~~~(a ||| (b ||| c)) + 20 * ~~~(a ||| ( ~~~b ||| c)) - 14 * ~~~( ~~~a ||| (b ||| c)) - 15 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 3 * ( ~~~a &&& (b &&& c)) + 10 * (a &&& ( ~~~b &&& c)) + 11 * (a &&& (b &&& c)) = - 7 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) - 11 * (a &&& b) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1845 (x y : BitVec w) : +theorem e_1845 : - 7 * (c ^^^ (a ||| ~~~b)) - 11 * ~~~(a &&& ( ~~~b ||| c)) + 1 * (b ||| c) - 1 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 7 * ((a ^^^ b) &&& (a ^^^ c)) + 2 * (b ^^^ ~~~(a ||| ~~~c)) + 3 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 6 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) - 1 * (c ^^^ ( ~~~a ||| (b ||| c))) - 1 * ((a ||| ~~~b) &&& (b ^^^ c)) - 2 * (b ^^^ ~~~(a &&& (b &&& c))) - 5 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 1 * ~~~(a ^^^ ( ~~~b &&& c)) - 1 * (a ||| ~~~c) + 5 * ~~~(a &&& (b &&& c)) + 1 * ~~~(a ^^^ b) - 2 * (b ||| ~~~(a ||| ~~~c)) - 1 * (c ^^^ (a &&& ~~~b)) - 7 * ( ~~~b &&& ~~~(a ^^^ c)) + 4 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) - 1 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 11 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) - 2 * ((a &&& b) ||| ~~~(b ^^^ c)) - 1 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) + 3 * ((a &&& b) ^^^ (b ||| ~~~c)) - 11 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) + 3 * (b ^^^ (a &&& (b ||| c))) - 7 * (c &&& ~~~(a &&& b)) - 1 * ~~~(a ||| ( ~~~b &&& c)) + 1 * ~~~( ~~~a ||| ( ~~~b &&& c)) + 5 * (c ^^^ ~~~(a ||| b)) + 3 * ((a ||| b) &&& ~~~(b ^^^ c)) + 1 * ( ~~~c ||| (a ^^^ b)) + 2 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) + 1 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) + 5 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) + 24 * ~~~(a ||| (b ||| c)) - 14 * ~~~(a ||| ( ~~~b ||| c)) - 10 * ~~~( ~~~a ||| (b ||| c)) + 17 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 10 * ( ~~~a &&& ( ~~~b &&& c)) + 13 * ( ~~~a &&& (b &&& c)) + 10 * (a &&& ( ~~~b &&& c)) - 5 * (a &&& (b &&& c)) = - 7 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1846 (x y : BitVec w) : +theorem e_1846 : 1 * (b ^^^ (a &&& (b ||| c))) + 7 * ~~~(a &&& b) - 2 * ((a ||| b) &&& ~~~(b ^^^ c)) - 11 * ~~~c + 2 * ~~~(a ||| (b &&& c)) - 3 * ( ~~~(a ||| b) ||| (b ^^^ c)) + 1 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 7 * (a &&& c) - 7 * ~~~(a ^^^ b) - 1 * ( ~~~b ||| ~~~(a ^^^ c)) + 2 * (c ^^^ ~~~(a &&& (b &&& c))) - 2 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) - 3 * (c ^^^ (a &&& ~~~b)) - 11 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) + 11 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) + 1 * (b &&& ~~~(a &&& c)) + 4 * (b &&& ~~~(a ^^^ c)) - 1 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) - 2 * ((a &&& c) ^^^ (b ||| c)) + 2 * (b ^^^ (a ||| ( ~~~b &&& c))) - 1 * ((a &&& b) ^^^ (b ||| c)) - 5 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) - 11 * a + 1 * (c &&& (a ||| ~~~b)) + 2 * (b ^^^ (a &&& ~~~c)) - 11 * ~~~( ~~~a ||| ( ~~~b &&& c)) + 3 * (a ^^^ (b ^^^ c)) + 1 * ( ~~~b ||| (a ^^^ c)) - 1 * (c ^^^ ~~~(a &&& (b ||| c))) + 1 * ((a &&& c) ||| (b &&& ~~~c)) + 2 * (c ^^^ (a ||| (b &&& c))) + 1 * (b ^^^ (a &&& (b ^^^ c))) - 2 * (a ||| ~~~c) + 4 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) + 2 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) + 2 * (b ^^^ (a &&& c)) + 9 * ~~~(a ||| (b ||| c)) - 16 * ~~~(a ||| ( ~~~b ||| c)) + 41 * ~~~( ~~~a ||| (b ||| c)) + 41 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 7 * ( ~~~a &&& ( ~~~b &&& c)) - 21 * ( ~~~a &&& (b &&& c)) + 5 * (a &&& ( ~~~b &&& c)) + 23 * (a &&& (b &&& c)) = 3 * (b &&& (a ^^^ c)) - 11 * ~~~(a ||| ~~~b) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1847 (x y : BitVec w) : +theorem e_1847 : - 1 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) + 11 * (b ^^^ ( ~~~a ||| (b ||| c))) + 5 * ~~~( ~~~a ||| (b &&& c)) - 3 * (b ^^^ ~~~(a ||| (b &&& c))) + 2 * (c ^^^ ( ~~~a ||| (b &&& c))) + 3 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 2 * (b ^^^ (a ||| (b &&& c))) + 3 * (b &&& ~~~(a ^^^ c)) - 3 * (b &&& ~~~(a &&& ~~~c)) + 2 * (a ^^^ ( ~~~b ||| c)) - 6 * ((b &&& c) ||| (a &&& (b ||| c))) - 11 * (b ^^^ ~~~(a &&& (b ||| c))) - 1 * (b ||| ~~~(a ||| c)) + 5 * (c ||| (a &&& b)) - 2 * b - 2 * (c ^^^ (a ||| (b &&& c))) + 7 * (c ||| ~~~(a ||| ~~~b)) + 2 * (a ||| c) - 3 * (c ^^^ (a ||| ( ~~~b ||| c))) - 2 * (b ^^^ ( ~~~a ||| (b ^^^ c))) + 1 * (c ^^^ ~~~(a &&& ~~~b)) - 1 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) - 2 * (b ||| ~~~(a ||| ~~~c)) + 1 * ( ~~~a &&& ( ~~~b ||| c)) + 7 * (b ^^^ (a ||| c)) + 4 * (b &&& (a ^^^ c)) - 1 * (c ^^^ ~~~(a ||| (b &&& c))) - 6 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) + 2 * ((a ^^^ b) &&& (a ^^^ c)) - 5 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) - 7 * (c ||| (a &&& ~~~b)) - 1 * ~~~(b ||| ~~~c) + 1 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) - 1 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 1 * (b ^^^ (a ||| ~~~c)) + 11 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) + 7 * (b ^^^ (a &&& (b ^^^ c))) + 9 * ~~~(a ||| (b ||| c)) - 24 * ~~~(a ||| ( ~~~b ||| c)) + 9 * ~~~( ~~~a ||| (b ||| c)) - 3 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 1 * ( ~~~a &&& (b &&& c)) - 25 * (a &&& ( ~~~b &&& c)) + 11 * (a &&& (b &&& c)) = 6 * ( ~~~a &&& ( ~~~b &&& c)) - 2 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1848 (x y : BitVec w) : +theorem e_1848 : 1 * (b ^^^ (a ||| (b ||| c))) + 1 * (b ^^^ ( ~~~a &&& (b ||| c))) - 1 * (b ||| ~~~(a ^^^ c)) - 2 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 2 * (c ||| (a ^^^ b)) - 2 * ~~~b - 11 * ~~~(a &&& ( ~~~b &&& c)) - 2 * (c ^^^ ~~~(a &&& ~~~b)) + 1 * ((a ||| b) &&& ~~~(b ^^^ c)) + 2 * (c ^^^ ( ~~~a ||| (b ||| c))) + 3 * (b ||| (a ^^^ c)) + 11 * (b ^^^ c) - 5 * ~~~(b &&& c) + 2 * (a ^^^ (b ||| c)) + 5 * (b &&& c) + 11 * (c ^^^ (a ||| ( ~~~b &&& c))) - 2 * (c ^^^ ~~~(a &&& b)) - 6 * (c ^^^ ~~~(a &&& (b ||| c))) + 4 * ~~~(b ||| ~~~c) - 1 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) + 11 * (b ^^^ (a ||| c)) - 5 * ((a &&& b) ||| ~~~(b ||| c)) + 2 * ~~~( ~~~a &&& (b ^^^ c)) - 1 * ((a ^^^ b) ||| ~~~(a ^^^ c)) + 2 * (a ^^^ ( ~~~b ||| c)) + 5 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) - 7 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) + 2 * (b ^^^ (a &&& ( ~~~b ||| c))) + 2 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) + 5 * (b ^^^ ~~~(a &&& (b ^^^ c))) + 3 * ~~~(a ||| (b &&& c)) - 1 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 7 * (b ^^^ (a ||| (b &&& c))) - 1 * (b ^^^ ~~~(a ||| c)) - 1 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) - 3 * (a ||| c) + 1 * (b ^^^ (a ||| ~~~c)) + 4 * (c ^^^ ~~~(a ||| ~~~b)) + 19 * ~~~(a ||| (b ||| c)) - 12 * ~~~(a ||| ( ~~~b ||| c)) - 8 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 20 * ( ~~~a &&& ( ~~~b &&& c)) - 16 * ( ~~~a &&& (b &&& c)) - 20 * (a &&& ( ~~~b &&& c)) + 19 * (a &&& (b &&& c)) = 3 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) + 4 * ~~~( ~~~a ||| (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1849 (x y : BitVec w) : +theorem e_1849 : - 7 * ~~~(a ^^^ b) + 5 * ( ~~~a ||| (b ||| c)) - 1 * ( ~~~c ||| ~~~(a ^^^ b)) + 3 * ~~~(a ||| (b &&& c)) - 5 * (c ^^^ (a &&& ~~~b)) + 1 * (a ^^^ (b &&& c)) + 1 * ( ~~~b ||| ~~~(a ^^^ c)) - 6 * (c ^^^ (a &&& b)) + 11 * ~~~(a &&& b) - 2 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 2 * (a ^^^ (b ^^^ c)) - 11 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) + 7 * ~~~(a &&& ( ~~~b ||| c)) - 11 * ~~~( ~~~a ||| (b ^^^ c)) - 1 * (a ||| (b &&& c)) - 7 * (c ^^^ ~~~(a &&& (b ||| c))) + 7 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 2 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 2 * (b ^^^ ~~~(a &&& (b ||| c))) + 11 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) - 1 * (c ^^^ ( ~~~a ||| (b ||| c))) - 1 * (c ||| ~~~(a ||| ~~~b)) + 1 * ~~~(a &&& ~~~b) - 11 * (b ||| (a &&& ~~~c)) + 1 * ((a &&& c) ||| (b &&& ~~~c)) + 1 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) + 2 * ~~~(a &&& ~~~a) + 5 * (b ^^^ (a ||| ~~~c)) - 3 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) + 3 * ( ~~~a &&& ( ~~~b ||| c)) + 7 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) + 4 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) + 2 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) - 2 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) - 6 * (b ^^^ ~~~(a ||| (b &&& c))) + 3 * (b ^^^ ~~~(a ||| ~~~c)) - 6 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 12 * ~~~(a ||| (b ||| c)) - 1 * ~~~(a ||| ( ~~~b ||| c)) + 22 * ~~~( ~~~a ||| (b ||| c)) + 18 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 39 * ( ~~~a &&& ( ~~~b &&& c)) - 6 * ( ~~~a &&& (b &&& c)) - 31 * (a &&& ( ~~~b &&& c)) + 38 * (a &&& (b &&& c)) = 1 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1850 (x y : BitVec w) : +theorem e_1850 : 11 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 1 * (b ^^^ (a ||| ( ~~~b &&& c))) - 1 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) + 11 * ( ~~~a &&& (b ||| c)) + 5 * ((a &&& b) ||| ~~~(b ^^^ c)) + 7 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 1 * ( ~~~a ||| ( ~~~b ||| c)) - 11 * ((a ||| b) &&& (b ^^^ c)) + 5 * ((a &&& b) ^^^ (b ||| c)) + 5 * ( ~~~b &&& (a ^^^ c)) + 1 * ~~~(a ||| ~~~c) + 2 * (a ||| (b &&& c)) - 2 * ~~~(a ||| ( ~~~b &&& c)) - 6 * (b ^^^ ~~~(a ||| c)) + 4 * ((a ^^^ b) ||| ~~~(a ^^^ c)) - 5 * (c ^^^ ~~~(a &&& (b ||| c))) - 6 * (b &&& ~~~c) - 6 * ~~~(a &&& ( ~~~b &&& c)) - 2 * ~~~(a ||| ~~~b) + 5 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) - 7 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 3 * (b ^^^ ~~~(a ||| (b ^^^ c))) - 11 * ((a ^^^ b) ||| (a ^^^ c)) - 1 * ~~~( ~~~a &&& (b ||| c)) - 1 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 3 * ~~~( ~~~a ||| (b ^^^ c)) + 4 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) + 2 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) - 1 * (b ^^^ (a ||| c)) - 7 * ~~~(a ^^^ ( ~~~b &&& c)) - 1 * (c ||| (a &&& ~~~b)) + 1 * (b ||| c) - 2 * (a &&& ~~~c) + 11 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) - 5 * ~~~c - 7 * (a ^^^ b) + 4 * (b ||| (a &&& ~~~c)) - 5 * ((a &&& b) ||| ~~~(b ||| ~~~c)) - 2 * (a ^^^ c) + 7 * ~~~(a ||| (b ||| c)) + 22 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 7 * ( ~~~a &&& ( ~~~b &&& c)) - 23 * ( ~~~a &&& (b &&& c)) + 9 * (a &&& ( ~~~b &&& c)) - 6 * (a &&& (b &&& c)) = - 42 * ~~~(a ||| ( ~~~b ||| c)) - 1 * (b ^^^ ( ~~~a &&& (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1851 (x y : BitVec w) : +theorem e_1851 : - 6 * (c ^^^ (a ||| (b &&& c))) - 2 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 1 * ~~~( ~~~a &&& (b ||| c)) - 3 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) + 2 * (b ||| ~~~(a ||| c)) - 1 * (c ^^^ ~~~(a ||| b)) + 2 * ((a ^^^ b) ||| (a ^^^ c)) - 1 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 7 * (c ^^^ ( ~~~a ||| (b ||| c))) + 11 * (c &&& ~~~(a ^^^ b)) - 2 * (c ||| ~~~(a ||| ~~~b)) + 1 * (b ^^^ (a ||| (b &&& c))) + 5 * (a &&& c) + 4 * (b ^^^ ~~~(a ||| c)) + 7 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) + 1 * ((a &&& b) ||| ~~~(b ||| c)) + 3 * (b ||| ~~~(a ||| ~~~c)) - 1 * ( ~~~b ||| (a ^^^ c)) - 3 * ((a ^^^ b) &&& ~~~(a ^^^ c)) - 7 * ((a &&& c) ^^^ (b ||| c)) + 5 * ~~~( ~~~a ||| ( ~~~b &&& c)) + 3 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) - 1 * ~~~(b &&& c) + 1 * (c &&& (a ||| ~~~b)) + 11 * ( ~~~c ||| ~~~(a ^^^ b)) + 5 * (b ^^^ (a ||| (b ^^^ c))) - 1 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) - 6 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) + 3 * ~~~( ~~~a ||| (b &&& c)) + 2 * (b ^^^ (a &&& ( ~~~b ||| c))) - 1 * ((a ||| b) &&& (b ^^^ c)) + 1 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) - 11 * (b ^^^ ~~~(a ||| (b &&& c))) + 11 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) + 7 * ~~~(a ^^^ b) + 11 * (a ||| ( ~~~b &&& c)) + 1 * ((b &&& c) ||| (a &&& (b ||| c))) - 11 * ~~~(a ||| (b ||| c)) - 34 * ~~~(a ||| ( ~~~b ||| c)) - 53 * ~~~( ~~~a ||| (b ||| c)) - 32 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 28 * ( ~~~a &&& ( ~~~b &&& c)) + 8 * ( ~~~a &&& (b &&& c)) - 17 * (a &&& ( ~~~b &&& c)) - 70 * (a &&& (b &&& c)) = 1 * ~~~(a &&& ~~~b) - 5 * ( ~~~a ||| (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1852 (x y : BitVec w) : +theorem e_1852 : 4 * ~~~( ~~~a ||| (b &&& c)) - 5 * ~~~(a &&& ~~~b) - 2 * (b ^^^ ~~~(a ||| ~~~c)) + 7 * (c ^^^ ~~~(a &&& ~~~b)) + 3 * (b ^^^ ( ~~~a ||| (b &&& c))) - 2 * ((a &&& c) ||| ~~~(b ||| c)) - 11 * ((a &&& ~~~b) ||| (b ^^^ c)) + 11 * ( ~~~a &&& ( ~~~b ||| c)) - 1 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 5 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) + 11 * ~~~(a ^^^ ( ~~~b &&& c)) - 5 * (b ^^^ (a ||| ~~~c)) - 6 * (b &&& (a ||| c)) + 2 * (b ^^^ (a ||| c)) - 6 * ((a &&& b) ^^^ (b ||| c)) - 5 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) + 1 * ~~~( ~~~a &&& (b &&& c)) + 5 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) + 3 * (b ^^^ c) - 11 * (a &&& b) + 7 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) + 7 * (a ||| b) + 11 * (c ^^^ (a &&& b)) - 11 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) - 6 * ~~~(a &&& ~~~a) + 7 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) + 1 * (c ^^^ (a &&& (b ||| c))) + 2 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 1 * (a ||| (b ^^^ c)) - 1 * ~~~(b ^^^ c) - 1 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 7 * (b ^^^ ~~~(a ||| (b &&& c))) + 4 * (c ^^^ ~~~(a &&& (b &&& c))) + 3 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 11 * ( ~~~a &&& (b ^^^ c)) + 2 * (c ^^^ ~~~(a &&& (b ||| c))) - 2 * (b ^^^ ( ~~~a ||| (b ^^^ c))) - 12 * ~~~(a ||| (b ||| c)) - 21 * ~~~(a ||| ( ~~~b ||| c)) + 12 * ~~~( ~~~a ||| (b ||| c)) + 11 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 1 * ( ~~~a &&& ( ~~~b &&& c)) - 4 * ( ~~~a &&& (b &&& c)) - 28 * (a &&& ( ~~~b &&& c)) + 32 * (a &&& (b &&& c)) = 1 * ~~~( ~~~a ||| ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1853 (x y : BitVec w) : +theorem e_1853 : - 1 * ( ~~~a &&& ( ~~~b ||| c)) - 2 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 2 * (c ||| ~~~(a ||| b)) + 2 * ( ~~~(a ||| b) ||| (b ^^^ c)) + 1 * ~~~(b ||| ~~~c) - 3 * ~~~(b &&& ~~~c) - 1 * ~~~(a ||| c) + 7 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 5 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 7 * (c ||| ~~~(a ^^^ b)) + 11 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) + 4 * (b ^^^ ~~~(a &&& ~~~c)) - 6 * (c ||| (a &&& ~~~b)) + 5 * ~~~(a &&& c) - 7 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) - 1 * (a ||| ( ~~~b ||| c)) - 1 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) - 6 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) + 5 * ((a &&& b) ||| (b ^^^ c)) + 2 * (b ^^^ (a &&& (b ||| c))) - 1 * (b ^^^ (a ||| ~~~c)) - 1 * (b ^^^ (a ||| (b &&& c))) - 1 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 2 * ( ~~~b ||| ~~~(a ^^^ c)) + 2 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 3 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) - 3 * (b &&& ~~~(a &&& c)) - 2 * (c ||| (a &&& b)) + 2 * ~~~(a ^^^ b) - 1 * (c ^^^ ~~~(a ||| (b &&& c))) - 3 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) + 1 * (b ||| ~~~(a ||| c)) + 1 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) + 1 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) + 4 * (b ||| ~~~(a ||| ~~~c)) + 1 * (a &&& ( ~~~b ||| c)) - 1 * ~~~( ~~~a &&& (b ^^^ c)) - 1 * (b ^^^ (a &&& c)) - 7 * ~~~(a ||| ( ~~~b ||| c)) + 26 * ~~~( ~~~a ||| (b ||| c)) + 17 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 15 * ( ~~~a &&& ( ~~~b &&& c)) + 10 * ( ~~~a &&& (b &&& c)) + 12 * (a &&& ( ~~~b &&& c)) + 2 * (a &&& (b &&& c)) = - 2 * ~~~(a ||| (b ||| c)) + 5 * ( ~~~c ||| (a ^^^ b)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1854 (x y : BitVec w) : +theorem e_1854 : - 11 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) - 5 * ~~~(a ^^^ ( ~~~b ||| c)) - 6 * ((a ||| b) &&& (b ^^^ c)) - 11 * (a ^^^ (b ^^^ c)) - 3 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) - 1 * (a ||| b) + 11 * (a ||| ( ~~~b ||| c)) + 1 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) - 7 * (a ||| ~~~c) - 1 * ((a ||| b) &&& ~~~(b ^^^ c)) + 11 * ~~~(b ||| c) - 1 * (b &&& ~~~(a ^^^ c)) + 4 * (b ^^^ ~~~(a &&& (b ||| c))) - 1 * (a ||| (b ^^^ c)) - 1 * ( ~~~b ||| ~~~(a ^^^ c)) - 3 * (c ||| ~~~(a ||| b)) + 3 * ( ~~~a &&& (b ^^^ c)) - 1 * ( ~~~b &&& (a ^^^ c)) - 2 * (b ^^^ c) - 7 * (a ||| (b &&& c)) + 3 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) - 3 * ( ~~~a &&& (b ||| c)) + 2 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 2 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) - 1 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 5 * ((a &&& ~~~b) ||| (b ^^^ c)) + 2 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) + 7 * (b ^^^ ~~~(a &&& c)) + 11 * (b ^^^ ~~~(a ||| ~~~c)) + 1 * ~~~(a ^^^ b) - 2 * ~~~(a &&& (b &&& c)) - 1 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) + 11 * ((a &&& b) ||| ~~~(b ||| ~~~c)) - 1 * ~~~( ~~~a &&& (b ^^^ c)) + 5 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 5 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) - 1 * (c ||| ~~~(a ^^^ b)) - 16 * ~~~(a ||| (b ||| c)) + 26 * ~~~(a ||| ( ~~~b ||| c)) + 1 * ~~~( ~~~a ||| (b ||| c)) - 3 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 30 * ( ~~~a &&& ( ~~~b &&& c)) + 9 * ( ~~~a &&& (b &&& c)) + 13 * (a &&& ( ~~~b &&& c)) + 6 * (a &&& (b &&& c)) = 3 * ~~~(a ||| ( ~~~b &&& c)) - 3 * ~~~a := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1855 (x y : BitVec w) : +theorem e_1855 : - 7 * ( ~~~b &&& (a ^^^ c)) - 1 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) + 4 * ~~~( ~~~a ||| (b &&& c)) + 2 * (c ^^^ ~~~(a ||| b)) - 3 * ((a ||| ~~~b) &&& (b ^^^ c)) - 5 * ~~~(a ||| ( ~~~b &&& c)) + 2 * ( ~~~c ||| (a ^^^ b)) + 2 * (c ^^^ (a ||| ( ~~~b &&& c))) - 2 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) + 2 * (c ^^^ ~~~(a ||| ~~~b)) - 6 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) + 1 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) + 7 * ~~~(a &&& (b &&& c)) + 7 * (b ^^^ (a &&& (b ||| c))) + 4 * ~~~(a &&& b) + 1 * ~~~(a &&& c) + 7 * ~~~( ~~~a ||| (b ^^^ c)) - 11 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) - 2 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 2 * (b ^^^ ~~~(a &&& c)) + 1 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) - 3 * (b ^^^ ~~~(a &&& ~~~c)) + 2 * (b ^^^ ~~~(a &&& (b ||| c))) - 5 * (a ||| ( ~~~b ||| c)) + 1 * ~~~(a ||| b) - 1 * ~~~b - 11 * (c &&& (a ^^^ b)) - 2 * (c ||| (a ^^^ b)) + 1 * ~~~( ~~~a &&& (b ^^^ c)) - 1 * ((a &&& ~~~b) ||| (b ^^^ c)) + 5 * (b ^^^ (a &&& c)) + 5 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) + 5 * (c ^^^ (a ||| ( ~~~b ||| c))) + 3 * (b ^^^ ( ~~~a &&& (b ||| c))) + 3 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) - 1 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 1 * ((b &&& c) ||| (a &&& (b ||| c))) - 2 * ~~~(a ||| ~~~c) + 21 * ~~~(a ||| (b ||| c)) + 4 * ~~~(a ||| ( ~~~b ||| c)) - 9 * ~~~( ~~~a ||| (b ||| c)) - 19 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 16 * ( ~~~a &&& ( ~~~b &&& c)) + 1 * ( ~~~a &&& (b &&& c)) + 22 * (a &&& ( ~~~b &&& c)) = 1 * (a &&& (b &&& c)) + 11 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1856 (x y : BitVec w) : +theorem e_1856 : 1 * ~~~(a ^^^ ( ~~~b &&& c)) - 1 * (c ^^^ ( ~~~a ||| (b &&& c))) + 4 * (c ^^^ (a ||| b)) + 1 * (b ^^^ (a &&& c)) - 3 * (a ||| (b &&& c)) + 4 * ( ~~~c ||| ~~~(a ^^^ b)) + 2 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 1 * ((a &&& c) ^^^ (b ||| c)) - 11 * (c ^^^ ~~~(a &&& ~~~b)) + 1 * ~~~(b &&& c) - 6 * (c &&& ~~~(a &&& ~~~b)) - 1 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) + 7 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 6 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) + 5 * (c ^^^ ( ~~~a &&& (b ||| c))) - 2 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 11 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) - 7 * ( ~~~a ||| ( ~~~b &&& c)) - 1 * ((a ^^^ b) &&& ~~~(a ^^^ c)) + 2 * (b ^^^ ~~~(a ||| ~~~c)) + 11 * (c ^^^ (a ||| ( ~~~b &&& c))) - 3 * ( ~~~b ||| (a ^^^ c)) + 11 * ((a &&& b) ^^^ (b ||| ~~~c)) + 1 * (a ||| ( ~~~b &&& c)) - 5 * ~~~b + 4 * (c ^^^ (a &&& (b ||| c))) - 1 * (b ||| (a &&& c)) - 6 * (c ||| ~~~(a ||| b)) + 3 * (b ^^^ c) + 2 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) + 1 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 6 * (c ||| ~~~(a ^^^ b)) - 1 * ~~~(a ^^^ (b ||| c)) + 4 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) - 3 * (b ||| (a &&& ~~~c)) + 3 * (b ||| ~~~c) + 2 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) + 14 * ~~~(a ||| (b ||| c)) - 18 * ~~~(a ||| ( ~~~b ||| c)) - 10 * ~~~( ~~~a ||| (b ||| c)) - 14 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 11 * ( ~~~a &&& ( ~~~b &&& c)) + 14 * ( ~~~a &&& (b &&& c)) + 45 * (a &&& ( ~~~b &&& c)) + 15 * (a &&& (b &&& c)) = 11 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1857 (x y : BitVec w) : +theorem e_1857 : - 2 * (c &&& ~~~(a &&& ~~~b)) - 5 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) + 1 * (a ^^^ (b &&& c)) - 1 * (c ^^^ (a ||| (b &&& c))) - 6 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) + 2 * ((a ^^^ b) &&& ~~~(a ^^^ c)) + 1 * ~~~(a &&& ( ~~~b &&& c)) - 11 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) + 1 * ~~~a - 7 * (b ^^^ (a &&& (b ^^^ c))) - 2 * (b &&& ~~~(a ^^^ c)) + 4 * ~~~( ~~~a &&& ( ~~~b ||| c)) - 5 * (b ^^^ (a ||| (b ^^^ c))) - 5 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 7 * ((a ^^^ b) &&& (a ^^^ c)) - 1 * (c ^^^ ~~~(a ||| b)) - 3 * (b ^^^ (a &&& ~~~c)) - 1 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) - 2 * (c ^^^ ( ~~~a &&& (b ||| c))) + 2 * (a ^^^ b) + 7 * (a &&& ~~~b) - 3 * ~~~(a ||| (b &&& c)) - 2 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 1 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 11 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) - 2 * ( ~~~a ||| (b ^^^ c)) + 4 * ~~~(a &&& (b ||| c)) - 3 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) + 2 * (b ^^^ c) - 11 * (b &&& c) + 7 * (a ^^^ ( ~~~b ||| c)) - 1 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) + 11 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) - 1 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) + 1 * (b ^^^ (a ||| (b ||| c))) + 5 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) + 4 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 19 * ~~~(a ||| (b ||| c)) + 27 * ~~~(a ||| ( ~~~b ||| c)) - 1 * ~~~( ~~~a ||| (b ||| c)) + 3 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 16 * ( ~~~a &&& ( ~~~b &&& c)) + 51 * ( ~~~a &&& (b &&& c)) + 21 * (a &&& ( ~~~b &&& c)) + 39 * (a &&& (b &&& c)) = 7 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1858 (x y : BitVec w) : +theorem e_1858 : 1 * (c ^^^ ~~~(a &&& b)) + 2 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 2 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 7 * (b ^^^ ~~~(a ||| (b ^^^ c))) - 3 * (b &&& ~~~c) + 2 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 7 * (c ^^^ (a ||| (b ||| c))) + 7 * (b ^^^ (a ||| ~~~c)) - 1 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) - 3 * (b ^^^ ( ~~~a ||| (b &&& c))) - 7 * ((a &&& ~~~b) ||| (b ^^^ c)) - 1 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) - 1 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) - 1 * (a &&& (b ||| c)) + 11 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 1 * (b ^^^ (a &&& (b ^^^ c))) + 1 * (c ^^^ ( ~~~a ||| (b &&& c))) - 1 * ((a &&& b) ||| ~~~(b ^^^ c)) + 7 * (c &&& ~~~(a ^^^ b)) + 11 * (b &&& ~~~(a ^^^ c)) - 1 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) + 1 * (c ^^^ (a &&& ~~~b)) - 3 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) - 7 * ~~~(b ^^^ c) + 5 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) - 3 * ~~~(a ^^^ ( ~~~b ||| c)) + 3 * (c ^^^ (a ||| ( ~~~b &&& c))) - 1 * ~~~( ~~~a ||| (b &&& c)) + 5 * (c ^^^ (a ||| b)) + 3 * ( ~~~a ||| ( ~~~b &&& c)) + 11 * ~~~( ~~~a &&& ( ~~~b &&& c)) + 2 * (a &&& ( ~~~b ||| c)) + 2 * (b ^^^ (a &&& ( ~~~b ||| c))) - 6 * (b ^^^ ~~~(a ||| (b &&& c))) + 7 * (c &&& (a ^^^ b)) - 1 * (a ||| c) - 6 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) - 3 * (c &&& (a ||| b)) + 5 * (b ^^^ c) - 3 * ~~~(a ||| (b ||| c)) - 17 * ~~~(a ||| ( ~~~b ||| c)) - 14 * ~~~( ~~~a ||| (b ||| c)) - 18 * ( ~~~a &&& ( ~~~b &&& c)) - 19 * ( ~~~a &&& (b &&& c)) - 34 * (a &&& ( ~~~b &&& c)) - 4 * (a &&& (b &&& c)) = 2 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1859 (x y : BitVec w) : +theorem e_1859 : - 2 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) - 1 * ( ~~~a &&& (b ^^^ c)) - 2 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 11 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) + 2 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) + 1 * (c ^^^ ( ~~~a ||| (b ||| c))) + 1 * (b &&& (a ^^^ c)) - 11 * (b &&& c) - 2 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) - 1 * (b ^^^ (a ||| ( ~~~b ||| c))) - 6 * (c &&& ~~~(a &&& ~~~b)) + 1 * ((a &&& b) ||| ~~~(b ||| ~~~c)) + 11 * ~~~(a &&& (b &&& c)) + 3 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) + 1 * (c ^^^ (a ||| b)) - 11 * ~~~( ~~~a &&& (b ||| c)) + 1 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) - 2 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) + 3 * (c ||| (a &&& b)) - 6 * ~~~( ~~~a &&& ( ~~~b &&& c)) - 3 * ( ~~~c &&& (a ^^^ b)) - 5 * ~~~(a &&& c) - 3 * ( ~~~a &&& (b ||| c)) - 6 * ((a ||| ~~~b) &&& (b ^^^ c)) - 1 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) + 2 * ( ~~~a ||| ( ~~~b &&& c)) - 2 * (c ^^^ ~~~(a &&& (b ||| c))) + 7 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) - 1 * ( ~~~c &&& ~~~(a ^^^ b)) + 1 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 1 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) - 1 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 7 * (b ^^^ ( ~~~a ||| (b &&& c))) - 2 * (c ^^^ ~~~(a ||| (b &&& c))) + 2 * ~~~(a ^^^ ( ~~~b &&& c)) + 2 * ((a &&& b) ^^^ (b ||| ~~~c)) + 7 * (c &&& ~~~(a &&& b)) + 2 * ~~~(a ||| ~~~b) - 6 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) + 18 * ~~~(a ||| (b ||| c)) + 14 * ~~~(a ||| ( ~~~b ||| c)) + 32 * ~~~( ~~~a ||| (b ||| c)) + 24 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 3 * ( ~~~a &&& ( ~~~b &&& c)) + 19 * (a &&& ( ~~~b &&& c)) + 29 * (a &&& (b &&& c)) = - 2 * (a ^^^ c) - 2 * (c ||| ~~~(a ||| ~~~b)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1860 (x y : BitVec w) : +theorem e_1860 : - 2 * (a ^^^ b) - 7 * (a ||| ( ~~~b ||| c)) + 3 * ((a &&& c) ||| ~~~(b ||| c)) - 1 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) + 7 * (b ^^^ ( ~~~a &&& (b ||| c))) - 1 * ( ~~~c &&& ~~~(a ^^^ b)) - 3 * ( ~~~a &&& (b ||| c)) + 2 * (b ||| (a &&& c)) - 1 * (b ||| ~~~(a ^^^ c)) - 2 * (b ^^^ ~~~(a &&& (b ||| c))) - 11 * (c ^^^ (a ||| ~~~b)) - 2 * (c ^^^ (a &&& (b ||| c))) + 7 * (a &&& b) + 1 * ~~~( ~~~a ||| (b &&& c)) + 1 * (c ^^^ (a ||| (b &&& c))) + 2 * (c ||| ~~~(a ||| ~~~b)) + 2 * (c ^^^ ~~~(a ||| ~~~b)) - 1 * ( ~~~c ||| (a ^^^ b)) + 7 * ((a &&& b) ||| ~~~(b ^^^ c)) + 1 * ( ~~~(a &&& b) &&& (b ^^^ c)) - 1 * ~~~(a &&& ~~~b) - 6 * (a ||| ( ~~~b &&& c)) - 2 * (b ^^^ (a &&& c)) - 1 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) + 2 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 2 * ~~~(a &&& ~~~c) + 7 * (c ^^^ ( ~~~a ||| (b ||| c))) + 7 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) + 1 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) + 5 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) + 2 * (c ^^^ ~~~(a &&& (b &&& c))) - 5 * (c ^^^ (a ||| ( ~~~b &&& c))) + 11 * (c ^^^ (a ||| (b ||| c))) + 7 * ~~~( ~~~a ||| ( ~~~b &&& c)) - 6 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 4 * (c &&& ~~~(a &&& ~~~b)) - 2 * (b ^^^ (a &&& ~~~c)) - 7 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) - 2 * (b ^^^ ~~~(a ||| ~~~c)) - 13 * ~~~(a ||| ( ~~~b ||| c)) + 6 * ~~~( ~~~a ||| (b ||| c)) - 4 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 13 * ( ~~~a &&& ( ~~~b &&& c)) + 19 * ( ~~~a &&& (b &&& c)) - 5 * (a &&& ( ~~~b &&& c)) - 29 * (a &&& (b &&& c)) = - 3 * (c ^^^ ~~~(a ||| (b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1861 (x y : BitVec w) : +theorem e_1861 : - 5 * ( ~~~c ||| ~~~(a ^^^ b)) - 7 * ~~~(a &&& ~~~c) - 2 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) - 2 * (c &&& ~~~(a ^^^ b)) + 4 * (c ^^^ (a ||| ( ~~~b ||| c))) + 1 * (b &&& ~~~(a &&& ~~~c)) - 3 * (b ^^^ ~~~(a &&& (b ^^^ c))) + 1 * (b ^^^ ~~~(a &&& c)) + 2 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 2 * (a ^^^ ( ~~~b &&& c)) + 1 * ~~~(b ||| ~~~c) - 1 * (b ^^^ (a &&& ~~~c)) + 4 * ~~~( ~~~a &&& ( ~~~b ||| c)) + 1 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 1 * ( ~~~b ||| (a ^^^ c)) + 5 * (b ^^^ (a ||| ~~~c)) + 1 * (b ^^^ (a &&& (b ^^^ c))) - 2 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) - 1 * ~~~(a &&& ( ~~~b ||| c)) - 11 * (a ^^^ b) + 1 * ~~~( ~~~a ||| (b ^^^ c)) + 2 * ((a &&& b) ^^^ (b ||| c)) + 3 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) + 2 * ( ~~~c ||| (a ^^^ b)) + 7 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) - 1 * ~~~(a &&& ~~~b) + 5 * ~~~( ~~~a &&& (b ||| c)) + 1 * c - 6 * ( ~~~a ||| ( ~~~b ||| c)) - 3 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) + 1 * ( ~~~a ||| (b ^^^ c)) - 7 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 5 * (b ||| ~~~(a ||| ~~~c)) + 2 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) + 11 * (c ^^^ (a ||| ( ~~~b &&& c))) - 5 * ~~~(a ||| c) - 3 * (a &&& c) - 7 * ~~~(a ||| ( ~~~b &&& c)) + 20 * ~~~(a ||| (b ||| c)) + 25 * ~~~(a ||| ( ~~~b ||| c)) + 8 * ~~~( ~~~a ||| (b ||| c)) - 16 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 15 * ( ~~~a &&& ( ~~~b &&& c)) + 19 * ( ~~~a &&& (b &&& c)) + 18 * (a &&& ( ~~~b &&& c)) + 3 * (a &&& (b &&& c)) = 5 * ((a ^^^ b) ||| (a ^^^ c)) + 2 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1862 (x y : BitVec w) : +theorem e_1862 : 2 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 1 * (b ^^^ ( ~~~a &&& (b ^^^ c))) - 1 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) + 4 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) + 2 * ((a &&& c) ||| ~~~(b ||| c)) - 7 * (b ^^^ (a &&& c)) + 5 * (c ||| ~~~(a ^^^ b)) + 11 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) + 2 * ((a &&& b) ^^^ (b ||| ~~~c)) + 2 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) - 2 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) + 7 * (a ||| c) + 1 * (b ^^^ (a &&& (b ^^^ c))) - 2 * ~~~(a ^^^ ( ~~~b &&& c)) + 1 * ( ~~~a &&& (b ||| c)) - 6 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) + 7 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) - 1 * (b ^^^ (a &&& (b ||| c))) - 2 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) - 2 * (a ||| ( ~~~b ||| c)) - 2 * ~~~(a ||| (b &&& c)) + 1 * ~~~(b &&& c) + 1 * ( ~~~b ||| ~~~(a ^^^ c)) - 1 * (c &&& (a ^^^ b)) + 2 * (c &&& ~~~(a &&& ~~~b)) - 1 * ~~~(a ||| ( ~~~b &&& c)) + 3 * ~~~(b ||| c) - 2 * (b ^^^ ( ~~~a ||| (b ^^^ c))) - 6 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) - 1 * (a &&& (b ^^^ c)) - 3 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 1 * ~~~(a &&& ~~~c) - 3 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) - 7 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 11 * (b &&& (a ||| c)) - 6 * ~~~(a &&& ~~~a) - 1 * ~~~(a ||| b) + 1 * (a &&& b) + 4 * ~~~(a ||| (b ||| c)) + 7 * ~~~(a ||| ( ~~~b ||| c)) - 32 * ~~~( ~~~a ||| (b ||| c)) - 35 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 1 * ( ~~~a &&& ( ~~~b &&& c)) - 17 * ( ~~~a &&& (b &&& c)) + 6 * (a &&& ( ~~~b &&& c)) - 41 * (a &&& (b &&& c)) = - 4 * (a &&& ~~~c) - 11 * ~~~( ~~~a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1863 (x y : BitVec w) : +theorem e_1863 : - 7 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) - 6 * ~~~b + 4 * ~~~(a &&& ~~~b) + 7 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 5 * (b ^^^ (a &&& ( ~~~b ||| c))) + 7 * ((b &&& c) ||| (a &&& (b ||| c))) - 2 * (a ||| ~~~b) + 5 * (b ||| ~~~(a ||| ~~~c)) + 7 * ~~~(a &&& c) + 2 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 1 * ~~~(a &&& b) + 1 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) + 4 * ~~~(b &&& c) + 5 * ~~~(b ||| ~~~c) + 1 * ((a &&& b) ||| ~~~(b ^^^ c)) - 2 * ( ~~~(a ||| b) ||| (b ^^^ c)) - 1 * (b ||| (a ^^^ c)) - 11 * (a &&& (b ^^^ c)) + 11 * ~~~(a &&& (b &&& c)) - 7 * (b ^^^ ( ~~~a ||| (b ^^^ c))) + 2 * (b ^^^ (a &&& ~~~c)) + 3 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 11 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) - 11 * (c ^^^ (a ||| ~~~b)) - 2 * (c &&& ~~~(a &&& b)) + 4 * ( ~~~b &&& ~~~(a ^^^ c)) - 2 * ( ~~~a &&& (b ||| c)) - 3 * (a ||| (b &&& c)) - 7 * (b ^^^ (a &&& c)) - 1 * ~~~(a ^^^ (b ^^^ c)) + 2 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) + 11 * (b ^^^ ( ~~~a &&& (b ||| c))) + 1 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) - 2 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) + 2 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 7 * (a &&& c) - 1 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) + 4 * (b ^^^ (a &&& (b ||| c))) + 1 * (a &&& (b ||| c)) + 3 * ~~~(a ||| (b ||| c)) - 21 * ~~~(a ||| ( ~~~b ||| c)) - 11 * ~~~( ~~~a ||| (b ||| c)) - 4 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 30 * ( ~~~a &&& ( ~~~b &&& c)) - 32 * ( ~~~a &&& (b &&& c)) + 13 * (a &&& ( ~~~b &&& c)) = 1 * (b ^^^ (a ||| (b &&& c))) + 6 * (a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1864 (x y : BitVec w) : +theorem e_1864 : 7 * (c &&& ~~~(a &&& b)) + 3 * (c ^^^ ~~~(a &&& (b ||| c))) - 2 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) - 1 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 11 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) - 7 * ((a &&& b) ||| ~~~(b ||| c)) + 7 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) + 3 * (a &&& ~~~c) + 3 * ~~~(b &&& c) - 3 * ~~~c + 4 * ( ~~~c &&& (a ^^^ b)) - 6 * (b ^^^ (a &&& (b ||| c))) + 5 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 11 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 2 * (c ^^^ ( ~~~a ||| (b &&& c))) + 1 * ~~~( ~~~a &&& (b ^^^ c)) + 2 * (b ||| ~~~(a ||| c)) - 7 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) - 1 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) - 1 * (b ||| c) - 6 * (a &&& ~~~b) - 3 * ~~~(a ||| ( ~~~b &&& c)) + 1 * ~~~( ~~~a ||| (b ^^^ c)) - 11 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) + 1 * (b ^^^ (a ||| ( ~~~b &&& c))) - 11 * (b ^^^ (a &&& (b ^^^ c))) - 5 * ( ~~~a &&& (b ^^^ c)) - 6 * (b ^^^ ~~~(a ||| ~~~c)) + 5 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) + 7 * ~~~(a &&& (b ||| c)) - 7 * (c &&& ~~~(a ^^^ b)) - 1 * (c ^^^ ~~~(a &&& b)) + 4 * (b ^^^ (a ||| ( ~~~b ||| c))) + 11 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) - 1 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) + 1 * ( ~~~(a &&& b) &&& (b ^^^ c)) - 1 * ( ~~~(a ||| b) ||| (b ^^^ c)) - 2 * ~~~(a ||| (b &&& c)) + 5 * ( ~~~b &&& ~~~(a ^^^ c)) + 1 * ~~~(a ||| (b ||| c)) + 27 * ~~~(a ||| ( ~~~b ||| c)) - 1 * ~~~( ~~~a ||| (b ||| c)) + 20 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 18 * ( ~~~a &&& (b &&& c)) + 10 * (a &&& ( ~~~b &&& c)) + 40 * (a &&& (b &&& c)) = 7 * (b &&& (a ||| ~~~c)) + 2 * ~~~(a &&& c) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1865 (x y : BitVec w) : +theorem e_1865 : - 1 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 5 * (a ^^^ ( ~~~b &&& c)) + 2 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) - 2 * ~~~(a ||| ~~~c) + 1 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 7 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) - 3 * ~~~(a &&& (b ^^^ c)) + 1 * (b ^^^ ( ~~~a &&& (b ^^^ c))) + 4 * (a ^^^ ( ~~~b ||| c)) + 1 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) + 11 * ~~~a + 11 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) + 11 * (a &&& (b ^^^ c)) + 1 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) + 1 * ~~~(a ^^^ c) + 11 * ~~~(a &&& b) + 5 * (a &&& (b ||| c)) + 5 * ~~~( ~~~a &&& (b &&& c)) - 3 * (a &&& c) - 2 * (c ^^^ (a ||| ( ~~~b ||| c))) + 4 * (a ||| (b ^^^ c)) - 7 * (b ^^^ (a ||| (b ^^^ c))) + 3 * (b ||| (a &&& c)) - 3 * (b &&& (a ||| ~~~c)) - 1 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) + 1 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) + 1 * ((a &&& c) ^^^ (b ||| c)) - 7 * ( ~~~c &&& ~~~(a ^^^ b)) - 1 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) + 2 * (b ^^^ ~~~(a ||| c)) - 11 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) + 5 * ~~~(a &&& c) + 2 * (a ||| c) - 6 * (b ||| ~~~(a ||| ~~~c)) - 11 * (a ^^^ (b ||| c)) + 4 * (c &&& (a ^^^ b)) - 5 * (c ||| (a &&& ~~~b)) - 2 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 2 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) - 24 * ~~~(a ||| (b ||| c)) - 23 * ~~~(a ||| ( ~~~b ||| c)) + 22 * ~~~( ~~~a ||| (b ||| c)) - 20 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 4 * ( ~~~a &&& ( ~~~b &&& c)) - 4 * ( ~~~a &&& (b &&& c)) - 1 * (a &&& (b &&& c)) = 35 * (a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1866 (x y : BitVec w) : +theorem e_1866 : 4 * ((a &&& c) ^^^ (b ||| c)) - 5 * ~~~(a ^^^ ( ~~~b &&& c)) - 7 * ( ~~~a ||| ( ~~~b ||| c)) + 11 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) - 11 * ~~~( ~~~a ||| ( ~~~b &&& c)) - 1 * (b ||| ~~~c) - 5 * (c ^^^ ~~~(a ||| (b &&& c))) + 1 * (c ^^^ (a ||| ( ~~~b &&& c))) + 1 * ( ~~~a &&& ( ~~~b ||| c)) + 1 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) + 2 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) - 1 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) + 4 * (c ^^^ (a ||| (b ||| c))) - 2 * (a ||| ~~~c) + 2 * (b ^^^ ~~~(a ||| (b ^^^ c))) - 7 * (b &&& (a ||| c)) + 2 * (c ||| ~~~(a ||| ~~~b)) + 2 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 1 * ~~~(a &&& ( ~~~b ||| c)) - 6 * (b &&& ~~~(a &&& c)) - 1 * (a ||| ( ~~~b &&& c)) + 7 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 7 * (b ^^^ (a ||| (b &&& c))) - 1 * ((a &&& b) ^^^ (b ||| ~~~c)) + 1 * ~~~(a ||| ~~~c) - 1 * ~~~a + 2 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 2 * (c ^^^ ~~~(a &&& (b ||| c))) + 2 * (a ^^^ c) - 5 * (b ^^^ (a &&& c)) + 7 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) - 2 * ((a ||| ~~~b) &&& (b ^^^ c)) - 11 * (b ^^^ (a ||| (b ^^^ c))) - 2 * ~~~(a &&& b) + 11 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) + 1 * (b ^^^ ~~~(a &&& (b ||| c))) + 7 * ( ~~~c ||| ~~~(a ^^^ b)) + 2 * ( ~~~b &&& ~~~(a ^^^ c)) + 8 * ~~~(a ||| (b ||| c)) + 32 * ~~~(a ||| ( ~~~b ||| c)) + 6 * ~~~( ~~~a ||| (b ||| c)) - 12 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 16 * ( ~~~a &&& ( ~~~b &&& c)) + 11 * ( ~~~a &&& (b &&& c)) + 28 * (a &&& ( ~~~b &&& c)) + 13 * (a &&& (b &&& c)) = 11 * ~~~(a &&& (b ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1867 (x y : BitVec w) : +theorem e_1867 : 3 * ~~~( ~~~a &&& (b &&& c)) - 2 * (b &&& (a ||| c)) + 7 * ((a ^^^ b) ||| ~~~(a ^^^ c)) + 4 * ~~~( ~~~a &&& (b ||| c)) + 4 * ~~~(a ||| (b &&& c)) - 5 * ( ~~~a &&& (b ^^^ c)) + 7 * ((a &&& b) ^^^ (b ||| c)) + 1 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 1 * (a ^^^ (b ||| c)) + 2 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) + 3 * (c ^^^ (a ||| ( ~~~b ||| c))) + 2 * (b ^^^ ( ~~~a &&& (b ^^^ c))) + 11 * (c ^^^ ~~~(a &&& (b ||| c))) - 2 * (a &&& ( ~~~b ||| c)) + 2 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) - 1 * ((a ||| b) &&& ~~~(b ^^^ c)) - 1 * (c ||| ~~~(a ||| b)) + 3 * (b &&& ~~~c) + 11 * ~~~(a ||| b) - 3 * (b &&& c) - 3 * ( ~~~a ||| ( ~~~b &&& c)) - 5 * (b ^^^ ~~~(a &&& ~~~c)) - 3 * ~~~(a ^^^ (b &&& c)) + 4 * (b ^^^ (a ||| ( ~~~b &&& c))) + 2 * (b ^^^ (a &&& c)) + 4 * (c ^^^ ~~~(a ||| ~~~b)) + 7 * b - 2 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) - 1 * ( ~~~c &&& ~~~(a ^^^ b)) + 1 * ((a ^^^ b) &&& ~~~(a ^^^ c)) + 3 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) + 1 * ( ~~~c ||| ~~~(a ^^^ b)) + 2 * (b ^^^ ~~~(a &&& (b ||| c))) + 1 * ~~~(a &&& (b &&& c)) + 5 * ((a ||| ~~~b) &&& (b ^^^ c)) - 1 * ((a &&& c) ||| (b &&& ~~~c)) - 1 * (b ^^^ (a ||| c)) + 11 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) - 44 * ~~~(a ||| (b ||| c)) - 46 * ~~~(a ||| ( ~~~b ||| c)) - 51 * ~~~( ~~~a ||| (b ||| c)) - 25 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 44 * ( ~~~a &&& ( ~~~b &&& c)) - 24 * ( ~~~a &&& (b &&& c)) - 38 * (a &&& ( ~~~b &&& c)) - 43 * (a &&& (b &&& c)) = - 5 * (b ^^^ ~~~(a &&& c)) + 1 * ~~~(a &&& ~~~a) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1868 (x y : BitVec w) : +theorem e_1868 : - 5 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) + 1 * (b ^^^ (a ||| c)) - 1 * (b ^^^ (a ||| (b &&& c))) + 7 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 5 * ((a ^^^ b) ||| (a ^^^ c)) - 2 * ((a &&& b) ||| ~~~(b ||| c)) - 1 * ~~~(a ||| ( ~~~b &&& c)) - 7 * (a &&& c) + 7 * ((a &&& b) ||| ~~~(b ^^^ c)) + 5 * ((a ||| b) &&& (b ^^^ c)) + 11 * (b ^^^ ~~~(a &&& c)) - 1 * (b ^^^ ~~~(a ||| (b &&& c))) - 1 * ~~~(a ||| ~~~b) + 4 * (c ^^^ (a ||| (b &&& c))) - 1 * (b ^^^ ~~~(a ||| ~~~c)) + 7 * ~~~(b &&& c) + 1 * (c ^^^ (a ||| ( ~~~b &&& c))) - 1 * ( ~~~a ||| (b &&& c)) - 1 * (b ^^^ (a ||| ( ~~~b &&& c))) + 2 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) + 3 * (b &&& (a ||| ~~~c)) - 1 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) + 3 * ((a &&& c) ||| ~~~(b ||| c)) - 6 * (b ||| ~~~(a ||| ~~~c)) - 1 * ( ~~~a ||| ( ~~~b &&& c)) - 11 * (c &&& ~~~(a &&& b)) + 4 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) + 7 * b - 6 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) + 7 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) - 11 * (a ||| (b ^^^ c)) + 7 * (a ||| ~~~b) - 11 * ((a &&& c) ^^^ (b ||| c)) - 1 * (c ^^^ (a ||| ~~~b)) - 6 * (c ^^^ ( ~~~a &&& (b ||| c))) + 11 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 5 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) - 2 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 5 * (c ^^^ (a &&& ( ~~~b ||| c))) - 49 * ~~~(a ||| (b ||| c)) - 6 * ~~~(a ||| ( ~~~b ||| c)) - 18 * ~~~( ~~~a ||| (b ||| c)) - 3 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 30 * ( ~~~a &&& (b &&& c)) + 12 * (a &&& ( ~~~b &&& c)) - 15 * (a &&& (b &&& c)) = - 2 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 22 * ( ~~~a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1869 (x y : BitVec w) : +theorem e_1869 : - 2 * (b ^^^ c) + 1 * (b ||| (a ^^^ c)) + 1 * ( ~~~a ||| (b &&& c)) + 1 * (b &&& (a ^^^ c)) + 1 * (c ^^^ (a ||| b)) - 2 * ~~~(a ||| (b &&& c)) - 11 * ~~~(b &&& ~~~c) + 2 * (c ^^^ ~~~(a &&& b)) + 7 * ~~~(b &&& c) - 3 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) + 7 * (c ||| (a ^^^ b)) - 11 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) - 3 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) - 1 * (c ^^^ ~~~(a &&& (b ||| c))) - 7 * (b ^^^ ~~~(a &&& ~~~c)) + 7 * (b ^^^ ~~~(a &&& (b &&& c))) + 1 * ( ~~~b &&& ~~~(a ^^^ c)) + 1 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 1 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) + 3 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 3 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) + 5 * (b ^^^ (a &&& (b ||| c))) + 7 * ~~~(a ||| ~~~b) - 1 * ( ~~~a &&& (b ||| c)) - 11 * ( ~~~c &&& (a ^^^ b)) + 7 * (c ||| ~~~(a ||| b)) + 11 * ~~~c + 4 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 5 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 4 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) - 2 * (b ^^^ ~~~(a &&& c)) + 2 * ~~~(a ||| ( ~~~b &&& c)) + 1 * (b ^^^ ( ~~~a ||| (b ^^^ c))) - 5 * (b ^^^ ( ~~~a ||| (b &&& c))) + 1 * ((a &&& b) ^^^ (b ||| ~~~c)) + 2 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) - 2 * ((a &&& c) ^^^ (b ||| c)) - 7 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 5 * ~~~(a ||| (b ||| c)) - 32 * ~~~(a ||| ( ~~~b ||| c)) - 13 * ~~~( ~~~a ||| (b ||| c)) + 10 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 14 * ( ~~~a &&& ( ~~~b &&& c)) - 24 * ( ~~~a &&& (b &&& c)) - 6 * (a &&& ( ~~~b &&& c)) - 15 * (a &&& (b &&& c)) = - 3 * (b ^^^ (a &&& (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1870 (x y : BitVec w) : +theorem e_1870 : 2 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) - 6 * (c ||| (a ^^^ b)) + 1 * ~~~( ~~~a &&& ( ~~~b &&& c)) + 1 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) - 2 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) - 11 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) - 6 * ((b &&& c) ||| (a &&& (b ||| c))) - 1 * ( ~~~a &&& ( ~~~b ||| c)) + 4 * ~~~( ~~~a &&& (b ||| c)) - 1 * (a ^^^ b) + 1 * (c ^^^ (a ||| ( ~~~b &&& c))) - 5 * (a &&& c) - 1 * (b ^^^ ~~~(a ||| ~~~c)) - 2 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 4 * (c ^^^ ~~~(a ||| b)) + 3 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) + 2 * ((a ^^^ b) ||| (a ^^^ c)) + 1 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 11 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) + 1 * ((a ^^^ b) &&& ~~~(a ^^^ c)) - 5 * (b ^^^ (a &&& (b ^^^ c))) + 4 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 1 * (b ^^^ ( ~~~a &&& (b ||| c))) - 1 * ~~~a + 4 * ~~~(b ||| c) - 1 * ~~~(a ^^^ (b ^^^ c)) - 3 * ~~~(a ^^^ (b ||| c)) - 2 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 7 * (c ^^^ (a &&& b)) + 3 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) - 1 * ~~~(a ||| b) + 2 * (b ^^^ (a ||| ~~~c)) + 1 * (a ^^^ (b ||| c)) - 3 * ((a &&& ~~~b) ||| (b ^^^ c)) - 1 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) - 5 * (c ||| ~~~(a ||| ~~~b)) - 3 * (b ^^^ ( ~~~a ||| (b ^^^ c))) + 7 * (a ^^^ (b ^^^ c)) + 1 * ( ~~~a ||| (b ||| c)) + 7 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) - 8 * ~~~(a ||| (b ||| c)) - 1 * ~~~(a ||| ( ~~~b ||| c)) + 3 * ~~~( ~~~a ||| (b ||| c)) + 8 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 18 * ( ~~~a &&& ( ~~~b &&& c)) + 26 * ( ~~~a &&& (b &&& c)) + 36 * (a &&& (b &&& c)) = - 35 * (a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1871 (x y : BitVec w) : +theorem e_1871 : 11 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 2 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) + 7 * (b ||| (a &&& ~~~c)) + 1 * ( ~~~b ||| (a ^^^ c)) - 2 * (a ||| b) + 1 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) - 3 * (c ||| (a ^^^ b)) + 1 * (c ^^^ (a &&& ( ~~~b ||| c))) + 1 * ((a &&& c) ||| (b &&& ~~~c)) - 11 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) + 7 * ~~~(a &&& ( ~~~b ||| c)) - 6 * (b ||| ~~~(a ^^^ c)) - 7 * (c ^^^ ( ~~~a ||| (b &&& c))) - 5 * (b &&& (a ^^^ c)) - 11 * ((a ||| ~~~b) &&& (b ^^^ c)) + 1 * ~~~(a ||| (b ^^^ c)) + 3 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 5 * (b ||| (a &&& c)) + 2 * ~~~(a &&& ~~~a) + 11 * ( ~~~a ||| (b ^^^ c)) - 2 * (a ^^^ c) + 2 * (b ^^^ (a ||| (b &&& c))) + 11 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) + 5 * ~~~(a ^^^ (b &&& c)) - 1 * (b &&& ~~~(a ^^^ c)) - 2 * (c ^^^ ~~~(a &&& b)) - 1 * (c &&& ~~~(a &&& b)) - 1 * (c ||| ~~~(a ||| ~~~b)) - 1 * (b ^^^ ~~~(a ||| (b ^^^ c))) - 6 * (a &&& ~~~b) - 1 * ( ~~~c &&& (a ^^^ b)) - 11 * ~~~(a ^^^ b) - 2 * (a ||| ( ~~~b &&& c)) + 1 * ((a &&& b) ||| (b ^^^ c)) + 4 * (c ||| (a &&& b)) - 1 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 1 * ((a &&& b) ^^^ (b ||| ~~~c)) - 7 * ~~~(b ^^^ c) - 7 * ( ~~~(a ||| b) ||| (b ^^^ c)) - 8 * ~~~(a ||| (b ||| c)) + 2 * ~~~(a ||| ( ~~~b ||| c)) + 13 * ~~~( ~~~a ||| (b ||| c)) - 4 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 8 * ( ~~~a &&& ( ~~~b &&& c)) - 11 * ( ~~~a &&& (b &&& c)) + 6 * (a &&& ( ~~~b &&& c)) + 12 * (a &&& (b &&& c)) = 1 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1872 (x y : BitVec w) : +theorem e_1872 : - 11 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) - 1 * (c ^^^ (a ||| b)) - 1 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) + 3 * ( ~~~b &&& (a ^^^ c)) + 1 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 11 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 1 * ( ~~~a &&& ( ~~~b ||| c)) - 7 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) - 1 * ~~~(a &&& ( ~~~b ||| c)) + 4 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 5 * (c ^^^ ( ~~~a &&& (b ||| c))) + 7 * (c ||| (a &&& ~~~b)) - 7 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) + 1 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) + 7 * (a &&& ( ~~~b ||| c)) + 4 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) - 3 * ~~~(a ^^^ (b &&& c)) + 1 * ( ~~~a ||| (b &&& c)) - 3 * (a ||| b) - 6 * ( ~~~a ||| (b ||| c)) + 1 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) + 2 * ((a ^^^ b) ||| ~~~(a ^^^ c)) + 7 * (c ||| ~~~(a ||| b)) + 1 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) + 1 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) - 6 * ~~~(a ||| c) + 11 * ~~~(b ||| ~~~c) - 1 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) - 1 * (c ^^^ ~~~(a &&& b)) + 3 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) + 2 * (c &&& (a ||| b)) - 2 * (c ^^^ ~~~(a &&& ~~~b)) - 2 * (c ^^^ (a &&& ( ~~~b ||| c))) - 2 * ((a &&& b) ^^^ (b ||| ~~~c)) - 5 * (a ^^^ ( ~~~b ||| c)) - 5 * ~~~(a &&& c) + 2 * (b ^^^ (a &&& (b ||| c))) - 1 * (a ||| ~~~c) - 2 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) + 41 * ~~~(a ||| (b ||| c)) + 15 * ~~~(a ||| ( ~~~b ||| c)) + 16 * ~~~( ~~~a ||| (b ||| c)) + 36 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 1 * ( ~~~a &&& ( ~~~b &&& c)) + 7 * ( ~~~a &&& (b &&& c)) - 13 * (a &&& ( ~~~b &&& c)) - 18 * (a &&& (b &&& c)) = - 3 * (c ||| ~~~(a ^^^ b)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1873 (x y : BitVec w) : +theorem e_1873 : 2 * (c ^^^ (a ||| (b ||| c))) + 2 * (b ||| ~~~(a ||| ~~~c)) - 3 * (b ^^^ (a &&& ~~~c)) - 7 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 1 * (a ||| (b ||| c)) - 5 * ~~~(a ^^^ (b &&& c)) + 2 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) - 11 * (c ^^^ (a &&& ~~~b)) - 6 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) + 4 * ~~~(a &&& b) + 2 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) + 2 * ((a ^^^ b) ||| ~~~(a ^^^ c)) + 1 * ~~~(a ||| c) + 4 * (c ^^^ ~~~(a &&& b)) - 1 * (a &&& ~~~c) - 7 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) + 5 * (c ^^^ ~~~(a &&& (b ||| c))) - 6 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 1 * ~~~( ~~~a ||| ( ~~~b &&& c)) - 6 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) + 1 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) + 1 * (c ^^^ ( ~~~a ||| (b ||| c))) - 7 * ( ~~~c &&& ~~~(a ^^^ b)) + 7 * ~~~(a ||| (b ^^^ c)) + 11 * (b ^^^ ( ~~~a ||| (b &&& c))) - 11 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) - 3 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) + 1 * ((a ^^^ b) ||| (a ^^^ c)) + 2 * ( ~~~(a ||| b) ||| (b ^^^ c)) - 2 * ~~~a + 4 * (c ^^^ ~~~(a ||| ~~~b)) - 6 * ~~~( ~~~a &&& (b ||| c)) - 5 * (c ^^^ ( ~~~a &&& (b ||| c))) - 11 * ((b &&& c) ||| (a &&& (b ||| c))) - 5 * (a ||| ~~~c) - 1 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 3 * (a ||| b) - 3 * (b ||| ~~~(a ||| c)) - 1 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) + 45 * ~~~(a ||| (b ||| c)) + 31 * ~~~(a ||| ( ~~~b ||| c)) + 43 * ~~~( ~~~a ||| (b ||| c)) + 46 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 16 * ( ~~~a &&& ( ~~~b &&& c)) + 41 * ( ~~~a &&& (b &&& c)) + 22 * (a &&& ( ~~~b &&& c)) + 67 * (a &&& (b &&& c)) = 11 * (c ^^^ ~~~(a &&& (b &&& c))) - 1 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1874 (x y : BitVec w) : +theorem e_1874 : 2 * (b ^^^ (a &&& ~~~c)) - 1 * ~~~(a ^^^ (b &&& c)) - 7 * ~~~(a &&& ( ~~~b ||| c)) + 1 * (a ^^^ (b &&& c)) + 7 * (c ^^^ ( ~~~a ||| (b &&& c))) - 11 * (a &&& ~~~b) - 2 * (c ^^^ (a ||| ( ~~~b &&& c))) + 2 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 2 * ((a ||| b) &&& (b ^^^ c)) + 3 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) - 6 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) - 5 * ((a ^^^ b) &&& (a ^^^ c)) - 1 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) + 7 * ~~~(a ^^^ (b ||| c)) - 2 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) + 2 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) + 2 * (b ^^^ (a ||| (b ||| c))) - 7 * ~~~(a &&& ~~~b) + 1 * (c ^^^ ~~~(a ||| ~~~b)) - 1 * (c ^^^ (a &&& ( ~~~b ||| c))) - 5 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) + 11 * (a &&& (b ||| c)) - 11 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 1 * ((a &&& b) ||| ~~~(b ||| ~~~c)) - 11 * (a ||| ~~~b) - 11 * ~~~(b &&& ~~~c) - 1 * (b ^^^ (a &&& (b ^^^ c))) + 4 * (b ^^^ ~~~(a &&& (b ^^^ c))) + 7 * ~~~(a ||| b) + 4 * ( ~~~c ||| (a ^^^ b)) - 1 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 2 * (c &&& (a ||| b)) + 1 * (b ^^^ ~~~(a ||| ~~~c)) - 11 * (c &&& (a ^^^ b)) - 6 * (b ||| (a &&& c)) + 1 * ((a ^^^ b) ||| ~~~(a ^^^ c)) - 6 * (b ||| ~~~(a ^^^ c)) + 1 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) - 1 * ~~~c + 36 * ~~~(a ||| (b ||| c)) + 22 * ~~~(a ||| ( ~~~b ||| c)) + 30 * ~~~( ~~~a ||| (b ||| c)) + 26 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 17 * ( ~~~a &&& ( ~~~b &&& c)) + 51 * ( ~~~a &&& (b &&& c)) + 44 * (a &&& ( ~~~b &&& c)) + 14 * (a &&& (b &&& c)) = - 11 * (b ^^^ ( ~~~a &&& (b ||| c))) - 1 * (b ||| ~~~c) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1875 (x y : BitVec w) : +theorem e_1875 : 1 * (b ^^^ (a &&& (b ^^^ c))) + 3 * (b &&& ~~~(a &&& c)) - 7 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) + 2 * ~~~b - 3 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) - 6 * (c ||| (a &&& b)) - 7 * ~~~(a &&& (b ||| c)) + 11 * (b ||| ~~~(a ||| ~~~c)) + 11 * ( ~~~c &&& ~~~(a ^^^ b)) - 2 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) + 4 * (b &&& ~~~(a ^^^ c)) + 5 * ( ~~~c &&& (a ^^^ b)) + 4 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) - 1 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) - 1 * ( ~~~b ||| ~~~(a ^^^ c)) + 1 * ((a &&& b) ||| ~~~(b ^^^ c)) + 2 * (c ^^^ (a &&& b)) - 2 * ~~~(a ||| (b ^^^ c)) + 5 * (b &&& ~~~c) - 1 * (c &&& (a ^^^ b)) + 2 * (b ^^^ ~~~(a &&& (b ^^^ c))) + 1 * ((a &&& b) ||| ~~~(b ||| c)) - 11 * (b &&& (a ||| c)) + 4 * (c ^^^ ~~~(a &&& b)) + 1 * ~~~(a ||| (b &&& c)) + 1 * ~~~(a &&& b) - 1 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) - 1 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) + 1 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 7 * (c ^^^ (a ||| b)) + 3 * (b ^^^ ~~~(a ||| (b ^^^ c))) - 2 * (c ||| (a &&& ~~~b)) + 1 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 1 * ~~~( ~~~a ||| (b &&& c)) + 2 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 2 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) + 1 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) - 6 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) - 3 * (a &&& ~~~b) - 7 * ~~~(a ||| (b ||| c)) - 14 * ~~~(a ||| ( ~~~b ||| c)) + 2 * ~~~( ~~~a ||| (b ||| c)) - 16 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 21 * ( ~~~a &&& ( ~~~b &&& c)) + 6 * ( ~~~a &&& (b &&& c)) + 9 * (a &&& ( ~~~b &&& c)) + 4 * (a &&& (b &&& c)) = - 1 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1876 (x y : BitVec w) : +theorem e_1876 : - 2 * ~~~(a &&& b) + 2 * (c ||| (a &&& ~~~b)) - 6 * ( ~~~a &&& (b ||| c)) - 1 * ( ~~~a ||| (b &&& c)) - 5 * (b ^^^ (a &&& c)) - 5 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) + 2 * ~~~c + 1 * ((a &&& b) ^^^ (b ||| c)) + 7 * (a ||| (b ||| c)) + 4 * (a ^^^ c) - 3 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) - 7 * ~~~(a &&& ~~~c) - 1 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) - 3 * ~~~(a ||| (b ^^^ c)) - 1 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 1 * ~~~(a ^^^ ( ~~~b ||| c)) + 1 * (b ^^^ (a ||| (b ^^^ c))) + 1 * ~~~(a ||| ( ~~~b &&& c)) + 1 * ~~~( ~~~a &&& ( ~~~b &&& c)) - 7 * (b ^^^ ~~~(a ||| c)) - 1 * (c ||| (a ^^^ b)) - 2 * ( ~~~c ||| (a ^^^ b)) + 1 * (c ^^^ (a ||| ( ~~~b &&& c))) + 1 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) + 4 * (b ^^^ (a &&& ( ~~~b ||| c))) - 7 * ((a &&& ~~~b) ||| (b ^^^ c)) + 1 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) + 11 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 6 * ((a ^^^ b) ||| (a ^^^ c)) - 6 * ((a ^^^ b) ||| ~~~(a ^^^ c)) - 7 * ~~~(a ||| ~~~b) - 1 * (b ^^^ ~~~(a &&& (b &&& c))) - 3 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) + 5 * ~~~(a ^^^ c) - 1 * (c &&& (a ||| b)) + 2 * ((a ^^^ b) &&& (a ^^^ c)) + 2 * ~~~( ~~~a &&& (b ^^^ c)) + 1 * ((a ^^^ b) &&& ~~~(a ^^^ c)) - 1 * (c ^^^ (a ||| b)) + 15 * ~~~(a ||| (b ||| c)) + 40 * ~~~(a ||| ( ~~~b ||| c)) + 1 * ~~~( ~~~a ||| (b ||| c)) - 5 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 16 * ( ~~~a &&& ( ~~~b &&& c)) + 20 * ( ~~~a &&& (b &&& c)) + 22 * (a &&& ( ~~~b &&& c)) + 6 * (a &&& (b &&& c)) = - 1 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) - 4 * (b ^^^ ~~~(a &&& (b ||| c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1877 (x y : BitVec w) : +theorem e_1877 : 7 * (b ||| ~~~(a ||| c)) - 3 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) - 1 * ( ~~~b &&& (a ^^^ c)) - 7 * ((a &&& c) ||| (b &&& ~~~c)) + 11 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) - 6 * (c ||| ~~~(a ||| b)) - 1 * (b &&& (a ||| c)) - 3 * (b ^^^ (a ||| ( ~~~b ||| c))) + 2 * ~~~(a ||| b) + 1 * (b ^^^ ~~~(a &&& ~~~c)) - 2 * ( ~~~c &&& (a ^^^ b)) - 2 * ~~~(a ||| (b ^^^ c)) - 2 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) + 7 * (c ||| (a &&& b)) - 1 * (a &&& ~~~b) - 1 * (c &&& (a ^^^ b)) - 1 * ~~~(a &&& (b ^^^ c)) - 5 * (b ^^^ (a ||| ~~~c)) - 6 * ((a ^^^ b) ||| ~~~(a ^^^ c)) + 4 * (b &&& ~~~c) - 7 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) + 2 * ~~~( ~~~a &&& ( ~~~b &&& c)) + 7 * (c ^^^ ( ~~~a ||| (b &&& c))) + 2 * (b ^^^ (a &&& (b ^^^ c))) - 7 * ~~~( ~~~a &&& (b ^^^ c)) + 4 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) - 1 * ~~~( ~~~a &&& (b &&& c)) + 7 * ( ~~~a ||| (b ||| c)) + 4 * (b &&& ~~~(a &&& c)) - 6 * ((a &&& c) ||| ~~~(b ||| c)) - 6 * (b ^^^ c) + 3 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 1 * (b &&& ~~~(a ^^^ c)) + 5 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 1 * ~~~(a ||| c) + 11 * (c ^^^ ~~~(a &&& (b ||| c))) - 3 * ((b &&& c) ||| (a &&& (b ||| c))) + 1 * ~~~(b ||| ~~~c) - 11 * (b ||| c) - 19 * ~~~(a ||| (b ||| c)) - 21 * ~~~(a ||| ( ~~~b ||| c)) + 18 * ~~~( ~~~a ||| (b ||| c)) - 1 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 2 * ( ~~~a &&& ( ~~~b &&& c)) + 15 * ( ~~~a &&& (b &&& c)) + 10 * (a &&& ( ~~~b &&& c)) + 12 * (a &&& (b &&& c)) = - 3 * ~~~(a ^^^ ( ~~~b ||| c)) + 5 * ~~~(a &&& ~~~b) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1878 (x y : BitVec w) : +theorem e_1878 : - 1 * (c &&& (a ||| ~~~b)) - 2 * (b ^^^ (a &&& ~~~c)) + 3 * ( ~~~(a ||| b) ||| (b ^^^ c)) + 3 * (b ||| (a ^^^ c)) + 1 * (c ^^^ ~~~(a ||| ~~~b)) + 1 * (a ^^^ ( ~~~b ||| c)) - 5 * (b ^^^ ~~~(a ||| ~~~c)) + 1 * ( ~~~c &&& ~~~(a ^^^ b)) - 1 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) - 7 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 7 * ~~~( ~~~a ||| (b ^^^ c)) + 11 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) - 1 * (a &&& ~~~c) + 11 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) + 2 * (b &&& (a ||| ~~~c)) + 11 * (b ^^^ (a ||| (b &&& c))) - 3 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) - 2 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 4 * ~~~(a &&& b) + 11 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) + 7 * (a ^^^ (b &&& c)) - 6 * ~~~(a ^^^ b) + 4 * ~~~(a ||| b) + 1 * ((a &&& b) ^^^ (b ||| ~~~c)) + 2 * ~~~(a &&& c) - 5 * (b ^^^ ~~~(a &&& c)) - 3 * (b &&& (a ||| c)) - 1 * (b ^^^ ~~~(a ||| (b &&& c))) + 1 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) - 2 * (c &&& ~~~(a &&& b)) + 1 * ~~~(a ||| (b ^^^ c)) - 7 * (a &&& ( ~~~b ||| c)) + 11 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) - 7 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) - 5 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) + 5 * ((a &&& b) ||| (b ^^^ c)) + 4 * ( ~~~a &&& (b ^^^ c)) - 2 * ((a ^^^ b) &&& ~~~(a ^^^ c)) + 1 * ~~~(b ||| ~~~c) - 30 * ~~~(a ||| (b ||| c)) - 19 * ~~~(a ||| ( ~~~b ||| c)) - 14 * ~~~( ~~~a ||| (b ||| c)) + 1 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 30 * ( ~~~a &&& ( ~~~b &&& c)) - 28 * ( ~~~a &&& (b &&& c)) - 41 * (a &&& ( ~~~b &&& c)) + 18 * (a &&& (b &&& c)) = 1 * (c ^^^ (a ||| ~~~b)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1879 (x y : BitVec w) : +theorem e_1879 : 5 * (c &&& ~~~(a &&& ~~~b)) + 1 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) - 6 * ~~~a - 6 * (c &&& (a ||| ~~~b)) + 11 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) - 11 * ( ~~~c &&& (a ^^^ b)) + 5 * (c ||| ~~~(a ||| ~~~b)) - 11 * (b ||| ~~~(a ||| c)) + 2 * ~~~(a &&& c) + 2 * ( ~~~a ||| (b ^^^ c)) + 11 * (a &&& b) - 1 * (c ^^^ (a ||| (b ||| c))) - 6 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) - 6 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 1 * (b &&& c) - 3 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) - 3 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 7 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) + 3 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) - 7 * ~~~(a &&& ( ~~~b ||| c)) - 2 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) + 1 * (c ||| (a &&& b)) - 5 * (b ^^^ (a &&& ~~~c)) + 1 * (a ||| ~~~c) + 1 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) - 6 * (b ^^^ (a ||| (b ^^^ c))) + 1 * ( ~~~a ||| (b &&& c)) - 1 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) + 5 * (b ^^^ ~~~(a &&& ~~~c)) + 11 * (a ^^^ c) + 1 * ( ~~~c ||| ~~~(a ^^^ b)) - 1 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) - 3 * ~~~(a ^^^ c) - 1 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) - 2 * (b &&& (a ^^^ c)) + 1 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) + 1 * (c ^^^ (a ||| b)) - 5 * ~~~(a ^^^ (b ||| c)) + 4 * (a &&& ~~~b) + 2 * (a &&& ~~~c) + 25 * ~~~(a ||| (b ||| c)) + 5 * ~~~( ~~~a ||| (b ||| c)) - 6 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 12 * ( ~~~a &&& ( ~~~b &&& c)) - 9 * ( ~~~a &&& (b &&& c)) + 1 * (a &&& ( ~~~b &&& c)) + 4 * (a &&& (b &&& c)) = - 17 * ~~~(a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1880 (x y : BitVec w) : +theorem e_1880 : 11 * ~~~(a &&& ~~~a) - 6 * ( ~~~c &&& ~~~(a ^^^ b)) - 2 * (b &&& (a ||| c)) - 7 * (b ||| (a ^^^ c)) + 4 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) - 11 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 1 * ~~~( ~~~a &&& ( ~~~b ||| c)) + 7 * (a ||| c) - 1 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) + 2 * (b ||| (a &&& c)) - 6 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) + 2 * (a &&& (b ||| c)) - 5 * ((a &&& b) ||| ~~~(b ^^^ c)) + 1 * (a ||| (b ^^^ c)) + 1 * (b ^^^ (a &&& ~~~c)) - 1 * (b &&& ~~~(a &&& ~~~c)) - 7 * (c ||| (a &&& b)) - 2 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) + 2 * ( ~~~a ||| (b ||| c)) + 2 * ~~~(a &&& ~~~b) - 6 * (b ^^^ ~~~(a ||| (b ^^^ c))) + 2 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) + 2 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) - 6 * ( ~~~a &&& (b ^^^ c)) - 11 * (b ^^^ ~~~(a ||| (b &&& c))) + 1 * ( ~~~c ||| (a ^^^ b)) + 2 * (b ||| c) + 1 * ((a &&& b) ^^^ (b ||| c)) - 7 * (c ^^^ (a &&& b)) - 2 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) - 3 * ~~~(a &&& (b ^^^ c)) - 2 * ((b &&& c) ||| (a &&& (b ||| c))) + 7 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) + 3 * (a ||| (b ||| c)) - 7 * (c ^^^ ~~~(a ||| b)) + 1 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 3 * (b ^^^ ~~~(a &&& c)) + 4 * ~~~(a ||| b) - 1 * (b ^^^ (a &&& (b ||| c))) - 3 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 11 * (a ||| ~~~b) + 11 * (c ||| ~~~(a ||| ~~~b)) + 39 * ~~~(a ||| (b ||| c)) - 13 * ~~~(a ||| ( ~~~b ||| c)) + 9 * ~~~( ~~~a ||| (b ||| c)) + 54 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 16 * (a &&& ( ~~~b &&& c)) + 14 * (a &&& (b &&& c)) = 8 * ( ~~~a &&& ( ~~~b &&& c)) - 11 * ( ~~~a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1881 (x y : BitVec w) : +theorem e_1881 : - 1 * (a ||| ~~~b) - 1 * (b ^^^ (a ||| (b ^^^ c))) + 5 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) + 4 * ( ~~~a ||| (b ||| c)) - 2 * (b ^^^ (a &&& ~~~c)) + 1 * (a ||| ( ~~~b ||| c)) + 4 * ~~~c - 5 * ~~~(a ||| ( ~~~b &&& c)) - 11 * (c ^^^ (a ||| (b ||| c))) - 3 * (c ^^^ (a ||| (b &&& c))) + 7 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) - 3 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) - 1 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) - 2 * (b &&& ~~~(a &&& ~~~c)) + 7 * ~~~( ~~~a &&& (b &&& c)) + 1 * (c &&& (a ||| ~~~b)) + 4 * (c ^^^ ~~~(a ||| b)) - 6 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) - 7 * (b ^^^ (a &&& ( ~~~b ||| c))) + 5 * ~~~(a ^^^ ( ~~~b ||| c)) - 7 * ((a &&& b) ^^^ (b ||| ~~~c)) + 3 * ~~~(a &&& ~~~a) + 5 * (a &&& ~~~c) + 4 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 1 * ( ~~~b &&& (a ^^^ c)) - 5 * (b ^^^ (a &&& (b ^^^ c))) + 2 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) + 4 * (c ||| ~~~(a ||| b)) + 2 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) - 1 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) - 2 * ~~~(a ^^^ (b ||| c)) - 7 * ((a &&& c) ||| ~~~(b ||| c)) + 1 * (c ||| ~~~(a ||| ~~~b)) - 11 * ( ~~~c ||| (a ^^^ b)) - 1 * (b ^^^ ~~~(a ||| ~~~c)) - 2 * (c ^^^ ~~~(a ||| (b &&& c))) + 11 * (a &&& ( ~~~b ||| c)) + 1 * (b &&& ~~~c) - 1 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 1 * ~~~(a &&& ( ~~~b ||| c)) + 1 * ~~~(a ||| (b ||| c)) + 29 * ~~~(a ||| ( ~~~b ||| c)) - 3 * ~~~( ~~~a ||| (b ||| c)) + 4 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 19 * ( ~~~a &&& ( ~~~b &&& c)) + 29 * ( ~~~a &&& (b &&& c)) - 14 * (a &&& ( ~~~b &&& c)) - 19 * (a &&& (b &&& c)) = - 2 * ( ~~~a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1882 (x y : BitVec w) : +theorem e_1882 : 5 * ((a &&& b) ||| (b ^^^ c)) + 5 * (c &&& ~~~(a &&& ~~~b)) - 5 * ~~~( ~~~a &&& ( ~~~b &&& c)) - 1 * (a &&& (b ||| c)) + 4 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) + 11 * (a ^^^ ( ~~~b ||| c)) + 11 * (a ||| c) - 7 * b - 1 * ~~~(a ^^^ (b ^^^ c)) - 3 * (b &&& ~~~(a ^^^ c)) - 2 * ( ~~~a &&& (b ||| c)) - 7 * ( ~~~(a &&& b) &&& (b ^^^ c)) - 11 * ( ~~~a ||| (b ||| c)) - 1 * (a &&& ~~~b) - 1 * (b ||| ~~~(a ||| c)) + 4 * (a ^^^ (b ^^^ c)) + 5 * (b ||| (a &&& ~~~c)) + 2 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) + 7 * ~~~( ~~~a &&& (b &&& c)) - 1 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) + 4 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) - 3 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) + 11 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) + 1 * ((a &&& ~~~b) ||| (b ^^^ c)) - 3 * (c ^^^ (a ||| ( ~~~b &&& c))) - 2 * (b ^^^ ~~~(a &&& ~~~c)) + 2 * ( ~~~b ||| ~~~(a ^^^ c)) - 1 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) + 4 * (a &&& c) - 2 * ( ~~~a ||| ( ~~~b &&& c)) - 11 * (a ||| ( ~~~b &&& c)) - 2 * (b &&& (a ^^^ c)) + 4 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) - 1 * ~~~(a ||| b) - 1 * (c ||| ~~~(a ||| b)) + 4 * (a ^^^ b) + 3 * (b ^^^ ( ~~~a &&& (b ^^^ c))) + 1 * (b ^^^ (a &&& (b ||| c))) - 1 * ~~~(a ^^^ (b &&& c)) + 3 * (b ^^^ (a ||| (b &&& c))) - 1 * ~~~(a ||| (b ||| c)) + 7 * ~~~(a ||| ( ~~~b ||| c)) - 29 * ~~~( ~~~a ||| (b ||| c)) - 11 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 31 * ( ~~~a &&& ( ~~~b &&& c)) - 20 * ( ~~~a &&& (b &&& c)) - 1 * (a &&& ( ~~~b &&& c)) - 14 * (a &&& (b &&& c)) = 2 * (b ^^^ ~~~(a ||| ~~~c)) - 1 * (c ||| (a &&& b)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1883 (x y : BitVec w) : +theorem e_1883 : - 11 * (b &&& (a ||| ~~~c)) - 2 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) - 1 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) - 1 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) + 1 * (a ||| (b &&& c)) + 3 * (b ||| ~~~(a ^^^ c)) + 11 * (a ^^^ (b ^^^ c)) - 6 * ~~~(a ^^^ b) + 3 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 4 * (b ^^^ ~~~(a &&& c)) - 2 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) + 1 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) - 2 * ~~~(a ^^^ ( ~~~b ||| c)) - 2 * ~~~(a &&& ~~~c) - 1 * (a ||| b) - 1 * (b ^^^ ( ~~~a &&& (b ^^^ c))) + 11 * ( ~~~(a &&& b) &&& (b ^^^ c)) - 2 * (a ^^^ (b &&& c)) + 3 * ((a &&& b) ||| (b ^^^ c)) - 1 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 1 * (a ^^^ ( ~~~b &&& c)) + 2 * ~~~(a ||| (b ^^^ c)) - 1 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 1 * ~~~(a ||| c) - 1 * ~~~b - 1 * ( ~~~c &&& ~~~(a ^^^ b)) - 3 * (c ^^^ ~~~(a &&& (b &&& c))) + 1 * (c ^^^ ( ~~~a ||| (b &&& c))) - 2 * (c ^^^ (a ||| b)) - 11 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) + 7 * ~~~(a &&& ~~~b) + 1 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) + 1 * (c &&& (a ||| ~~~b)) + 4 * ~~~(a &&& b) - 7 * (b ^^^ ~~~(a ||| (b ^^^ c))) - 2 * ( ~~~b &&& ~~~(a ^^^ c)) + 2 * (b ^^^ c) - 3 * (c ^^^ ~~~(a &&& b)) + 11 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) - 11 * (a &&& c) + 8 * ~~~(a ||| (b ||| c)) + 4 * ~~~(a ||| ( ~~~b ||| c)) - 3 * ~~~( ~~~a ||| (b ||| c)) + 22 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 40 * ( ~~~a &&& ( ~~~b &&& c)) + 5 * ( ~~~a &&& (b &&& c)) - 13 * (a &&& ( ~~~b &&& c)) - 1 * (a &&& (b &&& c)) = - 11 * (a &&& b) + 2 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1884 (x y : BitVec w) : +theorem e_1884 : 2 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) + 1 * (c ||| ~~~(a ||| b)) + 4 * (c ^^^ ~~~(a ||| (b &&& c))) + 4 * ( ~~~a ||| (b &&& c)) + 11 * ~~~( ~~~a &&& (b ||| c)) + 2 * ((a ^^^ b) &&& ~~~(a ^^^ c)) - 1 * ((a &&& b) ^^^ (b ||| c)) + 1 * ( ~~~c &&& ~~~(a ^^^ b)) + 7 * (a ||| b) + 3 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) + 7 * (b ^^^ ( ~~~a &&& (b ^^^ c))) + 7 * (a &&& (b ^^^ c)) - 11 * ~~~(a ^^^ (b &&& c)) - 6 * ~~~(b ||| ~~~c) + 1 * (b ||| ~~~c) + 2 * b - 11 * ~~~(a &&& ~~~a) - 1 * (c &&& (a ||| b)) + 1 * ( ~~~b &&& ~~~(a ^^^ c)) - 7 * (c &&& (a ||| ~~~b)) - 2 * (b ||| ~~~(a ||| ~~~c)) - 7 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) + 2 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) + 1 * ( ~~~a ||| (b ||| c)) + 1 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) - 2 * (a ^^^ ( ~~~b &&& c)) + 1 * (a ||| ~~~c) - 1 * (b ^^^ ~~~(a ||| (b ^^^ c))) + 11 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) + 2 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) + 3 * (c &&& ~~~(a &&& b)) + 7 * ( ~~~b &&& (a ^^^ c)) + 11 * (c ^^^ ~~~(a &&& ~~~b)) - 1 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) + 5 * ((a ^^^ b) ||| ~~~(a ^^^ c)) - 2 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 3 * (b ^^^ (a ||| ( ~~~b ||| c))) + 7 * (c ||| ~~~(a ^^^ b)) - 1 * (c ^^^ ~~~(a &&& (b &&& c))) + 1 * (a &&& b) - 34 * ~~~(a ||| (b ||| c)) - 3 * ~~~(a ||| ( ~~~b ||| c)) - 24 * ~~~( ~~~a ||| (b ||| c)) - 40 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 22 * ( ~~~a &&& ( ~~~b &&& c)) - 37 * ( ~~~a &&& (b &&& c)) - 34 * (a &&& ( ~~~b &&& c)) - 15 * (a &&& (b &&& c)) = - 1 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 2 * ( ~~~a &&& (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1885 (x y : BitVec w) : +theorem e_1885 : - 1 * (c &&& ~~~(a &&& b)) - 1 * ((a &&& c) ||| (b &&& ~~~c)) + 1 * ((a &&& c) ||| ~~~(b ||| c)) - 2 * (c ^^^ (a &&& b)) + 4 * ~~~(a ^^^ ( ~~~b &&& c)) + 2 * (c ^^^ ~~~(a &&& (b ||| c))) - 3 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) - 7 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) + 3 * (b ^^^ ~~~(a &&& (b &&& c))) - 6 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) + 1 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) - 5 * (c ^^^ (a &&& ( ~~~b ||| c))) + 3 * ~~~( ~~~a &&& ( ~~~b &&& c)) - 1 * (b ||| c) + 2 * (c ^^^ (a &&& (b ||| c))) + 1 * ( ~~~c &&& (a ^^^ b)) - 1 * (b ^^^ ~~~(a ||| (b &&& c))) + 5 * ~~~(b &&& ~~~c) - 6 * (a ^^^ ( ~~~b ||| c)) + 1 * (a ^^^ c) - 6 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) - 7 * (b &&& (a ^^^ c)) + 11 * a - 1 * (b ^^^ ( ~~~a &&& (b ||| c))) - 1 * ~~~(a &&& ~~~b) + 11 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) - 1 * (b ||| (a &&& ~~~c)) + 2 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 7 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) + 1 * (b &&& c) + 3 * ~~~(b ^^^ c) + 1 * (c ^^^ (a &&& ~~~b)) - 3 * (b &&& (a ||| c)) - 1 * ~~~( ~~~a ||| (b ^^^ c)) - 6 * ( ~~~c ||| (a ^^^ b)) - 2 * ~~~(a &&& (b ||| c)) + 1 * (b ^^^ (a ||| ( ~~~b &&& c))) + 1 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) - 2 * ((a ||| b) &&& (b ^^^ c)) - 2 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) - 1 * (a ||| (b ||| c)) + 14 * ~~~(a ||| (b ||| c)) + 18 * ~~~(a ||| ( ~~~b ||| c)) + 3 * ~~~( ~~~a ||| (b ||| c)) + 21 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 19 * ( ~~~a &&& (b &&& c)) - 13 * (a &&& ( ~~~b &&& c)) - 22 * (a &&& (b &&& c)) = - 10 * ( ~~~a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1886 (x y : BitVec w) : +theorem e_1886 : - 1 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) - 1 * (c ^^^ ~~~(a &&& b)) - 6 * (c &&& (a ||| b)) - 11 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 1 * (b ^^^ ~~~(a ||| (b ^^^ c))) - 3 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) - 1 * (b &&& ~~~c) - 2 * (c ^^^ ~~~(a &&& (b &&& c))) + 5 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) - 6 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) + 11 * (b ^^^ (a ||| c)) + 4 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 7 * ((b &&& c) ||| (a &&& (b ||| c))) - 1 * (a ||| (b ||| c)) + 7 * (a ^^^ b) + 7 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) - 1 * (a ||| (b &&& c)) + 3 * ~~~(a ||| ~~~c) + 4 * (c ^^^ (a ||| ~~~b)) - 1 * (b ^^^ (a ||| ( ~~~b &&& c))) + 7 * ((a &&& b) ^^^ (b ||| ~~~c)) + 11 * (c ^^^ ~~~(a ||| (b &&& c))) + 3 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) + 1 * (b &&& (a ^^^ c)) - 7 * ( ~~~(a &&& b) &&& (b ^^^ c)) - 6 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) + 2 * ( ~~~b &&& (a ^^^ c)) + 2 * (c &&& ~~~(a &&& b)) - 2 * ((a &&& ~~~b) ||| (b ^^^ c)) + 1 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) - 7 * (c ^^^ (a ||| b)) - 1 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 3 * ( ~~~a ||| (b &&& c)) + 2 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) + 1 * ( ~~~a &&& (b ||| c)) - 11 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 6 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) + 2 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) - 7 * ( ~~~a &&& ( ~~~b ||| c)) - 3 * (c ^^^ (a &&& b)) - 2 * ~~~(a &&& ~~~c) - 7 * ~~~(a ||| (b ||| c)) + 3 * ~~~(a ||| ( ~~~b ||| c)) + 6 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 17 * ( ~~~a &&& ( ~~~b &&& c)) - 11 * ( ~~~a &&& (b &&& c)) + 20 * (a &&& ( ~~~b &&& c)) + 24 * (a &&& (b &&& c)) = - 4 * ~~~(a &&& (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1887 (x y : BitVec w) : +theorem e_1887 : 2 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 3 * (b ^^^ (a ||| ~~~c)) + 11 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 1 * ~~~(a ||| (b &&& c)) + 4 * ~~~(a &&& ~~~c) + 11 * ~~~(a &&& ~~~b) - 11 * (b &&& (a ||| ~~~c)) + 2 * (c ^^^ ~~~(a &&& (b ||| c))) - 1 * (a ^^^ b) - 1 * (b ^^^ ~~~(a ||| (b ^^^ c))) + 1 * ~~~(a ||| ~~~b) - 1 * (b ^^^ (a ||| ( ~~~b &&& c))) - 3 * (b ^^^ ( ~~~a &&& (b ^^^ c))) + 2 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 7 * (c ^^^ ~~~(a ||| (b &&& c))) - 5 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) + 7 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 1 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) + 4 * ( ~~~c &&& ~~~(a ^^^ b)) + 1 * ((a &&& b) ^^^ (b ||| ~~~c)) + 5 * ( ~~~c ||| ~~~(a ^^^ b)) + 2 * (b ^^^ (a ||| c)) + 4 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) + 1 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) - 2 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 1 * (a ^^^ (b ||| c)) - 2 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 2 * ~~~a + 2 * (b ||| ~~~c) - 11 * (b ^^^ (a &&& ( ~~~b ||| c))) + 1 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) + 1 * (c ||| ~~~(a ^^^ b)) - 7 * (b ^^^ ~~~(a &&& (b &&& c))) - 7 * (b &&& (a ^^^ c)) - 5 * ( ~~~c &&& (a ^^^ b)) - 2 * ( ~~~a ||| (b ^^^ c)) - 1 * (a ||| ~~~c) - 1 * (b &&& ~~~c) - 2 * (b ^^^ (a ||| (b ||| c))) - 1 * (c ^^^ ~~~(a &&& b)) - 25 * ~~~(a ||| (b ||| c)) - 3 * ~~~(a ||| ( ~~~b ||| c)) + 10 * ~~~( ~~~a ||| (b ||| c)) + 8 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 10 * ( ~~~a &&& ( ~~~b &&& c)) + 7 * ( ~~~a &&& (b &&& c)) + 24 * (a &&& ( ~~~b &&& c)) + 1 * (a &&& (b &&& c)) = - 3 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1888 (x y : BitVec w) : +theorem e_1888 : 2 * ((a ||| b) &&& (b ^^^ c)) - 3 * ( ~~~(a ||| b) ||| (b ^^^ c)) - 1 * (b ^^^ (a &&& (b ||| c))) - 1 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) + 1 * ~~~(b ^^^ c) + 7 * (b ^^^ (a ||| (b ^^^ c))) + 11 * (c &&& (a ^^^ b)) - 3 * (b ^^^ (a ||| ( ~~~b ||| c))) + 2 * ( ~~~b ||| (a ^^^ c)) + 4 * (b ^^^ (a ||| c)) + 7 * ~~~(a &&& c) - 11 * ~~~(b ||| ~~~c) - 6 * ((b &&& c) ||| (a &&& (b ||| c))) - 3 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) + 7 * (a ^^^ (b &&& c)) - 5 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) + 3 * (a ||| ~~~c) + 5 * (c ^^^ ~~~(a &&& ~~~b)) - 7 * ~~~(a ||| ~~~b) + 1 * ~~~(b ||| c) + 1 * ( ~~~a &&& ( ~~~b ||| c)) - 11 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) + 7 * (c ^^^ (a ||| ( ~~~b &&& c))) + 5 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 7 * ~~~(a &&& ~~~c) - 1 * (b ^^^ ~~~(a &&& ~~~c)) - 5 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 2 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) - 1 * (a ||| ~~~b) - 7 * ~~~( ~~~a &&& ( ~~~b &&& c)) - 1 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) + 2 * (a ||| ( ~~~b &&& c)) - 1 * ((a ||| b) &&& ~~~(b ^^^ c)) - 6 * (b &&& c) + 1 * (b ^^^ (a ||| (b &&& c))) - 5 * ((a &&& b) ^^^ (b ||| ~~~c)) - 3 * (c ^^^ ~~~(a &&& (b &&& c))) + 7 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) + 7 * ~~~(a ^^^ (b ||| c)) + 1 * ~~~(a ||| (b ^^^ c)) - 7 * ~~~(a ||| (b ||| c)) + 10 * ~~~(a ||| ( ~~~b ||| c)) - 11 * ~~~( ~~~a ||| (b ||| c)) - 4 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 6 * ( ~~~a &&& ( ~~~b &&& c)) + 9 * ( ~~~a &&& (b &&& c)) - 13 * (a &&& ( ~~~b &&& c)) + 29 * (a &&& (b &&& c)) = - 2 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) - 5 * ~~~b := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1889 (x y : BitVec w) : +theorem e_1889 : - 2 * ((a &&& b) ||| (b ^^^ c)) - 11 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) + 2 * ( ~~~a ||| (b &&& c)) + 11 * ~~~(a ^^^ ( ~~~b &&& c)) + 7 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 1 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 1 * (c &&& ~~~(a ^^^ b)) - 3 * ( ~~~b &&& (a ^^^ c)) + 1 * (b ^^^ ~~~(a ||| c)) + 1 * (b ^^^ (a ||| c)) - 1 * ( ~~~(a &&& b) &&& (b ^^^ c)) + 2 * ((a &&& ~~~b) ||| (b ^^^ c)) - 6 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) - 2 * (c ^^^ (a &&& ~~~b)) + 7 * (b ^^^ (a &&& ( ~~~b ||| c))) - 7 * (a ||| ~~~c) + 1 * c + 7 * (c ^^^ (a &&& (b ||| c))) + 2 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 1 * (a ||| (b ^^^ c)) + 1 * (a &&& ~~~c) + 11 * ~~~(a &&& (b ^^^ c)) - 2 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) + 11 * (a ^^^ ( ~~~b &&& c)) - 5 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 1 * ( ~~~a ||| (b ||| c)) + 2 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) - 6 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) - 1 * (c ^^^ (a ||| b)) + 4 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) + 3 * (b ^^^ ~~~(a &&& (b ||| c))) + 4 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) - 11 * (b ^^^ (a ||| ( ~~~b &&& c))) - 3 * (a &&& b) + 1 * (a ||| (b &&& c)) - 1 * (a ||| ( ~~~b &&& c)) + 4 * (b ^^^ (a &&& ~~~c)) - 1 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) - 1 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) - 6 * ~~~( ~~~a &&& (b ^^^ c)) - 14 * ~~~(a ||| (b ||| c)) - 21 * ~~~(a ||| ( ~~~b ||| c)) + 8 * ~~~( ~~~a ||| (b ||| c)) - 33 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 8 * ( ~~~a &&& ( ~~~b &&& c)) - 16 * ( ~~~a &&& (b &&& c)) - 2 * (a &&& ( ~~~b &&& c)) - 7 * (a &&& (b &&& c)) = - 5 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 3 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1890 (x y : BitVec w) : +theorem e_1890 : - 7 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) + 11 * (a &&& (b ||| c)) + 4 * (b &&& ~~~(a &&& c)) + 2 * ( ~~~b ||| ~~~(a ^^^ c)) - 3 * (c ^^^ (a &&& ( ~~~b ||| c))) - 1 * ~~~( ~~~a &&& (b ^^^ c)) + 11 * ((a ||| ~~~b) &&& (b ^^^ c)) - 3 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 1 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) - 11 * ( ~~~(a ||| b) ||| (b ^^^ c)) + 2 * (a &&& b) - 5 * (b ^^^ (a ||| c)) + 11 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 1 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) + 5 * ( ~~~a ||| (b ^^^ c)) + 3 * ~~~(a ||| (b &&& c)) + 2 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) + 1 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) + 1 * (a ^^^ (b ^^^ c)) + 3 * ( ~~~(a &&& b) &&& (b ^^^ c)) + 5 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) + 1 * (a &&& c) - 1 * ( ~~~a ||| ( ~~~b ||| c)) - 7 * ~~~(a ^^^ ( ~~~b ||| c)) + 7 * (b ||| (a ^^^ c)) - 2 * ( ~~~a ||| (b &&& c)) - 1 * ~~~(a &&& (b ^^^ c)) - 11 * (c ^^^ ~~~(a ||| ~~~b)) - 2 * (c ^^^ (a ||| (b &&& c))) + 2 * ~~~(a &&& ( ~~~b ||| c)) - 1 * a - 5 * ~~~(b ||| c) - 6 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) + 1 * (c ||| (a &&& b)) + 11 * ( ~~~c &&& ~~~(a ^^^ b)) - 1 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) + 1 * (b ^^^ ~~~(a ||| (b &&& c))) - 1 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 2 * (b ^^^ ~~~(a &&& c)) + 7 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) - 6 * ((a &&& b) ||| (b ^^^ c)) - 1 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) + 5 * (c ^^^ ( ~~~a ||| (b &&& c))) - 22 * ~~~(a ||| (b ||| c)) - 36 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 2 * ( ~~~a &&& ( ~~~b &&& c)) - 17 * ( ~~~a &&& (b &&& c)) - 18 * (a &&& ( ~~~b &&& c)) + 4 * (a &&& (b &&& c)) = - 21 * ~~~(a ||| ( ~~~b ||| c)) - 2 * ~~~( ~~~a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1891 (x y : BitVec w) : +theorem e_1891 : 7 * (b &&& (a ||| c)) + 3 * ~~~(a &&& (b &&& c)) - 7 * ( ~~~(a ||| b) ||| (b ^^^ c)) + 2 * ( ~~~a ||| ( ~~~b &&& c)) - 3 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 1 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) - 5 * (b ^^^ c) + 11 * ~~~( ~~~a &&& ( ~~~b ||| c)) - 1 * (c ||| ~~~(a ||| ~~~b)) + 2 * ~~~(a ^^^ c) + 2 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) + 1 * ((a ^^^ b) ||| ~~~(a ^^^ c)) + 1 * (b ^^^ ~~~(a ||| c)) - 6 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) - 1 * ((a &&& b) ||| ~~~(b ||| c)) - 1 * (c ^^^ (a &&& b)) + 5 * ( ~~~a ||| (b ||| c)) - 11 * (c ^^^ ( ~~~a &&& (b ||| c))) - 1 * (b &&& ~~~(a ^^^ c)) + 2 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 1 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 5 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 3 * (c ^^^ (a ||| b)) - 3 * ((a &&& ~~~b) ||| (b ^^^ c)) - 1 * (c ^^^ (a ||| ~~~b)) - 11 * ~~~a - 11 * (c ^^^ (a ||| (b ||| c))) - 7 * (b ^^^ ( ~~~a ||| (b &&& c))) - 5 * (c ||| (a ^^^ b)) + 1 * (c &&& (a ||| ~~~b)) + 1 * (b ||| (a ^^^ c)) + 1 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) + 7 * ~~~( ~~~a ||| (b &&& c)) + 2 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) + 1 * ~~~(a &&& b) - 1 * (a ||| ~~~b) + 4 * ~~~(a &&& ( ~~~b &&& c)) + 5 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) + 7 * (b ^^^ ( ~~~a &&& (b ||| c))) - 2 * (b &&& ~~~c) - 7 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) + 23 * ~~~(a ||| (b ||| c)) + 21 * ~~~(a ||| ( ~~~b ||| c)) - 4 * ~~~( ~~~a ||| (b ||| c)) - 12 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 11 * ( ~~~a &&& ( ~~~b &&& c)) - 3 * ( ~~~a &&& (b &&& c)) + 7 * (a &&& ( ~~~b &&& c)) - 7 * (a &&& (b &&& c)) = 3 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1892 (x y : BitVec w) : +theorem e_1892 : 7 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 1 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 5 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) - 1 * ~~~(a ^^^ c) - 5 * ~~~(b ^^^ c) - 1 * ((a &&& b) ^^^ (b ||| c)) + 11 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) - 1 * ( ~~~a ||| (b ^^^ c)) - 6 * ( ~~~c ||| ~~~(a ^^^ b)) - 1 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) + 7 * (b ^^^ (a &&& ~~~c)) - 1 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) - 3 * (a ||| (b ||| c)) - 1 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) + 1 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) + 11 * ~~~( ~~~a &&& (b &&& c)) - 2 * (b ^^^ (a ||| c)) - 7 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) - 7 * ~~~(a &&& (b ||| c)) + 7 * ~~~(a ||| (b ^^^ c)) - 6 * (c &&& ~~~(a &&& ~~~b)) + 1 * (a &&& ~~~b) + 2 * (a ^^^ (b ||| c)) + 2 * (b ||| (a &&& c)) - 3 * (b &&& (a ^^^ c)) - 6 * ~~~(a ||| ~~~c) + 1 * (b ^^^ ( ~~~a ||| (b ||| c))) + 2 * ~~~(a &&& (b ^^^ c)) - 2 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) - 6 * (a &&& ( ~~~b ||| c)) + 1 * (c ||| ~~~(a ||| b)) + 1 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 11 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) - 5 * ( ~~~c &&& (a ^^^ b)) + 2 * ((a &&& b) ||| (b ^^^ c)) - 1 * (b ||| ~~~(a ||| ~~~c)) + 5 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) + 1 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) - 1 * (c ^^^ (a &&& b)) - 1 * (a ||| ~~~c) - 6 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) - 23 * ~~~(a ||| (b ||| c)) - 10 * ~~~(a ||| ( ~~~b ||| c)) + 3 * ~~~( ~~~a ||| (b ||| c)) - 6 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 16 * ( ~~~a &&& ( ~~~b &&& c)) - 7 * ( ~~~a &&& (b &&& c)) - 5 * (a &&& ( ~~~b &&& c)) - 4 * (a &&& (b &&& c)) = 3 * ((a &&& b) ^^^ (b ||| ~~~c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1893 (x y : BitVec w) : +theorem e_1893 : 11 * ((a &&& b) ^^^ (b ||| c)) + 4 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) + 2 * (c ^^^ ~~~(a &&& ~~~b)) + 5 * (b ^^^ (a &&& ~~~c)) + 5 * (b ^^^ (a ||| c)) + 5 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) - 2 * ((a &&& b) ^^^ (b ||| ~~~c)) + 11 * (a ||| (b ^^^ c)) + 3 * (a &&& (b ^^^ c)) + 7 * (b &&& ~~~c) + 7 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) + 3 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) - 5 * (c ||| (a ^^^ b)) - 3 * (b ||| c) - 1 * (b ||| ~~~(a ^^^ c)) - 11 * (a ^^^ (b &&& c)) + 7 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 7 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 11 * ~~~(a ^^^ c) + 2 * (c ^^^ (a ||| ~~~b)) - 1 * ( ~~~c ||| (a ^^^ b)) - 2 * (b ^^^ ( ~~~a &&& (b ^^^ c))) - 7 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) + 1 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) - 3 * (b ||| ~~~(a ||| c)) - 2 * (b ||| ~~~(a ||| ~~~c)) + 7 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 1 * (c ^^^ ~~~(a ||| ~~~b)) - 6 * ((b &&& c) ||| (a &&& (b ||| c))) + 1 * ~~~(b ^^^ c) + 3 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) - 5 * ~~~(a &&& b) - 6 * ( ~~~(a ||| b) ||| (b ^^^ c)) + 3 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) + 4 * (a ||| b) + 11 * ( ~~~c ||| ~~~(a ^^^ b)) + 1 * (b ^^^ c) - 7 * ~~~( ~~~a &&& ( ~~~b ||| c)) - 7 * ~~~(a &&& ~~~a) - 2 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) - 2 * (c ^^^ (a ||| ( ~~~b ||| c))) - 13 * ~~~(a ||| (b ||| c)) - 34 * ~~~(a ||| ( ~~~b ||| c)) - 10 * ~~~( ~~~a ||| (b ||| c)) - 14 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 30 * ( ~~~a &&& ( ~~~b &&& c)) + 3 * ( ~~~a &&& (b &&& c)) - 1 * (a &&& ( ~~~b &&& c)) - 22 * (a &&& (b &&& c)) = - 2 * (b ^^^ ~~~(a ||| (b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1894 (x y : BitVec w) : +theorem e_1894 : - 1 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) + 1 * (c ^^^ ( ~~~a &&& (b ||| c))) - 1 * (c ^^^ ~~~(a &&& (b ||| c))) - 6 * ( ~~~b &&& (a ^^^ c)) - 2 * ((a &&& c) ||| (b &&& ~~~c)) - 6 * ~~~(a ^^^ ( ~~~b ||| c)) - 1 * ~~~(a ||| c) - 7 * (a ||| ~~~c) - 1 * ~~~(b &&& c) + 4 * ((a ^^^ b) ||| (a ^^^ c)) - 7 * b + 2 * ~~~(b ^^^ c) + 11 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) + 1 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) + 3 * (c ^^^ ~~~(a &&& ~~~b)) + 4 * (b ^^^ ~~~(a &&& c)) + 4 * (c ^^^ ~~~(a ||| (b &&& c))) - 6 * ( ~~~b &&& ~~~(a ^^^ c)) + 2 * c - 3 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) + 2 * ( ~~~c ||| (a ^^^ b)) + 5 * ~~~(a &&& ~~~c) - 2 * (b ^^^ ~~~(a ||| c)) + 2 * ((a ||| ~~~b) &&& (b ^^^ c)) + 11 * (c ^^^ (a &&& b)) + 5 * ((a ||| b) &&& (b ^^^ c)) - 1 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) - 11 * ~~~(a &&& ~~~b) + 4 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) - 3 * ((a ^^^ b) &&& (a ^^^ c)) + 11 * (a ||| ( ~~~b ||| c)) - 11 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) - 7 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) - 1 * ((a ^^^ b) &&& ~~~(a ^^^ c)) + 2 * (c ^^^ ~~~(a ||| ~~~b)) + 1 * (b ^^^ (a ||| (b ||| c))) - 1 * ~~~(a ^^^ (b ||| c)) - 5 * ( ~~~a ||| (b ||| c)) - 3 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) + 4 * (a &&& (b ||| c)) + 3 * ((a &&& b) ||| ~~~(b ||| ~~~c)) + 7 * ( ~~~c &&& (a ^^^ b)) + 19 * ~~~(a ||| (b ||| c)) + 31 * ~~~(a ||| ( ~~~b ||| c)) - 4 * ~~~( ~~~a ||| (b ||| c)) - 10 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 10 * ( ~~~a &&& (b &&& c)) - 21 * (a &&& ( ~~~b &&& c)) + 16 * (a &&& (b &&& c)) = - 2 * (c &&& ~~~(a &&& b)) + 11 * (c &&& ~~~(a ^^^ b)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1895 (x y : BitVec w) : +theorem e_1895 : - 2 * (b ^^^ (a ||| ~~~c)) - 7 * (c ^^^ (a ||| ( ~~~b &&& c))) + 2 * (b ^^^ (a &&& (b ^^^ c))) - 1 * (c ^^^ (a &&& ( ~~~b ||| c))) - 5 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) + 5 * ~~~( ~~~a &&& (b &&& c)) - 1 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) - 6 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 5 * (c ^^^ ~~~(a &&& b)) + 3 * (b ^^^ (a ||| (b ||| c))) + 1 * c - 1 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 1 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) + 4 * (b ||| ~~~(a ||| c)) + 2 * (c ^^^ (a &&& (b ||| c))) - 1 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) - 11 * ~~~c - 7 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) + 1 * (b ||| ~~~(a ^^^ c)) - 1 * ( ~~~c ||| ~~~(a ^^^ b)) + 1 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 7 * ((a ^^^ b) &&& ~~~(a ^^^ c)) - 11 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) + 1 * ( ~~~a &&& (b ^^^ c)) - 2 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) + 11 * ( ~~~a &&& (b ||| c)) - 1 * ~~~(a ^^^ ( ~~~b &&& c)) - 11 * (b ^^^ c) + 7 * (c ^^^ (a &&& ~~~b)) + 4 * (a &&& ~~~b) - 5 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) - 3 * ~~~(b &&& ~~~c) - 2 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) - 7 * (c ^^^ ( ~~~a ||| (b &&& c))) + 2 * (a ^^^ (b &&& c)) + 7 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) + 7 * ~~~(a &&& ( ~~~b &&& c)) - 1 * (a &&& (b ||| c)) + 2 * (c ^^^ (a &&& b)) + 11 * ~~~(a ^^^ (b ^^^ c)) - 6 * (a ||| c) + 11 * (a &&& c) + 27 * ~~~(a ||| (b ||| c)) + 5 * ~~~(a ||| ( ~~~b ||| c)) + 1 * ~~~( ~~~a ||| (b ||| c)) - 4 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 3 * ( ~~~a &&& (b &&& c)) - 13 * (a &&& ( ~~~b &&& c)) - 22 * (a &&& (b &&& c)) = - 11 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) + 3 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1896 (x y : BitVec w) : +theorem e_1896 : 7 * (b ^^^ (a &&& ~~~c)) - 3 * (a &&& b) - 3 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) - 6 * ( ~~~(a &&& b) &&& (b ^^^ c)) - 6 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) + 5 * ~~~(a ||| (b &&& c)) - 11 * ~~~b + 1 * (b ^^^ c) + 1 * (b ||| ~~~c) + 1 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 5 * ((a &&& b) ^^^ (b ||| ~~~c)) + 4 * ~~~(a ||| ~~~c) + 1 * (b ^^^ ( ~~~a &&& (b ^^^ c))) + 1 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) - 2 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) + 11 * (c &&& ~~~(a &&& b)) + 1 * (c ^^^ ~~~(a &&& (b &&& c))) + 3 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) - 1 * ~~~(b ||| ~~~c) - 1 * ~~~(b ^^^ c) + 5 * ( ~~~(a ||| b) ||| (b ^^^ c)) + 11 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) + 1 * (b ||| ~~~(a ^^^ c)) + 2 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) - 5 * ~~~(a ||| ( ~~~b &&& c)) - 6 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 7 * (a ||| (b ||| c)) - 1 * (c ^^^ (a &&& ~~~b)) + 2 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 3 * (a ^^^ (b &&& c)) + 2 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 1 * (c ^^^ (a ||| ~~~b)) - 2 * (b ^^^ (a &&& (b ||| c))) - 1 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) - 5 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) + 11 * (c ||| ~~~(a ||| ~~~b)) + 1 * (a ||| c) + 2 * (b &&& (a ||| c)) - 11 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 1 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) + 7 * ((a &&& ~~~b) ||| (b ^^^ c)) - 2 * ~~~(a ||| (b ||| c)) - 10 * ~~~(a ||| ( ~~~b ||| c)) + 9 * ~~~( ~~~a ||| (b ||| c)) - 17 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 24 * ( ~~~a &&& ( ~~~b &&& c)) - 17 * ( ~~~a &&& (b &&& c)) + 7 * (a &&& ( ~~~b &&& c)) + 1 * (a &&& (b &&& c)) = 7 * (a ^^^ c) - 1 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1897 (x y : BitVec w) : +theorem e_1897 : - 2 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) - 6 * (a ^^^ b) - 3 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) + 7 * ~~~(a ||| c) - 11 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) + 7 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) + 2 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) - 1 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) + 3 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) + 11 * (b ||| ~~~(a ^^^ c)) - 11 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) - 1 * ~~~( ~~~a &&& ( ~~~b ||| c)) - 7 * ~~~(a &&& (b ||| c)) + 3 * (b ^^^ (a ||| c)) - 1 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) + 2 * ((a ^^^ b) ||| (a ^^^ c)) + 1 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) + 1 * ~~~(a &&& (b &&& c)) + 4 * (b ^^^ c) - 7 * ((a &&& b) ||| ~~~(b ||| c)) - 11 * (b ^^^ ~~~(a ||| (b ^^^ c))) + 1 * (a ||| (b &&& c)) - 11 * ( ~~~b &&& (a ^^^ c)) - 2 * ( ~~~a ||| (b &&& c)) + 4 * (b &&& c) + 7 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 1 * (c ^^^ (a ||| ~~~b)) - 1 * ( ~~~c &&& ~~~(a ^^^ b)) + 7 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) + 1 * (a &&& ~~~c) - 11 * ~~~(a &&& ~~~b) - 6 * (b ^^^ ~~~(a ||| c)) + 5 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 1 * (c ^^^ ~~~(a &&& (b &&& c))) - 3 * (a ||| c) + 7 * ~~~(a &&& c) - 1 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) + 1 * ~~~(a ||| b) - 6 * (c ||| (a &&& b)) + 1 * ( ~~~a ||| ( ~~~b ||| c)) + 5 * ~~~(a ^^^ (b ||| c)) + 9 * ~~~(a ||| (b ||| c)) - 5 * ~~~(a ||| ( ~~~b ||| c)) - 13 * ~~~( ~~~a ||| (b ||| c)) + 28 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 14 * ( ~~~a &&& ( ~~~b &&& c)) + 16 * ( ~~~a &&& (b &&& c)) - 17 * (a &&& ( ~~~b &&& c)) + 29 * (a &&& (b &&& c)) = - 3 * (a ^^^ (b ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1898 (x y : BitVec w) : +theorem e_1898 : - 1 * ((a &&& b) ||| ~~~(b ^^^ c)) + 2 * (b ^^^ ( ~~~a ||| (b ^^^ c))) + 7 * ~~~(a &&& (b ^^^ c)) + 3 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 7 * (c ^^^ (a ||| b)) - 5 * ~~~(a ||| (b ^^^ c)) + 11 * a + 1 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) - 3 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) - 1 * c - 1 * ~~~(a ||| ( ~~~b &&& c)) + 5 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) + 11 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 5 * ~~~(a ^^^ b) + 2 * (c ^^^ ~~~(a &&& (b ||| c))) + 1 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) - 11 * (c &&& (a ^^^ b)) + 4 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) - 5 * ((a &&& c) ||| ~~~(b ||| c)) + 11 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) - 1 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) + 3 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) - 1 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) - 6 * ( ~~~b &&& ~~~(a ^^^ c)) - 1 * ~~~(a ||| b) + 1 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) - 1 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) + 1 * (a ||| ( ~~~b ||| c)) - 11 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 11 * ~~~(b &&& ~~~c) + 2 * (c &&& (a ||| ~~~b)) - 6 * ((a &&& b) ||| ~~~(b ||| c)) - 5 * (c ^^^ ~~~(a &&& (b &&& c))) + 1 * (c ^^^ ~~~(a &&& ~~~b)) + 1 * (a &&& ( ~~~b ||| c)) + 3 * (c ^^^ (a ||| (b &&& c))) - 7 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) + 4 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 6 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) + 4 * ~~~(a &&& c) + 5 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) - 1 * ~~~(b ||| c) + 9 * ~~~(a ||| (b ||| c)) - 39 * ~~~(a ||| ( ~~~b ||| c)) - 7 * ~~~( ~~~a ||| (b ||| c)) - 31 * ( ~~~a &&& ( ~~~b &&& c)) + 7 * ( ~~~a &&& (b &&& c)) + 25 * (a &&& ( ~~~b &&& c)) - 4 * (a &&& (b &&& c)) = 50 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 1 * (a ||| (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1899 (x y : BitVec w) : +theorem e_1899 : 2 * (a ^^^ ( ~~~b &&& c)) + 5 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 6 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) - 1 * ~~~(b &&& ~~~c) - 6 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 1 * (b ^^^ (a &&& (b ||| c))) + 11 * (c ^^^ (a &&& b)) + 3 * (b ^^^ ~~~(a &&& (b ^^^ c))) + 4 * (b ||| ~~~(a ||| c)) - 2 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) - 6 * ~~~(a ^^^ ( ~~~b &&& c)) + 11 * (b ^^^ ~~~(a ||| ~~~c)) - 2 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 2 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) + 1 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) + 3 * ~~~(a ^^^ c) + 5 * ~~~(b &&& c) + 1 * ( ~~~b &&& (a ^^^ c)) - 5 * (c ^^^ (a ||| (b &&& c))) - 5 * (b ^^^ (a ||| ( ~~~b &&& c))) + 11 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 3 * (a ^^^ (b ||| c)) - 1 * (c ^^^ (a ||| (b ||| c))) + 3 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) + 2 * ( ~~~a &&& (b ||| c)) - 6 * (b ||| (a &&& ~~~c)) - 1 * ~~~(a &&& (b ^^^ c)) + 4 * ~~~(a ||| (b ^^^ c)) + 2 * ( ~~~b &&& ~~~(a ^^^ c)) - 3 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) + 3 * (b ^^^ ~~~(a &&& ~~~c)) - 7 * c - 1 * (c ^^^ ~~~(a &&& (b ||| c))) - 11 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) + 2 * ~~~(a ||| ( ~~~b &&& c)) - 1 * ~~~(a &&& ( ~~~b ||| c)) - 11 * b - 2 * ~~~(a &&& (b &&& c)) + 5 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) - 6 * ~~~( ~~~a &&& ( ~~~b &&& c)) + 1 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) - 1 * ~~~(a ||| (b ||| c)) + 12 * ~~~(a ||| ( ~~~b ||| c)) + 45 * ~~~( ~~~a ||| (b ||| c)) - 9 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 2 * ( ~~~a &&& ( ~~~b &&& c)) + 30 * ( ~~~a &&& (b &&& c)) + 12 * (a &&& ( ~~~b &&& c)) + 18 * (a &&& (b &&& c)) = 5 * (c ||| (a &&& ~~~b)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1900 (x y : BitVec w) : +theorem e_1900 : 2 * (b ^^^ (a &&& ~~~c)) - 11 * (b ^^^ ~~~(a &&& (b ^^^ c))) - 3 * (b &&& ~~~(a &&& ~~~c)) - 1 * (b ^^^ (a ||| ~~~c)) - 2 * (a ||| ( ~~~b &&& c)) + 11 * ( ~~~a ||| (b ||| c)) + 2 * (c ||| (a &&& ~~~b)) - 1 * (a ||| b) - 5 * (c ^^^ (a &&& b)) + 7 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) + 4 * ~~~(b &&& ~~~c) + 7 * (a ^^^ c) - 1 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) + 7 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 11 * (b ^^^ ( ~~~a ||| (b &&& c))) + 1 * (b &&& c) + 1 * ((a ^^^ b) ||| (a ^^^ c)) - 5 * (b ^^^ (a ||| (b ^^^ c))) - 6 * (a &&& (b ||| c)) - 2 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) + 7 * ~~~(a ^^^ (b ||| c)) + 2 * ~~~(a ||| (b &&& c)) - 7 * ( ~~~b &&& ~~~(a ^^^ c)) + 3 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) - 6 * c - 2 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 11 * ~~~(a &&& ~~~b) - 3 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 7 * ~~~(a ||| ~~~b) + 2 * (a &&& ~~~c) - 11 * ~~~(a &&& ~~~c) + 11 * ~~~( ~~~a &&& (b ||| c)) - 2 * (b ^^^ ( ~~~a &&& (b ||| c))) + 4 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) + 4 * (a ^^^ (b &&& c)) + 1 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 2 * ~~~(b ||| ~~~c) + 1 * ( ~~~b ||| ~~~(a ^^^ c)) + 2 * ~~~(b &&& c) + 11 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) + 1 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) - 56 * ~~~(a ||| (b ||| c)) - 28 * ~~~(a ||| ( ~~~b ||| c)) - 27 * ~~~( ~~~a ||| (b ||| c)) - 52 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 24 * ( ~~~a &&& ( ~~~b &&& c)) - 18 * ( ~~~a &&& (b &&& c)) + 5 * (a &&& ( ~~~b &&& c)) - 37 * (a &&& (b &&& c)) = - 1 * ((a &&& ~~~b) ||| (b ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1901 (x y : BitVec w) : +theorem e_1901 : - 3 * (b ^^^ ~~~(a ||| (b &&& c))) - 1 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 5 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) + 7 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) + 1 * (b &&& (a ^^^ c)) - 5 * (b &&& ~~~(a ^^^ c)) + 5 * (a ||| ( ~~~b &&& c)) + 2 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) - 6 * ((a &&& b) ^^^ (b ||| c)) - 2 * (b ^^^ (a &&& (b ||| c))) + 2 * (a ||| (b ||| c)) - 6 * (a &&& ~~~c) - 6 * (b ^^^ (a &&& ( ~~~b ||| c))) - 5 * (b ^^^ ~~~(a ||| ~~~c)) + 4 * ~~~(b &&& c) - 1 * ((a ^^^ b) ||| (a ^^^ c)) - 2 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 2 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) + 1 * (c ^^^ (a ||| b)) + 1 * (a ^^^ ( ~~~b ||| c)) + 11 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) - 7 * (c ^^^ (a &&& b)) + 3 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 2 * ((a ||| ~~~b) &&& (b ^^^ c)) + 4 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) - 11 * (b ||| (a ^^^ c)) - 3 * (b &&& ~~~(a &&& c)) + 1 * (b ^^^ ~~~(a ||| (b ^^^ c))) - 1 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) - 11 * (c &&& ~~~(a ^^^ b)) - 6 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 7 * ((a &&& b) ||| (b ^^^ c)) - 2 * ~~~(a &&& (b ||| c)) - 11 * (b ||| ~~~(a ||| ~~~c)) - 7 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 1 * ((a ||| b) &&& (b ^^^ c)) + 1 * ~~~( ~~~a &&& (b ^^^ c)) + 11 * ( ~~~(a ||| b) ||| (b ^^^ c)) + 4 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) + 1 * ( ~~~b &&& ~~~(a ^^^ c)) - 1 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) - 18 * ~~~(a ||| (b ||| c)) + 17 * ~~~(a ||| ( ~~~b ||| c)) + 7 * ~~~( ~~~a ||| (b ||| c)) + 26 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 6 * ( ~~~a &&& ( ~~~b &&& c)) + 33 * ( ~~~a &&& (b &&& c)) - 9 * (a &&& ( ~~~b &&& c)) + 36 * (a &&& (b &&& c)) = 2 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) - 1 * (b ^^^ ( ~~~a &&& (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1902 (x y : BitVec w) : +theorem e_1902 : 5 * ((b &&& c) ||| (a &&& (b ||| c))) + 11 * (b ||| (a ^^^ c)) - 2 * (a ^^^ (b ||| c)) - 3 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 7 * (b &&& ~~~(a &&& ~~~c)) + 1 * (c ^^^ ~~~(a &&& ~~~b)) - 1 * ~~~( ~~~a ||| (b ^^^ c)) + 7 * (b ^^^ (a ||| (b ^^^ c))) - 7 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) + 2 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) + 5 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) + 11 * ~~~(a &&& (b ^^^ c)) + 7 * ~~~a - 7 * (a ||| ( ~~~b &&& c)) + 5 * (b &&& ~~~(a ^^^ c)) - 1 * ((a ^^^ b) ||| (a ^^^ c)) + 3 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) + 3 * (b ^^^ ~~~(a ||| c)) + 2 * (c ^^^ (a ||| (b ||| c))) + 5 * ( ~~~b ||| (a ^^^ c)) + 2 * ((a &&& c) ||| ~~~(b ||| c)) + 11 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) - 3 * (c ^^^ (a ||| ~~~b)) - 7 * (a ^^^ ( ~~~b ||| c)) - 3 * ( ~~~b ||| ~~~(a ^^^ c)) - 7 * (a ||| (b &&& c)) - 5 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) + 2 * (c ||| (a &&& b)) - 6 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) - 2 * ~~~(a ^^^ b) + 2 * (a ||| ~~~b) - 2 * (a &&& c) + 1 * (b ^^^ (a &&& c)) + 3 * ~~~(a ||| (b &&& c)) - 11 * ((a &&& c) ||| (b &&& ~~~c)) + 2 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 5 * ~~~( ~~~a &&& ( ~~~b ||| c)) - 1 * (b ^^^ (a &&& (b ||| c))) - 2 * ~~~(a ||| ~~~b) - 5 * (b &&& c) - 2 * ((a ||| b) &&& (b ^^^ c)) - 11 * ~~~(a ||| (b ||| c)) - 34 * ~~~(a ||| ( ~~~b ||| c)) - 15 * ~~~( ~~~a ||| (b ||| c)) + 20 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 28 * ( ~~~a &&& ( ~~~b &&& c)) - 13 * ( ~~~a &&& (b &&& c)) + 13 * (a &&& ( ~~~b &&& c)) + 7 * (a &&& (b &&& c)) = 5 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1903 (x y : BitVec w) : +theorem e_1903 : 7 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) + 1 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 5 * ( ~~~a &&& (b ^^^ c)) + 1 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 1 * (c ^^^ (a &&& (b ||| c))) + 1 * ~~~(a ^^^ (b ^^^ c)) + 1 * (b ||| ~~~(a ^^^ c)) - 6 * (b ^^^ ~~~(a &&& (b &&& c))) + 3 * (b &&& (a ^^^ c)) + 1 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) - 2 * (c ^^^ (a ||| (b &&& c))) - 6 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) - 5 * (a &&& ~~~c) + 1 * ( ~~~b ||| (a ^^^ c)) + 2 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) - 1 * (c &&& (a ^^^ b)) + 11 * (b &&& ~~~c) - 6 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) + 3 * ( ~~~a &&& (b ||| c)) + 1 * ~~~(b ||| ~~~c) - 2 * (b ||| (a ^^^ c)) - 1 * ~~~( ~~~a &&& ( ~~~b ||| c)) - 5 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) + 3 * (b ^^^ ( ~~~a &&& (b ||| c))) + 2 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) + 5 * (a ||| ~~~b) - 6 * ((a &&& c) ||| ~~~(b ||| c)) + 11 * ((a &&& b) ^^^ (b ||| ~~~c)) + 2 * ~~~a + 1 * (b &&& (a ||| ~~~c)) - 7 * (b ^^^ (a &&& ( ~~~b ||| c))) - 2 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) + 4 * (b ^^^ ~~~(a &&& (b ||| c))) - 7 * (a &&& (b ^^^ c)) - 6 * (b ||| ~~~(a ||| c)) - 1 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 1 * (a ^^^ (b ||| c)) - 1 * (a ^^^ b) + 1 * (b ^^^ (a ||| ~~~c)) + 7 * ~~~(b &&& c) - 1 * a - 12 * ~~~(a ||| (b ||| c)) - 22 * ~~~(a ||| ( ~~~b ||| c)) + 12 * ~~~( ~~~a ||| (b ||| c)) - 10 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 20 * ( ~~~a &&& ( ~~~b &&& c)) + 14 * ( ~~~a &&& (b &&& c)) - 3 * (a &&& ( ~~~b &&& c)) + 13 * (a &&& (b &&& c)) = - 5 * ( ~~~b &&& ~~~(a ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1904 (x y : BitVec w) : +theorem e_1904 : 1 * ~~~(b &&& c) - 7 * ( ~~~a ||| (b ^^^ c)) + 11 * ((a &&& b) ^^^ (b ||| ~~~c)) + 4 * (a ^^^ ( ~~~b &&& c)) - 2 * (c ^^^ (a &&& b)) - 5 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) + 7 * ~~~(a &&& (b ^^^ c)) - 1 * (b ^^^ ( ~~~a ||| (b ^^^ c))) - 5 * ~~~(a ^^^ (b ||| c)) + 2 * (b ^^^ (a ||| (b ||| c))) - 7 * ~~~(a &&& ( ~~~b &&& c)) + 1 * (c ^^^ (a ||| ( ~~~b &&& c))) - 3 * (b &&& ~~~(a ^^^ c)) - 2 * ( ~~~b ||| ~~~(a ^^^ c)) - 2 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 7 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 1 * ((a ^^^ b) ||| ~~~(a ^^^ c)) + 3 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) + 3 * ( ~~~a ||| ( ~~~b &&& c)) + 1 * ~~~( ~~~a ||| (b ^^^ c)) - 7 * (b ||| ~~~c) + 2 * (a ||| ~~~c) - 1 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) - 3 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 11 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) + 3 * (b ^^^ ~~~(a &&& (b &&& c))) - 5 * (b ||| (a &&& ~~~c)) + 2 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 2 * (b &&& ~~~(a &&& c)) - 11 * ((a ||| b) &&& (b ^^^ c)) - 6 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) - 1 * (a ^^^ c) + 7 * ((a &&& ~~~b) ||| (b ^^^ c)) - 5 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 2 * (c &&& ~~~(a &&& b)) + 2 * (b ^^^ (a ||| ~~~c)) + 5 * (c ^^^ ~~~(a &&& (b ||| c))) - 5 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 3 * ( ~~~a ||| ( ~~~b ||| c)) + 3 * ((a &&& b) ^^^ (b ||| c)) - 5 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 7 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) + 23 * ~~~(a ||| (b ||| c)) + 19 * ~~~(a ||| ( ~~~b ||| c)) - 6 * ~~~( ~~~a ||| (b ||| c)) + 56 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 2 * ( ~~~a &&& ( ~~~b &&& c)) + 23 * ( ~~~a &&& (b &&& c)) + 11 * (a &&& ( ~~~b &&& c)) + 31 * (a &&& (b &&& c)) = 7 * (b &&& (a ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1905 (x y : BitVec w) : +theorem e_1905 : 1 * (a ^^^ c) + 1 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) - 5 * (a ||| ( ~~~b &&& c)) + 2 * ( ~~~b ||| ~~~(a ^^^ c)) + 1 * (a &&& ~~~c) + 5 * ( ~~~c &&& ~~~(a ^^^ b)) + 3 * ((a &&& ~~~b) ||| (b ^^^ c)) - 7 * ~~~(b ^^^ c) + 2 * (a ||| c) + 7 * ((a &&& c) ||| (b &&& ~~~c)) - 2 * ( ~~~(a ||| b) ||| (b ^^^ c)) + 1 * (a ^^^ ( ~~~b ||| c)) - 3 * ~~~(b &&& ~~~c) - 2 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) + 4 * (a ||| ( ~~~b ||| c)) - 1 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) - 1 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) + 1 * (c ^^^ (a ||| (b &&& c))) - 7 * (c ^^^ (a &&& ~~~b)) + 1 * ( ~~~a ||| ( ~~~b &&& c)) - 11 * (b &&& c) - 2 * ~~~(a ^^^ ( ~~~b &&& c)) + 5 * (a ||| b) - 1 * (b &&& (a ||| ~~~c)) + 1 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) - 1 * ~~~(a ||| c) - 5 * a + 11 * (a &&& (b ||| c)) + 2 * (a ^^^ (b ^^^ c)) - 1 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) - 6 * (c &&& (a ^^^ b)) - 3 * ~~~(a &&& ( ~~~b &&& c)) - 3 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 1 * (a &&& ( ~~~b ||| c)) + 3 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) - 1 * (c ^^^ ~~~(a &&& (b ||| c))) + 2 * ((a &&& b) ||| ~~~(b ||| c)) + 4 * ~~~(a &&& (b ^^^ c)) + 3 * ( ~~~a ||| (b ||| c)) + 2 * (c &&& ~~~(a &&& ~~~b)) + 1 * (b ||| ~~~(a ^^^ c)) + 11 * (b ^^^ ( ~~~a &&& (b ^^^ c))) - 2 * (a &&& (b ^^^ c)) - 28 * ~~~(a ||| ( ~~~b ||| c)) + 6 * ~~~( ~~~a ||| (b ||| c)) - 42 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 22 * ( ~~~a &&& ( ~~~b &&& c)) + 3 * ( ~~~a &&& (b &&& c)) - 21 * (a &&& ( ~~~b &&& c)) - 18 * (a &&& (b &&& c)) = - 3 * (b ^^^ (a &&& (b ^^^ c))) - 4 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1906 (x y : BitVec w) : +theorem e_1906 : 4 * (a &&& ~~~c) - 1 * (a ^^^ b) - 5 * ~~~(b ^^^ c) + 7 * ( ~~~a ||| (b &&& c)) + 4 * (b ^^^ (a ||| (b ^^^ c))) - 5 * (c &&& (a ||| b)) - 1 * (a ||| b) - 1 * (c &&& ~~~(a &&& ~~~b)) + 3 * ~~~(a ^^^ (b ^^^ c)) + 7 * a + 5 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) + 4 * (c ^^^ (a ||| ( ~~~b &&& c))) - 1 * (c ^^^ (a &&& ( ~~~b ||| c))) + 1 * ( ~~~a &&& ( ~~~b ||| c)) + 3 * (b ||| ~~~c) - 2 * (c ^^^ (a &&& (b ||| c))) + 1 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) - 1 * (a &&& (b ^^^ c)) - 1 * (a ||| ~~~b) - 3 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 3 * ~~~(a ^^^ (b ||| c)) + 1 * ~~~b - 1 * (a &&& b) + 2 * (a &&& ~~~b) + 7 * (b ^^^ c) - 2 * ~~~( ~~~a &&& ( ~~~b ||| c)) + 5 * (c ^^^ ~~~(a &&& (b ||| c))) + 2 * (b ^^^ (a &&& c)) + 7 * (b ^^^ ~~~(a ||| c)) - 7 * ( ~~~(a &&& b) &&& (b ^^^ c)) + 1 * ( ~~~c ||| (a ^^^ b)) + 3 * (b &&& (a ^^^ c)) + 1 * ~~~(a ^^^ b) - 3 * (a ^^^ (b ^^^ c)) - 2 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) + 11 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 11 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 1 * (c ^^^ ( ~~~a &&& (b ||| c))) - 11 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) + 1 * c + 7 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 7 * ((a &&& b) ^^^ (b ||| ~~~c)) + 2 * (c ^^^ ( ~~~a ||| (b ||| c))) + 1 * ( ~~~a ||| (b ||| c)) - 27 * ~~~(a ||| (b ||| c)) - 18 * ~~~(a ||| ( ~~~b ||| c)) - 2 * ~~~( ~~~a ||| (b ||| c)) - 44 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 9 * ( ~~~a &&& (b &&& c)) + 1 * (a &&& (b &&& c)) = 10 * (a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1907 (x y : BitVec w) : +theorem e_1907 : - 2 * (a &&& ( ~~~b ||| c)) + 7 * ((a &&& c) ||| ~~~(b ||| c)) - 6 * ( ~~~a ||| (b ||| c)) + 11 * (b ^^^ (a ||| (b ||| c))) - 7 * (a &&& (b ^^^ c)) - 11 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) + 2 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 2 * (b ^^^ (a ||| (b &&& c))) + 1 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 5 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) + 2 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) + 1 * (c &&& (a ||| b)) - 11 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) + 1 * ~~~(a &&& (b ||| c)) + 11 * ((a &&& c) ||| (b &&& ~~~c)) - 1 * ~~~(a ^^^ ( ~~~b ||| c)) - 7 * ~~~(b ^^^ c) - 5 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) + 2 * (c ^^^ (a ||| ( ~~~b ||| c))) + 2 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) - 6 * ~~~( ~~~a &&& ( ~~~b ||| c)) - 2 * (b ^^^ (a &&& ~~~c)) - 2 * (b ^^^ ~~~(a ||| ~~~c)) + 3 * ~~~c - 6 * ~~~(b &&& ~~~c) - 7 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) + 1 * ~~~( ~~~a &&& ( ~~~b &&& c)) - 3 * ~~~(a &&& ~~~a) + 11 * (b &&& ~~~c) + 4 * ~~~( ~~~a ||| (b &&& c)) - 5 * (b &&& c) - 6 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 1 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) + 5 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 7 * (c ^^^ ~~~(a ||| b)) - 2 * (c ^^^ ~~~(a &&& b)) + 3 * (c ^^^ ( ~~~a ||| (b ||| c))) + 4 * (c ^^^ ~~~(a &&& (b &&& c))) + 5 * (a ||| ~~~c) - 2 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) - 2 * ((b &&& c) ||| (a &&& (b ||| c))) + 2 * ~~~(a ||| (b &&& c)) - 1 * ((a &&& ~~~b) ||| (b ^^^ c)) + 14 * ~~~(a ||| (b ||| c)) + 9 * ~~~(a ||| ( ~~~b ||| c)) + 7 * ~~~( ~~~a ||| (b ||| c)) + 18 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 39 * ( ~~~a &&& ( ~~~b &&& c)) + 64 * ( ~~~a &&& (b &&& c)) + 25 * (a &&& (b &&& c)) = - 14 * (a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1908 (x y : BitVec w) : +theorem e_1908 : - 6 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) - 2 * ((a &&& c) ||| (b &&& ~~~c)) - 6 * (c &&& (a ^^^ b)) - 7 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) + 11 * (c &&& (a ||| ~~~b)) - 7 * (b ||| c) + 7 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) + 1 * a - 1 * (c ^^^ (a ||| ( ~~~b ||| c))) + 3 * ~~~(a &&& ~~~a) + 5 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) + 1 * (b ^^^ ~~~(a &&& ~~~c)) - 7 * (b &&& ~~~(a &&& c)) - 1 * (c ^^^ ~~~(a &&& (b &&& c))) + 2 * (a &&& ~~~b) + 11 * ( ~~~b &&& (a ^^^ c)) - 1 * (b ||| (a ^^^ c)) + 11 * (b ^^^ ~~~(a &&& c)) + 7 * (a ||| (b ^^^ c)) + 11 * (c ^^^ (a ||| (b &&& c))) - 1 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 11 * ( ~~~(a &&& b) &&& (b ^^^ c)) - 2 * (a ||| ( ~~~b ||| c)) + 7 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) - 1 * (b ^^^ (a &&& c)) - 7 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) - 1 * (c ^^^ (a &&& (b ||| c))) - 3 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 1 * (c ||| (a ^^^ b)) + 1 * ~~~(a ||| (b ^^^ c)) + 5 * (b ||| ~~~(a ||| ~~~c)) + 1 * ~~~(b ||| c) - 6 * ~~~(b &&& ~~~c) - 1 * (a &&& ~~~c) - 5 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 11 * (b ^^^ (a &&& ~~~c)) + 7 * ~~~(a ^^^ b) + 4 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) + 3 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) + 1 * (b ^^^ (a &&& (b ^^^ c))) - 11 * ( ~~~c &&& ~~~(a ^^^ b)) - 2 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) + 11 * ~~~(a ||| (b ||| c)) + 4 * ~~~(a ||| ( ~~~b ||| c)) - 41 * ~~~( ~~~a ||| (b ||| c)) - 4 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 28 * ( ~~~a &&& ( ~~~b &&& c)) + 39 * ( ~~~a &&& (b &&& c)) + 12 * (a &&& ( ~~~b &&& c)) - 20 * (a &&& (b &&& c)) = - 7 * (b ^^^ (a &&& ( ~~~b ||| c))) + 3 * (b ^^^ (a &&& (b ||| c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1909 (x y : BitVec w) : +theorem e_1909 : 11 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) + 3 * ~~~(a &&& (b &&& c)) + 11 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) + 5 * (c ^^^ ( ~~~a ||| (b &&& c))) - 7 * (b ||| ~~~c) + 1 * ((a &&& b) ||| ~~~(b ||| ~~~c)) - 7 * ~~~(a ^^^ ( ~~~b ||| c)) - 3 * ( ~~~a &&& (b ||| c)) - 7 * (b ||| c) + 1 * (a ^^^ b) - 1 * (b ^^^ (a ||| c)) - 1 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) - 11 * (a ||| b) - 1 * (a ||| ( ~~~b ||| c)) + 4 * (c ^^^ ~~~(a &&& (b &&& c))) + 7 * (b ^^^ (a ||| (b &&& c))) + 11 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 2 * (b ||| (a ^^^ c)) + 1 * (c &&& ~~~(a ^^^ b)) + 11 * (c ^^^ (a &&& ( ~~~b ||| c))) + 1 * ( ~~~a ||| (b ||| c)) - 2 * (c ^^^ ~~~(a &&& ~~~b)) + 1 * (a ||| (b ||| c)) - 2 * (c ^^^ (a ||| ( ~~~b ||| c))) + 3 * ( ~~~b &&& ~~~(a ^^^ c)) + 4 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 2 * ~~~(b ||| ~~~c) - 1 * (a ^^^ c) + 1 * ~~~(b &&& c) + 3 * (c &&& ~~~(a &&& b)) - 3 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) - 1 * (a ^^^ (b &&& c)) - 6 * ~~~(a ||| c) - 1 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) - 11 * (b ^^^ ( ~~~a &&& (b ||| c))) + 1 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 2 * ((a &&& b) ^^^ (b ||| ~~~c)) - 7 * (a ||| ~~~c) - 3 * (c &&& (a ^^^ b)) + 11 * ~~~(a &&& c) - 2 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) + 2 * (c ||| ~~~(a ||| ~~~b)) - 13 * ~~~(a ||| (b ||| c)) - 5 * ~~~(a ||| ( ~~~b ||| c)) - 9 * ~~~( ~~~a ||| (b ||| c)) + 27 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 36 * ( ~~~a &&& ( ~~~b &&& c)) + 6 * ( ~~~a &&& (b &&& c)) - 5 * (a &&& ( ~~~b &&& c)) + 8 * (a &&& (b &&& c)) = 2 * (c ^^^ (a &&& (b ||| c))) + 11 * (b ^^^ ( ~~~a ||| (b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1910 (x y : BitVec w) : +theorem e_1910 : 7 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) - 6 * (a ||| b) + 1 * ( ~~~a &&& (b ^^^ c)) + 2 * (b &&& ~~~c) - 7 * ~~~( ~~~a &&& (b ^^^ c)) - 1 * (b ^^^ (a ||| ~~~c)) + 4 * (b ^^^ (a &&& c)) + 2 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 6 * ~~~(a ^^^ (b ^^^ c)) - 1 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) + 11 * (b ^^^ (a &&& (b ||| c))) - 3 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) - 6 * ~~~(a ||| b) - 2 * (c ^^^ (a ||| (b &&& c))) - 11 * ( ~~~(a ||| b) ||| (b ^^^ c)) + 7 * (b ^^^ ( ~~~a &&& (b ^^^ c))) + 2 * (a &&& (b ^^^ c)) - 3 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) - 5 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 6 * ((a &&& b) ^^^ (b ||| ~~~c)) + 11 * (c ^^^ (a &&& (b ||| c))) - 2 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 3 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) + 1 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) - 1 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) + 7 * (b ^^^ (a &&& (b ^^^ c))) + 1 * (b ||| (a ^^^ c)) - 7 * ( ~~~b &&& ~~~(a ^^^ c)) + 4 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 5 * (b ^^^ (a ||| (b ||| c))) + 3 * (a ^^^ c) - 11 * (a &&& ~~~b) + 7 * (b ||| ~~~(a ^^^ c)) + 1 * (b ^^^ (a ||| c)) + 2 * ( ~~~a ||| (b ^^^ c)) - 1 * ~~~( ~~~a &&& (b &&& c)) + 5 * ((a ^^^ b) &&& ~~~(a ^^^ c)) - 2 * ( ~~~a ||| ( ~~~b &&& c)) + 3 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) + 1 * ~~~b - 1 * (a &&& b) - 5 * (a ||| (b ||| c)) + 35 * ~~~(a ||| (b ||| c)) - 17 * ~~~(a ||| ( ~~~b ||| c)) + 18 * ~~~( ~~~a ||| (b ||| c)) - 2 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 2 * ( ~~~a &&& ( ~~~b &&& c)) - 31 * ( ~~~a &&& (b &&& c)) + 8 * (a &&& ( ~~~b &&& c)) - 11 * (a &&& (b &&& c)) = - 4 * (a ||| (b &&& c)) - 3 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1911 (x y : BitVec w) : +theorem e_1911 : - 6 * (a &&& c) - 1 * (a ||| (b &&& c)) - 6 * (b ^^^ (a ||| c)) - 5 * ( ~~~a ||| ( ~~~b &&& c)) - 11 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 2 * ~~~(a ||| b) - 1 * ((a &&& ~~~b) ||| (b ^^^ c)) - 6 * ((a &&& b) ^^^ (b ||| c)) + 1 * (b ^^^ ~~~(a &&& (b ||| c))) - 2 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) + 3 * ~~~(a ^^^ b) - 2 * ( ~~~b &&& (a ^^^ c)) - 2 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) - 11 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 11 * (c ^^^ (a &&& b)) - 1 * ~~~(a ||| ( ~~~b &&& c)) + 11 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) - 5 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) - 6 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) - 5 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) - 1 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) + 1 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 5 * (c ^^^ (a &&& ( ~~~b ||| c))) + 1 * ~~~(a ^^^ (b ||| c)) - 3 * ((a &&& b) ||| ~~~(b ||| c)) - 7 * ( ~~~a ||| (b &&& c)) + 2 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 1 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) - 1 * (b ^^^ ~~~(a ||| ~~~c)) + 2 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) - 5 * (b ^^^ c) - 2 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) - 1 * (b ^^^ (a &&& c)) - 11 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) - 7 * (a ^^^ (b ||| c)) + 1 * ~~~(a ||| (b ^^^ c)) + 3 * ~~~(a ||| ~~~b) + 3 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) - 1 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) + 2 * ~~~(b &&& c) + 5 * ~~~(a ^^^ (b ^^^ c)) - 2 * (b ^^^ ~~~(a ||| (b &&& c))) + 2 * (c &&& (a ||| b)) + 9 * ~~~(a ||| (b ||| c)) + 67 * ~~~(a ||| ( ~~~b ||| c)) + 42 * ~~~( ~~~a ||| (b ||| c)) + 24 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 70 * ( ~~~a &&& ( ~~~b &&& c)) + 71 * ( ~~~a &&& (b &&& c)) + 48 * (a &&& ( ~~~b &&& c)) = - 40 * (a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1912 (x y : BitVec w) : +theorem e_1912 : 1 * (c ^^^ (a ||| (b &&& c))) + 11 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 2 * (a ||| ( ~~~b &&& c)) - 1 * (b ^^^ (a &&& ~~~c)) + 2 * (b &&& (a ^^^ c)) - 1 * (b ^^^ ( ~~~a &&& (b ^^^ c))) + 1 * ((a &&& b) ||| (b ^^^ c)) + 2 * (c &&& ~~~(a &&& ~~~b)) - 6 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) - 2 * (a ||| ( ~~~b ||| c)) - 5 * (c &&& (a ^^^ b)) - 1 * ( ~~~a ||| (b ^^^ c)) + 5 * (c ||| (a &&& ~~~b)) - 2 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) - 7 * ~~~(a ^^^ (b &&& c)) - 2 * (b ||| (a &&& c)) + 1 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) - 6 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) - 1 * (b ^^^ (a &&& (b ^^^ c))) + 3 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 2 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) - 6 * (c ||| ~~~(a ||| ~~~b)) - 2 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) - 6 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) - 1 * (b ||| c) + 2 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) - 11 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) + 2 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) + 4 * (b ||| ~~~(a ^^^ c)) + 2 * ~~~(b ^^^ c) - 3 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 6 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 1 * (c &&& ~~~(a &&& b)) - 2 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) - 3 * ~~~( ~~~a &&& ( ~~~b &&& c)) + 5 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) + 2 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) - 1 * (b ^^^ c) + 1 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 5 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) + 1 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 2 * ~~~(b &&& c) + 24 * ~~~(a ||| (b ||| c)) + 8 * ~~~(a ||| ( ~~~b ||| c)) + 14 * ~~~( ~~~a ||| (b ||| c)) + 29 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 22 * ( ~~~a &&& ( ~~~b &&& c)) + 34 * ( ~~~a &&& (b &&& c)) + 17 * (a &&& ( ~~~b &&& c)) + 20 * (a &&& (b &&& c)) = 7 * ( ~~~c &&& ~~~(a ^^^ b)) + 3 * ((a ^^^ b) &&& (a ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1913 (x y : BitVec w) : +theorem e_1913 : 5 * ( ~~~a ||| ( ~~~b ||| c)) - 1 * ( ~~~a &&& ( ~~~b ||| c)) + 1 * ~~~b - 5 * (b ||| (a &&& c)) + 2 * ((a &&& c) ||| (b &&& ~~~c)) + 11 * ~~~a - 1 * (b ^^^ (a ||| ~~~c)) + 5 * ~~~( ~~~a ||| (b &&& c)) - 1 * (c ||| (a ^^^ b)) + 5 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) - 11 * ( ~~~b &&& ~~~(a ^^^ c)) - 1 * ((a &&& b) ||| ~~~(b ||| ~~~c)) + 11 * (b ||| ~~~(a ||| c)) - 2 * ( ~~~c &&& (a ^^^ b)) - 5 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 1 * (a ^^^ ( ~~~b ||| c)) - 5 * (b ^^^ ~~~(a &&& (b ||| c))) + 3 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) - 2 * ((a ^^^ b) ||| ~~~(a ^^^ c)) + 7 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) + 4 * ~~~(a ||| ~~~c) + 1 * (c &&& (a ||| ~~~b)) + 7 * (a &&& (b ^^^ c)) - 6 * (b ||| ~~~(a ||| ~~~c)) + 11 * ((a ^^^ b) ||| (a ^^^ c)) + 2 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) - 1 * ~~~(a ||| ~~~b) - 1 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) + 2 * ~~~( ~~~a &&& (b ^^^ c)) + 3 * ( ~~~b &&& (a ^^^ c)) + 2 * (c ^^^ ~~~(a &&& (b &&& c))) - 3 * (b ^^^ ( ~~~a ||| (b ^^^ c))) + 1 * ~~~(a ^^^ (b ^^^ c)) + 1 * (c &&& ~~~(a &&& b)) - 2 * (b ||| ~~~(a ^^^ c)) + 7 * (c ^^^ ( ~~~a &&& (b ||| c))) + 11 * ( ~~~c ||| ~~~(a ^^^ b)) + 3 * (a ^^^ ( ~~~b &&& c)) + 1 * b - 3 * ((a &&& b) ||| ~~~(b ||| c)) + 2 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 7 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) - 21 * ~~~(a ||| (b ||| c)) - 48 * ~~~(a ||| ( ~~~b ||| c)) - 25 * ~~~( ~~~a ||| (b ||| c)) - 25 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 45 * ( ~~~a &&& ( ~~~b &&& c)) - 24 * ( ~~~a &&& (b &&& c)) - 13 * (a &&& ( ~~~b &&& c)) - 13 * (a &&& (b &&& c)) = 3 * (a ||| ~~~b) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1914 (x y : BitVec w) : +theorem e_1914 : - 6 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 1 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) - 2 * (a ||| b) - 1 * ~~~(b &&& ~~~c) - 6 * (c ^^^ (a &&& (b ||| c))) - 1 * (b ^^^ ~~~(a &&& c)) - 1 * (b ^^^ (a ||| ( ~~~b ||| c))) - 2 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 1 * ~~~(b ||| ~~~c) - 3 * (c ^^^ ( ~~~a ||| (b ||| c))) - 5 * (b ^^^ ~~~(a &&& (b &&& c))) - 11 * (b ^^^ ~~~(a ||| (b ^^^ c))) + 7 * ~~~(a ||| ~~~b) + 3 * (c ^^^ ~~~(a ||| b)) - 6 * (b ||| (a &&& ~~~c)) - 2 * ( ~~~(a &&& b) &&& (b ^^^ c)) + 5 * ~~~(a &&& ~~~c) + 4 * (b &&& ~~~(a ^^^ c)) + 2 * (b ||| c) + 1 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 3 * ( ~~~a &&& ( ~~~b ||| c)) + 3 * ~~~(a &&& c) + 11 * (c ^^^ (a &&& ( ~~~b ||| c))) + 1 * (c ^^^ ~~~(a &&& (b &&& c))) + 1 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) - 7 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) + 1 * (a ||| ~~~c) - 5 * (b &&& ~~~c) + 2 * (b ||| (a &&& c)) + 4 * (b ^^^ (a &&& ~~~c)) - 5 * ( ~~~a ||| (b ||| c)) - 7 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) - 7 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) - 3 * ((a &&& b) ||| (b ^^^ c)) + 4 * ( ~~~c &&& (a ^^^ b)) - 1 * ( ~~~c &&& ~~~(a ^^^ b)) - 2 * ~~~(b &&& c) + 2 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) - 1 * ~~~(a &&& (b ||| c)) + 11 * ~~~(a ^^^ c) + 1 * ~~~(a ^^^ b) - 6 * ~~~(a ^^^ (b ^^^ c)) + 20 * ~~~(a ||| (b ||| c)) - 2 * ~~~(a ||| ( ~~~b ||| c)) + 22 * ~~~( ~~~a ||| (b ||| c)) + 38 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 13 * ( ~~~a &&& ( ~~~b &&& c)) + 7 * ( ~~~a &&& (b &&& c)) + 14 * (a &&& ( ~~~b &&& c)) + 15 * (a &&& (b &&& c)) = 7 * (a &&& ~~~b) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1915 (x y : BitVec w) : +theorem e_1915 : - 2 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) - 2 * ~~~(a &&& (b ^^^ c)) + 4 * (a ^^^ ( ~~~b ||| c)) + 3 * ~~~(b &&& c) + 1 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) - 5 * (a ||| (b ||| c)) + 2 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) - 1 * ~~~a - 7 * ~~~(a ^^^ b) + 4 * (b ^^^ (a ||| ( ~~~b ||| c))) - 6 * (b ^^^ ( ~~~a &&& (b ^^^ c))) - 1 * (a ||| b) - 1 * ( ~~~(a &&& b) &&& (b ^^^ c)) - 3 * (c ^^^ ( ~~~a &&& (b ||| c))) - 1 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) - 5 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) + 4 * ~~~( ~~~a &&& ( ~~~b ||| c)) - 6 * a - 1 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 5 * (b ||| ~~~c) + 2 * (c ||| (a &&& b)) - 1 * ~~~(a ^^^ c) - 11 * (a &&& c) - 2 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 1 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) - 6 * (b &&& (a ||| ~~~c)) - 3 * ((a ^^^ b) &&& ~~~(a ^^^ c)) - 7 * ~~~(a ||| ( ~~~b &&& c)) + 11 * ~~~(a ||| ~~~c) + 4 * (b &&& ~~~(a ^^^ c)) + 1 * (c ||| ~~~(a ||| ~~~b)) - 1 * ~~~( ~~~a &&& (b ^^^ c)) + 1 * (c &&& (a ||| ~~~b)) - 3 * (a ||| ~~~c) - 1 * (c &&& ~~~(a ^^^ b)) + 11 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) + 2 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) - 1 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) + 4 * ( ~~~c &&& ~~~(a ^^^ b)) + 2 * ~~~(a &&& (b &&& c)) + 7 * (c ^^^ ( ~~~a ||| (b ||| c))) - 5 * (c ^^^ (a ||| (b &&& c))) - 7 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) - 11 * ( ~~~b ||| (a ^^^ c)) + 18 * ~~~(a ||| (b ||| c)) + 23 * ~~~( ~~~a ||| (b ||| c)) + 27 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 3 * ( ~~~a &&& ( ~~~b &&& c)) + 8 * ( ~~~a &&& (b &&& c)) + 39 * (a &&& (b &&& c)) = - 35 * (a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1916 (x y : BitVec w) : +theorem e_1916 : 7 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) - 5 * (b ^^^ (a ||| (b &&& c))) + 1 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 6 * (b &&& ~~~(a &&& c)) - 7 * (b ^^^ ( ~~~a &&& (b ^^^ c))) - 5 * ~~~(a ^^^ c) + 1 * (b ^^^ ( ~~~a &&& (b ||| c))) - 3 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) + 1 * (c ^^^ ~~~(a ||| b)) - 6 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) - 1 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) + 2 * ~~~( ~~~a &&& (b &&& c)) + 11 * (b ^^^ (a ||| ~~~c)) + 3 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 3 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) + 5 * (c ^^^ ~~~(a &&& b)) - 1 * (c &&& (a ||| b)) + 4 * (a &&& b) + 5 * ( ~~~c ||| ~~~(a ^^^ b)) - 1 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) + 1 * ( ~~~a ||| ( ~~~b ||| c)) + 1 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 1 * (a ||| b) - 2 * ~~~(a &&& ( ~~~b ||| c)) - 3 * ((a &&& ~~~b) ||| (b ^^^ c)) + 3 * b + 1 * (a ^^^ (b ||| c)) - 5 * ~~~(b ^^^ c) - 5 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 5 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) + 7 * (b ^^^ (a ||| ( ~~~b &&& c))) + 1 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 2 * (b ^^^ ~~~(a ||| ~~~c)) - 1 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) - 5 * ~~~a - 2 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 11 * (a ||| ~~~b) - 1 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) + 5 * ~~~(a &&& c) + 3 * ~~~(a ||| c) - 11 * ~~~( ~~~a ||| (b &&& c)) - 1 * (b ||| ~~~c) + 1 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) - 32 * ~~~(a ||| (b ||| c)) - 13 * ~~~(a ||| ( ~~~b ||| c)) - 23 * ~~~( ~~~a ||| (b ||| c)) + 7 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 19 * ( ~~~a &&& ( ~~~b &&& c)) + 1 * ( ~~~a &&& (b &&& c)) - 10 * (a &&& ( ~~~b &&& c)) - 19 * (a &&& (b &&& c)) = - 4 * (b ^^^ (a &&& (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1917 (x y : BitVec w) : +theorem e_1917 : 7 * ~~~(a ||| (b ^^^ c)) + 4 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) - 3 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) - 6 * (b ^^^ (a &&& ~~~c)) - 6 * ((a ||| b) &&& (b ^^^ c)) + 2 * (b &&& ~~~(a &&& ~~~c)) - 6 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) - 6 * (b &&& ~~~(a &&& c)) + 4 * (b ^^^ (a &&& (b ||| c))) - 6 * (c &&& (a ^^^ b)) + 1 * (b ||| ~~~(a ||| c)) + 4 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 1 * ~~~(a &&& ( ~~~b &&& c)) + 5 * ( ~~~b ||| (a ^^^ c)) - 3 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 11 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) + 1 * (a &&& ( ~~~b ||| c)) + 1 * ~~~( ~~~a &&& (b ||| c)) - 1 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 1 * ~~~(a ^^^ ( ~~~b ||| c)) - 1 * ((a &&& c) ||| (b &&& ~~~c)) + 2 * (c ^^^ (a &&& ~~~b)) + 4 * (b ||| ~~~(a ^^^ c)) - 7 * (b ^^^ (a ||| ~~~c)) + 7 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) - 1 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 7 * ( ~~~c ||| ~~~(a ^^^ b)) + 3 * (c ^^^ ~~~(a &&& ~~~b)) + 1 * ( ~~~c &&& (a ^^^ b)) - 11 * ~~~(a ^^^ (b ||| c)) - 1 * (b ||| ~~~(a ||| ~~~c)) - 2 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) - 11 * ((a &&& b) ^^^ (b ||| ~~~c)) + 11 * (b ^^^ ~~~(a &&& (b &&& c))) + 5 * ((a &&& b) ||| ~~~(b ||| c)) + 2 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) + 11 * (c ^^^ (a &&& ( ~~~b ||| c))) + 1 * (c ||| ~~~(a ||| ~~~b)) + 4 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 5 * ~~~(a ||| ~~~c) - 7 * (b ^^^ ~~~(a ||| ~~~c)) + 5 * (b ||| (a ^^^ c)) + 1 * (b ^^^ ( ~~~a &&& (b ^^^ c))) - 7 * ~~~( ~~~a ||| ( ~~~b &&& c)) + 2 * ~~~(a ||| ( ~~~b ||| c)) - 42 * ~~~( ~~~a ||| (b ||| c)) + 9 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 44 * ( ~~~a &&& ( ~~~b &&& c)) - 10 * ( ~~~a &&& (b &&& c)) - 8 * (a &&& ( ~~~b &&& c)) - 28 * (a &&& (b &&& c)) = 11 * ~~~(a ||| (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1918 (x y : BitVec w) : +theorem e_1918 : - 11 * ~~~(a &&& (b ^^^ c)) - 1 * ((a &&& c) ||| ~~~(b ||| c)) - 11 * (c &&& (a ^^^ b)) - 1 * (a ||| ~~~b) - 5 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) + 1 * (b ^^^ ~~~(a &&& (b &&& c))) + 1 * (c &&& ~~~(a &&& b)) + 2 * (c ||| (a ^^^ b)) + 1 * ( ~~~c ||| ~~~(a ^^^ b)) + 7 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) - 2 * (b ^^^ ~~~(a ||| ~~~c)) + 2 * ( ~~~a ||| (b ||| c)) + 2 * (c &&& (a ||| b)) + 11 * ( ~~~a ||| ( ~~~b &&& c)) + 5 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) - 3 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) + 1 * ((a &&& c) ||| (b &&& ~~~c)) - 2 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) + 1 * (a &&& (b ||| c)) - 7 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) + 11 * ~~~( ~~~a &&& (b ||| c)) + 2 * (c ^^^ ~~~(a ||| ~~~b)) - 6 * (c ^^^ (a ||| (b &&& c))) - 1 * (b ^^^ ~~~(a ||| (b ^^^ c))) + 2 * (c ||| ~~~(a ||| b)) - 6 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) + 2 * (b ^^^ ( ~~~a &&& (b ^^^ c))) + 7 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 5 * (b ^^^ ~~~(a &&& ~~~c)) - 2 * ((a ||| ~~~b) &&& (b ^^^ c)) - 6 * ( ~~~a &&& ( ~~~b ||| c)) + 5 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) + 4 * ~~~(a ||| (b ^^^ c)) + 4 * (a ^^^ (b ^^^ c)) + 2 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) - 11 * ~~~(a ^^^ (b ||| c)) + 5 * ( ~~~a &&& (b ^^^ c)) - 1 * b - 2 * (a &&& c) - 1 * ~~~(a &&& c) + 2 * ((a ||| b) &&& ~~~(b ^^^ c)) + 2 * (b ^^^ (a &&& ~~~c)) + 7 * (a &&& ( ~~~b ||| c)) - 1 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) - 5 * ~~~(a ||| (b ||| c)) - 18 * ~~~( ~~~a ||| (b ||| c)) + 10 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 10 * ( ~~~a &&& ( ~~~b &&& c)) - 4 * ( ~~~a &&& (b &&& c)) - 4 * (a &&& ( ~~~b &&& c)) - 14 * (a &&& (b &&& c)) = - 2 * ~~~b := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1919 (x y : BitVec w) : +theorem e_1919 : 3 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 1 * ((a &&& b) ||| ~~~(b ||| c)) - 7 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 5 * ~~~(a &&& (b ||| c)) - 3 * (c ||| ~~~(a ^^^ b)) + 1 * ((a &&& b) ^^^ (b ||| ~~~c)) + 1 * (b ^^^ ~~~(a &&& (b ||| c))) + 2 * ~~~( ~~~a &&& ( ~~~b &&& c)) - 5 * (c ^^^ (a &&& ( ~~~b ||| c))) - 5 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) + 2 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) - 1 * ~~~(a ^^^ ( ~~~b ||| c)) - 11 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) + 5 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 2 * ~~~c - 11 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) - 1 * (c &&& ~~~(a &&& b)) - 5 * (c ^^^ (a ||| ( ~~~b &&& c))) + 7 * (b ||| ~~~(a ||| ~~~c)) + 2 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) - 1 * ( ~~~a ||| (b ||| c)) - 3 * b + 1 * ~~~(a ^^^ c) + 1 * (a ||| c) + 3 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) + 2 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) + 4 * (c ||| (a &&& b)) + 3 * (c &&& (a ||| ~~~b)) + 2 * (b ^^^ ~~~(a ||| c)) - 6 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) + 1 * (a &&& (b ||| c)) + 7 * (b ^^^ ( ~~~a ||| (b ||| c))) + 2 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) + 2 * (c ^^^ (a &&& b)) - 11 * (b ^^^ (a ||| (b ^^^ c))) + 4 * (b ^^^ (a ||| ( ~~~b ||| c))) + 3 * ~~~(b ||| c) + 4 * ( ~~~a ||| ( ~~~b &&& c)) - 7 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 3 * (a &&& (b ^^^ c)) - 1 * (b &&& (a ||| c)) - 11 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 3 * (c &&& ~~~(a &&& ~~~b)) + 15 * ~~~(a ||| (b ||| c)) + 6 * ~~~(a ||| ( ~~~b ||| c)) + 26 * ~~~( ~~~a ||| (b ||| c)) + 6 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 26 * ( ~~~a &&& ( ~~~b &&& c)) + 4 * ( ~~~a &&& (b &&& c)) - 7 * (a &&& ( ~~~b &&& c)) + 13 * (a &&& (b &&& c)) = - 1 * ( ~~~b &&& ~~~(a ^^^ c)) + 1 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1920 (x y : BitVec w) : +theorem e_1920 : - 11 * ~~~(a &&& b) + 2 * (c &&& ~~~(a &&& b)) - 11 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) - 5 * (a ^^^ c) - 2 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) - 5 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) + 1 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) - 2 * (a &&& b) + 7 * (b ||| c) + 2 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 11 * (a ||| (b ||| c)) + 2 * ( ~~~a &&& ( ~~~b ||| c)) - 2 * ((a &&& b) ||| ~~~(b ^^^ c)) - 2 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 5 * (b &&& (a ||| c)) - 5 * ((a &&& b) ||| ~~~(b ||| ~~~c)) + 7 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) - 2 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) + 2 * (a &&& ~~~b) - 1 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 1 * a + 11 * ~~~(a ||| b) + 2 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 7 * ~~~(a ^^^ (b ||| c)) - 1 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 3 * (a ^^^ ( ~~~b ||| c)) + 4 * ( ~~~c ||| (a ^^^ b)) - 2 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) + 1 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 6 * (a ||| c) + 7 * ( ~~~c ||| ~~~(a ^^^ b)) + 3 * (a &&& ( ~~~b ||| c)) + 11 * (b &&& (a ^^^ c)) - 5 * (a ||| ( ~~~b ||| c)) - 6 * (a &&& (b ^^^ c)) + 3 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) + 1 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) - 1 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) + 1 * (c ||| ~~~(a ^^^ b)) - 1 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) + 5 * ~~~( ~~~a &&& (b ^^^ c)) - 2 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) + 11 * ~~~(a ^^^ ( ~~~b ||| c)) - 17 * ~~~(a ||| (b ||| c)) - 6 * ~~~(a ||| ( ~~~b ||| c)) + 13 * ~~~( ~~~a ||| (b ||| c)) - 3 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 13 * ( ~~~a &&& ( ~~~b &&& c)) - 9 * ( ~~~a &&& (b &&& c)) - 31 * (a &&& ( ~~~b &&& c)) - 23 * (a &&& (b &&& c)) = 3 * (c ^^^ (a ||| (b ||| c))) + 7 * (c ^^^ ~~~(a &&& (b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1921 (x y : BitVec w) : +theorem e_1921 : - 2 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) - 5 * ~~~(b &&& ~~~c) - 1 * ( ~~~b &&& (a ^^^ c)) + 11 * (b &&& ~~~c) - 6 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) - 6 * (c ||| (a &&& b)) + 4 * (a ||| (b ||| c)) + 11 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 7 * (c &&& (a ||| ~~~b)) + 2 * ~~~( ~~~a &&& ( ~~~b &&& c)) - 1 * (b ||| c) + 2 * (a ^^^ (b ^^^ c)) + 1 * ~~~(a ||| c) - 2 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) + 7 * ~~~(a &&& ( ~~~b ||| c)) + 11 * ( ~~~b &&& ~~~(a ^^^ c)) - 1 * ((a ^^^ b) ||| ~~~(a ^^^ c)) + 2 * (a &&& ( ~~~b ||| c)) + 3 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) + 1 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) + 4 * ( ~~~a &&& (b ^^^ c)) + 1 * ((b &&& c) ||| (a &&& (b ||| c))) - 3 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) - 7 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) + 7 * (c &&& (a ^^^ b)) - 7 * ( ~~~(a ||| b) ||| (b ^^^ c)) - 5 * (b &&& ~~~(a ^^^ c)) - 6 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 3 * ((a &&& b) ^^^ (b ||| ~~~c)) + 11 * (c ||| ~~~(a ^^^ b)) - 11 * ~~~(a ^^^ (b &&& c)) + 3 * (c ^^^ (a ||| ( ~~~b ||| c))) + 7 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 2 * ~~~(a ^^^ ( ~~~b ||| c)) - 1 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 5 * (b ^^^ ~~~(a &&& (b ^^^ c))) - 1 * (c ^^^ (a ||| ( ~~~b &&& c))) - 1 * (a &&& ~~~c) + 1 * (a ^^^ b) + 1 * ((a &&& c) ||| ~~~(b ||| c)) + 2 * (c ^^^ ~~~(a ||| b)) - 2 * (b ||| ~~~(a ||| c)) - 2 * ~~~(a &&& ~~~c) - 2 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 20 * ~~~(a ||| (b ||| c)) - 6 * ~~~( ~~~a ||| (b ||| c)) - 34 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 11 * ( ~~~a &&& ( ~~~b &&& c)) - 9 * ( ~~~a &&& (b &&& c)) + 2 * (a &&& ( ~~~b &&& c)) + 20 * (a &&& (b &&& c)) = - 3 * (b ^^^ ( ~~~a ||| (b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1922 (x y : BitVec w) : +theorem e_1922 : - 1 * (b ^^^ ~~~(a ||| (b ^^^ c))) - 2 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) - 6 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) + 2 * (c ^^^ ( ~~~a ||| (b ||| c))) + 3 * (a ||| (b &&& c)) - 2 * ( ~~~b &&& (a ^^^ c)) + 7 * ~~~( ~~~a ||| ( ~~~b &&& c)) - 3 * ~~~(a ||| ~~~c) - 6 * (c ^^^ ~~~(a ||| b)) + 1 * (b ^^^ (a &&& ~~~c)) + 2 * (b ^^^ ~~~(a &&& (b ||| c))) - 1 * ~~~(a &&& c) - 11 * (a ||| c) + 7 * (b ||| ~~~c) + 1 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) + 5 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) + 2 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) - 6 * ~~~(a ^^^ (b &&& c)) + 5 * ~~~( ~~~a &&& ( ~~~b ||| c)) - 7 * (c ||| (a &&& ~~~b)) - 2 * (c ^^^ ( ~~~a &&& (b ||| c))) - 11 * (b ^^^ (a ||| ( ~~~b &&& c))) - 3 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 1 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 11 * (a &&& (b ^^^ c)) - 2 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) - 1 * ~~~(a &&& ~~~a) - 2 * (b ^^^ (a ||| (b ||| c))) + 11 * (c &&& (a ||| ~~~b)) + 3 * (a ^^^ (b ^^^ c)) - 1 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) + 1 * ( ~~~c &&& (a ^^^ b)) - 7 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) - 5 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 1 * ( ~~~b &&& ~~~(a ^^^ c)) - 1 * ~~~(a &&& b) + 7 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) + 1 * (b &&& ~~~(a &&& ~~~c)) - 2 * (a ||| ( ~~~b ||| c)) + 1 * (b ^^^ (a &&& c)) - 5 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 1 * ~~~(a &&& (b ||| c)) - 5 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 12 * ~~~(a ||| (b ||| c)) - 7 * ~~~(a ||| ( ~~~b ||| c)) + 23 * ~~~( ~~~a ||| (b ||| c)) - 2 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 29 * ( ~~~a &&& ( ~~~b &&& c)) + 30 * ( ~~~a &&& (b &&& c)) + 41 * (a &&& ( ~~~b &&& c)) - 4 * (a &&& (b &&& c)) = - 7 * ~~~(b &&& c) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1923 (x y : BitVec w) : +theorem e_1923 : - 7 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) + 1 * ((a &&& b) ^^^ (b ||| c)) + 1 * (b ^^^ (a ||| ( ~~~b &&& c))) + 2 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) + 1 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) - 6 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) - 5 * ~~~(a ||| ~~~c) - 11 * (c &&& ~~~(a &&& b)) - 2 * (a &&& (b ^^^ c)) - 6 * ((a &&& b) ||| (b ^^^ c)) + 1 * (c ^^^ ( ~~~a &&& (b ||| c))) - 2 * (a &&& ( ~~~b ||| c)) - 7 * (b ||| (a ^^^ c)) - 6 * (a &&& b) + 7 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) - 1 * (a ||| ( ~~~b &&& c)) + 5 * (c ^^^ (a ||| ( ~~~b ||| c))) - 1 * (a ^^^ (b ^^^ c)) + 2 * (b ^^^ (a &&& c)) - 3 * (b ^^^ ~~~(a ||| (b ^^^ c))) + 1 * (b ^^^ (a ||| (b ||| c))) + 11 * (c ^^^ ~~~(a ||| ~~~b)) - 2 * b + 11 * ((a &&& b) ||| ~~~(b ||| c)) + 2 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) - 1 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) - 3 * (b ||| ~~~(a ^^^ c)) + 3 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) - 1 * (c &&& ~~~(a ^^^ b)) + 1 * ~~~(a &&& ~~~c) - 3 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) + 5 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) + 1 * ( ~~~a ||| (b &&& c)) + 1 * (a &&& ~~~b) - 5 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) - 1 * (c &&& ~~~(a &&& ~~~b)) - 5 * ( ~~~b ||| ~~~(a ^^^ c)) + 3 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 4 * ~~~(a ^^^ c) - 11 * (b ^^^ ( ~~~a ||| (b &&& c))) - 2 * (b ^^^ (a ||| (b &&& c))) + 7 * ~~~c + 4 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 7 * (c ||| (a &&& ~~~b)) + 3 * ~~~(a ||| (b ||| c)) - 15 * ~~~(a ||| ( ~~~b ||| c)) - 11 * ~~~( ~~~a ||| (b ||| c)) + 21 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 17 * ( ~~~a &&& ( ~~~b &&& c)) + 9 * ( ~~~a &&& (b &&& c)) - 4 * (a &&& ( ~~~b &&& c)) = 1 * ( ~~~c ||| ~~~(a ^^^ b)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1924 (x y : BitVec w) : +theorem e_1924 : - 3 * ((a &&& b) ||| (b ^^^ c)) + 3 * ~~~( ~~~a ||| (b &&& c)) - 6 * (a ||| ( ~~~b ||| c)) + 1 * (a ||| (b ^^^ c)) + 2 * (a &&& ~~~b) + 1 * ~~~(b &&& c) + 11 * (a &&& ( ~~~b ||| c)) - 7 * ~~~( ~~~a &&& (b ||| c)) - 7 * (a ^^^ (b &&& c)) + 3 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) + 4 * ((a &&& ~~~b) ||| (b ^^^ c)) + 11 * ~~~(a ||| c) - 1 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) + 1 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) - 1 * ~~~(a ||| ( ~~~b &&& c)) - 7 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 11 * (b &&& (a ||| ~~~c)) + 5 * (b ^^^ (a &&& (b ||| c))) - 1 * (a ||| ~~~c) - 3 * ( ~~~a ||| (b &&& c)) - 11 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) + 1 * ( ~~~b &&& (a ^^^ c)) + 11 * ((a &&& b) ||| ~~~(b ^^^ c)) + 4 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) - 2 * ~~~(a ^^^ b) - 5 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) - 1 * ((a ||| ~~~b) &&& (b ^^^ c)) - 2 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 7 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 5 * ( ~~~a &&& ( ~~~b ||| c)) + 1 * (b &&& (a ||| c)) - 5 * (b ^^^ ( ~~~a ||| (b &&& c))) - 2 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) + 1 * (b ^^^ (a &&& ( ~~~b ||| c))) - 1 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 4 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 1 * (b ^^^ ~~~(a &&& (b ^^^ c))) + 2 * ( ~~~a ||| ( ~~~b ||| c)) + 1 * ((a &&& c) ||| (b &&& ~~~c)) + 2 * ((a ^^^ b) ||| (a ^^^ c)) - 3 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 2 * (b ^^^ (a &&& ~~~c)) - 5 * ((a ||| b) &&& (b ^^^ c)) - 1 * ~~~(a &&& (b ^^^ c)) + 27 * ~~~(a ||| (b ||| c)) - 5 * ~~~( ~~~a ||| (b ||| c)) + 9 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 8 * ( ~~~a &&& ( ~~~b &&& c)) + 17 * ( ~~~a &&& (b &&& c)) - 4 * (a &&& ( ~~~b &&& c)) + 11 * (a &&& (b &&& c)) = 11 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) - 11 * ~~~(a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1925 (x y : BitVec w) : +theorem e_1925 : 7 * (c ^^^ ~~~(a &&& ~~~b)) + 1 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 3 * ((b &&& c) ||| (a &&& (b ||| c))) + 1 * ( ~~~b ||| (a ^^^ c)) - 1 * ~~~(a ^^^ ( ~~~b ||| c)) - 3 * (c ||| ~~~(a ||| ~~~b)) + 1 * ( ~~~a ||| ( ~~~b &&& c)) - 7 * ~~~( ~~~a &&& ( ~~~b ||| c)) - 6 * ~~~( ~~~a ||| ( ~~~b &&& c)) + 4 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 1 * (c ^^^ ( ~~~a ||| (b ||| c))) + 11 * ( ~~~c ||| ~~~(a ^^^ b)) - 1 * (c ||| (a &&& b)) + 11 * (b ^^^ ~~~(a &&& (b ^^^ c))) - 7 * (a ||| (b ||| c)) + 4 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 11 * (b &&& c) + 1 * (a &&& ( ~~~b ||| c)) + 5 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) + 2 * ((a &&& c) ^^^ (b ||| c)) + 7 * ~~~(a &&& b) + 2 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) + 7 * ((a &&& c) ||| ~~~(b ||| c)) - 5 * ( ~~~a ||| ( ~~~b ||| c)) + 3 * (b ^^^ ~~~(a &&& (b ||| c))) + 7 * b - 6 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) - 6 * ((a &&& ~~~b) ||| (b ^^^ c)) - 1 * ( ~~~a &&& (b ^^^ c)) + 3 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) + 2 * (b ^^^ ~~~(a &&& (b &&& c))) + 3 * ~~~c + 1 * ( ~~~c &&& ~~~(a ^^^ b)) - 3 * ( ~~~a &&& ( ~~~b ||| c)) + 1 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 7 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) + 1 * (a ||| (b &&& c)) - 11 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 7 * (c ^^^ (a &&& b)) - 3 * (c ^^^ (a &&& ( ~~~b ||| c))) - 2 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) + 2 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) - 11 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 6 * (a &&& (b ^^^ c)) - 43 * ~~~(a ||| (b ||| c)) + 5 * ~~~(a ||| ( ~~~b ||| c)) + 8 * ~~~( ~~~a ||| (b ||| c)) - 17 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 19 * ( ~~~a &&& ( ~~~b &&& c)) + 6 * ( ~~~a &&& (b &&& c)) - 14 * (a &&& (b &&& c)) = 5 * (c ^^^ ( ~~~a &&& (b ||| c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1926 (x y : BitVec w) : +theorem e_1926 : - 3 * (a ^^^ (b ^^^ c)) + 11 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 5 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) - 3 * (c &&& (a ||| b)) - 1 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) + 1 * a - 11 * (c ^^^ ( ~~~a ||| (b ||| c))) - 1 * (b ||| (a &&& ~~~c)) + 2 * (a &&& ~~~c) + 3 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) - 1 * c + 11 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) - 3 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) - 11 * ( ~~~a ||| (b ^^^ c)) - 1 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) - 3 * (b &&& c) - 1 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) - 5 * ((a ||| b) &&& (b ^^^ c)) - 1 * (b ||| (a &&& c)) + 5 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) + 1 * ( ~~~a &&& (b ^^^ c)) + 2 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) - 2 * (c &&& ~~~(a &&& b)) + 4 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) - 6 * (a ||| (b &&& c)) - 3 * ((a &&& b) ^^^ (b ||| c)) + 1 * (a ||| c) + 4 * ((a ^^^ b) ||| ~~~(a ^^^ c)) - 2 * (b ^^^ ~~~(a &&& (b &&& c))) - 11 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) + 1 * (c ^^^ ~~~(a &&& (b &&& c))) + 7 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) - 1 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 1 * (b ^^^ (a &&& (b ||| c))) + 7 * (b ^^^ (a ||| c)) - 11 * (b ^^^ ~~~(a &&& (b ^^^ c))) - 1 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) - 5 * (c ||| ~~~(a ||| ~~~b)) + 2 * (a ^^^ ( ~~~b &&& c)) + 5 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) - 2 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) + 1 * ~~~(a &&& ( ~~~b ||| c)) + 2 * ~~~( ~~~a ||| (b &&& c)) - 6 * (c ^^^ ~~~(a &&& (b ||| c))) + 21 * ~~~(a ||| (b ||| c)) + 28 * ~~~(a ||| ( ~~~b ||| c)) - 2 * ~~~( ~~~a ||| (b ||| c)) + 5 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 6 * ( ~~~a &&& ( ~~~b &&& c)) + 15 * ( ~~~a &&& (b &&& c)) + 9 * (a &&& (b &&& c)) = - 13 * (a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1927 (x y : BitVec w) : +theorem e_1927 : - 11 * ~~~(a &&& (b &&& c)) - 7 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) + 4 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) + 2 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 11 * (c ^^^ ~~~(a ||| ~~~b)) + 2 * (b ^^^ c) + 3 * ~~~(b &&& c) - 1 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) + 1 * ~~~(a ||| b) - 2 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) + 4 * ~~~(a ^^^ (b ^^^ c)) - 7 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) + 11 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) + 5 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) + 1 * ~~~(b ^^^ c) + 11 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 1 * (a &&& ( ~~~b ||| c)) - 5 * ~~~(a &&& b) + 4 * (a ||| (b &&& c)) - 5 * ~~~c - 2 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) - 2 * (b &&& (a ||| ~~~c)) + 7 * ( ~~~a ||| ( ~~~b ||| c)) + 1 * (b ||| c) + 11 * (b ^^^ ( ~~~a &&& (b ^^^ c))) + 1 * ~~~(b &&& ~~~c) - 2 * ~~~a + 2 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) - 11 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) - 6 * ( ~~~b ||| (a ^^^ c)) - 6 * (b &&& ~~~c) - 1 * (c ^^^ ( ~~~a ||| (b &&& c))) + 11 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) + 1 * (b ||| (a &&& ~~~c)) + 1 * (b &&& ~~~(a &&& ~~~c)) - 11 * ( ~~~a ||| (b ||| c)) - 1 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 1 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) + 7 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 1 * ~~~(a ||| ( ~~~b &&& c)) - 7 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 1 * ~~~(a ^^^ ( ~~~b &&& c)) + 1 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) - 1 * (b ^^^ (a ||| ( ~~~b ||| c))) + 12 * ~~~(a ||| (b ||| c)) - 4 * ~~~(a ||| ( ~~~b ||| c)) + 1 * ~~~( ~~~a ||| (b ||| c)) + 23 * ( ~~~a &&& ( ~~~b &&& c)) - 8 * ( ~~~a &&& (b &&& c)) - 11 * (a &&& ( ~~~b &&& c)) - 31 * (a &&& (b &&& c)) = - 35 * ~~~( ~~~a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1928 (x y : BitVec w) : +theorem e_1928 : - 1 * (a &&& ~~~c) + 1 * (a &&& (b ||| c)) + 1 * ~~~( ~~~a &&& (b &&& c)) - 11 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) + 1 * b + 7 * ( ~~~a ||| (b &&& c)) + 11 * ~~~(b ||| ~~~c) + 2 * (b ||| ~~~(a ||| c)) - 1 * ((a &&& c) ||| (b &&& ~~~c)) + 5 * ~~~(a ^^^ b) + 1 * (b ||| (a &&& c)) + 3 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 11 * (b ||| (a ^^^ c)) + 4 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) - 3 * ((a ^^^ b) &&& (a ^^^ c)) - 2 * ((a &&& b) ^^^ (b ||| ~~~c)) - 3 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) - 6 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 3 * (c ^^^ (a &&& b)) + 5 * ((a &&& b) ^^^ (b ||| c)) - 5 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) - 7 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) + 3 * (a &&& b) + 1 * ((a ^^^ b) ||| ~~~(a ^^^ c)) - 1 * ~~~(a ||| (b &&& c)) - 2 * (c ^^^ ~~~(a &&& (b &&& c))) - 1 * ((a ||| ~~~b) &&& (b ^^^ c)) - 1 * (b ^^^ ~~~(a &&& (b ||| c))) + 11 * ((a &&& b) ||| ~~~(b ||| ~~~c)) - 3 * (a ^^^ ( ~~~b &&& c)) - 6 * (b ||| c) + 3 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 2 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) + 3 * ~~~( ~~~a &&& ( ~~~b &&& c)) - 2 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) + 4 * (a &&& ( ~~~b ||| c)) - 1 * ((a &&& c) ^^^ (b ||| c)) - 11 * (b ^^^ (a &&& (b ^^^ c))) - 1 * (b &&& ~~~(a &&& c)) + 1 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) + 5 * (c ^^^ (a &&& ( ~~~b ||| c))) - 2 * (a ^^^ c) + 2 * (c ^^^ ~~~(a &&& (b ||| c))) - 22 * ~~~(a ||| (b ||| c)) + 19 * ~~~(a ||| ( ~~~b ||| c)) + 7 * ~~~( ~~~a ||| (b ||| c)) - 19 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 31 * ( ~~~a &&& ( ~~~b &&& c)) - 13 * ( ~~~a &&& (b &&& c)) - 11 * (a &&& ( ~~~b &&& c)) - 36 * (a &&& (b &&& c)) = - 11 * (b ^^^ ~~~(a ||| c)) + 3 * ~~~( ~~~a ||| ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1929 (x y : BitVec w) : +theorem e_1929 : 1 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) + 1 * ((a ^^^ b) &&& (a ^^^ c)) + 1 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) + 1 * ((a &&& ~~~b) ||| (b ^^^ c)) - 1 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) - 11 * ( ~~~c &&& ~~~(a ^^^ b)) - 2 * (c ^^^ ( ~~~a &&& (b ||| c))) + 1 * (c ^^^ (a ||| ( ~~~b ||| c))) - 1 * (a &&& ( ~~~b ||| c)) + 1 * ((a &&& b) ||| (b ^^^ c)) - 1 * (c ^^^ (a ||| b)) - 5 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) + 5 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) - 3 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 1 * (c ||| (a &&& b)) - 6 * (a ^^^ (b ||| c)) + 5 * (c &&& (a ^^^ b)) - 6 * (c ||| (a &&& ~~~b)) + 4 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) - 5 * ((a &&& b) ^^^ (b ||| ~~~c)) - 1 * (a ^^^ b) - 2 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 2 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) + 4 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 5 * ~~~(a &&& ~~~a) - 11 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) - 1 * (b ^^^ ~~~(a &&& (b ^^^ c))) - 3 * (c ^^^ (a ||| (b ||| c))) + 2 * (c ^^^ (a &&& (b ||| c))) - 5 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) - 11 * (b ^^^ ( ~~~a &&& (b ^^^ c))) - 3 * ( ~~~b ||| (a ^^^ c)) - 1 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 2 * (b ^^^ c) + 4 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) + 3 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 7 * (b &&& (a ||| c)) + 1 * ~~~( ~~~a ||| ( ~~~b &&& c)) - 6 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) - 1 * (c &&& (a ||| ~~~b)) + 11 * ((a &&& c) ^^^ (b ||| c)) + 7 * (c ^^^ (a ||| (b &&& c))) - 7 * ~~~b - 1 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 39 * ~~~(a ||| (b ||| c)) - 10 * ~~~(a ||| ( ~~~b ||| c)) + 19 * ~~~( ~~~a ||| (b ||| c)) - 8 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 28 * ( ~~~a &&& ( ~~~b &&& c)) + 13 * ( ~~~a &&& (b &&& c)) + 25 * (a &&& ( ~~~b &&& c)) + 14 * (a &&& (b &&& c)) = - 2 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 1 * (a ||| ~~~b) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1930 (x y : BitVec w) : +theorem e_1930 : - 1 * (c ^^^ ( ~~~a ||| (b ||| c))) - 7 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) + 1 * ~~~( ~~~a ||| (b ^^^ c)) - 1 * (b &&& c) + 7 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) + 11 * (c ||| (a ^^^ b)) - 2 * (a ^^^ ( ~~~b ||| c)) - 1 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) - 3 * (c ^^^ ~~~(a &&& b)) - 3 * (b ^^^ ~~~(a &&& c)) + 1 * (c &&& ~~~(a ^^^ b)) + 7 * ((a &&& c) ||| ~~~(b ||| c)) - 7 * (b ^^^ ( ~~~a ||| (b ||| c))) + 2 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 5 * ~~~(a ^^^ (b ^^^ c)) - 1 * (c ^^^ (a ||| (b &&& c))) - 6 * (c ^^^ ~~~(a ||| b)) - 5 * (a ^^^ (b &&& c)) + 2 * ((a ||| b) &&& (b ^^^ c)) + 1 * c + 1 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 1 * (c ^^^ ~~~(a ||| ~~~b)) + 4 * (a ||| (b ^^^ c)) - 6 * ~~~(a &&& (b ||| c)) - 11 * (c ^^^ ( ~~~a ||| (b &&& c))) - 3 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 3 * (b ^^^ (a &&& (b ^^^ c))) + 1 * ((b &&& c) ||| (a &&& (b ||| c))) + 1 * (c ^^^ (a &&& b)) - 7 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) + 4 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 3 * (a ^^^ b) - 7 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) + 1 * (b ||| ~~~(a ^^^ c)) - 2 * (c ^^^ ~~~(a &&& (b ||| c))) - 2 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 1 * ~~~(a ^^^ c) + 2 * (b ||| (a ^^^ c)) + 5 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) - 11 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) + 7 * (a ||| b) + 1 * ( ~~~a &&& (b ^^^ c)) + 4 * ~~~(a ||| ~~~b) + 5 * ~~~( ~~~a &&& (b &&& c)) + 38 * ~~~(a ||| (b ||| c)) + 9 * ~~~(a ||| ( ~~~b ||| c)) - 10 * ~~~( ~~~a ||| (b ||| c)) - 21 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 9 * ( ~~~a &&& ( ~~~b &&& c)) + 3 * ( ~~~a &&& (b &&& c)) - 7 * (a &&& ( ~~~b &&& c)) - 5 * (a &&& (b &&& c)) = - 1 * (b ^^^ ~~~(a &&& ~~~c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1931 (x y : BitVec w) : +theorem e_1931 : 4 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) - 6 * (b ^^^ ~~~(a ||| c)) + 2 * (b ^^^ ( ~~~a ||| (b &&& c))) + 2 * (c ^^^ (a ||| ( ~~~b ||| c))) - 3 * (b &&& ~~~(a &&& ~~~c)) + 1 * ~~~(a &&& (b ||| c)) - 1 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) + 3 * (b ^^^ ~~~(a &&& (b ^^^ c))) + 4 * ((a ^^^ b) ||| ~~~(a ^^^ c)) - 7 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) - 1 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) - 1 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) - 5 * (a &&& b) - 11 * ( ~~~a ||| ( ~~~b ||| c)) - 2 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) - 1 * (a &&& ( ~~~b ||| c)) + 11 * (c ^^^ (a ||| (b ||| c))) + 7 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 2 * (a ||| c) + 5 * ((a &&& b) ^^^ (b ||| ~~~c)) + 2 * (c ^^^ ( ~~~a ||| (b &&& c))) + 1 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 5 * (b ^^^ (a ||| (b ||| c))) - 6 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) - 5 * (c ^^^ ~~~(a &&& b)) + 1 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) + 1 * ~~~( ~~~a ||| (b ^^^ c)) + 11 * ~~~(a &&& b) - 2 * (c ^^^ (a &&& (b ||| c))) + 3 * ~~~(a ^^^ ( ~~~b &&& c)) - 2 * ~~~(a ^^^ (b ^^^ c)) - 2 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) - 1 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) - 5 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 1 * (b ||| (a &&& ~~~c)) + 3 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) + 2 * ~~~b + 1 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) - 1 * (b &&& ~~~(a ^^^ c)) + 2 * ((b &&& c) ||| (a &&& (b ||| c))) - 2 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) - 2 * ((a ||| b) &&& ~~~(b ^^^ c)) + 1 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) + 5 * (c ^^^ (a ||| ~~~b)) + 1 * ~~~( ~~~a &&& (b ||| c)) - 1 * ( ~~~(a &&& b) &&& (b ^^^ c)) - 13 * ~~~(a ||| ( ~~~b ||| c)) - 31 * ~~~( ~~~a ||| (b ||| c)) - 15 * ( ~~~a &&& ( ~~~b &&& c)) - 4 * ( ~~~a &&& (b &&& c)) - 16 * (a &&& ( ~~~b &&& c)) + 35 * (a &&& (b &&& c)) = 7 * ~~~(a ||| (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1932 (x y : BitVec w) : +theorem e_1932 : 5 * ((a &&& b) ^^^ (b ||| c)) - 5 * (a &&& ~~~c) - 7 * ~~~(b ^^^ c) - 3 * ( ~~~a ||| (b &&& c)) - 1 * ((a ||| ~~~b) &&& (b ^^^ c)) + 5 * ~~~(a &&& (b ||| c)) - 1 * (b ^^^ (a ||| ~~~c)) - 2 * (c ||| (a &&& ~~~b)) - 1 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) - 1 * (b ||| (a &&& c)) - 1 * ~~~(a ||| ~~~c) + 5 * (b ^^^ ( ~~~a ||| (b ^^^ c))) - 5 * (c &&& (a ||| b)) + 11 * ~~~(a &&& b) + 2 * ~~~(a ||| ( ~~~b &&& c)) - 1 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) - 2 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) - 3 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 2 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 2 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) - 2 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 1 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) + 1 * (a ||| (b ||| c)) + 7 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 3 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) + 4 * (b ^^^ (a ||| ( ~~~b &&& c))) - 1 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) + 2 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) + 2 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 2 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) + 1 * ((a ^^^ b) &&& ~~~(a ^^^ c)) + 7 * (b ^^^ ~~~(a &&& ~~~c)) - 11 * (c ^^^ (a &&& ~~~b)) + 1 * ~~~(a ^^^ ( ~~~b ||| c)) + 4 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) + 1 * (b ||| ~~~(a ||| ~~~c)) - 7 * ~~~(b ||| ~~~c) - 6 * (b ^^^ ( ~~~a ||| (b ||| c))) + 2 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) + 1 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) + 7 * (a ^^^ (b &&& c)) - 1 * ((a ||| b) &&& (b ^^^ c)) - 6 * ~~~( ~~~a ||| ( ~~~b &&& c)) + 1 * (c ^^^ ~~~(a &&& (b &&& c))) - 23 * ~~~(a ||| (b ||| c)) - 41 * ~~~(a ||| ( ~~~b ||| c)) - 6 * ~~~( ~~~a ||| (b ||| c)) - 6 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 13 * ( ~~~a &&& ( ~~~b &&& c)) - 15 * ( ~~~a &&& (b &&& c)) - 22 * (a &&& ( ~~~b &&& c)) + 25 * (a &&& (b &&& c)) = - 2 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1933 (x y : BitVec w) : +theorem e_1933 : 7 * ((a ||| b) &&& (b ^^^ c)) + 3 * ( ~~~a ||| (b ||| c)) - 1 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) - 6 * ((a &&& b) ^^^ (b ||| c)) + 4 * (a ^^^ c) - 5 * (b ||| ~~~(a ^^^ c)) - 1 * (c ^^^ (a ||| (b ||| c))) - 1 * ((a &&& b) ||| (b ^^^ c)) - 6 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) - 1 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 1 * ( ~~~a &&& ( ~~~b ||| c)) + 1 * ~~~( ~~~a &&& ( ~~~b &&& c)) - 5 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) - 2 * (b &&& c) + 2 * ~~~(a &&& b) + 1 * ~~~(a ^^^ (b ||| c)) + 1 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) + 11 * ((a ^^^ b) &&& (a ^^^ c)) + 11 * ~~~(a ^^^ c) - 1 * (c ^^^ ~~~(a ||| ~~~b)) + 4 * (c ^^^ (a &&& ~~~b)) + 1 * (b ^^^ (a &&& (b ^^^ c))) - 2 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) - 2 * ( ~~~(a &&& b) &&& (b ^^^ c)) - 6 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) - 3 * (c ||| ~~~(a ||| b)) + 2 * ((a &&& b) ||| ~~~(b ||| ~~~c)) + 1 * ( ~~~a ||| ( ~~~b &&& c)) - 1 * (a ^^^ ( ~~~b ||| c)) + 1 * (a ||| ( ~~~b ||| c)) - 7 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) + 5 * ( ~~~a &&& (b ^^^ c)) + 5 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) - 7 * (a &&& (b ||| c)) + 4 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 4 * (b ||| (a &&& ~~~c)) + 3 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) - 1 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) + 2 * (b ^^^ ( ~~~a ||| (b ^^^ c))) - 2 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 1 * (c &&& (a ||| ~~~b)) - 11 * (b ^^^ c) + 7 * ((a ^^^ b) &&& ~~~(a ^^^ c)) - 2 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) + 11 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) - 5 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) - 2 * ~~~(a ||| (b ||| c)) + 2 * ~~~(a ||| ( ~~~b ||| c)) - 2 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 2 * ( ~~~a &&& ( ~~~b &&& c)) - 18 * (a &&& ( ~~~b &&& c)) + 6 * (a &&& (b &&& c)) = 16 * ~~~( ~~~a ||| (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1934 (x y : BitVec w) : +theorem e_1934 : 4 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) + 11 * (a ^^^ (b &&& c)) - 6 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) + 11 * (c &&& (a ||| b)) - 5 * (c ^^^ ( ~~~a ||| (b ||| c))) - 7 * (b &&& (a ||| ~~~c)) + 1 * (c ||| (a ^^^ b)) + 1 * b + 7 * (c ||| (a &&& ~~~b)) - 2 * c - 1 * (c ^^^ (a &&& ( ~~~b ||| c))) - 1 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) - 2 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) - 6 * ~~~( ~~~a &&& (b ^^^ c)) + 1 * (c ||| ~~~(a ||| ~~~b)) - 1 * ~~~a - 11 * ~~~(a &&& c) + 5 * ~~~(a ||| (b &&& c)) - 6 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 2 * ~~~(b ||| ~~~c) + 1 * (a ||| c) - 7 * (a ||| ~~~c) + 2 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) - 11 * (c ^^^ (a ||| ( ~~~b &&& c))) + 2 * (c ^^^ ~~~(a &&& b)) - 3 * (b ^^^ (a &&& c)) - 2 * ~~~( ~~~a ||| (b ^^^ c)) - 11 * ~~~(a ||| (b ^^^ c)) + 2 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 1 * ( ~~~a ||| (b ||| c)) - 11 * ( ~~~c ||| ~~~(a ^^^ b)) + 4 * (b ^^^ (a ||| (b ||| c))) + 3 * (c &&& (a ||| ~~~b)) - 1 * (c ^^^ ~~~(a ||| b)) + 2 * ((a &&& b) ||| ~~~(b ||| c)) + 4 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) - 1 * ((a &&& c) ||| (b &&& ~~~c)) - 2 * ((a ^^^ b) &&& ~~~(a ^^^ c)) - 11 * (b ||| (a &&& c)) + 1 * (c ||| ~~~(a ||| b)) + 2 * ( ~~~a ||| ( ~~~b &&& c)) - 6 * (b ^^^ (a &&& ( ~~~b ||| c))) + 4 * (b ^^^ ~~~(a ||| (b ^^^ c))) - 1 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 43 * ~~~(a ||| (b ||| c)) + 52 * ~~~(a ||| ( ~~~b ||| c)) + 29 * ~~~( ~~~a ||| (b ||| c)) + 55 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 1 * ( ~~~a &&& ( ~~~b &&& c)) + 39 * ( ~~~a &&& (b &&& c)) - 2 * (a &&& ( ~~~b &&& c)) + 23 * (a &&& (b &&& c)) = 2 * (b ^^^ (a ||| ~~~c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1935 (x y : BitVec w) : +theorem e_1935 : 4 * (a &&& (b ^^^ c)) + 11 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 5 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) - 11 * (a &&& c) - 3 * (b ^^^ ( ~~~a &&& (b ^^^ c))) - 5 * ~~~(a &&& ( ~~~b &&& c)) - 1 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) - 2 * (b ||| (a ^^^ c)) + 11 * (c &&& ~~~(a &&& ~~~b)) - 2 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) + 4 * ((a ^^^ b) ||| ~~~(a ^^^ c)) + 2 * (c ^^^ (a &&& ~~~b)) - 3 * (c ^^^ ~~~(a ||| b)) - 2 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 7 * ~~~(a &&& ~~~c) - 3 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) + 2 * (c ^^^ ( ~~~a ||| (b &&& c))) - 2 * (c ^^^ (a ||| b)) - 1 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) + 1 * (b ^^^ (a ||| ~~~c)) - 3 * (c ||| (a &&& ~~~b)) + 5 * ~~~(b &&& ~~~c) + 11 * b + 1 * a - 5 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 1 * ((a ^^^ b) &&& (a ^^^ c)) - 1 * (b ^^^ (a &&& (b ^^^ c))) - 6 * ((a ||| b) &&& ~~~(b ^^^ c)) - 1 * ~~~(a ||| ~~~b) + 4 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) + 1 * (b ^^^ (a ||| c)) - 1 * (a ||| ~~~b) - 1 * (a ||| (b &&& c)) - 6 * (b ||| ~~~(a ||| c)) - 2 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) - 1 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) + 5 * (c ^^^ (a &&& ( ~~~b ||| c))) + 3 * ((a ||| b) &&& (b ^^^ c)) - 1 * ~~~(a ||| ~~~c) - 11 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 1 * (b ^^^ (a &&& ~~~c)) + 11 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 2 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 1 * (b ^^^ (a &&& ( ~~~b ||| c))) - 12 * ~~~(a ||| (b ||| c)) - 15 * ~~~(a ||| ( ~~~b ||| c)) - 15 * ~~~( ~~~a ||| (b ||| c)) + 10 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 16 * ( ~~~a &&& ( ~~~b &&& c)) - 19 * ( ~~~a &&& (b &&& c)) - 15 * (a &&& ( ~~~b &&& c)) - 27 * (a &&& (b &&& c)) = - 11 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1936 (x y : BitVec w) : +theorem e_1936 : - 1 * (c ^^^ ( ~~~a ||| (b &&& c))) + 2 * ((a &&& b) ^^^ (b ||| ~~~c)) + 5 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) - 1 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) + 2 * (b ^^^ (a &&& ( ~~~b ||| c))) - 5 * ( ~~~b ||| (a ^^^ c)) - 11 * (b ^^^ ~~~(a &&& (b ||| c))) + 5 * (b ^^^ (a &&& (b ||| c))) - 6 * ~~~(a &&& c) + 4 * (c &&& ~~~(a ^^^ b)) + 3 * (c ^^^ ( ~~~a &&& (b ||| c))) + 1 * c - 1 * ((a &&& b) ||| ~~~(b ||| ~~~c)) - 11 * (b ^^^ ~~~(a &&& ~~~c)) + 7 * ~~~a - 1 * ( ~~~a ||| (b ||| c)) + 11 * (a &&& c) - 7 * (b &&& ~~~(a ^^^ c)) + 4 * ~~~(a &&& (b ^^^ c)) - 7 * (c &&& (a ^^^ b)) + 3 * ( ~~~c &&& ~~~(a ^^^ b)) + 11 * (c ^^^ ~~~(a &&& (b ||| c))) + 5 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) - 3 * (a ^^^ (b ||| c)) + 11 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 2 * (a ^^^ (b &&& c)) - 1 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 2 * ((a &&& c) ||| (b &&& ~~~c)) + 5 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) + 4 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) + 5 * (b ^^^ (a ||| ~~~c)) - 2 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) + 2 * ((a &&& b) ||| (b ^^^ c)) + 4 * ( ~~~c ||| ~~~(a ^^^ b)) - 6 * ((a ^^^ b) ||| (a ^^^ c)) - 3 * (a ^^^ ( ~~~b ||| c)) + 1 * (c ^^^ ~~~(a &&& ~~~b)) - 1 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) + 11 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) + 1 * ~~~(b ||| ~~~c) - 7 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 5 * ~~~(a ||| ( ~~~b &&& c)) - 11 * ~~~(a &&& ~~~a) + 1 * ~~~(a ^^^ ( ~~~b ||| c)) + 3 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) + 4 * (b &&& (a ||| c)) - 4 * ~~~(a ||| (b ||| c)) - 22 * ~~~(a ||| ( ~~~b ||| c)) + 14 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 7 * ( ~~~a &&& ( ~~~b &&& c)) + 1 * (a &&& ( ~~~b &&& c)) - 15 * (a &&& (b &&& c)) = 25 * ~~~( ~~~a ||| (b ||| c)) + 24 * ( ~~~a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1937 (x y : BitVec w) : +theorem e_1937 : - 1 * (c ^^^ ~~~(a ||| ~~~b)) - 5 * (b ^^^ (a ||| (b ||| c))) + 11 * (c ^^^ (a &&& b)) + 1 * (c &&& (a ||| ~~~b)) + 1 * (c &&& (a ^^^ b)) - 11 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) - 11 * (c &&& ~~~(a &&& b)) + 11 * ~~~(a &&& ~~~b) + 2 * b - 11 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) + 2 * (b ^^^ (a ||| (b ^^^ c))) - 1 * ( ~~~a ||| ( ~~~b ||| c)) - 5 * ( ~~~b ||| (a ^^^ c)) - 1 * (a ||| ~~~b) + 4 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) + 3 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 2 * (a ^^^ b) - 6 * (c ^^^ (a ||| ( ~~~b ||| c))) - 6 * ((a ||| b) &&& ~~~(b ^^^ c)) - 1 * ((a ^^^ b) &&& (a ^^^ c)) - 1 * ~~~( ~~~a &&& ( ~~~b &&& c)) + 1 * (a ||| ( ~~~b &&& c)) + 2 * (c &&& ~~~(a &&& ~~~b)) + 2 * ( ~~~c ||| ~~~(a ^^^ b)) + 7 * (b ^^^ ~~~(a &&& c)) - 1 * (c ||| ~~~(a ^^^ b)) - 6 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 1 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) + 4 * ~~~(a ^^^ ( ~~~b &&& c)) - 6 * (c ^^^ (a &&& (b ||| c))) + 3 * ((a &&& b) ^^^ (b ||| c)) - 7 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) - 5 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) - 11 * ((a &&& b) ^^^ (b ||| ~~~c)) + 7 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) - 7 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) + 2 * (b ^^^ (a ||| (b &&& c))) - 1 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) - 5 * (b ^^^ (a ||| c)) + 1 * ~~~(a ||| (b ^^^ c)) + 2 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) - 1 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) + 5 * (a &&& b) + 7 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) + 1 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 37 * ~~~(a ||| (b ||| c)) + 1 * ~~~(a ||| ( ~~~b ||| c)) + 28 * ~~~( ~~~a ||| (b ||| c)) - 8 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 14 * ( ~~~a &&& ( ~~~b &&& c)) + 4 * ( ~~~a &&& (b &&& c)) + 6 * (a &&& ( ~~~b &&& c)) + 7 * (a &&& (b &&& c)) = - 2 * ( ~~~(a ||| b) ||| (b ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1938 (x y : BitVec w) : +theorem e_1938 : - 1 * ~~~(a ||| ( ~~~b &&& c)) + 3 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) + 1 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 11 * (a ^^^ (b &&& c)) + 2 * (b ||| (a &&& ~~~c)) - 11 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) - 6 * (b ^^^ ( ~~~a ||| (b ||| c))) - 11 * ((a ^^^ b) ||| (a ^^^ c)) + 11 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) - 1 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) + 5 * (b ||| ~~~(a ||| c)) + 1 * ( ~~~a ||| (b ^^^ c)) - 1 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) + 4 * ~~~(a ^^^ (b &&& c)) - 7 * (a ^^^ (b ||| c)) + 1 * (a &&& ( ~~~b ||| c)) - 6 * (b ^^^ (a ||| ( ~~~b &&& c))) - 1 * ( ~~~b &&& (a ^^^ c)) + 1 * (c ||| ~~~(a ||| ~~~b)) + 1 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) - 7 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) + 1 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) + 2 * ~~~(a ||| ~~~b) + 1 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) + 2 * (a ||| ( ~~~b ||| c)) - 6 * b + 7 * (a ||| (b ||| c)) + 2 * ~~~(a ^^^ (b ||| c)) - 11 * (a ^^^ c) - 1 * ~~~(b ^^^ c) + 1 * (b ^^^ ( ~~~a ||| (b ^^^ c))) + 2 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) + 1 * ~~~(a &&& c) - 7 * (a ||| (b &&& c)) + 1 * (b ^^^ ~~~(a ||| ~~~c)) + 2 * ((a &&& b) ||| (b ^^^ c)) + 11 * ((a &&& b) ^^^ (b ||| ~~~c)) - 7 * (b ^^^ ~~~(a &&& (b &&& c))) - 2 * ~~~( ~~~a &&& ( ~~~b &&& c)) + 2 * (c ^^^ (a &&& (b ||| c))) - 11 * (c ||| ~~~(a ^^^ b)) - 1 * ~~~(a ^^^ ( ~~~b ||| c)) + 1 * (c ^^^ (a ||| (b &&& c))) + 5 * (a ^^^ b) - 7 * (b ^^^ (a ||| ~~~c)) + 14 * ~~~(a ||| (b ||| c)) + 5 * ~~~(a ||| ( ~~~b ||| c)) + 43 * ~~~( ~~~a ||| (b ||| c)) + 43 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 34 * ( ~~~a &&& ( ~~~b &&& c)) + 47 * ( ~~~a &&& (b &&& c)) + 31 * (a &&& ( ~~~b &&& c)) - 3 * (a &&& (b &&& c)) = 5 * ( ~~~c ||| ~~~(a ^^^ b)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1939 (x y : BitVec w) : +theorem e_1939 : 3 * (c ||| ~~~(a ||| ~~~b)) + 2 * (c ^^^ ~~~(a &&& b)) - 11 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) + 11 * (a &&& c) + 2 * ( ~~~a &&& ( ~~~b ||| c)) - 6 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) - 5 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) - 2 * (a ||| ( ~~~b ||| c)) + 11 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) - 1 * ( ~~~a &&& (b ||| c)) - 1 * (a ||| ( ~~~b &&& c)) + 1 * (b ||| ~~~(a ^^^ c)) + 2 * (a ||| ~~~b) - 7 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 2 * (c &&& ~~~(a &&& b)) + 2 * (c ^^^ (a &&& (b ||| c))) + 1 * (c ^^^ ( ~~~a ||| (b &&& c))) + 5 * (b &&& ~~~c) - 7 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 11 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 1 * (b ^^^ (a ||| (b ||| c))) - 11 * (b ^^^ ( ~~~a &&& (b ||| c))) - 1 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) + 3 * (b &&& ~~~(a ^^^ c)) + 11 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) + 7 * ((b &&& c) ||| (a &&& (b ||| c))) + 1 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) + 1 * (a ||| ~~~c) + 5 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) - 7 * ~~~(a &&& b) + 1 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) + 5 * (b ||| ~~~(a ||| c)) + 11 * (b ^^^ (a ||| (b ^^^ c))) + 7 * ( ~~~b ||| (a ^^^ c)) - 5 * ( ~~~a ||| (b ^^^ c)) - 1 * (b ^^^ ~~~(a ||| (b ^^^ c))) + 4 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) - 5 * ( ~~~a ||| ( ~~~b &&& c)) - 6 * ~~~c + 4 * ((a &&& ~~~b) ||| (b ^^^ c)) - 1 * (c ^^^ (a ||| ( ~~~b ||| c))) + 3 * ( ~~~c &&& (a ^^^ b)) - 11 * (b &&& (a ^^^ c)) + 1 * ( ~~~b &&& (a ^^^ c)) - 3 * (b ^^^ ( ~~~a ||| (b ||| c))) + 17 * ~~~(a ||| (b ||| c)) + 6 * ~~~(a ||| ( ~~~b ||| c)) - 9 * ~~~( ~~~a ||| (b ||| c)) + 18 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 8 * ( ~~~a &&& ( ~~~b &&& c)) - 1 * ( ~~~a &&& (b &&& c)) - 2 * (a &&& ( ~~~b &&& c)) - 14 * (a &&& (b &&& c)) = - 3 * ( ~~~a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1940 (x y : BitVec w) : +theorem e_1940 : - 7 * ~~~(a &&& (b &&& c)) - 11 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) + 1 * (c ^^^ ~~~(a &&& (b &&& c))) + 5 * (c ^^^ ~~~(a &&& ~~~b)) - 3 * (b ^^^ ( ~~~a ||| (b &&& c))) - 1 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 2 * (c ^^^ (a &&& ~~~b)) - 1 * (a ||| ( ~~~b &&& c)) - 2 * ( ~~~c ||| ~~~(a ^^^ b)) + 7 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) - 1 * (c &&& ~~~(a &&& b)) + 11 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) - 1 * ~~~(a ^^^ (b ^^^ c)) - 7 * (a &&& ( ~~~b ||| c)) - 5 * ((a &&& b) ||| ~~~(b ^^^ c)) - 1 * ((a ||| ~~~b) &&& (b ^^^ c)) - 7 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) + 1 * ((a ||| b) &&& (b ^^^ c)) - 2 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 1 * (a ||| ~~~b) + 1 * (a ^^^ ( ~~~b &&& c)) - 2 * ((a ^^^ b) &&& ~~~(a ^^^ c)) - 2 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 4 * (b ||| ~~~c) - 2 * (a ||| c) - 1 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) - 2 * ((a &&& b) ||| (b ^^^ c)) - 7 * ~~~( ~~~a ||| (b &&& c)) + 5 * ~~~(a ||| c) - 6 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 11 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) + 1 * ~~~(a ||| b) + 2 * (b ^^^ ~~~(a &&& (b &&& c))) + 2 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) - 6 * ~~~( ~~~a &&& (b ||| c)) - 2 * ( ~~~a ||| (b &&& c)) + 2 * (b ^^^ ~~~(a ||| (b &&& c))) + 4 * ~~~(a ^^^ ( ~~~b &&& c)) - 1 * (c ||| (a &&& ~~~b)) - 2 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) + 3 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 5 * (b ^^^ ~~~(a ||| (b ^^^ c))) - 1 * (b ||| (a ^^^ c)) - 5 * (b ^^^ c) + 3 * (c ||| (a &&& b)) + 5 * ~~~(a ||| (b ||| c)) + 16 * ~~~(a ||| ( ~~~b ||| c)) + 32 * ~~~( ~~~a ||| (b ||| c)) + 35 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 19 * ( ~~~a &&& ( ~~~b &&& c)) + 9 * ( ~~~a &&& (b &&& c)) + 36 * (a &&& ( ~~~b &&& c)) + 37 * (a &&& (b &&& c)) = - 5 * (b &&& (a ||| c)) - 2 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1941 (x y : BitVec w) : +theorem e_1941 : - 6 * ( ~~~a ||| (b &&& c)) - 1 * (b ^^^ ~~~(a ||| (b &&& c))) - 7 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 7 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 1 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) - 3 * ~~~(a ||| ( ~~~b &&& c)) - 1 * (b ^^^ (a &&& (b ^^^ c))) - 6 * (b ^^^ ~~~(a &&& ~~~c)) - 7 * (a &&& (b ^^^ c)) + 2 * ~~~(b &&& c) + 11 * (a &&& ( ~~~b ||| c)) + 1 * (b ^^^ (a &&& c)) - 6 * ~~~( ~~~a &&& ( ~~~b &&& c)) + 4 * ~~~a - 11 * (c ^^^ ~~~(a &&& (b &&& c))) - 11 * ~~~(a &&& b) + 5 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) + 3 * (c ^^^ ( ~~~a &&& (b ||| c))) - 1 * (b ^^^ (a ||| (b ^^^ c))) + 7 * ~~~(b ||| c) - 5 * ~~~( ~~~a &&& (b ^^^ c)) - 2 * (b &&& ~~~(a ^^^ c)) - 11 * ((b &&& c) ||| (a &&& (b ||| c))) + 2 * (b ^^^ ( ~~~a &&& (b ||| c))) + 1 * (c ^^^ ~~~(a &&& b)) + 4 * (c ^^^ (a ||| (b ||| c))) + 1 * (c ^^^ ~~~(a ||| b)) + 1 * ((a &&& b) ||| ~~~(b ||| c)) - 6 * (c ^^^ ~~~(a ||| (b &&& c))) + 5 * (b ^^^ ~~~(a &&& c)) + 2 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 1 * ( ~~~b ||| ~~~(a ^^^ c)) + 2 * ( ~~~c ||| ~~~(a ^^^ b)) - 2 * (b ||| c) - 11 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 2 * (c ^^^ ( ~~~a ||| (b ||| c))) + 4 * ~~~(a ||| ~~~c) - 7 * (b &&& c) + 4 * (c ||| (a &&& ~~~b)) - 3 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 5 * ((a &&& b) ||| ~~~(b ||| ~~~c)) - 1 * ~~~c + 4 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) + 1 * ~~~(a ||| b) - 1 * b + 24 * ~~~(a ||| (b ||| c)) + 30 * ~~~(a ||| ( ~~~b ||| c)) + 7 * ~~~( ~~~a ||| (b ||| c)) + 30 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 1 * ( ~~~a &&& ( ~~~b &&& c)) + 34 * ( ~~~a &&& (b &&& c)) + 16 * (a &&& ( ~~~b &&& c)) + 16 * (a &&& (b &&& c)) = - 7 * ( ~~~b ||| (a ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1942 (x y : BitVec w) : +theorem e_1942 : - 2 * ~~~b + 2 * ~~~(b ||| c) + 4 * (b ^^^ (a &&& ~~~c)) + 3 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) - 1 * (b ^^^ ~~~(a ||| (b ^^^ c))) - 7 * ~~~(a ^^^ ( ~~~b ||| c)) - 2 * (c &&& ~~~(a &&& b)) - 3 * (a ||| ( ~~~b &&& c)) - 2 * (b ^^^ (a &&& c)) - 2 * ~~~(b ||| ~~~c) + 1 * ~~~(a ^^^ (b ^^^ c)) + 4 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) - 11 * (c ^^^ ( ~~~a &&& (b ||| c))) - 11 * (b ^^^ ~~~(a &&& ~~~c)) + 2 * ~~~( ~~~a &&& ( ~~~b ||| c)) + 3 * (a &&& ( ~~~b ||| c)) - 1 * ~~~(a ||| ~~~b) - 3 * ( ~~~b ||| ~~~(a ^^^ c)) + 1 * (c ||| (a &&& ~~~b)) - 3 * ~~~(a &&& (b &&& c)) - 1 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) + 4 * (c ^^^ ~~~(a &&& ~~~b)) - 1 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 5 * a - 6 * (b ^^^ ~~~(a ||| c)) - 1 * (a ||| ( ~~~b ||| c)) + 2 * (c ^^^ (a &&& (b ||| c))) + 2 * ( ~~~b &&& (a ^^^ c)) + 1 * (b ||| (a &&& c)) + 2 * (c ^^^ ~~~(a &&& (b &&& c))) + 5 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) + 5 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) + 2 * (c ^^^ (a ||| ( ~~~b &&& c))) + 1 * (a &&& (b ^^^ c)) + 1 * (a ^^^ ( ~~~b ||| c)) - 1 * (c ^^^ (a ||| b)) - 3 * ((a ^^^ b) &&& ~~~(a ^^^ c)) + 1 * ~~~(a ||| (b &&& c)) + 2 * ~~~( ~~~a &&& (b ||| c)) + 1 * ~~~(a ||| ( ~~~b &&& c)) - 7 * b + 11 * (b &&& (a ^^^ c)) - 2 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) + 1 * (a ||| (b ^^^ c)) - 3 * ~~~(a &&& (b ^^^ c)) + 14 * ~~~(a ||| (b ||| c)) + 26 * ~~~(a ||| ( ~~~b ||| c)) + 7 * ~~~( ~~~a ||| (b ||| c)) + 8 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 18 * ( ~~~a &&& ( ~~~b &&& c)) - 2 * ( ~~~a &&& (b &&& c)) + 37 * (a &&& ( ~~~b &&& c)) + 22 * (a &&& (b &&& c)) = 5 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 1 * (b ^^^ c) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1943 (x y : BitVec w) : +theorem e_1943 : 5 * (b ||| ~~~(a ^^^ c)) - 11 * ((a &&& b) ^^^ (b ||| c)) - 2 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) + 4 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) + 1 * ~~~(b &&& ~~~c) + 1 * ~~~(a ^^^ b) - 1 * ~~~(a ||| (b &&& c)) + 1 * (c ^^^ ~~~(a &&& (b &&& c))) - 2 * ~~~(a &&& ~~~b) - 7 * ~~~(a &&& c) + 7 * (c ^^^ (a ||| b)) + 3 * (b ^^^ (a &&& c)) - 1 * (a ||| ~~~b) - 7 * (b ||| (a &&& ~~~c)) + 5 * (b ^^^ (a ||| (b ||| c))) - 2 * (c ^^^ ~~~(a ||| (b &&& c))) + 1 * (a ^^^ (b ^^^ c)) + 11 * ((a ^^^ b) &&& ~~~(a ^^^ c)) + 4 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) - 6 * (c ^^^ ( ~~~a ||| (b ||| c))) + 2 * ((a ^^^ b) ||| ~~~(a ^^^ c)) + 2 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) + 7 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) + 11 * ( ~~~c &&& ~~~(a ^^^ b)) - 2 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) - 2 * ( ~~~b &&& ~~~(a ^^^ c)) - 2 * (c ^^^ ~~~(a &&& b)) + 1 * ~~~a + 3 * (b ^^^ ( ~~~a &&& (b ||| c))) + 4 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 7 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 7 * ~~~(a &&& (b &&& c)) - 1 * (c &&& (a ^^^ b)) - 2 * (c ^^^ ~~~(a ||| ~~~b)) - 3 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 2 * ((a &&& b) ||| ~~~(b ||| c)) - 1 * ~~~(b &&& c) - 1 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) + 3 * (c ^^^ (a ||| (b &&& c))) + 1 * ( ~~~a ||| (b &&& c)) + 1 * ((a &&& b) ||| ~~~(b ||| ~~~c)) - 2 * (c ^^^ (a &&& b)) + 7 * ((a ^^^ b) ||| (a ^^^ c)) - 1 * ((a &&& ~~~b) ||| (b ^^^ c)) - 1 * ((a &&& b) ^^^ (b ||| ~~~c)) + 5 * (b ^^^ (a ||| c)) - 25 * ~~~(a ||| (b ||| c)) - 21 * ~~~(a ||| ( ~~~b ||| c)) - 23 * ~~~( ~~~a ||| (b ||| c)) - 38 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 26 * ( ~~~a &&& ( ~~~b &&& c)) - 35 * (a &&& ( ~~~b &&& c)) - 8 * (a &&& (b &&& c)) = - 4 * ~~~(a ||| ( ~~~b &&& c)) + 9 * ( ~~~a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1944 (x y : BitVec w) : +theorem e_1944 : - 7 * (b &&& (a ||| ~~~c)) + 7 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) + 1 * (a ^^^ c) - 11 * ((b &&& c) ||| (a &&& (b ||| c))) - 1 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) - 1 * (b &&& c) - 5 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) + 3 * ~~~(a ^^^ (b &&& c)) - 3 * (a &&& c) + 4 * ( ~~~b ||| ~~~(a ^^^ c)) - 1 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 6 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) - 1 * ((a &&& b) ||| ~~~(b ^^^ c)) - 2 * (c &&& (a ||| ~~~b)) + 3 * ~~~(a ^^^ (b ^^^ c)) - 1 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) + 1 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) + 1 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) + 1 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) - 11 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 3 * ( ~~~a &&& (b ||| c)) + 11 * ( ~~~(a &&& b) &&& (b ^^^ c)) - 2 * (a ||| (b ^^^ c)) - 1 * (c ||| ~~~(a ||| ~~~b)) - 1 * (b &&& ~~~c) - 2 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) + 5 * ~~~(a &&& (b &&& c)) - 2 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) - 11 * ~~~(a &&& (b ^^^ c)) - 1 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 2 * (b ||| (a &&& c)) + 11 * ~~~(a ^^^ b) - 7 * (c ^^^ ~~~(a &&& ~~~b)) + 1 * (b ^^^ (a ||| (b ||| c))) + 5 * ((a &&& b) ||| ~~~(b ||| c)) - 2 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) + 5 * (a ^^^ ( ~~~b ||| c)) + 7 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) - 1 * ~~~(a ||| c) + 11 * (c ^^^ (a ||| ~~~b)) - 1 * (a ||| ( ~~~b &&& c)) + 3 * ( ~~~a ||| ( ~~~b ||| c)) - 11 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) + 2 * (c ^^^ (a ||| b)) - 11 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) + 10 * ~~~(a ||| (b ||| c)) + 7 * ~~~(a ||| ( ~~~b ||| c)) - 4 * ~~~( ~~~a ||| (b ||| c)) + 14 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 2 * ( ~~~a &&& ( ~~~b &&& c)) + 1 * ( ~~~a &&& (b &&& c)) + 24 * (a &&& ( ~~~b &&& c)) + 56 * (a &&& (b &&& c)) = - 3 * (c &&& ~~~(a &&& b)) + 2 * ( ~~~a ||| ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1945 (x y : BitVec w) : +theorem e_1945 : - 5 * ( ~~~a ||| ( ~~~b ||| c)) - 11 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) + 1 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) - 11 * ( ~~~c &&& (a ^^^ b)) - 2 * ( ~~~a ||| (b ||| c)) - 7 * ( ~~~a &&& ( ~~~b ||| c)) + 3 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 7 * ~~~(a &&& (b ^^^ c)) - 2 * ~~~(a &&& b) - 3 * (c ^^^ ~~~(a &&& (b ||| c))) + 11 * (b ^^^ (a &&& c)) + 5 * (b ^^^ (a &&& (b ||| c))) + 1 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) + 4 * (a &&& (b ||| c)) + 1 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) - 2 * (a ||| ~~~b) + 2 * (c ||| (a &&& b)) + 5 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) + 1 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) - 3 * (a ||| b) + 2 * ~~~(a ||| (b &&& c)) + 11 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) - 1 * (a ||| (b &&& c)) + 1 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) - 5 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) - 1 * ~~~(a &&& ( ~~~b ||| c)) - 1 * ((a ^^^ b) &&& (a ^^^ c)) + 1 * (b ^^^ ( ~~~a ||| (b &&& c))) + 4 * ( ~~~c ||| (a ^^^ b)) + 5 * (c ^^^ (a &&& b)) + 1 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 1 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) + 1 * (b &&& c) + 11 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 11 * ~~~(a ||| ~~~c) + 1 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) + 11 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 4 * ( ~~~a ||| (b &&& c)) - 5 * (b ^^^ ~~~(a &&& (b ||| c))) + 3 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) - 2 * ~~~(a ||| c) - 1 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) - 1 * (b ^^^ ( ~~~a ||| (b ||| c))) + 3 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) - 2 * (c ^^^ (a &&& ( ~~~b ||| c))) + 2 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 14 * ~~~(a ||| (b ||| c)) - 19 * ~~~(a ||| ( ~~~b ||| c)) - 14 * ~~~( ~~~a ||| (b ||| c)) - 20 * ( ~~~a &&& ( ~~~b &&& c)) - 15 * ( ~~~a &&& (b &&& c)) - 45 * (a &&& ( ~~~b &&& c)) - 7 * (a &&& (b &&& c)) = 32 * ~~~( ~~~a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1946 (x y : BitVec w) : +theorem e_1946 : 7 * (c &&& ~~~(a ^^^ b)) + 7 * ~~~(a ||| (b ^^^ c)) + 2 * ~~~(a ||| ~~~c) + 2 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) - 5 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) + 11 * (c ^^^ ~~~(a &&& ~~~b)) - 1 * ((a &&& b) ||| ~~~(b ||| c)) - 1 * ( ~~~c ||| (a ^^^ b)) + 2 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) - 7 * b + 2 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 3 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) - 1 * (c ||| (a &&& b)) + 1 * (b ^^^ ~~~(a &&& (b &&& c))) + 5 * (a ^^^ (b ||| c)) - 1 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 2 * (b &&& c) - 11 * ((a ^^^ b) &&& ~~~(a ^^^ c)) + 2 * (c ^^^ ~~~(a ||| ~~~b)) + 11 * ~~~(a &&& b) - 11 * (b ^^^ (a ||| ( ~~~b ||| c))) + 5 * (a ^^^ ( ~~~b ||| c)) + 4 * ( ~~~b &&& (a ^^^ c)) + 7 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) - 1 * (c ^^^ ~~~(a &&& (b ||| c))) - 2 * ((a &&& b) ^^^ (b ||| c)) - 1 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) + 5 * ~~~(a ||| b) - 3 * ( ~~~a ||| ( ~~~b ||| c)) + 11 * ~~~( ~~~a &&& ( ~~~b &&& c)) + 2 * ~~~(a ^^^ (b ||| c)) - 7 * ~~~(b &&& ~~~c) + 4 * ((a ^^^ b) ||| (a ^^^ c)) - 1 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) - 2 * (b ^^^ (a ||| ( ~~~b &&& c))) - 2 * ((a &&& b) ||| (b ^^^ c)) + 2 * (a &&& ( ~~~b ||| c)) - 2 * ( ~~~b &&& ~~~(a ^^^ c)) - 11 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) + 2 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) - 6 * (c &&& (a ||| ~~~b)) + 1 * (c ^^^ ( ~~~a &&& (b ||| c))) - 1 * (c ^^^ (a &&& b)) + 5 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) + 3 * (c ^^^ (a ||| ~~~b)) - 23 * ~~~(a ||| (b ||| c)) - 2 * ~~~(a ||| ( ~~~b ||| c)) + 10 * ~~~( ~~~a ||| (b ||| c)) - 15 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 4 * ( ~~~a &&& ( ~~~b &&& c)) - 22 * ( ~~~a &&& (b &&& c)) + 17 * (a &&& ( ~~~b &&& c)) + 7 * (a &&& (b &&& c)) = 11 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 6 * (b ^^^ (a ||| ~~~c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1947 (x y : BitVec w) : +theorem e_1947 : 7 * (b ^^^ (a &&& c)) - 1 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) + 2 * (b &&& ~~~c) - 5 * (c ||| (a &&& ~~~b)) - 1 * (b &&& c) - 7 * (b ^^^ ~~~(a ||| (b &&& c))) + 11 * ((a &&& b) ^^^ (b ||| c)) - 2 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) + 2 * ( ~~~a ||| (b ^^^ c)) - 3 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) + 5 * (a ^^^ b) - 1 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 7 * ~~~(a ^^^ c) + 11 * ~~~(b ||| c) + 1 * ~~~(a &&& ( ~~~b &&& c)) - 7 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) - 1 * (b ^^^ ~~~(a ||| c)) + 4 * ~~~( ~~~a &&& ( ~~~b ||| c)) - 3 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) + 7 * ((a &&& b) ||| (b ^^^ c)) - 1 * ( ~~~a ||| ( ~~~b &&& c)) - 2 * ~~~(a ||| (b &&& c)) + 2 * (b ||| ~~~(a ||| ~~~c)) - 5 * ~~~( ~~~a ||| (b ^^^ c)) + 2 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) + 3 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 7 * (b ^^^ ( ~~~a ||| (b ||| c))) - 2 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 3 * ((a &&& b) ||| ~~~(b ||| ~~~c)) + 5 * (c ^^^ ( ~~~a ||| (b ||| c))) - 1 * (b ^^^ (a ||| c)) - 3 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 3 * (c ||| ~~~(a ||| b)) + 4 * ((a ||| ~~~b) &&& (b ^^^ c)) - 1 * (c ^^^ (a ||| b)) + 1 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 4 * (b ||| ~~~(a ^^^ c)) - 2 * b + 1 * ~~~(a &&& ( ~~~b ||| c)) + 2 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) - 2 * ~~~(a ^^^ (b ||| c)) - 2 * (b ^^^ ~~~(a &&& ~~~c)) + 3 * ( ~~~a ||| ( ~~~b ||| c)) - 3 * ~~~(a ^^^ b) - 1 * (b ^^^ (a ||| ( ~~~b &&& c))) - 7 * ~~~(a ||| (b ||| c)) - 37 * ~~~(a ||| ( ~~~b ||| c)) + 1 * ~~~( ~~~a ||| (b ||| c)) - 6 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 17 * ( ~~~a &&& ( ~~~b &&& c)) - 9 * ( ~~~a &&& (b &&& c)) - 28 * (a &&& ( ~~~b &&& c)) + 10 * (a &&& (b &&& c)) = - 1 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1948 (x y : BitVec w) : +theorem e_1948 : - 2 * (b &&& ~~~(a &&& c)) + 4 * ((a &&& b) ||| ~~~(b ||| ~~~c)) + 2 * (a ||| b) - 1 * (b ^^^ (a ||| ( ~~~b ||| c))) + 3 * ~~~(a &&& ~~~c) + 5 * ( ~~~b &&& ~~~(a ^^^ c)) + 2 * ~~~(a ^^^ (b &&& c)) + 7 * (a &&& (b ||| c)) + 1 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 3 * ~~~(a ^^^ ( ~~~b ||| c)) + 4 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) - 5 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 2 * (c ||| ~~~(a ^^^ b)) - 5 * (c &&& (a ||| b)) + 1 * (b ^^^ ~~~(a &&& ~~~c)) - 1 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) - 1 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) + 11 * (b ^^^ ~~~(a ||| c)) - 5 * (b ||| (a ^^^ c)) + 1 * a - 2 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) - 1 * (a ||| (b &&& c)) - 1 * (b ^^^ (a ||| ( ~~~b &&& c))) + 2 * (a ||| (b ||| c)) + 11 * ~~~(a ||| ~~~c) - 6 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) - 11 * (a ||| ( ~~~b ||| c)) - 6 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 11 * (b ^^^ ~~~(a ||| ~~~c)) - 2 * ( ~~~b ||| ~~~(a ^^^ c)) - 3 * ( ~~~a ||| ( ~~~b ||| c)) - 5 * (c ^^^ ( ~~~a ||| (b ||| c))) + 2 * (b ^^^ ~~~(a &&& (b ^^^ c))) + 2 * ( ~~~a &&& (b ^^^ c)) - 1 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) + 3 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) - 2 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) - 3 * (a ^^^ (b ||| c)) - 11 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) - 1 * (a &&& c) + 7 * (b ||| ~~~(a ||| c)) - 2 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) - 2 * (b ^^^ (a ||| (b &&& c))) + 7 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) + 3 * (b ^^^ (a ||| ~~~c)) + 27 * ~~~(a ||| (b ||| c)) + 3 * ~~~(a ||| ( ~~~b ||| c)) + 29 * ~~~( ~~~a ||| (b ||| c)) + 2 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 4 * ( ~~~a &&& ( ~~~b &&& c)) + 16 * ( ~~~a &&& (b &&& c)) + 34 * (a &&& ( ~~~b &&& c)) - 8 * (a &&& (b &&& c)) = 6 * ~~~c := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1949 (x y : BitVec w) : +theorem e_1949 : - 1 * (b ||| ~~~(a ^^^ c)) + 5 * ((b &&& c) ||| (a &&& (b ||| c))) + 11 * ~~~(a &&& ( ~~~b ||| c)) - 2 * (c ^^^ ~~~(a &&& (b ||| c))) - 5 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) - 7 * (c ^^^ ( ~~~a ||| (b &&& c))) - 7 * ( ~~~a &&& (b ^^^ c)) - 6 * ( ~~~a &&& (b ||| c)) - 5 * (b ^^^ ( ~~~a ||| (b ^^^ c))) + 1 * (b ||| ~~~(a ||| ~~~c)) - 2 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) + 2 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) + 11 * ~~~(a ^^^ ( ~~~b &&& c)) + 3 * ~~~(a ^^^ c) + 2 * (b ^^^ ~~~(a &&& (b ||| c))) - 5 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) - 3 * ((a ||| b) &&& ~~~(b ^^^ c)) + 2 * ((a ||| ~~~b) &&& (b ^^^ c)) + 11 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) + 7 * ~~~b + 7 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) - 6 * (b ^^^ (a ||| (b &&& c))) + 2 * ((a ^^^ b) &&& ~~~(a ^^^ c)) - 1 * ((a ^^^ b) ||| (a ^^^ c)) - 11 * ~~~(a ||| ( ~~~b &&& c)) - 3 * ~~~(a ^^^ (b ^^^ c)) + 1 * (b ^^^ ( ~~~a &&& (b ||| c))) - 2 * ~~~(a &&& (b ^^^ c)) + 1 * (c ^^^ ~~~(a ||| b)) + 1 * (a ||| ( ~~~b &&& c)) - 1 * ( ~~~a ||| (b ^^^ c)) - 11 * ~~~( ~~~a ||| ( ~~~b &&& c)) + 1 * (b ^^^ ~~~(a ||| ~~~c)) - 6 * ~~~( ~~~a ||| (b ^^^ c)) - 3 * (b &&& ~~~(a &&& ~~~c)) + 1 * (a &&& ( ~~~b ||| c)) + 5 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 3 * (c ^^^ (a &&& b)) + 2 * ~~~(a &&& (b ||| c)) - 3 * (c &&& (a ||| ~~~b)) + 4 * ( ~~~c &&& ~~~(a ^^^ b)) - 1 * ( ~~~b &&& (a ^^^ c)) - 5 * (c ^^^ ( ~~~a ||| (b ||| c))) + 2 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) + 3 * (b ^^^ ~~~(a ||| (b ^^^ c))) - 26 * ~~~(a ||| (b ||| c)) + 5 * ~~~(a ||| ( ~~~b ||| c)) + 20 * ~~~( ~~~a ||| (b ||| c)) - 19 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 16 * ( ~~~a &&& ( ~~~b &&& c)) - 13 * ( ~~~a &&& (b &&& c)) - 17 * (a &&& ( ~~~b &&& c)) + 18 * (a &&& (b &&& c)) = - 4 * ~~~(a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1950 (x y : BitVec w) : +theorem e_1950 : 11 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 1 * ~~~( ~~~a ||| (b ^^^ c)) - 3 * ~~~( ~~~a ||| ( ~~~b &&& c)) + 1 * (b &&& (a ^^^ c)) - 7 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) - 5 * ( ~~~c &&& ~~~(a ^^^ b)) + 1 * (c ^^^ (a &&& (b ||| c))) + 1 * ( ~~~(a ||| b) ||| (b ^^^ c)) - 1 * (b ^^^ ~~~(a &&& (b &&& c))) - 2 * ~~~(a &&& ( ~~~b ||| c)) + 3 * ( ~~~a &&& (b ^^^ c)) - 1 * ((a &&& b) ^^^ (b ||| c)) - 1 * (b ^^^ ~~~(a ||| c)) - 5 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) + 5 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) - 1 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) + 2 * (b ^^^ ~~~(a &&& c)) - 11 * ~~~( ~~~a ||| (b &&& c)) - 3 * (c ^^^ ( ~~~a ||| (b &&& c))) - 5 * ~~~(b ^^^ c) + 11 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 1 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) - 1 * (b &&& ~~~c) - 1 * ( ~~~b &&& ~~~(a ^^^ c)) + 1 * (c &&& (a ||| ~~~b)) + 2 * (b ^^^ ( ~~~a &&& (b ^^^ c))) - 7 * (a &&& (b ||| c)) - 2 * (b ^^^ (a &&& ( ~~~b ||| c))) + 1 * (c ^^^ (a ||| b)) + 5 * ((a ||| ~~~b) &&& (b ^^^ c)) - 1 * ((a &&& b) ||| ~~~(b ||| c)) + 2 * ~~~(a &&& (b &&& c)) + 7 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) - 2 * ~~~( ~~~a &&& (b ||| c)) - 1 * (b &&& c) + 2 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 2 * (b ||| ~~~(a ||| c)) + 4 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) + 3 * (b &&& ~~~(a &&& ~~~c)) + 1 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) - 3 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) + 7 * (b ^^^ (a ||| (b ^^^ c))) + 1 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) - 3 * ~~~c + 5 * ( ~~~c ||| (a ^^^ b)) - 7 * c - 5 * ~~~(a &&& (b ||| c)) - 8 * ~~~(a ||| (b ||| c)) - 13 * ~~~(a ||| ( ~~~b ||| c)) - 8 * ~~~( ~~~a ||| (b ||| c)) + 9 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 6 * ( ~~~a &&& ( ~~~b &&& c)) - 12 * ( ~~~a &&& (b &&& c)) - 1 * (a &&& (b &&& c)) = - 3 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 2 * ((a ||| b) &&& ~~~(b ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1951 (x y : BitVec w) : +theorem e_1951 : 7 * ((a ||| b) &&& ~~~(b ^^^ c)) + 4 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 2 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) + 7 * ~~~(a &&& (b ||| c)) - 5 * ( ~~~a ||| (b ||| c)) + 5 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) + 1 * (b &&& ~~~(a ^^^ c)) + 1 * (a ^^^ (b ||| c)) + 4 * (a ^^^ b) - 11 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) - 2 * (c &&& ~~~(a &&& b)) - 11 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) - 2 * b - 2 * ~~~(a ^^^ ( ~~~b &&& c)) - 6 * ((a &&& c) ||| (b &&& ~~~c)) - 11 * ((a ^^^ b) ||| (a ^^^ c)) + 1 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) + 1 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 1 * ( ~~~c ||| (a ^^^ b)) + 7 * (a ^^^ (b ^^^ c)) + 5 * (b ||| ~~~(a ||| c)) + 2 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 2 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) + 1 * (c ^^^ (a ||| (b ||| c))) + 3 * ( ~~~a ||| (b ^^^ c)) - 7 * ( ~~~a &&& (b ||| c)) - 6 * (c &&& ~~~(a ^^^ b)) - 1 * ~~~(a ||| ~~~b) + 2 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) + 4 * (b ^^^ (a &&& ~~~c)) + 2 * (a ||| (b &&& c)) + 5 * ~~~(a ||| c) + 3 * (a ||| ( ~~~b &&& c)) + 1 * (a ||| (b ||| c)) + 11 * (a &&& b) + 2 * (a &&& (b ||| c)) + 2 * ((a ||| ~~~b) &&& (b ^^^ c)) - 1 * ((a &&& b) ||| ~~~(b ||| ~~~c)) - 2 * (b ^^^ ~~~(a &&& c)) - 1 * (c ^^^ ( ~~~a ||| (b ||| c))) - 1 * ( ~~~a &&& ( ~~~b ||| c)) - 1 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) - 5 * ((a ^^^ b) &&& (a ^^^ c)) - 1 * (c ^^^ (a &&& (b ||| c))) - 1 * (a ||| b) - 1 * ~~~(b ||| ~~~c) + 9 * ~~~(a ||| (b ||| c)) + 14 * ~~~(a ||| ( ~~~b ||| c)) - 1 * ~~~( ~~~a ||| (b ||| c)) - 1 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 19 * ( ~~~a &&& ( ~~~b &&& c)) + 8 * ( ~~~a &&& (b &&& c)) + 8 * (a &&& ( ~~~b &&& c)) - 4 * (a &&& (b &&& c)) = 7 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) - 2 * (c ^^^ ~~~(a ||| (b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1952 (x y : BitVec w) : +theorem e_1952 : - 11 * (c ^^^ (a ||| (b ||| c))) - 3 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 1 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) - 2 * ( ~~~(a ||| b) ||| (b ^^^ c)) - 3 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 1 * c - 2 * (c ^^^ ~~~(a ||| b)) + 3 * (a ^^^ c) - 2 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 6 * (c ^^^ (a &&& ~~~b)) + 7 * ( ~~~a ||| ( ~~~b &&& c)) + 2 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 7 * (a &&& c) + 1 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) - 2 * (b ^^^ (a &&& ~~~c)) - 3 * (b ^^^ ~~~(a ||| (b ^^^ c))) + 7 * (b ^^^ ( ~~~a &&& (b ||| c))) - 1 * (c ||| (a &&& ~~~b)) + 11 * ~~~(a ^^^ b) - 1 * (b &&& (a ^^^ c)) + 4 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 5 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 5 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) + 4 * (a ||| ~~~c) - 1 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) + 2 * (c ^^^ ( ~~~a &&& (b ||| c))) + 2 * (a ||| c) - 1 * (c ||| ~~~(a ||| ~~~b)) - 7 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) - 1 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 2 * ((a ^^^ b) &&& ~~~(a ^^^ c)) + 4 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 2 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) + 4 * (b &&& ~~~(a ^^^ c)) + 1 * (b ^^^ (a ||| (b ||| c))) - 5 * (a ^^^ (b ||| c)) + 5 * ((a ^^^ b) &&& (a ^^^ c)) - 6 * (b &&& ~~~(a &&& ~~~c)) + 11 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) + 1 * (c ^^^ (a ||| (b &&& c))) - 2 * (a ^^^ (b ^^^ c)) - 1 * (c ^^^ (a &&& b)) - 1 * (b ||| ~~~c) + 3 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) + 4 * (c ^^^ (a ||| b)) - 2 * (b ^^^ ~~~(a ||| ~~~c)) - 28 * ~~~(a ||| (b ||| c)) + 12 * ~~~(a ||| ( ~~~b ||| c)) - 8 * ~~~( ~~~a ||| (b ||| c)) - 24 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 13 * ( ~~~a &&& ( ~~~b &&& c)) - 9 * ( ~~~a &&& (b &&& c)) - 6 * (a &&& ( ~~~b &&& c)) + 8 * (a &&& (b &&& c)) = 1 * ((a &&& ~~~b) ||| (b ^^^ c)) + 5 * (a ||| b) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1953 (x y : BitVec w) : +theorem e_1953 : - 11 * ~~~(a &&& ~~~b) - 5 * ((a &&& b) ||| (b ^^^ c)) - 1 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) - 7 * (b ^^^ ( ~~~a ||| (b ^^^ c))) - 1 * (a &&& (b ^^^ c)) - 6 * ~~~(a ^^^ ( ~~~b &&& c)) + 7 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) - 2 * (a ^^^ ( ~~~b ||| c)) + 2 * (b ^^^ ~~~(a &&& ~~~c)) - 1 * (b ^^^ (a ||| (b &&& c))) + 2 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 5 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) + 7 * (a &&& ~~~b) - 1 * (b &&& ~~~(a ^^^ c)) + 1 * ~~~(b ||| c) + 2 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 5 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 4 * (c ^^^ ( ~~~a ||| (b ||| c))) - 2 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) + 2 * (b ^^^ (a &&& ( ~~~b ||| c))) + 3 * (b &&& ~~~(a &&& c)) + 1 * ~~~(a ||| b) - 1 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) + 1 * (c ^^^ (a ||| ( ~~~b ||| c))) + 7 * (b &&& (a ||| ~~~c)) - 2 * ( ~~~c &&& ~~~(a ^^^ b)) + 11 * (c ^^^ ~~~(a ||| b)) + 1 * (a &&& c) - 5 * (c &&& (a ||| b)) + 4 * (b ^^^ (a &&& ~~~c)) - 1 * (b ^^^ (a &&& (b ^^^ c))) - 6 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) - 6 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 11 * ~~~(a ||| (b ^^^ c)) - 1 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) + 4 * ~~~( ~~~a &&& (b ^^^ c)) - 7 * ( ~~~a ||| (b ||| c)) - 1 * (a ^^^ c) + 3 * ((a &&& b) ^^^ (b ||| c)) - 1 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 1 * ~~~( ~~~a ||| ( ~~~b &&& c)) - 1 * (a ||| b) + 2 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) - 2 * (a ||| ~~~c) - 1 * ((b &&& c) ||| (a &&& (b ||| c))) + 4 * ~~~(a ||| ( ~~~b &&& c)) + 11 * ~~~(a &&& b) - 13 * ~~~(a ||| (b ||| c)) + 10 * ~~~(a ||| ( ~~~b ||| c)) - 14 * ~~~( ~~~a ||| (b ||| c)) + 12 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 26 * ( ~~~a &&& ( ~~~b &&& c)) - 6 * (a &&& ( ~~~b &&& c)) + 10 * (a &&& (b &&& c)) = 18 * ( ~~~a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1954 (x y : BitVec w) : +theorem e_1954 : 2 * (c ^^^ ~~~(a &&& ~~~b)) - 11 * ((a &&& b) ||| (b ^^^ c)) - 3 * ~~~(a ||| b) - 5 * (a &&& ~~~c) - 2 * (b ||| (a ^^^ c)) - 1 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) + 2 * ( ~~~a &&& ( ~~~b ||| c)) + 2 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) + 5 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 1 * ( ~~~c ||| (a ^^^ b)) + 5 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) + 5 * ~~~(a ||| (b ^^^ c)) + 1 * ~~~(a &&& (b &&& c)) + 1 * (b ^^^ (a &&& (b ^^^ c))) + 4 * ( ~~~c &&& ~~~(a ^^^ b)) - 1 * (c ||| ~~~(a ||| b)) + 4 * (b ^^^ (a ||| (b ||| c))) - 2 * (c ^^^ ~~~(a ||| ~~~b)) - 2 * ~~~(a ^^^ ( ~~~b ||| c)) - 1 * ( ~~~(a ||| b) ||| (b ^^^ c)) + 1 * (c &&& ~~~(a ^^^ b)) + 7 * (b ^^^ c) + 4 * ~~~( ~~~a ||| (b ^^^ c)) + 1 * ~~~(a &&& ( ~~~b &&& c)) - 1 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) + 5 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) - 2 * ~~~(a ||| c) - 1 * (a ^^^ b) + 1 * (b ^^^ ~~~(a &&& c)) - 1 * ~~~b + 7 * (b ^^^ (a ||| ( ~~~b &&& c))) + 5 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) - 1 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) + 11 * ~~~(a &&& c) + 1 * (c ^^^ ~~~(a &&& (b &&& c))) - 2 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) + 4 * (b ^^^ ~~~(a ||| (b ^^^ c))) - 2 * (c &&& (a ^^^ b)) - 1 * ~~~( ~~~a ||| ( ~~~b &&& c)) + 11 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) - 1 * ( ~~~a ||| ( ~~~b &&& c)) - 6 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) + 11 * ~~~(a &&& b) - 11 * (a &&& (b ||| c)) - 5 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) + 1 * (c ^^^ ~~~(a ||| b)) + 1 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) - 42 * ~~~(a ||| (b ||| c)) - 47 * ~~~(a ||| ( ~~~b ||| c)) - 24 * ~~~( ~~~a ||| (b ||| c)) - 19 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 21 * ( ~~~a &&& (b &&& c)) + 1 * (a &&& ( ~~~b &&& c)) + 15 * (a &&& (b &&& c)) = 34 * ( ~~~a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1955 (x y : BitVec w) : +theorem e_1955 : - 11 * (a &&& (b ||| c)) + 5 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) - 6 * ( ~~~b &&& (a ^^^ c)) + 1 * ( ~~~(a ||| b) ||| (b ^^^ c)) - 5 * (c ^^^ ~~~(a &&& b)) + 3 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) - 1 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) + 1 * (b ^^^ ( ~~~a &&& (b ^^^ c))) + 1 * (c ^^^ (a &&& b)) + 7 * (b ^^^ ( ~~~a ||| (b ||| c))) - 1 * ( ~~~a ||| ( ~~~b &&& c)) + 2 * (c &&& (a ||| b)) + 7 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) - 6 * ~~~(a ||| (b &&& c)) + 2 * (b ||| ~~~(a ||| c)) - 6 * ((a ^^^ b) ||| (a ^^^ c)) + 3 * ((a &&& b) ||| ~~~(b ||| c)) - 1 * ((a ||| b) &&& ~~~(b ^^^ c)) - 2 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) + 5 * (b ||| (a ^^^ c)) + 1 * (b ^^^ (a &&& (b ^^^ c))) - 2 * (a ||| ~~~c) + 2 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 1 * ((a &&& c) ||| (b &&& ~~~c)) + 2 * ( ~~~c ||| ~~~(a ^^^ b)) - 1 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) + 1 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) + 3 * (b &&& ~~~c) + 4 * (c ^^^ ( ~~~a ||| (b &&& c))) + 1 * (a ^^^ (b ^^^ c)) + 11 * (a ||| ~~~b) + 1 * ~~~(a ||| ~~~b) - 2 * (a ^^^ ( ~~~b &&& c)) - 3 * (b &&& (a ^^^ c)) - 1 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 2 * ~~~(a &&& b) + 5 * (c ^^^ (a ||| b)) + 2 * ((a &&& b) ^^^ (b ||| ~~~c)) + 4 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) - 7 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) - 2 * ~~~(a &&& ( ~~~b &&& c)) + 2 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 3 * ((a ||| b) &&& (b ^^^ c)) + 1 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) - 5 * ~~~( ~~~a ||| (b ^^^ c)) - 2 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) - 24 * ~~~(a ||| (b ||| c)) - 3 * ~~~(a ||| ( ~~~b ||| c)) + 9 * ~~~( ~~~a ||| (b ||| c)) - 11 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 17 * ( ~~~a &&& ( ~~~b &&& c)) + 6 * ( ~~~a &&& (b &&& c)) - 8 * (a &&& ( ~~~b &&& c)) - 15 * (a &&& (b &&& c)) = - 3 * ((a &&& b) ||| ~~~(b ^^^ c)) + 5 * (c ^^^ ( ~~~a ||| (b ||| c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1956 (x y : BitVec w) : +theorem e_1956 : - 11 * ((a &&& c) ||| ~~~(b ||| c)) + 7 * (c ^^^ ~~~(a &&& (b &&& c))) - 1 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) + 1 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 1 * ((a ||| b) &&& (b ^^^ c)) + 5 * (b ^^^ ( ~~~a &&& (b ||| c))) - 6 * ~~~(a ^^^ (b ^^^ c)) + 11 * (c ^^^ ( ~~~a ||| (b &&& c))) - 2 * ((a &&& b) ||| ~~~(b ||| c)) + 2 * (b ^^^ (a ||| ~~~c)) - 7 * ~~~(a ||| ~~~c) + 11 * ( ~~~a &&& (b ||| c)) - 5 * (b ^^^ (a ||| ( ~~~b ||| c))) + 4 * ((a &&& b) ||| ~~~(b ||| ~~~c)) + 1 * ~~~(a ^^^ b) + 3 * (c ^^^ ~~~(a ||| (b &&& c))) - 11 * ~~~(a &&& ( ~~~b &&& c)) + 2 * (b ||| ~~~(a ^^^ c)) + 2 * (b ||| (a &&& ~~~c)) - 3 * ~~~(a ^^^ (b ||| c)) - 1 * (a ||| c) + 1 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) - 1 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) - 2 * (a &&& c) + 2 * (b &&& (a ||| ~~~c)) - 3 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 3 * ( ~~~a &&& ( ~~~b ||| c)) + 1 * (a ||| ~~~b) + 1 * (c ^^^ (a ||| ( ~~~b &&& c))) - 5 * (b ^^^ ( ~~~a ||| (b ^^^ c))) - 6 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) - 6 * (c ^^^ (a ||| ~~~b)) - 2 * (c ||| (a &&& ~~~b)) - 3 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) + 1 * ( ~~~b ||| (a ^^^ c)) - 2 * (c ^^^ (a &&& b)) - 3 * (a ^^^ c) + 1 * (b ^^^ c) - 1 * b + 7 * ~~~(a ||| c) - 5 * ~~~( ~~~a ||| ( ~~~b &&& c)) + 4 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 3 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) + 7 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) - 6 * ~~~( ~~~a ||| (b ^^^ c)) + 1 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) + 19 * ~~~(a ||| (b ||| c)) - 32 * ~~~(a ||| ( ~~~b ||| c)) + 36 * ~~~( ~~~a ||| (b ||| c)) + 11 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 16 * ( ~~~a &&& ( ~~~b &&& c)) + 15 * ( ~~~a &&& (b &&& c)) + 13 * (a &&& ( ~~~b &&& c)) + 17 * (a &&& (b &&& c)) = - 5 * (c ^^^ (a &&& (b ||| c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1957 (x y : BitVec w) : +theorem e_1957 : 1 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 1 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 11 * ( ~~~a ||| (b ||| c)) + 5 * (b &&& (a ^^^ c)) + 4 * (b &&& ~~~(a &&& ~~~c)) + 2 * ~~~(a ||| c) + 11 * (c ^^^ (a &&& b)) + 4 * ~~~(a &&& (b ||| c)) - 1 * (b &&& ~~~(a ^^^ c)) - 11 * (a ^^^ (b &&& c)) - 3 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) - 1 * ~~~(a &&& (b ^^^ c)) + 3 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 7 * ((a &&& b) ||| ~~~(b ||| ~~~c)) + 4 * (c &&& ~~~(a ^^^ b)) - 6 * (b ^^^ (a ||| ~~~c)) - 2 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 1 * ((a ||| ~~~b) &&& (b ^^^ c)) + 11 * (c ^^^ ~~~(a &&& (b ||| c))) - 1 * (c &&& ~~~(a &&& ~~~b)) + 2 * ((a &&& b) ^^^ (b ||| ~~~c)) + 5 * (b &&& c) - 2 * (a &&& (b ||| c)) - 5 * ~~~(a ||| ~~~b) - 11 * ~~~(b ||| c) - 3 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) - 6 * ~~~( ~~~a &&& (b ||| c)) - 1 * (c ||| (a &&& ~~~b)) - 1 * ( ~~~c &&& ~~~(a ^^^ b)) + 1 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) - 2 * (b ^^^ ( ~~~a ||| (b ||| c))) + 1 * (b ^^^ ~~~(a ||| (b &&& c))) + 2 * (b ^^^ ~~~(a &&& (b ||| c))) + 3 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) - 1 * ( ~~~a ||| ( ~~~b ||| c)) - 1 * ((a &&& b) ||| ~~~(b ^^^ c)) + 1 * (c ^^^ (a ||| ~~~b)) + 4 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) + 2 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) + 5 * (b ^^^ (a ||| (b &&& c))) - 1 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) + 1 * ((a ^^^ b) &&& ~~~(a ^^^ c)) - 7 * ((a &&& b) ^^^ (b ||| c)) + 11 * (a ||| c) + 1 * (a ||| (b &&& c)) + 1 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 5 * (b ^^^ ( ~~~a ||| (b ^^^ c))) - 6 * ~~~(a ||| (b ||| c)) - 35 * ~~~(a ||| ( ~~~b ||| c)) - 33 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 34 * ( ~~~a &&& ( ~~~b &&& c)) - 26 * ( ~~~a &&& (b &&& c)) - 19 * (a &&& ( ~~~b &&& c)) - 48 * (a &&& (b &&& c)) = - 2 * ((a ^^^ b) ||| (a ^^^ c)) - 1 * ~~~( ~~~a ||| (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1958 (x y : BitVec w) : +theorem e_1958 : 7 * a - 5 * ~~~( ~~~a &&& (b ||| c)) - 1 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 6 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) + 7 * (c ^^^ ~~~(a ||| b)) + 1 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) + 1 * ( ~~~a &&& (b ^^^ c)) - 7 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) - 2 * ~~~(a ^^^ c) + 2 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 5 * ~~~(a &&& ~~~c) - 6 * ~~~(a ||| ~~~c) - 1 * ( ~~~b &&& (a ^^^ c)) + 2 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) + 1 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 2 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) - 7 * ~~~(a ||| (b ^^^ c)) + 11 * (c ^^^ (a ||| b)) + 11 * ~~~(a &&& (b &&& c)) + 1 * (c ^^^ ~~~(a &&& (b &&& c))) + 1 * ~~~a - 5 * ( ~~~c ||| (a ^^^ b)) - 11 * ~~~(a &&& ~~~a) + 1 * (b ^^^ ~~~(a &&& (b &&& c))) - 7 * ~~~(b &&& c) + 4 * ~~~(a &&& ( ~~~b ||| c)) + 5 * ( ~~~(a &&& b) &&& (b ^^^ c)) + 1 * (c ^^^ (a ||| (b ||| c))) + 11 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) + 3 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) - 7 * ( ~~~a ||| (b &&& c)) - 1 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) - 1 * (b ^^^ (a &&& (b ^^^ c))) + 3 * (a ||| ~~~c) - 2 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) + 5 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) + 5 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) + 4 * (b ^^^ (a ||| (b ||| c))) - 11 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) - 3 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 3 * (c ^^^ (a &&& b)) - 5 * (b ||| ~~~(a ||| c)) + 7 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) - 11 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) - 7 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) + 11 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) + 11 * (b ^^^ ( ~~~a ||| (b &&& c))) - 3 * ~~~(a ||| (b ||| c)) - 12 * ~~~( ~~~a ||| (b ||| c)) + 11 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 13 * ( ~~~a &&& ( ~~~b &&& c)) + 11 * ( ~~~a &&& (b &&& c)) - 6 * (a &&& ( ~~~b &&& c)) + 12 * (a &&& (b &&& c)) = - 9 * ~~~(a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1959 (x y : BitVec w) : +theorem e_1959 : - 3 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 2 * ~~~(a &&& (b ^^^ c)) + 1 * (a ^^^ (b ||| c)) - 3 * (b ^^^ ~~~(a ||| c)) + 5 * (b ^^^ ~~~(a &&& ~~~c)) + 2 * (b &&& ~~~c) - 5 * ~~~(a ^^^ ( ~~~b ||| c)) - 3 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) - 7 * ( ~~~c ||| ~~~(a ^^^ b)) + 3 * ~~~( ~~~a &&& ( ~~~b ||| c)) - 1 * ~~~(a &&& ( ~~~b &&& c)) - 7 * b - 7 * (b ^^^ (a ||| ( ~~~b &&& c))) + 2 * ((a &&& b) ^^^ (b ||| ~~~c)) - 2 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) - 5 * (b ^^^ (a &&& ~~~c)) - 1 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) + 1 * ( ~~~b &&& ~~~(a ^^^ c)) - 6 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) + 3 * ~~~(a ^^^ c) + 5 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) - 2 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 5 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 1 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) + 2 * (b ^^^ (a ||| (b ^^^ c))) - 3 * (a ^^^ b) - 2 * (b ||| ~~~c) - 1 * ((a ||| ~~~b) &&& (b ^^^ c)) - 2 * (c &&& ~~~(a &&& b)) + 1 * (b ^^^ ~~~(a &&& c)) + 1 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) + 3 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 2 * ~~~(b ^^^ c) - 1 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) - 1 * (a ^^^ c) + 1 * (a ||| ( ~~~b ||| c)) - 1 * (c ^^^ (a &&& b)) + 5 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) - 11 * (b &&& c) - 6 * (c ^^^ (a &&& (b ||| c))) + 11 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) + 5 * (a ^^^ (b ^^^ c)) - 7 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 5 * (b ^^^ ~~~(a &&& (b ^^^ c))) + 1 * ((a ^^^ b) ||| ~~~(a ^^^ c)) + 2 * ~~~(a &&& c) - 11 * ((a &&& c) ||| ~~~(b ||| c)) - 3 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 7 * ~~~(a ||| ( ~~~b ||| c)) + 35 * ~~~( ~~~a ||| (b ||| c)) + 32 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 28 * ( ~~~a &&& ( ~~~b &&& c)) + 42 * ( ~~~a &&& (b &&& c)) + 2 * (a &&& ( ~~~b &&& c)) + 50 * (a &&& (b &&& c)) = 2 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 6 * (a ||| ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1960 (x y : BitVec w) : +theorem e_1960 : - 1 * (a ^^^ b) - 5 * ( ~~~b ||| ~~~(a ^^^ c)) - 11 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) + 2 * ((a &&& b) ||| ~~~(b ^^^ c)) - 1 * ~~~(a ^^^ ( ~~~b &&& c)) + 5 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 2 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) + 7 * ((a &&& b) ||| ~~~(b ||| c)) - 11 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) + 11 * (a ||| c) - 5 * (a &&& (b ^^^ c)) - 6 * (c &&& (a ||| ~~~b)) + 5 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) - 3 * ((a ^^^ b) ||| (a ^^^ c)) - 2 * (c &&& (a ||| b)) + 5 * (a ||| (b ||| c)) - 2 * (b ^^^ ( ~~~a ||| (b &&& c))) + 3 * (c ^^^ (a &&& ( ~~~b ||| c))) - 1 * ((a &&& c) ||| ~~~(b ||| c)) - 3 * (b ^^^ (a ||| (b &&& c))) - 1 * ~~~(a ^^^ c) + 5 * c + 2 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) + 11 * (a &&& ( ~~~b ||| c)) + 1 * ( ~~~a ||| (b ||| c)) + 2 * b - 3 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) + 1 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 6 * ( ~~~(a &&& b) &&& (b ^^^ c)) - 5 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) + 3 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) - 1 * ((a ||| b) &&& ~~~(b ^^^ c)) - 7 * (b &&& (a ||| c)) - 1 * ~~~(a ||| (b &&& c)) - 3 * (c ||| ~~~(a ||| b)) + 5 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) - 6 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 3 * (c &&& ~~~(a &&& ~~~b)) + 4 * ~~~(a &&& ~~~c) + 2 * (a ||| ( ~~~b ||| c)) + 1 * (b ^^^ ~~~(a &&& (b ||| c))) + 1 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) - 2 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) - 2 * ( ~~~a ||| (b ^^^ c)) - 5 * (c ^^^ (a ||| (b &&& c))) - 2 * ~~~b - 7 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) + 16 * ~~~(a ||| (b ||| c)) + 40 * ~~~(a ||| ( ~~~b ||| c)) - 12 * ~~~( ~~~a ||| (b ||| c)) + 23 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 9 * ( ~~~a &&& ( ~~~b &&& c)) - 17 * ( ~~~a &&& (b &&& c)) + 8 * (a &&& ( ~~~b &&& c)) - 17 * (a &&& (b &&& c)) = - 2 * (c ||| (a &&& ~~~b)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1961 (x y : BitVec w) : +theorem e_1961 : 1 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) + 2 * ( ~~~c &&& ~~~(a ^^^ b)) - 7 * (b &&& ~~~(a ^^^ c)) - 5 * (c ^^^ (a ||| ( ~~~b &&& c))) + 11 * ~~~( ~~~a &&& ( ~~~b &&& c)) - 1 * (b &&& ~~~(a &&& c)) + 1 * (c &&& ~~~(a ^^^ b)) + 1 * (a ^^^ ( ~~~b &&& c)) + 1 * (c ^^^ (a ||| ( ~~~b ||| c))) + 1 * ~~~(b ||| c) + 5 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) - 2 * (c &&& ~~~(a &&& ~~~b)) - 2 * (b ^^^ ~~~(a &&& (b &&& c))) - 2 * (b &&& ~~~(a &&& ~~~c)) - 5 * ((a &&& b) ||| (b ^^^ c)) - 11 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 5 * (a ^^^ ( ~~~b ||| c)) - 2 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) + 2 * (b ^^^ ~~~(a &&& ~~~c)) - 1 * ( ~~~a ||| (b ^^^ c)) - 1 * (c ||| (a ^^^ b)) - 5 * (b ^^^ ( ~~~a &&& (b ||| c))) - 6 * ~~~(a &&& (b &&& c)) + 1 * (c &&& (a ^^^ b)) - 11 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) + 2 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) + 3 * (a &&& c) + 1 * ~~~(a ^^^ ( ~~~b ||| c)) + 2 * (c ^^^ ~~~(a ||| ~~~b)) - 1 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) - 11 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) - 3 * ( ~~~(a ||| b) ||| (b ^^^ c)) - 5 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) + 4 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 1 * (c &&& (a ||| b)) - 2 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) - 1 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 6 * (b ^^^ ~~~(a &&& (b ||| c))) - 2 * (b ^^^ (a &&& (b ||| c))) + 3 * (b ^^^ c) + 3 * (b ||| ~~~c) - 1 * ~~~( ~~~a &&& (b &&& c)) - 6 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) + 2 * (c ^^^ ( ~~~a ||| (b ||| c))) - 1 * (c ^^^ (a ||| (b &&& c))) - 7 * ( ~~~a &&& ( ~~~b ||| c)) + 7 * (c ||| (a &&& ~~~b)) + 31 * ~~~(a ||| (b ||| c)) + 43 * ~~~(a ||| ( ~~~b ||| c)) + 33 * ~~~( ~~~a ||| (b ||| c)) + 41 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 55 * ( ~~~a &&& ( ~~~b &&& c)) + 37 * ( ~~~a &&& (b &&& c)) - 6 * (a &&& ( ~~~b &&& c)) + 12 * (a &&& (b &&& c)) = 5 * ~~~( ~~~a &&& (b ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1962 (x y : BitVec w) : +theorem e_1962 : 1 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) - 11 * (b &&& c) - 7 * (c ^^^ ~~~(a &&& (b &&& c))) + 1 * (c ||| ~~~(a ||| ~~~b)) + 4 * ( ~~~c ||| ~~~(a ^^^ b)) + 1 * ~~~(a ^^^ (b ^^^ c)) - 11 * (a ||| b) - 1 * ~~~( ~~~a ||| (b &&& c)) - 1 * (b &&& ~~~(a ^^^ c)) + 1 * (c ||| (a &&& b)) - 5 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 3 * ~~~(a &&& (b &&& c)) + 11 * ((a &&& b) ^^^ (b ||| c)) + 1 * (b &&& ~~~(a &&& c)) - 7 * ~~~(a &&& ~~~b) + 1 * (a &&& ( ~~~b ||| c)) + 11 * (c ^^^ ~~~(a ||| (b &&& c))) + 3 * ( ~~~a &&& ( ~~~b ||| c)) + 2 * (c ^^^ ( ~~~a ||| (b &&& c))) + 4 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) - 11 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 5 * (a ^^^ ( ~~~b &&& c)) + 2 * (b ||| ~~~c) - 3 * (b ||| (a ^^^ c)) - 11 * ~~~(a ||| c) + 7 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) + 2 * ~~~( ~~~a ||| (b ^^^ c)) - 1 * (a &&& (b ^^^ c)) - 2 * (b ^^^ ~~~(a &&& (b ||| c))) + 1 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) + 5 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 1 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) + 1 * (b ^^^ ~~~(a ||| c)) - 5 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 6 * ~~~(a ^^^ (b &&& c)) - 1 * ( ~~~c &&& (a ^^^ b)) - 1 * (b ^^^ (a ||| (b ^^^ c))) - 1 * (a &&& ~~~b) + 7 * (a ||| ( ~~~b ||| c)) - 2 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) - 2 * ~~~(a ^^^ (b ||| c)) - 1 * ( ~~~a ||| (b &&& c)) + 1 * (a &&& (b ||| c)) - 2 * (c ^^^ ~~~(a ||| b)) + 2 * (a &&& ~~~c) + 5 * ( ~~~a &&& (b ^^^ c)) - 5 * (a ^^^ (b &&& c)) - 3 * (a ^^^ c) + 16 * ~~~(a ||| (b ||| c)) + 30 * ~~~(a ||| ( ~~~b ||| c)) + 21 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 10 * ( ~~~a &&& ( ~~~b &&& c)) + 1 * ( ~~~a &&& (b &&& c)) - 7 * (a &&& ( ~~~b &&& c)) + 29 * (a &&& (b &&& c)) = 3 * ~~~( ~~~a &&& ( ~~~b &&& c)) - 27 * ~~~( ~~~a ||| (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1963 (x y : BitVec w) : +theorem e_1963 : - 2 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 5 * ((a &&& c) ||| (b &&& ~~~c)) - 7 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 2 * (b ||| c) - 1 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) + 1 * ( ~~~c &&& ~~~(a ^^^ b)) - 7 * (c ||| ~~~(a ||| ~~~b)) + 11 * (c ^^^ (a ||| ~~~b)) + 1 * (b &&& ~~~c) + 3 * ( ~~~(a &&& b) &&& (b ^^^ c)) - 7 * (c ^^^ (a ||| b)) + 2 * (a ||| (b &&& c)) - 6 * (a &&& (b ||| c)) - 7 * ~~~(a &&& (b &&& c)) - 1 * (a ^^^ (b ^^^ c)) + 2 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) + 3 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 5 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 1 * ~~~(a &&& c) - 7 * (c &&& (a ^^^ b)) - 2 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) + 4 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) + 3 * ( ~~~a &&& ( ~~~b ||| c)) - 5 * ((a &&& c) ^^^ (b ||| c)) + 7 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) - 6 * (b ^^^ ( ~~~a &&& (b ^^^ c))) - 3 * (b ^^^ ( ~~~a ||| (b ||| c))) - 1 * a + 7 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) + 7 * ((a &&& b) ||| ~~~(b ||| ~~~c)) - 1 * (c &&& ~~~(a ^^^ b)) - 11 * (b &&& ~~~(a &&& c)) - 1 * (a ^^^ (b &&& c)) + 3 * ( ~~~b ||| (a ^^^ c)) + 2 * ~~~a + 5 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) - 5 * ~~~(a ||| (b &&& c)) + 5 * (b ^^^ ~~~(a ||| (b &&& c))) + 1 * ~~~(a ||| ( ~~~b &&& c)) - 5 * (c ^^^ ( ~~~a &&& (b ||| c))) - 1 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) + 1 * (c ||| (a &&& ~~~b)) + 2 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) - 11 * (b &&& c) - 5 * ((a ||| ~~~b) &&& (b ^^^ c)) + 7 * ~~~(a ^^^ (b ^^^ c)) + 1 * (b ||| ~~~(a ||| c)) - 25 * ~~~(a ||| (b ||| c)) + 42 * ~~~(a ||| ( ~~~b ||| c)) - 11 * ~~~( ~~~a ||| (b ||| c)) + 7 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 33 * ( ~~~a &&& ( ~~~b &&& c)) + 13 * ( ~~~a &&& (b &&& c)) + 22 * (a &&& ( ~~~b &&& c)) + 14 * (a &&& (b &&& c)) = - 3 * (b ^^^ (a &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1964 (x y : BitVec w) : +theorem e_1964 : - 6 * ~~~(a &&& (b &&& c)) - 2 * (a ^^^ (b ^^^ c)) + 1 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) - 1 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 3 * (b &&& (a ||| ~~~c)) - 1 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 5 * ~~~(a ^^^ ( ~~~b ||| c)) - 11 * (a &&& ~~~b) - 5 * (c &&& ~~~(a &&& ~~~b)) + 7 * (b ^^^ ~~~(a &&& c)) + 1 * ( ~~~c &&& (a ^^^ b)) - 3 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) + 1 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 1 * (b ^^^ (a &&& ( ~~~b ||| c))) - 1 * ~~~(a ^^^ b) + 1 * ((a ||| ~~~b) &&& (b ^^^ c)) + 11 * (a ||| ( ~~~b &&& c)) + 1 * (c ^^^ ~~~(a ||| b)) + 2 * ~~~(a ^^^ c) + 2 * (b ^^^ (a &&& (b ||| c))) - 3 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) + 5 * (a ^^^ (b &&& c)) - 1 * ~~~(a ^^^ (b ^^^ c)) - 6 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) + 7 * (a ||| ~~~c) - 3 * (c ^^^ (a &&& ~~~b)) + 2 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 7 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 1 * (c ^^^ ~~~(a &&& (b ||| c))) + 4 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) + 2 * ~~~(a &&& (b ^^^ c)) - 5 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) + 1 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) + 7 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) + 1 * ( ~~~(a ||| b) ||| (b ^^^ c)) - 5 * ( ~~~a &&& (b ||| c)) - 2 * ~~~( ~~~a &&& (b ||| c)) + 1 * (a &&& (b ||| c)) + 3 * (b ^^^ (a ||| ~~~c)) + 11 * (c ^^^ (a ||| ( ~~~b ||| c))) - 5 * ~~~(a &&& b) - 2 * ~~~(a &&& ( ~~~b ||| c)) - 7 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) + 1 * ( ~~~a ||| (b ||| c)) - 3 * (b ^^^ (a ||| ( ~~~b &&& c))) - 3 * (b ^^^ (a &&& c)) - 11 * ~~~(b ||| ~~~c) - 12 * ~~~(a ||| (b ||| c)) + 12 * ~~~(a ||| ( ~~~b ||| c)) - 18 * ~~~( ~~~a ||| (b ||| c)) - 29 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 26 * ( ~~~a &&& ( ~~~b &&& c)) + 37 * ( ~~~a &&& (b &&& c)) + 10 * (a &&& ( ~~~b &&& c)) + 2 * (a &&& (b &&& c)) = 3 * (a ||| c) + 1 * ~~~(b ^^^ c) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1965 (x y : BitVec w) : +theorem e_1965 : 1 * (b ^^^ ~~~(a ||| (b &&& c))) - 6 * (b ^^^ ~~~(a ||| c)) - 6 * (c ||| ~~~(a ||| b)) + 7 * ( ~~~b &&& (a ^^^ c)) + 2 * (c &&& (a ^^^ b)) - 1 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 1 * ( ~~~a ||| (b ||| c)) + 5 * (a ||| ~~~c) + 7 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 7 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) - 11 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) + 1 * ~~~(a ^^^ ( ~~~b &&& c)) + 7 * ~~~(a ||| c) + 2 * (b &&& c) - 5 * (c ^^^ (a ||| b)) - 1 * (b ^^^ ~~~(a &&& c)) - 1 * ~~~( ~~~a &&& (b &&& c)) - 1 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) - 7 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) - 5 * ( ~~~c &&& (a ^^^ b)) - 6 * (c ||| ~~~(a ||| ~~~b)) - 2 * (c ||| (a &&& ~~~b)) + 7 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) + 2 * ( ~~~c ||| (a ^^^ b)) + 3 * (c ^^^ (a &&& (b ||| c))) + 3 * (a ^^^ c) - 1 * (c ^^^ ( ~~~a ||| (b ||| c))) - 3 * (a ^^^ b) + 1 * ( ~~~b ||| ~~~(a ^^^ c)) + 1 * ((a &&& b) ||| ~~~(b ^^^ c)) - 6 * ~~~( ~~~a &&& (b ^^^ c)) + 1 * (b ^^^ ( ~~~a ||| (b &&& c))) - 6 * ((a &&& b) ||| ~~~(b ||| c)) - 7 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) - 2 * ((a &&& b) ||| (b ^^^ c)) - 1 * (a ||| (b ^^^ c)) + 2 * ~~~(a &&& c) + 2 * ((a &&& b) ^^^ (b ||| c)) + 2 * ( ~~~(a &&& b) &&& (b ^^^ c)) - 11 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 1 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 5 * (b ^^^ ~~~(a &&& (b &&& c))) + 7 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) - 5 * (b ^^^ (a &&& ~~~c)) + 4 * (c ^^^ ~~~(a ||| (b &&& c))) - 3 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) + 3 * (c &&& ~~~(a &&& ~~~b)) + 9 * ~~~(a ||| (b ||| c)) + 11 * ~~~(a ||| ( ~~~b ||| c)) + 13 * ~~~( ~~~a ||| (b ||| c)) - 1 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 3 * ( ~~~a &&& ( ~~~b &&& c)) + 8 * ( ~~~a &&& (b &&& c)) + 7 * (a &&& ( ~~~b &&& c)) + 34 * (a &&& (b &&& c)) = 11 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) - 4 * (b &&& (a ||| ~~~c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1966 (x y : BitVec w) : +theorem e_1966 : - 1 * ~~~(a &&& ~~~a) + 5 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 3 * (b ^^^ ~~~(a &&& (b ||| c))) + 7 * ( ~~~a &&& (b ||| c)) - 3 * ~~~(a &&& ~~~b) + 1 * (a ||| c) - 3 * (b ||| ~~~(a ^^^ c)) - 1 * (b ^^^ ( ~~~a &&& (b ||| c))) - 1 * (c ^^^ (a ||| (b ||| c))) + 2 * ~~~(b &&& c) - 2 * (a ^^^ ( ~~~b ||| c)) - 7 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) + 3 * (b ^^^ ~~~(a &&& (b &&& c))) - 6 * (c ||| ~~~(a ^^^ b)) + 5 * ( ~~~a ||| ( ~~~b ||| c)) + 4 * (a ||| b) + 5 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 1 * (c ||| ~~~(a ||| b)) - 5 * ~~~(a ^^^ ( ~~~b ||| c)) - 6 * ( ~~~c &&& (a ^^^ b)) + 1 * (b ^^^ ( ~~~a ||| (b ^^^ c))) - 1 * (b ^^^ ~~~(a &&& ~~~c)) - 11 * (b ^^^ (a &&& (b ^^^ c))) - 7 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) + 1 * (b &&& ~~~(a ^^^ c)) + 1 * ~~~(a ||| (b ^^^ c)) + 1 * (a ^^^ (b ^^^ c)) - 11 * (c ^^^ ~~~(a ||| (b &&& c))) + 2 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) + 3 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) + 1 * ~~~(a &&& b) + 1 * ~~~( ~~~a ||| ( ~~~b &&& c)) - 6 * ((a ||| b) &&& ~~~(b ^^^ c)) + 11 * ~~~(a ||| b) - 1 * (b ^^^ ( ~~~a ||| (b &&& c))) - 7 * ((a &&& c) ||| (b &&& ~~~c)) - 3 * ~~~(a ^^^ b) + 11 * (a &&& b) + 1 * ((a &&& b) ||| ~~~(b ^^^ c)) + 1 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) + 1 * (b ^^^ (a ||| (b ^^^ c))) - 2 * ((a &&& b) ||| (b ^^^ c)) - 7 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 7 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) - 1 * (b &&& ~~~(a &&& ~~~c)) + 1 * (b ^^^ c) - 2 * ( ~~~c &&& ~~~(a ^^^ b)) + 17 * ~~~(a ||| (b ||| c)) + 34 * ~~~(a ||| ( ~~~b ||| c)) - 4 * ~~~( ~~~a ||| (b ||| c)) + 16 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 9 * ( ~~~a &&& ( ~~~b &&& c)) + 22 * ( ~~~a &&& (b &&& c)) + 33 * (a &&& ( ~~~b &&& c)) + 37 * (a &&& (b &&& c)) = - 4 * (a &&& (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1967 (x y : BitVec w) : +theorem e_1967 : - 1 * (c ^^^ (a &&& ~~~b)) - 1 * (b &&& ~~~(a &&& c)) + 4 * ~~~(a ||| ( ~~~b &&& c)) + 3 * (b ^^^ (a &&& ( ~~~b ||| c))) - 6 * (b ^^^ (a ||| ( ~~~b ||| c))) + 4 * (b ^^^ ~~~(a ||| (b &&& c))) + 4 * (c &&& (a ^^^ b)) + 1 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) + 1 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 2 * ~~~( ~~~a &&& (b ||| c)) - 5 * ~~~(b &&& c) + 4 * (a &&& (b ^^^ c)) - 2 * ( ~~~a ||| ( ~~~b &&& c)) - 2 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) - 11 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) + 1 * ~~~( ~~~a ||| (b &&& c)) - 1 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 5 * ~~~(a ^^^ (b ^^^ c)) - 1 * (c ^^^ (a &&& b)) + 1 * ((a &&& c) ||| ~~~(b ||| c)) + 11 * (c ^^^ ~~~(a &&& (b ||| c))) - 2 * ((a ||| ~~~b) &&& (b ^^^ c)) - 7 * (b ^^^ (a ||| ( ~~~b &&& c))) - 6 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) - 1 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) - 2 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) - 5 * (c &&& ~~~(a &&& ~~~b)) + 3 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 5 * ( ~~~c ||| ~~~(a ^^^ b)) + 1 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) - 1 * (b ^^^ (a &&& (b ||| c))) + 2 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) + 1 * ((a ||| b) &&& (b ^^^ c)) - 1 * (b ^^^ (a &&& ~~~c)) + 1 * (a ||| (b ||| c)) - 7 * (a ^^^ (b ||| c)) - 2 * (c ||| (a ^^^ b)) - 1 * ((a &&& b) ^^^ (b ||| c)) - 7 * (a ^^^ (b ^^^ c)) + 1 * (c ^^^ ~~~(a ||| b)) + 1 * ~~~(a ^^^ c) - 3 * (c ^^^ ~~~(a &&& ~~~b)) - 1 * ((a &&& ~~~b) ||| (b ^^^ c)) + 1 * ((a ^^^ b) &&& (a ^^^ c)) + 2 * ~~~(a ||| ~~~b) - 7 * (b ^^^ ~~~(a &&& (b ^^^ c))) - 6 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 1 * (b ^^^ (a ||| (b ^^^ c))) + 2 * ~~~(a ^^^ b) - 2 * (c ^^^ ( ~~~a ||| (b &&& c))) + 9 * ~~~(a ||| (b ||| c)) + 45 * ~~~( ~~~a ||| (b ||| c)) + 42 * ( ~~~a &&& ( ~~~b &&& c)) + 29 * ( ~~~a &&& (b &&& c)) + 9 * (a &&& ( ~~~b &&& c)) + 2 * (a &&& (b &&& c)) = - 7 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) - 26 * ~~~(a ||| ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1968 (x y : BitVec w) : +theorem e_1968 : 7 * (c ^^^ ~~~(a &&& ~~~b)) - 1 * ~~~(a ^^^ ( ~~~b ||| c)) - 2 * ((a ||| b) &&& (b ^^^ c)) + 4 * (b &&& ~~~(a &&& c)) - 2 * ( ~~~b &&& ~~~(a ^^^ c)) + 1 * ~~~c + 4 * b - 11 * ~~~(a &&& ~~~c) - 1 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) - 6 * ~~~(b ||| ~~~c) + 11 * (a ||| ( ~~~b &&& c)) + 2 * ( ~~~c &&& (a ^^^ b)) - 3 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 5 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 1 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) - 7 * (b &&& ~~~c) - 6 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 11 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) + 7 * (b ^^^ ~~~(a &&& (b &&& c))) - 7 * (a ^^^ c) + 1 * (c &&& ~~~(a &&& b)) + 1 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 5 * (c ||| (a &&& b)) + 3 * (b ||| ~~~(a ^^^ c)) + 3 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) + 3 * (c ||| ~~~(a ^^^ b)) + 1 * ((a &&& b) ^^^ (b ||| ~~~c)) - 7 * ~~~( ~~~a &&& ( ~~~b ||| c)) - 11 * (b ||| c) - 7 * ~~~(a &&& b) + 7 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) + 2 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 6 * ( ~~~(a &&& b) &&& (b ^^^ c)) - 7 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 5 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) + 2 * (a ||| (b ||| c)) - 11 * (b ^^^ ~~~(a ||| (b &&& c))) - 6 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) + 1 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 2 * (c &&& (a ||| b)) - 1 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) + 1 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) - 11 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) + 11 * ~~~(a ||| c) - 1 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) - 1 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) + 7 * (b ^^^ ( ~~~a &&& (b ^^^ c))) - 6 * ((a ^^^ b) ||| ~~~(a ^^^ c)) + 7 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) - 8 * ~~~(a ||| (b ||| c)) + 30 * ~~~(a ||| ( ~~~b ||| c)) + 32 * ~~~( ~~~a ||| (b ||| c)) + 18 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 32 * ( ~~~a &&& (b &&& c)) + 26 * (a &&& ( ~~~b &&& c)) + 11 * (a &&& (b &&& c)) = 6 * (c ^^^ (a &&& ~~~b)) - 33 * ( ~~~a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1969 (x y : BitVec w) : +theorem e_1969 : - 7 * ~~~(a &&& ~~~a) + 2 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) + 1 * (a ^^^ ( ~~~b ||| c)) + 1 * ( ~~~c &&& (a ^^^ b)) - 1 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) + 3 * (c &&& ~~~(a &&& ~~~b)) + 1 * (b ^^^ ~~~(a ||| (b ^^^ c))) + 7 * (a &&& (b ||| c)) + 1 * ~~~(b ^^^ c) + 4 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) + 5 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) - 1 * (a ||| ( ~~~b ||| c)) + 2 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) - 3 * ((a &&& ~~~b) ||| (b ^^^ c)) + 11 * ~~~(a ^^^ c) - 2 * (b ^^^ ~~~(a &&& (b ||| c))) - 7 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 6 * ~~~(a ^^^ (b &&& c)) + 11 * (a ||| (b ^^^ c)) + 5 * ((a &&& b) ^^^ (b ||| ~~~c)) + 4 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) - 2 * ( ~~~(a ||| b) ||| (b ^^^ c)) + 11 * (b ^^^ ( ~~~a &&& (b ^^^ c))) - 1 * ~~~( ~~~a &&& ( ~~~b ||| c)) + 2 * (b ||| ~~~(a ||| c)) - 6 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) - 7 * (c ^^^ ~~~(a ||| b)) + 2 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 1 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) - 3 * (b ^^^ ( ~~~a ||| (b ||| c))) + 4 * ~~~(a ||| ~~~c) + 3 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) + 4 * ( ~~~(a &&& b) &&& (b ^^^ c)) - 3 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) - 2 * c + 1 * (c ^^^ ( ~~~a &&& (b ||| c))) + 2 * ( ~~~a ||| ( ~~~b &&& c)) + 2 * ~~~(a ^^^ (b ||| c)) - 7 * (b ^^^ ( ~~~a ||| (b &&& c))) + 1 * (c ||| ~~~(a ||| b)) + 1 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) - 5 * (c &&& ~~~(a ^^^ b)) - 1 * ((a &&& c) ||| ~~~(b ||| c)) - 6 * ((b &&& c) ||| (a &&& (b ||| c))) + 1 * (c ||| (a &&& b)) + 1 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 1 * (b ||| c) + 3 * ((a &&& b) ^^^ (b ||| c)) + 4 * ~~~(a ||| (b ||| c)) - 21 * ~~~(a ||| ( ~~~b ||| c)) - 12 * ~~~( ~~~a ||| (b ||| c)) + 3 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 13 * ( ~~~a &&& ( ~~~b &&& c)) - 20 * ( ~~~a &&& (b &&& c)) - 15 * (a &&& ( ~~~b &&& c)) - 22 * (a &&& (b &&& c)) = 3 * ( ~~~c ||| (a ^^^ b)) - 3 * (a ||| ~~~c) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1970 (x y : BitVec w) : +theorem e_1970 : 7 * ( ~~~b &&& ~~~(a ^^^ c)) + 2 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 6 * ~~~(a &&& (b ^^^ c)) + 1 * (a ||| (b &&& c)) - 1 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 1 * (b ||| (a &&& c)) + 5 * (b ^^^ ~~~(a &&& ~~~c)) + 1 * ( ~~~(a &&& b) &&& (b ^^^ c)) - 3 * (c ^^^ ~~~(a &&& b)) - 1 * (c ^^^ ~~~(a ||| b)) - 1 * (c &&& ~~~(a &&& ~~~b)) + 11 * ( ~~~a &&& ( ~~~b ||| c)) + 2 * (b ||| c) - 2 * (c ||| (a &&& b)) + 2 * ((a &&& b) ||| ~~~(b ||| ~~~c)) + 1 * ~~~(a ||| c) - 1 * (c ^^^ (a &&& ~~~b)) - 11 * (a ||| ~~~c) + 5 * (b &&& (a ||| ~~~c)) - 3 * ( ~~~c &&& (a ^^^ b)) - 5 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) - 2 * ((a ||| ~~~b) &&& (b ^^^ c)) + 3 * ~~~(a &&& (b &&& c)) + 5 * (b ^^^ (a &&& (b ||| c))) - 2 * ( ~~~a ||| (b &&& c)) - 2 * (a ^^^ (b &&& c)) + 11 * ~~~(a &&& ( ~~~b ||| c)) + 7 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) + 11 * (b ||| (a ^^^ c)) - 2 * (a ^^^ (b ^^^ c)) + 11 * ( ~~~b &&& (a ^^^ c)) + 1 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) - 11 * ~~~(b ||| ~~~c) + 7 * (c &&& (a ||| b)) - 7 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) + 1 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) - 2 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) - 1 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 7 * (a ^^^ ( ~~~b &&& c)) - 1 * (c &&& (a ||| ~~~b)) - 3 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 6 * ~~~(b &&& ~~~c) + 4 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) + 1 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) - 2 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) + 5 * (a ||| b) - 11 * ( ~~~a ||| (b ||| c)) - 1 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) + 5 * ((a ||| b) &&& ~~~(b ^^^ c)) + 1 * (b ||| (a &&& ~~~c)) + 8 * ~~~(a ||| ( ~~~b ||| c)) + 11 * ~~~( ~~~a ||| (b ||| c)) - 4 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 1 * ( ~~~a &&& ( ~~~b &&& c)) - 28 * ( ~~~a &&& (b &&& c)) + 9 * (a &&& (b &&& c)) = - 1 * ~~~(a ||| (b ||| c)) - 21 * (a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1971 (x y : BitVec w) : +theorem e_1971 : 11 * (b ^^^ ( ~~~a ||| (b ||| c))) + 4 * (c ^^^ ( ~~~a ||| (b &&& c))) - 3 * (c ||| ~~~(a ^^^ b)) + 3 * ~~~(b ||| c) + 5 * (b ||| ~~~(a ||| c)) - 1 * ((b &&& c) ||| (a &&& (b ||| c))) + 4 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) + 3 * ~~~(b ^^^ c) + 1 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 4 * (b ^^^ (a ||| ~~~c)) - 5 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) - 6 * (c &&& (a ||| ~~~b)) + 11 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) + 1 * ~~~(a &&& ( ~~~b ||| c)) - 2 * (c ||| (a &&& ~~~b)) - 7 * ( ~~~b &&& ~~~(a ^^^ c)) - 1 * ( ~~~a &&& (b ^^^ c)) + 4 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) - 2 * (c ^^^ (a ||| ( ~~~b ||| c))) - 2 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) + 2 * (b ^^^ (a ||| (b &&& c))) + 2 * (b &&& ~~~(a &&& c)) + 11 * (c ||| ~~~(a ||| b)) - 1 * (b ^^^ ~~~(a ||| ~~~c)) + 2 * (c ^^^ ~~~(a ||| ~~~b)) + 5 * ~~~(a &&& (b ||| c)) + 1 * a + 2 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) + 1 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) + 2 * ~~~(a &&& (b ^^^ c)) - 1 * (a &&& (b ||| c)) + 1 * ( ~~~a &&& ( ~~~b ||| c)) + 2 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) - 5 * ~~~(a ^^^ (b ||| c)) + 3 * (a ||| c) + 1 * ~~~(a &&& ~~~c) - 1 * (b ^^^ ( ~~~a ||| (b &&& c))) - 6 * (a &&& c) - 5 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 7 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) - 2 * ~~~(a ^^^ (b &&& c)) - 3 * ( ~~~a ||| (b &&& c)) + 7 * (b ^^^ ~~~(a &&& (b ||| c))) - 11 * ((a &&& ~~~b) ||| (b ^^^ c)) + 1 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) + 1 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) + 1 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) - 1 * ( ~~~a &&& (b ||| c)) - 34 * ~~~(a ||| (b ||| c)) - 10 * ~~~(a ||| ( ~~~b ||| c)) - 27 * ~~~( ~~~a ||| (b ||| c)) + 1 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 21 * ( ~~~a &&& ( ~~~b &&& c)) - 21 * ( ~~~a &&& (b &&& c)) + 4 * (a &&& ( ~~~b &&& c)) - 14 * (a &&& (b &&& c)) = 11 * ~~~(a ||| (b &&& c)) + 2 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1972 (x y : BitVec w) : +theorem e_1972 : 1 * (b ||| ~~~c) + 2 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 7 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) + 2 * (a &&& c) - 2 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 1 * ((a ^^^ b) ||| (a ^^^ c)) + 4 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) + 1 * (c ^^^ (a ||| ~~~b)) - 3 * (a ||| b) + 4 * (b ^^^ ~~~(a &&& c)) - 2 * (c ^^^ (a ||| (b ||| c))) - 11 * (c ||| (a ^^^ b)) + 7 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 2 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 1 * (c ^^^ ~~~(a ||| (b &&& c))) - 11 * ~~~(a &&& ~~~b) - 1 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) + 7 * (c ^^^ (a ||| ( ~~~b &&& c))) - 6 * ~~~(a &&& c) + 1 * (c ^^^ (a &&& (b ||| c))) + 2 * ~~~(a &&& ( ~~~b ||| c)) - 1 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) - 7 * (c ^^^ ( ~~~a &&& (b ||| c))) - 11 * (a ||| ~~~c) + 5 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) - 1 * ~~~(a ||| (b ^^^ c)) + 5 * ~~~(a ||| ~~~c) - 6 * (a ||| (b ^^^ c)) + 1 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) - 7 * ~~~(a &&& ~~~c) + 3 * ~~~(a ||| (b &&& c)) + 2 * ( ~~~c ||| (a ^^^ b)) - 1 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) + 1 * (c ||| ~~~(a ^^^ b)) - 1 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) - 6 * (a ||| ( ~~~b &&& c)) - 1 * (a &&& ~~~c) + 4 * ~~~(a ||| ( ~~~b &&& c)) - 11 * ((a &&& c) ^^^ (b ||| c)) - 5 * (b ^^^ ( ~~~a ||| (b &&& c))) + 1 * ((a ||| ~~~b) &&& (b ^^^ c)) + 1 * (a &&& ( ~~~b ||| c)) + 7 * (c ^^^ ~~~(a ||| ~~~b)) - 5 * (a ^^^ c) + 3 * ~~~(a ^^^ c) + 3 * ( ~~~b ||| (a ^^^ c)) + 3 * (c &&& ~~~(a ^^^ b)) + 1 * ~~~(b ||| c) + 1 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) + 6 * ~~~(a ||| (b ||| c)) + 45 * ~~~(a ||| ( ~~~b ||| c)) + 28 * ~~~( ~~~a ||| (b ||| c)) + 41 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 43 * ( ~~~a &&& ( ~~~b &&& c)) + 29 * (a &&& ( ~~~b &&& c)) + 46 * (a &&& (b &&& c)) = - 15 * ( ~~~a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1973 (x y : BitVec w) : +theorem e_1973 : 1 * (b ^^^ ~~~(a &&& (b &&& c))) + 3 * ( ~~~a ||| (b ^^^ c)) + 4 * (a ||| (b ||| c)) - 1 * (b ^^^ ( ~~~a ||| (b ^^^ c))) + 7 * (b ^^^ ~~~(a &&& c)) + 11 * ((a ^^^ b) &&& (a ^^^ c)) + 2 * ~~~(a ||| ~~~c) - 11 * (b &&& (a ^^^ c)) + 1 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) + 1 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) - 2 * (b &&& ~~~(a &&& c)) + 2 * (c ||| (a &&& b)) + 3 * ~~~(a &&& (b ^^^ c)) - 2 * c - 2 * (b &&& (a ||| c)) - 1 * (c ^^^ ~~~(a ||| ~~~b)) - 1 * ((a &&& c) ||| (b &&& ~~~c)) + 1 * ~~~(b ^^^ c) - 6 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) + 7 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) - 7 * ((a &&& c) ||| ~~~(b ||| c)) - 6 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) - 6 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) - 11 * ( ~~~c ||| (a ^^^ b)) - 5 * ~~~(a ^^^ ( ~~~b ||| c)) + 5 * ~~~(a &&& ( ~~~b &&& c)) + 7 * ~~~(a ^^^ (b &&& c)) - 1 * (b ||| ~~~(a ||| c)) + 4 * (b &&& ~~~(a ^^^ c)) + 7 * ( ~~~b &&& (a ^^^ c)) - 1 * (b ^^^ (a &&& ~~~c)) + 1 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) + 7 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) - 1 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) - 7 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) - 2 * (c ||| (a &&& ~~~b)) + 11 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) - 2 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) - 6 * ( ~~~b &&& ~~~(a ^^^ c)) + 11 * (b ||| (a &&& ~~~c)) + 5 * (c ^^^ (a &&& (b ||| c))) - 3 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 5 * ~~~(a ||| c) + 5 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) + 3 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) - 1 * (c ||| ~~~(a ||| ~~~b)) - 1 * ~~~(a &&& ~~~c) + 2 * (b ^^^ (a ||| ~~~c)) + 9 * ~~~(a ||| (b ||| c)) - 11 * ~~~(a ||| ( ~~~b ||| c)) - 43 * ~~~( ~~~a ||| (b ||| c)) - 17 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 61 * ( ~~~a &&& ( ~~~b &&& c)) - 27 * ( ~~~a &&& (b &&& c)) + 19 * (a &&& ( ~~~b &&& c)) - 22 * (a &&& (b &&& c)) = - 3 * (b &&& (a ||| ~~~c)) - 2 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1974 (x y : BitVec w) : +theorem e_1974 : 3 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) - 2 * (a ^^^ ( ~~~b &&& c)) + 5 * (a ||| b) + 7 * (a ||| c) - 7 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) - 1 * (a ^^^ (b &&& c)) - 3 * ~~~( ~~~a ||| (b ^^^ c)) + 2 * ((a ||| b) &&& (b ^^^ c)) - 1 * (c ^^^ ~~~(a ||| b)) + 4 * ( ~~~a &&& (b ^^^ c)) - 11 * (a ||| (b ||| c)) + 3 * ~~~c - 3 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 2 * (b ^^^ (a &&& (b ^^^ c))) + 1 * (a ||| ( ~~~b ||| c)) + 1 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) + 11 * b - 5 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) - 5 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) + 7 * (c &&& ~~~(a &&& ~~~b)) - 1 * ((a &&& c) ^^^ (b ||| c)) - 5 * ( ~~~(a ||| b) ||| (b ^^^ c)) + 4 * ( ~~~b &&& (a ^^^ c)) + 1 * (b &&& ~~~c) - 2 * (c ^^^ (a ||| (b &&& c))) - 11 * (b &&& (a ||| c)) - 2 * (c ^^^ (a ||| ( ~~~b &&& c))) - 1 * ~~~(b &&& c) + 2 * (c &&& (a ||| ~~~b)) - 1 * (c ^^^ (a &&& ( ~~~b ||| c))) - 1 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) + 2 * (a &&& (b ||| c)) - 1 * (c ^^^ ~~~(a &&& ~~~b)) + 2 * (b &&& ~~~(a &&& c)) - 7 * ~~~( ~~~a &&& (b &&& c)) - 5 * ((a &&& b) ||| ~~~(b ^^^ c)) + 3 * (a ^^^ (b ||| c)) + 11 * (a ||| ( ~~~b &&& c)) + 5 * (b ^^^ ~~~(a &&& (b ^^^ c))) + 1 * ((a &&& b) ||| ~~~(b ||| c)) + 7 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) + 1 * ~~~(a ||| c) + 2 * (b ^^^ ~~~(a &&& (b ||| c))) + 7 * ( ~~~b ||| ~~~(a ^^^ c)) - 7 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) - 1 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 1 * ((a &&& b) ^^^ (b ||| c)) - 6 * (b ^^^ ( ~~~a ||| (b ^^^ c))) - 6 * (b ||| ~~~(a ||| ~~~c)) + 7 * ~~~(a ||| (b ||| c)) - 4 * ~~~(a ||| ( ~~~b ||| c)) - 7 * ~~~( ~~~a ||| (b ||| c)) - 4 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 8 * ( ~~~a &&& (b &&& c)) + 5 * (a &&& ( ~~~b &&& c)) + 10 * (a &&& (b &&& c)) = - 7 * (b ||| (a ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1975 (x y : BitVec w) : +theorem e_1975 : 1 * (b ||| ~~~(a ||| ~~~c)) + 1 * c - 5 * (c ^^^ ~~~(a ||| ~~~b)) - 1 * (b ||| ~~~c) + 11 * (c &&& ~~~(a ^^^ b)) + 2 * ~~~(a &&& b) - 5 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) - 1 * (c ||| (a ^^^ b)) + 7 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) - 2 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 7 * ((a &&& b) ||| ~~~(b ||| ~~~c)) + 1 * (c &&& ~~~(a &&& b)) - 1 * ( ~~~c &&& ~~~(a ^^^ b)) - 11 * (a ||| (b ^^^ c)) + 1 * (c ||| (a &&& b)) + 1 * ~~~( ~~~a &&& ( ~~~b ||| c)) + 4 * (c &&& (a ^^^ b)) - 7 * (a ||| ~~~b) + 5 * (b ^^^ ~~~(a &&& (b ^^^ c))) + 11 * (b ^^^ ~~~(a ||| (b ^^^ c))) - 3 * ~~~(b &&& ~~~c) + 5 * (c ||| ~~~(a ||| b)) - 2 * (a ||| b) - 1 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) - 6 * (c ^^^ (a &&& (b ||| c))) - 3 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 1 * ((a ^^^ b) &&& (a ^^^ c)) - 5 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 3 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) + 2 * ~~~b + 3 * ( ~~~b ||| (a ^^^ c)) - 2 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) + 1 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) - 1 * ~~~(a ||| ~~~c) - 11 * (b ^^^ ( ~~~a &&& (b ^^^ c))) - 7 * (c ^^^ ( ~~~a ||| (b ||| c))) - 6 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) - 2 * (c ^^^ (a ||| (b ||| c))) + 3 * ((a &&& b) ||| (b ^^^ c)) + 4 * (b ||| c) - 2 * (b &&& (a ||| c)) + 7 * (c ^^^ ~~~(a &&& (b ||| c))) + 11 * (b ^^^ (a ||| (b ^^^ c))) - 1 * ( ~~~a &&& ( ~~~b ||| c)) - 1 * ~~~(a ^^^ ( ~~~b ||| c)) - 11 * ((a ^^^ b) ||| (a ^^^ c)) - 11 * (a ||| ( ~~~b &&& c)) + 5 * (a ||| ~~~c) + 1 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 2 * ~~~(a ||| c) - 17 * ~~~(a ||| (b ||| c)) + 10 * ~~~(a ||| ( ~~~b ||| c)) + 29 * ~~~( ~~~a ||| (b ||| c)) + 54 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 26 * ( ~~~a &&& ( ~~~b &&& c)) + 6 * ( ~~~a &&& (b &&& c)) + 9 * (a &&& (b &&& c)) = - 6 * (a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1976 (x y : BitVec w) : +theorem e_1976 : - 5 * ( ~~~c ||| ~~~(a ^^^ b)) - 1 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 11 * (a ^^^ (b ^^^ c)) - 2 * ~~~(a &&& (b ||| c)) - 5 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) + 5 * (c ^^^ ~~~(a &&& (b ||| c))) - 1 * ((a &&& b) ^^^ (b ||| c)) - 1 * ~~~( ~~~a &&& ( ~~~b ||| c)) + 2 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 1 * (b ^^^ ( ~~~a ||| (b ||| c))) + 11 * (c ^^^ (a ||| (b &&& c))) + 7 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) - 2 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) - 11 * ( ~~~b ||| ~~~(a ^^^ c)) + 1 * (b ^^^ ~~~(a &&& ~~~c)) + 11 * (a ||| ~~~b) - 7 * ~~~c + 1 * (b ^^^ (a &&& (b ||| c))) + 11 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) - 1 * (c ^^^ (a ||| ( ~~~b &&& c))) - 2 * (b ^^^ (a ||| (b ^^^ c))) + 11 * (a ^^^ (b ||| c)) + 1 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) - 11 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) + 1 * (b ^^^ (a &&& c)) - 3 * ~~~(b ||| c) + 7 * (c ^^^ (a &&& ~~~b)) - 6 * (b ^^^ (a ||| ( ~~~b &&& c))) - 1 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) - 3 * (b ^^^ (a &&& (b ^^^ c))) + 1 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 2 * ~~~(b ^^^ c) + 1 * ( ~~~c ||| (a ^^^ b)) - 11 * ((a ^^^ b) &&& ~~~(a ^^^ c)) + 7 * ((a &&& c) ||| ~~~(b ||| c)) + 2 * (a ||| c) + 7 * (b ||| ~~~(a ||| ~~~c)) - 1 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 5 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 1 * (c ||| ~~~(a ||| b)) - 3 * (b ^^^ (a ||| ~~~c)) + 2 * (c &&& (a ^^^ b)) - 3 * ~~~(a ^^^ ( ~~~b &&& c)) + 1 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 4 * c - 1 * ( ~~~b &&& (a ^^^ c)) - 5 * (b ^^^ c) + 3 * (c ||| (a ^^^ b)) - 5 * (b ^^^ ~~~(a ||| ~~~c)) - 5 * ~~~( ~~~a &&& (b &&& c)) - 8 * ~~~(a ||| (b ||| c)) + 31 * ~~~(a ||| ( ~~~b ||| c)) - 18 * ~~~( ~~~a ||| (b ||| c)) + 8 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 23 * ( ~~~a &&& (b &&& c)) + 6 * (a &&& ( ~~~b &&& c)) - 35 * (a &&& (b &&& c)) = 32 * ( ~~~a &&& ( ~~~b &&& c)) - 3 * ~~~( ~~~a ||| ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1977 (x y : BitVec w) : +theorem e_1977 : - 5 * ((a &&& c) ||| ~~~(b ||| c)) - 1 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 1 * (a ||| ( ~~~b &&& c)) + 3 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 5 * (b ||| ~~~c) - 7 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) + 4 * (b &&& ~~~(a &&& c)) - 1 * ( ~~~b ||| ~~~(a ^^^ c)) - 2 * ~~~(b ^^^ c) + 1 * ((a &&& c) ^^^ ~~~(a ^^^ ( ~~~b &&& c))) + 1 * (a ||| b) + 2 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) - 1 * (c ^^^ ~~~(a &&& (b &&& c))) + 2 * (b ^^^ (a ||| c)) + 11 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 2 * ~~~(b ||| c) + 3 * ( ~~~b ||| (a ^^^ c)) - 3 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) - 1 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) + 7 * ~~~(a &&& c) - 6 * (b ^^^ ~~~(a &&& (b ^^^ c))) + 2 * ( ~~~c ||| ~~~(a ^^^ b)) + 3 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) - 1 * ( ~~~a &&& (b ^^^ c)) - 1 * ~~~a + 11 * ~~~(a &&& (b &&& c)) + 1 * ~~~(a ^^^ (b &&& c)) + 1 * ( ~~~a ||| (b &&& c)) - 2 * ( ~~~c ||| (a ^^^ b)) + 11 * ~~~(a ^^^ (b ^^^ c)) - 11 * (c ^^^ ( ~~~a ||| (b &&& c))) - 6 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) - 1 * (b ^^^ ( ~~~a ||| (b ^^^ c))) - 2 * ~~~(a &&& b) - 3 * ( ~~~(a &&& b) &&& (b ^^^ c)) + 2 * (c ^^^ (a &&& ~~~b)) + 11 * (b &&& c) - 2 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) + 2 * (c ^^^ ( ~~~a ||| (b ||| c))) - 1 * (c ^^^ ~~~(a ||| (b &&& c))) - 1 * ~~~(a ||| ~~~b) - 1 * (b ||| ~~~(a ^^^ c)) + 11 * (a ^^^ (b &&& c)) - 7 * ( ~~~a ||| ( ~~~b &&& c)) + 7 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 1 * ((a ^^^ b) &&& (a ^^^ c)) - 6 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 3 * ((a &&& ~~~b) ||| (b ^^^ c)) + 5 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 16 * ~~~(a ||| (b ||| c)) + 10 * ~~~(a ||| ( ~~~b ||| c)) - 14 * ~~~( ~~~a ||| (b ||| c)) - 57 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 19 * ( ~~~a &&& ( ~~~b &&& c)) - 65 * ( ~~~a &&& (b &&& c)) - 16 * (a &&& ( ~~~b &&& c)) - 5 * (a &&& (b &&& c)) = - 1 * (c ^^^ (a ||| ~~~b)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1978 (x y : BitVec w) : +theorem e_1978 : - 1 * (c ^^^ ~~~(a &&& b)) - 3 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) - 1 * ((a &&& b) ||| ~~~(b ^^^ c)) + 1 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) + 7 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) + 7 * (c ^^^ (a &&& (b ||| c))) - 1 * (c &&& ~~~(a ^^^ b)) + 7 * (a &&& ~~~c) + 2 * (a &&& ~~~b) + 1 * ((a ||| ~~~b) &&& (b ^^^ c)) + 5 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) + 1 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 2 * (b ^^^ c) - 6 * ( ~~~a &&& (b ^^^ c)) + 1 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) + 4 * ( ~~~(a &&& b) &&& (b ^^^ c)) - 1 * ((b &&& c) ||| (a &&& (b ||| c))) + 2 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) - 2 * (c ^^^ (a &&& b)) + 11 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) + 2 * (c ||| (a ^^^ b)) - 5 * (b ||| ~~~(a ^^^ c)) - 5 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 2 * (b ^^^ ( ~~~a &&& (b ||| c))) - 1 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 11 * (b ^^^ ~~~(a &&& ~~~c)) - 1 * ((a &&& b) ||| (b ^^^ c)) - 1 * (c ^^^ (a &&& ~~~b)) + 11 * ( ~~~b &&& (a ^^^ c)) - 2 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) + 3 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) + 5 * ( ~~~a ||| ( ~~~b ||| c)) - 2 * (a ||| b) + 11 * ~~~(a ^^^ ( ~~~b &&& c)) - 1 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) + 4 * (a ^^^ b) - 6 * (c ^^^ ~~~(a ||| b)) - 11 * (b ||| ~~~(a ||| ~~~c)) + 5 * ~~~( ~~~a ||| (b &&& c)) + 11 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) + 5 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) - 2 * ~~~(a &&& ( ~~~b &&& c)) - 1 * (b ^^^ ( ~~~a ||| (b ||| c))) - 2 * (a ||| (b ||| c)) + 4 * (c ^^^ (a ||| ( ~~~b &&& c))) + 1 * ((a &&& ~~~b) ||| (b ^^^ c)) - 7 * ( ~~~c &&& ~~~(a ^^^ b)) + 3 * (b ^^^ (a ||| ( ~~~b ||| c))) - 7 * ~~~(a ^^^ b) - 4 * ~~~(a ||| (b ||| c)) - 11 * ~~~(a ||| ( ~~~b ||| c)) - 43 * ~~~( ~~~a ||| (b ||| c)) + 8 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 1 * ( ~~~a &&& ( ~~~b &&& c)) - 4 * ( ~~~a &&& (b &&& c)) - 22 * (a &&& ( ~~~b &&& c)) + 8 * (a &&& (b &&& c)) = - 2 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1979 (x y : BitVec w) : +theorem e_1979 : 2 * (a ^^^ b) + 5 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) + 1 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) - 5 * ( ~~~a ||| (b ||| c)) + 11 * (c ^^^ ~~~(a &&& b)) + 1 * (a ||| (b &&& c)) + 1 * ( ~~~(a &&& b) &&& (b ^^^ c)) + 5 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) + 4 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 2 * (a ^^^ (b &&& c)) - 5 * (b ^^^ ~~~(a ||| (b &&& c))) - 6 * (b ^^^ (a ||| ~~~c)) - 2 * (c ^^^ (a ||| (b ||| c))) - 2 * (b ^^^ ~~~(a ||| (b ^^^ c))) + 1 * (c ^^^ (a ||| ( ~~~b ||| c))) - 6 * ~~~(b &&& c) + 1 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) - 6 * (c ^^^ ( ~~~a &&& (b ||| c))) + 1 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) + 5 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) - 7 * ((b &&& c) ||| (a &&& (b ||| c))) - 1 * (a ||| b) + 11 * (b ^^^ (a &&& ( ~~~b ||| c))) + 7 * ~~~( ~~~a &&& ( ~~~b &&& c)) - 2 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) + 3 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) + 3 * ~~~(a ^^^ (b ^^^ c)) + 4 * (a ||| ( ~~~b ||| c)) - 7 * (a ||| c) + 7 * (c ^^^ (a ||| b)) - 1 * ((a &&& b) ||| (b ^^^ c)) + 1 * ~~~(a ||| ~~~c) + 1 * (c ||| (a &&& ~~~b)) + 3 * (b ^^^ (a ||| (b &&& c))) + 11 * (c &&& (a ^^^ b)) - 2 * ((a ^^^ b) ||| ~~~(a ^^^ c)) - 2 * ~~~(b ||| c) - 3 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) + 1 * ( ~~~a ||| (b ^^^ c)) + 11 * ~~~(b &&& ~~~c) - 11 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) + 1 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) - 1 * (a &&& ( ~~~b ||| c)) - 7 * (a &&& (b ||| c)) + 7 * ~~~(b ^^^ c) + 1 * (a &&& ~~~b) - 6 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) - 11 * ( ~~~a &&& ( ~~~b ||| c)) - 5 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) + 1 * ~~~(a ||| (b ||| c)) - 20 * ~~~(a ||| ( ~~~b ||| c)) - 31 * ~~~( ~~~a ||| (b ||| c)) - 1 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 11 * ( ~~~a &&& ( ~~~b &&& c)) - 19 * ( ~~~a &&& (b &&& c)) - 15 * (a &&& ( ~~~b &&& c)) - 2 * (a &&& (b &&& c)) = - 2 * (b ^^^ (a ||| (b ||| c))) + 1 * (a ^^^ ( ~~~b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1980 (x y : BitVec w) : +theorem e_1980 : - 6 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 2 * ~~~(a ^^^ (b &&& c)) - 3 * (c ^^^ (a &&& b)) - 7 * ( ~~~(a ||| b) ||| (b ^^^ c)) - 11 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) - 5 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) + 7 * (c &&& (a ||| ~~~b)) + 5 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) - 11 * (b &&& (a ^^^ c)) - 1 * (b ||| ~~~(a ^^^ c)) - 7 * ((a &&& b) ^^^ (b ||| c)) + 7 * ~~~(b &&& ~~~c) + 1 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) + 11 * ~~~(a ||| (b ^^^ c)) - 11 * ~~~(a ^^^ (b ^^^ c)) + 1 * (b ^^^ ~~~(a ||| (b ^^^ c))) + 3 * ( ~~~b ||| ~~~(a ^^^ c)) - 7 * ~~~(a ^^^ ( ~~~b ||| c)) - 1 * (c &&& ~~~(a &&& ~~~b)) + 1 * (a &&& b) + 1 * (c ^^^ ( ~~~a ||| (b &&& c))) + 3 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) - 3 * (c ^^^ (a ||| b)) + 7 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) - 2 * (b ^^^ (a ||| ( ~~~b &&& c))) - 2 * ~~~(b &&& c) - 1 * ( ~~~a &&& (b ^^^ c)) + 5 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) + 4 * (b ^^^ (a ||| (b ^^^ c))) - 7 * (b ^^^ (a &&& ~~~c)) + 3 * (a &&& (b ^^^ c)) + 11 * (b ^^^ ~~~(a &&& (b &&& c))) - 3 * (c &&& (a ||| b)) + 1 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) - 2 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) - 1 * ~~~b - 2 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) - 2 * ~~~(a &&& (b &&& c)) - 2 * (c ^^^ (a &&& ~~~b)) + 2 * (b ^^^ (a ||| ~~~c)) + 2 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) + 1 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) - 5 * (b ^^^ ~~~(a &&& ~~~c)) + 3 * (c ^^^ ~~~(a ||| b)) + 5 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) + 2 * (b ^^^ ( ~~~a ||| (b &&& c))) - 1 * (b ||| ~~~(a ||| c)) + 2 * ( ~~~a &&& (b ||| c)) + 2 * (b ^^^ (a &&& c)) + 13 * ~~~(a ||| (b ||| c)) + 27 * ~~~(a ||| ( ~~~b ||| c)) + 2 * ~~~( ~~~a ||| (b ||| c)) + 45 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 14 * ( ~~~a &&& ( ~~~b &&& c)) + 35 * ( ~~~a &&& (b &&& c)) + 10 * (a &&& ( ~~~b &&& c)) - 17 * (a &&& (b &&& c)) = 6 * ~~~(a &&& b) + 1 * ~~~( ~~~a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1981 (x y : BitVec w) : +theorem e_1981 : - 1 * ( ~~~(a &&& b) &&& (b ^^^ c)) + 3 * (a &&& c) - 11 * ( ~~~b ||| (a ^^^ c)) + 5 * ~~~(a ||| ~~~c) - 1 * (b ||| (a &&& ~~~c)) - 1 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) + 2 * ~~~(a &&& (b ||| c)) - 3 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 1 * (a ||| (b ||| c)) - 1 * (c ||| ~~~(a ||| ~~~b)) - 11 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) + 3 * (a ^^^ (b &&& c)) + 7 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) + 11 * ((a ||| b) &&& ~~~(b ^^^ c)) + 1 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) - 6 * (c ^^^ (a ||| b)) - 7 * (a ||| ~~~c) - 5 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) - 1 * ~~~(a &&& c) + 1 * ( ~~~a &&& ( ~~~b ||| c)) - 2 * ~~~(a ||| c) + 7 * (b ^^^ ( ~~~a ||| (b ||| c))) - 3 * ~~~( ~~~a &&& ( ~~~b ||| c)) - 5 * (c &&& ~~~(a &&& ~~~b)) + 1 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) - 1 * ((b &&& c) ||| (a &&& (b ||| c))) - 6 * (c ^^^ (a &&& b)) - 2 * (c ||| ~~~(a ||| b)) + 1 * (b ||| ~~~(a ^^^ c)) - 3 * ((a &&& b) ^^^ (b ||| c)) + 1 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) - 1 * (a ||| b) + 5 * (c ^^^ ~~~(a &&& (b &&& c))) - 11 * (b &&& c) + 2 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) + 3 * (a ^^^ (b ^^^ c)) + 5 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) + 3 * c - 7 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 1 * (b ^^^ (a ||| (b ||| c))) + 4 * ~~~(a &&& ~~~b) - 11 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) - 5 * (b ^^^ ~~~(a ||| (b ^^^ c))) + 3 * ( ~~~a ||| (b ||| c)) - 7 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) + 7 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 2 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) + 1 * (a &&& b) + 4 * ~~~(a &&& ~~~c) + 19 * ~~~(a ||| (b ||| c)) + 13 * ~~~(a ||| ( ~~~b ||| c)) + 14 * ~~~( ~~~a ||| (b ||| c)) + 57 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 9 * ( ~~~a &&& ( ~~~b &&& c)) + 3 * ( ~~~a &&& (b &&& c)) + 7 * (a &&& ( ~~~b &&& c)) - 11 * (a &&& (b &&& c)) = - 11 * (b ^^^ (a &&& (b ||| c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1982 (x y : BitVec w) : +theorem e_1982 : 2 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 1 * (b ||| (a &&& ~~~c)) - 2 * (b &&& ~~~(a &&& c)) - 1 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) + 2 * (c ^^^ ( ~~~a ||| (b ||| c))) + 5 * ((a &&& c) ||| (b &&& ~~~c)) - 6 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) + 5 * ( ~~~(a ||| b) ||| (b ^^^ c)) - 1 * (b &&& ~~~(a ^^^ c)) + 1 * ~~~(a ^^^ (b ^^^ c)) + 2 * ~~~( ~~~a ||| (b &&& c)) + 4 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) - 1 * ((b &&& c) ||| (a &&& (b ||| c))) + 2 * (b ^^^ ( ~~~a &&& (b ||| c))) - 1 * a - 6 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) + 7 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 2 * ((a &&& b) ||| ~~~(b ||| c)) - 2 * (a &&& (b ||| c)) + 11 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 1 * ~~~(b ^^^ c) - 1 * ((a &&& c) ||| ~~~(b ||| c)) + 11 * (a ||| b) - 6 * (c ^^^ (a &&& (b ||| c))) + 2 * (a &&& ~~~b) + 2 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) + 7 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) + 3 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 11 * ( ~~~a &&& ( ~~~b ||| c)) + 2 * (a ||| ~~~b) + 1 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) - 7 * ~~~(a ^^^ b) - 3 * ~~~(a &&& ~~~b) + 5 * (c ^^^ ( ~~~a &&& (b ||| c))) - 1 * ~~~(a &&& ~~~c) - 2 * ~~~( ~~~a &&& ( ~~~b &&& c)) - 2 * (c ^^^ (a &&& ( ~~~b ||| c))) + 4 * ((a ||| b) &&& (b ^^^ c)) - 1 * ~~~(a ||| (b &&& c)) - 1 * ~~~(a ||| b) + 1 * ( ~~~b &&& ~~~(a ^^^ c)) + 3 * (a ^^^ (b ^^^ c)) - 7 * (b ^^^ ~~~(a &&& (b ^^^ c))) - 2 * (b ^^^ ( ~~~a ||| (b ||| c))) - 3 * (b ||| c) - 11 * (a ^^^ b) + 1 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) - 7 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) - 2 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 18 * ~~~(a ||| (b ||| c)) - 7 * ~~~(a ||| ( ~~~b ||| c)) - 12 * ~~~( ~~~a ||| (b ||| c)) + 4 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 19 * ( ~~~a &&& ( ~~~b &&& c)) + 32 * ( ~~~a &&& (b &&& c)) - 22 * (a &&& ( ~~~b &&& c)) + 12 * (a &&& (b &&& c)) = 11 * (b ||| ~~~(a ||| ~~~c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1983 (x y : BitVec w) : +theorem e_1983 : 2 * (b ^^^ ~~~(a &&& c)) - 2 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 11 * (c ^^^ ~~~(a &&& (b ||| c))) + 1 * ~~~( ~~~a &&& (b ||| c)) + 5 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 11 * (a ^^^ ( ~~~b &&& c)) + 1 * (b ^^^ (a &&& ~~~c)) - 2 * ~~~(a ^^^ ( ~~~b &&& c)) + 1 * ~~~(a ||| c) + 11 * ( ~~~c ||| (a ^^^ b)) + 3 * (b ^^^ (a ||| ~~~c)) + 4 * ((a ^^^ b) &&& ~~~(a ^^^ c)) - 2 * ((a &&& b) ||| ~~~(b ^^^ c)) + 3 * ~~~(a ^^^ c) - 7 * ((a ||| ~~~b) &&& (b ^^^ c)) + 5 * (c ^^^ ( ~~~a &&& (b ||| c))) + 4 * (c ^^^ (a &&& b)) - 7 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 7 * ( ~~~b &&& (a ^^^ c)) - 11 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) - 1 * (b &&& c) - 6 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) + 7 * ( ~~~a &&& (b ||| c)) + 2 * (b ^^^ ~~~(a &&& (b &&& c))) - 11 * ((a ^^^ b) ||| ~~~(a ^^^ c)) + 1 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) - 2 * ( ~~~a ||| (b ||| c)) + 5 * (a &&& ~~~c) + 3 * (b ^^^ ~~~(a &&& (b ||| c))) + 7 * (a ^^^ (b ^^^ c)) + 2 * ~~~(a ^^^ (b ^^^ c)) - 5 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) + 4 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) - 1 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) - 1 * ~~~(a &&& (b ||| c)) - 7 * ( ~~~a &&& (b ^^^ c)) - 1 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) - 2 * ((a &&& c) ||| (b &&& ~~~c)) + 7 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) + 11 * ~~~(a ||| ~~~c) - 6 * (c ^^^ (a ||| ~~~b)) - 5 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) + 2 * (b ^^^ ~~~(a ||| (b &&& c))) - 2 * ~~~(b ||| ~~~c) + 3 * (b ||| ~~~(a ||| c)) - 6 * ( ~~~c ||| ~~~(a ^^^ b)) + 7 * (c ^^^ (a &&& (b ||| c))) + 7 * (c ||| ~~~(a ^^^ b)) + 3 * (b ^^^ ~~~(a &&& ~~~c)) + 1 * (c ^^^ (a &&& ( ~~~b ||| c))) - 14 * ~~~(a ||| (b ||| c)) - 2 * ~~~(a ||| ( ~~~b ||| c)) + 15 * ~~~( ~~~a ||| (b ||| c)) - 1 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 33 * ( ~~~a &&& (b &&& c)) - 35 * (a &&& ( ~~~b &&& c)) - 10 * (a &&& (b &&& c)) = 1 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) + 7 * ~~~(a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1984 (x y : BitVec w) : +theorem e_1984 : - 1 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) - 2 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) + 2 * (a ||| b) + 1 * (a ^^^ ( ~~~b &&& c)) - 1 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) + 3 * ~~~(a &&& ~~~b) + 5 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 5 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 6 * (c ^^^ ( ~~~a ||| (b ||| c))) - 6 * (a ||| ~~~b) + 11 * c - 11 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) + 2 * (b ^^^ (a &&& (b ^^^ c))) + 4 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) - 1 * (b ^^^ ~~~(a &&& ~~~c)) - 5 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) + 7 * (a &&& ~~~c) - 2 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 3 * (b ||| (a &&& ~~~c)) + 7 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 2 * ( ~~~a &&& ( ~~~b ||| c)) + 2 * (c ^^^ ~~~(a &&& b)) - 5 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) + 2 * ~~~(a &&& (b ^^^ c)) + 2 * (a &&& ~~~b) + 1 * (b &&& ~~~(a &&& ~~~c)) - 7 * ( ~~~(a ||| b) ||| (b ^^^ c)) - 3 * (a ||| (b &&& c)) + 1 * ~~~(a ||| (b ^^^ c)) + 3 * ((a ||| b) &&& ~~~(b ^^^ c)) - 1 * ~~~b + 1 * a + 1 * ((a &&& b) ^^^ (b ||| c)) + 5 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) - 11 * (a ^^^ b) + 3 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) + 4 * ( ~~~b &&& ~~~(a ^^^ c)) - 2 * ~~~( ~~~a &&& (b ||| c)) + 7 * ((a &&& b) ||| ~~~(b ^^^ c)) + 4 * (a ||| (b ^^^ c)) + 11 * (b ||| (a ^^^ c)) + 4 * ~~~(b ^^^ c) - 7 * (b &&& (a ^^^ c)) + 2 * ((a &&& b) ||| (b ^^^ c)) - 11 * ((a &&& b) ||| ~~~(b ||| ~~~c)) + 2 * ~~~(a ||| ~~~b) - 7 * ~~~(a ||| b) - 2 * (b ^^^ ( ~~~a ||| (b ||| c))) - 1 * (a &&& b) - 2 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) + 26 * ~~~(a ||| (b ||| c)) + 3 * ~~~(a ||| ( ~~~b ||| c)) + 1 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 1 * ( ~~~a &&& ( ~~~b &&& c)) - 17 * ( ~~~a &&& (b &&& c)) + 17 * (a &&& ( ~~~b &&& c)) - 31 * (a &&& (b &&& c)) = 7 * (c &&& (a ^^^ b)) + 31 * ~~~( ~~~a ||| (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1985 (x y : BitVec w) : +theorem e_1985 : 1 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 1 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) - 3 * (a ||| b) - 5 * (c ^^^ (a &&& ( ~~~b ||| c))) + 4 * (c ||| ~~~(a ||| ~~~b)) + 1 * (c ^^^ ( ~~~a ||| (b ||| c))) - 2 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) - 1 * (b &&& (a ||| c)) - 3 * (a ||| (b ^^^ c)) - 1 * (b ^^^ ( ~~~a ||| (b ^^^ c))) - 2 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) + 7 * (c ^^^ (a ||| ~~~b)) - 1 * ~~~a + 1 * ~~~( ~~~a ||| (b ^^^ c)) - 2 * (c ^^^ (a &&& b)) + 11 * (b &&& c) - 3 * (b ||| ~~~(a ||| c)) - 11 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) - 7 * (a ^^^ ( ~~~b ||| c)) - 2 * ((b &&& ~~~c) ^^^ ( ~~~a ||| (b ^^^ c))) - 6 * ( ~~~c &&& (a ^^^ b)) - 1 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 7 * ((a &&& b) ||| ~~~(b ||| c)) - 5 * ( ~~~(a ||| b) ||| (b ^^^ c)) - 3 * (c ^^^ ~~~(a ||| ~~~b)) - 6 * (c ^^^ (a ||| ( ~~~b ||| c))) + 7 * (a &&& ~~~c) + 11 * ( ~~~a ||| (b ||| c)) - 5 * (c ^^^ (a ||| ( ~~~b &&& c))) - 5 * (a &&& ( ~~~b ||| c)) - 2 * ( ~~~b &&& (a ^^^ c)) + 1 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) + 5 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) + 7 * (a ^^^ (b &&& c)) + 3 * ((a ^^^ b) &&& (a ^^^ c)) - 7 * ~~~(a ||| ~~~b) - 2 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 1 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) - 5 * c + 5 * ( ~~~a ||| (b ^^^ c)) - 2 * ~~~(a ^^^ (b &&& c)) - 2 * ((a ||| b) &&& ~~~(b ^^^ c)) + 2 * (b ^^^ (a &&& c)) + 7 * (b ^^^ ~~~(a &&& c)) + 3 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 2 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) + 2 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) - 1 * (b ^^^ ( ~~~a &&& (b ||| c))) - 1 * ~~~(a &&& (b ||| c)) + 2 * (b ^^^ ~~~(a &&& ~~~c)) - 1 * (b ||| ~~~c) - 6 * ~~~(a ||| (b ||| c)) + 13 * ~~~(a ||| ( ~~~b ||| c)) + 22 * ~~~( ~~~a ||| (b ||| c)) - 1 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 20 * ( ~~~a &&& ( ~~~b &&& c)) - 14 * ( ~~~a &&& (b &&& c)) + 11 * (a &&& (b &&& c)) = - 13 * (a &&& ( ~~~b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1986 (x y : BitVec w) : +theorem e_1986 : - 2 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) - 1 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) - 6 * (c ||| (a &&& b)) - 2 * (c ||| ~~~(a ||| ~~~b)) - 3 * ( ~~~a ||| (b &&& c)) - 6 * ((a &&& c) ^^^ (b ||| c)) - 5 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 1 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) + 1 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) - 1 * ~~~(a ||| c) - 3 * ~~~(a &&& b) - 11 * (b ||| c) - 2 * (a ^^^ ( ~~~b &&& c)) + 2 * (b &&& (a ||| ~~~c)) + 2 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) - 7 * ~~~(a &&& ~~~c) - 1 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) + 2 * (b ^^^ (a ||| (b ^^^ c))) - 2 * ( ~~~a ||| ( ~~~b ||| c)) + 1 * (c ^^^ ( ~~~a ||| (b ||| c))) - 7 * b - 7 * ( ~~~c &&& (a ^^^ b)) + 5 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) + 7 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) + 1 * (b ^^^ ~~~( ~~~a &&& (b &&& c))) - 1 * (a ||| ( ~~~b ||| c)) - 1 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 2 * ((a &&& b) ^^^ (b ||| c)) + 5 * ~~~(a &&& ~~~a) - 11 * (b ^^^ ~~~(a ||| c)) + 7 * (b &&& ~~~(a &&& c)) + 7 * (c ^^^ ~~~(a &&& b)) - 2 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) + 1 * (c ^^^ (a &&& ~~~b)) + 3 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) + 5 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) - 2 * ((a &&& ~~~b) ||| (b ^^^ c)) + 1 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) - 2 * (b ^^^ (a &&& ( ~~~b ||| c))) - 6 * (c &&& (a ||| b)) - 6 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) - 7 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) - 1 * (a ||| (b ^^^ c)) + 1 * ~~~b + 4 * (c ^^^ (a &&& ( ~~~b ||| c))) - 2 * ~~~(a &&& ~~~b) + 1 * ~~~( ~~~a ||| (b ^^^ c)) + 4 * ((a &&& c) ||| ~~~(b ||| c)) + 2 * ( ~~~b &&& ~~~(a ^^^ c)) + 1 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) + 11 * ~~~(a ||| (b ||| c)) + 29 * ~~~(a ||| ( ~~~b ||| c)) - 5 * ~~~( ~~~a ||| (b ||| c)) + 23 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 27 * ( ~~~a &&& ( ~~~b &&& c)) + 50 * ( ~~~a &&& (b &&& c)) + 28 * (a &&& ( ~~~b &&& c)) + 50 * (a &&& (b &&& c)) = - 2 * (c &&& ~~~(a &&& ~~~b)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1987 (x y : BitVec w) : +theorem e_1987 : - 3 * (b ||| ~~~(a ||| ~~~c)) + 3 * (a &&& ( ~~~b ||| c)) - 11 * ( ~~~a ||| ( ~~~b ||| c)) - 7 * b - 3 * ~~~( ~~~a ||| (b &&& c)) + 1 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) - 2 * ~~~(a &&& (b ^^^ c)) - 7 * (c ^^^ (a ||| (b ||| c))) + 1 * ( ~~~b &&& (a ^^^ c)) + 1 * (b ^^^ ( ~~~a ||| (b &&& c))) - 2 * (b ^^^ (a ||| ( ~~~b &&& c))) - 6 * ( ~~~(a &&& b) &&& (b ^^^ c)) - 1 * ~~~(a ||| b) + 3 * (c &&& ~~~(a &&& ~~~b)) - 3 * (c ^^^ (a ||| (b &&& c))) - 2 * (b ^^^ (a &&& (b ^^^ c))) - 2 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) - 11 * ~~~(b ||| ~~~c) + 7 * (b ^^^ ~~~(a &&& c)) + 2 * (b ^^^ (a ||| c)) - 1 * ~~~(b &&& c) + 3 * ~~~(a &&& ~~~b) - 1 * (a &&& ~~~c) + 1 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) + 4 * (c ^^^ (a ||| b)) + 11 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 1 * ~~~(a ||| ~~~b) - 11 * (c ^^^ ~~~(a &&& ~~~b)) - 1 * ( ~~~a ||| (b &&& c)) - 5 * (b ^^^ ~~~(a ||| ~~~c)) - 1 * ((a ^^^ b) &&& (a ^^^ c)) + 4 * (a ||| (b ^^^ c)) + 1 * ( ~~~(a &&& ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 2 * (b ^^^ c) + 11 * (b ||| ~~~(a ||| c)) + 1 * (b ||| c) - 3 * (c ||| (a ^^^ b)) + 5 * (c ^^^ (a &&& b)) - 6 * ~~~(a ||| (b ^^^ c)) - 1 * ((a &&& b) ||| ~~~(b ||| ~~~c)) - 3 * (a &&& (b ^^^ c)) + 7 * ~~~(a ||| ~~~c) + 4 * ((a ^^^ b) ||| (a ^^^ c)) - 1 * ~~~(a &&& b) - 2 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) - 5 * (b ^^^ ~~~(a ||| c)) - 2 * (b ^^^ (a &&& (b ||| c))) - 1 * (a &&& (b ||| c)) - 1 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) + 3 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) - 4 * ~~~(a ||| (b ||| c)) + 29 * ~~~(a ||| ( ~~~b ||| c)) - 5 * ~~~( ~~~a ||| (b ||| c)) + 9 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 5 * ( ~~~a &&& ( ~~~b &&& c)) + 8 * ( ~~~a &&& (b &&& c)) + 21 * (a &&& ( ~~~b &&& c)) + 10 * (a &&& (b &&& c)) = - 5 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) - 3 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1988 (x y : BitVec w) : +theorem e_1988 : - 2 * ~~~(a ^^^ (b ^^^ c)) + 11 * (b ^^^ ( ~~~a ||| (b ^^^ c))) + 5 * ~~~(a &&& b) + 4 * (b ||| (a &&& c)) + 4 * ~~~(b ||| c) + 7 * ( ~~~a ||| ( ~~~b ||| c)) + 2 * (b ^^^ ~~~(a &&& ~~~c)) + 1 * (a ||| (b ||| c)) - 1 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) + 2 * (b ^^^ ~~~(a &&& (b ||| c))) + 1 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) - 7 * (a ^^^ b) - 2 * (c ^^^ (a ||| b)) + 11 * (c ||| (a &&& ~~~b)) - 1 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) - 7 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) + 1 * (a ||| (b ^^^ c)) + 2 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) - 2 * (c ^^^ ( ~~~a &&& (b ||| c))) + 5 * b - 1 * (b ^^^ (a &&& c)) + 5 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 6 * ~~~(a ||| (b &&& c)) - 7 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 1 * (b ^^^ ~~~(a &&& (b ^^^ c))) - 6 * ~~~(a ^^^ b) + 3 * (c ||| ~~~(a ^^^ b)) - 11 * ~~~(a ||| ~~~c) - 1 * c + 4 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) - 2 * ~~~( ~~~a &&& (b ||| c)) - 7 * (b &&& (a ||| ~~~c)) + 1 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 5 * (c ^^^ (a ||| (b &&& c))) + 2 * (a &&& c) + 4 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) - 3 * (a &&& ( ~~~b ||| c)) - 2 * ( ~~~b &&& ~~~(a ^^^ c)) + 2 * ~~~a + 2 * ~~~(b ||| ~~~c) - 11 * ~~~c - 2 * ( ~~~b ||| (a ^^^ c)) - 7 * (a ^^^ ( ~~~b ||| c)) + 1 * (a ||| ~~~c) + 7 * (b ||| (a ^^^ c)) - 7 * (b ^^^ (a ||| ~~~c)) + 2 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) - 5 * (c ^^^ (a ||| ~~~b)) + 1 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) + 3 * ~~~(a &&& ~~~b) - 3 * ~~~(a ||| (b ||| c)) - 6 * ~~~(a ||| ( ~~~b ||| c)) - 16 * ~~~( ~~~a ||| (b ||| c)) - 7 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 38 * ( ~~~a &&& ( ~~~b &&& c)) - 8 * ( ~~~a &&& (b &&& c)) - 25 * (a &&& ( ~~~b &&& c)) - 33 * (a &&& (b &&& c)) = - 5 * (a ||| ~~~b) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1989 (x y : BitVec w) : +theorem e_1989 : 1 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) - 1 * (b ^^^ (a &&& (b ^^^ c))) - 1 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 5 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 6 * ~~~( ~~~a &&& (b ||| c)) + 1 * (b &&& c) + 3 * (b ^^^ (a &&& (b ||| c))) + 4 * b - 7 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 11 * ~~~(a ||| b) + 2 * ( ~~~(a ||| b) ||| (b ^^^ c)) + 1 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 4 * (c ^^^ (a ||| b)) + 1 * (b ||| (a ^^^ c)) - 3 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) + 3 * ~~~(a &&& b) - 11 * ( ~~~a ||| (b ^^^ c)) - 1 * ~~~c - 1 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 6 * ~~~(a ||| ~~~b) - 2 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) + 1 * ~~~(a &&& ~~~c) + 5 * ~~~( ~~~a &&& (b ^^^ c)) + 3 * (c ^^^ ~~~(a ||| ~~~b)) + 7 * ~~~(a &&& (b &&& c)) - 3 * ~~~(b ||| c) + 7 * ((a ^^^ b) ||| ~~~(a ^^^ c)) + 4 * ~~~(a &&& ~~~a) + 1 * ((a &&& ~~~b) ||| (b ^^^ c)) - 1 * (c &&& (a ^^^ b)) - 7 * (b ^^^ ~~~(a ||| (b &&& c))) - 11 * ~~~b - 1 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) + 1 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) + 1 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) - 1 * ~~~( ~~~a ||| (b &&& c)) - 2 * (c ^^^ ~~~(a ||| (b &&& c))) - 2 * ( ~~~a ||| (b &&& c)) - 1 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 5 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) - 1 * ~~~(a ^^^ b) + 2 * (c &&& ~~~(a ^^^ b)) - 6 * ((a ^^^ b) &&& (a ^^^ c)) + 2 * (b ^^^ (a ||| ( ~~~b ||| c))) - 1 * ~~~(a ^^^ c) + 2 * (b ^^^ ~~~(a ||| c)) + 2 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 11 * (a &&& ~~~c) - 7 * (b ^^^ (a &&& ( ~~~b ||| c))) + 1 * (a &&& (b ^^^ c)) + 30 * ~~~(a ||| (b ||| c)) + 13 * ~~~(a ||| ( ~~~b ||| c)) + 9 * ~~~( ~~~a ||| (b ||| c)) + 4 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 24 * ( ~~~a &&& ( ~~~b &&& c)) + 20 * ( ~~~a &&& (b &&& c)) + 21 * (a &&& ( ~~~b &&& c)) + 14 * (a &&& (b &&& c)) = 7 * (b ^^^ (a ||| ( ~~~b &&& c))) + 2 * ((a &&& c) ||| (b &&& ~~~c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1990 (x y : BitVec w) : +theorem e_1990 : 1 * ~~~(a ||| ~~~b) - 1 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) + 2 * ~~~( ~~~a &&& ( ~~~b &&& c)) - 6 * ((a &&& b) ||| ~~~(b ||| c)) - 7 * (c ^^^ (a ||| b)) - 3 * (b ^^^ (a ||| c)) + 1 * (c &&& (a ^^^ b)) - 7 * (c ^^^ ~~~(a &&& ~~~b)) + 2 * (a ||| ~~~c) - 5 * (b ^^^ (a ||| (b ||| c))) + 2 * ~~~( ~~~a ||| (b &&& c)) + 4 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) + 4 * ~~~(a &&& (b &&& c)) + 4 * ~~~(a &&& ~~~b) - 1 * ~~~( ~~~a &&& ( ~~~b ||| c)) - 7 * (b ^^^ ( ~~~a &&& (b ||| c))) + 1 * (c ^^^ ( ~~~a ||| (b ||| c))) + 1 * ( ~~~a ||| (b ^^^ c)) - 2 * (b ||| ~~~(a ||| ~~~c)) - 1 * ~~~(a &&& (b ||| c)) - 5 * ~~~(a ^^^ (b ||| c)) + 2 * (a ^^^ ( ~~~b ||| c)) + 4 * ( ~~~b &&& ~~~(a ^^^ c)) + 11 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) - 11 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) - 6 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) + 5 * b + 3 * ~~~a - 1 * (b ^^^ (a ||| ( ~~~b &&& c))) + 1 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) - 1 * (c &&& (a ||| b)) - 2 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) - 3 * (b ^^^ (a ||| (b &&& c))) + 2 * (b ^^^ ( ~~~a &&& (b ^^^ c))) - 5 * ( ~~~c ||| (a ^^^ b)) - 3 * a + 2 * ~~~( ~~~a ||| ( ~~~b &&& c)) + 1 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) + 5 * (a &&& c) + 7 * ( ~~~c &&& (a ^^^ b)) + 2 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 7 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) - 3 * ~~~(a &&& (b ^^^ c)) + 7 * ~~~(b ||| ~~~c) + 1 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) + 3 * (b ^^^ (a ||| ~~~c)) + 2 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) + 11 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) - 5 * (c ^^^ ~~~(a ||| b)) + 1 * (a &&& ~~~c) + 5 * ~~~(a ||| (b ||| c)) - 3 * ~~~(a ||| ( ~~~b ||| c)) - 14 * ~~~( ~~~a ||| (b ||| c)) + 1 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 26 * ( ~~~a &&& ( ~~~b &&& c)) - 20 * ( ~~~a &&& (b &&& c)) + 12 * (a &&& ( ~~~b &&& c)) - 5 * (a &&& (b &&& c)) = - 1 * ( ~~~a ||| (b ||| c)) - 11 * ( ~~~b ||| (a ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1991 (x y : BitVec w) : +theorem e_1991 : - 11 * ((a &&& ~~~b) ||| (b ^^^ c)) - 2 * (b ^^^ ( ~~~a ||| (b ^^^ c))) - 1 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) - 2 * (b ^^^ (a &&& ( ~~~b ||| c))) - 6 * (a ^^^ (b ||| c)) + 4 * ( ~~~(a ||| b) ||| ~~~(b ^^^ c)) - 1 * (c &&& (a ||| ~~~b)) - 1 * (a ||| ( ~~~b ||| c)) + 1 * (b ||| c) - 11 * ~~~(a &&& (b ^^^ c)) - 11 * ~~~( ~~~a ||| (b ^^^ c)) + 4 * ((a &&& b) ||| ~~~(b ^^^ c)) - 11 * ~~~(a ^^^ b) - 2 * (a ^^^ ( ~~~b &&& c)) - 1 * ~~~(a ||| b) + 2 * (c ^^^ (a ||| ( ~~~b ||| c))) - 6 * (b ^^^ ~~~(a ||| (b ^^^ c))) + 7 * ((a &&& c) ||| (b &&& ~~~c)) + 5 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) + 11 * ~~~(a ^^^ (b &&& c)) + 1 * ( ~~~(a ^^^ b) &&& ~~~(a ^^^ c)) + 2 * (c ||| ~~~(a ||| b)) - 5 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) - 6 * ~~~( ~~~a &&& ( ~~~b &&& c)) - 11 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) - 3 * (b ||| (a ^^^ c)) + 5 * ~~~(a &&& ~~~a) - 7 * (b ||| (a &&& ~~~c)) - 5 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) + 1 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) + 3 * (c ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 5 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) + 1 * (c &&& (a ||| b)) - 1 * (b ^^^ ~~~(a &&& (b ||| c))) - 6 * ~~~(a ^^^ (b ^^^ c)) + 1 * ~~~( ~~~a &&& (b ||| c)) + 5 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) - 6 * (b ^^^ (a ||| ( ~~~b &&& c))) - 3 * ( ~~~(a ||| b) ||| (b ^^^ c)) - 2 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 2 * ((a &&& c) ^^^ (b ||| c)) - 11 * (c ^^^ ( ~~~a ||| (b &&& c))) - 5 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) - 6 * ( ~~~a ||| (b ||| c)) - 5 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) + 2 * ~~~(a &&& ~~~b) + 3 * (c ^^^ ~~~(a ||| ~~~b)) - 1 * (a &&& (b ^^^ c)) - 2 * ( ~~~(a ||| b) ||| ~~~(a ^^^ (b ^^^ c))) - 7 * ((a ^^^ b) &&& (a ^^^ c)) + 48 * ~~~(a ||| (b ||| c)) + 69 * ~~~(a ||| ( ~~~b ||| c)) + 66 * ~~~( ~~~a ||| (b ||| c)) + 42 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 55 * ( ~~~a &&& ( ~~~b &&& c)) + 57 * ( ~~~a &&& (b &&& c)) + 40 * (a &&& ( ~~~b &&& c)) + 56 * (a &&& (b &&& c)) = - 4 * ~~~(a ||| (b ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1992 (x y : BitVec w) : +theorem e_1992 : 4 * (c ||| (a &&& ~~~b)) - 1 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) - 2 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) - 2 * (b ^^^ (a ||| (b ||| c))) + 1 * (b ||| (a &&& c)) - 7 * (b ^^^ (a &&& c)) + 1 * (b ||| (a &&& ~~~c)) - 1 * ~~~(a ^^^ (b ^^^ c)) - 2 * (c ^^^ ~~~(a &&& b)) - 2 * ~~~(a &&& (b ||| c)) + 2 * (b ^^^ c) - 2 * ~~~(a ||| c) + 4 * (b ^^^ ( ~~~a &&& (b ||| c))) - 1 * ( ~~~a ||| (b ||| c)) - 1 * (c ^^^ ~~~(a &&& (b &&& c))) - 5 * ( ~~~b ||| (a ^^^ c)) + 1 * ~~~a - 2 * ((a ^^^ b) ||| ~~~(a ^^^ c)) - 1 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 7 * (b ^^^ ~~~(a &&& (b &&& c))) - 3 * ( ~~~a &&& ( ~~~b ||| c)) - 7 * (b ||| (a ^^^ c)) + 1 * ( ~~~a &&& (b ^^^ c)) - 1 * (b ^^^ ~~~(a ||| (b ^^^ c))) + 4 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) + 1 * ~~~(a ^^^ (b ||| c)) + 7 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) - 11 * ((a &&& b) ^^^ (b ||| c)) + 1 * c + 2 * ~~~(a &&& b) + 2 * (b ^^^ (a ||| ( ~~~b &&& c))) + 1 * ~~~(a ||| ~~~b) + 11 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) + 4 * (a ^^^ c) - 11 * (a ||| ( ~~~b ||| c)) + 11 * (c &&& ~~~(a &&& ~~~b)) - 3 * ((b &&& c) ||| (a &&& (b ||| c))) - 1 * ~~~(a ^^^ ( ~~~b ||| c)) - 11 * ((a ||| b) &&& (b ^^^ c)) - 2 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) + 7 * ~~~(a ^^^ (b &&& c)) - 1 * ( ~~~c ||| (a ^^^ b)) - 5 * (c &&& ~~~(a &&& b)) - 1 * ~~~(a &&& ~~~c) - 11 * ~~~( ~~~a &&& (b &&& c)) + 1 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 1 * (a &&& ~~~b) - 5 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) + 1 * ~~~( ~~~a ||| (b ^^^ c)) - 7 * ((a ^^^ b) &&& ~~~(a ^^^ c)) + 16 * ~~~(a ||| (b ||| c)) + 57 * ~~~(a ||| ( ~~~b ||| c)) + 29 * ~~~( ~~~a ||| (b ||| c)) + 55 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 11 * ( ~~~a &&& ( ~~~b &&& c)) + 25 * ( ~~~a &&& (b &&& c)) + 58 * (a &&& ( ~~~b &&& c)) - 8 * (a &&& (b &&& c)) = - 3 * (c ^^^ ( ~~~a &&& (b ||| c))) + 6 * ((a ^^^ b) ||| (a ^^^ c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1993 (x y : BitVec w) : +theorem e_1993 : - 2 * ( ~~~c ||| ~~~(a ^^^ b)) - 7 * (b ^^^ ~~~(a ||| (b ^^^ c))) - 11 * (a ||| ~~~b) - 5 * ((a &&& c) ||| (b &&& ~~~c)) + 1 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 1 * (b ^^^ (a &&& ( ~~~b ||| c))) - 2 * (c ^^^ (a &&& ~~~b)) - 11 * b - 1 * ~~~(b ||| c) - 2 * (b &&& c) + 2 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) + 11 * ((a ^^^ b) &&& ~~~(a ^^^ c)) + 3 * (a ^^^ (b ||| c)) - 1 * (c ^^^ (a &&& b)) + 5 * ~~~(a &&& (b ||| c)) + 1 * (b ^^^ ~~~(a &&& ~~~c)) + 1 * ~~~(a &&& b) - 5 * (b ^^^ ~~~(a &&& c)) + 1 * (c ^^^ (a ||| (b &&& c))) + 2 * (b ^^^ ( ~~~a &&& (b ^^^ c))) + 4 * (a ^^^ c) - 1 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) - 6 * ((b &&& c) ^^^ ~~~(a &&& (b ^^^ c))) - 3 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) - 2 * (c &&& ~~~(a &&& ~~~b)) + 1 * ((b &&& c) ||| (a &&& (b ||| c))) - 1 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) + 3 * (c &&& (a ^^^ b)) - 1 * (b ^^^ ( ~~~a ||| (b ||| c))) + 7 * (c ^^^ ( ~~~a ||| ( ~~~b ||| c))) + 5 * (b ^^^ ~~~(a ||| c)) + 4 * (c ^^^ (a ||| ( ~~~b &&& c))) - 6 * (a &&& c) + 5 * ~~~(a ^^^ c) + 2 * ~~~( ~~~a &&& (b ||| c)) + 5 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) + 1 * (b &&& (a ||| c)) + 5 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) + 7 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) - 11 * (c ^^^ (a &&& (b ||| c))) + 4 * ( ~~~c &&& (a ^^^ b)) - 2 * (c ^^^ (a ||| (b ||| c))) - 3 * (c ^^^ ~~~(a &&& (b &&& c))) + 5 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 6 * (b &&& ~~~c) - 1 * (a &&& (b ^^^ c)) + 3 * (b ^^^ ( ~~~a &&& (b ||| c))) + 7 * (c &&& ~~~(a ^^^ b)) + 7 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 2 * (b ||| (a &&& c)) - 15 * ~~~(a ||| (b ||| c)) + 5 * ~~~(a ||| ( ~~~b ||| c)) - 16 * ~~~( ~~~a ||| (b ||| c)) + 36 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 13 * ( ~~~a &&& ( ~~~b &&& c)) - 8 * ( ~~~a &&& (b &&& c)) - 10 * (a &&& ( ~~~b &&& c)) + 21 * (a &&& (b &&& c)) = - 2 * ((a ^^^ b) &&& (a ^^^ c)) + 1 * (c ||| (a &&& ~~~b)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1994 (x y : BitVec w) : +theorem e_1994 : 1 * ( ~~~(a ^^^ b) ||| (a ^^^ c)) - 1 * ( ~~~a ||| (b &&& c)) + 3 * ((a &&& c) ^^^ ~~~(b &&& ~~~c)) + 1 * ~~~(a ||| (b ^^^ c)) + 7 * (b ^^^ ( ~~~a ||| (b ||| c))) + 2 * ( ~~~(a ||| ~~~b) ||| (a ^^^ (b ^^^ c))) - 7 * ((a ^^^ b) ||| (a ^^^ c)) - 1 * (c ^^^ ~~~(a ||| b)) + 1 * (a ||| ~~~b) + 1 * ( ~~~(a ||| ~~~b) ||| ~~~(b ^^^ c)) + 2 * (c &&& (a ||| ~~~b)) + 2 * (b ^^^ (a ||| ( ~~~b &&& c))) + 5 * ( ~~~a ||| ( ~~~b &&& c)) - 1 * (b ^^^ ~~~(a &&& (b ^^^ c))) - 7 * (c ^^^ ~~~(a &&& (b ||| c))) + 4 * (b &&& ~~~(a &&& c)) - 1 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) - 5 * ~~~(a ^^^ ( ~~~b &&& c)) - 1 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 3 * ~~~( ~~~a &&& ( ~~~b ||| c)) + 11 * ( ~~~b &&& (a ^^^ c)) - 1 * (a &&& (b ||| c)) - 2 * (a ||| ( ~~~b &&& c)) - 2 * ( ~~~a &&& (b ^^^ c)) - 2 * (b ^^^ ~~~(a &&& ~~~c)) - 5 * (a ^^^ (b ^^^ c)) - 5 * ( ~~~a ||| (b ||| c)) - 2 * (a ||| b) + 5 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) + 1 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) + 1 * ((a &&& b) ||| ~~~(b ^^^ c)) - 6 * ~~~(a ||| b) + 4 * ~~~b - 3 * (b ||| (a &&& c)) + 7 * (b ||| (a &&& ~~~c)) - 11 * ~~~(b ||| c) + 11 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 3 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) - 2 * ( ~~~c &&& ~~~(a ^^^ b)) + 7 * (a &&& c) + 4 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) - 1 * (b ^^^ ~~~( ~~~a ||| ( ~~~b &&& c))) - 1 * ((a ||| b) &&& ~~~(b ^^^ c)) - 6 * (b ^^^ (a ||| c)) + 3 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) - 11 * (c ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) + 4 * (c ^^^ (a ||| ( ~~~b &&& c))) + 1 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) + 11 * (b ||| ~~~(a ^^^ c)) + 1 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) + 1 * (c ^^^ ~~~( ~~~a &&& (b ||| c))) - 5 * ((a &&& b) ^^^ (b ||| ~~~c)) + 17 * ~~~(a ||| ( ~~~b ||| c)) + 1 * ~~~( ~~~a ||| (b ||| c)) - 4 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 4 * ( ~~~a &&& ( ~~~b &&& c)) - 23 * ( ~~~a &&& (b &&& c)) - 9 * (a &&& ( ~~~b &&& c)) - 8 * (a &&& (b &&& c)) = 2 * ~~~(a ||| (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1995 (x y : BitVec w) : +theorem e_1995 : - 1 * ~~~(a &&& (b ||| c)) + 1 * (b ^^^ ~~~(a &&& ~~~c)) - 2 * ~~~b + 1 * ~~~( ~~~a ||| (b ^^^ c)) - 6 * (a &&& (b ||| c)) + 4 * (a ^^^ (b ||| c)) - 1 * (c ^^^ ~~~(a &&& b)) - 6 * (b ^^^ (a &&& (b ||| c))) + 1 * ~~~(a ||| (b &&& c)) + 11 * ( ~~~b &&& ~~~(a ^^^ c)) - 11 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 7 * ((a &&& ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 2 * ~~~(a &&& ~~~a) - 11 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 11 * (b ^^^ (a &&& ~~~c)) + 7 * (c ^^^ ~~~(a ||| (b &&& c))) - 1 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) + 11 * (b &&& ~~~c) + 1 * ((a &&& b) ||| ~~~(b ||| c)) - 1 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) + 2 * ~~~(b ||| ~~~c) + 1 * (b ^^^ ~~~(a ||| (b ^^^ c))) - 2 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) - 2 * (a ||| b) + 1 * ~~~(a ^^^ b) - 2 * (b ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 3 * (b ^^^ ~~~(a &&& (b ^^^ c))) + 1 * ( ~~~a ||| ( ~~~b &&& c)) - 2 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) - 7 * (c &&& (a ^^^ b)) + 2 * (a ||| ( ~~~b &&& c)) - 5 * ~~~a + 2 * ( ~~~b ||| (a ^^^ c)) + 5 * (a &&& b) + 2 * (b ^^^ ~~~(a &&& ( ~~~b &&& c))) + 7 * ( ~~~a &&& (b ||| c)) + 3 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) + 5 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) + 1 * (a ^^^ c) - 1 * (b ||| ~~~(a ||| c)) - 2 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) + 1 * (c ^^^ ~~~(a &&& ~~~b)) + 2 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 1 * (b ||| (a &&& ~~~c)) + 3 * (c ^^^ ~~~( ~~~a ||| (b &&& c))) - 7 * (c ^^^ ~~~(a &&& (b ||| c))) + 4 * ((a &&& ~~~b) ||| (b ^^^ c)) - 2 * (b ||| ~~~(a ^^^ c)) - 6 * (a &&& ( ~~~b ||| c)) - 1 * (b ^^^ (a &&& (b ^^^ c))) - 2 * ~~~(a ^^^ ( ~~~b ||| c)) + 6 * ~~~(a ||| (b ||| c)) - 13 * ~~~(a ||| ( ~~~b ||| c)) - 5 * ~~~( ~~~a ||| (b ||| c)) - 11 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 15 * ( ~~~a &&& ( ~~~b &&& c)) - 16 * ( ~~~a &&& (b &&& c)) + 30 * (a &&& ( ~~~b &&& c)) + 18 * (a &&& (b &&& c)) = - 1 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1996 (x y : BitVec w) : +theorem e_1996 : 5 * (b ^^^ (a ||| (b ^^^ c))) - 5 * ( ~~~(a &&& b) &&& ~~~(a ^^^ (b ^^^ c))) + 3 * ~~~(a ||| ~~~b) - 2 * ~~~(a ||| ~~~c) - 1 * (b ^^^ (a &&& (b ^^^ c))) - 2 * ( ~~~(a &&& ~~~b) &&& (b ^^^ c)) - 11 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) + 11 * (c ^^^ ~~~(a &&& ( ~~~b ||| c))) - 2 * (b ^^^ ~~~(a &&& ~~~c)) - 6 * (c ^^^ (a ||| ( ~~~b ||| c))) - 11 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 7 * (a ^^^ b) + 5 * (b ^^^ (a ||| (b &&& c))) - 5 * ((a ^^^ b) ||| ~~~(a ^^^ c)) - 5 * (c ^^^ ~~~(a &&& ~~~b)) + 2 * ((a ^^^ b) ||| (a ^^^ c)) - 6 * (c ^^^ (a ||| (b &&& c))) + 11 * ~~~(a ||| (b &&& c)) + 2 * (c ^^^ (a &&& ~~~b)) - 5 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) - 1 * (a &&& (b ^^^ c)) + 1 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) + 1 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) + 1 * ( ~~~a ||| (b ^^^ c)) + 4 * (b ||| ~~~(a ||| ~~~c)) + 1 * (a ^^^ ( ~~~b &&& c)) + 7 * (c ^^^ ~~~(a &&& (b &&& c))) - 6 * (b ^^^ ~~~(a ||| (b ^^^ c))) + 1 * (c &&& ~~~(a &&& ~~~b)) + 1 * ( ~~~a &&& ( ~~~b ||| c)) - 6 * ~~~(a &&& c) - 1 * (b ^^^ (a ||| ( ~~~b ||| c))) + 7 * (c ||| (a &&& b)) - 1 * (b ^^^ (a ||| ~~~c)) + 4 * b - 1 * ~~~( ~~~a ||| (b ^^^ c)) - 2 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) - 1 * ((a ^^^ b) &&& ~~~(a ^^^ c)) + 2 * ((a ||| b) &&& (a ^^^ (b ^^^ c))) - 5 * ~~~(a ||| ( ~~~b &&& c)) - 6 * ( ~~~(a &&& b) &&& (b ^^^ c)) + 5 * (a &&& c) - 5 * ~~~(b ||| c) - 11 * (b ^^^ ~~~(a &&& (b ||| c))) + 1 * ~~~( ~~~a &&& ( ~~~b &&& c)) + 3 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) - 11 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) + 1 * (a ||| (b &&& c)) + 1 * ~~~(a &&& ( ~~~b &&& c)) + 3 * (a ||| b) - 3 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 56 * ~~~(a ||| (b ||| c)) + 6 * ~~~(a ||| ( ~~~b ||| c)) + 27 * ~~~( ~~~a ||| (b ||| c)) + 15 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 5 * ( ~~~a &&& ( ~~~b &&& c)) + 37 * ( ~~~a &&& (b &&& c)) + 16 * (a &&& ( ~~~b &&& c)) + 13 * (a &&& (b &&& c)) = 1 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1997 (x y : BitVec w) : +theorem e_1997 : 1 * ~~~( ~~~a ||| (b ^^^ c)) + 3 * ((a &&& b) ^^^ (a ^^^ (b &&& c))) + 3 * (b ^^^ ~~~( ~~~a &&& (b ||| c))) - 2 * ((b &&& ~~~c) ^^^ (a ||| (b ^^^ c))) + 11 * ~~~c - 2 * ( ~~~b ||| (a ^^^ c)) - 1 * (b &&& ~~~(a ^^^ c)) + 2 * ( ~~~(a ||| ~~~b) ||| ~~~(a ^^^ (b ^^^ c))) - 5 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) + 1 * (b &&& (a ^^^ c)) - 7 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) + 7 * (c ^^^ ( ~~~a &&& ( ~~~b ||| c))) + 2 * c - 3 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) - 6 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 4 * (a &&& b) + 3 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) + 11 * (c ^^^ ( ~~~a ||| (b &&& c))) + 11 * ( ~~~a &&& ( ~~~b ||| c)) - 2 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) - 1 * (c ^^^ (a ||| b)) + 1 * ~~~(a ||| ( ~~~b &&& c)) + 1 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) - 2 * ~~~(a ||| (b &&& c)) - 2 * (b ^^^ ( ~~~a ||| (b ||| c))) + 1 * ( ~~~a ||| (b &&& c)) + 5 * (a ||| ~~~b) - 1 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) + 2 * ( ~~~(a &&& b) &&& ~~~(b ^^^ c)) - 1 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) + 1 * ( ~~~b ||| ~~~(a ^^^ c)) + 1 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 5 * (b ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) + 2 * (c ^^^ ~~~(a &&& ~~~b)) + 4 * (c ^^^ (a ||| ( ~~~b ||| c))) - 3 * ((b &&& ~~~c) ||| ~~~( ~~~a ||| ( ~~~b &&& c))) + 1 * (c ^^^ (a &&& (b ||| c))) + 3 * ((a &&& ~~~b) ||| (a ^^^ (b ^^^ c))) + 4 * (a ||| ( ~~~b &&& c)) - 3 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 1 * (a &&& (b ^^^ c)) - 6 * ((a &&& b) ||| ~~~(b ||| ~~~c)) + 2 * (c ^^^ (a ||| (b &&& c))) + 2 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) - 3 * (b ||| (a &&& c)) - 11 * ( ~~~a &&& (b ||| c)) - 5 * ((a &&& b) ||| ~~~(a ^^^ (b ^^^ c))) - 1 * (b ^^^ (a ||| ( ~~~b ||| c))) - 11 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) - 7 * ((b &&& c) ||| ( ~~~a &&& (b ||| c))) - 11 * (c ^^^ ~~~(a &&& b)) + 4 * (c &&& ~~~(a ^^^ b)) - 22 * ~~~(a ||| (b ||| c)) + 36 * ~~~(a ||| ( ~~~b ||| c)) - 16 * ~~~( ~~~a ||| (b ||| c)) + 5 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 28 * ( ~~~a &&& ( ~~~b &&& c)) + 12 * ( ~~~a &&& (b &&& c)) - 21 * (a &&& ( ~~~b &&& c)) = - 12 * (a &&& (b &&& c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1998 (x y : BitVec w) : +theorem e_1998 : - 11 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 7 * ( ~~~a ||| (b &&& c)) + 2 * (c ||| ~~~(a ||| ~~~b)) + 7 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) + 1 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) + 4 * (a &&& ~~~c) - 2 * ~~~( ~~~a ||| (b ^^^ c)) - 7 * (c &&& (a ||| b)) + 3 * (b &&& ~~~c) - 5 * ((a &&& ~~~b) ||| ~~~(b ^^^ c)) + 5 * (b ^^^ (a &&& c)) + 2 * (b ^^^ ( ~~~a ||| ( ~~~b ||| c))) - 5 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) - 11 * ~~~(a ^^^ b) + 2 * (c ^^^ (a &&& ~~~b)) - 3 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) - 6 * ((a &&& b) ^^^ (a ^^^ ( ~~~b ||| c))) + 11 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 1 * ~~~(a ^^^ (b &&& c)) - 6 * (b ^^^ (a ||| ( ~~~b ||| c))) + 1 * (a ||| ( ~~~b ||| c)) - 2 * ~~~(b &&& ~~~c) + 1 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) + 3 * ~~~(a ||| (b ^^^ c)) - 1 * b - 7 * (b ^^^ ~~~(a ||| (b ^^^ c))) + 11 * ~~~(a ^^^ c) - 1 * ~~~(a ^^^ ( ~~~b &&& c)) - 1 * ~~~(b &&& c) + 7 * (b ^^^ (a ||| ( ~~~b &&& c))) + 1 * ~~~( ~~~a &&& ( ~~~b ||| c)) + 2 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) - 5 * (a &&& (b ^^^ c)) - 3 * (b ^^^ ( ~~~a &&& (b ^^^ c))) + 4 * ((a &&& b) ||| ~~~(b ||| c)) + 7 * (b ^^^ ( ~~~a ||| (b &&& c))) + 3 * (c ||| (a &&& b)) + 2 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) - 1 * (b ^^^ ( ~~~a ||| (b ^^^ c))) + 2 * (b ^^^ ~~~(a &&& ( ~~~b ||| c))) - 2 * ( ~~~(a &&& b) &&& (a ^^^ (b ^^^ c))) - 2 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) + 5 * a - 6 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) + 2 * ((a ||| ~~~b) &&& (a ^^^ (b ^^^ c))) + 4 * ((a &&& c) ||| (b &&& ~~~c)) - 1 * (b ^^^ (a &&& (b ||| c))) - 6 * (b ^^^ (a ||| (b ^^^ c))) + 11 * (b ^^^ ~~~( ~~~a &&& ( ~~~b &&& c))) - 5 * ((a ||| ~~~b) &&& (b ^^^ c)) + 1 * (b ^^^ ( ~~~a &&& (b ||| c))) - 18 * ~~~(a ||| (b ||| c)) - 26 * ~~~(a ||| ( ~~~b ||| c)) - 16 * ~~~( ~~~a ||| (b ||| c)) - 12 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 15 * ( ~~~a &&& ( ~~~b &&& c)) + 25 * ( ~~~a &&& (b &&& c)) - 23 * (a &&& ( ~~~b &&& c)) + 4 * (a &&& (b &&& c)) = - 11 * ( ~~~(a ^^^ b) ||| ~~~(a ^^^ c)) - 1 * (c ^^^ ~~~(a &&& (b &&& c))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_1999 (x y : BitVec w) : +theorem e_1999 : 2 * (c &&& (a ^^^ b)) + 11 * ~~~(b &&& c) - 7 * ~~~(b &&& ~~~c) + 4 * (a ^^^ c) - 6 * (b ^^^ c) - 6 * (c &&& ~~~(a &&& b)) - 3 * ~~~a + 1 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) - 2 * ( ~~~a ||| (b ^^^ c)) + 4 * ((a &&& c) ^^^ (a ^^^ ( ~~~b &&& c))) + 5 * (b ||| ~~~(a ^^^ c)) - 2 * ( ~~~(a &&& ~~~b) &&& ~~~(b ^^^ c)) - 5 * (b ^^^ ( ~~~a ||| (b ||| c))) - 5 * (b &&& c) + 5 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) - 11 * (c ^^^ (a ||| ~~~b)) - 1 * (c ^^^ (a ||| b)) + 7 * (b ^^^ (a &&& c)) - 1 * ( ~~~b ||| ~~~(a ^^^ c)) + 1 * ((a ^^^ b) &&& ~~~(a ^^^ c)) - 1 * (c ^^^ ~~~( ~~~a &&& ( ~~~b ||| c))) - 2 * ~~~(a &&& (b ||| c)) + 1 * ( ~~~a ||| (b ||| c)) - 2 * (a &&& c) - 3 * (a &&& ~~~b) + 1 * ((a &&& c) ^^^ ~~~(a ^^^ (b &&& c))) + 1 * ( ~~~a ||| ( ~~~b &&& c)) + 1 * (c ^^^ ( ~~~a ||| (b &&& c))) - 6 * (b &&& ~~~(a ^^^ c)) - 1 * ~~~b + 5 * (b ^^^ ~~~(a &&& (b &&& c))) + 2 * (b &&& (a ^^^ c)) - 7 * ((a &&& c) ||| (b &&& ~~~c)) + 4 * (b &&& (a ||| c)) + 3 * ( ~~~(a ||| b) ||| (a ^^^ (b ^^^ c))) + 1 * (b ^^^ (a ||| ( ~~~b &&& c))) + 3 * ((a &&& b) ^^^ (b ||| ~~~c)) + 1 * (a ^^^ ( ~~~b ||| c)) - 2 * ( ~~~(a &&& ~~~b) &&& (a ^^^ (b ^^^ c))) - 11 * (c ^^^ ~~~(a &&& ( ~~~b &&& c))) - 6 * ~~~( ~~~a &&& ( ~~~b ||| c)) + 5 * ~~~c + 11 * ( ~~~(a ||| ~~~b) ||| (b ^^^ c)) + 3 * (a &&& ( ~~~b ||| c)) - 11 * (b ||| ~~~c) - 2 * ((a &&& b) ^^^ ~~~(a ^^^ ( ~~~b ||| c))) + 3 * (b ^^^ ~~~(a &&& c)) + 4 * (b ^^^ ~~~( ~~~a ||| (b &&& c))) + 1 * (b ^^^ (a &&& (b ^^^ c))) - 11 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 1 * ((a &&& c) ^^^ (b ||| c)) + 3 * ( ~~~a &&& (b ||| c)) + 11 * (c ^^^ ( ~~~a ||| ( ~~~b &&& c))) - 14 * ~~~(a ||| ( ~~~b ||| c)) - 6 * ~~~( ~~~a ||| (b ||| c)) - 2 * ~~~( ~~~a ||| ( ~~~b ||| c)) - 11 * ( ~~~a &&& ( ~~~b &&& c)) - 5 * ( ~~~a &&& (b &&& c)) + 9 * (a &&& (b &&& c)) = - 11 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) - 4 * ~~~(a ||| (b ||| c)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2000 (x y : BitVec w) : +theorem e_2000 : 11 * ~~~(a &&& (b &&& c)) + 4 * ~~~( ~~~a ||| ( ~~~b &&& c)) - 3 * ~~~a - 3 * (b ^^^ ( ~~~a ||| ( ~~~b &&& c))) + 2 * ( ~~~a &&& ( ~~~b ||| c)) - 1 * ((b &&& ~~~c) ||| ~~~(a ||| ( ~~~b &&& c))) + 11 * (b ^^^ ( ~~~a ||| (b ||| c))) - 1 * (c ^^^ ~~~(a ||| ( ~~~b &&& c))) - 1 * (c ^^^ ~~~( ~~~a &&& (b &&& c))) + 1 * (c ^^^ ~~~(a &&& (b ||| c))) - 11 * (a ^^^ c) - 6 * ((a ||| b) &&& ~~~(a ^^^ (b ^^^ c))) + 1 * ((a ||| ~~~b) &&& ~~~(b ^^^ c)) + 1 * ((b &&& c) ^^^ ~~~( ~~~a &&& (b ^^^ c))) + 2 * (a ^^^ ( ~~~b &&& c)) - 1 * (b ^^^ ~~~(a ||| ~~~c)) + 5 * ~~~(a ||| b) + 3 * (c ^^^ ( ~~~a &&& (b ||| c))) + 2 * ((a &&& b) ^^^ ~~~(a ^^^ (b &&& c))) - 1 * ( ~~~(a ^^^ b) &&& (a ^^^ c)) - 2 * ~~~(a &&& b) + 5 * ((a &&& c) ^^^ (a ^^^ (b &&& c))) + 1 * (c ||| (a &&& b)) + 1 * (c ^^^ ( ~~~a ||| (b ||| c))) - 7 * (a &&& ~~~b) + 3 * (b ^^^ ( ~~~a &&& ( ~~~b ||| c))) - 3 * ( ~~~a ||| (b ^^^ c)) - 7 * ~~~(b &&& c) + 2 * ((a ^^^ b) ||| ~~~(a ^^^ c)) - 3 * ((a ||| ~~~b) &&& ~~~(a ^^^ (b ^^^ c))) - 7 * ((a ||| ~~~b) &&& (b ^^^ c)) - 11 * ((a &&& b) ||| ~~~(b ^^^ c)) + 2 * (c ^^^ ( ~~~a ||| (b &&& c))) + 1 * (b ^^^ (a ||| (b ||| c))) + 1 * (c ^^^ (a &&& b)) - 2 * ( ~~~a ||| ( ~~~b &&& c)) + 5 * (b ^^^ ( ~~~a ||| (b ^^^ c))) + 4 * (b ^^^ (a &&& c)) - 7 * ( ~~~a &&& (b ^^^ c)) + 4 * (b ||| (a &&& c)) + 7 * ~~~(a ||| ( ~~~b &&& c)) + 1 * (c ^^^ (a ||| ( ~~~b ||| c))) - 3 * ((a &&& b) ||| ~~~(b ||| ~~~c)) - 2 * ~~~( ~~~a ||| (b ^^^ c)) + 3 * (b ^^^ ~~~(a &&& (b ^^^ c))) + 2 * ((a ^^^ b) &&& ~~~(a ^^^ c)) + 7 * (a ||| b) - 3 * (b &&& ~~~(a ^^^ c)) + 2 * (b &&& (a ^^^ c)) + 1 * (b ^^^ ~~~( ~~~a ||| (b ^^^ c))) - 5 * ((a &&& b) ||| (a ^^^ (b ^^^ c))) - 16 * ~~~(a ||| (b ||| c)) - 15 * ~~~(a ||| ( ~~~b ||| c)) + 5 * ~~~( ~~~a ||| (b ||| c)) + 15 * ~~~( ~~~a ||| ( ~~~b ||| c)) + 9 * ( ~~~a &&& ( ~~~b &&& c)) - 7 * ( ~~~a &&& (b &&& c)) - 13 * (a &&& ( ~~~b &&& c)) - 4 * (a &&& (b &&& c)) = 6 * (b ^^^ ~~~(a ||| ( ~~~b &&& c))) - 1 * (a ||| ~~~c) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2001 (x y : BitVec w) : +theorem e_2001 : - 6 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 2 * ~~~(d ^^^ ( ~~~e ||| f)) - 7 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 1 * (f ^^^ (d &&& ~~~e)) + 2 * (f ^^^ (d &&& e)) + 1 * (f ^^^ ~~~(d &&& e)) - 5 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 3 * (d ^^^ f) + 1 * (d &&& ~~~f) - 1 * (e ^^^ (d ||| ( ~~~e &&& f))) + 1 * ~~~(d &&& ( ~~~e ||| f)) - 3 * (e ^^^ ( ~~~d ||| (e ||| f))) - 2 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 6 * (f ||| (d &&& ~~~e)) + 1 * (d ||| ~~~e) + 1 * (e ^^^ (d &&& ~~~f)) + 3 * ~~~(d ^^^ e) + 11 * (e &&& ~~~f) + 1 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 5 * ~~~(e ||| ~~~f) - 3 * (d ^^^ ( ~~~e &&& f)) + 7 * ~~~(d &&& f) + 4 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 11 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 23 * ~~~(d ||| (e ||| f)) - 27 * ~~~(d ||| ( ~~~e ||| f)) + 7 * ~~~( ~~~d ||| (e ||| f)) - 20 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 5 * ( ~~~d &&& ( ~~~e &&& f)) + 12 * ( ~~~d &&& (e &&& f)) + 4 * (d &&& ( ~~~e &&& f)) + 10 * (d &&& (e &&& f)) = 1 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 3 * ~~~(e &&& f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2002 (x y : BitVec w) : +theorem e_2002 : 4 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 5 * (e ||| (d ^^^ f)) + 1 * ~~~(d &&& ( ~~~e &&& f)) - 6 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 11 * f - 11 * ( ~~~e &&& (d ^^^ f)) - 3 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 7 * ~~~(d &&& ~~~d) + 7 * (d ^^^ e) + 11 * ~~~(e ||| f) + 1 * (e &&& ~~~(d &&& f)) - 7 * (e &&& ~~~f) + 11 * ~~~(d &&& ( ~~~e ||| f)) - 2 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * (e ^^^ (d ||| ( ~~~e ||| f))) - 5 * (f ^^^ (d &&& ( ~~~e ||| f))) + 7 * (e ^^^ f) - 1 * (d ||| e) - 7 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 5 * (d ||| (e &&& f)) + 1 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 3 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 1 * ( ~~~d ||| ( ~~~e ||| f)) + 3 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 5 * (d &&& ( ~~~e ||| f)) + 2 * (d ^^^ (e ^^^ f)) - 22 * ~~~(d ||| (e ||| f)) - 13 * ~~~(d ||| ( ~~~e ||| f)) + 17 * ~~~( ~~~d ||| (e ||| f)) - 6 * ( ~~~d &&& ( ~~~e &&& f)) - 13 * ( ~~~d &&& (e &&& f)) - 5 * (d &&& ( ~~~e &&& f)) = 7 * (d &&& (e &&& f)) + 4 * ~~~( ~~~d ||| ( ~~~e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2003 (x y : BitVec w) : +theorem e_2003 : 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 2 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 1 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 2 * (d &&& (e ||| f)) - 1 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 11 * (f &&& (d ||| ~~~e)) - 2 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 1 * (e ^^^ ~~~(d &&& f)) + 5 * d - 7 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 5 * (e ^^^ (d ||| (e &&& f))) - 6 * (e &&& f) - 2 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 7 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 1 * (f ^^^ (d ||| (e ||| f))) + 1 * (e &&& (d ||| f)) + 1 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 5 * (f &&& ~~~(d &&& ~~~e)) - 11 * ~~~(d ^^^ ( ~~~e ||| f)) - 1 * (e ||| ~~~f) + 7 * ~~~(d ^^^ ( ~~~e &&& f)) + 7 * ~~~(d ^^^ (e ||| f)) + 11 * (f ^^^ (d ||| e)) - 2 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 10 * ~~~(d ||| (e ||| f)) + 5 * ~~~(d ||| ( ~~~e ||| f)) + 13 * ~~~( ~~~d ||| (e ||| f)) - 18 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 29 * ( ~~~d &&& ( ~~~e &&& f)) + 12 * ( ~~~d &&& (e &&& f)) - 11 * (d &&& ( ~~~e &&& f)) - 1 * (d &&& (e &&& f)) = 1 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 11 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2004 (x y : BitVec w) : +theorem e_2004 : - 2 * (f ||| ~~~(d ||| ~~~e)) + 4 * ( ~~~f &&& (d ^^^ e)) - 1 * (d &&& ~~~f) + 1 * ( ~~~d ||| ( ~~~e ||| f)) + 4 * ~~~(d ^^^ ( ~~~e ||| f)) - 3 * (e &&& (d ||| f)) + 5 * (f &&& (d ||| e)) - 2 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 7 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 3 * (f ||| (d &&& ~~~e)) + 5 * ~~~(d ^^^ (e &&& f)) + 1 * (d ||| ( ~~~e ||| f)) - 2 * ((d &&& e) ^^^ (e ||| ~~~f)) + 1 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 2 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 11 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 3 * (e &&& ~~~f) - 1 * (e &&& f) + 7 * (d ^^^ e) - 1 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 5 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 5 * (d ||| (e &&& f)) + 7 * (f ^^^ ( ~~~d ||| (e ||| f))) - 2 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 27 * ~~~(d ||| (e ||| f)) - 23 * ~~~(d ||| ( ~~~e ||| f)) - 22 * ~~~( ~~~d ||| (e ||| f)) - 14 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 12 * ( ~~~d &&& ( ~~~e &&& f)) - 14 * ( ~~~d &&& (e &&& f)) - 15 * (d &&& ( ~~~e &&& f)) - 26 * (d &&& (e &&& f)) = - 5 * ((d &&& f) ||| ~~~(e ||| f)) - 2 * ~~~(d ||| ~~~f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2005 (x y : BitVec w) : +theorem e_2005 : 1 * (f ||| (d &&& e)) - 2 * ( ~~~f ||| ~~~(d ^^^ e)) + 5 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 2 * ((d ||| e) &&& (e ^^^ f)) - 1 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 4 * (f ^^^ ~~~(d ||| (e &&& f))) + 2 * ((d ^^^ e) ||| (d ^^^ f)) - 5 * ( ~~~d ||| (e ||| f)) - 7 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 1 * (e &&& (d ^^^ f)) - 1 * (e ^^^ ~~~(d &&& (e ||| f))) - 5 * ( ~~~d ||| (e &&& f)) + 5 * (f ^^^ (d &&& ( ~~~e ||| f))) - 1 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 6 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 1 * ~~~(e &&& f) - 2 * ( ~~~e &&& (d ^^^ f)) - 2 * (f ^^^ ( ~~~d ||| (e &&& f))) + 3 * (e ^^^ (d ||| f)) + 1 * ~~~(d ||| (e ^^^ f)) - 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 7 * ~~~(d &&& ( ~~~e ||| f)) - 1 * (d ^^^ (e ^^^ f)) - 2 * (d &&& (e ||| f)) + 22 * ~~~(d ||| (e ||| f)) + 13 * ~~~(d ||| ( ~~~e ||| f)) - 7 * ~~~( ~~~d ||| (e ||| f)) + 4 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 5 * ( ~~~d &&& ( ~~~e &&& f)) - 4 * ( ~~~d &&& (e &&& f)) - 6 * (d &&& ( ~~~e &&& f)) + 13 * (d &&& (e &&& f)) = - 1 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 11 * ~~~(d &&& (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2006 (x y : BitVec w) : +theorem e_2006 : - 1 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 2 * ((d ^^^ e) &&& (d ^^^ f)) - 7 * ((d &&& e) ||| (e ^^^ f)) + 7 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 2 * ( ~~~e &&& ~~~(d ^^^ f)) - 1 * (f ^^^ ~~~(d &&& (e &&& f))) + 1 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 3 * (e ||| (d &&& ~~~f)) + 11 * ~~~(d &&& ( ~~~e &&& f)) + 5 * (d &&& ~~~f) + 2 * (e ||| (d ^^^ f)) - 1 * (f ||| (d &&& e)) + 1 * (d ||| ~~~e) - 2 * ( ~~~e ||| ~~~(d ^^^ f)) + 2 * ~~~(d &&& ~~~f) - 11 * ( ~~~d ||| ( ~~~e ||| f)) - 1 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 11 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 1 * (d ||| ( ~~~e ||| f)) + 7 * (e ^^^ ~~~(d &&& ~~~f)) + 7 * (e ^^^ f) + 1 * ~~~(d ||| (e &&& f)) + 4 * ~~~(d &&& ( ~~~e ||| f)) + 11 * (e &&& ~~~(d &&& ~~~f)) - 5 * (e &&& f) - 28 * ~~~(d ||| (e ||| f)) - 31 * ~~~(d ||| ( ~~~e ||| f)) - 7 * ~~~( ~~~d ||| (e ||| f)) - 40 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 24 * ( ~~~d &&& ( ~~~e &&& f)) - 13 * ( ~~~d &&& (e &&& f)) + 2 * (d &&& ( ~~~e &&& f)) - 13 * (d &&& (e &&& f)) = 2 * (f ^^^ (d &&& e)) - 1 * ((d ||| e) &&& ~~~(e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2007 (x y : BitVec w) : +theorem e_2007 : 1 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 1 * (f ^^^ ( ~~~d &&& (e ||| f))) + 11 * ~~~(e ^^^ f) + 1 * ~~~(e &&& f) + 11 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 1 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 1 * ( ~~~d &&& ( ~~~e ||| f)) + 1 * (e &&& (d ||| f)) + 5 * (e ^^^ (d &&& (e ||| f))) - 5 * (d ^^^ f) - 2 * (e ||| (d &&& ~~~f)) + 1 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 11 * (f &&& ~~~(d ^^^ e)) + 7 * (d ^^^ e) - 3 * ~~~(d &&& ( ~~~e &&& f)) - 3 * ((d &&& e) ^^^ (e ||| f)) + 4 * ~~~(d &&& f) + 1 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 5 * (d ^^^ ( ~~~e ||| f)) + 1 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 7 * (f ^^^ ~~~(d ||| e)) + 3 * (f ^^^ ( ~~~d ||| (e ||| f))) - 2 * (e ^^^ (d &&& ( ~~~e ||| f))) - 6 * (d ||| (e ^^^ f)) - 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 18 * ~~~(d ||| (e ||| f)) - 20 * ~~~( ~~~d ||| (e ||| f)) + 12 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 1 * ( ~~~d &&& ( ~~~e &&& f)) - 13 * ( ~~~d &&& (e &&& f)) - 18 * (d &&& ( ~~~e &&& f)) - 27 * (d &&& (e &&& f)) = 3 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 3 * ~~~(d ||| ( ~~~e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2008 (x y : BitVec w) : +theorem e_2008 : - 11 * (e ^^^ ( ~~~d ||| (e &&& f))) + 1 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 4 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 2 * ~~~(e &&& ~~~f) + 1 * ( ~~~d &&& (e ||| f)) + 1 * ((d ^^^ e) &&& (d ^^^ f)) - 1 * d - 3 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 1 * ~~~(d &&& ~~~e) + 2 * (e ^^^ (d &&& (e ||| f))) - 6 * (d ||| ~~~f) + 7 * (d ^^^ e) - 5 * (e ^^^ (d &&& f)) + 3 * (e ||| f) - 11 * (e ^^^ ~~~(d &&& (e &&& f))) - 5 * ((d &&& ~~~e) ||| (e ^^^ f)) + 2 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 1 * ( ~~~f &&& ~~~(d ^^^ e)) - 2 * ~~~( ~~~d &&& (e ^^^ f)) - 2 * (f ^^^ (d &&& ~~~e)) - 11 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 2 * ((d &&& e) ||| (e ^^^ f)) + 1 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * ~~~e + 1 * (e ||| (d ^^^ f)) + 7 * (e ^^^ ( ~~~d &&& (e ||| f))) + 17 * ~~~(d ||| (e ||| f)) + 10 * ~~~(d ||| ( ~~~e ||| f)) + 13 * ~~~( ~~~d ||| (e ||| f)) + 13 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 9 * ( ~~~d &&& (e &&& f)) + 30 * (d &&& ( ~~~e &&& f)) + 5 * (d &&& (e &&& f)) = - 2 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 26 * ( ~~~d &&& ( ~~~e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2009 (x y : BitVec w) : +theorem e_2009 : - 3 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 1 * ((d &&& e) ||| ~~~(e ||| f)) + 5 * (e ^^^ (d ||| f)) - 11 * ((d ||| ~~~e) &&& (e ^^^ f)) - 2 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 1 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 2 * ( ~~~d ||| ( ~~~e &&& f)) + 1 * ~~~(d ||| ~~~f) - 6 * ( ~~~f ||| ~~~(d ^^^ e)) + 2 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 4 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 2 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 11 * (e ^^^ ~~~(d &&& ~~~f)) - 7 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 1 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 6 * (e ||| (d &&& ~~~f)) - 1 * (f ^^^ (d ||| (e &&& f))) + 1 * ((d &&& e) ||| (e ^^^ f)) + 3 * (f ^^^ ~~~(d ||| ~~~e)) + 2 * ~~~(d ^^^ (e &&& f)) + 2 * (e ^^^ ( ~~~d &&& (e ||| f))) + 1 * ((d ^^^ e) &&& (d ^^^ f)) + 3 * (e ||| (d &&& f)) + 2 * (e &&& (d ||| f)) + 5 * (d &&& f) - 1 * ~~~(d ^^^ f) - 6 * ~~~(d ||| (e ||| f)) + 13 * ~~~(d ||| ( ~~~e ||| f)) + 11 * ~~~( ~~~d ||| (e ||| f)) + 16 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 4 * ( ~~~d &&& ( ~~~e &&& f)) - 3 * ( ~~~d &&& (e &&& f)) - 7 * (d &&& ( ~~~e &&& f)) = 2 * (d &&& (e &&& f)) + 1 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2010 (x y : BitVec w) : +theorem e_2010 : 2 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 3 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 1 * (f ^^^ ~~~(d &&& ~~~e)) - 1 * (f ^^^ (d &&& ~~~e)) + 11 * ~~~(d &&& e) - 6 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 2 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 2 * (f &&& (d ^^^ e)) - 7 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 1 * (f &&& ~~~(d &&& ~~~e)) - 2 * ((d &&& f) ^^^ (e ||| f)) + 4 * ~~~(d &&& ( ~~~e ||| f)) + 4 * (e ||| f) + 4 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 11 * ~~~(d ||| (e ^^^ f)) - 3 * (f ^^^ (d ||| e)) + 2 * ( ~~~e ||| (d ^^^ f)) + 11 * (e &&& ~~~(d ^^^ f)) - 5 * ~~~(d &&& (e &&& f)) + 7 * (e ^^^ (d ||| (e ||| f))) - 11 * (e ^^^ ~~~(d &&& (e &&& f))) - 7 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 2 * ~~~(d ^^^ (e ^^^ f)) - 2 * (d &&& (e ||| f)) - 3 * ((d &&& e) ^^^ (e ||| ~~~f)) + 13 * ~~~(d ||| (e ||| f)) - 8 * ~~~(d ||| ( ~~~e ||| f)) + 22 * ~~~( ~~~d ||| (e ||| f)) + 13 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 6 * ( ~~~d &&& ( ~~~e &&& f)) + 5 * ( ~~~d &&& (e &&& f)) - 2 * (d &&& ( ~~~e &&& f)) + 15 * (d &&& (e &&& f)) = 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2011 (x y : BitVec w) : +theorem e_2011 : 7 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 2 * (e ^^^ (d ||| (e &&& f))) - 1 * (f ^^^ (d &&& ~~~e)) - 2 * (d &&& (e ||| f)) - 2 * (f ^^^ ~~~(d &&& e)) - 7 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 2 * (f ^^^ ~~~(d ||| e)) + 2 * ~~~(d &&& ( ~~~e ||| f)) + 11 * (e ||| ~~~(d ||| f)) - 1 * ( ~~~d ||| (e ^^^ f)) - 6 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 5 * (e ^^^ (d &&& (e ||| f))) + 11 * (d ^^^ (e ^^^ f)) - 11 * (e ^^^ (d &&& f)) + 2 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 11 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 7 * ~~~(d ||| ( ~~~e &&& f)) - 1 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 2 * (f ||| (d ^^^ e)) - 11 * (f ^^^ ( ~~~d ||| (e &&& f))) + 1 * ((d &&& e) ^^^ (e ||| f)) - 7 * (f ^^^ ~~~(d ||| ~~~e)) + 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * ((d ^^^ e) &&& (d ^^^ f)) - 5 * (f ^^^ (d &&& ( ~~~e ||| f))) - 11 * ~~~(d ||| (e ||| f)) + 16 * ~~~(d ||| ( ~~~e ||| f)) - 10 * ~~~( ~~~d ||| (e ||| f)) - 8 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 4 * ( ~~~d &&& ( ~~~e &&& f)) - 13 * ( ~~~d &&& (e &&& f)) + 38 * (d &&& ( ~~~e &&& f)) - 21 * (d &&& (e &&& f)) = 5 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2012 (x y : BitVec w) : +theorem e_2012 : - 5 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 4 * (f ||| ~~~(d ^^^ e)) - 3 * (e ^^^ (d ||| ~~~f)) - 1 * (f ^^^ ~~~(d &&& ~~~e)) + 4 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 2 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 6 * (e ^^^ (d ||| (e &&& f))) - 1 * (f ^^^ (d ||| (e &&& f))) - 5 * ~~~(e ||| f) - 7 * ( ~~~d &&& ( ~~~e ||| f)) + 11 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 4 * ~~~(d ^^^ (e ^^^ f)) - 6 * (f ^^^ (d ||| (e ||| f))) - 6 * ~~~(d &&& f) - 7 * ((d &&& e) ^^^ (e ||| f)) - 1 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 3 * ~~~(d ^^^ ( ~~~e &&& f)) + 2 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 5 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 2 * (e ||| ~~~(d ^^^ f)) + 3 * ( ~~~d ||| (e &&& f)) + 3 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 7 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 1 * (e ^^^ ~~~(d &&& (e &&& f))) - 11 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 3 * (e ^^^ (d &&& (e ||| f))) + 11 * ~~~(d ||| (e ||| f)) + 18 * ( ~~~d &&& ( ~~~e &&& f)) + 12 * ( ~~~d &&& (e &&& f)) - 1 * (d &&& ( ~~~e &&& f)) - 2 * (d &&& (e &&& f)) = - 42 * ~~~( ~~~d ||| (e ||| f)) - 41 * ~~~(d ||| ( ~~~e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2013 (x y : BitVec w) : +theorem e_2013 : 5 * (e ||| ~~~(d ||| f)) - 3 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 3 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 11 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 2 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 5 * ~~~(e ||| f) - 11 * ((d &&& e) ||| ~~~(e ||| f)) - 6 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 2 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 7 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 6 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 7 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 2 * (e ^^^ f) + 1 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 2 * (e ^^^ (d ||| (e &&& f))) + 5 * ~~~(e ||| ~~~f) - 11 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 5 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 5 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 5 * (f ^^^ (d ||| (e &&& f))) + 4 * ((d &&& ~~~e) ||| (e ^^^ f)) + 2 * (f ^^^ ~~~(d &&& e)) + 4 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 10 * ~~~(d ||| (e ||| f)) - 1 * ~~~(d ||| ( ~~~e ||| f)) + 11 * ~~~( ~~~d ||| (e ||| f)) + 26 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 14 * ( ~~~d &&& ( ~~~e &&& f)) - 4 * ( ~~~d &&& (e &&& f)) + 13 * (d &&& ( ~~~e &&& f)) + 18 * (d &&& (e &&& f)) = 1 * (e ^^^ ~~~(d ||| (e &&& f))) + 3 * (d &&& ~~~f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2014 (x y : BitVec w) : +theorem e_2014 : - 1 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 6 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 7 * ~~~(d ^^^ ( ~~~e &&& f)) - 2 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 6 * (e &&& (d ||| ~~~f)) - 1 * (d ||| ~~~e) + 1 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 1 * (e ^^^ (d &&& ~~~f)) + 5 * (e ||| (d ^^^ f)) + 1 * ~~~(d &&& (e &&& f)) - 1 * ((d &&& e) ||| ~~~(e ||| f)) - 5 * (f ^^^ (d ||| (e &&& f))) + 7 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * (e ^^^ ~~~(d ||| f)) + 4 * (d ||| ( ~~~e ||| f)) - 3 * ( ~~~f &&& (d ^^^ e)) + 3 * f - 1 * (f ^^^ ~~~(d ||| ~~~e)) - 1 * (e ||| (d &&& f)) - 7 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 7 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * ( ~~~d ||| (e ^^^ f)) - 11 * (d ^^^ (e ^^^ f)) + 5 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 2 * (f ^^^ (d ||| e)) - 5 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 1 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 8 * ~~~(d ||| (e ||| f)) + 24 * ~~~(d ||| ( ~~~e ||| f)) + 6 * ( ~~~d &&& ( ~~~e &&& f)) - 15 * ( ~~~d &&& (e &&& f)) - 7 * (d &&& ( ~~~e &&& f)) + 14 * (d &&& (e &&& f)) = - 7 * (d ||| (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2015 (x y : BitVec w) : +theorem e_2015 : 5 * (f ^^^ (d &&& e)) + 11 * ( ~~~e &&& ~~~(d ^^^ f)) + 4 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 1 * (e ||| ~~~(d ||| f)) + 2 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 2 * (f ^^^ ~~~(d &&& e)) + 2 * ~~~(d ^^^ e) + 3 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 1 * (f ^^^ (d ||| (e &&& f))) - 3 * ~~~( ~~~d &&& (e &&& f)) + 3 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 1 * (e ||| ~~~f) + 1 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 5 * (d &&& (e ^^^ f)) - 11 * ( ~~~d ||| (e ^^^ f)) - 6 * e + 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 2 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 11 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 3 * (e ||| (d ^^^ f)) + 4 * ((d ^^^ e) ||| (d ^^^ f)) + 11 * (d ||| e) + 1 * (d ||| (e ^^^ f)) - 11 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 11 * ~~~(d &&& (e ^^^ f)) - 11 * (e &&& ~~~(d &&& f)) - 18 * ~~~(d ||| (e ||| f)) - 9 * ~~~(d ||| ( ~~~e ||| f)) - 34 * ~~~( ~~~d ||| (e ||| f)) - 7 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 18 * ( ~~~d &&& ( ~~~e &&& f)) + 1 * ( ~~~d &&& (e &&& f)) - 7 * (d &&& ( ~~~e &&& f)) - 23 * (d &&& (e &&& f)) = - 7 * ((d &&& e) ||| ~~~(e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2016 (x y : BitVec w) : +theorem e_2016 : - 1 * ((e &&& f) ||| (d &&& (e ||| f))) + 7 * (f ||| (d ^^^ e)) + 1 * ((d &&& e) ||| (e ^^^ f)) + 1 * (e ^^^ ~~~(d ||| ~~~f)) + 2 * ( ~~~e &&& ~~~(d ^^^ f)) - 1 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * (d ^^^ ( ~~~e &&& f)) - 1 * (d ||| (e &&& f)) - 2 * (e ^^^ (d &&& f)) + 2 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 3 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 1 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 5 * (e ||| ~~~f) + 2 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 3 * (e ^^^ ( ~~~d ||| (e &&& f))) - 2 * (e ^^^ ~~~(d &&& (e &&& f))) - 7 * (d ||| f) + 2 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 1 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 1 * ( ~~~f &&& ~~~(d ^^^ e)) + 1 * (d &&& ~~~f) - 1 * ((d ||| e) &&& ~~~(e ^^^ f)) + 1 * (f &&& ~~~(d &&& e)) - 6 * (e ^^^ ~~~(d &&& f)) - 6 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 2 * d + 24 * ~~~(d ||| (e ||| f)) + 3 * ~~~(d ||| ( ~~~e ||| f)) + 22 * ~~~( ~~~d ||| (e ||| f)) + 18 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 14 * ( ~~~d &&& ( ~~~e &&& f)) + 9 * (d &&& ( ~~~e &&& f)) + 15 * (d &&& (e &&& f)) = 2 * (f ^^^ ~~~(d ||| (e &&& f))) - 14 * ( ~~~d &&& (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2017 (x y : BitVec w) : +theorem e_2017 : - 1 * ( ~~~e &&& ~~~(d ^^^ f)) - 7 * ((d &&& f) ||| ~~~(e ||| f)) + 7 * ((d ^^^ e) &&& (d ^^^ f)) + 4 * (f ||| (d &&& ~~~e)) + 4 * (f &&& ~~~(d &&& ~~~e)) + 1 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 2 * (d ^^^ (e &&& f)) + 1 * (e ||| (d &&& ~~~f)) + 2 * (e ||| f) - 2 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 2 * (f &&& ~~~(d &&& e)) - 2 * ~~~(d ||| ( ~~~e &&& f)) - 6 * ((d &&& e) ^^^ (e ||| f)) - 7 * (e ^^^ ~~~(d &&& ~~~f)) - 5 * (d ||| (e ^^^ f)) + 1 * ~~~(d ||| e) + 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 11 * (e ^^^ (d &&& (e ||| f))) + 1 * (f ||| ~~~(d ^^^ e)) - 5 * (e &&& ~~~f) - 1 * (d &&& ~~~e) - 3 * ((d &&& e) ||| ~~~(e ||| f)) + 7 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 1 * (f ^^^ ( ~~~d &&& (e ||| f))) - 3 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 11 * (f ^^^ (d ||| ~~~e)) + 2 * ~~~(d &&& (e ^^^ f)) - 1 * ~~~(d ||| (e ||| f)) - 15 * ~~~( ~~~d ||| (e ||| f)) + 1 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 4 * ( ~~~d &&& ( ~~~e &&& f)) - 19 * ( ~~~d &&& (e &&& f)) + 24 * (d &&& ( ~~~e &&& f)) - 6 * (d &&& (e &&& f)) = - 16 * ~~~(d ||| ( ~~~e ||| f)) - 2 * (e ^^^ (d ||| (e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2018 (x y : BitVec w) : +theorem e_2018 : 1 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 11 * ((d &&& f) ||| (e &&& ~~~f)) - 6 * (e ^^^ ~~~(d &&& (e &&& f))) + 1 * (e ^^^ (d ||| ~~~f)) - 1 * (f ^^^ (d &&& ~~~e)) - 1 * f + 5 * (f ||| ~~~(d ^^^ e)) + 7 * (e ||| ~~~(d ||| f)) - 1 * ~~~(d &&& ~~~f) + 2 * (e ^^^ ~~~(d &&& (e ||| f))) + 2 * ( ~~~f &&& ~~~(d ^^^ e)) - 7 * (d &&& ~~~e) + 7 * (e ^^^ f) + 7 * ( ~~~e ||| (d ^^^ f)) - 1 * e - 1 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 6 * ~~~( ~~~d ||| (e ^^^ f)) + 11 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 2 * (f &&& (d ||| ~~~e)) - 1 * (d ^^^ f) - 1 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 5 * (f ^^^ ( ~~~d ||| (e &&& f))) - 7 * (e ^^^ (d &&& ( ~~~e ||| f))) - 1 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 1 * (e ^^^ ~~~(d &&& f)) + 1 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 24 * ~~~(d ||| (e ||| f)) - 13 * ~~~(d ||| ( ~~~e ||| f)) + 3 * ~~~( ~~~d ||| (e ||| f)) - 33 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 27 * ( ~~~d &&& ( ~~~e &&& f)) - 9 * ( ~~~d &&& (e &&& f)) - 6 * (d &&& ( ~~~e &&& f)) - 12 * (d &&& (e &&& f)) = - 1 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 2 * (e ^^^ (d &&& ~~~f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2019 (x y : BitVec w) : +theorem e_2019 : 4 * ~~~( ~~~d &&& (e ^^^ f)) - 1 * (f ^^^ ( ~~~d ||| (e &&& f))) + 1 * (e &&& f) + 1 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 7 * (e &&& (d ||| ~~~f)) - 2 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 2 * (f ^^^ ~~~(d &&& e)) - 3 * (d &&& ( ~~~e ||| f)) - 1 * ((d &&& e) ||| ~~~(e ^^^ f)) + 3 * (e ^^^ (d &&& f)) - 3 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 1 * (e &&& ~~~(d ^^^ f)) - 6 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 1 * (f ^^^ (d &&& e)) - 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 1 * ((d &&& e) ^^^ (e ||| f)) - 5 * ~~~( ~~~d ||| (e ^^^ f)) - 6 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 5 * ( ~~~e ||| (d ^^^ f)) - 2 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 7 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 2 * ~~~(d ||| ( ~~~e &&& f)) - 2 * (e ^^^ (d ||| f)) + 1 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 5 * ~~~(d ^^^ e) + 9 * ~~~(d ||| (e ||| f)) + 1 * ~~~(d ||| ( ~~~e ||| f)) + 29 * ~~~( ~~~d ||| (e ||| f)) - 9 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 22 * ( ~~~d &&& ( ~~~e &&& f)) + 17 * ( ~~~d &&& (e &&& f)) + 14 * (d &&& ( ~~~e &&& f)) - 3 * (d &&& (e &&& f)) = 1 * ((d &&& e) ^^^ (e ||| ~~~f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2020 (x y : BitVec w) : +theorem e_2020 : 1 * (d ||| ( ~~~e &&& f)) + 2 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 7 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 2 * (f ||| (d &&& ~~~e)) - 6 * (e ^^^ f) - 1 * (e &&& f) - 5 * (e ^^^ (d ||| f)) - 6 * (d ||| (e &&& f)) + 3 * ((d &&& e) ||| ~~~(e ^^^ f)) - 1 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 4 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 3 * (d ||| f) + 5 * (e ^^^ (d ||| (e ^^^ f))) - 5 * ((d ^^^ e) ||| ~~~(d ^^^ f)) + 1 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 3 * (e ||| (d &&& f)) + 2 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 11 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 1 * (d ||| ( ~~~e ||| f)) - 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 11 * (d &&& (e ^^^ f)) - 2 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 4 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 1 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 11 * (e ^^^ ( ~~~d ||| (e &&& f))) - 3 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 11 * (e ^^^ ~~~(d ||| (e &&& f))) + 11 * (f ||| ~~~(d ||| ~~~e)) + 7 * ~~~(d ||| (e ||| f)) - 4 * ~~~( ~~~d ||| (e ||| f)) + 45 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 12 * ( ~~~d &&& ( ~~~e &&& f)) - 14 * ( ~~~d &&& (e &&& f)) - 7 * (d &&& ( ~~~e &&& f)) = - 11 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 7 * ~~~(d ||| ( ~~~e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2021 (x y : BitVec w) : +theorem e_2021 : - 6 * ((d &&& e) ^^^ (e ||| f)) + 5 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 3 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 6 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 2 * (e ^^^ (d ||| (e ^^^ f))) + 1 * ( ~~~e ||| ~~~(d ^^^ f)) - 5 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 7 * ~~~(e &&& ~~~f) + 2 * ~~~(d ^^^ (e &&& f)) - 1 * ( ~~~d &&& (e ||| f)) - 5 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 4 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 2 * (d ||| (e ^^^ f)) - 1 * (f &&& ~~~(d ^^^ e)) + 2 * ~~~(d ^^^ ( ~~~e &&& f)) + 3 * (d ^^^ (e ||| f)) - 5 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 11 * ((d &&& ~~~e) ||| (e ^^^ f)) + 4 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 1 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 3 * ~~~(d &&& ~~~f) + 2 * (e ^^^ (d &&& f)) + 1 * ((d ||| e) &&& (e ^^^ f)) + 11 * ~~~(d ^^^ ( ~~~e ||| f)) - 1 * ~~~(d ||| (e ^^^ f)) - 6 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 3 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 6 * ~~~(d ||| (e ||| f)) + 5 * ~~~(d ||| ( ~~~e ||| f)) + 3 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 16 * ( ~~~d &&& ( ~~~e &&& f)) - 6 * ( ~~~d &&& (e &&& f)) - 1 * (d &&& ( ~~~e &&& f)) - 12 * (d &&& (e &&& f)) = - 4 * (e ||| (d ^^^ f)) - 1 * (f ^^^ (d &&& (e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2022 (x y : BitVec w) : +theorem e_2022 : - 1 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 5 * (d &&& f) + 1 * ((e &&& f) ||| (d &&& (e ||| f))) - 2 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 1 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 7 * ~~~(d &&& (e &&& f)) + 2 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 11 * ((d ^^^ e) ||| (d ^^^ f)) + 2 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 1 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 3 * ~~~(d ^^^ (e &&& f)) - 1 * (f ^^^ ( ~~~d ||| (e &&& f))) + 1 * ~~~(d &&& ( ~~~e &&& f)) + 2 * (f ^^^ (d ||| ( ~~~e &&& f))) + 4 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 1 * f - 2 * ~~~( ~~~d ||| (e &&& f)) - 6 * (e ^^^ (d ||| f)) - 7 * ( ~~~f &&& (d ^^^ e)) + 4 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 7 * (e &&& ~~~f) + 3 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 5 * ~~~( ~~~d &&& (e ||| f)) + 1 * ( ~~~d ||| (e ||| f)) + 11 * (d &&& ( ~~~e ||| f)) + 2 * ( ~~~d &&& (e ||| f)) + 1 * ((d ^^^ e) &&& (d ^^^ f)) - 9 * ~~~(d ||| (e ||| f)) - 3 * ~~~(d ||| ( ~~~e ||| f)) - 24 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 9 * ( ~~~d &&& ( ~~~e &&& f)) - 15 * ( ~~~d &&& (e &&& f)) - 29 * (d &&& ( ~~~e &&& f)) - 26 * (d &&& (e &&& f)) = 12 * ~~~( ~~~d ||| (e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2023 (x y : BitVec w) : +theorem e_2023 : - 1 * (f ^^^ ( ~~~d ||| (e ||| f))) + 2 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 3 * (e ^^^ (d &&& ( ~~~e ||| f))) - 11 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 3 * (e &&& ~~~(d ^^^ f)) - 2 * ((d &&& f) ^^^ (e ||| f)) - 7 * ((d ||| e) &&& (e ^^^ f)) - 6 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 2 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 7 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 1 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 11 * ~~~(d ||| e) + 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 1 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 6 * (d ||| ( ~~~e ||| f)) + 2 * ~~~f + 2 * ( ~~~d &&& (e ||| f)) - 1 * ( ~~~d ||| (e &&& f)) + 1 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 3 * (d ^^^ f) - 7 * (d &&& (e ||| f)) - 1 * (d ||| (e ||| f)) - 1 * (e ^^^ (d ||| (e ||| f))) + 3 * (e ^^^ ( ~~~d &&& (e ||| f))) + 1 * (e ^^^ ~~~(d &&& (e ||| f))) + 4 * (e ^^^ ( ~~~d ||| (e ||| f))) - 9 * ~~~(d ||| (e ||| f)) + 13 * ~~~(d ||| ( ~~~e ||| f)) + 15 * ~~~( ~~~d ||| (e ||| f)) + 36 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 8 * ( ~~~d &&& ( ~~~e &&& f)) + 25 * ( ~~~d &&& (e &&& f)) + 29 * (d &&& ( ~~~e &&& f)) + 18 * (d &&& (e &&& f)) = 1 * ( ~~~d ||| (e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2024 (x y : BitVec w) : +theorem e_2024 : 3 * (e ^^^ ~~~(d &&& ~~~f)) + 3 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 7 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 2 * ~~~( ~~~d ||| (e &&& f)) + 1 * ( ~~~d ||| ( ~~~e ||| f)) - 2 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 1 * (e ^^^ ~~~(d &&& (e ||| f))) - 6 * (d ^^^ f) + 11 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 1 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 3 * (e &&& ~~~(d &&& ~~~f)) - 2 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 7 * (f ^^^ ~~~(d ||| ~~~e)) - 1 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 11 * ( ~~~d &&& (e ^^^ f)) + 5 * ( ~~~d ||| (e ^^^ f)) + 2 * (f ^^^ (d &&& (e ||| f))) - 5 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 5 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 4 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 2 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 1 * (e &&& ~~~(d &&& f)) + 2 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 2 * ~~~( ~~~d &&& (e ||| f)) + 3 * (f ^^^ ~~~(d &&& (e ||| f))) + 5 * (d &&& ~~~f) + 4 * (d &&& e) - 6 * ((d &&& e) ||| (e ^^^ f)) - 30 * ~~~(d ||| (e ||| f)) - 8 * ~~~( ~~~d ||| (e ||| f)) - 5 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 21 * ( ~~~d &&& ( ~~~e &&& f)) + 1 * (d &&& ( ~~~e &&& f)) = 3 * (d ||| (e ||| f)) + 19 * ( ~~~d &&& (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2025 (x y : BitVec w) : +theorem e_2025 : 3 * (f ^^^ (d &&& (e ||| f))) + 4 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 1 * ((d ^^^ e) &&& (d ^^^ f)) - 1 * (e ^^^ ~~~(d ||| ~~~f)) - 6 * ~~~(d ||| ~~~e) - 5 * (e ^^^ ~~~(d ||| f)) + 1 * ((d ^^^ e) ||| ~~~(d ^^^ f)) + 5 * d - 1 * ~~~f - 5 * (e ^^^ ~~~(d &&& (e &&& f))) + 2 * (e ^^^ ( ~~~d &&& (e ||| f))) - 1 * e - 11 * (e ^^^ ( ~~~d ||| (e ||| f))) + 2 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 11 * (d ^^^ (e ^^^ f)) + 1 * ~~~(d ||| (e &&& f)) + 4 * (e &&& ~~~(d ^^^ f)) + 1 * (f &&& (d ||| e)) + 5 * (f &&& ~~~(d &&& e)) - 1 * ((d &&& e) ||| (e ^^^ f)) + 2 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 7 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 1 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 5 * (f ^^^ (d ||| (e ||| f))) - 2 * (f ^^^ ~~~(d ||| ~~~e)) - 2 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 4 * ~~~(d ||| (e ||| f)) - 17 * ~~~(d ||| ( ~~~e ||| f)) - 18 * ~~~( ~~~d ||| (e ||| f)) - 6 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 13 * ( ~~~d &&& ( ~~~e &&& f)) - 4 * ( ~~~d &&& (e &&& f)) + 2 * (d &&& ( ~~~e &&& f)) - 21 * (d &&& (e &&& f)) = 2 * (d ||| f) - 1 * (f ^^^ (d ||| (e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2026 (x y : BitVec w) : +theorem e_2026 : 7 * ~~~(d &&& (e &&& f)) - 1 * ~~~f - 1 * (d ^^^ (e ||| f)) - 2 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 11 * ~~~(d ||| ~~~f) - 7 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 2 * ~~~(e &&& f) + 1 * ~~~(e &&& ~~~f) + 2 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 2 * (f ||| ~~~(d ^^^ e)) + 2 * ((d &&& e) ||| ~~~(e ||| f)) + 11 * ( ~~~d ||| (e &&& f)) - 11 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 3 * ~~~(d &&& ~~~f) + 3 * (d &&& ( ~~~e ||| f)) + 4 * (f &&& ~~~(d &&& ~~~e)) + 7 * ~~~( ~~~d &&& (e &&& f)) - 1 * (d &&& e) - 3 * (e ^^^ ~~~(d &&& (e ||| f))) - 1 * ~~~(d ||| ~~~e) - 1 * (f ^^^ (d ||| (e ||| f))) - 3 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 11 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 7 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 5 * ( ~~~d ||| (e ^^^ f)) - 3 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 2 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 12 * ~~~(d ||| ( ~~~e ||| f)) + 1 * ~~~( ~~~d ||| (e ||| f)) - 12 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 5 * ( ~~~d &&& ( ~~~e &&& f)) + 28 * ( ~~~d &&& (e &&& f)) - 2 * (d &&& ( ~~~e &&& f)) + 5 * (d &&& (e &&& f)) = 4 * ~~~(d ||| (e ||| f)) + 1 * ~~~e := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2027 (x y : BitVec w) : +theorem e_2027 : - 3 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 6 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 11 * ( ~~~e &&& (d ^^^ f)) + 2 * ~~~( ~~~d &&& (e &&& f)) - 6 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 2 * ~~~f + 5 * (f &&& ~~~(d &&& e)) - 2 * ((d &&& ~~~e) ||| (e ^^^ f)) + 1 * (f ^^^ (d ||| e)) + 7 * ( ~~~f &&& ~~~(d ^^^ e)) + 5 * (d ||| (e &&& f)) - 11 * ~~~(d ||| (e ^^^ f)) - 3 * ((d &&& f) ||| (e &&& ~~~f)) - 5 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 1 * (e ^^^ (d ||| (e ^^^ f))) + 3 * (f ||| ~~~(d ||| ~~~e)) + 3 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * d - 1 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 11 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 5 * (e ||| ~~~f) + 7 * ( ~~~d ||| ( ~~~e ||| f)) - 7 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 7 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 7 * ( ~~~d ||| ( ~~~e &&& f)) + 7 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 2 * (e ^^^ ~~~(d ||| (e &&& f))) - 11 * ~~~(d ||| (e ||| f)) - 19 * ~~~(d ||| ( ~~~e ||| f)) - 21 * ~~~( ~~~d ||| (e ||| f)) - 28 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 42 * ( ~~~d &&& ( ~~~e &&& f)) - 34 * ( ~~~d &&& (e &&& f)) - 19 * (d &&& ( ~~~e &&& f)) - 23 * (d &&& (e &&& f)) = 1 * ~~~( ~~~d &&& ( ~~~e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2028 (x y : BitVec w) : +theorem e_2028 : - 5 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 4 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 5 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 2 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 1 * (e ^^^ (d ||| f)) + 11 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 4 * (f ||| ~~~(d ^^^ e)) + 1 * (f ^^^ (d &&& ~~~e)) - 1 * ( ~~~d ||| ( ~~~e ||| f)) + 2 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 6 * (f ^^^ ~~~(d &&& e)) + 1 * (e ^^^ (d ||| ~~~f)) + 4 * (f &&& ~~~(d &&& e)) + 1 * (e &&& ~~~(d &&& f)) - 3 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 7 * ((d &&& f) ||| ~~~(e ||| f)) + 2 * (d ||| ~~~e) + 3 * ( ~~~f &&& ~~~(d ^^^ e)) - 5 * (d &&& (e ||| f)) + 2 * (d &&& ~~~f) + 3 * (f ^^^ ( ~~~d ||| (e &&& f))) - 11 * (f ^^^ ~~~(d &&& (e ||| f))) - 1 * (e ||| ~~~(d ^^^ f)) + 11 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 5 * (e &&& (d ^^^ f)) + 1 * ( ~~~d &&& ( ~~~e ||| f)) - 2 * (f ||| (d &&& ~~~e)) - 22 * ~~~(d ||| (e ||| f)) + 8 * ~~~(d ||| ( ~~~e ||| f)) + 6 * ~~~( ~~~d ||| (e ||| f)) + 12 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 5 * ( ~~~d &&& ( ~~~e &&& f)) - 18 * ( ~~~d &&& (e &&& f)) - 2 * (d &&& ( ~~~e &&& f)) + 5 * (d &&& (e &&& f)) = 1 * (f ||| (d ^^^ e)) + 7 * (d &&& (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2029 (x y : BitVec w) : +theorem e_2029 : 11 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 1 * ((d &&& f) ||| ~~~(e ||| f)) - 1 * (d ^^^ f) - 3 * (d ||| f) + 4 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 7 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 7 * ~~~(d ^^^ ( ~~~e ||| f)) - 3 * (d ^^^ (e ^^^ f)) + 5 * (e ||| ~~~(d ^^^ f)) + 5 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 2 * (f ^^^ ~~~(d ||| ~~~e)) + 5 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 2 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 1 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 5 * (f ||| ~~~(d ||| e)) + 1 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 7 * ~~~f - 2 * (d ^^^ (e ||| f)) - 2 * (f ^^^ ( ~~~d ||| (e &&& f))) - 3 * ( ~~~f &&& ~~~(d ^^^ e)) + 11 * ~~~(d ||| (e &&& f)) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 7 * ((d ^^^ e) ||| (d ^^^ f)) + 5 * ~~~( ~~~d &&& (e &&& f)) - 2 * (f ^^^ (d ||| ( ~~~e ||| f))) + 2 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 7 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 31 * ~~~(d ||| (e ||| f)) - 30 * ~~~(d ||| ( ~~~e ||| f)) - 14 * ~~~( ~~~d ||| (e ||| f)) - 33 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 40 * ( ~~~d &&& ( ~~~e &&& f)) - 17 * ( ~~~d &&& (e &&& f)) - 48 * (d &&& ( ~~~e &&& f)) - 18 * (d &&& (e &&& f)) = 1 * (e &&& (d ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2030 (x y : BitVec w) : +theorem e_2030 : - 2 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 7 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 1 * ( ~~~d ||| (e ^^^ f)) - 1 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 11 * (f ^^^ ~~~(d ||| (e &&& f))) - 5 * (d ^^^ (e ||| f)) + 5 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 3 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 7 * (e ||| f) + 5 * (f ||| (d &&& ~~~e)) + 4 * ~~~(d ^^^ ( ~~~e &&& f)) + 2 * (e &&& ~~~f) + 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 5 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 11 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 7 * ~~~(d ||| (e &&& f)) - 1 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 2 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 11 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 3 * (e ^^^ (d &&& (e ^^^ f))) - 7 * ( ~~~d ||| (e &&& f)) - 3 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 5 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 2 * ((d ||| e) &&& ~~~(e ^^^ f)) - 1 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 4 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 4 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 42 * ~~~(d ||| (e ||| f)) + 52 * ~~~(d ||| ( ~~~e ||| f)) + 18 * ~~~( ~~~d ||| (e ||| f)) - 3 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 25 * ( ~~~d &&& ( ~~~e &&& f)) + 36 * ( ~~~d &&& (e &&& f)) + 16 * (d &&& ( ~~~e &&& f)) + 44 * (d &&& (e &&& f)) = 2 * (e ^^^ (d &&& (e ||| f))) - 3 * ((d ^^^ e) ||| (d ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2031 (x y : BitVec w) : +theorem e_2031 : - 6 * (f &&& (d ^^^ e)) - 5 * ~~~(d ^^^ ( ~~~e ||| f)) - 6 * (e &&& ~~~(d &&& ~~~f)) + 1 * ~~~(d ^^^ f) + 1 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 2 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 6 * ((d ^^^ e) ||| (d ^^^ f)) - 1 * (f ||| ~~~(d ||| ~~~e)) - 1 * ~~~(d &&& f) - 1 * (e ^^^ (d ||| ~~~f)) + 2 * (d ||| (e ||| f)) + 7 * ((d &&& ~~~e) ||| (e ^^^ f)) - 11 * ( ~~~d ||| (e ||| f)) - 1 * (e ||| (d ^^^ f)) + 11 * (f ^^^ (d ||| (e &&& f))) - 2 * ((d &&& e) ||| ~~~(e ^^^ f)) - 11 * (f ^^^ (d ||| e)) - 1 * (f ^^^ ( ~~~d ||| (e &&& f))) - 1 * (e ^^^ (d ||| (e ||| f))) + 2 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 7 * (e ^^^ ~~~(d &&& (e &&& f))) - 11 * (d &&& ~~~e) - 5 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 1 * (e ^^^ ~~~(d ||| (e &&& f))) - 11 * (e ||| ~~~(d ^^^ f)) - 7 * ((d ||| ~~~e) &&& (e ^^^ f)) - 5 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 38 * ~~~(d ||| (e ||| f)) + 46 * ~~~(d ||| ( ~~~e ||| f)) + 32 * ~~~( ~~~d ||| (e ||| f)) + 34 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 30 * ( ~~~d &&& ( ~~~e &&& f)) + 47 * ( ~~~d &&& (e &&& f)) + 63 * (d &&& ( ~~~e &&& f)) + 43 * (d &&& (e &&& f)) = 5 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * ~~~(d ^^^ (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2032 (x y : BitVec w) : +theorem e_2032 : 11 * (e ^^^ (d ||| ( ~~~e ||| f))) - 1 * ~~~(e ^^^ f) + 11 * ( ~~~d ||| (e &&& f)) - 3 * (f &&& ~~~(d &&& e)) + 3 * ((d &&& e) ^^^ (e ||| ~~~f)) - 2 * ~~~(d &&& (e &&& f)) + 1 * (f ||| ~~~(d ^^^ e)) - 2 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 6 * (f ^^^ (d ||| (e ||| f))) + 4 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 4 * ~~~( ~~~d &&& (e &&& f)) + 1 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 5 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 2 * (f ^^^ (d ||| ( ~~~e ||| f))) - 5 * ( ~~~d ||| ( ~~~e &&& f)) - 3 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 2 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 11 * ~~~( ~~~d ||| (e ^^^ f)) + 7 * (e ||| ~~~(d ^^^ f)) + 3 * ((d ||| e) &&& ~~~(e ^^^ f)) + 11 * (e ^^^ ~~~(d &&& f)) - 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 2 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 7 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 41 * ~~~(d ||| (e ||| f)) - 19 * ~~~(d ||| ( ~~~e ||| f)) - 37 * ~~~( ~~~d ||| (e ||| f)) - 11 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 19 * ( ~~~d &&& ( ~~~e &&& f)) - 8 * ( ~~~d &&& (e &&& f)) - 7 * (d &&& ( ~~~e &&& f)) - 54 * (d &&& (e &&& f)) = - 1 * ((d &&& e) ||| ~~~(e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2033 (x y : BitVec w) : +theorem e_2033 : 1 * ~~~(d &&& f) - 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 5 * (e ^^^ ( ~~~d ||| (e ||| f))) - 5 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 2 * (f ^^^ ~~~(d &&& e)) - 3 * (e &&& (d ^^^ f)) + 2 * (e &&& ~~~f) - 2 * ( ~~~d ||| (e &&& f)) + 11 * (d ^^^ f) + 2 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 11 * (e ||| (d &&& f)) - 11 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 2 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 3 * (d ||| ~~~e) - 2 * ((d &&& f) ^^^ (e ||| f)) + 1 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 1 * (d &&& ~~~f) + 5 * (d ||| (e &&& f)) - 5 * (e ^^^ ~~~(d ||| f)) + 4 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 1 * ((d &&& e) ||| ~~~(e ||| f)) + 1 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 1 * ~~~(d &&& ( ~~~e ||| f)) - 6 * (d ^^^ (e ^^^ f)) - 1 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 1 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 1 * (e &&& f) + 4 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 4 * ~~~(d ||| (e ||| f)) - 16 * ~~~( ~~~d ||| (e ||| f)) - 21 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 12 * ( ~~~d &&& ( ~~~e &&& f)) - 17 * ( ~~~d &&& (e &&& f)) - 18 * (d &&& ( ~~~e &&& f)) + 4 * (d &&& (e &&& f)) = 8 * ~~~(d ||| ( ~~~e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2034 (x y : BitVec w) : +theorem e_2034 : - 2 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 1 * ~~~f + 3 * (f &&& ~~~(d ^^^ e)) - 6 * ~~~( ~~~d ||| (e &&& f)) - 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 2 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 5 * (d ||| ( ~~~e &&& f)) - 3 * (f ^^^ ( ~~~d ||| (e ||| f))) - 3 * ~~~(d &&& ~~~f) + 3 * (f ^^^ (d &&& e)) + 5 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 7 * (d ||| e) - 5 * (e ^^^ (d ||| ( ~~~e &&& f))) - 7 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 5 * (f ^^^ (d &&& (e ||| f))) + 4 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 1 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 7 * ((d ||| e) &&& ~~~(e ^^^ f)) + 2 * (d &&& ~~~e) - 5 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 11 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 1 * (e ||| ~~~f) + 2 * (e ^^^ ~~~(d &&& (e &&& f))) + 2 * (e ^^^ ( ~~~d ||| (e &&& f))) - 1 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 1 * ((d &&& e) ^^^ (e ||| ~~~f)) - 3 * (f ||| (d ^^^ e)) + 18 * ~~~(d ||| (e ||| f)) + 7 * ~~~(d ||| ( ~~~e ||| f)) + 13 * ~~~( ~~~d ||| (e ||| f)) + 10 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 12 * ( ~~~d &&& ( ~~~e &&& f)) - 2 * ( ~~~d &&& (e &&& f)) + 3 * (d &&& ( ~~~e &&& f)) + 7 * (d &&& (e &&& f)) = - 2 * (f ^^^ ~~~(d &&& e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2035 (x y : BitVec w) : +theorem e_2035 : - 5 * ~~~(d &&& (e ||| f)) - 7 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 7 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 7 * ( ~~~d ||| ( ~~~e &&& f)) + 5 * (e ^^^ (d ||| ( ~~~e &&& f))) - 6 * (e ^^^ f) + 2 * ~~~(d &&& (e &&& f)) - 2 * (d &&& (e ||| f)) + 1 * (d ||| e) - 5 * (d ||| ( ~~~e &&& f)) + 7 * (f ^^^ (d &&& e)) + 11 * ((d &&& f) ^^^ (e ||| f)) - 1 * ( ~~~f ||| (d ^^^ e)) + 1 * ((d &&& e) ||| ~~~(e ||| f)) - 2 * (f &&& ~~~(d &&& e)) - 1 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 11 * (f ^^^ ~~~(d &&& (e ||| f))) - 6 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 2 * (d &&& ( ~~~e ||| f)) - 2 * ~~~d - 3 * (e ^^^ ~~~(d &&& (e ||| f))) + 2 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 2 * ((d ^^^ e) &&& (d ^^^ f)) - 11 * (e &&& ~~~(d &&& f)) + 11 * ~~~(d ^^^ ( ~~~e ||| f)) + 2 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 4 * ((d &&& e) ^^^ (e ||| ~~~f)) - 3 * (f ^^^ (d &&& ~~~e)) + 2 * e + 34 * ~~~(d ||| (e ||| f)) + 4 * ~~~( ~~~d ||| (e ||| f)) + 7 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 4 * ( ~~~d &&& ( ~~~e &&& f)) - 5 * ( ~~~d &&& (e &&& f)) + 13 * (d &&& ( ~~~e &&& f)) + 15 * (d &&& (e &&& f)) = - 14 * ~~~(d ||| ( ~~~e ||| f)) + 1 * (d ||| ~~~f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2036 (x y : BitVec w) : +theorem e_2036 : 2 * (f ^^^ ~~~(d &&& ~~~e)) + 7 * ~~~(d ^^^ ( ~~~e &&& f)) - 1 * ~~~(e ||| f) - 1 * (f &&& (d ||| e)) + 2 * ( ~~~d &&& (e ||| f)) + 1 * (d &&& ~~~e) - 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 2 * ((d ||| e) &&& ~~~(e ^^^ f)) + 2 * ~~~(e ^^^ f) - 7 * (d ^^^ (e ||| f)) + 4 * (f &&& ~~~(d ^^^ e)) - 5 * ~~~(d ||| f) - 1 * (d ||| f) + 3 * ~~~(d ^^^ (e ^^^ f)) - 7 * (f ^^^ ( ~~~d &&& (e ||| f))) - 2 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 5 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 11 * ~~~(e &&& f) - 2 * ~~~(d ^^^ ( ~~~e ||| f)) - 7 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 7 * ~~~(d &&& e) + 2 * ~~~f - 6 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * (f ^^^ ~~~(d ||| e)) + 11 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 2 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 2 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 2 * ~~~(d &&& (e ^^^ f)) - 1 * ~~~(d ||| (e ^^^ f)) + 18 * ~~~(d ||| (e ||| f)) + 9 * ~~~(d ||| ( ~~~e ||| f)) + 11 * ~~~( ~~~d ||| (e ||| f)) + 21 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 6 * ( ~~~d &&& ( ~~~e &&& f)) + 16 * (d &&& ( ~~~e &&& f)) + 16 * (d &&& (e &&& f)) = - 1 * ( ~~~d &&& (e ^^^ f)) - 2 * ( ~~~d &&& (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2037 (x y : BitVec w) : +theorem e_2037 : 3 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 2 * (f ^^^ (d ||| (e &&& f))) - 2 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 11 * ~~~(d ^^^ (e &&& f)) + 3 * ((d &&& ~~~e) ||| (e ^^^ f)) + 5 * (f ^^^ ~~~(d ||| e)) - 5 * (e ^^^ (d ||| ( ~~~e ||| f))) - 3 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 11 * ( ~~~f &&& ~~~(d ^^^ e)) - 6 * ~~~(d &&& (e ||| f)) + 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 7 * (f ||| ~~~(d ^^^ e)) + 3 * ( ~~~d ||| (e ^^^ f)) + 5 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * (e ^^^ (d &&& (e ||| f))) - 7 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 11 * ~~~(e ||| ~~~f) + 3 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 11 * ( ~~~f ||| ~~~(d ^^^ e)) + 1 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 7 * ((d &&& e) ||| (e ^^^ f)) - 5 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 1 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 1 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 1 * (e &&& ~~~(d &&& ~~~f)) - 1 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 1 * ((d &&& e) ||| ~~~(e ||| f)) - 6 * ~~~(d ||| (e ||| f)) + 9 * ~~~(d ||| ( ~~~e ||| f)) + 27 * ~~~( ~~~d ||| (e ||| f)) - 13 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 18 * ( ~~~d &&& ( ~~~e &&& f)) + 5 * ( ~~~d &&& (e &&& f)) - 6 * (d &&& ( ~~~e &&& f)) - 12 * (d &&& (e &&& f)) = - 2 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2038 (x y : BitVec w) : +theorem e_2038 : - 6 * f + 5 * ( ~~~e &&& ~~~(d ^^^ f)) - 1 * ~~~(d &&& (e &&& f)) - 11 * ~~~(d ||| ( ~~~e &&& f)) - 2 * ~~~(d &&& e) + 3 * ( ~~~d &&& (e ||| f)) - 2 * ( ~~~e ||| (d ^^^ f)) + 3 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 2 * (e &&& (d ||| f)) + 11 * (f ||| ~~~(d ||| e)) + 1 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 5 * (d ^^^ e) - 1 * (f ^^^ ( ~~~d &&& (e ||| f))) - 5 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 1 * (e ||| ~~~f) + 1 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 3 * ((d ||| e) &&& ~~~(e ^^^ f)) - 5 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 1 * ((d &&& f) ||| ~~~(e ||| f)) + 11 * ~~~(d &&& ~~~e) - 6 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 5 * ((d ^^^ e) ||| (d ^^^ f)) - 11 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 7 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * (d ||| (e ^^^ f)) - 1 * ~~~(d ^^^ (e ^^^ f)) - 7 * (d ^^^ f) + 2 * (f ^^^ (d ||| ( ~~~e &&& f))) + 3 * ~~~(d &&& ( ~~~e &&& f)) + 16 * ~~~(d ||| (e ||| f)) + 3 * ~~~(d ||| ( ~~~e ||| f)) + 24 * ~~~( ~~~d ||| (e ||| f)) + 12 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 2 * ( ~~~d &&& ( ~~~e &&& f)) + 13 * ( ~~~d &&& (e &&& f)) - 20 * (d &&& (e &&& f)) = - 16 * (d &&& ( ~~~e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2039 (x y : BitVec w) : +theorem e_2039 : 11 * ((d ^^^ e) ||| (d ^^^ f)) + 1 * (f ^^^ ~~~(d ||| ~~~e)) - 6 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 2 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 1 * (e ^^^ ~~~(d &&& f)) + 2 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * ( ~~~d &&& (e ^^^ f)) - 2 * ((d ||| e) &&& (e ^^^ f)) - 1 * ( ~~~e ||| ~~~(d ^^^ f)) - 1 * ~~~( ~~~d &&& (e &&& f)) - 1 * ~~~(d &&& (e &&& f)) + 11 * (e ^^^ ~~~(d &&& (e ||| f))) - 2 * (e ^^^ (d ||| f)) + 5 * ((e &&& f) ||| (d &&& (e ||| f))) + 3 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 4 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 2 * (f ^^^ ~~~(d &&& (e &&& f))) - 1 * ~~~(d &&& (e ||| f)) - 5 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 1 * (e ^^^ ~~~(d ||| ~~~f)) - 1 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 1 * ~~~(d &&& ( ~~~e ||| f)) - 5 * (d ^^^ ( ~~~e &&& f)) + 1 * (f &&& ~~~(d ^^^ e)) - 3 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 1 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 2 * (f ||| ~~~(d ||| e)) - 3 * ~~~(d ||| (e ||| f)) + 3 * ~~~(d ||| ( ~~~e ||| f)) + 1 * ~~~( ~~~d ||| (e ||| f)) - 8 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 2 * ( ~~~d &&& ( ~~~e &&& f)) - 21 * ( ~~~d &&& (e &&& f)) - 1 * (d &&& ( ~~~e &&& f)) - 10 * (d &&& (e &&& f)) = 3 * (d ||| ~~~e) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2040 (x y : BitVec w) : +theorem e_2040 : 4 * (f ||| (d &&& e)) + 1 * (f &&& ~~~(d &&& e)) - 2 * (f ^^^ (d &&& ~~~e)) + 5 * (d ^^^ ( ~~~e &&& f)) - 1 * (e ||| ~~~f) - 5 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 1 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 1 * ((d ||| e) &&& ~~~(e ^^^ f)) + 4 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 1 * ( ~~~e &&& (d ^^^ f)) - 3 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 5 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 4 * (e ^^^ ~~~(d &&& ~~~f)) - 3 * ~~~(d ||| (e ^^^ f)) + 1 * (f ^^^ ~~~(d &&& e)) + 1 * ( ~~~f ||| ~~~(d ^^^ e)) - 7 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (e ^^^ (d ||| ( ~~~e ||| f))) - 6 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 11 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 11 * ~~~(d &&& f) + 7 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 11 * (e ^^^ ( ~~~d &&& (e ||| f))) - 7 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 5 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 7 * (e ^^^ ( ~~~d ||| (e &&& f))) + 3 * ((d &&& f) ^^^ (e ||| f)) - 6 * (f ^^^ ~~~(d ||| e)) - 13 * ~~~(d ||| (e ||| f)) - 14 * ~~~(d ||| ( ~~~e ||| f)) - 16 * ~~~( ~~~d ||| (e ||| f)) - 20 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 32 * ( ~~~d &&& ( ~~~e &&& f)) + 2 * ( ~~~d &&& (e &&& f)) + 8 * (d &&& ( ~~~e &&& f)) + 2 * (d &&& (e &&& f)) = - 2 * ((d ^^^ e) ||| (d ^^^ f)) - 1 * ( ~~~(d ||| e) ||| (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2041 (x y : BitVec w) : +theorem e_2041 : 5 * (d ||| ~~~e) + 5 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 2 * ~~~(e ||| ~~~f) - 7 * (e ^^^ (d ||| (e ||| f))) - 2 * ~~~(d ||| (e ^^^ f)) + 11 * (f &&& (d ||| e)) - 11 * (d ||| (e ^^^ f)) - 3 * ~~~(d &&& ( ~~~e ||| f)) + 1 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 11 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 2 * (d ||| ( ~~~e &&& f)) - 3 * (f ^^^ ( ~~~d ||| (e ||| f))) - 1 * (e ^^^ (d &&& f)) + 5 * (e ^^^ (d ||| ( ~~~e ||| f))) + 1 * ~~~(d ||| (e &&& f)) - 3 * ~~~(d &&& (e ^^^ f)) - 7 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 4 * ~~~(d &&& f) + 7 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 1 * ((d &&& f) ||| (e &&& ~~~f)) + 3 * (f ^^^ ~~~(d ||| e)) - 6 * ( ~~~f ||| ~~~(d ^^^ e)) - 3 * ((d &&& e) ^^^ (e ||| f)) - 7 * ~~~(d ||| ~~~e) + 3 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 5 * ((d ||| e) &&& (e ^^^ f)) - 11 * (e &&& ~~~(d &&& ~~~f)) + 1 * (f ^^^ (d ||| (e &&& f))) - 1 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 22 * ~~~(d ||| (e ||| f)) + 45 * ~~~(d ||| ( ~~~e ||| f)) + 8 * ~~~( ~~~d ||| (e ||| f)) + 20 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 1 * ( ~~~d &&& ( ~~~e &&& f)) - 28 * (d &&& ( ~~~e &&& f)) - 16 * (d &&& (e &&& f)) = - 3 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 7 * (e ^^^ ( ~~~d ||| (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2042 (x y : BitVec w) : +theorem e_2042 : - 7 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * ~~~( ~~~d &&& (e ||| f)) + 1 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 11 * (e ||| (d &&& ~~~f)) + 3 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 1 * ~~~(d ||| (e ^^^ f)) + 3 * ~~~f - 3 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 1 * (e &&& f) - 11 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 7 * ( ~~~d &&& (e ||| f)) + 1 * (f &&& (d ^^^ e)) - 1 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 3 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 3 * ( ~~~d &&& ( ~~~e ||| f)) + 2 * (d ^^^ f) + 11 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 5 * ( ~~~f ||| ~~~(d ^^^ e)) - 1 * (d ||| f) + 7 * ~~~(d ^^^ ( ~~~e ||| f)) - 1 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 3 * (e ^^^ (d ||| ( ~~~e &&& f))) - 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 2 * ~~~(d &&& f) + 4 * (e ^^^ ~~~(d ||| ~~~f)) + 1 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 3 * (d &&& (e ^^^ f)) - 4 * ~~~(d ||| (e ||| f)) + 19 * ~~~(d ||| ( ~~~e ||| f)) + 29 * ~~~( ~~~d ||| (e ||| f)) + 26 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 8 * ( ~~~d &&& ( ~~~e &&& f)) + 21 * ( ~~~d &&& (e &&& f)) + 5 * (d &&& ( ~~~e &&& f)) + 9 * (d &&& (e &&& f)) = 1 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2043 (x y : BitVec w) : +theorem e_2043 : - 2 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 5 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 5 * ( ~~~f ||| ~~~(d ^^^ e)) + 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 1 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 1 * ((d ||| e) &&& ~~~(e ^^^ f)) - 1 * ( ~~~d ||| (e ^^^ f)) - 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 3 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 1 * (e ^^^ ~~~(d ||| ~~~f)) - 2 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 1 * (e ||| (d &&& f)) - 2 * ~~~(d ^^^ f) + 2 * (f ||| ~~~(d ^^^ e)) - 7 * (e ||| (d &&& ~~~f)) - 2 * (e ^^^ (d ||| ~~~f)) - 5 * (e ||| ~~~(d ||| f)) + 2 * ~~~(d &&& (e ^^^ f)) - 2 * (e ||| f) + 11 * ( ~~~f &&& ~~~(d ^^^ e)) + 3 * ~~~(d &&& (e ||| f)) - 1 * (e ^^^ (d ||| (e ^^^ f))) + 5 * (d ||| e) - 2 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 1 * (f ||| (d ^^^ e)) - 1 * d + 2 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 11 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 11 * ( ~~~e &&& (d ^^^ f)) - 10 * ~~~(d ||| (e ||| f)) + 1 * ~~~(d ||| ( ~~~e ||| f)) - 13 * ~~~( ~~~d ||| (e ||| f)) - 1 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 9 * ( ~~~d &&& (e &&& f)) + 2 * (d &&& ( ~~~e &&& f)) + 17 * (d &&& (e &&& f)) = 23 * ( ~~~d &&& ( ~~~e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2044 (x y : BitVec w) : +theorem e_2044 : 5 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 11 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 4 * ((d &&& e) ||| (e ^^^ f)) - 6 * ( ~~~d &&& (e ||| f)) + 1 * (f ^^^ (d &&& e)) + 4 * (e ^^^ (d &&& ( ~~~e ||| f))) + 1 * (f ^^^ (d ||| (e &&& f))) + 4 * ~~~(e ^^^ f) + 3 * (e ^^^ (d ||| f)) - 1 * ~~~(d &&& ~~~d) - 3 * (f ^^^ (d &&& (e ||| f))) - 1 * ( ~~~e &&& (d ^^^ f)) + 7 * ((d &&& e) ||| ~~~(e ^^^ f)) - 1 * ~~~( ~~~d &&& (e &&& f)) - 6 * (e ^^^ (d ||| ( ~~~e ||| f))) - 5 * ~~~e + 2 * (d ||| (e ^^^ f)) + 11 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 3 * (f &&& (d ||| ~~~e)) - 6 * (e ^^^ ~~~(d ||| (e &&& f))) - 2 * e - 5 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 1 * ( ~~~d &&& (e ^^^ f)) + 5 * (f ^^^ (d ||| ( ~~~e &&& f))) - 11 * (e ^^^ (d &&& f)) + 4 * (e &&& ~~~(d &&& ~~~f)) + 3 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 2 * ~~~(d &&& ~~~f) - 6 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 12 * ~~~(d ||| (e ||| f)) + 8 * ~~~(d ||| ( ~~~e ||| f)) - 15 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 16 * ( ~~~d &&& ( ~~~e &&& f)) + 2 * ( ~~~d &&& (e &&& f)) + 3 * (d &&& ( ~~~e &&& f)) - 19 * (d &&& (e &&& f)) = - 5 * ~~~(d ||| ( ~~~e &&& f)) - 2 * ((d &&& ~~~e) ||| (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2045 (x y : BitVec w) : +theorem e_2045 : 1 * (f &&& ~~~(d ^^^ e)) - 2 * ((d ||| e) &&& (e ^^^ f)) - 1 * (e ||| ~~~(d ^^^ f)) - 2 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 5 * (f ^^^ ( ~~~d ||| (e ||| f))) - 2 * (f ^^^ (d ||| (e ||| f))) - 11 * (e ^^^ (d &&& ( ~~~e ||| f))) + 2 * (f ^^^ ( ~~~d &&& (e ||| f))) - 2 * (d ^^^ e) - 7 * ( ~~~f &&& ~~~(d ^^^ e)) - 11 * ~~~(e ||| ~~~f) - 1 * (d &&& ( ~~~e ||| f)) + 4 * ~~~(d ^^^ ( ~~~e &&& f)) - 1 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 7 * ~~~(d ^^^ ( ~~~e ||| f)) + 5 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 11 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 2 * (f ||| (d ^^^ e)) - 1 * ((d &&& e) ||| ~~~(e ^^^ f)) - 11 * (f &&& (d ^^^ e)) + 3 * ~~~(d ||| ~~~f) + 2 * (d ||| e) + 2 * ( ~~~d &&& ( ~~~e ||| f)) + 4 * ~~~(d &&& f) + 2 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 7 * (e ^^^ (d ||| ( ~~~e ||| f))) + 3 * (f ^^^ ~~~(d ||| ~~~e)) + 7 * (f ^^^ (d ||| ( ~~~e ||| f))) - 2 * (d ||| (e ^^^ f)) - 36 * ~~~(d ||| (e ||| f)) - 21 * ~~~(d ||| ( ~~~e ||| f)) - 12 * ~~~( ~~~d ||| (e ||| f)) + 7 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 7 * ( ~~~d &&& (e &&& f)) + 13 * (d &&& ( ~~~e &&& f)) - 25 * (d &&& (e &&& f)) = 21 * ( ~~~d &&& ( ~~~e &&& f)) + 2 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2046 (x y : BitVec w) : +theorem e_2046 : - 5 * (e &&& ~~~f) - 7 * ~~~(d ^^^ (e ||| f)) + 11 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 1 * ~~~( ~~~d &&& (e ||| f)) - 2 * (d ||| (e ^^^ f)) + 2 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 7 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 11 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 2 * ~~~(d &&& ~~~f) - 2 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 1 * (e ||| ~~~(d ||| f)) - 1 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 1 * ~~~(e ^^^ f) + 5 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * (e ||| f) - 3 * ~~~(d &&& ( ~~~e &&& f)) - 3 * ~~~(d ||| ~~~e) - 1 * d - 5 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 5 * (d ^^^ (e &&& f)) - 2 * (e ^^^ (d &&& (e ^^^ f))) - 1 * (d ^^^ (e ^^^ f)) + 5 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 3 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (d &&& ( ~~~e ||| f)) + 1 * ((e &&& f) ||| (d &&& (e ||| f))) + 11 * (e ^^^ ~~~(d ||| ~~~f)) + 8 * ~~~(d ||| (e ||| f)) + 8 * ~~~(d ||| ( ~~~e ||| f)) + 34 * ~~~( ~~~d ||| (e ||| f)) - 6 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 6 * ( ~~~d &&& ( ~~~e &&& f)) + 20 * ( ~~~d &&& (e &&& f)) + 7 * (d &&& ( ~~~e &&& f)) - 1 * (d &&& (e &&& f)) = 7 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 2 * (f ||| ~~~(d ^^^ e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2047 (x y : BitVec w) : +theorem e_2047 : - 7 * ~~~(e ||| ~~~f) - 5 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 5 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 11 * (f ^^^ (d &&& e)) - 11 * (f ||| (d ^^^ e)) + 1 * ~~~(e ||| f) - 2 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 1 * (f ^^^ (d ||| ~~~e)) - 1 * ((d &&& e) ^^^ (e ||| f)) - 6 * ( ~~~d &&& (e ||| f)) - 2 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 1 * ~~~( ~~~d ||| (e ^^^ f)) - 11 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 1 * ~~~(d &&& f) + 5 * (d ||| ( ~~~e &&& f)) - 1 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 5 * d - 1 * (d &&& ( ~~~e ||| f)) - 2 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 7 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 6 * (e ^^^ ~~~(d &&& ~~~f)) + 1 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 5 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 2 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 11 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 11 * (e ^^^ (d &&& (e ^^^ f))) - 1 * (d &&& (e ^^^ f)) - 2 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 5 * (e ^^^ (d ||| ( ~~~e ||| f))) + 3 * (f ^^^ ~~~(d &&& (e &&& f))) + 41 * ~~~(d ||| (e ||| f)) + 46 * ~~~(d ||| ( ~~~e ||| f)) + 26 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 43 * ( ~~~d &&& ( ~~~e &&& f)) + 53 * ( ~~~d &&& (e &&& f)) + 79 * (d &&& ( ~~~e &&& f)) + 35 * (d &&& (e &&& f)) = - 20 * ~~~( ~~~d ||| (e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2048 (x y : BitVec w) : +theorem e_2048 : 1 * (e ^^^ (d ||| f)) - 7 * (d ^^^ (e ^^^ f)) - 1 * ~~~(d &&& ( ~~~e &&& f)) + 4 * (e &&& ~~~(d ^^^ f)) - 2 * (e &&& (d ||| f)) - 5 * (e ^^^ (d &&& (e ^^^ f))) + 3 * (e ||| (d &&& f)) + 1 * ~~~(d ||| (e ^^^ f)) + 2 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 1 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * (d ^^^ f) + 2 * ( ~~~d ||| ( ~~~e &&& f)) - 5 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 3 * ~~~(d &&& e) - 2 * (f ||| (d &&& e)) - 11 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 7 * ~~~(d ^^^ e) + 3 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 11 * ~~~(d ^^^ (e &&& f)) + 2 * (e ||| ~~~(d ||| f)) - 1 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 1 * ( ~~~e &&& ~~~(d ^^^ f)) + 11 * ~~~(e ||| ~~~f) + 11 * ( ~~~d ||| (e &&& f)) + 2 * ~~~d - 2 * ~~~(e &&& ~~~f) - 7 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 3 * (f ^^^ (d &&& (e ||| f))) + 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 18 * ~~~(d ||| (e ||| f)) - 10 * ~~~(d ||| ( ~~~e ||| f)) + 25 * ~~~( ~~~d ||| (e ||| f)) - 1 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 16 * ( ~~~d &&& ( ~~~e &&& f)) + 3 * ( ~~~d &&& (e &&& f)) + 7 * (d &&& ( ~~~e &&& f)) - 9 * (d &&& (e &&& f)) = 1 * ( ~~~d ||| (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2049 (x y : BitVec w) : +theorem e_2049 : 2 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 2 * (f ^^^ ~~~(d ||| e)) - 2 * ((d &&& e) ||| (e ^^^ f)) - 2 * ((d &&& f) ||| (e &&& ~~~f)) + 2 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 3 * (f ^^^ (d ||| ( ~~~e ||| f))) + 4 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 3 * ~~~(d &&& e) + 2 * (f ^^^ (d &&& e)) - 5 * ~~~( ~~~d ||| (e ^^^ f)) - 1 * (e ^^^ ~~~(d &&& (e &&& f))) + 2 * ~~~( ~~~d &&& (e ||| f)) + 5 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 7 * (d ||| ( ~~~e ||| f)) + 4 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 3 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 3 * (f ||| (d ^^^ e)) - 2 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 1 * ~~~(d &&& f) + 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 11 * (f ||| (d &&& e)) - 11 * ~~~(d &&& (e ^^^ f)) + 11 * (e ||| ~~~(d ||| ~~~f)) + 11 * ( ~~~e &&& ~~~(d ^^^ f)) + 1 * ( ~~~d &&& (e ||| f)) + 1 * (e ^^^ (d ||| (e ^^^ f))) - 5 * (d ||| (e ^^^ f)) + 11 * (f &&& (d ^^^ e)) + 5 * ( ~~~f ||| ~~~(d ^^^ e)) + 6 * ~~~(d ||| ( ~~~e ||| f)) + 9 * ~~~( ~~~d ||| (e ||| f)) - 22 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 3 * ( ~~~d &&& ( ~~~e &&& f)) - 9 * ( ~~~d &&& (e &&& f)) - 22 * (d &&& ( ~~~e &&& f)) + 3 * (d &&& (e &&& f)) = 27 * ~~~(d ||| (e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2050 (x y : BitVec w) : +theorem e_2050 : - 11 * ~~~(d ^^^ (e ^^^ f)) - 6 * ~~~(d ^^^ e) - 3 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 6 * (f ^^^ (d ||| ~~~e)) - 2 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 11 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 6 * (e ||| (d &&& ~~~f)) - 11 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 3 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 1 * (d ||| ~~~f) + 5 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 11 * ( ~~~f &&& ~~~(d ^^^ e)) + 1 * (f &&& (d ||| ~~~e)) - 11 * ((d &&& f) ||| (e &&& ~~~f)) - 1 * ~~~(e ^^^ f) - 1 * (e ^^^ ~~~(d ||| f)) + 2 * ( ~~~d &&& (e ^^^ f)) + 11 * (f &&& (d ^^^ e)) + 4 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 1 * (f ^^^ (d ||| e)) + 2 * (e ^^^ (d ||| ( ~~~e &&& f))) - 11 * (f ^^^ (d ||| ( ~~~e ||| f))) - 6 * (f ^^^ (d &&& (e ||| f))) - 5 * ( ~~~e &&& ~~~(d ^^^ f)) - 1 * (f ^^^ ~~~(d &&& ~~~e)) - 1 * (f ||| (d &&& ~~~e)) + 5 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 1 * (e &&& ~~~(d &&& ~~~f)) + 1 * (e ^^^ (d &&& ( ~~~e ||| f))) + 17 * ~~~(d ||| (e ||| f)) - 4 * ~~~(d ||| ( ~~~e ||| f)) + 13 * ~~~( ~~~d ||| (e ||| f)) + 41 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 18 * ( ~~~d &&& ( ~~~e &&& f)) - 11 * ( ~~~d &&& (e &&& f)) - 1 * (d &&& ( ~~~e &&& f)) + 16 * (d &&& (e &&& f)) = - 11 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2051 (x y : BitVec w) : +theorem e_2051 : - 2 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 3 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 11 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 1 * (e ^^^ ~~~(d ||| f)) + 1 * ( ~~~f ||| (d ^^^ e)) + 7 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 7 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 7 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 11 * f + 5 * ~~~(d ||| f) + 4 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 3 * ~~~e + 1 * ((d &&& f) ||| (e &&& ~~~f)) - 3 * ((d &&& e) ||| ~~~(e ||| f)) - 6 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 1 * ~~~(d &&& ~~~e) + 1 * (e &&& ~~~(d &&& f)) - 5 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 3 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 1 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 11 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 5 * ~~~(d ||| (e ^^^ f)) - 1 * (d ^^^ (e ||| f)) + 2 * ( ~~~d &&& ( ~~~e ||| f)) + 3 * (f &&& ~~~(d ^^^ e)) + 11 * (d ^^^ f) - 3 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 7 * ~~~f + 1 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 1 * ~~~(d ||| (e ||| f)) - 6 * ~~~(d ||| ( ~~~e ||| f)) - 18 * ~~~( ~~~d ||| (e ||| f)) - 14 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 11 * ( ~~~d &&& ( ~~~e &&& f)) - 41 * ( ~~~d &&& (e &&& f)) + 5 * (d &&& ( ~~~e &&& f)) + 10 * (d &&& (e &&& f)) = 1 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2052 (x y : BitVec w) : +theorem e_2052 : 5 * (e ^^^ ~~~(d ||| ~~~f)) + 11 * ~~~(d ^^^ (e ^^^ f)) + 5 * ~~~(d &&& ~~~d) - 2 * (f ^^^ (d ||| ( ~~~e &&& f))) - 11 * (d ||| ~~~e) + 1 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 2 * ~~~(d &&& ( ~~~e ||| f)) + 2 * (f &&& ~~~(d ^^^ e)) + 11 * (d ||| f) - 1 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 5 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 6 * (e ^^^ (d ||| (e ||| f))) - 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 5 * (d ||| (e ||| f)) - 3 * (e ^^^ ( ~~~d &&& (e ||| f))) + 2 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 2 * ( ~~~d ||| ( ~~~e ||| f)) + 5 * (f ^^^ ~~~(d ||| e)) + 1 * (e &&& ~~~(d &&& f)) - 3 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 1 * ((d ^^^ e) &&& (d ^^^ f)) + 3 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 2 * ~~~( ~~~d ||| (e ^^^ f)) - 1 * (d &&& (e ||| f)) + 1 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 1 * ~~~(d ||| (e &&& f)) - 3 * ~~~(e &&& ~~~f) - 6 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 5 * (e ^^^ (d &&& (e ^^^ f))) + 1 * (f ^^^ ~~~(d ||| (e &&& f))) - 5 * ~~~(d ||| (e ||| f)) - 3 * ~~~(d ||| ( ~~~e ||| f)) + 17 * ~~~( ~~~d ||| (e ||| f)) + 8 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 24 * ( ~~~d &&& ( ~~~e &&& f)) - 10 * ( ~~~d &&& (e &&& f)) + 1 * (d &&& ( ~~~e &&& f)) = 6 * (d ^^^ f) - 9 * (d &&& (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2053 (x y : BitVec w) : +theorem e_2053 : 7 * ~~~(d ||| ~~~f) - 1 * ~~~(d ||| (e ^^^ f)) - 1 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 1 * (d ||| ( ~~~e ||| f)) + 5 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 1 * (f &&& ~~~(d ^^^ e)) - 1 * (d ^^^ (e &&& f)) + 1 * (e ||| (d ^^^ f)) - 7 * (f ||| (d ^^^ e)) + 1 * ~~~(d &&& ( ~~~e ||| f)) - 5 * ~~~(e ^^^ f) - 11 * (f &&& (d ||| ~~~e)) - 7 * ~~~(d ^^^ ( ~~~e &&& f)) - 11 * (f ^^^ (d ||| (e ||| f))) - 2 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 1 * ((d ||| e) &&& (e ^^^ f)) + 5 * (d ||| ( ~~~e &&& f)) - 2 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 4 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 2 * ( ~~~f &&& ~~~(d ^^^ e)) - 6 * (d &&& e) - 3 * (d &&& ( ~~~e ||| f)) - 1 * ~~~(e &&& f) - 5 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 2 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * ~~~(d ||| e) + 3 * (e ||| ~~~f) + 11 * (d ||| (e &&& f)) - 2 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 1 * ((d &&& f) ^^^ (e ||| f)) + 7 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 2 * ~~~(d ||| (e ||| f)) + 12 * ~~~(d ||| ( ~~~e ||| f)) + 9 * ~~~( ~~~d ||| (e ||| f)) + 5 * ( ~~~d &&& ( ~~~e &&& f)) - 4 * ( ~~~d &&& (e &&& f)) + 6 * (d &&& (e &&& f)) = - 4 * (d &&& ( ~~~e &&& f)) - 4 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2054 (x y : BitVec w) : +theorem e_2054 : - 11 * (e ||| ~~~f) + 7 * (d ||| ~~~f) - 7 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 2 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 5 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 1 * (e ^^^ (d ||| ( ~~~e &&& f))) - 1 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 11 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 7 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 6 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 3 * (e &&& f) + 4 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 3 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 4 * (e ^^^ (d &&& ( ~~~e ||| f))) + 11 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 3 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 6 * ((d &&& f) ^^^ (e ||| f)) + 7 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 2 * ~~~(d ||| e) + 1 * (f ^^^ (d &&& (e ||| f))) - 5 * (d ||| ( ~~~e &&& f)) - 7 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 1 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 3 * (e ||| (d &&& ~~~f)) + 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 5 * (f ^^^ (d ||| ( ~~~e ||| f))) + 4 * ( ~~~d ||| ( ~~~e &&& f)) + 1 * ( ~~~e &&& (d ^^^ f)) + 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 4 * ~~~(d ||| (e ||| f)) - 7 * ~~~(d ||| ( ~~~e ||| f)) - 6 * ~~~( ~~~d ||| (e ||| f)) + 22 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 3 * ( ~~~d &&& ( ~~~e &&& f)) + 19 * ( ~~~d &&& (e &&& f)) + 33 * (d &&& (e &&& f)) = - 11 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 1 * ( ~~~d ||| ( ~~~e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2055 (x y : BitVec w) : +theorem e_2055 : - 5 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 4 * (f ^^^ (d &&& ( ~~~e ||| f))) + 2 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 4 * (f ^^^ (d ||| ( ~~~e &&& f))) - 1 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 1 * (d ^^^ (e &&& f)) - 1 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 1 * (d ||| ( ~~~e &&& f)) - 7 * ~~~(e ^^^ f) - 1 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 3 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 7 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 5 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 1 * (e ^^^ (d &&& ( ~~~e ||| f))) + 1 * (e ^^^ (d ||| (e ||| f))) - 2 * ((d &&& e) ||| (e ^^^ f)) + 7 * ~~~(d &&& ( ~~~e &&& f)) + 11 * (f ^^^ ~~~(d ||| ~~~e)) + 2 * (f &&& (d ||| e)) - 2 * (e &&& (d ||| f)) - 11 * (f ||| (d ^^^ e)) + 1 * ~~~( ~~~d &&& (e ^^^ f)) + 7 * (e ||| (d &&& ~~~f)) - 11 * (e ^^^ f) - 6 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * ~~~(d &&& ~~~e) - 11 * (e ||| (d ^^^ f)) + 2 * (f &&& ~~~(d &&& ~~~e)) - 10 * ~~~(d ||| (e ||| f)) + 12 * ~~~(d ||| ( ~~~e ||| f)) - 4 * ~~~( ~~~d ||| (e ||| f)) + 14 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 21 * ( ~~~d &&& ( ~~~e &&& f)) - 3 * ( ~~~d &&& (e &&& f)) + 7 * (d &&& ( ~~~e &&& f)) + 1 * (d &&& (e &&& f)) = - 4 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2056 (x y : BitVec w) : +theorem e_2056 : 5 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 2 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 2 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 1 * (f ^^^ (d &&& e)) + 7 * ~~~( ~~~d &&& (e ^^^ f)) - 1 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 2 * (d &&& (e ^^^ f)) + 2 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 3 * ~~~(d ||| ~~~f) + 7 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 5 * (e ^^^ ( ~~~d &&& (e ||| f))) - 5 * (d ||| ~~~f) + 2 * (e &&& f) - 5 * (f &&& ~~~(d ^^^ e)) + 1 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 3 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 2 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * (f ^^^ ( ~~~d &&& (e ||| f))) - 5 * (e ^^^ ( ~~~d ||| (e ||| f))) - 7 * ((d ^^^ e) &&& (d ^^^ f)) - 3 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 11 * (e ^^^ ~~~(d ||| ~~~f)) - 1 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 4 * (e &&& (d ^^^ f)) - 1 * (f ^^^ ~~~(d &&& e)) - 11 * ~~~(d ||| (e &&& f)) - 1 * (e ||| ~~~f) - 5 * ~~~(d ^^^ f) + 16 * ~~~(d ||| (e ||| f)) + 12 * ~~~(d ||| ( ~~~e ||| f)) - 2 * ~~~( ~~~d ||| (e ||| f)) - 22 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 30 * ( ~~~d &&& ( ~~~e &&& f)) - 15 * ( ~~~d &&& (e &&& f)) + 16 * (d &&& ( ~~~e &&& f)) + 3 * (d &&& (e &&& f)) = - 5 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 11 * ( ~~~(d &&& e) &&& (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2057 (x y : BitVec w) : +theorem e_2057 : - 11 * (d ^^^ f) + 5 * ((d &&& ~~~e) ||| (e ^^^ f)) + 7 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 2 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 3 * (d ||| ~~~f) - 1 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 1 * (f ^^^ (d &&& (e ||| f))) + 1 * (f ^^^ ~~~(d &&& e)) + 4 * (e ^^^ f) - 1 * (f ||| (d &&& e)) - 1 * (f ^^^ ~~~(d &&& (e &&& f))) + 11 * ( ~~~d ||| ( ~~~e ||| f)) - 1 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 4 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 7 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 2 * ~~~(d ^^^ f) - 2 * d + 2 * ((d &&& e) ||| ~~~(e ||| f)) + 11 * (d &&& e) + 11 * ~~~(d ||| (e &&& f)) - 11 * ~~~(d ^^^ e) - 1 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 7 * (e &&& ~~~(d &&& f)) - 3 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 3 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 1 * (e ^^^ ( ~~~d ||| (e &&& f))) - 1 * (f ^^^ (d ||| (e ||| f))) + 4 * (e ||| (d ^^^ f)) - 3 * (d ^^^ (e ^^^ f)) + 1 * (e ||| (d &&& f)) - 37 * ~~~(d ||| ( ~~~e ||| f)) - 8 * ~~~( ~~~d ||| (e ||| f)) - 14 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 3 * ( ~~~d &&& ( ~~~e &&& f)) - 18 * ( ~~~d &&& (e &&& f)) - 13 * (d &&& ( ~~~e &&& f)) - 20 * (d &&& (e &&& f)) = 17 * ~~~(d ||| (e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2058 (x y : BitVec w) : +theorem e_2058 : - 2 * ~~~(d ||| e) + 5 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 1 * (e ^^^ ~~~(d &&& (e ||| f))) + 11 * ((d &&& ~~~e) ||| (e ^^^ f)) + 7 * ~~~(e ||| ~~~f) - 11 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 1 * (e ^^^ (d ||| (e ||| f))) - 6 * ~~~(d &&& ~~~d) + 1 * (e ^^^ f) - 11 * (e ^^^ (d &&& f)) + 4 * (d ||| ~~~f) - 11 * (e ||| ~~~(d ^^^ f)) - 11 * ((d &&& f) ||| ~~~(e ||| f)) - 1 * ( ~~~f &&& ~~~(d ^^^ e)) + 2 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 7 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 4 * (e ^^^ (d ||| ( ~~~e &&& f))) - 5 * (e ^^^ ~~~(d &&& f)) + 1 * ((d &&& e) ||| ~~~(e ||| f)) - 1 * ~~~(d &&& (e ^^^ f)) + 3 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 5 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 1 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 3 * (e ||| (d &&& ~~~f)) - 7 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 1 * ~~~( ~~~d &&& (e ||| f)) - 11 * ~~~(e ||| f) + 1 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 1 * (e &&& f) + 34 * ~~~(d ||| (e ||| f)) + 3 * ~~~(d ||| ( ~~~e ||| f)) - 2 * ~~~( ~~~d ||| (e ||| f)) - 2 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 19 * ( ~~~d &&& ( ~~~e &&& f)) + 29 * ( ~~~d &&& (e &&& f)) + 14 * (d &&& ( ~~~e &&& f)) + 14 * (d &&& (e &&& f)) = - 7 * ~~~(d ^^^ ( ~~~e ||| f)) + 3 * ~~~(d ||| ~~~e) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2059 (x y : BitVec w) : +theorem e_2059 : 2 * (f ^^^ ~~~(d ||| ~~~e)) - 1 * (e ||| (d &&& f)) + 3 * ((e &&& f) ||| (d &&& (e ||| f))) + 11 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 1 * (d &&& e) - 1 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 6 * (e ^^^ (d ||| ( ~~~e &&& f))) - 1 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 7 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 3 * (e ^^^ ( ~~~d ||| (e ||| f))) + 7 * (f &&& (d ^^^ e)) - 1 * (f &&& ~~~(d ^^^ e)) - 11 * (f ^^^ ~~~(d ||| (e &&& f))) - 2 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 2 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 1 * ~~~(d &&& ~~~f) + 1 * ~~~(d ||| ( ~~~e &&& f)) - 3 * (f &&& ~~~(d &&& ~~~e)) + 1 * ~~~(d &&& ( ~~~e ||| f)) + 5 * (e ^^^ (d ||| (e &&& f))) - 3 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 7 * (e &&& ~~~(d &&& f)) - 1 * ~~~(d ||| (e &&& f)) - 3 * ( ~~~e &&& (d ^^^ f)) - 7 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 1 * (f ^^^ ~~~(d &&& ~~~e)) - 5 * ( ~~~d &&& (e ||| f)) + 1 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 11 * ~~~(d ||| e) + 12 * ~~~(d ||| (e ||| f)) + 5 * ~~~(d ||| ( ~~~e ||| f)) - 1 * ~~~( ~~~d ||| (e ||| f)) + 4 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 23 * ( ~~~d &&& ( ~~~e &&& f)) + 9 * ( ~~~d &&& (e &&& f)) - 9 * (d &&& ( ~~~e &&& f)) + 8 * (d &&& (e &&& f)) = - 1 * (d ||| ~~~f) - 2 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2060 (x y : BitVec w) : +theorem e_2060 : - 2 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 5 * (f ^^^ ~~~(d ||| e)) - 11 * ~~~(d ^^^ (e ^^^ f)) - 1 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 7 * (d &&& ~~~f) - 11 * (e ^^^ ~~~(d &&& ~~~f)) + 11 * ( ~~~d ||| (e ^^^ f)) + 4 * (e ||| (d &&& f)) - 11 * ((d &&& e) ^^^ (e ||| ~~~f)) - 1 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 1 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 5 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 2 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 4 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 7 * ( ~~~e &&& ~~~(d ^^^ f)) + 7 * (e ||| f) + 2 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 4 * (e ^^^ (d ||| (e &&& f))) + 11 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 6 * ((d ^^^ e) ||| (d ^^^ f)) - 5 * ~~~e + 1 * (f ^^^ (d ||| ( ~~~e &&& f))) - 6 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 1 * (d ||| f) - 3 * (f ^^^ (d &&& (e ||| f))) - 2 * ~~~(d ^^^ ( ~~~e &&& f)) + 2 * (f ^^^ (d ||| (e &&& f))) - 6 * (e &&& ~~~(d &&& ~~~f)) - 5 * (d ||| e) + 21 * ~~~(d ||| (e ||| f)) + 2 * ~~~(d ||| ( ~~~e ||| f)) + 13 * ~~~( ~~~d ||| (e ||| f)) + 1 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 4 * ( ~~~d &&& ( ~~~e &&& f)) + 34 * ( ~~~d &&& (e &&& f)) + 11 * (d &&& ( ~~~e &&& f)) = - 15 * (d &&& (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2061 (x y : BitVec w) : +theorem e_2061 : 7 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 1 * ((d &&& f) ||| ~~~(e ||| f)) - 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 2 * (e ^^^ (d &&& ( ~~~e ||| f))) + 5 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 1 * ~~~(d &&& (e ||| f)) - 1 * (d ||| ~~~f) - 11 * (d ||| ( ~~~e ||| f)) - 2 * (f ^^^ ( ~~~d ||| (e ||| f))) + 1 * (e ^^^ ( ~~~d ||| (e &&& f))) + 1 * (f ||| (d ^^^ e)) + 1 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 1 * (e &&& (d ||| f)) + 5 * ((d &&& e) ^^^ (e ||| ~~~f)) - 7 * ~~~d + 1 * (d &&& ~~~e) + 2 * ~~~(d ^^^ ( ~~~e &&& f)) - 11 * (e ^^^ (d &&& (e ||| f))) - 7 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * ~~~(d ^^^ (e ^^^ f)) - 1 * (f ^^^ ~~~(d &&& (e ||| f))) - 5 * (e ^^^ (d ||| (e &&& f))) + 2 * (f ^^^ ~~~(d ||| (e &&& f))) + 5 * (f &&& (d ||| ~~~e)) + 4 * (f ^^^ (d ||| e)) - 2 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 5 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 2 * (f ^^^ (d &&& e)) + 1 * (f ^^^ ~~~(d &&& ~~~e)) - 11 * (f ^^^ (d &&& (e ||| f))) + 17 * ~~~(d ||| (e ||| f)) + 19 * ~~~(d ||| ( ~~~e ||| f)) + 8 * ~~~( ~~~d ||| (e ||| f)) + 25 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 12 * ( ~~~d &&& ( ~~~e &&& f)) + 31 * ( ~~~d &&& (e &&& f)) + 35 * (d &&& ( ~~~e &&& f)) + 8 * (d &&& (e &&& f)) = 3 * (e ^^^ (d ||| ( ~~~e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2062 (x y : BitVec w) : +theorem e_2062 : 11 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 2 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 7 * (e ^^^ (d &&& ~~~f)) - 5 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 3 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 2 * (d ||| e) - 1 * (f ||| (d ^^^ e)) + 1 * ( ~~~e &&& (d ^^^ f)) + 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 1 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 1 * ((d ||| e) &&& (e ^^^ f)) - 6 * ~~~(d ||| (e ^^^ f)) - 3 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 2 * ~~~(d ^^^ ( ~~~e ||| f)) - 11 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 2 * ~~~(d ^^^ e) - 1 * ((d &&& e) ||| (e ^^^ f)) - 2 * (e ||| ~~~f) - 6 * ~~~(d ^^^ (e ||| f)) + 2 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 2 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 6 * (f &&& (d ||| e)) - 2 * (d ^^^ ( ~~~e ||| f)) + 5 * (e ^^^ ~~~(d &&& (e ||| f))) - 5 * ( ~~~d &&& (e ^^^ f)) - 11 * (e &&& ~~~f) + 5 * (f ||| ~~~(d ^^^ e)) - 11 * (d ||| (e ||| f)) + 5 * ~~~(d ^^^ (e &&& f)) + 3 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 4 * ~~~(d ||| (e ||| f)) + 26 * ~~~(d ||| ( ~~~e ||| f)) - 1 * ~~~( ~~~d ||| (e ||| f)) + 16 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 7 * ( ~~~d &&& ( ~~~e &&& f)) + 25 * ( ~~~d &&& (e &&& f)) + 13 * (d &&& ( ~~~e &&& f)) + 11 * (d &&& (e &&& f)) = - 2 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2063 (x y : BitVec w) : +theorem e_2063 : - 1 * ~~~( ~~~d ||| (e &&& f)) + 1 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 11 * (e ^^^ ~~~(d &&& (e ||| f))) + 4 * (d ||| ( ~~~e &&& f)) + 5 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 7 * (e ||| (d &&& f)) - 6 * (e ^^^ ~~~(d ||| (e &&& f))) + 7 * ~~~f - 3 * (d &&& (e ^^^ f)) - 2 * ( ~~~f &&& ~~~(d ^^^ e)) + 2 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 2 * (e ^^^ (d &&& ( ~~~e ||| f))) + 4 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 2 * (f ^^^ ( ~~~d ||| (e ||| f))) - 1 * (e ||| ~~~(d ||| f)) - 11 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 2 * (e ^^^ (d ||| ( ~~~e &&& f))) + 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 3 * (f &&& (d ||| e)) + 3 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 5 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 1 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * (f ||| ~~~(d ^^^ e)) + 2 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 2 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 7 * ~~~(d &&& (e ||| f)) + 3 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 2 * (e ^^^ (d ||| ( ~~~e ||| f))) + 1 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * ~~~(d ||| (e ||| f)) + 9 * ~~~(d ||| ( ~~~e ||| f)) - 20 * ~~~( ~~~d ||| (e ||| f)) - 20 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 2 * ( ~~~d &&& ( ~~~e &&& f)) - 6 * ( ~~~d &&& (e &&& f)) - 3 * (d &&& ( ~~~e &&& f)) - 29 * (d &&& (e &&& f)) = 2 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2064 (x y : BitVec w) : +theorem e_2064 : 1 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 1 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 5 * (e ^^^ ~~~(d ||| ~~~f)) + 11 * (f ||| ~~~(d ||| ~~~e)) - 1 * ~~~(d ||| e) - 3 * (e ^^^ ~~~(d &&& f)) + 3 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 4 * ( ~~~d ||| (e ^^^ f)) - 2 * ~~~(e &&& f) + 1 * ( ~~~f ||| (d ^^^ e)) - 11 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 2 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 3 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 11 * (e ^^^ (d ||| (e ||| f))) - 3 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 2 * ~~~( ~~~d ||| (e &&& f)) - 1 * (f ^^^ ~~~(d ||| e)) - 7 * ((d &&& e) ||| ~~~(e ^^^ f)) - 7 * (e &&& (d ||| ~~~f)) + 1 * (f &&& (d ||| ~~~e)) + 5 * e + 2 * (e ^^^ (d &&& f)) + 11 * (d &&& ~~~e) + 1 * (e ^^^ (d &&& ( ~~~e ||| f))) + 7 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 7 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 1 * (e ^^^ (d ||| (e ^^^ f))) + 1 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 3 * ~~~(d ^^^ (e ^^^ f)) + 11 * (f ||| ~~~(d ||| e)) + 9 * ~~~(d ||| (e ||| f)) - 2 * ~~~(d ||| ( ~~~e ||| f)) + 16 * ~~~( ~~~d ||| (e ||| f)) + 6 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 3 * ( ~~~d &&& ( ~~~e &&& f)) - 34 * ( ~~~d &&& (e &&& f)) - 32 * (d &&& ( ~~~e &&& f)) + 15 * (d &&& (e &&& f)) = 1 * ~~~(d &&& f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2065 (x y : BitVec w) : +theorem e_2065 : 2 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 7 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 6 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 5 * (d ||| (e &&& f)) - 1 * (e ^^^ (d ||| (e &&& f))) - 1 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 1 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 7 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 6 * ~~~(d ^^^ ( ~~~e ||| f)) - 2 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 4 * ((d ^^^ e) &&& (d ^^^ f)) + 1 * (e &&& ~~~(d &&& ~~~f)) - 1 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 1 * (f ^^^ (d &&& (e ||| f))) + 1 * ~~~( ~~~d &&& (e ||| f)) - 1 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 3 * (f ||| (d ^^^ e)) + 7 * ((d &&& e) ^^^ (e ||| ~~~f)) - 3 * (e ||| ~~~f) - 1 * ((d ||| ~~~e) &&& (e ^^^ f)) + 5 * ( ~~~e ||| ~~~(d ^^^ f)) + 2 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 5 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 2 * ~~~(d ||| f) + 2 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 1 * (d ^^^ (e ||| f)) - 7 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 1 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 2 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 11 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 3 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 2 * ~~~(d ||| (e ||| f)) + 11 * ~~~(d ||| ( ~~~e ||| f)) + 12 * ~~~( ~~~d ||| (e ||| f)) + 41 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 18 * ( ~~~d &&& ( ~~~e &&& f)) + 6 * ( ~~~d &&& (e &&& f)) + 7 * (d &&& ( ~~~e &&& f)) + 21 * (d &&& (e &&& f)) = - 4 * ~~~( ~~~d &&& ( ~~~e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2066 (x y : BitVec w) : +theorem e_2066 : - 2 * (e ^^^ (d &&& (e ||| f))) - 7 * (f &&& ~~~(d ^^^ e)) + 11 * ~~~(d &&& ~~~e) - 7 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 2 * (e ||| ~~~(d ||| f)) + 2 * ~~~(d &&& (e ^^^ f)) + 5 * (f ^^^ ~~~(d ||| ~~~e)) - 11 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 2 * ((d ^^^ e) &&& (d ^^^ f)) + 2 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 3 * ~~~(d ||| ( ~~~e &&& f)) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 1 * (e ^^^ ( ~~~d ||| (e &&& f))) - 3 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 4 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 1 * (d ||| ~~~f) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 2 * (e &&& ~~~f) + 2 * (d ^^^ (e &&& f)) - 6 * (d &&& (e ||| f)) - 1 * (f ||| (d &&& ~~~e)) - 1 * (e ^^^ (d ||| ~~~f)) - 1 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 1 * ~~~(d ^^^ f) - 3 * ~~~(d ||| ~~~f) - 2 * ( ~~~d ||| ( ~~~e ||| f)) - 3 * ((d &&& e) ||| (e ^^^ f)) - 1 * (e ^^^ ( ~~~d &&& (e ||| f))) + 7 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * (f ^^^ (d ||| e)) - 6 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 7 * ~~~(d ||| (e ||| f)) - 13 * ~~~(d ||| ( ~~~e ||| f)) + 24 * ~~~( ~~~d ||| (e ||| f)) + 7 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 3 * ( ~~~d &&& ( ~~~e &&& f)) + 5 * ( ~~~d &&& (e &&& f)) + 9 * (d &&& ( ~~~e &&& f)) + 10 * (d &&& (e &&& f)) = 1 * ~~~(d &&& ~~~d) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2067 (x y : BitVec w) : +theorem e_2067 : - 1 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 11 * (e &&& (d ||| ~~~f)) - 11 * (f ^^^ (d &&& (e ||| f))) + 2 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 1 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 1 * (d ||| ~~~e) - 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 2 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 6 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 1 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 3 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 1 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 1 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 6 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 7 * ( ~~~d ||| ( ~~~e ||| f)) + 2 * (e ^^^ ~~~(d ||| f)) - 5 * (d ||| ~~~f) - 2 * (e ||| ~~~(d ||| f)) - 2 * (f ^^^ ~~~(d &&& (e ||| f))) + 1 * (e ||| ~~~(d ||| ~~~f)) + 3 * ( ~~~d &&& (e ^^^ f)) + 1 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 1 * (e ^^^ (d ||| ( ~~~e &&& f))) + 1 * (e ||| (d ^^^ f)) + 11 * ( ~~~e ||| (d ^^^ f)) + 11 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 1 * (f ^^^ ~~~(d ||| ~~~e)) + 2 * (f &&& (d ||| ~~~e)) + 1 * (d ^^^ f) - 1 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 4 * ~~~(d ||| (e ||| f)) + 33 * ~~~(d ||| ( ~~~e ||| f)) - 2 * ~~~( ~~~d ||| (e ||| f)) + 16 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 10 * ( ~~~d &&& ( ~~~e &&& f)) - 9 * ( ~~~d &&& (e &&& f)) - 11 * (d &&& ( ~~~e &&& f)) + 19 * (d &&& (e &&& f)) = - 3 * ~~~( ~~~d &&& (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2068 (x y : BitVec w) : +theorem e_2068 : 11 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 1 * ~~~(e ||| f) + 7 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 1 * ((d &&& f) ||| ~~~(e ||| f)) + 2 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 1 * (f ||| (d &&& e)) - 1 * (e &&& (d ||| ~~~f)) - 1 * ( ~~~d &&& (e ||| f)) - 6 * ~~~(d &&& ~~~f) - 2 * ( ~~~f &&& (d ^^^ e)) + 4 * f + 5 * ( ~~~f ||| ~~~(d ^^^ e)) + 3 * (f ^^^ ~~~(d ||| (e &&& f))) + 5 * ( ~~~d ||| (e &&& f)) + 3 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 1 * (e ^^^ (d ||| (e ^^^ f))) - 2 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 7 * ~~~(d &&& ( ~~~e ||| f)) + 1 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 1 * (e &&& ~~~(d ^^^ f)) - 11 * ( ~~~f &&& ~~~(d ^^^ e)) + 1 * (e ^^^ (d ||| ( ~~~e ||| f))) - 2 * (f ||| (d ^^^ e)) + 5 * ( ~~~e ||| (d ^^^ f)) + 2 * (f ^^^ ~~~(d ||| ~~~e)) + 7 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 3 * (f ^^^ ~~~(d &&& (e &&& f))) - 3 * ((d &&& e) ||| ~~~(e ||| f)) - 3 * (f ^^^ ~~~(d &&& ~~~e)) + 5 * (e ^^^ (d &&& (e ||| f))) - 1 * (f ^^^ (d &&& ~~~e)) - 17 * ~~~(d ||| (e ||| f)) - 12 * ~~~(d ||| ( ~~~e ||| f)) - 20 * ~~~( ~~~d ||| (e ||| f)) - 6 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 12 * ( ~~~d &&& ( ~~~e &&& f)) - 26 * ( ~~~d &&& (e &&& f)) - 18 * (d &&& ( ~~~e &&& f)) - 17 * (d &&& (e &&& f)) = 3 * (e ^^^ ~~~(d &&& (e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2069 (x y : BitVec w) : +theorem e_2069 : - 7 * (e ^^^ (d &&& ~~~f)) - 6 * (e ^^^ (d ||| ( ~~~e &&& f))) + 11 * (f ||| ~~~(d ||| e)) + 1 * (f &&& ~~~(d &&& e)) - 1 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 1 * ((d ||| e) &&& ~~~(e ^^^ f)) - 1 * ~~~(d ^^^ ( ~~~e &&& f)) - 2 * (d &&& ~~~e) + 7 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 1 * ~~~(d &&& ( ~~~e ||| f)) - 11 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 2 * (f ^^^ (d ||| ( ~~~e &&& f))) - 2 * ((d &&& e) ||| (e ^^^ f)) + 1 * (f ^^^ (d ||| ~~~e)) - 1 * (f ||| (d &&& e)) + 5 * (e ||| ~~~(d ^^^ f)) + 1 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 2 * ((d ||| e) &&& (e ^^^ f)) + 2 * ~~~(d &&& (e ||| f)) - 1 * (e ^^^ ~~~(d &&& (e ||| f))) - 11 * (f ^^^ ~~~(d ||| (e &&& f))) - 1 * (e ^^^ ( ~~~d ||| (e ||| f))) - 11 * ((d ^^^ e) &&& (d ^^^ f)) - 2 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 1 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 11 * (d ||| (e &&& f)) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 3 * (d ||| (e ||| f)) + 2 * (f ^^^ (d ||| e)) - 7 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 3 * (d ^^^ ( ~~~e ||| f)) - 11 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 2 * ~~~(d ||| (e ||| f)) + 11 * ~~~(d ||| ( ~~~e ||| f)) + 14 * ~~~( ~~~d ||| (e ||| f)) - 15 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 16 * ( ~~~d &&& ( ~~~e &&& f)) + 5 * ( ~~~d &&& (e &&& f)) + 3 * (d &&& ( ~~~e &&& f)) - 4 * (d &&& (e &&& f)) = - 5 * ((d &&& e) ^^^ (e ||| ~~~f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2070 (x y : BitVec w) : +theorem e_2070 : - 7 * ((d ^^^ e) &&& (d ^^^ f)) - 7 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 7 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 5 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 1 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 7 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 2 * ~~~( ~~~d ||| (e ^^^ f)) + 2 * (e ||| ~~~(d ^^^ f)) - 2 * (e ^^^ (d ||| ~~~f)) + 2 * e - 1 * (f &&& (d ^^^ e)) + 3 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 11 * (f &&& ~~~(d ^^^ e)) - 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 6 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 2 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 2 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 4 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 1 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 1 * ( ~~~d ||| (e ^^^ f)) + 2 * (f &&& ~~~(d &&& ~~~e)) + 5 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 2 * ~~~(d ^^^ (e ^^^ f)) - 6 * (f ^^^ (d &&& e)) + 7 * (e &&& f) + 4 * (e ^^^ (d ||| (e &&& f))) - 7 * (f ^^^ (d &&& (e ||| f))) + 7 * ~~~(d &&& ~~~d) + 1 * ~~~( ~~~d &&& (e ^^^ f)) + 11 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 11 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 8 * ~~~(d ||| (e ||| f)) - 2 * ~~~(d ||| ( ~~~e ||| f)) + 2 * ~~~( ~~~d ||| (e ||| f)) - 16 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 17 * ( ~~~d &&& ( ~~~e &&& f)) - 4 * ( ~~~d &&& (e &&& f)) - 8 * (d &&& ( ~~~e &&& f)) - 44 * (d &&& (e &&& f)) = - 5 * (f ^^^ ~~~(d ||| e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2071 (x y : BitVec w) : +theorem e_2071 : 5 * ~~~(d ||| e) - 1 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 5 * (e &&& (d ||| f)) - 6 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 2 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 5 * (d ||| (e ||| f)) - 7 * ((d ||| e) &&& ~~~(e ^^^ f)) - 1 * (d ^^^ (e ||| f)) + 1 * (e ^^^ (d &&& (e ||| f))) + 2 * (e &&& ~~~f) - 2 * (e ^^^ ( ~~~d ||| (e ||| f))) - 2 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 5 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 3 * (e ^^^ f) - 2 * ~~~(d ||| (e ^^^ f)) + 1 * (e ^^^ (d &&& f)) - 2 * ~~~(e &&& f) - 1 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 1 * (f ^^^ ~~~(d ||| ~~~e)) + 2 * (f ^^^ ~~~(d ||| e)) + 2 * ~~~(d ^^^ f) - 1 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 3 * ~~~(d &&& (e ^^^ f)) - 2 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 3 * (f ||| ~~~(d ||| e)) + 4 * ( ~~~e &&& (d ^^^ f)) + 1 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 1 * (e &&& ~~~(d &&& f)) - 7 * (e ||| ~~~(d ||| ~~~f)) - 1 * (e ^^^ (d &&& ~~~f)) + 11 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 1 * ( ~~~d ||| (e &&& f)) + 1 * ~~~(d ||| (e ||| f)) - 4 * ~~~(d ||| ( ~~~e ||| f)) + 7 * ~~~( ~~~d ||| (e ||| f)) + 3 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 4 * ( ~~~d &&& ( ~~~e &&& f)) + 10 * ( ~~~d &&& (e &&& f)) + 4 * (d &&& ( ~~~e &&& f)) + 3 * (d &&& (e &&& f)) = 1 * (e ^^^ ~~~(d &&& (e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2072 (x y : BitVec w) : +theorem e_2072 : - 3 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 7 * (d ^^^ (e ||| f)) + 7 * ~~~(d ||| e) + 3 * (f ^^^ ( ~~~d &&& (e ||| f))) + 5 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 4 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 1 * (d ||| (e ||| f)) - 1 * ~~~(d &&& e) + 7 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 6 * ( ~~~d ||| ( ~~~e &&& f)) + 1 * ~~~( ~~~d ||| (e ^^^ f)) + 11 * ~~~(d &&& ( ~~~e ||| f)) + 2 * ((d &&& e) ||| ~~~(e ^^^ f)) - 2 * (f &&& (d ||| e)) - 1 * ~~~(d &&& ( ~~~e &&& f)) + 2 * (e &&& ~~~f) - 11 * (e ^^^ (d &&& f)) - 3 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 2 * e + 2 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 1 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 7 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * (e ^^^ ( ~~~d &&& (e ||| f))) - 5 * ( ~~~f ||| ~~~(d ^^^ e)) + 1 * (f ^^^ ( ~~~d ||| (e ||| f))) - 2 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 1 * ~~~(d ||| (e ^^^ f)) + 3 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 2 * (f ^^^ ~~~(d &&& ~~~e)) + 5 * (e ^^^ (d ||| (e &&& f))) + 11 * ~~~(e &&& f) - 3 * (f ||| ~~~(d ||| ~~~e)) - 35 * ~~~(d ||| (e ||| f)) - 5 * ~~~(d ||| ( ~~~e ||| f)) - 14 * ~~~( ~~~d ||| (e ||| f)) - 19 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 10 * ( ~~~d &&& ( ~~~e &&& f)) + 5 * ( ~~~d &&& (e &&& f)) - 3 * (d &&& ( ~~~e &&& f)) + 4 * (d &&& (e &&& f)) = 1 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 1 * ~~~(d &&& ~~~d) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2073 (x y : BitVec w) : +theorem e_2073 : - 7 * (e &&& (d ^^^ f)) - 1 * (d ^^^ ( ~~~e &&& f)) - 6 * ~~~( ~~~d ||| (e ^^^ f)) - 1 * (d ||| ( ~~~e ||| f)) + 2 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 4 * ~~~(d &&& ~~~d) + 7 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 11 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 5 * ~~~(d &&& f) - 3 * (f ^^^ ( ~~~d ||| (e ||| f))) + 2 * ~~~(d &&& (e ||| f)) + 11 * ~~~(d ||| (e &&& f)) + 3 * (e ^^^ (d ||| f)) - 3 * ( ~~~d ||| ( ~~~e &&& f)) - 2 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 11 * ((d &&& f) ^^^ (e ||| f)) + 2 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 11 * ~~~(d ^^^ (e &&& f)) + 1 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 3 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 11 * (d &&& (e ||| f)) - 11 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 1 * (f ^^^ ~~~(d ||| e)) + 1 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 4 * (e ^^^ (d &&& (e ||| f))) - 1 * (e ||| ~~~f) - 6 * ( ~~~f &&& ~~~(d ^^^ e)) - 1 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 6 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 1 * ~~~(d &&& e) + 2 * ~~~( ~~~d &&& (e ||| f)) - 1 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 1 * (e ||| (d &&& f)) + 14 * ~~~(d ||| (e ||| f)) - 18 * ~~~(d ||| ( ~~~e ||| f)) - 10 * ~~~( ~~~d ||| (e ||| f)) - 16 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 11 * ( ~~~d &&& ( ~~~e &&& f)) - 22 * (d &&& ( ~~~e &&& f)) - 9 * (d &&& (e &&& f)) = 30 * ( ~~~d &&& (e &&& f)) - 7 * (d &&& f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2074 (x y : BitVec w) : +theorem e_2074 : 1 * (e ^^^ (d ||| (e ||| f))) + 1 * ~~~(d ^^^ ( ~~~e ||| f)) - 6 * (f ^^^ (d &&& e)) - 1 * (f &&& (d ||| ~~~e)) + 2 * (f ^^^ (d ||| ~~~e)) - 5 * ((d &&& e) ||| ~~~(e ||| f)) - 11 * ( ~~~e ||| (d ^^^ f)) + 11 * ~~~(d ||| (e &&& f)) - 5 * (d ^^^ ( ~~~e &&& f)) + 1 * (e ^^^ (d ||| f)) + 1 * (e ^^^ (d &&& (e ||| f))) - 2 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 5 * (d &&& ~~~e) + 4 * (f ^^^ (d ||| (e &&& f))) + 4 * (d ||| ( ~~~e ||| f)) + 4 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 6 * ((d ||| e) &&& (e ^^^ f)) + 7 * ~~~(d &&& ( ~~~e &&& f)) + 3 * ( ~~~f &&& ~~~(d ^^^ e)) + 5 * (f &&& (d ^^^ e)) + 11 * (d &&& (e ^^^ f)) + 3 * (f ^^^ ~~~(d &&& (e &&& f))) + 5 * (e ^^^ ( ~~~d &&& (e ||| f))) - 11 * (f ^^^ ~~~(d &&& ~~~e)) - 1 * (e ^^^ ~~~(d &&& (e &&& f))) + 2 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 1 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 1 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 2 * (e &&& (d ||| f)) - 3 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 1 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 5 * ((d ^^^ e) ||| ~~~(d ^^^ f)) + 3 * ~~~(d ||| (e ||| f)) + 1 * ~~~(d ||| ( ~~~e ||| f)) + 5 * ~~~( ~~~d ||| (e ||| f)) + 5 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 7 * ( ~~~d &&& ( ~~~e &&& f)) + 6 * ( ~~~d &&& (e &&& f)) + 20 * (d &&& ( ~~~e &&& f)) + 4 * (d &&& (e &&& f)) = 1 * (e ^^^ (d &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2075 (x y : BitVec w) : +theorem e_2075 : - 3 * (f &&& (d ||| ~~~e)) + 1 * (e ^^^ (d &&& (e ||| f))) - 5 * ( ~~~d ||| (e ||| f)) + 1 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 5 * (f ^^^ (d ||| ( ~~~e &&& f))) - 1 * (f ||| ~~~(d ||| ~~~e)) + 1 * ~~~(d &&& e) - 2 * ( ~~~d ||| ( ~~~e &&& f)) - 1 * ~~~(d &&& (e ^^^ f)) - 3 * (f ^^^ ~~~(d ||| e)) - 2 * ((d ||| ~~~e) &&& (e ^^^ f)) - 3 * (e ^^^ ~~~(d ||| (e &&& f))) - 1 * ~~~( ~~~d &&& (e ||| f)) - 1 * (d ||| (e ^^^ f)) + 1 * ~~~(d &&& f) + 2 * (f ^^^ ~~~(d &&& (e &&& f))) - 11 * ( ~~~e ||| ~~~(d ^^^ f)) - 1 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 2 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 6 * ( ~~~d &&& (e ^^^ f)) + 2 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 2 * (e ^^^ ~~~(d ||| f)) + 4 * (e ^^^ ( ~~~d &&& (e ||| f))) - 6 * ( ~~~d ||| (e &&& f)) - 1 * (d &&& f) + 11 * (d ||| e) + 11 * (f ^^^ (d &&& ( ~~~e ||| f))) - 2 * (e ^^^ (d &&& (e ^^^ f))) - 7 * (f ^^^ ( ~~~d ||| (e ||| f))) - 2 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 7 * ~~~(d ^^^ (e ^^^ f)) + 1 * ( ~~~f &&& (d ^^^ e)) + 2 * (f &&& ~~~(d ^^^ e)) + 28 * ~~~(d ||| (e ||| f)) + 23 * ~~~(d ||| ( ~~~e ||| f)) - 10 * ~~~( ~~~d ||| (e ||| f)) + 2 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 21 * ( ~~~d &&& ( ~~~e &&& f)) - 4 * ( ~~~d &&& (e &&& f)) + 20 * (d &&& (e &&& f)) = - 10 * (d &&& ( ~~~e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2076 (x y : BitVec w) : +theorem e_2076 : - 1 * ( ~~~e &&& (d ^^^ f)) + 11 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 3 * ~~~(e ||| f) - 1 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 1 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 5 * (e ^^^ (d ||| ( ~~~e &&& f))) + 1 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 11 * (f ^^^ (d ||| ( ~~~e ||| f))) - 3 * (d ^^^ f) + 3 * (e &&& (d ||| f)) - 11 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 5 * (f ^^^ ~~~(d ||| (e &&& f))) + 2 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 1 * ( ~~~d ||| ( ~~~e ||| f)) - 2 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 7 * ( ~~~e &&& ~~~(d ^^^ f)) + 2 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 3 * ( ~~~f &&& ~~~(d ^^^ e)) - 2 * ~~~(d &&& ~~~e) + 3 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 6 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 2 * ~~~(d &&& ~~~f) - 5 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 7 * (d &&& (e ^^^ f)) + 5 * ((d &&& e) ^^^ (e ||| f)) - 1 * (f &&& (d ||| ~~~e)) + 3 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 5 * ((d &&& e) ^^^ (e ||| ~~~f)) + 4 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (f ||| (d ^^^ e)) - 5 * (d ||| (e &&& f)) + 2 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 3 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 2 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 19 * ~~~(d ||| (e ||| f)) - 7 * ~~~(d ||| ( ~~~e ||| f)) - 1 * ~~~( ~~~d ||| (e ||| f)) + 2 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 13 * ( ~~~d &&& ( ~~~e &&& f)) + 5 * (d &&& (e &&& f)) = - 11 * ~~~(d ^^^ (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2077 (x y : BitVec w) : +theorem e_2077 : 3 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 4 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 7 * (d ^^^ f) - 1 * ((d &&& e) ||| (e ^^^ f)) - 2 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 5 * (e ^^^ ~~~(d &&& f)) + 1 * ( ~~~e ||| (d ^^^ f)) + 4 * ( ~~~d ||| (e &&& f)) - 2 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 2 * ~~~(d ||| ( ~~~e &&& f)) - 11 * ~~~( ~~~d &&& (e ^^^ f)) + 2 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 1 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 11 * (f ^^^ (d ||| e)) - 11 * ( ~~~e &&& ~~~(d ^^^ f)) + 4 * ( ~~~f ||| (d ^^^ e)) - 5 * (f ||| ~~~(d ||| e)) + 5 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 2 * (e ^^^ (d ||| (e &&& f))) + 5 * (f ||| (d &&& ~~~e)) - 1 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 7 * (d ^^^ (e &&& f)) - 6 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 1 * (f ||| (d ^^^ e)) - 7 * ~~~f + 4 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 1 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 1 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 1 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 1 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 32 * ~~~(d ||| (e ||| f)) - 22 * ~~~(d ||| ( ~~~e ||| f)) + 12 * ~~~( ~~~d ||| (e ||| f)) + 11 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 3 * ( ~~~d &&& ( ~~~e &&& f)) + 27 * ( ~~~d &&& (e &&& f)) + 14 * (d &&& ( ~~~e &&& f)) + 11 * (d &&& (e &&& f)) = - 2 * ~~~(d ^^^ (e &&& f)) + 2 * (d ||| (e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2078 (x y : BitVec w) : +theorem e_2078 : - 11 * ( ~~~d ||| (e ||| f)) + 7 * (e ||| (d &&& f)) + 3 * (e ^^^ ~~~(d ||| f)) + 1 * (f ^^^ ~~~(d ||| (e &&& f))) - 3 * ((d &&& e) ||| ~~~(e ^^^ f)) + 2 * ( ~~~f &&& ~~~(d ^^^ e)) + 1 * (e ^^^ ( ~~~d ||| (e &&& f))) + 2 * ~~~(d &&& ( ~~~e &&& f)) + 7 * (f ^^^ ( ~~~d ||| (e ||| f))) - 1 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 1 * (e ^^^ ~~~(d &&& (e &&& f))) - 2 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 7 * ~~~e + 3 * ~~~(d &&& ~~~f) + 3 * (d ||| ( ~~~e &&& f)) + 2 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 11 * (f ||| (d ^^^ e)) + 1 * (f ||| (d &&& ~~~e)) + 2 * (d &&& ( ~~~e ||| f)) - 7 * (d ||| (e ^^^ f)) + 5 * ( ~~~d ||| ( ~~~e &&& f)) + 2 * ((d ||| ~~~e) &&& (e ^^^ f)) - 2 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 3 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 5 * ((d &&& e) ^^^ (e ||| f)) + 1 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 7 * ~~~(d &&& ( ~~~e ||| f)) - 6 * ~~~(d ^^^ e) - 1 * ~~~(d &&& e) + 2 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 1 * (d ^^^ (e &&& f)) - 11 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 7 * ~~~( ~~~d &&& (e ^^^ f)) - 5 * ( ~~~e &&& ~~~(d ^^^ f)) + 11 * ~~~(d ||| (e ||| f)) + 9 * ~~~(d ||| ( ~~~e ||| f)) + 2 * ~~~( ~~~d ||| (e ||| f)) - 2 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 8 * ( ~~~d &&& ( ~~~e &&& f)) + 18 * (d &&& ( ~~~e &&& f)) + 34 * (d &&& (e &&& f)) = - 11 * ~~~(d &&& f) - 4 * (f ^^^ (d &&& ~~~e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2079 (x y : BitVec w) : +theorem e_2079 : - 2 * ~~~(d &&& ( ~~~e &&& f)) - 7 * ((d &&& e) ||| ~~~(e ^^^ f)) + 1 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 5 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 1 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 11 * (e ^^^ (d &&& f)) + 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 1 * (f ||| (d &&& ~~~e)) - 2 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 5 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 1 * (d ||| ~~~f) + 2 * (e ^^^ ~~~(d &&& (e &&& f))) + 2 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 3 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 4 * (f &&& (d ||| e)) + 7 * (f ^^^ ( ~~~d ||| (e ||| f))) + 4 * (f ||| ~~~(d ||| ~~~e)) + 1 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 4 * (f &&& (d ^^^ e)) - 1 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 2 * (e &&& (d ||| f)) + 1 * (f ^^^ ~~~(d ||| e)) - 1 * ( ~~~e &&& (d ^^^ f)) - 1 * (e ^^^ ( ~~~d ||| (e ||| f))) - 1 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 3 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 7 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 1 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 2 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 2 * (d ^^^ e) + 7 * (f ^^^ ~~~(d &&& (e ||| f))) + 11 * ( ~~~d &&& (e ||| f)) + 3 * (e ^^^ ~~~(d &&& f)) + 5 * ~~~(d ||| (e ||| f)) - 34 * ~~~(d ||| ( ~~~e ||| f)) + 2 * ~~~( ~~~d ||| (e ||| f)) - 11 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 27 * ( ~~~d &&& (e &&& f)) - 24 * (d &&& ( ~~~e &&& f)) - 1 * (d &&& (e &&& f)) = 5 * ( ~~~d &&& ( ~~~e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2080 (x y : BitVec w) : +theorem e_2080 : - 7 * ~~~(d ||| (e ^^^ f)) - 1 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 5 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * (e ||| (d &&& ~~~f)) + 11 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 1 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 1 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 11 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 2 * (f ||| (d &&& e)) + 1 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 11 * (d ||| (e ||| f)) + 1 * ~~~(d ^^^ f) + 1 * (e ||| ~~~(d ^^^ f)) + 11 * (e ^^^ (d &&& ~~~f)) - 3 * (e ^^^ (d &&& (e ||| f))) + 7 * (f ^^^ ( ~~~d ||| (e ||| f))) + 1 * ~~~(d &&& (e ^^^ f)) - 1 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 2 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 2 * (e ^^^ (d &&& ( ~~~e ||| f))) + 4 * (e ||| (d ^^^ f)) - 11 * (e ^^^ (d &&& f)) + 2 * (d ^^^ (e ^^^ f)) + 2 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 5 * (e ^^^ ~~~(d &&& (e ||| f))) - 11 * (e ^^^ ~~~(d ||| ~~~f)) + 4 * ( ~~~e ||| ~~~(d ^^^ f)) + 2 * (f ^^^ ( ~~~d &&& (e ||| f))) - 1 * (e ^^^ (d &&& (e ^^^ f))) - 2 * f + 3 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 22 * ~~~(d ||| (e ||| f)) - 39 * ~~~(d ||| ( ~~~e ||| f)) - 52 * ~~~( ~~~d ||| (e ||| f)) + 4 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 17 * ( ~~~d &&& ( ~~~e &&& f)) - 10 * ( ~~~d &&& (e &&& f)) - 2 * (d &&& ( ~~~e &&& f)) - 29 * (d &&& (e &&& f)) = 1 * (e ^^^ ~~~(d ||| (e &&& f))) + 3 * (e &&& ~~~(d &&& ~~~f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2081 (x y : BitVec w) : +theorem e_2081 : - 11 * (d ^^^ ( ~~~e &&& f)) - 2 * (d ||| ~~~e) - 2 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 4 * ( ~~~d &&& ( ~~~e ||| f)) + 5 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 1 * (e ||| f) - 7 * (f ^^^ ( ~~~d ||| (e &&& f))) - 2 * ~~~(d ^^^ e) - 5 * ~~~(d &&& ( ~~~e &&& f)) + 2 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 7 * ~~~(d ||| f) - 2 * (f ^^^ ~~~(d ||| e)) + 1 * (d &&& ~~~e) + 2 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 2 * (f &&& ~~~(d ^^^ e)) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 1 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 3 * (e ^^^ (d ||| (e &&& f))) + 11 * ((d &&& f) ||| ~~~(e ||| f)) + 7 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 2 * ((d ^^^ e) &&& (d ^^^ f)) + 5 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 3 * ((d &&& e) ^^^ (e ||| f)) - 7 * (e ^^^ (d &&& f)) - 2 * ( ~~~e &&& (d ^^^ f)) - 11 * ((e &&& f) ||| (d &&& (e ||| f))) + 1 * (e ^^^ ~~~(d &&& (e &&& f))) - 1 * (e ^^^ ~~~(d ||| f)) - 5 * ~~~(d &&& (e ||| f)) - 6 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 7 * ~~~(d ^^^ (e ^^^ f)) - 1 * (e ^^^ (d ||| ( ~~~e &&& f))) - 1 * (f ^^^ (d &&& ~~~e)) - 8 * ~~~(d ||| (e ||| f)) + 16 * ~~~(d ||| ( ~~~e ||| f)) + 5 * ~~~( ~~~d ||| (e ||| f)) + 35 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 17 * ( ~~~d &&& ( ~~~e &&& f)) + 21 * ( ~~~d &&& (e &&& f)) + 9 * (d &&& ( ~~~e &&& f)) + 26 * (d &&& (e &&& f)) = 6 * ~~~( ~~~d &&& (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2082 (x y : BitVec w) : +theorem e_2082 : - 3 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 7 * (f ^^^ (d &&& (e ||| f))) - 7 * (e ^^^ ~~~(d &&& (e &&& f))) + 4 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 7 * (e &&& ~~~(d ^^^ f)) + 4 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 4 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * (f ^^^ (d ||| ( ~~~e ||| f))) + 1 * ~~~(d &&& (e &&& f)) + 1 * (e ^^^ (d &&& ( ~~~e ||| f))) + 1 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 1 * ~~~(d ^^^ e) - 2 * ( ~~~d ||| ( ~~~e ||| f)) - 11 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 5 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 3 * (f ||| ~~~(d ||| ~~~e)) - 6 * (f ||| ~~~(d ||| e)) - 7 * (e ^^^ (d ||| f)) - 3 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 1 * ~~~(d ||| ~~~e) + 1 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 4 * (d ||| ( ~~~e &&& f)) - 3 * (d &&& f) + 11 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 1 * (f &&& ~~~(d &&& e)) + 3 * (e ||| (d &&& f)) + 7 * (d ||| e) + 3 * (f ^^^ (d &&& e)) + 3 * ( ~~~f &&& (d ^^^ e)) - 1 * ( ~~~e &&& (d ^^^ f)) + 2 * (e &&& (d ||| f)) + 2 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 7 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 5 * ~~~(d ||| (e ||| f)) - 31 * ~~~(d ||| ( ~~~e ||| f)) - 1 * ~~~( ~~~d ||| (e ||| f)) - 39 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 10 * ( ~~~d &&& ( ~~~e &&& f)) - 39 * ( ~~~d &&& (e &&& f)) - 2 * (d &&& ( ~~~e &&& f)) + 7 * (d &&& (e &&& f)) = - 2 * (f ||| (d ^^^ e)) - 1 * (f &&& (d ||| e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2083 (x y : BitVec w) : +theorem e_2083 : 4 * (d ^^^ (e ^^^ f)) + 2 * (e ^^^ (d &&& ~~~f)) - 2 * ( ~~~d &&& ( ~~~e ||| f)) + 11 * (f ^^^ (d &&& ( ~~~e ||| f))) + 1 * (e ^^^ ~~~(d &&& ~~~f)) + 4 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 1 * ( ~~~d ||| (e ||| f)) + 1 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * ((d &&& f) ^^^ (e ||| f)) + 7 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 1 * ( ~~~f ||| (d ^^^ e)) + 5 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 2 * ~~~(d &&& e) - 1 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 3 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 6 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * (e &&& (d ||| ~~~f)) - 11 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 1 * ((d &&& f) ||| (e &&& ~~~f)) - 1 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 3 * ((d ^^^ e) ||| (d ^^^ f)) - 1 * ~~~(d &&& (e &&& f)) + 7 * (f ^^^ (d ||| (e ||| f))) - 2 * ~~~( ~~~d &&& (e ||| f)) - 2 * (e &&& f) - 11 * ((d ^^^ e) &&& (d ^^^ f)) + 3 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 7 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 7 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 2 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 2 * ~~~(d ||| ( ~~~e &&& f)) + 3 * (d &&& e) + 7 * ~~~(d ||| (e ||| f)) - 7 * ~~~(d ||| ( ~~~e ||| f)) + 11 * ~~~( ~~~d ||| (e ||| f)) - 11 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 17 * ( ~~~d &&& ( ~~~e &&& f)) + 37 * ( ~~~d &&& (e &&& f)) + 8 * (d &&& ( ~~~e &&& f)) + 18 * (d &&& (e &&& f)) = - 2 * (e ^^^ ( ~~~d ||| (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2084 (x y : BitVec w) : +theorem e_2084 : 7 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 2 * (e &&& ~~~(d &&& f)) - 1 * (f ^^^ (d &&& e)) + 1 * (f ^^^ (d ||| ( ~~~e ||| f))) + 4 * (f ^^^ ( ~~~d ||| (e &&& f))) - 5 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 1 * ( ~~~e &&& ~~~(d ^^^ f)) + 1 * ( ~~~f ||| ~~~(d ^^^ e)) - 5 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 7 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 1 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 4 * ((d &&& ~~~e) ||| (e ^^^ f)) + 2 * e + 5 * ( ~~~f &&& (d ^^^ e)) - 1 * (e ^^^ (d &&& ( ~~~e ||| f))) - 2 * (e ^^^ ( ~~~d ||| (e &&& f))) + 11 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 3 * ~~~(d ^^^ (e ^^^ f)) - 3 * ((d ||| e) &&& (e ^^^ f)) + 11 * (d &&& ~~~e) + 1 * (f ^^^ ~~~(d &&& ~~~e)) - 6 * (d ^^^ (e ^^^ f)) - 5 * ( ~~~f &&& ~~~(d ^^^ e)) + 1 * (e ||| (d ^^^ f)) + 2 * ~~~(d ||| ( ~~~e &&& f)) - 6 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 2 * (e ^^^ (d ||| f)) + 1 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 1 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 3 * (e ^^^ (d &&& f)) - 3 * ~~~(d ^^^ ( ~~~e ||| f)) - 1 * (d &&& ~~~f) + 2 * ((d &&& e) ||| ~~~(e ||| f)) - 8 * ~~~(d ||| (e ||| f)) - 20 * ~~~(d ||| ( ~~~e ||| f)) - 16 * ~~~( ~~~d ||| (e ||| f)) - 16 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 1 * ( ~~~d &&& ( ~~~e &&& f)) - 11 * ( ~~~d &&& (e &&& f)) - 20 * (d &&& ( ~~~e &&& f)) + 16 * (d &&& (e &&& f)) = - 5 * (e &&& ~~~f) + 2 * ((d &&& e) ||| ~~~(e ||| ~~~f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2085 (x y : BitVec w) : +theorem e_2085 : - 7 * ~~~(d ||| ( ~~~e &&& f)) - 3 * (f ^^^ ~~~(d ||| (e &&& f))) - 1 * (e ^^^ ~~~(d ||| (e &&& f))) + 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 2 * (d &&& ~~~e) + 1 * (e ^^^ (d &&& ~~~f)) + 5 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 5 * ~~~(d ^^^ ( ~~~e ||| f)) + 4 * (e ^^^ (d ||| (e ^^^ f))) - 1 * (d &&& ( ~~~e ||| f)) - 11 * ~~~(e ||| ~~~f) - 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 2 * ((d &&& e) ||| ~~~(e ||| f)) + 1 * (f ^^^ ~~~(d ||| ~~~e)) - 3 * ((d ||| e) &&& (e ^^^ f)) + 2 * ~~~e + 7 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 6 * (d ||| e) + 2 * ~~~(d &&& (e ||| f)) - 6 * ((d &&& e) ||| (e ^^^ f)) + 2 * (e ^^^ (d ||| ( ~~~e ||| f))) - 2 * (f ^^^ ~~~(d &&& ~~~e)) + 3 * (e ^^^ ~~~(d &&& (e &&& f))) - 3 * (f &&& ~~~(d ^^^ e)) + 2 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 6 * ((d &&& f) ^^^ (e ||| f)) - 1 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 1 * d - 5 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 7 * (d ||| (e &&& f)) - 1 * (f ^^^ (d ||| (e ||| f))) - 1 * (e ^^^ ( ~~~d ||| (e ||| f))) + 3 * (e ||| (d &&& ~~~f)) - 1 * ~~~(d ||| (e ||| f)) + 13 * ~~~(d ||| ( ~~~e ||| f)) + 2 * ~~~( ~~~d ||| (e ||| f)) + 18 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 14 * ( ~~~d &&& ( ~~~e &&& f)) + 17 * ( ~~~d &&& (e &&& f)) + 31 * (d &&& ( ~~~e &&& f)) + 16 * (d &&& (e &&& f)) = - 5 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2086 (x y : BitVec w) : +theorem e_2086 : 2 * (f &&& (d ^^^ e)) - 1 * (d &&& (e ^^^ f)) - 1 * (d ||| ~~~f) + 1 * (e ||| f) - 1 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 1 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 11 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 2 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 6 * ( ~~~f ||| ~~~(d ^^^ e)) + 11 * (e ^^^ ~~~(d &&& f)) + 3 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 6 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 2 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 11 * (e ||| (d &&& f)) - 1 * ~~~(e ^^^ f) + 3 * ~~~(d ||| e) - 2 * ~~~( ~~~d ||| (e ^^^ f)) + 4 * (d &&& ( ~~~e ||| f)) + 5 * (d ||| e) + 5 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 1 * (f ^^^ ( ~~~d ||| (e &&& f))) - 5 * (e &&& f) - 11 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 5 * (f ^^^ (d ||| (e ||| f))) + 2 * (d ||| ( ~~~e &&& f)) + 2 * (d ^^^ ( ~~~e &&& f)) + 1 * ~~~e - 6 * ~~~(d &&& ( ~~~e &&& f)) - 2 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 7 * ~~~(d ||| (e ^^^ f)) - 6 * (d ^^^ e) - 1 * (d ^^^ f) + 4 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 8 * ~~~(d ||| (e ||| f)) + 29 * ~~~(d ||| ( ~~~e ||| f)) - 8 * ~~~( ~~~d ||| (e ||| f)) + 33 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 15 * ( ~~~d &&& ( ~~~e &&& f)) + 7 * ( ~~~d &&& (e &&& f)) - 2 * (d &&& ( ~~~e &&& f)) - 9 * (d &&& (e &&& f)) = 2 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2087 (x y : BitVec w) : +theorem e_2087 : - 11 * (e ^^^ (d &&& f)) - 3 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 1 * (d ||| ~~~f) + 5 * ~~~(d ^^^ ( ~~~e ||| f)) + 7 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 5 * (e ^^^ (d ||| ~~~f)) + 4 * (d ||| (e ||| f)) + 11 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 11 * ~~~(d &&& (e ||| f)) + 4 * (f ^^^ (d &&& (e ||| f))) - 1 * (e ^^^ ( ~~~d ||| (e ||| f))) + 4 * (e ^^^ (d ||| (e ||| f))) - 7 * ~~~(d ^^^ (e ||| f)) - 2 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 2 * ~~~( ~~~d &&& (e ^^^ f)) + 5 * ( ~~~e &&& (d ^^^ f)) - 2 * ~~~(d ||| (e ^^^ f)) + 1 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 2 * (e ||| ~~~f) + 1 * (f ^^^ ~~~(d &&& (e ||| f))) - 3 * (d ^^^ f) - 2 * ~~~(d ^^^ ( ~~~e &&& f)) - 11 * (f ^^^ ~~~(d ||| e)) + 1 * (f ^^^ ( ~~~d ||| (e &&& f))) + 4 * (e ^^^ ~~~(d ||| f)) + 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 4 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 3 * (f &&& ~~~(d ^^^ e)) - 5 * ~~~(d &&& ~~~d) + 7 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 2 * ~~~(d &&& f) - 6 * ( ~~~d ||| ( ~~~e &&& f)) - 2 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 5 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 9 * ~~~(d ||| ( ~~~e ||| f)) - 15 * ~~~( ~~~d ||| (e ||| f)) + 10 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 5 * ( ~~~d &&& ( ~~~e &&& f)) + 32 * ( ~~~d &&& (e &&& f)) + 18 * (d &&& ( ~~~e &&& f)) + 8 * (d &&& (e &&& f)) = - 1 * (d &&& (e ||| f)) - 37 * ~~~(d ||| (e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2088 (x y : BitVec w) : +theorem e_2088 : - 1 * (d ^^^ e) - 1 * ~~~(e ||| f) - 2 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 11 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 7 * (f ||| (d &&& ~~~e)) + 5 * (d ^^^ ( ~~~e ||| f)) - 3 * ((d &&& ~~~e) ||| (e ^^^ f)) + 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 7 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 3 * ((d &&& f) ^^^ (e ||| f)) - 3 * (e ^^^ (d ||| ( ~~~e ||| f))) + 7 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 1 * (e ^^^ ~~~(d &&& (e ||| f))) + 11 * (f &&& (d ^^^ e)) + 3 * ~~~(d ^^^ ( ~~~e &&& f)) - 3 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 2 * ~~~(e ||| ~~~f) - 1 * ((d ||| ~~~e) &&& (e ^^^ f)) + 1 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 6 * ( ~~~f ||| (d ^^^ e)) + 4 * (d ^^^ f) - 5 * (e ||| ~~~(d ||| f)) - 2 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 2 * ~~~(d ||| ( ~~~e &&& f)) - 1 * ((d ^^^ e) &&& (d ^^^ f)) + 1 * (f ||| (d &&& e)) + 3 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 7 * ~~~(d ||| (e ^^^ f)) - 5 * (f &&& ~~~(d &&& ~~~e)) - 11 * ( ~~~f &&& ~~~(d ^^^ e)) + 1 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 11 * (f ^^^ ~~~(d &&& ~~~e)) + 11 * (e ^^^ (d ||| (e ^^^ f))) + 14 * ~~~(d ||| (e ||| f)) + 22 * ~~~(d ||| ( ~~~e ||| f)) + 7 * ~~~( ~~~d ||| (e ||| f)) + 42 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 9 * ( ~~~d &&& ( ~~~e &&& f)) - 26 * ( ~~~d &&& (e &&& f)) - 5 * (d &&& ( ~~~e &&& f)) + 9 * (d &&& (e &&& f)) = - 11 * (f ^^^ ~~~(d ||| ~~~e)) - 2 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2089 (x y : BitVec w) : +theorem e_2089 : - 1 * ( ~~~d &&& (e ^^^ f)) + 1 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 11 * (f ||| (d &&& e)) - 1 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 6 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 7 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 1 * ~~~(d &&& ( ~~~e ||| f)) - 7 * ~~~(d ||| ~~~e) + 1 * ((d &&& f) ||| ~~~(e ||| f)) + 5 * ~~~(d ^^^ ( ~~~e ||| f)) - 7 * ~~~(e ||| f) + 1 * (d ^^^ (e ^^^ f)) - 1 * (e ^^^ ( ~~~d ||| (e &&& f))) + 5 * (d &&& ~~~e) - 3 * ((d ^^^ e) ||| (d ^^^ f)) - 1 * (e ||| ~~~(d ||| f)) - 1 * ~~~( ~~~d ||| (e ^^^ f)) + 11 * (d ||| (e &&& f)) + 1 * (d ^^^ ( ~~~e ||| f)) + 2 * ((d &&& e) ^^^ (e ||| ~~~f)) - 11 * (f ^^^ ~~~(d &&& e)) - 7 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 2 * (e ^^^ (d &&& ( ~~~e ||| f))) + 7 * ~~~(d &&& f) + 1 * (d ||| e) - 6 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 1 * (e ^^^ (d ||| f)) - 5 * (e ||| (d ^^^ f)) - 1 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 1 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 1 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 1 * f - 7 * (e ||| (d &&& f)) + 39 * ~~~(d ||| (e ||| f)) + 32 * ~~~(d ||| ( ~~~e ||| f)) + 15 * ~~~( ~~~d ||| (e ||| f)) + 16 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 33 * ( ~~~d &&& ( ~~~e &&& f)) + 18 * ( ~~~d &&& (e &&& f)) + 11 * (d &&& ( ~~~e &&& f)) + 23 * (d &&& (e &&& f)) = 1 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2090 (x y : BitVec w) : +theorem e_2090 : 2 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 1 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 7 * (e ||| ~~~(d ||| ~~~f)) - 7 * ((d &&& ~~~e) ||| (e ^^^ f)) - 3 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * f - 2 * ~~~(e &&& ~~~f) - 5 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 3 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 4 * (f &&& ~~~(d &&& ~~~e)) - 6 * (f ^^^ (d ||| (e &&& f))) + 1 * ~~~(d ||| ~~~f) - 2 * (e ^^^ (d &&& f)) - 5 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 2 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 2 * (e ||| (d &&& ~~~f)) - 6 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 11 * (d ||| ~~~e) + 11 * ( ~~~e ||| ~~~(d ^^^ f)) + 7 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (e ^^^ ~~~(d &&& (e ||| f))) - 1 * ~~~(d ||| (e &&& f)) - 5 * (d ^^^ (e ||| f)) - 7 * ((d &&& f) ||| ~~~(e ||| f)) + 1 * ((d &&& f) ^^^ (e ||| f)) + 4 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 2 * (e ||| (d &&& f)) + 4 * ~~~(d &&& ( ~~~e &&& f)) + 2 * (e &&& (d ||| ~~~f)) + 5 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 11 * (f ^^^ (d ||| (e ||| f))) + 11 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 5 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 11 * ~~~(d ||| (e ||| f)) + 3 * ~~~(d ||| ( ~~~e ||| f)) + 27 * ~~~( ~~~d ||| (e ||| f)) + 11 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 11 * ( ~~~d &&& ( ~~~e &&& f)) - 32 * ( ~~~d &&& (e &&& f)) + 6 * (d &&& ( ~~~e &&& f)) - 5 * (d &&& (e &&& f)) = - 5 * ((d ^^^ e) &&& (d ^^^ f)) - 3 * ((d &&& e) ||| (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2091 (x y : BitVec w) : +theorem e_2091 : - 1 * (d ||| ( ~~~e ||| f)) - 6 * (d &&& (e ^^^ f)) + 3 * (d &&& ( ~~~e ||| f)) + 1 * ((d &&& f) ^^^ (e ||| f)) - 11 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 6 * (d ^^^ ( ~~~e ||| f)) - 11 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 1 * ~~~(d ||| (e ^^^ f)) + 11 * ( ~~~f &&& (d ^^^ e)) - 2 * ((d ||| ~~~e) &&& (e ^^^ f)) + 2 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 4 * ~~~(e ||| ~~~f) + 1 * (f ^^^ ~~~(d &&& ~~~e)) - 1 * ( ~~~f &&& ~~~(d ^^^ e)) + 1 * (e ^^^ (d ||| ( ~~~e &&& f))) - 2 * ~~~(d &&& (e &&& f)) - 3 * ~~~(d &&& ~~~e) - 1 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 7 * ~~~(d ^^^ ( ~~~e ||| f)) + 2 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 1 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 5 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 11 * (f ^^^ (d ||| (e &&& f))) + 2 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 1 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 6 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 3 * (f &&& (d ^^^ e)) - 1 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 3 * (e ^^^ (d ||| ~~~f)) + 2 * ~~~(d &&& ~~~d) - 11 * ~~~(d &&& (e ^^^ f)) - 11 * (d ^^^ ( ~~~e &&& f)) + 1 * (f ^^^ ~~~(d &&& e)) + 2 * (f ^^^ ~~~(d ||| ~~~e)) + 50 * ~~~(d ||| (e ||| f)) + 8 * ~~~(d ||| ( ~~~e ||| f)) - 1 * ~~~( ~~~d ||| (e ||| f)) + 34 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 38 * ( ~~~d &&& ( ~~~e &&& f)) + 22 * ( ~~~d &&& (e &&& f)) + 5 * (d &&& ( ~~~e &&& f)) + 43 * (d &&& (e &&& f)) = 11 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2092 (x y : BitVec w) : +theorem e_2092 : - 7 * (f ^^^ ( ~~~d &&& (e ||| f))) + 2 * (e ^^^ (d &&& ( ~~~e ||| f))) - 11 * ~~~(d ^^^ (e &&& f)) + 5 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 2 * (e ||| ~~~(d ||| ~~~f)) - 3 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 1 * ((d ||| ~~~e) &&& (e ^^^ f)) + 5 * (f ||| (d ^^^ e)) - 7 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 4 * (e ^^^ (d &&& f)) - 6 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 3 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 1 * ~~~( ~~~d &&& (e ||| f)) + 1 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 4 * ((d ||| e) &&& (e ^^^ f)) + 1 * ( ~~~d ||| (e &&& f)) + 4 * (f ^^^ ( ~~~d ||| (e &&& f))) + 1 * (f &&& ~~~(d &&& ~~~e)) - 1 * ((d &&& e) ^^^ (e ||| f)) + 3 * (d ||| ( ~~~e ||| f)) + 7 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 3 * ~~~(e &&& f) + 2 * ( ~~~e ||| (d ^^^ f)) + 3 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 7 * (f ^^^ (d ||| (e ||| f))) - 11 * (e ||| (d &&& ~~~f)) - 2 * (f ^^^ ~~~(d ||| (e &&& f))) + 4 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 11 * ((d &&& f) ||| ~~~(e ||| f)) - 1 * ~~~f - 2 * (e ^^^ ~~~(d &&& (e &&& f))) - 2 * (d ^^^ (e &&& f)) + 2 * (f ^^^ ~~~(d &&& ~~~e)) + 19 * ~~~(d ||| (e ||| f)) + 22 * ~~~(d ||| ( ~~~e ||| f)) + 42 * ~~~( ~~~d ||| (e ||| f)) + 26 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 14 * ( ~~~d &&& ( ~~~e &&& f)) - 15 * ( ~~~d &&& (e &&& f)) + 12 * (d &&& ( ~~~e &&& f)) + 34 * (d &&& (e &&& f)) = 5 * ( ~~~f ||| ~~~(d ^^^ e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2093 (x y : BitVec w) : +theorem e_2093 : - 5 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 6 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 1 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 3 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 4 * (e ^^^ ~~~(d &&& (e &&& f))) - 11 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 1 * (d &&& ~~~e) + 4 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 5 * ~~~(e ||| f) + 7 * ~~~(d ||| f) + 2 * ~~~(d &&& ~~~f) - 1 * (f ||| ~~~(d ||| ~~~e)) - 3 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 1 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 2 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 2 * ~~~(d ^^^ e) + 1 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 1 * (e ^^^ f) + 1 * ~~~( ~~~d &&& (e ||| f)) + 1 * ~~~(d ^^^ ( ~~~e &&& f)) + 2 * ((d ||| ~~~e) &&& (e ^^^ f)) + 2 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 1 * (e ||| (d &&& ~~~f)) - 2 * (d &&& f) - 7 * ( ~~~f ||| ~~~(d ^^^ e)) + 4 * ~~~d - 7 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 2 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 6 * (f ^^^ (d ||| e)) + 7 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 11 * (e ^^^ ~~~(d ||| ~~~f)) + 11 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 5 * (d &&& ( ~~~e ||| f)) - 3 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 2 * ( ~~~d ||| (e ^^^ f)) - 4 * ~~~(d ||| (e ||| f)) - 12 * ~~~(d ||| ( ~~~e ||| f)) + 18 * ~~~( ~~~d ||| (e ||| f)) + 13 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 11 * ( ~~~d &&& ( ~~~e &&& f)) - 15 * ( ~~~d &&& (e &&& f)) - 22 * (d &&& (e &&& f)) = - 9 * (d &&& ( ~~~e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2094 (x y : BitVec w) : +theorem e_2094 : 1 * (f ^^^ ( ~~~d &&& (e ||| f))) + 2 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 5 * ~~~( ~~~d ||| (e &&& f)) - 3 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 1 * ~~~(d &&& f) - 1 * (f ^^^ (d ||| (e ||| f))) + 4 * ~~~(d ||| ~~~e) - 3 * (d ^^^ e) + 7 * (e ^^^ ~~~(d ||| (e &&& f))) - 1 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 11 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 2 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 3 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * ~~~(d &&& (e ^^^ f)) - 5 * (d &&& ( ~~~e ||| f)) - 3 * ~~~(d &&& (e &&& f)) + 1 * ((d &&& e) ^^^ (e ||| f)) - 7 * (e ||| ~~~(d ||| ~~~f)) - 7 * (f ||| (d ^^^ e)) + 4 * (d ^^^ (e ^^^ f)) - 2 * (d ||| ( ~~~e &&& f)) - 3 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 1 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 3 * ~~~(e &&& f) + 1 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 1 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 3 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 5 * (e ||| ~~~(d ||| f)) - 3 * ~~~(d &&& ~~~e) - 7 * (e ^^^ (d ||| f)) + 1 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 2 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 2 * ~~~(d ^^^ e) - 1 * (f &&& (d ||| ~~~e)) + 1 * (d &&& (e ^^^ f)) - 1 * (f ^^^ ~~~(d ||| e)) - 6 * ((d ||| e) &&& ~~~(e ^^^ f)) - 13 * ~~~(d ||| (e ||| f)) + 18 * ~~~(d ||| ( ~~~e ||| f)) + 26 * ( ~~~d &&& (e &&& f)) + 16 * (d &&& ( ~~~e &&& f)) + 19 * (d &&& (e &&& f)) = 15 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 12 * ~~~( ~~~d ||| (e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2095 (x y : BitVec w) : +theorem e_2095 : - 1 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 11 * ~~~(d &&& ~~~e) + 1 * (e ||| ~~~(d ||| f)) + 4 * (f ^^^ ~~~(d &&& (e ||| f))) + 1 * ~~~(d ||| ~~~e) - 11 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 5 * (e ^^^ ( ~~~d ||| (e ||| f))) + 7 * ~~~(d ^^^ (e &&& f)) - 1 * ( ~~~d ||| ( ~~~e &&& f)) + 1 * ~~~(d &&& e) - 3 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 3 * (e ^^^ ~~~(d ||| ~~~f)) - 7 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 7 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 6 * ((d &&& f) ||| ~~~(e ||| f)) + 11 * (e ^^^ (d ||| (e ^^^ f))) + 4 * ((d &&& e) ||| (e ^^^ f)) - 1 * ~~~d - 11 * (f ^^^ (d ||| ~~~e)) + 1 * (f ||| (d ^^^ e)) + 2 * (d ^^^ (e ^^^ f)) - 2 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 5 * ( ~~~d ||| ( ~~~e ||| f)) - 7 * (f ^^^ (d &&& e)) - 1 * (e &&& ~~~(d &&& ~~~f)) + 1 * (f &&& (d ||| e)) + 1 * ( ~~~f ||| (d ^^^ e)) - 5 * (d ^^^ ( ~~~e &&& f)) - 1 * ~~~(d ^^^ ( ~~~e ||| f)) + 7 * ((d &&& e) ||| ~~~(e ||| f)) + 2 * (f ||| ~~~(d ^^^ e)) + 11 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 6 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 5 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 7 * (f ^^^ ~~~(d ||| e)) + 45 * ~~~(d ||| (e ||| f)) - 1 * ~~~( ~~~d ||| (e ||| f)) + 53 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 26 * ( ~~~d &&& ( ~~~e &&& f)) + 40 * ( ~~~d &&& (e &&& f)) + 23 * (d &&& ( ~~~e &&& f)) + 18 * (d &&& (e &&& f)) = - 7 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 5 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2096 (x y : BitVec w) : +theorem e_2096 : - 6 * (f ^^^ (d ||| ( ~~~e ||| f))) - 5 * (e &&& ~~~f) + 11 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 6 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 5 * ~~~(e ||| ~~~f) + 11 * (d ^^^ ( ~~~e &&& f)) + 2 * ( ~~~d ||| (e ^^^ f)) - 2 * (e ^^^ f) + 2 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 4 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 1 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 3 * (f ^^^ ~~~(d &&& (e ||| f))) - 1 * (e ||| ~~~(d ||| ~~~f)) + 2 * (f ||| (d &&& e)) + 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 2 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 1 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 7 * (f ^^^ (d ||| e)) + 3 * (f ^^^ (d ||| ( ~~~e &&& f))) - 5 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 1 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 11 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 3 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 4 * (e ^^^ ~~~(d &&& f)) + 1 * ((d ||| ~~~e) &&& (e ^^^ f)) - 2 * (e &&& ~~~(d &&& f)) - 1 * ( ~~~e ||| ~~~(d ^^^ f)) + 7 * (e ||| ~~~(d ^^^ f)) + 1 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 6 * ( ~~~d ||| ( ~~~e ||| f)) + 1 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 3 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 1 * ~~~(d ||| (e ||| f)) + 4 * ~~~(d ||| ( ~~~e ||| f)) - 12 * ~~~( ~~~d ||| (e ||| f)) - 26 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 17 * ( ~~~d &&& ( ~~~e &&& f)) - 14 * ( ~~~d &&& (e &&& f)) - 1 * (d &&& ( ~~~e &&& f)) - 28 * (d &&& (e &&& f)) = 1 * (d &&& e) - 4 * ~~~(d ||| ( ~~~e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2097 (x y : BitVec w) : +theorem e_2097 : - 1 * (e &&& (d ^^^ f)) + 2 * (f ||| ~~~(d ^^^ e)) + 4 * (f ^^^ (d &&& ( ~~~e ||| f))) + 1 * ~~~( ~~~d ||| (e &&& f)) + 2 * ~~~(d ||| f) - 1 * (e ^^^ (d &&& ( ~~~e ||| f))) - 7 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 7 * ~~~( ~~~d &&& (e ^^^ f)) + 5 * (f ^^^ ~~~(d &&& (e ||| f))) + 1 * (d ^^^ (e &&& f)) - 3 * (f ^^^ (d &&& ~~~e)) + 11 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 5 * (d &&& f) - 2 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 1 * ~~~(d ||| ( ~~~e &&& f)) - 5 * (f ^^^ (d ||| (e ||| f))) + 1 * (d ^^^ (e ||| f)) + 7 * (f ^^^ ~~~(d &&& ~~~e)) + 11 * (d &&& (e ^^^ f)) - 2 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 5 * (f &&& (d ^^^ e)) - 3 * (e ||| ~~~(d ^^^ f)) - 2 * (d ||| e) + 5 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * ~~~(e ||| f) - 1 * (f ||| ~~~(d ||| ~~~e)) + 4 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 1 * (e ^^^ (d ||| (e ^^^ f))) - 5 * (e ^^^ (d ||| ( ~~~e &&& f))) - 11 * (f ||| (d &&& e)) - 6 * ((d &&& f) ||| (e &&& ~~~f)) + 11 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 7 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 11 * ((d &&& ~~~e) ||| (e ^^^ f)) - 1 * ~~~(e ^^^ f) - 19 * ~~~(d ||| ( ~~~e ||| f)) + 5 * ~~~( ~~~d ||| (e ||| f)) + 22 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 2 * ( ~~~d &&& ( ~~~e &&& f)) + 19 * ( ~~~d &&& (e &&& f)) - 12 * (d &&& ( ~~~e &&& f)) + 6 * (d &&& (e &&& f)) = - 2 * ~~~(d ^^^ f) - 5 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2098 (x y : BitVec w) : +theorem e_2098 : - 1 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 5 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 6 * (e ^^^ ( ~~~d &&& (e ||| f))) + 7 * (e ^^^ (d &&& (e ^^^ f))) - 11 * ~~~(d ||| f) + 5 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 2 * (e ^^^ (d ||| (e ||| f))) - 1 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 7 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (f ||| ~~~(d ||| ~~~e)) + 3 * ~~~(d ||| (e &&& f)) - 5 * (e ^^^ f) - 2 * ~~~(e ||| ~~~f) - 3 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 7 * (e &&& ~~~(d &&& f)) + 2 * ~~~(d &&& e) + 5 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 1 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 1 * (f ^^^ ( ~~~d ||| (e &&& f))) + 1 * (e ^^^ ( ~~~d ||| (e &&& f))) - 6 * (e ||| ~~~(d ||| f)) - 1 * (f ^^^ (d &&& ~~~e)) + 2 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 1 * ( ~~~f &&& (d ^^^ e)) + 1 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 3 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 1 * ~~~f - 1 * ( ~~~d ||| ( ~~~e &&& f)) - 5 * ((d &&& f) ||| (e &&& ~~~f)) + 1 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 7 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 6 * ( ~~~d &&& ( ~~~e ||| f)) - 5 * ~~~(d &&& ~~~e) + 2 * d + 1 * (d ||| ( ~~~e &&& f)) - 2 * ~~~(d ||| (e ||| f)) + 1 * ~~~(d ||| ( ~~~e ||| f)) - 22 * ~~~( ~~~d ||| (e ||| f)) - 12 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 10 * ( ~~~d &&& ( ~~~e &&& f)) - 19 * ( ~~~d &&& (e &&& f)) - 17 * (d &&& ( ~~~e &&& f)) = - 7 * ~~~(e &&& f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2099 (x y : BitVec w) : +theorem e_2099 : 3 * ~~~(d ||| ( ~~~e &&& f)) - 11 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 11 * ( ~~~f &&& ~~~(d ^^^ e)) - 2 * (f &&& ~~~(d &&& e)) - 7 * (e ^^^ (d ||| f)) - 5 * ((d ^^^ e) ||| (d ^^^ f)) + 3 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 3 * (e ^^^ ~~~(d &&& f)) - 1 * ~~~(d ||| (e ^^^ f)) + 7 * (d &&& ~~~f) - 1 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 4 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 6 * ( ~~~f ||| ~~~(d ^^^ e)) - 3 * (f ||| ~~~(d ^^^ e)) - 2 * (e ^^^ ( ~~~d ||| (e ||| f))) + 1 * (f ^^^ ( ~~~d ||| (e &&& f))) + 7 * (f ^^^ (d &&& ~~~e)) + 1 * (f ^^^ ( ~~~d ||| (e ||| f))) + 1 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * ((d ^^^ e) &&& (d ^^^ f)) - 2 * (f ||| ~~~(d ||| ~~~e)) - 2 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 2 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 7 * ~~~(d ||| ~~~e) - 5 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 6 * ( ~~~d ||| ( ~~~e ||| f)) + 1 * ( ~~~d ||| (e ||| f)) + 2 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 1 * (e ||| ~~~(d ||| f)) + 4 * (e ^^^ ~~~(d &&& (e &&& f))) - 1 * ( ~~~d ||| (e &&& f)) + 1 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 7 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 3 * ((d &&& e) ||| ~~~(e ||| f)) + 18 * ~~~(d ||| (e ||| f)) + 33 * ~~~(d ||| ( ~~~e ||| f)) + 21 * ~~~( ~~~d ||| (e ||| f)) + 28 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 15 * ( ~~~d &&& ( ~~~e &&& f)) + 15 * ( ~~~d &&& (e &&& f)) + 20 * (d &&& ( ~~~e &&& f)) + 17 * (d &&& (e &&& f)) = 1 * (f ||| (d &&& ~~~e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2100 (x y : BitVec w) : +theorem e_2100 : 2 * ~~~(d &&& ( ~~~e &&& f)) + 1 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 2 * (e ^^^ ~~~(d &&& (e ||| f))) - 1 * ~~~(d ||| ~~~e) - 1 * (d &&& ( ~~~e ||| f)) - 5 * ~~~(e ||| ~~~f) + 5 * ( ~~~d &&& (e ^^^ f)) + 3 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 2 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 11 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 7 * (e ||| (d &&& f)) - 2 * ~~~(d ||| (e ^^^ f)) + 11 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 11 * ~~~(d &&& ( ~~~e ||| f)) + 7 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 2 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 1 * (e &&& ~~~f) + 1 * (d ||| (e ||| f)) - 3 * (d ^^^ (e ||| f)) - 6 * (e ^^^ (d &&& (e ||| f))) - 6 * (f ^^^ ~~~(d ||| (e &&& f))) - 1 * (f ^^^ (d &&& ~~~e)) - 1 * ~~~( ~~~d ||| (e &&& f)) + 1 * ~~~( ~~~d &&& (e ||| f)) + 1 * ( ~~~d ||| (e ^^^ f)) + 2 * (d ||| ~~~f) + 5 * d - 3 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 3 * ~~~(d ^^^ f) - 1 * (f &&& (d ||| ~~~e)) + 5 * ( ~~~f &&& ~~~(d ^^^ e)) - 11 * ( ~~~d ||| ( ~~~e ||| f)) + 2 * (e ||| ~~~(d ||| f)) + 1 * (e &&& ~~~(d &&& f)) + 11 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 4 * ((d &&& e) ^^^ (e ||| f)) + 5 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 18 * ~~~(d ||| (e ||| f)) - 7 * ~~~(d ||| ( ~~~e ||| f)) - 17 * ~~~( ~~~d ||| (e ||| f)) - 54 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 6 * ( ~~~d &&& (e &&& f)) - 13 * (d &&& ( ~~~e &&& f)) = - 1 * (d ||| (e ^^^ f)) - 1 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2101 (x y : BitVec w) : +theorem e_2101 : - 6 * (e ^^^ (d ||| ( ~~~e ||| f))) - 1 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 3 * ( ~~~e ||| (d ^^^ f)) + 3 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 11 * (e ^^^ (d ||| f)) - 7 * ( ~~~d &&& (e ^^^ f)) - 1 * ~~~(d &&& (e ||| f)) - 11 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (e ^^^ (d ||| ( ~~~e &&& f))) - 2 * (d &&& (e ||| f)) - 6 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * ~~~(d ^^^ e) + 4 * ~~~(d ^^^ ( ~~~e &&& f)) - 3 * ~~~(d &&& f) + 1 * (f ||| ~~~(d ||| ~~~e)) - 3 * ~~~(d ||| ~~~e) - 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 4 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 1 * (f ^^^ ~~~(d ||| ~~~e)) - 5 * (d ^^^ e) - 1 * (e ^^^ ( ~~~d ||| (e &&& f))) + 7 * ((d &&& f) ^^^ (e ||| f)) + 11 * ~~~(d ||| ( ~~~e &&& f)) - 1 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 1 * (d &&& ( ~~~e ||| f)) + 2 * (e &&& f) - 2 * d - 2 * ((d &&& e) ^^^ (e ||| ~~~f)) + 1 * ~~~(d ||| (e &&& f)) + 2 * (e ||| ~~~(d ||| ~~~f)) - 2 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 2 * (f ||| ~~~(d ^^^ e)) + 5 * (f ^^^ ~~~(d &&& ~~~e)) - 1 * (e ^^^ ( ~~~d &&& (e ||| f))) - 2 * ~~~(d ||| (e ||| f)) + 6 * ~~~(d ||| ( ~~~e ||| f)) + 46 * ~~~( ~~~d ||| (e ||| f)) + 8 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 9 * ( ~~~d &&& ( ~~~e &&& f)) + 7 * ( ~~~d &&& (e &&& f)) + 30 * (d &&& ( ~~~e &&& f)) - 5 * (d &&& (e &&& f)) = - 3 * ~~~(d ||| e) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2102 (x y : BitVec w) : +theorem e_2102 : - 2 * (f ^^^ (d ||| (e ||| f))) - 5 * (f ^^^ ~~~(d &&& ~~~e)) + 2 * ((d ||| e) &&& ~~~(e ^^^ f)) - 3 * (e &&& (d ||| f)) + 11 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 1 * (f ^^^ (d ||| ( ~~~e &&& f))) - 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 4 * ((e &&& f) ||| (d &&& (e ||| f))) - 1 * (f ^^^ ~~~(d &&& (e ||| f))) - 2 * (e &&& ~~~f) + 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 1 * (e &&& ~~~(d &&& f)) - 5 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * (e ^^^ f) + 11 * (e ^^^ ( ~~~d ||| (e ||| f))) + 5 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 2 * (d ||| e) + 4 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 5 * (f ^^^ ~~~(d ||| e)) - 5 * (e ^^^ (d &&& ~~~f)) - 1 * (e ^^^ ~~~(d ||| ~~~f)) - 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 5 * (e ^^^ ~~~(d &&& ~~~f)) + 2 * (f ^^^ ( ~~~d ||| (e &&& f))) - 2 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 1 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 5 * (f ||| (d &&& ~~~e)) + 3 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 4 * (f ||| ~~~(d ||| ~~~e)) + 1 * ~~~(e ||| f) + 1 * ~~~(d &&& (e ||| f)) + 2 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 2 * (f ||| ~~~(d ||| e)) - 11 * (f &&& (d ^^^ e)) + 11 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 4 * (e ^^^ ~~~(d ||| (e &&& f))) - 40 * ~~~(d ||| (e ||| f)) + 8 * ~~~(d ||| ( ~~~e ||| f)) + 2 * ~~~( ~~~d ||| (e ||| f)) - 5 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 41 * ( ~~~d &&& ( ~~~e &&& f)) - 3 * ( ~~~d &&& (e &&& f)) - 30 * (d &&& (e &&& f)) = 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2103 (x y : BitVec w) : +theorem e_2103 : 2 * (f &&& (d ^^^ e)) + 5 * ((d &&& ~~~e) ||| (e ^^^ f)) - 1 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 6 * ((d ^^^ e) &&& (d ^^^ f)) - 5 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 1 * f - 1 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 1 * ((d ||| e) &&& (e ^^^ f)) - 7 * (e ^^^ f) - 1 * (f ^^^ (d &&& e)) + 2 * ~~~(d &&& ( ~~~e ||| f)) - 2 * ~~~(d ||| ~~~f) - 1 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 4 * ((d &&& e) ||| ~~~(e ||| f)) - 1 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 7 * ((d ||| e) &&& ~~~(e ^^^ f)) - 2 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 11 * ((d &&& e) ||| (e ^^^ f)) - 7 * ~~~(d ||| f) - 3 * (e ^^^ ~~~(d ||| (e &&& f))) + 1 * ~~~(d &&& ~~~e) + 1 * ~~~(d &&& (e ||| f)) + 1 * (e &&& ~~~(d ^^^ f)) + 11 * (d ^^^ f) - 1 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 2 * ~~~(d &&& ~~~f) - 3 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * (e ^^^ ~~~(d &&& f)) + 7 * ~~~f + 7 * (e &&& ~~~(d &&& f)) + 2 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 4 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 7 * (e ||| ~~~(d ||| f)) + 1 * ( ~~~e ||| (d ^^^ f)) - 2 * ~~~(d ^^^ ( ~~~e &&& f)) - 3 * ~~~(d ||| (e ||| f)) - 12 * ~~~(d ||| ( ~~~e ||| f)) - 1 * ~~~( ~~~d ||| (e ||| f)) - 35 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 11 * ( ~~~d &&& ( ~~~e &&& f)) - 3 * (d &&& ( ~~~e &&& f)) - 3 * (d &&& (e &&& f)) = 11 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 9 * ( ~~~d &&& (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2104 (x y : BitVec w) : +theorem e_2104 : 7 * (f &&& ~~~(d ^^^ e)) + 11 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 6 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 3 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 1 * (e ||| ~~~(d ||| ~~~f)) - 5 * ~~~(d ||| (e ^^^ f)) + 1 * ~~~(d ^^^ ( ~~~e &&& f)) + 1 * ~~~(d ^^^ (e ||| f)) - 1 * (d &&& ~~~f) - 2 * (e ||| ~~~f) + 7 * (e ^^^ ~~~(d &&& (e ||| f))) + 2 * ~~~(d ||| (e &&& f)) + 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 2 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 1 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 3 * ~~~(d &&& (e ||| f)) + 2 * ( ~~~e &&& ~~~(d ^^^ f)) - 2 * ((d &&& f) ||| (e &&& ~~~f)) + 4 * ( ~~~d ||| (e ||| f)) + 11 * (f ^^^ ~~~(d ||| e)) + 1 * ~~~(e &&& f) - 3 * (e &&& (d ||| ~~~f)) + 5 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 6 * ( ~~~d ||| (e ^^^ f)) + 1 * ((d ^^^ e) ||| ~~~(d ^^^ f)) + 11 * ~~~(d &&& f) + 5 * ~~~( ~~~d &&& (e ^^^ f)) + 11 * ( ~~~d &&& (e ^^^ f)) - 6 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 11 * (f ^^^ ( ~~~d ||| (e &&& f))) + 3 * (e ^^^ (d &&& ~~~f)) + 11 * ~~~(d ^^^ ( ~~~e ||| f)) - 1 * ((d &&& e) ||| (e ^^^ f)) + 1 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 3 * ~~~(d &&& ( ~~~e ||| f)) - 33 * ~~~(d ||| (e ||| f)) - 24 * ~~~(d ||| ( ~~~e ||| f)) - 44 * ~~~( ~~~d ||| (e ||| f)) - 24 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 30 * ( ~~~d &&& ( ~~~e &&& f)) - 33 * ( ~~~d &&& (e &&& f)) - 32 * (d &&& ( ~~~e &&& f)) - 42 * (d &&& (e &&& f)) = - 1 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2105 (x y : BitVec w) : +theorem e_2105 : 1 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 2 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 11 * ~~~(e &&& f) - 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 1 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 7 * ((d ||| e) &&& (e ^^^ f)) - 5 * (f ||| (d &&& e)) - 2 * (f &&& (d ||| e)) + 3 * ( ~~~f ||| ~~~(d ^^^ e)) - 5 * (f ^^^ ~~~(d &&& (e &&& f))) + 7 * (f ^^^ ~~~(d ||| (e &&& f))) + 2 * (d ||| e) + 1 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 1 * (e ^^^ (d &&& (e ^^^ f))) - 1 * (e ^^^ (d ||| ( ~~~e ||| f))) - 11 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 7 * (e ^^^ ~~~(d ||| ~~~f)) - 11 * (f ^^^ (d &&& (e ||| f))) - 2 * (e ^^^ (d &&& ~~~f)) - 2 * ~~~(d ||| ~~~f) - 1 * ~~~( ~~~d ||| (e &&& f)) + 3 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 1 * ~~~(d &&& ~~~e) + 5 * (e ^^^ (d &&& ( ~~~e ||| f))) - 2 * ( ~~~e &&& ~~~(d ^^^ f)) + 2 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 11 * ( ~~~f &&& ~~~(d ^^^ e)) - 2 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * (f ^^^ (d &&& ( ~~~e ||| f))) - 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 1 * (d ^^^ f) + 11 * ((d &&& f) ||| ~~~(e ||| f)) - 11 * (f ^^^ (d &&& ~~~e)) - 1 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 2 * (d ^^^ (e &&& f)) + 2 * (f ^^^ ( ~~~d ||| (e ||| f))) - 17 * ~~~(d ||| (e ||| f)) + 17 * ~~~(d ||| ( ~~~e ||| f)) + 25 * ~~~( ~~~d ||| (e ||| f)) + 35 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 54 * ( ~~~d &&& ( ~~~e &&& f)) + 31 * ( ~~~d &&& (e &&& f)) + 2 * (d &&& (e &&& f)) = - 10 * (d &&& ( ~~~e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2106 (x y : BitVec w) : +theorem e_2106 : - 1 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 11 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 1 * (e ^^^ (d &&& ( ~~~e ||| f))) - 6 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 1 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 1 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 11 * ~~~( ~~~d &&& (e ^^^ f)) + 4 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 6 * (e ^^^ (d ||| ( ~~~e ||| f))) + 4 * (f ^^^ ( ~~~d ||| (e ||| f))) - 2 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 3 * (d &&& (e ||| f)) + 5 * ~~~(d ||| ~~~f) - 1 * (e ||| ~~~f) + 1 * ( ~~~f &&& ~~~(d ^^^ e)) + 2 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 1 * ( ~~~d &&& (e ||| f)) + 1 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 11 * (d ||| e) + 1 * (d ||| (e ^^^ f)) + 5 * ( ~~~d &&& ( ~~~e ||| f)) + 3 * (e ^^^ ( ~~~d &&& (e ||| f))) + 1 * (f ^^^ (d ||| (e &&& f))) - 1 * (e ^^^ (d &&& f)) - 5 * d + 2 * ~~~f - 2 * ~~~(d &&& ~~~d) + 5 * ((d &&& e) ^^^ (e ||| ~~~f)) + 2 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 6 * ((d &&& e) ||| (e ^^^ f)) + 2 * ( ~~~d ||| (e ^^^ f)) + 2 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 11 * ( ~~~f ||| ~~~(d ^^^ e)) - 2 * (e ^^^ ~~~(d &&& ~~~f)) - 6 * (d ^^^ (e &&& f)) + 1 * (f &&& (d ||| e)) - 27 * ~~~(d ||| ( ~~~e ||| f)) + 15 * ~~~( ~~~d ||| (e ||| f)) - 1 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 10 * ( ~~~d &&& ( ~~~e &&& f)) - 2 * ( ~~~d &&& (e &&& f)) - 5 * (d &&& (e &&& f)) = - 25 * (d &&& ( ~~~e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2107 (x y : BitVec w) : +theorem e_2107 : - 1 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 11 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * ~~~(d &&& ~~~d) - 1 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 7 * (d ^^^ f) - 1 * (f ^^^ ~~~(d &&& (e &&& f))) + 1 * (d ||| e) + 1 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * (d ||| ~~~f) + 11 * ~~~(d &&& e) - 2 * (e ||| (d ^^^ f)) - 6 * ~~~( ~~~d &&& (e ^^^ f)) - 6 * (f ^^^ ~~~(d &&& (e ||| f))) + 2 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 11 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 2 * (d ^^^ (e ||| f)) - 1 * (e ||| (d &&& ~~~f)) - 1 * (e ^^^ (d ||| (e ||| f))) + 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 4 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 3 * (e ||| (d &&& f)) - 6 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 2 * ( ~~~e ||| (d ^^^ f)) - 2 * (f ^^^ ( ~~~d &&& (e ||| f))) - 2 * (d &&& f) + 5 * ((d &&& ~~~e) ||| (e ^^^ f)) - 1 * (e ^^^ (d ||| ( ~~~e &&& f))) - 1 * (e ^^^ ( ~~~d ||| (e ||| f))) + 3 * ~~~(d &&& ~~~e) - 5 * (e ||| f) - 2 * (e ^^^ (d ||| ~~~f)) - 5 * (d &&& (e ^^^ f)) + 4 * ~~~e - 2 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 7 * ( ~~~d &&& ( ~~~e ||| f)) - 5 * (d ||| (e ||| f)) - 11 * ~~~(d &&& (e &&& f)) + 11 * ~~~(d ||| (e ||| f)) + 3 * ~~~( ~~~d ||| (e ||| f)) + 16 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 8 * ( ~~~d &&& ( ~~~e &&& f)) + 8 * ( ~~~d &&& (e &&& f)) + 9 * (d &&& ( ~~~e &&& f)) + 33 * (d &&& (e &&& f)) = - 19 * ~~~(d ||| ( ~~~e ||| f)) + 5 * (e ^^^ ( ~~~d ||| (e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2108 (x y : BitVec w) : +theorem e_2108 : - 5 * (e ||| ~~~(d ||| f)) - 3 * (d &&& (e ||| f)) - 6 * ((d &&& e) ^^^ (e ||| ~~~f)) - 5 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 2 * (f ^^^ ~~~(d ||| e)) + 5 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 2 * ~~~(d ||| ~~~e) - 2 * (d &&& (e ^^^ f)) + 1 * (f ^^^ ~~~(d &&& (e &&& f))) + 2 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 7 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 11 * (f ^^^ (d ||| ( ~~~e ||| f))) + 4 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 11 * (d &&& ~~~f) + 11 * ((d &&& f) ||| (e &&& ~~~f)) + 1 * ~~~(e ^^^ f) - 2 * ((d &&& e) ^^^ (e ||| f)) + 5 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 6 * (d ^^^ ( ~~~e &&& f)) - 3 * ( ~~~d ||| (e ^^^ f)) - 2 * ~~~(d &&& ( ~~~e ||| f)) + 7 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 1 * (e &&& ~~~f) - 1 * ~~~(d &&& ( ~~~e &&& f)) + 2 * (e ^^^ (d &&& f)) - 7 * (e ^^^ ~~~(d ||| f)) - 6 * (d ||| ~~~e) - 3 * (d ^^^ f) + 1 * (d ||| (e ||| f)) - 2 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 1 * (f &&& (d ||| e)) + 1 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 7 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 3 * (e ^^^ ~~~(d ||| ~~~f)) + 3 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 3 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 3 * ~~~(d ||| (e ||| f)) - 2 * ~~~(d ||| ( ~~~e ||| f)) + 4 * ~~~( ~~~d ||| (e ||| f)) + 11 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 30 * ( ~~~d &&& ( ~~~e &&& f)) + 19 * ( ~~~d &&& (e &&& f)) + 8 * (d &&& ( ~~~e &&& f)) + 26 * (d &&& (e &&& f)) = - 4 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2109 (x y : BitVec w) : +theorem e_2109 : - 5 * (e ^^^ ~~~(d ||| ~~~f)) + 1 * ~~~(d ||| ( ~~~e &&& f)) + 5 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 5 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 11 * (e ^^^ ( ~~~d ||| (e &&& f))) - 2 * (d ||| e) + 1 * ~~~(e ||| f) + 11 * (e ||| (d ^^^ f)) - 5 * (d ^^^ ( ~~~e ||| f)) - 1 * (e &&& ~~~f) + 1 * (d ^^^ f) - 2 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (e ^^^ (d &&& ~~~f)) - 1 * (e ^^^ ~~~(d &&& f)) - 3 * ( ~~~e ||| ~~~(d ^^^ f)) + 2 * (f ^^^ (d &&& ~~~e)) + 1 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 4 * (d ||| (e &&& f)) + 4 * (e ||| f) - 3 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 6 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (e ^^^ (d ||| (e &&& f))) - 2 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 2 * (e ^^^ ~~~(d &&& (e &&& f))) - 3 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 3 * ~~~(d ^^^ (e ||| f)) - 3 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 5 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 7 * (f &&& ~~~(d &&& ~~~e)) - 2 * ((e &&& f) ||| (d &&& (e ||| f))) + 3 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 7 * ( ~~~f &&& ~~~(d ^^^ e)) - 2 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 2 * (e ^^^ (d ||| ( ~~~e &&& f))) - 1 * (f ^^^ (d ||| (e ||| f))) + 5 * (d ^^^ (e ^^^ f)) + 29 * ~~~(d ||| (e ||| f)) - 10 * ~~~( ~~~d ||| (e ||| f)) + 16 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 13 * ( ~~~d &&& ( ~~~e &&& f)) + 10 * ( ~~~d &&& (e &&& f)) - 12 * (d &&& ( ~~~e &&& f)) - 5 * (d &&& (e &&& f)) = - 1 * ~~~(d ||| ( ~~~e ||| f)) + 6 * ~~~(d &&& (e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2110 (x y : BitVec w) : +theorem e_2110 : 11 * (f ^^^ (d ||| ( ~~~e ||| f))) - 2 * ~~~(e ^^^ f) + 1 * ~~~d + 2 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 3 * ~~~(d &&& (e ||| f)) - 6 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 11 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 3 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 6 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 2 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 2 * ~~~(d ||| ~~~e) + 1 * ((d &&& e) ||| ~~~(e ||| f)) - 2 * ( ~~~d ||| ( ~~~e ||| f)) - 1 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 1 * (e ^^^ ~~~(d ||| ~~~f)) + 5 * (f &&& (d ^^^ e)) - 3 * (f ||| ~~~(d ||| ~~~e)) + 11 * ( ~~~d &&& (e ^^^ f)) - 5 * ( ~~~e ||| ~~~(d ^^^ f)) - 2 * ~~~(d ^^^ f) - 11 * ( ~~~d ||| (e ^^^ f)) - 1 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 5 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 5 * (f &&& (d ||| e)) - 1 * (e ^^^ ~~~(d ||| f)) - 5 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 5 * (e ^^^ ~~~(d ||| (e &&& f))) - 3 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 11 * (d ^^^ (e ^^^ f)) + 1 * (e ||| (d ^^^ f)) + 4 * (f ^^^ (d ||| e)) + 3 * (f ^^^ (d ||| (e &&& f))) + 1 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 7 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 11 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 2 * ~~~(d ||| (e ||| f)) + 10 * ~~~(d ||| ( ~~~e ||| f)) + 15 * ~~~( ~~~d ||| (e ||| f)) - 18 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 1 * ( ~~~d &&& ( ~~~e &&& f)) + 1 * ( ~~~d &&& (e &&& f)) + 3 * (d &&& ( ~~~e &&& f)) + 22 * (d &&& (e &&& f)) = - 1 * (d &&& (e ^^^ f)) - 2 * (d ^^^ ( ~~~e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2111 (x y : BitVec w) : +theorem e_2111 : 7 * ~~~(d ||| ~~~f) + 1 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (e ^^^ (d ||| ( ~~~e &&& f))) - 5 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 5 * (f ^^^ ( ~~~d ||| (e ||| f))) - 1 * (f &&& (d ^^^ e)) - 6 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 3 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 1 * ~~~(d ^^^ ( ~~~e &&& f)) + 5 * (f ||| ~~~(d ^^^ e)) + 1 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 2 * (f &&& (d ||| ~~~e)) - 5 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 3 * ( ~~~d ||| ( ~~~e ||| f)) - 1 * (f ^^^ ( ~~~d ||| (e &&& f))) - 11 * (d &&& ( ~~~e ||| f)) - 1 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 2 * (e ^^^ (d ||| ~~~f)) - 2 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 7 * ~~~(d &&& f) - 1 * ((d &&& f) ||| ~~~(e ||| f)) + 3 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 6 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 5 * ((d &&& e) ^^^ (e ||| f)) - 1 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 11 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 7 * (e &&& f) + 2 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 1 * (e ||| ~~~f) - 6 * (e ||| ~~~(d ^^^ f)) - 7 * (d &&& f) - 11 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 2 * ~~~(d &&& e) - 2 * (e ||| (d &&& ~~~f)) + 1 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 1 * ( ~~~e &&& ~~~(d ^^^ f)) - 9 * ~~~(d ||| (e ||| f)) + 14 * ~~~(d ||| ( ~~~e ||| f)) + 15 * ~~~( ~~~d ||| (e ||| f)) + 7 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 13 * ( ~~~d &&& ( ~~~e &&& f)) + 8 * ( ~~~d &&& (e &&& f)) + 43 * (d &&& ( ~~~e &&& f)) + 14 * (d &&& (e &&& f)) = - 5 * (e ^^^ ~~~(d &&& (e ||| f))) - 1 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2112 (x y : BitVec w) : +theorem e_2112 : 4 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * ((d ^^^ e) ||| ~~~(d ^^^ f)) + 2 * ~~~(d &&& f) - 3 * (f &&& ~~~(d &&& e)) + 2 * (d ||| ~~~f) + 11 * (d ||| f) - 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 3 * (e &&& (d ^^^ f)) - 2 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 11 * (f &&& (d ||| e)) + 1 * (f ^^^ (d ||| ~~~e)) + 3 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 7 * (e ||| ~~~(d ||| ~~~f)) + 1 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 5 * ( ~~~d ||| ( ~~~e ||| f)) + 7 * ~~~(d ^^^ e) - 3 * (f ^^^ (d &&& (e ||| f))) + 1 * (f ^^^ ( ~~~d ||| (e &&& f))) - 1 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 4 * (f &&& (d ^^^ e)) - 2 * (e ^^^ (d ||| (e ^^^ f))) + 2 * (e ^^^ (d ||| f)) - 1 * (e &&& ~~~(d &&& f)) + 11 * (d ^^^ f) - 7 * ~~~(e &&& ~~~f) + 1 * (e ^^^ ~~~(d ||| (e &&& f))) + 2 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 2 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 1 * (d &&& (e ||| f)) - 3 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 6 * (e ^^^ ~~~(d &&& (e &&& f))) + 2 * ~~~(d ^^^ (e &&& f)) + 1 * ( ~~~f &&& ~~~(d ^^^ e)) - 2 * ~~~(d ^^^ f) + 7 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 1 * (e &&& (d ||| f)) + 3 * ((d &&& ~~~e) ||| (e ^^^ f)) - 3 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 2 * ~~~(d ||| (e ||| f)) - 6 * ~~~(d ||| ( ~~~e ||| f)) - 30 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 12 * ( ~~~d &&& ( ~~~e &&& f)) + 1 * ( ~~~d &&& (e &&& f)) + 11 * (d &&& (e &&& f)) = - 12 * (d &&& ( ~~~e &&& f)) + 10 * ~~~( ~~~d ||| (e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2113 (x y : BitVec w) : +theorem e_2113 : - 11 * ((d &&& f) ^^^ (e ||| f)) - 3 * ( ~~~d ||| (e &&& f)) - 1 * (e ||| (d ^^^ f)) + 5 * (f &&& ~~~(d ^^^ e)) + 7 * ( ~~~f &&& (d ^^^ e)) + 3 * (f ^^^ (d &&& (e ||| f))) - 6 * ( ~~~d ||| ( ~~~e ||| f)) + 3 * ( ~~~d ||| (e ^^^ f)) + 1 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 1 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 3 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 1 * ~~~(d &&& ( ~~~e ||| f)) + 2 * (e ^^^ ~~~(d &&& ~~~f)) + 2 * ~~~(e ^^^ f) - 6 * ~~~(e &&& ~~~f) - 5 * (d &&& f) + 2 * (f ^^^ ~~~(d ||| e)) + 2 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 5 * (e ^^^ ~~~(d &&& (e &&& f))) - 2 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 3 * (d ^^^ (e ||| f)) + 11 * ( ~~~e &&& ~~~(d ^^^ f)) + 1 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 3 * (f ||| (d &&& ~~~e)) + 7 * (f &&& (d ||| e)) - 5 * (e ^^^ (d &&& ~~~f)) - 2 * (e &&& (d ^^^ f)) + 5 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 11 * (d ||| (e &&& f)) - 5 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 1 * (f ||| ~~~(d ||| e)) - 11 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 1 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 5 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * ( ~~~e ||| (d ^^^ f)) + 4 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 13 * ~~~(d ||| (e ||| f)) + 21 * ~~~(d ||| ( ~~~e ||| f)) + 18 * ~~~( ~~~d ||| (e ||| f)) - 7 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 39 * ( ~~~d &&& ( ~~~e &&& f)) + 12 * ( ~~~d &&& (e &&& f)) - 8 * (d &&& ( ~~~e &&& f)) + 9 * (d &&& (e &&& f)) = - 1 * (d ^^^ (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2114 (x y : BitVec w) : +theorem e_2114 : - 7 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (d ||| ( ~~~e &&& f)) - 1 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 1 * (f ^^^ (d ||| ( ~~~e &&& f))) + 2 * (d &&& e) + 3 * (e ^^^ ( ~~~d ||| (e ||| f))) + 1 * (e ^^^ (d ||| (e &&& f))) - 5 * ( ~~~f &&& (d ^^^ e)) - 2 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 5 * (f &&& (d ||| ~~~e)) + 7 * (e ||| ~~~(d ||| f)) + 4 * ~~~d + 11 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (e ^^^ (d ||| (e ||| f))) - 6 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 2 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 1 * (f ^^^ ( ~~~d ||| (e ||| f))) + 2 * ( ~~~d ||| ( ~~~e &&& f)) + 2 * ~~~( ~~~d ||| (e ^^^ f)) - 1 * d - 1 * ~~~f - 3 * (e &&& ~~~(d &&& ~~~f)) + 7 * ( ~~~f ||| (d ^^^ e)) - 1 * ( ~~~e ||| ~~~(d ^^^ f)) + 3 * (f &&& ~~~(d &&& e)) - 2 * ~~~( ~~~d ||| (e &&& f)) + 7 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 4 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 2 * ~~~(d &&& ( ~~~e &&& f)) - 7 * (f ^^^ ~~~(d &&& ~~~e)) - 3 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 6 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 2 * (e &&& f) + 1 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 3 * (d ||| (e ^^^ f)) + 4 * ((d &&& e) ^^^ (e ||| f)) - 19 * ~~~(d ||| (e ||| f)) - 12 * ~~~(d ||| ( ~~~e ||| f)) - 12 * ~~~( ~~~d ||| (e ||| f)) - 8 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 9 * ( ~~~d &&& ( ~~~e &&& f)) - 27 * ( ~~~d &&& (e &&& f)) - 18 * (d &&& ( ~~~e &&& f)) - 8 * (d &&& (e &&& f)) = - 5 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2115 (x y : BitVec w) : +theorem e_2115 : 5 * (e ||| ~~~(d ^^^ f)) - 6 * (e ^^^ ~~~(d &&& f)) + 2 * (e &&& ~~~f) + 3 * (d &&& e) - 1 * (e ^^^ (d ||| ( ~~~e ||| f))) - 1 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 11 * (f ^^^ ~~~(d &&& (e &&& f))) + 11 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 2 * ~~~f - 2 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 2 * (d ^^^ (e &&& f)) - 3 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 7 * (d ||| ( ~~~e ||| f)) - 1 * ~~~(d ^^^ (e &&& f)) + 5 * ~~~(d &&& (e ^^^ f)) + 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 3 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 5 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 3 * (e ^^^ ~~~(d ||| f)) + 1 * ((d &&& e) ||| ~~~(e ^^^ f)) + 7 * (f &&& (d ||| ~~~e)) + 1 * (e ||| ~~~f) + 1 * (d &&& (e ^^^ f)) + 3 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 5 * ( ~~~d ||| (e &&& f)) + 7 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 1 * (f &&& ~~~(d ^^^ e)) - 1 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 1 * ~~~(d &&& ( ~~~e &&& f)) - 6 * (f ||| ~~~(d ||| ~~~e)) - 11 * e - 6 * (d ||| (e &&& f)) + 5 * (f ^^^ (d &&& (e ||| f))) + 1 * (e ^^^ (d &&& (e ^^^ f))) + 2 * ~~~( ~~~d ||| (e ^^^ f)) - 2 * ~~~(e ||| f) - 17 * ~~~(d ||| (e ||| f)) + 8 * ~~~(d ||| ( ~~~e ||| f)) + 7 * ~~~( ~~~d ||| (e ||| f)) + 2 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 3 * ( ~~~d &&& ( ~~~e &&& f)) + 9 * ( ~~~d &&& (e &&& f)) - 13 * (d &&& ( ~~~e &&& f)) + 2 * (d &&& (e &&& f)) = - 11 * ~~~(e &&& ~~~f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2116 (x y : BitVec w) : +theorem e_2116 : 2 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 2 * (e ||| f) - 11 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 7 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 6 * (e ^^^ (d &&& (e ^^^ f))) - 2 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 7 * ~~~(d &&& ( ~~~e &&& f)) + 4 * (e &&& ~~~(d ^^^ f)) - 2 * ((d ||| e) &&& (e ^^^ f)) - 2 * ~~~(d ^^^ (e &&& f)) + 5 * (e &&& (d ||| ~~~f)) - 1 * (f &&& (d ^^^ e)) - 1 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 2 * ( ~~~f ||| (d ^^^ e)) - 3 * (f ||| (d ^^^ e)) + 2 * ( ~~~e &&& (d ^^^ f)) - 2 * (e &&& (d ^^^ f)) - 6 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 4 * ~~~(e &&& f) + 3 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 3 * ( ~~~d &&& (e ||| f)) - 1 * (f ^^^ (d ||| ( ~~~e ||| f))) - 1 * (f ^^^ ~~~(d &&& e)) - 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 1 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 11 * (e ^^^ ( ~~~d &&& (e ||| f))) - 2 * (f ||| ~~~(d ||| ~~~e)) - 2 * (e ^^^ ~~~(d &&& ~~~f)) + 4 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 2 * ((d ^^^ e) &&& (d ^^^ f)) - 1 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 1 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 1 * ( ~~~d &&& (e ^^^ f)) - 2 * ~~~( ~~~d ||| (e &&& f)) + 11 * (e ^^^ ~~~(d &&& (e ||| f))) + 11 * ((d &&& e) ^^^ (e ||| f)) - 6 * ~~~(d ||| (e ||| f)) - 21 * ~~~(d ||| ( ~~~e ||| f)) - 31 * ~~~( ~~~d ||| (e ||| f)) - 39 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 33 * ( ~~~d &&& ( ~~~e &&& f)) - 9 * (d &&& ( ~~~e &&& f)) - 20 * (d &&& (e &&& f)) = 4 * ( ~~~d &&& (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2117 (x y : BitVec w) : +theorem e_2117 : - 5 * ~~~(d ||| ~~~e) + 1 * (f &&& (d ||| ~~~e)) - 1 * ((d &&& e) ||| ~~~(e ||| f)) - 11 * ( ~~~d ||| (e &&& f)) - 7 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 11 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 1 * (e &&& f) + 11 * (d &&& e) + 2 * (d ||| ( ~~~e ||| f)) + 4 * (e ^^^ (d ||| ( ~~~e &&& f))) + 3 * (e ^^^ ~~~(d &&& ~~~f)) - 3 * ~~~(d &&& ( ~~~e &&& f)) - 2 * (d ^^^ e) + 3 * (f &&& ~~~(d ^^^ e)) - 2 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 3 * d - 5 * ~~~(d &&& ( ~~~e ||| f)) - 11 * (e ^^^ ( ~~~d ||| (e ||| f))) - 2 * (e &&& ~~~(d &&& f)) + 2 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 7 * ( ~~~d ||| (e ^^^ f)) + 5 * ~~~(d ^^^ (e ||| f)) + 2 * (e ||| ~~~f) + 1 * e - 2 * (f ^^^ (d &&& ~~~e)) + 7 * ((d &&& e) ^^^ (e ||| ~~~f)) + 3 * (f &&& (d ^^^ e)) + 11 * ~~~(d &&& (e ||| f)) + 4 * (e ||| ~~~(d ^^^ f)) + 5 * ~~~( ~~~d &&& (e &&& f)) + 1 * (e ^^^ ~~~(d &&& f)) + 5 * (f ^^^ (d ||| ~~~e)) - 1 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 3 * ( ~~~d ||| (e ||| f)) + 3 * (e ^^^ (d ||| (e ||| f))) + 2 * (f ^^^ ( ~~~d ||| (e ||| f))) - 2 * ~~~(d ||| (e ||| f)) + 5 * ~~~(d ||| ( ~~~e ||| f)) - 34 * ~~~( ~~~d ||| (e ||| f)) - 26 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 2 * ( ~~~d &&& ( ~~~e &&& f)) - 14 * ( ~~~d &&& (e &&& f)) - 8 * (d &&& ( ~~~e &&& f)) - 7 * (d &&& (e &&& f)) = - 2 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2118 (x y : BitVec w) : +theorem e_2118 : 5 * (d ^^^ (e ||| f)) + 1 * (e ^^^ ~~~(d &&& (e &&& f))) + 1 * ~~~d - 11 * ((d &&& ~~~e) ||| (e ^^^ f)) - 2 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 1 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 7 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 7 * (d ||| ~~~f) + 11 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 2 * ( ~~~d ||| (e ^^^ f)) - 3 * (f ^^^ ~~~(d &&& (e ||| f))) + 4 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 7 * ( ~~~e ||| ~~~(d ^^^ f)) + 1 * (d ||| ( ~~~e &&& f)) + 5 * (e &&& ~~~(d ^^^ f)) + 1 * ~~~(d ^^^ ( ~~~e ||| f)) - 7 * (d &&& ~~~f) - 11 * ((d &&& e) ||| ~~~(e ||| f)) - 1 * ((d ^^^ e) ||| (d ^^^ f)) - 7 * ((d &&& f) ||| ~~~(e ||| f)) - 5 * (f ^^^ (d &&& ( ~~~e ||| f))) + 3 * ((d ^^^ e) &&& (d ^^^ f)) - 11 * (d ^^^ ( ~~~e ||| f)) + 4 * (e &&& ~~~(d &&& f)) + 2 * (f ^^^ ~~~(d &&& ~~~e)) - 2 * (f ^^^ ~~~(d ||| (e &&& f))) - 1 * ~~~( ~~~d &&& (e ||| f)) - 1 * ( ~~~f &&& ~~~(d ^^^ e)) + 5 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 1 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 11 * (f ^^^ (d ||| (e ||| f))) - 1 * ~~~(d &&& ( ~~~e ||| f)) - 6 * (f ^^^ (d ||| e)) + 11 * ((d &&& e) ^^^ (e ||| f)) - 1 * (e ^^^ (d ||| (e ||| f))) - 2 * (f ^^^ ~~~(d ||| e)) + 5 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 2 * (f &&& (d ^^^ e)) + 7 * ~~~(d ||| ( ~~~e ||| f)) + 60 * ~~~( ~~~d ||| (e ||| f)) + 60 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 11 * ( ~~~d &&& (e &&& f)) + 13 * (d &&& ( ~~~e &&& f)) + 14 * (d &&& (e &&& f)) = - 52 * ~~~(d ||| (e ||| f)) - 7 * ( ~~~d &&& ( ~~~e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2119 (x y : BitVec w) : +theorem e_2119 : 2 * (e ^^^ (d &&& f)) - 2 * ~~~( ~~~d &&& (e ||| f)) + 1 * (f ^^^ ~~~(d &&& (e ||| f))) + 1 * (e ^^^ f) + 7 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 1 * ((d &&& ~~~e) ||| (e ^^^ f)) + 1 * (e ^^^ ~~~(d &&& ~~~f)) + 11 * ( ~~~f &&& (d ^^^ e)) - 11 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 7 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 11 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 5 * (d ||| ( ~~~e &&& f)) + 1 * ( ~~~d ||| ( ~~~e ||| f)) - 2 * (f ^^^ (d ||| ( ~~~e ||| f))) + 11 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 3 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 1 * (f &&& ~~~(d &&& ~~~e)) - 3 * (f ^^^ ~~~(d ||| (e &&& f))) + 1 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 4 * ( ~~~e ||| ~~~(d ^^^ f)) - 1 * ~~~(d ||| ( ~~~e &&& f)) - 2 * (e ^^^ ( ~~~d &&& (e ||| f))) + 2 * ~~~(d &&& ~~~f) + 4 * (e ||| ~~~(d ||| ~~~f)) + 1 * (f &&& ~~~(d &&& e)) - 2 * (f ||| (d ^^^ e)) - 5 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * d - 1 * (f ^^^ ~~~(d ||| e)) - 2 * (d ||| e) - 1 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 3 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 2 * ~~~(d &&& f) - 1 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 7 * (f ^^^ (d &&& e)) - 1 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 4 * ~~~( ~~~d &&& (e ^^^ f)) + 1 * (e ^^^ (d ||| ~~~f)) + 8 * ~~~(d ||| (e ||| f)) - 28 * ~~~(d ||| ( ~~~e ||| f)) + 1 * ~~~( ~~~d ||| (e ||| f)) + 4 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 8 * ( ~~~d &&& ( ~~~e &&& f)) + 19 * ( ~~~d &&& (e &&& f)) + 20 * (d &&& ( ~~~e &&& f)) = - 3 * (d ^^^ (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2120 (x y : BitVec w) : +theorem e_2120 : - 1 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 3 * (d &&& e) - 5 * ( ~~~d ||| ( ~~~e &&& f)) - 2 * (e ||| ~~~(d ||| ~~~f)) - 2 * ((d ||| ~~~e) &&& (e ^^^ f)) + 2 * ((d &&& e) ||| ~~~(e ^^^ f)) - 1 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 11 * (e ^^^ (d ||| (e ||| f))) + 11 * ((d ^^^ e) &&& (d ^^^ f)) + 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 5 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 11 * (e ^^^ ~~~(d ||| ~~~f)) - 6 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 6 * ( ~~~d ||| (e ||| f)) - 5 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 1 * ((e &&& f) ||| (d &&& (e ||| f))) + 4 * ~~~(d &&& (e &&& f)) - 7 * (e &&& ~~~(d ^^^ f)) + 1 * (f &&& (d ||| ~~~e)) + 7 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 5 * (f ^^^ (d ||| ( ~~~e ||| f))) - 7 * (e ^^^ (d ||| ( ~~~e ||| f))) - 5 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 11 * e - 1 * ((d &&& e) ^^^ (e ||| ~~~f)) - 7 * (e ^^^ f) + 5 * (e ^^^ (d &&& f)) - 1 * (d ||| (e &&& f)) + 11 * (d ^^^ (e ||| f)) + 11 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 4 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 1 * (d ^^^ f) + 11 * ~~~(d &&& ~~~e) + 2 * f - 2 * ( ~~~f &&& ~~~(d ^^^ e)) - 7 * ((d &&& f) ^^^ (e ||| f)) - 3 * ~~~(e ||| ~~~f) - 1 * ~~~(d ||| (e ||| f)) + 41 * ~~~(d ||| ( ~~~e ||| f)) + 12 * ~~~( ~~~d ||| (e ||| f)) + 31 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 9 * ( ~~~d &&& ( ~~~e &&& f)) + 1 * ( ~~~d &&& (e &&& f)) + 28 * (d &&& ( ~~~e &&& f)) + 12 * (d &&& (e &&& f)) = 2 * (e ^^^ ~~~(d ||| f)) + 1 * (f ||| ~~~(d ||| ~~~e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2121 (x y : BitVec w) : +theorem e_2121 : 2 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 4 * (e ^^^ ( ~~~d ||| (e &&& f))) - 1 * ~~~(d ^^^ (e &&& f)) - 2 * ~~~(e ||| ~~~f) + 2 * ((d ||| e) &&& (e ^^^ f)) + 1 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 11 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 1 * ((d &&& e) ||| ~~~(e ^^^ f)) + 11 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 6 * (d &&& e) - 3 * ~~~(d &&& ( ~~~e ||| f)) + 1 * ((d ||| e) &&& ~~~(e ^^^ f)) + 5 * ( ~~~e ||| (d ^^^ f)) + 7 * ~~~(d ||| (e &&& f)) + 1 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 11 * (e ^^^ (d ||| (e ^^^ f))) - 3 * ((d &&& e) ^^^ (e ||| ~~~f)) - 1 * ( ~~~d ||| (e ^^^ f)) + 5 * (e ^^^ (d &&& ( ~~~e ||| f))) - 2 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 1 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 7 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * ((d &&& f) ^^^ (e ||| f)) + 3 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 2 * (f &&& ~~~(d &&& e)) - 1 * (e ^^^ ~~~(d ||| f)) + 2 * (f &&& (d ^^^ e)) + 5 * (f ^^^ ~~~(d ||| e)) + 4 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 2 * ~~~(d &&& (e ^^^ f)) - 6 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 1 * (d &&& ~~~e) - 3 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 7 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 1 * (d ||| (e ||| f)) + 2 * (f &&& (d ||| e)) - 19 * ~~~(d ||| (e ||| f)) - 26 * ~~~(d ||| ( ~~~e ||| f)) + 26 * ~~~( ~~~d ||| (e ||| f)) - 16 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 9 * ( ~~~d &&& ( ~~~e &&& f)) + 3 * ( ~~~d &&& (e &&& f)) + 8 * (d &&& ( ~~~e &&& f)) + 7 * (d &&& (e &&& f)) = - 4 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 3 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2122 (x y : BitVec w) : +theorem e_2122 : 4 * (d &&& ~~~e) - 2 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (d &&& e) + 4 * (e ^^^ ~~~(d &&& ~~~f)) + 5 * (f &&& ~~~(d &&& ~~~e)) + 11 * ( ~~~d &&& (e ||| f)) - 1 * ~~~(d ^^^ e) + 11 * ~~~(d &&& ~~~d) - 7 * ~~~(d &&& e) - 2 * (e ||| (d ^^^ f)) + 2 * (e &&& ~~~(d &&& ~~~f)) - 2 * ((d &&& f) ||| ~~~(e ||| f)) + 3 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 7 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 5 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 1 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 11 * ~~~(d &&& f) + 2 * ( ~~~d ||| ( ~~~e ||| f)) + 3 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 6 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 11 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 2 * (e ^^^ (d &&& ( ~~~e ||| f))) + 4 * (e &&& (d ||| ~~~f)) + 1 * (f ||| (d &&& e)) - 3 * ((e &&& f) ||| (d &&& (e ||| f))) - 11 * ~~~(d &&& (e ||| f)) + 1 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 7 * (e ^^^ f) - 7 * (d ||| e) - 1 * (f ^^^ (d &&& ~~~e)) - 2 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 11 * ( ~~~d ||| (e &&& f)) - 5 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 7 * (e ^^^ ( ~~~d ||| (e &&& f))) - 2 * (e ||| (d &&& ~~~f)) + 3 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 3 * (e ^^^ (d ||| ~~~f)) + 9 * ~~~(d ||| (e ||| f)) + 1 * ~~~(d ||| ( ~~~e ||| f)) + 40 * ~~~( ~~~d ||| (e ||| f)) + 40 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 15 * ( ~~~d &&& ( ~~~e &&& f)) + 11 * ( ~~~d &&& (e &&& f)) + 12 * (d &&& ( ~~~e &&& f)) - 12 * (d &&& (e &&& f)) = 7 * ~~~( ~~~d &&& (e ||| f)) - 1 * ~~~(e &&& f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2123 (x y : BitVec w) : +theorem e_2123 : - 1 * ~~~f + 3 * ((d ^^^ e) &&& (d ^^^ f)) - 3 * (d ||| ~~~e) + 5 * ((d &&& e) ^^^ (e ||| f)) - 2 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 1 * ~~~(d ^^^ e) + 1 * ~~~(d ||| (e &&& f)) + 2 * ~~~(d ^^^ (e ^^^ f)) - 5 * (d ||| ( ~~~e &&& f)) - 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 3 * (f ^^^ (d &&& e)) + 2 * (e ||| (d &&& ~~~f)) + 4 * ~~~(d ||| e) + 2 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 3 * (e ^^^ ~~~(d &&& f)) + 4 * (e ^^^ f) + 11 * d - 1 * (f ^^^ (d ||| (e ||| f))) - 6 * ((d ||| e) &&& ~~~(e ^^^ f)) + 2 * ( ~~~d &&& (e ||| f)) - 1 * (e ||| ~~~(d ||| ~~~f)) - 3 * (e ^^^ (d &&& ( ~~~e ||| f))) - 2 * (d &&& (e ||| f)) - 1 * ( ~~~f ||| (d ^^^ e)) - 7 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 4 * (e ^^^ (d &&& (e ||| f))) + 5 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 5 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 2 * (f &&& ~~~(d &&& ~~~e)) + 1 * ( ~~~f ||| ~~~(d ^^^ e)) + 5 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 7 * ( ~~~e &&& (d ^^^ f)) - 1 * (f ^^^ (d ||| ~~~e)) + 11 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 7 * ~~~( ~~~d ||| (e ^^^ f)) + 4 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 21 * ~~~(d ||| (e ||| f)) - 28 * ~~~(d ||| ( ~~~e ||| f)) + 7 * ~~~( ~~~d ||| (e ||| f)) + 13 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 33 * ( ~~~d &&& ( ~~~e &&& f)) - 4 * ( ~~~d &&& (e &&& f)) - 32 * (d &&& ( ~~~e &&& f)) + 14 * (d &&& (e &&& f)) = 7 * (d &&& (e ^^^ f)) + 11 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2124 (x y : BitVec w) : +theorem e_2124 : - 11 * (d ^^^ ( ~~~e &&& f)) + 7 * (f ^^^ (d &&& e)) + 11 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 3 * (e ^^^ (d &&& ~~~f)) + 5 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 7 * (e ^^^ (d ||| ( ~~~e &&& f))) + 1 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * ~~~(d &&& ~~~d) - 1 * ~~~f + 1 * (f ^^^ ( ~~~d ||| (e ||| f))) + 1 * ~~~(d ||| (e &&& f)) - 11 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 11 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 4 * ~~~(e &&& ~~~f) - 2 * ( ~~~d &&& (e ^^^ f)) + 3 * (e ^^^ (d &&& ( ~~~e ||| f))) - 7 * (d ||| ( ~~~e ||| f)) - 6 * (f ^^^ (d &&& ( ~~~e ||| f))) - 3 * ~~~(d &&& ( ~~~e &&& f)) - 3 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 2 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 2 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 11 * ( ~~~d &&& ( ~~~e ||| f)) + 11 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 1 * (d &&& e) + 1 * ((d &&& f) ||| (e &&& ~~~f)) + 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 7 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 1 * (e ^^^ ( ~~~d ||| (e &&& f))) + 3 * (e &&& ~~~(d &&& ~~~f)) - 6 * (e ^^^ ( ~~~d &&& (e ||| f))) + 2 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 1 * ((e &&& f) ||| (d &&& (e ||| f))) - 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 1 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 11 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 5 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 34 * ~~~(d ||| (e ||| f)) + 17 * ~~~(d ||| ( ~~~e ||| f)) + 13 * ~~~( ~~~d ||| (e ||| f)) + 5 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 3 * ( ~~~d &&& ( ~~~e &&& f)) - 24 * ( ~~~d &&& (e &&& f)) + 12 * (d &&& ( ~~~e &&& f)) - 11 * (d &&& (e &&& f)) = 2 * (f ||| (d ^^^ e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2125 (x y : BitVec w) : +theorem e_2125 : 1 * (e &&& ~~~(d ^^^ f)) + 7 * (e ^^^ (d ||| ( ~~~e ||| f))) - 7 * ~~~(d &&& ( ~~~e ||| f)) + 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 1 * (e ^^^ (d &&& f)) - 7 * ~~~( ~~~d &&& (e ||| f)) + 1 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 1 * (e ^^^ (d &&& ~~~f)) - 5 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (f &&& ~~~(d ^^^ e)) + 7 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 7 * (e &&& (d ||| f)) + 7 * (e ||| ~~~(d ||| ~~~f)) - 6 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 7 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 5 * ((d &&& e) ||| (e ^^^ f)) + 3 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 3 * (d ^^^ f) - 5 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 2 * (e ||| ~~~(d ^^^ f)) - 1 * ~~~(d ^^^ (e &&& f)) - 3 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 6 * ( ~~~d ||| ( ~~~e &&& f)) - 3 * (d ||| ~~~e) + 5 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 5 * ((d &&& f) ||| ~~~(e ||| f)) - 1 * ( ~~~f ||| (d ^^^ e)) - 2 * ~~~(d &&& ~~~d) - 7 * (e ^^^ ( ~~~d ||| (e ||| f))) - 1 * d + 2 * ~~~(d ||| ~~~f) - 2 * ~~~(d ^^^ (e ||| f)) - 1 * ~~~(d ||| ~~~e) + 1 * (e &&& ~~~(d &&& ~~~f)) + 2 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 2 * (e &&& f) - 1 * (d ||| f) - 6 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 14 * ~~~(d ||| (e ||| f)) + 3 * ~~~(d ||| ( ~~~e ||| f)) + 9 * ~~~( ~~~d ||| (e ||| f)) + 14 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 16 * ( ~~~d &&& ( ~~~e &&& f)) + 9 * ( ~~~d &&& (e &&& f)) + 1 * (d &&& ( ~~~e &&& f)) = 3 * e := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2126 (x y : BitVec w) : +theorem e_2126 : 5 * ((d &&& f) ^^^ (e ||| f)) - 7 * ~~~( ~~~d &&& (e ||| f)) + 11 * (f ^^^ (d &&& ( ~~~e ||| f))) - 5 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 2 * ~~~( ~~~d &&& (e ^^^ f)) + 7 * ~~~(d ||| e) - 5 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 5 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 5 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 11 * (f &&& (d ^^^ e)) + 5 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 6 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 1 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 2 * (d ||| (e ^^^ f)) - 5 * ( ~~~d &&& ( ~~~e ||| f)) + 4 * (f ||| ~~~(d ^^^ e)) + 7 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 1 * (f &&& ~~~(d &&& e)) + 7 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 2 * ( ~~~e &&& ~~~(d ^^^ f)) + 2 * (e ^^^ (d &&& (e ||| f))) - 7 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 4 * ( ~~~d ||| (e ||| f)) + 2 * ((d ^^^ e) &&& (d ^^^ f)) + 2 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 1 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 5 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 2 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 1 * ( ~~~d ||| ( ~~~e ||| f)) - 1 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 4 * ((d &&& e) ^^^ (e ||| f)) - 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 3 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 1 * (e ||| ~~~(d ||| f)) - 6 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 1 * (f &&& (d ||| ~~~e)) + 11 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 19 * ~~~(d ||| ( ~~~e ||| f)) - 10 * ~~~( ~~~d ||| (e ||| f)) - 18 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 21 * ( ~~~d &&& ( ~~~e &&& f)) - 25 * ( ~~~d &&& (e &&& f)) - 12 * (d &&& ( ~~~e &&& f)) - 4 * (d &&& (e &&& f)) = - 4 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 11 * ~~~(d ||| (e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2127 (x y : BitVec w) : +theorem e_2127 : 5 * ( ~~~d ||| ( ~~~e ||| f)) + 2 * ((d ^^^ e) ||| (d ^^^ f)) + 4 * (e ||| (d &&& f)) + 3 * ~~~(d ^^^ (e ||| f)) - 6 * (e ^^^ (d ||| (e ^^^ f))) - 1 * (e ||| (d ^^^ f)) + 1 * f - 2 * (f ||| (d &&& ~~~e)) + 2 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 11 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 3 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 3 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 2 * (e ^^^ ~~~(d &&& ~~~f)) - 11 * ~~~(d &&& ( ~~~e ||| f)) - 1 * (e ^^^ ~~~(d &&& f)) - 5 * (e ^^^ (d &&& ~~~f)) - 1 * (d ^^^ (e ^^^ f)) - 5 * ~~~(d ^^^ ( ~~~e ||| f)) + 2 * ~~~e - 6 * (f ^^^ (d &&& (e ||| f))) - 5 * (e ^^^ (d ||| (e &&& f))) - 2 * ( ~~~f &&& ~~~(d ^^^ e)) + 7 * ~~~(e &&& ~~~f) - 11 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 2 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 1 * ~~~(d &&& (e ||| f)) - 6 * ((d &&& f) ||| ~~~(e ||| f)) - 2 * (e &&& f) - 2 * (e ^^^ (d ||| ( ~~~e &&& f))) + 7 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 5 * (d ||| ( ~~~e &&& f)) + 4 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 2 * ~~~(e ^^^ f) + 2 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 4 * (f ^^^ (d ||| ( ~~~e ||| f))) + 5 * ((d &&& e) ||| (e ^^^ f)) - 5 * ~~~(d ||| (e ||| f)) + 14 * ~~~(d ||| ( ~~~e ||| f)) + 16 * ~~~( ~~~d ||| (e ||| f)) - 14 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 3 * ( ~~~d &&& ( ~~~e &&& f)) + 2 * ( ~~~d &&& (e &&& f)) - 19 * (d &&& ( ~~~e &&& f)) - 10 * (d &&& (e &&& f)) = 1 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2128 (x y : BitVec w) : +theorem e_2128 : 11 * (e ||| (d &&& ~~~f)) + 1 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 1 * (f ^^^ ~~~(d &&& (e ||| f))) - 1 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 5 * (d &&& ~~~f) + 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 11 * ~~~e - 2 * d - 6 * (d ^^^ e) + 1 * ~~~(d ^^^ ( ~~~e &&& f)) - 3 * (f ^^^ (d ||| (e ||| f))) - 5 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 3 * (e &&& ~~~(d &&& f)) - 2 * (e ^^^ ~~~(d &&& f)) - 6 * (d ||| ( ~~~e &&& f)) + 2 * ~~~(e &&& ~~~f) + 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 1 * ( ~~~e ||| ~~~(d ^^^ f)) - 2 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 2 * (e ||| ~~~f) - 1 * ( ~~~d ||| ( ~~~e &&& f)) + 7 * (d ||| e) + 11 * (d ^^^ (e &&& f)) - 5 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 11 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 3 * ~~~(e &&& f) + 1 * (e ^^^ (d &&& ( ~~~e ||| f))) - 1 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 7 * (f ^^^ (d ||| ( ~~~e ||| f))) - 1 * (f ^^^ ( ~~~d ||| (e ||| f))) - 1 * (d &&& (e ||| f)) - 6 * (d ||| (e &&& f)) + 11 * ~~~(d ^^^ (e &&& f)) + 3 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 7 * (e ^^^ (d ||| (e ||| f))) + 11 * (f ||| ~~~(d ||| e)) - 5 * (f ||| (d ^^^ e)) - 1 * ~~~(d &&& (e ^^^ f)) + 20 * ~~~(d ||| (e ||| f)) - 4 * ~~~(d ||| ( ~~~e ||| f)) + 29 * ~~~( ~~~d ||| (e ||| f)) + 21 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 30 * ( ~~~d &&& ( ~~~e &&& f)) - 24 * ( ~~~d &&& (e &&& f)) + 34 * (d &&& ( ~~~e &&& f)) = 6 * (d &&& (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2129 (x y : BitVec w) : +theorem e_2129 : - 7 * ~~~(d &&& ( ~~~e &&& f)) + 11 * ~~~(e &&& ~~~f) - 3 * ((d ||| ~~~e) &&& (e ^^^ f)) + 7 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 1 * (e &&& (d ^^^ f)) - 2 * (f ||| ~~~(d ||| ~~~e)) + 7 * (e ^^^ (d ||| ( ~~~e &&& f))) - 2 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 2 * ((d ||| e) &&& ~~~(e ^^^ f)) - 2 * (e &&& ~~~f) - 11 * ~~~(d &&& ~~~f) + 2 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 4 * (e ^^^ ~~~(d ||| f)) - 1 * (e ^^^ ~~~(d ||| (e &&& f))) - 11 * (f ^^^ (d ||| e)) - 2 * (d ||| (e ||| f)) + 1 * (e ^^^ ( ~~~d ||| (e ||| f))) + 11 * (d ^^^ f) + 1 * (e ^^^ (d ||| ( ~~~e ||| f))) - 2 * (d ^^^ (e ||| f)) + 3 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 5 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * ~~~(e ||| f) + 7 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 2 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * (e ^^^ (d &&& (e ||| f))) + 1 * (d ^^^ ( ~~~e &&& f)) - 11 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 11 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 3 * (e ^^^ ~~~(d ||| ~~~f)) + 2 * (d ^^^ (e ^^^ f)) + 7 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 11 * ~~~(d ||| f) - 1 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 3 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 2 * ((d &&& f) ||| (e &&& ~~~f)) - 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 7 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * ~~~(d ||| (e ||| f)) + 5 * ~~~(d ||| ( ~~~e ||| f)) - 16 * ~~~( ~~~d ||| (e ||| f)) - 19 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 18 * ( ~~~d &&& ( ~~~e &&& f)) - 11 * ( ~~~d &&& (e &&& f)) - 15 * (d &&& ( ~~~e &&& f)) - 24 * (d &&& (e &&& f)) = - 1 * (e ^^^ (d ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2130 (x y : BitVec w) : +theorem e_2130 : 1 * (e ^^^ (d ||| (e ^^^ f))) - 1 * ((d &&& f) ^^^ (e ||| f)) + 5 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 3 * (e &&& f) + 7 * ~~~(d &&& ( ~~~e &&& f)) + 5 * (f ^^^ ~~~(d &&& e)) + 2 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 7 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 7 * (e ||| ~~~(d ||| ~~~f)) - 2 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 1 * ((d &&& e) ^^^ (e ||| ~~~f)) - 11 * (f ^^^ ( ~~~d ||| (e ||| f))) + 3 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 1 * ( ~~~d &&& (e ||| f)) + 11 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 7 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 11 * (f ^^^ (d &&& ( ~~~e ||| f))) - 7 * ~~~(e &&& f) + 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 1 * ( ~~~d ||| (e ^^^ f)) + 1 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 1 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 5 * ~~~(e &&& ~~~f) - 11 * ~~~(d &&& (e ^^^ f)) + 11 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 1 * ( ~~~d ||| ( ~~~e &&& f)) + 11 * ~~~(d ||| ( ~~~e &&& f)) + 2 * (e ^^^ f) + 3 * ~~~(d &&& (e ||| f)) + 1 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 7 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 2 * (d ||| ( ~~~e &&& f)) - 1 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 4 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 6 * (d &&& (e ^^^ f)) + 3 * (d &&& ~~~f) - 11 * ~~~(d ||| (e ||| f)) - 6 * ~~~(d ||| ( ~~~e ||| f)) + 2 * ~~~( ~~~d ||| (e ||| f)) + 11 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 2 * ( ~~~d &&& ( ~~~e &&& f)) - 31 * ( ~~~d &&& (e &&& f)) - 8 * (d &&& ( ~~~e &&& f)) - 15 * (d &&& (e &&& f)) = - 4 * (e ^^^ (d &&& ~~~f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2131 (x y : BitVec w) : +theorem e_2131 : 3 * (d &&& (e ^^^ f)) - 1 * (e ^^^ (d &&& (e ^^^ f))) - 7 * ( ~~~f ||| ~~~(d ^^^ e)) - 1 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 3 * (d ^^^ (e &&& f)) - 1 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 7 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * (f ^^^ (d ||| ~~~e)) + 4 * (f ^^^ ~~~(d &&& ~~~e)) + 1 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 1 * (e ||| (d ^^^ f)) + 5 * (f ^^^ ~~~(d &&& (e &&& f))) + 2 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 2 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 3 * ~~~(d &&& ~~~f) - 1 * ~~~(d &&& ( ~~~e ||| f)) + 11 * (f &&& (d ^^^ e)) - 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 2 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 11 * ( ~~~d ||| (e ^^^ f)) + 1 * (d ^^^ ( ~~~e &&& f)) - 2 * (d ||| ( ~~~e ||| f)) + 4 * (e &&& ~~~f) - 2 * (e ^^^ ~~~(d ||| ~~~f)) - 6 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 5 * (e &&& ~~~(d &&& f)) + 1 * (f ^^^ (d &&& ~~~e)) - 5 * ~~~( ~~~d ||| (e &&& f)) + 1 * (e ^^^ ~~~(d ||| (e &&& f))) - 6 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 2 * (d &&& e) + 2 * ~~~(d ||| (e ^^^ f)) - 1 * (e &&& ~~~(d ^^^ f)) - 1 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 2 * ~~~(d ||| (e &&& f)) + 1 * (f ^^^ (d &&& e)) - 3 * (f ^^^ (d ||| ( ~~~e ||| f))) + 7 * (e ^^^ (d ||| (e &&& f))) + 9 * ~~~(d ||| (e ||| f)) + 16 * ~~~(d ||| ( ~~~e ||| f)) + 17 * ~~~( ~~~d ||| (e ||| f)) + 27 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 24 * ( ~~~d &&& ( ~~~e &&& f)) + 6 * ( ~~~d &&& (e &&& f)) + 14 * (d &&& ( ~~~e &&& f)) + 14 * (d &&& (e &&& f)) = - 2 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 1 * ( ~~~d &&& ( ~~~e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2132 (x y : BitVec w) : +theorem e_2132 : 3 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 1 * (e ^^^ (d &&& f)) - 11 * ( ~~~d &&& (e ||| f)) + 2 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 1 * (f ^^^ ( ~~~d ||| (e &&& f))) - 1 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 1 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 7 * (f ^^^ (d &&& (e ||| f))) + 1 * ~~~(d &&& f) + 5 * (f ^^^ (d ||| ( ~~~e ||| f))) + 7 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 3 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 1 * ~~~(d ||| f) - 3 * ((d &&& f) ||| (e &&& ~~~f)) - 11 * (e ^^^ (d ||| ( ~~~e ||| f))) + 3 * (f ^^^ (d &&& e)) - 2 * ~~~( ~~~d &&& (e &&& f)) + 2 * (f ||| (d &&& e)) - 11 * (e ^^^ (d ||| ~~~f)) + 1 * ~~~(d ^^^ (e &&& f)) - 1 * ~~~(d &&& ~~~e) + 7 * ~~~( ~~~d ||| (e ^^^ f)) - 5 * ~~~(d ^^^ ( ~~~e &&& f)) + 4 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 11 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 3 * (e ^^^ (d ||| (e ^^^ f))) - 7 * ~~~(d &&& (e ||| f)) + 11 * (d &&& e) - 11 * (f &&& (d ||| e)) - 1 * ((d &&& f) ||| ~~~(e ||| f)) - 3 * (d ^^^ ( ~~~e ||| f)) + 4 * ~~~(d ^^^ ( ~~~e ||| f)) + 2 * ~~~(e ||| f) - 1 * ( ~~~d ||| (e &&& f)) - 1 * ~~~( ~~~d &&& (e ^^^ f)) + 4 * ~~~(d ^^^ (e ||| f)) - 7 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 5 * (d &&& ~~~f) + 28 * ~~~(d ||| (e ||| f)) + 40 * ~~~(d ||| ( ~~~e ||| f)) + 30 * ~~~( ~~~d ||| (e ||| f)) - 24 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 2 * ( ~~~d &&& ( ~~~e &&& f)) + 46 * ( ~~~d &&& (e &&& f)) + 32 * (d &&& ( ~~~e &&& f)) - 12 * (d &&& (e &&& f)) = 7 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 7 * (d ||| e) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2133 (x y : BitVec w) : +theorem e_2133 : 3 * (d &&& ~~~f) + 2 * ~~~(e ||| ~~~f) + 1 * (f ^^^ ~~~(d ||| e)) - 2 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 5 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 1 * (f ^^^ ~~~(d &&& e)) + 11 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 1 * (f ^^^ (d ||| ~~~e)) + 2 * (d ||| ~~~f) + 11 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 2 * ( ~~~d &&& (e ^^^ f)) - 2 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 1 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 7 * (d &&& (e ||| f)) + 11 * (f ||| (d &&& ~~~e)) - 1 * ~~~(d ^^^ (e &&& f)) - 11 * ((d &&& f) ||| ~~~(e ||| f)) + 2 * (d ^^^ ( ~~~e ||| f)) + 5 * ( ~~~d ||| ( ~~~e ||| f)) - 7 * ~~~(d &&& (e ^^^ f)) - 3 * (f ^^^ (d &&& (e ||| f))) + 5 * ~~~(d ||| ( ~~~e &&& f)) - 2 * ~~~(d &&& e) - 6 * ( ~~~d &&& ( ~~~e ||| f)) - 3 * (f ^^^ ( ~~~d &&& (e ||| f))) - 1 * ((d &&& e) ||| (e ^^^ f)) - 2 * ( ~~~d ||| (e &&& f)) - 1 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 5 * ~~~( ~~~d ||| (e ^^^ f)) - 11 * (e &&& f) + 3 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 5 * (f ^^^ ( ~~~d ||| (e ||| f))) - 5 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 7 * ~~~(e &&& f) + 5 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 2 * ( ~~~d &&& (e ||| f)) + 3 * (f &&& (d ||| ~~~e)) - 11 * (d &&& ( ~~~e ||| f)) - 5 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 32 * ~~~(d ||| (e ||| f)) - 9 * ~~~(d ||| ( ~~~e ||| f)) + 23 * ~~~( ~~~d ||| (e ||| f)) + 3 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 9 * ( ~~~d &&& (e &&& f)) + 10 * (d &&& ( ~~~e &&& f)) + 9 * (d &&& (e &&& f)) = 5 * ( ~~~d &&& ( ~~~e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2134 (x y : BitVec w) : +theorem e_2134 : - 1 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 2 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 3 * ~~~(e ||| ~~~f) + 1 * ~~~(d ^^^ (e &&& f)) + 5 * (d ||| (e &&& f)) - 7 * (e &&& ~~~f) + 4 * (d ^^^ (e &&& f)) - 6 * (e ^^^ ~~~(d &&& ~~~f)) - 1 * (f ^^^ (d ||| ( ~~~e ||| f))) - 5 * (d ^^^ (e ^^^ f)) + 11 * (d ||| ~~~e) + 2 * (f ||| (d ^^^ e)) + 1 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 2 * (e ^^^ (d ||| f)) - 1 * (e ||| (d &&& ~~~f)) - 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 1 * (d ||| ( ~~~e &&& f)) + 5 * (e ^^^ (d ||| ( ~~~e &&& f))) - 2 * (f ||| (d &&& e)) - 11 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 7 * ( ~~~d &&& ( ~~~e ||| f)) + 1 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 1 * ((d &&& f) ^^^ (e ||| f)) + 2 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 3 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * (e ^^^ (d &&& (e ||| f))) + 1 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 11 * (d &&& ( ~~~e ||| f)) - 6 * ( ~~~e &&& (d ^^^ f)) + 1 * ~~~(e ||| f) - 1 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 1 * f + 2 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 1 * (f ^^^ ~~~(d ||| e)) + 2 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * ~~~(d ||| ~~~e) - 3 * ((d &&& e) ||| (e ^^^ f)) - 3 * (d ||| ~~~f) + 5 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 9 * ~~~(d ||| (e ||| f)) + 26 * ~~~(d ||| ( ~~~e ||| f)) - 11 * ~~~( ~~~d ||| (e ||| f)) + 6 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 20 * ( ~~~d &&& ( ~~~e &&& f)) - 9 * ( ~~~d &&& (e &&& f)) - 29 * (d &&& (e &&& f)) = 5 * (e ^^^ (d ||| (e ^^^ f))) + 6 * ((d &&& ~~~e) ||| (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2135 (x y : BitVec w) : +theorem e_2135 : - 7 * ~~~(e ||| f) + 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 11 * ((d &&& e) ||| ~~~(e ^^^ f)) - 6 * (e ||| ~~~(d ^^^ f)) + 1 * ( ~~~e &&& (d ^^^ f)) - 7 * (d ||| ~~~e) + 5 * (e ^^^ ~~~(d &&& f)) + 1 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 1 * (e ^^^ ( ~~~d ||| (e &&& f))) - 5 * (f ^^^ ( ~~~d ||| (e &&& f))) + 7 * ( ~~~e ||| (d ^^^ f)) - 2 * (f ^^^ ~~~(d ||| (e &&& f))) + 1 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 5 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 3 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 1 * (f ^^^ ~~~(d &&& (e ||| f))) - 1 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 1 * ~~~(d &&& f) - 5 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 1 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 2 * f + 2 * ~~~(e ^^^ f) + 2 * (f &&& (d ^^^ e)) + 5 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 2 * ~~~(d &&& e) + 3 * ~~~(d ||| ( ~~~e &&& f)) + 2 * (f &&& ~~~(d &&& e)) - 2 * ~~~(d &&& (e ||| f)) - 3 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 2 * (f ||| (d ^^^ e)) + 1 * ~~~(d &&& ~~~d) - 1 * ( ~~~d ||| (e ||| f)) - 3 * ( ~~~f &&& (d ^^^ e)) - 1 * (d ||| e) - 1 * (f ||| ~~~(d ||| e)) + 4 * (d &&& (e ||| f)) - 11 * ~~~(d ||| (e ||| f)) + 10 * ~~~(d ||| ( ~~~e ||| f)) - 11 * ~~~( ~~~d ||| (e ||| f)) - 21 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 1 * ( ~~~d &&& ( ~~~e &&& f)) - 23 * ( ~~~d &&& (e &&& f)) - 3 * (d &&& ( ~~~e &&& f)) - 4 * (d &&& (e &&& f)) = - 3 * ((d ||| e) &&& ~~~(e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2136 (x y : BitVec w) : +theorem e_2136 : - 5 * ~~~( ~~~d ||| (e &&& f)) + 3 * (e ^^^ ( ~~~d &&& (e ||| f))) + 2 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * (e &&& f) + 7 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 7 * ~~~(d ^^^ ( ~~~e ||| f)) + 1 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 1 * (d ||| (e &&& f)) + 7 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 3 * ((d &&& e) ^^^ (e ||| ~~~f)) + 4 * (f &&& (d ||| e)) - 3 * (e &&& (d ||| ~~~f)) - 1 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 2 * (f ^^^ ~~~(d ||| e)) - 2 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 7 * (f ^^^ (d ||| (e ||| f))) - 7 * ~~~( ~~~d &&& (e ||| f)) + 2 * ( ~~~e &&& (d ^^^ f)) - 11 * ~~~(d ^^^ f) + 7 * ~~~(d &&& (e ^^^ f)) + 2 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 5 * (f ||| ~~~(d ^^^ e)) + 4 * (d ||| ( ~~~e ||| f)) + 11 * (f ^^^ ( ~~~d &&& (e ||| f))) + 1 * (e ^^^ (d ||| (e ^^^ f))) - 1 * ~~~(e ||| ~~~f) - 2 * ~~~(e &&& f) + 4 * ~~~(d &&& e) - 6 * ((d &&& e) ^^^ (e ||| f)) + 3 * (f ^^^ (d &&& ~~~e)) - 2 * ( ~~~d ||| (e ^^^ f)) + 11 * (e ||| (d ^^^ f)) + 1 * ~~~(d &&& f) + 5 * (e ^^^ (d &&& f)) - 7 * (e ^^^ (d ||| ( ~~~e &&& f))) - 6 * (e ^^^ ~~~(d &&& ~~~f)) + 4 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 7 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 5 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 2 * ~~~(d ||| (e ||| f)) - 30 * ~~~(d ||| ( ~~~e ||| f)) - 16 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 18 * ( ~~~d &&& ( ~~~e &&& f)) - 51 * ( ~~~d &&& (e &&& f)) + 7 * (d &&& ( ~~~e &&& f)) - 34 * (d &&& (e &&& f)) = - 1 * (e ^^^ (d ||| f)) + 39 * ~~~( ~~~d ||| (e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2137 (x y : BitVec w) : +theorem e_2137 : 11 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 5 * ((d &&& e) ^^^ (e ||| f)) + 2 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 2 * ( ~~~d ||| (e ||| f)) + 4 * (d &&& (e ^^^ f)) + 5 * (f ||| (d &&& ~~~e)) - 5 * (f ^^^ (d ||| e)) + 7 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 1 * ( ~~~d &&& ( ~~~e ||| f)) + 2 * ( ~~~f &&& ~~~(d ^^^ e)) - 2 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 5 * ( ~~~e &&& (d ^^^ f)) - 1 * ~~~(d ^^^ (e ^^^ f)) + 11 * (d ||| (e &&& f)) - 1 * ~~~(e &&& f) - 3 * (e ^^^ (d ||| f)) + 2 * (e ^^^ ~~~(d &&& ~~~f)) - 5 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 4 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 1 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 11 * (f &&& (d ||| ~~~e)) - 1 * ~~~( ~~~d ||| (e &&& f)) - 5 * (e ^^^ f) - 1 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 1 * ~~~(d ^^^ (e &&& f)) - 5 * (e ^^^ (d &&& ~~~f)) - 1 * (d ||| (e ||| f)) + 4 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 11 * (e ^^^ (d &&& ( ~~~e ||| f))) + 2 * ((d &&& e) ||| ~~~(e ||| f)) - 6 * ( ~~~d ||| ( ~~~e &&& f)) - 1 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 7 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 6 * ~~~e - 11 * ~~~(d &&& (e ^^^ f)) + 3 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * (e ^^^ (d ||| ~~~f)) - 11 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 15 * ~~~(d ||| (e ||| f)) + 8 * ~~~( ~~~d ||| (e ||| f)) + 3 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 12 * ( ~~~d &&& ( ~~~e &&& f)) + 21 * ( ~~~d &&& (e &&& f)) + 28 * (d &&& ( ~~~e &&& f)) - 8 * (d &&& (e &&& f)) = - 36 * ~~~(d ||| ( ~~~e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2138 (x y : BitVec w) : +theorem e_2138 : - 2 * (e ||| ~~~f) - 6 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 1 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 2 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 5 * (f ^^^ ( ~~~d ||| (e ||| f))) + 1 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 2 * (f ^^^ ( ~~~d &&& (e ||| f))) + 2 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 3 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 7 * ~~~(d ^^^ e) + 1 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (f &&& ~~~(d &&& ~~~e)) - 1 * (e ^^^ (d ||| (e &&& f))) - 1 * ~~~(d ^^^ ( ~~~e ||| f)) + 11 * (f &&& ~~~(d ^^^ e)) - 1 * (d &&& ( ~~~e ||| f)) + 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 7 * ((d &&& f) ||| ~~~(e ||| f)) + 4 * (f &&& (d ||| e)) + 4 * ( ~~~d &&& (e ||| f)) + 3 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 7 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 11 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 6 * ( ~~~f ||| (d ^^^ e)) + 1 * (d ^^^ (e ||| f)) - 7 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 1 * (e ^^^ ~~~(d ||| ~~~f)) + 1 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 2 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * (d ||| (e ||| f)) - 1 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 2 * ((e &&& f) ||| (d &&& (e ||| f))) - 1 * ( ~~~f &&& (d ^^^ e)) - 1 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 1 * (f &&& (d ||| ~~~e)) + 5 * d + 2 * ( ~~~e &&& ~~~(d ^^^ f)) - 11 * ( ~~~d &&& ( ~~~e ||| f)) - 6 * ((d &&& e) ||| ~~~(e ^^^ f)) + 32 * ~~~(d ||| (e ||| f)) + 22 * ~~~(d ||| ( ~~~e ||| f)) + 26 * ~~~( ~~~d ||| (e ||| f)) + 33 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 17 * ( ~~~d &&& ( ~~~e &&& f)) + 44 * ( ~~~d &&& (e &&& f)) - 6 * (d &&& (e &&& f)) = 2 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2139 (x y : BitVec w) : +theorem e_2139 : - 5 * (e ||| (d &&& f)) - 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 3 * (f &&& (d ||| e)) - 6 * (e &&& (d ||| f)) + 3 * (f ^^^ (d ||| ( ~~~e &&& f))) + 7 * ( ~~~f ||| ~~~(d ^^^ e)) + 1 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 1 * (f ^^^ (d ||| (e ||| f))) + 1 * ~~~(d ||| f) - 7 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 1 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 1 * (f ^^^ (d ||| (e &&& f))) - 1 * (e ^^^ ( ~~~d &&& (e ||| f))) - 2 * (e ||| ~~~(d ^^^ f)) + 1 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 1 * (d ||| ~~~e) + 4 * ((d ^^^ e) ||| ~~~(d ^^^ f)) + 1 * (f ^^^ ( ~~~d ||| (e &&& f))) + 5 * (e ^^^ ( ~~~d ||| (e &&& f))) + 11 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 2 * ( ~~~e ||| (d ^^^ f)) + 1 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 5 * (d ||| ~~~f) - 1 * (e ^^^ (d &&& (e ||| f))) - 5 * ~~~(e ||| f) - 7 * (d ||| ( ~~~e &&& f)) + 7 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 5 * (e &&& ~~~(d ^^^ f)) + 2 * (f ^^^ ~~~(d ||| ~~~e)) - 11 * ~~~(d &&& (e ||| f)) + 3 * (f ^^^ (d ||| ~~~e)) - 7 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 11 * (d &&& (e ||| f)) + 3 * ~~~e - 11 * (f ||| (d ^^^ e)) - 5 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 6 * ~~~(d &&& ( ~~~e &&& f)) + 1 * (d ^^^ ( ~~~e ||| f)) - 14 * ~~~(d ||| (e ||| f)) + 12 * ~~~(d ||| ( ~~~e ||| f)) - 2 * ~~~( ~~~d ||| (e ||| f)) - 15 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 2 * ( ~~~d &&& ( ~~~e &&& f)) + 21 * ( ~~~d &&& (e &&& f)) - 23 * (d &&& ( ~~~e &&& f)) + 11 * (d &&& (e &&& f)) = - 11 * ~~~( ~~~d &&& (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2140 (x y : BitVec w) : +theorem e_2140 : 1 * (f ^^^ ~~~(d ||| (e &&& f))) + 1 * ((d &&& ~~~e) ||| (e ^^^ f)) - 5 * (d ||| ( ~~~e &&& f)) + 1 * (e ||| (d &&& ~~~f)) - 7 * (d &&& (e ||| f)) - 1 * ((d &&& e) ||| (e ^^^ f)) - 7 * ~~~(d &&& (e ||| f)) + 7 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 2 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 5 * ~~~(d ||| e) + 1 * ~~~(d ^^^ (e ^^^ f)) + 2 * (f ^^^ (d ||| ( ~~~e &&& f))) + 1 * (e ||| f) + 1 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 6 * ~~~(d &&& ~~~f) - 5 * ( ~~~d &&& (e ||| f)) - 2 * ( ~~~f ||| ~~~(d ^^^ e)) + 2 * (e ^^^ ( ~~~d &&& (e ||| f))) + 2 * (f ^^^ (d ||| e)) - 1 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 2 * (e ^^^ (d ||| ( ~~~e &&& f))) - 11 * (f &&& ~~~(d &&& ~~~e)) - 6 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 11 * (d &&& (e ^^^ f)) + 11 * (e &&& ~~~(d &&& f)) - 5 * (e &&& (d ||| f)) + 7 * ~~~( ~~~d ||| (e &&& f)) + 3 * ~~~f + 11 * (e ||| (d ^^^ f)) + 3 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 5 * ~~~(d &&& e) + 3 * ~~~(d ||| f) - 1 * (f &&& (d ||| e)) - 2 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 3 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 2 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 1 * (e ^^^ ( ~~~d ||| (e &&& f))) - 1 * ((d &&& f) ^^^ (e ||| f)) + 11 * (f &&& ~~~(d &&& e)) + 18 * ~~~(d ||| (e ||| f)) - 19 * ~~~(d ||| ( ~~~e ||| f)) - 16 * ~~~( ~~~d ||| (e ||| f)) - 29 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 2 * ( ~~~d &&& ( ~~~e &&& f)) - 9 * ( ~~~d &&& (e &&& f)) - 23 * (d &&& ( ~~~e &&& f)) + 18 * (d &&& (e &&& f)) = 7 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2141 (x y : BitVec w) : +theorem e_2141 : - 3 * ((d &&& f) ||| (e &&& ~~~f)) - 5 * (d ||| (e &&& f)) + 3 * (f ^^^ (d ||| e)) - 5 * ~~~(e &&& ~~~f) - 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 11 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 7 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * (f ^^^ ~~~(d ||| ~~~e)) + 1 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 2 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 1 * (e &&& ~~~(d &&& f)) + 5 * (f ||| (d &&& e)) - 1 * (e ^^^ ~~~(d ||| (e &&& f))) + 7 * (f ^^^ ~~~(d &&& (e ||| f))) + 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 4 * (d ||| ~~~f) + 7 * e + 1 * (f ^^^ (d ||| ~~~e)) + 3 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 2 * ( ~~~d &&& (e ||| f)) - 1 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 4 * (f &&& ~~~(d &&& e)) - 5 * ~~~(d &&& e) - 3 * (e &&& (d ||| f)) + 2 * (f ^^^ (d &&& ( ~~~e ||| f))) + 5 * ( ~~~e &&& ~~~(d ^^^ f)) - 1 * ~~~( ~~~d &&& (e ^^^ f)) - 6 * ~~~(d ^^^ (e ||| f)) + 3 * (f ^^^ (d &&& ~~~e)) + 1 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 11 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 4 * ~~~(d &&& (e ^^^ f)) + 2 * (d &&& ~~~e) + 1 * (f ^^^ (d ||| (e ||| f))) + 7 * (e ||| (d ^^^ f)) - 5 * ((d &&& e) ||| ~~~(e ||| f)) + 11 * d + 1 * ~~~(d ||| ~~~f) + 2 * ( ~~~f &&& ~~~(d ^^^ e)) - 27 * ~~~(d ||| ( ~~~e ||| f)) - 9 * ~~~( ~~~d ||| (e ||| f)) - 25 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 11 * ( ~~~d &&& ( ~~~e &&& f)) - 23 * ( ~~~d &&& (e &&& f)) - 27 * (d &&& ( ~~~e &&& f)) - 4 * (d &&& (e &&& f)) = - 9 * ~~~(d ||| (e ||| f)) - 2 * (e ^^^ (d ||| ( ~~~e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2142 (x y : BitVec w) : +theorem e_2142 : - 2 * (d &&& (e ^^^ f)) + 1 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 6 * (e ^^^ (d ||| ( ~~~e &&& f))) - 2 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 1 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 2 * ( ~~~d &&& ( ~~~e ||| f)) - 1 * (e ^^^ ( ~~~d ||| (e ||| f))) - 1 * ~~~( ~~~d &&& (e &&& f)) - 2 * ( ~~~e &&& (d ^^^ f)) - 2 * ~~~(d ||| (e &&& f)) - 11 * (e ^^^ ~~~(d &&& (e ||| f))) + 1 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 2 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 1 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 11 * ( ~~~e ||| ~~~(d ^^^ f)) + 4 * (e &&& ~~~(d &&& ~~~f)) - 1 * ~~~(d &&& (e ||| f)) + 3 * (f ^^^ ~~~(d &&& (e &&& f))) + 2 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 5 * ~~~f - 5 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 7 * (e ^^^ (d &&& f)) + 3 * ( ~~~d ||| ( ~~~e ||| f)) + 3 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 11 * ~~~(e ^^^ f) + 4 * (e ^^^ ~~~(d &&& ~~~f)) + 1 * (e ^^^ (d &&& ( ~~~e ||| f))) + 1 * ((d &&& e) ^^^ (e ||| ~~~f)) - 2 * ~~~d - 6 * (d &&& f) + 1 * ((d &&& f) ^^^ (e ||| f)) + 2 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 3 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 2 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 4 * (f ^^^ ~~~(d ||| ~~~e)) + 1 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 3 * ((d &&& e) ^^^ (e ||| f)) + 5 * ( ~~~d ||| (e ||| f)) - 11 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 2 * (e ||| ~~~(d ||| ~~~f)) + 24 * ~~~(d ||| (e ||| f)) - 17 * ~~~(d ||| ( ~~~e ||| f)) + 37 * ~~~( ~~~d ||| (e ||| f)) + 26 * ( ~~~d &&& ( ~~~e &&& f)) - 8 * ( ~~~d &&& (e &&& f)) + 7 * (d &&& ( ~~~e &&& f)) + 18 * (d &&& (e &&& f)) = - 7 * (f ||| ~~~(d ||| ~~~e)) - 1 * (e ||| ~~~(d ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2143 (x y : BitVec w) : +theorem e_2143 : 3 * ( ~~~d &&& (e ^^^ f)) + 4 * ~~~(e &&& ~~~f) - 5 * (e &&& ~~~f) + 7 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 4 * d + 4 * ~~~(d &&& (e ^^^ f)) - 1 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 1 * (f ^^^ (d ||| e)) + 2 * (d ||| e) - 7 * ( ~~~f ||| (d ^^^ e)) + 11 * ~~~(d &&& e) + 4 * ((d &&& e) ||| ~~~(e ||| f)) - 1 * (f ^^^ ~~~(d ||| ~~~e)) - 1 * (d ||| ~~~f) - 2 * (e &&& ~~~(d ^^^ f)) - 1 * (f ^^^ ~~~(d &&& (e &&& f))) + 5 * ( ~~~d ||| (e ^^^ f)) - 1 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 1 * (e ^^^ ~~~(d &&& f)) + 5 * ((d &&& e) ^^^ (e ||| ~~~f)) + 2 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 1 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 3 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * ~~~f + 3 * (e ^^^ ~~~(d ||| (e &&& f))) - 3 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 3 * (e ||| ~~~(d ||| ~~~f)) + 1 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 6 * ~~~(d &&& ( ~~~e ||| f)) - 3 * ( ~~~f &&& (d ^^^ e)) - 2 * ~~~(e ||| f) - 1 * (f &&& (d ||| ~~~e)) + 1 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 2 * ~~~(d &&& (e ||| f)) - 11 * ( ~~~d ||| ( ~~~e &&& f)) - 1 * (d ^^^ f) + 1 * (f ^^^ (d ||| ( ~~~e ||| f))) - 1 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 2 * (e ^^^ (d &&& (e ||| f))) - 24 * ~~~(d ||| (e ||| f)) + 7 * ~~~(d ||| ( ~~~e ||| f)) - 19 * ~~~( ~~~d ||| (e ||| f)) - 26 * ( ~~~d &&& ( ~~~e &&& f)) - 16 * ( ~~~d &&& (e &&& f)) - 12 * (d &&& ( ~~~e &&& f)) - 19 * (d &&& (e &&& f)) = - 7 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 1 * ( ~~~e &&& (d ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2144 (x y : BitVec w) : +theorem e_2144 : 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 3 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 1 * ((d ||| e) &&& (e ^^^ f)) - 7 * ~~~(e ||| f) - 3 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 1 * ~~~(d &&& (e &&& f)) + 7 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 7 * ~~~( ~~~d &&& (e ^^^ f)) + 1 * ((e &&& f) ||| (d &&& (e ||| f))) + 1 * (e ^^^ (d ||| ( ~~~e &&& f))) + 5 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 4 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 2 * (e ||| (d &&& ~~~f)) + 7 * ((d &&& f) ||| ~~~(e ||| f)) - 1 * ( ~~~d &&& (e ||| f)) - 1 * ((d &&& e) ^^^ (e ||| ~~~f)) + 2 * ~~~(d ||| f) + 4 * (f ^^^ (d &&& ~~~e)) + 7 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 1 * (f &&& (d ||| e)) + 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 2 * ((d &&& e) ||| ~~~(e ||| f)) + 5 * (d &&& e) + 1 * (f &&& (d ||| ~~~e)) + 11 * (f ^^^ (d ||| ( ~~~e &&& f))) + 1 * (d ^^^ ( ~~~e ||| f)) - 5 * (e ^^^ (d &&& ~~~f)) - 6 * ((d ^^^ e) ||| (d ^^^ f)) - 5 * ~~~(e &&& f) + 2 * ((d ||| ~~~e) &&& (e ^^^ f)) - 7 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 11 * (d &&& ~~~e) - 2 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 11 * (d ||| ( ~~~e ||| f)) + 1 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 2 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 11 * ( ~~~d ||| (e ^^^ f)) + 2 * ~~~(e ||| ~~~f) - 2 * ((d &&& e) ^^^ (e ||| f)) + 7 * ~~~(d ||| (e ||| f)) + 34 * ~~~(d ||| ( ~~~e ||| f)) - 12 * ~~~( ~~~d ||| (e ||| f)) - 1 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 6 * ( ~~~d &&& ( ~~~e &&& f)) + 12 * ( ~~~d &&& (e &&& f)) - 1 * (d &&& ( ~~~e &&& f)) - 26 * (d &&& (e &&& f)) = 7 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * ( ~~~d ||| ( ~~~e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2145 (x y : BitVec w) : +theorem e_2145 : - 2 * ~~~(d ||| f) - 6 * (e ^^^ (d ||| f)) + 7 * (d ||| ~~~f) + 2 * (f ||| ~~~(d ||| ~~~e)) + 2 * ((d &&& e) ||| (e ^^^ f)) + 2 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 4 * ((d &&& f) ||| ~~~(e ||| f)) - 1 * (d &&& ~~~e) - 11 * ( ~~~f &&& ~~~(d ^^^ e)) + 11 * (f ||| (d &&& ~~~e)) + 2 * (f &&& (d ^^^ e)) - 7 * (f ^^^ ~~~(d &&& (e &&& f))) - 5 * (d ||| ( ~~~e &&& f)) - 1 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 11 * (f ^^^ (d &&& ~~~e)) + 5 * (d &&& ~~~f) - 2 * (f &&& ~~~(d &&& e)) - 2 * (f ^^^ (d &&& e)) + 4 * ~~~(d ||| e) + 4 * ~~~(d &&& ~~~d) + 2 * ~~~(d &&& (e ^^^ f)) + 5 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 1 * (e ||| f) + 4 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 5 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 2 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 11 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 2 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 1 * (f ^^^ ~~~(d &&& ~~~e)) - 1 * (f &&& ~~~(d ^^^ e)) - 1 * (f ^^^ ~~~(d ||| e)) + 3 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 1 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 2 * (e ||| ~~~(d ||| ~~~f)) + 1 * (d ||| ~~~e) - 7 * (d ^^^ (e ^^^ f)) - 3 * (e ^^^ ( ~~~d ||| (e &&& f))) - 3 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 1 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 8 * ~~~(d ||| (e ||| f)) - 7 * ~~~(d ||| ( ~~~e ||| f)) + 12 * ~~~( ~~~d ||| (e ||| f)) - 4 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 6 * ( ~~~d &&& ( ~~~e &&& f)) - 5 * ( ~~~d &&& (e &&& f)) - 26 * (d &&& ( ~~~e &&& f)) - 21 * (d &&& (e &&& f)) = - 3 * ( ~~~(d &&& e) &&& (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2146 (x y : BitVec w) : +theorem e_2146 : - 5 * (e ^^^ (d &&& ( ~~~e ||| f))) - 1 * (e &&& (d ||| f)) - 1 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 3 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 3 * (d &&& f) - 6 * ( ~~~f &&& (d ^^^ e)) - 6 * ~~~f + 7 * ~~~(d ^^^ (e &&& f)) - 1 * (d ^^^ (e ||| f)) - 11 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 1 * ( ~~~d ||| ( ~~~e &&& f)) + 4 * (e ||| f) - 1 * ( ~~~f &&& ~~~(d ^^^ e)) - 1 * ~~~(d &&& e) + 2 * (d &&& ~~~e) - 1 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 6 * (f &&& (d ^^^ e)) - 5 * (f ^^^ (d &&& ~~~e)) + 4 * (e ^^^ ~~~(d &&& (e &&& f))) - 2 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 1 * (e ||| (d ^^^ f)) - 6 * ( ~~~d &&& (e ||| f)) - 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 2 * ~~~(d &&& ~~~f) + 7 * ~~~(d ||| ~~~f) - 2 * ~~~(d &&& ~~~e) + 7 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 1 * (e &&& ~~~(d ^^^ f)) + 1 * (e ^^^ (d &&& (e ^^^ f))) + 2 * ( ~~~d ||| ( ~~~e ||| f)) - 7 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 1 * (d ||| (e &&& f)) + 7 * (f ||| ~~~(d ^^^ e)) - 2 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 2 * (f ^^^ (d ||| e)) - 1 * ~~~(d &&& (e ^^^ f)) - 1 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 1 * ~~~(e ||| f) + 5 * ~~~(e &&& f) - 27 * ~~~(d ||| (e ||| f)) + 16 * ~~~(d ||| ( ~~~e ||| f)) + 29 * ~~~( ~~~d ||| (e ||| f)) - 8 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 29 * ( ~~~d &&& ( ~~~e &&& f)) - 9 * ( ~~~d &&& (e &&& f)) - 6 * (d &&& ( ~~~e &&& f)) - 7 * (d &&& (e &&& f)) = - 11 * (e ^^^ ~~~(d ||| (e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2147 (x y : BitVec w) : +theorem e_2147 : 2 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 2 * (d &&& (e ^^^ f)) - 1 * (e ^^^ (d &&& ( ~~~e ||| f))) - 5 * (e ||| ~~~(d ||| f)) + 11 * (f ^^^ ~~~(d ||| ~~~e)) + 3 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 3 * (d ^^^ e) - 11 * ~~~( ~~~d &&& (e &&& f)) - 2 * (d ||| (e ||| f)) + 3 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 1 * ~~~(d ^^^ f) - 11 * ~~~(d ||| ~~~e) - 3 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 6 * ~~~d - 1 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 1 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 3 * ~~~(e ||| f) - 1 * ((d &&& e) ^^^ (e ||| f)) - 7 * (f ||| (d &&& ~~~e)) - 3 * ((d &&& ~~~e) ||| (e ^^^ f)) + 3 * (e ^^^ ( ~~~d ||| (e &&& f))) - 3 * (d ||| ( ~~~e ||| f)) + 5 * (e ^^^ (d ||| ~~~f)) - 1 * ( ~~~f ||| (d ^^^ e)) - 7 * (f ^^^ (d ||| (e &&& f))) - 2 * ~~~( ~~~d ||| (e ^^^ f)) - 1 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 3 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 1 * (e &&& ~~~(d &&& ~~~f)) - 2 * ~~~e - 7 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 2 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 5 * ((d ^^^ e) ||| (d ^^^ f)) - 6 * (e ||| (d &&& f)) + 5 * (e ^^^ (d ||| (e &&& f))) + 11 * ((d &&& e) ^^^ (e ||| ~~~f)) - 6 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 11 * ( ~~~f ||| ~~~(d ^^^ e)) + 4 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 15 * ~~~(d ||| (e ||| f)) + 14 * ~~~(d ||| ( ~~~e ||| f)) + 31 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 26 * ( ~~~d &&& ( ~~~e &&& f)) + 27 * ( ~~~d &&& (e &&& f)) + 26 * (d &&& ( ~~~e &&& f)) + 8 * (d &&& (e &&& f)) = 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 20 * ~~~( ~~~d ||| (e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2148 (x y : BitVec w) : +theorem e_2148 : - 5 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 11 * (d ^^^ (e ||| f)) - 1 * ((d &&& ~~~e) ||| (e ^^^ f)) - 6 * ~~~( ~~~d ||| (e &&& f)) + 4 * (d ||| ( ~~~e ||| f)) + 4 * (e &&& (d ||| ~~~f)) - 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 2 * (f &&& (d ^^^ e)) - 11 * ((d &&& f) ||| ~~~(e ||| f)) + 11 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 1 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 7 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 2 * (e ^^^ (d &&& ~~~f)) - 2 * (e ||| (d ^^^ f)) - 11 * (e ^^^ ~~~(d ||| ~~~f)) + 3 * (d ||| ~~~f) - 2 * ( ~~~e ||| (d ^^^ f)) + 2 * ( ~~~d ||| (e ||| f)) + 1 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 2 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * (d &&& (e ^^^ f)) - 1 * (f &&& ~~~(d ^^^ e)) + 1 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 1 * ((d ||| ~~~e) &&& (e ^^^ f)) + 7 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 3 * ~~~(e &&& f) + 1 * ((d &&& e) ^^^ (e ||| f)) - 6 * (e &&& ~~~(d ^^^ f)) - 1 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 1 * (e &&& (d ||| f)) - 1 * (e ^^^ (d ||| ( ~~~e &&& f))) - 1 * ( ~~~d ||| (e &&& f)) - 2 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 2 * (e ^^^ ~~~(d &&& (e ||| f))) - 7 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 1 * (f &&& (d ||| e)) - 6 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * (f ^^^ (d &&& ~~~e)) + 2 * ((d ^^^ e) ||| (d ^^^ f)) - 9 * ~~~(d ||| (e ||| f)) - 4 * ~~~(d ||| ( ~~~e ||| f)) + 19 * ~~~( ~~~d ||| (e ||| f)) - 1 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 4 * ( ~~~d &&& ( ~~~e &&& f)) + 1 * ( ~~~d &&& (e &&& f)) - 12 * (d &&& ( ~~~e &&& f)) + 9 * (d &&& (e &&& f)) = - 11 * ( ~~~(d ||| e) ||| (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2149 (x y : BitVec w) : +theorem e_2149 : - 1 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 2 * ~~~( ~~~d &&& (e ||| f)) + 2 * (e ^^^ ~~~(d ||| f)) + 1 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 4 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 1 * ((d ^^^ e) &&& (d ^^^ f)) - 1 * ( ~~~d &&& ( ~~~e ||| f)) - 1 * ( ~~~d ||| (e ||| f)) - 1 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 1 * (e &&& (d ||| f)) + 11 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (e ^^^ (d ||| (e ||| f))) + 1 * ~~~(d ||| ~~~e) + 3 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 3 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 6 * ~~~(d ^^^ (e ||| f)) - 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 1 * ~~~e + 7 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * ~~~(e ||| f) + 1 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 4 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 4 * (f ||| ~~~(d ||| e)) - 5 * (f &&& ~~~(d &&& e)) - 11 * (e ^^^ ( ~~~d ||| (e &&& f))) - 1 * (d ||| ~~~e) - 3 * ~~~(d ||| (e ^^^ f)) + 1 * (f ^^^ (d ||| ( ~~~e &&& f))) - 11 * (e ^^^ (d &&& (e ||| f))) + 2 * (e ^^^ ~~~(d &&& (e &&& f))) - 1 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 6 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 2 * ( ~~~e ||| (d ^^^ f)) + 4 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 2 * (d &&& (e ||| f)) + 5 * (f &&& (d ^^^ e)) + 3 * ~~~(d &&& (e ^^^ f)) - 7 * ~~~(d &&& f) + 11 * ~~~( ~~~d &&& (e ^^^ f)) - 3 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 2 * (d &&& ( ~~~e ||| f)) - 5 * ~~~(e ||| ~~~f) - 18 * ~~~( ~~~d ||| (e ||| f)) + 1 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 31 * ( ~~~d &&& (e &&& f)) + 5 * (d &&& ( ~~~e &&& f)) - 21 * (d &&& (e &&& f)) = - 7 * ~~~(d ||| ( ~~~e ||| f)) - 15 * ( ~~~d &&& ( ~~~e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2150 (x y : BitVec w) : +theorem e_2150 : 2 * ( ~~~d ||| ( ~~~e &&& f)) + 7 * (d ||| (e ||| f)) + 11 * (f &&& ~~~(d &&& e)) - 1 * ~~~(d &&& f) + 11 * ( ~~~d &&& (e ||| f)) + 7 * (f ||| (d &&& e)) - 1 * (e ^^^ ~~~(d &&& ~~~f)) + 5 * (d &&& e) - 5 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 2 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 1 * ((d &&& f) ||| ~~~(e ||| f)) - 5 * ~~~(e &&& f) + 1 * (e ^^^ ( ~~~d ||| (e &&& f))) - 1 * ((d &&& e) ^^^ (e ||| f)) - 7 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 3 * (f ^^^ ( ~~~d ||| (e &&& f))) + 11 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 2 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 1 * (d &&& f) + 2 * ((d ^^^ e) &&& (d ^^^ f)) + 3 * ( ~~~f &&& (d ^^^ e)) + 1 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * (d ^^^ (e ^^^ f)) - 11 * ( ~~~d &&& ( ~~~e ||| f)) - 11 * ( ~~~e &&& ~~~(d ^^^ f)) - 2 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 11 * (d ||| ~~~f) - 1 * (f ^^^ (d ||| e)) - 2 * (e ^^^ (d ||| (e ||| f))) + 11 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 6 * ((e &&& f) ||| (d &&& (e ||| f))) - 1 * ~~~(d ||| (e &&& f)) - 1 * (d &&& (e ^^^ f)) + 3 * ~~~( ~~~d &&& (e ^^^ f)) - 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 5 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 11 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 5 * f + 7 * (e ^^^ (d &&& (e ||| f))) + 8 * ~~~(d ||| (e ||| f)) - 14 * ~~~(d ||| ( ~~~e ||| f)) - 4 * ~~~( ~~~d ||| (e ||| f)) + 1 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 37 * ( ~~~d &&& ( ~~~e &&& f)) - 56 * ( ~~~d &&& (e &&& f)) - 16 * (d &&& ( ~~~e &&& f)) + 9 * (d &&& (e &&& f)) = 7 * ( ~~~d &&& (e ^^^ f)) - 7 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2151 (x y : BitVec w) : +theorem e_2151 : 2 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 1 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 1 * (f &&& (d ||| e)) - 2 * ( ~~~d ||| (e ^^^ f)) - 2 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * ((d &&& f) ||| (e &&& ~~~f)) - 3 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 11 * ((e &&& f) ||| (d &&& (e ||| f))) + 1 * ((d &&& e) ||| ~~~(e ^^^ f)) - 2 * (d ^^^ e) + 7 * (f ^^^ ( ~~~d ||| (e &&& f))) + 1 * (d &&& f) + 1 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 7 * e - 1 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 7 * ~~~( ~~~d ||| (e ^^^ f)) - 1 * (d &&& e) + 11 * ((d &&& ~~~e) ||| (e ^^^ f)) - 7 * (e ||| (d ^^^ f)) - 2 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 1 * (f ^^^ ( ~~~d ||| (e ||| f))) + 1 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 4 * (e ^^^ (d &&& ( ~~~e ||| f))) + 4 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 5 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 2 * (f &&& ~~~(d &&& ~~~e)) - 6 * ~~~( ~~~d ||| (e &&& f)) - 1 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 5 * ((d &&& f) ||| ~~~(e ||| f)) + 11 * ~~~(e ||| f) - 5 * (f ^^^ (d ||| ( ~~~e &&& f))) + 7 * (e ^^^ (d ||| ( ~~~e &&& f))) - 5 * (f ||| ~~~(d ||| ~~~e)) - 2 * (e ^^^ f) + 3 * (e ^^^ (d ||| f)) + 2 * (f ||| (d &&& ~~~e)) + 3 * (d ||| ~~~e) - 3 * ((d &&& e) ||| (e ^^^ f)) + 11 * (e &&& ~~~(d ^^^ f)) - 28 * ~~~(d ||| (e ||| f)) - 30 * ~~~(d ||| ( ~~~e ||| f)) - 22 * ~~~( ~~~d ||| (e ||| f)) - 18 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 8 * ( ~~~d &&& ( ~~~e &&& f)) - 15 * ( ~~~d &&& (e &&& f)) - 35 * (d &&& ( ~~~e &&& f)) - 26 * (d &&& (e &&& f)) = 1 * ~~~(d ^^^ f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2152 (x y : BitVec w) : +theorem e_2152 : - 11 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 2 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 1 * (f ||| ~~~(d ^^^ e)) + 4 * (d &&& (e ^^^ f)) + 1 * ((d ||| e) &&& (e ^^^ f)) + 3 * (d ^^^ (e &&& f)) - 1 * (d ^^^ (e ||| f)) - 1 * ( ~~~d ||| (e &&& f)) - 2 * ~~~(d ||| ~~~e) - 1 * (e ||| f) + 3 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 2 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 3 * d + 7 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 1 * (e ^^^ ( ~~~d ||| (e ||| f))) - 2 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * (f &&& ~~~(d &&& e)) - 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 11 * ( ~~~e &&& ~~~(d ^^^ f)) + 11 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 5 * ~~~(d ||| f) - 11 * ((d ^^^ e) ||| (d ^^^ f)) + 1 * ~~~( ~~~d &&& (e ||| f)) - 1 * ~~~(d &&& ( ~~~e ||| f)) + 5 * ~~~(d &&& ( ~~~e &&& f)) - 7 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 1 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 7 * ~~~(d ^^^ f) - 3 * (f ^^^ (d ||| ( ~~~e ||| f))) + 4 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 11 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 2 * (f ^^^ ~~~(d ||| ~~~e)) + 1 * (e ^^^ (d ||| (e &&& f))) + 3 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 5 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 11 * ~~~(d &&& (e &&& f)) + 2 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 11 * ( ~~~d ||| ( ~~~e &&& f)) - 1 * ( ~~~d ||| (e ||| f)) + 1 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 2 * ~~~(d ||| (e ||| f)) + 16 * ~~~(d ||| ( ~~~e ||| f)) + 11 * ~~~( ~~~d ||| (e ||| f)) - 2 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 16 * ( ~~~d &&& ( ~~~e &&& f)) + 2 * ( ~~~d &&& (e &&& f)) + 22 * (d &&& ( ~~~e &&& f)) - 5 * (d &&& (e &&& f)) = 6 * (d ||| e) - 5 * (f ^^^ (d ||| (e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2153 (x y : BitVec w) : +theorem e_2153 : 1 * (e ^^^ (d &&& (e ||| f))) + 5 * ( ~~~d &&& ( ~~~e ||| f)) + 1 * ~~~(d ||| e) - 1 * ( ~~~e &&& (d ^^^ f)) - 1 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * (f &&& ~~~(d &&& e)) - 3 * (e ^^^ ( ~~~d ||| (e ||| f))) + 5 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 7 * ~~~(d ||| ~~~e) + 11 * (d ^^^ (e ^^^ f)) + 4 * ~~~(d &&& e) + 3 * (d ^^^ e) - 1 * (e ||| ~~~(d ||| ~~~f)) - 5 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 2 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 2 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 7 * (e ^^^ (d ||| (e ^^^ f))) + 5 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 1 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 6 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 11 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 2 * ((d &&& ~~~e) ||| (e ^^^ f)) + 2 * (f ^^^ ~~~(d &&& ~~~e)) + 2 * (e ^^^ ( ~~~d ||| (e &&& f))) + 2 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * ~~~(d &&& (e ^^^ f)) + 11 * (d ^^^ ( ~~~e ||| f)) + 4 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 5 * (f ^^^ ( ~~~d ||| (e &&& f))) + 1 * ( ~~~d ||| (e ^^^ f)) + 7 * ~~~(e ^^^ f) - 3 * (f ||| (d &&& ~~~e)) - 2 * (f &&& (d ||| e)) - 2 * ( ~~~f &&& (d ^^^ e)) - 1 * (f ^^^ ( ~~~d &&& (e ||| f))) + 11 * ~~~(d ^^^ (e ||| f)) + 3 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 11 * ~~~(d ^^^ (e &&& f)) - 2 * ~~~(d &&& (e &&& f)) - 1 * (d ||| ( ~~~e &&& f)) - 11 * (d &&& (e ^^^ f)) - 42 * ~~~(d ||| (e ||| f)) - 19 * ~~~(d ||| ( ~~~e ||| f)) - 31 * ~~~( ~~~d ||| (e ||| f)) - 24 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 2 * ( ~~~d &&& ( ~~~e &&& f)) - 43 * ( ~~~d &&& (e &&& f)) + 3 * (d &&& ( ~~~e &&& f)) = 13 * (d &&& (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2154 (x y : BitVec w) : +theorem e_2154 : 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 5 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 1 * (f &&& ~~~(d ^^^ e)) - 2 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 7 * ~~~(d &&& f) + 1 * (e &&& f) + 2 * ~~~(e ^^^ f) - 1 * ~~~( ~~~d ||| (e &&& f)) + 5 * (e ^^^ ( ~~~d &&& (e ||| f))) + 5 * ( ~~~d ||| ( ~~~e ||| f)) + 2 * ( ~~~d &&& ( ~~~e ||| f)) - 1 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 11 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 7 * (f ^^^ ( ~~~d &&& (e ||| f))) - 11 * (f ^^^ (d &&& ( ~~~e ||| f))) + 2 * ( ~~~f &&& (d ^^^ e)) - 3 * (f &&& (d ^^^ e)) + 11 * ((d ^^^ e) ||| ~~~(d ^^^ f)) + 3 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 5 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 11 * (d &&& ( ~~~e ||| f)) - 1 * (e ||| ~~~f) + 2 * (d ^^^ (e ^^^ f)) + 1 * (f ^^^ ( ~~~d ||| (e ||| f))) - 5 * ~~~(d ||| (e ^^^ f)) + 7 * (d ||| (e ||| f)) + 2 * ~~~(d &&& e) + 1 * ~~~(e &&& f) - 5 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 1 * (e ^^^ ( ~~~d ||| (e &&& f))) - 1 * (f ^^^ ~~~(d &&& (e &&& f))) - 6 * ~~~( ~~~d &&& (e &&& f)) + 1 * d - 5 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 3 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 11 * (f ^^^ ~~~(d &&& (e ||| f))) + 5 * ~~~e + 11 * (f &&& (d ||| e)) + 3 * (f ^^^ (d ||| (e &&& f))) - 2 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 16 * ~~~(d ||| (e ||| f)) - 41 * ~~~(d ||| ( ~~~e ||| f)) - 12 * ~~~( ~~~d ||| (e ||| f)) + 11 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 16 * ( ~~~d &&& ( ~~~e &&& f)) - 32 * ( ~~~d &&& (e &&& f)) - 18 * (d &&& ( ~~~e &&& f)) - 38 * (d &&& (e &&& f)) = 2 * ((d &&& e) ||| (e ^^^ f)) + 11 * ~~~( ~~~d &&& (e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2155 (x y : BitVec w) : +theorem e_2155 : - 7 * ((d ^^^ e) &&& (d ^^^ f)) + 1 * ~~~e - 5 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 7 * ~~~(d &&& ( ~~~e &&& f)) + 11 * ~~~(e &&& ~~~f) + 2 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 1 * (f ^^^ ~~~(d &&& ~~~e)) + 2 * (d ||| ~~~e) - 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 2 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 1 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 3 * ~~~(e ^^^ f) + 4 * ~~~(d &&& ~~~e) + 1 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 2 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 5 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 4 * (d &&& ~~~f) - 5 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 1 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 2 * (d ||| e) - 3 * (f ^^^ ~~~(d ||| (e &&& f))) + 5 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 11 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 1 * ( ~~~d ||| (e ||| f)) + 7 * ~~~( ~~~d ||| (e ^^^ f)) - 1 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 3 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 11 * (e &&& ~~~(d ^^^ f)) - 7 * ~~~( ~~~d &&& (e ||| f)) + 2 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 11 * ~~~(d ||| e) + 3 * ~~~(d ^^^ ( ~~~e &&& f)) + 5 * (e ^^^ (d ||| (e ||| f))) - 2 * (f ^^^ (d &&& (e ||| f))) + 5 * ( ~~~e ||| (d ^^^ f)) + 5 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 1 * (d &&& ( ~~~e ||| f)) + 7 * (e ||| ~~~(d ||| f)) - 6 * (f ^^^ ~~~(d &&& (e &&& f))) - 1 * ~~~(d ||| (e ||| f)) + 4 * ~~~(d ||| ( ~~~e ||| f)) - 9 * ~~~( ~~~d ||| (e ||| f)) - 12 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 7 * ( ~~~d &&& ( ~~~e &&& f)) - 8 * ( ~~~d &&& (e &&& f)) - 24 * (d &&& ( ~~~e &&& f)) - 11 * (d &&& (e &&& f)) = 2 * ( ~~~d ||| (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2156 (x y : BitVec w) : +theorem e_2156 : - 11 * ~~~(d ||| f) + 7 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 11 * ( ~~~d &&& (e ||| f)) + 11 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 1 * ( ~~~f ||| ~~~(d ^^^ e)) - 2 * ( ~~~e &&& (d ^^^ f)) + 2 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 7 * ( ~~~e ||| (d ^^^ f)) - 1 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 7 * (e ^^^ (d ||| (e ||| f))) + 5 * (f ^^^ ( ~~~d ||| (e ||| f))) - 5 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 1 * (d &&& (e ^^^ f)) - 1 * ( ~~~d &&& ( ~~~e ||| f)) - 1 * (f &&& ~~~(d &&& e)) - 2 * (e ^^^ (d ||| ( ~~~e &&& f))) - 7 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 2 * ~~~(d ^^^ (e ||| f)) - 11 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 7 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 1 * ~~~(d &&& (e ^^^ f)) - 2 * (d ^^^ (e ||| f)) - 2 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * ( ~~~f &&& (d ^^^ e)) - 6 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 4 * ~~~(d &&& ( ~~~e &&& f)) + 3 * ( ~~~f ||| (d ^^^ e)) - 11 * (f ^^^ (d &&& ~~~e)) - 7 * (f &&& (d ||| e)) - 6 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 4 * ((d &&& e) ||| (e ^^^ f)) + 1 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 2 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 2 * (f ||| (d &&& ~~~e)) - 3 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 4 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 2 * ~~~(d &&& ~~~d) - 1 * (e ||| ~~~(d ^^^ f)) + 1 * ~~~( ~~~d ||| (e ^^^ f)) - 7 * ~~~(d ||| (e ||| f)) - 38 * ~~~(d ||| ( ~~~e ||| f)) + 14 * ~~~( ~~~d ||| (e ||| f)) - 47 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 16 * ( ~~~d &&& ( ~~~e &&& f)) + 14 * ( ~~~d &&& (e &&& f)) + 21 * (d &&& ( ~~~e &&& f)) + 13 * (d &&& (e &&& f)) = - 3 * (f ||| (d &&& e)) - 4 * (e ^^^ ( ~~~d ||| (e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2157 (x y : BitVec w) : +theorem e_2157 : - 1 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 2 * ( ~~~d ||| (e ^^^ f)) + 2 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 1 * ( ~~~d &&& ( ~~~e ||| f)) + 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * ~~~(d ^^^ f) - 1 * (e ^^^ (d &&& (e ^^^ f))) - 2 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 1 * ~~~(d ||| ~~~e) - 6 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 11 * (e ||| (d &&& f)) + 1 * ~~~(d ||| (e ^^^ f)) - 6 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 6 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 1 * ((d &&& e) ||| (e ^^^ f)) - 1 * (e &&& (d ||| ~~~f)) + 11 * ~~~(d &&& ~~~d) - 3 * ~~~( ~~~d ||| (e &&& f)) + 3 * (d &&& e) + 1 * ((d &&& e) ^^^ (e ||| ~~~f)) - 11 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 5 * (e ^^^ (d ||| (e &&& f))) - 2 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 1 * (f &&& (d ||| ~~~e)) + 1 * (f ^^^ (d ||| ( ~~~e ||| f))) + 2 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * (e ^^^ ~~~(d &&& f)) + 1 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 4 * ((d ^^^ e) ||| (d ^^^ f)) + 2 * (f ^^^ ( ~~~d ||| (e &&& f))) + 1 * ((d &&& f) ||| (e &&& ~~~f)) - 3 * ~~~(d ||| f) - 6 * (e ^^^ (d ||| ~~~f)) + 4 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 11 * (e &&& ~~~(d &&& ~~~f)) - 7 * ~~~( ~~~d &&& (e ^^^ f)) + 2 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 7 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 5 * (d ||| (e ||| f)) - 2 * ~~~(d &&& (e ^^^ f)) - 3 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 15 * ~~~(d ||| (e ||| f)) - 1 * ~~~(d ||| ( ~~~e ||| f)) - 8 * ~~~( ~~~d ||| (e ||| f)) + 6 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 1 * ( ~~~d &&& ( ~~~e &&& f)) + 22 * (d &&& ( ~~~e &&& f)) + 7 * (d &&& (e &&& f)) = - 2 * ( ~~~d ||| (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2158 (x y : BitVec w) : +theorem e_2158 : 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 3 * (f ^^^ (d &&& (e ||| f))) - 7 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 6 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 7 * ((d &&& e) ^^^ (e ||| ~~~f)) + 5 * (d ||| ~~~f) + 7 * (f ||| ~~~(d ^^^ e)) - 7 * (e ^^^ ~~~(d ||| ~~~f)) + 2 * (d ^^^ ( ~~~e ||| f)) - 1 * ((d &&& f) ||| ~~~(e ||| f)) + 3 * ~~~(d ||| (e &&& f)) + 2 * ~~~( ~~~d ||| (e &&& f)) + 3 * (f ||| ~~~(d ||| ~~~e)) - 2 * (e ^^^ ( ~~~d &&& (e ||| f))) - 1 * (e ^^^ (d &&& (e ^^^ f))) - 7 * ((d ||| e) &&& (e ^^^ f)) + 11 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 11 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 1 * ~~~( ~~~d &&& (e &&& f)) - 5 * ( ~~~e &&& (d ^^^ f)) + 1 * ((d &&& e) ||| ~~~(e ||| f)) + 2 * (f &&& (d ^^^ e)) + 3 * ~~~(d ||| ~~~e) - 1 * (e ^^^ (d ||| f)) + 11 * (d &&& (e ||| f)) + 5 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 2 * (f ^^^ ~~~(d &&& ~~~e)) + 1 * ~~~(d ^^^ e) - 6 * ( ~~~f &&& (d ^^^ e)) - 3 * (e ||| ~~~(d ||| f)) + 5 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 5 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 11 * (e &&& (d ^^^ f)) + 1 * (f ^^^ (d &&& ( ~~~e ||| f))) + 4 * ~~~(d &&& ~~~d) - 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 2 * d - 6 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 11 * (f ^^^ ( ~~~d ||| (e &&& f))) - 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 48 * ~~~(d ||| (e ||| f)) - 14 * ~~~(d ||| ( ~~~e ||| f)) + 1 * ~~~( ~~~d ||| (e ||| f)) - 24 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 40 * ( ~~~d &&& ( ~~~e &&& f)) - 43 * ( ~~~d &&& (e &&& f)) - 33 * (d &&& ( ~~~e &&& f)) - 21 * (d &&& (e &&& f)) = 1 * (e ||| ~~~(d ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2159 (x y : BitVec w) : +theorem e_2159 : - 2 * (e &&& ~~~(d ^^^ f)) + 1 * (e ^^^ ~~~(d ||| (e &&& f))) - 7 * ~~~(d ||| e) - 3 * (f ||| ~~~(d ^^^ e)) - 1 * (f ^^^ ~~~(d &&& (e &&& f))) + 11 * (e ^^^ (d &&& f)) - 11 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 3 * (e ^^^ (d &&& (e ||| f))) - 1 * ((d ^^^ e) &&& (d ^^^ f)) + 2 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 2 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 2 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 1 * ( ~~~f &&& (d ^^^ e)) + 2 * (d ||| ~~~e) + 3 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 6 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 5 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 2 * ~~~(d ^^^ f) + 4 * (e ^^^ (d ||| (e &&& f))) + 7 * ((d &&& e) ^^^ (e ||| f)) + 5 * ~~~(d ||| ~~~e) + 1 * (d &&& (e ||| f)) + 5 * ( ~~~d &&& (e ||| f)) + 1 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 6 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 11 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * ((d &&& e) ^^^ (e ||| ~~~f)) + 4 * ~~~(d ^^^ ( ~~~e ||| f)) - 3 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 1 * (f ^^^ (d ||| ( ~~~e ||| f))) + 5 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 1 * (d &&& (e ^^^ f)) + 4 * ( ~~~e &&& (d ^^^ f)) + 3 * ((d &&& f) ||| ~~~(e ||| f)) + 5 * ( ~~~d ||| ( ~~~e ||| f)) - 1 * (f ^^^ (d ||| ( ~~~e &&& f))) - 1 * ~~~(d ^^^ e) + 1 * ~~~(d &&& f) - 7 * ~~~f + 1 * (f &&& ~~~(d &&& e)) + 24 * ~~~(d ||| (e ||| f)) - 23 * ~~~(d ||| ( ~~~e ||| f)) - 3 * ~~~( ~~~d ||| (e ||| f)) + 10 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 12 * ( ~~~d &&& ( ~~~e &&& f)) - 14 * ( ~~~d &&& (e &&& f)) - 8 * (d &&& ( ~~~e &&& f)) - 16 * (d &&& (e &&& f)) = - 1 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 1 * (f &&& (d ||| ~~~e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2160 (x y : BitVec w) : +theorem e_2160 : - 1 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 7 * (e &&& (d ||| f)) + 5 * ~~~(d &&& (e ^^^ f)) + 4 * ((d ||| ~~~e) &&& (e ^^^ f)) + 3 * (e ^^^ ~~~(d &&& ~~~f)) + 2 * (f ^^^ ~~~(d &&& (e &&& f))) - 2 * ((d &&& f) ||| ~~~(e ||| f)) - 6 * (d &&& ~~~f) - 11 * ~~~(e ||| ~~~f) - 7 * (e &&& (d ^^^ f)) + 4 * ~~~(e ||| f) + 1 * ((d ||| e) &&& ~~~(e ^^^ f)) - 1 * e - 3 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 1 * (e ||| ~~~(d ^^^ f)) - 6 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 3 * (f &&& ~~~(d &&& e)) + 2 * ((e &&& f) ||| (d &&& (e ||| f))) - 2 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 2 * (e ^^^ (d &&& (e ||| f))) + 1 * (f ^^^ (d &&& ~~~e)) + 5 * (e &&& ~~~f) + 5 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 5 * (e ^^^ f) - 6 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 2 * (e ^^^ (d ||| f)) + 1 * ~~~(d &&& ~~~e) - 7 * ~~~e - 7 * ~~~(d ||| ~~~e) + 1 * ~~~(d ||| f) - 1 * (f &&& ~~~(d &&& ~~~e)) + 2 * (f &&& (d ||| ~~~e)) - 1 * (e ^^^ ~~~(d ||| ~~~f)) - 2 * (e ||| ~~~(d ||| f)) - 5 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 7 * (e ^^^ (d &&& (e ^^^ f))) - 11 * ~~~( ~~~d ||| (e &&& f)) + 4 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 11 * ~~~(d ||| (e ^^^ f)) - 5 * (f ||| (d ^^^ e)) + 1 * (d ^^^ e) - 1 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 4 * ~~~(d ||| (e ||| f)) + 15 * ~~~(d ||| ( ~~~e ||| f)) + 26 * ~~~( ~~~d ||| (e ||| f)) + 14 * ( ~~~d &&& ( ~~~e &&& f)) + 30 * (d &&& ( ~~~e &&& f)) - 13 * (d &&& (e &&& f)) = 1 * (e &&& ~~~(d &&& ~~~f)) - 14 * ~~~( ~~~d ||| ( ~~~e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2161 (x y : BitVec w) : +theorem e_2161 : - 1 * (e ^^^ (d ||| (e ^^^ f))) - 2 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 1 * (e &&& ~~~(d ^^^ f)) - 11 * ~~~(e &&& f) + 3 * ~~~(d &&& ~~~e) - 2 * (e ^^^ ~~~(d ||| ~~~f)) + 4 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 2 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 4 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 2 * ( ~~~d ||| (e ^^^ f)) + 1 * (d ||| (e &&& f)) - 1 * (e &&& (d ||| ~~~f)) - 7 * (f ^^^ ~~~(d &&& (e ||| f))) - 2 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 2 * ( ~~~d ||| ( ~~~e ||| f)) - 1 * (d ||| f) - 3 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 3 * (d &&& ( ~~~e ||| f)) - 1 * (e ||| (d &&& ~~~f)) + 11 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 5 * (f &&& ~~~(d &&& e)) - 11 * (d ||| ( ~~~e ||| f)) + 3 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 3 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 6 * (d ^^^ (e ||| f)) - 1 * ~~~(d ^^^ f) - 11 * ~~~(d ^^^ ( ~~~e ||| f)) + 11 * (e ^^^ (d &&& (e ^^^ f))) + 3 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * (d ^^^ ( ~~~e ||| f)) - 5 * ( ~~~e &&& ~~~(d ^^^ f)) - 7 * ((d &&& f) ||| ~~~(e ||| f)) + 1 * ( ~~~d ||| (e &&& f)) + 7 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 3 * ~~~(d ^^^ e) - 5 * ((e &&& f) ||| (d &&& (e ||| f))) + 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 2 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 2 * (f &&& ~~~(d &&& ~~~e)) - 2 * (d ^^^ (e ^^^ f)) + 16 * ~~~(d ||| (e ||| f)) + 19 * ~~~(d ||| ( ~~~e ||| f)) + 43 * ~~~( ~~~d ||| (e ||| f)) + 19 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 8 * ( ~~~d &&& ( ~~~e &&& f)) - 17 * ( ~~~d &&& (e &&& f)) + 38 * (d &&& ( ~~~e &&& f)) + 3 * (d &&& (e &&& f)) = - 2 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 5 * (e ^^^ ~~~(d &&& ~~~f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2162 (x y : BitVec w) : +theorem e_2162 : - 3 * (e &&& ~~~(d &&& f)) + 4 * ((d &&& e) ||| ~~~(e ^^^ f)) - 3 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 1 * (f ||| (d ^^^ e)) - 7 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 5 * ((d ||| e) &&& (e ^^^ f)) + 3 * ~~~(d ^^^ ( ~~~e &&& f)) - 7 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 11 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 2 * (d &&& f) - 1 * (f ^^^ ~~~(d &&& (e ||| f))) + 1 * ( ~~~d &&& ( ~~~e ||| f)) - 2 * ( ~~~d ||| ( ~~~e ||| f)) + 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 5 * (f ^^^ (d ||| (e ||| f))) + 5 * ~~~(d ||| f) + 2 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 5 * ~~~(d ||| e) + 1 * (e ^^^ (d &&& ~~~f)) + 11 * (e ^^^ (d ||| (e ||| f))) + 3 * ((e &&& f) ||| (d &&& (e ||| f))) - 3 * f - 2 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 1 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 7 * (d ||| f) + 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 11 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 2 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 1 * (d ||| ~~~e) + 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 5 * ( ~~~d ||| (e ^^^ f)) - 1 * ( ~~~f ||| ~~~(d ^^^ e)) - 5 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 7 * (f ^^^ ~~~(d ||| e)) - 6 * (f ^^^ (d ||| ~~~e)) - 3 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 2 * (f &&& (d ^^^ e)) + 2 * ~~~(e ||| f) + 11 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 1 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 3 * (d ||| ( ~~~e &&& f)) + 25 * ~~~(d ||| (e ||| f)) + 2 * ~~~(d ||| ( ~~~e ||| f)) - 4 * ~~~( ~~~d ||| (e ||| f)) + 5 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 5 * ( ~~~d &&& ( ~~~e &&& f)) - 15 * ( ~~~d &&& (e &&& f)) + 2 * (d &&& ( ~~~e &&& f)) - 11 * (d &&& (e &&& f)) = - 1 * ~~~( ~~~d ||| (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2163 (x y : BitVec w) : +theorem e_2163 : - 5 * ((d ^^^ e) &&& (d ^^^ f)) + 3 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 1 * (e ^^^ ~~~(d ||| ~~~f)) + 5 * ( ~~~f &&& ~~~(d ^^^ e)) + 1 * ((d &&& e) ||| ~~~(e ^^^ f)) - 7 * (e ^^^ f) - 1 * ((e &&& f) ||| (d &&& (e ||| f))) + 11 * (f ^^^ ~~~(d ||| ~~~e)) - 6 * (f ^^^ (d ||| (e &&& f))) + 2 * ( ~~~d ||| (e ^^^ f)) - 6 * ( ~~~e &&& (d ^^^ f)) + 7 * (e &&& ~~~f) - 11 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 3 * ~~~(d ||| (e ^^^ f)) + 11 * (d ^^^ (e &&& f)) + 3 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 2 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 1 * (e &&& (d ||| ~~~f)) + 1 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 1 * (e ^^^ ~~~(d ||| (e &&& f))) - 1 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 2 * (e ^^^ (d &&& f)) - 7 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 2 * ( ~~~d &&& (e ^^^ f)) + 1 * (e ^^^ ( ~~~d ||| (e &&& f))) + 7 * ~~~(d ^^^ (e ^^^ f)) + 5 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 6 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 2 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 1 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 2 * ( ~~~e &&& ~~~(d ^^^ f)) - 2 * ~~~(d ^^^ (e ||| f)) + 5 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 1 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 1 * (f ^^^ ~~~(d &&& (e &&& f))) - 7 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 2 * (e ||| ~~~f) - 5 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 3 * (e ||| ~~~(d ||| ~~~f)) - 1 * (f &&& ~~~(d ^^^ e)) - 5 * ~~~(d ||| (e ||| f)) - 2 * ~~~(d ||| ( ~~~e ||| f)) + 13 * ~~~( ~~~d ||| (e ||| f)) - 12 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 9 * ( ~~~d &&& ( ~~~e &&& f)) + 2 * ( ~~~d &&& (e &&& f)) - 25 * (d &&& ( ~~~e &&& f)) + 4 * (d &&& (e &&& f)) = - 7 * ~~~( ~~~d &&& (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2164 (x y : BitVec w) : +theorem e_2164 : - 1 * ( ~~~e ||| (d ^^^ f)) + 11 * ((d ||| e) &&& (e ^^^ f)) - 3 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 2 * ( ~~~f &&& (d ^^^ e)) + 5 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 7 * (d ||| (e ^^^ f)) + 3 * (f ^^^ (d ||| ~~~e)) - 11 * (f ^^^ ~~~(d ||| ~~~e)) - 1 * (e ^^^ (d &&& ~~~f)) + 5 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 5 * ~~~(d ^^^ (e ||| f)) - 7 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 3 * (e ^^^ ~~~(d ||| f)) + 11 * ((e &&& f) ||| (d &&& (e ||| f))) - 3 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 11 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 5 * (f ^^^ ~~~(d ||| (e &&& f))) - 6 * ~~~(d ^^^ ( ~~~e &&& f)) + 1 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 4 * (f &&& (d ||| ~~~e)) + 1 * (e ^^^ ( ~~~d ||| (e &&& f))) - 5 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 2 * (f ||| (d ^^^ e)) - 1 * ~~~(d ||| ( ~~~e &&& f)) + 1 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 6 * ( ~~~d ||| (e ^^^ f)) + 2 * (e ^^^ (d &&& ( ~~~e ||| f))) - 6 * ~~~( ~~~d &&& (e ^^^ f)) - 2 * ~~~(d ^^^ ( ~~~e ||| f)) - 2 * ~~~(d ^^^ (e &&& f)) - 11 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 4 * ~~~(d ||| ~~~e) - 3 * (f ^^^ (d ||| e)) + 5 * (d ^^^ (e &&& f)) + 3 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 7 * (d ^^^ e) - 2 * ~~~( ~~~d &&& (e &&& f)) + 1 * ((d &&& f) ||| (e &&& ~~~f)) - 2 * (f ||| ~~~(d ||| e)) - 1 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 5 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 32 * ~~~(d ||| (e ||| f)) + 21 * ~~~(d ||| ( ~~~e ||| f)) + 15 * ~~~( ~~~d ||| (e ||| f)) - 19 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 38 * ( ~~~d &&& ( ~~~e &&& f)) + 18 * ( ~~~d &&& (e &&& f)) + 24 * (d &&& ( ~~~e &&& f)) + 8 * (d &&& (e &&& f)) = 7 * ( ~~~e &&& ~~~(d ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2165 (x y : BitVec w) : +theorem e_2165 : 7 * (e ^^^ ~~~(d &&& (e &&& f))) - 2 * ~~~(d ^^^ (e ||| f)) - 1 * (d ^^^ f) - 7 * (d ||| (e &&& f)) + 5 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 11 * ~~~(d ||| ( ~~~e &&& f)) - 7 * ~~~d + 4 * (e ^^^ ~~~(d &&& f)) + 1 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 3 * ( ~~~d &&& (e ^^^ f)) + 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 11 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 1 * (f ^^^ (d ||| ( ~~~e ||| f))) - 2 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 2 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 3 * (f ^^^ ~~~(d ||| e)) + 4 * ~~~(d ||| ~~~f) - 3 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 1 * ~~~f - 2 * ~~~(d &&& ~~~e) + 5 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 2 * (e ^^^ ( ~~~d ||| (e &&& f))) - 5 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * (e ^^^ (d ||| ~~~f)) - 7 * (e ^^^ (d &&& (e ^^^ f))) - 2 * (e ^^^ ~~~(d &&& (e ||| f))) + 5 * (e ^^^ (d ||| (e ^^^ f))) + 1 * ~~~(d ^^^ e) + 5 * ~~~(d &&& ( ~~~e ||| f)) + 7 * (d &&& ( ~~~e ||| f)) + 2 * (f ^^^ ( ~~~d &&& (e ||| f))) - 1 * (d &&& (e ||| f)) + 2 * (e &&& f) + 7 * (e ^^^ ~~~(d &&& ~~~f)) - 6 * (f ^^^ (d &&& ~~~e)) + 1 * (e ^^^ (d ||| ( ~~~e ||| f))) - 11 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 3 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 3 * ( ~~~e ||| (d ^^^ f)) - 3 * (f ||| ~~~(d ^^^ e)) - 3 * ~~~(d ||| f) + 5 * ~~~(d ||| (e ||| f)) + 2 * ~~~(d ||| ( ~~~e ||| f)) + 10 * ~~~( ~~~d ||| (e ||| f)) + 21 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 9 * ( ~~~d &&& ( ~~~e &&& f)) + 9 * ( ~~~d &&& (e &&& f)) + 7 * (d &&& ( ~~~e &&& f)) + 24 * (d &&& (e &&& f)) = - 1 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2166 (x y : BitVec w) : +theorem e_2166 : - 6 * (f &&& (d ^^^ e)) + 11 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 1 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 2 * (d ||| ~~~e) + 11 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 6 * ~~~(d ^^^ (e ||| f)) - 7 * ( ~~~d ||| ( ~~~e &&& f)) - 2 * ( ~~~e &&& ~~~(d ^^^ f)) + 7 * (d &&& ( ~~~e ||| f)) + 1 * (f ^^^ ( ~~~d ||| (e &&& f))) + 5 * ( ~~~f ||| ~~~(d ^^^ e)) - 2 * ~~~(d &&& ( ~~~e ||| f)) + 2 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 2 * ~~~(e ||| ~~~f) - 5 * (e ^^^ ( ~~~d &&& (e ||| f))) - 2 * ~~~( ~~~d ||| (e ^^^ f)) - 7 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 2 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 1 * (d ||| ~~~f) + 2 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 4 * ~~~(d &&& f) - 11 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 4 * ((d &&& e) ||| (e ^^^ f)) + 3 * (e ^^^ (d ||| f)) + 7 * (e ^^^ (d ||| (e &&& f))) - 11 * (f ^^^ ~~~(d &&& e)) - 5 * (f ^^^ ( ~~~d &&& (e ||| f))) + 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 1 * ((d &&& e) ^^^ (e ||| ~~~f)) + 7 * ( ~~~d &&& ( ~~~e ||| f)) + 2 * ((d ^^^ e) ||| (d ^^^ f)) + 4 * ~~~(d &&& e) + 1 * ( ~~~d ||| (e ^^^ f)) - 2 * (e ^^^ ~~~(d ||| (e &&& f))) + 7 * (f ^^^ (d ||| e)) + 2 * f - 6 * (e ||| (d ^^^ f)) + 1 * (e &&& ~~~f) - 1 * ~~~(d &&& (e &&& f)) - 2 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 7 * (f ||| ~~~(d ||| e)) + 7 * ~~~(d ||| (e ||| f)) + 1 * ~~~(d ||| ( ~~~e ||| f)) - 16 * ~~~( ~~~d ||| (e ||| f)) + 10 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 8 * ( ~~~d &&& ( ~~~e &&& f)) + 19 * ( ~~~d &&& (e &&& f)) + 17 * (d &&& ( ~~~e &&& f)) + 9 * (d &&& (e &&& f)) = 7 * (d ^^^ ( ~~~e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2167 (x y : BitVec w) : +theorem e_2167 : - 2 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 3 * (f ^^^ (d ||| ( ~~~e &&& f))) - 1 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 7 * f + 4 * ((d ||| e) &&& ~~~(e ^^^ f)) - 1 * (e &&& (d ^^^ f)) - 1 * ~~~(e ^^^ f) + 4 * (f ^^^ ~~~(d &&& (e ||| f))) - 2 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 5 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 1 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 2 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 2 * (e ||| ~~~(d ^^^ f)) - 6 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 11 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 6 * ~~~( ~~~d &&& (e ^^^ f)) - 1 * (f ||| (d &&& ~~~e)) - 1 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 4 * ((d &&& f) ||| ~~~(e ||| f)) + 1 * (e &&& ~~~(d &&& ~~~f)) - 7 * ( ~~~f &&& ~~~(d ^^^ e)) - 7 * (e ^^^ (d ||| ( ~~~e ||| f))) + 1 * ( ~~~f &&& (d ^^^ e)) + 3 * (e ^^^ (d &&& (e ||| f))) + 5 * ~~~( ~~~d ||| (e &&& f)) - 2 * ( ~~~f ||| ~~~(d ^^^ e)) + 11 * (f ^^^ ~~~(d ||| ~~~e)) + 11 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 2 * ~~~(d ^^^ (e &&& f)) - 5 * (d &&& e) - 1 * ~~~(d &&& (e ||| f)) + 1 * (f &&& ~~~(d &&& e)) + 2 * (f &&& ~~~(d ^^^ e)) + 1 * (e ^^^ (d ||| f)) - 6 * ~~~(d &&& (e ^^^ f)) - 2 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (e &&& f) + 5 * ~~~(d ^^^ f) + 1 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 11 * (e ^^^ (d ||| (e &&& f))) + 7 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 13 * ~~~(d ||| (e ||| f)) - 18 * ~~~(d ||| ( ~~~e ||| f)) + 1 * ~~~( ~~~d ||| (e ||| f)) + 26 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 7 * ( ~~~d &&& ( ~~~e &&& f)) - 2 * ( ~~~d &&& (e &&& f)) - 51 * (d &&& ( ~~~e &&& f)) - 17 * (d &&& (e &&& f)) = 1 * (d &&& ~~~f) - 2 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2168 (x y : BitVec w) : +theorem e_2168 : - 2 * ((d ||| e) &&& ~~~(e ^^^ f)) - 1 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 7 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 11 * ( ~~~f &&& (d ^^^ e)) + 4 * ~~~(e ^^^ f) + 2 * (f ^^^ (d &&& (e ||| f))) - 2 * (e ^^^ ( ~~~d ||| (e &&& f))) - 7 * ( ~~~d ||| (e ^^^ f)) + 3 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 5 * ~~~(d ^^^ f) + 11 * (e &&& ~~~(d ^^^ f)) + 11 * (f ^^^ ( ~~~d ||| (e ||| f))) + 3 * ( ~~~e ||| (d ^^^ f)) + 1 * (e ^^^ (d &&& ( ~~~e ||| f))) + 2 * (f ^^^ (d ||| ( ~~~e &&& f))) + 7 * (f ^^^ ~~~(d ||| e)) - 1 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 7 * (e ^^^ ~~~(d ||| (e &&& f))) - 1 * (e ||| (d &&& ~~~f)) + 1 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 1 * (e ||| f) + 1 * ((d &&& f) ||| ~~~(e ||| f)) - 1 * (d ^^^ (e &&& f)) - 3 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 1 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 5 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 3 * (f ^^^ ( ~~~d ||| (e &&& f))) - 6 * (e ^^^ ~~~(d &&& f)) + 4 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 1 * ( ~~~d &&& (e ^^^ f)) + 1 * ~~~(d &&& e) + 4 * ~~~f + 1 * ( ~~~f &&& ~~~(d ^^^ e)) - 11 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 5 * ((d ||| ~~~e) &&& (e ^^^ f)) - 3 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 1 * ~~~( ~~~d ||| (e &&& f)) + 7 * (f &&& (d ^^^ e)) - 43 * ~~~(d ||| (e ||| f)) - 28 * ~~~(d ||| ( ~~~e ||| f)) + 7 * ~~~( ~~~d ||| (e ||| f)) - 2 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 17 * ( ~~~d &&& ( ~~~e &&& f)) - 4 * ( ~~~d &&& (e &&& f)) - 10 * (d &&& ( ~~~e &&& f)) - 25 * (d &&& (e &&& f)) = 1 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 3 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2169 (x y : BitVec w) : +theorem e_2169 : - 5 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 1 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 11 * (d ^^^ e) + 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 1 * (e ^^^ (d ||| ( ~~~e ||| f))) - 7 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 7 * (f ^^^ ~~~(d ||| ~~~e)) + 1 * ~~~(d &&& (e ^^^ f)) - 1 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 3 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 1 * (e ^^^ (d &&& (e ||| f))) + 5 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 2 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 5 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 2 * ~~~(d ^^^ (e ^^^ f)) + 2 * (f ||| (d ^^^ e)) - 3 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 1 * (f ^^^ ~~~(d &&& e)) - 11 * (e ^^^ (d &&& f)) - 11 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 4 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 1 * e - 1 * (e &&& (d ||| f)) + 2 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 1 * ( ~~~f ||| ~~~(d ^^^ e)) - 2 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 1 * ~~~(d &&& ( ~~~e &&& f)) + 1 * ~~~f + 11 * ( ~~~d &&& (e ||| f)) - 3 * (f ^^^ (d &&& (e ||| f))) + 4 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 11 * ~~~(d &&& f) - 11 * (f &&& ~~~(d &&& e)) + 1 * (e ^^^ ~~~(d &&& (e &&& f))) + 1 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 1 * (d ^^^ f) - 7 * (e &&& ~~~(d ^^^ f)) + 3 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 7 * ~~~(d ||| f) + 1 * (d &&& (e ||| f)) + 12 * ~~~(d ||| (e ||| f)) - 2 * ~~~(d ||| ( ~~~e ||| f)) - 22 * ~~~( ~~~d ||| (e ||| f)) + 42 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 5 * ( ~~~d &&& ( ~~~e &&& f)) - 4 * (d &&& ( ~~~e &&& f)) - 3 * (d &&& (e &&& f)) = - 3 * ~~~(e ^^^ f) - 22 * ( ~~~d &&& (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2170 (x y : BitVec w) : +theorem e_2170 : - 2 * (f &&& ~~~(d &&& ~~~e)) - 1 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 3 * (d &&& e) + 1 * (f &&& (d ^^^ e)) - 11 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 2 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 5 * ~~~(d ||| ~~~e) + 4 * ((d &&& e) ^^^ (e ||| ~~~f)) - 3 * (f ^^^ (d ||| ( ~~~e &&& f))) - 2 * ~~~d - 5 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 1 * (d ||| ( ~~~e ||| f)) - 1 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 7 * (e ^^^ ~~~(d &&& (e ||| f))) - 7 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 11 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 4 * (f ^^^ (d ||| e)) + 1 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 3 * (f ^^^ (d ||| (e ||| f))) - 11 * (f ^^^ (d &&& e)) + 11 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 7 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 2 * (f ^^^ (d &&& ( ~~~e ||| f))) + 5 * ~~~( ~~~d &&& (e &&& f)) - 11 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 4 * (d &&& (e ||| f)) - 11 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * e + 7 * ~~~(d ^^^ (e &&& f)) + 1 * (f ||| ~~~(d ^^^ e)) + 5 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 2 * ~~~( ~~~d &&& (e ^^^ f)) - 1 * ((d ||| e) &&& ~~~(e ^^^ f)) + 2 * (d ||| ~~~e) - 6 * (d &&& (e ^^^ f)) - 2 * ((d &&& f) ||| (e &&& ~~~f)) - 3 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 1 * ~~~(d &&& ~~~e) + 11 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 2 * ~~~(d &&& ( ~~~e ||| f)) - 3 * ~~~(d ||| ~~~f) - 3 * ~~~(d ||| (e ||| f)) - 16 * ~~~(d ||| ( ~~~e ||| f)) + 24 * ~~~( ~~~d ||| (e ||| f)) - 2 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 1 * ( ~~~d &&& ( ~~~e &&& f)) - 3 * ( ~~~d &&& (e &&& f)) + 18 * (d &&& ( ~~~e &&& f)) = 27 * (d &&& (e &&& f)) + 1 * ((d &&& e) ||| ~~~(e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2171 (x y : BitVec w) : +theorem e_2171 : 3 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 1 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 11 * ~~~( ~~~d ||| (e &&& f)) + 7 * ((d ^^^ e) ||| ~~~(d ^^^ f)) + 4 * (e ^^^ ~~~(d &&& ~~~f)) - 11 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 11 * (f ^^^ (d ||| e)) + 3 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 2 * ~~~(d &&& ~~~d) - 3 * ~~~(e &&& ~~~f) + 1 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 2 * (d &&& (e ^^^ f)) + 4 * (e ^^^ (d ||| ( ~~~e ||| f))) - 1 * (d ||| (e ^^^ f)) + 7 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 2 * (f &&& ~~~(d ^^^ e)) + 1 * ~~~(d &&& ~~~e) - 1 * (d ||| ( ~~~e &&& f)) + 3 * (e ^^^ f) - 1 * (e ||| (d &&& f)) - 7 * (d ^^^ (e ^^^ f)) - 6 * ( ~~~d ||| ( ~~~e &&& f)) - 2 * (e ^^^ ( ~~~d ||| (e &&& f))) - 1 * (f &&& (d ^^^ e)) - 5 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 2 * (f ^^^ ( ~~~d &&& (e ||| f))) - 2 * (f ^^^ ~~~(d &&& e)) - 1 * (e &&& (d ||| f)) - 3 * (f ^^^ (d ||| (e ||| f))) + 11 * (d ^^^ e) + 11 * ( ~~~d ||| (e &&& f)) + 1 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 11 * (e &&& ~~~(d &&& ~~~f)) - 6 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 4 * ((d ^^^ e) ||| (d ^^^ f)) - 6 * ~~~(d ^^^ f) - 6 * (f &&& ~~~(d &&& ~~~e)) + 3 * ~~~(d &&& e) - 3 * (f ^^^ ~~~(d &&& (e &&& f))) - 1 * (f ^^^ ( ~~~d ||| (e &&& f))) - 11 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 1 * ~~~(d ||| (e ||| f)) - 15 * ~~~(d ||| ( ~~~e ||| f)) - 14 * ~~~( ~~~d ||| (e ||| f)) - 17 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 6 * ( ~~~d &&& ( ~~~e &&& f)) - 19 * (d &&& ( ~~~e &&& f)) + 19 * (d &&& (e &&& f)) = 6 * ~~~(e ^^^ f) - 2 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2172 (x y : BitVec w) : +theorem e_2172 : - 1 * (e ^^^ (d &&& (e ||| f))) + 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 1 * ((d &&& e) ||| ~~~(e ||| f)) - 3 * ((d ||| ~~~e) &&& (e ^^^ f)) + 5 * (f ^^^ ~~~(d ||| ~~~e)) - 2 * ( ~~~d ||| ( ~~~e ||| f)) - 7 * ~~~(d ||| f) - 6 * (d ||| ( ~~~e &&& f)) - 7 * ~~~(d ^^^ f) - 5 * (e ||| (d &&& f)) - 2 * ((d &&& f) ||| (e &&& ~~~f)) + 2 * ((d &&& e) ||| ~~~(e ^^^ f)) - 11 * ( ~~~d &&& (e ||| f)) + 1 * (d &&& ( ~~~e ||| f)) + 1 * (e ^^^ (d &&& ~~~f)) - 6 * (e ||| f) - 1 * ( ~~~e ||| (d ^^^ f)) + 4 * (f ^^^ (d &&& (e ||| f))) - 1 * (d ^^^ (e ^^^ f)) - 2 * (e ^^^ f) - 3 * ~~~(d ||| (e &&& f)) + 1 * ~~~(e ||| ~~~f) + 1 * (d ||| (e &&& f)) - 1 * (f ^^^ (d ||| (e ||| f))) - 1 * (e &&& ~~~(d &&& f)) + 7 * (f ^^^ (d &&& ~~~e)) + 2 * ~~~(d ||| (e ^^^ f)) - 1 * (f ^^^ ~~~(d &&& ~~~e)) + 1 * ((d ^^^ e) ||| (d ^^^ f)) + 1 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 1 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 11 * d + 4 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (f &&& (d ||| e)) - 2 * (e ^^^ ( ~~~d ||| (e ||| f))) - 1 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 5 * ( ~~~e &&& ~~~(d ^^^ f)) + 2 * (e ^^^ (d ||| ( ~~~e ||| f))) - 11 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 1 * (e ^^^ (d &&& (e ^^^ f))) - 2 * ~~~(d ^^^ (e ||| f)) + 20 * ~~~(d ||| (e ||| f)) + 33 * ~~~(d ||| ( ~~~e ||| f)) + 18 * ~~~( ~~~d ||| (e ||| f)) + 41 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 29 * ( ~~~d &&& ( ~~~e &&& f)) + 14 * ( ~~~d &&& (e &&& f)) + 38 * (d &&& ( ~~~e &&& f)) + 35 * (d &&& (e &&& f)) = - 1 * (f ^^^ ( ~~~d ||| (e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2173 (x y : BitVec w) : +theorem e_2173 : 2 * (e ||| ~~~f) + 3 * (f &&& (d ^^^ e)) + 1 * ~~~f - 1 * (f ^^^ (d ||| e)) + 5 * ~~~( ~~~d ||| (e &&& f)) + 7 * (d ||| (e ||| f)) + 2 * (e ^^^ f) + 1 * ((e &&& f) ||| (d &&& (e ||| f))) + 5 * (e ^^^ (d ||| ~~~f)) + 2 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 7 * ((d ^^^ e) ||| (d ^^^ f)) + 1 * (e ^^^ (d ||| ( ~~~e &&& f))) + 1 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 11 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 3 * (f ||| ~~~(d ||| e)) - 1 * ( ~~~e ||| (d ^^^ f)) + 11 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 11 * ((d &&& e) ||| ~~~(e ^^^ f)) + 2 * (d ||| f) - 1 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 5 * (e ||| ~~~(d ||| f)) - 6 * (e ^^^ ~~~(d &&& (e ||| f))) + 4 * ~~~(d &&& ( ~~~e &&& f)) + 5 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 6 * (f ^^^ ~~~(d ||| ~~~e)) + 7 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 11 * ~~~(d ||| ~~~e) + 4 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 5 * (d ^^^ (e ^^^ f)) - 5 * (f ^^^ (d ||| ( ~~~e ||| f))) + 2 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 2 * ( ~~~f ||| (d ^^^ e)) + 1 * (f ^^^ ~~~(d &&& (e ||| f))) - 1 * (e &&& ~~~(d &&& f)) + 3 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 3 * (f ^^^ (d ||| ( ~~~e &&& f))) - 2 * (e ^^^ ( ~~~d ||| (e &&& f))) - 3 * ~~~(d &&& ~~~d) - 6 * (e ^^^ (d &&& f)) - 1 * (f ^^^ ( ~~~d &&& (e ||| f))) - 2 * (f &&& ~~~(d &&& e)) - 5 * (f &&& (d ||| e)) - 18 * ~~~(d ||| (e ||| f)) - 7 * ~~~(d ||| ( ~~~e ||| f)) - 28 * ~~~( ~~~d ||| (e ||| f)) - 26 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 13 * ( ~~~d &&& ( ~~~e &&& f)) - 34 * (d &&& ( ~~~e &&& f)) + 11 * (d &&& (e &&& f)) = - 4 * (e ^^^ ~~~(d &&& ~~~f)) + 11 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2174 (x y : BitVec w) : +theorem e_2174 : 2 * (e ^^^ (d &&& ~~~f)) - 1 * (f ^^^ (d &&& e)) + 2 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * ~~~(d &&& (e ||| f)) + 3 * (e ^^^ (d ||| ( ~~~e ||| f))) + 7 * (f ^^^ (d ||| (e ||| f))) - 1 * (e ||| (d ^^^ f)) + 1 * (f ||| (d &&& ~~~e)) + 1 * (e &&& (d ^^^ f)) - 1 * ~~~(d ^^^ ( ~~~e ||| f)) - 6 * (f ^^^ (d ||| e)) + 1 * (e ||| f) + 7 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 3 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 5 * ( ~~~e &&& ~~~(d ^^^ f)) + 1 * ~~~(e ^^^ f) + 2 * ~~~(e &&& ~~~f) - 1 * (d ^^^ (e &&& f)) - 5 * (d ^^^ (e ||| f)) - 7 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 4 * (e ^^^ ~~~(d &&& (e &&& f))) - 2 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 11 * ( ~~~d ||| ( ~~~e &&& f)) + 1 * ( ~~~f ||| (d ^^^ e)) - 1 * (d &&& f) + 3 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * ~~~(d ||| (e &&& f)) - 5 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 4 * (f &&& (d ||| ~~~e)) + 1 * (d &&& ( ~~~e ||| f)) - 2 * (e ^^^ ( ~~~d ||| (e ||| f))) - 7 * ~~~(d ^^^ (e ||| f)) - 11 * ~~~(d ||| (e ^^^ f)) - 6 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 1 * (f ||| (d &&& e)) + 2 * (e ^^^ ~~~(d &&& ~~~f)) - 3 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 2 * (e ^^^ (d ||| (e ||| f))) - 1 * (e ||| ~~~(d ||| ~~~f)) - 11 * ~~~(d &&& ( ~~~e ||| f)) + 1 * f + 11 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 4 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 23 * ~~~(d ||| (e ||| f)) + 18 * ~~~(d ||| ( ~~~e ||| f)) + 23 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 9 * ( ~~~d &&& ( ~~~e &&& f)) + 39 * ( ~~~d &&& (e &&& f)) - 21 * (d &&& ( ~~~e &&& f)) - 8 * (d &&& (e &&& f)) = 3 * ~~~( ~~~d &&& (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2175 (x y : BitVec w) : +theorem e_2175 : - 3 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 7 * (d ||| ( ~~~e &&& f)) + 2 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 1 * ~~~(d &&& f) + 3 * (e ^^^ ( ~~~d ||| (e &&& f))) - 3 * (e ^^^ ~~~(d ||| (e &&& f))) - 7 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 1 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 7 * (e ||| ~~~f) + 11 * ~~~(d ||| ( ~~~e &&& f)) - 1 * (d ||| (e &&& f)) - 3 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 1 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 5 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 3 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 7 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 11 * (e ||| (d &&& ~~~f)) + 5 * ((d ||| e) &&& (e ^^^ f)) + 3 * ~~~( ~~~d ||| (e &&& f)) + 1 * (e ||| ~~~(d ||| ~~~f)) + 1 * ( ~~~e ||| ~~~(d ^^^ f)) - 2 * (e ^^^ f) - 3 * ~~~(d ^^^ ( ~~~e ||| f)) - 1 * (f ^^^ (d ||| (e ||| f))) + 2 * (e ^^^ (d &&& ( ~~~e ||| f))) + 3 * (e &&& (d ||| ~~~f)) + 2 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 6 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 2 * ~~~(d ||| (e &&& f)) + 2 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 7 * (f ^^^ ~~~(d &&& (e &&& f))) - 2 * (e ||| ~~~(d ^^^ f)) - 1 * ((d &&& f) ^^^ (e ||| f)) + 1 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 11 * ~~~(e ||| ~~~f) - 5 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 2 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 5 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 2 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 11 * (f ^^^ ~~~(d &&& (e ||| f))) + 4 * ( ~~~d ||| (e ^^^ f)) - 5 * ~~~(d ||| (e ||| f)) + 16 * ~~~(d ||| ( ~~~e ||| f)) + 17 * ~~~( ~~~d ||| (e ||| f)) + 21 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 10 * ( ~~~d &&& ( ~~~e &&& f)) + 20 * ( ~~~d &&& (e &&& f)) - 1 * (d &&& ( ~~~e &&& f)) + 19 * (d &&& (e &&& f)) = 11 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2176 (x y : BitVec w) : +theorem e_2176 : - 1 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 5 * (d ||| ~~~f) + 1 * ((d ^^^ e) &&& (d ^^^ f)) + 7 * ~~~(d &&& ~~~f) + 11 * ~~~(d &&& (e &&& f)) - 1 * (e &&& ~~~(d &&& f)) + 7 * (e ^^^ f) - 1 * (f ||| ~~~(d ^^^ e)) + 1 * (f ^^^ (d &&& e)) + 5 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 2 * (f ^^^ (d &&& ~~~e)) - 1 * (f ^^^ (d &&& ( ~~~e ||| f))) - 11 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (d &&& ~~~f) - 7 * ( ~~~f &&& ~~~(d ^^^ e)) + 2 * (e ^^^ (d ||| (e ||| f))) + 1 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 1 * (d ||| ( ~~~e &&& f)) + 1 * (e &&& (d ||| ~~~f)) + 2 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * ~~~(e ||| f) - 6 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 5 * ~~~(d ||| ~~~f) + 3 * ~~~(d ^^^ (e ^^^ f)) - 1 * (f ^^^ ~~~(d ||| e)) - 1 * ~~~(d ^^^ (e &&& f)) - 11 * (f ||| (d &&& ~~~e)) + 2 * ( ~~~e &&& (d ^^^ f)) - 5 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 2 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 1 * ~~~( ~~~d &&& (e ^^^ f)) - 1 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 11 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 1 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 3 * (e ^^^ ( ~~~d &&& (e ||| f))) + 4 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 1 * (e ^^^ (d &&& ( ~~~e ||| f))) + 7 * ((d &&& ~~~e) ||| (e ^^^ f)) + 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 6 * (f ^^^ ~~~(d &&& (e ||| f))) + 19 * ~~~(d ||| (e ||| f)) - 11 * ~~~(d ||| ( ~~~e ||| f)) + 3 * ~~~( ~~~d ||| (e ||| f)) + 12 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 31 * ( ~~~d &&& ( ~~~e &&& f)) + 16 * ( ~~~d &&& (e &&& f)) + 11 * (d &&& ( ~~~e &&& f)) + 41 * (d &&& (e &&& f)) = 1 * (d ||| (e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2177 (x y : BitVec w) : +theorem e_2177 : 5 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 3 * (e ^^^ (d &&& ~~~f)) - 11 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 1 * ((d ||| ~~~e) &&& (e ^^^ f)) + 1 * (d ||| ~~~e) + 2 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 1 * (f ^^^ (d ||| (e &&& f))) + 7 * ((d &&& ~~~e) ||| (e ^^^ f)) + 1 * ~~~( ~~~d &&& (e ||| f)) + 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 3 * ~~~d + 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 1 * ( ~~~d &&& (e ^^^ f)) + 5 * ((d &&& f) ||| ~~~(e ||| f)) + 4 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 11 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 1 * ( ~~~e ||| ~~~(d ^^^ f)) - 7 * (e ^^^ ( ~~~d &&& (e ||| f))) + 1 * ~~~(d ^^^ e) - 6 * (f ^^^ ~~~(d ||| e)) - 2 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 7 * (f &&& (d ||| ~~~e)) + 2 * (f ||| ~~~(d ||| e)) - 3 * ~~~(d ||| (e &&& f)) - 2 * (e ^^^ (d &&& (e ||| f))) - 2 * ~~~(d ^^^ (e ||| f)) + 11 * (f ^^^ ~~~(d &&& (e &&& f))) + 2 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 2 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 1 * ~~~(d &&& ( ~~~e &&& f)) + 2 * ~~~f + 3 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 2 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 3 * (e ^^^ (d &&& ( ~~~e ||| f))) + 2 * (e ||| ~~~(d ||| f)) - 5 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 11 * (e ^^^ ~~~(d &&& f)) + 1 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 6 * (d ^^^ e) - 7 * (d &&& f) + 11 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 3 * (d ^^^ (e ^^^ f)) - 1 * ~~~(d ||| f) - 6 * d - 25 * ~~~(d ||| ( ~~~e ||| f)) + 1 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 16 * ( ~~~d &&& ( ~~~e &&& f)) + 2 * ( ~~~d &&& (e &&& f)) + 7 * (d &&& ( ~~~e &&& f)) + 15 * (d &&& (e &&& f)) = 23 * ~~~( ~~~d ||| (e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2178 (x y : BitVec w) : +theorem e_2178 : 2 * (f &&& ~~~(d ^^^ e)) - 6 * ( ~~~f &&& ~~~(d ^^^ e)) + 7 * ((d &&& e) ||| ~~~(e ^^^ f)) - 3 * (f ^^^ (d &&& ( ~~~e ||| f))) + 2 * ( ~~~d &&& (e ||| f)) + 2 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 5 * ( ~~~d &&& ( ~~~e ||| f)) - 1 * (d ^^^ (e ^^^ f)) - 2 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 4 * ~~~(d ||| f) + 2 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 1 * e + 1 * (e ^^^ ~~~(d ||| ~~~f)) + 2 * ((d ^^^ e) &&& (d ^^^ f)) + 4 * (d ||| ( ~~~e ||| f)) - 7 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 5 * (d ||| ~~~f) + 1 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 1 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 1 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 2 * (f ^^^ (d &&& ~~~e)) - 1 * ( ~~~e ||| ~~~(d ^^^ f)) + 7 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 11 * ((d ||| e) &&& (e ^^^ f)) + 2 * (e ^^^ (d ||| (e ^^^ f))) - 2 * (f &&& (d ||| ~~~e)) + 1 * (e ^^^ (d ||| f)) + 4 * (d ||| f) - 1 * (d &&& ( ~~~e ||| f)) - 1 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 3 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 2 * (d ^^^ f) + 5 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 11 * (e &&& ~~~f) - 2 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 1 * (e &&& f) - 1 * ~~~(d ^^^ ( ~~~e ||| f)) - 6 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 6 * (f ^^^ ~~~(d ||| (e &&& f))) - 3 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 5 * (f ^^^ (d ||| ( ~~~e &&& f))) + 7 * (d ^^^ ( ~~~e ||| f)) + 11 * ~~~(d ||| (e ||| f)) + 23 * ~~~(d ||| ( ~~~e ||| f)) - 7 * ~~~( ~~~d ||| (e ||| f)) + 7 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 16 * ( ~~~d &&& ( ~~~e &&& f)) - 11 * ( ~~~d &&& (e &&& f)) + 35 * (d &&& ( ~~~e &&& f)) + 2 * (d &&& (e &&& f)) = - 3 * (f ^^^ (d ||| (e ||| f))) + 1 * ((d ||| ~~~e) &&& (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2179 (x y : BitVec w) : +theorem e_2179 : 2 * (f ^^^ ( ~~~d ||| (e ||| f))) + 5 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 1 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 1 * (f ^^^ ~~~(d &&& e)) - 11 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 6 * (f ^^^ (d &&& e)) + 7 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 1 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 7 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 1 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 11 * (d ^^^ e) + 11 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 3 * ~~~(e ^^^ f) - 2 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 2 * (f ||| ~~~(d ^^^ e)) + 11 * (d ||| (e &&& f)) - 6 * ~~~(e ||| f) - 2 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 11 * (d ^^^ (e ||| f)) + 1 * (f &&& (d ^^^ e)) + 4 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 2 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 11 * (e ^^^ (d &&& (e ^^^ f))) - 1 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 2 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 2 * (f ^^^ ( ~~~d &&& (e ||| f))) + 7 * ((d &&& ~~~e) ||| (e ^^^ f)) - 5 * ~~~(d ^^^ f) + 7 * (f ^^^ (d &&& ~~~e)) + 4 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 4 * ~~~(d &&& (e ^^^ f)) - 5 * ~~~(d &&& (e &&& f)) - 7 * (d ||| f) + 2 * (f &&& ~~~(d &&& ~~~e)) - 11 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 3 * (f &&& (d ||| e)) + 1 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 3 * ((d &&& e) ^^^ (e ||| ~~~f)) - 3 * ~~~( ~~~d ||| (e ^^^ f)) + 1 * ~~~(d &&& ~~~e) + 11 * ( ~~~e &&& (d ^^^ f)) + 1 * ( ~~~d ||| ( ~~~e ||| f)) + 5 * ~~~(d ||| (e ||| f)) - 8 * ~~~(d ||| ( ~~~e ||| f)) - 57 * ~~~( ~~~d ||| (e ||| f)) - 11 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 9 * ( ~~~d &&& ( ~~~e &&& f)) - 27 * ( ~~~d &&& (e &&& f)) + 13 * (d &&& ( ~~~e &&& f)) + 20 * (d &&& (e &&& f)) = - 1 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2180 (x y : BitVec w) : +theorem e_2180 : 1 * (d ^^^ (e ||| f)) - 6 * ( ~~~e &&& ~~~(d ^^^ f)) + 2 * (e ^^^ (d ||| (e &&& f))) - 1 * ( ~~~d &&& (e ||| f)) + 7 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 7 * (e ||| (d ^^^ f)) - 1 * (e ^^^ (d &&& (e ^^^ f))) - 7 * ~~~(e ^^^ f) + 2 * (f ^^^ ~~~(d &&& ~~~e)) - 2 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 7 * (f ^^^ (d &&& ( ~~~e ||| f))) + 1 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 5 * ~~~(d ^^^ e) - 1 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 1 * ( ~~~f ||| (d ^^^ e)) + 3 * (e &&& f) + 1 * ( ~~~f &&& ~~~(d ^^^ e)) + 3 * (f ||| (d ^^^ e)) - 11 * ~~~(d ^^^ (e &&& f)) + 7 * (d ||| (e ^^^ f)) + 2 * ~~~(d ||| ~~~e) - 3 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 3 * (f &&& (d ^^^ e)) + 1 * ( ~~~d ||| (e ||| f)) + 11 * (f ^^^ ( ~~~d ||| (e ||| f))) - 2 * ~~~(d ^^^ ( ~~~e ||| f)) + 11 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 4 * ~~~( ~~~d ||| (e ^^^ f)) - 1 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 2 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * (e ^^^ (d &&& ( ~~~e ||| f))) + 5 * (d ^^^ f) + 1 * ~~~(d ^^^ f) - 3 * ( ~~~e ||| ~~~(d ^^^ f)) + 2 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 11 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 1 * (e ||| (d &&& ~~~f)) + 7 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 4 * (e ^^^ ~~~(d &&& ~~~f)) + 2 * (f ^^^ (d ||| ( ~~~e &&& f))) + 3 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 1 * ( ~~~f &&& (d ^^^ e)) - 5 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 24 * ~~~(d ||| (e ||| f)) - 20 * ~~~(d ||| ( ~~~e ||| f)) - 2 * ~~~( ~~~d ||| (e ||| f)) - 26 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 1 * ( ~~~d &&& ( ~~~e &&& f)) - 1 * ( ~~~d &&& (e &&& f)) - 18 * (d &&& ( ~~~e &&& f)) = 1 * ((d ^^^ e) &&& (d ^^^ f)) + 11 * (e ^^^ ~~~(d &&& (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2181 (x y : BitVec w) : +theorem e_2181 : 2 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (f ||| (d &&& ~~~e)) + 3 * ( ~~~d &&& (e ||| f)) + 1 * (e ^^^ ~~~(d &&& f)) + 1 * ((d &&& f) ^^^ (e ||| f)) - 2 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 2 * (f ^^^ (d ||| e)) - 1 * (f ^^^ ~~~(d ||| ~~~e)) - 5 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * (d &&& ~~~e) - 11 * (f ^^^ (d &&& (e ||| f))) - 6 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 5 * ~~~(d &&& (e ||| f)) + 2 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (e ^^^ ( ~~~d ||| (e &&& f))) + 2 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 3 * (d ^^^ (e &&& f)) - 11 * ~~~(d ||| e) + 1 * (f &&& ~~~(d &&& ~~~e)) - 2 * (f ||| ~~~(d ||| e)) + 7 * (e ||| f) + 4 * (e &&& (d ||| f)) - 11 * (e ^^^ (d ||| ~~~f)) - 7 * d + 1 * ~~~( ~~~d ||| (e &&& f)) - 2 * ( ~~~d &&& (e ^^^ f)) - 1 * (f ||| (d &&& e)) - 2 * ~~~( ~~~d &&& (e ||| f)) - 6 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 1 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 5 * (e ^^^ (d ||| ( ~~~e ||| f))) - 2 * ((d &&& e) ^^^ (e ||| f)) - 6 * ((d &&& f) ||| (e &&& ~~~f)) + 2 * ~~~(e &&& ~~~f) + 1 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 5 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 11 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 2 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 1 * ( ~~~e ||| ~~~(d ^^^ f)) + 1 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 2 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 10 * ~~~(d ||| (e ||| f)) - 20 * ~~~(d ||| ( ~~~e ||| f)) - 14 * ~~~( ~~~d ||| (e ||| f)) + 4 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 1 * ( ~~~d &&& ( ~~~e &&& f)) + 5 * ( ~~~d &&& (e &&& f)) + 17 * (d &&& ( ~~~e &&& f)) - 7 * (d &&& (e &&& f)) = 1 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2182 (x y : BitVec w) : +theorem e_2182 : - 3 * ~~~(d ^^^ (e &&& f)) - 1 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 6 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 2 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 6 * ~~~d - 1 * (e &&& (d ||| f)) - 2 * (f &&& (d ^^^ e)) + 1 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 5 * (e ||| ~~~(d ^^^ f)) - 1 * (e ^^^ (d ||| (e &&& f))) + 1 * (d ^^^ (e &&& f)) + 1 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 11 * ~~~(d ^^^ ( ~~~e &&& f)) - 1 * ~~~(e ||| ~~~f) + 2 * (f ^^^ ~~~(d &&& (e &&& f))) - 1 * ~~~(d &&& e) - 5 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 3 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 2 * (d ||| ~~~f) + 7 * ~~~(d &&& (e &&& f)) - 1 * (e &&& f) - 11 * ~~~(d ||| f) - 2 * (d ||| e) + 3 * ~~~( ~~~d ||| (e ^^^ f)) + 5 * ~~~f + 4 * ( ~~~d &&& (e ||| f)) - 6 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 2 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 5 * (d &&& (e ||| f)) + 11 * ~~~e + 5 * ( ~~~f ||| ~~~(d ^^^ e)) + 4 * ~~~( ~~~d &&& (e ^^^ f)) + 4 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 3 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 2 * ( ~~~e ||| (d ^^^ f)) + 2 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 3 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 2 * (d &&& e) - 1 * ((d &&& ~~~e) ||| (e ^^^ f)) - 3 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 3 * (d ||| f) - 2 * ( ~~~d &&& ( ~~~e ||| f)) - 10 * ~~~(d ||| (e ||| f)) + 7 * ~~~(d ||| ( ~~~e ||| f)) - 29 * ~~~( ~~~d ||| (e ||| f)) - 1 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 9 * ( ~~~d &&& ( ~~~e &&& f)) + 3 * ( ~~~d &&& (e &&& f)) - 15 * (d &&& ( ~~~e &&& f)) + 11 * (d &&& (e &&& f)) = 6 * ~~~(e ^^^ f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2183 (x y : BitVec w) : +theorem e_2183 : 2 * (f ^^^ ~~~(d ||| ~~~e)) - 2 * ((d &&& e) ^^^ (e ||| f)) - 1 * (e &&& (d ||| ~~~f)) + 11 * (e ^^^ (d ||| f)) + 4 * ~~~(d ||| e) + 7 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 1 * ( ~~~d ||| ( ~~~e &&& f)) - 1 * (d ||| ( ~~~e ||| f)) - 3 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 3 * ((d &&& f) ^^^ (e ||| f)) - 2 * ( ~~~d ||| (e ^^^ f)) + 3 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 5 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * (f ^^^ ~~~(d &&& ~~~e)) + 7 * (d ||| (e ||| f)) + 11 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 6 * ( ~~~f &&& (d ^^^ e)) + 5 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 1 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 5 * ~~~(d &&& (e &&& f)) + 1 * (e ^^^ (d &&& ~~~f)) - 1 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 11 * (e ^^^ ( ~~~d ||| (e ||| f))) + 4 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 5 * (e ^^^ (d ||| ( ~~~e &&& f))) + 7 * (d &&& (e ||| f)) + 3 * (f ^^^ (d ||| ~~~e)) + 1 * ~~~(d ^^^ (e ||| f)) + 4 * ~~~(d ^^^ e) + 2 * ~~~(d ||| ~~~f) - 2 * (f &&& ~~~(d ^^^ e)) - 5 * ((d &&& ~~~e) ||| (e ^^^ f)) + 1 * ((d ^^^ e) ||| (d ^^^ f)) + 5 * ( ~~~e ||| (d ^^^ f)) - 3 * (f &&& (d ^^^ e)) - 7 * ((d ||| e) &&& (e ^^^ f)) + 11 * (e ||| (d &&& f)) - 3 * (f ^^^ (d &&& ~~~e)) - 2 * (d ^^^ ( ~~~e &&& f)) - 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 11 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 7 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 32 * ~~~(d ||| (e ||| f)) - 29 * ~~~(d ||| ( ~~~e ||| f)) - 46 * ~~~( ~~~d ||| (e ||| f)) - 34 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 32 * ( ~~~d &&& ( ~~~e &&& f)) - 36 * ( ~~~d &&& (e &&& f)) - 54 * (d &&& ( ~~~e &&& f)) - 34 * (d &&& (e &&& f)) = - 3 * (e ||| f) - 2 * (f ^^^ (d ||| (e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2184 (x y : BitVec w) : +theorem e_2184 : - 1 * (f ^^^ ~~~(d ||| e)) - 3 * ( ~~~f ||| (d ^^^ e)) + 11 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 6 * (d ^^^ ( ~~~e &&& f)) + 1 * ((d &&& e) ||| ~~~(e ||| f)) + 4 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 3 * (e &&& ~~~(d &&& ~~~f)) + 1 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 2 * d - 3 * (e ^^^ ~~~(d &&& f)) - 11 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 3 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 4 * (d ||| f) - 2 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 5 * (e ^^^ (d ||| (e ^^^ f))) + 2 * ~~~(d ||| ~~~f) + 11 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 7 * (d ^^^ (e ||| f)) - 6 * ((d ||| e) &&& (e ^^^ f)) + 2 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 7 * ~~~(d ^^^ e) - 2 * ((d &&& e) ^^^ (e ||| ~~~f)) + 2 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 7 * (d ||| ( ~~~e &&& f)) + 3 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 4 * ~~~(e ||| f) - 2 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 11 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 2 * (e ^^^ ~~~(d &&& (e &&& f))) - 1 * ~~~d + 11 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 1 * f + 5 * (f ^^^ ~~~(d ||| ~~~e)) - 5 * (f ^^^ (d ||| ( ~~~e &&& f))) - 1 * ~~~(d &&& ~~~d) - 1 * (f ||| (d ^^^ e)) - 1 * ~~~(d ^^^ (e ||| f)) - 2 * (d ^^^ f) + 2 * ( ~~~d ||| (e ^^^ f)) + 2 * (f &&& (d ||| ~~~e)) - 2 * ( ~~~e ||| ~~~(d ^^^ f)) + 1 * ( ~~~d ||| ( ~~~e &&& f)) + 2 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 7 * ~~~(d ||| (e ||| f)) + 5 * ~~~(d ||| ( ~~~e ||| f)) + 12 * ~~~( ~~~d ||| (e ||| f)) - 15 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 10 * ( ~~~d &&& ( ~~~e &&& f)) - 21 * (d &&& ( ~~~e &&& f)) - 7 * (d &&& (e &&& f)) = - 2 * (f ^^^ (d &&& e)) - 5 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2185 (x y : BitVec w) : +theorem e_2185 : - 11 * ~~~(d ^^^ ( ~~~e ||| f)) + 2 * (d &&& ( ~~~e ||| f)) - 11 * ((d &&& e) ^^^ (e ||| ~~~f)) - 2 * (f ||| (d &&& e)) + 1 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 5 * ~~~( ~~~d ||| (e &&& f)) - 6 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 5 * (d ^^^ f) - 2 * ( ~~~d ||| ( ~~~e &&& f)) - 3 * ( ~~~d &&& (e ^^^ f)) - 6 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 1 * ~~~d - 1 * ((d &&& e) ||| ~~~(e ||| f)) + 2 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 1 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 7 * ~~~e - 2 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 1 * (f ^^^ ~~~(d ||| (e &&& f))) + 3 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 1 * (d ||| ( ~~~e &&& f)) + 4 * (e &&& f) - 6 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 6 * (e &&& ~~~(d ^^^ f)) - 1 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 1 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 2 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 11 * (e ^^^ ~~~(d &&& ~~~f)) - 2 * (e ^^^ (d ||| ( ~~~e &&& f))) - 2 * (e ^^^ ~~~(d &&& f)) + 4 * (f &&& (d ||| ~~~e)) + 2 * (f ^^^ (d &&& ( ~~~e ||| f))) - 2 * (f &&& ~~~(d ^^^ e)) + 4 * ~~~(d &&& ( ~~~e &&& f)) - 3 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 1 * ((d &&& e) ^^^ (e ||| f)) + 1 * (f ^^^ ( ~~~d &&& (e ||| f))) - 7 * (d ^^^ e) - 7 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * ((d ||| e) &&& (e ^^^ f)) + 1 * (e &&& ~~~f) + 1 * ( ~~~d ||| (e &&& f)) - 5 * (e ^^^ (d ||| ( ~~~e ||| f))) + 19 * ~~~(d ||| (e ||| f)) + 47 * ~~~(d ||| ( ~~~e ||| f)) + 44 * ~~~( ~~~d ||| (e ||| f)) - 2 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 4 * ( ~~~d &&& ( ~~~e &&& f)) + 19 * ( ~~~d &&& (e &&& f)) + 37 * (d &&& ( ~~~e &&& f)) + 10 * (d &&& (e &&& f)) = - 11 * ~~~(d ^^^ e) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2186 (x y : BitVec w) : +theorem e_2186 : - 2 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 5 * (f ||| (d &&& e)) - 7 * (f ^^^ ~~~(d &&& ~~~e)) - 3 * (e ^^^ ( ~~~d ||| (e ||| f))) + 2 * (e &&& (d ||| ~~~f)) - 1 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 7 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 2 * (d ||| (e ^^^ f)) + 11 * ~~~d + 2 * (e ^^^ (d &&& ( ~~~e ||| f))) + 1 * ( ~~~d ||| (e ^^^ f)) - 11 * (f &&& ~~~(d &&& ~~~e)) - 1 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 3 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 1 * ( ~~~d ||| (e ||| f)) + 4 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 1 * (e ^^^ ~~~(d ||| ~~~f)) + 3 * ( ~~~f ||| (d ^^^ e)) + 2 * (e &&& (d ||| f)) + 3 * (f ||| (d &&& ~~~e)) - 3 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 11 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 2 * (f ^^^ ( ~~~d ||| (e &&& f))) + 2 * (e ||| (d &&& ~~~f)) - 2 * (e &&& ~~~(d &&& ~~~f)) - 1 * ((d &&& f) ^^^ (e ||| f)) - 3 * ~~~(d ||| (e &&& f)) + 1 * (d ^^^ ( ~~~e &&& f)) - 2 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * (d &&& (e ||| f)) - 1 * (e &&& ~~~(d ^^^ f)) + 11 * d + 5 * ~~~(e &&& f) - 2 * ((d &&& e) ^^^ (e ||| ~~~f)) + 1 * (f ^^^ ~~~(d ||| (e &&& f))) + 5 * ((d ||| e) &&& ~~~(e ^^^ f)) + 1 * (f &&& (d ||| ~~~e)) + 11 * (e ^^^ (d &&& (e ^^^ f))) + 2 * (e ||| ~~~(d ||| ~~~f)) + 2 * (d ^^^ ( ~~~e ||| f)) + 4 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 5 * ~~~(d ||| e) + 1 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 18 * ~~~(d ||| (e ||| f)) - 10 * ~~~(d ||| ( ~~~e ||| f)) - 28 * ~~~( ~~~d ||| (e ||| f)) - 15 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 9 * ( ~~~d &&& ( ~~~e &&& f)) - 22 * ( ~~~d &&& (e &&& f)) - 23 * (d &&& ( ~~~e &&& f)) - 16 * (d &&& (e &&& f)) = - 11 * ((d &&& ~~~e) ||| (e ^^^ f)) + 1 * (f ^^^ ~~~(d ||| ~~~e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2187 (x y : BitVec w) : +theorem e_2187 : - 3 * (e ^^^ (d ||| (e ||| f))) + 1 * ~~~(d ||| ~~~e) + 3 * ( ~~~f ||| (d ^^^ e)) - 2 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 2 * (f ||| (d ^^^ e)) + 11 * ( ~~~f &&& ~~~(d ^^^ e)) + 1 * (e ^^^ ~~~(d ||| ~~~f)) - 2 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 1 * (d ||| (e ^^^ f)) - 5 * (e &&& f) + 1 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 3 * ~~~( ~~~d &&& (e ||| f)) + 1 * ~~~(d &&& (e ^^^ f)) - 7 * (f &&& (d ^^^ e)) - 1 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 7 * ( ~~~d &&& (e ||| f)) + 2 * ~~~( ~~~d ||| (e ^^^ f)) + 7 * (d ||| ~~~e) - 6 * ( ~~~d ||| (e &&& f)) - 5 * (e ^^^ (d ||| (e ^^^ f))) + 1 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 6 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 7 * ~~~(d ^^^ (e ||| f)) + 1 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 1 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 7 * (e ^^^ (d ||| ( ~~~e &&& f))) + 7 * (d ^^^ ( ~~~e &&& f)) + 4 * ~~~( ~~~d &&& (e ^^^ f)) - 3 * (f ^^^ (d ||| ~~~e)) + 2 * ((d ||| ~~~e) &&& (e ^^^ f)) - 1 * (e &&& (d ||| f)) + 5 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 11 * (f ^^^ ~~~(d &&& (e ||| f))) - 1 * (e ^^^ ~~~(d &&& (e ||| f))) + 1 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 1 * e + 4 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 1 * (e &&& ~~~(d &&& f)) + 2 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 11 * (d &&& f) - 1 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 6 * (f ^^^ (d &&& e)) - 3 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 11 * (e &&& ~~~f) + 5 * (d ^^^ (e ||| f)) - 34 * ~~~(d ||| (e ||| f)) - 41 * ~~~( ~~~d ||| (e ||| f)) - 38 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 14 * ( ~~~d &&& (e &&& f)) - 37 * (d &&& ( ~~~e &&& f)) - 42 * (d &&& (e &&& f)) = 3 * ( ~~~d &&& ( ~~~e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2188 (x y : BitVec w) : +theorem e_2188 : 11 * ( ~~~d &&& (e ^^^ f)) - 11 * ~~~( ~~~d ||| (e &&& f)) + 1 * ( ~~~e &&& ~~~(d ^^^ f)) + 7 * (e ^^^ (d &&& f)) + 4 * (e ^^^ (d ||| (e ||| f))) + 2 * (f ||| ~~~(d ||| e)) + 11 * (e ^^^ (d ||| ~~~f)) - 11 * e + 2 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 4 * ~~~(d ||| (e &&& f)) + 2 * (e ^^^ ~~~(d &&& (e ||| f))) - 2 * ( ~~~e ||| ~~~(d ^^^ f)) + 1 * (f ^^^ ~~~(d ||| (e &&& f))) - 3 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 3 * (e ||| f) - 5 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 5 * (f ^^^ ~~~(d &&& e)) - 7 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 6 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 1 * (e ||| ~~~(d ||| f)) - 5 * (e ||| ~~~(d ||| ~~~f)) + 2 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 5 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 5 * ( ~~~d ||| ( ~~~e ||| f)) - 1 * (d &&& (e ^^^ f)) + 7 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 1 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (f &&& ~~~(d &&& ~~~e)) + 5 * (f ^^^ ( ~~~d ||| (e ||| f))) + 1 * (e &&& (d ^^^ f)) - 1 * (e ^^^ (d ||| (e ^^^ f))) + 11 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 3 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 1 * (f &&& (d ||| e)) - 3 * (e ^^^ (d ||| ( ~~~e &&& f))) - 6 * (f ^^^ (d &&& e)) - 2 * (f ||| (d ^^^ e)) - 7 * (d ||| ( ~~~e &&& f)) + 2 * (f ||| (d &&& e)) - 7 * (d ||| f) - 1 * ~~~( ~~~d ||| (e ^^^ f)) - 5 * ( ~~~d &&& (e ||| f)) + 1 * (d ^^^ e) - 16 * ~~~(d ||| (e ||| f)) + 4 * ~~~(d ||| ( ~~~e ||| f)) + 11 * ~~~( ~~~d ||| (e ||| f)) + 44 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 1 * ( ~~~d &&& ( ~~~e &&& f)) + 15 * ( ~~~d &&& (e &&& f)) + 3 * (d &&& ( ~~~e &&& f)) + 44 * (d &&& (e &&& f)) = 7 * ~~~( ~~~d ||| ( ~~~e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2189 (x y : BitVec w) : +theorem e_2189 : - 7 * (f ^^^ ~~~(d &&& e)) + 1 * (e &&& (d ||| ~~~f)) - 2 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 2 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 1 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 7 * (f &&& (d ||| e)) - 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 5 * ~~~(d &&& ~~~e) - 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 2 * (f ^^^ (d &&& e)) + 1 * (e ^^^ ~~~(d &&& (e ||| f))) - 11 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 1 * ( ~~~d &&& (e ||| f)) + 4 * ( ~~~d ||| ( ~~~e ||| f)) + 3 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 7 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 5 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 1 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 3 * (d &&& e) + 1 * ((d ^^^ e) ||| (d ^^^ f)) - 11 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 1 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 11 * (e &&& f) + 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 7 * (d &&& ~~~e) + 7 * (d ||| ~~~e) + 4 * (f ||| ~~~(d ||| ~~~e)) - 5 * (e ^^^ (d &&& (e ||| f))) + 7 * (f ^^^ (d ||| ( ~~~e &&& f))) - 1 * ( ~~~f &&& (d ^^^ e)) - 2 * (d ^^^ f) + 4 * ~~~(d &&& ( ~~~e &&& f)) + 1 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 11 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 1 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 5 * ( ~~~f ||| (d ^^^ e)) + 1 * (e &&& ~~~(d ^^^ f)) + 1 * ~~~(d &&& ~~~d) - 11 * ~~~f - 1 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 3 * (d ||| ( ~~~e ||| f)) - 11 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 5 * e + 11 * ~~~(d ||| (e ||| f)) - 4 * ~~~(d ||| ( ~~~e ||| f)) + 12 * ~~~( ~~~d ||| (e ||| f)) + 17 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 11 * ( ~~~d &&& ( ~~~e &&& f)) - 13 * ( ~~~d &&& (e &&& f)) + 13 * (d &&& ( ~~~e &&& f)) - 18 * (d &&& (e &&& f)) = 3 * ~~~(e &&& f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2190 (x y : BitVec w) : +theorem e_2190 : - 7 * (e ^^^ ( ~~~d ||| (e &&& f))) - 5 * (e &&& (d ^^^ f)) - 2 * ~~~(d ||| ( ~~~e &&& f)) + 5 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 1 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 1 * (f ^^^ ~~~(d &&& (e &&& f))) - 2 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 1 * (e ^^^ (d ||| ( ~~~e ||| f))) + 11 * (f ^^^ (d &&& ~~~e)) - 11 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * (d ^^^ ( ~~~e ||| f)) + 1 * (d &&& ~~~f) - 6 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 5 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 2 * (f ||| (d &&& ~~~e)) + 3 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 6 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 1 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 11 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 2 * (f &&& ~~~(d ^^^ e)) - 1 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 1 * ( ~~~d &&& ( ~~~e ||| f)) + 1 * (e ^^^ (d &&& (e ||| f))) - 2 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 3 * (e &&& (d ||| f)) - 1 * ( ~~~f &&& ~~~(d ^^^ e)) - 2 * (e ||| ~~~(d ^^^ f)) - 6 * (e ^^^ ~~~(d &&& (e ||| f))) + 2 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 1 * ~~~( ~~~d &&& (e ||| f)) + 1 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 6 * (e ||| ~~~(d ||| f)) + 11 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 3 * ~~~(e ^^^ f) - 1 * (f ^^^ ~~~(d &&& (e ||| f))) - 2 * ((d &&& e) ^^^ (e ||| f)) - 1 * ~~~(d &&& f) - 7 * ~~~(e &&& f) + 2 * ( ~~~e &&& (d ^^^ f)) + 5 * (f ^^^ ( ~~~d ||| (e &&& f))) + 5 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 2 * (f ^^^ ~~~(d &&& ~~~e)) - 11 * (d ^^^ e) + 39 * ~~~(d ||| (e ||| f)) + 32 * ~~~(d ||| ( ~~~e ||| f)) + 10 * ~~~( ~~~d ||| (e ||| f)) + 35 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 25 * ( ~~~d &&& (e &&& f)) + 21 * (d &&& ( ~~~e &&& f)) + 9 * (d &&& (e &&& f)) = - 2 * (e &&& ~~~(d ^^^ f)) - 5 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2191 (x y : BitVec w) : +theorem e_2191 : 5 * ((d &&& e) ||| ~~~(e ^^^ f)) + 3 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 2 * (f &&& (d ||| e)) + 1 * ~~~(d ^^^ ( ~~~e &&& f)) - 3 * (e &&& ~~~(d ^^^ f)) - 6 * (f ||| (d ^^^ e)) + 1 * (d ||| ~~~f) + 2 * ~~~(d ||| e) - 3 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 1 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 3 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 1 * ~~~(d ||| ( ~~~e &&& f)) - 1 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 2 * ( ~~~f &&& (d ^^^ e)) + 2 * (e ^^^ (d ||| ~~~f)) + 11 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 5 * (d &&& f) - 7 * (e &&& (d ||| f)) + 5 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 3 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 4 * (e ^^^ ~~~(d ||| (e &&& f))) - 3 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 7 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 11 * ( ~~~d &&& (e ||| f)) + 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * (f ^^^ ~~~(d &&& (e &&& f))) - 11 * ((d &&& e) ^^^ (e ||| f)) - 7 * (f ^^^ (d ||| (e &&& f))) - 3 * (f ^^^ ( ~~~d &&& (e ||| f))) + 1 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * (d ^^^ (e &&& f)) + 7 * (e ^^^ ( ~~~d ||| (e ||| f))) - 6 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 7 * (d ||| f) + 3 * ~~~(d &&& ( ~~~e ||| f)) + 11 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 1 * (f ^^^ ~~~(d &&& e)) + 1 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 2 * (f ^^^ (d &&& ~~~e)) - 2 * (f ^^^ (d &&& (e ||| f))) - 1 * ((d &&& f) ||| ~~~(e ||| f)) + 5 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 54 * ~~~(d ||| (e ||| f)) - 16 * ~~~(d ||| ( ~~~e ||| f)) - 36 * ~~~( ~~~d ||| (e ||| f)) - 8 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 1 * ( ~~~d &&& ( ~~~e &&& f)) - 7 * ( ~~~d &&& (e &&& f)) + 5 * (d &&& ( ~~~e &&& f)) - 32 * (d &&& (e &&& f)) = - 11 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2192 (x y : BitVec w) : +theorem e_2192 : 11 * ~~~(e ^^^ f) - 1 * ~~~(e ||| ~~~f) + 4 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 1 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 1 * ~~~( ~~~d ||| (e ^^^ f)) - 1 * (e ^^^ ~~~(d ||| ~~~f)) + 1 * (f ^^^ (d ||| ( ~~~e ||| f))) - 6 * ~~~(d &&& ~~~f) - 3 * ~~~(d ^^^ e) - 3 * ( ~~~d ||| (e &&& f)) - 11 * (e ^^^ ~~~(d ||| f)) - 2 * (f ||| ~~~(d ||| e)) + 2 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 3 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 2 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 2 * f + 11 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 11 * (f ^^^ (d ||| (e &&& f))) + 2 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 7 * (d &&& (e ||| f)) - 2 * (f ^^^ (d &&& ( ~~~e ||| f))) + 3 * ~~~(d ^^^ (e ^^^ f)) - 2 * (d ||| (e ||| f)) + 2 * (f ^^^ ~~~(d ||| (e &&& f))) - 3 * (f ^^^ (d &&& e)) - 1 * (e &&& f) - 5 * (d ^^^ (e &&& f)) + 4 * e + 1 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 4 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * ~~~(d &&& ~~~e) - 1 * ((d &&& ~~~e) ||| (e ^^^ f)) + 1 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 11 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 11 * ((e &&& f) ||| (d &&& (e ||| f))) + 2 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 5 * ( ~~~e ||| (d ^^^ f)) + 2 * (e ||| (d ^^^ f)) - 7 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 5 * (d ||| ( ~~~e ||| f)) - 2 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 11 * ~~~(e ||| f) + 3 * (e ^^^ (d ||| ( ~~~e ||| f))) + 30 * ~~~(d ||| (e ||| f)) - 3 * ~~~(d ||| ( ~~~e ||| f)) + 14 * ~~~( ~~~d ||| (e ||| f)) + 12 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 1 * ( ~~~d &&& ( ~~~e &&& f)) + 29 * ( ~~~d &&& (e &&& f)) + 12 * (d &&& ( ~~~e &&& f)) + 9 * (d &&& (e &&& f)) = 3 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 4 * ((d &&& e) ||| (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2193 (x y : BitVec w) : +theorem e_2193 : - 5 * (d ||| (e &&& f)) - 6 * ((d &&& f) ||| ~~~(e ||| f)) - 11 * ~~~(d &&& f) - 7 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 3 * (e &&& ~~~(d &&& ~~~f)) - 3 * (f ^^^ (d ||| (e &&& f))) - 3 * ~~~e + 2 * (d &&& (e ||| f)) + 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 3 * (f &&& ~~~(d &&& e)) - 1 * ~~~(d ||| (e &&& f)) + 4 * ( ~~~d &&& (e ||| f)) - 2 * (f ||| ~~~(d ||| e)) - 1 * ~~~(d ||| ( ~~~e &&& f)) + 7 * (e ^^^ ~~~(d &&& ~~~f)) + 1 * (e ^^^ (d &&& ( ~~~e ||| f))) + 1 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 4 * (f ^^^ (d ||| ~~~e)) - 3 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 2 * ~~~f - 7 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 1 * (f ^^^ (d &&& ~~~e)) + 1 * ( ~~~f ||| ~~~(d ^^^ e)) - 2 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 2 * ~~~d - 1 * ((d &&& e) ^^^ (e ||| f)) + 4 * ~~~(d ||| e) + 7 * (f &&& (d ^^^ e)) + 1 * (e ||| ~~~f) - 1 * (d ||| ~~~e) - 2 * ( ~~~f ||| (d ^^^ e)) + 11 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 2 * (e &&& ~~~(d &&& f)) - 1 * (e ||| f) - 2 * ( ~~~d ||| ( ~~~e &&& f)) - 7 * (d &&& ( ~~~e ||| f)) + 11 * ~~~(d &&& (e ^^^ f)) - 11 * ~~~(d &&& (e &&& f)) - 1 * ((d &&& e) ||| (e ^^^ f)) - 5 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 5 * ~~~(d ||| ~~~e) + 1 * (d ^^^ e) - 11 * ~~~(d ^^^ e) + 29 * ~~~(d ||| (e ||| f)) + 22 * ~~~(d ||| ( ~~~e ||| f)) + 58 * ~~~( ~~~d ||| (e ||| f)) + 47 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 24 * ( ~~~d &&& ( ~~~e &&& f)) + 29 * ( ~~~d &&& (e &&& f)) + 25 * (d &&& ( ~~~e &&& f)) + 25 * (d &&& (e &&& f)) = 6 * (d ||| ( ~~~e &&& f)) + 3 * (e ^^^ (d ||| (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2194 (x y : BitVec w) : +theorem e_2194 : - 3 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 11 * (f ^^^ (d ||| (e &&& f))) + 3 * (d &&& ( ~~~e ||| f)) + 2 * (d ^^^ (e &&& f)) - 11 * ~~~(d ||| ~~~e) - 2 * ((d &&& e) ||| (e ^^^ f)) - 5 * (e ^^^ (d &&& (e ||| f))) - 1 * ( ~~~e ||| (d ^^^ f)) + 2 * (e &&& ~~~(d &&& f)) - 7 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 5 * (d ||| e) - 2 * d + 2 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 2 * (e ^^^ (d ||| ( ~~~e ||| f))) + 3 * e - 1 * (e ||| ~~~(d ||| ~~~f)) + 1 * (e ||| (d &&& ~~~f)) - 7 * (e ^^^ ~~~(d &&& ~~~f)) - 11 * (f ^^^ (d ||| e)) - 7 * ( ~~~d &&& ( ~~~e ||| f)) + 1 * (e ^^^ (d &&& ( ~~~e ||| f))) - 5 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 3 * (f ^^^ (d &&& e)) - 2 * (f &&& (d ^^^ e)) + 11 * (e ^^^ (d &&& f)) - 1 * f - 6 * (e ^^^ (d ||| (e &&& f))) + 1 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 4 * ~~~(d &&& ~~~e) + 1 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 6 * ((d &&& e) ^^^ (e ||| ~~~f)) + 2 * (e ||| ~~~(d ||| f)) + 1 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 7 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 1 * ~~~(d ^^^ (e ||| f)) + 1 * ~~~(e ^^^ f) + 3 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 11 * (e &&& ~~~(d ^^^ f)) - 6 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 1 * (d ^^^ ( ~~~e ||| f)) + 1 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 11 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 1 * (f ^^^ ~~~(d ||| (e &&& f))) + 13 * ~~~(d ||| (e ||| f)) + 34 * ~~~(d ||| ( ~~~e ||| f)) + 20 * ~~~( ~~~d ||| (e ||| f)) - 1 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 30 * ( ~~~d &&& ( ~~~e &&& f)) + 3 * ( ~~~d &&& (e &&& f)) + 2 * (d &&& ( ~~~e &&& f)) - 1 * (d &&& (e &&& f)) = 2 * ~~~(d ^^^ ( ~~~e &&& f)) + 5 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2195 (x y : BitVec w) : +theorem e_2195 : 5 * ( ~~~f ||| ~~~(d ^^^ e)) + 1 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 4 * ((d &&& f) ||| (e &&& ~~~f)) + 2 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 3 * (e ^^^ ~~~(d &&& (e &&& f))) - 6 * ~~~(d &&& (e ||| f)) - 5 * (e &&& f) + 4 * (d ||| (e &&& f)) - 7 * e - 1 * ( ~~~e ||| (d ^^^ f)) + 11 * ~~~(d &&& (e &&& f)) - 6 * ((d &&& e) ||| ~~~(e ^^^ f)) - 11 * ~~~(d ||| f) + 2 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 7 * ~~~(e ||| f) - 2 * ( ~~~f ||| (d ^^^ e)) - 1 * (f &&& ~~~(d &&& e)) + 4 * ~~~f + 11 * ~~~(d &&& ~~~d) + 5 * ((d ||| ~~~e) &&& (e ^^^ f)) + 1 * (e ^^^ (d ||| f)) + 11 * (d ^^^ e) - 3 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 2 * (d ||| ~~~f) - 3 * (f ^^^ ~~~(d &&& (e &&& f))) - 6 * ( ~~~d ||| (e ^^^ f)) - 1 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 2 * ~~~(d ||| (e &&& f)) - 1 * ( ~~~d ||| ( ~~~e &&& f)) - 1 * (d &&& (e ||| f)) + 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 7 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 3 * (f ||| (d &&& e)) + 1 * (e ^^^ ~~~(d ||| ~~~f)) + 1 * (e &&& (d ||| f)) - 2 * (e ^^^ (d &&& ~~~f)) - 1 * (e ^^^ ~~~(d ||| (e &&& f))) - 2 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 2 * (f ^^^ (d ||| ~~~e)) + 2 * (f ^^^ (d ||| ( ~~~e ||| f))) + 3 * (e ^^^ (d &&& ( ~~~e ||| f))) - 1 * (d ^^^ (e &&& f)) + 1 * (d ^^^ f) + 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 1 * ~~~(d ||| (e ||| f)) - 33 * ~~~( ~~~d ||| (e ||| f)) - 20 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 14 * ( ~~~d &&& ( ~~~e &&& f)) + 6 * ( ~~~d &&& (e &&& f)) - 32 * (d &&& ( ~~~e &&& f)) - 3 * (d &&& (e &&& f)) = 12 * ~~~(d ||| ( ~~~e ||| f)) + 2 * ~~~(d ^^^ (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2196 (x y : BitVec w) : +theorem e_2196 : - 2 * ~~~(d &&& f) - 1 * ~~~(d ^^^ (e ||| f)) - 1 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 6 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 11 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 1 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 1 * (f ^^^ ~~~(d &&& (e &&& f))) - 1 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 1 * ( ~~~e ||| ~~~(d ^^^ f)) - 5 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 11 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 7 * (f &&& ~~~(d ^^^ e)) - 11 * ~~~( ~~~d &&& (e ^^^ f)) - 1 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 2 * (e &&& ~~~(d &&& f)) + 2 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 7 * (e &&& (d ||| ~~~f)) + 7 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 3 * ~~~(d ||| ~~~e) - 7 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 5 * (f ^^^ ~~~(d &&& e)) - 1 * ((d ^^^ e) &&& (d ^^^ f)) - 2 * ~~~(d ^^^ f) + 3 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 3 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 7 * (e ^^^ (d ||| ( ~~~e ||| f))) + 1 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (e &&& f) - 3 * (f ^^^ (d ||| (e &&& f))) + 2 * (e ||| ~~~f) - 1 * ~~~(d ||| ( ~~~e &&& f)) + 1 * ((d ^^^ e) ||| (d ^^^ f)) + 11 * ~~~(d ^^^ ( ~~~e &&& f)) + 1 * (d ||| ( ~~~e &&& f)) - 2 * d + 2 * (f ^^^ ( ~~~d &&& (e ||| f))) - 1 * ~~~(d &&& ~~~d) + 3 * (e ^^^ ~~~(d &&& ~~~f)) + 2 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 6 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 4 * (e ^^^ ~~~(d ||| ~~~f)) - 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 1 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 7 * (d ||| ~~~e) - 21 * ~~~(d ||| ( ~~~e ||| f)) + 1 * ~~~( ~~~d ||| (e ||| f)) + 3 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 7 * ( ~~~d &&& ( ~~~e &&& f)) + 2 * ( ~~~d &&& (e &&& f)) - 7 * (d &&& ( ~~~e &&& f)) - 1 * (d &&& (e &&& f)) = 30 * ~~~(d ||| (e ||| f)) - 3 * (f &&& (d ^^^ e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2197 (x y : BitVec w) : +theorem e_2197 : - 3 * ((d &&& e) ^^^ (e ||| ~~~f)) + 1 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (f &&& ~~~(d ^^^ e)) - 1 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 1 * (e &&& (d ||| f)) + 1 * ( ~~~d ||| (e ^^^ f)) - 1 * (d ||| f) - 1 * (f ^^^ ~~~(d ||| (e &&& f))) + 2 * (e ^^^ ~~~(d &&& f)) + 4 * (e ^^^ ~~~(d &&& (e ||| f))) - 6 * ( ~~~f ||| ~~~(d ^^^ e)) - 2 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 2 * (e ^^^ ~~~(d &&& (e &&& f))) + 1 * (e ^^^ ~~~(d ||| ~~~f)) - 11 * (e ^^^ (d &&& ~~~f)) - 1 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 3 * ((d ||| e) &&& ~~~(e ^^^ f)) + 5 * (f &&& ~~~(d &&& e)) - 7 * ~~~(d ||| ~~~e) - 2 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 1 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 2 * (f &&& (d ^^^ e)) + 11 * (e ||| f) + 1 * ((d ^^^ e) ||| (d ^^^ f)) - 1 * (f ||| (d &&& ~~~e)) + 11 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 2 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 2 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 2 * (f ^^^ ~~~(d &&& e)) + 5 * (e ||| ~~~(d ||| ~~~f)) - 11 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 11 * ( ~~~d &&& ( ~~~e ||| f)) - 3 * ((d ||| ~~~e) &&& (e ^^^ f)) - 7 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 2 * (e ^^^ (d ||| (e ^^^ f))) - 3 * (e ^^^ ~~~(d &&& ~~~f)) + 1 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 1 * (f ^^^ ( ~~~d ||| (e &&& f))) - 1 * ~~~(d &&& (e &&& f)) - 1 * ((e &&& f) ||| (d &&& (e ||| f))) + 4 * (d ^^^ (e ||| f)) + 1 * (e ||| (d &&& f)) + 22 * ~~~(d ||| (e ||| f)) + 28 * ~~~(d ||| ( ~~~e ||| f)) + 17 * ~~~( ~~~d ||| (e ||| f)) - 25 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 5 * ( ~~~d &&& ( ~~~e &&& f)) + 26 * ( ~~~d &&& (e &&& f)) + 11 * (d &&& ( ~~~e &&& f)) + 19 * (d &&& (e &&& f)) = 6 * ~~~(d &&& ~~~f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2198 (x y : BitVec w) : +theorem e_2198 : - 5 * (e ^^^ (d ||| (e ^^^ f))) - 6 * ~~~(e ||| f) + 7 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 3 * ~~~( ~~~d &&& (e ^^^ f)) - 3 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 1 * ~~~(d ||| e) + 2 * (f ^^^ (d ||| ( ~~~e ||| f))) - 2 * ~~~(d &&& (e ^^^ f)) + 11 * ~~~(d &&& e) - 7 * (e ^^^ (d &&& (e ^^^ f))) + 4 * (f ||| ~~~(d ^^^ e)) + 5 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 11 * ~~~(d &&& ~~~e) + 1 * ~~~(e ^^^ f) + 1 * ~~~(d &&& ~~~d) + 2 * (e ^^^ (d ||| (e &&& f))) + 7 * (d ||| (e ^^^ f)) - 3 * ~~~(d ^^^ f) + 2 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 5 * (d ||| ~~~e) - 1 * (e ||| ~~~(d ^^^ f)) - 1 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 2 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 3 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 1 * (e &&& ~~~f) + 1 * ~~~d + 2 * (f ^^^ ~~~(d ||| e)) - 2 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 3 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 1 * (d ^^^ f) - 2 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 3 * ((d &&& e) ||| ~~~(e ||| f)) + 3 * ((d &&& e) ^^^ (e ||| ~~~f)) + 2 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * (f &&& ~~~(d ^^^ e)) - 7 * ~~~(d &&& f) - 2 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 4 * (e ||| ~~~(d ||| ~~~f)) - 2 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * ~~~(d &&& ( ~~~e ||| f)) - 3 * ((d ^^^ e) &&& (d ^^^ f)) - 2 * (e ^^^ ~~~(d ||| f)) + 7 * (e ^^^ ~~~(d ||| (e &&& f))) - 12 * ~~~(d ||| (e ||| f)) + 7 * ~~~(d ||| ( ~~~e ||| f)) - 11 * ~~~( ~~~d ||| (e ||| f)) - 1 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 16 * ( ~~~d &&& ( ~~~e &&& f)) + 8 * ( ~~~d &&& (e &&& f)) - 16 * (d &&& ( ~~~e &&& f)) + 5 * (d &&& (e &&& f)) = - 2 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2199 (x y : BitVec w) : +theorem e_2199 : - 1 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 5 * (e ^^^ ~~~(d ||| ~~~f)) + 4 * (e ^^^ ~~~(d &&& ~~~f)) + 1 * (e ^^^ (d ||| ( ~~~e ||| f))) + 1 * (f ||| ~~~(d ||| e)) + 4 * ~~~( ~~~d &&& (e &&& f)) + 2 * ( ~~~f ||| (d ^^^ e)) - 2 * (e ^^^ ~~~(d &&& f)) + 5 * d + 1 * ((d &&& f) ||| ~~~(e ||| f)) + 7 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 2 * (f ||| (d &&& e)) + 1 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 1 * (e &&& ~~~(d &&& f)) + 3 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 4 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 3 * (f &&& ~~~(d &&& e)) + 11 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 7 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 5 * ((d &&& e) ^^^ (e ||| f)) - 5 * (f &&& (d ||| e)) - 2 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 11 * (e ||| ~~~(d ^^^ f)) - 7 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 3 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 4 * ~~~(d &&& ~~~f) + 1 * ((d &&& e) ^^^ (e ||| ~~~f)) + 7 * ((d &&& e) ||| (e ^^^ f)) - 1 * ~~~(d ||| ~~~f) - 1 * (f ^^^ ~~~(d &&& ~~~e)) - 5 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 1 * ((d &&& e) ||| ~~~(e ||| f)) - 1 * ~~~(d ||| f) - 11 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 4 * (f &&& (d ^^^ e)) + 5 * (f ^^^ ~~~(d ||| (e &&& f))) + 2 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 7 * ~~~(e ||| ~~~f) - 5 * (e ^^^ ~~~(d &&& (e ||| f))) - 7 * ~~~(d &&& e) + 1 * ~~~(d ||| e) - 1 * ( ~~~f &&& (d ^^^ e)) - 2 * (e &&& ~~~f) - 1 * ((d ^^^ e) ||| (d ^^^ f)) + 3 * ~~~(d ||| (e ||| f)) + 7 * ~~~(d ||| ( ~~~e ||| f)) - 2 * ~~~( ~~~d ||| (e ||| f)) + 16 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 2 * ( ~~~d &&& ( ~~~e &&& f)) + 20 * ( ~~~d &&& (e &&& f)) - 29 * (d &&& ( ~~~e &&& f)) + 5 * (d &&& (e &&& f)) = 3 * ( ~~~d &&& (e ^^^ f)) - 2 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2200 (x y : BitVec w) : +theorem e_2200 : - 3 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 1 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 5 * (e ^^^ (d ||| (e ^^^ f))) + 7 * ~~~( ~~~d &&& (e &&& f)) + 5 * ~~~(e ||| f) - 1 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 5 * ~~~(d &&& (e ^^^ f)) - 7 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 3 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 1 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 3 * ((d ^^^ e) &&& (d ^^^ f)) + 1 * ~~~(d ^^^ ( ~~~e ||| f)) - 6 * (e ||| ~~~(d ^^^ f)) - 1 * ~~~(d ||| ( ~~~e &&& f)) - 5 * (f &&& (d ||| e)) + 5 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 11 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 3 * (e ^^^ ~~~(d ||| f)) - 3 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 11 * ((d &&& e) ^^^ (e ||| f)) + 2 * ((d ||| ~~~e) &&& (e ^^^ f)) + 7 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 4 * ((d ||| e) &&& ~~~(e ^^^ f)) + 2 * (e ^^^ ( ~~~d ||| (e &&& f))) + 1 * ( ~~~f &&& ~~~(d ^^^ e)) + 3 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 11 * (f &&& ~~~(d &&& e)) - 6 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 2 * (e ^^^ ( ~~~d &&& (e ||| f))) - 1 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 2 * ( ~~~d &&& (e ^^^ f)) - 1 * ~~~( ~~~d ||| (e &&& f)) - 1 * (d ||| (e &&& f)) + 1 * (d ^^^ (e &&& f)) + 2 * (f ^^^ (d &&& (e ||| f))) - 2 * ( ~~~d &&& ( ~~~e ||| f)) - 6 * (e ^^^ (d ||| (e &&& f))) + 3 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 1 * (f ^^^ ( ~~~d &&& (e ||| f))) + 2 * ~~~(d &&& (e ||| f)) - 1 * ((d &&& e) ^^^ (e ||| ~~~f)) - 2 * ~~~(d ||| ~~~e) + 3 * ~~~(d ||| e) + 2 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 4 * ~~~(d ||| ( ~~~e ||| f)) - 24 * ~~~( ~~~d ||| (e ||| f)) - 3 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 20 * ( ~~~d &&& ( ~~~e &&& f)) + 19 * (d &&& ( ~~~e &&& f)) - 5 * (d &&& (e &&& f)) = - 1 * (d ^^^ e) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2201 (x y : BitVec w) : +theorem e_2201 : - 5 * (f ^^^ (d ||| ( ~~~e &&& f))) - 2 * (f &&& ~~~(d &&& ~~~e)) + 2 * (f ^^^ (d ||| e)) - 11 * (d ||| f) + 7 * ~~~(d &&& (e ||| f)) - 11 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 11 * (d ||| ( ~~~e ||| f)) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 4 * ~~~( ~~~d &&& (e ||| f)) - 1 * ~~~f + 1 * (d ^^^ f) - 3 * ~~~(d &&& ~~~f) - 5 * (e ^^^ ( ~~~d &&& (e ||| f))) + 1 * (e &&& f) + 1 * (e ^^^ (d &&& (e ||| f))) - 6 * (f &&& ~~~(d ^^^ e)) + 5 * (d ||| ~~~e) + 5 * (d ||| (e ||| f)) - 7 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 1 * ~~~(d &&& ( ~~~e ||| f)) - 3 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 2 * (d ^^^ ( ~~~e ||| f)) - 1 * ((d &&& e) ||| ~~~(e ^^^ f)) + 7 * ( ~~~d ||| ( ~~~e &&& f)) - 5 * (f ^^^ (d ||| ( ~~~e ||| f))) - 5 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 3 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 7 * (e ^^^ (d &&& ( ~~~e ||| f))) - 6 * ((d &&& ~~~e) ||| (e ^^^ f)) - 7 * (e ||| ~~~(d ^^^ f)) - 11 * ( ~~~f ||| ~~~(d ^^^ e)) + 2 * (e ||| (d &&& ~~~f)) - 1 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 1 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 2 * (e ^^^ ~~~(d &&& (e &&& f))) - 2 * ~~~(d ||| ~~~e) + 5 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 2 * (d ||| e) + 7 * (f ^^^ (d &&& e)) + 1 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 7 * ~~~(e ||| ~~~f) + 3 * ((d &&& e) ^^^ (e ||| f)) - 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 4 * (f ||| ~~~(d ||| e)) + 44 * ~~~( ~~~d ||| (e ||| f)) + 33 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 12 * ( ~~~d &&& ( ~~~e &&& f)) + 17 * ( ~~~d &&& (e &&& f)) + 30 * (d &&& ( ~~~e &&& f)) + 35 * (d &&& (e &&& f)) = - 19 * ~~~(d ||| (e ||| f)) - 24 * ~~~(d ||| ( ~~~e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2202 (x y : BitVec w) : +theorem e_2202 : - 2 * (e ||| (d ^^^ f)) - 1 * (e ^^^ ( ~~~d ||| (e ||| f))) + 5 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 1 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 3 * (e ^^^ (d ||| (e &&& f))) - 1 * (e ||| (d &&& ~~~f)) - 2 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 1 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 2 * (f ||| (d &&& ~~~e)) - 6 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 3 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 5 * ( ~~~d &&& (e ||| f)) - 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 7 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 2 * (f ^^^ ~~~(d ||| (e &&& f))) - 11 * ~~~(d &&& ~~~d) + 11 * ~~~(e &&& ~~~f) - 5 * ~~~( ~~~d ||| (e &&& f)) + 1 * ( ~~~f ||| ~~~(d ^^^ e)) + 2 * (e ^^^ f) - 5 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 11 * (e ^^^ (d ||| f)) - 7 * (e ^^^ (d &&& f)) + 3 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 1 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 2 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 2 * (e ^^^ (d ||| (e ^^^ f))) - 6 * ~~~d + 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 7 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 5 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 2 * ((d &&& e) ^^^ (e ||| ~~~f)) - 7 * (e &&& ~~~f) - 5 * ((d &&& e) ||| ~~~(e ||| f)) + 1 * ~~~(d ||| ~~~e) - 6 * ((d &&& f) ||| (e &&& ~~~f)) + 4 * ~~~(d ^^^ (e ||| f)) + 1 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 11 * ~~~(d &&& f) + 11 * (d &&& (e ^^^ f)) - 6 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 11 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 5 * ~~~(d ||| ( ~~~e &&& f)) - 11 * ~~~(d &&& ( ~~~e ||| f)) + 12 * ~~~(d ||| (e ||| f)) + 47 * ~~~(d ||| ( ~~~e ||| f)) - 5 * ~~~( ~~~d ||| (e ||| f)) + 44 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 9 * ( ~~~d &&& ( ~~~e &&& f)) + 12 * ( ~~~d &&& (e &&& f)) - 20 * (d &&& ( ~~~e &&& f)) + 17 * (d &&& (e &&& f)) = - 1 * (f ||| ~~~(d ||| ~~~e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2203 (x y : BitVec w) : +theorem e_2203 : 2 * (e ^^^ ~~~(d &&& (e &&& f))) + 11 * (d &&& e) - 7 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * (e &&& (d ^^^ f)) - 11 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 2 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 5 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 7 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 11 * (f ^^^ ~~~(d &&& e)) - 3 * ~~~( ~~~d &&& (e &&& f)) - 2 * (e ^^^ ~~~(d &&& ~~~f)) - 1 * (f ^^^ (d &&& (e ||| f))) + 11 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 4 * ~~~(d ||| e) - 1 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 1 * (f ^^^ (d ||| (e &&& f))) - 11 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 7 * (e ^^^ ( ~~~d &&& (e ||| f))) - 3 * (e &&& ~~~(d ^^^ f)) - 1 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 2 * (f ^^^ ~~~(d &&& (e &&& f))) - 11 * (e &&& (d ||| f)) + 1 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 1 * ~~~(d ^^^ (e ^^^ f)) - 1 * ~~~(d ^^^ (e &&& f)) + 3 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 4 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 1 * ((d &&& f) ||| ~~~(e ||| f)) - 1 * ( ~~~d ||| (e &&& f)) + 5 * ((d ||| ~~~e) &&& (e ^^^ f)) - 6 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 3 * ( ~~~d ||| ( ~~~e ||| f)) + 2 * ~~~(d ^^^ f) - 1 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 11 * (d &&& ~~~f) - 2 * (e &&& ~~~f) + 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 11 * (e ^^^ (d ||| (e &&& f))) + 4 * (f ^^^ ~~~(d ||| e)) + 2 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 1 * ((d &&& e) ||| ~~~(e ^^^ f)) - 6 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 3 * ( ~~~f ||| (d ^^^ e)) - 1 * ~~~(d &&& ~~~d) - 6 * ~~~(d ||| ~~~e) + 34 * ~~~(d ||| (e ||| f)) + 41 * ~~~(d ||| ( ~~~e ||| f)) + 57 * ~~~( ~~~d ||| (e ||| f)) + 42 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 3 * ( ~~~d &&& ( ~~~e &&& f)) + 47 * ( ~~~d &&& (e &&& f)) + 29 * (d &&& (e &&& f)) = - 11 * (d &&& ( ~~~e &&& f)) + 7 * (d ||| ~~~e) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2204 (x y : BitVec w) : +theorem e_2204 : 4 * (e ^^^ (d ||| (e &&& f))) + 4 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 11 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 3 * ~~~(d ||| ~~~e) - 2 * (d ||| ~~~e) - 7 * ((d ^^^ e) &&& (d ^^^ f)) - 1 * ~~~(d &&& ~~~d) + 5 * (e ^^^ ~~~(d &&& (e &&& f))) - 1 * (e ^^^ ( ~~~d ||| (e &&& f))) + 1 * ((d ||| e) &&& ~~~(e ^^^ f)) - 6 * ~~~(d ^^^ ( ~~~e ||| f)) - 2 * (f ^^^ (d &&& ( ~~~e ||| f))) + 5 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 5 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 11 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 6 * (e ^^^ ~~~(d ||| (e &&& f))) - 1 * ((d &&& e) ||| ~~~(e ||| f)) + 5 * ~~~(d ||| ~~~f) - 11 * ~~~(d ^^^ (e ||| f)) + 1 * (e ||| ~~~(d ^^^ f)) + 11 * (e &&& ~~~f) - 6 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 3 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 2 * (f ^^^ ~~~(d &&& (e ||| f))) + 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 1 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 6 * (d &&& (e ||| f)) + 7 * ( ~~~e ||| ~~~(d ^^^ f)) - 1 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 4 * ~~~(d ^^^ (e ^^^ f)) + 1 * (e ^^^ (d ||| ~~~f)) - 2 * ((d &&& f) ||| (e &&& ~~~f)) + 5 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 11 * (f ^^^ ~~~(d &&& (e &&& f))) - 5 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 7 * ~~~(d &&& e) - 7 * (d &&& f) - 1 * (e ^^^ ~~~(d &&& f)) + 2 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 1 * (d &&& ~~~e) - 1 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 2 * ~~~(e ||| f) + 2 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 2 * ~~~(d &&& ( ~~~e ||| f)) - 11 * ~~~(d ||| (e ||| f)) - 40 * ~~~(d ||| ( ~~~e ||| f)) + 11 * ~~~( ~~~d ||| (e ||| f)) - 11 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 6 * ( ~~~d &&& ( ~~~e &&& f)) + 15 * ( ~~~d &&& (e &&& f)) + 21 * (d &&& ( ~~~e &&& f)) + 17 * (d &&& (e &&& f)) = 3 * (d ||| ( ~~~e &&& f)) - 1 * ((d ||| ~~~e) &&& (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2205 (x y : BitVec w) : +theorem e_2205 : - 5 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 1 * (e &&& ~~~f) - 1 * ~~~( ~~~d &&& (e ||| f)) + 1 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 4 * ( ~~~d ||| (e ^^^ f)) + 7 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 2 * (d ^^^ (e &&& f)) - 1 * (e ||| (d &&& f)) - 7 * (e ^^^ ~~~(d ||| (e &&& f))) + 1 * (d &&& ~~~e) + 2 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 5 * (f ^^^ ~~~(d &&& ~~~e)) + 4 * (f &&& ~~~(d &&& ~~~e)) + 1 * e - 6 * (d ||| ( ~~~e &&& f)) - 1 * (f ^^^ (d &&& e)) + 7 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 3 * (e ||| (d ^^^ f)) - 5 * (f ^^^ ~~~(d ||| (e &&& f))) + 7 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 11 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 2 * (d ||| e) + 11 * (e ||| ~~~(d ||| ~~~f)) - 1 * (e ^^^ ( ~~~d ||| (e &&& f))) - 5 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 1 * (f ^^^ ~~~(d &&& e)) + 11 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 7 * ((d &&& e) ||| ~~~(e ||| f)) + 1 * ~~~(d ^^^ ( ~~~e ||| f)) - 11 * (d &&& (e ||| f)) + 2 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 3 * ~~~(e ||| ~~~f) + 5 * (e ^^^ ~~~(d ||| ~~~f)) + 1 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 1 * ((d &&& ~~~e) ||| (e ^^^ f)) - 7 * (d &&& ~~~f) - 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 1 * ~~~f - 11 * (f ^^^ ( ~~~d ||| (e ||| f))) - 5 * ~~~(d ||| ~~~e) + 4 * (e &&& f) - 2 * (e ^^^ (d ||| f)) - 6 * ~~~(d &&& ~~~e) + 2 * (e ^^^ (d &&& (e ||| f))) - 1 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 13 * ~~~(d ||| ( ~~~e ||| f)) - 4 * ~~~( ~~~d ||| (e ||| f)) + 37 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 17 * ( ~~~d &&& ( ~~~e &&& f)) - 29 * ( ~~~d &&& (e &&& f)) + 4 * (d &&& ( ~~~e &&& f)) - 23 * (d &&& (e &&& f)) = - 11 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2206 (x y : BitVec w) : +theorem e_2206 : - 11 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 6 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 5 * (f ^^^ ~~~(d &&& (e &&& f))) - 7 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 2 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 7 * (e ^^^ ~~~(d ||| f)) + 2 * ( ~~~f ||| ~~~(d ^^^ e)) - 1 * ((d &&& f) ||| ~~~(e ||| f)) - 2 * ( ~~~e ||| ~~~(d ^^^ f)) + 1 * (e &&& ~~~(d ^^^ f)) + 11 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 3 * (f &&& ~~~(d &&& ~~~e)) - 2 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 1 * (f ||| (d &&& e)) + 2 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * (e ^^^ (d &&& ( ~~~e ||| f))) - 2 * ~~~( ~~~d &&& (e &&& f)) + 3 * ~~~(d ^^^ ( ~~~e ||| f)) + 4 * (d ^^^ f) - 5 * (e ^^^ (d &&& (e ^^^ f))) + 5 * (d ^^^ (e &&& f)) - 2 * ((d &&& e) ||| ~~~(e ||| f)) + 5 * (f ||| (d &&& ~~~e)) + 1 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 7 * (d ^^^ ( ~~~e ||| f)) - 11 * ( ~~~d &&& ( ~~~e ||| f)) - 1 * (f ^^^ (d &&& ~~~e)) - 1 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 2 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 6 * (f ^^^ (d &&& (e ||| f))) - 1 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 5 * (f ||| (d ^^^ e)) - 3 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 4 * f - 1 * ((d &&& e) ^^^ (e ||| ~~~f)) - 2 * (f ||| ~~~(d ||| e)) - 11 * ~~~(d ||| ( ~~~e &&& f)) - 1 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 7 * ~~~(d ^^^ e) - 3 * ( ~~~f ||| (d ^^^ e)) - 3 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 11 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 3 * (d ||| (e ||| f)) + 2 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 1 * (d ||| e) + 18 * ~~~(d ||| (e ||| f)) + 15 * ~~~(d ||| ( ~~~e ||| f)) - 18 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 38 * ( ~~~d &&& ( ~~~e &&& f)) + 26 * ( ~~~d &&& (e &&& f)) - 10 * (d &&& ( ~~~e &&& f)) - 8 * (d &&& (e &&& f)) = 14 * ~~~( ~~~d ||| (e ||| f)) - 5 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2207 (x y : BitVec w) : +theorem e_2207 : 1 * ~~~(d ||| ~~~f) + 5 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 2 * ( ~~~d &&& (e ^^^ f)) - 6 * ~~~(d ||| (e &&& f)) + 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 3 * ((d ||| ~~~e) &&& (e ^^^ f)) - 5 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 11 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 1 * ((d ||| e) &&& ~~~(e ^^^ f)) - 2 * ~~~(d &&& ~~~e) + 3 * ~~~(e ||| f) + 7 * (d ^^^ e) - 1 * (d ||| ( ~~~e ||| f)) + 1 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 3 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 7 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 1 * (e &&& ~~~(d &&& f)) + 2 * ~~~(e &&& ~~~f) - 3 * (e ^^^ (d &&& f)) + 3 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 7 * ~~~(d &&& e) - 2 * (e &&& f) + 3 * (f ^^^ (d ||| ( ~~~e &&& f))) + 1 * ( ~~~d &&& (e ||| f)) - 11 * ~~~e + 4 * ~~~(d &&& (e ^^^ f)) - 2 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 1 * (d ^^^ ( ~~~e ||| f)) - 1 * (e ||| ~~~(d ||| ~~~f)) + 1 * ~~~(d ||| ~~~e) - 11 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 7 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 5 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 2 * ~~~(d ||| (e ^^^ f)) + 4 * (f &&& ~~~(d &&& e)) + 11 * (f ^^^ (d ||| e)) + 7 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 1 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 1 * ~~~( ~~~d ||| (e &&& f)) + 1 * ~~~( ~~~d &&& (e &&& f)) + 4 * (f ||| (d &&& e)) - 2 * ((d &&& e) ||| ~~~(e ^^^ f)) + 3 * (f ^^^ ~~~(d ||| ~~~e)) + 3 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 7 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 47 * ~~~(d ||| (e ||| f)) - 17 * ~~~(d ||| ( ~~~e ||| f)) + 5 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 23 * ( ~~~d &&& ( ~~~e &&& f)) + 7 * ( ~~~d &&& (e &&& f)) + 13 * (d &&& ( ~~~e &&& f)) + 15 * (d &&& (e &&& f)) = 2 * (d ^^^ ( ~~~e &&& f)) - 7 * (e &&& ~~~f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2208 (x y : BitVec w) : +theorem e_2208 : 4 * (f ^^^ ( ~~~d ||| (e &&& f))) + 3 * ((d ^^^ e) &&& (d ^^^ f)) + 1 * ~~~(d &&& ~~~d) - 11 * (f ||| (d ^^^ e)) + 1 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 1 * (e ||| ~~~(d ||| ~~~f)) + 3 * (f ^^^ ~~~(d ||| (e &&& f))) - 2 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 4 * (e ^^^ (d &&& (e ||| f))) - 5 * (e ^^^ (d &&& ( ~~~e ||| f))) + 11 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 1 * (e ^^^ (d &&& ~~~f)) - 1 * (e ^^^ ~~~(d ||| ~~~f)) - 5 * ((d &&& e) ^^^ (e ||| f)) - 1 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 3 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 1 * ((d &&& ~~~e) ||| (e ^^^ f)) + 2 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * ((d &&& e) ||| ~~~(e ^^^ f)) - 7 * ((d &&& f) ||| (e &&& ~~~f)) + 11 * ((d &&& e) ||| (e ^^^ f)) + 1 * (d ^^^ e) + 1 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 1 * (e &&& ~~~(d ^^^ f)) - 2 * (f ||| ~~~(d ^^^ e)) + 2 * (f ^^^ (d ||| ( ~~~e ||| f))) - 6 * (f &&& (d ||| ~~~e)) - 2 * (d ||| ~~~f) - 7 * ( ~~~d ||| ( ~~~e ||| f)) + 3 * ~~~(d ^^^ e) + 7 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 6 * (f ||| ~~~(d ||| ~~~e)) + 1 * (e ^^^ f) - 5 * (d &&& (e ||| f)) + 11 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 5 * ~~~(d ^^^ (e ^^^ f)) - 6 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 4 * ( ~~~e &&& (d ^^^ f)) - 1 * ~~~( ~~~d &&& (e ^^^ f)) + 2 * (f ^^^ (d ||| e)) - 3 * (f &&& ~~~(d &&& ~~~e)) + 1 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 2 * ~~~(d ^^^ ( ~~~e &&& f)) + 1 * (e &&& (d ^^^ f)) + 1 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 11 * ~~~(d ||| (e ||| f)) - 3 * ~~~( ~~~d ||| (e ||| f)) - 4 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 21 * ( ~~~d &&& ( ~~~e &&& f)) + 4 * ( ~~~d &&& (e &&& f)) + 36 * (d &&& ( ~~~e &&& f)) + 23 * (d &&& (e &&& f)) = - 12 * ~~~(d ||| ( ~~~e ||| f)) - 3 * (e ^^^ (d ||| ~~~f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2209 (x y : BitVec w) : +theorem e_2209 : - 3 * ((d &&& e) ^^^ (e ||| ~~~f)) + 2 * (e &&& ~~~f) - 1 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 3 * ~~~(d &&& e) - 1 * ~~~(d ||| ~~~e) + 7 * (e &&& (d ^^^ f)) - 5 * (e ||| ~~~f) - 1 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 6 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 7 * (e ^^^ (d &&& f)) + 7 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 11 * (d ^^^ ( ~~~e ||| f)) - 3 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 6 * ~~~(d ^^^ e) - 1 * (e ^^^ (d ||| ( ~~~e &&& f))) - 7 * (f ||| (d &&& e)) - 1 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 7 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 3 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 5 * ~~~( ~~~d &&& (e ^^^ f)) - 2 * ~~~(d ^^^ f) + 1 * ~~~e - 2 * ((d ^^^ e) ||| (d ^^^ f)) - 5 * ~~~(d &&& ( ~~~e ||| f)) + 3 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 7 * ( ~~~d &&& (e ^^^ f)) + 4 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 5 * ((d &&& ~~~e) ||| (e ^^^ f)) - 7 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 1 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 4 * (f ||| ~~~(d ^^^ e)) - 2 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 1 * ( ~~~f &&& ~~~(d ^^^ e)) - 1 * ((d &&& f) ||| ~~~(e ||| f)) - 2 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 3 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 2 * (e ^^^ (d ||| (e ^^^ f))) - 11 * ((d ||| e) &&& ~~~(e ^^^ f)) + 2 * (d &&& (e ^^^ f)) - 11 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (d ||| ( ~~~e ||| f)) - 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 5 * (f ^^^ ~~~(d ||| (e &&& f))) - 2 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 18 * ~~~(d ||| (e ||| f)) + 32 * ~~~(d ||| ( ~~~e ||| f)) + 24 * ~~~( ~~~d ||| (e ||| f)) - 3 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 25 * ( ~~~d &&& ( ~~~e &&& f)) + 29 * ( ~~~d &&& (e &&& f)) + 9 * (d &&& ( ~~~e &&& f)) + 45 * (d &&& (e &&& f)) = 1 * (e ^^^ ~~~(d ||| ~~~f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2210 (x y : BitVec w) : +theorem e_2210 : 11 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 5 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 2 * ~~~(d &&& ~~~f) + 1 * (e ^^^ (d &&& (e ||| f))) + 4 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 4 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 1 * ((d &&& e) ||| ~~~(e ^^^ f)) + 11 * ( ~~~e &&& (d ^^^ f)) - 6 * (d ^^^ ( ~~~e ||| f)) + 11 * ~~~(d ^^^ e) + 1 * (d &&& (e ||| f)) - 7 * ~~~e - 6 * (e ^^^ (d ||| ~~~f)) - 2 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 1 * ~~~(e ^^^ f) + 7 * (f ^^^ (d ||| ( ~~~e ||| f))) + 7 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 5 * (e ^^^ (d ||| (e ^^^ f))) + 7 * (d ||| (e ^^^ f)) - 1 * ~~~f - 3 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * ((d ^^^ e) ||| ~~~(d ^^^ f)) + 4 * (f &&& (d ||| e)) - 2 * ( ~~~e ||| (d ^^^ f)) + 3 * f + 11 * ~~~(e ||| f) - 2 * (f ^^^ (d &&& e)) - 1 * (f ^^^ (d &&& (e ||| f))) + 1 * ( ~~~e ||| ~~~(d ^^^ f)) + 3 * (f ||| (d &&& e)) + 2 * (f &&& (d ||| ~~~e)) - 7 * ~~~(d ^^^ f) + 1 * ((d &&& e) ^^^ (e ||| f)) + 2 * (e ^^^ f) - 5 * (f ^^^ (d ||| (e ||| f))) + 1 * ( ~~~f &&& ~~~(d ^^^ e)) - 1 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 1 * ((d &&& e) ||| (e ^^^ f)) + 1 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 3 * (e ^^^ ~~~(d ||| f)) + 2 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 2 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 1 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 2 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 3 * (e &&& ~~~(d &&& ~~~f)) - 4 * ~~~(d ||| (e ||| f)) - 3 * ~~~(d ||| ( ~~~e ||| f)) - 27 * ~~~( ~~~d ||| (e ||| f)) - 22 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 59 * ( ~~~d &&& ( ~~~e &&& f)) - 5 * ( ~~~d &&& (e &&& f)) - 15 * (d &&& ( ~~~e &&& f)) = 43 * (d &&& (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2211 (x y : BitVec w) : +theorem e_2211 : 4 * (e ||| ~~~(d ^^^ f)) + 5 * (f ^^^ ~~~(d &&& (e ||| f))) + 7 * (e &&& f) - 2 * (e ||| (d &&& ~~~f)) - 7 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 4 * (e ^^^ ~~~(d ||| ~~~f)) - 6 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 7 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 11 * ( ~~~d ||| (e ^^^ f)) + 3 * (e ^^^ (d &&& (e ||| f))) - 1 * (f &&& (d ||| e)) - 6 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 7 * (d &&& f) + 4 * ( ~~~d &&& (e ^^^ f)) - 1 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 2 * (f ^^^ ~~~(d ||| ~~~e)) - 7 * ~~~(d &&& ( ~~~e &&& f)) + 4 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 2 * (f ^^^ ( ~~~d ||| (e ||| f))) - 1 * ( ~~~e ||| (d ^^^ f)) - 2 * (e ^^^ f) + 1 * ~~~( ~~~d &&& (e &&& f)) + 11 * ( ~~~e &&& (d ^^^ f)) + 2 * ((d &&& e) ||| ~~~(e ||| f)) - 2 * ((d ^^^ e) ||| ~~~(d ^^^ f)) + 5 * (d &&& e) + 1 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 4 * ~~~(d ||| (e &&& f)) + 3 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 1 * ( ~~~e &&& ~~~(d ^^^ f)) + 2 * (e ^^^ (d &&& (e ^^^ f))) - 5 * (d ||| e) - 2 * (d ||| ( ~~~e ||| f)) - 2 * (e ||| ~~~(d ||| ~~~f)) + 1 * (e ^^^ (d &&& f)) - 3 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 3 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 5 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 3 * (d &&& ~~~f) + 2 * ((d ||| e) &&& ~~~(e ^^^ f)) + 5 * ~~~( ~~~d ||| (e ^^^ f)) - 6 * ~~~(e ||| f) + 1 * ((d &&& e) ||| (e ^^^ f)) - 5 * d - 1 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 3 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 23 * ~~~(d ||| (e ||| f)) + 11 * ~~~(d ||| ( ~~~e ||| f)) + 22 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 24 * ( ~~~d &&& ( ~~~e &&& f)) + 38 * ( ~~~d &&& (e &&& f)) + 20 * (d &&& ( ~~~e &&& f)) + 21 * (d &&& (e &&& f)) = 11 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 35 * ~~~( ~~~d ||| (e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2212 (x y : BitVec w) : +theorem e_2212 : - 2 * (d ^^^ e) + 1 * ~~~(d ^^^ ( ~~~e ||| f)) - 5 * (e ^^^ (d ||| f)) + 5 * (e ^^^ (d &&& (e ^^^ f))) + 1 * (f ^^^ (d ||| ( ~~~e ||| f))) - 6 * (d &&& f) - 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 1 * ( ~~~f &&& ~~~(d ^^^ e)) + 4 * ~~~(d &&& (e &&& f)) - 1 * ( ~~~e &&& ~~~(d ^^^ f)) + 7 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 7 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 3 * (f ^^^ ~~~(d ||| ~~~e)) - 2 * (d &&& ~~~f) - 1 * (d ^^^ ( ~~~e &&& f)) + 1 * (d ||| e) + 1 * (d &&& ( ~~~e ||| f)) - 2 * (e &&& (d ^^^ f)) - 11 * ~~~(d ||| (e &&& f)) + 11 * ~~~(d ||| ~~~f) - 2 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 5 * ~~~e + 2 * (e ^^^ (d ||| ~~~f)) - 1 * (e ^^^ ~~~(d ||| (e &&& f))) + 11 * ~~~(e ^^^ f) - 6 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 4 * ( ~~~d &&& ( ~~~e ||| f)) - 11 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 1 * (f ||| (d ^^^ e)) + 2 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 4 * ~~~( ~~~d ||| (e &&& f)) + 3 * (d &&& (e ^^^ f)) + 5 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 1 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 5 * ( ~~~d &&& (e ^^^ f)) - 7 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 1 * ( ~~~e &&& (d ^^^ f)) + 3 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 11 * (e ||| ~~~(d ^^^ f)) + 4 * ( ~~~d ||| ( ~~~e &&& f)) - 7 * (f &&& ~~~(d &&& e)) + 11 * ~~~(d &&& ~~~f) + 11 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (f ||| ~~~(d ||| ~~~e)) + 1 * ~~~(e ||| f) - 43 * ~~~(d ||| (e ||| f)) - 24 * ~~~(d ||| ( ~~~e ||| f)) + 3 * ~~~( ~~~d ||| (e ||| f)) - 42 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 8 * ( ~~~d &&& ( ~~~e &&& f)) - 67 * ( ~~~d &&& (e &&& f)) - 20 * (d &&& ( ~~~e &&& f)) - 40 * (d &&& (e &&& f)) = - 2 * e := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2213 (x y : BitVec w) : +theorem e_2213 : - 2 * (f ^^^ (d ||| ( ~~~e ||| f))) + 11 * ~~~(d &&& (e ^^^ f)) - 11 * ( ~~~f &&& (d ^^^ e)) - 1 * ( ~~~d ||| ( ~~~e ||| f)) - 1 * (d &&& ( ~~~e ||| f)) + 2 * ((d &&& e) ||| (e ^^^ f)) + 5 * e - 2 * (d ||| f) - 11 * ((d ||| e) &&& ~~~(e ^^^ f)) + 1 * ( ~~~e ||| (d ^^^ f)) - 11 * (e &&& (d ||| ~~~f)) - 1 * (e ^^^ ~~~(d &&& (e &&& f))) - 1 * (f &&& ~~~(d &&& e)) + 2 * ( ~~~f ||| (d ^^^ e)) + 7 * (f &&& (d ^^^ e)) + 7 * ( ~~~d ||| (e &&& f)) - 11 * f + 1 * (f ^^^ ( ~~~d ||| (e &&& f))) + 3 * (e ^^^ (d ||| f)) + 2 * ( ~~~d &&& (e ||| f)) + 11 * (e ^^^ (d &&& (e ||| f))) + 2 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 1 * (e ^^^ (d ||| (e ^^^ f))) + 7 * ~~~(d ^^^ f) - 5 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 1 * (d ||| (e ^^^ f)) - 3 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 7 * ( ~~~d &&& ( ~~~e ||| f)) + 7 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 1 * (d &&& e) + 3 * (d ||| e) - 2 * ~~~(d &&& f) - 6 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 6 * ~~~(d ^^^ e) + 1 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 4 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 7 * (d ||| ( ~~~e &&& f)) + 4 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * (d ^^^ (e &&& f)) + 1 * (f ^^^ (d ||| (e &&& f))) - 6 * (f ||| ~~~(d ||| e)) + 1 * (f ^^^ (d &&& e)) - 6 * (f &&& (d ||| e)) + 2 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 7 * (e ^^^ ~~~(d ||| ~~~f)) - 4 * ~~~(d ||| (e ||| f)) - 28 * ~~~(d ||| ( ~~~e ||| f)) + 14 * ~~~( ~~~d ||| (e ||| f)) + 11 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 14 * ( ~~~d &&& ( ~~~e &&& f)) + 2 * ( ~~~d &&& (e &&& f)) - 5 * (d &&& ( ~~~e &&& f)) + 31 * (d &&& (e &&& f)) = 2 * (d &&& f) - 5 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2214 (x y : BitVec w) : +theorem e_2214 : - 3 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 2 * (d &&& (e ||| f)) - 11 * (f &&& ~~~(d ^^^ e)) - 1 * (d &&& ( ~~~e ||| f)) - 6 * ~~~(d ^^^ f) - 1 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 7 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 6 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 2 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 1 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 2 * ~~~(d ^^^ (e ^^^ f)) + 7 * (f ^^^ ( ~~~d ||| (e &&& f))) + 1 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 2 * ~~~(d &&& ( ~~~e &&& f)) + 1 * ~~~(d ||| f) - 2 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * ( ~~~d ||| (e ||| f)) + 5 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 11 * ((d &&& e) ||| ~~~(e ^^^ f)) + 1 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 2 * (d &&& f) + 1 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 2 * ~~~e - 7 * (f ^^^ (d ||| (e ||| f))) + 11 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 2 * (d &&& e) + 5 * (d ||| ~~~e) + 3 * ((d ||| e) &&& ~~~(e ^^^ f)) + 1 * ((d &&& f) ^^^ (e ||| f)) - 1 * ~~~(d ||| ~~~e) + 4 * ~~~(d ^^^ e) - 3 * (f ^^^ (d ||| (e &&& f))) - 1 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 11 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 1 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 7 * ( ~~~d ||| ( ~~~e &&& f)) - 5 * ( ~~~f &&& ~~~(d ^^^ e)) + 1 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 4 * (f ^^^ (d &&& ( ~~~e ||| f))) + 7 * (e ^^^ ( ~~~d &&& (e ||| f))) + 7 * (d &&& ~~~f) + 2 * ~~~(d ||| (e ||| f)) + 28 * ~~~(d ||| ( ~~~e ||| f)) + 17 * ~~~( ~~~d ||| (e ||| f)) + 17 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 2 * ( ~~~d &&& ( ~~~e &&& f)) + 7 * ( ~~~d &&& (e &&& f)) - 2 * (d &&& ( ~~~e &&& f)) + 3 * (d &&& (e &&& f)) = - 1 * (e &&& ~~~(d &&& ~~~f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2215 (x y : BitVec w) : +theorem e_2215 : - 1 * (f ^^^ (d ||| ( ~~~e ||| f))) + 5 * e - 5 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 3 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 1 * ~~~d - 7 * ( ~~~d ||| ( ~~~e &&& f)) - 1 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 1 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 11 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 7 * ((d ^^^ e) &&& (d ^^^ f)) + 7 * ( ~~~d &&& (e ||| f)) - 3 * (d ||| f) + 11 * (f ^^^ (d &&& ( ~~~e ||| f))) - 5 * ~~~(d ^^^ ( ~~~e ||| f)) - 3 * ( ~~~e &&& ~~~(d ^^^ f)) + 2 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 11 * (e ^^^ (d ||| ~~~f)) + 3 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 7 * (f ||| (d &&& ~~~e)) - 2 * f + 4 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 1 * ~~~(d ^^^ ( ~~~e &&& f)) + 3 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 2 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 4 * ~~~(d ||| ~~~f) + 1 * ~~~(e &&& ~~~f) + 4 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 2 * (d ||| (e &&& f)) + 5 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 6 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 1 * ~~~(e ||| ~~~f) + 2 * (d &&& ( ~~~e ||| f)) + 4 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 2 * (d ||| ( ~~~e &&& f)) + 1 * (f ^^^ ~~~(d ||| e)) - 7 * (e ^^^ f) + 2 * d + 11 * ((d &&& f) ||| ~~~(e ||| f)) - 5 * ~~~(d &&& ( ~~~e &&& f)) + 1 * (e ^^^ (d &&& (e ||| f))) + 7 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 6 * (e ^^^ (d ||| ( ~~~e ||| f))) - 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 2 * ~~~e - 3 * ~~~(d ||| (e ||| f)) - 1 * ~~~(d ||| ( ~~~e ||| f)) - 15 * ~~~( ~~~d ||| (e ||| f)) - 13 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 7 * ( ~~~d &&& ( ~~~e &&& f)) - 18 * ( ~~~d &&& (e &&& f)) + 2 * (d &&& ( ~~~e &&& f)) - 8 * (d &&& (e &&& f)) = 2 * (e &&& (d ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2216 (x y : BitVec w) : +theorem e_2216 : - 1 * ( ~~~f ||| (d ^^^ e)) + 4 * (e &&& ~~~f) - 6 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 2 * ~~~(d ^^^ e) - 3 * (f ||| ~~~(d ||| ~~~e)) + 1 * (e ^^^ ~~~(d &&& ~~~f)) - 6 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * ~~~(d ^^^ (e ||| f)) - 1 * ((d &&& e) ^^^ (e ||| f)) - 1 * ( ~~~d ||| ( ~~~e ||| f)) - 3 * (f &&& ~~~(d &&& e)) - 2 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 1 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 2 * ( ~~~d &&& (e ||| f)) + 11 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 1 * (e &&& ~~~(d &&& ~~~f)) + 11 * ((d ||| e) &&& ~~~(e ^^^ f)) - 7 * (f ^^^ (d ||| ( ~~~e ||| f))) - 5 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 2 * ~~~e + 5 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 7 * (f ^^^ ~~~(d ||| e)) + 7 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (e ^^^ (d ||| (e ^^^ f))) + 2 * ((d ^^^ e) ||| (d ^^^ f)) + 2 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 1 * ( ~~~d ||| ( ~~~e &&& f)) - 6 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 11 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 6 * (f ^^^ (d &&& e)) - 5 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 7 * (d ||| f) + 4 * (e ^^^ ( ~~~d &&& (e ||| f))) + 3 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 7 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 11 * (e ||| f) + 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 1 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 1 * ~~~d + 5 * (e ||| ~~~f) + 5 * (f ||| (d ^^^ e)) + 11 * (e &&& ~~~(d &&& f)) - 2 * ((d ||| ~~~e) &&& (e ^^^ f)) + 2 * e - 7 * ~~~(d ||| (e ||| f)) - 16 * ~~~(d ||| ( ~~~e ||| f)) + 6 * ~~~( ~~~d ||| (e ||| f)) + 4 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 17 * ( ~~~d &&& ( ~~~e &&& f)) + 2 * ( ~~~d &&& (e &&& f)) + 21 * (d &&& ( ~~~e &&& f)) - 6 * (d &&& (e &&& f)) = 2 * (f ||| ~~~(d ||| e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2217 (x y : BitVec w) : +theorem e_2217 : 5 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 1 * ( ~~~d ||| ( ~~~e ||| f)) + 1 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 1 * (d &&& ~~~e) - 1 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 7 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 1 * (f ||| (d &&& e)) - 2 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 11 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 1 * (d &&& (e ^^^ f)) - 1 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 2 * ~~~(d ^^^ e) - 6 * (e ||| ~~~(d ^^^ f)) + 3 * (d ||| ~~~f) - 3 * ~~~(d ||| f) + 1 * ~~~(d &&& e) - 6 * (e &&& ~~~(d &&& ~~~f)) - 5 * (d ||| (e ||| f)) + 2 * (f ^^^ ~~~(d &&& (e ||| f))) + 5 * (d &&& f) - 1 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 1 * ( ~~~d &&& (e ^^^ f)) - 2 * (e ||| ~~~(d ||| ~~~f)) + 3 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 1 * (d ||| (e &&& f)) + 7 * ((d &&& e) ||| ~~~(e ^^^ f)) + 5 * ~~~(d &&& ( ~~~e ||| f)) + 1 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 1 * (e ^^^ ~~~(d ||| ~~~f)) + 11 * ~~~(d &&& f) + 11 * ~~~(d ||| ~~~f) + 2 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 5 * (e ^^^ (d ||| f)) - 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 2 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 1 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 1 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 11 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 11 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 1 * ~~~(d ||| e) - 2 * f + 1 * ((d &&& f) ||| ~~~(e ||| f)) + 2 * (e &&& (d ||| f)) + 4 * (d ||| ( ~~~e &&& f)) - 11 * (f ^^^ (d &&& ( ~~~e ||| f))) - 2 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 19 * ~~~(d ||| ( ~~~e ||| f)) - 23 * ~~~( ~~~d ||| (e ||| f)) - 36 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 23 * ( ~~~d &&& ( ~~~e &&& f)) - 11 * ( ~~~d &&& (e &&& f)) + 6 * (d &&& ( ~~~e &&& f)) - 21 * (d &&& (e &&& f)) = 37 * ~~~(d ||| (e ||| f)) - 2 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2218 (x y : BitVec w) : +theorem e_2218 : 4 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 2 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 5 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * ( ~~~d &&& (e ^^^ f)) + 7 * (f ^^^ (d ||| ( ~~~e ||| f))) - 1 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 2 * (d ||| ( ~~~e ||| f)) + 1 * (d ||| (e ^^^ f)) - 11 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 7 * ~~~(d &&& ( ~~~e &&& f)) + 5 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 5 * (e ^^^ ~~~(d ||| f)) - 2 * (e ||| ~~~(d ^^^ f)) + 1 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 6 * (d &&& (e ^^^ f)) - 1 * (e ^^^ (d ||| (e ^^^ f))) - 2 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 3 * (e ^^^ ( ~~~d ||| (e &&& f))) - 1 * (f ||| (d &&& e)) + 7 * ~~~(d ||| ~~~f) + 1 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * (e ^^^ (d ||| ~~~f)) + 2 * (f ^^^ ~~~(d &&& (e &&& f))) + 1 * ( ~~~d &&& (e ||| f)) + 2 * ( ~~~e &&& (d ^^^ f)) - 7 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 5 * ~~~(d ||| ~~~e) + 2 * (f ^^^ ~~~(d ||| e)) + 1 * ( ~~~d ||| (e ||| f)) - 6 * (f &&& ~~~(d &&& e)) + 11 * (f ||| (d &&& ~~~e)) + 2 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 1 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 3 * ~~~d - 7 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * (f ^^^ ~~~(d &&& (e ||| f))) - 7 * (e ^^^ ~~~(d &&& (e &&& f))) + 2 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 11 * ~~~(e ^^^ f) - 1 * (d ^^^ (e ||| f)) + 3 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 5 * (f ||| ~~~(d ||| e)) - 2 * (f ^^^ (d &&& e)) - 11 * (e &&& f) + 31 * ~~~(d ||| (e ||| f)) - 20 * ~~~( ~~~d ||| (e ||| f)) + 33 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 13 * ( ~~~d &&& ( ~~~e &&& f)) + 18 * ( ~~~d &&& (e &&& f)) + 22 * (d &&& ( ~~~e &&& f)) + 19 * (d &&& (e &&& f)) = 11 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2219 (x y : BitVec w) : +theorem e_2219 : - 6 * ((d ||| e) &&& (e ^^^ f)) + 2 * ~~~(d &&& (e ^^^ f)) + 1 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 7 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 3 * ( ~~~d ||| (e &&& f)) - 5 * (f &&& ~~~(d &&& ~~~e)) + 1 * (f ||| ~~~(d ^^^ e)) + 4 * ( ~~~d &&& ( ~~~e ||| f)) - 5 * (d &&& e) + 11 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 11 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 4 * (d ||| f) - 2 * (e ^^^ (d &&& (e ^^^ f))) - 2 * (f &&& ~~~(d &&& e)) + 1 * (f ^^^ (d ||| (e &&& f))) - 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 1 * (e ^^^ ~~~(d &&& ~~~f)) + 2 * ~~~(d ||| ( ~~~e &&& f)) - 1 * ~~~(d ||| (e &&& f)) - 7 * ~~~(e &&& ~~~f) + 5 * ((d &&& e) ^^^ (e ||| f)) - 1 * (d ||| (e ^^^ f)) + 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 7 * (e ||| ~~~(d ^^^ f)) + 1 * (d &&& (e ^^^ f)) - 2 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 3 * ((d &&& e) ||| (e ^^^ f)) - 1 * ~~~(e ||| f) - 11 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 3 * ~~~(d ^^^ e) + 7 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 3 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 2 * ~~~( ~~~d &&& (e &&& f)) + 3 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 6 * ~~~(d &&& ~~~e) + 5 * (e ||| ~~~f) + 4 * ~~~(e ^^^ f) - 7 * ~~~(d ^^^ f) + 1 * (e &&& (d ||| f)) + 2 * (e ||| (d &&& f)) + 1 * (f ||| (d ^^^ e)) + 4 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 5 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 1 * (f ^^^ (d &&& ( ~~~e ||| f))) - 2 * ~~~f + 41 * ~~~(d ||| ( ~~~e ||| f)) - 6 * ~~~( ~~~d ||| (e ||| f)) + 10 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 24 * ( ~~~d &&& ( ~~~e &&& f)) - 21 * ( ~~~d &&& (e &&& f)) - 10 * (d &&& ( ~~~e &&& f)) + 19 * (d &&& (e &&& f)) = - 12 * ~~~(d ||| (e ||| f)) + 11 * (f ^^^ ~~~(d &&& e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2220 (x y : BitVec w) : +theorem e_2220 : 11 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 5 * (f ||| (d &&& ~~~e)) - 1 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 1 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 6 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 1 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 11 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 6 * (d ^^^ ( ~~~e ||| f)) - 3 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 5 * ~~~(d ^^^ e) - 6 * ((e &&& f) ||| (d &&& (e ||| f))) + 11 * (d ||| ( ~~~e &&& f)) - 1 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 2 * (e ^^^ (d ||| ( ~~~e ||| f))) - 5 * (e ||| ~~~(d ||| f)) - 3 * (f &&& (d ||| ~~~e)) + 1 * ((d &&& e) ^^^ (e ||| f)) - 1 * ((d ^^^ e) ||| (d ^^^ f)) + 1 * (d &&& f) + 3 * d + 2 * ~~~(d ^^^ (e ^^^ f)) - 1 * (f ^^^ (d &&& ~~~e)) - 11 * (f ^^^ (d &&& ( ~~~e ||| f))) + 2 * ~~~(d &&& ~~~d) + 2 * (f &&& ~~~(d &&& ~~~e)) - 11 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 4 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 1 * (f ^^^ ~~~(d ||| (e &&& f))) + 5 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 11 * ((d &&& e) ^^^ (e ||| ~~~f)) - 2 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 1 * (f &&& (d ||| e)) - 1 * (e &&& (d ||| ~~~f)) - 2 * ~~~(d ^^^ ( ~~~e ||| f)) + 2 * (e ^^^ (d &&& (e ^^^ f))) - 2 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 7 * (e ^^^ ( ~~~d ||| (e &&& f))) + 1 * (f ||| (d ^^^ e)) + 11 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 3 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 4 * (d ||| ~~~f) + 2 * (d ^^^ (e ||| f)) - 3 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 5 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 2 * (f ^^^ ( ~~~d ||| (e &&& f))) + 7 * (d ^^^ ( ~~~e &&& f)) - 31 * ~~~(d ||| (e ||| f)) - 10 * ~~~(d ||| ( ~~~e ||| f)) - 17 * ~~~( ~~~d ||| (e ||| f)) - 26 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 13 * ( ~~~d &&& ( ~~~e &&& f)) + 34 * ( ~~~d &&& (e &&& f)) - 14 * (d &&& ( ~~~e &&& f)) - 32 * (d &&& (e &&& f)) = - 1 * (e ^^^ (d &&& ( ~~~e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2221 (x y : BitVec w) : +theorem e_2221 : - 1 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 3 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 1 * ((d ||| ~~~e) &&& (e ^^^ f)) - 2 * (d &&& ~~~f) + 1 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 5 * ((d &&& e) ^^^ (e ||| f)) + 4 * ( ~~~d &&& (e ^^^ f)) - 1 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 1 * (e ^^^ (d ||| ~~~f)) - 7 * (d ||| ~~~e) - 5 * (f ^^^ (d ||| ( ~~~e &&& f))) - 2 * (e ^^^ (d ||| f)) + 2 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 3 * ~~~(d &&& (e ^^^ f)) + 11 * ( ~~~f ||| (d ^^^ e)) + 4 * (f ^^^ ~~~(d ||| e)) - 1 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 2 * (e &&& (d ||| f)) + 1 * (e ||| ~~~(d ^^^ f)) + 7 * (e &&& (d ||| ~~~f)) + 7 * (e ^^^ ~~~(d ||| ~~~f)) + 2 * ( ~~~d ||| ( ~~~e &&& f)) + 1 * (f ||| ~~~(d ||| e)) + 4 * (e &&& f) + 7 * (d ||| ( ~~~e &&& f)) - 6 * (e ||| ~~~(d ||| f)) - 2 * (d ||| ~~~f) - 1 * (f ^^^ ~~~(d &&& ~~~e)) - 6 * (e &&& ~~~(d &&& ~~~f)) - 2 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 5 * (e &&& (d ^^^ f)) - 1 * (f ||| ~~~(d ^^^ e)) - 1 * (f ^^^ (d ||| (e ||| f))) - 1 * (d ||| f) - 5 * (e ^^^ ~~~(d ||| (e &&& f))) + 4 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 2 * ~~~(d ^^^ (e &&& f)) + 1 * ((d ^^^ e) ||| (d ^^^ f)) - 3 * ~~~f - 2 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 2 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 11 * ~~~( ~~~d &&& (e &&& f)) + 2 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 2 * (e ^^^ (d &&& ~~~f)) + 4 * ((d &&& f) ^^^ (e ||| f)) - 3 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 20 * ~~~(d ||| (e ||| f)) - 16 * ~~~(d ||| ( ~~~e ||| f)) + 13 * ~~~( ~~~d ||| (e ||| f)) + 6 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 11 * ( ~~~d &&& ( ~~~e &&& f)) - 16 * ( ~~~d &&& (e &&& f)) + 2 * (d &&& (e &&& f)) = - 5 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2222 (x y : BitVec w) : +theorem e_2222 : - 5 * (e ^^^ ~~~(d &&& f)) - 1 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 1 * (d ^^^ e) - 3 * ~~~(d ||| f) - 5 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 2 * (f ^^^ ~~~(d ||| e)) - 2 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 2 * ~~~d - 1 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 1 * (d ^^^ (e ^^^ f)) - 6 * (e ^^^ (d &&& f)) + 1 * ( ~~~d &&& (e ^^^ f)) - 5 * (e ^^^ ~~~(d &&& (e ||| f))) + 7 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 3 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 11 * ~~~(d &&& ( ~~~e &&& f)) - 7 * ((e &&& f) ||| (d &&& (e ||| f))) - 6 * (e ||| (d ^^^ f)) + 1 * ( ~~~e ||| ~~~(d ^^^ f)) + 5 * (f ^^^ ~~~(d &&& e)) - 1 * (d &&& f) + 4 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 2 * (f &&& ~~~(d &&& e)) + 1 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 1 * ~~~(d &&& (e &&& f)) + 11 * (f ^^^ (d &&& ~~~e)) - 1 * ( ~~~d ||| ( ~~~e &&& f)) + 4 * (e ^^^ (d ||| (e &&& f))) + 2 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 2 * ~~~(d ^^^ ( ~~~e ||| f)) + 2 * (e &&& (d ||| ~~~f)) + 5 * ~~~(d ||| (e &&& f)) - 3 * ~~~(d &&& f) + 7 * ~~~(d &&& ( ~~~e ||| f)) + 2 * (e ^^^ (d ||| (e ||| f))) + 5 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (d ||| ( ~~~e ||| f)) + 3 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 11 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 11 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 3 * ~~~( ~~~d &&& (e ||| f)) - 1 * (e ^^^ (d ||| (e ^^^ f))) + 2 * (f ||| (d &&& ~~~e)) - 3 * ( ~~~d ||| (e &&& f)) - 6 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * ~~~(d ||| ( ~~~e ||| f)) - 1 * ~~~( ~~~d ||| (e ||| f)) + 19 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 19 * ( ~~~d &&& ( ~~~e &&& f)) + 15 * ( ~~~d &&& (e &&& f)) + 1 * (d &&& ( ~~~e &&& f)) + 24 * (d &&& (e &&& f)) = - 1 * ((d &&& e) ||| ~~~(e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2223 (x y : BitVec w) : +theorem e_2223 : 5 * ~~~(e ||| f) + 3 * (d ||| f) - 2 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 7 * (e ||| ~~~f) + 5 * (e ^^^ (d &&& (e ||| f))) + 1 * ((e &&& f) ||| (d &&& (e ||| f))) - 1 * ((d &&& e) ^^^ (e ||| f)) - 1 * ~~~d - 5 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 1 * (d ||| e) + 3 * ( ~~~d &&& (e ||| f)) - 11 * ( ~~~e ||| ~~~(d ^^^ f)) + 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 7 * (e ^^^ ~~~(d &&& ~~~f)) + 11 * (e ^^^ (d ||| (e &&& f))) - 1 * (f &&& (d ||| ~~~e)) - 1 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 7 * ((d &&& f) ||| ~~~(e ||| f)) - 2 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 5 * (f ||| (d &&& ~~~e)) - 11 * (f ^^^ ( ~~~d ||| (e ||| f))) + 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 11 * (e ^^^ ~~~(d &&& (e ||| f))) + 11 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 2 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * ( ~~~d ||| ( ~~~e ||| f)) + 4 * (d ^^^ ( ~~~e &&& f)) - 2 * (e &&& (d ||| f)) + 2 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 2 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 11 * ~~~e + 5 * (f ^^^ (d ||| ~~~e)) + 2 * ~~~(e ||| ~~~f) - 11 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 2 * ( ~~~d ||| ( ~~~e &&& f)) - 6 * ~~~(d ^^^ e) + 11 * (d ||| ~~~f) + 2 * (d ^^^ e) + 1 * (d ||| (e ^^^ f)) - 3 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 3 * ((d &&& f) ^^^ (e ||| f)) - 1 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 7 * (e ^^^ (d ||| (e ^^^ f))) - 3 * (e ^^^ (d ||| ( ~~~e &&& f))) + 1 * (e ^^^ ~~~(d &&& f)) + 4 * ((d &&& e) ||| ~~~(e ^^^ f)) - 5 * ((d ||| e) &&& (e ^^^ f)) - 19 * ~~~(d ||| (e ||| f)) - 16 * ~~~(d ||| ( ~~~e ||| f)) - 76 * ~~~( ~~~d ||| (e ||| f)) - 14 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 12 * ( ~~~d &&& (e &&& f)) - 18 * (d &&& ( ~~~e &&& f)) - 17 * (d &&& (e &&& f)) = 10 * ( ~~~d &&& ( ~~~e &&& f)) + 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2224 (x y : BitVec w) : +theorem e_2224 : - 7 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 5 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 5 * ~~~(d ^^^ e) - 2 * ~~~(d ^^^ ( ~~~e ||| f)) - 11 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 6 * (e ^^^ ~~~(d ||| f)) - 5 * (d ^^^ ( ~~~e &&& f)) + 7 * ~~~(d ^^^ ( ~~~e &&& f)) + 1 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 5 * (d ^^^ f) - 3 * ((d &&& e) ||| ~~~(e ||| f)) + 5 * (f ^^^ ~~~(d &&& ~~~e)) + 2 * ~~~(d ^^^ (e ||| f)) - 1 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 6 * (f ^^^ ( ~~~d &&& (e ||| f))) + 7 * (d &&& ( ~~~e ||| f)) + 1 * (d &&& ~~~f) + 1 * ~~~(d ||| ~~~f) + 4 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 11 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 1 * (e &&& ~~~(d ^^^ f)) - 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * (d ^^^ (e &&& f)) + 11 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 7 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 3 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 2 * (e ^^^ (d &&& (e ||| f))) + 2 * ((d &&& f) ^^^ (e ||| f)) + 4 * ((d &&& e) ||| ~~~(e ^^^ f)) - 1 * f + 2 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 2 * ~~~(d ||| f) - 1 * d - 1 * ~~~(d &&& e) + 5 * ( ~~~e ||| ~~~(d ^^^ f)) + 2 * (f ^^^ ~~~(d ||| ~~~e)) - 1 * e + 1 * (d ||| ( ~~~e &&& f)) - 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 5 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 6 * (e ||| ~~~(d ^^^ f)) + 7 * (e ^^^ (d &&& f)) - 1 * (d &&& e) - 2 * ( ~~~e &&& ~~~(d ^^^ f)) + 1 * (d ||| (e ^^^ f)) + 3 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 10 * ~~~(d ||| (e ||| f)) - 11 * ~~~(d ||| ( ~~~e ||| f)) + 8 * ~~~( ~~~d ||| (e ||| f)) + 12 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 27 * ( ~~~d &&& ( ~~~e &&& f)) + 6 * ( ~~~d &&& (e &&& f)) - 2 * (d &&& ( ~~~e &&& f)) + 30 * (d &&& (e &&& f)) = 1 * (e ^^^ (d &&& ( ~~~e ||| f))) + 5 * (f ||| (d &&& e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2225 (x y : BitVec w) : +theorem e_2225 : - 6 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 3 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 4 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 1 * (f ||| (d &&& e)) - 7 * (f ^^^ ~~~(d &&& e)) + 1 * (e ||| ~~~(d ^^^ f)) - 2 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 7 * ~~~(d &&& (e &&& f)) + 2 * ((d ||| e) &&& (e ^^^ f)) - 1 * ~~~( ~~~d ||| (e &&& f)) + 1 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 2 * (e ||| (d ^^^ f)) + 5 * (d &&& ( ~~~e ||| f)) + 4 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 1 * (d ^^^ ( ~~~e ||| f)) + 2 * (d ||| (e ^^^ f)) - 6 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 11 * ~~~( ~~~d &&& (e &&& f)) - 11 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 7 * (d ||| ( ~~~e &&& f)) - 7 * ( ~~~d &&& (e ^^^ f)) + 7 * ~~~(d ^^^ e) - 1 * (d ||| ~~~e) + 1 * ((d ^^^ e) ||| (d ^^^ f)) - 11 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 1 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 7 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 2 * (e ||| (d &&& f)) - 6 * (f &&& ~~~(d ^^^ e)) + 1 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 1 * (f &&& ~~~(d &&& e)) + 11 * ((d &&& e) ||| ~~~(e ||| f)) - 2 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 1 * ~~~(d ||| (e &&& f)) - 6 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 2 * ~~~(d ||| (e ^^^ f)) - 1 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 1 * (f ||| ~~~(d ||| ~~~e)) + 5 * (e ^^^ (d ||| ( ~~~e ||| f))) - 2 * (e ^^^ (d &&& (e ^^^ f))) + 1 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 5 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 3 * (f ^^^ (d &&& e)) + 3 * ~~~(d ^^^ ( ~~~e ||| f)) + 1 * ( ~~~f ||| ~~~(d ^^^ e)) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 15 * ~~~(d ||| (e ||| f)) - 3 * ~~~(d ||| ( ~~~e ||| f)) - 35 * ~~~( ~~~d ||| (e ||| f)) - 19 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 2 * ( ~~~d &&& ( ~~~e &&& f)) + 5 * ( ~~~d &&& (e &&& f)) - 22 * (d &&& ( ~~~e &&& f)) - 4 * (d &&& (e &&& f)) = 6 * ( ~~~d ||| (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2226 (x y : BitVec w) : +theorem e_2226 : - 6 * (d ^^^ (e ||| f)) + 1 * ((d ^^^ e) ||| (d ^^^ f)) + 2 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 1 * ( ~~~d &&& (e ||| f)) + 1 * (e ||| (d ^^^ f)) + 2 * (d ^^^ ( ~~~e &&& f)) + 11 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 7 * (d ||| e) - 1 * (e &&& ~~~(d &&& ~~~f)) + 7 * (e ^^^ ( ~~~d &&& (e ||| f))) - 11 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 5 * (d &&& ~~~f) + 1 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 1 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 5 * (f ^^^ (d &&& (e ||| f))) + 1 * (d ||| ( ~~~e &&& f)) + 11 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 1 * (e &&& f) + 1 * ((d &&& e) ||| ~~~(e ^^^ f)) - 7 * (f ^^^ ( ~~~d &&& (e ||| f))) - 1 * (e ^^^ ~~~(d &&& (e &&& f))) + 3 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 2 * ((d &&& f) ||| ~~~(e ||| f)) - 3 * (f ^^^ (d &&& ( ~~~e ||| f))) + 4 * (d &&& ( ~~~e ||| f)) - 11 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 1 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 3 * (f ||| (d ^^^ e)) + 4 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 2 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 7 * ( ~~~d &&& ( ~~~e ||| f)) - 1 * ((d &&& e) ^^^ (e ||| ~~~f)) - 1 * (d &&& (e ^^^ f)) - 2 * (f ^^^ (d ||| (e ||| f))) - 6 * ~~~(d ^^^ ( ~~~e ||| f)) - 6 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 1 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 4 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * (f &&& (d ||| e)) + 2 * ~~~(d ^^^ (e &&& f)) + 2 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 1 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 2 * ( ~~~e &&& ~~~(d ^^^ f)) + 4 * ((d &&& f) ^^^ (e ||| f)) - 1 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 2 * (f ^^^ (d &&& e)) + 1 * ~~~(d ||| ~~~f) - 14 * ~~~(d ||| (e ||| f)) + 15 * ~~~(d ||| ( ~~~e ||| f)) - 6 * ~~~( ~~~d ||| (e ||| f)) - 13 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 18 * ( ~~~d &&& (e &&& f)) + 13 * (d &&& ( ~~~e &&& f)) - 8 * (d &&& (e &&& f)) = 3 * ( ~~~d &&& ( ~~~e &&& f)) + 7 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2227 (x y : BitVec w) : +theorem e_2227 : - 3 * (e ^^^ ~~~(d ||| (e &&& f))) - 6 * ~~~(e ^^^ f) - 3 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * ~~~(d ^^^ (e ||| f)) - 2 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 3 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 11 * ( ~~~d ||| ( ~~~e ||| f)) - 6 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 1 * (f ||| (d &&& e)) - 2 * ((d &&& e) ^^^ (e ||| f)) - 1 * ~~~(d &&& f) - 2 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 1 * (f ^^^ (d ||| ( ~~~e ||| f))) - 3 * ((d ||| e) &&& (e ^^^ f)) - 7 * (f ^^^ (d &&& (e ||| f))) - 1 * ~~~( ~~~d ||| (e &&& f)) - 2 * (e ^^^ (d ||| ( ~~~e ||| f))) + 2 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 2 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 1 * (e ^^^ (d &&& (e ||| f))) + 11 * ~~~(e &&& ~~~f) - 1 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 1 * (d &&& f) - 5 * ((d ^^^ e) ||| ~~~(d ^^^ f)) + 1 * ~~~(d ^^^ (e ^^^ f)) + 3 * ~~~(d &&& e) - 1 * (f ^^^ ( ~~~d ||| (e ||| f))) + 5 * (d ||| (e ||| f)) + 7 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 1 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 7 * ( ~~~d ||| ( ~~~e &&& f)) + 7 * ((d &&& ~~~e) ||| (e ^^^ f)) - 1 * ((d &&& e) ^^^ (e ||| ~~~f)) - 6 * ~~~(d ^^^ ( ~~~e &&& f)) + 2 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 1 * ( ~~~e &&& (d ^^^ f)) - 5 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 2 * (f ^^^ (d ||| (e ||| f))) - 5 * (d ^^^ (e ^^^ f)) + 7 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 11 * (e ||| (d &&& ~~~f)) - 5 * f + 3 * (d ||| ( ~~~e &&& f)) + 2 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * (f ||| ~~~(d ^^^ e)) - 1 * ~~~(d ||| (e ||| f)) - 27 * ~~~(d ||| ( ~~~e ||| f)) - 20 * ~~~( ~~~d ||| (e ||| f)) - 14 * ( ~~~d &&& ( ~~~e &&& f)) - 16 * ( ~~~d &&& (e &&& f)) - 17 * (d &&& ( ~~~e &&& f)) - 27 * (d &&& (e &&& f)) = - 2 * (f ^^^ ~~~(d &&& e)) + 1 * ~~~( ~~~d ||| ( ~~~e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2228 (x y : BitVec w) : +theorem e_2228 : - 11 * (e ^^^ (d &&& ~~~f)) + 11 * ~~~e + 4 * ( ~~~d &&& (e ^^^ f)) + 11 * (f ^^^ (d ||| ( ~~~e &&& f))) - 7 * (f ^^^ ~~~(d &&& (e ||| f))) + 3 * (d ^^^ (e &&& f)) - 1 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 1 * ( ~~~e ||| (d ^^^ f)) - 2 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 7 * ((d &&& e) ^^^ (e ||| f)) - 1 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 11 * ~~~(d ||| f) + 2 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 4 * ( ~~~d &&& ( ~~~e ||| f)) - 1 * (e &&& f) + 1 * ~~~(d &&& ( ~~~e ||| f)) + 2 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 1 * (d ^^^ ( ~~~e &&& f)) + 1 * ~~~(d &&& ~~~e) + 11 * (d ||| (e ||| f)) - 1 * (e &&& (d ||| ~~~f)) - 6 * ~~~(d ||| (e ^^^ f)) + 7 * (e ^^^ (d ||| ~~~f)) + 1 * (d ^^^ (e ^^^ f)) + 3 * f + 7 * ((d &&& e) ||| ~~~(e ||| f)) - 2 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 1 * (d ^^^ ( ~~~e ||| f)) + 3 * ~~~(d ||| (e &&& f)) - 1 * ( ~~~d ||| ( ~~~e ||| f)) - 1 * ~~~(d &&& f) + 2 * ~~~( ~~~d &&& (e &&& f)) - 1 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 2 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 5 * ~~~(e ||| ~~~f) - 2 * ( ~~~f ||| ~~~(d ^^^ e)) - 5 * ~~~(d ||| ~~~f) - 5 * d - 2 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 1 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 4 * ~~~(d ||| ~~~e) - 1 * (f ^^^ ( ~~~d &&& (e ||| f))) - 2 * (f &&& (d ^^^ e)) - 6 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 5 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 1 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 26 * ~~~(d ||| ( ~~~e ||| f)) - 15 * ~~~( ~~~d ||| (e ||| f)) - 19 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 33 * ( ~~~d &&& ( ~~~e &&& f)) - 2 * ( ~~~d &&& (e &&& f)) - 16 * (d &&& ( ~~~e &&& f)) + 18 * (d &&& (e &&& f)) = - 5 * ((d ^^^ e) ||| (d ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2229 (x y : BitVec w) : +theorem e_2229 : - 1 * ~~~f + 11 * ~~~(e ||| ~~~f) + 1 * (e ^^^ (d ||| ~~~f)) - 7 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 2 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 2 * (d &&& (e ||| f)) - 7 * (e ^^^ (d &&& (e ^^^ f))) + 1 * (e &&& ~~~(d ^^^ f)) + 7 * ~~~(d &&& ( ~~~e ||| f)) - 1 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 1 * (e ||| (d ^^^ f)) - 1 * (e ^^^ (d ||| (e ^^^ f))) - 6 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 6 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 1 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 11 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * (e ^^^ (d &&& ( ~~~e ||| f))) + 4 * ( ~~~d ||| (e ||| f)) + 2 * ((d &&& f) ||| (e &&& ~~~f)) - 5 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 11 * (d ||| ~~~f) - 1 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 1 * (d ||| e) - 3 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 2 * (e ^^^ (d ||| ( ~~~e ||| f))) + 3 * (e ^^^ ( ~~~d ||| (e ||| f))) - 5 * (e ||| ~~~(d ||| f)) + 2 * (f ^^^ (d ||| (e &&& f))) - 5 * (e ^^^ ~~~(d ||| f)) + 3 * (d ^^^ ( ~~~e &&& f)) - 1 * (e ^^^ ~~~(d ||| ~~~f)) + 5 * e + 4 * ~~~(d &&& e) + 2 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 3 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 5 * (d ||| f) - 2 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 4 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 4 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 3 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 1 * (f &&& ~~~(d &&& e)) + 11 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 2 * ~~~(d ^^^ (e ||| f)) + 1 * (e ^^^ f) + 1 * (f ^^^ ~~~(d &&& (e ||| f))) - 4 * ~~~(d ||| ( ~~~e ||| f)) + 3 * ~~~( ~~~d ||| (e ||| f)) + 19 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 26 * ( ~~~d &&& ( ~~~e &&& f)) - 6 * ( ~~~d &&& (e &&& f)) - 19 * (d &&& ( ~~~e &&& f)) - 18 * (d &&& (e &&& f)) = - 11 * (f ||| (d ^^^ e)) + 11 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2230 (x y : BitVec w) : +theorem e_2230 : 2 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 11 * (d ||| ~~~f) - 1 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 6 * ~~~(d &&& (e ||| f)) + 3 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 2 * (e ^^^ (d ||| ~~~f)) + 1 * ((d &&& e) ^^^ (e ||| ~~~f)) + 2 * (e &&& (d ||| f)) - 11 * (d ^^^ (e ^^^ f)) - 7 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 7 * ~~~(d &&& (e &&& f)) + 4 * (e &&& ~~~(d &&& f)) - 6 * ((d ||| ~~~e) &&& (e ^^^ f)) - 6 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 3 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 1 * (f ^^^ ~~~(d &&& (e &&& f))) + 7 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 5 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 2 * ~~~(d ^^^ f) + 1 * (e ^^^ (d ||| (e ||| f))) + 7 * (e &&& (d ^^^ f)) - 1 * (f &&& (d ||| ~~~e)) + 1 * ( ~~~e ||| ~~~(d ^^^ f)) - 7 * (e ^^^ (d &&& ( ~~~e ||| f))) - 1 * ~~~( ~~~d ||| (e ^^^ f)) - 3 * ~~~( ~~~d &&& (e &&& f)) + 2 * ~~~(d ^^^ (e &&& f)) - 7 * ~~~(d ||| ( ~~~e &&& f)) + 1 * (e ^^^ ( ~~~d ||| (e &&& f))) - 5 * (e ^^^ ~~~(d &&& (e &&& f))) + 7 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 5 * (f ^^^ ~~~(d &&& ~~~e)) + 4 * (e &&& ~~~f) - 3 * (f ||| ~~~(d ^^^ e)) - 5 * ((d &&& f) ||| ~~~(e ||| f)) - 2 * (f ^^^ ( ~~~d ||| (e &&& f))) + 2 * ~~~(d ||| f) - 1 * (d ||| e) + 3 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 5 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 11 * ~~~(d ^^^ ( ~~~e &&& f)) + 2 * (f ^^^ (d &&& ~~~e)) + 4 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 3 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 4 * ((d &&& e) ||| ~~~(e ||| f)) - 11 * (e ||| ~~~(d ||| ~~~f)) - 1 * (e &&& ~~~(d &&& ~~~f)) + 2 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 31 * ~~~(d ||| (e ||| f)) + 5 * ~~~(d ||| ( ~~~e ||| f)) - 13 * ~~~( ~~~d ||| (e ||| f)) - 5 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 12 * ( ~~~d &&& (e &&& f)) - 1 * (d &&& ( ~~~e &&& f)) - 15 * (d &&& (e &&& f)) = - 11 * (e ^^^ ~~~(d &&& f)) - 5 * ( ~~~d &&& ( ~~~e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2231 (x y : BitVec w) : +theorem e_2231 : - 1 * (d ^^^ ( ~~~e ||| f)) - 5 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 5 * (d ||| ( ~~~e &&& f)) - 2 * (e ^^^ (d ||| (e &&& f))) + 2 * (d ||| (e &&& f)) - 3 * (f ^^^ ~~~(d &&& ~~~e)) + 1 * (d ^^^ (e ^^^ f)) - 7 * (e &&& ~~~(d ^^^ f)) - 7 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 3 * ((d ||| e) &&& ~~~(e ^^^ f)) - 3 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 1 * ((d &&& e) ||| ~~~(e ^^^ f)) + 5 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 11 * ~~~(d &&& e) - 11 * (e ^^^ ~~~(d &&& (e ||| f))) + 1 * ( ~~~f ||| ~~~(d ^^^ e)) - 1 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 6 * ( ~~~d &&& (e ^^^ f)) + 2 * (e &&& ~~~(d &&& f)) + 3 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * (e &&& ~~~f) + 11 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 3 * (e ||| ~~~f) - 6 * (f ^^^ ( ~~~d ||| (e &&& f))) - 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 2 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 11 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 5 * ( ~~~d ||| (e ^^^ f)) - 7 * (f ^^^ ~~~(d ||| ~~~e)) + 1 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 7 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * ~~~( ~~~d &&& (e ^^^ f)) + 7 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 11 * (f ^^^ (d ||| ~~~e)) + 1 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 2 * (f ^^^ (d ||| ( ~~~e ||| f))) + 7 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 3 * (e ||| (d &&& f)) - 2 * (e ^^^ ~~~(d ||| ~~~f)) - 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 11 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 3 * ~~~(e &&& f) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * (f ||| ~~~(d ||| ~~~e)) - 2 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 5 * (e ^^^ (d ||| ( ~~~e &&& f))) + 38 * ~~~(d ||| (e ||| f)) + 49 * ~~~(d ||| ( ~~~e ||| f)) - 6 * ~~~( ~~~d ||| (e ||| f)) - 15 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 6 * ( ~~~d &&& ( ~~~e &&& f)) - 14 * ( ~~~d &&& (e &&& f)) + 4 * (d &&& ( ~~~e &&& f)) + 5 * (d &&& (e &&& f)) = - 4 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 3 * (f ^^^ (d ||| ( ~~~e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2232 (x y : BitVec w) : +theorem e_2232 : - 7 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 2 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 1 * (f ^^^ ( ~~~d ||| (e ||| f))) - 5 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 11 * ~~~(d ^^^ ( ~~~e &&& f)) + 7 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 6 * (d ||| (e ||| f)) + 3 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 11 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 2 * ( ~~~d ||| (e ||| f)) - 6 * ~~~(d ||| (e ^^^ f)) + 1 * (f ^^^ (d ||| (e &&& f))) + 11 * ( ~~~f ||| (d ^^^ e)) - 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 5 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 5 * (f &&& ~~~(d &&& e)) + 1 * ((d &&& ~~~e) ||| (e ^^^ f)) - 2 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 2 * (f ||| (d &&& e)) + 2 * (e ||| ~~~(d ||| ~~~f)) - 2 * ( ~~~e ||| ~~~(d ^^^ f)) + 1 * (d ^^^ ( ~~~e ||| f)) + 2 * ~~~(d ||| e) + 2 * ~~~(d ^^^ f) + 5 * (f ||| ~~~(d ^^^ e)) + 7 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 7 * ~~~(d ||| ( ~~~e &&& f)) - 7 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 11 * (e ^^^ (d &&& ( ~~~e ||| f))) - 3 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 4 * ((d &&& e) ^^^ (e ||| f)) + 2 * (e ^^^ ( ~~~d ||| (e &&& f))) - 3 * ((d ^^^ e) ||| (d ^^^ f)) + 3 * ~~~d - 1 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 1 * (f ^^^ ~~~(d ||| e)) - 1 * (f ||| (d ^^^ e)) - 1 * (e ^^^ ~~~(d ||| f)) - 6 * (f ^^^ ( ~~~d ||| (e &&& f))) + 1 * (f ^^^ (d ||| ( ~~~e ||| f))) + 2 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 1 * (f ^^^ (d &&& e)) - 5 * (f &&& (d ^^^ e)) + 5 * (e ^^^ ~~~(d &&& (e ||| f))) + 1 * ~~~(d ||| (e ||| f)) + 3 * ~~~(d ||| ( ~~~e ||| f)) - 35 * ~~~( ~~~d ||| (e ||| f)) - 17 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 26 * ( ~~~d &&& ( ~~~e &&& f)) - 2 * ( ~~~d &&& (e &&& f)) + 12 * (d &&& ( ~~~e &&& f)) - 1 * (d &&& (e &&& f)) = - 3 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2233 (x y : BitVec w) : +theorem e_2233 : 1 * ~~~(d ^^^ f) - 2 * ( ~~~d &&& (e ^^^ f)) + 11 * ( ~~~d ||| (e &&& f)) + 2 * (d &&& e) + 1 * (e ^^^ (d &&& ~~~f)) + 2 * ~~~(d ||| ~~~e) - 1 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 1 * (f ^^^ ( ~~~d &&& (e ||| f))) - 1 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 4 * ~~~(e ||| ~~~f) - 1 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 1 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 2 * (e &&& ~~~(d &&& f)) - 11 * (e ||| f) - 1 * (e ||| (d ^^^ f)) - 2 * (e ^^^ ~~~(d &&& (e &&& f))) + 2 * (e ^^^ ( ~~~d ||| (e ||| f))) + 1 * (d ||| e) + 7 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 3 * ((d &&& f) ^^^ (e ||| f)) - 2 * (f ^^^ ~~~(d &&& e)) + 7 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 5 * (e ^^^ (d ||| ( ~~~e ||| f))) - 2 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 4 * (f ^^^ (d &&& e)) - 2 * (f ||| (d &&& e)) + 3 * ((d ^^^ e) ||| (d ^^^ f)) - 6 * (f ^^^ (d &&& ( ~~~e ||| f))) + 11 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 3 * f - 7 * ~~~d - 11 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 2 * (d &&& f) - 7 * (e ^^^ ~~~(d &&& (e ||| f))) + 3 * ~~~(d ^^^ ( ~~~e ||| f)) - 3 * (f ^^^ (d ||| ~~~e)) - 6 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 1 * ((d &&& e) ||| (e ^^^ f)) - 7 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 2 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 1 * ( ~~~e ||| ~~~(d ^^^ f)) - 3 * (e &&& ~~~f) - 2 * ~~~( ~~~d &&& (e &&& f)) - 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 7 * ( ~~~e &&& (d ^^^ f)) - 1 * (f ^^^ ( ~~~d ||| (e ||| f))) + 1 * (e ^^^ ~~~(d ||| f)) + 9 * ~~~(d ||| (e ||| f)) - 6 * ~~~(d ||| ( ~~~e ||| f)) + 13 * ~~~( ~~~d ||| (e ||| f)) + 24 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 5 * ( ~~~d &&& ( ~~~e &&& f)) + 23 * ( ~~~d &&& (e &&& f)) + 11 * (d &&& ( ~~~e &&& f)) - 8 * (d &&& (e &&& f)) = 2 * ( ~~~d &&& ( ~~~e ||| f)) - 7 * ( ~~~f &&& (d ^^^ e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2234 (x y : BitVec w) : +theorem e_2234 : - 6 * (f &&& (d ||| e)) - 2 * ( ~~~f &&& (d ^^^ e)) - 5 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 5 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 5 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 3 * (d ||| f) - 11 * ~~~( ~~~d &&& (e ^^^ f)) - 7 * ~~~(d ||| e) - 2 * (e ^^^ f) + 11 * ~~~e - 7 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 11 * (e &&& f) - 6 * (e ^^^ ~~~(d ||| (e &&& f))) - 11 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 5 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 1 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * (f &&& ~~~(d &&& e)) - 2 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 4 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 5 * ~~~(d ||| ~~~f) - 7 * (e ^^^ (d ||| ( ~~~e &&& f))) + 1 * ((d ||| ~~~e) &&& (e ^^^ f)) + 5 * ~~~(e &&& ~~~f) - 1 * ( ~~~e &&& (d ^^^ f)) + 3 * (e ^^^ (d &&& ( ~~~e ||| f))) - 1 * ((d &&& e) ^^^ (e ||| f)) - 2 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 1 * ~~~(d &&& e) + 7 * ~~~(e ||| f) - 6 * (f ^^^ ~~~(d &&& ~~~e)) + 1 * (d &&& ~~~e) - 2 * ~~~( ~~~d &&& (e &&& f)) - 1 * (d &&& ( ~~~e ||| f)) + 2 * (d &&& f) + 11 * (d ||| (e ||| f)) - 7 * (f ||| (d &&& ~~~e)) - 6 * (e &&& (d ||| f)) - 2 * (d ||| (e ^^^ f)) + 5 * ~~~( ~~~d ||| (e &&& f)) - 6 * (e ^^^ ( ~~~d &&& (e ||| f))) + 2 * (f ^^^ (d &&& ~~~e)) + 11 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 1 * ((d &&& f) ||| ~~~(e ||| f)) + 1 * (e ^^^ (d &&& (e ||| f))) - 1 * (d ^^^ e) + 10 * ~~~(d ||| (e ||| f)) + 11 * ~~~(d ||| ( ~~~e ||| f)) + 23 * ~~~( ~~~d ||| (e ||| f)) + 42 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 15 * ( ~~~d &&& ( ~~~e &&& f)) + 21 * ( ~~~d &&& (e &&& f)) - 2 * (d &&& ( ~~~e &&& f)) + 21 * (d &&& (e &&& f)) = 6 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 1 * ~~~(d &&& (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2235 (x y : BitVec w) : +theorem e_2235 : - 2 * ~~~(d &&& e) + 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 5 * ((d ^^^ e) ||| (d ^^^ f)) - 3 * (f ||| (d &&& ~~~e)) - 1 * ( ~~~d ||| (e ||| f)) + 4 * ~~~(d ^^^ ( ~~~e &&& f)) - 6 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 1 * (e ^^^ (d ||| (e &&& f))) + 1 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 2 * (e ||| f) + 5 * ~~~(d &&& (e ||| f)) - 2 * (f ^^^ ~~~(d &&& (e ||| f))) + 1 * (f ^^^ (d &&& e)) + 3 * ~~~(d &&& ~~~e) - 2 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 2 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 3 * ((d ^^^ e) &&& (d ^^^ f)) + 1 * ~~~(d ||| ~~~f) + 2 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 1 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 1 * (e &&& (d ^^^ f)) + 5 * (f ^^^ ( ~~~d &&& (e ||| f))) + 1 * f - 2 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 1 * (d &&& ( ~~~e ||| f)) - 3 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 2 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 5 * (e ||| ~~~(d ^^^ f)) - 6 * ( ~~~f &&& (d ^^^ e)) - 1 * ~~~(d &&& ~~~d) + 3 * (e ^^^ (d ||| ( ~~~e ||| f))) + 5 * ( ~~~d ||| ( ~~~e ||| f)) + 5 * ~~~(d &&& (e ^^^ f)) - 1 * ~~~(d ^^^ (e ||| f)) - 11 * ~~~(d &&& (e &&& f)) + 2 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 5 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 1 * ~~~(d ||| ( ~~~e &&& f)) + 2 * ( ~~~d &&& ( ~~~e ||| f)) - 1 * e + 2 * (f &&& ~~~(d &&& ~~~e)) - 2 * (d ||| (e ^^^ f)) + 7 * ((e &&& f) ||| (d &&& (e ||| f))) + 11 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 2 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 7 * (f ^^^ (d ||| ( ~~~e &&& f))) - 11 * (f ^^^ ~~~(d &&& (e &&& f))) + 2 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 5 * ~~~(d ||| (e ||| f)) + 7 * ~~~(d ||| ( ~~~e ||| f)) + 19 * ~~~( ~~~d ||| (e ||| f)) + 8 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 4 * ( ~~~d &&& ( ~~~e &&& f)) - 9 * ( ~~~d &&& (e &&& f)) + 11 * (d &&& ( ~~~e &&& f)) = - 1 * (d &&& (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2236 (x y : BitVec w) : +theorem e_2236 : 4 * (f ^^^ (d &&& e)) + 1 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 1 * d + 2 * (e ||| (d &&& ~~~f)) - 6 * (f &&& (d ||| e)) + 1 * ~~~(d ||| e) + 5 * (e &&& (d ^^^ f)) + 2 * (f ^^^ ( ~~~d ||| (e ||| f))) - 1 * (d &&& ~~~f) + 2 * (e ^^^ ~~~(d ||| f)) + 5 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 1 * ~~~( ~~~d &&& (e ^^^ f)) + 3 * ( ~~~d &&& (e ||| f)) - 6 * ((d ^^^ e) ||| (d ^^^ f)) - 6 * ( ~~~d ||| ( ~~~e ||| f)) + 4 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 3 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 1 * ( ~~~f &&& (d ^^^ e)) + 7 * ~~~(d &&& (e ^^^ f)) - 1 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 4 * (e ^^^ f) - 11 * (d ||| ( ~~~e ||| f)) + 5 * (d ||| ~~~f) + 11 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 3 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 3 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 1 * (f &&& (d ^^^ e)) + 2 * (f ^^^ (d ||| ~~~e)) - 11 * (e ||| ~~~(d ||| ~~~f)) - 2 * ~~~(d &&& ~~~e) + 4 * (d &&& e) + 2 * (e ^^^ ~~~(d ||| ~~~f)) + 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 11 * ~~~(d &&& (e &&& f)) - 7 * ~~~( ~~~d &&& (e &&& f)) - 1 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 5 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 2 * (d ||| e) - 1 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 5 * ~~~(d ^^^ f) + 7 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 2 * ( ~~~f ||| (d ^^^ e)) + 4 * (f ^^^ (d ||| ( ~~~e &&& f))) + 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 5 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 2 * ~~~(d ||| (e ||| f)) + 16 * ~~~(d ||| ( ~~~e ||| f)) + 22 * ~~~( ~~~d ||| (e ||| f)) - 1 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 35 * ( ~~~d &&& ( ~~~e &&& f)) + 9 * ( ~~~d &&& (e &&& f)) + 40 * (d &&& ( ~~~e &&& f)) + 25 * (d &&& (e &&& f)) = 1 * ~~~( ~~~d ||| (e ^^^ f)) - 2 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2237 (x y : BitVec w) : +theorem e_2237 : 2 * (f &&& ~~~(d &&& e)) + 1 * ((d &&& f) ||| ~~~(e ||| f)) + 3 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 3 * ~~~(d &&& ( ~~~e &&& f)) - 7 * (f ^^^ (d ||| ( ~~~e ||| f))) - 1 * ~~~(d &&& (e ^^^ f)) - 1 * (e ^^^ ~~~(d ||| (e &&& f))) + 1 * ~~~(e &&& ~~~f) - 1 * ~~~(d ^^^ (e &&& f)) + 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 2 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 5 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 11 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 2 * (e ||| ~~~(d ||| ~~~f)) - 1 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * (d &&& (e ^^^ f)) + 5 * (d &&& f) - 2 * ((d &&& e) ||| ~~~(e ||| f)) - 1 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 2 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 5 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 5 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 11 * ( ~~~f ||| ~~~(d ^^^ e)) - 11 * (f ^^^ (d &&& ~~~e)) - 1 * (f ^^^ ~~~(d ||| ~~~e)) - 5 * (d ^^^ (e &&& f)) + 1 * ((d ||| ~~~e) &&& (e ^^^ f)) - 2 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 6 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 2 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 2 * (f ^^^ ~~~(d &&& (e &&& f))) - 3 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 2 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 11 * (e &&& f) - 11 * ~~~(d &&& ( ~~~e ||| f)) - 1 * ( ~~~f ||| (d ^^^ e)) + 1 * (e ^^^ (d ||| (e &&& f))) - 3 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 1 * ( ~~~e &&& (d ^^^ f)) + 4 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 5 * ((d &&& e) ||| ~~~(e ^^^ f)) + 5 * (e &&& ~~~(d &&& ~~~f)) + 1 * ((d &&& f) ^^^ (e ||| f)) - 1 * (e &&& ~~~(d ^^^ f)) - 6 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 6 * (d ^^^ f) - 3 * e + 6 * ~~~(d ||| (e ||| f)) - 12 * ~~~(d ||| ( ~~~e ||| f)) + 14 * ~~~( ~~~d ||| (e ||| f)) - 2 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 39 * ( ~~~d &&& ( ~~~e &&& f)) + 4 * ( ~~~d &&& (e &&& f)) - 18 * (d &&& ( ~~~e &&& f)) - 9 * (d &&& (e &&& f)) = - 11 * ~~~(d ^^^ (e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2238 (x y : BitVec w) : +theorem e_2238 : 4 * (e ^^^ f) + 2 * ~~~( ~~~d &&& (e &&& f)) - 11 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 2 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 1 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 7 * (d ||| ( ~~~e &&& f)) + 1 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 6 * (f ^^^ ~~~(d ||| (e &&& f))) + 5 * (e &&& (d ||| f)) + 2 * ( ~~~f ||| ~~~(d ^^^ e)) + 7 * (e &&& f) - 3 * ~~~(d ||| e) + 1 * ( ~~~d ||| (e ^^^ f)) - 3 * (f ||| ~~~(d ||| ~~~e)) - 7 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 2 * (d ||| f) + 3 * ((d &&& e) ^^^ (e ||| f)) - 2 * (e ||| f) - 2 * ~~~(d &&& ~~~f) + 2 * ((d ||| e) &&& ~~~(e ^^^ f)) - 2 * (d &&& ~~~f) - 1 * ( ~~~f ||| (d ^^^ e)) + 2 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 11 * (d ^^^ (e ^^^ f)) + 5 * ( ~~~d ||| (e ||| f)) + 1 * (f ||| (d ^^^ e)) - 2 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 5 * ( ~~~f &&& ~~~(d ^^^ e)) + 1 * ~~~(d &&& e) - 7 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 1 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 1 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 1 * ((d ||| e) &&& (e ^^^ f)) - 5 * (f &&& (d ||| ~~~e)) - 3 * ~~~(e ^^^ f) + 4 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 3 * ~~~(d &&& ( ~~~e ||| f)) + 5 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 11 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 4 * (e ^^^ (d &&& (e ^^^ f))) - 1 * ~~~(d ||| (e ^^^ f)) + 7 * (f ^^^ (d &&& ~~~e)) - 5 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * (d ||| e) - 3 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 2 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 1 * (e ||| ~~~f) - 12 * ~~~(d ||| (e ||| f)) - 6 * ~~~(d ||| ( ~~~e ||| f)) - 6 * ~~~( ~~~d ||| (e ||| f)) - 15 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 27 * ( ~~~d &&& ( ~~~e &&& f)) - 10 * ( ~~~d &&& (e &&& f)) - 7 * (d &&& ( ~~~e &&& f)) - 26 * (d &&& (e &&& f)) = 2 * ~~~( ~~~d &&& (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2239 (x y : BitVec w) : +theorem e_2239 : - 1 * ( ~~~d ||| (e ||| f)) + 1 * (d &&& ~~~f) - 1 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 1 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 11 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 1 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 1 * ~~~(e &&& ~~~f) + 3 * (e ^^^ ~~~(d ||| ~~~f)) - 3 * (d ||| (e &&& f)) + 7 * ((e &&& f) ||| (d &&& (e ||| f))) - 5 * ~~~(e ||| f) - 2 * e - 3 * ~~~( ~~~d &&& (e ||| f)) + 4 * ~~~(d ||| ~~~e) - 2 * (f &&& ~~~(d &&& e)) - 5 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 7 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 1 * ( ~~~f ||| ~~~(d ^^^ e)) + 5 * (f ||| (d &&& e)) - 2 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 5 * (d ||| ~~~e) + 1 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 7 * ~~~(d &&& ( ~~~e ||| f)) - 1 * (d ||| ~~~f) + 1 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 6 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 11 * (f ^^^ ~~~(d ||| e)) + 7 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 7 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 11 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 2 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 3 * ~~~f + 7 * (e ^^^ ( ~~~d &&& (e ||| f))) + 2 * ((d &&& ~~~e) ||| (e ^^^ f)) + 11 * ( ~~~d &&& (e ^^^ f)) + 7 * (f ||| ~~~(d ||| e)) + 2 * ((d &&& e) ^^^ (e ||| f)) + 3 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 1 * (f ^^^ (d &&& ~~~e)) - 7 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 2 * (d ||| f) - 5 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 6 * ( ~~~e ||| ~~~(d ^^^ f)) - 3 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 1 * (f ||| ~~~(d ^^^ e)) + 5 * ( ~~~d ||| ( ~~~e &&& f)) + 11 * (e ||| ~~~f) + 5 * (e &&& (d ||| ~~~f)) - 18 * ~~~(d ||| (e ||| f)) - 51 * ~~~(d ||| ( ~~~e ||| f)) - 2 * ~~~( ~~~d ||| (e ||| f)) - 26 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 44 * ( ~~~d &&& ( ~~~e &&& f)) - 45 * ( ~~~d &&& (e &&& f)) - 8 * (d &&& ( ~~~e &&& f)) - 51 * (d &&& (e &&& f)) = - 1 * ~~~(d &&& ( ~~~e &&& f)) + 1 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2240 (x y : BitVec w) : +theorem e_2240 : - 1 * (e &&& f) - 7 * (d ||| ~~~e) - 3 * (e ||| ~~~(d ^^^ f)) + 4 * (f ^^^ ~~~(d &&& ~~~e)) + 1 * (d &&& (e ||| f)) + 2 * (e ||| (d &&& f)) + 4 * (d &&& ~~~e) + 2 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 1 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 11 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 3 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 1 * ( ~~~d &&& (e ||| f)) - 5 * (e &&& ~~~(d &&& f)) + 2 * (d ^^^ (e ||| f)) + 3 * (e ^^^ ~~~(d &&& ~~~f)) - 2 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 1 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 3 * ~~~(d ^^^ e) + 7 * (f ^^^ ( ~~~d ||| (e &&& f))) - 2 * ( ~~~e &&& (d ^^^ f)) + 3 * ( ~~~f ||| ~~~(d ^^^ e)) - 6 * ~~~(d ||| f) - 2 * (f ^^^ (d &&& e)) + 11 * (d ^^^ e) + 2 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 2 * (e &&& ~~~f) + 2 * ( ~~~f ||| (d ^^^ e)) - 1 * (f ^^^ ~~~(d &&& (e ||| f))) - 6 * (f ||| (d ^^^ e)) + 1 * ((d ^^^ e) &&& (d ^^^ f)) - 11 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 5 * (d &&& e) + 1 * ~~~(d &&& e) - 2 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 5 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 11 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 5 * (d ^^^ f) + 1 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 11 * f + 1 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 11 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 1 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 7 * ~~~(e ||| ~~~f) + 5 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 5 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 4 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 7 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * ((d &&& e) ^^^ (e ||| f)) - 1 * ( ~~~d ||| (e ||| f)) - 12 * ~~~(d ||| (e ||| f)) - 16 * ~~~(d ||| ( ~~~e ||| f)) - 9 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 37 * ( ~~~d &&& ( ~~~e &&& f)) - 20 * ( ~~~d &&& (e &&& f)) - 6 * (d &&& ( ~~~e &&& f)) + 26 * (d &&& (e &&& f)) = 20 * ~~~( ~~~d ||| (e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2241 (x y : BitVec w) : +theorem e_2241 : 1 * (e ^^^ (d ||| ~~~f)) - 1 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * ( ~~~f &&& (d ^^^ e)) - 6 * (e ||| ~~~f) + 5 * ((d ^^^ e) ||| (d ^^^ f)) + 1 * (e ^^^ (d ||| (e &&& f))) - 11 * ((d &&& f) ^^^ (e ||| f)) - 3 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 2 * (d &&& (e ||| f)) - 1 * (e ^^^ (d &&& (e ||| f))) - 1 * ~~~(d &&& ~~~e) - 5 * (e ^^^ (d &&& (e ^^^ f))) - 6 * (f ^^^ (d &&& e)) + 4 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 1 * ~~~e + 4 * ((d &&& f) ||| (e &&& ~~~f)) + 2 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 3 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 11 * ~~~(d &&& ( ~~~e &&& f)) - 5 * ~~~(e &&& ~~~f) + 5 * (f ^^^ ~~~(d ||| ~~~e)) - 2 * ~~~( ~~~d ||| (e &&& f)) - 7 * (e ^^^ ( ~~~d &&& (e ||| f))) + 1 * ( ~~~e ||| ~~~(d ^^^ f)) + 2 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 5 * (f &&& (d ^^^ e)) - 3 * ((d &&& e) ||| ~~~(e ^^^ f)) + 3 * (e &&& ~~~(d &&& ~~~f)) - 7 * ((d ||| ~~~e) &&& (e ^^^ f)) + 1 * (e ^^^ (d &&& ~~~f)) + 7 * (f &&& (d ||| e)) + 3 * (d &&& ~~~f) + 1 * (e ||| ~~~(d ||| f)) - 1 * (d ||| f) - 1 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 1 * (f ^^^ ~~~(d ||| e)) - 2 * ((d ||| e) &&& ~~~(e ^^^ f)) - 1 * (d ||| (e &&& f)) - 3 * (d &&& f) + 5 * (f &&& ~~~(d ^^^ e)) + 2 * (e ^^^ (d &&& ( ~~~e ||| f))) + 2 * (e ||| f) + 3 * (f ^^^ ~~~(d ||| (e &&& f))) - 1 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 1 * (e ^^^ (d ||| (e ^^^ f))) - 3 * e + 3 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 7 * (d &&& (e ^^^ f)) - 4 * ~~~(d ||| (e ||| f)) - 19 * ~~~(d ||| ( ~~~e ||| f)) - 10 * ~~~( ~~~d ||| (e ||| f)) + 29 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 7 * ( ~~~d &&& ( ~~~e &&& f)) + 13 * ( ~~~d &&& (e &&& f)) + 12 * (d &&& ( ~~~e &&& f)) - 2 * (d &&& (e &&& f)) = - 1 * ~~~(d &&& f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2242 (x y : BitVec w) : +theorem e_2242 : - 1 * (e ||| ~~~f) + 1 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 5 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 11 * ( ~~~d ||| (e ||| f)) - 1 * ((d ||| ~~~e) &&& (e ^^^ f)) + 1 * ~~~(d ||| (e ^^^ f)) - 2 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 7 * (f ^^^ (d &&& ~~~e)) - 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 2 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 7 * (d ||| ~~~e) + 1 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 1 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 3 * (f ^^^ (d &&& e)) - 5 * (e ^^^ (d ||| (e ||| f))) - 7 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 1 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 1 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 2 * f + 1 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * (e ^^^ (d &&& f)) - 1 * ((e &&& f) ||| (d &&& (e ||| f))) + 1 * (d ||| (e ||| f)) + 11 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 1 * ((d &&& e) ||| ~~~(e ||| f)) - 7 * (d &&& ( ~~~e ||| f)) + 2 * (f ^^^ ~~~(d ||| (e &&& f))) + 3 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 5 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 1 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 11 * ~~~(e ||| f) - 1 * (e ||| ~~~(d ||| ~~~f)) + 5 * ~~~(d &&& (e ||| f)) + 4 * (e ^^^ ~~~(d &&& ~~~f)) + 7 * ((d &&& f) ^^^ (e ||| f)) - 11 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 2 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 6 * ~~~(d &&& ~~~e) + 3 * ((d &&& e) ^^^ (e ||| f)) - 2 * ~~~(d &&& ~~~f) - 6 * (d ||| ~~~f) + 1 * (d ||| (e &&& f)) - 1 * ~~~(d ^^^ f) - 5 * ~~~(d &&& f) - 6 * ~~~( ~~~d &&& (e ||| f)) + 7 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 1 * (f ^^^ ~~~(d ||| ~~~e)) + 27 * ~~~(d ||| (e ||| f)) + 8 * ~~~(d ||| ( ~~~e ||| f)) + 50 * ~~~( ~~~d ||| (e ||| f)) + 15 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 9 * ( ~~~d &&& ( ~~~e &&& f)) + 1 * ( ~~~d &&& (e &&& f)) + 35 * (d &&& ( ~~~e &&& f)) + 54 * (d &&& (e &&& f)) = - 11 * ~~~(d ||| ~~~f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2243 (x y : BitVec w) : +theorem e_2243 : 1 * ~~~(d ^^^ e) - 2 * (e ^^^ (d ||| (e &&& f))) + 4 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 2 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 11 * (d ^^^ ( ~~~e ||| f)) + 11 * (e ^^^ ~~~(d &&& (e ||| f))) - 3 * (e ^^^ (d ||| (e ^^^ f))) - 7 * ~~~( ~~~d &&& (e &&& f)) + 1 * (d ||| ~~~e) + 1 * (d ^^^ ( ~~~e &&& f)) - 7 * ~~~(d &&& ~~~d) + 1 * (d &&& ~~~e) - 1 * (d ^^^ (e &&& f)) - 11 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 4 * (f ^^^ (d ||| ( ~~~e &&& f))) + 2 * (e ^^^ (d &&& ( ~~~e ||| f))) + 1 * (f ||| (d ^^^ e)) - 7 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 5 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 1 * (d ^^^ e) - 2 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 7 * (f ||| ~~~(d ||| ~~~e)) + 3 * (d ||| e) - 2 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 11 * ~~~(d ||| ~~~e) + 1 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 2 * ~~~(d &&& e) - 2 * (e &&& ~~~(d &&& ~~~f)) - 2 * (d &&& ( ~~~e ||| f)) - 1 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 2 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 1 * ~~~(e ||| ~~~f) - 1 * (e ||| ~~~(d ^^^ f)) - 6 * (e ^^^ ~~~(d ||| f)) - 1 * (f &&& ~~~(d &&& e)) - 3 * (e ^^^ (d &&& (e ||| f))) - 5 * ~~~(d &&& (e ||| f)) + 2 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 7 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 2 * (f ^^^ (d ||| ~~~e)) + 7 * ( ~~~d ||| (e ^^^ f)) + 3 * (d &&& (e ^^^ f)) - 5 * (f &&& (d ||| e)) - 1 * (f ^^^ (d ||| (e &&& f))) - 1 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 2 * (d ||| f) + 2 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 3 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 1 * ~~~(d ^^^ f) + 31 * ~~~(d ||| ( ~~~e ||| f)) - 3 * ~~~( ~~~d ||| (e ||| f)) - 11 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 10 * ( ~~~d &&& ( ~~~e &&& f)) + 21 * ( ~~~d &&& (e &&& f)) + 13 * (d &&& ( ~~~e &&& f)) + 3 * (d &&& (e &&& f)) = - 5 * (d ||| ~~~f) - 1 * ~~~(d ||| (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2244 (x y : BitVec w) : +theorem e_2244 : 7 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 3 * (e &&& ~~~(d &&& f)) - 1 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 2 * ~~~(d ||| ( ~~~e &&& f)) - 1 * ~~~( ~~~d &&& (e ^^^ f)) - 5 * ( ~~~d ||| ( ~~~e ||| f)) + 3 * (d ^^^ f) + 11 * ~~~d + 1 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 3 * (e &&& ~~~(d &&& ~~~f)) + 1 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 7 * ~~~(d ^^^ (e &&& f)) + 4 * ((d ^^^ e) &&& (d ^^^ f)) - 3 * ( ~~~d ||| ( ~~~e &&& f)) - 2 * ~~~(d &&& ~~~e) - 1 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 2 * (e ^^^ (d &&& ~~~f)) + 11 * (f ^^^ ~~~(d &&& (e &&& f))) - 1 * (e ||| ~~~(d ^^^ f)) + 2 * d - 5 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 7 * ~~~( ~~~d &&& (e ||| f)) - 3 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 1 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 4 * (f ^^^ (d ||| (e ||| f))) - 1 * ((d &&& e) ^^^ (e ||| f)) - 11 * (e ^^^ (d ||| f)) - 1 * ( ~~~e &&& (d ^^^ f)) + 2 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 5 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 7 * (f ^^^ ( ~~~d ||| (e &&& f))) + 2 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 2 * (f ||| ~~~(d ||| ~~~e)) + 2 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 3 * ~~~(d ||| ~~~f) + 1 * ~~~(d ||| e) - 1 * ( ~~~e ||| ~~~(d ^^^ f)) + 5 * (f ^^^ (d ||| ~~~e)) + 1 * (f ^^^ (d ||| (e &&& f))) + 7 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 2 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 2 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 5 * (f ^^^ ~~~(d ||| ~~~e)) - 7 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * (f ||| ~~~(d ^^^ e)) + 1 * ~~~(e &&& ~~~f) + 2 * (d ||| ~~~e) - 11 * ((d &&& e) ||| ~~~(e ||| f)) + 4 * ~~~(d ||| (e ||| f)) + 7 * ~~~(d ||| ( ~~~e ||| f)) + 2 * ~~~( ~~~d ||| (e ||| f)) + 15 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 4 * ( ~~~d &&& ( ~~~e &&& f)) - 2 * ( ~~~d &&& (e &&& f)) + 47 * (d &&& ( ~~~e &&& f)) + 4 * (d &&& (e &&& f)) = 2 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2245 (x y : BitVec w) : +theorem e_2245 : 2 * ~~~(d &&& ~~~d) - 1 * (f ||| ~~~(d ||| e)) + 4 * ((d &&& e) ^^^ (e ||| ~~~f)) - 6 * (e ^^^ ~~~(d &&& (e &&& f))) - 2 * (d ^^^ e) - 2 * ((d &&& e) ||| (e ^^^ f)) + 1 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 6 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 5 * (d &&& f) - 3 * (f ^^^ (d ||| ( ~~~e ||| f))) + 1 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 5 * (f ||| (d &&& e)) - 5 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 3 * (e ||| f) + 4 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 5 * (f ^^^ ~~~(d ||| e)) - 1 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 7 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 7 * ~~~(e ^^^ f) - 3 * (d &&& (e ^^^ f)) + 7 * (e &&& (d ||| f)) + 7 * (f &&& ~~~(d &&& e)) + 11 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 6 * (e ^^^ ~~~(d ||| (e &&& f))) + 1 * ((d ||| e) &&& (e ^^^ f)) - 1 * (e ||| ~~~(d ||| f)) - 1 * ~~~e + 1 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 5 * ( ~~~d ||| ( ~~~e ||| f)) + 1 * ((d &&& e) ^^^ (e ||| f)) - 1 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 2 * ~~~(d &&& f) + 2 * (f ^^^ ~~~(d &&& e)) - 3 * ~~~( ~~~d &&& (e ^^^ f)) + 5 * ((d &&& f) ^^^ (e ||| f)) - 1 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 1 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 2 * ( ~~~d ||| (e &&& f)) + 2 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 1 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * (d &&& ~~~e) + 11 * ( ~~~d &&& (e ||| f)) + 4 * ((d ^^^ e) ||| (d ^^^ f)) + 11 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 3 * (f &&& ~~~(d ^^^ e)) - 1 * (e ^^^ ~~~(d &&& (e ||| f))) - 6 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 1 * ( ~~~f ||| ~~~(d ^^^ e)) + 11 * ( ~~~f &&& (d ^^^ e)) - 23 * ~~~(d ||| (e ||| f)) - 53 * ~~~(d ||| ( ~~~e ||| f)) - 19 * ~~~( ~~~d ||| (e ||| f)) - 27 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 23 * ( ~~~d &&& ( ~~~e &&& f)) - 43 * ( ~~~d &&& (e &&& f)) - 33 * (d &&& ( ~~~e &&& f)) - 45 * (d &&& (e &&& f)) = - 5 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 2 * ((d ||| e) &&& ~~~(e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2246 (x y : BitVec w) : +theorem e_2246 : 4 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 2 * (e ^^^ ( ~~~d &&& (e ||| f))) - 3 * e + 1 * ~~~( ~~~d &&& (e &&& f)) + 5 * (e ||| ~~~(d ||| f)) + 4 * (f ^^^ ~~~(d &&& (e &&& f))) + 3 * (d ||| e) + 11 * ~~~(d ^^^ (e ^^^ f)) + 2 * (e ^^^ (d ||| ( ~~~e &&& f))) + 1 * (d ||| (e ^^^ f)) + 1 * ~~~(d ||| ( ~~~e &&& f)) + 7 * (d ^^^ ( ~~~e ||| f)) - 11 * (f ^^^ (d &&& ~~~e)) - 7 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 5 * (e &&& (d ^^^ f)) - 2 * ~~~(d &&& (e ||| f)) + 7 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 5 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 4 * (e &&& (d ||| ~~~f)) + 1 * (f ||| (d ^^^ e)) + 2 * ( ~~~f ||| ~~~(d ^^^ e)) + 3 * ~~~(e &&& f) + 1 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 2 * (d &&& ~~~f) - 3 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 1 * (f ||| ~~~(d ^^^ e)) + 1 * ( ~~~e ||| ~~~(d ^^^ f)) + 1 * (e ||| (d ^^^ f)) - 2 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 3 * ((d &&& ~~~e) ||| (e ^^^ f)) + 1 * (f &&& ~~~(d &&& ~~~e)) - 5 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 11 * ((d &&& e) ^^^ (e ||| ~~~f)) - 1 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 7 * (f ^^^ ~~~(d ||| ~~~e)) - 3 * (f ^^^ (d &&& e)) - 2 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (d ||| ( ~~~e &&& f)) + 11 * (d &&& f) - 2 * (d ||| f) + 2 * (f &&& (d ^^^ e)) - 11 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 6 * (d ^^^ e) + 3 * (e ^^^ ~~~(d &&& ~~~f)) + 11 * (f ^^^ (d ||| ( ~~~e &&& f))) + 3 * ~~~(d ^^^ ( ~~~e ||| f)) - 7 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 11 * ((d ||| ~~~e) &&& (e ^^^ f)) - 47 * ~~~(d ||| (e ||| f)) - 39 * ~~~(d ||| ( ~~~e ||| f)) + 2 * ~~~( ~~~d ||| (e ||| f)) - 36 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 4 * ( ~~~d &&& ( ~~~e &&& f)) - 12 * ( ~~~d &&& (e &&& f)) - 39 * (d &&& ( ~~~e &&& f)) - 27 * (d &&& (e &&& f)) = - 1 * (f ^^^ ~~~(d ||| (e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2247 (x y : BitVec w) : +theorem e_2247 : - 1 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 7 * (e ^^^ (d ||| ( ~~~e &&& f))) + 1 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 5 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 2 * (e ^^^ (d ||| (e &&& f))) - 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 2 * (f &&& ~~~(d &&& ~~~e)) + 1 * (e ^^^ ( ~~~d &&& (e ||| f))) + 2 * ~~~(d ||| ~~~e) + 11 * (f ||| (d ^^^ e)) + 7 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 7 * ( ~~~f ||| (d ^^^ e)) - 2 * (d ||| (e &&& f)) - 1 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 1 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 7 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 11 * (e ^^^ ~~~(d &&& ~~~f)) - 1 * ~~~(d ||| f) - 11 * (d ^^^ e) + 4 * ((d ||| e) &&& ~~~(e ^^^ f)) + 11 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 1 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 2 * (e ^^^ ( ~~~d ||| (e ||| f))) - 5 * ((d ||| e) &&& (e ^^^ f)) - 11 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 7 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 6 * (f ||| (d &&& ~~~e)) + 2 * (d &&& ~~~f) - 1 * (e ||| (d &&& f)) + 11 * ((d &&& e) ||| (e ^^^ f)) - 1 * ~~~(d ^^^ f) + 1 * (d ||| ( ~~~e ||| f)) + 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 4 * (d &&& ~~~e) + 2 * (f &&& (d ||| ~~~e)) + 2 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 1 * ~~~(d &&& (e ||| f)) + 5 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 3 * (e ||| f) + 5 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 7 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 2 * (e ||| ~~~(d ||| ~~~f)) + 1 * (e ||| ~~~f) - 1 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 11 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 3 * (f ^^^ (d ||| e)) + 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 28 * ~~~(d ||| (e ||| f)) - 26 * ~~~(d ||| ( ~~~e ||| f)) - 19 * ~~~( ~~~d ||| (e ||| f)) - 25 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 19 * ( ~~~d &&& ( ~~~e &&& f)) - 21 * ( ~~~d &&& (e &&& f)) - 10 * (d &&& ( ~~~e &&& f)) - 40 * (d &&& (e &&& f)) = - 3 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 2 * (d ||| ~~~e) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2248 (x y : BitVec w) : +theorem e_2248 : 2 * (e ||| f) + 7 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 5 * (f ^^^ ~~~(d ||| e)) - 7 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 2 * (f ^^^ (d ||| ( ~~~e &&& f))) + 11 * (f ^^^ ~~~(d ||| (e &&& f))) + 1 * (d ||| ( ~~~e ||| f)) + 2 * ~~~(d &&& (e ^^^ f)) + 1 * ((d ||| e) &&& ~~~(e ^^^ f)) + 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 3 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 1 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 4 * (f ^^^ (d ||| (e &&& f))) - 6 * ~~~f + 3 * (f ^^^ ~~~(d &&& ~~~e)) - 7 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 6 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 2 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 1 * (d &&& ~~~e) - 5 * ((d &&& e) ^^^ (e ||| f)) + 5 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 2 * (d &&& e) - 2 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 6 * ~~~e - 2 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 11 * ~~~(d ||| (e ^^^ f)) + 11 * ~~~(e ||| f) - 1 * ((d ||| ~~~e) &&& (e ^^^ f)) + 4 * (e ^^^ (d ||| ( ~~~e ||| f))) + 5 * (f ||| (d ^^^ e)) - 1 * (f ||| ~~~(d ^^^ e)) - 2 * ( ~~~d ||| ( ~~~e ||| f)) + 5 * d + 2 * ~~~(d ^^^ (e ^^^ f)) - 2 * (e ^^^ f) - 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 2 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 1 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 7 * ( ~~~f &&& ~~~(d ^^^ e)) + 7 * (f ^^^ (d ||| e)) + 3 * (d ||| ( ~~~e &&& f)) + 2 * (e ^^^ (d ||| f)) + 1 * (e ^^^ ~~~(d &&& (e &&& f))) - 7 * ~~~(d ||| e) - 11 * ~~~( ~~~d &&& (e &&& f)) - 2 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 2 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 6 * ((d &&& f) ||| ~~~(e ||| f)) - 15 * ~~~(d ||| (e ||| f)) - 34 * ~~~(d ||| ( ~~~e ||| f)) - 11 * ~~~( ~~~d ||| (e ||| f)) - 14 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 5 * ( ~~~d &&& ( ~~~e &&& f)) - 37 * ( ~~~d &&& (e &&& f)) - 9 * (d &&& ( ~~~e &&& f)) - 17 * (d &&& (e &&& f)) = - 11 * ( ~~~d ||| ( ~~~e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2249 (x y : BitVec w) : +theorem e_2249 : - 7 * ~~~(d &&& ~~~e) - 3 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 11 * (e ||| ~~~(d ^^^ f)) - 1 * (f ^^^ (d ||| e)) - 1 * (f ||| (d &&& ~~~e)) + 1 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 1 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 11 * (d ||| (e &&& f)) + 1 * (e &&& (d ||| f)) + 11 * (d &&& ~~~e) + 1 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 2 * (e ^^^ (d ||| (e ^^^ f))) - 2 * ~~~(d ^^^ f) - 11 * f - 2 * ((d ^^^ e) ||| (d ^^^ f)) - 3 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 5 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 7 * ~~~(d &&& e) - 1 * (f ^^^ (d ||| ( ~~~e ||| f))) - 6 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 1 * ~~~(d ||| (e &&& f)) + 2 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 3 * (f ^^^ (d ||| ~~~e)) - 11 * (f ^^^ (d &&& e)) + 3 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 5 * ~~~(d &&& ~~~d) + 3 * ~~~( ~~~d ||| (e ^^^ f)) + 4 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 2 * (e ^^^ ~~~(d &&& (e &&& f))) + 11 * (e ^^^ (d &&& ~~~f)) - 1 * (f ||| (d &&& e)) - 7 * ( ~~~e ||| (d ^^^ f)) + 7 * ~~~(d ||| ~~~f) - 1 * (e ^^^ ~~~(d &&& ~~~f)) + 2 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 1 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 11 * (e &&& ~~~f) - 3 * ((d &&& e) ||| ~~~(e ^^^ f)) - 2 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 1 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 6 * (e ^^^ (d ||| (e ||| f))) - 1 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 1 * (e &&& (d ^^^ f)) + 7 * ( ~~~e ||| ~~~(d ^^^ f)) + 7 * ( ~~~f ||| ~~~(d ^^^ e)) + 7 * ( ~~~d &&& ( ~~~e ||| f)) - 6 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 30 * ~~~(d ||| (e ||| f)) - 33 * ~~~(d ||| ( ~~~e ||| f)) - 30 * ~~~( ~~~d ||| (e ||| f)) + 10 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 6 * ( ~~~d &&& ( ~~~e &&& f)) - 11 * ( ~~~d &&& (e &&& f)) + 13 * (d &&& ( ~~~e &&& f)) - 13 * (d &&& (e &&& f)) = - 1 * (f ^^^ (d &&& (e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2250 (x y : BitVec w) : +theorem e_2250 : 11 * (f ^^^ (d &&& ( ~~~e ||| f))) - 2 * ( ~~~e ||| (d ^^^ f)) - 6 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 3 * (f &&& (d ||| ~~~e)) - 11 * (e ^^^ (d ||| ~~~f)) - 2 * (e ||| ~~~(d ||| f)) + 2 * (f ^^^ (d &&& e)) - 1 * (f ^^^ (d ||| ( ~~~e ||| f))) - 5 * ( ~~~d &&& ( ~~~e ||| f)) - 5 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 7 * (d ^^^ ( ~~~e &&& f)) + 1 * ~~~(e ||| f) + 3 * (e &&& ~~~(d &&& f)) + 1 * ~~~(d &&& ~~~d) - 2 * (d ^^^ f) + 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 7 * ~~~(d &&& (e &&& f)) + 7 * (e ^^^ (d ||| (e ||| f))) + 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 1 * ~~~(d ||| ~~~f) - 6 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 1 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 1 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 7 * ~~~(d &&& e) + 3 * (f &&& ~~~(d &&& e)) - 5 * (f ^^^ (d ||| ( ~~~e &&& f))) - 2 * (e &&& (d ||| f)) + 1 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 6 * (e ||| ~~~(d ^^^ f)) + 5 * (d &&& (e ^^^ f)) + 3 * (e ^^^ (d ||| ( ~~~e &&& f))) - 1 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 5 * (f ^^^ (d ||| ~~~e)) + 1 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 5 * ~~~(d &&& (e ||| f)) + 2 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 6 * (d ^^^ (e &&& f)) - 1 * ( ~~~e &&& (d ^^^ f)) + 1 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * ~~~(d ^^^ ( ~~~e &&& f)) - 1 * ((d ||| e) &&& (e ^^^ f)) - 3 * (f ^^^ ~~~(d &&& (e &&& f))) - 2 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 1 * (f &&& (d ||| e)) - 5 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * ~~~(d ^^^ e) + 2 * ~~~(e ||| ~~~f) + 7 * e - 1 * ~~~(d ||| f) - 3 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 37 * ~~~(d ||| (e ||| f)) + 10 * ~~~(d ||| ( ~~~e ||| f)) + 19 * ~~~( ~~~d ||| (e ||| f)) + 33 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 2 * ( ~~~d &&& ( ~~~e &&& f)) + 20 * ( ~~~d &&& (e &&& f)) + 10 * (d &&& ( ~~~e &&& f)) = - 28 * (d &&& (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2251 (x y : BitVec w) : +theorem e_2251 : - 2 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 11 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 5 * (f ^^^ (d ||| ( ~~~e ||| f))) + 2 * (e ^^^ ~~~(d &&& ~~~f)) - 6 * ((d &&& e) ||| (e ^^^ f)) - 7 * ( ~~~f ||| (d ^^^ e)) + 5 * (f ^^^ (d &&& ( ~~~e ||| f))) + 1 * (e ^^^ ~~~(d &&& (e &&& f))) + 1 * (d ^^^ f) + 7 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * ~~~(e &&& f) + 1 * ~~~(e &&& ~~~f) - 1 * (f ^^^ (d &&& ~~~e)) - 11 * (e ^^^ (d ||| (e &&& f))) - 2 * (e ^^^ (d ||| ( ~~~e ||| f))) - 1 * (e &&& ~~~(d &&& f)) - 5 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 7 * (f ^^^ (d ||| e)) + 2 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 3 * ~~~(e ||| f) + 5 * (e ^^^ (d &&& ~~~f)) + 7 * (f ^^^ ~~~(d &&& (e ||| f))) - 6 * (e &&& ~~~(d &&& ~~~f)) - 6 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 5 * (f &&& ~~~(d ^^^ e)) - 7 * ( ~~~d &&& (e ||| f)) - 5 * (e ||| (d &&& ~~~f)) - 3 * ~~~(d ||| ~~~e) + 5 * ~~~(d &&& ( ~~~e ||| f)) + 5 * f - 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 6 * (d ||| (e ^^^ f)) - 1 * (e ^^^ ~~~(d &&& (e ||| f))) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 1 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * ~~~( ~~~d &&& (e ||| f)) - 2 * ( ~~~e &&& ~~~(d ^^^ f)) + 4 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 2 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * (e ^^^ (d &&& f)) - 1 * (f ^^^ ~~~(d ||| e)) + 1 * (d ^^^ ( ~~~e ||| f)) + 1 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 11 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * (f &&& (d ||| e)) - 3 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 1 * (f &&& (d ^^^ e)) + 7 * (f ^^^ (d ||| (e &&& f))) + 11 * (e ^^^ (d ||| (e ^^^ f))) - 12 * ~~~(d ||| (e ||| f)) + 26 * ~~~(d ||| ( ~~~e ||| f)) - 10 * ~~~( ~~~d ||| (e ||| f)) + 2 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 2 * ( ~~~d &&& ( ~~~e &&& f)) - 12 * ( ~~~d &&& (e &&& f)) - 16 * (d &&& ( ~~~e &&& f)) - 8 * (d &&& (e &&& f)) = 1 * d - 4 * ~~~( ~~~d &&& (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2252 (x y : BitVec w) : +theorem e_2252 : 2 * ( ~~~e ||| (d ^^^ f)) + 2 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 3 * (e ^^^ ~~~(d &&& f)) - 1 * (e ||| ~~~(d ||| f)) + 1 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 6 * ~~~e + 5 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 6 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 6 * (d ^^^ ( ~~~e ||| f)) + 7 * (e ||| ~~~(d ^^^ f)) - 5 * (f &&& (d ||| e)) - 3 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 5 * ~~~(d &&& (e ||| f)) + 7 * ( ~~~e &&& (d ^^^ f)) + 2 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 11 * (e ^^^ ~~~(d &&& ~~~f)) + 4 * ~~~(e &&& f) + 7 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 2 * (e ^^^ (d &&& (e ^^^ f))) + 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 2 * ((d ^^^ e) &&& (d ^^^ f)) - 1 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 2 * ( ~~~d ||| (e ^^^ f)) + 2 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 11 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (f ^^^ (d &&& ( ~~~e ||| f))) - 3 * (f ||| (d &&& ~~~e)) - 1 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 2 * ( ~~~d ||| (e ||| f)) + 7 * (d &&& f) + 3 * (e &&& (d ||| f)) - 2 * (e ^^^ (d ||| (e ^^^ f))) + 4 * (f ^^^ ~~~(d &&& ~~~e)) - 1 * ~~~(e ||| f) + 11 * (f ^^^ (d &&& ~~~e)) - 3 * ~~~(d ||| ~~~f) + 1 * (d &&& (e ||| f)) + 1 * ((d &&& e) ||| ~~~(e ^^^ f)) + 2 * (f &&& ~~~(d &&& ~~~e)) - 5 * ~~~(d &&& ( ~~~e ||| f)) + 11 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 2 * ( ~~~f &&& (d ^^^ e)) - 7 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 11 * (e ^^^ ~~~(d ||| f)) - 1 * ~~~( ~~~d ||| (e &&& f)) + 7 * (e ^^^ (d ||| ~~~f)) + 1 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 3 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 2 * ~~~(d ||| e) - 34 * ~~~(d ||| (e ||| f)) - 11 * ~~~(d ||| ( ~~~e ||| f)) - 30 * ~~~( ~~~d ||| (e ||| f)) - 54 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 61 * ( ~~~d &&& ( ~~~e &&& f)) - 13 * ( ~~~d &&& (e &&& f)) - 47 * (d &&& ( ~~~e &&& f)) - 29 * (d &&& (e &&& f)) = - 2 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2253 (x y : BitVec w) : +theorem e_2253 : 1 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 1 * ~~~(d ||| (e &&& f)) - 2 * ( ~~~e ||| (d ^^^ f)) + 1 * (f ^^^ ( ~~~d ||| (e ||| f))) + 2 * (e &&& f) - 11 * (e ^^^ (d ||| ( ~~~e &&& f))) - 2 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 6 * ~~~(d &&& ( ~~~e ||| f)) - 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 4 * ~~~( ~~~d &&& (e ||| f)) - 11 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 6 * (e ^^^ ~~~(d &&& (e ||| f))) - 11 * (d ||| ( ~~~e &&& f)) + 1 * ~~~(e ||| f) - 7 * ~~~(d &&& ( ~~~e &&& f)) - 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 1 * (d &&& e) - 2 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 1 * (f &&& (d ||| ~~~e)) + 5 * ( ~~~d ||| ( ~~~e &&& f)) + 1 * ~~~(d ||| ~~~e) + 11 * ~~~( ~~~d ||| (e ^^^ f)) + 11 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 5 * (e ||| f) - 2 * d - 6 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 1 * (e ^^^ ( ~~~d ||| (e &&& f))) + 3 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 11 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 5 * (e &&& ~~~f) + 1 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 7 * ~~~d + 2 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 7 * (d ^^^ (e ^^^ f)) + 4 * (d ||| ~~~e) - 2 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 2 * ~~~(e ||| ~~~f) - 6 * (e ||| ~~~f) - 2 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 6 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 3 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 3 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 5 * (e ^^^ (d ||| (e &&& f))) + 1 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 7 * ~~~( ~~~d ||| (e &&& f)) - 3 * ((d ||| e) &&& (e ^^^ f)) + 7 * (e ^^^ ( ~~~d ||| (e ||| f))) + 7 * ( ~~~e &&& ~~~(d ^^^ f)) - 17 * ~~~(d ||| (e ||| f)) + 27 * ~~~(d ||| ( ~~~e ||| f)) + 26 * ~~~( ~~~d ||| (e ||| f)) + 43 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 36 * ( ~~~d &&& ( ~~~e &&& f)) + 33 * ( ~~~d &&& (e &&& f)) + 18 * (d &&& ( ~~~e &&& f)) + 21 * (d &&& (e &&& f)) = - 2 * (f ^^^ ~~~(d ||| (e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2254 (x y : BitVec w) : +theorem e_2254 : 2 * (d ||| (e ||| f)) + 2 * (d ||| f) + 1 * (f ^^^ (d ||| (e ||| f))) + 1 * (d ||| e) - 1 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 3 * (e ^^^ (d ||| (e ||| f))) - 1 * ((d ^^^ e) ||| ~~~(d ^^^ f)) + 2 * ( ~~~f ||| (d ^^^ e)) + 2 * ~~~( ~~~d &&& (e ||| f)) - 1 * (e ||| (d ^^^ f)) - 7 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 2 * ((d &&& e) ||| ~~~(e ^^^ f)) + 11 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 2 * ~~~(d ||| (e &&& f)) + 3 * ((d ||| ~~~e) &&& (e ^^^ f)) + 3 * ( ~~~d ||| ( ~~~e ||| f)) - 11 * (f &&& ~~~(d &&& ~~~e)) + 4 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 5 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 7 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 1 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 5 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 3 * (f ^^^ ( ~~~d ||| (e &&& f))) - 6 * (d ^^^ ( ~~~e &&& f)) - 3 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 2 * ((d ||| e) &&& (e ^^^ f)) - 3 * ~~~(d ||| ~~~e) + 11 * (f ^^^ ( ~~~d ||| (e ||| f))) - 5 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 5 * ~~~(d &&& ~~~d) - 1 * ~~~(d ^^^ ( ~~~e &&& f)) - 7 * (f ||| ~~~(d ||| e)) - 2 * ~~~( ~~~d ||| (e &&& f)) + 4 * ( ~~~f &&& ~~~(d ^^^ e)) + 1 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 5 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 11 * ~~~(d ||| e) + 7 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 4 * (d &&& ~~~e) + 11 * ((d &&& f) ^^^ (e ||| f)) - 11 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 4 * (e ^^^ (d &&& ~~~f)) - 1 * (f ^^^ ~~~(d ||| e)) - 2 * (e ||| ~~~(d ||| ~~~f)) - 2 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 11 * ( ~~~e &&& ~~~(d ^^^ f)) + 7 * (d &&& ( ~~~e ||| f)) - 1 * ((e &&& f) ||| (d &&& (e ||| f))) + 1 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 19 * ~~~(d ||| (e ||| f)) - 28 * ~~~(d ||| ( ~~~e ||| f)) - 26 * ~~~( ~~~d ||| (e ||| f)) - 35 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 8 * ( ~~~d &&& ( ~~~e &&& f)) + 1 * ( ~~~d &&& (e &&& f)) - 17 * (d &&& ( ~~~e &&& f)) + 13 * (d &&& (e &&& f)) = 1 * ((d &&& e) ||| ~~~(e ||| ~~~f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2255 (x y : BitVec w) : +theorem e_2255 : - 5 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 11 * ~~~(d ^^^ e) - 2 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 3 * ((d &&& e) ||| ~~~(e ||| f)) - 3 * (e ^^^ f) + 2 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 2 * ~~~(d &&& f) + 1 * (d ||| (e &&& f)) - 11 * (d ^^^ (e ^^^ f)) - 6 * (f ^^^ ( ~~~d ||| (e ||| f))) - 11 * (e ^^^ (d &&& f)) + 5 * (f ^^^ ( ~~~d ||| (e &&& f))) - 2 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 1 * (f ^^^ (d &&& (e ||| f))) + 3 * ( ~~~e ||| (d ^^^ f)) + 11 * ( ~~~d ||| (e ||| f)) + 5 * (d ||| f) - 6 * ~~~(e ||| f) + 7 * ((d &&& f) ||| ~~~(e ||| f)) - 2 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 2 * (d ||| (e ||| f)) - 5 * ((d ^^^ e) ||| ~~~(d ^^^ f)) + 11 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 5 * f - 7 * ( ~~~f ||| ~~~(d ^^^ e)) - 2 * (d &&& (e ^^^ f)) - 2 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 4 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 7 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 4 * (e ^^^ (d ||| f)) - 5 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 1 * ~~~(d ^^^ (e ||| f)) - 7 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 11 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 2 * (e ^^^ (d ||| ( ~~~e &&& f))) - 1 * (f ||| (d &&& ~~~e)) + 2 * ((d &&& f) ||| (e &&& ~~~f)) + 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 1 * ( ~~~f &&& ~~~(d ^^^ e)) - 2 * (d &&& ~~~f) - 2 * ~~~(d &&& ~~~e) + 1 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 7 * (f ^^^ (d ||| ( ~~~e ||| f))) - 5 * (f &&& (d ^^^ e)) - 1 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * (e ||| ~~~(d ||| f)) - 6 * (d ^^^ (e ||| f)) - 1 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 5 * (e ^^^ (d ||| (e ^^^ f))) - 1 * ((d &&& e) ^^^ (e ||| f)) - 5 * ~~~(d ||| (e ||| f)) + 29 * ~~~(d ||| ( ~~~e ||| f)) - 7 * ~~~( ~~~d ||| (e ||| f)) + 30 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 29 * ( ~~~d &&& ( ~~~e &&& f)) + 18 * ( ~~~d &&& (e &&& f)) + 5 * (d &&& ( ~~~e &&& f)) + 15 * (d &&& (e &&& f)) = - 1 * ( ~~~d ||| ( ~~~e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2256 (x y : BitVec w) : +theorem e_2256 : - 1 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 5 * ((d &&& e) ||| (e ^^^ f)) + 1 * (e ^^^ (d ||| (e ^^^ f))) + 4 * (f ^^^ (d ||| (e ||| f))) - 3 * (e ^^^ (d ||| f)) + 2 * (d ||| (e &&& f)) - 2 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 3 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * (f ||| ~~~(d ||| e)) + 2 * (e ^^^ (d ||| ( ~~~e ||| f))) + 5 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 6 * (e ||| (d &&& ~~~f)) - 3 * ~~~(d ||| (e &&& f)) - 1 * (f ^^^ (d &&& e)) - 2 * ((d &&& f) ^^^ (e ||| f)) + 5 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 1 * ((d &&& e) ||| ~~~(e ||| f)) - 2 * ~~~(d &&& ~~~e) + 2 * ((d &&& e) ||| ~~~(e ^^^ f)) - 11 * ~~~d - 1 * (e ||| f) - 1 * (d ^^^ (e ^^^ f)) - 5 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 1 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 2 * e - 3 * (f ^^^ (d &&& (e ||| f))) - 7 * (e ^^^ (d &&& (e ||| f))) + 1 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 6 * (d ||| ~~~f) + 3 * (e ^^^ ~~~(d ||| (e &&& f))) + 1 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 3 * (f ^^^ ~~~(d ||| e)) + 1 * (f ^^^ ~~~(d ||| (e &&& f))) + 4 * (e ^^^ ~~~(d &&& f)) + 1 * (e ||| ~~~f) - 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 2 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 4 * ~~~(d ^^^ e) - 1 * (d &&& ( ~~~e ||| f)) - 6 * ~~~(d &&& (e &&& f)) - 1 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 5 * (d &&& ~~~f) + 7 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 7 * ~~~(d ||| ~~~f) - 2 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 3 * (d &&& (e ||| f)) + 4 * ~~~(d &&& ( ~~~e ||| f)) + 2 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 1 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 11 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 5 * ~~~(d ||| (e ||| f)) + 36 * ~~~(d ||| ( ~~~e ||| f)) - 35 * ~~~( ~~~d ||| (e ||| f)) - 16 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 2 * ( ~~~d &&& ( ~~~e &&& f)) + 17 * ( ~~~d &&& (e &&& f)) + 9 * (d &&& ( ~~~e &&& f)) - 10 * (d &&& (e &&& f)) = - 11 * ~~~( ~~~d ||| (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2257 (x y : BitVec w) : +theorem e_2257 : 2 * (f ^^^ (d ||| ~~~e)) + 7 * (e &&& ~~~(d &&& ~~~f)) - 2 * (e &&& ~~~(d ^^^ f)) - 5 * (f ||| ~~~(d ^^^ e)) + 5 * ~~~(d &&& (e &&& f)) + 3 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 6 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 2 * (d &&& ( ~~~e ||| f)) - 7 * ~~~(d ||| ( ~~~e &&& f)) - 1 * (f ^^^ ~~~(d &&& (e &&& f))) - 2 * (e ^^^ (d ||| ( ~~~e ||| f))) - 1 * ( ~~~e ||| (d ^^^ f)) + 1 * (e ^^^ ~~~(d &&& f)) + 3 * ( ~~~d ||| (e ||| f)) - 2 * ~~~e + 1 * ((d &&& ~~~e) ||| (e ^^^ f)) + 3 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 11 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 4 * ( ~~~d ||| (e &&& f)) - 3 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 6 * (e &&& (d ^^^ f)) - 5 * (f ||| ~~~(d ||| e)) + 2 * ((d &&& e) ^^^ (e ||| ~~~f)) + 7 * ((d &&& e) ^^^ (e ||| f)) + 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 1 * (d ^^^ ( ~~~e ||| f)) - 5 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 4 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 5 * (d ^^^ (e ^^^ f)) - 1 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 4 * (e ^^^ (d ||| ~~~f)) + 3 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 7 * (f ||| (d &&& ~~~e)) + 11 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 1 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 1 * ~~~(d ||| e) + 4 * ((d &&& e) ||| ~~~(e ^^^ f)) + 1 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * (e ^^^ ( ~~~d ||| (e &&& f))) + 1 * ~~~(e ||| f) + 5 * (d ||| (e ^^^ f)) + 1 * (f ^^^ (d ||| ( ~~~e ||| f))) - 7 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 5 * ~~~(d ^^^ ( ~~~e ||| f)) + 1 * ( ~~~f &&& (d ^^^ e)) - 1 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 11 * (e ||| (d ^^^ f)) + 2 * (f &&& ~~~(d ^^^ e)) + 5 * (f ^^^ (d &&& (e ||| f))) - 3 * ~~~(d &&& f) - 6 * ~~~(d ||| (e ||| f)) + 5 * ~~~(d ||| ( ~~~e ||| f)) - 12 * ~~~( ~~~d ||| (e ||| f)) + 32 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 8 * ( ~~~d &&& ( ~~~e &&& f)) - 10 * ( ~~~d &&& (e &&& f)) - 4 * (d &&& ( ~~~e &&& f)) + 14 * (d &&& (e &&& f)) = 1 * (d ^^^ e) + 7 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2258 (x y : BitVec w) : +theorem e_2258 : - 2 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 2 * (d ||| ~~~e) - 1 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 6 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 7 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 2 * ~~~(d ^^^ ( ~~~e &&& f)) + 5 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 1 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 2 * ~~~(d &&& (e &&& f)) + 1 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 11 * (f ^^^ ( ~~~d ||| (e ||| f))) - 1 * (f &&& (d ||| ~~~e)) + 11 * (e ||| ~~~(d ||| ~~~f)) + 3 * (f ^^^ (d ||| ( ~~~e ||| f))) - 5 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 1 * (f ^^^ ~~~(d &&& e)) - 7 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 1 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 11 * (d ||| (e &&& f)) + 3 * ((d &&& e) ||| (e ^^^ f)) + 3 * (f ^^^ (d &&& (e ||| f))) - 6 * (e &&& ~~~(d &&& ~~~f)) + 3 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 2 * (e ^^^ ( ~~~d ||| (e ||| f))) - 1 * (e ^^^ (d &&& ( ~~~e ||| f))) - 3 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 6 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 1 * (d &&& f) - 2 * (f ||| (d &&& e)) - 1 * (e ^^^ (d ||| ~~~f)) - 7 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 11 * (f ^^^ ~~~(d ||| e)) - 7 * ~~~(d ^^^ ( ~~~e ||| f)) - 2 * ((d &&& e) ||| ~~~(e ||| f)) - 1 * ( ~~~d &&& (e ^^^ f)) + 11 * (e ^^^ (d ||| (e ^^^ f))) + 7 * (d ||| (e ||| f)) + 2 * ( ~~~e &&& ~~~(d ^^^ f)) + 11 * ~~~(e &&& ~~~f) - 1 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 5 * (e ^^^ ~~~(d &&& (e &&& f))) - 1 * (d ||| ( ~~~e ||| f)) + 3 * ((d &&& f) ||| (e &&& ~~~f)) + 1 * (f ||| (d ^^^ e)) + 4 * ( ~~~d ||| (e ^^^ f)) - 3 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 5 * (f ^^^ (d ||| e)) + 2 * ((d &&& e) ||| ~~~(e ^^^ f)) + 1 * ~~~(d ||| ~~~e) - 11 * ~~~(d ||| (e ||| f)) + 9 * ~~~(d ||| ( ~~~e ||| f)) - 29 * ~~~( ~~~d ||| (e ||| f)) - 22 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 45 * ( ~~~d &&& ( ~~~e &&& f)) - 32 * ( ~~~d &&& (e &&& f)) - 35 * (d &&& ( ~~~e &&& f)) - 32 * (d &&& (e &&& f)) = 11 * (e ||| (d &&& ~~~f)) - 5 * (e ^^^ ( ~~~d &&& (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2259 (x y : BitVec w) : +theorem e_2259 : 2 * ((d ||| e) &&& (e ^^^ f)) + 7 * ((e &&& f) ||| (d &&& (e ||| f))) - 5 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 7 * (e ^^^ ( ~~~d ||| (e ||| f))) + 3 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 2 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 2 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 2 * (e ||| (d &&& f)) + 4 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 7 * f + 11 * ( ~~~e ||| (d ^^^ f)) - 3 * (f ||| ~~~(d ||| e)) + 1 * ( ~~~e &&& ~~~(d ^^^ f)) - 1 * (e ^^^ ~~~(d ||| ~~~f)) + 1 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 3 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 1 * ~~~e - 2 * (e ||| ~~~(d ||| ~~~f)) - 3 * (f ||| (d &&& ~~~e)) - 6 * ((d &&& f) ^^^ (e ||| f)) - 5 * ~~~(d ^^^ e) - 11 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 11 * ~~~(d &&& (e ||| f)) + 2 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 1 * (e ^^^ (d &&& f)) + 11 * (f &&& ~~~(d &&& ~~~e)) - 11 * (d ||| (e ^^^ f)) + 1 * (e ||| (d &&& ~~~f)) - 1 * (e ^^^ (d &&& ( ~~~e ||| f))) + 1 * (d ||| ~~~e) - 1 * (f &&& (d ^^^ e)) - 11 * (d ^^^ (e ^^^ f)) + 11 * ((d ^^^ e) ||| (d ^^^ f)) + 5 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 11 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 5 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 1 * (e ^^^ ~~~(d &&& f)) - 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * (e &&& (d ^^^ f)) + 3 * ~~~(d &&& ~~~e) + 7 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 3 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 1 * (e ^^^ ~~~(d ||| (e &&& f))) - 7 * (e ^^^ f) - 3 * ( ~~~d &&& ( ~~~e ||| f)) + 3 * ~~~(d ^^^ (e &&& f)) - 2 * ( ~~~d &&& (e ||| f)) + 2 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 20 * ~~~(d ||| (e ||| f)) + 12 * ~~~(d ||| ( ~~~e ||| f)) - 13 * ~~~( ~~~d ||| (e ||| f)) - 4 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 18 * ( ~~~d &&& ( ~~~e &&& f)) - 39 * ( ~~~d &&& (e &&& f)) + 14 * (d &&& ( ~~~e &&& f)) + 22 * (d &&& (e &&& f)) = 1 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 11 * ((d &&& e) ||| ~~~(e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2260 (x y : BitVec w) : +theorem e_2260 : 7 * (e ||| f) + 5 * (d ||| ( ~~~e ||| f)) + 5 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 2 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 5 * (f ^^^ ~~~(d ||| e)) + 2 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 2 * (d ||| ( ~~~e &&& f)) - 1 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 1 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 2 * (e ^^^ (d &&& ~~~f)) + 3 * ~~~(d &&& e) - 5 * ( ~~~f ||| ~~~(d ^^^ e)) + 2 * (e ^^^ (d &&& (e ^^^ f))) - 11 * (e ^^^ ~~~(d ||| f)) - 2 * f - 6 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 1 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 6 * (f ^^^ ( ~~~d ||| (e &&& f))) + 7 * (f ^^^ (d ||| ~~~e)) - 1 * (d ^^^ ( ~~~e &&& f)) - 2 * (e &&& ~~~(d &&& f)) + 5 * ~~~(d &&& ~~~d) - 1 * (f ||| (d &&& ~~~e)) - 7 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 2 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 1 * (f ^^^ (d ||| ( ~~~e &&& f))) + 2 * ((d &&& f) ||| ~~~(e ||| f)) + 1 * (f ^^^ ~~~(d &&& (e ||| f))) - 3 * (f ^^^ (d &&& e)) + 11 * ~~~(d ^^^ (e ^^^ f)) + 3 * (e &&& (d ||| ~~~f)) - 5 * (f ^^^ ~~~(d &&& ~~~e)) - 5 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 1 * ((d &&& e) ||| ~~~(e ||| f)) - 1 * (d &&& (e ||| f)) - 2 * ( ~~~f &&& ~~~(d ^^^ e)) - 1 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 11 * ~~~(d &&& ( ~~~e &&& f)) + 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 2 * (d ^^^ ( ~~~e ||| f)) - 7 * ~~~( ~~~d &&& (e ^^^ f)) + 7 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 2 * (f ^^^ ~~~(d &&& e)) + 7 * (e ^^^ (d &&& ( ~~~e ||| f))) + 7 * (f ||| ~~~(d ||| e)) + 7 * ((d ^^^ e) ||| (d ^^^ f)) - 1 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 1 * (f ^^^ ~~~(d ||| ~~~e)) - 1 * (d &&& ~~~e) - 1 * ~~~(d ||| (e ||| f)) - 8 * ~~~(d ||| ( ~~~e ||| f)) - 13 * ~~~( ~~~d ||| (e ||| f)) + 13 * ( ~~~d &&& ( ~~~e &&& f)) - 27 * ( ~~~d &&& (e &&& f)) - 38 * (d &&& ( ~~~e &&& f)) + 14 * (d &&& (e &&& f)) = - 11 * ~~~( ~~~d ||| ( ~~~e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2261 (x y : BitVec w) : +theorem e_2261 : 2 * ~~~(d &&& f) + 4 * (d &&& e) - 11 * ~~~(e &&& f) - 1 * ((d &&& e) ||| ~~~(e ||| f)) - 3 * (f &&& ~~~(d &&& e)) + 1 * (e &&& ~~~(d ^^^ f)) - 3 * (f ^^^ ~~~(d ||| (e &&& f))) + 5 * ( ~~~f &&& (d ^^^ e)) - 7 * (f &&& (d ^^^ e)) + 5 * (f &&& ~~~(d ^^^ e)) + 11 * (e ^^^ ~~~(d &&& (e &&& f))) - 1 * (e ^^^ (d &&& ( ~~~e ||| f))) + 4 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 1 * (e ^^^ (d &&& f)) + 7 * (e ||| f) - 7 * ((e &&& f) ||| (d &&& (e ||| f))) + 7 * (d ^^^ ( ~~~e &&& f)) - 3 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 4 * ~~~(d &&& ~~~d) - 1 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 1 * (e ^^^ ~~~(d &&& ~~~f)) - 1 * ( ~~~e &&& ~~~(d ^^^ f)) + 1 * ~~~(d ^^^ (e ^^^ f)) - 2 * (f ||| (d &&& ~~~e)) + 1 * (f ^^^ (d &&& (e ||| f))) + 5 * ~~~(d &&& (e ^^^ f)) - 3 * (d ||| (e ||| f)) + 2 * e + 11 * ((d &&& e) ^^^ (e ||| f)) - 3 * (f &&& (d ||| ~~~e)) - 11 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 2 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 11 * ( ~~~d &&& (e ||| f)) - 6 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 2 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 5 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 5 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 1 * ~~~( ~~~d &&& (e &&& f)) + 4 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 5 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 3 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 5 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 11 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 7 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 6 * ~~~f + 5 * ((d ^^^ e) ||| (d ^^^ f)) + 1 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 5 * f + 3 * (e ^^^ (d ||| ( ~~~e ||| f))) - 7 * (d &&& ( ~~~e ||| f)) + 5 * ~~~(d ||| (e ||| f)) + 21 * ~~~(d ||| ( ~~~e ||| f)) + 27 * ~~~( ~~~d ||| (e ||| f)) - 7 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 14 * ( ~~~d &&& ( ~~~e &&& f)) - 17 * ( ~~~d &&& (e &&& f)) + 4 * (d &&& ( ~~~e &&& f)) - 11 * (d &&& (e &&& f)) = 5 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2262 (x y : BitVec w) : +theorem e_2262 : - 5 * ( ~~~f ||| ~~~(d ^^^ e)) + 7 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 7 * (d ||| f) - 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 2 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 2 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 11 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 1 * (e ^^^ (d ||| ( ~~~e ||| f))) - 1 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 11 * (d &&& f) + 2 * (e ^^^ (d &&& f)) + 1 * ~~~( ~~~d &&& (e ||| f)) + 5 * ((d &&& e) ^^^ (e ||| ~~~f)) - 1 * (e ^^^ (d ||| ( ~~~e &&& f))) - 1 * (f ^^^ (d ||| ( ~~~e ||| f))) + 1 * ( ~~~d ||| ( ~~~e &&& f)) - 7 * ~~~( ~~~d ||| (e &&& f)) - 7 * (e ^^^ ~~~(d &&& (e ||| f))) - 2 * (f ||| (d &&& e)) - 1 * (e ||| ~~~(d ||| ~~~f)) + 4 * (d ||| ~~~f) - 3 * ((d &&& e) ||| (e ^^^ f)) + 5 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 5 * (d ^^^ ( ~~~e &&& f)) + 1 * (f ^^^ ( ~~~d ||| (e &&& f))) + 1 * (f ^^^ ~~~(d &&& (e ||| f))) - 3 * ~~~(e &&& f) - 3 * ( ~~~e &&& ~~~(d ^^^ f)) + 2 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 7 * f + 2 * (e &&& ~~~(d &&& ~~~f)) + 4 * (e ^^^ (d &&& ~~~f)) + 1 * ((d &&& e) ||| ~~~(e ||| f)) + 11 * (f &&& (d ||| ~~~e)) - 2 * (e ^^^ (d ||| (e ||| f))) + 5 * ((d &&& e) ||| ~~~(e ^^^ f)) - 11 * (f ^^^ ( ~~~d &&& (e ||| f))) - 2 * ~~~e - 2 * (f ||| ~~~(d ||| e)) + 1 * (f ^^^ ~~~(d &&& ~~~e)) + 2 * (f ^^^ (d ||| (e ||| f))) + 2 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 3 * (e ^^^ ~~~(d &&& f)) - 6 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 2 * ~~~(e ^^^ f) + 3 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 3 * (f ^^^ ~~~(d ||| (e &&& f))) + 7 * ((d &&& f) ||| (e &&& ~~~f)) - 1 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 3 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 11 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 29 * ~~~(d ||| (e ||| f)) - 6 * ~~~(d ||| ( ~~~e ||| f)) + 6 * ~~~( ~~~d ||| (e ||| f)) + 24 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 30 * ( ~~~d &&& ( ~~~e &&& f)) - 9 * ( ~~~d &&& (e &&& f)) + 2 * (d &&& (e &&& f)) = 2 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2263 (x y : BitVec w) : +theorem e_2263 : 3 * (e ^^^ (d ||| ~~~f)) - 1 * (e ||| (d &&& f)) + 1 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 5 * ((d ||| e) &&& ~~~(e ^^^ f)) + 3 * ~~~(d &&& ~~~e) + 2 * ~~~(d ||| (e &&& f)) - 5 * (d ^^^ (e ^^^ f)) + 7 * (e ||| (d ^^^ f)) + 5 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 7 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 1 * (f ^^^ (d &&& (e ||| f))) - 1 * ((e &&& f) ||| (d &&& (e ||| f))) - 11 * (f ^^^ (d ||| (e ||| f))) - 11 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 2 * (f ^^^ (d &&& ( ~~~e ||| f))) + 5 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 5 * (e ^^^ (d ||| (e &&& f))) + 1 * (f &&& (d ||| e)) - 6 * (f ||| ~~~(d ||| e)) - 1 * (e ||| ~~~(d ||| ~~~f)) + 2 * (d ||| f) + 2 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 7 * ~~~d + 2 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 11 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 2 * ( ~~~e &&& (d ^^^ f)) + 1 * ~~~(d ^^^ (e ||| f)) - 7 * (f &&& (d ^^^ e)) - 2 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 7 * (f ^^^ (d ||| ( ~~~e ||| f))) + 1 * (f ^^^ (d &&& e)) - 1 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 1 * ~~~(d ||| (e ^^^ f)) - 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 5 * (f ^^^ (d &&& ~~~e)) + 11 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 5 * (e ^^^ ( ~~~d ||| (e ||| f))) - 7 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 1 * (e ^^^ (d &&& ~~~f)) - 1 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 3 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 3 * (f ^^^ ~~~(d ||| (e &&& f))) - 1 * (d ||| ( ~~~e &&& f)) + 1 * ( ~~~d &&& ( ~~~e ||| f)) - 11 * ~~~(e &&& ~~~f) + 1 * d + 1 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 5 * (e ^^^ (d &&& (e ^^^ f))) - 7 * ~~~( ~~~d ||| (e ^^^ f)) + 11 * (e ^^^ (d &&& f)) - 47 * ~~~(d ||| (e ||| f)) - 21 * ~~~(d ||| ( ~~~e ||| f)) + 1 * ~~~( ~~~d ||| (e ||| f)) - 25 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 21 * ( ~~~d &&& ( ~~~e &&& f)) - 50 * ( ~~~d &&& (e &&& f)) - 23 * (d &&& ( ~~~e &&& f)) - 9 * (d &&& (e &&& f)) = - 1 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 11 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2264 (x y : BitVec w) : +theorem e_2264 : 2 * (e ^^^ f) + 2 * (e ^^^ (d ||| ( ~~~e &&& f))) - 11 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 1 * (f ^^^ (d &&& ~~~e)) - 1 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 4 * ~~~(e ^^^ f) + 7 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 7 * ( ~~~f &&& (d ^^^ e)) - 1 * (f ^^^ (d ||| ( ~~~e &&& f))) + 1 * (e ^^^ (d ||| (e ||| f))) - 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 5 * ~~~(d &&& ( ~~~e &&& f)) + 2 * ~~~(d ^^^ f) + 1 * ~~~(e &&& f) + 11 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 1 * (f &&& (d ^^^ e)) - 1 * (e ||| ~~~f) + 11 * (e ^^^ ~~~(d &&& (e ||| f))) + 1 * (e ^^^ ~~~(d &&& ~~~f)) - 2 * (f &&& (d ||| e)) + 2 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 5 * ( ~~~e &&& ~~~(d ^^^ f)) + 1 * (e ^^^ (d ||| (e ^^^ f))) - 6 * (e &&& (d ||| f)) - 11 * ( ~~~e &&& (d ^^^ f)) + 2 * (e &&& (d ||| ~~~f)) - 2 * f - 1 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 1 * ~~~(d ^^^ ( ~~~e ||| f)) + 2 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 4 * ((d ^^^ e) &&& (d ^^^ f)) + 11 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 5 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 1 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * (e ^^^ ~~~(d &&& f)) - 7 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 6 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 1 * ~~~(d &&& f) - 11 * (e ||| ~~~(d ||| ~~~f)) - 11 * (e ||| ~~~(d ^^^ f)) - 2 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 3 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 7 * ~~~( ~~~d ||| (e &&& f)) + 11 * (f ||| ~~~(d ^^^ e)) - 11 * (e ||| ~~~(d ||| f)) + 1 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 11 * ( ~~~d &&& (e ||| f)) - 5 * (e ||| (d ^^^ f)) + 2 * (e ^^^ (d ||| f)) - 11 * ~~~(d ||| (e ||| f)) + 23 * ~~~(d ||| ( ~~~e ||| f)) + 8 * ~~~( ~~~d ||| (e ||| f)) + 1 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 8 * ( ~~~d &&& ( ~~~e &&& f)) + 9 * ( ~~~d &&& (e &&& f)) - 23 * (d &&& ( ~~~e &&& f)) + 24 * (d &&& (e &&& f)) = 1 * (e ^^^ ~~~(d ||| ~~~f)) - 4 * ~~~(d ||| f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2265 (x y : BitVec w) : +theorem e_2265 : - 1 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 2 * (f ^^^ ( ~~~d ||| (e &&& f))) - 5 * ((d &&& f) ^^^ (e ||| f)) + 5 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 11 * ( ~~~f ||| ~~~(d ^^^ e)) - 7 * ~~~(d ^^^ f) - 1 * (f ^^^ ~~~(d &&& (e ||| f))) - 3 * (e ||| f) + 1 * ((d &&& e) ^^^ (e ||| f)) - 3 * (f ||| (d ^^^ e)) + 7 * (e ^^^ (d &&& (e ||| f))) + 1 * (f ||| (d &&& ~~~e)) + 3 * (f ^^^ ~~~(d ||| e)) - 6 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 11 * (d ^^^ (e &&& f)) + 7 * ( ~~~d &&& (e ^^^ f)) + 1 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 11 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 11 * (e &&& ~~~(d ^^^ f)) - 3 * ~~~(e ^^^ f) + 2 * ~~~( ~~~d &&& (e ||| f)) + 11 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 4 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 5 * d - 2 * ((d ||| e) &&& (e ^^^ f)) - 11 * ~~~( ~~~d ||| (e ^^^ f)) + 2 * (f ^^^ (d ||| (e ||| f))) - 3 * (d ||| ~~~f) - 7 * (e ^^^ ~~~(d ||| f)) + 1 * ( ~~~f ||| (d ^^^ e)) - 2 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 1 * ~~~(e &&& f) + 7 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 1 * ~~~e - 7 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 5 * ((d &&& f) ||| (e &&& ~~~f)) + 2 * ~~~(d ^^^ (e ^^^ f)) - 1 * (e ^^^ ( ~~~d &&& (e ||| f))) - 7 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 2 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 6 * (e ^^^ (d ||| ( ~~~e &&& f))) - 1 * ~~~(d &&& (e ^^^ f)) + 1 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 7 * ~~~(d &&& ~~~f) + 2 * (f &&& (d ||| e)) - 2 * (f ^^^ ~~~(d &&& e)) + 7 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 7 * ( ~~~e &&& (d ^^^ f)) + 3 * ~~~(d ||| (e ^^^ f)) - 2 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 1 * (e ^^^ (d ||| (e &&& f))) + 2 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 23 * ~~~(d ||| ( ~~~e ||| f)) + 51 * ~~~( ~~~d ||| (e ||| f)) + 29 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 9 * ( ~~~d &&& ( ~~~e &&& f)) + 21 * ( ~~~d &&& (e &&& f)) + 32 * (d &&& ( ~~~e &&& f)) + 19 * (d &&& (e &&& f)) = 1 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * (e ||| ~~~(d ||| ~~~f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2266 (x y : BitVec w) : +theorem e_2266 : 2 * (d ||| ~~~e) - 1 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 4 * ((d ||| e) &&& (e ^^^ f)) + 11 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 5 * ~~~(e &&& ~~~f) - 5 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 7 * ((d ^^^ e) ||| (d ^^^ f)) + 5 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 5 * ~~~(e &&& f) + 1 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 7 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 5 * (d ||| f) - 1 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 4 * ((d &&& ~~~e) ||| (e ^^^ f)) - 6 * ( ~~~e ||| (d ^^^ f)) - 1 * (e ^^^ (d &&& f)) + 7 * (e ^^^ ( ~~~d ||| (e &&& f))) + 1 * (d ^^^ (e ^^^ f)) + 1 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 5 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 3 * (e ^^^ f) - 1 * ( ~~~d &&& (e ||| f)) + 5 * (e ^^^ (d ||| (e ^^^ f))) + 5 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 2 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 2 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 2 * (f ||| ~~~(d ||| ~~~e)) + 1 * (f &&& (d ^^^ e)) + 2 * (e ^^^ ~~~(d &&& (e &&& f))) - 1 * (d ||| ( ~~~e ||| f)) + 1 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 11 * ((d &&& e) ||| (e ^^^ f)) + 4 * ((d &&& e) ||| ~~~(e ^^^ f)) + 1 * (d &&& ( ~~~e ||| f)) + 1 * ( ~~~d ||| (e &&& f)) - 1 * (f ^^^ (d &&& ( ~~~e ||| f))) - 11 * ~~~(d &&& e) + 3 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 2 * ( ~~~d &&& (e ^^^ f)) - 1 * ( ~~~d ||| (e ||| f)) + 11 * (f ^^^ (d ||| e)) - 2 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 7 * (d ||| ~~~f) - 2 * ~~~( ~~~d &&& (e ^^^ f)) - 7 * ((d &&& f) ||| (e &&& ~~~f)) + 2 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 2 * (d ||| e) - 6 * ~~~(d ||| (e ^^^ f)) + 2 * ((d ||| e) &&& ~~~(e ^^^ f)) + 4 * (e ^^^ ( ~~~d ||| (e ||| f))) + 2 * (f ^^^ ( ~~~d ||| (e &&& f))) - 1 * ~~~(d ||| (e ||| f)) - 7 * ~~~(d ||| ( ~~~e ||| f)) - 2 * ~~~( ~~~d ||| (e ||| f)) - 11 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 10 * ( ~~~d &&& ( ~~~e &&& f)) + 36 * ( ~~~d &&& (e &&& f)) + 10 * (d &&& ( ~~~e &&& f)) - 12 * (d &&& (e &&& f)) = 2 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 11 * ~~~(d &&& f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2267 (x y : BitVec w) : +theorem e_2267 : 3 * (f &&& ~~~(d &&& e)) + 4 * ((d &&& f) ^^^ (e ||| f)) + 4 * (d ^^^ e) - 11 * ~~~( ~~~d &&& (e &&& f)) + 1 * ~~~(d ||| f) - 2 * ~~~(d ^^^ e) - 3 * (f ^^^ (d &&& ( ~~~e ||| f))) + 1 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 1 * ( ~~~d &&& (e ||| f)) + 2 * ~~~(d ||| e) + 1 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 3 * ~~~( ~~~d &&& (e ^^^ f)) - 1 * (f ^^^ ~~~(d &&& e)) - 5 * ~~~(d &&& e) + 5 * ( ~~~d &&& ( ~~~e ||| f)) - 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 1 * (e ^^^ ~~~(d ||| ~~~f)) + 5 * ~~~(d ||| ( ~~~e &&& f)) + 1 * (d &&& ~~~f) + 1 * (f ||| ~~~(d ^^^ e)) + 1 * (f &&& (d ||| ~~~e)) + 1 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 1 * (e &&& (d ||| ~~~f)) - 11 * (f &&& ~~~(d &&& ~~~e)) - 11 * ~~~(d &&& (e ^^^ f)) + 3 * ~~~(e ||| f) - 5 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 2 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * ( ~~~e ||| ~~~(d ^^^ f)) + 4 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 11 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 2 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 3 * (e &&& ~~~(d &&& f)) + 3 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 1 * (e ^^^ (d ||| (e &&& f))) - 2 * (e ^^^ ( ~~~d ||| (e &&& f))) + 3 * ~~~(d ||| ~~~f) - 1 * (d &&& (e ||| f)) + 2 * (e ^^^ ~~~(d ||| f)) - 7 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 6 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 1 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 3 * (f ^^^ (d &&& e)) + 2 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 7 * (d ||| e) - 11 * ~~~(d &&& ( ~~~e &&& f)) - 5 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 1 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 1 * ~~~(e &&& ~~~f) - 6 * (e ||| ~~~f) + 30 * ~~~(d ||| (e ||| f)) + 16 * ~~~(d ||| ( ~~~e ||| f)) + 46 * ~~~( ~~~d ||| (e ||| f)) + 15 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 27 * ( ~~~d &&& ( ~~~e &&& f)) + 21 * ( ~~~d &&& (e &&& f)) - 2 * (d &&& ( ~~~e &&& f)) + 54 * (d &&& (e &&& f)) = - 7 * ~~~(d &&& ( ~~~e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2268 (x y : BitVec w) : +theorem e_2268 : 2 * (e &&& (d ^^^ f)) - 11 * ( ~~~e ||| (d ^^^ f)) - 6 * (e ^^^ (d &&& ( ~~~e ||| f))) + 1 * (d ||| ~~~e) + 1 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 2 * (f ||| ~~~(d ||| ~~~e)) - 3 * (e ^^^ ~~~(d ||| f)) + 5 * ((d ||| e) &&& (e ^^^ f)) - 7 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 7 * (e ^^^ (d ||| (e &&& f))) + 5 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 6 * (e ^^^ ~~~(d &&& f)) - 2 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 5 * (d ^^^ (e ||| f)) + 7 * (e ^^^ (d ||| (e ^^^ f))) - 2 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 7 * e - 1 * (f ^^^ (d &&& (e ||| f))) + 4 * (d ||| ( ~~~e ||| f)) - 6 * ( ~~~f &&& (d ^^^ e)) - 2 * (d ||| (e ||| f)) - 1 * (f ^^^ ( ~~~d ||| (e &&& f))) + 5 * (e &&& (d ||| f)) - 1 * ((d &&& f) ||| (e &&& ~~~f)) + 3 * ( ~~~d ||| (e &&& f)) + 11 * ~~~(d &&& ~~~f) - 5 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 1 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 6 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 3 * (d ||| ~~~f) - 11 * (e ||| ~~~(d ||| ~~~f)) - 1 * ~~~( ~~~d &&& (e ||| f)) + 2 * (e &&& ~~~(d &&& f)) + 3 * ~~~(e ^^^ f) + 4 * (e ||| ~~~(d ^^^ f)) - 2 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 11 * (f ^^^ ~~~(d ||| (e &&& f))) + 1 * ~~~(d ^^^ ( ~~~e ||| f)) + 1 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 7 * ~~~(d ||| ~~~e) + 5 * ~~~(d ^^^ (e &&& f)) - 2 * (f ||| (d &&& e)) + 3 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 2 * ~~~( ~~~d &&& (e ^^^ f)) - 1 * (d ^^^ ( ~~~e ||| f)) - 7 * (f ^^^ (d ||| ( ~~~e &&& f))) - 3 * (e &&& (d ||| ~~~f)) + 7 * ( ~~~e &&& (d ^^^ f)) + 1 * (f ^^^ (d ||| (e &&& f))) - 1 * ((d ^^^ e) &&& (d ^^^ f)) + 1 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 7 * ~~~(d ||| (e ||| f)) + 16 * ~~~(d ||| ( ~~~e ||| f)) + 30 * ~~~( ~~~d ||| (e ||| f)) + 36 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 5 * ( ~~~d &&& ( ~~~e &&& f)) + 13 * ( ~~~d &&& (e &&& f)) + 7 * (d &&& ( ~~~e &&& f)) + 12 * (d &&& (e &&& f)) = 7 * ~~~(d &&& f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2269 (x y : BitVec w) : +theorem e_2269 : - 6 * (d ^^^ (e &&& f)) - 1 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 1 * ~~~(e ||| ~~~f) - 1 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 1 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * ((d &&& e) ^^^ (e ||| ~~~f)) - 1 * ((d &&& e) ||| ~~~(e ^^^ f)) + 2 * ((d &&& e) ||| ~~~(e ||| f)) - 2 * (f ^^^ ( ~~~d ||| (e ||| f))) - 6 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 11 * ((d ||| ~~~e) &&& (e ^^^ f)) + 1 * (e ||| f) - 2 * ~~~( ~~~d ||| (e &&& f)) - 2 * (e ^^^ (d ||| (e &&& f))) + 5 * (e ||| (d &&& ~~~f)) + 11 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 2 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 3 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 7 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 11 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 3 * (e ||| (d &&& f)) + 1 * (e ^^^ (d &&& ~~~f)) + 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 11 * (e ^^^ ~~~(d ||| (e &&& f))) + 1 * ~~~(d &&& f) + 11 * (f ^^^ ~~~(d &&& ~~~e)) + 7 * ~~~(d ||| (e ^^^ f)) - 1 * (f ||| ~~~(d ||| ~~~e)) + 1 * ( ~~~e &&& (d ^^^ f)) + 3 * ~~~(d ^^^ e) + 7 * (e &&& f) + 7 * (d &&& e) + 2 * (d &&& (e ||| f)) + 1 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 6 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 1 * (f ^^^ ~~~(d ||| (e &&& f))) - 6 * ( ~~~d &&& (e ||| f)) + 5 * (f ^^^ (d ||| (e &&& f))) - 5 * (d &&& ( ~~~e ||| f)) + 3 * ~~~d + 5 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 11 * ~~~(d &&& (e ||| f)) + 2 * (e ^^^ ( ~~~d ||| (e ||| f))) - 7 * (f ||| (d &&& ~~~e)) - 2 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 5 * ( ~~~d ||| ( ~~~e ||| f)) - 3 * (e ^^^ (d ||| (e ||| f))) + 4 * ~~~( ~~~d &&& (e ^^^ f)) + 2 * ~~~(d &&& ~~~f) + 3 * ( ~~~d ||| (e &&& f)) + 1 * ( ~~~d ||| (e ^^^ f)) - 49 * ~~~(d ||| (e ||| f)) - 31 * ~~~(d ||| ( ~~~e ||| f)) + 19 * ~~~( ~~~d ||| (e ||| f)) - 39 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 8 * ( ~~~d &&& ( ~~~e &&& f)) - 4 * ( ~~~d &&& (e &&& f)) + 13 * (d &&& ( ~~~e &&& f)) - 54 * (d &&& (e &&& f)) = 1 * (e ||| ~~~(d ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2270 (x y : BitVec w) : +theorem e_2270 : 4 * ( ~~~d &&& (e ||| f)) + 7 * ~~~(d ||| ( ~~~e &&& f)) - 1 * (e ||| (d &&& f)) - 11 * ( ~~~e &&& ~~~(d ^^^ f)) - 7 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 2 * ( ~~~f ||| ~~~(d ^^^ e)) - 2 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 1 * ( ~~~d ||| ( ~~~e &&& f)) - 2 * (f ||| (d &&& ~~~e)) - 2 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 2 * (d ||| ~~~e) + 1 * (f ^^^ (d ||| ~~~e)) + 3 * (d &&& f) - 2 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 7 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 4 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 3 * ~~~( ~~~d ||| (e ^^^ f)) + 7 * ( ~~~f &&& ~~~(d ^^^ e)) - 2 * ((d &&& e) ||| ~~~(e ||| f)) - 6 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 2 * (f ^^^ (d ||| e)) + 11 * ( ~~~d ||| (e &&& f)) + 4 * ((d &&& f) ^^^ (e ||| f)) - 3 * (e &&& ~~~(d &&& f)) - 3 * ~~~(d ^^^ e) + 3 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 1 * (f ^^^ ( ~~~d ||| (e &&& f))) - 1 * (d ^^^ ( ~~~e ||| f)) + 5 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 6 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 2 * ~~~(d &&& f) + 2 * (f ^^^ (d ||| ( ~~~e &&& f))) + 1 * ~~~(d &&& ( ~~~e &&& f)) - 5 * ~~~(d ||| (e ^^^ f)) - 7 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 2 * (f &&& ~~~(d &&& e)) - 1 * ( ~~~f &&& (d ^^^ e)) + 1 * ((d ^^^ e) &&& (d ^^^ f)) + 1 * (e ^^^ (d ||| ~~~f)) - 1 * (e ^^^ ~~~(d ||| (e &&& f))) + 2 * ~~~(d &&& e) + 11 * e - 1 * (d ||| f) - 6 * (f ||| ~~~(d ^^^ e)) - 5 * (f ^^^ (d ||| (e ||| f))) - 1 * (f ^^^ ~~~(d &&& ~~~e)) - 6 * ((d ||| e) &&& ~~~(e ^^^ f)) - 5 * (d ^^^ e) - 1 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 3 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 11 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 20 * ~~~(d ||| (e ||| f)) - 15 * ~~~(d ||| ( ~~~e ||| f)) + 33 * ~~~( ~~~d ||| (e ||| f)) - 7 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 23 * (d &&& ( ~~~e &&& f)) - 1 * (d &&& (e &&& f)) = 6 * ( ~~~d &&& (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2271 (x y : BitVec w) : +theorem e_2271 : 3 * ~~~(d ||| ( ~~~e &&& f)) - 1 * ((d ^^^ e) &&& (d ^^^ f)) - 2 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 6 * ((d &&& ~~~e) ||| (e ^^^ f)) + 1 * (f ^^^ (d &&& e)) - 11 * ~~~(d ||| e) - 6 * (e ||| (d &&& ~~~f)) + 7 * (d ^^^ e) + 1 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 7 * (f ^^^ (d ||| (e ||| f))) - 5 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 2 * ( ~~~d ||| (e &&& f)) + 1 * (e ^^^ (d ||| ( ~~~e &&& f))) - 2 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 4 * (f ^^^ (d ||| (e &&& f))) + 5 * (d &&& (e ^^^ f)) - 3 * ~~~( ~~~d ||| (e &&& f)) - 1 * (e ^^^ ~~~(d ||| f)) - 2 * ((e &&& f) ||| (d &&& (e ||| f))) + 4 * ((d &&& e) ||| (e ^^^ f)) - 5 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 1 * (f ^^^ ~~~(d &&& (e ||| f))) - 11 * ~~~(d &&& ~~~d) + 11 * (f ^^^ (d &&& ~~~e)) - 1 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 7 * (d ||| (e ||| f)) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 1 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 2 * ( ~~~e ||| (d ^^^ f)) + 2 * (e ^^^ (d ||| f)) - 2 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 1 * (e ||| ~~~f) + 7 * ~~~( ~~~d ||| (e ^^^ f)) - 6 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 5 * ((d &&& e) ^^^ (e ||| f)) - 7 * (e ||| ~~~(d ^^^ f)) - 3 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 1 * ((d ^^^ e) ||| (d ^^^ f)) + 1 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 7 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 1 * ~~~(d ||| ~~~f) + 5 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 5 * (e &&& f) - 1 * ~~~( ~~~d &&& (e ^^^ f)) - 6 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 7 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 1 * ~~~(d ||| (e &&& f)) - 2 * (d &&& e) + 1 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 4 * (f &&& (d ||| e)) + 2 * (e ||| ~~~(d ||| ~~~f)) + 28 * ~~~(d ||| (e ||| f)) + 14 * ~~~( ~~~d ||| (e ||| f)) + 43 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 35 * ( ~~~d &&& ( ~~~e &&& f)) + 39 * ( ~~~d &&& (e &&& f)) + 43 * (d &&& ( ~~~e &&& f)) + 40 * (d &&& (e &&& f)) = - 25 * ~~~(d ||| ( ~~~e ||| f)) + 5 * (d &&& ( ~~~e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2272 (x y : BitVec w) : +theorem e_2272 : 1 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 4 * ( ~~~e &&& ~~~(d ^^^ f)) - 2 * (f ^^^ (d ||| ( ~~~e ||| f))) - 2 * (f ||| (d &&& ~~~e)) - 2 * (f ^^^ (d &&& ~~~e)) + 3 * (e ^^^ (d ||| (e ^^^ f))) + 5 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 1 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 11 * (f ^^^ (d ||| e)) - 2 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 7 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 11 * ((d ||| ~~~e) &&& (e ^^^ f)) - 1 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 11 * (f ^^^ ( ~~~d ||| (e ||| f))) + 1 * (d ||| e) + 11 * (e ^^^ (d ||| ~~~f)) + 3 * (e &&& ~~~(d &&& f)) - 2 * ~~~(d ^^^ ( ~~~e ||| f)) - 1 * (e ^^^ (d &&& ( ~~~e ||| f))) - 1 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 2 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 5 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 11 * (e &&& f) + 1 * (f &&& (d ||| ~~~e)) + 11 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 7 * (f &&& (d ||| e)) + 2 * (e ||| (d ^^^ f)) - 6 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 1 * (e ^^^ ~~~(d &&& (e &&& f))) + 2 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 1 * (e &&& ~~~(d ^^^ f)) + 1 * ~~~(d &&& ( ~~~e &&& f)) + 7 * ~~~(d ||| f) - 3 * ~~~(d ||| (e &&& f)) - 6 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 5 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 3 * (f &&& ~~~(d ^^^ e)) + 3 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 7 * ~~~( ~~~d &&& (e ||| f)) - 11 * (e &&& (d ^^^ f)) + 1 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 3 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 5 * ( ~~~d &&& (e ^^^ f)) + 3 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 1 * (e &&& ~~~(d &&& ~~~f)) - 1 * ((d &&& e) ||| ~~~(e ^^^ f)) + 5 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 4 * (d &&& e) - 11 * ~~~e - 4 * ~~~(d ||| (e ||| f)) - 15 * ~~~(d ||| ( ~~~e ||| f)) - 8 * ~~~( ~~~d ||| (e ||| f)) - 8 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 1 * ( ~~~d &&& ( ~~~e &&& f)) + 12 * ( ~~~d &&& (e &&& f)) - 18 * (d &&& ( ~~~e &&& f)) + 23 * (d &&& (e &&& f)) = 5 * ~~~(d &&& (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2273 (x y : BitVec w) : +theorem e_2273 : - 3 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 4 * ( ~~~e &&& ~~~(d ^^^ f)) - 3 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 4 * (e ^^^ ~~~(d ||| ~~~f)) + 7 * ~~~(d &&& (e &&& f)) + 2 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 5 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 2 * (e ^^^ (d ||| f)) - 11 * ((d &&& e) ^^^ (e ||| f)) - 1 * ~~~(e ||| f) - 7 * ~~~(d ^^^ e) - 3 * (f &&& ~~~(d &&& ~~~e)) - 1 * (f ^^^ (d &&& ( ~~~e ||| f))) - 5 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * (e ||| ~~~(d ||| f)) + 4 * ((d &&& e) ^^^ (e ||| ~~~f)) - 1 * ~~~(e ^^^ f) + 2 * ( ~~~d ||| ( ~~~e ||| f)) + 2 * (f ^^^ (d &&& ~~~e)) - 3 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 11 * (e &&& ~~~(d &&& f)) - 6 * ~~~(d &&& (e ^^^ f)) - 1 * (e ^^^ (d ||| ~~~f)) + 1 * ~~~(d ||| (e ^^^ f)) + 1 * ~~~(d &&& f) + 1 * (e ||| (d &&& f)) - 1 * ~~~( ~~~d ||| (e ^^^ f)) - 2 * (f ^^^ ( ~~~d ||| (e ||| f))) - 1 * (f ||| ~~~(d ||| ~~~e)) + 1 * (e ||| ~~~f) - 1 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 1 * (d ||| e) - 11 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 6 * (d ||| (e ^^^ f)) - 6 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (e ^^^ f) + 7 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 2 * (e ^^^ ~~~(d &&& f)) - 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 3 * d + 7 * ~~~(d ||| ~~~f) - 1 * ( ~~~f &&& ~~~(d ^^^ e)) - 1 * (d ||| ~~~f) - 5 * (e ||| (d ^^^ f)) + 1 * (e ^^^ ~~~(d ||| f)) - 7 * (f ||| ~~~(d ||| e)) - 6 * (d ^^^ f) + 2 * (e ^^^ (d &&& f)) + 1 * (d ^^^ ( ~~~e &&& f)) + 1 * (e ^^^ (d ||| (e ||| f))) + 5 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 1 * ~~~(d ||| (e ||| f)) + 23 * ~~~( ~~~d ||| (e ||| f)) + 16 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 23 * ( ~~~d &&& ( ~~~e &&& f)) + 32 * ( ~~~d &&& (e &&& f)) + 27 * (d &&& ( ~~~e &&& f)) + 32 * (d &&& (e &&& f)) = 1 * ~~~(d ||| ( ~~~e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2274 (x y : BitVec w) : +theorem e_2274 : 5 * ( ~~~d &&& (e ||| f)) - 1 * (f &&& (d ||| e)) - 3 * (e ||| (d &&& f)) + 2 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 7 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 3 * (e ^^^ f) - 1 * (e ^^^ ~~~(d ||| f)) + 3 * (d &&& e) + 11 * (e ^^^ (d &&& (e ^^^ f))) - 7 * (d ||| ~~~f) - 3 * (f ^^^ ~~~(d ||| ~~~e)) - 1 * (f ||| (d &&& e)) + 7 * (e ^^^ ~~~(d &&& f)) - 6 * (d ^^^ (e &&& f)) - 2 * ((d &&& e) ||| ~~~(e ||| f)) - 6 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 1 * ((d ^^^ e) ||| ~~~(d ^^^ f)) + 2 * ((d ^^^ e) ||| (d ^^^ f)) + 2 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 2 * (f ^^^ ~~~(d &&& ~~~e)) - 2 * ((d ||| ~~~e) &&& (e ^^^ f)) + 1 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 1 * ~~~(d &&& e) - 7 * (d ^^^ (e ^^^ f)) - 1 * (e &&& (d ||| ~~~f)) + 5 * (e ^^^ ~~~(d &&& (e &&& f))) - 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 6 * (f &&& ~~~(d ^^^ e)) - 2 * (e &&& ~~~(d &&& f)) + 4 * (d &&& ~~~e) + 7 * ~~~(d ^^^ ( ~~~e ||| f)) + 4 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 2 * (d ^^^ ( ~~~e &&& f)) - 1 * ~~~(d &&& f) + 1 * (d ||| ( ~~~e &&& f)) - 3 * ~~~(d ||| ( ~~~e &&& f)) - 1 * ~~~(d &&& ~~~f) + 3 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 11 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 7 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 2 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 7 * ~~~( ~~~d &&& (e ||| f)) + 3 * (e ||| ~~~(d ||| ~~~f)) + 4 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 11 * (f &&& ~~~(d &&& ~~~e)) + 1 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 1 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 5 * (e ^^^ (d ||| (e ^^^ f))) - 7 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 3 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 12 * ~~~(d ||| (e ||| f)) + 5 * ~~~(d ||| ( ~~~e ||| f)) + 6 * ~~~( ~~~d ||| (e ||| f)) + 43 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 36 * ( ~~~d &&& ( ~~~e &&& f)) - 14 * ( ~~~d &&& (e &&& f)) - 14 * (d &&& ( ~~~e &&& f)) + 12 * (d &&& (e &&& f)) = - 7 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 5 * (e ^^^ (d ||| (e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2275 (x y : BitVec w) : +theorem e_2275 : - 3 * ~~~(d &&& (e ||| f)) + 2 * (f ^^^ (d &&& ( ~~~e ||| f))) - 2 * (f ^^^ (d &&& (e ||| f))) + 2 * (f &&& (d ^^^ e)) - 1 * (f ^^^ ( ~~~d &&& (e ||| f))) + 1 * (d ||| f) - 5 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 2 * (d ^^^ (e ^^^ f)) + 2 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 5 * ((d ||| e) &&& ~~~(e ^^^ f)) + 11 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 11 * ((d ^^^ e) &&& (d ^^^ f)) + 1 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 4 * (f ^^^ ~~~(d ||| ~~~e)) + 3 * (e ||| (d &&& ~~~f)) + 1 * (e ^^^ ~~~(d &&& (e ||| f))) + 2 * (f ^^^ (d ||| ( ~~~e ||| f))) + 4 * ~~~(d ^^^ ( ~~~e &&& f)) - 5 * (d ||| (e ^^^ f)) - 3 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 2 * (d &&& ( ~~~e ||| f)) + 1 * ~~~(d ||| (e ^^^ f)) - 7 * (f &&& ~~~(d ^^^ e)) - 7 * (f ^^^ (d ||| e)) - 2 * (e &&& ~~~(d &&& ~~~f)) + 7 * ~~~f + 1 * ( ~~~e &&& ~~~(d ^^^ f)) - 5 * ((e &&& f) ||| (d &&& (e ||| f))) - 6 * ( ~~~e ||| (d ^^^ f)) + 7 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 1 * (d ^^^ ( ~~~e ||| f)) + 1 * ~~~(d ^^^ (e ||| f)) - 6 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 11 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 1 * ( ~~~e ||| ~~~(d ^^^ f)) - 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 4 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 2 * ~~~( ~~~d &&& (e ||| f)) + 3 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 1 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 7 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 5 * (d &&& ~~~e) + 7 * (e ^^^ (d &&& (e ^^^ f))) - 1 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 2 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 1 * (e ||| (d &&& f)) - 11 * (e ^^^ ~~~(d &&& f)) + 5 * (f ^^^ (d ||| ~~~e)) + 1 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (d ||| e) - 16 * ~~~(d ||| (e ||| f)) - 22 * ~~~(d ||| ( ~~~e ||| f)) + 2 * ~~~( ~~~d ||| (e ||| f)) + 10 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 11 * ( ~~~d &&& ( ~~~e &&& f)) - 8 * ( ~~~d &&& (e &&& f)) - 17 * (d &&& ( ~~~e &&& f)) - 10 * (d &&& (e &&& f)) = 7 * ((d ||| e) &&& (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2276 (x y : BitVec w) : +theorem e_2276 : 11 * (f ^^^ ~~~(d ||| ~~~e)) + 4 * (e &&& (d ||| ~~~f)) + 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 11 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 7 * ~~~(d ||| (e &&& f)) + 5 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 11 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 3 * (e ||| ~~~f) + 2 * (d ^^^ (e &&& f)) - 7 * (d ^^^ e) + 3 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 1 * (e ^^^ (d ||| ( ~~~e &&& f))) + 2 * (e ^^^ ~~~(d &&& (e ||| f))) - 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 4 * (f &&& ~~~(d &&& e)) + 1 * ((d &&& f) ||| (e &&& ~~~f)) + 7 * (f ^^^ ~~~(d &&& e)) + 2 * (f ^^^ ( ~~~d ||| (e &&& f))) - 3 * ~~~( ~~~d ||| (e ^^^ f)) + 1 * (e ^^^ (d &&& ~~~f)) - 1 * (e &&& (d ||| f)) + 3 * (d ||| (e &&& f)) + 7 * (e ||| ~~~(d ||| f)) + 4 * ((d &&& e) ||| (e ^^^ f)) - 2 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 1 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 6 * (d &&& (e ||| f)) - 3 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 2 * (f &&& (d ^^^ e)) + 5 * (f ||| (d &&& ~~~e)) + 3 * ( ~~~d &&& (e ^^^ f)) + 2 * (d ||| ( ~~~e ||| f)) - 3 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * (e ^^^ (d &&& ( ~~~e ||| f))) + 2 * (f ^^^ (d ||| (e &&& f))) - 7 * f + 2 * (e &&& f) + 2 * (d ^^^ ( ~~~e &&& f)) + 1 * ((e &&& f) ||| (d &&& (e ||| f))) - 6 * (e ^^^ ~~~(d ||| f)) - 1 * (e &&& ~~~(d ^^^ f)) + 7 * (f ^^^ ( ~~~d ||| (e ||| f))) - 1 * (f ^^^ (d ||| ( ~~~e ||| f))) - 2 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 1 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 5 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 1 * ~~~(e ||| ~~~f) - 6 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 11 * ((d &&& e) ^^^ (e ||| ~~~f)) + 5 * (d ||| ~~~f) - 3 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 2 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 1 * ~~~(d ||| (e ||| f)) - 35 * ~~~(d ||| ( ~~~e ||| f)) - 1 * ~~~( ~~~d ||| (e ||| f)) - 7 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 1 * ( ~~~d &&& ( ~~~e &&& f)) + 26 * ( ~~~d &&& (e &&& f)) + 14 * (d &&& ( ~~~e &&& f)) - 26 * (d &&& (e &&& f)) = 1 * (e &&& ~~~f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2277 (x y : BitVec w) : +theorem e_2277 : - 6 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 3 * (e ^^^ (d &&& ~~~f)) + 11 * (d ||| (e ^^^ f)) - 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 2 * ( ~~~d &&& (e ||| f)) + 2 * (e ^^^ (d &&& (e ^^^ f))) + 4 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 6 * (f ^^^ ~~~(d &&& (e ||| f))) + 3 * (e ^^^ ( ~~~d ||| (e ||| f))) + 1 * ((d ||| e) &&& (e ^^^ f)) - 1 * ~~~(d &&& ( ~~~e ||| f)) + 4 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 7 * (e ^^^ ( ~~~d &&& (e ||| f))) - 2 * (e ^^^ (d ||| (e ||| f))) - 1 * ~~~(d &&& ~~~f) - 2 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 11 * (e &&& (d ^^^ f)) + 7 * (e ^^^ ~~~(d ||| (e &&& f))) + 11 * (d ^^^ f) + 2 * ~~~( ~~~d ||| (e &&& f)) + 1 * (e &&& ~~~(d &&& ~~~f)) - 7 * (e ^^^ f) - 1 * (e ^^^ ~~~(d ||| f)) - 1 * ( ~~~f &&& (d ^^^ e)) - 7 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 7 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 1 * ( ~~~e &&& (d ^^^ f)) - 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 1 * d + 7 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 4 * ((d &&& e) ||| ~~~(e ||| f)) - 7 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 1 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 2 * (e ||| ~~~f) - 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 1 * (e ^^^ (d &&& (e ||| f))) + 5 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 11 * (f ^^^ ( ~~~d ||| (e &&& f))) - 11 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 2 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 2 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 2 * ( ~~~d &&& ( ~~~e ||| f)) - 1 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 6 * ~~~(d ||| ( ~~~e &&& f)) - 11 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 4 * ((d &&& f) ||| ~~~(e ||| f)) + 5 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 3 * ~~~(e ||| f) + 4 * ( ~~~d ||| ( ~~~e ||| f)) - 3 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 2 * (e ^^^ (d ||| (e ^^^ f))) + 23 * ~~~(d ||| (e ||| f)) - 14 * ~~~( ~~~d ||| (e ||| f)) + 21 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 19 * ( ~~~d &&& ( ~~~e &&& f)) + 41 * ( ~~~d &&& (e &&& f)) + 2 * (d &&& ( ~~~e &&& f)) - 16 * (d &&& (e &&& f)) = - 1 * (f &&& (d ||| e)) - 43 * ~~~(d ||| ( ~~~e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2278 (x y : BitVec w) : +theorem e_2278 : - 7 * ~~~(e &&& f) + 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 11 * (d ^^^ (e ||| f)) + 4 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 3 * ((d ^^^ e) &&& (d ^^^ f)) - 6 * (e ^^^ (d ||| (e &&& f))) + 1 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 11 * ~~~f + 7 * ~~~(d ^^^ ( ~~~e &&& f)) - 11 * ~~~(d &&& ~~~d) - 1 * (d ||| ( ~~~e ||| f)) - 3 * e + 2 * (d ||| f) + 5 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 1 * (f &&& (d ||| ~~~e)) - 3 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 2 * (e ^^^ (d ||| ( ~~~e &&& f))) + 1 * ~~~(d &&& ( ~~~e &&& f)) - 7 * (d ||| (e ^^^ f)) + 3 * ((d &&& e) ||| ~~~(e ^^^ f)) + 7 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 6 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * ((d &&& ~~~e) ||| (e ^^^ f)) + 2 * ( ~~~d ||| ( ~~~e &&& f)) + 3 * (f ^^^ ( ~~~d ||| (e ||| f))) + 4 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 2 * ~~~( ~~~d ||| (e &&& f)) + 2 * ~~~( ~~~d ||| (e ^^^ f)) - 7 * (e ^^^ ~~~(d ||| (e &&& f))) - 11 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 5 * (e ^^^ ~~~(d &&& (e ||| f))) + 5 * (f ||| ~~~(d ||| e)) - 1 * (f ^^^ (d ||| ~~~e)) + 1 * ((d &&& e) ||| (e ^^^ f)) - 11 * ( ~~~f ||| (d ^^^ e)) - 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 4 * ( ~~~d ||| ( ~~~e ||| f)) + 3 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 5 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 11 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 3 * ~~~(d ^^^ f) + 4 * ( ~~~d &&& (e ^^^ f)) - 6 * ((d &&& f) ^^^ (e ||| f)) - 1 * (f &&& ~~~(d ^^^ e)) + 7 * d + 1 * (d &&& f) + 11 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 3 * ~~~(d ^^^ (e &&& f)) - 3 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 5 * ( ~~~d &&& ( ~~~e ||| f)) + 3 * ~~~(d ||| (e ||| f)) + 18 * ~~~(d ||| ( ~~~e ||| f)) + 20 * ~~~( ~~~d ||| (e ||| f)) - 4 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 41 * ( ~~~d &&& ( ~~~e &&& f)) + 20 * ( ~~~d &&& (e &&& f)) + 2 * (d &&& ( ~~~e &&& f)) - 8 * (d &&& (e &&& f)) = 1 * (e ^^^ ~~~(d &&& (e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2279 (x y : BitVec w) : +theorem e_2279 : - 2 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 1 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 1 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 2 * ~~~(d ^^^ e) - 1 * (f ^^^ ( ~~~d &&& (e ||| f))) - 1 * ~~~( ~~~d &&& (e ||| f)) + 1 * ~~~(d ||| (e &&& f)) + 5 * (f ^^^ ~~~(d &&& (e &&& f))) - 2 * (f ^^^ (d ||| ( ~~~e ||| f))) + 3 * ( ~~~f ||| (d ^^^ e)) - 7 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 3 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 2 * (f ^^^ (d ||| (e ||| f))) + 3 * ( ~~~d ||| ( ~~~e &&& f)) - 3 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 1 * ~~~(d &&& e) + 2 * (e ^^^ (d ||| ( ~~~e &&& f))) - 2 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 6 * ((d ^^^ e) ||| (d ^^^ f)) - 3 * (f ^^^ (d &&& ~~~e)) - 6 * e - 11 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 1 * (d ^^^ e) + 7 * (e ^^^ ~~~(d ||| ~~~f)) - 1 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 4 * ~~~( ~~~d &&& (e ^^^ f)) + 4 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 11 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 1 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 2 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 3 * (e ||| (d &&& f)) - 1 * ~~~(d &&& ~~~e) + 4 * ~~~(d ||| e) + 5 * (e ^^^ ( ~~~d ||| (e &&& f))) + 1 * ((d ^^^ e) &&& (d ^^^ f)) - 5 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 1 * (f ||| (d &&& e)) + 11 * (d &&& (e ||| f)) + 5 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 11 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 5 * (f ^^^ (d ||| e)) + 2 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 1 * (f ||| ~~~(d ^^^ e)) + 1 * (d ^^^ (e ||| f)) - 2 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * (f &&& (d ||| ~~~e)) - 2 * (d ||| ( ~~~e &&& f)) - 1 * (f ^^^ (d ||| ( ~~~e &&& f))) - 2 * (e ||| ~~~(d ^^^ f)) - 2 * ((d &&& f) ||| ~~~(e ||| f)) - 1 * ~~~(d ||| ~~~e) + 10 * ~~~(d ||| (e ||| f)) + 22 * ~~~(d ||| ( ~~~e ||| f)) + 25 * ~~~( ~~~d ||| (e ||| f)) + 1 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 11 * ( ~~~d &&& ( ~~~e &&& f)) + 29 * ( ~~~d &&& (e &&& f)) + 17 * (d &&& ( ~~~e &&& f)) - 6 * (d &&& (e &&& f)) = - 1 * (e ^^^ (d ||| (e ||| f))) - 3 * (e ^^^ ~~~(d &&& (e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2280 (x y : BitVec w) : +theorem e_2280 : 3 * (f ^^^ ~~~(d &&& ~~~e)) + 5 * ( ~~~d &&& (e ||| f)) + 1 * (f ||| (d &&& ~~~e)) - 6 * (f ^^^ ( ~~~d ||| (e ||| f))) - 2 * (e ^^^ (d ||| (e ||| f))) - 7 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 2 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 3 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 1 * (d ||| e) + 1 * ~~~(d ||| ( ~~~e &&& f)) - 7 * ( ~~~d ||| ( ~~~e &&& f)) - 1 * (e ^^^ ~~~(d ||| f)) + 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 1 * ( ~~~d &&& ( ~~~e ||| f)) + 1 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 1 * ~~~(e ||| f) + 4 * (f &&& (d ||| ~~~e)) - 6 * ( ~~~f &&& ~~~(d ^^^ e)) + 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 4 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 5 * ~~~( ~~~d ||| (e ^^^ f)) + 5 * (f ||| (d &&& e)) + 2 * (e ^^^ ~~~(d &&& f)) + 2 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 7 * (f ^^^ (d &&& ~~~e)) + 1 * (e ^^^ ( ~~~d ||| (e &&& f))) - 1 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 7 * (f ^^^ (d ||| ( ~~~e ||| f))) + 1 * (e ^^^ ~~~(d &&& ~~~f)) - 1 * (e &&& (d ||| ~~~f)) - 1 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 2 * (e &&& ~~~(d ^^^ f)) + 1 * (f &&& (d ^^^ e)) - 5 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 1 * (f ^^^ (d &&& (e ||| f))) - 2 * ~~~( ~~~d &&& (e ||| f)) + 2 * (d ^^^ ( ~~~e &&& f)) + 5 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 7 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 11 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 2 * ((d &&& ~~~e) ||| (e ^^^ f)) + 1 * (f ||| ~~~(d ||| ~~~e)) - 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 5 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 2 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 2 * ~~~(d ||| ~~~f) - 1 * d + 1 * (d ^^^ (e ^^^ f)) + 2 * (e ||| (d &&& f)) - 1 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 6 * (e &&& ~~~(d &&& f)) + 2 * (d ^^^ ( ~~~e ||| f)) + 22 * ~~~(d ||| (e ||| f)) - 8 * ~~~(d ||| ( ~~~e ||| f)) - 24 * ~~~( ~~~d ||| (e ||| f)) - 3 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 27 * ( ~~~d &&& ( ~~~e &&& f)) - 17 * ( ~~~d &&& (e &&& f)) - 2 * (d &&& ( ~~~e &&& f)) - 50 * (d &&& (e &&& f)) = - 11 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 6 * (e ^^^ (d &&& ~~~f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2281 (x y : BitVec w) : +theorem e_2281 : 4 * (e ^^^ ~~~(d ||| f)) - 7 * ( ~~~e &&& ~~~(d ^^^ f)) + 1 * (f ^^^ ~~~(d ||| ~~~e)) + 5 * (f &&& (d ^^^ e)) - 6 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 11 * (e ^^^ f) + 1 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 2 * ~~~(d ||| (e ^^^ f)) - 2 * ~~~f + 3 * (f &&& ~~~(d ^^^ e)) + 1 * (d ^^^ f) - 11 * ((d ||| e) &&& ~~~(e ^^^ f)) + 1 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 2 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 2 * ~~~(d &&& e) + 2 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 4 * ~~~(d &&& f) - 2 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 7 * (f ^^^ ( ~~~d ||| (e &&& f))) - 3 * (f ||| (d ^^^ e)) + 1 * ((d &&& e) ||| (e ^^^ f)) - 1 * ~~~(d &&& ~~~f) + 5 * (f ^^^ (d &&& ( ~~~e ||| f))) - 1 * (e &&& f) - 1 * (f ||| ~~~(d ^^^ e)) + 7 * ( ~~~d ||| ( ~~~e ||| f)) - 11 * ~~~(d &&& ( ~~~e &&& f)) - 1 * ~~~d + 7 * (f ^^^ ~~~(d &&& ~~~e)) + 5 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 1 * (f ^^^ (d ||| (e ||| f))) + 2 * ( ~~~f ||| (d ^^^ e)) - 7 * (e ||| ~~~(d ^^^ f)) - 7 * ~~~( ~~~d &&& (e &&& f)) + 2 * (e ||| (d &&& ~~~f)) + 3 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 2 * (f ^^^ ~~~(d &&& (e &&& f))) - 2 * (f ^^^ ~~~(d ||| e)) + 5 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 5 * ~~~(e &&& ~~~f) - 1 * ~~~(d ||| f) - 11 * ( ~~~d ||| (e ||| f)) + 3 * (d ||| ~~~e) - 6 * (f ^^^ (d ||| ~~~e)) + 5 * (f &&& (d ||| ~~~e)) - 3 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 7 * ~~~( ~~~d ||| (e ^^^ f)) - 6 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 3 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 5 * ( ~~~f &&& ~~~(d ^^^ e)) + 7 * (e ^^^ (d ||| f)) + 1 * (d ^^^ (e ^^^ f)) + 20 * ~~~(d ||| (e ||| f)) - 22 * ~~~(d ||| ( ~~~e ||| f)) + 6 * ~~~( ~~~d ||| (e ||| f)) + 9 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 16 * ( ~~~d &&& ( ~~~e &&& f)) + 19 * ( ~~~d &&& (e &&& f)) - 25 * (d &&& ( ~~~e &&& f)) + 8 * (d &&& (e &&& f)) = - 1 * ~~~(d &&& (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2282 (x y : BitVec w) : +theorem e_2282 : 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 11 * ~~~(d &&& (e &&& f)) + 4 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 1 * (d &&& ~~~f) - 1 * (e ^^^ ~~~(d &&& (e ||| f))) + 5 * (f ^^^ ~~~(d &&& (e ||| f))) - 2 * ((d ^^^ e) &&& (d ^^^ f)) + 1 * (d ^^^ ( ~~~e &&& f)) + 2 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 1 * (e ||| (d ^^^ f)) + 4 * (f ||| ~~~(d ^^^ e)) + 5 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (d ^^^ (e ^^^ f)) - 1 * ( ~~~d ||| ( ~~~e &&& f)) - 1 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 4 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 2 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 2 * ~~~e - 5 * ((d &&& f) ^^^ (e ||| f)) - 5 * ~~~(d &&& e) + 4 * (d ||| (e &&& f)) - 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 2 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 2 * ~~~d + 7 * ~~~(d ||| ( ~~~e &&& f)) + 3 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 3 * ((d &&& e) ^^^ (e ||| f)) - 7 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 11 * ~~~( ~~~d &&& (e ||| f)) - 6 * ((d ||| e) &&& ~~~(e ^^^ f)) + 7 * ((e &&& f) ||| (d &&& (e ||| f))) + 11 * (d &&& ~~~e) - 1 * ~~~(d ||| ~~~f) - 1 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 11 * ( ~~~d &&& (e ||| f)) - 1 * (e &&& (d ||| f)) + 1 * ~~~(d ^^^ (e ||| f)) - 1 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 2 * ( ~~~e &&& ~~~(d ^^^ f)) - 11 * ~~~(e &&& f) + 2 * (e ^^^ (d ||| (e ||| f))) + 4 * (e ^^^ ( ~~~d ||| (e &&& f))) + 3 * (f &&& (d ^^^ e)) + 2 * (e ^^^ (d ||| ( ~~~e &&& f))) - 6 * (f ^^^ (d &&& e)) + 2 * ( ~~~e ||| ~~~(d ^^^ f)) - 7 * ~~~(d ^^^ (e ^^^ f)) - 11 * ~~~(e &&& ~~~f) - 11 * (d ||| f) - 11 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 7 * ( ~~~d &&& (e ^^^ f)) + 2 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 25 * ~~~(d ||| (e ||| f)) + 4 * ~~~(d ||| ( ~~~e ||| f)) + 44 * ~~~( ~~~d ||| (e ||| f)) + 13 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 33 * ( ~~~d &&& ( ~~~e &&& f)) + 28 * ( ~~~d &&& (e &&& f)) + 7 * (d &&& ( ~~~e &&& f)) + 33 * (d &&& (e &&& f)) = 5 * (d ^^^ (e ||| f)) + 7 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2283 (x y : BitVec w) : +theorem e_2283 : - 1 * (f ^^^ ( ~~~d ||| (e &&& f))) - 5 * ( ~~~d ||| (e &&& f)) - 6 * ((d ||| e) &&& ~~~(e ^^^ f)) + 2 * (f ^^^ (d ||| (e &&& f))) + 11 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 3 * ( ~~~f ||| ~~~(d ^^^ e)) - 2 * ~~~(d ^^^ e) - 2 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 1 * (e ^^^ (d ||| ~~~f)) - 6 * (e ^^^ ~~~(d ||| f)) + 4 * (e ||| (d &&& ~~~f)) + 11 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 3 * ( ~~~e ||| ~~~(d ^^^ f)) - 3 * ~~~( ~~~d ||| (e &&& f)) + 4 * (e ||| f) + 5 * (f ^^^ (d &&& ~~~e)) - 3 * ~~~(d ^^^ ( ~~~e &&& f)) + 2 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 7 * (f ^^^ ( ~~~d &&& (e ||| f))) - 11 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 5 * ~~~(d ^^^ f) + 1 * (f &&& (d ||| e)) - 6 * ( ~~~d ||| ( ~~~e ||| f)) + 1 * (e ^^^ (d &&& ~~~f)) - 2 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 7 * (d &&& (e ||| f)) + 2 * ( ~~~f ||| (d ^^^ e)) + 7 * ~~~(d &&& (e &&& f)) - 7 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 2 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 2 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 11 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 5 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * ~~~( ~~~d ||| (e ^^^ f)) + 2 * (e ^^^ (d ||| (e ||| f))) - 11 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 5 * ~~~d - 1 * (d ||| ( ~~~e &&& f)) + 11 * (f ^^^ ~~~(d &&& ~~~e)) + 1 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 3 * ( ~~~e &&& ~~~(d ^^^ f)) - 1 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 7 * (e ^^^ ( ~~~d ||| (e ||| f))) - 6 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 2 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 5 * (f ^^^ (d ||| e)) + 11 * (f ^^^ (d &&& e)) + 1 * (e ^^^ ~~~(d ||| ~~~f)) - 2 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 11 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 5 * (f &&& ~~~(d &&& ~~~e)) + 4 * ((d ||| e) &&& (e ^^^ f)) - 1 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 7 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 9 * ~~~(d ||| (e ||| f)) + 15 * ~~~( ~~~d ||| (e ||| f)) - 7 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 8 * ( ~~~d &&& ( ~~~e &&& f)) - 9 * ( ~~~d &&& (e &&& f)) - 7 * (d &&& ( ~~~e &&& f)) = - 57 * (d &&& (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2284 (x y : BitVec w) : +theorem e_2284 : - 1 * ~~~(e ^^^ f) + 7 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 1 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 1 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 3 * (f ||| ~~~(d ||| e)) - 2 * (d &&& ( ~~~e ||| f)) + 11 * (f ^^^ ~~~(d &&& (e &&& f))) - 5 * (f ^^^ (d ||| ( ~~~e ||| f))) + 7 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 1 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 7 * ((d &&& f) ^^^ (e ||| f)) + 3 * (f ||| (d ^^^ e)) + 1 * (d ||| (e &&& f)) - 1 * ~~~e + 1 * (d ^^^ (e ^^^ f)) - 3 * (e ^^^ (d &&& f)) - 2 * (f ^^^ ~~~(d ||| ~~~e)) + 5 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 7 * (d ^^^ ( ~~~e &&& f)) - 3 * ~~~(d ||| ~~~f) + 4 * (d ||| ~~~e) + 2 * ~~~(d ||| ( ~~~e &&& f)) + 7 * (f &&& (d ^^^ e)) + 7 * ~~~(d &&& ( ~~~e ||| f)) + 1 * (e &&& ~~~f) - 2 * ~~~(d ^^^ ( ~~~e &&& f)) - 11 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 3 * f - 2 * ((d &&& e) ^^^ (e ||| ~~~f)) - 2 * (e &&& ~~~(d ^^^ f)) - 1 * (e ||| (d &&& f)) - 1 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 4 * (f ^^^ (d &&& ~~~e)) - 11 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 3 * ((d ^^^ e) ||| (d ^^^ f)) - 5 * d - 6 * ~~~(e &&& ~~~f) - 6 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 1 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 2 * ((d &&& f) ||| (e &&& ~~~f)) + 2 * ~~~(e ||| f) + 11 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 5 * (d ^^^ (e ||| f)) + 2 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 3 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 1 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 11 * (e ^^^ (d &&& (e ||| f))) - 6 * (f ^^^ ~~~(d &&& ~~~e)) - 11 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 11 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 3 * ( ~~~e &&& (d ^^^ f)) - 2 * ((d ||| e) &&& ~~~(e ^^^ f)) - 11 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 27 * ~~~(d ||| (e ||| f)) - 27 * ~~~(d ||| ( ~~~e ||| f)) - 26 * ~~~( ~~~d ||| (e ||| f)) - 10 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 17 * ( ~~~d &&& ( ~~~e &&& f)) + 4 * ( ~~~d &&& (e &&& f)) + 34 * (d &&& ( ~~~e &&& f)) - 7 * (d &&& (e &&& f)) = - 1 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2285 (x y : BitVec w) : +theorem e_2285 : 1 * ( ~~~d ||| (e ^^^ f)) - 1 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 4 * (d ^^^ (e &&& f)) - 1 * (d &&& e) - 1 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 5 * ~~~(d &&& ( ~~~e ||| f)) - 5 * (d ||| ( ~~~e ||| f)) + 3 * ~~~(e ||| f) + 2 * ~~~(d &&& (e ||| f)) + 5 * (e ^^^ ( ~~~d ||| (e ||| f))) + 1 * ((d &&& e) ||| (e ^^^ f)) - 3 * ~~~( ~~~d &&& (e &&& f)) - 7 * (e ^^^ (d &&& f)) + 1 * (d ||| ~~~f) - 1 * (e ^^^ ~~~(d ||| f)) + 7 * ~~~(e ^^^ f) - 5 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 2 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 7 * (e ||| f) - 1 * (e ||| (d &&& f)) - 6 * ~~~(d &&& (e &&& f)) + 1 * d - 3 * (e ^^^ (d ||| ( ~~~e &&& f))) + 1 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 1 * f - 5 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 5 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 2 * ((d &&& f) ||| (e &&& ~~~f)) + 2 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 1 * ~~~(d ||| e) + 1 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 11 * (f ^^^ ~~~(d &&& ~~~e)) + 1 * (f ^^^ (d ||| e)) + 2 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * ~~~(d &&& ~~~d) - 5 * ~~~(d ||| (e ^^^ f)) - 1 * (d ^^^ ( ~~~e ||| f)) + 1 * ~~~(d ^^^ e) + 1 * ( ~~~e ||| (d ^^^ f)) - 2 * (e ^^^ (d ||| (e ^^^ f))) + 3 * (f ^^^ (d ||| ( ~~~e ||| f))) + 2 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 2 * ( ~~~d &&& (e ^^^ f)) - 1 * ((d ^^^ e) &&& (d ^^^ f)) + 3 * (f ||| (d &&& ~~~e)) - 11 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 1 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 11 * ~~~(e &&& f) + 2 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 11 * (d ^^^ e) - 1 * ( ~~~f &&& (d ^^^ e)) - 3 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 2 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 16 * ~~~(d ||| (e ||| f)) + 9 * ~~~(d ||| ( ~~~e ||| f)) - 9 * ~~~( ~~~d ||| (e ||| f)) - 2 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 4 * ( ~~~d &&& ( ~~~e &&& f)) + 27 * ( ~~~d &&& (e &&& f)) + 11 * (d &&& ( ~~~e &&& f)) + 24 * (d &&& (e &&& f)) = - 4 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2286 (x y : BitVec w) : +theorem e_2286 : 1 * (e ||| (d ^^^ f)) - 6 * (f ^^^ ~~~(d ||| (e &&& f))) + 5 * ~~~(d ^^^ (e ||| f)) + 1 * (f ^^^ (d ||| (e ||| f))) - 3 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 4 * ~~~(d ||| ~~~f) - 7 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 6 * (d ||| (e ||| f)) - 3 * ~~~( ~~~d &&& (e ||| f)) + 4 * (e ^^^ ~~~(d &&& (e &&& f))) + 1 * ~~~(d ||| ~~~e) + 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 3 * (e ^^^ (d ||| f)) - 3 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 2 * (f ^^^ ~~~(d ||| e)) + 4 * ~~~(d ||| e) - 2 * ( ~~~d &&& (e ^^^ f)) + 7 * (f &&& (d ||| e)) + 11 * ~~~(d &&& ( ~~~e &&& f)) + 3 * ((d &&& ~~~e) ||| (e ^^^ f)) - 3 * (f ^^^ (d ||| ( ~~~e &&& f))) - 2 * (e ||| f) + 11 * ((d &&& e) ||| ~~~(e ||| f)) + 2 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 5 * (f ^^^ (d ||| e)) - 7 * ( ~~~d &&& (e ||| f)) + 7 * (f ^^^ ~~~(d ||| ~~~e)) - 7 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 11 * (e ^^^ ~~~(d ||| (e &&& f))) + 2 * ((d &&& f) ||| ~~~(e ||| f)) - 1 * ~~~(e ||| f) - 6 * (d ^^^ ( ~~~e &&& f)) + 1 * (d &&& e) + 7 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 1 * (e &&& (d ||| ~~~f)) + 7 * (f ||| ~~~(d ^^^ e)) + 5 * (e &&& (d ^^^ f)) + 2 * ~~~(d ^^^ ( ~~~e ||| f)) - 2 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 11 * (f ^^^ ~~~(d &&& (e &&& f))) - 1 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 2 * (e ^^^ ~~~(d ||| f)) + 2 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 11 * (d ^^^ (e &&& f)) - 5 * (d ||| (e &&& f)) - 7 * ((e &&& f) ||| (d &&& (e ||| f))) - 1 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 3 * ((d &&& e) ||| (e ^^^ f)) + 2 * ( ~~~e ||| (d ^^^ f)) - 1 * (d ||| f) - 2 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 3 * (e ^^^ ~~~(d &&& f)) - 51 * ~~~(d ||| (e ||| f)) - 7 * ~~~(d ||| ( ~~~e ||| f)) - 8 * ~~~( ~~~d ||| (e ||| f)) - 34 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 12 * ( ~~~d &&& ( ~~~e &&& f)) + 3 * ( ~~~d &&& (e &&& f)) - 5 * (d &&& ( ~~~e &&& f)) - 27 * (d &&& (e &&& f)) = 5 * ( ~~~d ||| (e &&& f)) - 2 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2287 (x y : BitVec w) : +theorem e_2287 : 2 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 2 * (f ^^^ ( ~~~d ||| (e ||| f))) - 1 * (d ^^^ (e &&& f)) - 5 * ( ~~~d ||| (e ^^^ f)) + 11 * ((d ||| ~~~e) &&& (e ^^^ f)) - 1 * (f ^^^ ~~~(d ||| (e &&& f))) - 2 * ~~~(d ||| ( ~~~e &&& f)) - 1 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 5 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * ( ~~~e ||| (d ^^^ f)) + 3 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 11 * d - 11 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 4 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 7 * (f &&& ~~~(d &&& ~~~e)) + 2 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 3 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 1 * ~~~(d &&& ~~~e) + 5 * (d ||| (e ^^^ f)) - 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 2 * (e ||| (d &&& f)) - 1 * ~~~(d ^^^ e) + 2 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 7 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 5 * (f ||| (d &&& e)) + 1 * (e &&& (d ||| ~~~f)) - 1 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 3 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 1 * ~~~(d &&& e) + 1 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 7 * (e &&& ~~~(d &&& ~~~f)) - 1 * (f ||| (d ^^^ e)) - 5 * (e ^^^ ~~~(d ||| f)) + 2 * ~~~(d ||| (e ^^^ f)) + 7 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 1 * (d &&& e) + 2 * ( ~~~d ||| (e ||| f)) + 2 * (d ^^^ (e ^^^ f)) + 5 * (e ||| ~~~(d ||| f)) - 3 * ((d ^^^ e) ||| (d ^^^ f)) - 2 * (f ^^^ (d ||| (e ||| f))) - 11 * ~~~(d ||| f) - 2 * (d ||| f) - 7 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 7 * ~~~(d &&& ~~~f) + 1 * (f ^^^ (d &&& (e ||| f))) + 1 * e + 2 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 1 * ~~~(d &&& ( ~~~e ||| f)) + 3 * ( ~~~f &&& (d ^^^ e)) + 7 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 4 * ((d &&& ~~~e) ||| (e ^^^ f)) + 1 * ~~~(d ^^^ (e ^^^ f)) + 5 * ~~~(d ||| (e ||| f)) + 4 * ~~~(d ||| ( ~~~e ||| f)) - 20 * ~~~( ~~~d ||| (e ||| f)) - 31 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 16 * ( ~~~d &&& ( ~~~e &&& f)) + 13 * ( ~~~d &&& (e &&& f)) - 16 * (d &&& ( ~~~e &&& f)) - 12 * (d &&& (e &&& f)) = 6 * (e ^^^ (d ||| (e ||| f))) + 1 * (e ^^^ (d &&& ~~~f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2288 (x y : BitVec w) : +theorem e_2288 : 1 * ~~~(e &&& f) - 1 * f - 6 * (e &&& ~~~(d &&& f)) + 2 * ((d &&& ~~~e) ||| (e ^^^ f)) + 4 * (d &&& e) - 11 * d + 3 * (d ||| f) + 7 * ~~~(e ^^^ f) - 1 * ~~~(d ||| e) - 6 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * ( ~~~e ||| ~~~(d ^^^ f)) - 1 * ~~~(d ^^^ ( ~~~e ||| f)) + 2 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 5 * ~~~(d ||| ~~~e) - 7 * (e ^^^ ~~~(d &&& (e ||| f))) - 1 * ~~~(d ^^^ (e ||| f)) - 5 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 6 * (f ||| ~~~(d ||| e)) + 2 * (e ||| ~~~(d ||| ~~~f)) + 7 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 1 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 1 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 1 * (d ||| e) + 3 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 1 * (e ||| (d &&& f)) - 11 * (f &&& (d ||| e)) - 11 * (f ||| ~~~(d ||| ~~~e)) + 1 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 11 * (f ^^^ (d &&& ~~~e)) + 5 * (e &&& ~~~f) - 3 * ~~~e + 1 * (e ^^^ ~~~(d ||| (e &&& f))) - 1 * (f ^^^ ~~~(d &&& (e ||| f))) - 2 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 1 * (d ^^^ e) + 1 * (f ^^^ ~~~(d ||| e)) - 6 * ~~~(d ^^^ (e &&& f)) - 1 * (f &&& (d ||| ~~~e)) + 4 * ( ~~~d &&& (e ^^^ f)) - 3 * ~~~(d &&& (e ||| f)) + 3 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 5 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 2 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 11 * ( ~~~f &&& (d ^^^ e)) + 11 * ((d ^^^ e) ||| (d ^^^ f)) - 11 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 2 * (f ^^^ ~~~(d &&& e)) + 7 * (e ^^^ f) - 5 * (e ^^^ (d &&& (e ||| f))) + 2 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 3 * (f ^^^ ~~~(d ||| ~~~e)) - 2 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 11 * (d ||| ~~~f) + 11 * ~~~(d ||| (e ||| f)) - 12 * ~~~(d ||| ( ~~~e ||| f)) - 12 * ~~~( ~~~d ||| (e ||| f)) - 30 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 4 * ( ~~~d &&& ( ~~~e &&& f)) + 17 * ( ~~~d &&& (e &&& f)) + 22 * (d &&& ( ~~~e &&& f)) + 47 * (d &&& (e &&& f)) = - 2 * (d ^^^ (e &&& f)) - 1 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2289 (x y : BitVec w) : +theorem e_2289 : - 7 * ~~~(d ^^^ (e ||| f)) + 2 * (f ||| (d &&& ~~~e)) + 2 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 1 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 1 * (e ^^^ (d &&& ~~~f)) + 3 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 2 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 2 * ~~~(d ^^^ ( ~~~e &&& f)) - 5 * (f ^^^ ( ~~~d ||| (e &&& f))) + 2 * (e &&& f) - 7 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 3 * (f ^^^ (d ||| ( ~~~e ||| f))) - 7 * ( ~~~d ||| ( ~~~e ||| f)) + 11 * ((d ^^^ e) ||| (d ^^^ f)) + 2 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 2 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 1 * ~~~(d ||| f) + 2 * (d ^^^ ( ~~~e &&& f)) + 4 * ( ~~~f ||| (d ^^^ e)) - 11 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * (e &&& (d ||| ~~~f)) + 2 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 1 * ~~~(d ^^^ ( ~~~e ||| f)) + 5 * ( ~~~d ||| (e &&& f)) + 1 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 7 * ~~~( ~~~d &&& (e ^^^ f)) + 11 * (f ^^^ (d &&& e)) - 3 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 7 * ((d &&& e) ||| ~~~(e ||| f)) - 1 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 7 * (f ||| ~~~(d ||| e)) + 1 * (d ||| ( ~~~e ||| f)) - 1 * (e ^^^ (d &&& (e ||| f))) - 7 * (e ^^^ ( ~~~d &&& (e ||| f))) - 3 * ~~~(d ^^^ (e ^^^ f)) - 1 * (e &&& ~~~(d &&& ~~~f)) + 11 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 3 * ~~~(d ||| (e ^^^ f)) + 1 * (f ^^^ ~~~(d &&& (e &&& f))) + 1 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (e ^^^ (d ||| ( ~~~e &&& f))) + 2 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 6 * ( ~~~f &&& (d ^^^ e)) - 2 * (e ^^^ ( ~~~d ||| (e &&& f))) - 11 * (e ||| (d &&& f)) - 2 * ~~~( ~~~d &&& (e ||| f)) - 2 * (e ^^^ (d ||| (e &&& f))) - 3 * ~~~(d ^^^ f) - 2 * ((d &&& f) ||| ~~~(e ||| f)) - 2 * ~~~(d &&& (e ||| f)) - 6 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 11 * (d &&& ( ~~~e ||| f)) - 1 * (e &&& ~~~(d &&& f)) + 3 * ~~~(d ||| (e ||| f)) + 8 * ~~~(d ||| ( ~~~e ||| f)) + 8 * ~~~( ~~~d ||| (e ||| f)) + 8 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 14 * ( ~~~d &&& ( ~~~e &&& f)) - 36 * ( ~~~d &&& (e &&& f)) + 9 * (d &&& ( ~~~e &&& f)) + 38 * (d &&& (e &&& f)) = - 7 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 5 * e := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2290 (x y : BitVec w) : +theorem e_2290 : - 3 * (e ||| ~~~(d ^^^ f)) - 1 * (f &&& (d ^^^ e)) - 6 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 1 * ~~~( ~~~d ||| (e &&& f)) + 11 * (f ^^^ ~~~(d &&& (e ||| f))) + 1 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 2 * (f ^^^ ~~~(d &&& (e &&& f))) - 5 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 1 * (e ||| ~~~(d ||| f)) + 5 * ( ~~~d &&& (e ||| f)) - 11 * ( ~~~d ||| (e ||| f)) - 1 * (f ^^^ (d ||| e)) + 11 * (f ^^^ ~~~(d ||| ~~~e)) + 2 * ~~~(d ^^^ e) - 6 * ~~~(d ||| ~~~f) + 11 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 2 * (f ^^^ (d &&& (e ||| f))) + 4 * ((d &&& f) ^^^ (e ||| f)) + 5 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 2 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 2 * ~~~(d &&& (e &&& f)) - 6 * (f &&& (d ||| ~~~e)) + 1 * (d ^^^ ( ~~~e &&& f)) - 1 * ((d &&& e) ||| ~~~(e ^^^ f)) - 7 * (d ^^^ ( ~~~e ||| f)) - 1 * (d &&& e) + 1 * ~~~(e ^^^ f) - 7 * ( ~~~e &&& ~~~(d ^^^ f)) + 4 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 3 * (e ^^^ ~~~(d &&& (e &&& f))) - 6 * ~~~e + 3 * (d ^^^ (e ^^^ f)) + 2 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * (e &&& (d ^^^ f)) + 1 * (e &&& ~~~(d &&& ~~~f)) + 1 * e + 7 * ( ~~~d ||| ( ~~~e &&& f)) + 2 * (e ^^^ (d ||| (e &&& f))) - 3 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 3 * (e ^^^ (d ||| f)) - 2 * ((d ||| e) &&& ~~~(e ^^^ f)) + 5 * (f ^^^ ~~~(d ||| (e &&& f))) + 4 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 2 * ~~~(d &&& ~~~e) - 2 * (e ^^^ ~~~(d &&& (e ||| f))) - 2 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 1 * ~~~(e &&& ~~~f) + 11 * (f ^^^ (d ||| ( ~~~e &&& f))) - 11 * ~~~(d &&& (e ^^^ f)) - 7 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 7 * (e ||| (d &&& ~~~f)) + 13 * ~~~(d ||| (e ||| f)) - 37 * ~~~(d ||| ( ~~~e ||| f)) + 2 * ~~~( ~~~d ||| (e ||| f)) - 16 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 29 * ( ~~~d &&& ( ~~~e &&& f)) + 20 * ( ~~~d &&& (e &&& f)) - 12 * (d &&& ( ~~~e &&& f)) + 11 * (d &&& (e &&& f)) = 5 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2291 (x y : BitVec w) : +theorem e_2291 : - 6 * ~~~(e ||| f) + 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * e + 7 * (f ^^^ ~~~(d &&& ~~~e)) - 2 * (e ||| (d &&& f)) + 5 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 1 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 1 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 1 * (e ^^^ (d &&& (e ^^^ f))) - 2 * (e ^^^ ~~~(d &&& f)) - 7 * ~~~(d &&& ( ~~~e &&& f)) + 2 * ~~~d - 1 * (e &&& f) + 3 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 2 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 11 * (e ^^^ (d &&& ( ~~~e ||| f))) - 2 * (e ^^^ ~~~(d ||| (e &&& f))) - 1 * (f ^^^ (d &&& ~~~e)) + 11 * ((d &&& e) ||| (e ^^^ f)) + 2 * (f ^^^ ( ~~~d &&& (e ||| f))) + 11 * (d ^^^ (e ||| f)) + 11 * (e ^^^ ( ~~~d ||| (e &&& f))) + 1 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 2 * ~~~(d &&& (e ||| f)) + 1 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 5 * (f ||| ~~~(d ^^^ e)) + 1 * (f ^^^ ~~~(d &&& e)) + 1 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 6 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 11 * ~~~(d &&& ( ~~~e ||| f)) + 3 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 7 * ~~~( ~~~d ||| (e &&& f)) - 3 * ~~~(d ^^^ e) - 1 * f + 4 * ((d &&& f) ||| (e &&& ~~~f)) - 5 * ((d ^^^ e) ||| (d ^^^ f)) + 5 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 2 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 1 * ( ~~~d ||| ( ~~~e &&& f)) - 2 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 11 * (e ^^^ (d &&& f)) - 11 * (e ^^^ ~~~(d &&& (e &&& f))) - 6 * (f ||| (d &&& ~~~e)) - 1 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 1 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 1 * ~~~(d &&& f) + 2 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 5 * ~~~(d ^^^ f) + 5 * (f ^^^ (d &&& e)) - 1 * (e ^^^ f) - 2 * (e ||| f) - 1 * ~~~(d &&& ~~~e) - 2 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 13 * ~~~(d ||| (e ||| f)) - 16 * ~~~(d ||| ( ~~~e ||| f)) + 49 * ~~~( ~~~d ||| (e ||| f)) - 7 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 17 * ( ~~~d &&& ( ~~~e &&& f)) + 30 * ( ~~~d &&& (e &&& f)) + 12 * (d &&& ( ~~~e &&& f)) = - 12 * (d &&& (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2292 (x y : BitVec w) : +theorem e_2292 : 2 * ~~~(d ||| f) - 11 * (e &&& f) + 11 * ~~~(e &&& ~~~f) + 7 * (f ^^^ ( ~~~d &&& (e ||| f))) + 4 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 7 * (d ||| ( ~~~e &&& f)) + 1 * ~~~( ~~~d ||| (e &&& f)) - 2 * (d ||| ~~~e) - 2 * (e ^^^ ~~~(d &&& f)) + 1 * ~~~(d &&& e) + 2 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 6 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 1 * (d &&& e) + 2 * (e &&& (d ||| ~~~f)) + 7 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 7 * (f ^^^ (d &&& (e ||| f))) - 3 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 1 * (e ^^^ (d &&& ( ~~~e ||| f))) - 7 * (d ^^^ ( ~~~e &&& f)) - 1 * ~~~(d ^^^ ( ~~~e ||| f)) - 7 * ((d ||| e) &&& ~~~(e ^^^ f)) + 5 * ~~~(d ^^^ ( ~~~e &&& f)) + 2 * ~~~(d ||| e) + 1 * (f ^^^ (d &&& e)) - 1 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 11 * ( ~~~d ||| ( ~~~e ||| f)) + 7 * (e ^^^ ~~~(d ||| ~~~f)) + 2 * ((d &&& f) ||| ~~~(e ||| f)) + 1 * (e &&& ~~~(d &&& ~~~f)) + 11 * ( ~~~f ||| ~~~(d ^^^ e)) - 5 * ~~~(d ||| (e ^^^ f)) - 1 * (d ||| (e &&& f)) + 2 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 3 * ( ~~~d ||| (e ^^^ f)) + 2 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 2 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 11 * (e ^^^ ( ~~~d ||| (e ||| f))) - 11 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 2 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 5 * ~~~(e &&& f) + 4 * (d ||| e) - 1 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 3 * ((e &&& f) ||| (d &&& (e ||| f))) + 4 * ( ~~~d &&& (e ^^^ f)) - 11 * ~~~(d ||| (e &&& f)) - 1 * d - 2 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 2 * ~~~(d &&& f) - 3 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 2 * (e ||| ~~~(d ||| f)) + 1 * ~~~( ~~~d &&& (e ||| f)) + 11 * ~~~(d &&& ~~~f) + 2 * (f ^^^ (d ||| (e &&& f))) - 51 * ~~~(d ||| (e ||| f)) - 43 * ~~~(d ||| ( ~~~e ||| f)) - 11 * ~~~( ~~~d ||| (e ||| f)) - 5 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 41 * ( ~~~d &&& ( ~~~e &&& f)) - 32 * ( ~~~d &&& (e &&& f)) - 53 * (d &&& ( ~~~e &&& f)) - 25 * (d &&& (e &&& f)) = - 7 * (f &&& (d ^^^ e)) + 1 * ~~~(d &&& (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2293 (x y : BitVec w) : +theorem e_2293 : - 1 * ((d &&& ~~~e) ||| (e ^^^ f)) + 3 * (d &&& ~~~e) - 5 * ~~~(e ||| ~~~f) + 2 * (f ^^^ (d ||| e)) + 2 * ((d ||| ~~~e) &&& (e ^^^ f)) - 1 * (f ^^^ (d ||| ( ~~~e &&& f))) - 6 * (f ^^^ ( ~~~d ||| (e &&& f))) - 3 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 2 * (f ^^^ (d &&& ~~~e)) - 3 * ((d ^^^ e) &&& (d ^^^ f)) - 1 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 11 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * ((d &&& e) ^^^ (e ||| ~~~f)) - 7 * (f ^^^ ( ~~~d ||| (e ||| f))) - 2 * (e ^^^ ~~~(d ||| f)) + 4 * ( ~~~d &&& (e ^^^ f)) - 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 2 * ~~~(d ^^^ ( ~~~e ||| f)) + 7 * (e ||| (d ^^^ f)) - 1 * ~~~(e &&& f) - 7 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 3 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 6 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 5 * (e ||| ~~~f) + 5 * ~~~(d ||| f) + 1 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 2 * ( ~~~d ||| (e &&& f)) + 2 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 5 * (e ^^^ ~~~(d &&& (e ||| f))) + 4 * (e ||| (d &&& ~~~f)) + 2 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 1 * (f ^^^ ~~~(d ||| e)) - 11 * ~~~(d &&& ~~~f) - 5 * ~~~(d ||| ~~~e) - 2 * ( ~~~d &&& (e ||| f)) - 6 * (e ^^^ (d ||| ~~~f)) - 3 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 5 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 2 * ~~~d - 5 * ( ~~~e ||| (d ^^^ f)) + 11 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 1 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * ((d ||| e) &&& ~~~(e ^^^ f)) - 3 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 2 * (e ^^^ ~~~(d ||| (e &&& f))) + 11 * ~~~(d ^^^ ( ~~~e &&& f)) + 4 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 3 * (e &&& f) + 11 * (d ^^^ (e ||| f)) - 1 * ~~~(d &&& ~~~e) + 1 * (f ^^^ ( ~~~d &&& (e ||| f))) + 1 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 5 * ~~~(d ||| (e ||| f)) - 23 * ~~~(d ||| ( ~~~e ||| f)) - 17 * ~~~( ~~~d ||| (e ||| f)) - 5 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 13 * ( ~~~d &&& ( ~~~e &&& f)) - 16 * ( ~~~d &&& (e &&& f)) + 3 * (d &&& ( ~~~e &&& f)) - 27 * (d &&& (e &&& f)) = - 4 * (e ^^^ (d ||| ( ~~~e &&& f))) - 3 * (f &&& (d ||| ~~~e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2294 (x y : BitVec w) : +theorem e_2294 : 4 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 1 * (e ^^^ ~~~(d ||| f)) + 1 * (d &&& (e ||| f)) - 2 * (e ^^^ (d &&& (e ^^^ f))) + 11 * ((d &&& e) ^^^ (e ||| f)) - 11 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 7 * ((d ^^^ e) &&& (d ^^^ f)) - 1 * ~~~(d ^^^ (e ||| f)) + 1 * (d &&& e) + 2 * ~~~( ~~~d ||| (e &&& f)) - 2 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 7 * (e &&& (d ||| ~~~f)) - 6 * (e ^^^ (d ||| (e ||| f))) + 7 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 5 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 1 * (e ^^^ (d ||| (e &&& f))) + 3 * e + 7 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 2 * ~~~( ~~~d &&& (e &&& f)) + 3 * ( ~~~d &&& (e ^^^ f)) - 2 * ( ~~~f &&& ~~~(d ^^^ e)) + 1 * (e ^^^ (d ||| (e ^^^ f))) + 1 * ( ~~~e ||| (d ^^^ f)) + 4 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 1 * (e ||| ~~~(d ^^^ f)) - 1 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 1 * (f ||| (d &&& e)) - 2 * (f ^^^ (d &&& (e ||| f))) - 11 * (d ||| e) + 3 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 1 * (f &&& (d ||| e)) + 1 * (e ^^^ ~~~(d &&& (e ||| f))) - 6 * (f &&& ~~~(d ^^^ e)) + 2 * ~~~(e &&& f) - 7 * ~~~(d &&& f) - 1 * ~~~( ~~~d &&& (e ^^^ f)) + 3 * (e ||| (d ^^^ f)) + 7 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 2 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 1 * (f &&& ~~~(d &&& e)) + 2 * (d ||| ~~~f) - 5 * (e ^^^ (d &&& f)) - 3 * f + 2 * (e ^^^ ( ~~~d ||| (e &&& f))) - 1 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 1 * (d ||| (e ||| f)) - 1 * ~~~(d &&& ( ~~~e &&& f)) - 1 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 3 * (f &&& (d ||| ~~~e)) + 5 * (d ^^^ (e ||| f)) - 6 * (e ^^^ (d ||| f)) - 3 * (e &&& (d ^^^ f)) - 6 * (e &&& ~~~(d ^^^ f)) - 15 * ~~~(d ||| (e ||| f)) - 5 * ~~~(d ||| ( ~~~e ||| f)) - 7 * ~~~( ~~~d ||| (e ||| f)) - 1 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 11 * ( ~~~d &&& ( ~~~e &&& f)) - 13 * ( ~~~d &&& (e &&& f)) - 5 * (d &&& ( ~~~e &&& f)) + 3 * (d &&& (e &&& f)) = - 5 * ((d &&& e) ||| ~~~(e ^^^ f)) + 5 * ((d ||| ~~~e) &&& (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2295 (x y : BitVec w) : +theorem e_2295 : 5 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * ( ~~~d &&& (e ^^^ f)) - 2 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * (e ^^^ (d ||| (e &&& f))) + 4 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 5 * ( ~~~d ||| (e ^^^ f)) - 7 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 5 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 1 * (e ^^^ (d &&& f)) + 4 * (f ^^^ (d &&& ( ~~~e ||| f))) - 2 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 7 * (d &&& e) - 11 * ((d &&& f) ||| (e &&& ~~~f)) + 5 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 1 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 2 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 1 * (f ^^^ ~~~(d &&& (e &&& f))) - 11 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 7 * (f ^^^ (d &&& e)) + 3 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 3 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 3 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 7 * (e ^^^ ( ~~~d ||| (e ||| f))) + 1 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 1 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 1 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 3 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 5 * (f ^^^ ~~~(d ||| ~~~e)) + 3 * ~~~(d &&& e) - 5 * (d ||| f) + 5 * (f &&& ~~~(d &&& e)) + 1 * ((d &&& e) ^^^ (e ||| f)) + 2 * (f ^^^ ( ~~~d &&& (e ||| f))) - 5 * (e ^^^ (d ||| ( ~~~e &&& f))) - 7 * ~~~( ~~~d ||| (e ^^^ f)) + 2 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 2 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 6 * (f ||| ~~~(d ||| ~~~e)) + 1 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 5 * (f ^^^ ( ~~~d ||| (e &&& f))) + 11 * e + 2 * ~~~(d ||| ~~~e) - 3 * ~~~(d ||| ( ~~~e &&& f)) - 3 * (d &&& ~~~e) - 5 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 11 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 1 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 5 * ((d &&& e) ||| (e ^^^ f)) + 2 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 2 * (e &&& f) + 4 * ~~~(d &&& ( ~~~e &&& f)) - 3 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 11 * (f ||| (d &&& ~~~e)) + 11 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 4 * ~~~(d ||| (e ||| f)) - 10 * ~~~(d ||| ( ~~~e ||| f)) + 4 * ~~~( ~~~d ||| (e ||| f)) + 4 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 9 * ( ~~~d &&& ( ~~~e &&& f)) + 1 * ( ~~~d &&& (e &&& f)) + 24 * (d &&& (e &&& f)) = - 7 * ( ~~~f ||| (d ^^^ e)) - 9 * (d &&& ( ~~~e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2296 (x y : BitVec w) : +theorem e_2296 : 1 * ~~~(e &&& f) + 5 * (e ^^^ ~~~(d ||| ~~~f)) - 7 * (d ||| ( ~~~e &&& f)) + 1 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 7 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 3 * (e ^^^ (d &&& (e ||| f))) - 2 * ~~~(d &&& ~~~e) + 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 11 * (e ^^^ ( ~~~d &&& (e ||| f))) - 5 * (d ||| ~~~e) + 11 * ~~~(d &&& ~~~f) - 2 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 1 * (e &&& ~~~(d ^^^ f)) - 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 3 * (f ^^^ ~~~(d &&& e)) - 6 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 1 * (d ||| f) - 1 * ( ~~~e ||| ~~~(d ^^^ f)) + 1 * (e ^^^ ~~~(d ||| f)) + 2 * (e ^^^ (d ||| ~~~f)) - 6 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 1 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 1 * (f ^^^ (d &&& ( ~~~e ||| f))) + 2 * (d ||| (e &&& f)) - 11 * ((d &&& e) ||| ~~~(e ^^^ f)) - 1 * (f &&& (d ^^^ e)) + 1 * ((d &&& f) ||| (e &&& ~~~f)) - 6 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 2 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 7 * ((d ^^^ e) ||| (d ^^^ f)) - 5 * (e ||| (d &&& f)) + 11 * ~~~(d ||| (e &&& f)) + 5 * (e ^^^ (d ||| (e ^^^ f))) + 1 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 5 * ((d ||| ~~~e) &&& (e ^^^ f)) + 1 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 7 * (e ^^^ ~~~(d ||| (e &&& f))) + 2 * ~~~(d ||| ( ~~~e &&& f)) - 1 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 1 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 6 * (e ||| ~~~(d ^^^ f)) + 7 * ~~~(d &&& (e &&& f)) + 5 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 2 * ~~~(d ||| ~~~f) + 1 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 11 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 5 * ~~~(d ||| (e ^^^ f)) + 4 * ~~~(d &&& ( ~~~e &&& f)) - 7 * (f ^^^ (d ||| e)) - 11 * ~~~(d ^^^ f) - 11 * ~~~(d ^^^ (e ||| f)) + 1 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 1 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 23 * ~~~(d ||| (e ||| f)) - 5 * ~~~(d ||| ( ~~~e ||| f)) + 11 * ~~~( ~~~d ||| (e ||| f)) + 49 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 12 * ( ~~~d &&& ( ~~~e &&& f)) - 40 * ( ~~~d &&& (e &&& f)) - 1 * (d &&& ( ~~~e &&& f)) + 35 * (d &&& (e &&& f)) = 6 * ( ~~~(d &&& e) &&& (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2297 (x y : BitVec w) : +theorem e_2297 : - 3 * (f ||| ~~~(d ^^^ e)) + 3 * ~~~( ~~~d &&& (e ^^^ f)) + 1 * (e ^^^ ( ~~~d ||| (e ||| f))) - 3 * (f ||| (d &&& ~~~e)) - 5 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 7 * ~~~(e &&& f) + 2 * (e ^^^ ~~~(d ||| ~~~f)) - 6 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 5 * ~~~( ~~~d &&& (e &&& f)) - 3 * (e ^^^ (d ||| (e ^^^ f))) - 2 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 4 * (d ||| (e ^^^ f)) - 5 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 1 * ( ~~~f &&& ~~~(d ^^^ e)) + 5 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * ( ~~~d ||| ( ~~~e &&& f)) + 7 * ~~~(d ||| ~~~e) - 1 * (f ^^^ (d ||| (e ||| f))) + 2 * ( ~~~f &&& (d ^^^ e)) - 1 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 1 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 5 * (e ||| (d &&& ~~~f)) + 4 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 7 * (e ^^^ ~~~(d &&& f)) - 2 * (f ^^^ ( ~~~d ||| (e &&& f))) - 2 * ( ~~~d ||| (e &&& f)) - 11 * (e &&& (d ||| f)) + 1 * (e ^^^ ~~~(d ||| f)) - 5 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 2 * ~~~(d ^^^ (e ||| f)) + 7 * ~~~(d ||| e) + 11 * ~~~( ~~~d ||| (e &&& f)) + 1 * ((d ^^^ e) ||| (d ^^^ f)) + 7 * (f ||| ~~~(d ||| e)) + 4 * ~~~(e ^^^ f) + 1 * (d ||| (e ||| f)) + 2 * (f ^^^ (d ||| (e &&& f))) - 1 * (d ^^^ ( ~~~e ||| f)) - 1 * ( ~~~d ||| (e ||| f)) + 2 * ((d ||| e) &&& ~~~(e ^^^ f)) - 5 * (d ^^^ ( ~~~e &&& f)) - 11 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 2 * (e ^^^ f) - 3 * ((d &&& e) ^^^ (e ||| f)) - 3 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 1 * (d &&& f) + 1 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 11 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 6 * ~~~(d &&& ( ~~~e ||| f)) - 11 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 5 * ( ~~~e &&& (d ^^^ f)) - 11 * (e &&& (d ||| ~~~f)) - 1 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 6 * ~~~(d &&& ( ~~~e &&& f)) + 6 * ~~~(d ||| (e ||| f)) + 27 * ~~~(d ||| ( ~~~e ||| f)) + 2 * ~~~( ~~~d ||| (e ||| f)) + 46 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 20 * ( ~~~d &&& ( ~~~e &&& f)) + 6 * (d &&& ( ~~~e &&& f)) + 23 * (d &&& (e &&& f)) = - 25 * ( ~~~d &&& (e &&& f)) - 1 * (f ^^^ ~~~(d &&& (e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2298 (x y : BitVec w) : +theorem e_2298 : - 1 * ( ~~~d &&& ( ~~~e ||| f)) - 5 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 5 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 1 * ~~~(e ^^^ f) + 1 * (f &&& (d ^^^ e)) - 3 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 2 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 3 * ((d ^^^ e) &&& (d ^^^ f)) + 3 * ~~~(d ^^^ (e ||| f)) + 1 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 2 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 3 * ( ~~~d ||| ( ~~~e &&& f)) + 7 * (e ^^^ ~~~(d ||| ~~~f)) + 4 * (e ||| f) + 7 * (d ||| (e ^^^ f)) + 1 * ((d &&& e) ||| ~~~(e ||| f)) - 3 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 3 * e - 2 * ( ~~~f &&& ~~~(d ^^^ e)) + 1 * ~~~f + 1 * (f ^^^ (d &&& (e ||| f))) + 11 * (e ^^^ ( ~~~d ||| (e &&& f))) - 3 * (f ^^^ ( ~~~d &&& (e ||| f))) - 6 * (e ||| (d &&& ~~~f)) + 5 * (e ^^^ (d ||| ( ~~~e &&& f))) + 4 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 1 * (f &&& ~~~(d &&& ~~~e)) - 5 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 3 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 2 * (e ^^^ (d ||| (e &&& f))) - 6 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 7 * (f ||| (d &&& ~~~e)) - 6 * ~~~(d &&& ~~~d) - 7 * ~~~e - 1 * (f &&& (d ||| e)) + 5 * (f ^^^ (d ||| e)) - 1 * ((d ||| e) &&& ~~~(e ^^^ f)) - 11 * ( ~~~e ||| (d ^^^ f)) + 1 * (e &&& ~~~(d ^^^ f)) - 1 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 2 * ( ~~~d &&& (e ^^^ f)) - 5 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 3 * (e ^^^ (d &&& (e ^^^ f))) - 2 * (f ^^^ (d ||| (e &&& f))) + 7 * (f ^^^ (d ||| ~~~e)) - 6 * (d ||| ~~~f) - 1 * (e ||| (d ^^^ f)) + 1 * ~~~(d ||| (e &&& f)) + 1 * (e ||| ~~~f) - 1 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 1 * (e ^^^ f) - 11 * (f ^^^ ~~~(d &&& e)) + 2 * ( ~~~d ||| (e ^^^ f)) + 35 * ~~~(d ||| (e ||| f)) - 3 * ~~~(d ||| ( ~~~e ||| f)) + 53 * ~~~( ~~~d ||| (e ||| f)) - 12 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 2 * ( ~~~d &&& ( ~~~e &&& f)) + 24 * ( ~~~d &&& (e &&& f)) + 19 * (d &&& ( ~~~e &&& f)) + 21 * (d &&& (e &&& f)) = 1 * (f ^^^ (d ||| ( ~~~e &&& f))) - 1 * (f ^^^ (d ||| (e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2299 (x y : BitVec w) : +theorem e_2299 : 1 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 11 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 5 * (e ^^^ ( ~~~d ||| (e &&& f))) + 7 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * ( ~~~d ||| (e ||| f)) + 1 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 1 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 3 * ((d &&& e) ^^^ (e ||| f)) + 5 * ~~~(d ||| ~~~f) - 11 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 3 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 11 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * e + 7 * (e ^^^ (d ||| (e ^^^ f))) - 1 * ~~~(d &&& ~~~e) - 2 * (e &&& (d ||| ~~~f)) - 5 * ( ~~~d &&& (e ^^^ f)) + 4 * (e ^^^ (d ||| ( ~~~e &&& f))) - 11 * (e ^^^ (d ||| f)) - 7 * ~~~(d &&& ~~~f) - 1 * ~~~(e &&& ~~~f) - 1 * ~~~(d &&& ( ~~~e &&& f)) + 11 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 1 * d + 3 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * (d ||| ( ~~~e &&& f)) - 5 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 1 * (f ^^^ (d ||| (e ||| f))) + 3 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 2 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 7 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 7 * (e ^^^ (d &&& (e ||| f))) + 11 * ~~~(e &&& f) + 1 * (f ^^^ ~~~(d &&& ~~~e)) - 11 * (d &&& (e ^^^ f)) - 7 * ( ~~~e ||| ~~~(d ^^^ f)) + 4 * ~~~(d ||| f) + 1 * (d ||| f) + 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 5 * ~~~( ~~~d ||| (e ^^^ f)) + 5 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 1 * (f ^^^ ~~~(d ||| ~~~e)) + 4 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 1 * (d ^^^ (e ||| f)) + 1 * (e ^^^ ( ~~~d &&& (e ||| f))) + 2 * ((d &&& ~~~e) ||| (e ^^^ f)) + 2 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 5 * ( ~~~d ||| ( ~~~e &&& f)) - 3 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 3 * ((d &&& f) ||| ~~~(e ||| f)) + 1 * (f ^^^ (d &&& e)) - 2 * ~~~(d ^^^ f) - 6 * ~~~( ~~~d &&& (e ^^^ f)) - 2 * (e &&& ~~~(d &&& ~~~f)) - 4 * ~~~(d ||| (e ||| f)) + 22 * ~~~(d ||| ( ~~~e ||| f)) - 14 * ~~~( ~~~d ||| (e ||| f)) - 8 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 5 * ( ~~~d &&& ( ~~~e &&& f)) - 11 * ( ~~~d &&& (e &&& f)) + 6 * (d &&& ( ~~~e &&& f)) + 8 * (d &&& (e &&& f)) = 7 * ((d &&& f) ^^^ (e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2300 (x y : BitVec w) : +theorem e_2300 : - 11 * ( ~~~d &&& (e ||| f)) + 3 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 1 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 3 * (e &&& ~~~(d &&& f)) + 1 * ~~~(d ^^^ f) - 5 * (f ^^^ ~~~(d ||| ~~~e)) - 1 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 2 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 11 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 3 * ((d &&& f) ^^^ (e ||| f)) - 7 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 2 * ~~~( ~~~d ||| (e &&& f)) - 1 * (e &&& f) - 1 * ((d ||| ~~~e) &&& (e ^^^ f)) - 2 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 3 * ~~~(e &&& f) - 1 * (e ^^^ (d ||| ~~~f)) + 3 * ~~~(d &&& ~~~e) - 1 * ((d ^^^ e) ||| (d ^^^ f)) - 3 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 2 * ( ~~~d ||| ( ~~~e ||| f)) - 2 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 1 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 2 * ~~~(d ||| ~~~e) + 11 * ((d ^^^ e) &&& (d ^^^ f)) + 4 * (e ^^^ ~~~(d ||| (e &&& f))) - 2 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 11 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 1 * (e ^^^ ~~~(d &&& ~~~f)) + 7 * ~~~(d ||| ~~~f) - 1 * (e ^^^ (d &&& (e ^^^ f))) - 2 * ~~~(d &&& ~~~f) + 4 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 7 * (e ^^^ (d ||| f)) + 4 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 7 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 2 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 6 * ~~~(d ^^^ ( ~~~e &&& f)) + 7 * (e ||| (d ^^^ f)) - 2 * ~~~(e ||| f) - 11 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 1 * (d ||| ~~~e) + 2 * (d ||| ( ~~~e &&& f)) - 2 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 1 * (f ^^^ (d ||| (e ||| f))) + 5 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 1 * (d ^^^ f) - 1 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 1 * ~~~(d &&& (e &&& f)) - 5 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * (e &&& (d ||| ~~~f)) + 37 * ~~~(d ||| (e ||| f)) + 29 * ~~~(d ||| ( ~~~e ||| f)) + 12 * ~~~( ~~~d ||| (e ||| f)) + 9 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 20 * ( ~~~d &&& ( ~~~e &&& f)) + 36 * ( ~~~d &&& (e &&& f)) + 12 * (d &&& ( ~~~e &&& f)) + 25 * (d &&& (e &&& f)) = - 1 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 1 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2301 (x y : BitVec w) : +theorem e_2301 : - 1 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 1 * (f ^^^ (d ||| ~~~e)) + 11 * (e &&& (d ^^^ f)) - 6 * ((d ||| e) &&& ~~~(e ^^^ f)) - 6 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 6 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 3 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 7 * ~~~(e ||| ~~~f) + 2 * (d ^^^ ( ~~~e ||| f)) + 1 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 3 * (d ||| (e ^^^ f)) - 2 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 5 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 1 * (f ^^^ ~~~(d ||| (e &&& f))) - 11 * (f &&& (d ^^^ e)) + 4 * (f ^^^ ~~~(d &&& ~~~e)) - 2 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 11 * ( ~~~d &&& ( ~~~e ||| f)) - 2 * (f ^^^ ~~~(d ||| e)) + 7 * (f ^^^ (d ||| e)) - 1 * (f ^^^ (d ||| ( ~~~e &&& f))) + 2 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 4 * ~~~(e ||| f) - 2 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 1 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 3 * ~~~(d ^^^ f) - 7 * ((d &&& e) ||| (e ^^^ f)) - 7 * (e ^^^ ~~~(d ||| ~~~f)) + 3 * ~~~(d &&& ~~~f) + 5 * ( ~~~d ||| ( ~~~e ||| f)) - 1 * (f ^^^ ( ~~~d ||| (e &&& f))) - 2 * ((d &&& e) ^^^ (e ||| ~~~f)) + 11 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 2 * ((d &&& e) ^^^ (e ||| f)) + 2 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 3 * (e ^^^ ~~~(d ||| (e &&& f))) - 3 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 7 * (f ||| (d &&& ~~~e)) - 3 * (d ||| (e &&& f)) - 7 * (f ^^^ (d ||| ( ~~~e ||| f))) - 2 * (e ^^^ (d ||| f)) + 1 * (e ||| f) - 7 * ( ~~~d &&& (e ^^^ f)) + 3 * ( ~~~d ||| (e &&& f)) + 4 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 7 * (f &&& ~~~(d &&& ~~~e)) + 2 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 2 * ~~~(d ||| (e &&& f)) + 3 * ((d ^^^ e) ||| (d ^^^ f)) - 1 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 1 * (d ^^^ (e &&& f)) + 4 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 2 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 4 * (f ^^^ ~~~(d &&& e)) - 1 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 1 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 8 * ~~~(d ||| ( ~~~e ||| f)) - 9 * ~~~( ~~~d ||| (e ||| f)) - 20 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 23 * ( ~~~d &&& ( ~~~e &&& f)) + 8 * ( ~~~d &&& (e &&& f)) - 1 * (d &&& ( ~~~e &&& f)) = 8 * ~~~(d ||| (e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2302 (x y : BitVec w) : +theorem e_2302 : 2 * (e &&& (d ||| ~~~f)) + 4 * ~~~( ~~~d ||| (e &&& f)) + 1 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 1 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 3 * (d &&& ( ~~~e ||| f)) - 2 * (e &&& (d ^^^ f)) - 3 * (f ^^^ ~~~(d ||| ~~~e)) + 7 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 7 * ~~~( ~~~d &&& (e &&& f)) - 5 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 5 * ~~~(d ||| ~~~e) + 11 * ~~~(d ^^^ (e ^^^ f)) - 1 * ~~~( ~~~d &&& (e ||| f)) - 2 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 2 * (f ^^^ (d &&& ( ~~~e ||| f))) - 11 * (e ^^^ (d &&& ( ~~~e ||| f))) - 2 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 2 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 5 * (e ^^^ f) - 2 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * ~~~(d ||| (e &&& f)) + 1 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 7 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 1 * (f &&& ~~~(d &&& e)) - 11 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 2 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 1 * (e &&& ~~~(d &&& f)) - 6 * ~~~(d &&& ( ~~~e ||| f)) + 7 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 6 * (e &&& f) - 3 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 5 * (d ||| e) + 2 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 3 * (f &&& (d ^^^ e)) - 11 * ~~~(d ||| ( ~~~e &&& f)) - 1 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (d &&& (e ^^^ f)) - 6 * (d ^^^ (e ||| f)) + 1 * (d ||| ( ~~~e ||| f)) + 1 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 3 * (d ||| (e ^^^ f)) - 11 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 2 * (e &&& ~~~f) - 2 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 3 * (f ||| ~~~(d ^^^ e)) + 11 * (e ^^^ ~~~(d &&& (e &&& f))) - 1 * (d ^^^ e) - 5 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 7 * (f &&& (d ||| e)) + 1 * ~~~(d &&& (e ||| f)) - 1 * ~~~(d ||| f) + 2 * (f &&& ~~~(d ^^^ e)) + 2 * ~~~(d ||| ~~~f) + 2 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 17 * ~~~(d ||| (e ||| f)) + 46 * ~~~(d ||| ( ~~~e ||| f)) + 20 * ~~~( ~~~d ||| (e ||| f)) + 3 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 4 * ( ~~~d &&& ( ~~~e &&& f)) + 46 * ( ~~~d &&& (e &&& f)) + 16 * (d &&& ( ~~~e &&& f)) + 37 * (d &&& (e &&& f)) = - 5 * (e ||| (d ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2303 (x y : BitVec w) : +theorem e_2303 : 11 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 2 * ~~~(d ||| e) + 1 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 4 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 7 * ~~~( ~~~d &&& (e ||| f)) - 7 * ~~~e + 4 * ( ~~~d &&& (e ||| f)) + 11 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 2 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 6 * ~~~(d ||| ~~~f) - 5 * (e ^^^ (d &&& (e ||| f))) - 1 * ~~~(d &&& ~~~e) + 1 * ( ~~~e &&& (d ^^^ f)) - 3 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 3 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 2 * ~~~(d ||| ( ~~~e &&& f)) + 7 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 5 * ~~~(d ^^^ e) + 5 * (f ^^^ ~~~(d ||| (e &&& f))) - 7 * (f ^^^ ~~~(d &&& (e &&& f))) + 3 * (f ||| ~~~(d ||| ~~~e)) - 11 * (f ^^^ ( ~~~d ||| (e &&& f))) + 5 * ( ~~~f &&& ~~~(d ^^^ e)) + 3 * (f ||| ~~~(d ^^^ e)) + 2 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 7 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 1 * (d ^^^ ( ~~~e ||| f)) + 4 * ~~~(d ^^^ (e ||| f)) - 5 * (d &&& e) + 11 * (d ^^^ (e ^^^ f)) - 6 * (e ^^^ (d &&& ~~~f)) + 2 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 1 * ~~~(d &&& (e &&& f)) - 1 * (f ^^^ (d ||| ( ~~~e &&& f))) + 1 * (d ||| ( ~~~e &&& f)) - 3 * ~~~(d &&& (e ||| f)) + 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 5 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 1 * (d &&& (e ||| f)) + 2 * ((d &&& e) ||| ~~~(e ||| f)) + 5 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 3 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 5 * ( ~~~d ||| ( ~~~e &&& f)) - 2 * (f ^^^ ( ~~~d ||| (e ||| f))) + 3 * ( ~~~f ||| ~~~(d ^^^ e)) - 2 * ( ~~~d ||| (e ^^^ f)) + 7 * ((d ^^^ e) ||| ~~~(d ^^^ f)) + 1 * (f ^^^ ~~~(d &&& e)) - 2 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 1 * ~~~(d ||| (e ^^^ f)) - 7 * (e &&& ~~~(d &&& ~~~f)) + 4 * (d ||| f) + 2 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 25 * ~~~(d ||| (e ||| f)) - 12 * ~~~(d ||| ( ~~~e ||| f)) - 11 * ~~~( ~~~d ||| (e ||| f)) - 9 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 34 * ( ~~~d &&& ( ~~~e &&& f)) - 8 * ( ~~~d &&& (e &&& f)) - 20 * (d &&& ( ~~~e &&& f)) - 43 * (d &&& (e &&& f)) = 11 * (d ^^^ ( ~~~e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2304 (x y : BitVec w) : +theorem e_2304 : - 1 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 7 * (f ^^^ (d &&& (e ||| f))) + 1 * ((d &&& e) ^^^ (e ||| f)) - 2 * (f &&& (d ||| ~~~e)) + 2 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 2 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 5 * (d ||| (e ^^^ f)) - 1 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 7 * (e ^^^ ~~~(d ||| (e &&& f))) - 2 * (e ^^^ (d &&& ( ~~~e ||| f))) - 1 * (f ^^^ (d ||| ( ~~~e &&& f))) + 11 * (e &&& ~~~f) + 3 * (e &&& ~~~(d &&& f)) - 2 * (e ||| (d &&& ~~~f)) - 1 * ~~~(d &&& ~~~f) - 2 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 2 * ( ~~~d ||| (e ||| f)) - 11 * (f ^^^ (d &&& ~~~e)) - 1 * (e ||| ~~~(d ||| ~~~f)) + 4 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 2 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 3 * ~~~(d ||| (e ^^^ f)) + 11 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 11 * (f ^^^ ~~~(d &&& ~~~e)) + 5 * ((d ||| ~~~e) &&& (e ^^^ f)) - 6 * (f ^^^ ~~~(d ||| (e &&& f))) + 2 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 7 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 1 * (e ^^^ ( ~~~d ||| (e ||| f))) + 3 * ~~~( ~~~d ||| (e ^^^ f)) + 3 * ( ~~~d &&& (e ^^^ f)) - 5 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 2 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 3 * (f ^^^ ~~~(d &&& (e &&& f))) + 2 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 5 * (f ^^^ (d ||| (e ||| f))) + 11 * ~~~(d ||| ~~~e) - 5 * (d &&& e) - 3 * ~~~(d ||| (e &&& f)) - 3 * ((d &&& e) ||| ~~~(e ||| f)) + 7 * ( ~~~e ||| ~~~(d ^^^ f)) - 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 1 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 11 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 6 * (d ^^^ ( ~~~e ||| f)) + 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (e ^^^ ~~~(d &&& (e ||| f))) - 2 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 3 * ~~~(d ^^^ ( ~~~e ||| f)) - 1 * (e ^^^ f) - 1 * (d &&& ( ~~~e ||| f)) - 1 * (e ||| ~~~(d ||| f)) - 6 * (d &&& (e ||| f)) + 2 * (e ||| (d ^^^ f)) + 26 * ~~~(d ||| (e ||| f)) - 5 * ~~~(d ||| ( ~~~e ||| f)) + 20 * ~~~( ~~~d ||| (e ||| f)) + 15 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 2 * ( ~~~d &&& ( ~~~e &&& f)) + 41 * ( ~~~d &&& (e &&& f)) + 18 * (d &&& ( ~~~e &&& f)) + 35 * (d &&& (e &&& f)) = 2 * (e ^^^ ~~~(d &&& f)) - 11 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2305 (x y : BitVec w) : +theorem e_2305 : 4 * (e ^^^ (d ||| f)) - 6 * (d ||| (e ||| f)) - 11 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 11 * (d ||| ( ~~~e ||| f)) + 11 * (f ^^^ (d &&& e)) + 1 * ~~~(d ^^^ (e ^^^ f)) - 1 * (e ^^^ (d &&& ~~~f)) + 5 * ~~~(d &&& ~~~e) + 2 * (d &&& ~~~f) + 1 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 11 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 4 * (f ^^^ ~~~(d ||| ~~~e)) - 6 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 4 * ((d ||| e) &&& ~~~(e ^^^ f)) - 1 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 2 * (f ^^^ (d &&& ~~~e)) + 4 * ~~~(e ||| ~~~f) + 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 7 * (f &&& (d ||| e)) - 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 2 * ((d ||| ~~~e) &&& (e ^^^ f)) - 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * (d ^^^ ( ~~~e ||| f)) - 7 * ((d ^^^ e) &&& (d ^^^ f)) + 2 * ~~~(e &&& f) + 1 * ~~~e + 7 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 1 * ( ~~~f ||| (d ^^^ e)) - 6 * (f ^^^ ~~~(d &&& (e &&& f))) + 3 * (d ^^^ f) + 5 * (e ^^^ ~~~(d &&& f)) + 1 * (e ^^^ (d ||| ( ~~~e &&& f))) + 7 * ~~~(d &&& ~~~d) - 2 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 4 * e + 7 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * (e ^^^ (d ||| (e ^^^ f))) - 7 * ((d &&& e) ^^^ (e ||| f)) - 2 * (f ||| (d ^^^ e)) - 7 * (d ||| (e &&& f)) - 2 * (e &&& f) + 1 * (e ||| (d ^^^ f)) - 2 * (d &&& ~~~e) - 3 * (f &&& ~~~(d &&& ~~~e)) - 1 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 2 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 7 * (f ||| (d &&& ~~~e)) - 2 * f + 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 2 * (f ^^^ ( ~~~d &&& (e ||| f))) - 11 * ( ~~~f &&& ~~~(d ^^^ e)) - 11 * (f ^^^ (d &&& (e ||| f))) + 3 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 1 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 3 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 1 * ( ~~~d ||| (e &&& f)) - 4 * ~~~(d ||| (e ||| f)) + 3 * ~~~(d ||| ( ~~~e ||| f)) + 11 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 22 * ( ~~~d &&& ( ~~~e &&& f)) + 12 * ( ~~~d &&& (e &&& f)) - 6 * (d &&& ( ~~~e &&& f)) = - 15 * (d &&& (e &&& f)) + 3 * ~~~( ~~~d ||| (e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2306 (x y : BitVec w) : +theorem e_2306 : 5 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 6 * (e &&& ~~~(d ^^^ f)) - 11 * ((d &&& e) ||| ~~~(e ||| f)) - 2 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 1 * ((d ^^^ e) &&& (d ^^^ f)) + 1 * (e ^^^ (d ||| (e ||| f))) - 5 * ~~~(d &&& ~~~f) + 2 * (e ^^^ ( ~~~d &&& (e ||| f))) - 11 * ~~~e + 11 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 7 * (d ||| (e &&& f)) - 11 * (d ||| f) + 4 * (e ||| (d &&& f)) + 5 * ~~~f + 1 * (e ||| (d &&& ~~~f)) - 2 * ~~~(d &&& f) - 2 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 7 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 7 * ((d ^^^ e) ||| (d ^^^ f)) - 1 * ~~~(d ^^^ (e ^^^ f)) + 1 * (d ^^^ (e ||| f)) - 7 * (d ||| ( ~~~e ||| f)) - 5 * (e ^^^ ~~~(d &&& (e &&& f))) - 3 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 2 * (e ||| ~~~(d ||| f)) + 5 * ~~~(d &&& (e ||| f)) - 11 * (e ||| (d ^^^ f)) + 4 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 5 * ~~~(d &&& ~~~e) - 1 * (e ^^^ ( ~~~d ||| (e ||| f))) + 3 * e + 11 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 5 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 1 * (e ^^^ (d &&& ~~~f)) - 2 * ((d &&& f) ||| (e &&& ~~~f)) - 2 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 2 * (f ^^^ (d &&& ~~~e)) + 11 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 11 * ( ~~~f &&& ~~~(d ^^^ e)) - 5 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 3 * (f ^^^ (d ||| ( ~~~e ||| f))) - 1 * (e ^^^ ~~~(d &&& f)) + 4 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 2 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 4 * (d &&& ( ~~~e ||| f)) - 3 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 2 * (d &&& (e ||| f)) - 1 * (e &&& f) + 3 * ~~~(d &&& ( ~~~e ||| f)) - 7 * (e &&& ~~~(d &&& f)) - 3 * (f ||| ~~~(d ||| ~~~e)) - 5 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 1 * ~~~(e ||| ~~~f) + 1 * (e ^^^ f) - 6 * ~~~(d ^^^ f) + 6 * ~~~(d ||| (e ||| f)) + 11 * ~~~(d ||| ( ~~~e ||| f)) + 30 * ~~~( ~~~d ||| (e ||| f)) - 11 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 40 * ( ~~~d &&& ( ~~~e &&& f)) - 12 * ( ~~~d &&& (e &&& f)) + 35 * (d &&& ( ~~~e &&& f)) + 19 * (d &&& (e &&& f)) = - 11 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 1 * (d ||| ~~~e) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2307 (x y : BitVec w) : +theorem e_2307 : 1 * (e &&& ~~~f) - 2 * ~~~(d &&& ~~~e) + 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * (e ^^^ (d &&& ~~~f)) + 2 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 5 * (f ^^^ (d &&& (e ||| f))) + 3 * (d ||| (e &&& f)) + 7 * ~~~(d &&& ~~~f) + 11 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 2 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 7 * (d ||| ~~~f) - 1 * ~~~(e ^^^ f) - 2 * ~~~(d ^^^ (e ^^^ f)) + 1 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 6 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 1 * (f &&& (d ||| ~~~e)) - 6 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 2 * (d ^^^ f) - 3 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 1 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 3 * ( ~~~f ||| ~~~(d ^^^ e)) + 1 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 4 * ~~~(d &&& (e &&& f)) + 11 * ~~~e + 1 * (f ||| (d &&& ~~~e)) - 11 * ( ~~~e &&& (d ^^^ f)) - 11 * ~~~(d ||| ~~~f) - 6 * ~~~(d &&& (e ^^^ f)) - 3 * ~~~(d &&& ~~~d) + 2 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 11 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 2 * ~~~(e ||| f) - 6 * (d &&& ~~~f) - 1 * (f &&& (d ^^^ e)) - 6 * ((d &&& e) ^^^ (e ||| ~~~f)) + 11 * (f ^^^ ~~~(d &&& (e ||| f))) - 2 * ~~~(d &&& (e ||| f)) + 2 * (f ^^^ (d &&& e)) + 5 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 11 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 11 * (f &&& (d ||| e)) - 1 * ~~~(d ^^^ f) + 1 * ( ~~~f &&& ~~~(d ^^^ e)) - 3 * (e ^^^ (d ||| f)) - 5 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 4 * ~~~d + 3 * (f ^^^ ~~~(d ||| ~~~e)) - 5 * ( ~~~d ||| ( ~~~e ||| f)) + 4 * ~~~(d ||| f) + 3 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 2 * (f ^^^ ~~~(d &&& e)) + 1 * ( ~~~e ||| (d ^^^ f)) - 1 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 5 * (f ^^^ (d &&& ~~~e)) + 4 * (d ^^^ e) - 12 * ~~~(d ||| (e ||| f)) + 12 * ~~~(d ||| ( ~~~e ||| f)) + 20 * ~~~( ~~~d ||| (e ||| f)) - 29 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 17 * ( ~~~d &&& ( ~~~e &&& f)) - 14 * ( ~~~d &&& (e &&& f)) - 24 * (d &&& ( ~~~e &&& f)) - 26 * (d &&& (e &&& f)) = 7 * (d &&& ( ~~~e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2308 (x y : BitVec w) : +theorem e_2308 : - 1 * (e ^^^ f) - 2 * (d ||| ( ~~~e ||| f)) + 3 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * ~~~(d &&& ~~~d) + 7 * (e ^^^ ( ~~~d &&& (e ||| f))) - 1 * ~~~(d ^^^ ( ~~~e ||| f)) - 3 * ((d &&& f) ^^^ (e ||| f)) + 5 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 4 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 5 * ( ~~~d ||| (e ^^^ f)) + 4 * (f ^^^ (d &&& ~~~e)) - 1 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 5 * (d ||| (e ||| f)) - 6 * (d ^^^ (e ||| f)) + 7 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 3 * (f ^^^ (d &&& ( ~~~e ||| f))) + 7 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 7 * (f ||| (d &&& e)) + 1 * (f ^^^ ~~~(d ||| (e &&& f))) - 7 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 3 * ((d ||| ~~~e) &&& (e ^^^ f)) + 2 * (f &&& (d ^^^ e)) - 1 * ((d &&& ~~~e) ||| (e ^^^ f)) + 4 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 1 * (e ^^^ (d &&& f)) + 3 * ((d &&& e) ^^^ (e ||| f)) - 2 * (f ||| (d &&& ~~~e)) - 6 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 1 * ~~~(d ||| ( ~~~e &&& f)) - 1 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 2 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 2 * (e ^^^ (d ||| (e ||| f))) - 11 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 7 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 4 * (e ^^^ (d ||| (e ^^^ f))) - 1 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 1 * (f ^^^ ~~~(d &&& (e &&& f))) - 3 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 4 * (f ^^^ ~~~(d ||| e)) + 2 * (d ||| ~~~f) - 1 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 3 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 11 * (e ^^^ ~~~(d &&& f)) + 5 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 11 * ~~~e + 2 * (e ||| f) - 6 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 1 * (e &&& (d ^^^ f)) - 7 * ~~~( ~~~d &&& (e &&& f)) - 5 * ~~~(d ^^^ (e ||| f)) + 1 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 2 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 5 * (e &&& (d ||| ~~~f)) - 1 * ~~~(d ^^^ f) - 27 * ~~~(d ||| (e ||| f)) + 4 * ~~~(d ||| ( ~~~e ||| f)) - 1 * ~~~( ~~~d ||| (e ||| f)) + 3 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 30 * ( ~~~d &&& ( ~~~e &&& f)) + 3 * ( ~~~d &&& (e &&& f)) + 11 * (d &&& (e &&& f)) = - 4 * ( ~~~e ||| (d ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2309 (x y : BitVec w) : +theorem e_2309 : - 5 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 3 * (f ^^^ ~~~(d &&& (e &&& f))) - 2 * ( ~~~e ||| ~~~(d ^^^ f)) + 5 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 5 * (e ^^^ ~~~(d &&& f)) - 6 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 3 * ~~~(d ||| (e ^^^ f)) - 1 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 3 * (e ^^^ (d ||| (e ||| f))) - 3 * ((d &&& e) ||| ~~~(e ^^^ f)) - 7 * (f ^^^ (d ||| (e ||| f))) - 7 * ( ~~~f ||| ~~~(d ^^^ e)) - 5 * (e ||| (d &&& ~~~f)) + 3 * (e &&& (d ||| ~~~f)) - 2 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 1 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 3 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * ((d ^^^ e) ||| (d ^^^ f)) + 7 * ~~~(d ^^^ (e ||| f)) - 2 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 3 * (e ^^^ ( ~~~d &&& (e ||| f))) + 11 * (f ^^^ ~~~(d &&& e)) - 1 * ( ~~~d &&& (e ^^^ f)) + 2 * (f ^^^ (d ||| ~~~e)) + 3 * d - 1 * ~~~(d &&& f) + 4 * ~~~(e &&& ~~~f) + 3 * (d ^^^ e) + 7 * ~~~( ~~~d ||| (e &&& f)) + 2 * (e ^^^ (d &&& (e ^^^ f))) - 6 * (d &&& ~~~e) - 1 * ~~~d + 1 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (f ^^^ (d &&& ~~~e)) + 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 5 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 7 * (d ||| f) + 2 * ~~~(d ||| ~~~e) + 3 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 1 * ~~~(e ^^^ f) + 1 * (e ^^^ ~~~(d &&& (e ||| f))) - 2 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 11 * (f ^^^ ( ~~~d &&& (e ||| f))) - 6 * (e &&& ~~~f) + 1 * (d ^^^ ( ~~~e &&& f)) + 4 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 11 * (e ||| ~~~(d ^^^ f)) - 5 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 1 * (f ^^^ ~~~(d ||| (e &&& f))) - 7 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 2 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 1 * (d ^^^ ( ~~~e ||| f)) + 11 * (e ^^^ ( ~~~d ||| (e &&& f))) + 1 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 51 * ~~~(d ||| (e ||| f)) + 26 * ~~~(d ||| ( ~~~e ||| f)) - 9 * ~~~( ~~~d ||| (e ||| f)) - 12 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 7 * ( ~~~d &&& ( ~~~e &&& f)) - 1 * ( ~~~d &&& (e &&& f)) - 2 * (d &&& ( ~~~e &&& f)) + 17 * (d &&& (e &&& f)) = 1 * (e ^^^ (d &&& ~~~f)) + 6 * (f ^^^ ~~~(d ||| ~~~e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2310 (x y : BitVec w) : +theorem e_2310 : - 1 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 5 * ( ~~~d &&& ( ~~~e ||| f)) + 5 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 1 * ~~~(d &&& f) + 1 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 2 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 3 * (e ^^^ (d &&& (e ||| f))) + 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 7 * ( ~~~e ||| (d ^^^ f)) - 11 * ~~~(e ||| ~~~f) + 4 * (f ||| ~~~(d ^^^ e)) + 4 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * (d ^^^ ( ~~~e ||| f)) + 1 * ~~~(d &&& (e &&& f)) + 2 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 7 * (e ^^^ ~~~(d &&& (e &&& f))) - 5 * ((d &&& e) ^^^ (e ||| ~~~f)) + 2 * (d ^^^ (e ^^^ f)) + 5 * (d ||| ~~~f) - 7 * (d &&& (e ^^^ f)) + 2 * ( ~~~f &&& ~~~(d ^^^ e)) - 3 * ~~~(d &&& ~~~e) - 6 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 11 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 1 * (f ^^^ (d &&& ( ~~~e ||| f))) - 3 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 11 * ~~~(e &&& f) - 2 * (d &&& ( ~~~e ||| f)) + 11 * (e ^^^ (d ||| (e ^^^ f))) + 4 * ~~~(d ^^^ f) - 3 * (e &&& (d ||| ~~~f)) + 1 * (e ||| ~~~(d ||| ~~~f)) - 3 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 2 * ( ~~~f ||| (d ^^^ e)) + 2 * ~~~(d ^^^ ( ~~~e ||| f)) + 5 * ~~~(d ||| e) - 2 * (d ^^^ (e &&& f)) - 1 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 1 * (e ^^^ (d ||| f)) - 11 * (f ^^^ ~~~(d &&& ~~~e)) - 2 * (f ||| (d &&& ~~~e)) + 2 * ~~~( ~~~d &&& (e ||| f)) + 7 * (e ^^^ (d &&& ( ~~~e ||| f))) + 4 * ~~~(d ^^^ ( ~~~e &&& f)) - 5 * ~~~(e ^^^ f) + 7 * (d &&& ~~~e) + 11 * ~~~(d &&& ( ~~~e &&& f)) - 5 * ~~~e + 5 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 1 * (e ^^^ (d ||| (e ||| f))) + 1 * ((d &&& e) ||| ~~~(e ||| f)) + 7 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 2 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 6 * ~~~(d ||| f) + 2 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 6 * ~~~(d ||| (e ||| f)) + 14 * ~~~(d ||| ( ~~~e ||| f)) - 18 * ~~~( ~~~d ||| (e ||| f)) + 5 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 22 * ( ~~~d &&& ( ~~~e &&& f)) - 13 * ( ~~~d &&& (e &&& f)) + 6 * (d &&& ( ~~~e &&& f)) - 21 * (d &&& (e &&& f)) = 3 * (e &&& (d ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2311 (x y : BitVec w) : +theorem e_2311 : 1 * ~~~(d &&& e) - 2 * (f ^^^ ~~~(d &&& (e &&& f))) + 1 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * ( ~~~d ||| (e ||| f)) + 1 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 1 * (f &&& (d ||| e)) - 6 * (d ^^^ e) + 4 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 2 * ( ~~~e &&& (d ^^^ f)) + 4 * ((d ^^^ e) &&& (d ^^^ f)) + 2 * (e &&& ~~~(d &&& f)) - 1 * ~~~(d ^^^ (e ||| f)) - 1 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 2 * (e ^^^ (d ||| ( ~~~e &&& f))) + 11 * (d &&& (e ||| f)) - 1 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 4 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 3 * ( ~~~e ||| (d ^^^ f)) - 7 * ( ~~~f ||| ~~~(d ^^^ e)) + 2 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 5 * ~~~(e &&& ~~~f) + 1 * (e &&& f) + 7 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 1 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 7 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 1 * d - 2 * ~~~( ~~~d &&& (e &&& f)) - 1 * (d ^^^ (e ||| f)) + 4 * (d ^^^ f) - 2 * (f ^^^ (d ||| (e &&& f))) + 5 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 1 * (e ||| (d &&& f)) - 6 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 1 * (f ^^^ (d &&& ~~~e)) - 11 * (e &&& (d ^^^ f)) - 1 * e - 2 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 2 * (f ^^^ (d ||| ~~~e)) - 2 * ( ~~~d ||| ( ~~~e ||| f)) + 5 * (e ^^^ (d ||| ( ~~~e ||| f))) - 1 * ( ~~~d &&& ( ~~~e ||| f)) - 2 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 3 * (f ||| ~~~(d ^^^ e)) - 1 * (d ||| ( ~~~e ||| f)) + 3 * ((d &&& f) ||| (e &&& ~~~f)) + 11 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 3 * ~~~(d &&& f) - 11 * (e ^^^ ( ~~~d ||| (e ||| f))) - 2 * ~~~(d ||| ~~~f) + 1 * ~~~(d &&& (e ^^^ f)) + 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 4 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 6 * ~~~( ~~~d &&& (e ^^^ f)) - 1 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 11 * (e ^^^ (d &&& f)) + 23 * ~~~(d ||| (e ||| f)) + 7 * ~~~(d ||| ( ~~~e ||| f)) + 34 * ~~~( ~~~d ||| (e ||| f)) + 3 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 4 * ( ~~~d &&& ( ~~~e &&& f)) + 11 * ( ~~~d &&& (e &&& f)) + 3 * (d &&& ( ~~~e &&& f)) + 1 * (d &&& (e &&& f)) = 6 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 11 * ((d &&& e) ^^^ (e ||| ~~~f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2312 (x y : BitVec w) : +theorem e_2312 : 5 * (d &&& ~~~e) + 1 * (d &&& e) + 1 * ~~~(d &&& f) - 2 * (e &&& ~~~(d ^^^ f)) + 3 * (d ||| ( ~~~e &&& f)) - 2 * (d ^^^ (e &&& f)) + 11 * ( ~~~d ||| (e ||| f)) + 3 * (d &&& ~~~f) - 5 * ~~~(d ||| ( ~~~e &&& f)) - 3 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 1 * (f ^^^ ~~~(d &&& (e &&& f))) - 1 * (d ^^^ f) + 7 * (f ^^^ (d ||| ~~~e)) + 3 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 1 * (e ^^^ f) - 11 * ~~~(d &&& (e &&& f)) - 1 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 11 * (e ^^^ ~~~(d ||| ~~~f)) - 7 * e - 3 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 11 * f + 1 * (d ^^^ (e ^^^ f)) - 5 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 2 * ( ~~~d ||| (e ^^^ f)) - 2 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 7 * ( ~~~f ||| ~~~(d ^^^ e)) - 1 * ~~~(d ||| ~~~f) - 2 * (e &&& ~~~(d &&& ~~~f)) + 1 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 7 * (f ^^^ (d ||| (e ||| f))) + 1 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 11 * (d &&& ( ~~~e ||| f)) + 2 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 5 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * ( ~~~e ||| ~~~(d ^^^ f)) + 11 * (d ||| ( ~~~e ||| f)) - 5 * (f ^^^ (d &&& ( ~~~e ||| f))) - 11 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * (e &&& ~~~f) + 2 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 7 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 6 * ~~~( ~~~d ||| (e &&& f)) - 11 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * ( ~~~d &&& (e ^^^ f)) + 5 * ~~~d - 3 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 11 * (f ^^^ ( ~~~d &&& (e ||| f))) - 1 * (d ||| f) - 1 * ~~~f + 4 * (e ||| (d &&& f)) - 1 * (f ^^^ (d &&& (e ||| f))) - 3 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 2 * (e ^^^ ~~~(d ||| (e &&& f))) + 13 * ~~~(d ||| (e ||| f)) + 27 * ~~~(d ||| ( ~~~e ||| f)) + 14 * ~~~( ~~~d ||| (e ||| f)) + 10 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 20 * ( ~~~d &&& ( ~~~e &&& f)) + 33 * ( ~~~d &&& (e &&& f)) - 7 * (d &&& ( ~~~e &&& f)) - 20 * (d &&& (e &&& f)) = 1 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 11 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2313 (x y : BitVec w) : +theorem e_2313 : - 1 * (f ^^^ ~~~(d &&& e)) + 2 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 2 * (e &&& ~~~(d &&& ~~~f)) + 1 * (e &&& (d ||| ~~~f)) + 3 * (e ^^^ ~~~(d ||| ~~~f)) - 3 * ~~~(d &&& ( ~~~e ||| f)) + 5 * (e ^^^ ( ~~~d &&& (e ||| f))) + 4 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 7 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 4 * ~~~(d &&& (e ^^^ f)) - 2 * (f ^^^ ~~~(d &&& (e ||| f))) + 11 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 11 * ~~~(d ||| ~~~e) + 2 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 3 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 3 * (e ||| (d &&& f)) + 1 * ((d &&& e) ||| ~~~(e ^^^ f)) - 5 * (f ^^^ ~~~(d ||| e)) - 7 * ( ~~~d &&& (e ||| f)) - 5 * (f ^^^ (d ||| (e ||| f))) - 3 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 1 * (e ^^^ (d ||| (e ||| f))) + 4 * ((d &&& e) ^^^ (e ||| ~~~f)) + 5 * (f ^^^ (d &&& ~~~e)) + 1 * (d ^^^ e) - 11 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 2 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 11 * ((d &&& e) ||| ~~~(e ||| f)) + 1 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 1 * (f ^^^ (d &&& e)) - 1 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 6 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 7 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 11 * ( ~~~e ||| ~~~(d ^^^ f)) - 2 * (d ||| (e ^^^ f)) + 11 * ~~~(d ^^^ ( ~~~e ||| f)) - 1 * ~~~(d &&& (e ||| f)) - 2 * (e ^^^ ~~~(d &&& (e &&& f))) + 2 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 5 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 1 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 5 * (d ||| (e &&& f)) + 7 * ~~~( ~~~d &&& (e ||| f)) + 3 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * (e &&& f) - 5 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 2 * (d ^^^ f) - 1 * (e &&& ~~~(d &&& f)) - 5 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 5 * (e ^^^ (d &&& ~~~f)) - 7 * ~~~(d ^^^ e) - 2 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 7 * ((d ||| ~~~e) &&& (e ^^^ f)) - 5 * ((d ||| e) &&& (e ^^^ f)) + 1 * ((d &&& e) ^^^ (e ||| f)) + 11 * ~~~(d ||| (e ||| f)) + 20 * ~~~(d ||| ( ~~~e ||| f)) - 5 * ~~~( ~~~d ||| (e ||| f)) + 11 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 20 * ( ~~~d &&& ( ~~~e &&& f)) - 12 * ( ~~~d &&& (e &&& f)) - 8 * (d &&& ( ~~~e &&& f)) - 10 * (d &&& (e &&& f)) = - 7 * ((e &&& f) ||| (d &&& (e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2314 (x y : BitVec w) : +theorem e_2314 : - 2 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 7 * (f &&& (d ||| e)) + 1 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 7 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 7 * ~~~(d &&& ~~~f) + 2 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 1 * ((d ^^^ e) ||| (d ^^^ f)) - 6 * (f ^^^ (d ||| ( ~~~e ||| f))) + 11 * ~~~(d &&& ( ~~~e &&& f)) - 2 * (e ^^^ (d &&& ( ~~~e ||| f))) - 2 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 5 * (e ||| ~~~f) - 6 * (e ^^^ (d ||| ~~~f)) - 5 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 5 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 1 * (f &&& ~~~(d &&& ~~~e)) - 6 * (d ^^^ (e ^^^ f)) - 1 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 1 * ( ~~~d &&& ( ~~~e ||| f)) + 1 * (d ||| (e &&& f)) - 11 * (d &&& e) - 3 * (e &&& ~~~(d &&& ~~~f)) + 2 * (f ^^^ (d &&& e)) + 11 * (d ||| f) - 1 * (f ^^^ (d ||| ~~~e)) - 3 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 3 * ((e &&& f) ||| (d &&& (e ||| f))) + 11 * (e ^^^ (d &&& ~~~f)) - 2 * ((d &&& e) ||| (e ^^^ f)) + 1 * (e ^^^ (d ||| f)) + 5 * ((d &&& e) ^^^ (e ||| f)) - 2 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 6 * (d &&& (e ||| f)) + 11 * ((d &&& f) ^^^ (e ||| f)) + 7 * (d ||| (e ||| f)) + 4 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 1 * ( ~~~d &&& (e ||| f)) + 3 * (e &&& ~~~(d ^^^ f)) - 11 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 5 * (e ||| (d &&& f)) + 1 * ~~~(e &&& f) + 1 * ~~~f - 1 * (f ^^^ ~~~(d &&& ~~~e)) - 11 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 2 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 7 * ((d &&& e) ^^^ (e ||| ~~~f)) + 2 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 1 * ~~~(d ||| (e ^^^ f)) + 1 * ~~~(d ^^^ (e ^^^ f)) - 1 * (e ^^^ (d ||| (e ^^^ f))) + 4 * ~~~(e ||| f) + 3 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 4 * (d ^^^ (e &&& f)) + 5 * (f ^^^ ~~~(d ||| e)) + 15 * ~~~(d ||| (e ||| f)) - 24 * ~~~(d ||| ( ~~~e ||| f)) - 12 * ~~~( ~~~d ||| (e ||| f)) - 25 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 52 * ( ~~~d &&& ( ~~~e &&& f)) + 11 * (d &&& ( ~~~e &&& f)) + 5 * (d &&& (e &&& f)) = 30 * ( ~~~d &&& (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2315 (x y : BitVec w) : +theorem e_2315 : 1 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 2 * ~~~f - 6 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 4 * ( ~~~d ||| ( ~~~e &&& f)) + 11 * (e ^^^ ~~~(d ||| ~~~f)) + 7 * (e ^^^ ~~~(d &&& ~~~f)) + 3 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 11 * (e &&& ~~~f) + 5 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 2 * ~~~(e ^^^ f) - 1 * (f ^^^ (d ||| e)) - 5 * ~~~( ~~~d &&& (e &&& f)) - 1 * ((d &&& e) ||| ~~~(e ||| f)) + 1 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 11 * ~~~(d &&& ~~~d) - 3 * (d ||| f) + 4 * (f ||| ~~~(d ^^^ e)) + 5 * ~~~(d ||| (e &&& f)) - 7 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 5 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 11 * ~~~(d &&& ( ~~~e &&& f)) + 3 * d + 2 * ~~~(d ^^^ (e ^^^ f)) - 1 * (d ^^^ ( ~~~e &&& f)) + 1 * (e ^^^ ( ~~~d ||| (e &&& f))) + 2 * (f ^^^ (d ||| (e &&& f))) + 2 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 6 * (e &&& (d ||| f)) - 2 * (e ||| ~~~(d ^^^ f)) - 2 * (e ||| (d &&& ~~~f)) + 11 * (e ^^^ ~~~(d ||| f)) - 2 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 2 * ((d &&& ~~~e) ||| (e ^^^ f)) + 1 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 2 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (f ^^^ (d ||| ~~~e)) - 2 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 1 * ( ~~~d ||| (e ||| f)) + 7 * ~~~(d &&& (e &&& f)) + 1 * (f &&& (d ||| e)) - 1 * (f ^^^ ~~~(d ||| e)) - 2 * (f ^^^ (d ||| ( ~~~e &&& f))) - 2 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 11 * (f ||| (d ^^^ e)) - 6 * ( ~~~f &&& (d ^^^ e)) + 1 * ~~~(e &&& ~~~f) + 11 * (f ^^^ ( ~~~d ||| (e ||| f))) - 3 * (d ^^^ (e ||| f)) + 3 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 2 * (f ^^^ ~~~(d ||| (e &&& f))) - 2 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 7 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 1 * (f &&& ~~~(d ^^^ e)) - 5 * e - 7 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 6 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 55 * ~~~(d ||| (e ||| f)) - 8 * ~~~(d ||| ( ~~~e ||| f)) + 6 * ~~~( ~~~d ||| (e ||| f)) - 15 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 30 * ( ~~~d &&& ( ~~~e &&& f)) - 25 * ( ~~~d &&& (e &&& f)) - 12 * (d &&& ( ~~~e &&& f)) - 20 * (d &&& (e &&& f)) = - 2 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2316 (x y : BitVec w) : +theorem e_2316 : 3 * ~~~(d &&& ( ~~~e ||| f)) + 1 * (f &&& ~~~(d &&& e)) + 7 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * ~~~( ~~~d &&& (e &&& f)) - 1 * (e ^^^ ~~~(d ||| ~~~f)) - 1 * (f ^^^ (d &&& ( ~~~e ||| f))) - 1 * (e ||| ~~~(d ||| f)) - 7 * (e ^^^ ( ~~~d ||| (e ||| f))) - 7 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 1 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 11 * (d ^^^ (e ||| f)) + 5 * ~~~(e &&& ~~~f) + 7 * (e ^^^ (d ||| (e &&& f))) - 6 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 5 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 5 * ~~~(d ||| ~~~f) - 1 * ~~~(d ^^^ e) + 1 * ~~~d - 2 * ( ~~~d ||| (e &&& f)) + 2 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 1 * (e &&& ~~~f) - 11 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 3 * (e ^^^ (d &&& ( ~~~e ||| f))) - 2 * (f &&& ~~~(d &&& ~~~e)) - 2 * ~~~(e ||| f) + 11 * ~~~(d &&& ~~~f) - 11 * ((d &&& e) ^^^ (e ||| ~~~f)) + 3 * (d ||| ( ~~~e &&& f)) + 1 * (f ^^^ (d &&& e)) + 2 * (d ||| ~~~e) + 2 * (e ^^^ (d &&& (e ||| f))) - 11 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 7 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 1 * (d &&& ~~~f) - 1 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 1 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 7 * (f ||| ~~~(d ||| ~~~e)) + 2 * ((d ||| e) &&& (e ^^^ f)) + 1 * (e ||| (d &&& f)) + 5 * (e ^^^ ~~~(d &&& (e ||| f))) - 5 * ~~~( ~~~d ||| (e ^^^ f)) - 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 2 * ( ~~~d ||| (e ||| f)) - 3 * ~~~(d ^^^ (e ||| f)) - 6 * (e ^^^ (d &&& f)) + 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 2 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 11 * ((d &&& e) ||| ~~~(e ^^^ f)) - 3 * ( ~~~e &&& ~~~(d ^^^ f)) - 2 * (d ||| (e ^^^ f)) + 3 * (e ^^^ (d ||| (e ||| f))) - 3 * ((d &&& e) ||| ~~~(e ||| f)) + 3 * ((d ^^^ e) &&& (d ^^^ f)) + 5 * (f ^^^ ( ~~~d ||| (e ||| f))) - 1 * (e ^^^ ~~~(d &&& ~~~f)) + 24 * ~~~(d ||| (e ||| f)) + 28 * ~~~(d ||| ( ~~~e ||| f)) + 1 * ~~~( ~~~d ||| (e ||| f)) - 6 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 26 * ( ~~~d &&& ( ~~~e &&& f)) - 3 * ( ~~~d &&& (e &&& f)) - 11 * (d &&& ( ~~~e &&& f)) - 16 * (d &&& (e &&& f)) = - 11 * (e &&& f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2317 (x y : BitVec w) : +theorem e_2317 : 3 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 1 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 1 * ( ~~~d &&& (e ^^^ f)) + 11 * (f ^^^ (d &&& e)) - 11 * ~~~(d &&& (e ||| f)) + 11 * (e ^^^ (d &&& ( ~~~e ||| f))) - 7 * (e &&& (d ||| f)) - 7 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 6 * ~~~(d &&& f) - 1 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 6 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 11 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 1 * ( ~~~f ||| ~~~(d ^^^ e)) + 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 4 * (f ^^^ ~~~(d &&& ~~~e)) - 7 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 4 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 11 * (d &&& f) + 4 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 1 * ~~~(d ||| e) - 2 * (f ^^^ (d &&& ~~~e)) - 7 * (f ^^^ ~~~(d &&& (e ||| f))) + 5 * (e &&& ~~~(d &&& f)) + 7 * (f ^^^ ~~~(d ||| (e &&& f))) - 5 * ~~~(d ||| ~~~e) + 2 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 2 * ((d &&& f) ^^^ (e ||| f)) - 3 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 6 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 1 * ~~~(d ^^^ f) + 1 * ~~~(d &&& ~~~e) - 1 * (d ||| (e &&& f)) - 7 * (d ||| (e ||| f)) + 7 * ~~~(e ||| f) - 3 * (e ^^^ (d ||| f)) - 6 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 2 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 11 * ~~~(d ||| ~~~f) - 7 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 3 * (e ^^^ (d &&& (e ^^^ f))) - 6 * (f &&& ~~~(d &&& e)) + 5 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 2 * (e &&& ~~~(d ^^^ f)) + 1 * (f ^^^ (d &&& ( ~~~e ||| f))) + 3 * (d ||| ( ~~~e &&& f)) + 4 * ~~~(d ^^^ (e ^^^ f)) - 5 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 7 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 5 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 5 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 11 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 3 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 1 * (e &&& (d ||| ~~~f)) - 3 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 2 * (f ^^^ (d ||| ~~~e)) + 3 * ~~~(d ||| (e ||| f)) + 19 * ~~~(d ||| ( ~~~e ||| f)) + 57 * ~~~( ~~~d ||| (e ||| f)) - 7 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 72 * ( ~~~d &&& ( ~~~e &&& f)) + 45 * ( ~~~d &&& (e &&& f)) + 30 * (d &&& ( ~~~e &&& f)) + 75 * (d &&& (e &&& f)) = - 2 * (f ^^^ (d ||| (e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2318 (x y : BitVec w) : +theorem e_2318 : 7 * (e &&& ~~~(d &&& ~~~f)) - 2 * ((d &&& f) ||| ~~~(e ||| f)) + 2 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 5 * (d &&& ~~~e) + 2 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 2 * (d ^^^ e) - 11 * ~~~(d ^^^ ( ~~~e ||| f)) - 6 * (f ^^^ ~~~(d ||| (e &&& f))) - 2 * ~~~(d &&& f) - 11 * ((d ||| ~~~e) &&& (e ^^^ f)) - 2 * (d ||| e) - 3 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 2 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (f ^^^ ( ~~~d ||| (e ||| f))) + 11 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 1 * (e ^^^ (d ||| (e ||| f))) + 1 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 7 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 2 * (e ^^^ ~~~(d ||| ~~~f)) - 1 * (d ||| (e ^^^ f)) - 2 * (e ||| (d &&& ~~~f)) - 3 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 1 * (f ||| (d ^^^ e)) + 1 * ((d ||| e) &&& ~~~(e ^^^ f)) - 11 * (e ^^^ (d ||| ( ~~~e &&& f))) - 5 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 5 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 2 * (e ^^^ ( ~~~d ||| (e &&& f))) + 1 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 1 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 1 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 7 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * (f ^^^ ( ~~~d &&& (e ||| f))) - 2 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 4 * ~~~(d &&& e) + 5 * (e ^^^ ( ~~~d ||| (e ||| f))) + 2 * ~~~(e &&& ~~~f) + 3 * (e ^^^ (d ||| f)) - 11 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 2 * ( ~~~d ||| ( ~~~e ||| f)) - 2 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 4 * ( ~~~f ||| (d ^^^ e)) - 2 * ~~~(d ^^^ e) - 7 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 6 * (f ^^^ ~~~(d &&& (e ||| f))) + 7 * (f ^^^ ~~~(d &&& e)) + 3 * (e ^^^ ~~~(d ||| f)) + 5 * ~~~(d ||| (e &&& f)) + 1 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 7 * ~~~( ~~~d &&& (e &&& f)) + 1 * ~~~(d ^^^ (e ^^^ f)) + 1 * ~~~(d &&& ( ~~~e ||| f)) - 1 * ~~~(d ^^^ (e &&& f)) - 1 * (d ^^^ f) - 19 * ~~~(d ||| (e ||| f)) + 11 * ~~~(d ||| ( ~~~e ||| f)) + 23 * ~~~( ~~~d ||| (e ||| f)) + 25 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 49 * ( ~~~d &&& ( ~~~e &&& f)) - 17 * ( ~~~d &&& (e &&& f)) + 42 * (d &&& ( ~~~e &&& f)) + 48 * (d &&& (e &&& f)) = 11 * (e ^^^ ( ~~~d &&& (e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2319 (x y : BitVec w) : +theorem e_2319 : 11 * (e ||| ~~~f) + 1 * ~~~(d &&& ( ~~~e &&& f)) + 5 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * ( ~~~d ||| (e ||| f)) - 2 * (f ||| (d &&& ~~~e)) - 7 * (e ^^^ (d &&& ~~~f)) + 4 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 1 * ( ~~~d ||| ( ~~~e ||| f)) - 1 * (d ||| (e &&& f)) + 2 * ( ~~~d ||| (e &&& f)) - 1 * (e ^^^ (d &&& (e ||| f))) - 1 * (f &&& ~~~(d ^^^ e)) + 3 * ~~~(d ^^^ f) - 7 * ((d &&& f) ||| (e &&& ~~~f)) + 7 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 3 * ( ~~~e ||| (d ^^^ f)) + 2 * ( ~~~e ||| ~~~(d ^^^ f)) - 5 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 2 * (e ^^^ ~~~(d &&& (e &&& f))) - 3 * ~~~(e &&& f) + 1 * (e ^^^ ~~~(d ||| ~~~f)) + 2 * (e ^^^ (d ||| (e ^^^ f))) + 11 * (f ^^^ ~~~(d &&& (e &&& f))) - 11 * (d &&& ( ~~~e ||| f)) + 1 * (f ^^^ (d ||| (e &&& f))) + 2 * (d &&& ~~~f) + 7 * (f ^^^ ~~~(d &&& ~~~e)) - 1 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 2 * (e ||| ~~~(d ^^^ f)) - 6 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 5 * (e ^^^ f) + 5 * ~~~(d ||| (e ^^^ f)) - 2 * (e ^^^ ~~~(d ||| f)) - 6 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 4 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 1 * (d ||| ( ~~~e &&& f)) + 5 * ( ~~~f ||| (d ^^^ e)) - 3 * (e ^^^ ~~~(d ||| (e &&& f))) + 3 * ( ~~~d &&& (e ||| f)) - 1 * (f ^^^ ( ~~~d &&& (e ||| f))) + 5 * (d ^^^ ( ~~~e ||| f)) - 5 * ((d ^^^ e) ||| ~~~(d ^^^ f)) + 1 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 1 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 7 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 2 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 4 * (e &&& (d ||| f)) - 6 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 1 * (e ^^^ (d ||| (e &&& f))) - 2 * ~~~(d ^^^ (e ||| f)) + 11 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 7 * ( ~~~d ||| ( ~~~e &&& f)) + 2 * (d ||| e) + 5 * ~~~(d ||| f) + 11 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 52 * ~~~(d ||| (e ||| f)) - 5 * ~~~(d ||| ( ~~~e ||| f)) - 13 * ~~~( ~~~d ||| (e ||| f)) - 29 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 9 * ( ~~~d &&& ( ~~~e &&& f)) - 33 * ( ~~~d &&& (e &&& f)) + 5 * (d &&& ( ~~~e &&& f)) - 32 * (d &&& (e &&& f)) = 1 * d - 7 * (f ^^^ ~~~(d ||| e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2320 (x y : BitVec w) : +theorem e_2320 : 4 * ~~~(d ^^^ (e ||| f)) + 3 * (e ||| (d &&& f)) - 3 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 7 * (f ||| (d &&& e)) + 11 * (d ^^^ (e &&& f)) + 1 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 5 * ~~~(d &&& ~~~e) - 11 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 7 * (e ^^^ (d ||| f)) - 11 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 7 * (d ^^^ (e ^^^ f)) - 1 * ((d &&& f) ^^^ (e ||| f)) - 1 * (f ^^^ ~~~(d ||| (e &&& f))) - 6 * (d ||| e) + 5 * ~~~(d &&& ( ~~~e &&& f)) - 1 * (f ^^^ ( ~~~d ||| (e ||| f))) + 2 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 2 * ~~~(d ||| ( ~~~e &&& f)) + 3 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 1 * (e ||| ~~~(d ^^^ f)) + 11 * ( ~~~d ||| ( ~~~e ||| f)) + 7 * (f ^^^ (d &&& e)) + 11 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 5 * ~~~(d ||| ~~~e) + 1 * (f ||| ~~~(d ^^^ e)) + 2 * ~~~(d ||| ~~~f) - 1 * (f ^^^ ( ~~~d &&& (e ||| f))) + 5 * (e ^^^ (d &&& ( ~~~e ||| f))) - 1 * (e ^^^ ( ~~~d &&& (e ||| f))) - 6 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 1 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 2 * (d &&& ( ~~~e ||| f)) + 4 * ((d &&& f) ||| ~~~(e ||| f)) - 5 * ( ~~~e &&& ~~~(d ^^^ f)) - 2 * (e ||| ~~~(d ||| f)) - 3 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 4 * ( ~~~d &&& ( ~~~e ||| f)) - 2 * (e ^^^ ~~~(d &&& f)) + 5 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * d + 2 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 4 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 7 * ((d &&& ~~~e) ||| (e ^^^ f)) + 11 * (f ^^^ ( ~~~d ||| (e &&& f))) + 11 * ~~~(e ^^^ f) - 5 * (d ^^^ e) - 1 * (d ||| (e &&& f)) - 11 * (d ^^^ ( ~~~e ||| f)) + 4 * ~~~d + 4 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 6 * ~~~(d ^^^ e) + 1 * (f ||| (d ^^^ e)) + 3 * e - 1 * ~~~(e ||| ~~~f) + 2 * (f ^^^ (d ||| (e &&& f))) + 1 * ( ~~~e &&& (d ^^^ f)) - 14 * ~~~(d ||| (e ||| f)) - 8 * ~~~(d ||| ( ~~~e ||| f)) - 32 * ~~~( ~~~d ||| (e ||| f)) - 9 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 11 * ( ~~~d &&& ( ~~~e &&& f)) - 57 * ( ~~~d &&& (e &&& f)) - 33 * (d &&& ( ~~~e &&& f)) - 16 * (d &&& (e &&& f)) = - 1 * (d ||| ~~~f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2321 (x y : BitVec w) : +theorem e_2321 : - 11 * ~~~(e ^^^ f) + 2 * (e ^^^ (d &&& (e ^^^ f))) + 2 * ( ~~~f ||| ~~~(d ^^^ e)) - 11 * ( ~~~d ||| (e ||| f)) + 3 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 7 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 3 * (f &&& ~~~(d &&& e)) - 7 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 1 * (d &&& ( ~~~e ||| f)) + 1 * ~~~(d &&& ( ~~~e ||| f)) - 1 * (d &&& ~~~f) + 1 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 11 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 2 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 2 * ~~~(d &&& (e ^^^ f)) - 2 * (e ||| ~~~(d ||| f)) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 11 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 11 * (d ^^^ (e ^^^ f)) - 1 * ( ~~~d ||| (e &&& f)) - 1 * ((d ||| e) &&& ~~~(e ^^^ f)) + 2 * ( ~~~f &&& ~~~(d ^^^ e)) - 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 1 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 1 * (e ^^^ (d &&& f)) + 1 * ~~~(d ^^^ (e &&& f)) - 2 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 4 * (d ||| ~~~e) + 11 * ( ~~~d &&& (e ||| f)) - 3 * (d &&& e) + 7 * (e ^^^ ~~~(d ||| f)) + 3 * (e &&& ~~~(d &&& ~~~f)) + 7 * (f ^^^ (d ||| ( ~~~e ||| f))) - 1 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 3 * ( ~~~d &&& (e ^^^ f)) - 6 * ((d ||| e) &&& (e ^^^ f)) - 5 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 3 * (f &&& (d ||| e)) + 1 * ((d &&& ~~~e) ||| (e ^^^ f)) - 3 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 11 * (e ^^^ (d ||| f)) - 11 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 1 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 11 * (f &&& ~~~(d &&& ~~~e)) + 1 * (f ^^^ ( ~~~d ||| (e &&& f))) + 5 * ((d ^^^ e) &&& (d ^^^ f)) - 5 * (e ^^^ (d &&& (e ||| f))) - 1 * (d ||| (e &&& f)) + 2 * (e ^^^ (d ||| ~~~f)) + 1 * (d ||| ~~~f) - 7 * (f ||| ~~~(d ^^^ e)) - 5 * ~~~( ~~~d ||| (e &&& f)) + 1 * ~~~d + 3 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 11 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 7 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 14 * ~~~(d ||| (e ||| f)) + 38 * ~~~(d ||| ( ~~~e ||| f)) - 13 * ~~~( ~~~d ||| (e ||| f)) + 23 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 23 * ( ~~~d &&& ( ~~~e &&& f)) - 18 * ( ~~~d &&& (e &&& f)) + 66 * (d &&& ( ~~~e &&& f)) - 12 * (d &&& (e &&& f)) = - 2 * (e ^^^ ~~~(d ||| (e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2322 (x y : BitVec w) : +theorem e_2322 : 5 * ~~~( ~~~d &&& (e ^^^ f)) + 4 * ~~~(d &&& ( ~~~e &&& f)) - 1 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 7 * (e ^^^ (d ||| f)) - 1 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 1 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 11 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * ( ~~~e &&& (d ^^^ f)) + 5 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 1 * (f ^^^ (d ||| (e ||| f))) - 2 * ~~~(d &&& f) + 1 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 5 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 5 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 5 * ~~~e - 1 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 1 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 11 * (e ^^^ ~~~(d &&& (e ||| f))) + 3 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 4 * (f ^^^ (d &&& ( ~~~e ||| f))) + 2 * (e &&& f) - 6 * ( ~~~d ||| (e ^^^ f)) + 5 * (e ^^^ (d ||| ~~~f)) + 11 * (e ^^^ (d &&& (e ^^^ f))) + 7 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 1 * ~~~(d ||| e) - 6 * ~~~(d &&& (e &&& f)) + 1 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 7 * (e ^^^ (d &&& (e ||| f))) + 4 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 3 * ~~~(e &&& ~~~f) + 1 * (f &&& ~~~(d ^^^ e)) + 2 * (f ^^^ ~~~(d ||| e)) - 1 * (e ^^^ ~~~(d &&& ~~~f)) - 11 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * ~~~(d ||| (e ^^^ f)) - 1 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 2 * d - 6 * (f ^^^ (d ||| (e &&& f))) - 2 * ~~~(d ^^^ (e ^^^ f)) + 1 * (e &&& (d ^^^ f)) + 7 * (e ^^^ (d &&& f)) - 1 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 1 * ( ~~~d &&& (e ^^^ f)) - 2 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 7 * (e ^^^ ~~~(d ||| f)) + 7 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 2 * ~~~(d &&& (e ^^^ f)) - 1 * (d &&& (e ||| f)) + 3 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 3 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 4 * ((d &&& f) ||| ~~~(e ||| f)) + 2 * ((d &&& f) ||| (e &&& ~~~f)) - 11 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 1 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 5 * ( ~~~d ||| (e &&& f)) - 1 * ~~~(d ||| (e ||| f)) - 18 * ~~~(d ||| ( ~~~e ||| f)) + 9 * ~~~( ~~~d ||| (e ||| f)) + 12 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 7 * ( ~~~d &&& ( ~~~e &&& f)) - 31 * ( ~~~d &&& (e &&& f)) - 37 * (d &&& (e &&& f)) = 38 * (d &&& ( ~~~e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2323 (x y : BitVec w) : +theorem e_2323 : - 5 * (e ^^^ ( ~~~d ||| (e ||| f))) - 11 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 11 * (f &&& ~~~(d &&& ~~~e)) + 5 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 3 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 7 * (f ^^^ (d ||| ( ~~~e ||| f))) + 5 * ( ~~~d &&& (e ||| f)) + 2 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 3 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 7 * (e ^^^ (d &&& (e ^^^ f))) - 2 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 5 * ( ~~~e ||| ~~~(d ^^^ f)) + 1 * ( ~~~e &&& ~~~(d ^^^ f)) + 5 * (d ^^^ e) + 1 * ~~~(d &&& ~~~f) + 2 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 5 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 3 * (e ||| ~~~(d ^^^ f)) + 2 * ((d ^^^ e) &&& (d ^^^ f)) - 2 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 11 * (f &&& ~~~(d ^^^ e)) + 2 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 7 * (f ^^^ (d ||| ~~~e)) - 5 * ( ~~~e ||| (d ^^^ f)) + 7 * (e ^^^ (d &&& ~~~f)) - 1 * ~~~(e ||| ~~~f) - 2 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 7 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 3 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 11 * (e ^^^ (d ||| ( ~~~e ||| f))) + 5 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 6 * (e ^^^ ~~~(d &&& (e ||| f))) - 5 * (f ^^^ (d &&& ( ~~~e ||| f))) - 1 * ~~~(e &&& f) + 1 * ~~~(d ^^^ (e ||| f)) + 4 * (f ||| ~~~(d ^^^ e)) + 11 * (f ^^^ (d &&& (e ||| f))) - 5 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 1 * (e ^^^ ( ~~~d ||| (e &&& f))) + 11 * (e ^^^ (d &&& ( ~~~e ||| f))) - 2 * (f &&& (d ^^^ e)) - 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 1 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 1 * f - 6 * ( ~~~d ||| ( ~~~e ||| f)) + 2 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 11 * ((d &&& ~~~e) ||| (e ^^^ f)) + 1 * ( ~~~f &&& (d ^^^ e)) + 7 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 2 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 1 * (f &&& ~~~(d &&& e)) + 1 * (e ||| (d &&& ~~~f)) - 3 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 7 * (d &&& e) + 15 * ~~~(d ||| (e ||| f)) - 26 * ~~~(d ||| ( ~~~e ||| f)) - 7 * ~~~( ~~~d ||| (e ||| f)) - 12 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 4 * ( ~~~d &&& ( ~~~e &&& f)) - 10 * ( ~~~d &&& (e &&& f)) - 1 * (d &&& ( ~~~e &&& f)) + 25 * (d &&& (e &&& f)) = 1 * ~~~(d ^^^ (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2324 (x y : BitVec w) : +theorem e_2324 : 1 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 3 * (e ^^^ f) + 5 * ~~~(d &&& (e ||| f)) - 2 * ~~~(e ^^^ f) + 7 * (f ^^^ (d &&& ( ~~~e ||| f))) - 11 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 4 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 6 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 11 * ~~~(d &&& ~~~f) + 2 * (f ||| ~~~(d ^^^ e)) - 3 * ( ~~~d ||| ( ~~~e &&& f)) - 6 * ((e &&& f) ||| (d &&& (e ||| f))) + 1 * (e &&& f) - 3 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 1 * (e ||| ~~~(d ||| ~~~f)) + 2 * (e ^^^ ~~~(d &&& f)) + 1 * ~~~f - 5 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 5 * f + 2 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 1 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 7 * (d &&& ~~~e) - 7 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 2 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * (d ||| (e ^^^ f)) - 1 * (f ||| ~~~(d ||| e)) - 11 * ( ~~~f ||| ~~~(d ^^^ e)) - 5 * (f ^^^ (d ||| ~~~e)) + 11 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 11 * (e ||| f) + 7 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 11 * (f ^^^ ~~~(d &&& ~~~e)) - 1 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 1 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 2 * (d &&& ( ~~~e ||| f)) + 4 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 6 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * ( ~~~f ||| (d ^^^ e)) + 2 * ((d ||| ~~~e) &&& (e ^^^ f)) - 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 7 * ( ~~~e ||| ~~~(d ^^^ f)) + 3 * (e ^^^ (d ||| ~~~f)) + 7 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 1 * d + 2 * (f ||| (d &&& e)) - 1 * (e &&& (d ||| f)) - 2 * (d ||| (e &&& f)) + 4 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 3 * ~~~(d ^^^ ( ~~~e &&& f)) - 6 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 1 * (f ^^^ (d &&& ~~~e)) + 3 * ~~~(d ||| (e ^^^ f)) + 4 * ~~~(d &&& ~~~d) - 5 * ((d &&& e) ||| ~~~(e ||| f)) - 11 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 2 * ( ~~~e &&& ~~~(d ^^^ f)) + 12 * ~~~(d ||| (e ||| f)) - 31 * ~~~(d ||| ( ~~~e ||| f)) + 34 * ~~~( ~~~d ||| (e ||| f)) + 18 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 12 * ( ~~~d &&& ( ~~~e &&& f)) - 11 * (d &&& ( ~~~e &&& f)) - 13 * (d &&& (e &&& f)) = 24 * ( ~~~d &&& (e &&& f)) + 1 * (f ^^^ (d ||| ( ~~~e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2325 (x y : BitVec w) : +theorem e_2325 : 1 * (e ^^^ (d ||| ( ~~~e &&& f))) - 1 * ~~~(d &&& (e ^^^ f)) + 2 * (e ^^^ ~~~(d ||| f)) + 1 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 6 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 3 * (e ||| ~~~(d ||| f)) - 1 * ~~~(d ^^^ (e &&& f)) + 4 * ( ~~~d ||| (e &&& f)) + 1 * (e ^^^ f) + 11 * ((d &&& f) ^^^ (e ||| f)) - 1 * (e ^^^ ~~~(d &&& (e &&& f))) + 7 * (e ^^^ (d &&& f)) + 2 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 2 * (e ||| ~~~f) - 1 * ~~~(d &&& e) - 11 * (f &&& (d ^^^ e)) - 7 * ( ~~~f &&& ~~~(d ^^^ e)) - 2 * ~~~( ~~~d &&& (e ^^^ f)) - 1 * ~~~( ~~~d &&& (e ||| f)) + 3 * (d &&& (e ^^^ f)) + 1 * (e ^^^ ~~~(d ||| (e &&& f))) + 7 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 1 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 6 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 1 * (f ^^^ (d ||| (e ||| f))) - 11 * ~~~(e ||| f) + 2 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 3 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 1 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 2 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * (d ^^^ (e &&& f)) + 3 * ~~~(d &&& ( ~~~e &&& f)) + 5 * ~~~(d ^^^ ( ~~~e ||| f)) + 1 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 5 * ~~~( ~~~d ||| (e ^^^ f)) + 4 * ( ~~~e &&& ~~~(d ^^^ f)) - 5 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 5 * (d &&& ~~~e) + 7 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 7 * (f ^^^ ( ~~~d &&& (e ||| f))) - 1 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 6 * ((d ^^^ e) &&& (d ^^^ f)) + 2 * (e ||| ~~~(d ^^^ f)) + 1 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 7 * ((d ||| e) &&& (e ^^^ f)) + 11 * (f ^^^ ~~~(d &&& e)) - 2 * (e ^^^ ( ~~~d ||| (e &&& f))) + 7 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 4 * ( ~~~d &&& (e ||| f)) + 2 * ~~~(d ^^^ e) + 3 * ~~~( ~~~d ||| (e &&& f)) + 5 * (f ^^^ ( ~~~d ||| (e ||| f))) - 6 * (f ^^^ ~~~(d ||| e)) - 5 * ((d &&& e) ||| ~~~(e ^^^ f)) + 2 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 2 * (d ||| f) + 6 * ~~~(d ||| (e ||| f)) - 47 * ~~~(d ||| ( ~~~e ||| f)) - 10 * ~~~( ~~~d ||| (e ||| f)) - 27 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 23 * ( ~~~d &&& ( ~~~e &&& f)) - 10 * ( ~~~d &&& (e &&& f)) - 22 * (d &&& ( ~~~e &&& f)) - 26 * (d &&& (e &&& f)) = - 2 * (f ||| ~~~(d ||| e)) + 3 * ~~~(d ||| (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2326 (x y : BitVec w) : +theorem e_2326 : - 2 * ~~~(d &&& f) + 11 * (e ||| (d &&& f)) + 1 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 6 * (e ^^^ ~~~(d &&& (e &&& f))) + 1 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 3 * (e &&& f) - 5 * (d &&& ( ~~~e ||| f)) - 1 * ( ~~~e &&& (d ^^^ f)) - 11 * ((d ||| e) &&& (e ^^^ f)) + 2 * ( ~~~e ||| (d ^^^ f)) - 11 * ~~~f + 3 * ( ~~~d &&& (e ||| f)) - 5 * (e &&& (d ^^^ f)) + 1 * (e ^^^ ~~~(d &&& (e ||| f))) + 1 * (d ^^^ (e ^^^ f)) + 1 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (d &&& f) - 7 * ~~~( ~~~d &&& (e &&& f)) + 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 7 * ( ~~~d ||| ( ~~~e &&& f)) + 2 * ( ~~~e ||| ~~~(d ^^^ f)) + 11 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 7 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 5 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 2 * (f ^^^ ( ~~~d ||| (e &&& f))) + 2 * ~~~d + 2 * (d ^^^ f) + 11 * (e ^^^ (d ||| f)) + 5 * (e ^^^ (d ||| (e &&& f))) - 6 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * (f ^^^ ( ~~~d ||| (e ||| f))) + 2 * (f ||| ~~~(d ||| e)) - 6 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 1 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 1 * ~~~(d ||| ~~~e) - 1 * (f ^^^ ~~~(d ||| (e &&& f))) + 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 4 * (f ^^^ ~~~(d &&& (e ||| f))) + 5 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 7 * ~~~( ~~~d ||| (e ^^^ f)) + 4 * (f ^^^ (d &&& ( ~~~e ||| f))) - 2 * ( ~~~f &&& ~~~(d ^^^ e)) - 1 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 3 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 2 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 7 * ((e &&& f) ||| (d &&& (e ||| f))) + 3 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 2 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 11 * ( ~~~f &&& (d ^^^ e)) + 1 * ((d &&& e) ||| (e ^^^ f)) - 1 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 11 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 2 * ((d &&& f) ||| (e &&& ~~~f)) + 2 * (e ||| (d &&& ~~~f)) - 5 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 5 * ~~~(d ||| (e ^^^ f)) - 22 * ~~~(d ||| (e ||| f)) - 25 * ~~~(d ||| ( ~~~e ||| f)) - 18 * ~~~( ~~~d ||| (e ||| f)) - 22 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 28 * ( ~~~d &&& ( ~~~e &&& f)) - 62 * ( ~~~d &&& (e &&& f)) - 39 * (d &&& ( ~~~e &&& f)) - 38 * (d &&& (e &&& f)) = - 1 * (d ^^^ (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2327 (x y : BitVec w) : +theorem e_2327 : 1 * ((d ^^^ e) ||| (d ^^^ f)) - 1 * ~~~(d ^^^ ( ~~~e &&& f)) - 5 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 2 * ( ~~~f &&& (d ^^^ e)) + 1 * (e ^^^ f) + 1 * ~~~d + 11 * (d ||| (e ^^^ f)) + 1 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 7 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 2 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 2 * (e ||| ~~~(d ||| ~~~f)) + 7 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 6 * ~~~(d ||| (e &&& f)) - 2 * (f ^^^ ( ~~~d &&& (e ||| f))) + 4 * ( ~~~d ||| (e &&& f)) - 11 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 5 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 5 * ( ~~~f ||| (d ^^^ e)) + 7 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 3 * ~~~(d &&& ( ~~~e &&& f)) + 1 * (e ^^^ ~~~(d ||| (e &&& f))) + 7 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 6 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 1 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 3 * (f ^^^ (d ||| (e ||| f))) + 1 * (f ^^^ ~~~(d &&& (e &&& f))) - 2 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 4 * (d &&& (e ^^^ f)) + 2 * ~~~(d &&& ~~~d) - 7 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (e &&& ~~~(d &&& f)) + 5 * (f ||| (d &&& e)) + 3 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 4 * ~~~(d &&& ~~~e) - 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 2 * ~~~(d &&& ( ~~~e ||| f)) + 7 * (d ^^^ ( ~~~e ||| f)) - 2 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 2 * ~~~(d &&& e) + 5 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 5 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 2 * ~~~(d &&& (e ^^^ f)) + 1 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 1 * (f ^^^ ~~~(d &&& e)) + 1 * (f ^^^ ( ~~~d ||| (e &&& f))) + 2 * (e ^^^ (d ||| (e &&& f))) - 5 * (e ^^^ ~~~(d &&& f)) - 11 * (e ||| (d &&& f)) - 3 * (e ^^^ (d ||| ~~~f)) - 1 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * (e ^^^ (d &&& ~~~f)) - 11 * (f ||| (d ^^^ e)) - 1 * (d &&& f) + 1 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 2 * (e &&& ~~~(d ^^^ f)) + 5 * ( ~~~d ||| (e ^^^ f)) + 11 * ~~~(e &&& f) - 11 * ~~~(d ||| (e ||| f)) - 21 * ~~~(d ||| ( ~~~e ||| f)) - 23 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 32 * ( ~~~d &&& ( ~~~e &&& f)) - 4 * ( ~~~d &&& (e &&& f)) - 6 * (d &&& ( ~~~e &&& f)) + 2 * (d &&& (e &&& f)) = - 4 * (e &&& (d ^^^ f)) + 6 * (f ^^^ (d &&& (e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2328 (x y : BitVec w) : +theorem e_2328 : 2 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 7 * (d ||| f) + 3 * ~~~(d ||| (e ^^^ f)) - 11 * (e ||| (d ^^^ f)) - 11 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 5 * (f ||| ~~~(d ||| ~~~e)) + 1 * ((d &&& e) ^^^ (e ||| f)) - 2 * (e ||| (d &&& f)) + 1 * ~~~(d ^^^ (e ^^^ f)) - 2 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 2 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 1 * (e &&& ~~~(d &&& f)) + 1 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 5 * ((d ||| e) &&& ~~~(e ^^^ f)) + 11 * ~~~(d &&& ~~~d) - 3 * (f &&& (d ||| e)) - 1 * ((d &&& f) ||| (e &&& ~~~f)) - 3 * (e ^^^ ( ~~~d ||| (e &&& f))) + 5 * (f ||| (d ^^^ e)) + 1 * ((d &&& e) ||| (e ^^^ f)) - 6 * (d ^^^ f) + 7 * (e &&& (d ||| ~~~f)) - 6 * f + 4 * ~~~(d ||| ~~~f) + 7 * ( ~~~d ||| ( ~~~e ||| f)) + 5 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 5 * ( ~~~f ||| ~~~(d ^^^ e)) + 11 * (d ^^^ ( ~~~e ||| f)) - 1 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 2 * ~~~(d ||| e) - 2 * (f ^^^ (d ||| ( ~~~e &&& f))) + 2 * (d ^^^ (e ^^^ f)) - 5 * (e ^^^ (d &&& ~~~f)) - 1 * (e ^^^ (d ||| (e &&& f))) + 7 * (f ^^^ (d ||| (e &&& f))) + 1 * ~~~d + 3 * ((d &&& e) ||| ~~~(e ||| f)) - 1 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 5 * (e ^^^ f) + 2 * ~~~(e &&& f) - 3 * (f ||| ~~~(d ||| e)) - 1 * ~~~( ~~~d ||| (e &&& f)) - 5 * (e ^^^ ~~~(d ||| f)) + 2 * (f ^^^ (d ||| ( ~~~e ||| f))) + 3 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 1 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 3 * ((d &&& e) ||| ~~~(e ^^^ f)) - 6 * (e ^^^ ~~~(d ||| ~~~f)) - 6 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 3 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 2 * ( ~~~e ||| ~~~(d ^^^ f)) + 4 * (e &&& ~~~(d &&& ~~~f)) - 1 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 6 * ~~~e + 4 * (f ^^^ (d &&& ~~~e)) - 1 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 7 * ~~~( ~~~d &&& (e ^^^ f)) - 7 * ~~~(d ||| (e ||| f)) + 12 * ~~~(d ||| ( ~~~e ||| f)) - 11 * ~~~( ~~~d ||| (e ||| f)) + 5 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 2 * ( ~~~d &&& ( ~~~e &&& f)) - 5 * (d &&& ( ~~~e &&& f)) - 10 * (d &&& (e &&& f)) = 15 * ( ~~~d &&& (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2329 (x y : BitVec w) : +theorem e_2329 : 7 * ( ~~~e ||| ~~~(d ^^^ f)) - 7 * (f &&& (d ||| e)) - 1 * ~~~(d ^^^ (e ||| f)) + 2 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 3 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * ( ~~~e &&& (d ^^^ f)) + 1 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 11 * ( ~~~f &&& (d ^^^ e)) + 1 * (f ||| (d &&& ~~~e)) - 2 * ~~~(d &&& ~~~f) - 7 * (e &&& ~~~(d ^^^ f)) - 3 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 2 * d - 7 * ~~~(d &&& (e &&& f)) - 1 * ( ~~~d &&& ( ~~~e ||| f)) - 2 * ~~~( ~~~d &&& (e &&& f)) + 5 * ((e &&& f) ||| (d &&& (e ||| f))) + 1 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 2 * ~~~(d &&& e) + 1 * (e ^^^ ~~~(d &&& (e ||| f))) + 2 * ( ~~~e &&& ~~~(d ^^^ f)) + 2 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 1 * (f ||| ~~~(d ||| e)) - 5 * (e ^^^ (d ||| ( ~~~e ||| f))) - 6 * ~~~(e &&& ~~~f) + 1 * (f ^^^ (d ||| (e ||| f))) - 1 * (e ^^^ ( ~~~d &&& (e ||| f))) - 6 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 1 * ~~~(e &&& f) + 1 * (f &&& ~~~(d ^^^ e)) + 4 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 1 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 2 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 1 * (e ||| ~~~(d ^^^ f)) + 1 * ~~~(d ||| e) + 1 * ( ~~~f &&& ~~~(d ^^^ e)) - 11 * (d ||| ( ~~~e ||| f)) - 11 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 6 * (e ^^^ (d ||| ( ~~~e &&& f))) + 2 * (e ^^^ (d &&& f)) - 11 * (f ^^^ (d ||| ( ~~~e ||| f))) + 2 * (d ||| (e &&& f)) - 11 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 4 * (d ||| (e ||| f)) - 7 * (e ^^^ (d ||| ~~~f)) - 7 * ~~~(d ||| ~~~f) - 5 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 3 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 2 * (e &&& (d ||| f)) + 3 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 2 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 3 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 7 * ( ~~~f ||| ~~~(d ^^^ e)) - 2 * (e ||| ~~~(d ||| ~~~f)) + 1 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 6 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 82 * ~~~(d ||| (e ||| f)) + 13 * ~~~(d ||| ( ~~~e ||| f)) + 30 * ~~~( ~~~d ||| (e ||| f)) + 46 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 46 * ( ~~~d &&& ( ~~~e &&& f)) + 59 * ( ~~~d &&& (e &&& f)) + 41 * (d &&& ( ~~~e &&& f)) + 37 * (d &&& (e &&& f)) = - 4 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 2 * ((d ^^^ e) ||| (d ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2330 (x y : BitVec w) : +theorem e_2330 : 7 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 5 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 1 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 2 * (e ^^^ ( ~~~d ||| (e ||| f))) + 1 * (d ||| (e &&& f)) - 1 * ( ~~~d &&& ( ~~~e ||| f)) + 11 * (d ||| ~~~f) + 5 * ( ~~~f ||| ~~~(d ^^^ e)) + 2 * (f ||| ~~~(d ^^^ e)) - 1 * (f &&& ~~~(d ^^^ e)) - 3 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 7 * d + 11 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 6 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 1 * ( ~~~d ||| (e ^^^ f)) + 1 * (d &&& ~~~f) + 3 * ((d &&& f) ||| (e &&& ~~~f)) - 2 * ( ~~~e ||| (d ^^^ f)) + 3 * (d ^^^ (e &&& f)) - 1 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 11 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 11 * (e ^^^ ~~~(d &&& f)) + 3 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 7 * (f ^^^ ~~~(d &&& e)) + 4 * (e &&& ~~~(d ^^^ f)) + 5 * (e ||| (d &&& f)) + 4 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * ~~~(d ||| ( ~~~e &&& f)) + 11 * (e ||| ~~~(d ||| ~~~f)) + 1 * ((e &&& f) ||| (d &&& (e ||| f))) - 2 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * ~~~(d &&& ( ~~~e &&& f)) - 6 * ( ~~~e &&& (d ^^^ f)) + 1 * (e &&& ~~~f) + 1 * ~~~(d &&& (e ^^^ f)) - 2 * (f ||| (d &&& ~~~e)) - 7 * (f ^^^ ~~~(d ||| (e &&& f))) - 3 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 2 * (e ^^^ (d ||| ( ~~~e &&& f))) - 2 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 4 * ~~~(d &&& (e &&& f)) - 1 * (e ^^^ (d &&& (e ||| f))) - 3 * (d ^^^ f) + 3 * ((d ^^^ e) &&& (d ^^^ f)) - 5 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 2 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 5 * (f ||| (d &&& e)) - 11 * ((d ||| e) &&& ~~~(e ^^^ f)) + 1 * ~~~(e ^^^ f) - 11 * ~~~(d ||| ~~~e) - 3 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 2 * (e &&& (d ^^^ f)) - 11 * (e ^^^ ( ~~~d ||| (e &&& f))) - 2 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 5 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 13 * ~~~(d ||| (e ||| f)) - 39 * ~~~(d ||| ( ~~~e ||| f)) + 35 * ~~~( ~~~d ||| (e ||| f)) - 33 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 29 * ( ~~~d &&& ( ~~~e &&& f)) + 10 * ( ~~~d &&& (e &&& f)) - 15 * (d &&& ( ~~~e &&& f)) + 10 * (d &&& (e &&& f)) = - 1 * ( ~~~d ||| (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2331 (x y : BitVec w) : +theorem e_2331 : - 1 * ((d &&& e) ||| ~~~(e ||| f)) - 7 * ~~~(d ||| ~~~f) - 7 * ( ~~~e &&& ~~~(d ^^^ f)) + 1 * (e ||| ~~~(d ||| f)) + 4 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 1 * ~~~f + 1 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 1 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 3 * (f ^^^ (d ||| (e &&& f))) + 3 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * ~~~(d &&& (e &&& f)) - 2 * (e &&& (d ||| ~~~f)) - 1 * ((d ^^^ e) ||| (d ^^^ f)) - 2 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 2 * (e ||| ~~~f) + 3 * (e ^^^ (d &&& (e ^^^ f))) - 2 * (e ||| (d ^^^ f)) - 2 * (e ^^^ (d ||| ~~~f)) - 1 * (e ^^^ (d &&& ~~~f)) - 5 * (e ^^^ ( ~~~d ||| (e &&& f))) + 2 * ( ~~~d &&& (e ^^^ f)) - 5 * ~~~(d &&& ( ~~~e &&& f)) - 7 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 11 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 2 * ~~~( ~~~d &&& (e ^^^ f)) - 3 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 6 * ~~~(d ^^^ ( ~~~e ||| f)) + 5 * (f ^^^ (d ||| ( ~~~e &&& f))) - 6 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 11 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 3 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 3 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 1 * (f ^^^ ~~~(d &&& (e ||| f))) + 2 * (f ^^^ (d &&& e)) + 2 * (d ||| ~~~f) - 1 * (e ||| (d &&& ~~~f)) + 1 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 5 * ~~~(d ^^^ ( ~~~e &&& f)) - 6 * ~~~( ~~~d &&& (e ||| f)) + 7 * ~~~( ~~~d &&& (e &&& f)) + 1 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 7 * ~~~(e ||| ~~~f) + 1 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * ( ~~~d ||| (e &&& f)) - 2 * ((d &&& f) ^^^ (e ||| f)) + 11 * (f ^^^ ~~~(d &&& (e &&& f))) + 1 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 11 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 6 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 7 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 1 * (f ^^^ ~~~(d ||| (e &&& f))) + 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 3 * ~~~(d ||| e) - 6 * f + 1 * (e ^^^ ~~~(d ||| f)) - 5 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 11 * e + 18 * ~~~(d ||| (e ||| f)) + 34 * ~~~(d ||| ( ~~~e ||| f)) + 10 * ~~~( ~~~d ||| (e ||| f)) + 8 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 31 * ( ~~~d &&& ( ~~~e &&& f)) + 24 * ( ~~~d &&& (e &&& f)) + 26 * (d &&& ( ~~~e &&& f)) + 12 * (d &&& (e &&& f)) = - 4 * (e ^^^ ~~~(d &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2332 (x y : BitVec w) : +theorem e_2332 : - 2 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 5 * (e ^^^ ~~~(d &&& ~~~f)) + 5 * (d ^^^ (e &&& f)) - 1 * (e ^^^ ~~~(d ||| f)) + 7 * (d ||| (e ||| f)) + 1 * (e &&& ~~~f) - 3 * (e ^^^ ( ~~~d ||| (e ||| f))) - 1 * (e ^^^ (d ||| ( ~~~e &&& f))) + 7 * ~~~(d &&& ( ~~~e &&& f)) - 2 * (e ^^^ ~~~(d &&& (e ||| f))) - 1 * (d ^^^ f) - 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 2 * (f ^^^ (d ||| e)) - 1 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 3 * (f &&& (d ||| e)) - 1 * ((d &&& e) ||| ~~~(e ||| f)) - 3 * (f ||| (d &&& ~~~e)) + 4 * ~~~(e &&& f) + 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 1 * (f ^^^ (d &&& ( ~~~e ||| f))) - 6 * (e ^^^ (d ||| f)) - 5 * ~~~(d ||| ~~~f) - 6 * (f ^^^ ~~~(d &&& (e ||| f))) - 7 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 2 * (f ||| (d &&& e)) - 6 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 5 * ~~~(d &&& (e ||| f)) + 4 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 1 * (f ^^^ (d &&& e)) + 5 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 7 * (f ^^^ ( ~~~d &&& (e ||| f))) - 7 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 2 * ~~~(e ||| f) - 11 * ~~~(d ||| f) - 1 * ((d ||| e) &&& (e ^^^ f)) - 5 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 3 * (e ^^^ (d ||| (e &&& f))) + 2 * ~~~(d &&& ~~~f) + 7 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 2 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 6 * ~~~(d ^^^ (e &&& f)) - 11 * ( ~~~e &&& ~~~(d ^^^ f)) + 4 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * ( ~~~f &&& (d ^^^ e)) - 11 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 1 * (d ||| ~~~f) + 1 * ( ~~~e &&& (d ^^^ f)) - 2 * (e &&& (d ||| f)) + 2 * (e ||| f) + 1 * (d &&& ~~~f) - 7 * ( ~~~d ||| (e ^^^ f)) - 1 * ~~~(d ||| (e ^^^ f)) - 1 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 1 * (e ||| (d &&& ~~~f)) + 36 * ~~~(d ||| (e ||| f)) - 4 * ~~~(d ||| ( ~~~e ||| f)) - 1 * ~~~( ~~~d ||| (e ||| f)) + 3 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 21 * ( ~~~d &&& ( ~~~e &&& f)) - 15 * ( ~~~d &&& (e &&& f)) + 10 * (d &&& ( ~~~e &&& f)) + 18 * (d &&& (e &&& f)) = 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 2 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2333 (x y : BitVec w) : +theorem e_2333 : - 3 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 1 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 5 * ~~~(d ||| ~~~f) - 2 * (f &&& (d ^^^ e)) - 7 * (d ^^^ (e ||| f)) - 1 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 11 * (f ^^^ (d ||| ~~~e)) - 2 * ~~~(e ||| f) + 11 * ( ~~~f &&& (d ^^^ e)) + 1 * (e ^^^ ~~~(d &&& ~~~f)) - 1 * ~~~(d &&& (e ||| f)) - 3 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 11 * ~~~d - 7 * ~~~(d ^^^ e) + 1 * ( ~~~f &&& ~~~(d ^^^ e)) - 1 * ~~~(d &&& ~~~f) + 3 * f - 2 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 1 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 5 * (e ^^^ ( ~~~d &&& (e ||| f))) - 2 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 11 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 6 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 3 * (f ^^^ ( ~~~d ||| (e &&& f))) + 1 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 3 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 2 * ( ~~~f ||| (d ^^^ e)) + 7 * ((d ||| e) &&& (e ^^^ f)) + 1 * ( ~~~d &&& (e ^^^ f)) + 2 * ((d &&& ~~~e) ||| (e ^^^ f)) + 4 * (f ||| ~~~(d ||| ~~~e)) - 1 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 1 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 1 * ( ~~~d ||| ( ~~~e &&& f)) + 1 * (f ^^^ ~~~(d &&& ~~~e)) + 2 * (e ^^^ f) - 2 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 2 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 11 * ~~~(d ||| (e &&& f)) + 5 * ((d &&& e) ^^^ (e ||| ~~~f)) - 1 * ~~~( ~~~d &&& (e ||| f)) + 3 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 7 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 11 * ~~~(d ^^^ ( ~~~e ||| f)) - 1 * e - 6 * ~~~(d ||| f) - 1 * (d ^^^ ( ~~~e &&& f)) - 1 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 3 * ((d &&& f) ||| ~~~(e ||| f)) + 5 * ~~~(d ^^^ (e ^^^ f)) - 1 * (f ^^^ ~~~(d &&& e)) + 2 * ( ~~~d &&& (e ||| f)) - 2 * (f ^^^ ~~~(d ||| (e &&& f))) - 6 * (e &&& f) + 2 * (e &&& (d ||| f)) + 4 * (e ||| ~~~(d ^^^ f)) - 5 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 49 * ~~~(d ||| (e ||| f)) - 24 * ~~~(d ||| ( ~~~e ||| f)) + 30 * ~~~( ~~~d ||| (e ||| f)) + 6 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 9 * ( ~~~d &&& ( ~~~e &&& f)) + 44 * ( ~~~d &&& (e &&& f)) - 21 * (d &&& ( ~~~e &&& f)) = - 11 * (e ^^^ ~~~(d ||| ~~~f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2334 (x y : BitVec w) : +theorem e_2334 : 1 * ~~~(d ||| (e &&& f)) + 2 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 6 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 1 * (f &&& (d ||| e)) - 7 * ~~~(d ^^^ f) + 11 * (f &&& ~~~(d &&& ~~~e)) - 5 * (f ^^^ (d ||| ~~~e)) + 11 * ((e &&& f) ||| (d &&& (e ||| f))) - 1 * (f ||| (d ^^^ e)) - 2 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * ~~~( ~~~d ||| (e ^^^ f)) - 2 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 1 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 11 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 3 * (f ^^^ ~~~(d ||| ~~~e)) - 3 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 2 * (d &&& e) - 1 * (f ||| ~~~(d ||| e)) - 11 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 2 * (f ||| ~~~(d ^^^ e)) + 11 * (d &&& (e ^^^ f)) + 2 * (e ^^^ (d ||| (e &&& f))) - 3 * (d ||| f) - 5 * (d &&& (e ||| f)) + 2 * ((d &&& e) ||| (e ^^^ f)) - 1 * (e ^^^ f) + 7 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 1 * ~~~(d &&& (e ||| f)) + 11 * ~~~(d &&& ( ~~~e &&& f)) + 7 * (e ^^^ ( ~~~d ||| (e ||| f))) + 2 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 5 * ((d &&& f) ||| ~~~(e ||| f)) + 1 * ~~~(e ^^^ f) + 4 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 6 * ( ~~~d ||| ( ~~~e ||| f)) + 4 * (d ^^^ ( ~~~e ||| f)) + 5 * (e ||| (d &&& f)) + 1 * ( ~~~e &&& ~~~(d ^^^ f)) + 1 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 1 * (f ^^^ (d ||| ( ~~~e ||| f))) - 1 * (f ^^^ (d ||| ( ~~~e &&& f))) - 11 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * (e ||| (d ^^^ f)) + 4 * (e ^^^ ( ~~~d ||| (e &&& f))) - 2 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 5 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 1 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 1 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 2 * (f ||| (d &&& e)) - 1 * ~~~(d ||| e) + 3 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 5 * (e ^^^ (d ||| ( ~~~e &&& f))) + 1 * (e ^^^ ~~~(d &&& ~~~f)) - 1 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 5 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 3 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 6 * ~~~(d &&& ( ~~~e ||| f)) + 1 * ~~~(d ^^^ (e ||| f)) - 26 * ~~~(d ||| (e ||| f)) + 16 * ~~~(d ||| ( ~~~e ||| f)) + 17 * ~~~( ~~~d ||| (e ||| f)) - 7 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 32 * ( ~~~d &&& ( ~~~e &&& f)) - 23 * (d &&& ( ~~~e &&& f)) - 31 * (d &&& (e &&& f)) = 1 * ~~~(e ||| ~~~f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2335 (x y : BitVec w) : +theorem e_2335 : - 1 * (d &&& (e ^^^ f)) - 5 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 1 * (e ^^^ (d ||| (e &&& f))) + 7 * ( ~~~d &&& (e ||| f)) - 6 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 1 * (e &&& ~~~f) + 2 * e - 1 * ~~~d + 1 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 2 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 1 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 4 * ~~~(d &&& ~~~d) - 11 * (d ^^^ e) + 1 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 1 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 11 * (f ^^^ (d ||| ( ~~~e ||| f))) + 1 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 1 * ( ~~~e ||| (d ^^^ f)) + 3 * (d &&& e) + 1 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 1 * ( ~~~d &&& (e ^^^ f)) + 5 * (d ||| e) + 3 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 1 * (d &&& ~~~f) - 3 * (d ^^^ (e &&& f)) - 11 * (e ^^^ ( ~~~d ||| (e ||| f))) + 2 * (e &&& (d ^^^ f)) - 5 * ((d &&& e) ||| (e ^^^ f)) + 5 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 1 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 1 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 2 * (f ^^^ ( ~~~d &&& (e ||| f))) + 11 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 7 * (d ||| ( ~~~e &&& f)) - 7 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 2 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 3 * ~~~(d ^^^ ( ~~~e &&& f)) - 2 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 5 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 1 * ~~~( ~~~d ||| (e &&& f)) + 1 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 1 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 11 * ( ~~~e &&& ~~~(d ^^^ f)) + 4 * (d ^^^ (e ||| f)) + 1 * (d ^^^ f) + 5 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 2 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 7 * (e ^^^ (d &&& (e ^^^ f))) - 7 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 2 * (f &&& ~~~(d &&& e)) - 1 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 2 * (e ||| (d ^^^ f)) - 1 * ~~~(d ^^^ (e ||| f)) - 5 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 2 * ~~~(d &&& e) - 2 * (f ^^^ ~~~(d &&& e)) + 1 * ~~~(d &&& f) - 20 * ~~~(d ||| (e ||| f)) + 26 * ~~~(d ||| ( ~~~e ||| f)) + 14 * ~~~( ~~~d ||| (e ||| f)) - 31 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 14 * ( ~~~d &&& ( ~~~e &&& f)) + 23 * ( ~~~d &&& (e &&& f)) + 21 * (d &&& ( ~~~e &&& f)) + 15 * (d &&& (e &&& f)) = - 7 * (f ||| ~~~(d ||| e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2336 (x y : BitVec w) : +theorem e_2336 : 1 * ( ~~~f ||| ~~~(d ^^^ e)) - 1 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 2 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 2 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 4 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 11 * (d ||| ( ~~~e &&& f)) + 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 1 * ~~~(d &&& e) + 2 * (d ||| f) - 5 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 3 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 11 * (d ^^^ (e ^^^ f)) - 1 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 3 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 6 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 1 * ((d &&& f) ||| ~~~(e ||| f)) + 1 * ~~~( ~~~d ||| (e &&& f)) + 2 * (f ||| ~~~(d ||| e)) - 1 * (f ^^^ (d &&& (e ||| f))) + 1 * ~~~(e ||| ~~~f) + 4 * (f ^^^ (d ||| (e ||| f))) - 1 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 1 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 3 * (e ^^^ (d ||| (e &&& f))) - 11 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 11 * ((d &&& f) ^^^ (e ||| f)) - 6 * f + 11 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 2 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 1 * (d ||| ~~~e) - 6 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 7 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 3 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 2 * ((d ||| e) &&& ~~~(e ^^^ f)) - 2 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 3 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 5 * ~~~(d ||| ~~~e) - 1 * ~~~(d ||| (e &&& f)) - 2 * ~~~(d &&& ~~~e) - 3 * (f &&& (d ||| e)) + 2 * (e ||| ~~~(d ||| f)) - 7 * (e ^^^ (d ||| f)) - 6 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 1 * (e ^^^ ~~~(d ||| f)) + 7 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 5 * (e ||| f) - 1 * ((e &&& f) ||| (d &&& (e ||| f))) - 5 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 2 * (f ||| (d ^^^ e)) - 1 * (d ||| (e ||| f)) - 11 * (e ^^^ (d ||| (e ||| f))) - 1 * (e &&& (d ||| f)) + 11 * e + 7 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 6 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 2 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * ((d ||| e) &&& (e ^^^ f)) + 11 * (f ^^^ (d ||| ~~~e)) + 7 * ~~~(d ||| (e ||| f)) + 18 * ~~~(d ||| ( ~~~e ||| f)) + 19 * ~~~( ~~~d ||| (e ||| f)) - 26 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 35 * ( ~~~d &&& ( ~~~e &&& f)) + 55 * (d &&& ( ~~~e &&& f)) + 31 * (d &&& (e &&& f)) = 6 * (e ^^^ (d ||| ( ~~~e &&& f))) - 8 * ( ~~~d &&& (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2337 (x y : BitVec w) : +theorem e_2337 : 4 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 6 * ~~~(d ^^^ (e &&& f)) - 11 * (e ^^^ ~~~(d &&& (e ||| f))) + 2 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 7 * (f ^^^ (d ||| (e &&& f))) - 1 * (d &&& ( ~~~e ||| f)) + 7 * ( ~~~f ||| ~~~(d ^^^ e)) + 7 * ((d &&& e) ||| ~~~(e ||| f)) + 1 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 5 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 4 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 1 * ( ~~~e ||| (d ^^^ f)) - 1 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 11 * ((d ^^^ e) ||| ~~~(d ^^^ f)) + 7 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 11 * (d &&& f) + 11 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 1 * (f ||| ~~~(d ||| ~~~e)) + 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 3 * ( ~~~f &&& ~~~(d ^^^ e)) + 5 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 11 * (d ^^^ (e ||| f)) - 1 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 1 * ( ~~~f ||| (d ^^^ e)) - 2 * ~~~(d ^^^ ( ~~~e &&& f)) + 5 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 2 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 1 * ( ~~~d ||| (e &&& f)) + 2 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 1 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 5 * (e ^^^ ~~~(d ||| f)) + 2 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 3 * ~~~( ~~~d ||| (e ^^^ f)) - 3 * (e ^^^ ( ~~~d ||| (e &&& f))) - 7 * (e ^^^ ( ~~~d &&& (e ||| f))) - 5 * (e ^^^ (d &&& (e ||| f))) - 6 * ~~~(d ^^^ ( ~~~e ||| f)) + 2 * ((e &&& f) ||| (d &&& (e ||| f))) + 4 * (d ^^^ (e &&& f)) + 2 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * ((d ||| ~~~e) &&& (e ^^^ f)) - 6 * (f ^^^ ~~~(d ||| (e &&& f))) + 1 * (d ||| f) + 1 * (e ^^^ (d ||| ~~~f)) + 2 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 1 * (f ^^^ (d ||| ( ~~~e &&& f))) + 2 * (f ^^^ (d &&& ( ~~~e ||| f))) - 7 * (d &&& ~~~e) + 1 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 1 * (e ^^^ ~~~(d &&& ~~~f)) + 4 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 1 * ~~~(d ||| e) - 5 * (d ^^^ ( ~~~e &&& f)) + 1 * (f ^^^ ~~~(d &&& (e &&& f))) + 1 * ~~~( ~~~d ||| (e &&& f)) - 2 * (d &&& (e ^^^ f)) + 3 * ( ~~~d &&& ( ~~~e ||| f)) - 38 * ~~~(d ||| (e ||| f)) - 9 * ~~~(d ||| ( ~~~e ||| f)) - 16 * ~~~( ~~~d ||| (e ||| f)) - 50 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 15 * ( ~~~d &&& ( ~~~e &&& f)) - 14 * ( ~~~d &&& (e &&& f)) - 18 * (d &&& ( ~~~e &&& f)) - 41 * (d &&& (e &&& f)) = - 11 * ~~~(d ^^^ e) + 2 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2338 (x y : BitVec w) : +theorem e_2338 : - 1 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 1 * ~~~(d &&& (e ^^^ f)) + 1 * ((d ||| e) &&& ~~~(e ^^^ f)) - 11 * (d ^^^ e) - 6 * (f ||| ~~~(d ||| ~~~e)) - 5 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 2 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 1 * f - 1 * ((d ^^^ e) ||| ~~~(d ^^^ f)) + 5 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 1 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 6 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 7 * ~~~( ~~~d &&& (e ^^^ f)) + 1 * ~~~(d ^^^ f) + 1 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 7 * ((d &&& e) ^^^ (e ||| ~~~f)) - 2 * (f ^^^ ~~~(d ||| e)) - 11 * (d ||| (e &&& f)) - 7 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 7 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 11 * (f ||| ~~~(d ^^^ e)) + 11 * (e ^^^ (d &&& (e ^^^ f))) - 1 * (e ^^^ (d ||| ( ~~~e &&& f))) - 11 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 2 * ~~~d - 11 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 11 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 3 * e - 7 * ~~~(d &&& ~~~e) - 6 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 1 * (f ^^^ (d &&& (e ||| f))) - 1 * (d ||| ( ~~~e ||| f)) + 2 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 7 * (f ^^^ (d ||| ( ~~~e ||| f))) + 5 * ((d ||| e) &&& (e ^^^ f)) + 1 * (d ||| ~~~e) + 7 * ( ~~~e &&& (d ^^^ f)) - 1 * (f ^^^ (d &&& e)) - 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 6 * ~~~(e ||| ~~~f) - 1 * (d ^^^ ( ~~~e ||| f)) - 1 * (e ||| f) - 1 * ~~~(e &&& ~~~f) - 2 * ( ~~~d ||| (e ^^^ f)) + 7 * ~~~(d &&& ~~~d) - 3 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 3 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 7 * (e ^^^ ( ~~~d ||| (e ||| f))) + 1 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 3 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 3 * (d ^^^ (e ^^^ f)) + 2 * ( ~~~f &&& ~~~(d ^^^ e)) - 3 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 4 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 1 * ( ~~~e ||| (d ^^^ f)) + 1 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 2 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 13 * ~~~(d ||| (e ||| f)) + 33 * ~~~(d ||| ( ~~~e ||| f)) + 48 * ~~~( ~~~d ||| (e ||| f)) + 5 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 2 * ( ~~~d &&& ( ~~~e &&& f)) + 31 * ( ~~~d &&& (e &&& f)) + 21 * (d &&& ( ~~~e &&& f)) - 3 * (d &&& (e &&& f)) = - 4 * (f &&& ~~~(d &&& e)) - 2 * ~~~(d ||| f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2339 (x y : BitVec w) : +theorem e_2339 : 2 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 1 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 4 * ~~~(d &&& (e &&& f)) + 11 * ~~~( ~~~d &&& (e &&& f)) + 2 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 11 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 4 * (e ^^^ ~~~(d &&& f)) + 3 * ((e &&& f) ||| (d &&& (e ||| f))) + 7 * (f &&& ~~~(d ^^^ e)) - 5 * (e ^^^ (d ||| (e ^^^ f))) - 2 * (e ^^^ ( ~~~d &&& (e ||| f))) - 6 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 7 * e - 5 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 1 * ~~~( ~~~d &&& (e ||| f)) + 2 * (f ^^^ ~~~(d &&& ~~~e)) + 5 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 2 * ~~~(d &&& ~~~e) - 3 * (d ||| f) - 6 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 1 * (e ^^^ ~~~(d ||| (e &&& f))) + 7 * (e ^^^ (d ||| (e &&& f))) + 11 * (d ^^^ (e ||| f)) + 11 * ~~~(e &&& ~~~f) + 5 * (d ||| ~~~f) - 6 * ((d &&& f) ||| ~~~(e ||| f)) + 2 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (f ||| ~~~(d ||| e)) + 4 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 11 * (d ^^^ e) - 3 * (f ^^^ ( ~~~d &&& (e ||| f))) + 5 * ~~~(e &&& f) + 5 * (e ||| (d ^^^ f)) - 1 * ((d ||| e) &&& (e ^^^ f)) - 1 * (d &&& ~~~f) + 3 * (d ||| (e ||| f)) - 6 * ((d ||| ~~~e) &&& (e ^^^ f)) - 1 * ((d &&& f) ^^^ (e ||| f)) - 5 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 1 * ~~~(d ^^^ (e ^^^ f)) - 2 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 1 * ~~~(d &&& ( ~~~e &&& f)) - 1 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 11 * (e ||| ~~~f) - 5 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 2 * (f ^^^ ~~~(d ||| (e &&& f))) + 5 * ((d &&& e) ^^^ (e ||| ~~~f)) + 1 * ~~~(d ^^^ ( ~~~e &&& f)) - 3 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 7 * ~~~(d &&& ( ~~~e ||| f)) - 7 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 5 * ~~~( ~~~d ||| (e ^^^ f)) + 1 * (e &&& f) - 5 * (d ||| ~~~e) + 1 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 2 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 11 * (e ^^^ (d &&& ( ~~~e ||| f))) + 10 * ~~~(d ||| (e ||| f)) - 4 * ~~~(d ||| ( ~~~e ||| f)) + 12 * ~~~( ~~~d ||| (e ||| f)) + 20 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 18 * ( ~~~d &&& ( ~~~e &&& f)) + 23 * ( ~~~d &&& (e &&& f)) + 12 * (d &&& ( ~~~e &&& f)) + 18 * (d &&& (e &&& f)) = - 2 * ( ~~~d &&& (e ||| f)) + 2 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2340 (x y : BitVec w) : +theorem e_2340 : - 5 * (e ^^^ ~~~(d &&& ~~~f)) - 1 * (f ||| ~~~(d ||| ~~~e)) - 3 * (e ||| (d ^^^ f)) - 11 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 2 * (d ^^^ (e &&& f)) + 3 * (e ||| (d &&& ~~~f)) + 2 * ( ~~~d &&& ( ~~~e ||| f)) + 1 * ~~~(d ^^^ ( ~~~e &&& f)) - 3 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 5 * ~~~(e ^^^ f) + 1 * (e ^^^ ~~~(d ||| ~~~f)) + 3 * (e ||| ~~~f) + 4 * (e ||| ~~~(d ||| ~~~f)) + 1 * ( ~~~f ||| (d ^^^ e)) - 5 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 1 * (e ^^^ (d ||| (e &&& f))) + 1 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 1 * ((d ||| e) &&& (e ^^^ f)) + 7 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 6 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 4 * ((d &&& e) ||| (e ^^^ f)) - 5 * ~~~(d &&& e) + 2 * (e ^^^ (d ||| ~~~f)) - 1 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 1 * ~~~(d ^^^ e) + 7 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 7 * ( ~~~e ||| (d ^^^ f)) - 2 * (f &&& ~~~(d ^^^ e)) - 3 * ( ~~~d ||| ( ~~~e ||| f)) - 1 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 1 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 3 * (f ^^^ (d ||| ( ~~~e ||| f))) + 11 * (e ||| (d &&& f)) - 6 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 1 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 1 * ~~~(d ||| (e &&& f)) - 2 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 2 * (e &&& (d ^^^ f)) + 11 * ~~~(d &&& (e ||| f)) + 7 * ( ~~~d ||| (e ||| f)) - 6 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 2 * ((d &&& f) ||| ~~~(e ||| f)) - 11 * (e &&& ~~~(d ^^^ f)) - 1 * ~~~(d &&& ( ~~~e &&& f)) - 11 * ~~~(d &&& ~~~e) + 1 * ((d &&& e) ||| ~~~(e ||| f)) + 4 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 3 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 7 * ((d &&& e) ||| ~~~(e ^^^ f)) - 5 * (d &&& f) - 7 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 5 * ~~~(d ^^^ (e ||| f)) + 3 * ~~~(d ^^^ (e &&& f)) + 2 * (f ^^^ (d ||| ( ~~~e &&& f))) + 11 * ( ~~~f ||| ~~~(d ^^^ e)) + 2 * (e &&& f) + 5 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 1 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 4 * ~~~(d ||| (e ||| f)) - 24 * ~~~(d ||| ( ~~~e ||| f)) - 11 * ~~~( ~~~d ||| (e ||| f)) - 20 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 13 * ( ~~~d &&& ( ~~~e &&& f)) - 5 * ( ~~~d &&& (e &&& f)) - 13 * (d &&& ( ~~~e &&& f)) - 3 * (d &&& (e &&& f)) = - 5 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2341 (x y : BitVec w) : +theorem e_2341 : - 1 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 7 * (e ||| f) - 2 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 7 * ~~~(e ^^^ f) - 2 * (e ^^^ ~~~(d &&& (e ||| f))) - 5 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 2 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 4 * (e ^^^ (d &&& f)) + 4 * e + 2 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 1 * ~~~(d &&& (e &&& f)) + 1 * ~~~( ~~~d ||| (e &&& f)) - 11 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 7 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 2 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 1 * ~~~(d ||| ~~~e) - 3 * (d ^^^ ( ~~~e &&& f)) - 11 * (e &&& ~~~(d &&& ~~~f)) + 5 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 11 * ~~~(d &&& ~~~d) - 11 * (f &&& ~~~(d &&& ~~~e)) + 7 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 1 * ((d &&& e) ^^^ (e ||| ~~~f)) + 1 * ~~~(e &&& ~~~f) - 3 * (f ^^^ (d &&& ( ~~~e ||| f))) + 1 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 3 * ( ~~~e &&& (d ^^^ f)) - 1 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 5 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 11 * (e ||| ~~~(d ^^^ f)) - 2 * (e ^^^ (d ||| ( ~~~e &&& f))) + 1 * (e ^^^ ~~~(d &&& (e &&& f))) + 1 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 2 * ~~~(e &&& f) + 11 * ~~~(d ^^^ (e ||| f)) + 3 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 5 * ~~~(d ^^^ (e &&& f)) - 7 * ((e &&& f) ||| (d &&& (e ||| f))) + 1 * (d ||| ~~~f) - 3 * (e ^^^ (d ||| (e ||| f))) - 1 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 1 * (f ||| (d &&& ~~~e)) + 4 * (e &&& ~~~(d ^^^ f)) + 1 * ( ~~~d &&& (e ^^^ f)) - 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 5 * (e &&& (d ||| f)) - 2 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 11 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 7 * ( ~~~d ||| ( ~~~e &&& f)) - 11 * ( ~~~e ||| ~~~(d ^^^ f)) + 3 * ((d &&& e) ||| (e ^^^ f)) + 3 * (e ^^^ (d &&& ~~~f)) - 6 * ~~~( ~~~d &&& (e ||| f)) - 7 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 4 * ~~~(d ||| ~~~f) - 13 * ~~~(d ||| (e ||| f)) - 39 * ~~~(d ||| ( ~~~e ||| f)) + 31 * ~~~( ~~~d ||| (e ||| f)) - 14 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 7 * ( ~~~d &&& ( ~~~e &&& f)) - 4 * ( ~~~d &&& (e &&& f)) + 2 * (d &&& ( ~~~e &&& f)) - 11 * (d &&& (e &&& f)) = 5 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 5 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2342 (x y : BitVec w) : +theorem e_2342 : - 7 * (e ||| f) - 7 * (e ^^^ ~~~(d ||| (e &&& f))) - 6 * ((d ||| e) &&& ~~~(e ^^^ f)) - 1 * (e &&& (d ^^^ f)) + 4 * (f ^^^ (d &&& ( ~~~e ||| f))) + 11 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 4 * ~~~(d ^^^ (e &&& f)) + 4 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 7 * (e ||| ~~~(d ^^^ f)) + 1 * ((d ^^^ e) ||| ~~~(d ^^^ f)) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 3 * ( ~~~d &&& (e ^^^ f)) - 2 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * ((d &&& f) ||| (e &&& ~~~f)) + 1 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * ( ~~~f &&& (d ^^^ e)) + 2 * (e ^^^ (d ||| ~~~f)) + 4 * ((d &&& ~~~e) ||| (e ^^^ f)) + 2 * ~~~(d ^^^ (e ^^^ f)) + 5 * (e &&& (d ||| ~~~f)) - 2 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 2 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 3 * ( ~~~e ||| (d ^^^ f)) - 2 * (d ^^^ ( ~~~e &&& f)) + 5 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 1 * ( ~~~d ||| (e ||| f)) - 6 * (f ^^^ ( ~~~d &&& (e ||| f))) + 1 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 1 * (e ^^^ (d ||| ( ~~~e &&& f))) - 5 * (d ||| f) + 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 7 * ( ~~~f &&& ~~~(d ^^^ e)) - 5 * (e ^^^ ~~~(d ||| ~~~f)) + 5 * (f ^^^ ~~~(d &&& e)) - 11 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 5 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 3 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 1 * ~~~( ~~~d &&& (e ||| f)) + 11 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 6 * ~~~(d &&& (e ^^^ f)) + 5 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 5 * (f ^^^ (d &&& (e ||| f))) + 1 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 11 * (f ^^^ ~~~(d ||| e)) + 3 * ~~~(d ||| ~~~e) + 4 * (e ^^^ (d ||| (e &&& f))) - 1 * ( ~~~e &&& (d ^^^ f)) - 2 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 7 * (d ||| e) + 4 * ~~~(d &&& ( ~~~e &&& f)) - 1 * (e ^^^ (d &&& (e ||| f))) - 2 * ((d ||| ~~~e) &&& (e ^^^ f)) - 2 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 1 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 7 * ~~~( ~~~d ||| (e ^^^ f)) + 2 * ( ~~~f ||| (d ^^^ e)) - 1 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 18 * ~~~(d ||| (e ||| f)) - 19 * ~~~(d ||| ( ~~~e ||| f)) - 39 * ~~~( ~~~d ||| (e ||| f)) + 16 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 34 * ( ~~~d &&& ( ~~~e &&& f)) + 15 * ( ~~~d &&& (e &&& f)) - 2 * (d &&& ( ~~~e &&& f)) = - 20 * (d &&& (e &&& f)) + 2 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2343 (x y : BitVec w) : +theorem e_2343 : - 1 * (f ||| (d &&& ~~~e)) + 11 * (e ||| ~~~(d ||| ~~~f)) + 2 * (e ^^^ (d ||| f)) + 1 * ~~~( ~~~d ||| (e ^^^ f)) + 7 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 1 * ~~~(d &&& ( ~~~e &&& f)) - 7 * (f ^^^ (d ||| (e &&& f))) - 7 * (e ^^^ ~~~(d &&& ~~~f)) + 3 * (f ^^^ (d &&& (e ||| f))) - 1 * (e &&& (d ||| ~~~f)) - 6 * (d ^^^ e) + 2 * ~~~( ~~~d &&& (e &&& f)) + 5 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 11 * ~~~(d &&& e) + 4 * (e ||| ~~~(d ||| f)) + 4 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 2 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 1 * ~~~( ~~~d &&& (e ||| f)) - 1 * ~~~(d &&& (e ||| f)) + 3 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 5 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 3 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 1 * ~~~( ~~~d ||| (e &&& f)) - 5 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 1 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 11 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 4 * (e &&& ~~~(d &&& f)) - 7 * ~~~(d ||| (e ^^^ f)) + 1 * (d &&& (e ^^^ f)) - 1 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 1 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 2 * ~~~(d ||| ~~~f) + 2 * (f ^^^ ~~~(d ||| ~~~e)) - 7 * ~~~e - 2 * (d ||| (e ^^^ f)) + 7 * (e ^^^ (d ||| ( ~~~e &&& f))) - 2 * ((d ^^^ e) ||| (d ^^^ f)) + 1 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 7 * (f ^^^ ~~~(d &&& (e &&& f))) + 5 * ~~~(d ^^^ (e ^^^ f)) + 11 * ( ~~~d &&& ( ~~~e ||| f)) + 2 * (e &&& (d ^^^ f)) + 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * ( ~~~d &&& (e ||| f)) + 1 * (f ||| ~~~(d ||| ~~~e)) + 1 * (d &&& e) - 5 * (d ^^^ (e &&& f)) + 1 * (e ^^^ f) - 1 * ~~~(e ||| ~~~f) - 6 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (e ^^^ (d &&& (e ^^^ f))) - 1 * (e ^^^ ~~~(d &&& (e &&& f))) - 5 * ((d &&& f) ^^^ (e ||| f)) + 1 * (e ||| (d &&& ~~~f)) + 1 * ~~~(d &&& (e ^^^ f)) - 3 * (f ^^^ (d &&& ~~~e)) - 5 * (e ^^^ ( ~~~d ||| (e &&& f))) + 2 * ( ~~~d ||| ( ~~~e ||| f)) - 20 * ~~~(d ||| (e ||| f)) - 39 * ~~~(d ||| ( ~~~e ||| f)) + 1 * ( ~~~d &&& ( ~~~e &&& f)) - 29 * ( ~~~d &&& (e &&& f)) - 7 * (d &&& ( ~~~e &&& f)) - 16 * (d &&& (e &&& f)) = 5 * ~~~( ~~~d ||| ( ~~~e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2344 (x y : BitVec w) : +theorem e_2344 : - 1 * ~~~d - 5 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 2 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 11 * ((d ^^^ e) ||| (d ^^^ f)) + 1 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 3 * (d ||| e) - 11 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 11 * ~~~(d ^^^ (e &&& f)) - 3 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 6 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 7 * (f ^^^ (d &&& e)) + 2 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 2 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * (e ||| (d &&& f)) - 1 * ~~~(d ||| (e ^^^ f)) + 1 * (e ||| ~~~(d ||| f)) - 5 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 7 * (d ^^^ e) + 11 * (f ^^^ (d &&& (e ||| f))) + 1 * (e &&& ~~~(d ^^^ f)) - 7 * (e ||| (d ^^^ f)) - 1 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 1 * ~~~(d ||| ~~~e) + 1 * (e ^^^ ( ~~~d &&& (e ||| f))) - 6 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 1 * (e &&& ~~~(d &&& ~~~f)) + 2 * ~~~( ~~~d ||| (e &&& f)) - 1 * ( ~~~d ||| ( ~~~e &&& f)) - 1 * ( ~~~f ||| (d ^^^ e)) + 1 * (f ^^^ ~~~(d &&& (e &&& f))) + 5 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 4 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 1 * ~~~(e &&& ~~~f) - 6 * ( ~~~d &&& (e ||| f)) + 2 * ~~~( ~~~d &&& (e &&& f)) + 2 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 1 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 11 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 3 * (d ||| ~~~e) - 11 * (f ^^^ (d ||| ( ~~~e ||| f))) + 5 * (e ^^^ ( ~~~d ||| (e &&& f))) + 4 * ~~~(d &&& ~~~d) - 1 * (f &&& ~~~(d &&& e)) + 5 * (f ^^^ ~~~(d &&& ~~~e)) + 5 * (e &&& ~~~f) + 1 * ( ~~~e &&& (d ^^^ f)) + 1 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 1 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 5 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 2 * ( ~~~e ||| ~~~(d ^^^ f)) + 11 * ( ~~~f &&& (d ^^^ e)) + 1 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 3 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 2 * (f &&& ~~~(d &&& ~~~e)) + 2 * (e ^^^ (d &&& ( ~~~e ||| f))) - 3 * (e &&& f) + 2 * (f ^^^ (d &&& ~~~e)) + 34 * ~~~(d ||| (e ||| f)) + 7 * ~~~(d ||| ( ~~~e ||| f)) + 18 * ~~~( ~~~d ||| (e ||| f)) - 13 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 8 * ( ~~~d &&& ( ~~~e &&& f)) + 3 * ( ~~~d &&& (e &&& f)) + 1 * (d &&& ( ~~~e &&& f)) + 34 * (d &&& (e &&& f)) = - 1 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 1 * (e ||| (d &&& ~~~f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2345 (x y : BitVec w) : +theorem e_2345 : - 2 * ~~~(d ||| e) - 7 * ~~~(d ^^^ ( ~~~e ||| f)) + 5 * ((d &&& f) ^^^ (e ||| f)) - 7 * (f ||| ~~~(d ^^^ e)) - 11 * (f ^^^ ~~~(d ||| ~~~e)) + 3 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 2 * (f ||| (d &&& ~~~e)) + 2 * ((d &&& e) ||| ~~~(e ^^^ f)) + 1 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 1 * (d &&& ~~~f) - 3 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 2 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 3 * ~~~(d ||| ~~~e) - 5 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 11 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 2 * ((e &&& f) ||| (d &&& (e ||| f))) + 1 * (f ^^^ ~~~(d ||| e)) + 1 * ~~~f + 1 * ((d &&& e) ||| (e ^^^ f)) + 2 * ~~~(d &&& ( ~~~e &&& f)) - 5 * (d ^^^ e) - 1 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 11 * (d &&& ( ~~~e ||| f)) + 1 * ~~~(d &&& ~~~e) - 1 * ( ~~~d ||| (e &&& f)) - 2 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 1 * ((d &&& f) ||| ~~~(e ||| f)) - 11 * ( ~~~d &&& (e ||| f)) + 1 * (e ^^^ (d &&& ( ~~~e ||| f))) + 4 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 1 * (f ^^^ (d &&& ~~~e)) - 7 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 11 * ~~~( ~~~d ||| (e ^^^ f)) - 1 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 3 * ( ~~~e &&& (d ^^^ f)) + 11 * (d ^^^ (e &&& f)) + 1 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 4 * (f ^^^ (d ||| (e &&& f))) + 4 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 1 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 1 * ( ~~~d ||| ( ~~~e &&& f)) - 2 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 1 * (f ^^^ ~~~(d &&& ~~~e)) - 1 * (e &&& ~~~(d ^^^ f)) - 2 * (d ||| (e &&& f)) + 5 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 2 * (e ^^^ (d ||| ( ~~~e &&& f))) - 2 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 5 * ~~~(d &&& f) + 7 * ~~~(e ^^^ f) + 2 * ~~~(d &&& (e &&& f)) - 3 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 6 * ~~~(d &&& (e ^^^ f)) + 1 * ~~~( ~~~d &&& (e &&& f)) + 1 * (e ||| (d ^^^ f)) - 2 * (d ||| (e ||| f)) - 3 * ~~~(d ^^^ ( ~~~e &&& f)) + 3 * (d ^^^ f) + 33 * ~~~(d ||| (e ||| f)) + 39 * ~~~(d ||| ( ~~~e ||| f)) - 9 * ~~~( ~~~d ||| (e ||| f)) - 34 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 41 * ( ~~~d &&& ( ~~~e &&& f)) + 14 * ( ~~~d &&& (e &&& f)) + 51 * (d &&& ( ~~~e &&& f)) + 13 * (d &&& (e &&& f)) = - 11 * (d &&& (e ||| f)) + 1 * ~~~(e ||| ~~~f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2346 (x y : BitVec w) : +theorem e_2346 : - 2 * (f &&& ~~~(d &&& ~~~e)) - 2 * (f ^^^ (d ||| ( ~~~e &&& f))) + 4 * (f ||| (d &&& ~~~e)) + 2 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 1 * (e ^^^ (d &&& ~~~f)) + 7 * ( ~~~e &&& ~~~(d ^^^ f)) + 2 * ( ~~~d ||| (e ^^^ f)) - 7 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * (f ^^^ (d ||| ( ~~~e ||| f))) + 2 * (f ^^^ ( ~~~d ||| (e &&& f))) + 5 * ( ~~~d &&& ( ~~~e ||| f)) + 2 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 5 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 1 * (d &&& ~~~f) + 11 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 3 * ~~~(d &&& ( ~~~e ||| f)) - 1 * ~~~(d &&& ~~~d) - 1 * ( ~~~d ||| ( ~~~e &&& f)) + 2 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 4 * ( ~~~e ||| (d ^^^ f)) - 1 * d - 7 * (e ^^^ ( ~~~d &&& (e ||| f))) + 5 * (d ^^^ (e &&& f)) - 11 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 2 * ~~~(d &&& (e ||| f)) - 6 * ((d &&& e) ||| ~~~(e ^^^ f)) - 2 * ~~~(d ^^^ (e ^^^ f)) - 3 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 3 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 6 * ((d &&& e) ||| (e ^^^ f)) - 6 * (e ||| ~~~(d ||| f)) + 4 * (e &&& (d ^^^ f)) - 3 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 1 * ((d ||| ~~~e) &&& (e ^^^ f)) + 5 * (e ^^^ (d ||| ~~~f)) - 1 * (f ||| ~~~(d ||| e)) - 11 * (f ^^^ (d &&& e)) - 6 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 1 * ((d ^^^ e) &&& (d ^^^ f)) - 2 * (e ||| ~~~(d ^^^ f)) - 3 * (e ^^^ (d &&& (e ^^^ f))) - 11 * (e ^^^ (d ||| ( ~~~e &&& f))) - 1 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 2 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 3 * ~~~(d ||| ~~~f) + 1 * (d ||| (e ||| f)) + 1 * ~~~(d &&& (e &&& f)) - 2 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 5 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 5 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 2 * ~~~e - 1 * (f ||| (d &&& e)) - 1 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 2 * (f ||| ~~~(d ^^^ e)) + 4 * ~~~(d ^^^ (e &&& f)) + 1 * ~~~(d &&& ( ~~~e &&& f)) - 1 * e - 2 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 12 * ~~~(d ||| (e ||| f)) + 34 * ~~~(d ||| ( ~~~e ||| f)) + 5 * ~~~( ~~~d ||| (e ||| f)) + 57 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 38 * ( ~~~d &&& ( ~~~e &&& f)) + 16 * ( ~~~d &&& (e &&& f)) + 23 * (d &&& ( ~~~e &&& f)) + 54 * (d &&& (e &&& f)) = 5 * ( ~~~f &&& ~~~(d ^^^ e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2347 (x y : BitVec w) : +theorem e_2347 : - 5 * (f ^^^ ( ~~~d &&& (e ||| f))) + 2 * (d ||| f) - 6 * ( ~~~d &&& (e ^^^ f)) + 3 * ~~~(d ^^^ e) + 5 * (f ^^^ ~~~(d &&& (e ||| f))) + 3 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 5 * ~~~(d &&& ~~~e) - 6 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 2 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 2 * (e ^^^ (d ||| ~~~f)) + 5 * (e ||| (d ^^^ f)) + 7 * (f ||| ~~~(d ||| ~~~e)) - 1 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 2 * ~~~(d &&& (e ^^^ f)) - 2 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * (e ^^^ (d ||| ( ~~~e &&& f))) + 4 * (e ^^^ ~~~(d &&& (e &&& f))) + 3 * ~~~(d ||| (e ^^^ f)) - 3 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 1 * (f ||| (d &&& ~~~e)) - 1 * (e ^^^ ~~~(d ||| (e &&& f))) - 2 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 2 * (e &&& f) + 4 * (e ^^^ (d &&& ( ~~~e ||| f))) + 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 11 * ( ~~~f &&& ~~~(d ^^^ e)) - 3 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 2 * ((d &&& e) ^^^ (e ||| f)) + 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 1 * ~~~( ~~~d &&& (e ^^^ f)) + 1 * (d &&& ~~~e) - 1 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 7 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 3 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 7 * (f ^^^ (d ||| ~~~e)) - 7 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 7 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 3 * ((d ^^^ e) ||| (d ^^^ f)) + 11 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 1 * (e ^^^ (d ||| ( ~~~e ||| f))) - 1 * ((e &&& f) ||| (d &&& (e ||| f))) + 5 * ( ~~~d ||| (e ^^^ f)) + 4 * ~~~(d ||| f) - 7 * (e ||| (d &&& ~~~f)) - 6 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 2 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 3 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 3 * ((d &&& e) ^^^ (e ||| ~~~f)) + 5 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 5 * (f ||| ~~~(d ||| e)) + 1 * (e &&& ~~~(d &&& f)) - 1 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 2 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 1 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 1 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 3 * (e ||| ~~~(d ||| ~~~f)) - 11 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 5 * ( ~~~f ||| (d ^^^ e)) + 11 * ~~~(d ||| (e ||| f)) - 1 * ~~~( ~~~d ||| (e ||| f)) + 6 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 10 * ( ~~~d &&& ( ~~~e &&& f)) - 6 * ( ~~~d &&& (e &&& f)) + 18 * (d &&& ( ~~~e &&& f)) + 4 * (d &&& (e &&& f)) = - 7 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 3 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2348 (x y : BitVec w) : +theorem e_2348 : 1 * ((d ||| ~~~e) &&& (e ^^^ f)) + 3 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 1 * (e ^^^ (d ||| (e ||| f))) - 1 * (e ^^^ ~~~(d ||| f)) - 3 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 1 * (e ^^^ (d &&& ( ~~~e ||| f))) - 2 * ( ~~~d ||| (e ||| f)) + 7 * ((d &&& e) ||| ~~~(e ^^^ f)) - 2 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 5 * (d ^^^ (e ||| f)) - 6 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 1 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 1 * (f ||| (d ^^^ e)) + 2 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 3 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 7 * ~~~(d &&& ~~~d) + 11 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 1 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 6 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 6 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * (e ||| (d &&& ~~~f)) + 7 * (e &&& ~~~(d &&& f)) + 1 * ( ~~~e &&& ~~~(d ^^^ f)) + 2 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 7 * ( ~~~e ||| (d ^^^ f)) - 5 * (e ||| ~~~f) + 1 * (f &&& (d ||| ~~~e)) - 11 * (f ^^^ ( ~~~d ||| (e ||| f))) + 5 * ((d &&& ~~~e) ||| (e ^^^ f)) - 2 * ( ~~~f &&& (d ^^^ e)) - 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 2 * (d ||| f) + 1 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 1 * (f &&& ~~~(d &&& e)) + 11 * (e ^^^ (d ||| ~~~f)) + 1 * ~~~(d ^^^ (e ^^^ f)) - 3 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 1 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 1 * (e ^^^ ~~~(d ||| ~~~f)) - 1 * (d ||| e) + 3 * (d ^^^ e) + 5 * (e &&& ~~~f) + 1 * ((d ||| e) &&& ~~~(e ^^^ f)) + 1 * (e ^^^ f) - 1 * ( ~~~d &&& (e ^^^ f)) - 6 * ~~~(e &&& ~~~f) + 7 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 7 * (d &&& ( ~~~e ||| f)) + 2 * (d &&& ~~~f) + 4 * ( ~~~d ||| ( ~~~e ||| f)) + 2 * (e &&& ~~~(d ^^^ f)) + 4 * ( ~~~e ||| ~~~(d ^^^ f)) - 1 * f - 11 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 3 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 11 * (f &&& ~~~(d ^^^ e)) - 2 * ~~~(d ^^^ e) - 5 * ~~~(e ||| ~~~f) - 7 * e + 8 * ~~~(d ||| (e ||| f)) + 16 * ~~~(d ||| ( ~~~e ||| f)) - 17 * ~~~( ~~~d ||| (e ||| f)) + 31 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 1 * ( ~~~d &&& ( ~~~e &&& f)) - 11 * ( ~~~d &&& (e &&& f)) + 4 * (d &&& ( ~~~e &&& f)) - 23 * (d &&& (e &&& f)) = - 4 * (f ^^^ (d &&& (e ||| f))) + 6 * ((d ||| e) &&& (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2349 (x y : BitVec w) : +theorem e_2349 : 4 * (f ^^^ ~~~(d ||| e)) - 1 * (f ||| (d ^^^ e)) - 2 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 5 * (f &&& ~~~(d &&& e)) - 3 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 11 * ~~~(e &&& ~~~f) + 7 * (e ||| ~~~(d ||| f)) + 5 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 7 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 1 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 1 * (f ^^^ ~~~(d ||| (e &&& f))) + 4 * (d ||| (e &&& f)) + 11 * (e ||| (d &&& f)) + 4 * (d &&& (e ||| f)) + 1 * ~~~(e &&& f) - 1 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 6 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 1 * (e ^^^ ~~~(d &&& f)) - 6 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 5 * ~~~(d ^^^ f) - 2 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 1 * ( ~~~d &&& (e ||| f)) - 5 * e - 1 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 1 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 1 * (f ^^^ ~~~(d &&& (e ||| f))) + 7 * (d &&& ( ~~~e ||| f)) - 11 * ~~~(d &&& (e ^^^ f)) + 3 * (d ^^^ e) + 5 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 2 * ~~~(d ||| ~~~e) - 1 * (e &&& (d ^^^ f)) + 2 * (f ^^^ (d &&& (e ||| f))) - 2 * ~~~(d &&& e) + 7 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 1 * ~~~f + 3 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 11 * (e ^^^ ~~~(d ||| f)) + 3 * (f &&& ~~~(d ^^^ e)) - 6 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 2 * ((d &&& f) ||| ~~~(e ||| f)) - 2 * ( ~~~d ||| ( ~~~e ||| f)) - 3 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 2 * (d ||| (e ^^^ f)) - 5 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 7 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 11 * ((d &&& e) ||| (e ^^^ f)) - 7 * ~~~( ~~~d ||| (e ^^^ f)) - 1 * (e &&& ~~~f) + 11 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * (e ||| f) - 7 * ( ~~~f ||| (d ^^^ e)) + 5 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 2 * (e &&& (d ||| ~~~f)) - 1 * ((e &&& f) ||| (d &&& (e ||| f))) + 2 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * (f ^^^ ~~~(d &&& e)) - 2 * ~~~(d ||| (e ||| f)) - 2 * ~~~(d ||| ( ~~~e ||| f)) + 4 * ~~~( ~~~d ||| (e ||| f)) - 17 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 43 * ( ~~~d &&& ( ~~~e &&& f)) - 4 * ( ~~~d &&& (e &&& f)) - 5 * (d &&& ( ~~~e &&& f)) - 12 * (d &&& (e &&& f)) = 5 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2350 (x y : BitVec w) : +theorem e_2350 : 1 * (f ^^^ (d ||| ( ~~~e &&& f))) + 11 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 5 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 2 * ((d ||| ~~~e) &&& (e ^^^ f)) - 6 * (f ^^^ (d ||| ( ~~~e ||| f))) - 1 * ( ~~~e &&& (d ^^^ f)) - 2 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 1 * (f ||| (d &&& ~~~e)) + 1 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 11 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 2 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 1 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 11 * (e ||| (d ^^^ f)) + 4 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 6 * (f &&& (d ^^^ e)) - 7 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 6 * ( ~~~d ||| ( ~~~e ||| f)) - 2 * (e ^^^ ~~~(d ||| ~~~f)) + 2 * ~~~(d &&& ( ~~~e ||| f)) + 2 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 1 * ~~~(d &&& f) - 11 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 1 * ((d &&& e) ||| (e ^^^ f)) + 11 * ((d ^^^ e) ||| (d ^^^ f)) - 6 * ~~~(d &&& ~~~d) - 3 * ((d &&& e) ^^^ (e ||| ~~~f)) + 4 * ((d &&& f) ^^^ (e ||| f)) - 3 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 1 * ( ~~~f ||| (d ^^^ e)) + 1 * ((d ||| e) &&& ~~~(e ^^^ f)) - 3 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 6 * ( ~~~e &&& ~~~(d ^^^ f)) + 3 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 5 * ~~~(d &&& e) - 2 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 3 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 4 * (d ^^^ e) - 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 3 * (f ||| ~~~(d ||| e)) - 5 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 2 * (d &&& ~~~f) + 1 * (f ||| (d ^^^ e)) + 1 * ((d &&& f) ||| (e &&& ~~~f)) - 7 * (e &&& (d ||| f)) + 2 * (f ||| ~~~(d ||| ~~~e)) - 7 * (e ^^^ (d &&& (e ||| f))) - 5 * ( ~~~d ||| (e &&& f)) + 7 * (e ^^^ (d ||| (e ^^^ f))) + 4 * (e &&& (d ^^^ f)) - 2 * ( ~~~d &&& (e ||| f)) - 1 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 3 * (d ^^^ (e &&& f)) - 3 * (e ^^^ ~~~(d ||| f)) - 2 * (f ||| ~~~(d ^^^ e)) + 7 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 2 * (e ||| f) + 1 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 1 * ~~~(d ||| ~~~f) + 1 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 7 * ~~~(d ||| (e ||| f)) + 15 * ~~~(d ||| ( ~~~e ||| f)) - 20 * ~~~( ~~~d ||| (e ||| f)) + 38 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 18 * ( ~~~d &&& ( ~~~e &&& f)) - 8 * ( ~~~d &&& (e &&& f)) - 15 * (d &&& ( ~~~e &&& f)) + 38 * (d &&& (e &&& f)) = - 2 * (f ^^^ ~~~(d &&& (e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2351 (x y : BitVec w) : +theorem e_2351 : - 7 * ((d &&& e) ||| (e ^^^ f)) + 5 * ~~~(d ^^^ ( ~~~e &&& f)) + 7 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 7 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 1 * (d ^^^ (e &&& f)) - 2 * (d &&& e) - 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 1 * ~~~(d &&& ( ~~~e ||| f)) - 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 11 * (d ||| e) + 2 * (e ||| (d &&& ~~~f)) + 2 * ~~~(d ||| ( ~~~e &&& f)) + 1 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 1 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 7 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 2 * (f ||| ~~~(d ^^^ e)) - 5 * (f ||| ~~~(d ||| e)) - 6 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 11 * (f ^^^ ( ~~~d ||| (e &&& f))) - 7 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 6 * (e ||| (d &&& f)) + 11 * ((d ||| e) &&& (e ^^^ f)) - 3 * ~~~( ~~~d ||| (e &&& f)) + 1 * ~~~(d ||| ~~~e) - 2 * (d &&& ( ~~~e ||| f)) + 1 * ~~~(d ^^^ (e &&& f)) + 4 * (f ^^^ ( ~~~d &&& (e ||| f))) - 2 * (f ^^^ ~~~(d ||| ~~~e)) + 5 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 1 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 1 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 7 * ~~~(d ^^^ e) + 2 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 4 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * (f ^^^ (d ||| (e ||| f))) + 1 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * ~~~(d ||| (e &&& f)) + 4 * (f &&& ~~~(d &&& e)) - 3 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 1 * ~~~(d ||| f) + 7 * (f ||| (d &&& e)) - 2 * ((e &&& f) ||| (d &&& (e ||| f))) - 11 * ~~~(d &&& f) + 2 * ( ~~~f ||| ~~~(d ^^^ e)) + 1 * ~~~(e &&& ~~~f) + 2 * ~~~( ~~~d &&& (e &&& f)) - 1 * ((d &&& e) ^^^ (e ||| ~~~f)) - 11 * (d ||| (e ^^^ f)) - 2 * (f &&& (d ||| e)) + 2 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 3 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 2 * (f ||| ~~~(d ||| ~~~e)) + 7 * (e ^^^ (d ||| f)) - 6 * ~~~(d &&& ( ~~~e &&& f)) - 1 * (e ^^^ ~~~(d &&& f)) - 1 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 5 * (f &&& (d ||| ~~~e)) + 1 * ( ~~~d ||| (e &&& f)) + 1 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 6 * ~~~(d ||| (e ||| f)) - 21 * ~~~(d ||| ( ~~~e ||| f)) + 19 * ~~~( ~~~d ||| (e ||| f)) - 3 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 10 * ( ~~~d &&& ( ~~~e &&& f)) + 11 * ( ~~~d &&& (e &&& f)) - 27 * (d &&& ( ~~~e &&& f)) + 20 * (d &&& (e &&& f)) = 1 * ~~~d := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2352 (x y : BitVec w) : +theorem e_2352 : - 3 * ((d &&& e) ||| ~~~(e ^^^ f)) + 5 * (e ^^^ ~~~(d &&& (e &&& f))) - 2 * ( ~~~d ||| ( ~~~e ||| f)) - 11 * (f ||| (d &&& e)) + 4 * ~~~(d &&& e) - 1 * (e &&& (d ||| f)) - 11 * (f ^^^ ( ~~~d ||| (e &&& f))) - 2 * ~~~(d &&& ~~~f) - 7 * (e &&& (d ||| ~~~f)) + 1 * ( ~~~d ||| (e ||| f)) + 3 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 1 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 3 * (f ||| ~~~(d ||| e)) + 5 * (f &&& ~~~(d ^^^ e)) - 1 * (d &&& ~~~f) + 2 * ~~~(e ^^^ f) - 7 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 11 * ~~~(d ||| ~~~f) - 2 * (e ^^^ (d ||| ( ~~~e &&& f))) + 4 * ((d ||| e) &&& ~~~(e ^^^ f)) - 11 * e - 3 * (e ^^^ (d ||| (e ^^^ f))) - 1 * (d ^^^ (e ^^^ f)) + 3 * ((d ||| e) &&& (e ^^^ f)) - 5 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 4 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 4 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 1 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 1 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 1 * (f ^^^ (d &&& e)) + 5 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 7 * (f ^^^ (d &&& (e ||| f))) + 5 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 1 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 7 * ((d &&& ~~~e) ||| (e ^^^ f)) - 7 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 1 * (d ||| ( ~~~e &&& f)) - 1 * (f ^^^ ~~~(d ||| e)) - 6 * (f ^^^ ~~~(d &&& (e ||| f))) - 11 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 7 * (e ||| f) - 6 * ~~~( ~~~d &&& (e &&& f)) + 2 * ( ~~~f ||| ~~~(d ^^^ e)) + 2 * (e ||| ~~~(d ^^^ f)) - 5 * ( ~~~d ||| (e &&& f)) + 7 * (e ^^^ ~~~(d ||| ~~~f)) - 2 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 2 * (d ||| (e ^^^ f)) + 4 * ((d ^^^ e) &&& (d ^^^ f)) + 4 * ~~~(d ||| (e &&& f)) - 5 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * (e &&& f) + 5 * ~~~(d ^^^ ( ~~~e ||| f)) + 7 * ((d ^^^ e) ||| ~~~(d ^^^ f)) + 2 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 7 * (d ||| ~~~f) - 2 * (e ^^^ (d ||| (e ||| f))) + 11 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 38 * ~~~(d ||| (e ||| f)) + 40 * ~~~(d ||| ( ~~~e ||| f)) - 12 * ~~~( ~~~d ||| (e ||| f)) + 24 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 28 * ( ~~~d &&& ( ~~~e &&& f)) + 1 * ( ~~~d &&& (e &&& f)) + 27 * (d &&& ( ~~~e &&& f)) + 40 * (d &&& (e &&& f)) = - 1 * ((d &&& f) ^^^ (e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2353 (x y : BitVec w) : +theorem e_2353 : - 5 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 11 * ( ~~~f &&& (d ^^^ e)) + 7 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 6 * ~~~(d ^^^ e) - 2 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 1 * (e ^^^ ~~~(d ||| ~~~f)) + 3 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 4 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 2 * ( ~~~f &&& ~~~(d ^^^ e)) - 2 * (d ^^^ ( ~~~e &&& f)) - 1 * (e ^^^ f) - 2 * ~~~( ~~~d &&& (e ||| f)) + 11 * (e ||| ~~~(d ||| ~~~f)) + 1 * (e ^^^ (d ||| (e ||| f))) - 2 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 1 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 1 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 3 * (e ||| ~~~f) + 11 * ~~~d + 5 * ~~~( ~~~d &&& (e ^^^ f)) + 5 * (e ^^^ ( ~~~d &&& (e ||| f))) + 5 * (d &&& e) + 1 * ((d &&& f) ^^^ (e ||| f)) - 1 * (e ^^^ ~~~(d ||| (e &&& f))) + 4 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 3 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 7 * ( ~~~e ||| (d ^^^ f)) - 5 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 7 * ~~~(d ^^^ ( ~~~e ||| f)) - 2 * (e ^^^ (d ||| ( ~~~e &&& f))) - 2 * ~~~(d &&& (e ||| f)) - 3 * ~~~(d &&& ( ~~~e &&& f)) + 2 * (f &&& (d ||| ~~~e)) - 6 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 5 * (f ^^^ ~~~(d &&& (e ||| f))) - 11 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 7 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 1 * (e ^^^ (d &&& ~~~f)) - 1 * ((d ||| ~~~e) &&& (e ^^^ f)) - 1 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 7 * (f ||| (d &&& e)) + 11 * ( ~~~d &&& (e ^^^ f)) + 5 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 11 * (d &&& f) - 6 * ( ~~~e &&& ~~~(d ^^^ f)) + 2 * (f ^^^ ~~~(d &&& ~~~e)) + 1 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 2 * ~~~(e ^^^ f) + 2 * (f ^^^ (d ||| e)) - 6 * ~~~(d &&& (e ^^^ f)) - 1 * e - 1 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 1 * ~~~(d &&& f) + 7 * (f ||| ~~~(d ||| e)) - 7 * ~~~(d ||| f) - 3 * (f ^^^ (d ||| ~~~e)) + 4 * (f ^^^ (d &&& ( ~~~e ||| f))) - 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 6 * ((d &&& f) ||| (e &&& ~~~f)) + 2 * (d &&& ~~~e) - 10 * ~~~(d ||| (e ||| f)) - 6 * ~~~(d ||| ( ~~~e ||| f)) - 11 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 28 * ( ~~~d &&& ( ~~~e &&& f)) - 44 * ( ~~~d &&& (e &&& f)) - 20 * (d &&& ( ~~~e &&& f)) - 8 * (d &&& (e &&& f)) = - 2 * (f ^^^ (d ||| (e ||| f))) + 14 * ~~~( ~~~d ||| (e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2354 (x y : BitVec w) : +theorem e_2354 : 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 2 * ~~~(d ^^^ (e ^^^ f)) - 3 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 1 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 2 * (e ||| (d ^^^ f)) + 11 * (e &&& ~~~(d ^^^ f)) - 7 * (f ^^^ ~~~(d ||| (e &&& f))) + 11 * ((d &&& f) ||| (e &&& ~~~f)) + 1 * (f ^^^ (d &&& ( ~~~e ||| f))) + 2 * ((d &&& e) ||| ~~~(e ^^^ f)) + 2 * (e &&& ~~~(d &&& ~~~f)) - 1 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 1 * (f ^^^ ~~~(d ||| ~~~e)) - 1 * d + 7 * (f ^^^ (d &&& (e ||| f))) + 1 * (e ^^^ ~~~(d &&& (e ||| f))) - 1 * (e ^^^ (d ||| (e ^^^ f))) - 1 * ( ~~~d ||| (e ^^^ f)) + 7 * ( ~~~d ||| ( ~~~e ||| f)) - 7 * (f ||| ~~~(d ||| ~~~e)) + 5 * ~~~(d &&& ~~~f) + 2 * (e &&& ~~~(d &&& f)) + 5 * (d ^^^ e) - 3 * (e ||| (d &&& ~~~f)) - 1 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 5 * (f ^^^ ( ~~~d &&& (e ||| f))) - 5 * (d ^^^ ( ~~~e &&& f)) + 7 * (d ||| ~~~f) + 1 * ( ~~~e &&& (d ^^^ f)) - 1 * (f ||| (d &&& e)) - 11 * (e ||| ~~~f) - 11 * (e ^^^ (d ||| ( ~~~e &&& f))) - 1 * (d &&& ( ~~~e ||| f)) - 2 * ~~~(d &&& ~~~d) - 1 * ( ~~~f &&& (d ^^^ e)) - 5 * (f ^^^ (d ||| (e &&& f))) - 2 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 2 * (d ||| (e ^^^ f)) - 3 * (d ^^^ (e &&& f)) + 5 * (f ^^^ ( ~~~d ||| (e ||| f))) + 7 * ~~~(e ||| ~~~f) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 5 * ((d &&& e) ^^^ (e ||| ~~~f)) + 2 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 11 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 3 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 2 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * ~~~(d ^^^ e) - 1 * (e ^^^ (d ||| f)) - 2 * ( ~~~d ||| (e ||| f)) - 6 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 1 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 5 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 2 * (e ^^^ ( ~~~d ||| (e ||| f))) - 1 * ((d ||| e) &&& (e ^^^ f)) + 11 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 1 * ~~~(e &&& ~~~f) - 6 * (e ^^^ ( ~~~d &&& (e ||| f))) + 7 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 3 * ~~~f + 1 * (f ||| (d &&& ~~~e)) - 17 * ~~~(d ||| (e ||| f)) - 7 * ~~~(d ||| ( ~~~e ||| f)) + 5 * ~~~( ~~~d ||| (e ||| f)) - 19 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 5 * ( ~~~d &&& ( ~~~e &&& f)) - 6 * (d &&& ( ~~~e &&& f)) - 22 * (d &&& (e &&& f)) = - 23 * ( ~~~d &&& (e &&& f)) - 2 * (f ^^^ (d ||| ( ~~~e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2355 (x y : BitVec w) : +theorem e_2355 : 7 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 11 * ( ~~~d ||| ( ~~~e &&& f)) - 1 * (f ^^^ (d ||| e)) + 1 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 3 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 1 * ( ~~~d &&& (e ^^^ f)) - 3 * (f ^^^ (d &&& ( ~~~e ||| f))) + 7 * (e ^^^ ( ~~~d &&& (e ||| f))) + 1 * ( ~~~f ||| (d ^^^ e)) + 7 * ~~~(d ||| ~~~e) - 7 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 1 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 1 * ( ~~~d ||| (e &&& f)) - 1 * (e ^^^ ~~~(d &&& f)) - 3 * (e ^^^ ( ~~~d ||| (e ||| f))) - 6 * ((d &&& e) ||| ~~~(e ^^^ f)) - 2 * (e ^^^ (d &&& (e ^^^ f))) - 5 * ((d ||| e) &&& ~~~(e ^^^ f)) - 6 * ~~~(d ||| ~~~f) - 2 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 3 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 1 * (f ^^^ ~~~(d &&& (e &&& f))) + 1 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 11 * (d ^^^ ( ~~~e ||| f)) - 2 * (e ^^^ (d ||| (e ^^^ f))) + 4 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 2 * (e ^^^ f) - 11 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 4 * (e ||| ~~~(d ||| ~~~f)) + 5 * (d ^^^ (e &&& f)) - 6 * ~~~(d ^^^ ( ~~~e ||| f)) - 11 * (f ^^^ ~~~(d ||| (e &&& f))) + 2 * (f ||| ~~~(d ||| e)) + 5 * (e ^^^ ~~~(d ||| ~~~f)) - 3 * (e ^^^ ~~~(d &&& ~~~f)) + 1 * (e ^^^ ~~~(d ||| f)) + 3 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 4 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (e &&& (d ||| f)) + 2 * (d &&& ( ~~~e ||| f)) - 7 * (e ^^^ (d ||| ( ~~~e &&& f))) - 1 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 1 * ( ~~~f &&& (d ^^^ e)) + 7 * ~~~(d ^^^ e) - 11 * (f &&& ~~~(d &&& ~~~e)) - 5 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 11 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 5 * (f ^^^ ~~~(d ||| e)) + 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * ~~~(d &&& (e ||| f)) + 1 * (e ||| (d ^^^ f)) - 1 * ~~~(d ||| f) + 5 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 5 * (f ^^^ ~~~(d ||| ~~~e)) - 2 * (e &&& f) - 1 * (e ||| ~~~f) - 7 * e + 3 * (d ||| ~~~f) - 6 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 2 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 48 * ~~~(d ||| (e ||| f)) + 49 * ~~~(d ||| ( ~~~e ||| f)) + 22 * ~~~( ~~~d ||| (e ||| f)) + 5 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 54 * ( ~~~d &&& ( ~~~e &&& f)) + 76 * ( ~~~d &&& (e &&& f)) + 40 * (d &&& ( ~~~e &&& f)) + 31 * (d &&& (e &&& f)) = 1 * ~~~(d &&& ~~~d) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2356 (x y : BitVec w) : +theorem e_2356 : 2 * ~~~(d &&& ~~~f) - 1 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 1 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 3 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 1 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 1 * ((d &&& f) ^^^ (e ||| f)) - 3 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 6 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (d &&& ( ~~~e ||| f)) - 1 * (e ||| (d ^^^ f)) - 2 * ~~~(d &&& ( ~~~e &&& f)) + 11 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 1 * (f ^^^ (d ||| (e &&& f))) + 7 * ( ~~~e ||| (d ^^^ f)) - 3 * ~~~(e ||| ~~~f) - 2 * (e ^^^ ( ~~~d &&& (e ||| f))) - 6 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 2 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 2 * (e ^^^ (d &&& ~~~f)) - 2 * (e ||| ~~~(d ||| ~~~f)) + 7 * (e ^^^ (d ||| (e ||| f))) + 1 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 3 * ( ~~~d ||| (e ^^^ f)) + 7 * (e ^^^ ~~~(d &&& f)) - 7 * (f ^^^ ~~~(d &&& e)) + 1 * (d &&& (e ||| f)) - 1 * ( ~~~d &&& ( ~~~e ||| f)) + 1 * (d ^^^ (e ||| f)) - 2 * ((d ^^^ e) &&& (d ^^^ f)) + 1 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 4 * ((d ||| ~~~e) &&& (e ^^^ f)) + 1 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 11 * ((d ||| e) &&& ~~~(e ^^^ f)) + 7 * (f ^^^ ( ~~~d &&& (e ||| f))) + 2 * (d ||| (e ||| f)) + 4 * (e ||| ~~~f) + 2 * ( ~~~d &&& (e ||| f)) - 1 * ( ~~~d &&& (e ^^^ f)) + 3 * (d ||| ( ~~~e ||| f)) + 5 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 2 * ( ~~~d ||| (e ||| f)) + 2 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 5 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 1 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 3 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 5 * (d &&& ~~~f) - 6 * ( ~~~e &&& ~~~(d ^^^ f)) + 3 * ((d &&& ~~~e) ||| (e ^^^ f)) - 11 * ~~~(d ^^^ f) + 1 * (f ^^^ (d &&& (e ||| f))) + 11 * ((d ^^^ e) ||| (d ^^^ f)) + 5 * (d ||| ( ~~~e &&& f)) + 3 * (f ^^^ (d &&& e)) + 1 * (e ||| (d &&& f)) - 2 * (f ^^^ (d &&& ~~~e)) - 3 * (e ^^^ (d ||| (e ^^^ f))) + 1 * (d ^^^ (e &&& f)) - 1 * ((d &&& e) ^^^ (e ||| ~~~f)) - 5 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 6 * ~~~(d &&& f) - 1 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 7 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 10 * ~~~(d ||| (e ||| f)) - 14 * ~~~(d ||| ( ~~~e ||| f)) - 27 * ~~~( ~~~d ||| (e ||| f)) - 23 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 41 * ( ~~~d &&& ( ~~~e &&& f)) - 51 * (d &&& ( ~~~e &&& f)) = 13 * ( ~~~d &&& (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2357 (x y : BitVec w) : +theorem e_2357 : - 6 * ~~~(d ||| (e ^^^ f)) + 1 * ( ~~~e ||| ~~~(d ^^^ f)) - 1 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 5 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * ~~~(d ||| f) + 3 * ( ~~~f &&& (d ^^^ e)) + 1 * ((d ^^^ e) ||| (d ^^^ f)) + 1 * (f ||| (d &&& ~~~e)) - 6 * (e &&& ~~~(d ^^^ f)) + 7 * ~~~(d ^^^ ( ~~~e &&& f)) + 4 * (f ||| (d &&& e)) + 7 * (d ||| (e &&& f)) + 11 * ( ~~~f ||| (d ^^^ e)) - 6 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 5 * (f &&& ~~~(d &&& e)) + 5 * (d &&& f) - 11 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 2 * (f ^^^ (d ||| (e ||| f))) + 7 * (d ||| (e ||| f)) + 3 * (f ^^^ ~~~(d &&& ~~~e)) - 3 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 1 * (f &&& (d ||| e)) - 11 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 2 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 5 * (f ^^^ (d &&& e)) + 7 * ( ~~~e ||| (d ^^^ f)) + 5 * ((d &&& e) ||| ~~~(e ^^^ f)) - 2 * ( ~~~d ||| (e &&& f)) - 2 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 1 * (e ^^^ ~~~(d &&& ~~~f)) - 1 * (e ||| ~~~f) - 2 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 5 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 11 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 2 * (e ||| ~~~(d ||| f)) + 4 * ~~~(d ^^^ e) + 4 * (e ^^^ (d &&& (e ||| f))) - 1 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 2 * (d &&& ~~~f) - 1 * ~~~f + 2 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 1 * (e ^^^ ( ~~~d ||| (e &&& f))) + 11 * ~~~( ~~~d &&& (e &&& f)) + 3 * (f ^^^ ~~~(d &&& (e ||| f))) - 1 * (e ^^^ ~~~(d &&& f)) - 1 * ((d ^^^ e) &&& (d ^^^ f)) - 1 * (d ^^^ (e ^^^ f)) + 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 5 * ~~~(d ||| ~~~f) + 2 * (f ^^^ ( ~~~d ||| (e &&& f))) + 2 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 3 * ((d &&& f) ||| ~~~(e ||| f)) - 7 * ~~~(d ^^^ (e ||| f)) - 3 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 7 * (f ^^^ ~~~(d ||| ~~~e)) - 1 * (e ^^^ ~~~(d &&& (e &&& f))) + 2 * (e ^^^ f) + 1 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 2 * ((d &&& f) ||| (e &&& ~~~f)) + 1 * ~~~(e &&& ~~~f) - 16 * ~~~(d ||| (e ||| f)) - 17 * ~~~(d ||| ( ~~~e ||| f)) - 38 * ~~~( ~~~d ||| (e ||| f)) - 5 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 27 * ( ~~~d &&& ( ~~~e &&& f)) - 6 * ( ~~~d &&& (e &&& f)) - 71 * (d &&& ( ~~~e &&& f)) - 18 * (d &&& (e &&& f)) = 3 * (e ^^^ (d ||| (e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2358 (x y : BitVec w) : +theorem e_2358 : - 2 * ((d ^^^ e) &&& (d ^^^ f)) + 4 * ~~~(d ^^^ (e ||| f)) - 5 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 2 * e - 11 * ((d &&& e) ^^^ (e ||| ~~~f)) + 1 * ~~~(e &&& ~~~f) - 7 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 1 * (e ^^^ (d ||| ( ~~~e &&& f))) + 2 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 3 * (d ||| ~~~e) - 1 * ~~~(d ||| ~~~f) + 3 * ~~~(d &&& ( ~~~e &&& f)) - 1 * (e &&& ~~~(d &&& ~~~f)) - 3 * (e ||| (d &&& f)) - 2 * (d ||| ( ~~~e &&& f)) - 6 * ( ~~~d &&& (e ^^^ f)) + 2 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 1 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 1 * ~~~(d &&& ~~~d) - 11 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 1 * ( ~~~d ||| (e &&& f)) - 2 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 11 * (f ^^^ ~~~(d &&& e)) - 5 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 3 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * (d ||| (e &&& f)) - 3 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 3 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 5 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 11 * ~~~( ~~~d &&& (e ^^^ f)) + 1 * (f ^^^ ~~~(d &&& ~~~e)) + 5 * ~~~(d ||| ( ~~~e &&& f)) - 11 * ((d ||| e) &&& ~~~(e ^^^ f)) + 1 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 5 * ~~~( ~~~d ||| (e &&& f)) - 3 * (f &&& ~~~(d &&& ~~~e)) + 3 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 1 * (f &&& (d ^^^ e)) + 2 * ( ~~~f &&& (d ^^^ e)) + 3 * ~~~(d ^^^ ( ~~~e &&& f)) - 2 * (e ^^^ ~~~(d &&& f)) - 5 * (e &&& ~~~(d ^^^ f)) + 5 * ~~~f - 11 * (f ||| (d &&& ~~~e)) - 1 * (e &&& f) + 4 * (d &&& ~~~f) - 6 * (f ^^^ ( ~~~d ||| (e &&& f))) - 6 * (e &&& ~~~f) - 2 * (d ^^^ (e ||| f)) + 2 * ((e &&& f) ||| (d &&& (e ||| f))) + 4 * ~~~(d &&& ~~~e) - 6 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 1 * (e ^^^ (d &&& ~~~f)) + 11 * (d ^^^ (e &&& f)) + 7 * (f ^^^ (d ||| ( ~~~e &&& f))) + 5 * ~~~(e ||| ~~~f) - 1 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 11 * (f &&& ~~~(d &&& e)) + 4 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 3 * ~~~(d ||| (e ||| f)) + 17 * ~~~(d ||| ( ~~~e ||| f)) - 10 * ~~~( ~~~d ||| (e ||| f)) - 17 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 41 * ( ~~~d &&& ( ~~~e &&& f)) + 13 * ( ~~~d &&& (e &&& f)) + 10 * (d &&& ( ~~~e &&& f)) + 29 * (d &&& (e &&& f)) = - 2 * (e ^^^ (d &&& (e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2359 (x y : BitVec w) : +theorem e_2359 : - 2 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 3 * (f ^^^ (d &&& ( ~~~e ||| f))) + 5 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 11 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 1 * ~~~(d &&& ( ~~~e &&& f)) + 3 * (e ^^^ ~~~(d &&& f)) - 1 * ~~~(d &&& ( ~~~e ||| f)) - 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 11 * (e &&& ~~~f) - 5 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 1 * (d ^^^ (e ||| f)) + 4 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 11 * ( ~~~e ||| (d ^^^ f)) + 1 * (f ^^^ (d ||| (e ||| f))) + 2 * ~~~(d ||| e) + 1 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 1 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 2 * (e ^^^ ( ~~~d &&& (e ||| f))) - 6 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * ~~~(d &&& (e ||| f)) + 1 * (f ^^^ ( ~~~d ||| (e &&& f))) - 6 * (f &&& (d ^^^ e)) - 5 * (e ||| (d &&& ~~~f)) - 11 * ~~~(d ^^^ (e ||| f)) - 6 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 1 * ((e &&& f) ||| (d &&& (e ||| f))) + 4 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 5 * ~~~(d &&& e) + 3 * (e ^^^ ~~~(d ||| ~~~f)) - 1 * (d ^^^ ( ~~~e ||| f)) + 2 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 3 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 2 * ((d &&& f) ||| ~~~(e ||| f)) - 7 * (e &&& ~~~(d ^^^ f)) - 11 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 3 * (e ^^^ (d ||| (e ||| f))) - 1 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 4 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 7 * (f ^^^ (d ||| ( ~~~e &&& f))) - 7 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 1 * ( ~~~d &&& ( ~~~e ||| f)) - 1 * (f ^^^ (d ||| e)) + 5 * (e ^^^ ~~~(d ||| f)) + 1 * ~~~(e ^^^ f) - 1 * ( ~~~f &&& (d ^^^ e)) + 3 * (d ||| (e ||| f)) + 5 * (f ^^^ (d ||| ~~~e)) - 7 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 7 * (f ||| (d &&& e)) + 7 * (d ||| ( ~~~e ||| f)) - 3 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 1 * ((d &&& f) ^^^ (e ||| f)) - 6 * (f ||| (d ^^^ e)) + 1 * ((d &&& e) ^^^ (e ||| ~~~f)) + 2 * f - 5 * ~~~( ~~~d &&& (e ^^^ f)) + 2 * (f ^^^ (d ||| ( ~~~e ||| f))) - 1 * (e &&& ~~~(d &&& f)) + 1 * ( ~~~d ||| ( ~~~e ||| f)) - 11 * ((d ^^^ e) &&& (d ^^^ f)) + 15 * ~~~(d ||| (e ||| f)) + 36 * ~~~(d ||| ( ~~~e ||| f)) + 7 * ~~~( ~~~d ||| (e ||| f)) + 56 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 11 * ( ~~~d &&& ( ~~~e &&& f)) + 48 * ( ~~~d &&& (e &&& f)) + 35 * (d &&& ( ~~~e &&& f)) + 34 * (d &&& (e &&& f)) = 1 * (d ^^^ (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2360 (x y : BitVec w) : +theorem e_2360 : - 1 * ( ~~~d ||| (e ||| f)) - 3 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 1 * ~~~(d ||| ~~~e) + 7 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 1 * (f ||| (d &&& e)) + 1 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 7 * ~~~(d ^^^ e) - 11 * ((d &&& e) ||| (e ^^^ f)) - 1 * (d ||| e) - 2 * (e ^^^ (d ||| (e &&& f))) + 2 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 11 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 3 * ( ~~~d ||| ( ~~~e ||| f)) + 1 * (e ^^^ ( ~~~d ||| (e ||| f))) + 5 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 5 * ((d &&& ~~~e) ||| (e ^^^ f)) - 5 * ~~~(d ||| (e ^^^ f)) - 5 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 11 * ( ~~~d &&& (e ^^^ f)) - 6 * ~~~(d &&& ~~~f) + 2 * (e &&& ~~~f) - 7 * ~~~(d &&& (e &&& f)) - 11 * ~~~(d &&& e) - 5 * (e ^^^ f) + 5 * ( ~~~f &&& (d ^^^ e)) + 1 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 4 * (e ^^^ ~~~(d ||| (e &&& f))) + 3 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 1 * ~~~e - 1 * (e ^^^ (d ||| ~~~f)) + 7 * ( ~~~f &&& ~~~(d ^^^ e)) - 11 * ~~~d - 1 * (e ^^^ ( ~~~d &&& (e ||| f))) - 1 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 4 * (f ^^^ (d &&& ( ~~~e ||| f))) + 1 * (d ^^^ ( ~~~e ||| f)) - 6 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (f ^^^ ~~~(d &&& (e ||| f))) + 2 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 1 * (e ||| (d &&& ~~~f)) + 4 * ~~~(d &&& ~~~d) - 2 * (d ^^^ (e ^^^ f)) + 1 * ((d ||| ~~~e) &&& (e ^^^ f)) + 2 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * (f ||| ~~~(d ||| e)) + 4 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * (d &&& ~~~e) + 5 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 4 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 7 * (d ||| ( ~~~e ||| f)) + 3 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 1 * (d &&& e) - 2 * ~~~(e ||| ~~~f) - 5 * ~~~(e ^^^ f) + 2 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 5 * (f &&& ~~~(d &&& ~~~e)) + 11 * ~~~(e &&& f) + 2 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 6 * (d &&& (e ^^^ f)) - 3 * ( ~~~e &&& (d ^^^ f)) + 17 * ~~~(d ||| (e ||| f)) - 7 * ~~~(d ||| ( ~~~e ||| f)) - 3 * ~~~( ~~~d ||| (e ||| f)) + 16 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 22 * ( ~~~d &&& ( ~~~e &&& f)) + 25 * ( ~~~d &&& (e &&& f)) + 24 * (d &&& ( ~~~e &&& f)) + 29 * (d &&& (e &&& f)) = 2 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2361 (x y : BitVec w) : +theorem e_2361 : - 7 * (d ||| ( ~~~e &&& f)) + 1 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 1 * ( ~~~d &&& (e ||| f)) - 2 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 7 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 2 * ((d &&& e) ^^^ (e ||| f)) - 3 * (e ||| ~~~f) + 11 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 2 * (f &&& ~~~(d &&& ~~~e)) + 5 * ( ~~~d &&& (e ^^^ f)) - 2 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 1 * ~~~( ~~~d ||| (e &&& f)) - 3 * (e &&& f) + 7 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 4 * (e ||| (d &&& f)) - 7 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 11 * (f &&& (d ||| e)) + 3 * ~~~e - 6 * ((d &&& e) ||| (e ^^^ f)) - 6 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 2 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 2 * (f &&& ~~~(d &&& e)) - 11 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 1 * ~~~(e &&& f) - 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 2 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 1 * (e ^^^ ~~~(d &&& f)) - 5 * (e ^^^ (d ||| (e ^^^ f))) + 1 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 1 * ( ~~~d ||| (e &&& f)) + 11 * ( ~~~d &&& ( ~~~e ||| f)) + 4 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 4 * (f ^^^ (d ||| (e &&& f))) - 6 * ~~~(d &&& e) + 3 * (e ^^^ (d &&& (e ^^^ f))) - 2 * ~~~(d ^^^ (e &&& f)) + 11 * ((d &&& f) ||| ~~~(e ||| f)) - 7 * (d ||| ~~~f) - 2 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 6 * ( ~~~f &&& (d ^^^ e)) - 2 * (f ^^^ (d &&& (e ||| f))) + 1 * (e &&& ~~~(d ^^^ f)) + 1 * (e &&& ~~~(d &&& f)) - 3 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 2 * (e ||| (d ^^^ f)) + 11 * ( ~~~e &&& (d ^^^ f)) - 2 * ( ~~~e ||| (d ^^^ f)) - 1 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 11 * (e ||| f) - 1 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 1 * ((d &&& f) ||| (e &&& ~~~f)) - 1 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 2 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 1 * (f &&& (d ||| ~~~e)) - 1 * (e ^^^ ~~~(d ||| (e &&& f))) + 1 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 11 * ~~~(e ||| f) - 6 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 7 * ~~~(e ^^^ f) - 17 * ~~~(d ||| (e ||| f)) + 38 * ~~~(d ||| ( ~~~e ||| f)) + 16 * ~~~( ~~~d ||| (e ||| f)) + 27 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 28 * ( ~~~d &&& ( ~~~e &&& f)) - 3 * ( ~~~d &&& (e &&& f)) + 2 * (d &&& ( ~~~e &&& f)) + 10 * (d &&& (e &&& f)) = - 5 * (f &&& (d ^^^ e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2362 (x y : BitVec w) : +theorem e_2362 : 2 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 5 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 2 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 3 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 2 * (e ^^^ (d ||| (e ^^^ f))) - 11 * ((d &&& e) ||| (e ^^^ f)) + 7 * (d ||| ~~~e) + 4 * (e &&& (d ||| f)) + 11 * ((d &&& ~~~e) ||| (e ^^^ f)) + 2 * (d &&& f) + 3 * (f ^^^ ( ~~~d &&& (e ||| f))) - 1 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 2 * ~~~(d ||| (e ^^^ f)) + 4 * ~~~(d &&& e) + 2 * (f ^^^ ~~~(d &&& e)) - 5 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 1 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 7 * ~~~(d ^^^ (e ||| f)) - 5 * (f &&& (d ^^^ e)) - 5 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 2 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 5 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 2 * ~~~(d ||| ~~~e) - 2 * ~~~(d &&& ~~~d) - 6 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 1 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 7 * ( ~~~e ||| (d ^^^ f)) - 11 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 3 * ~~~( ~~~d &&& (e &&& f)) + 2 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * ~~~(e &&& f) + 5 * ( ~~~f ||| ~~~(d ^^^ e)) + 2 * ( ~~~d ||| (e &&& f)) - 7 * (f &&& (d ||| e)) + 5 * (d &&& (e ^^^ f)) - 11 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 2 * ~~~( ~~~d &&& (e ^^^ f)) + 5 * (f ^^^ ~~~(d ||| e)) + 11 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 3 * ~~~(d &&& ( ~~~e &&& f)) + 3 * (f ^^^ ~~~(d ||| ~~~e)) + 1 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 2 * ((d &&& e) ||| ~~~(e ||| f)) + 5 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 2 * ~~~(d ^^^ (e ^^^ f)) - 1 * (f ||| (d ^^^ e)) - 7 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 5 * (e ^^^ (d ||| f)) - 1 * ~~~(d &&& (e ||| f)) - 11 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 1 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 1 * ( ~~~e &&& ~~~(d ^^^ f)) - 1 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 6 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 6 * (d ||| (e &&& f)) + 4 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 2 * (d ||| e) - 1 * ~~~(d ||| ( ~~~e &&& f)) + 1 * (f ^^^ (d ||| (e &&& f))) - 2 * (e ||| ~~~(d ||| ~~~f)) + 24 * ~~~(d ||| (e ||| f)) + 50 * ~~~(d ||| ( ~~~e ||| f)) + 39 * ~~~( ~~~d ||| (e ||| f)) + 34 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 22 * ( ~~~d &&& ( ~~~e &&& f)) + 26 * ( ~~~d &&& (e &&& f)) + 56 * (d &&& ( ~~~e &&& f)) + 45 * (d &&& (e &&& f)) = - 1 * (f ^^^ (d ||| (e ||| f))) + 7 * ((d ||| e) &&& (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2363 (x y : BitVec w) : +theorem e_2363 : - 6 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 1 * (e ^^^ ~~~(d &&& (e ||| f))) - 1 * ((d ||| ~~~e) &&& (e ^^^ f)) - 1 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 1 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 1 * (f &&& (d ^^^ e)) + 7 * ~~~f - 7 * (e ||| (d &&& f)) + 1 * ( ~~~f ||| ~~~(d ^^^ e)) - 5 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 2 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 11 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 7 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 11 * ( ~~~d &&& ( ~~~e ||| f)) - 2 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 7 * f + 7 * ~~~(e ||| f) - 3 * ~~~(d ^^^ e) - 1 * ~~~( ~~~d ||| (e &&& f)) + 1 * ((d &&& e) ||| ~~~(e ^^^ f)) - 2 * (f ^^^ (d ||| e)) - 5 * (f ^^^ ( ~~~d ||| (e &&& f))) - 6 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 2 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 2 * ~~~(d ^^^ (e ||| f)) + 1 * (e ||| ~~~(d ||| ~~~f)) + 1 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 7 * ( ~~~d ||| ( ~~~e ||| f)) - 6 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (f &&& ~~~(d &&& e)) - 1 * (d ||| ( ~~~e ||| f)) + 1 * (f ||| (d &&& ~~~e)) + 5 * (e ^^^ ~~~(d ||| f)) + 1 * ~~~(e ||| ~~~f) - 5 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 6 * (d &&& ~~~e) + 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 2 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 2 * ((d &&& e) ||| (e ^^^ f)) - 1 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 3 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 1 * (f ^^^ ~~~(d &&& (e &&& f))) + 2 * (e ^^^ (d &&& ( ~~~e ||| f))) + 2 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 4 * ((d &&& f) ^^^ (e ||| f)) + 1 * ~~~(d &&& ~~~f) - 6 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 7 * (f ^^^ (d &&& (e ||| f))) + 3 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 11 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 5 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 3 * ( ~~~e ||| ~~~(d ^^^ f)) - 3 * ( ~~~d &&& (e ^^^ f)) - 2 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 1 * (e ^^^ ~~~(d &&& (e &&& f))) - 11 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 7 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * (e &&& ~~~(d ^^^ f)) - 1 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 49 * ~~~(d ||| (e ||| f)) + 16 * ~~~(d ||| ( ~~~e ||| f)) - 9 * ~~~( ~~~d ||| (e ||| f)) + 26 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 40 * ( ~~~d &&& ( ~~~e &&& f)) + 23 * ( ~~~d &&& (e &&& f)) + 60 * (d &&& ( ~~~e &&& f)) + 23 * (d &&& (e &&& f)) = 5 * (d ||| ( ~~~e &&& f)) + 1 * (e ^^^ (d ||| (e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2364 (x y : BitVec w) : +theorem e_2364 : 2 * ~~~(d &&& f) + 1 * (e &&& ~~~(d ^^^ f)) - 7 * ( ~~~e &&& (d ^^^ f)) + 1 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * ~~~(d &&& (e &&& f)) - 2 * ((d &&& e) ^^^ (e ||| f)) + 3 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 7 * (e ||| ~~~(d ||| ~~~f)) - 1 * (e ||| (d &&& ~~~f)) - 11 * (f ^^^ (d ||| ~~~e)) - 1 * ~~~(d ^^^ (e ||| f)) + 1 * ~~~e + 4 * (e ||| ~~~(d ||| f)) - 5 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 1 * ~~~(d ^^^ (e ^^^ f)) - 6 * (d ||| ( ~~~e ||| f)) - 3 * (f &&& ~~~(d &&& ~~~e)) + 2 * (e ^^^ ~~~(d &&& (e ||| f))) + 3 * ~~~( ~~~d &&& (e ^^^ f)) + 4 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 2 * (f ^^^ ~~~(d &&& (e &&& f))) + 2 * ((d &&& e) ||| (e ^^^ f)) - 2 * ~~~(d &&& ~~~d) + 1 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 1 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 11 * (e ^^^ (d &&& ( ~~~e ||| f))) + 4 * ~~~(e &&& f) + 3 * (e &&& (d ||| ~~~f)) - 1 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 2 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 11 * (e ||| ~~~(d ^^^ f)) - 1 * (e ^^^ f) - 5 * ((d ^^^ e) ||| (d ^^^ f)) + 1 * ((d &&& f) ||| (e &&& ~~~f)) + 5 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 6 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 4 * (d ^^^ ( ~~~e &&& f)) + 2 * ~~~(d ||| (e &&& f)) + 2 * ((d &&& e) ^^^ (e ||| ~~~f)) - 2 * ~~~(d ||| ( ~~~e &&& f)) + 2 * ~~~(e ||| f) - 5 * (e ||| (d &&& f)) + 7 * (e ^^^ (d ||| (e ||| f))) - 3 * (d ^^^ ( ~~~e ||| f)) - 2 * (d &&& ~~~e) + 4 * ~~~( ~~~d &&& (e ||| f)) - 6 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 1 * ( ~~~f ||| ~~~(d ^^^ e)) + 1 * ~~~(e &&& ~~~f) + 11 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 1 * (f ^^^ ~~~(d ||| ~~~e)) - 2 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * (f ^^^ (d ||| (e ||| f))) - 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 5 * (d ||| ( ~~~e &&& f)) - 3 * ( ~~~e ||| (d ^^^ f)) + 3 * (e &&& (d ||| f)) - 1 * (f ||| ~~~(d ||| e)) - 1 * (e ^^^ (d &&& (e ||| f))) - 2 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 1 * (f ^^^ ~~~(d ||| e)) + 3 * ~~~(d ||| (e ||| f)) - 15 * ~~~(d ||| ( ~~~e ||| f)) - 28 * ~~~( ~~~d ||| (e ||| f)) + 7 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 9 * ( ~~~d &&& ( ~~~e &&& f)) + 44 * ( ~~~d &&& (e &&& f)) + 2 * (d &&& ( ~~~e &&& f)) = - 1 * ( ~~~e &&& ~~~(d ^^^ f)) - 2 * (e ^^^ ( ~~~d ||| (e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2365 (x y : BitVec w) : +theorem e_2365 : 1 * (f ^^^ (d &&& (e ||| f))) + 3 * ~~~(d ^^^ (e ^^^ f)) + 1 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 2 * ( ~~~f ||| (d ^^^ e)) + 1 * (d ^^^ e) - 2 * (d ||| (e ||| f)) - 1 * ~~~e + 1 * (e ||| (d ^^^ f)) + 11 * ~~~(d &&& ~~~e) - 6 * ~~~(d &&& ~~~d) + 1 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 1 * (e ^^^ (d ||| ( ~~~e &&& f))) + 3 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 7 * ~~~(e ||| f) + 1 * (e ^^^ (d ||| (e ^^^ f))) + 2 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (f ^^^ (d &&& ~~~e)) - 3 * ((d ^^^ e) &&& (d ^^^ f)) + 2 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 7 * ~~~(d &&& f) - 2 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 5 * ~~~(d &&& e) - 1 * ((d &&& ~~~e) ||| (e ^^^ f)) + 2 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 3 * ~~~(d ||| ~~~e) + 2 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 7 * (f ^^^ (d &&& ( ~~~e ||| f))) + 3 * (f ||| ~~~(d ||| e)) - 1 * (e ^^^ (d ||| ( ~~~e ||| f))) - 1 * ( ~~~d ||| (e ^^^ f)) + 11 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 1 * (f ^^^ (d ||| ( ~~~e ||| f))) - 3 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 1 * ~~~(e ^^^ f) - 11 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 4 * (d ||| (e &&& f)) - 3 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 1 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 5 * (e ||| ~~~(d ||| ~~~f)) - 5 * (e ^^^ (d ||| ~~~f)) + 1 * (f ||| ~~~(d ^^^ e)) - 7 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 1 * (f &&& ~~~(d &&& ~~~e)) + 7 * (f ^^^ ~~~(d ||| ~~~e)) + 3 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 6 * ((d ||| e) &&& (e ^^^ f)) - 2 * (e ^^^ ~~~(d ||| ~~~f)) + 1 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 5 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 5 * (d ^^^ ( ~~~e ||| f)) + 4 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 5 * (e &&& (d ||| ~~~f)) - 3 * (e ^^^ ~~~(d &&& (e ||| f))) + 7 * ( ~~~d ||| (e ||| f)) + 2 * ( ~~~d ||| ( ~~~e &&& f)) - 11 * ( ~~~d &&& (e ||| f)) - 3 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 1 * (d ||| e) + 7 * (d ^^^ (e ^^^ f)) + 7 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 7 * (d ||| f) + 10 * ~~~(d ||| (e ||| f)) - 20 * ~~~(d ||| ( ~~~e ||| f)) + 40 * ~~~( ~~~d ||| (e ||| f)) + 7 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 7 * ( ~~~d &&& ( ~~~e &&& f)) - 15 * ( ~~~d &&& (e &&& f)) + 17 * (d &&& ( ~~~e &&& f)) - 34 * (d &&& (e &&& f)) = - 3 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2366 (x y : BitVec w) : +theorem e_2366 : - 2 * (e ^^^ (d ||| f)) - 6 * ( ~~~d ||| (e ||| f)) - 1 * (f ^^^ (d &&& ( ~~~e ||| f))) + 1 * ~~~(d &&& (e ||| f)) - 1 * ((d ^^^ e) &&& (d ^^^ f)) - 2 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 5 * (e &&& ~~~(d &&& f)) - 3 * (f ^^^ ~~~(d &&& (e &&& f))) + 7 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 11 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * ( ~~~f ||| (d ^^^ e)) + 1 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 11 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 11 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 5 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 1 * (e ^^^ ( ~~~d &&& (e ||| f))) - 2 * ( ~~~f &&& ~~~(d ^^^ e)) + 1 * (f &&& ~~~(d &&& ~~~e)) + 2 * (e ||| ~~~(d ||| ~~~f)) - 7 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 6 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 2 * (e ^^^ ~~~(d ||| ~~~f)) - 5 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 1 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 3 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 11 * ~~~(d ^^^ ( ~~~e &&& f)) + 3 * ~~~(d ||| e) - 3 * ((d &&& f) ||| ~~~(e ||| f)) + 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 5 * ~~~( ~~~d &&& (e ^^^ f)) + 4 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 4 * (e &&& (d ^^^ f)) + 4 * (f ^^^ ~~~(d &&& (e ||| f))) - 1 * (e ^^^ ~~~(d &&& (e ||| f))) + 2 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 1 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 3 * (f ||| ~~~(d ||| ~~~e)) - 1 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 2 * ~~~f - 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 3 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 2 * (d ||| e) + 4 * (d ^^^ e) - 6 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 1 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 7 * (f ^^^ ~~~(d &&& ~~~e)) - 7 * (e ||| (d &&& f)) + 2 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 11 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 3 * (e ^^^ ( ~~~d ||| (e ||| f))) - 2 * ( ~~~e ||| ~~~(d ^^^ f)) + 1 * (f ||| (d &&& e)) + 1 * ~~~(d &&& (e &&& f)) - 3 * ~~~(d ||| f) + 2 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 5 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 11 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 1 * (d ||| ( ~~~e ||| f)) - 2 * (e ^^^ (d &&& ( ~~~e ||| f))) + 68 * ~~~(d ||| (e ||| f)) + 49 * ~~~(d ||| ( ~~~e ||| f)) + 49 * ~~~( ~~~d ||| (e ||| f)) + 48 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 44 * ( ~~~d &&& ( ~~~e &&& f)) + 32 * ( ~~~d &&& (e &&& f)) + 50 * (d &&& ( ~~~e &&& f)) + 64 * (d &&& (e &&& f)) = - 1 * ~~~(d &&& e) + 7 * (f ^^^ (d &&& ~~~e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2367 (x y : BitVec w) : +theorem e_2367 : - 3 * (d ||| ( ~~~e &&& f)) - 7 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 3 * (d &&& (e ||| f)) - 6 * ((d &&& f) ||| ~~~(e ||| f)) - 2 * ((d &&& e) ^^^ (e ||| ~~~f)) - 11 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 2 * (e ||| (d &&& ~~~f)) + 1 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 11 * ~~~(d ||| f) - 2 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 4 * (e ||| ~~~(d ||| ~~~f)) + 1 * (e &&& ~~~f) - 3 * (e ^^^ ~~~(d ||| f)) + 2 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 6 * ~~~(d &&& ~~~d) + 4 * (d ||| e) + 7 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 1 * (f ^^^ ~~~(d ||| e)) + 11 * ( ~~~d ||| (e ^^^ f)) - 1 * (f ^^^ ( ~~~d &&& (e ||| f))) + 3 * ((d &&& e) ||| (e ^^^ f)) - 2 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 5 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 1 * ( ~~~d &&& ( ~~~e ||| f)) - 2 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 3 * (e ^^^ (d ||| f)) - 1 * (f &&& (d ^^^ e)) + 7 * ~~~(d ^^^ f) - 1 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 2 * ~~~(d ||| (e &&& f)) + 5 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 3 * (d &&& ~~~e) - 2 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 5 * ~~~( ~~~d &&& (e ^^^ f)) + 1 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 5 * (f ^^^ (d ||| ( ~~~e &&& f))) - 1 * d + 1 * (f ^^^ (d &&& (e ||| f))) + 11 * (e ||| ~~~(d ^^^ f)) + 7 * (f ^^^ (d &&& e)) + 1 * (d ^^^ e) - 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 5 * ~~~(e ||| ~~~f) + 5 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 3 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 2 * (d ^^^ (e &&& f)) + 4 * ( ~~~f ||| ~~~(d ^^^ e)) - 2 * (d ||| ~~~f) + 1 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 5 * (f ^^^ ~~~(d ||| ~~~e)) - 1 * ( ~~~d ||| (e ||| f)) + 2 * (d ^^^ ( ~~~e ||| f)) - 1 * ( ~~~f &&& (d ^^^ e)) + 1 * (f ^^^ ~~~(d &&& e)) + 3 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 6 * (e &&& ~~~(d ^^^ f)) + 11 * (d &&& ~~~f) + 1 * (f ||| ~~~(d ^^^ e)) - 7 * ~~~e - 7 * ((d &&& e) ||| ~~~(e ||| f)) - 1 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 1 * (e ^^^ (d ||| ( ~~~e ||| f))) + 3 * ~~~(d ||| (e ||| f)) - 31 * ~~~(d ||| ( ~~~e ||| f)) + 28 * ~~~( ~~~d ||| (e ||| f)) - 27 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 12 * ( ~~~d &&& ( ~~~e &&& f)) - 8 * ( ~~~d &&& (e &&& f)) - 15 * (d &&& ( ~~~e &&& f)) = 1 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2368 (x y : BitVec w) : +theorem e_2368 : 3 * (d ||| e) - 7 * (e &&& ~~~(d &&& ~~~f)) - 1 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 6 * ( ~~~d &&& (e ||| f)) + 11 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 2 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 1 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 11 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 1 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 3 * (d &&& (e ^^^ f)) + 11 * ~~~(d &&& ( ~~~e ||| f)) - 11 * (f ||| ~~~(d ||| ~~~e)) - 1 * ((e &&& f) ||| (d &&& (e ||| f))) - 7 * (f &&& ~~~(d &&& e)) + 1 * ~~~(d ^^^ (e &&& f)) + 4 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 1 * (d ||| (e ^^^ f)) - 1 * ((d &&& e) ||| ~~~(e ^^^ f)) + 2 * ( ~~~d ||| (e ^^^ f)) + 11 * (e ^^^ ( ~~~d &&& (e ||| f))) - 7 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 7 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 2 * (f &&& ~~~(d ^^^ e)) + 2 * (d &&& f) - 11 * (e ^^^ (d &&& ( ~~~e ||| f))) + 2 * (e &&& ~~~(d &&& f)) + 3 * ((d &&& e) ||| ~~~(e ||| f)) - 5 * ~~~(d &&& ( ~~~e &&& f)) + 1 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 3 * ((d &&& ~~~e) ||| (e ^^^ f)) + 2 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 5 * ~~~(e &&& f) + 5 * ~~~( ~~~d ||| (e &&& f)) + 4 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * (e ||| (d &&& ~~~f)) - 11 * (f ^^^ ~~~(d ||| e)) - 2 * ((d &&& f) ||| ~~~(e ||| f)) - 1 * ( ~~~f ||| ~~~(d ^^^ e)) - 1 * (e &&& (d ||| f)) + 7 * ~~~(d ||| ( ~~~e &&& f)) + 1 * ~~~(d ||| (e &&& f)) - 5 * (d ^^^ (e ||| f)) + 5 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 1 * (e ^^^ (d ||| ~~~f)) - 5 * ( ~~~e ||| (d ^^^ f)) + 11 * (e ^^^ (d ||| ( ~~~e &&& f))) + 3 * ~~~(d ^^^ (e ^^^ f)) - 2 * ~~~( ~~~d ||| (e ^^^ f)) - 2 * (e ||| (d ^^^ f)) + 3 * ~~~d - 6 * (d ^^^ e) + 7 * (e &&& f) + 2 * (e ^^^ ~~~(d &&& f)) + 5 * ~~~(d ^^^ e) - 2 * (f ^^^ ~~~(d &&& ~~~e)) + 5 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 3 * (e ||| ~~~(d ||| ~~~f)) + 2 * (f &&& (d ^^^ e)) + 1 * ~~~( ~~~d &&& (e ^^^ f)) - 2 * ( ~~~e &&& (d ^^^ f)) + 1 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 27 * ~~~(d ||| (e ||| f)) + 17 * ~~~(d ||| ( ~~~e ||| f)) + 28 * ~~~( ~~~d ||| (e ||| f)) + 7 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 11 * ( ~~~d &&& ( ~~~e &&& f)) + 11 * ( ~~~d &&& (e &&& f)) + 37 * (d &&& ( ~~~e &&& f)) - 13 * (d &&& (e &&& f)) = 2 * (d ||| ~~~f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2369 (x y : BitVec w) : +theorem e_2369 : 4 * (d ^^^ (e ^^^ f)) - 1 * (e ^^^ (d ||| ~~~f)) - 3 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 5 * ~~~(d &&& ~~~d) + 5 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 6 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 2 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 5 * (f ^^^ (d ||| (e ||| f))) - 3 * d + 2 * ((e &&& f) ||| (d &&& (e ||| f))) + 7 * ~~~( ~~~d &&& (e ^^^ f)) + 5 * ~~~(e ||| f) + 11 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 1 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 3 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 1 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 7 * (d ||| ~~~e) - 2 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 11 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 2 * (e &&& ~~~(d &&& f)) - 5 * (e ^^^ ( ~~~d ||| (e ||| f))) + 1 * (e ^^^ (d ||| (e &&& f))) + 1 * (e &&& (d ||| ~~~f)) - 7 * (e ^^^ (d &&& (e ||| f))) + 11 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 1 * ~~~(d &&& ~~~f) + 1 * ((d ||| e) &&& (e ^^^ f)) + 11 * (e &&& ~~~f) - 2 * (e &&& f) + 7 * (f ^^^ (d ||| ( ~~~e ||| f))) - 2 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 11 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 1 * (d &&& ~~~e) - 11 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 2 * (e ||| ~~~f) + 3 * (e ^^^ (d &&& f)) + 4 * (e &&& (d ^^^ f)) - 11 * (e ^^^ (d ||| ( ~~~e ||| f))) + 3 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 7 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 2 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 2 * ~~~(e ||| ~~~f) + 1 * ((d &&& e) ||| ~~~(e ^^^ f)) - 3 * (f &&& ~~~(d ^^^ e)) - 2 * (f &&& ~~~(d &&& e)) + 1 * (e ^^^ ( ~~~d ||| (e &&& f))) + 1 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 3 * (f ||| (d ^^^ e)) + 3 * (e &&& (d ||| f)) + 2 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 1 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * ( ~~~f &&& (d ^^^ e)) - 5 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 7 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 1 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 2 * ~~~(d ^^^ e) - 2 * ( ~~~f ||| (d ^^^ e)) + 7 * ~~~(d &&& ~~~e) + 2 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 5 * (f ||| (d &&& ~~~e)) - 30 * ~~~(d ||| (e ||| f)) - 11 * ~~~(d ||| ( ~~~e ||| f)) - 13 * ~~~( ~~~d ||| (e ||| f)) - 66 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 12 * ( ~~~d &&& ( ~~~e &&& f)) - 41 * ( ~~~d &&& (e &&& f)) - 27 * (d &&& ( ~~~e &&& f)) - 16 * (d &&& (e &&& f)) = 1 * (d ||| e) + 6 * ( ~~~e &&& (d ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2370 (x y : BitVec w) : +theorem e_2370 : 7 * (f ||| ~~~(d ||| e)) - 11 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 11 * (e ||| (d ^^^ f)) - 1 * (d ||| f) + 3 * (e ^^^ (d ||| ( ~~~e ||| f))) - 3 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 7 * ((d &&& f) ^^^ (e ||| f)) + 2 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 5 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 1 * (e ^^^ f) - 1 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 11 * (f ^^^ (d &&& e)) - 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * (d &&& (e ||| f)) + 1 * (d &&& e) - 5 * (f ||| ~~~(d ||| ~~~e)) + 4 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 7 * (e ^^^ ~~~(d &&& ~~~f)) + 2 * (e ^^^ (d &&& ( ~~~e ||| f))) + 3 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 1 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 5 * ~~~(d ||| (e ^^^ f)) + 5 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 1 * (d ^^^ ( ~~~e ||| f)) - 2 * ~~~(d ||| (e &&& f)) + 11 * (f ||| (d ^^^ e)) - 1 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 1 * ( ~~~d &&& (e ^^^ f)) + 4 * (e ||| (d &&& f)) + 1 * (d &&& (e ^^^ f)) - 1 * ( ~~~f ||| (d ^^^ e)) - 1 * ~~~(e &&& ~~~f) - 7 * ~~~(d &&& (e ^^^ f)) - 3 * ~~~(d ||| ( ~~~e &&& f)) + 11 * ((d ||| ~~~e) &&& (e ^^^ f)) + 3 * (d ^^^ f) - 2 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 3 * (d ||| (e ^^^ f)) - 11 * (e ||| ~~~(d ||| f)) + 5 * ~~~e + 2 * (e &&& (d ||| ~~~f)) - 2 * ((d ||| e) &&& (e ^^^ f)) + 3 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 2 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 1 * (f ^^^ (d &&& (e ||| f))) - 1 * (f ^^^ ~~~(d ||| ~~~e)) - 2 * ~~~( ~~~d &&& (e ^^^ f)) - 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 1 * ((d &&& e) ^^^ (e ||| f)) + 7 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 1 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 6 * ((d &&& e) ||| ~~~(e ||| f)) - 2 * (f ^^^ ~~~(d &&& (e ||| f))) + 1 * (e ^^^ (d &&& (e ||| f))) + 3 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 5 * (f ^^^ ( ~~~d &&& (e ||| f))) - 1 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 7 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * ((e &&& f) ||| (d &&& (e ||| f))) + 2 * (f &&& (d ^^^ e)) - 10 * ~~~(d ||| (e ||| f)) - 23 * ~~~(d ||| ( ~~~e ||| f)) - 4 * ~~~( ~~~d ||| (e ||| f)) - 65 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 74 * ( ~~~d &&& ( ~~~e &&& f)) - 52 * ( ~~~d &&& (e &&& f)) - 76 * (d &&& ( ~~~e &&& f)) - 1 * (d &&& (e &&& f)) = - 2 * (d &&& f) - 5 * (e ||| ~~~(d ||| ~~~f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2371 (x y : BitVec w) : +theorem e_2371 : 2 * (d ||| (e ^^^ f)) - 6 * (d ||| ~~~e) - 2 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 1 * (f ^^^ (d &&& ~~~e)) + 1 * (e ^^^ ~~~(d ||| ~~~f)) - 1 * (d ||| (e ||| f)) - 1 * ~~~(d ||| (e &&& f)) + 7 * ( ~~~e ||| ~~~(d ^^^ f)) - 1 * (e &&& ~~~(d &&& ~~~f)) + 3 * ~~~(d &&& ~~~e) + 1 * ((d &&& ~~~e) ||| (e ^^^ f)) + 4 * (e ||| ~~~(d ^^^ f)) - 2 * ~~~(e ||| f) - 7 * (f ^^^ (d ||| ~~~e)) + 1 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 7 * (e &&& ~~~f) - 1 * (e ||| (d &&& ~~~f)) - 2 * (f ||| ~~~(d ||| ~~~e)) - 11 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 4 * (d ^^^ ( ~~~e &&& f)) - 7 * (f ^^^ ~~~(d &&& (e &&& f))) - 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 5 * (d ^^^ e) - 5 * ~~~(d &&& (e ||| f)) + 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 11 * (f ||| ~~~(d ^^^ e)) + 1 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 3 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 5 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 1 * ((d &&& e) ||| ~~~(e ||| f)) - 1 * (e ||| f) - 6 * ( ~~~e &&& (d ^^^ f)) + 3 * ((d &&& f) ||| ~~~(e ||| f)) + 7 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 2 * (e ||| ~~~(d ||| ~~~f)) + 3 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 2 * (e ^^^ ~~~(d &&& ~~~f)) + 7 * f - 5 * (d ^^^ (e &&& f)) + 11 * (d ^^^ f) + 1 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 1 * (e ^^^ (d &&& (e ||| f))) + 3 * ( ~~~e &&& ~~~(d ^^^ f)) + 2 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 1 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 2 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 1 * (e ||| ~~~(d ||| f)) - 2 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 11 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 1 * (e ^^^ (d &&& ( ~~~e ||| f))) + 1 * (f ^^^ (d ||| e)) - 6 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 11 * (e ^^^ (d &&& (e ^^^ f))) + 4 * (d ^^^ ( ~~~e ||| f)) - 5 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 5 * ( ~~~d ||| ( ~~~e ||| f)) - 2 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 2 * ((d &&& e) ||| (e ^^^ f)) - 11 * (e ^^^ (d &&& ~~~f)) + 1 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 7 * ((d ||| e) &&& ~~~(e ^^^ f)) - 10 * ~~~(d ||| (e ||| f)) - 4 * ~~~(d ||| ( ~~~e ||| f)) - 9 * ~~~( ~~~d ||| (e ||| f)) + 8 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 18 * ( ~~~d &&& ( ~~~e &&& f)) - 14 * ( ~~~d &&& (e &&& f)) - 42 * (d &&& ( ~~~e &&& f)) - 31 * (d &&& (e &&& f)) = - 4 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 1 * ~~~(d &&& (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2372 (x y : BitVec w) : +theorem e_2372 : 1 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 2 * ((d ||| ~~~e) &&& (e ^^^ f)) + 1 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 2 * (e ^^^ (d &&& (e ^^^ f))) - 2 * (f ^^^ (d &&& (e ||| f))) - 2 * ~~~(d ^^^ e) - 3 * (e ^^^ (d ||| (e ^^^ f))) + 11 * ( ~~~f ||| ~~~(d ^^^ e)) + 2 * ~~~(d ||| ( ~~~e &&& f)) - 3 * (d ^^^ f) - 7 * (e ^^^ ~~~(d ||| f)) - 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 2 * (d ||| (e ||| f)) + 1 * ~~~( ~~~d &&& (e ^^^ f)) + 1 * (e ^^^ ~~~(d &&& (e ||| f))) + 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 7 * (f ^^^ ~~~(d &&& e)) + 1 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 7 * (d ^^^ (e &&& f)) - 1 * (f ^^^ ( ~~~d ||| (e &&& f))) + 5 * ((d &&& ~~~e) ||| (e ^^^ f)) - 1 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 4 * (d ^^^ e) + 7 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 7 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 2 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 6 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 3 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 6 * (f ||| (d &&& ~~~e)) + 2 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 1 * ~~~(d &&& ~~~f) + 3 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 2 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 3 * e + 2 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 1 * ((d &&& e) ^^^ (e ||| f)) + 2 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 3 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 11 * ( ~~~e &&& ~~~(d ^^^ f)) + 11 * ~~~(d ||| (e ^^^ f)) + 1 * (f &&& (d ^^^ e)) - 5 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 3 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 4 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 2 * ~~~( ~~~d ||| (e &&& f)) + 5 * (e ^^^ (d ||| (e ||| f))) - 2 * (e ||| (d &&& f)) + 2 * (e ^^^ ~~~(d ||| ~~~f)) + 11 * (e &&& ~~~(d &&& ~~~f)) + 2 * f + 7 * (f ^^^ ~~~(d ||| e)) + 11 * (f ^^^ ~~~(d &&& (e ||| f))) + 1 * (f ^^^ (d &&& ~~~e)) - 1 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 1 * ~~~(d &&& (e &&& f)) + 4 * (f ^^^ ~~~(d ||| ~~~e)) + 1 * ( ~~~e &&& (d ^^^ f)) - 11 * (e ||| ~~~(d ||| f)) - 2 * (d ^^^ (e ||| f)) - 1 * (f ^^^ (d ||| ( ~~~e &&& f))) - 2 * (e ^^^ (d ||| (e &&& f))) - 8 * ~~~(d ||| (e ||| f)) - 13 * ~~~(d ||| ( ~~~e ||| f)) - 20 * ~~~( ~~~d ||| (e ||| f)) + 9 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 21 * ( ~~~d &&& ( ~~~e &&& f)) + 9 * ( ~~~d &&& (e &&& f)) - 14 * (d &&& ( ~~~e &&& f)) - 11 * (d &&& (e &&& f)) = 1 * (e ||| ~~~(d ||| ~~~f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2373 (x y : BitVec w) : +theorem e_2373 : - 1 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 3 * (e &&& (d ^^^ f)) - 11 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 4 * (f ^^^ (d ||| (e &&& f))) - 6 * (e ^^^ (d ||| f)) + 1 * ~~~(e ||| ~~~f) - 5 * (e ^^^ (d ||| (e &&& f))) + 11 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 7 * (f ^^^ ~~~(d &&& ~~~e)) + 1 * ~~~(d &&& (e ||| f)) + 11 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 1 * (d ||| e) - 11 * (e ^^^ ~~~(d &&& ~~~f)) - 1 * ~~~(d ^^^ (e &&& f)) + 2 * (e &&& (d ||| ~~~f)) + 1 * ~~~(d &&& ( ~~~e &&& f)) + 11 * (e ^^^ ( ~~~d ||| (e &&& f))) - 1 * (f &&& (d ^^^ e)) + 2 * (d &&& ~~~f) + 5 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 3 * f - 11 * ~~~(d ||| e) - 7 * ~~~(d &&& (e &&& f)) - 1 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 2 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 1 * (e ^^^ ~~~(d &&& (e ||| f))) - 7 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 11 * (e ^^^ f) - 1 * (e ^^^ (d &&& ~~~f)) - 1 * ~~~(e &&& f) - 2 * (d ||| ~~~e) - 2 * (d &&& (e ||| f)) - 3 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 7 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 1 * ~~~(d &&& ( ~~~e ||| f)) - 7 * (e ^^^ (d ||| ( ~~~e &&& f))) - 3 * (e ||| ~~~(d ||| f)) + 1 * (f ^^^ ( ~~~d ||| (e ||| f))) - 5 * ~~~(d ^^^ e) + 5 * ( ~~~d ||| (e ^^^ f)) + 11 * (e &&& ~~~(d &&& ~~~f)) + 3 * ((d &&& e) ||| (e ^^^ f)) - 1 * (e ||| (d ^^^ f)) - 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 3 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 5 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 7 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 4 * ( ~~~d ||| ( ~~~e ||| f)) + 2 * ~~~(d &&& ~~~f) - 2 * (d &&& (e ^^^ f)) - 2 * (f ^^^ (d ||| e)) + 4 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 4 * (e ||| f) - 3 * ((d ||| e) &&& ~~~(e ^^^ f)) - 7 * (f ^^^ (d ||| (e ||| f))) + 1 * ~~~(d ||| ~~~f) - 2 * (d ||| ( ~~~e &&& f)) - 11 * ( ~~~d ||| (e ||| f)) - 7 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 2 * ((d ||| e) &&& (e ^^^ f)) - 6 * ( ~~~d &&& (e ||| f)) - 2 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 23 * ~~~(d ||| (e ||| f)) + 5 * ~~~(d ||| ( ~~~e ||| f)) + 52 * ~~~( ~~~d ||| (e ||| f)) - 16 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 21 * ( ~~~d &&& ( ~~~e &&& f)) + 34 * ( ~~~d &&& (e &&& f)) - 1 * (d &&& ( ~~~e &&& f)) = 14 * (d &&& (e &&& f)) + 1 * (d ||| (e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2374 (x y : BitVec w) : +theorem e_2374 : - 5 * (d ||| (e &&& f)) + 11 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 1 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 1 * e - 2 * (e &&& (d ||| ~~~f)) + 3 * (e &&& f) - 3 * (e ^^^ (d &&& (e ||| f))) - 5 * ( ~~~d &&& (e ^^^ f)) + 2 * (f ^^^ (d ||| e)) - 2 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 2 * (e ^^^ (d &&& f)) + 1 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 6 * (d ^^^ (e ^^^ f)) + 11 * (f ^^^ (d &&& ~~~e)) - 11 * ~~~(e &&& ~~~f) - 2 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 2 * (e ^^^ (d ||| ~~~f)) + 2 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 5 * (e ^^^ f) - 2 * (d &&& (e ^^^ f)) + 2 * (f ^^^ ~~~(d &&& e)) + 11 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 5 * ~~~(d ||| ~~~f) + 2 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 2 * ( ~~~e &&& (d ^^^ f)) + 1 * (e &&& ~~~(d &&& ~~~f)) - 7 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 11 * ((d &&& f) ||| ~~~(e ||| f)) - 11 * (e ^^^ (d &&& (e ^^^ f))) - 1 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 3 * (e &&& ~~~(d ^^^ f)) - 1 * (d ||| (e ^^^ f)) - 3 * (e ||| ~~~(d ||| ~~~f)) - 11 * ((d &&& e) ||| ~~~(e ^^^ f)) + 2 * ~~~(d &&& (e ||| f)) - 6 * (f ||| (d &&& ~~~e)) + 2 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 2 * ~~~(e &&& f) + 7 * ~~~(d &&& ~~~d) - 2 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 5 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 1 * (e ||| f) + 1 * ~~~( ~~~d ||| (e &&& f)) + 1 * (f ^^^ (d &&& e)) + 2 * (f ^^^ ( ~~~d ||| (e ||| f))) + 4 * ~~~f + 7 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 1 * (e ^^^ (d ||| ( ~~~e ||| f))) - 1 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 11 * (f ||| ~~~(d ||| ~~~e)) + 4 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 2 * ~~~(d &&& ~~~f) - 6 * (f &&& (d ^^^ e)) + 2 * ~~~(d ^^^ (e &&& f)) + 1 * (e ||| (d &&& f)) + 2 * (f ^^^ ( ~~~d &&& (e ||| f))) - 11 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 5 * (e ^^^ (d ||| ( ~~~e &&& f))) - 3 * (e ^^^ (d ||| (e ^^^ f))) - 7 * ((d &&& f) ^^^ (e ||| f)) + 1 * ( ~~~f ||| ~~~(d ^^^ e)) - 27 * ~~~(d ||| (e ||| f)) - 8 * ~~~(d ||| ( ~~~e ||| f)) - 25 * ~~~( ~~~d ||| (e ||| f)) - 8 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 6 * ( ~~~d &&& ( ~~~e &&& f)) + 29 * ( ~~~d &&& (e &&& f)) - 10 * (d &&& ( ~~~e &&& f)) + 7 * (d &&& (e &&& f)) = - 4 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * (f ^^^ ( ~~~d ||| (e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2375 (x y : BitVec w) : +theorem e_2375 : - 3 * ~~~(d ^^^ ( ~~~e &&& f)) - 7 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 1 * (d &&& f) + 11 * (e ^^^ ~~~(d &&& (e ||| f))) + 1 * (e ^^^ (d &&& ~~~f)) + 7 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 7 * ( ~~~d ||| ( ~~~e ||| f)) - 3 * (d ^^^ ( ~~~e ||| f)) - 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 6 * (f ^^^ (d ||| (e &&& f))) - 7 * (d ||| ~~~f) + 11 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 11 * ( ~~~e ||| ~~~(d ^^^ f)) - 1 * (d ^^^ e) - 2 * (f ^^^ ~~~(d &&& (e &&& f))) - 6 * (d ||| (e ^^^ f)) - 1 * (d &&& (e ^^^ f)) - 1 * (e &&& ~~~(d &&& f)) - 1 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 3 * (f ^^^ ( ~~~d &&& (e ||| f))) + 11 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 1 * (f ||| ~~~(d ||| e)) + 5 * (e &&& (d ||| ~~~f)) + 1 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 5 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 5 * (d ^^^ f) - 6 * (e ^^^ (d &&& (e ^^^ f))) - 1 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 7 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 5 * ( ~~~d ||| (e ^^^ f)) - 11 * ~~~(d &&& ~~~d) + 5 * (d &&& ~~~e) - 2 * (e ^^^ ( ~~~d ||| (e ||| f))) - 2 * (f ^^^ ~~~(d &&& (e ||| f))) + 11 * (f ^^^ (d ||| ( ~~~e ||| f))) + 1 * (d ||| ~~~e) - 1 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 1 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 2 * ( ~~~f &&& ~~~(d ^^^ e)) - 1 * ~~~(d ||| f) - 2 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 7 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 1 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 2 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 6 * (f ||| (d &&& e)) - 11 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 4 * (e ^^^ (d ||| ( ~~~e &&& f))) + 2 * (f ^^^ (d ||| (e ||| f))) - 6 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 1 * ~~~(d &&& ~~~f) + 1 * (d &&& ( ~~~e ||| f)) + 2 * (f ^^^ ~~~(d &&& ~~~e)) - 5 * ( ~~~d &&& (e ^^^ f)) - 3 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 3 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 7 * ~~~(d ||| ( ~~~e &&& f)) + 1 * (d ^^^ (e ^^^ f)) + 1 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 5 * ~~~e + 4 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 11 * (d ||| f) - 1 * (f ^^^ ( ~~~d ||| (e ||| f))) + 5 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 21 * ~~~(d ||| (e ||| f)) + 35 * ~~~(d ||| ( ~~~e ||| f)) + 9 * ~~~( ~~~d ||| (e ||| f)) + 33 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 38 * ( ~~~d &&& ( ~~~e &&& f)) + 34 * ( ~~~d &&& (e &&& f)) + 6 * (d &&& ( ~~~e &&& f)) = - 39 * (d &&& (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2376 (x y : BitVec w) : +theorem e_2376 : 1 * (d ||| ( ~~~e &&& f)) - 2 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 2 * (e ^^^ (d ||| (e ^^^ f))) - 2 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 1 * (f ^^^ ~~~(d &&& (e &&& f))) - 2 * ( ~~~d ||| (e &&& f)) + 2 * (f ||| (d &&& e)) + 11 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 2 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 5 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 2 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * ( ~~~e ||| ~~~(d ^^^ f)) - 1 * (d &&& (e ||| f)) + 7 * ((d ||| ~~~e) &&& (e ^^^ f)) + 1 * (d ^^^ e) + 2 * ( ~~~f &&& ~~~(d ^^^ e)) - 6 * (f ^^^ (d ||| (e &&& f))) - 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 5 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 11 * ~~~(d &&& ~~~f) + 2 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 7 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 1 * (f ^^^ ( ~~~d ||| (e &&& f))) - 7 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 1 * (e &&& ~~~f) + 2 * ((d &&& e) ||| ~~~(e ||| f)) - 2 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 3 * (e &&& (d ||| ~~~f)) - 11 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 4 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 1 * (d ||| (e &&& f)) - 3 * (f ^^^ ~~~(d ||| (e &&& f))) - 1 * ((d &&& e) ^^^ (e ||| f)) - 1 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 3 * (e ||| f) - 7 * ( ~~~d &&& ( ~~~e ||| f)) + 1 * ((e &&& f) ||| (d &&& (e ||| f))) - 6 * ~~~(d &&& ( ~~~e ||| f)) - 11 * ( ~~~d ||| (e ^^^ f)) + 11 * (e &&& ~~~(d ^^^ f)) + 5 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 1 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * (d ||| (e ^^^ f)) + 2 * (e ^^^ ~~~(d &&& ~~~f)) + 1 * ~~~(d ||| ~~~f) - 6 * (f ^^^ (d ||| ~~~e)) - 1 * ~~~(d &&& ( ~~~e &&& f)) + 1 * (f &&& ~~~(d &&& ~~~e)) + 4 * (d ^^^ (e ||| f)) - 6 * (d ^^^ f) + 2 * ~~~(d ||| (e ^^^ f)) + 2 * (e ^^^ (d &&& f)) - 1 * (f ||| ~~~(d ^^^ e)) - 5 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 5 * (f ^^^ (d &&& ( ~~~e ||| f))) - 6 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 1 * (e ^^^ ~~~(d &&& f)) + 5 * ~~~(d &&& ~~~d) + 1 * ~~~f + 1 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 7 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 7 * (e ^^^ (d ||| (e ||| f))) - 2 * (d ||| ~~~f) + 60 * ~~~(d ||| (e ||| f)) + 29 * ~~~(d ||| ( ~~~e ||| f)) + 15 * ~~~( ~~~d ||| (e ||| f)) + 17 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 33 * ( ~~~d &&& ( ~~~e &&& f)) + 17 * (d &&& ( ~~~e &&& f)) + 6 * (d &&& (e &&& f)) = - 47 * ( ~~~d &&& (e &&& f)) + 1 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2377 (x y : BitVec w) : +theorem e_2377 : - 1 * (f ^^^ ~~~(d ||| ~~~e)) + 1 * (f ^^^ ~~~(d ||| (e &&& f))) - 1 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 7 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 1 * (e ^^^ ~~~(d ||| ~~~f)) - 1 * ~~~( ~~~d &&& (e ||| f)) + 3 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 5 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 3 * (e &&& ~~~(d &&& f)) - 1 * (e ||| (d &&& f)) - 5 * (d &&& ~~~e) + 4 * (d ||| ~~~f) + 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 7 * (e ^^^ ~~~(d &&& f)) - 1 * ~~~(d ^^^ f) + 11 * ( ~~~e ||| ~~~(d ^^^ f)) - 2 * ( ~~~d ||| (e ||| f)) - 1 * (e ^^^ (d ||| (e ||| f))) - 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 11 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 5 * (e &&& f) + 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 2 * ~~~d + 2 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * ((d ||| ~~~e) &&& (e ^^^ f)) + 2 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 1 * (f ^^^ (d ||| ~~~e)) - 3 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 5 * ((d ||| e) &&& ~~~(e ^^^ f)) + 3 * ~~~(d &&& ~~~e) + 5 * ( ~~~d &&& (e ^^^ f)) + 4 * (d ^^^ (e &&& f)) + 7 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 2 * (e ||| ~~~f) + 1 * ((d &&& ~~~e) ||| (e ^^^ f)) - 1 * ~~~(e ^^^ f) - 2 * (e ^^^ (d &&& (e ^^^ f))) - 5 * (f &&& ~~~(d &&& ~~~e)) - 1 * ((d &&& e) ^^^ (e ||| ~~~f)) + 2 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 4 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 5 * (f ^^^ (d ||| ( ~~~e ||| f))) - 6 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 7 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 11 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 11 * (f ||| (d &&& ~~~e)) - 3 * (e &&& (d ||| f)) + 2 * (e ||| ~~~(d ^^^ f)) + 11 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 2 * (d &&& ( ~~~e ||| f)) - 1 * (f ||| (d ^^^ e)) + 11 * (f ^^^ (d ||| ( ~~~e &&& f))) - 5 * (e ^^^ ~~~(d &&& (e &&& f))) - 2 * (f ^^^ (d &&& ( ~~~e ||| f))) - 1 * (d &&& (e ||| f)) - 1 * (f &&& (d ||| e)) - 2 * ~~~(d ^^^ e) + 11 * ~~~( ~~~d ||| (e &&& f)) + 2 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 11 * ~~~(d &&& ( ~~~e ||| f)) + 1 * (f ||| ~~~(d ||| ~~~e)) + 29 * ~~~(d ||| (e ||| f)) + 8 * ~~~(d ||| ( ~~~e ||| f)) - 35 * ~~~( ~~~d ||| (e ||| f)) - 29 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 20 * ( ~~~d &&& ( ~~~e &&& f)) + 20 * ( ~~~d &&& (e &&& f)) + 2 * (d &&& ( ~~~e &&& f)) + 21 * (d &&& (e &&& f)) = 11 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2378 (x y : BitVec w) : +theorem e_2378 : 1 * ((d &&& f) ||| (e &&& ~~~f)) - 1 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 1 * (e &&& f) - 5 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 6 * (f ^^^ (d ||| ( ~~~e ||| f))) - 3 * (f ^^^ ~~~(d ||| ~~~e)) + 2 * ~~~d + 5 * (e ^^^ ~~~(d &&& ~~~f)) + 2 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 2 * ((e &&& f) ||| (d &&& (e ||| f))) + 11 * (e ^^^ ( ~~~d ||| (e ||| f))) + 2 * ( ~~~e &&& ~~~(d ^^^ f)) - 6 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 4 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 7 * (f &&& ~~~(d &&& e)) - 3 * (e ^^^ ~~~(d ||| f)) + 4 * ((d &&& f) ||| ~~~(e ||| f)) + 5 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 11 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 5 * (e ||| (d ^^^ f)) + 7 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 4 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * (e &&& ~~~(d &&& f)) - 2 * d - 5 * (e &&& ~~~f) - 5 * ~~~(d ^^^ ( ~~~e &&& f)) + 1 * (e ||| (d &&& ~~~f)) - 11 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 5 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 11 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 1 * (e ^^^ ~~~(d &&& f)) + 2 * (f ^^^ ~~~(d ||| (e &&& f))) + 5 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 1 * ((d &&& e) ||| ~~~(e ^^^ f)) - 3 * (e ^^^ (d &&& (e ||| f))) - 6 * ((d &&& f) ^^^ (e ||| f)) - 5 * ( ~~~d ||| ( ~~~e &&& f)) - 2 * ~~~(d &&& (e ^^^ f)) - 2 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 1 * (e &&& ~~~(d ^^^ f)) - 3 * ~~~(d ^^^ (e ||| f)) - 11 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * (f ^^^ (d &&& (e ||| f))) - 2 * ( ~~~d ||| (e &&& f)) - 2 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * (f ^^^ ~~~(d ||| e)) + 1 * ~~~f - 6 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 4 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 1 * (e &&& (d ^^^ f)) - 1 * (d &&& (e ||| f)) - 7 * (d ^^^ e) + 2 * (d &&& ( ~~~e ||| f)) + 7 * ~~~(e ^^^ f) + 3 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 11 * (d ||| ~~~f) + 5 * (f ^^^ ( ~~~d ||| (e &&& f))) + 2 * (d ^^^ ( ~~~e ||| f)) + 7 * ( ~~~e ||| ~~~(d ^^^ f)) + 11 * ~~~(d ||| (e ^^^ f)) - 1 * (e &&& ~~~(d &&& ~~~f)) - 1 * ~~~( ~~~d ||| (e &&& f)) - 35 * ~~~(d ||| (e ||| f)) + 27 * ~~~(d ||| ( ~~~e ||| f)) - 3 * ~~~( ~~~d ||| (e ||| f)) + 17 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 18 * ( ~~~d &&& ( ~~~e &&& f)) - 4 * ( ~~~d &&& (e &&& f)) - 9 * (d &&& ( ~~~e &&& f)) - 27 * (d &&& (e &&& f)) = - 7 * ( ~~~(d ||| e) ||| (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2379 (x y : BitVec w) : +theorem e_2379 : - 3 * (e ||| ~~~f) - 1 * (e ^^^ (d ||| (e &&& f))) + 1 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 5 * ~~~(d ^^^ e) + 2 * (f ^^^ (d &&& (e ||| f))) - 7 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 3 * (e ||| ~~~(d ||| ~~~f)) + 1 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 3 * (e &&& f) - 2 * ~~~(d ^^^ (e ^^^ f)) + 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 2 * (e ^^^ ( ~~~d &&& (e ||| f))) + 1 * ~~~(e &&& f) + 11 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 4 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 2 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 5 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * (f &&& (d ||| e)) - 11 * ~~~( ~~~d ||| (e ^^^ f)) - 3 * ( ~~~e &&& ~~~(d ^^^ f)) + 7 * (e ^^^ (d ||| f)) + 11 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 6 * (d ^^^ ( ~~~e ||| f)) - 6 * ( ~~~e ||| ~~~(d ^^^ f)) - 7 * (d ||| (e ^^^ f)) - 5 * ~~~(d ||| ( ~~~e &&& f)) + 2 * (f ^^^ ~~~(d &&& (e &&& f))) + 2 * (f ^^^ ( ~~~d ||| (e ||| f))) + 5 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 5 * (e ||| ~~~(d ^^^ f)) + 2 * (d ^^^ (e &&& f)) - 2 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 1 * ~~~( ~~~d &&& (e ^^^ f)) + 5 * ~~~(d &&& ( ~~~e ||| f)) - 6 * ~~~(d ||| (e &&& f)) + 11 * (d ||| ( ~~~e ||| f)) - 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 3 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 4 * (d &&& ~~~f) + 1 * (f &&& (d ^^^ e)) + 7 * (e ^^^ (d ||| (e ^^^ f))) + 2 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 1 * (f ||| ~~~(d ||| e)) - 3 * (e ||| (d &&& f)) - 1 * (f ^^^ ( ~~~d ||| (e &&& f))) - 1 * ( ~~~e ||| (d ^^^ f)) + 7 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 5 * (f ^^^ (d ||| (e &&& f))) - 2 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 5 * ((d ^^^ e) ||| ~~~(d ^^^ f)) + 1 * (f ^^^ (d ||| (e ||| f))) + 7 * (e &&& (d ||| ~~~f)) - 7 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 11 * ~~~(e &&& ~~~f) - 6 * ~~~( ~~~d ||| (e &&& f)) + 5 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 4 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 6 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 1 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 4 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 7 * ~~~(d ||| (e ||| f)) - 7 * ~~~(d ||| ( ~~~e ||| f)) - 14 * ~~~( ~~~d ||| (e ||| f)) - 28 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 12 * ( ~~~d &&& ( ~~~e &&& f)) + 8 * ( ~~~d &&& (e &&& f)) - 7 * (d &&& ( ~~~e &&& f)) + 18 * (d &&& (e &&& f)) = - 2 * (d ||| (e &&& f)) + 2 * (d ^^^ ( ~~~e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2380 (x y : BitVec w) : +theorem e_2380 : - 3 * ((d &&& e) ||| (e ^^^ f)) - 5 * (f &&& ~~~(d &&& ~~~e)) + 1 * (d ||| e) + 1 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 4 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 3 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 1 * (f ^^^ (d ||| ( ~~~e &&& f))) + 2 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 3 * (d ||| ( ~~~e &&& f)) + 7 * ( ~~~f &&& (d ^^^ e)) + 3 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 4 * ~~~(d ||| (e ^^^ f)) + 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 1 * (d ||| ~~~e) + 1 * (d ^^^ f) - 11 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 1 * (e ||| (d ^^^ f)) - 3 * ~~~(d ||| (e &&& f)) + 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 5 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 5 * (f ||| (d &&& e)) + 7 * (d ^^^ e) + 1 * ((d &&& f) ||| ~~~(e ||| f)) + 3 * (f ^^^ (d ||| e)) - 1 * ((d ||| e) &&& (e ^^^ f)) + 11 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 11 * ~~~( ~~~d ||| (e &&& f)) + 1 * (e ^^^ (d ||| (e ||| f))) + 4 * (f ||| ~~~(d ||| ~~~e)) + 3 * (e ||| (d &&& f)) + 4 * (d ^^^ ( ~~~e ||| f)) + 2 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 1 * ((d &&& e) ^^^ (e ||| ~~~f)) + 1 * ~~~(e ^^^ f) + 4 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 2 * (f &&& (d ^^^ e)) - 5 * f + 11 * (e ^^^ (d &&& (e ^^^ f))) + 3 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 1 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 2 * (e ||| ~~~f) - 1 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 2 * (f ||| ~~~(d ^^^ e)) - 1 * (d &&& ~~~e) + 4 * (f ^^^ ( ~~~d &&& (e ||| f))) + 11 * (e &&& ~~~f) - 1 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 1 * (e ^^^ ~~~(d ||| ~~~f)) + 2 * ((d ||| e) &&& ~~~(e ^^^ f)) - 2 * ~~~(d &&& (e ^^^ f)) + 1 * (d ^^^ (e &&& f)) - 1 * ~~~(d ^^^ (e &&& f)) + 5 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 2 * ( ~~~d &&& ( ~~~e ||| f)) + 1 * (e &&& ~~~(d &&& f)) + 4 * ((d ^^^ e) &&& (d ^^^ f)) + 5 * (e &&& ~~~(d &&& ~~~f)) - 3 * (e &&& ~~~(d ^^^ f)) + 1 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 7 * ~~~( ~~~d &&& (e &&& f)) - 7 * (e ^^^ (d ||| (e &&& f))) - 21 * ~~~(d ||| (e ||| f)) - 61 * ~~~(d ||| ( ~~~e ||| f)) - 32 * ~~~( ~~~d ||| (e ||| f)) - 24 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 26 * ( ~~~d &&& ( ~~~e &&& f)) - 67 * ( ~~~d &&& (e &&& f)) - 19 * (d &&& ( ~~~e &&& f)) - 34 * (d &&& (e &&& f)) = - 11 * (e ||| f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2381 (x y : BitVec w) : +theorem e_2381 : - 2 * ~~~(d &&& ~~~d) - 1 * (e ^^^ ~~~(d ||| (e &&& f))) + 2 * (f ^^^ ( ~~~d &&& (e ||| f))) - 1 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 7 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 7 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 7 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 3 * (f ^^^ (d ||| (e &&& f))) + 1 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 11 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 6 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 1 * ( ~~~d ||| ( ~~~e &&& f)) - 11 * ((d &&& e) ||| ~~~(e ||| f)) - 2 * (e ^^^ (d ||| f)) - 1 * (f ^^^ ~~~(d &&& ~~~e)) - 5 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 4 * (f &&& ~~~(d ^^^ e)) + 4 * (e &&& (d ||| f)) + 1 * ~~~(d ^^^ (e ||| f)) - 1 * (d ||| ( ~~~e ||| f)) - 3 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 1 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 1 * (e ^^^ ( ~~~d &&& (e ||| f))) + 5 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 3 * (f &&& (d ^^^ e)) + 1 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 2 * (f ^^^ ~~~(d &&& (e ||| f))) - 3 * (e ||| ~~~f) + 3 * ~~~(d &&& ( ~~~e ||| f)) + 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 6 * ~~~(d &&& e) - 7 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 11 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 1 * ~~~(e &&& f) + 2 * ~~~(d ||| ~~~e) + 5 * (d ||| ~~~f) + 4 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 2 * ( ~~~d ||| (e ^^^ f)) + 3 * ~~~(d &&& f) - 6 * (e ^^^ ( ~~~d ||| (e &&& f))) + 1 * ~~~(e ^^^ f) + 2 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 7 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 1 * (d &&& (e ||| f)) - 5 * (e ^^^ (d &&& ( ~~~e ||| f))) - 6 * ( ~~~d ||| ( ~~~e ||| f)) + 2 * ( ~~~d ||| (e &&& f)) - 1 * (e ^^^ ( ~~~d ||| (e ||| f))) - 2 * (d ^^^ e) - 2 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 1 * ((d ||| ~~~e) &&& (e ^^^ f)) - 2 * (f ||| (d &&& e)) + 5 * ( ~~~f &&& ~~~(d ^^^ e)) + 4 * ((d ||| e) &&& ~~~(e ^^^ f)) - 11 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 3 * (d ^^^ (e &&& f)) + 1 * ~~~e - 11 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 11 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 3 * (e ^^^ ~~~(d &&& (e &&& f))) + 1 * (f ^^^ (d &&& ( ~~~e ||| f))) - 2 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 29 * ~~~(d ||| (e ||| f)) + 35 * ~~~(d ||| ( ~~~e ||| f)) + 42 * ~~~( ~~~d ||| (e ||| f)) + 6 * ( ~~~d &&& ( ~~~e &&& f)) + 30 * ( ~~~d &&& (e &&& f)) + 40 * (d &&& ( ~~~e &&& f)) + 6 * (d &&& (e &&& f)) = - 34 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 5 * (d &&& ~~~e) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2382 (x y : BitVec w) : +theorem e_2382 : 1 * (d ||| (e ||| f)) - 11 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 5 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 2 * ( ~~~e ||| (d ^^^ f)) - 11 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 4 * (d ||| e) - 5 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (e &&& (d ^^^ f)) + 1 * (f ^^^ ~~~(d &&& ~~~e)) + 3 * (d ^^^ ( ~~~e ||| f)) + 11 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 5 * ( ~~~f ||| ~~~(d ^^^ e)) - 2 * ~~~(d ||| f) - 2 * ~~~(d ||| e) + 5 * (e &&& ~~~(d &&& ~~~f)) + 11 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 7 * ~~~(d ^^^ ( ~~~e ||| f)) - 2 * (e ||| (d ^^^ f)) - 2 * (f ^^^ (d ||| e)) + 2 * (f ||| ~~~(d ||| e)) - 3 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 1 * (f ^^^ (d &&& (e ||| f))) + 1 * d + 4 * ( ~~~d &&& ( ~~~e ||| f)) + 2 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 7 * ( ~~~e ||| ~~~(d ^^^ f)) - 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 1 * ~~~( ~~~d &&& (e ||| f)) + 2 * (d ^^^ f) + 5 * ((d &&& e) ^^^ (e ||| ~~~f)) - 2 * (f &&& ~~~(d &&& ~~~e)) + 2 * (f ^^^ ~~~(d &&& (e &&& f))) - 6 * ((d &&& e) ||| (e ^^^ f)) - 11 * (e ^^^ (d ||| f)) - 6 * (f ||| ~~~(d ^^^ e)) - 1 * ~~~(d &&& (e ^^^ f)) + 2 * (d ||| f) - 5 * (e ^^^ (d &&& f)) - 1 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 1 * (d ^^^ e) - 11 * (e ^^^ ~~~(d ||| f)) - 1 * ((d &&& ~~~e) ||| (e ^^^ f)) + 7 * (e ||| ~~~(d ||| ~~~f)) - 11 * ( ~~~d &&& (e ^^^ f)) + 1 * (e ^^^ ~~~(d ||| ~~~f)) + 5 * ~~~(d &&& e) - 7 * ((d ^^^ e) ||| (d ^^^ f)) + 7 * (d ^^^ (e ^^^ f)) + 1 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 11 * ((d ||| e) &&& (e ^^^ f)) + 1 * ~~~(e ||| f) + 1 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 1 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 2 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 2 * (e ^^^ (d &&& ( ~~~e ||| f))) + 1 * ( ~~~f &&& (d ^^^ e)) - 7 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 1 * (d &&& ( ~~~e ||| f)) + 1 * ~~~(d ^^^ (e ||| f)) + 2 * (e &&& (d ||| f)) + 28 * ~~~(d ||| (e ||| f)) + 31 * ~~~(d ||| ( ~~~e ||| f)) + 21 * ~~~( ~~~d ||| (e ||| f)) + 56 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 49 * ( ~~~d &&& ( ~~~e &&& f)) + 10 * ( ~~~d &&& (e &&& f)) + 46 * (d &&& ( ~~~e &&& f)) + 29 * (d &&& (e &&& f)) = - 2 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 1 * (e ^^^ (d &&& ~~~f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2383 (x y : BitVec w) : +theorem e_2383 : - 2 * ((d &&& e) ||| (e ^^^ f)) + 2 * ((d &&& e) ^^^ (e ||| f)) - 1 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 5 * ( ~~~e &&& ~~~(d ^^^ f)) + 4 * (d ||| ( ~~~e &&& f)) + 4 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 2 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 1 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 5 * (e &&& (d ||| ~~~f)) - 6 * ( ~~~d &&& ( ~~~e ||| f)) - 6 * (f ^^^ ( ~~~d &&& (e ||| f))) - 11 * ( ~~~f &&& ~~~(d ^^^ e)) + 3 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * ( ~~~d ||| ( ~~~e &&& f)) + 5 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 1 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 7 * ( ~~~d ||| ( ~~~e ||| f)) - 11 * ~~~(d ||| (e ^^^ f)) + 2 * (f ^^^ ~~~(d &&& (e ||| f))) + 2 * (e ^^^ (d &&& ( ~~~e ||| f))) + 3 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 5 * ~~~( ~~~d ||| (e &&& f)) + 1 * ((d ||| e) &&& (e ^^^ f)) - 7 * ~~~(d ^^^ (e &&& f)) + 1 * (d ||| ~~~f) - 7 * (e ^^^ ~~~(d &&& (e ||| f))) - 2 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 2 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 1 * (e &&& ~~~(d &&& f)) + 5 * (e &&& ~~~(d &&& ~~~f)) + 1 * (f ^^^ (d ||| (e &&& f))) + 1 * ~~~(d &&& e) + 3 * (f ^^^ ~~~(d ||| e)) - 11 * ( ~~~f &&& (d ^^^ e)) - 1 * (e ^^^ (d ||| ( ~~~e &&& f))) + 4 * ~~~(e ||| ~~~f) + 7 * (f ||| (d &&& ~~~e)) - 7 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 2 * ( ~~~f ||| ~~~(d ^^^ e)) - 2 * ~~~(d ||| (e &&& f)) + 5 * ~~~d - 1 * (d ||| (e ||| f)) + 1 * (d ||| (e &&& f)) - 5 * ((d &&& e) ||| ~~~(e ^^^ f)) + 1 * (e ||| ~~~(d ^^^ f)) + 7 * ((d &&& f) ^^^ (e ||| f)) - 1 * (e &&& (d ^^^ f)) - 6 * (f ^^^ (d ||| e)) + 1 * ~~~(d ||| ~~~e) - 11 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 4 * (e ^^^ (d &&& f)) + 2 * (d &&& ~~~e) - 1 * (f ^^^ ~~~(d &&& ~~~e)) + 7 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 7 * (d &&& (e ^^^ f)) + 11 * (d ^^^ f) + 2 * ( ~~~d &&& (e ||| f)) + 2 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 1 * (f &&& (d ^^^ e)) - 6 * (e ^^^ ( ~~~d &&& (e ||| f))) + 4 * (d ||| ( ~~~e ||| f)) - 1 * (e &&& ~~~f) + 4 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 38 * ~~~(d ||| (e ||| f)) + 10 * ~~~(d ||| ( ~~~e ||| f)) - 4 * ~~~( ~~~d ||| (e ||| f)) - 27 * ( ~~~d &&& ( ~~~e &&& f)) - 39 * ( ~~~d &&& (e &&& f)) - 30 * (d &&& ( ~~~e &&& f)) + 15 * (d &&& (e &&& f)) = - 5 * (f &&& (d ||| e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2384 (x y : BitVec w) : +theorem e_2384 : 2 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 6 * ~~~(d ^^^ (e ^^^ f)) - 5 * (e ^^^ (d &&& f)) - 1 * ~~~(e ||| ~~~f) - 3 * (f ^^^ ~~~(d ||| (e &&& f))) - 6 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 2 * (e ||| ~~~f) - 6 * (e ||| (d &&& ~~~f)) + 1 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 4 * ~~~(d &&& ~~~d) + 11 * (f ^^^ (d &&& (e ||| f))) + 2 * ( ~~~d ||| ( ~~~e ||| f)) - 5 * (d ||| (e ||| f)) + 5 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 7 * (f ^^^ (d ||| ( ~~~e ||| f))) + 2 * (d &&& (e ||| f)) - 11 * ~~~e - 5 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 5 * ~~~(e &&& f) + 1 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 3 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 5 * ( ~~~e &&& ~~~(d ^^^ f)) - 3 * ~~~( ~~~d ||| (e &&& f)) - 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 2 * (f ^^^ (d ||| ~~~e)) + 2 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 2 * ( ~~~f ||| ~~~(d ^^^ e)) + 1 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 1 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * (e &&& ~~~(d &&& ~~~f)) - 2 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 1 * ((d &&& f) ||| ~~~(e ||| f)) - 1 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 7 * (e ^^^ ~~~(d &&& f)) + 2 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 11 * (e ^^^ f) + 3 * (f ^^^ ( ~~~d ||| (e &&& f))) + 3 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 2 * (f &&& (d ||| e)) - 2 * (e ^^^ (d &&& (e ||| f))) - 1 * (e ^^^ ( ~~~d &&& (e ||| f))) - 3 * (e ^^^ ( ~~~d ||| (e ||| f))) - 5 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 6 * ( ~~~d ||| ( ~~~e &&& f)) + 1 * (e &&& (d ||| ~~~f)) - 1 * ( ~~~e ||| (d ^^^ f)) - 1 * ((d ||| ~~~e) &&& (e ^^^ f)) + 3 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 2 * ~~~(d &&& e) - 11 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 1 * ~~~(d ||| ( ~~~e &&& f)) + 4 * (f ^^^ (d ||| (e &&& f))) + 2 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * ((d &&& ~~~e) ||| (e ^^^ f)) - 6 * (e ^^^ (d ||| (e ^^^ f))) + 2 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 1 * ~~~(d &&& (e ^^^ f)) - 1 * ( ~~~d &&& (e ||| f)) + 7 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 4 * (e ||| (d &&& f)) + 1 * ~~~(d &&& (e &&& f)) - 1 * (e &&& ~~~(d ^^^ f)) + 9 * ~~~(d ||| (e ||| f)) - 1 * ~~~(d ||| ( ~~~e ||| f)) + 32 * ~~~( ~~~d ||| (e ||| f)) - 26 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 2 * ( ~~~d &&& ( ~~~e &&& f)) + 20 * ( ~~~d &&& (e &&& f)) + 20 * (d &&& ( ~~~e &&& f)) - 9 * (d &&& (e &&& f)) = 1 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 2 * (f &&& (d ^^^ e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2385 (x y : BitVec w) : +theorem e_2385 : 4 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 2 * (f ^^^ ~~~(d &&& (e ||| f))) - 2 * (e ||| ~~~(d ||| f)) - 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 1 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 6 * (e ^^^ (d &&& (e ^^^ f))) - 6 * (d ^^^ f) + 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 7 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 5 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 3 * ((d ||| e) &&& (e ^^^ f)) - 11 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 3 * (f ^^^ (d ||| ( ~~~e &&& f))) - 7 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 4 * (f &&& (d ^^^ e)) - 5 * (e ^^^ ~~~(d &&& ~~~f)) - 2 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 3 * (d &&& f) - 5 * ( ~~~d &&& (e ^^^ f)) + 1 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 7 * ~~~(d &&& ~~~d) - 7 * ((d &&& e) ^^^ (e ||| ~~~f)) - 6 * (e ^^^ (d ||| (e ^^^ f))) - 3 * ~~~( ~~~d &&& (e ^^^ f)) + 7 * (e ^^^ ~~~(d &&& (e &&& f))) + 2 * ~~~e + 4 * ~~~(d ||| (e &&& f)) + 5 * (e ^^^ ( ~~~d ||| (e &&& f))) - 7 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 2 * ( ~~~d &&& ( ~~~e ||| f)) - 3 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 1 * ((d ||| e) &&& ~~~(e ^^^ f)) + 1 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 3 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 2 * (d ||| (e &&& f)) - 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 11 * (e &&& ~~~f) + 7 * (e ^^^ f) - 2 * (d ||| e) - 1 * (f ^^^ (d &&& ~~~e)) + 3 * (e ^^^ ( ~~~d &&& (e ||| f))) - 11 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 4 * (f ^^^ (d ||| (e &&& f))) + 1 * (e ^^^ (d ||| (e ||| f))) + 5 * (e ^^^ ~~~(d ||| ~~~f)) + 1 * (e ||| (d &&& ~~~f)) + 3 * ~~~(e ||| f) - 2 * ( ~~~d ||| (e ^^^ f)) + 1 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 1 * (d ||| (e ||| f)) - 6 * (d &&& (e ^^^ f)) + 11 * ~~~(e &&& ~~~f) + 11 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 11 * (e &&& (d ||| f)) + 3 * ~~~(d ^^^ (e ^^^ f)) + 5 * ~~~(d &&& (e ||| f)) - 5 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 2 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * (e ^^^ (d &&& ( ~~~e ||| f))) + 2 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 1 * (e ^^^ (d ||| (e &&& f))) - 11 * ~~~(d ||| (e ||| f)) + 34 * ~~~(d ||| ( ~~~e ||| f)) + 15 * ~~~( ~~~d ||| (e ||| f)) + 19 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 26 * ( ~~~d &&& ( ~~~e &&& f)) - 24 * ( ~~~d &&& (e &&& f)) + 21 * (d &&& ( ~~~e &&& f)) - 33 * (d &&& (e &&& f)) = 1 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2386 (x y : BitVec w) : +theorem e_2386 : 2 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 5 * (e ||| (d ^^^ f)) - 1 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 2 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 1 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 5 * (d ^^^ (e ||| f)) - 3 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 3 * ( ~~~d ||| (e ||| f)) + 7 * (d ^^^ ( ~~~e ||| f)) + 1 * (f ^^^ (d &&& ( ~~~e ||| f))) + 1 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 2 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 11 * (e ^^^ (d ||| (e ||| f))) + 4 * (e ^^^ ~~~(d &&& ~~~f)) - 7 * (f &&& ~~~(d &&& ~~~e)) + 3 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 3 * (e ^^^ ( ~~~d ||| (e ||| f))) + 1 * (d ^^^ ( ~~~e &&& f)) + 1 * (f ^^^ ( ~~~d ||| (e &&& f))) + 11 * ((d &&& e) ||| ~~~(e ||| f)) + 1 * ( ~~~d ||| (e ^^^ f)) - 3 * (f &&& ~~~(d &&& e)) - 2 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 1 * ( ~~~d &&& (e ||| f)) - 1 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 11 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 5 * ~~~(d ||| ~~~f) - 7 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 1 * (e ^^^ (d ||| ( ~~~e ||| f))) + 7 * (d ||| (e ||| f)) - 1 * (e ||| f) - 2 * (d &&& f) + 4 * (e &&& ~~~(d ^^^ f)) + 1 * (f ^^^ (d ||| e)) - 3 * (f ^^^ (d ||| (e ||| f))) + 1 * ~~~(e ^^^ f) + 7 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 3 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 1 * ((d &&& e) ||| ~~~(e ^^^ f)) + 2 * (f ||| ~~~(d ^^^ e)) - 2 * ( ~~~d ||| ( ~~~e &&& f)) + 1 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 1 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 7 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 11 * (f ^^^ (d &&& e)) - 2 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 5 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * ~~~( ~~~d &&& (e ||| f)) + 4 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 6 * (f &&& (d ||| e)) + 3 * (f ^^^ (d ||| ( ~~~e ||| f))) - 5 * ~~~(e &&& ~~~f) + 2 * (e ^^^ (d ||| ( ~~~e &&& f))) - 11 * ((d ||| e) &&& (e ^^^ f)) + 5 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 11 * ~~~(e &&& f) - 1 * ~~~( ~~~d ||| (e &&& f)) + 3 * d + 7 * (f ^^^ (d ||| ( ~~~e &&& f))) + 7 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 11 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 11 * ( ~~~d &&& ( ~~~e ||| f)) - 5 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 57 * ~~~(d ||| (e ||| f)) - 14 * ~~~(d ||| ( ~~~e ||| f)) - 13 * ~~~( ~~~d ||| (e ||| f)) - 57 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 4 * ( ~~~d &&& ( ~~~e &&& f)) - 16 * ( ~~~d &&& (e &&& f)) - 13 * (d &&& ( ~~~e &&& f)) - 3 * (d &&& (e &&& f)) = - 1 * (d &&& ~~~e) + 1 * ((d &&& f) ^^^ (e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2387 (x y : BitVec w) : +theorem e_2387 : 1 * ~~~(d &&& e) + 2 * (e &&& ~~~(d ^^^ f)) + 7 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 3 * ~~~(d ^^^ f) - 11 * (f &&& ~~~(d &&& ~~~e)) + 4 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 5 * (e ^^^ (d &&& (e ||| f))) + 11 * (d ^^^ (e ||| f)) - 2 * (f ^^^ ~~~(d &&& ~~~e)) + 2 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 3 * (d &&& ~~~e) + 7 * (d &&& (e ||| f)) + 4 * (f ^^^ (d ||| ( ~~~e ||| f))) + 5 * (f ^^^ (d &&& e)) + 3 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 2 * ( ~~~d &&& ( ~~~e ||| f)) - 1 * ~~~(d &&& ( ~~~e ||| f)) + 1 * (f ^^^ ~~~(d ||| ~~~e)) + 1 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 7 * ~~~(d ||| ~~~e) - 5 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 1 * (f ^^^ ~~~(d ||| e)) - 2 * (f ^^^ (d &&& (e ||| f))) + 11 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 2 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 3 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 3 * (d &&& (e ^^^ f)) + 1 * ~~~(d &&& (e &&& f)) - 7 * (e ^^^ (d ||| (e ||| f))) + 4 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 2 * (f ||| (d &&& e)) - 11 * ((d ^^^ e) ||| (d ^^^ f)) - 1 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 2 * (f ^^^ ~~~(d &&& (e &&& f))) - 2 * (d ||| (e ^^^ f)) - 5 * ~~~( ~~~d &&& (e ^^^ f)) - 2 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 11 * (e &&& (d ||| ~~~f)) + 1 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 2 * (e ||| (d ^^^ f)) - 1 * (d ^^^ ( ~~~e &&& f)) + 2 * (e ^^^ (d &&& ~~~f)) - 1 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 3 * ~~~(e &&& ~~~f) + 1 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 1 * f + 2 * (e ^^^ ~~~(d ||| f)) - 7 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 3 * ((d ||| e) &&& (e ^^^ f)) + 5 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 6 * (d ^^^ f) + 11 * (e &&& ~~~f) + 2 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 1 * (d &&& e) + 1 * ((d &&& e) ||| (e ^^^ f)) - 7 * (f &&& ~~~(d &&& e)) - 5 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 1 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 7 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 11 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 4 * (e ^^^ (d ||| f)) - 2 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 2 * d - 5 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 1 * ~~~(d ||| (e ||| f)) - 8 * ~~~(d ||| ( ~~~e ||| f)) - 4 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 8 * ( ~~~d &&& ( ~~~e &&& f)) + 44 * ( ~~~d &&& (e &&& f)) + 12 * (d &&& ( ~~~e &&& f)) + 22 * (d &&& (e &&& f)) = 6 * ~~~(d ^^^ (e &&& f)) - 1 * ((d &&& e) ||| ~~~(e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2388 (x y : BitVec w) : +theorem e_2388 : - 3 * ((d &&& e) ^^^ (e ||| ~~~f)) - 11 * ( ~~~d ||| (e &&& f)) - 7 * ~~~(d ||| ( ~~~e &&& f)) + 2 * (e ^^^ ~~~(d &&& f)) - 5 * (e ^^^ ~~~(d ||| (e &&& f))) + 1 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 2 * (f ||| ~~~(d ||| e)) + 1 * (d &&& e) + 3 * ~~~e - 7 * (d ^^^ e) + 1 * (f ||| (d ^^^ e)) - 5 * ~~~(e ||| f) - 11 * (f ^^^ (d &&& e)) - 5 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 1 * ((d ^^^ e) ||| ~~~(d ^^^ f)) + 4 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 7 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 2 * (f ^^^ ~~~(d ||| ~~~e)) + 1 * (d &&& ( ~~~e ||| f)) + 1 * (f ^^^ (d &&& ( ~~~e ||| f))) - 1 * (f ^^^ ~~~(d ||| e)) + 2 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 6 * (e ^^^ (d ||| ( ~~~e ||| f))) + 5 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (f ^^^ ( ~~~d ||| (e &&& f))) + 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * (e ^^^ ( ~~~d ||| (e ||| f))) - 6 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 1 * (e ^^^ ~~~(d &&& (e &&& f))) - 1 * ~~~(d ^^^ e) + 2 * (f &&& (d ^^^ e)) + 1 * (d &&& (e ^^^ f)) - 1 * ((d ^^^ e) ||| (d ^^^ f)) + 2 * (d ^^^ (e ^^^ f)) + 7 * (e ||| (d ^^^ f)) - 5 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 3 * (d ^^^ (e &&& f)) + 4 * ((d ^^^ e) &&& (d ^^^ f)) - 11 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 3 * (e ^^^ (d &&& (e ||| f))) + 4 * ((d &&& f) ||| (e &&& ~~~f)) + 11 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 2 * d - 1 * ~~~(d &&& ( ~~~e ||| f)) - 1 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 7 * (e &&& ~~~(d &&& f)) - 11 * ~~~(d ^^^ (e ||| f)) + 2 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 1 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 1 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * ((d &&& f) ^^^ (e ||| f)) + 1 * (f ^^^ ~~~(d &&& e)) + 5 * ( ~~~f ||| (d ^^^ e)) - 1 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 2 * (f &&& ~~~(d &&& ~~~e)) - 3 * ((d ||| ~~~e) &&& (e ^^^ f)) - 6 * ~~~d + 7 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 3 * ~~~(d ||| (e ^^^ f)) + 4 * (f ^^^ ~~~(d &&& (e ||| f))) + 11 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 2 * (f ^^^ (d ||| (e ||| f))) + 7 * ~~~(d ||| f) + 30 * ~~~(d ||| (e ||| f)) - 17 * ~~~( ~~~d ||| (e ||| f)) + 14 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 19 * ( ~~~d &&& ( ~~~e &&& f)) + 39 * ( ~~~d &&& (e &&& f)) + 30 * (d &&& ( ~~~e &&& f)) + 14 * (d &&& (e &&& f)) = - 1 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 5 * ~~~( ~~~d &&& (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2389 (x y : BitVec w) : +theorem e_2389 : - 1 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 11 * (e ^^^ ( ~~~d ||| (e &&& f))) + 2 * (f ^^^ ~~~(d &&& e)) + 4 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 2 * ((d &&& e) ^^^ (e ||| f)) + 1 * ((d &&& e) ||| ~~~(e ^^^ f)) + 2 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 2 * (e ^^^ (d &&& f)) + 1 * (f &&& ~~~(d ^^^ e)) - 5 * (f &&& (d ^^^ e)) - 1 * ( ~~~d ||| (e ||| f)) - 1 * (e ^^^ (d &&& (e ^^^ f))) - 2 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 5 * (e ^^^ (d ||| (e ^^^ f))) + 1 * (f ^^^ ~~~(d &&& (e &&& f))) + 11 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 7 * ~~~(d ^^^ (e ^^^ f)) - 1 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 2 * (d &&& ( ~~~e ||| f)) - 1 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 1 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 3 * ~~~(e ^^^ f) + 1 * ( ~~~d &&& ( ~~~e ||| f)) - 5 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 3 * (e ^^^ (d ||| (e ||| f))) + 1 * ~~~(d &&& (e ^^^ f)) + 1 * ((d &&& f) ||| ~~~(e ||| f)) - 7 * (f &&& (d ||| e)) + 2 * ( ~~~d ||| (e &&& f)) + 3 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 7 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 2 * ( ~~~f ||| ~~~(d ^^^ e)) - 2 * ((d ||| e) &&& (e ^^^ f)) + 2 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 1 * ((d &&& e) ||| ~~~(e ||| f)) - 5 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 6 * (d ^^^ ( ~~~e ||| f)) + 3 * ~~~(e &&& ~~~f) + 1 * (d &&& (e ||| f)) - 1 * (f ^^^ (d ||| (e &&& f))) - 6 * (d ||| ~~~e) - 11 * ((d ^^^ e) ||| (d ^^^ f)) - 1 * ~~~(d &&& f) - 2 * (f ^^^ ~~~(d ||| ~~~e)) - 3 * ~~~( ~~~d &&& (e &&& f)) + 11 * ~~~(d ||| f) - 2 * ~~~(d &&& ~~~f) - 1 * ((d &&& e) ^^^ (e ||| ~~~f)) + 1 * (f ^^^ (d ||| ( ~~~e ||| f))) + 11 * (f ||| ~~~(d ||| ~~~e)) - 1 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 7 * ( ~~~d ||| ( ~~~e &&& f)) - 2 * ((d &&& f) ^^^ (e ||| f)) + 1 * (f ^^^ ~~~(d ||| (e &&& f))) + 2 * (f ^^^ (d ||| e)) + 4 * (d ||| ( ~~~e ||| f)) - 11 * (f ^^^ (d &&& ~~~e)) + 1 * (f ^^^ ( ~~~d &&& (e ||| f))) - 5 * (d ||| ( ~~~e &&& f)) - 7 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 7 * (e ^^^ (d &&& ~~~f)) - 11 * ~~~(d ||| (e ||| f)) + 4 * ~~~(d ||| ( ~~~e ||| f)) + 20 * ~~~( ~~~d ||| (e ||| f)) + 25 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 17 * ( ~~~d &&& ( ~~~e &&& f)) + 26 * ( ~~~d &&& (e &&& f)) + 46 * (d &&& ( ~~~e &&& f)) + 8 * (d &&& (e &&& f)) = 11 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2390 (x y : BitVec w) : +theorem e_2390 : - 6 * (d ||| ( ~~~e &&& f)) - 1 * (d &&& ~~~e) + 3 * ( ~~~f ||| ~~~(d ^^^ e)) + 1 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 6 * (e ^^^ f) - 11 * (e ^^^ (d &&& (e ^^^ f))) + 1 * ( ~~~f ||| (d ^^^ e)) - 2 * (f ^^^ ~~~(d ||| e)) - 2 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 1 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 5 * (f ^^^ (d &&& ( ~~~e ||| f))) + 2 * ( ~~~d ||| (e ^^^ f)) + 2 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 3 * (d ||| ( ~~~e ||| f)) + 7 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 5 * (d &&& f) - 1 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 1 * (f ^^^ (d ||| ( ~~~e &&& f))) + 11 * ( ~~~e &&& (d ^^^ f)) + 5 * ~~~(d ||| (e &&& f)) - 5 * ~~~( ~~~d ||| (e ^^^ f)) - 2 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 2 * (d ^^^ (e &&& f)) - 3 * ( ~~~e ||| ~~~(d ^^^ f)) - 2 * (e ^^^ (d &&& ( ~~~e ||| f))) - 1 * (f ^^^ (d ||| (e &&& f))) - 1 * ((d ^^^ e) ||| (d ^^^ f)) - 5 * ((e &&& f) ||| (d &&& (e ||| f))) - 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 11 * (f ||| (d &&& ~~~e)) - 1 * (f &&& (d ||| e)) - 11 * (e ^^^ ( ~~~d ||| (e ||| f))) - 2 * ( ~~~d &&& (e ||| f)) - 5 * ~~~( ~~~d &&& (e ||| f)) - 2 * ~~~( ~~~d &&& (e ^^^ f)) - 7 * ~~~d + 2 * (e ^^^ ( ~~~d ||| (e &&& f))) - 1 * ~~~(e &&& f) + 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * ~~~( ~~~d ||| (e &&& f)) + 3 * (e ^^^ (d &&& ~~~f)) - 5 * (e ||| ~~~f) + 1 * (f &&& (d ||| ~~~e)) + 1 * (e ||| (d ^^^ f)) + 1 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 5 * ((d &&& e) ^^^ (e ||| f)) + 5 * (d ^^^ (e ||| f)) + 4 * (d &&& ( ~~~e ||| f)) + 11 * ~~~(d &&& ( ~~~e &&& f)) - 7 * (e &&& f) - 11 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 1 * (d ||| (e ||| f)) + 3 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 6 * ( ~~~d ||| (e &&& f)) + 7 * (f ||| ~~~(d ^^^ e)) - 6 * ~~~(d ||| ( ~~~e &&& f)) + 5 * (f ^^^ (d &&& ~~~e)) - 7 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 7 * (e ||| (d &&& f)) + 2 * ((d &&& f) ||| (e &&& ~~~f)) + 1 * ( ~~~d ||| ( ~~~e &&& f)) - 2 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 41 * ~~~(d ||| (e ||| f)) + 15 * ~~~(d ||| ( ~~~e ||| f)) - 9 * ~~~( ~~~d ||| (e ||| f)) + 21 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 28 * ( ~~~d &&& ( ~~~e &&& f)) + 11 * ( ~~~d &&& (e &&& f)) + 50 * (d &&& ( ~~~e &&& f)) + 16 * (d &&& (e &&& f)) = - 4 * (e &&& ~~~(d &&& ~~~f)) + 7 * ~~~(d ^^^ ( ~~~e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2391 (x y : BitVec w) : +theorem e_2391 : 2 * (f ||| (d ^^^ e)) + 4 * ( ~~~d &&& (e ^^^ f)) + 2 * (f ^^^ (d &&& ~~~e)) - 1 * (e ||| ~~~(d ||| f)) - 5 * ((d &&& ~~~e) ||| (e ^^^ f)) + 4 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 7 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 1 * ~~~(d ^^^ e) + 2 * ((d ||| ~~~e) &&& (e ^^^ f)) - 11 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 1 * (e ||| (d &&& ~~~f)) - 11 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 1 * (e ^^^ (d ||| ( ~~~e ||| f))) + 1 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 1 * (e ^^^ ~~~(d &&& ~~~f)) - 3 * ((e &&& f) ||| (d &&& (e ||| f))) + 5 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 7 * (f ^^^ (d ||| ( ~~~e ||| f))) - 7 * ( ~~~f ||| ~~~(d ^^^ e)) - 2 * (f ^^^ (d &&& e)) - 1 * (e ^^^ (d ||| (e &&& f))) + 5 * (d &&& (e ||| f)) + 4 * ( ~~~d ||| (e &&& f)) - 1 * (d ||| f) + 4 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 11 * (e ^^^ ~~~(d &&& f)) - 2 * (e ^^^ ~~~(d ||| ~~~f)) + 1 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 6 * ~~~d + 2 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 1 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 7 * ( ~~~e &&& ~~~(d ^^^ f)) - 5 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 4 * (f ^^^ (d &&& ( ~~~e ||| f))) + 1 * ~~~(e &&& f) + 7 * (f &&& (d ||| ~~~e)) - 5 * ~~~(d ||| f) + 1 * ~~~( ~~~d &&& (e ||| f)) + 5 * (d ^^^ ( ~~~e ||| f)) + 1 * (e ^^^ ~~~(d &&& (e ||| f))) + 1 * ~~~( ~~~d &&& (e &&& f)) - 6 * ~~~(d ||| ~~~f) + 5 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 7 * ((d ||| e) &&& (e ^^^ f)) - 6 * (f ^^^ ~~~(d ||| (e &&& f))) + 2 * (f &&& (d ||| e)) + 3 * ~~~(d ^^^ f) - 1 * ((d ^^^ e) &&& (d ^^^ f)) - 2 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 3 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 11 * (d ^^^ (e &&& f)) + 11 * ( ~~~f ||| (d ^^^ e)) - 11 * (e ^^^ (d &&& (e ^^^ f))) - 1 * (e ^^^ (d ||| ~~~f)) + 11 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 4 * ((d &&& e) ^^^ (e ||| f)) + 1 * (f ||| (d &&& ~~~e)) - 6 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 2 * ( ~~~e &&& (d ^^^ f)) + 5 * ~~~(d &&& ( ~~~e &&& f)) - 2 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 3 * ~~~(d &&& (e ||| f)) - 6 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 1 * ( ~~~d ||| (e ^^^ f)) + 40 * ~~~(d ||| (e ||| f)) + 21 * ~~~(d ||| ( ~~~e ||| f)) + 3 * ~~~( ~~~d ||| (e ||| f)) - 21 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 6 * ( ~~~d &&& ( ~~~e &&& f)) + 4 * ( ~~~d &&& (e &&& f)) - 15 * (d &&& ( ~~~e &&& f)) = 3 * (d ^^^ ( ~~~e &&& f)) - 6 * (d &&& (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2392 (x y : BitVec w) : +theorem e_2392 : 4 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 7 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 3 * (d ||| (e ||| f)) - 6 * (f ^^^ ~~~(d ||| e)) + 2 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 5 * ~~~(d ^^^ (e &&& f)) + 2 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 11 * ( ~~~d &&& ( ~~~e ||| f)) + 3 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 4 * ~~~d - 3 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 5 * ~~~(d &&& (e ||| f)) - 11 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 2 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 2 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 7 * (f ||| (d ^^^ e)) - 6 * ( ~~~f &&& (d ^^^ e)) + 4 * ((e &&& f) ||| (d &&& (e ||| f))) - 7 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 2 * (e ||| (d ^^^ f)) + 1 * (d ||| f) - 3 * (f ^^^ (d ||| (e &&& f))) - 7 * ( ~~~d &&& (e ||| f)) - 1 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 1 * (d ||| e) + 3 * ((d ||| e) &&& (e ^^^ f)) - 6 * (e ^^^ ~~~(d &&& f)) - 2 * (e ||| f) + 2 * (d ||| (e ^^^ f)) - 1 * (e ||| (d &&& f)) + 1 * ((d &&& ~~~e) ||| (e ^^^ f)) + 1 * (e ^^^ (d &&& ~~~f)) + 3 * ( ~~~e &&& (d ^^^ f)) - 1 * ~~~(e ||| f) - 11 * ~~~(d ^^^ e) + 1 * (d ^^^ f) + 3 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 1 * ~~~(d ||| ~~~f) + 7 * ~~~(d ^^^ (e ||| f)) + 7 * ((d ||| e) &&& ~~~(e ^^^ f)) + 1 * (f ^^^ (d ||| ( ~~~e &&& f))) + 11 * ~~~( ~~~d &&& (e ||| f)) + 2 * (d ||| ( ~~~e ||| f)) - 1 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 4 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 5 * ~~~(e ^^^ f) - 1 * ( ~~~f &&& ~~~(d ^^^ e)) - 6 * (e &&& (d ||| ~~~f)) + 7 * ((d &&& e) ^^^ (e ||| f)) + 2 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 3 * (f ^^^ (d &&& (e ||| f))) - 11 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 1 * (e ||| ~~~(d ||| f)) + 2 * (e ||| ~~~(d ||| ~~~f)) - 5 * (e ^^^ (d &&& f)) + 1 * ~~~(d ^^^ f) + 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 11 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 11 * (e ^^^ (d ||| ( ~~~e &&& f))) + 1 * (f ^^^ ~~~(d &&& e)) - 7 * (e ^^^ (d ||| ( ~~~e ||| f))) + 5 * ( ~~~d ||| ( ~~~e ||| f)) + 1 * ~~~(d &&& ( ~~~e ||| f)) - 2 * (d ||| (e &&& f)) - 1 * ~~~(d ||| (e ||| f)) + 38 * ~~~(d ||| ( ~~~e ||| f)) + 13 * ~~~( ~~~d ||| (e ||| f)) - 1 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 6 * ( ~~~d &&& ( ~~~e &&& f)) + 9 * (d &&& ( ~~~e &&& f)) + 19 * (d &&& (e &&& f)) = - 2 * (d ||| ( ~~~e &&& f)) - 26 * ( ~~~d &&& (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2393 (x y : BitVec w) : +theorem e_2393 : - 2 * (e &&& ~~~f) + 11 * ~~~f - 6 * (d ^^^ (e &&& f)) - 6 * ((d &&& e) ^^^ (e ||| ~~~f)) + 3 * (d ^^^ (e ^^^ f)) + 2 * (f ^^^ ~~~(d ||| ~~~e)) + 5 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 3 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 4 * (e ^^^ (d ||| ~~~f)) - 2 * (d ^^^ e) - 1 * (f ^^^ ~~~(d ||| (e &&& f))) - 1 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 2 * (e ^^^ (d ||| (e ^^^ f))) - 2 * ( ~~~e ||| ~~~(d ^^^ f)) - 7 * (f ^^^ ~~~(d &&& ~~~e)) - 2 * ~~~(d &&& (e ||| f)) + 11 * (e ||| f) + 1 * ~~~(e ||| f) - 5 * ~~~(d ||| ( ~~~e &&& f)) + 7 * (d ^^^ ( ~~~e ||| f)) - 2 * ~~~(d ||| ~~~e) + 11 * ~~~(d &&& ~~~e) + 2 * (e ||| (d ^^^ f)) - 3 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * ((d &&& f) ||| (e &&& ~~~f)) + 7 * (d ||| (e ||| f)) + 2 * (e &&& (d ||| ~~~f)) - 11 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 1 * (e ||| ~~~f) - 6 * (e ^^^ (d &&& f)) - 2 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 4 * (d ||| ( ~~~e ||| f)) + 1 * (d &&& e) + 5 * ( ~~~f ||| (d ^^^ e)) - 1 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 1 * ( ~~~f &&& ~~~(d ^^^ e)) + 1 * (e &&& ~~~(d &&& f)) - 7 * ~~~e + 11 * ((d ||| ~~~e) &&& (e ^^^ f)) - 6 * ( ~~~f ||| ~~~(d ^^^ e)) + 4 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 1 * ( ~~~e &&& (d ^^^ f)) + 5 * (f &&& ~~~(d &&& ~~~e)) + 5 * d + 5 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 2 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 3 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 3 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 11 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 1 * ((d ||| e) &&& ~~~(e ^^^ f)) - 2 * (e ^^^ ( ~~~d &&& (e ||| f))) - 3 * (f &&& (d ||| ~~~e)) + 3 * (e ^^^ (d ||| ( ~~~e ||| f))) - 11 * ((d &&& e) ||| ~~~(e ||| f)) + 1 * ( ~~~e ||| (d ^^^ f)) + 2 * ~~~(e ||| ~~~f) - 11 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 7 * ~~~(d ||| ~~~f) - 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 3 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 1 * (f ||| ~~~(d ||| ~~~e)) + 2 * ( ~~~e &&& ~~~(d ^^^ f)) - 7 * ( ~~~d ||| ( ~~~e &&& f)) - 1 * ~~~(d ||| (e ||| f)) - 9 * ~~~(d ||| ( ~~~e ||| f)) - 4 * ~~~( ~~~d ||| (e ||| f)) - 22 * ( ~~~d &&& ( ~~~e &&& f)) - 26 * ( ~~~d &&& (e &&& f)) - 22 * (d &&& ( ~~~e &&& f)) - 44 * (d &&& (e &&& f)) = 56 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 3 * (f ^^^ (d ||| e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2394 (x y : BitVec w) : +theorem e_2394 : 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 1 * (f ^^^ (d &&& ~~~e)) + 2 * (e ||| (d &&& ~~~f)) - 11 * (f ^^^ (d ||| (e &&& f))) - 1 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 11 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 11 * (e ||| (d ^^^ f)) - 6 * (e ^^^ ~~~(d &&& f)) - 5 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 1 * ~~~(e &&& f) + 5 * ((d &&& e) ^^^ (e ||| ~~~f)) + 5 * (d ||| (e ^^^ f)) - 1 * ~~~(d ||| e) + 7 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 5 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 5 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 2 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 7 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 1 * (e ||| ~~~(d ||| f)) + 1 * (d &&& e) - 6 * (e ^^^ (d ||| f)) + 4 * (e ^^^ ~~~(d &&& (e &&& f))) + 2 * (e &&& (d ||| f)) + 5 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 4 * (f ||| (d &&& e)) + 1 * (f ^^^ ~~~(d ||| (e &&& f))) + 7 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 3 * (f &&& (d ||| e)) + 1 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 1 * (d &&& (e ||| f)) - 7 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 1 * (e ||| f) - 3 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 11 * (f ^^^ (d ||| ( ~~~e &&& f))) - 2 * ~~~(d ||| ~~~f) - 3 * ~~~( ~~~d &&& (e ||| f)) - 1 * (d ||| f) + 2 * ~~~(d ^^^ (e &&& f)) + 4 * (f ^^^ (d &&& e)) - 3 * (f ^^^ ~~~(d ||| ~~~e)) - 3 * (d ^^^ (e ||| f)) + 4 * ((d &&& f) ^^^ (e ||| f)) - 7 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 5 * ( ~~~d ||| ( ~~~e &&& f)) - 2 * ~~~(d ||| f) - 1 * (e ^^^ ~~~(d ||| (e &&& f))) - 2 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 11 * ( ~~~f &&& (d ^^^ e)) - 11 * ~~~(e ^^^ f) - 1 * (f &&& ~~~(d &&& ~~~e)) + 3 * (e ^^^ (d ||| ( ~~~e &&& f))) - 1 * (e &&& f) - 2 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 7 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 2 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 3 * (d ||| ( ~~~e ||| f)) + 1 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 2 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 3 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 11 * ~~~(d &&& ( ~~~e ||| f)) + 7 * ((d ||| ~~~e) &&& (e ^^^ f)) - 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 23 * ~~~(d ||| (e ||| f)) + 6 * ~~~(d ||| ( ~~~e ||| f)) + 10 * ~~~( ~~~d ||| (e ||| f)) - 32 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 7 * ( ~~~d &&& (e &&& f)) - 8 * (d &&& ( ~~~e &&& f)) - 15 * (d &&& (e &&& f)) = - 14 * ( ~~~d &&& ( ~~~e &&& f)) + 7 * ~~~(d &&& e) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2395 (x y : BitVec w) : +theorem e_2395 : 3 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 1 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 7 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 3 * (e ^^^ (d ||| (e ^^^ f))) + 1 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 3 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 11 * (d &&& ~~~f) + 5 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 2 * (e ^^^ f) - 2 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 11 * (f ^^^ ~~~(d ||| ~~~e)) + 1 * ( ~~~f &&& (d ^^^ e)) + 5 * ((d &&& f) ||| ~~~(e ||| f)) + 1 * ~~~(d ||| f) - 2 * (d ^^^ ( ~~~e &&& f)) - 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 7 * (e ^^^ (d ||| f)) - 5 * ~~~(d &&& ( ~~~e ||| f)) + 2 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 3 * ( ~~~d &&& (e ^^^ f)) + 2 * (d ||| ( ~~~e &&& f)) - 11 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 1 * ((d ||| e) &&& ~~~(e ^^^ f)) + 11 * ( ~~~f ||| ~~~(d ^^^ e)) - 2 * (f ^^^ (d ||| e)) - 7 * (e ||| (d ^^^ f)) - 3 * (e ^^^ ( ~~~d ||| (e &&& f))) + 2 * ((d ^^^ e) &&& (d ^^^ f)) + 5 * (e &&& f) + 3 * (f ||| (d &&& e)) + 3 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 7 * (e ^^^ (d &&& ~~~f)) + 1 * (f ^^^ ~~~(d &&& e)) + 2 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 1 * (e ||| ~~~f) - 3 * ~~~(e ||| f) - 5 * ~~~(d ^^^ f) + 2 * (d ||| f) - 1 * ~~~(d ||| ( ~~~e &&& f)) + 2 * (f ^^^ ( ~~~d ||| (e &&& f))) + 2 * ~~~(e &&& ~~~f) + 4 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 11 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 2 * ~~~(d ^^^ (e &&& f)) + 1 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * (f ||| (d ^^^ e)) + 3 * (e &&& ~~~(d &&& f)) + 2 * ~~~(d ||| e) + 5 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 7 * ~~~(d ||| (e ^^^ f)) - 11 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 2 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 5 * (f ^^^ (d &&& e)) - 2 * ~~~( ~~~d &&& (e &&& f)) + 4 * (f ^^^ ( ~~~d &&& (e ||| f))) - 11 * (d &&& ~~~e) + 1 * ~~~(d &&& ( ~~~e &&& f)) + 1 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 2 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 1 * ~~~(e ^^^ f) - 2 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 6 * ( ~~~d &&& (e ||| f)) - 1 * (e &&& (d ||| f)) + 6 * ~~~(d ||| (e ||| f)) + 50 * ~~~(d ||| ( ~~~e ||| f)) + 49 * ~~~( ~~~d ||| (e ||| f)) + 38 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 42 * ( ~~~d &&& ( ~~~e &&& f)) + 8 * ( ~~~d &&& (e &&& f)) + 37 * (d &&& ( ~~~e &&& f)) + 11 * (d &&& (e &&& f)) = 3 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 2 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2396 (x y : BitVec w) : +theorem e_2396 : - 2 * (e ^^^ (d ||| f)) - 6 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 3 * (f ^^^ ~~~(d &&& (e &&& f))) - 5 * (e &&& (d ||| f)) - 7 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 7 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 11 * ~~~(d ^^^ (e &&& f)) - 1 * (e ^^^ (d ||| (e ||| f))) + 7 * f - 11 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 11 * (e ||| (d &&& ~~~f)) - 11 * ( ~~~e ||| ~~~(d ^^^ f)) + 1 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 1 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 2 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 1 * (e ^^^ ~~~(d &&& f)) - 3 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 2 * (d ^^^ (e ^^^ f)) - 1 * ~~~(e ^^^ f) + 11 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 1 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 3 * ~~~(d ||| ~~~f) - 6 * (d ||| ( ~~~e &&& f)) + 11 * ( ~~~d ||| ( ~~~e ||| f)) + 5 * (f ^^^ ( ~~~d ||| (e &&& f))) - 11 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 2 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 1 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 1 * (f ||| (d &&& e)) + 1 * d + 5 * (f ^^^ ~~~(d ||| (e &&& f))) - 11 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 5 * ((d &&& ~~~e) ||| (e ^^^ f)) - 2 * (f ||| ~~~(d ||| e)) + 1 * (f &&& (d ^^^ e)) + 3 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 5 * (e ||| f) + 11 * (d ||| (e ^^^ f)) + 2 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 5 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 7 * (f ^^^ ( ~~~d &&& (e ||| f))) + 4 * ~~~( ~~~d &&& (e ||| f)) - 1 * (e ^^^ ~~~(d &&& ~~~f)) + 1 * ~~~(d &&& e) + 4 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 2 * ~~~( ~~~d ||| (e ^^^ f)) - 2 * ( ~~~d &&& (e ^^^ f)) - 1 * ~~~(e ||| f) + 2 * (e &&& (d ^^^ f)) + 3 * (f ^^^ ~~~(d ||| ~~~e)) + 4 * ~~~(d ||| f) + 2 * (f ||| (d ^^^ e)) - 6 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 1 * ~~~(d ^^^ f) - 6 * (f ^^^ ~~~(d &&& e)) - 2 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 1 * (e ^^^ ( ~~~d ||| (e &&& f))) - 5 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 1 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 2 * ((d ||| e) &&& ~~~(e ^^^ f)) + 1 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 7 * ((d &&& f) ^^^ (e ||| f)) + 4 * ~~~(d ||| (e ||| f)) + 7 * ~~~(d ||| ( ~~~e ||| f)) + 14 * ~~~( ~~~d ||| (e ||| f)) + 34 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 4 * ( ~~~d &&& ( ~~~e &&& f)) - 31 * ( ~~~d &&& (e &&& f)) + 11 * (d &&& ( ~~~e &&& f)) + 7 * (d &&& (e &&& f)) = 1 * (e ||| ~~~(d ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2397 (x y : BitVec w) : +theorem e_2397 : - 11 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 2 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 3 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 3 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 3 * (d ||| (e &&& f)) + 2 * ((d ||| e) &&& (e ^^^ f)) - 2 * (f ^^^ ~~~(d &&& (e ||| f))) - 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 5 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 1 * (f ^^^ (d ||| ( ~~~e ||| f))) + 11 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 5 * ((d &&& ~~~e) ||| (e ^^^ f)) - 2 * (f &&& (d ||| e)) - 6 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 5 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * ~~~(d &&& ( ~~~e &&& f)) + 3 * (e &&& (d ^^^ f)) + 1 * (f ||| ~~~(d ||| ~~~e)) - 1 * (f ^^^ (d &&& (e ||| f))) - 7 * (e ^^^ (d &&& ~~~f)) + 2 * (d ^^^ (e ||| f)) + 1 * (f ^^^ ( ~~~d &&& (e ||| f))) - 1 * (d &&& ~~~e) + 1 * ~~~(d ^^^ ( ~~~e ||| f)) - 5 * (d ||| ~~~e) + 7 * (f ^^^ ~~~(d &&& (e &&& f))) - 2 * (d &&& ( ~~~e ||| f)) - 1 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 2 * ( ~~~d ||| ( ~~~e &&& f)) - 6 * ( ~~~e &&& (d ^^^ f)) - 1 * ~~~e - 6 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 5 * (f ^^^ (d &&& ( ~~~e ||| f))) + 1 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 2 * ((d &&& f) ^^^ (e ||| f)) - 2 * ~~~(d &&& (e ||| f)) + 2 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 1 * (d ^^^ ( ~~~e ||| f)) + 2 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 3 * ( ~~~e ||| ~~~(d ^^^ f)) - 7 * (f ^^^ (d ||| ~~~e)) - 5 * (f ^^^ (d ||| ( ~~~e &&& f))) + 7 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 1 * ((d &&& e) ||| ~~~(e ||| f)) + 11 * (e ||| (d ^^^ f)) + 1 * (f ^^^ (d &&& e)) - 6 * ~~~(d &&& ~~~d) + 7 * (f &&& ~~~(d &&& ~~~e)) - 2 * (f ^^^ (d ||| (e &&& f))) - 6 * ~~~(d ^^^ ( ~~~e &&& f)) + 1 * ((d ^^^ e) ||| (d ^^^ f)) + 2 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 1 * ( ~~~f &&& ~~~(d ^^^ e)) + 4 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 3 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 7 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 1 * (e ^^^ f) + 7 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 1 * ((d &&& f) ||| (e &&& ~~~f)) - 2 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 4 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 7 * (e ^^^ (d &&& (e ||| f))) - 1 * ( ~~~e &&& ~~~(d ^^^ f)) + 4 * (e ||| (d &&& ~~~f)) + 33 * ~~~(d ||| (e ||| f)) - 15 * ~~~(d ||| ( ~~~e ||| f)) + 33 * ~~~( ~~~d ||| (e ||| f)) - 19 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 21 * ( ~~~d &&& ( ~~~e &&& f)) + 1 * ( ~~~d &&& (e &&& f)) + 12 * (d &&& ( ~~~e &&& f)) - 1 * (d &&& (e &&& f)) = 7 * (f ^^^ ~~~(d &&& e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2398 (x y : BitVec w) : +theorem e_2398 : 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 7 * (e ^^^ (d ||| ( ~~~e ||| f))) + 1 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 6 * ((d &&& e) ^^^ (e ||| ~~~f)) - 1 * ((d ||| ~~~e) &&& (e ^^^ f)) - 1 * ( ~~~d ||| (e ||| f)) - 7 * ((d &&& e) ||| ~~~(e ^^^ f)) - 3 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 11 * (f ^^^ (d ||| ( ~~~e ||| f))) + 7 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 11 * ~~~(d &&& ~~~d) + 1 * ~~~(d ^^^ f) - 1 * (e ^^^ (d &&& f)) + 1 * (e ^^^ (d &&& ( ~~~e ||| f))) - 5 * ~~~(d &&& ( ~~~e &&& f)) - 2 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 5 * (e ||| (d &&& f)) - 1 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 3 * ~~~(d &&& (e ||| f)) + 11 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 2 * ((d ^^^ e) &&& (d ^^^ f)) + 11 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 1 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 2 * ( ~~~d &&& (e ^^^ f)) - 1 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 5 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 5 * ~~~(d &&& (e &&& f)) + 1 * (d ||| (e ||| f)) + 5 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 2 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 5 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 1 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 7 * (e ^^^ ~~~(d ||| ~~~f)) - 1 * (f ^^^ (d &&& (e ||| f))) + 1 * (d ||| ( ~~~e &&& f)) + 4 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 4 * (f &&& ~~~(d &&& e)) + 1 * (e ^^^ ( ~~~d &&& (e ||| f))) - 6 * ((d &&& e) ||| (e ^^^ f)) - 1 * e + 2 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 5 * (d ||| ~~~e) - 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 2 * ~~~(d ^^^ e) - 2 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 11 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 3 * (d ^^^ (e &&& f)) + 1 * ( ~~~f ||| ~~~(d ^^^ e)) - 1 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 3 * (f ^^^ (d &&& e)) - 7 * ~~~(d ^^^ (e ||| f)) + 1 * (e ^^^ ~~~(d &&& (e &&& f))) - 3 * ( ~~~e ||| (d ^^^ f)) - 2 * ( ~~~e &&& (d ^^^ f)) - 7 * ~~~(d &&& f) + 11 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * ((d &&& ~~~e) ||| (e ^^^ f)) + 5 * (f &&& (d ^^^ e)) + 1 * (f ||| (d &&& e)) + 3 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 4 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 1 * (f ^^^ (d ||| (e &&& f))) + 7 * ((d &&& e) ||| ~~~(e ||| f)) - 6 * (f ^^^ ~~~(d ||| e)) + 44 * ~~~(d ||| (e ||| f)) + 20 * ~~~(d ||| ( ~~~e ||| f)) + 30 * ~~~( ~~~d ||| (e ||| f)) + 8 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 1 * ( ~~~d &&& ( ~~~e &&& f)) + 16 * ( ~~~d &&& (e &&& f)) + 22 * (d &&& ( ~~~e &&& f)) + 22 * (d &&& (e &&& f)) = 11 * (e ^^^ (d ||| (e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2399 (x y : BitVec w) : +theorem e_2399 : - 1 * (f &&& (d ^^^ e)) + 1 * ((d ^^^ e) ||| ~~~(d ^^^ f)) + 3 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 5 * (f ^^^ (d &&& e)) - 5 * (e ^^^ ( ~~~d &&& (e ||| f))) + 11 * (d ^^^ e) - 2 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 7 * (f ^^^ ~~~(d &&& (e &&& f))) + 5 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 5 * ((d &&& e) ^^^ (e ||| f)) + 1 * (e ||| ~~~(d ^^^ f)) - 5 * (e ^^^ ( ~~~d ||| (e &&& f))) + 1 * (f ^^^ ~~~(d ||| (e &&& f))) - 3 * (f ^^^ (d ||| ( ~~~e ||| f))) + 3 * (e ||| (d &&& ~~~f)) + 2 * (f ||| ~~~(d ||| ~~~e)) - 5 * (f &&& ~~~(d ^^^ e)) + 4 * ( ~~~f ||| ~~~(d ^^^ e)) + 1 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 7 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 7 * (f ^^^ (d ||| e)) - 3 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 1 * (e ||| ~~~(d ||| f)) - 11 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 3 * (f ^^^ ( ~~~d &&& (e ||| f))) + 11 * (d ^^^ ( ~~~e &&& f)) - 7 * (e &&& (d ^^^ f)) + 1 * (f ^^^ (d ||| ~~~e)) - 11 * ( ~~~f &&& ~~~(d ^^^ e)) + 2 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 4 * ~~~( ~~~d &&& (e &&& f)) - 2 * (e &&& ~~~(d &&& f)) - 11 * (f ^^^ ~~~(d &&& ~~~e)) - 2 * ~~~(e &&& ~~~f) - 2 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 3 * ~~~(d &&& e) - 11 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 1 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 1 * e - 3 * (f ||| ~~~(d ||| e)) + 5 * ( ~~~e ||| (d ^^^ f)) - 1 * (e ^^^ ~~~(d ||| (e &&& f))) + 4 * (d &&& e) - 1 * ((d ^^^ e) ||| (d ^^^ f)) - 5 * (e ^^^ ~~~(d &&& ~~~f)) + 2 * (e &&& ~~~(d &&& ~~~f)) - 1 * (e ^^^ (d ||| (e ||| f))) + 4 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * (f ^^^ ~~~(d ||| e)) + 3 * ~~~(e ^^^ f) - 11 * (d ||| (e &&& f)) - 7 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 3 * (f ||| (d ^^^ e)) - 2 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 11 * ((d ||| e) &&& ~~~(e ^^^ f)) - 7 * (f ||| (d &&& e)) + 3 * (f ||| (d &&& ~~~e)) - 6 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 11 * ~~~(d ^^^ (e ||| f)) - 1 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 4 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 3 * (f &&& (d ||| e)) + 2 * (f ^^^ ~~~(d ||| ~~~e)) + 47 * ~~~(d ||| (e ||| f)) + 12 * ~~~(d ||| ( ~~~e ||| f)) + 6 * ~~~( ~~~d ||| (e ||| f)) + 34 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 48 * ( ~~~d &&& ( ~~~e &&& f)) + 38 * (d &&& ( ~~~e &&& f)) + 6 * (d &&& (e &&& f)) = - 42 * ( ~~~d &&& (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2400 (x y : BitVec w) : +theorem e_2400 : - 1 * (d ^^^ e) - 1 * f - 11 * (e ^^^ (d &&& f)) - 6 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 5 * ~~~( ~~~d ||| (e &&& f)) + 5 * (f ||| (d ^^^ e)) - 11 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 2 * (f &&& ~~~(d ^^^ e)) - 3 * ~~~(d &&& ( ~~~e ||| f)) - 11 * ( ~~~d &&& (e ||| f)) - 1 * (f ^^^ ~~~(d &&& (e &&& f))) - 3 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 7 * (e ^^^ (d &&& ~~~f)) + 1 * ( ~~~f &&& ~~~(d ^^^ e)) + 4 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 2 * ~~~(d ^^^ (e ||| f)) - 2 * (e ^^^ ~~~(d &&& ~~~f)) + 3 * (f &&& (d ^^^ e)) + 1 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 3 * ~~~(d ||| f) + 1 * ( ~~~e &&& ~~~(d ^^^ f)) + 2 * ((d ||| ~~~e) &&& (e ^^^ f)) - 6 * (f &&& (d ||| ~~~e)) + 2 * (e ^^^ (d ||| f)) + 1 * (e ||| (d &&& f)) + 2 * (e ^^^ (d &&& (e ||| f))) + 5 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 1 * (e ^^^ ( ~~~d ||| (e ||| f))) - 5 * (e ^^^ (d ||| (e &&& f))) + 2 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 3 * (d ||| ~~~e) + 5 * (e &&& ~~~(d &&& ~~~f)) - 6 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 2 * ~~~f + 3 * (e &&& (d ||| f)) - 7 * ( ~~~d ||| (e ^^^ f)) + 7 * ( ~~~d ||| (e &&& f)) - 7 * (d ||| (e &&& f)) + 2 * (d &&& (e ||| f)) + 11 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 11 * (f ^^^ ~~~(d &&& ~~~e)) + 11 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 1 * (f ^^^ ~~~(d ||| (e &&& f))) + 4 * (f ^^^ (d &&& ~~~e)) + 2 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * (e ||| f) - 1 * (f &&& ~~~(d &&& ~~~e)) - 2 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 1 * ( ~~~d ||| ( ~~~e &&& f)) - 7 * (f ^^^ ~~~(d ||| e)) - 2 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 2 * ~~~(e ||| ~~~f) + 1 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 4 * (e ^^^ (d &&& ( ~~~e ||| f))) + 3 * ~~~( ~~~d &&& (e ^^^ f)) + 11 * ~~~( ~~~d &&& (e ||| f)) - 5 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 2 * ~~~(d &&& (e ||| f)) - 1 * (e ||| ~~~f) - 1 * ~~~(d ||| (e &&& f)) - 6 * (f ||| (d &&& ~~~e)) - 3 * ~~~(d ^^^ ( ~~~e ||| f)) - 1 * (f ||| ~~~(d ^^^ e)) - 6 * ~~~(d &&& ~~~d) + 25 * ~~~(d ||| (e ||| f)) + 19 * ~~~(d ||| ( ~~~e ||| f)) + 1 * ~~~( ~~~d ||| (e ||| f)) + 21 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 29 * ( ~~~d &&& ( ~~~e &&& f)) + 19 * ( ~~~d &&& (e &&& f)) + 39 * (d &&& ( ~~~e &&& f)) - 2 * (d &&& (e &&& f)) = - 1 * (d &&& ~~~f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2401 (x y : BitVec w) : +theorem e_2401 : - 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 5 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 5 * ~~~(d ||| f) - 5 * (e ||| ~~~(d ||| ~~~f)) + 1 * (e ||| f) - 2 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 5 * ((d &&& e) ^^^ (e ||| ~~~f)) - 2 * f - 11 * (f ^^^ ~~~(d ||| ~~~e)) + 4 * ~~~(d ^^^ ( ~~~e ||| f)) + 1 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 3 * ( ~~~d ||| (e &&& f)) + 3 * (e ^^^ (d ||| (e &&& f))) + 3 * (f ^^^ ~~~(d &&& ~~~e)) + 11 * (e ^^^ (d ||| (e ^^^ f))) + 1 * ~~~(d ||| ( ~~~e &&& f)) - 1 * (e ||| (d &&& ~~~f)) - 1 * (d ^^^ ( ~~~e ||| f)) - 1 * (f ^^^ (d ||| ( ~~~e ||| f))) - 1 * (f &&& (d ||| e)) - 3 * (f ||| ~~~(d ^^^ e)) + 1 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 1 * (f ^^^ (d ||| (e ||| f))) + 4 * (d ^^^ f) + 1 * (e ||| ~~~(d ^^^ f)) - 6 * (f &&& (d ^^^ e)) - 5 * ~~~(d ||| ~~~e) + 2 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 5 * (e &&& ~~~(d ^^^ f)) - 1 * (e ^^^ (d ||| f)) + 1 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 2 * (f ||| (d &&& e)) + 2 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 7 * ~~~( ~~~d &&& (e ||| f)) + 5 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 7 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 6 * ((d &&& e) ||| ~~~(e ||| f)) + 1 * (f ^^^ ~~~(d ||| (e &&& f))) - 1 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 1 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 11 * (f ^^^ (d ||| e)) - 2 * (e ^^^ ~~~(d ||| f)) + 2 * ~~~(d &&& ~~~f) - 2 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 2 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 1 * (f ^^^ ~~~(d &&& (e ||| f))) - 5 * ~~~(d &&& (e ||| f)) - 6 * (d ^^^ (e ^^^ f)) - 3 * ( ~~~d ||| (e ^^^ f)) - 3 * e + 5 * (d ||| ~~~e) - 3 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 7 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 6 * ~~~(d ^^^ (e ^^^ f)) + 4 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * (e ^^^ ~~~(d ||| ~~~f)) - 1 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * (f ^^^ (d &&& ~~~e)) - 2 * (f ^^^ ( ~~~d ||| (e ||| f))) - 7 * ( ~~~e ||| (d ^^^ f)) - 1 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 11 * ((d ||| ~~~e) &&& (e ^^^ f)) + 1 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 13 * ~~~(d ||| (e ||| f)) + 18 * ~~~(d ||| ( ~~~e ||| f)) - 4 * ~~~( ~~~d ||| (e ||| f)) + 10 * ( ~~~d &&& ( ~~~e &&& f)) + 29 * ( ~~~d &&& (e &&& f)) - 7 * (d &&& ( ~~~e &&& f)) + 23 * (d &&& (e &&& f)) = 5 * (e ^^^ ~~~(d &&& f)) - 7 * ~~~( ~~~d ||| ( ~~~e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2402 (x y : BitVec w) : +theorem e_2402 : - 3 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 2 * ~~~(d &&& ( ~~~e ||| f)) + 1 * (d ||| ~~~f) - 11 * ~~~(e &&& f) - 7 * (e ||| ~~~(d ||| ~~~f)) - 5 * (e ^^^ ~~~(d &&& (e ||| f))) + 5 * (d ||| e) - 1 * ~~~d - 2 * ~~~(d &&& ( ~~~e &&& f)) + 7 * ((d ^^^ e) &&& (d ^^^ f)) - 1 * ~~~(d ||| f) + 2 * (d ||| (e ^^^ f)) - 6 * ( ~~~f ||| (d ^^^ e)) - 5 * ((d ^^^ e) ||| ~~~(d ^^^ f)) + 1 * (f ||| (d &&& ~~~e)) + 1 * (e ^^^ ~~~(d ||| ~~~f)) + 2 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 7 * (f ^^^ (d &&& e)) - 3 * ((d &&& ~~~e) ||| (e ^^^ f)) + 11 * (f ||| (d &&& e)) + 1 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 7 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 7 * (d ^^^ f) - 11 * (e ^^^ (d &&& (e ^^^ f))) + 3 * (f ^^^ ( ~~~d ||| (e ||| f))) + 3 * (e ^^^ (d &&& f)) + 5 * ((d ^^^ e) ||| (d ^^^ f)) - 2 * (e &&& ~~~(d &&& f)) + 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 3 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 1 * (f ||| (d ^^^ e)) - 6 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 11 * ( ~~~e ||| (d ^^^ f)) - 1 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 2 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 2 * (e ^^^ f) - 3 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 7 * (f ||| ~~~(d ||| e)) + 1 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 2 * (e &&& ~~~(d &&& ~~~f)) - 7 * ~~~(e &&& ~~~f) - 7 * ~~~(d &&& ~~~d) - 6 * ((d &&& f) ||| ~~~(e ||| f)) + 7 * ~~~(d ||| ~~~f) + 1 * ( ~~~d ||| ( ~~~e &&& f)) - 1 * (d ^^^ ( ~~~e &&& f)) + 4 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 2 * ~~~(d ^^^ ( ~~~e &&& f)) + 1 * f - 2 * ~~~(d &&& ~~~e) + 4 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 5 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * (f ^^^ ~~~(d ||| e)) + 11 * (f &&& (d ||| e)) + 1 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 7 * ( ~~~f ||| ~~~(d ^^^ e)) + 2 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 1 * (e ^^^ ~~~(d &&& (e &&& f))) - 1 * (f ^^^ (d ||| ( ~~~e ||| f))) - 1 * (e ||| (d ^^^ f)) - 1 * (f ^^^ ~~~(d &&& (e ||| f))) + 3 * (f &&& ~~~(d ^^^ e)) + 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 3 * (f ^^^ ~~~(d ||| (e &&& f))) + 37 * ~~~(d ||| (e ||| f)) + 27 * ~~~(d ||| ( ~~~e ||| f)) - 1 * ~~~( ~~~d ||| (e ||| f)) - 22 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 18 * ( ~~~d &&& ( ~~~e &&& f)) - 19 * ( ~~~d &&& (e &&& f)) + 4 * (d &&& (e &&& f)) = - 1 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 2 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2403 (x y : BitVec w) : +theorem e_2403 : 1 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 1 * (e ^^^ (d &&& ~~~f)) - 3 * ~~~e + 11 * (e ^^^ ~~~(d &&& f)) - 6 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 1 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 1 * (e ^^^ ~~~(d &&& (e ||| f))) + 3 * ~~~(d ||| ~~~e) + 11 * (e &&& (d ||| ~~~f)) - 5 * (f &&& ~~~(d &&& e)) + 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 3 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 4 * (e ^^^ (d &&& (e ||| f))) + 7 * (d ^^^ e) + 1 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 1 * f - 2 * ~~~(e &&& f) - 7 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 7 * (f ||| (d ^^^ e)) - 3 * (f ||| (d &&& ~~~e)) + 4 * (f ^^^ (d ||| ( ~~~e &&& f))) - 2 * (f ^^^ (d ||| (e &&& f))) + 11 * (f ^^^ ~~~(d &&& (e &&& f))) + 1 * (e ^^^ ( ~~~d ||| (e &&& f))) + 1 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 11 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 5 * (d ^^^ (e &&& f)) + 5 * (d ||| (e ^^^ f)) + 2 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 6 * ( ~~~e &&& (d ^^^ f)) - 1 * (f ||| ~~~(d ||| ~~~e)) + 5 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 4 * (d &&& ~~~f) + 2 * ~~~( ~~~d ||| (e &&& f)) + 7 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 11 * (d &&& f) + 2 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * ~~~(d ^^^ (e ^^^ f)) + 3 * (e ^^^ (d &&& ( ~~~e ||| f))) + 7 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 1 * ~~~(d &&& ( ~~~e ||| f)) + 1 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 3 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 1 * (e ||| (d ^^^ f)) + 7 * (e ^^^ ~~~(d ||| (e &&& f))) - 5 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 1 * ( ~~~f &&& ~~~(d ^^^ e)) - 3 * ~~~(d ^^^ e) + 3 * ( ~~~f ||| (d ^^^ e)) - 11 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * ~~~(d ^^^ (e ||| f)) - 2 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 3 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 5 * ~~~(d ||| ~~~f) + 2 * (e ^^^ f) - 6 * (f ^^^ (d ||| ~~~e)) + 1 * (e &&& (d ||| f)) - 5 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 3 * ( ~~~e &&& ~~~(d ^^^ f)) + 7 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 11 * (d ||| f) + 1 * (d ^^^ ( ~~~e ||| f)) - 25 * ~~~(d ||| (e ||| f)) - 23 * ~~~(d ||| ( ~~~e ||| f)) - 57 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 7 * ( ~~~d &&& ( ~~~e &&& f)) - 13 * ( ~~~d &&& (e &&& f)) + 23 * (d &&& ( ~~~e &&& f)) - 30 * (d &&& (e &&& f)) = 26 * ~~~( ~~~d ||| (e ||| f)) - 3 * ( ~~~(d ||| e) ||| (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2404 (x y : BitVec w) : +theorem e_2404 : 1 * ~~~(d ^^^ (e ||| f)) + 1 * ( ~~~e ||| ~~~(d ^^^ f)) - 2 * ~~~(d ||| e) + 1 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 3 * ((d ^^^ e) ||| (d ^^^ f)) - 6 * (e ^^^ f) - 3 * (f ^^^ ~~~(d ||| e)) - 1 * ((d ||| e) &&& (e ^^^ f)) + 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 1 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 3 * (f &&& (d ||| ~~~e)) - 7 * (e ^^^ ( ~~~d ||| (e ||| f))) + 2 * ~~~(d ||| ~~~f) + 5 * (f &&& (d ||| e)) - 6 * (d &&& ~~~e) - 7 * ~~~(d &&& ~~~d) - 7 * (e ||| (d &&& ~~~f)) + 4 * (f ^^^ ~~~(d ||| (e &&& f))) + 2 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 11 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 1 * (d ||| ~~~e) - 2 * (d ||| (e ^^^ f)) - 2 * (f ^^^ ~~~(d &&& (e &&& f))) - 3 * ~~~(e ^^^ f) + 1 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 1 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 3 * ((d &&& e) ^^^ (e ||| f)) - 11 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 6 * (e &&& ~~~f) - 1 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 11 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 1 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 1 * (e ^^^ (d &&& (e ||| f))) - 1 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 6 * (d ^^^ (e ||| f)) - 5 * ~~~(e ||| ~~~f) + 5 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 2 * (e ^^^ ~~~(d ||| f)) + 1 * (e &&& (d ^^^ f)) + 7 * ((d &&& f) ^^^ (e ||| f)) + 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 7 * (f ^^^ ( ~~~d ||| (e ||| f))) + 3 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 11 * ~~~(d ^^^ e) - 2 * (f ^^^ (d ||| e)) + 2 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 6 * (d ^^^ ( ~~~e ||| f)) + 1 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 1 * (d &&& ~~~f) + 3 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 3 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 11 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 1 * (e ^^^ ( ~~~d &&& (e ||| f))) - 1 * (e ||| ~~~(d ||| ~~~f)) - 2 * (e ||| ~~~(d ^^^ f)) - 2 * (d ^^^ e) - 3 * (e ^^^ ( ~~~d ||| (e &&& f))) + 4 * ~~~(d ^^^ (e &&& f)) - 5 * (f ^^^ ~~~(d &&& (e ||| f))) + 3 * (e ^^^ (d ||| (e &&& f))) + 1 * (f ^^^ (d ||| (e ||| f))) + 2 * ( ~~~f &&& ~~~(d ^^^ e)) - 7 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 2 * (f ^^^ ~~~(d ||| ~~~e)) + 49 * ~~~(d ||| (e ||| f)) - 1 * ~~~(d ||| ( ~~~e ||| f)) + 20 * ~~~( ~~~d ||| (e ||| f)) + 44 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 50 * ( ~~~d &&& ( ~~~e &&& f)) - 7 * ( ~~~d &&& (e &&& f)) + 23 * (d &&& ( ~~~e &&& f)) + 22 * (d &&& (e &&& f)) = - 5 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 1 * ( ~~~d &&& (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2405 (x y : BitVec w) : +theorem e_2405 : - 1 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 1 * (e ||| (d &&& ~~~f)) - 3 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 7 * d + 2 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 6 * ~~~(d ||| e) - 1 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 3 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 1 * (e ^^^ ( ~~~d ||| (e &&& f))) + 4 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 5 * (e ^^^ ~~~(d &&& ~~~f)) - 11 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 5 * ~~~e - 2 * ((d ||| e) &&& ~~~(e ^^^ f)) + 1 * (e ^^^ (d &&& ~~~f)) + 7 * (e ^^^ ~~~(d ||| f)) - 2 * (f &&& ~~~(d &&& ~~~e)) - 5 * ( ~~~e ||| (d ^^^ f)) + 2 * (f ^^^ (d ||| (e ||| f))) + 5 * ~~~(e &&& f) - 1 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 1 * (e ^^^ (d ||| f)) + 4 * ~~~d + 1 * ~~~(d ||| (e ^^^ f)) - 6 * (e ^^^ ~~~(d &&& (e &&& f))) + 2 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 3 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 7 * (d ^^^ f) + 2 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 11 * (d ||| ( ~~~e ||| f)) + 5 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 5 * (f ^^^ ~~~(d &&& (e &&& f))) - 5 * (f ^^^ ~~~(d ||| e)) - 11 * (f ^^^ (d ||| ~~~e)) + 2 * (f ^^^ (d ||| (e &&& f))) + 1 * (d &&& e) - 5 * ~~~( ~~~d &&& (e ||| f)) - 3 * ((d &&& e) ^^^ (e ||| ~~~f)) + 2 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 11 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 2 * ( ~~~f &&& (d ^^^ e)) + 11 * (f ^^^ (d ||| e)) + 1 * (e ^^^ (d ||| (e ^^^ f))) + 2 * ( ~~~d &&& (e ^^^ f)) - 2 * (d ^^^ e) + 7 * ((e &&& f) ||| (d &&& (e ||| f))) - 2 * (e ||| (d &&& f)) + 1 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 7 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 4 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 1 * (f &&& ~~~(d &&& e)) + 1 * ((d &&& e) ^^^ (e ||| f)) - 5 * (e &&& f) + 1 * ((d &&& e) ||| ~~~(e ||| f)) - 1 * (f ^^^ ~~~(d &&& e)) - 2 * (f &&& (d ||| ~~~e)) + 1 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (e ^^^ ( ~~~d &&& (e ||| f))) + 4 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 3 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 4 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 7 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 11 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 24 * ~~~(d ||| (e ||| f)) - 28 * ~~~(d ||| ( ~~~e ||| f)) + 29 * ~~~( ~~~d ||| (e ||| f)) + 10 * ( ~~~d &&& ( ~~~e &&& f)) + 12 * ( ~~~d &&& (e &&& f)) + 40 * (d &&& ( ~~~e &&& f)) + 17 * (d &&& (e &&& f)) = 1 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 3 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2406 (x y : BitVec w) : +theorem e_2406 : - 7 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 1 * (f ^^^ (d ||| (e ||| f))) - 11 * ~~~e - 6 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 1 * ((d &&& f) ^^^ (e ||| f)) - 1 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 2 * (e ^^^ (d &&& f)) + 1 * ((d &&& e) ||| ~~~(e ^^^ f)) + 11 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 2 * ((d ^^^ e) ||| (d ^^^ f)) - 5 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 5 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 6 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 2 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 1 * (e ||| ~~~(d ||| ~~~f)) + 3 * (f ^^^ (d ||| e)) - 1 * ( ~~~f ||| (d ^^^ e)) + 3 * (e &&& ~~~(d &&& f)) - 2 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 1 * (e ^^^ (d &&& (e ||| f))) + 1 * (f ^^^ (d ||| (e &&& f))) - 5 * (e ^^^ ~~~(d &&& (e &&& f))) - 6 * (e &&& ~~~(d &&& ~~~f)) - 6 * (f ^^^ (d &&& (e ||| f))) + 3 * (e ^^^ (d ||| (e ||| f))) + 3 * (d ^^^ f) + 1 * (e ||| ~~~f) + 2 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 1 * (d ||| (e ^^^ f)) - 1 * ( ~~~f &&& ~~~(d ^^^ e)) - 2 * ( ~~~f ||| ~~~(d ^^^ e)) - 1 * (f ^^^ (d ||| ~~~e)) - 3 * (d &&& e) + 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 1 * ( ~~~e ||| ~~~(d ^^^ f)) + 4 * ~~~(e &&& f) + 2 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 11 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 11 * ~~~( ~~~d &&& (e &&& f)) - 11 * ( ~~~d ||| (e ^^^ f)) - 2 * ~~~(d &&& ( ~~~e &&& f)) + 1 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 3 * (d ||| (e ||| f)) + 2 * ( ~~~e &&& ~~~(d ^^^ f)) + 7 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 1 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 2 * ((d ||| e) &&& (e ^^^ f)) - 7 * ~~~(d ^^^ f) - 2 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 2 * (f ||| ~~~(d ^^^ e)) + 5 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 7 * ~~~(d &&& ~~~e) + 5 * (d ||| ~~~f) + 3 * (d ||| ( ~~~e &&& f)) + 1 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 2 * ( ~~~d &&& (e ^^^ f)) - 11 * (e ^^^ (d ||| ~~~f)) + 7 * (e ||| (d &&& f)) + 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 1 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 5 * ~~~(d ^^^ e) + 11 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 1 * ~~~(d ^^^ (e ^^^ f)) + 1 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 25 * ~~~(d ||| (e ||| f)) + 19 * ~~~(d ||| ( ~~~e ||| f)) + 28 * ~~~( ~~~d ||| (e ||| f)) + 5 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 13 * ( ~~~d &&& ( ~~~e &&& f)) - 1 * ( ~~~d &&& (e &&& f)) + 28 * (d &&& ( ~~~e &&& f)) - 13 * (d &&& (e &&& f)) = - 3 * (f &&& ~~~(d ^^^ e)) + 1 * (f ^^^ (d &&& ( ~~~e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2407 (x y : BitVec w) : +theorem e_2407 : - 7 * (e ^^^ (d ||| ( ~~~e &&& f))) - 2 * (f ^^^ (d &&& ~~~e)) - 1 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 7 * (f &&& ~~~(d &&& ~~~e)) + 2 * (f ^^^ (d &&& e)) - 2 * e - 11 * (d ^^^ (e ^^^ f)) + 5 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 3 * ~~~(e &&& f) + 11 * ( ~~~d &&& ( ~~~e ||| f)) - 3 * ((d &&& e) ||| ~~~(e ^^^ f)) - 1 * (f ^^^ ~~~(d ||| ~~~e)) - 5 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 5 * (f ^^^ ~~~(d &&& (e &&& f))) + 2 * (d ^^^ f) - 3 * (f &&& (d ||| ~~~e)) + 4 * ~~~(d ||| e) + 5 * (d &&& ~~~f) - 1 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 1 * ~~~(d ^^^ (e &&& f)) + 11 * (e ||| ~~~(d ||| ~~~f)) - 7 * (d ^^^ (e &&& f)) - 11 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 1 * (d ||| (e ^^^ f)) - 5 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 6 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 2 * (f ^^^ ( ~~~d ||| (e &&& f))) + 1 * ((d ||| ~~~e) &&& (e ^^^ f)) - 1 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 1 * ((d &&& f) ^^^ (e ||| f)) - 1 * (f ^^^ ~~~(d ||| (e &&& f))) + 2 * (d ^^^ ( ~~~e &&& f)) + 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * ~~~( ~~~d &&& (e &&& f)) - 5 * ( ~~~e &&& ~~~(d ^^^ f)) - 2 * (e ^^^ (d ||| ( ~~~e ||| f))) + 2 * (d ||| (e ||| f)) + 5 * (f ||| (d &&& e)) + 2 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 5 * (e ^^^ (d &&& f)) - 2 * (d ||| (e &&& f)) + 4 * ~~~(e &&& ~~~f) - 1 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 6 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 11 * (f &&& ~~~(d &&& e)) - 11 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 6 * (f ^^^ (d &&& ( ~~~e ||| f))) - 1 * d + 7 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 7 * (f &&& (d ||| e)) + 4 * ~~~(d &&& (e &&& f)) + 4 * ((d &&& e) ||| ~~~(e ||| f)) + 1 * ~~~( ~~~d ||| (e &&& f)) - 1 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 1 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 2 * ((d &&& e) ^^^ (e ||| f)) + 7 * (f ^^^ ( ~~~d &&& (e ||| f))) + 11 * ((d &&& f) ||| (e &&& ~~~f)) - 2 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 7 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * ~~~( ~~~d ||| (e ^^^ f)) + 1 * (d &&& (e ||| f)) + 2 * (e &&& ~~~(d ^^^ f)) + 3 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 5 * ~~~(d ||| (e ||| f)) + 27 * ~~~(d ||| ( ~~~e ||| f)) + 59 * ~~~( ~~~d ||| (e ||| f)) - 6 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 20 * ( ~~~d &&& ( ~~~e &&& f)) - 6 * (d &&& ( ~~~e &&& f)) - 7 * (d &&& (e &&& f)) = 6 * (e ^^^ ~~~(d &&& (e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2408 (x y : BitVec w) : +theorem e_2408 : - 1 * (e &&& ~~~(d &&& f)) - 7 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 11 * (f ||| ~~~(d ^^^ e)) + 5 * (f ^^^ (d ||| ( ~~~e ||| f))) - 6 * ((d &&& ~~~e) ||| (e ^^^ f)) + 1 * ( ~~~d ||| (e ^^^ f)) + 3 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 5 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 1 * (e ^^^ ~~~(d ||| ~~~f)) - 1 * ( ~~~f ||| ~~~(d ^^^ e)) + 7 * ~~~(d &&& ~~~d) - 2 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 5 * ~~~(d ^^^ (e ^^^ f)) - 3 * (e ||| (d ^^^ f)) + 11 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 5 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (e ^^^ (d &&& (e ^^^ f))) - 1 * (d ||| (e &&& f)) + 1 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 7 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 6 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 2 * (d ||| ~~~e) - 6 * (d ^^^ f) - 7 * (e ^^^ f) + 11 * (e &&& (d ^^^ f)) - 1 * (d ||| ( ~~~e ||| f)) - 2 * (f ^^^ ~~~(d ||| e)) + 2 * (e ^^^ (d ||| ( ~~~e ||| f))) + 4 * ~~~(d ||| ( ~~~e &&& f)) + 7 * ~~~(e ^^^ f) - 3 * (d &&& f) - 2 * (e ||| ~~~(d ||| f)) - 1 * d - 11 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 1 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 1 * (f ^^^ (d &&& e)) + 2 * (e ^^^ ( ~~~d ||| (e &&& f))) + 1 * ((d ^^^ e) &&& (d ^^^ f)) + 1 * (e ^^^ (d ||| (e ^^^ f))) + 5 * (d ^^^ (e ||| f)) + 1 * ~~~d - 2 * ~~~( ~~~d ||| (e &&& f)) + 2 * (e &&& (d ||| f)) + 7 * (f &&& ~~~(d &&& ~~~e)) - 5 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 1 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 1 * (d &&& (e ^^^ f)) + 1 * (f ^^^ ~~~(d &&& (e &&& f))) + 4 * (f ^^^ ( ~~~d ||| (e ||| f))) - 11 * ((d &&& e) ^^^ (e ||| f)) + 3 * ( ~~~d &&& (e ||| f)) + 7 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 1 * ( ~~~f &&& (d ^^^ e)) - 2 * (f &&& ~~~(d &&& e)) + 2 * ~~~(d ^^^ (e ||| f)) + 1 * (e &&& ~~~(d ^^^ f)) - 6 * (d ||| f) + 5 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 7 * ~~~(d ^^^ e) + 5 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 7 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 2 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 5 * (f ^^^ ~~~(d ||| ~~~e)) + 2 * ( ~~~d &&& (e ^^^ f)) + 20 * ~~~(d ||| (e ||| f)) + 11 * ~~~(d ||| ( ~~~e ||| f)) + 5 * ~~~( ~~~d ||| (e ||| f)) + 30 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 43 * ( ~~~d &&& ( ~~~e &&& f)) - 2 * ( ~~~d &&& (e &&& f)) + 19 * (d &&& ( ~~~e &&& f)) + 24 * (d &&& (e &&& f)) = - 7 * (d &&& ( ~~~e ||| f)) - 2 * (f ||| ~~~(d ||| ~~~e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2409 (x y : BitVec w) : +theorem e_2409 : 3 * (e ||| ~~~(d ^^^ f)) + 3 * ~~~(d ||| f) + 4 * ((d &&& e) ^^^ (e ||| ~~~f)) + 4 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 2 * ( ~~~d &&& ( ~~~e ||| f)) - 1 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 7 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 5 * (e ||| (d ^^^ f)) + 5 * ~~~( ~~~d ||| (e &&& f)) - 1 * ~~~(d &&& f) + 2 * ~~~(d ||| (e &&& f)) + 2 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 1 * ~~~(e &&& f) - 5 * (e ^^^ ~~~(d &&& (e ||| f))) + 1 * (f ^^^ ~~~(d &&& ~~~e)) + 5 * (e ^^^ (d &&& ( ~~~e ||| f))) - 5 * ( ~~~d ||| (e ||| f)) - 2 * ~~~(d &&& ( ~~~e &&& f)) - 2 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 11 * (f ^^^ ~~~(d &&& (e ||| f))) - 7 * (e ^^^ ( ~~~d &&& (e ||| f))) + 1 * (d ||| ~~~f) - 6 * (f ^^^ ( ~~~d &&& (e ||| f))) - 2 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 1 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 1 * ((d &&& f) ||| ~~~(e ||| f)) + 2 * ( ~~~f &&& ~~~(d ^^^ e)) + 11 * (e ^^^ ( ~~~d ||| (e &&& f))) + 11 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 3 * (d ||| ( ~~~e &&& f)) + 4 * (e ||| ~~~(d ||| ~~~f)) + 5 * (e ||| f) + 11 * ~~~( ~~~d &&& (e ||| f)) - 3 * ( ~~~d ||| ( ~~~e ||| f)) - 2 * ~~~(d &&& ( ~~~e ||| f)) - 1 * e - 6 * ~~~(d ^^^ (e &&& f)) - 6 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 11 * ( ~~~d ||| (e &&& f)) + 2 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 1 * (e ^^^ ~~~(d &&& ~~~f)) - 3 * (f ^^^ ( ~~~d ||| (e ||| f))) - 5 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 4 * (d &&& ~~~f) + 2 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 2 * (d ^^^ f) + 1 * (e ^^^ (d &&& ~~~f)) + 2 * ~~~( ~~~d &&& (e &&& f)) + 3 * ((e &&& f) ||| (d &&& (e ||| f))) - 7 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 11 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 6 * (f &&& (d ||| ~~~e)) - 5 * (f ||| (d &&& ~~~e)) - 2 * (f ^^^ ( ~~~d ||| (e &&& f))) + 1 * (d ||| ~~~e) - 6 * ~~~(d ||| ~~~f) - 1 * (f ^^^ (d ||| (e &&& f))) - 1 * (e ^^^ (d ||| f)) - 1 * (d ||| (e ^^^ f)) - 6 * ((d &&& e) ||| (e ^^^ f)) + 2 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 1 * ( ~~~d &&& (e ||| f)) - 1 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 11 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 5 * ( ~~~f &&& (d ^^^ e)) + 1 * (e ^^^ (d ||| (e ^^^ f))) + 13 * ~~~(d ||| (e ||| f)) - 26 * ~~~( ~~~d ||| (e ||| f)) - 21 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 36 * ( ~~~d &&& ( ~~~e &&& f)) - 5 * ( ~~~d &&& (e &&& f)) - 16 * (d &&& ( ~~~e &&& f)) + 34 * (d &&& (e &&& f)) = - 19 * ~~~(d ||| ( ~~~e ||| f)) + 1 * (f ||| ~~~(d ||| e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2410 (x y : BitVec w) : +theorem e_2410 : 7 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 7 * (e ^^^ ~~~(d &&& f)) + 1 * ( ~~~e &&& (d ^^^ f)) - 6 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 2 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * ~~~( ~~~d &&& (e ||| f)) + 1 * ~~~(e &&& ~~~f) + 2 * ~~~(d &&& ( ~~~e &&& f)) + 1 * (e ^^^ ( ~~~d ||| (e &&& f))) - 2 * ((d ^^^ e) &&& (d ^^^ f)) - 5 * ~~~f - 1 * (e ||| ~~~(d ^^^ f)) - 2 * (f ^^^ (d &&& ~~~e)) + 1 * (e ^^^ ( ~~~d &&& (e ||| f))) - 3 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 1 * ~~~(e &&& f) + 5 * ((d ^^^ e) ||| (d ^^^ f)) + 4 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 4 * ((d ||| ~~~e) &&& (e ^^^ f)) - 11 * (e ^^^ (d &&& (e ^^^ f))) + 1 * (e ^^^ (d ||| ( ~~~e ||| f))) + 1 * (e ||| (d &&& ~~~f)) + 4 * (e &&& (d ||| f)) + 2 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 2 * (d ||| ~~~e) + 1 * (e ^^^ ( ~~~d ||| (e ||| f))) + 1 * (e ^^^ (d ||| (e &&& f))) + 5 * (f ^^^ (d ||| e)) + 1 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 5 * ( ~~~f &&& ~~~(d ^^^ e)) + 4 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 5 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 1 * ~~~(d ^^^ (e ||| f)) - 11 * ~~~(d ||| ~~~f) - 11 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 11 * ~~~(d &&& f) + 2 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 1 * ~~~(d ^^^ (e &&& f)) + 3 * ( ~~~f ||| (d ^^^ e)) + 7 * (e ^^^ (d &&& f)) - 2 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 3 * (f ^^^ ~~~(d &&& ~~~e)) + 11 * (e &&& f) + 5 * (d ||| e) - 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 7 * ~~~(d ||| e) - 2 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 6 * ((d ||| e) &&& ~~~(e ^^^ f)) + 3 * (f ^^^ (d ||| ~~~e)) - 7 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 3 * ( ~~~f &&& (d ^^^ e)) - 6 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 7 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 3 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 2 * (f &&& (d ||| ~~~e)) + 11 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 3 * (f ||| ~~~(d ||| ~~~e)) + 1 * ~~~(d &&& (e &&& f)) - 3 * ((d &&& f) ^^^ (e ||| f)) + 1 * ~~~(d ||| ~~~e) - 1 * (f ^^^ (d &&& ( ~~~e ||| f))) - 7 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 2 * (d ^^^ ( ~~~e &&& f)) - 2 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 15 * ~~~(d ||| (e ||| f)) - 30 * ~~~(d ||| ( ~~~e ||| f)) - 6 * ~~~( ~~~d ||| (e ||| f)) - 24 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 18 * ( ~~~d &&& ( ~~~e &&& f)) - 6 * ( ~~~d &&& (e &&& f)) - 1 * (d &&& ( ~~~e &&& f)) - 4 * (d &&& (e &&& f)) = - 2 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 1 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2411 (x y : BitVec w) : +theorem e_2411 : 3 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 3 * (e &&& (d ||| ~~~f)) - 6 * (f &&& ~~~(d &&& e)) + 11 * (f ^^^ (d ||| (e &&& f))) - 1 * (e ^^^ (d &&& (e ||| f))) + 4 * ~~~e - 3 * (f ^^^ ~~~(d ||| (e &&& f))) - 1 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 5 * ( ~~~d ||| (e &&& f)) - 5 * ~~~(d ||| ( ~~~e &&& f)) + 7 * (f ^^^ ~~~(d &&& (e &&& f))) - 1 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 2 * ~~~(d ||| ~~~f) + 11 * (e ||| f) - 1 * (d ||| ~~~f) + 2 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 2 * (d &&& f) - 7 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * ( ~~~f &&& ~~~(d ^^^ e)) - 1 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 7 * ~~~(d ||| (e ^^^ f)) - 6 * ( ~~~e ||| ~~~(d ^^^ f)) - 1 * (e ^^^ (d ||| ~~~f)) - 5 * d - 11 * (e ^^^ (d ||| (e &&& f))) - 1 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 2 * ~~~(e ||| ~~~f) + 11 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 2 * f - 5 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 4 * (e ^^^ ~~~(d &&& (e &&& f))) + 4 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 2 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 7 * ~~~(d &&& (e ^^^ f)) + 1 * ( ~~~e &&& ~~~(d ^^^ f)) + 3 * ~~~(d ^^^ (e ^^^ f)) + 2 * (e ||| ~~~(d ||| ~~~f)) + 1 * (e ^^^ ~~~(d &&& (e ||| f))) - 11 * (e ^^^ ( ~~~d ||| (e ||| f))) + 3 * ~~~( ~~~d &&& (e ^^^ f)) - 6 * (e ^^^ f) + 2 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 6 * (e ^^^ (d &&& (e ^^^ f))) - 2 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 7 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 2 * ~~~(e ||| f) + 1 * (d ^^^ ( ~~~e ||| f)) - 7 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 5 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 11 * (d &&& ( ~~~e ||| f)) + 5 * (f ||| ~~~(d ||| e)) - 5 * (e &&& ~~~(d &&& f)) + 7 * ((d &&& f) ||| (e &&& ~~~f)) + 1 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 2 * (f ^^^ (d &&& (e ||| f))) - 2 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 7 * (d ^^^ e) + 3 * (e ||| (d ^^^ f)) + 1 * ~~~(d &&& ~~~f) - 3 * (e &&& ~~~(d ^^^ f)) - 5 * (f ^^^ ~~~(d ||| e)) + 1 * (f ^^^ ( ~~~d ||| (e &&& f))) - 11 * ( ~~~d &&& (e ||| f)) + 1 * ~~~(d ||| (e ||| f)) + 10 * ~~~(d ||| ( ~~~e ||| f)) + 20 * ~~~( ~~~d ||| (e ||| f)) - 2 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 6 * ( ~~~d &&& ( ~~~e &&& f)) + 8 * ( ~~~d &&& (e &&& f)) + 33 * (d &&& ( ~~~e &&& f)) - 16 * (d &&& (e &&& f)) = 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2412 (x y : BitVec w) : +theorem e_2412 : - 1 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 1 * ((d ^^^ e) &&& (d ^^^ f)) + 11 * (f ^^^ (d ||| ( ~~~e &&& f))) - 3 * ~~~(d ^^^ (e &&& f)) - 2 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 3 * (f ^^^ ( ~~~d ||| (e &&& f))) + 1 * (e ||| ~~~(d ||| f)) + 1 * (f ^^^ ~~~(d ||| ~~~e)) - 1 * ~~~(d ^^^ (e ||| f)) + 4 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 2 * (d ||| ( ~~~e &&& f)) + 5 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 1 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 1 * (e ^^^ (d ||| ( ~~~e ||| f))) + 1 * (f ^^^ ~~~(d ||| e)) + 7 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 3 * (f &&& ~~~(d &&& ~~~e)) - 1 * (d &&& f) + 2 * ~~~(d &&& ( ~~~e &&& f)) - 1 * ~~~(d &&& ( ~~~e ||| f)) - 2 * (e ^^^ ~~~(d &&& ~~~f)) + 2 * (f ||| ~~~(d ||| e)) - 6 * (d ^^^ ( ~~~e &&& f)) - 11 * (f ^^^ (d ||| (e ||| f))) + 2 * (e ^^^ ~~~(d &&& (e ||| f))) + 3 * ~~~(d &&& (e &&& f)) + 1 * ~~~(d ||| ~~~e) + 1 * (d ||| e) + 1 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 2 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 7 * ~~~(e &&& f) + 3 * (d ||| ~~~f) - 1 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 11 * (e &&& ~~~f) - 5 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 11 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 11 * (e ||| ~~~(d ||| ~~~f)) - 7 * (e ^^^ (d ||| (e ||| f))) + 1 * ~~~(d &&& f) - 7 * (e &&& (d ||| f)) - 1 * (f ^^^ (d ||| e)) - 1 * (e &&& ~~~(d &&& ~~~f)) + 1 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 11 * ~~~( ~~~d &&& (e ||| f)) - 5 * (e ^^^ (d &&& (e ||| f))) - 5 * ( ~~~d ||| (e ||| f)) + 2 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 1 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 2 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 2 * (f ||| ~~~(d ||| ~~~e)) - 1 * (e &&& ~~~(d ^^^ f)) + 1 * (f ^^^ (d ||| ~~~e)) + 2 * ((d &&& f) ||| ~~~(e ||| f)) - 5 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 2 * (e &&& (d ^^^ f)) - 11 * (e ^^^ ( ~~~d ||| (e &&& f))) + 3 * (d &&& ( ~~~e ||| f)) - 7 * (d ||| (e &&& f)) - 6 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 6 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 6 * ~~~(e &&& ~~~f) - 2 * (d &&& (e ||| f)) + 5 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 4 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 7 * ~~~(d ||| (e ||| f)) - 20 * ~~~(d ||| ( ~~~e ||| f)) - 3 * ~~~( ~~~d ||| (e ||| f)) - 13 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 5 * ( ~~~d &&& ( ~~~e &&& f)) - 16 * ( ~~~d &&& (e &&& f)) + 18 * (d &&& ( ~~~e &&& f)) + 15 * (d &&& (e &&& f)) = - 4 * ~~~(e ||| f) - 7 * ((d &&& e) ||| ~~~(e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2413 (x y : BitVec w) : +theorem e_2413 : - 1 * (f ^^^ (d &&& e)) + 11 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 2 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * (f ||| (d &&& ~~~e)) + 5 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 4 * ~~~d - 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 7 * (f ^^^ ( ~~~d ||| (e &&& f))) + 1 * (e &&& ~~~f) + 1 * (e ||| ~~~(d ||| ~~~f)) - 1 * (f ^^^ (d ||| e)) + 3 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * (e &&& (d ||| f)) + 5 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 5 * ~~~(d ^^^ (e ^^^ f)) + 2 * (f ^^^ ~~~(d ||| ~~~e)) + 2 * ( ~~~d ||| (e ||| f)) + 2 * ~~~(d ^^^ ( ~~~e &&& f)) + 4 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 2 * (e ^^^ (d ||| ~~~f)) - 1 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 3 * ( ~~~d &&& ( ~~~e ||| f)) + 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 1 * ~~~( ~~~d &&& (e &&& f)) + 2 * ~~~(e ||| ~~~f) + 2 * ~~~(d &&& (e &&& f)) + 1 * (d &&& ( ~~~e ||| f)) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 7 * (e ||| (d &&& f)) - 1 * ~~~(d ^^^ f) - 6 * (f ^^^ ~~~(d ||| e)) + 2 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 6 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 6 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 7 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 3 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 5 * ~~~(d &&& (e ^^^ f)) - 11 * ((d &&& ~~~e) ||| (e ^^^ f)) - 11 * d - 7 * (e ^^^ ~~~(d ||| (e &&& f))) - 6 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 5 * (e ^^^ (d &&& (e ||| f))) - 3 * ((d ^^^ e) &&& (d ^^^ f)) - 2 * ~~~(e &&& f) - 1 * ( ~~~e ||| (d ^^^ f)) - 11 * (e ^^^ (d ||| ( ~~~e &&& f))) + 5 * ((d &&& e) ||| ~~~(e ||| f)) + 5 * ( ~~~f ||| (d ^^^ e)) + 3 * ~~~(d &&& ( ~~~e ||| f)) - 2 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 3 * (e ^^^ (d &&& (e ^^^ f))) + 11 * ~~~( ~~~d ||| (e &&& f)) - 2 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 3 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 11 * ( ~~~d ||| ( ~~~e &&& f)) - 5 * (f ^^^ (d ||| ~~~e)) + 4 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 1 * ~~~(d &&& ~~~d) + 1 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 2 * (f ||| ~~~(d ^^^ e)) + 1 * f + 2 * ~~~f + 7 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 5 * (e ^^^ ~~~(d &&& (e &&& f))) - 1 * ~~~(d &&& ~~~e) - 8 * ~~~(d ||| (e ||| f)) - 22 * ~~~(d ||| ( ~~~e ||| f)) + 24 * ~~~( ~~~d ||| (e ||| f)) + 1 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 6 * ( ~~~d &&& ( ~~~e &&& f)) - 4 * ( ~~~d &&& (e &&& f)) + 26 * (d &&& ( ~~~e &&& f)) - 7 * (d &&& (e &&& f)) = 1 * ( ~~~e ||| ~~~(d ^^^ f)) + 2 * (f &&& (d ||| ~~~e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2414 (x y : BitVec w) : +theorem e_2414 : 7 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 2 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 3 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 1 * (f ||| ~~~(d ||| e)) + 7 * (f ||| ~~~(d ^^^ e)) - 1 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 5 * ~~~(d ^^^ (e ||| f)) - 6 * (e ||| ~~~f) + 3 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 5 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 5 * (d ||| (e ^^^ f)) + 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 1 * (d &&& ~~~f) + 2 * ~~~( ~~~d &&& (e ^^^ f)) - 7 * ~~~(d ^^^ ( ~~~e ||| f)) - 3 * (d ^^^ e) - 3 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 1 * ~~~(d ||| f) - 3 * (e ^^^ (d ||| f)) - 11 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 1 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 11 * ( ~~~d &&& (e ^^^ f)) - 6 * (f ^^^ ~~~(d ||| e)) + 4 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 5 * (f &&& ~~~(d &&& e)) - 7 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 1 * (f ||| (d &&& e)) - 1 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 6 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 3 * (f ||| ~~~(d ||| ~~~e)) - 1 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 1 * (f ^^^ (d &&& (e ||| f))) - 3 * (e ^^^ ( ~~~d ||| (e ||| f))) + 2 * ~~~(d &&& ~~~e) - 2 * (f &&& (d ||| ~~~e)) + 2 * (e ^^^ (d &&& (e ^^^ f))) + 1 * ~~~d + 7 * ( ~~~f ||| (d ^^^ e)) + 1 * ~~~(e &&& ~~~f) + 5 * ~~~(d ||| ( ~~~e &&& f)) + 5 * ~~~(d &&& ( ~~~e &&& f)) - 2 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 11 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 1 * ~~~(d &&& e) - 7 * ( ~~~d ||| (e &&& f)) - 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 1 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 1 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 11 * (d ^^^ (e ^^^ f)) + 4 * ((d ^^^ e) &&& (d ^^^ f)) + 2 * (d &&& (e ^^^ f)) - 6 * ( ~~~d ||| (e ^^^ f)) + 11 * (f ^^^ ~~~(d &&& e)) + 11 * (e ^^^ ~~~(d ||| ~~~f)) + 2 * ( ~~~d &&& ( ~~~e ||| f)) + 4 * (d &&& ( ~~~e ||| f)) + 1 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 2 * (e ^^^ ~~~(d ||| (e &&& f))) - 2 * ~~~(d ||| (e ^^^ f)) - 7 * (f ^^^ (d &&& ( ~~~e ||| f))) + 4 * (e &&& ~~~(d &&& f)) + 7 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 6 * (d ||| ( ~~~e &&& f)) - 1 * (e &&& f) - 2 * ~~~(d ^^^ f) - 7 * (e ^^^ (d ||| ( ~~~e &&& f))) - 1 * ~~~(d ||| (e ||| f)) - 24 * ~~~(d ||| ( ~~~e ||| f)) + 9 * ~~~( ~~~d ||| (e ||| f)) - 27 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 15 * ( ~~~d &&& ( ~~~e &&& f)) + 19 * ( ~~~d &&& (e &&& f)) + 16 * (d &&& ( ~~~e &&& f)) + 23 * (d &&& (e &&& f)) = - 3 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 2 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2415 (x y : BitVec w) : +theorem e_2415 : - 2 * (d ||| ( ~~~e &&& f)) - 6 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 7 * d - 7 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 5 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 1 * ~~~(e ^^^ f) + 1 * ((d ||| e) &&& (e ^^^ f)) - 6 * ((d &&& e) ||| ~~~(e ^^^ f)) - 5 * (d ^^^ f) + 5 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 6 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * (e ||| (d &&& f)) + 7 * (d ^^^ ( ~~~e &&& f)) + 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 5 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 3 * (e ^^^ ( ~~~d ||| (e ||| f))) - 11 * (f ||| (d ^^^ e)) - 6 * ( ~~~f ||| ~~~(d ^^^ e)) - 11 * (e &&& (d ||| f)) + 7 * (e ||| ~~~f) - 2 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 1 * (f ^^^ (d ||| e)) + 1 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 5 * (d &&& (e ||| f)) - 2 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 1 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 1 * ~~~(d ^^^ (e ||| f)) - 2 * ~~~(d &&& ~~~d) - 1 * ( ~~~f ||| (d ^^^ e)) + 1 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 2 * ( ~~~f &&& (d ^^^ e)) + 2 * ( ~~~d ||| ( ~~~e ||| f)) + 3 * (e ^^^ ~~~(d ||| (e &&& f))) + 1 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 7 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 11 * ( ~~~f &&& ~~~(d ^^^ e)) - 6 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 3 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 3 * (d ^^^ e) + 4 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 4 * (f ^^^ (d &&& (e ||| f))) + 2 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 3 * (e ^^^ ~~~(d &&& ~~~f)) - 3 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 5 * (e ^^^ (d ||| ( ~~~e ||| f))) - 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * (e &&& ~~~(d &&& f)) - 1 * (f ^^^ ~~~(d &&& (e ||| f))) + 2 * (e ||| ~~~(d ||| ~~~f)) - 1 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 2 * ( ~~~e &&& (d ^^^ f)) - 11 * (f &&& (d ^^^ e)) - 1 * ((e &&& f) ||| (d &&& (e ||| f))) + 7 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 1 * ((d &&& f) ||| (e &&& ~~~f)) - 1 * (e ^^^ (d ||| (e &&& f))) + 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 7 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 1 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 11 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 2 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 2 * ((d &&& e) ||| ~~~(e ||| f)) - 7 * (d ||| e) + 3 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 2 * ~~~( ~~~d &&& (e ^^^ f)) - 2 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 3 * ~~~(d ||| (e ||| f)) + 33 * ~~~(d ||| ( ~~~e ||| f)) - 6 * ~~~( ~~~d ||| (e ||| f)) + 9 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 28 * ( ~~~d &&& ( ~~~e &&& f)) + 30 * ( ~~~d &&& (e &&& f)) + 44 * (d &&& ( ~~~e &&& f)) + 30 * (d &&& (e &&& f)) = 7 * ((d &&& f) ^^^ (e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2416 (x y : BitVec w) : +theorem e_2416 : - 3 * (d &&& ~~~e) + 1 * (f &&& ~~~(d &&& ~~~e)) - 3 * ((d &&& e) ||| ~~~(e ^^^ f)) + 5 * ((d ||| e) &&& (e ^^^ f)) + 1 * ((d &&& e) ||| (e ^^^ f)) - 1 * ~~~( ~~~d &&& (e ||| f)) - 7 * (e ^^^ (d ||| f)) - 1 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 1 * (e ||| f) + 1 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 7 * (e ^^^ (d ||| (e &&& f))) + 3 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 5 * (e ||| ~~~(d ||| ~~~f)) + 1 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 11 * ~~~d - 2 * (e ^^^ (d ||| ~~~f)) + 1 * ~~~(d &&& ( ~~~e &&& f)) - 7 * e - 6 * ~~~(d ^^^ (e ^^^ f)) - 11 * (e &&& (d ||| ~~~f)) - 2 * ~~~(d ||| e) + 1 * ~~~(d &&& ~~~e) + 4 * ~~~(e &&& f) - 1 * (d ^^^ (e ^^^ f)) + 3 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 6 * (e ^^^ f) + 1 * ((d ||| ~~~e) &&& (e ^^^ f)) + 2 * (e &&& ~~~(d &&& ~~~f)) + 1 * ( ~~~d &&& ( ~~~e ||| f)) - 3 * (e ^^^ ~~~(d ||| f)) - 11 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 1 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 11 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 1 * (e ||| (d ^^^ f)) + 5 * ((d ^^^ e) &&& (d ^^^ f)) + 1 * ( ~~~e ||| ~~~(d ^^^ f)) - 2 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * ((d &&& f) ||| ~~~(e ||| f)) + 7 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 3 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 7 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 1 * (e ||| (d &&& ~~~f)) - 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 2 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 5 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 6 * (d ||| f) - 2 * ~~~(d ||| ( ~~~e &&& f)) + 4 * (e ||| ~~~(d ^^^ f)) - 1 * (e ^^^ ~~~(d &&& (e &&& f))) - 11 * (f &&& ~~~(d &&& e)) + 5 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 11 * (f ^^^ (d &&& e)) + 3 * ((d &&& e) ^^^ (e ||| ~~~f)) + 1 * (e ^^^ (d &&& (e ||| f))) - 5 * (e ^^^ (d &&& f)) + 1 * (f ||| (d ^^^ e)) - 1 * (d &&& (e ||| f)) - 2 * (f &&& (d ||| ~~~e)) - 2 * ~~~(d &&& (e &&& f)) + 3 * (f ||| ~~~(d ||| e)) + 2 * (d ^^^ (e &&& f)) + 1 * (f ^^^ (d &&& ~~~e)) - 1 * (d ||| (e &&& f)) + 7 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 4 * ~~~(d &&& ~~~f) - 1 * (e ^^^ (d ||| ( ~~~e &&& f))) - 6 * ~~~(d ||| (e ||| f)) - 16 * ~~~(d ||| ( ~~~e ||| f)) + 17 * ~~~( ~~~d ||| (e ||| f)) + 33 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 2 * ( ~~~d &&& ( ~~~e &&& f)) + 32 * ( ~~~d &&& (e &&& f)) + 11 * (d &&& ( ~~~e &&& f)) + 11 * (d &&& (e &&& f)) = 6 * ~~~(d ||| ~~~e) + 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2417 (x y : BitVec w) : +theorem e_2417 : 11 * (d ^^^ e) - 1 * ~~~(d ^^^ (e ^^^ f)) - 5 * (d ^^^ (e ||| f)) - 1 * (e ^^^ (d ||| (e ^^^ f))) - 2 * (e ^^^ ~~~(d ||| ~~~f)) - 11 * (e ^^^ (d &&& ( ~~~e ||| f))) + 2 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 2 * (d ||| f) + 1 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 3 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 1 * (f &&& (d ||| ~~~e)) - 6 * (f ||| ~~~(d ^^^ e)) + 1 * ((d &&& e) ||| ~~~(e ^^^ f)) + 2 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 6 * (d &&& ~~~e) - 2 * (d ||| ( ~~~e ||| f)) + 11 * (d ^^^ (e ^^^ f)) - 5 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 5 * ((d &&& f) ||| (e &&& ~~~f)) + 1 * ((d ||| e) &&& (e ^^^ f)) - 6 * ~~~(d ^^^ ( ~~~e ||| f)) + 4 * (f ||| ~~~(d ||| e)) + 5 * (e ||| (d &&& ~~~f)) + 4 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 1 * ( ~~~d ||| (e &&& f)) + 2 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 2 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 4 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 1 * ~~~d - 3 * ( ~~~d ||| ( ~~~e ||| f)) - 2 * (f ^^^ ~~~(d ||| (e &&& f))) + 7 * (f ^^^ (d &&& ~~~e)) + 1 * ~~~( ~~~d &&& (e &&& f)) - 11 * (f ^^^ (d ||| (e &&& f))) + 1 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 2 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 3 * (e &&& (d ||| ~~~f)) + 1 * ( ~~~d &&& (e ^^^ f)) - 1 * ~~~(d &&& (e ||| f)) - 11 * ~~~(e ||| f) - 5 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 3 * (f ^^^ (d ||| e)) + 1 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 2 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 11 * (d &&& f) - 2 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 3 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 11 * ~~~( ~~~d ||| (e ^^^ f)) + 4 * ((d &&& e) ^^^ (e ||| f)) - 6 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 7 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 3 * ( ~~~f ||| ~~~(d ^^^ e)) + 2 * (e ||| ~~~(d ||| ~~~f)) + 2 * ( ~~~f &&& (d ^^^ e)) - 5 * ~~~(d &&& ~~~d) + 3 * ~~~(e &&& f) - 5 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 11 * (e ^^^ (d &&& (e ||| f))) - 1 * (f ^^^ (d ||| ~~~e)) + 1 * (f &&& (d ^^^ e)) + 1 * (e ||| f) + 2 * ((d ||| ~~~e) &&& (e ^^^ f)) - 1 * (e &&& (d ^^^ f)) - 7 * ~~~(d ^^^ (e ||| f)) - 1 * ( ~~~f &&& ~~~(d ^^^ e)) + 41 * ~~~(d ||| (e ||| f)) + 8 * ~~~(d ||| ( ~~~e ||| f)) + 36 * ~~~( ~~~d ||| (e ||| f)) + 26 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 7 * ( ~~~d &&& ( ~~~e &&& f)) + 27 * ( ~~~d &&& (e &&& f)) + 18 * (d &&& ( ~~~e &&& f)) - 21 * (d &&& (e &&& f)) = 1 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2418 (x y : BitVec w) : +theorem e_2418 : 1 * (d ^^^ (e &&& f)) - 1 * (f ^^^ ~~~(d &&& (e &&& f))) - 5 * (f ^^^ ( ~~~d ||| (e ||| f))) + 4 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 2 * ~~~(d &&& ~~~e) + 11 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 7 * ( ~~~d ||| (e ||| f)) - 1 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 11 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 7 * (e &&& ~~~(d &&& ~~~f)) - 3 * ((d ^^^ e) &&& (d ^^^ f)) - 1 * (f &&& ~~~(d ^^^ e)) + 5 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 2 * (e ^^^ (d &&& (e ||| f))) + 1 * (f ^^^ ( ~~~d ||| (e &&& f))) - 5 * (f ||| (d ^^^ e)) - 1 * (f ||| (d &&& e)) + 1 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 11 * d + 5 * ~~~(d ||| ~~~e) + 1 * (d &&& (e ||| f)) - 2 * (f &&& (d ^^^ e)) + 2 * (f ^^^ (d &&& e)) - 2 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 1 * (d &&& ~~~f) + 5 * ~~~(d ^^^ f) - 6 * e - 11 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 5 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 6 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 3 * (d &&& f) + 5 * ((d ||| e) &&& ~~~(e ^^^ f)) + 2 * (d &&& ~~~e) - 7 * (e &&& (d ||| ~~~f)) + 1 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 2 * ~~~(d ||| ~~~f) - 7 * (e ^^^ ~~~(d &&& ~~~f)) + 1 * (e ^^^ f) - 6 * (d ^^^ ( ~~~e ||| f)) + 4 * (e &&& (d ^^^ f)) - 1 * (e ||| ~~~(d ||| ~~~f)) + 2 * ~~~(d ^^^ ( ~~~e &&& f)) + 1 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 4 * (d ||| ( ~~~e &&& f)) + 1 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 2 * ( ~~~d ||| (e &&& f)) - 2 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 5 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 3 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 3 * (e ^^^ ~~~(d ||| ~~~f)) - 7 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * ( ~~~d ||| (e ^^^ f)) + 1 * ~~~(d ^^^ e) + 2 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 3 * ((d &&& e) ^^^ (e ||| f)) + 1 * ~~~(e ^^^ f) + 1 * ~~~(d &&& ~~~d) - 7 * (f ^^^ ~~~(d ||| e)) + 2 * (f ||| ~~~(d ||| e)) - 2 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 7 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 5 * (e ||| (d &&& f)) + 1 * (e ^^^ ~~~(d &&& (e ||| f))) + 7 * (f &&& ~~~(d &&& ~~~e)) - 1 * (e ^^^ (d &&& ( ~~~e ||| f))) + 1 * ~~~(d ||| ( ~~~e &&& f)) + 8 * ~~~(d ||| (e ||| f)) + 23 * ~~~(d ||| ( ~~~e ||| f)) - 25 * ~~~( ~~~d ||| (e ||| f)) + 23 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 1 * ( ~~~d &&& ( ~~~e &&& f)) + 3 * ( ~~~d &&& (e &&& f)) - 7 * (d &&& ( ~~~e &&& f)) - 9 * (d &&& (e &&& f)) = - 7 * (e &&& ~~~(d &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2419 (x y : BitVec w) : +theorem e_2419 : - 3 * ((d ||| e) &&& ~~~(e ^^^ f)) + 3 * ( ~~~d ||| (e ^^^ f)) + 3 * (f &&& ~~~(d ^^^ e)) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 2 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 2 * ~~~(d ^^^ f) + 7 * (e ^^^ (d ||| (e ^^^ f))) - 7 * ~~~d - 11 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 4 * (e ^^^ ~~~(d ||| (e &&& f))) + 5 * ( ~~~d ||| ( ~~~e ||| f)) - 6 * (e ||| (d &&& f)) - 2 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 1 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 1 * ~~~( ~~~d ||| (e &&& f)) + 11 * ((d ^^^ e) ||| ~~~(d ^^^ f)) + 1 * (f &&& ~~~(d &&& ~~~e)) + 1 * ((d ||| e) &&& (e ^^^ f)) - 1 * (e ^^^ (d &&& f)) - 1 * (f ^^^ (d &&& ~~~e)) + 5 * (e &&& ~~~(d &&& f)) + 11 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 2 * (f ^^^ (d ||| e)) + 1 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 7 * ((d &&& e) ||| ~~~(e ||| f)) + 3 * ( ~~~d &&& (e ^^^ f)) - 11 * (f ^^^ ~~~(d ||| e)) - 1 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 7 * ((d &&& f) ||| ~~~(e ||| f)) + 1 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 5 * (d &&& e) + 3 * ~~~(d ^^^ (e ||| f)) - 6 * (e ^^^ ~~~(d &&& f)) - 11 * (e &&& ~~~(d ^^^ f)) - 7 * (f &&& (d ^^^ e)) - 3 * (d &&& f) - 2 * (e ||| (d &&& ~~~f)) - 11 * (e ^^^ ~~~(d &&& (e &&& f))) - 2 * (e &&& f) - 7 * ~~~(d &&& ~~~e) + 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 2 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 3 * (d &&& (e ||| f)) - 1 * (d &&& ( ~~~e ||| f)) - 11 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 4 * (f ^^^ ~~~(d ||| ~~~e)) + 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 1 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 1 * (f ^^^ (d ||| ~~~e)) - 7 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 5 * ~~~(e ^^^ f) + 2 * (f ||| (d &&& ~~~e)) - 1 * ~~~(e ||| f) + 5 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 2 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 1 * ((d &&& e) ||| (e ^^^ f)) - 1 * ( ~~~f ||| ~~~(d ^^^ e)) + 4 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 2 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 2 * (e ^^^ ~~~(d ||| f)) + 2 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 2 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 5 * (e &&& ~~~f) - 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 4 * (f ^^^ ~~~(d &&& e)) - 5 * ~~~(e ||| ~~~f) + 30 * ~~~(d ||| (e ||| f)) + 10 * ~~~(d ||| ( ~~~e ||| f)) + 16 * ~~~( ~~~d ||| (e ||| f)) + 8 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 17 * ( ~~~d &&& ( ~~~e &&& f)) - 20 * ( ~~~d &&& (e &&& f)) + 23 * (d &&& ( ~~~e &&& f)) + 50 * (d &&& (e &&& f)) = - 7 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2420 (x y : BitVec w) : +theorem e_2420 : - 2 * ~~~(d ^^^ e) + 3 * (e ^^^ ~~~(d &&& ~~~f)) - 1 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 7 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 3 * (f ||| ~~~(d ^^^ e)) + 4 * (f ^^^ (d &&& ( ~~~e ||| f))) + 1 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 2 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 2 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 6 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 3 * (d &&& (e ||| f)) - 7 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 3 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 7 * ((d ||| e) &&& ~~~(e ^^^ f)) - 1 * ( ~~~d &&& (e ||| f)) - 11 * ~~~f + 1 * ( ~~~f &&& (d ^^^ e)) + 5 * ((d ||| ~~~e) &&& (e ^^^ f)) - 3 * ~~~(d &&& ( ~~~e &&& f)) - 7 * ((d &&& f) ^^^ (e ||| f)) - 2 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 6 * (e ^^^ (d &&& ( ~~~e ||| f))) + 7 * (d ||| e) - 11 * ~~~(e &&& f) + 4 * ((d ^^^ e) &&& (d ^^^ f)) + 11 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 2 * ((d &&& e) ||| ~~~(e ^^^ f)) + 2 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 2 * ( ~~~e ||| (d ^^^ f)) - 5 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 1 * (f ||| ~~~(d ||| ~~~e)) - 2 * ~~~(d ||| (e ^^^ f)) + 1 * (f ^^^ (d ||| ( ~~~e &&& f))) + 1 * (d &&& ~~~e) - 1 * (e ||| (d &&& ~~~f)) + 1 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 1 * (e ||| (d &&& f)) + 2 * (e ||| f) + 1 * (e ^^^ (d ||| f)) - 5 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 11 * ( ~~~d ||| (e ^^^ f)) + 1 * ~~~(d ||| ~~~f) - 1 * (d ^^^ (e ||| f)) - 5 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 5 * (f &&& (d ^^^ e)) + 1 * (e &&& (d ||| f)) + 11 * ( ~~~f ||| (d ^^^ e)) + 4 * ( ~~~d ||| ( ~~~e &&& f)) + 3 * (d ^^^ e) - 3 * (f ^^^ (d ||| ( ~~~e ||| f))) - 1 * (e ^^^ (d ||| (e ^^^ f))) - 1 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 11 * (e ^^^ ~~~(d ||| ~~~f)) - 6 * (f ||| ~~~(d ||| e)) - 1 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 11 * (e &&& ~~~(d &&& ~~~f)) - 3 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 2 * ~~~( ~~~d ||| (e ^^^ f)) + 11 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 1 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 1 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 1 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * ~~~( ~~~d ||| (e &&& f)) + 5 * (e ^^^ (d &&& ~~~f)) + 1 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 2 * ~~~d + 30 * ~~~(d ||| (e ||| f)) + 19 * ~~~(d ||| ( ~~~e ||| f)) + 17 * ~~~( ~~~d ||| (e ||| f)) + 3 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 4 * ( ~~~d &&& ( ~~~e &&& f)) + 20 * ( ~~~d &&& (e &&& f)) + 10 * (d &&& ( ~~~e &&& f)) + 5 * (d &&& (e &&& f)) = - 3 * e := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2421 (x y : BitVec w) : +theorem e_2421 : 4 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 1 * (f ^^^ (d &&& ( ~~~e ||| f))) + 1 * ((d ||| e) &&& (e ^^^ f)) + 1 * (d &&& (e ^^^ f)) - 1 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 7 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 1 * (d &&& ~~~e) + 2 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 6 * ~~~(d &&& ( ~~~e ||| f)) - 1 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 2 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 2 * d - 6 * (f &&& (d ^^^ e)) + 4 * ((d &&& e) ^^^ (e ||| ~~~f)) - 1 * (d &&& e) + 3 * (e ^^^ (d ||| ~~~f)) - 7 * ~~~(e ^^^ f) - 11 * (e &&& ~~~(d ^^^ f)) + 1 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 2 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 5 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 4 * (d ||| (e ^^^ f)) - 7 * (e &&& ~~~(d &&& f)) + 7 * (f ||| ~~~(d ||| e)) + 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 7 * (d ^^^ ( ~~~e ||| f)) - 1 * ~~~(d ^^^ ( ~~~e &&& f)) + 2 * ( ~~~d ||| ( ~~~e ||| f)) - 2 * ((d ||| e) &&& ~~~(e ^^^ f)) - 1 * (d ^^^ f) - 11 * ((d ^^^ e) ||| (d ^^^ f)) + 2 * ~~~(d ^^^ ( ~~~e ||| f)) + 1 * ~~~(d ||| ~~~f) + 1 * (e ^^^ ~~~(d &&& ~~~f)) - 3 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 4 * (d ^^^ e) - 7 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 7 * (f &&& (d ||| e)) - 3 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 11 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 5 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 2 * ( ~~~d &&& (e ^^^ f)) - 2 * (f ^^^ ~~~(d &&& (e &&& f))) + 2 * (d ||| (e ||| f)) + 3 * ~~~(e &&& ~~~f) - 1 * (f ^^^ (d ||| ( ~~~e &&& f))) - 2 * ~~~(d ^^^ (e ^^^ f)) - 11 * (e ^^^ (d &&& (e ||| f))) - 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 5 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 1 * (e ||| (d ^^^ f)) - 1 * (f ^^^ (d ||| ~~~e)) - 1 * (e &&& (d ||| f)) - 5 * (e ||| ~~~(d ^^^ f)) - 2 * (e ^^^ (d ||| (e ^^^ f))) - 2 * (f ^^^ ( ~~~d &&& (e ||| f))) - 11 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 2 * (f ||| (d &&& e)) - 3 * ((d &&& e) ||| ~~~(e ||| f)) + 4 * ( ~~~f ||| (d ^^^ e)) + 3 * (e &&& ~~~f) + 3 * (f ^^^ ~~~(d ||| ~~~e)) - 7 * (e &&& f) - 2 * (e ^^^ ~~~(d &&& (e ||| f))) + 1 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 5 * f + 16 * ~~~(d ||| (e ||| f)) + 7 * ~~~(d ||| ( ~~~e ||| f)) + 9 * ~~~( ~~~d ||| (e ||| f)) + 27 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 7 * ( ~~~d &&& ( ~~~e &&& f)) + 64 * ( ~~~d &&& (e &&& f)) - 19 * (d &&& ( ~~~e &&& f)) + 25 * (d &&& (e &&& f)) = 5 * (d ^^^ (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2422 (x y : BitVec w) : +theorem e_2422 : - 6 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 1 * ((d ||| e) &&& (e ^^^ f)) - 5 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 1 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 7 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 4 * ~~~(d ^^^ (e ^^^ f)) + 11 * ( ~~~f ||| ~~~(d ^^^ e)) - 7 * (e ^^^ ~~~(d ||| (e &&& f))) - 5 * (f ^^^ ( ~~~d &&& (e ||| f))) + 3 * (f &&& (d ||| ~~~e)) + 3 * (e ^^^ (d &&& f)) - 11 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * ~~~(d &&& ~~~e) + 7 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 4 * (f ^^^ (d ||| e)) - 1 * (e ^^^ ~~~(d &&& ~~~f)) - 1 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 7 * ~~~(d &&& ~~~f) - 5 * (e ||| (d ^^^ f)) - 6 * ~~~(d &&& (e ||| f)) + 3 * (f ||| ~~~(d ||| e)) - 6 * (f ^^^ ~~~(d &&& (e &&& f))) + 4 * (f &&& ~~~(d &&& e)) + 4 * ((d &&& e) ^^^ (e ||| f)) + 7 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 2 * (f ^^^ (d ||| (e ||| f))) - 2 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 5 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 1 * ~~~(d &&& (e &&& f)) - 11 * (e ^^^ (d ||| ~~~f)) + 2 * (f ||| ~~~(d ^^^ e)) + 2 * ~~~( ~~~d ||| (e ^^^ f)) + 5 * ( ~~~e &&& (d ^^^ f)) - 1 * (e ||| (d &&& f)) - 2 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 2 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 2 * ~~~(d &&& (e ^^^ f)) + 2 * (e ^^^ (d ||| (e &&& f))) - 6 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 3 * (e ^^^ (d &&& ~~~f)) + 4 * (f ||| (d &&& e)) + 1 * ((d &&& f) ^^^ (e ||| f)) - 11 * (f ||| (d &&& ~~~e)) - 11 * ~~~(d &&& ~~~d) + 1 * ~~~( ~~~d &&& (e ^^^ f)) - 6 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 5 * (f &&& (d ^^^ e)) + 3 * ~~~(d &&& f) - 2 * (e &&& (d ||| f)) + 2 * (f ^^^ (d ||| (e &&& f))) + 5 * ( ~~~d ||| (e ^^^ f)) + 3 * ((d ||| e) &&& ~~~(e ^^^ f)) - 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 11 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 2 * ~~~(d ^^^ e) - 11 * (d ^^^ ( ~~~e &&& f)) - 7 * ( ~~~d ||| (e ||| f)) - 11 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 2 * ~~~(e &&& ~~~f) - 2 * ~~~(d ^^^ (e &&& f)) - 3 * ((d &&& e) ||| ~~~(e ^^^ f)) + 2 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 1 * ~~~(e ||| f) + 11 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 7 * (e &&& ~~~(d &&& f)) + 28 * ~~~(d ||| (e ||| f)) + 7 * ~~~(d ||| ( ~~~e ||| f)) + 29 * ~~~( ~~~d ||| (e ||| f)) + 31 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 30 * ( ~~~d &&& ( ~~~e &&& f)) + 20 * ( ~~~d &&& (e &&& f)) + 4 * (d &&& ( ~~~e &&& f)) + 13 * (d &&& (e &&& f)) = 7 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 7 * ~~~(d ||| (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2423 (x y : BitVec w) : +theorem e_2423 : 1 * ((d &&& e) ^^^ (e ||| ~~~f)) - 6 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * ~~~(d &&& ( ~~~e &&& f)) - 3 * (d &&& f) + 2 * (f ||| (d ^^^ e)) - 6 * (d ||| (e ||| f)) + 5 * (d ||| e) - 1 * ~~~(d ^^^ f) - 1 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 11 * (e ^^^ (d &&& ( ~~~e ||| f))) - 1 * ((e &&& f) ||| (d &&& (e ||| f))) - 1 * (e ||| (d &&& f)) + 11 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 2 * (e ^^^ ~~~(d ||| f)) + 2 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 1 * ~~~( ~~~d &&& (e ^^^ f)) + 2 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 7 * ((d ||| e) &&& (e ^^^ f)) + 1 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 11 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * ~~~( ~~~d ||| (e &&& f)) + 1 * ((d ^^^ e) ||| (d ^^^ f)) - 1 * (e ||| (d &&& ~~~f)) - 1 * ~~~(d ^^^ (e &&& f)) + 2 * d + 1 * ~~~(d ||| ~~~f) + 3 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 2 * (f &&& ~~~(d &&& e)) + 3 * (e ^^^ (d ||| (e &&& f))) - 11 * (e &&& ~~~f) + 1 * (f ^^^ ~~~(d &&& (e ||| f))) - 6 * (f ^^^ (d ||| ~~~e)) + 1 * (e &&& f) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 3 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 2 * ( ~~~f ||| (d ^^^ e)) + 1 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 5 * (f &&& (d ^^^ e)) - 2 * (f ^^^ (d ||| (e &&& f))) - 1 * ((d ||| e) &&& ~~~(e ^^^ f)) - 1 * (f ^^^ (d ||| e)) + 5 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 11 * (e ||| ~~~(d ||| ~~~f)) - 2 * ~~~(e &&& f) - 7 * (f ^^^ (d &&& e)) - 11 * ~~~(e ||| f) + 1 * (d ||| (e &&& f)) - 7 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 2 * (d ^^^ (e ||| f)) + 2 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 1 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 4 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 1 * ~~~(d ||| ( ~~~e &&& f)) + 5 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 5 * (f ^^^ ~~~(d &&& ~~~e)) - 11 * (e ||| ~~~(d ||| f)) - 5 * (d ^^^ (e ^^^ f)) - 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 11 * ( ~~~d &&& (e ^^^ f)) + 4 * (e ^^^ (d ||| f)) + 3 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 2 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 7 * ~~~(d ||| (e ^^^ f)) - 1 * ~~~(e &&& ~~~f) - 7 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 5 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 28 * ~~~(d ||| (e ||| f)) - 2 * ~~~(d ||| ( ~~~e ||| f)) - 14 * ~~~( ~~~d ||| (e ||| f)) + 21 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 8 * ( ~~~d &&& (e &&& f)) - 7 * (d &&& ( ~~~e &&& f)) - 11 * (d &&& (e &&& f)) = - 1 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 4 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2424 (x y : BitVec w) : +theorem e_2424 : 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 11 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 2 * (e ^^^ ~~~(d ||| (e &&& f))) + 2 * (e ^^^ (d &&& f)) - 1 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 6 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 1 * (e ^^^ (d ||| (e ||| f))) + 3 * ( ~~~d &&& ( ~~~e ||| f)) + 5 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 1 * ( ~~~d ||| ( ~~~e &&& f)) - 7 * (e ^^^ (d ||| f)) + 3 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 5 * (f &&& ~~~(d &&& ~~~e)) - 11 * (f ||| ~~~(d ||| e)) + 5 * ((d &&& f) ||| (e &&& ~~~f)) + 2 * ( ~~~f &&& (d ^^^ e)) + 7 * ~~~(d ^^^ (e ||| f)) + 11 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 11 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (e ^^^ ( ~~~d &&& (e ||| f))) + 1 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 3 * (d ||| (e ^^^ f)) + 11 * (e ||| ~~~(d ||| ~~~f)) + 7 * (f ^^^ ~~~(d ||| e)) + 1 * (d ||| ( ~~~e ||| f)) - 6 * (e ^^^ ~~~(d ||| ~~~f)) - 1 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 3 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 1 * (e ||| (d ^^^ f)) + 7 * ~~~(d &&& e) - 6 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 3 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 6 * ~~~(d &&& f) - 7 * (d ^^^ e) - 1 * (d ||| f) - 1 * ~~~(d &&& (e ^^^ f)) - 1 * ( ~~~f &&& ~~~(d ^^^ e)) + 7 * (d ||| ~~~f) - 2 * (f ||| (d ^^^ e)) - 1 * (f ^^^ (d ||| (e &&& f))) + 4 * ( ~~~e &&& ~~~(d ^^^ f)) - 2 * ~~~( ~~~d ||| (e &&& f)) - 1 * (e ||| ~~~(d ^^^ f)) - 5 * ~~~(d ^^^ (e ^^^ f)) - 5 * (f ^^^ (d ||| ~~~e)) + 1 * (d ||| e) - 2 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 5 * (e ^^^ f) + 1 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 3 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 5 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 4 * (f &&& (d ||| e)) + 1 * ( ~~~f ||| (d ^^^ e)) - 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 2 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 1 * ( ~~~d ||| (e ||| f)) + 3 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 4 * ~~~(d &&& (e ||| f)) + 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 11 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 5 * (d &&& e) + 2 * ( ~~~e ||| (d ^^^ f)) + 4 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 11 * (e ^^^ (d ||| (e ^^^ f))) - 7 * ~~~(d ||| ~~~f) - 2 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 5 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 7 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 13 * ~~~(d ||| (e ||| f)) - 25 * ~~~(d ||| ( ~~~e ||| f)) + 11 * ~~~( ~~~d ||| (e ||| f)) - 26 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 1 * ( ~~~d &&& ( ~~~e &&& f)) - 2 * (d &&& ( ~~~e &&& f)) - 11 * (d &&& (e &&& f)) = - 24 * ( ~~~d &&& (e &&& f)) + 7 * ~~~(d &&& (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2425 (x y : BitVec w) : +theorem e_2425 : 3 * (d ||| ( ~~~e &&& f)) - 1 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 1 * (e ^^^ (d ||| (e ^^^ f))) + 11 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 2 * ~~~( ~~~d &&& (e &&& f)) - 5 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 6 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 1 * (e ^^^ (d &&& ( ~~~e ||| f))) + 11 * ~~~(d ||| ( ~~~e &&& f)) + 3 * ((d &&& e) ||| (e ^^^ f)) + 4 * (e ^^^ ~~~(d &&& (e ||| f))) + 2 * (f ^^^ ~~~(d ||| e)) - 11 * ( ~~~e &&& (d ^^^ f)) + 7 * ~~~( ~~~d &&& (e ||| f)) + 2 * ~~~(d ||| ~~~f) + 7 * ~~~(e ||| ~~~f) - 6 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 1 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 2 * ( ~~~f &&& ~~~(d ^^^ e)) + 7 * ((d &&& f) ^^^ (e ||| f)) - 1 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 1 * (d ||| e) - 3 * ((d ^^^ e) &&& (d ^^^ f)) + 3 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 3 * (f ||| ~~~(d ||| ~~~e)) + 2 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 5 * (f ^^^ ~~~(d &&& ~~~e)) + 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 2 * (e &&& (d ||| ~~~f)) + 5 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 2 * ((d &&& e) ||| ~~~(e ^^^ f)) - 2 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 1 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 2 * (e &&& f) + 1 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * (f ||| ~~~(d ^^^ e)) + 2 * (f ||| (d &&& ~~~e)) + 1 * (d ||| ~~~f) - 3 * ((d ||| e) &&& ~~~(e ^^^ f)) - 7 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 5 * (f &&& (d ^^^ e)) + 11 * (e &&& (d ||| f)) - 6 * (d ||| ( ~~~e ||| f)) - 6 * ~~~( ~~~d ||| (e ^^^ f)) + 5 * (e ^^^ (d ||| f)) - 2 * (e ^^^ ~~~(d ||| ~~~f)) - 11 * ~~~(d ^^^ (e &&& f)) + 2 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * (e ^^^ ~~~(d ||| (e &&& f))) - 7 * (d ^^^ (e &&& f)) - 7 * ( ~~~e &&& ~~~(d ^^^ f)) - 3 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 7 * (e ^^^ (d ||| ( ~~~e ||| f))) - 1 * (e ^^^ f) - 2 * ~~~(d &&& (e ||| f)) - 7 * (e ^^^ (d &&& (e ^^^ f))) + 2 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 11 * (e ^^^ (d ||| (e ||| f))) - 1 * (d ^^^ ( ~~~e ||| f)) - 3 * (e ||| f) + 11 * (d ^^^ (e ^^^ f)) - 5 * (d ||| (e ||| f)) - 1 * (f ^^^ (d ||| (e ||| f))) - 6 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 7 * (f ||| (d ^^^ e)) - 6 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 7 * ~~~(d ^^^ ( ~~~e &&& f)) + 30 * ~~~(d ||| (e ||| f)) - 16 * ~~~(d ||| ( ~~~e ||| f)) + 31 * ~~~( ~~~d ||| (e ||| f)) - 12 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 17 * ( ~~~d &&& ( ~~~e &&& f)) + 13 * ( ~~~d &&& (e &&& f)) + 10 * (d &&& ( ~~~e &&& f)) + 6 * (d &&& (e &&& f)) = - 1 * e := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2426 (x y : BitVec w) : +theorem e_2426 : - 6 * ~~~(d ||| (e &&& f)) - 1 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 1 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 1 * (d &&& ( ~~~e ||| f)) - 2 * ~~~(d ^^^ f) - 1 * (f ||| (d ^^^ e)) + 1 * ~~~(d ||| ~~~f) + 2 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 2 * (e ^^^ (d &&& ( ~~~e ||| f))) + 5 * ( ~~~d ||| (e ^^^ f)) - 2 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 6 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 7 * (f &&& (d ||| ~~~e)) - 7 * (e ^^^ ~~~(d &&& (e &&& f))) - 1 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 11 * (f ^^^ (d ||| (e &&& f))) + 5 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 7 * (e &&& f) + 1 * (e &&& ~~~(d ^^^ f)) + 3 * ~~~(d ^^^ (e ||| f)) - 3 * (e ||| ~~~(d ||| ~~~f)) + 3 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 1 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 11 * (e &&& (d ||| ~~~f)) - 1 * (d ||| (e ^^^ f)) - 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 1 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 2 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 1 * (d ^^^ ( ~~~e &&& f)) + 4 * (e ^^^ ~~~(d &&& ~~~f)) + 11 * (e ^^^ ~~~(d ||| (e &&& f))) + 2 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 2 * ((d &&& e) ||| ~~~(e ||| f)) + 3 * ~~~(d ||| (e ^^^ f)) + 2 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 7 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * ~~~(d &&& ~~~d) + 7 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 1 * ~~~(d &&& ( ~~~e &&& f)) - 2 * ~~~(e &&& ~~~f) + 1 * ( ~~~d &&& ( ~~~e ||| f)) - 2 * (f ^^^ ~~~(d &&& e)) - 11 * (d ^^^ (e &&& f)) - 2 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 1 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 7 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 5 * (d &&& f) - 1 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 6 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 5 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 11 * ( ~~~f &&& (d ^^^ e)) + 2 * ~~~e + 1 * ((d &&& e) ^^^ (e ||| f)) - 7 * (f ^^^ (d ||| (e ||| f))) - 2 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 5 * (e ||| (d ^^^ f)) + 2 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 1 * ~~~(d ^^^ (e &&& f)) + 2 * ( ~~~d ||| ( ~~~e ||| f)) + 5 * (f ^^^ (d &&& e)) - 1 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 3 * (f ^^^ (d &&& (e ||| f))) + 3 * (f &&& ~~~(d &&& e)) - 1 * (f ^^^ ~~~(d ||| (e &&& f))) + 3 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 5 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 7 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 21 * ~~~(d ||| (e ||| f)) - 17 * ~~~(d ||| ( ~~~e ||| f)) + 19 * ~~~( ~~~d ||| (e ||| f)) - 9 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 1 * ( ~~~d &&& ( ~~~e &&& f)) - 25 * ( ~~~d &&& (e &&& f)) + 10 * (d &&& ( ~~~e &&& f)) + 17 * (d &&& (e &&& f)) = 3 * (f &&& ~~~(d ^^^ e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2427 (x y : BitVec w) : +theorem e_2427 : - 5 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * ~~~(d ^^^ e) + 7 * ( ~~~e &&& (d ^^^ f)) - 3 * ( ~~~d ||| ( ~~~e &&& f)) + 4 * (f ^^^ (d ||| (e &&& f))) + 1 * ((d &&& f) ^^^ (e ||| f)) + 11 * (d ||| (e ^^^ f)) + 2 * (f ||| (d &&& ~~~e)) - 2 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 6 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 5 * ~~~( ~~~d ||| (e &&& f)) + 2 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 5 * (d ^^^ f) - 2 * ( ~~~f ||| ~~~(d ^^^ e)) - 2 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 6 * (d ||| e) + 1 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 3 * (f &&& (d ||| e)) - 2 * (f ^^^ ( ~~~d &&& (e ||| f))) + 3 * ~~~(d ||| f) - 1 * (e ^^^ (d &&& (e ^^^ f))) + 1 * ( ~~~d ||| (e ||| f)) + 1 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 1 * (f ||| ~~~(d ||| ~~~e)) + 1 * (d ||| ( ~~~e ||| f)) - 7 * (e ^^^ ~~~(d &&& (e ||| f))) + 7 * ( ~~~d ||| ( ~~~e ||| f)) + 2 * (f ^^^ (d ||| ( ~~~e ||| f))) - 1 * ~~~(d &&& ( ~~~e ||| f)) - 1 * (d &&& e) - 5 * ((d &&& e) ^^^ (e ||| f)) + 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 11 * (e &&& (d ||| f)) + 1 * (e ^^^ ~~~(d ||| f)) - 7 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 5 * ~~~(d &&& (e ||| f)) - 1 * ( ~~~d &&& ( ~~~e ||| f)) + 1 * ((d ||| ~~~e) &&& (e ^^^ f)) + 2 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 6 * ((d &&& e) ^^^ (e ||| ~~~f)) - 11 * (e ^^^ ( ~~~d ||| (e &&& f))) - 1 * ~~~( ~~~d ||| (e ^^^ f)) - 3 * (e ^^^ ~~~(d ||| ~~~f)) + 4 * (e ^^^ ~~~(d &&& f)) - 1 * (f ||| ~~~(d ^^^ e)) + 4 * (e &&& (d ^^^ f)) - 7 * (d ^^^ ( ~~~e ||| f)) + 2 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 7 * ((d ||| e) &&& ~~~(e ^^^ f)) - 2 * (e &&& f) - 3 * ~~~(d ^^^ (e ^^^ f)) + 5 * ((e &&& f) ||| (d &&& (e ||| f))) - 11 * (f ^^^ (d &&& ( ~~~e ||| f))) - 7 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 2 * (d &&& ~~~f) - 2 * ~~~(d &&& (e ^^^ f)) - 2 * d + 1 * ~~~(d &&& ~~~f) - 5 * (e ^^^ (d ||| f)) + 5 * (d ||| (e &&& f)) - 1 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 2 * ((d ||| e) &&& (e ^^^ f)) + 11 * (d ||| ~~~e) + 11 * (f ||| (d &&& e)) + 7 * ~~~(d ||| e) - 11 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 11 * ~~~(d &&& f) + 33 * ~~~(d ||| (e ||| f)) + 21 * ~~~(d ||| ( ~~~e ||| f)) - 6 * ~~~( ~~~d ||| (e ||| f)) + 8 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 13 * ( ~~~d &&& ( ~~~e &&& f)) + 36 * ( ~~~d &&& (e &&& f)) + 3 * (d &&& ( ~~~e &&& f)) + 4 * (d &&& (e &&& f)) = 6 * ~~~(e &&& f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2428 (x y : BitVec w) : +theorem e_2428 : - 2 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 7 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 1 * ((d ^^^ e) ||| ~~~(d ^^^ f)) + 1 * (f ^^^ (d &&& ( ~~~e ||| f))) - 6 * (e ||| ~~~(d ||| ~~~f)) + 2 * e + 7 * (f ^^^ ~~~(d ||| ~~~e)) - 1 * (e ^^^ f) - 3 * ~~~(d &&& ~~~e) - 2 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 4 * (f ^^^ ~~~(d ||| e)) + 2 * (f ^^^ (d ||| (e ||| f))) + 3 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 2 * (d ||| ( ~~~e ||| f)) + 7 * ~~~(e &&& f) + 11 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 3 * (e &&& (d ^^^ f)) - 1 * ~~~( ~~~d &&& (e ||| f)) + 7 * ~~~(d ^^^ (e ||| f)) - 1 * (e ^^^ ~~~(d ||| f)) + 5 * ~~~(d &&& ~~~d) + 7 * (d &&& ( ~~~e ||| f)) + 1 * ((d &&& f) ^^^ (e ||| f)) + 3 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 2 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 5 * (e ^^^ (d ||| ~~~f)) - 5 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * ~~~(d ^^^ f) + 2 * (d ^^^ (e ^^^ f)) + 1 * ~~~(d ^^^ e) + 5 * (e ^^^ (d &&& ( ~~~e ||| f))) + 1 * ~~~(d &&& ( ~~~e &&& f)) - 1 * (e ||| (d &&& f)) - 1 * (e ^^^ (d ||| (e ^^^ f))) + 11 * ~~~(e &&& ~~~f) + 3 * (f ^^^ (d ||| ( ~~~e &&& f))) + 4 * (e ^^^ (d ||| (e ||| f))) - 1 * (f &&& ~~~(d ^^^ e)) + 1 * ~~~( ~~~d &&& (e ^^^ f)) - 5 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 4 * (f ^^^ ~~~(d &&& (e &&& f))) + 3 * (e ||| ~~~(d ^^^ f)) + 1 * ( ~~~f &&& (d ^^^ e)) - 5 * (f ^^^ (d &&& ~~~e)) + 1 * ((d &&& e) ^^^ (e ||| ~~~f)) - 7 * ~~~(d &&& (e ^^^ f)) + 1 * ~~~( ~~~d ||| (e &&& f)) + 7 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * ((d ||| e) &&& ~~~(e ^^^ f)) - 2 * (e ^^^ (d ||| ( ~~~e ||| f))) - 5 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 2 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 11 * ((d &&& e) ^^^ (e ||| f)) - 2 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 11 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 11 * ~~~(d &&& f) + 5 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 2 * (d ^^^ ( ~~~e ||| f)) - 7 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 2 * (e ^^^ (d ||| (e &&& f))) + 1 * ~~~(d ||| (e &&& f)) - 1 * (e ^^^ (d &&& f)) + 11 * ~~~(d &&& (e ||| f)) - 7 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 3 * (e ^^^ ~~~(d ||| ~~~f)) - 2 * (d &&& ~~~e) - 1 * (f ||| ~~~(d ||| e)) - 25 * ~~~(d ||| (e ||| f)) - 16 * ~~~(d ||| ( ~~~e ||| f)) - 71 * ~~~( ~~~d ||| (e ||| f)) - 4 * ( ~~~d &&& ( ~~~e &&& f)) - 19 * ( ~~~d &&& (e &&& f)) - 64 * (d &&& ( ~~~e &&& f)) - 36 * (d &&& (e &&& f)) = 13 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 1 * (f ||| (d ^^^ e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2429 (x y : BitVec w) : +theorem e_2429 : - 1 * ~~~( ~~~d ||| (e &&& f)) + 5 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 1 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 2 * (e ^^^ (d &&& ~~~f)) - 7 * ~~~( ~~~d &&& (e ||| f)) + 4 * (e ||| ~~~(d ||| f)) + 11 * ~~~(e ||| f) - 1 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 3 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 7 * (f ^^^ ~~~(d &&& (e &&& f))) - 5 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 2 * (e ^^^ (d ||| ~~~f)) + 3 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 2 * (e ||| (d &&& ~~~f)) + 11 * (f ||| (d &&& ~~~e)) + 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 6 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 1 * ~~~(d &&& ( ~~~e &&& f)) - 1 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 11 * ~~~f - 11 * (e ^^^ (d ||| ( ~~~e &&& f))) + 7 * (f ^^^ (d ||| (e ||| f))) + 7 * (d ||| ~~~f) - 2 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 2 * (f ^^^ ~~~(d ||| ~~~e)) + 3 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 3 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 7 * (e ^^^ (d &&& f)) + 2 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 1 * (f ||| (d ^^^ e)) + 1 * (e &&& ~~~(d ^^^ f)) - 3 * (e ^^^ (d ||| (e &&& f))) - 1 * (d ^^^ e) - 6 * (d ^^^ (e ||| f)) + 7 * ~~~d + 1 * ~~~(d &&& ( ~~~e ||| f)) + 1 * ( ~~~d ||| ( ~~~e ||| f)) + 11 * (f ^^^ ~~~(d &&& e)) + 1 * (e ^^^ ~~~(d &&& f)) + 2 * ( ~~~e &&& ~~~(d ^^^ f)) - 2 * ~~~(d ||| ~~~f) + 1 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 6 * ~~~(d &&& (e &&& f)) - 2 * ~~~(d &&& ~~~e) - 3 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * (f &&& (d ||| ~~~e)) + 1 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 11 * ~~~(e &&& f) - 5 * ( ~~~d ||| (e ||| f)) - 6 * (f ^^^ (d &&& ~~~e)) - 2 * (f ^^^ ( ~~~d &&& (e ||| f))) + 1 * (e ^^^ (d &&& (e ||| f))) + 2 * ~~~(d ||| ( ~~~e &&& f)) + 11 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 3 * ((d &&& f) ||| (e &&& ~~~f)) - 5 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 1 * (d &&& f) - 5 * d + 4 * ((d &&& f) ^^^ (e ||| f)) + 5 * (e &&& ~~~(d &&& f)) - 1 * (d &&& ( ~~~e ||| f)) + 2 * (d ^^^ f) - 7 * (e &&& f) + 5 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 11 * (d ^^^ ( ~~~e &&& f)) - 9 * ~~~(d ||| (e ||| f)) + 16 * ~~~(d ||| ( ~~~e ||| f)) + 27 * ~~~( ~~~d ||| (e ||| f)) + 22 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 2 * ( ~~~d &&& ( ~~~e &&& f)) + 14 * ( ~~~d &&& (e &&& f)) + 28 * (d &&& ( ~~~e &&& f)) - 20 * (d &&& (e &&& f)) = - 2 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 2 * ~~~(d ^^^ ( ~~~e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2430 (x y : BitVec w) : +theorem e_2430 : 1 * e + 1 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 5 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 6 * (d ||| (e ^^^ f)) + 1 * (e ||| ~~~(d ||| ~~~f)) - 6 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 2 * (e ||| (d &&& ~~~f)) + 4 * (f ^^^ (d &&& ( ~~~e ||| f))) - 2 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 2 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 4 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 4 * (e ^^^ ( ~~~d &&& (e ||| f))) + 2 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 1 * ( ~~~d ||| ( ~~~e ||| f)) + 2 * (f ^^^ ( ~~~d ||| (e &&& f))) - 11 * ~~~(d &&& (e &&& f)) + 1 * ((d &&& e) ||| ~~~(e ^^^ f)) + 7 * (d ^^^ f) + 11 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 4 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 3 * (f ^^^ (d ||| ( ~~~e &&& f))) - 6 * (f ^^^ ~~~(d &&& (e &&& f))) + 5 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 5 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 5 * (f &&& ~~~(d &&& e)) + 1 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 7 * ~~~d + 3 * (d ^^^ (e ^^^ f)) + 2 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 5 * (f ^^^ (d &&& (e ||| f))) + 5 * ~~~(d &&& f) + 2 * (f ^^^ ~~~(d &&& (e ||| f))) - 2 * (f ^^^ ~~~(d ||| (e &&& f))) + 3 * (e ^^^ f) - 2 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 2 * ~~~( ~~~d &&& (e ||| f)) - 1 * ~~~( ~~~d &&& (e &&& f)) + 11 * (e ||| f) - 3 * (e &&& (d ||| f)) - 2 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 1 * (e ||| ~~~(d ||| f)) - 3 * ~~~(d ||| f) - 3 * (f ^^^ ~~~(d ||| e)) + 1 * ( ~~~d ||| ( ~~~e &&& f)) - 1 * (e &&& ~~~(d &&& f)) - 11 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 5 * ( ~~~d ||| (e ^^^ f)) + 11 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 2 * ~~~e + 11 * (d ^^^ e) + 2 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (e &&& (d ^^^ f)) - 7 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 3 * ~~~(d ^^^ ( ~~~e ||| f)) + 7 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 11 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 2 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 1 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 1 * ~~~(d ^^^ (e ^^^ f)) + 1 * ~~~(e &&& f) + 2 * ~~~(d ||| e) + 5 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 1 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 1 * (f ||| ~~~(d ||| ~~~e)) - 1 * ((d &&& f) ||| ~~~(e ||| f)) + 4 * (d ||| ~~~f) - 6 * (d ||| (e ||| f)) + 10 * ~~~(d ||| (e ||| f)) + 3 * ~~~(d ||| ( ~~~e ||| f)) - 8 * ~~~( ~~~d ||| (e ||| f)) - 10 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 5 * ( ~~~d &&& ( ~~~e &&& f)) + 9 * ( ~~~d &&& (e &&& f)) - 30 * (d &&& ( ~~~e &&& f)) - 1 * (d &&& (e &&& f)) = 7 * (e ^^^ ( ~~~d &&& (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2431 (x y : BitVec w) : +theorem e_2431 : 4 * (f ^^^ ( ~~~d &&& (e ||| f))) - 1 * ((d &&& e) ^^^ (e ||| f)) - 7 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 6 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 5 * (e ^^^ (d ||| ( ~~~e &&& f))) + 5 * ~~~( ~~~d &&& (e ^^^ f)) + 1 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 6 * ((d ^^^ e) ||| ~~~(d ^^^ f)) + 5 * (f ^^^ ( ~~~d ||| (e &&& f))) - 6 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 7 * (d ^^^ ( ~~~e ||| f)) + 1 * ~~~(d &&& f) + 2 * (d ||| ~~~f) - 2 * (f &&& (d ||| e)) + 1 * (d ^^^ (e &&& f)) + 2 * (e &&& (d ||| ~~~f)) - 2 * (f ^^^ ( ~~~d ||| (e ||| f))) + 3 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 5 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 6 * (f ^^^ ~~~(d ||| e)) + 4 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 7 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 3 * (e &&& ~~~(d ^^^ f)) - 11 * (e ^^^ (d ||| (e ^^^ f))) + 7 * (e ||| ~~~f) + 1 * (d ^^^ e) + 1 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 2 * ~~~(d ||| ~~~f) + 1 * (f ^^^ ~~~(d &&& (e &&& f))) - 1 * (d &&& ~~~f) - 2 * ( ~~~d ||| (e &&& f)) + 3 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 1 * ~~~(d &&& ~~~e) - 5 * ( ~~~d ||| ( ~~~e ||| f)) - 1 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 3 * e - 2 * (d &&& e) - 7 * (e ^^^ ( ~~~d ||| (e ||| f))) - 6 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 1 * (e ^^^ (d ||| (e &&& f))) + 4 * (f ^^^ ~~~(d &&& (e ||| f))) + 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 5 * ~~~(d ^^^ (e &&& f)) + 4 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 4 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 11 * ((d &&& e) ||| ~~~(e ^^^ f)) - 7 * ~~~(d ||| ( ~~~e &&& f)) + 11 * (e ^^^ (d ||| ~~~f)) + 1 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 11 * ((d &&& e) ||| ~~~(e ||| f)) + 3 * ((d &&& f) ^^^ (e ||| f)) - 2 * ~~~(e ^^^ f) - 1 * ((d ||| e) &&& ~~~(e ^^^ f)) - 11 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 3 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 11 * ( ~~~e &&& (d ^^^ f)) + 2 * (e ^^^ ~~~(d &&& ~~~f)) - 1 * ~~~(d &&& (e ^^^ f)) + 3 * (f &&& (d ^^^ e)) - 3 * (e ^^^ (d ||| ( ~~~e ||| f))) + 1 * (e ^^^ ~~~(d &&& f)) + 11 * ( ~~~f &&& (d ^^^ e)) + 5 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 6 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 1 * ~~~(d &&& ~~~d) + 1 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 2 * ~~~(d ^^^ ( ~~~e &&& f)) + 2 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 1 * (d ||| (e ^^^ f)) + 14 * ~~~(d ||| (e ||| f)) - 4 * ~~~( ~~~d ||| (e ||| f)) - 10 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 24 * ( ~~~d &&& ( ~~~e &&& f)) + 15 * ( ~~~d &&& (e &&& f)) + 16 * (d &&& (e &&& f)) = - 6 * (d &&& ( ~~~e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2432 (x y : BitVec w) : +theorem e_2432 : 11 * ( ~~~e ||| (d ^^^ f)) - 1 * (e &&& f) + 1 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 1 * ((d &&& ~~~e) ||| (e ^^^ f)) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 6 * (d ||| (e ||| f)) + 1 * (e &&& ~~~(d ^^^ f)) - 6 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 7 * (d ||| e) + 2 * (e ^^^ f) + 2 * (e ||| ~~~(d ^^^ f)) - 5 * (f ^^^ ~~~(d &&& ~~~e)) + 1 * (f ^^^ ~~~(d ||| (e &&& f))) - 7 * (f ^^^ ( ~~~d ||| (e ||| f))) + 3 * (d ^^^ e) - 6 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 5 * (e ||| ~~~f) + 1 * (d ^^^ f) - 2 * (e ||| (d ^^^ f)) - 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 3 * ~~~(d ||| ( ~~~e &&& f)) - 11 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 3 * ~~~(d ^^^ (e ^^^ f)) + 7 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 5 * (d ^^^ ( ~~~e &&& f)) + 4 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 3 * ~~~(d ^^^ ( ~~~e &&& f)) - 1 * ((d ^^^ e) &&& (d ^^^ f)) - 5 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 5 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 2 * ( ~~~f ||| (d ^^^ e)) + 1 * (e ^^^ ~~~(d &&& (e ||| f))) + 2 * (f ^^^ (d &&& (e ||| f))) + 1 * ((d ^^^ e) ||| (d ^^^ f)) + 2 * (d ^^^ (e &&& f)) - 5 * (e ||| ~~~(d ||| f)) - 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 4 * (e ^^^ ~~~(d &&& (e &&& f))) - 1 * (d ||| ( ~~~e &&& f)) + 7 * (f &&& (d ^^^ e)) + 5 * ~~~(d &&& ( ~~~e &&& f)) + 11 * (d &&& f) + 1 * (f &&& ~~~(d ^^^ e)) + 1 * d + 2 * (f &&& ~~~(d &&& ~~~e)) - 2 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 3 * ( ~~~d ||| ( ~~~e &&& f)) + 11 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 7 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 2 * ~~~( ~~~d &&& (e &&& f)) - 11 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 1 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 2 * (f ^^^ ~~~(d &&& (e ||| f))) - 2 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 5 * (d ^^^ (e ^^^ f)) + 2 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 7 * (e ||| (d &&& f)) - 1 * (d &&& ( ~~~e ||| f)) - 1 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 5 * ( ~~~d ||| (e ^^^ f)) + 5 * ( ~~~d ||| (e &&& f)) + 11 * (f ||| (d ^^^ e)) + 1 * ( ~~~d ||| (e ||| f)) + 2 * ((d &&& e) ||| ~~~(e ^^^ f)) - 2 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 1 * ( ~~~d &&& (e ||| f)) + 4 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 2 * ~~~(d ||| (e ||| f)) - 2 * ~~~(d ||| ( ~~~e ||| f)) + 16 * ~~~( ~~~d ||| (e ||| f)) + 15 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 41 * ( ~~~d &&& ( ~~~e &&& f)) - 26 * ( ~~~d &&& (e &&& f)) - 29 * (d &&& ( ~~~e &&& f)) - 17 * (d &&& (e &&& f)) = 1 * (e ||| (d &&& ~~~f)) - 4 * ~~~(d ^^^ ( ~~~e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2433 (x y : BitVec w) : +theorem e_2433 : 11 * ~~~(d &&& ~~~f) - 11 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 1 * (f ^^^ ~~~(d ||| (e &&& f))) - 3 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 1 * ~~~( ~~~d ||| (e &&& f)) - 1 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 5 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 7 * ~~~(d ^^^ (e &&& f)) + 5 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 6 * (d ||| ~~~e) - 1 * (d ^^^ f) + 1 * (e &&& (d ||| ~~~f)) + 5 * ~~~( ~~~d &&& (e ^^^ f)) - 5 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 1 * (e ^^^ (d ||| ( ~~~e &&& f))) + 11 * (f ||| ~~~(d ^^^ e)) - 3 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 3 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 2 * ( ~~~e ||| (d ^^^ f)) + 1 * ( ~~~f ||| (d ^^^ e)) + 4 * (d &&& (e ||| f)) + 3 * ( ~~~e ||| ~~~(d ^^^ f)) - 1 * ~~~(d ^^^ ( ~~~e ||| f)) + 3 * (d &&& f) - 2 * (e ^^^ ( ~~~d &&& (e ||| f))) - 1 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 4 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 5 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 7 * (d ||| (e ^^^ f)) - 6 * (d ^^^ ( ~~~e ||| f)) + 2 * ( ~~~e &&& ~~~(d ^^^ f)) - 3 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 2 * (e ^^^ ~~~(d ||| (e &&& f))) - 5 * ~~~(d ^^^ (e ||| f)) + 3 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 1 * ~~~(d ^^^ ( ~~~e &&& f)) + 5 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 1 * (d ||| f) + 11 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 2 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 7 * (f ^^^ ( ~~~d &&& (e ||| f))) - 6 * (e &&& ~~~f) - 5 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 2 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 11 * ((d &&& e) ||| ~~~(e ^^^ f)) - 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 4 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 5 * ( ~~~f &&& ~~~(d ^^^ e)) + 11 * (f ^^^ ~~~(d &&& e)) - 1 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 3 * (f ^^^ (d &&& (e ||| f))) + 4 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 1 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 2 * (e &&& ~~~(d &&& f)) - 1 * ~~~(d ^^^ (e ^^^ f)) + 1 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 1 * ~~~(d &&& ( ~~~e ||| f)) + 2 * ~~~(d &&& (e ^^^ f)) - 1 * (d &&& (e ^^^ f)) + 7 * ((d ||| e) &&& ~~~(e ^^^ f)) - 11 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 2 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 11 * (f ||| ~~~(d ||| e)) - 6 * (e ||| ~~~(d ||| f)) + 2 * (e ^^^ ~~~(d ||| f)) + 7 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 5 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 2 * ~~~(e &&& f) - 14 * ~~~(d ||| (e ||| f)) - 21 * ~~~(d ||| ( ~~~e ||| f)) - 18 * ~~~( ~~~d ||| (e ||| f)) + 56 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 12 * ( ~~~d &&& (e &&& f)) - 38 * (d &&& ( ~~~e &&& f)) - 1 * (d &&& (e &&& f)) = - 20 * ( ~~~d &&& ( ~~~e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2434 (x y : BitVec w) : +theorem e_2434 : 1 * (d ||| f) - 2 * ~~~(d ||| f) - 7 * (f &&& ~~~(d &&& ~~~e)) + 5 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 1 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 7 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 7 * (f ^^^ ~~~(d ||| (e &&& f))) - 7 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 2 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 11 * ~~~(d &&& ~~~e) - 3 * (d &&& ~~~e) + 1 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 5 * (e ^^^ ~~~(d ||| (e &&& f))) + 1 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 2 * (f &&& ~~~(d ^^^ e)) - 1 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 4 * ~~~(d ^^^ (e &&& f)) - 3 * (e ^^^ (d ||| f)) + 11 * (d ||| ~~~e) + 1 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 7 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 1 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 2 * (f ^^^ ~~~(d &&& (e &&& f))) - 5 * (e ^^^ (d ||| ( ~~~e ||| f))) + 3 * (d ||| ( ~~~e &&& f)) + 4 * ~~~( ~~~d &&& (e ^^^ f)) + 5 * (f ^^^ ~~~(d &&& (e ||| f))) - 6 * ~~~(d ^^^ (e ^^^ f)) + 11 * (d &&& ( ~~~e ||| f)) + 1 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 7 * ((d &&& e) ||| ~~~(e ^^^ f)) + 3 * (e &&& f) - 2 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * ((d &&& f) ||| ~~~(e ||| f)) - 11 * ~~~(d ^^^ ( ~~~e ||| f)) - 3 * (d ^^^ e) + 7 * (f ^^^ ~~~(d &&& e)) + 5 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 1 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 2 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 1 * (f ^^^ ( ~~~d ||| (e ||| f))) + 2 * (d &&& (e ^^^ f)) - 1 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 5 * ( ~~~f &&& ~~~(d ^^^ e)) - 7 * (f ^^^ ~~~(d ||| ~~~e)) - 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 11 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 4 * (e ^^^ ~~~(d ||| ~~~f)) + 3 * (d ||| ( ~~~e ||| f)) + 1 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 11 * ~~~(e ||| ~~~f) + 7 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 2 * ~~~(d &&& ~~~d) - 2 * (e ^^^ ~~~(d ||| f)) - 1 * e + 2 * ~~~(d &&& f) - 5 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 6 * ((e &&& f) ||| (d &&& (e ||| f))) + 1 * ~~~(e &&& f) + 2 * (e &&& ~~~(d &&& f)) - 2 * (e ^^^ (d ||| ( ~~~e &&& f))) - 11 * (e ||| ~~~f) + 5 * ~~~(d &&& (e ^^^ f)) - 1 * d + 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 7 * ((d &&& f) ||| (e &&& ~~~f)) + 1 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 1 * (d ||| (e &&& f)) - 29 * ~~~(d ||| (e ||| f)) + 25 * ~~~(d ||| ( ~~~e ||| f)) - 33 * ~~~( ~~~d ||| (e ||| f)) - 8 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 15 * ( ~~~d &&& ( ~~~e &&& f)) + 13 * ( ~~~d &&& (e &&& f)) - 23 * (d &&& ( ~~~e &&& f)) - 27 * (d &&& (e &&& f)) = 1 * (d ^^^ ( ~~~e &&& f)) + 6 * (e ^^^ ( ~~~d ||| (e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2435 (x y : BitVec w) : +theorem e_2435 : - 7 * (e ^^^ (d ||| ~~~f)) + 3 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 6 * (d ||| (e ^^^ f)) - 7 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 1 * (f &&& (d ||| e)) + 2 * (e ||| (d &&& ~~~f)) + 7 * (e ^^^ ~~~(d &&& f)) - 3 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 1 * ( ~~~d ||| (e ||| f)) - 6 * (e ^^^ ~~~(d ||| f)) - 11 * ~~~( ~~~d ||| (e &&& f)) + 1 * ((d &&& f) ||| (e &&& ~~~f)) + 5 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 1 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 1 * (e &&& ~~~(d &&& f)) + 1 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 2 * ~~~(d ^^^ (e ^^^ f)) - 11 * (f ||| ~~~(d ^^^ e)) + 7 * (f ^^^ ~~~(d ||| ~~~e)) - 2 * ~~~d - 3 * (f ^^^ ~~~(d &&& (e ||| f))) - 7 * (e ^^^ (d ||| (e ^^^ f))) + 7 * ~~~(d &&& (e ||| f)) + 7 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 1 * (f ||| (d ^^^ e)) + 7 * (e ^^^ (d ||| ( ~~~e &&& f))) - 6 * ( ~~~e &&& (d ^^^ f)) + 1 * ((d &&& f) ||| ~~~(e ||| f)) + 1 * ~~~(d ||| e) + 2 * (f ^^^ ( ~~~d ||| (e &&& f))) + 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 4 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 3 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 1 * (f &&& (d ^^^ e)) + 3 * ((d &&& e) ^^^ (e ||| ~~~f)) + 4 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 1 * (d ^^^ (e ^^^ f)) - 2 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 1 * ((d &&& e) ||| (e ^^^ f)) - 3 * ~~~( ~~~d &&& (e ^^^ f)) - 1 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 11 * (f ^^^ ~~~(d &&& ~~~e)) - 5 * ((d &&& f) ^^^ (e ||| f)) + 4 * (e ^^^ (d &&& f)) - 1 * (f ^^^ ~~~(d &&& e)) + 11 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 6 * (d &&& ~~~e) + 1 * ( ~~~d ||| ( ~~~e &&& f)) + 3 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * ( ~~~e ||| (d ^^^ f)) + 7 * (e ^^^ ~~~(d &&& (e ||| f))) - 1 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 11 * (f ^^^ ( ~~~d &&& (e ||| f))) - 2 * (d &&& (e ||| f)) - 1 * ( ~~~d &&& (e ||| f)) - 2 * ~~~(d ||| (e &&& f)) - 3 * ~~~(e &&& ~~~f) + 3 * (e ^^^ ~~~(d &&& (e &&& f))) - 2 * ~~~(d ^^^ (e ||| f)) - 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * e + 2 * (d ||| e) - 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 5 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 2 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 5 * ~~~(d ||| ~~~e) - 2 * ~~~(d &&& ( ~~~e ||| f)) - 7 * ~~~(d ||| (e ||| f)) - 13 * ~~~(d ||| ( ~~~e ||| f)) - 6 * ~~~( ~~~d ||| (e ||| f)) + 6 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 8 * ( ~~~d &&& ( ~~~e &&& f)) - 24 * ( ~~~d &&& (e &&& f)) + 24 * (d &&& ( ~~~e &&& f)) - 14 * (d &&& (e &&& f)) = - 11 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2436 (x y : BitVec w) : +theorem e_2436 : - 6 * ~~~(d &&& e) - 5 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 6 * ( ~~~f ||| (d ^^^ e)) + 1 * ( ~~~d ||| (e ^^^ f)) - 2 * (e &&& (d ||| ~~~f)) - 5 * ~~~d + 1 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 2 * ~~~(e &&& f) - 3 * ((e &&& f) ||| (d &&& (e ||| f))) - 11 * (d &&& f) - 11 * (f ||| ~~~(d ||| e)) + 2 * ( ~~~e ||| (d ^^^ f)) + 7 * ( ~~~d ||| ( ~~~e &&& f)) + 5 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 6 * ~~~(d ||| ~~~f) - 5 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 11 * ~~~(d ||| f) + 5 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 11 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 11 * ~~~(d ^^^ ( ~~~e &&& f)) + 11 * ~~~(d ^^^ (e ^^^ f)) - 3 * (e ^^^ (d ||| (e ^^^ f))) - 1 * (e ^^^ ~~~(d &&& (e ||| f))) + 2 * ~~~(d ||| (e ^^^ f)) + 2 * (f ^^^ (d ||| e)) - 1 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 7 * (d ^^^ ( ~~~e ||| f)) - 3 * (d ^^^ e) - 1 * ( ~~~d &&& (e ^^^ f)) - 2 * (f ^^^ (d &&& ~~~e)) + 5 * (e &&& (d ||| f)) + 7 * (d ^^^ ( ~~~e &&& f)) + 1 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 4 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 2 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 3 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * (f ^^^ ( ~~~d ||| (e &&& f))) - 7 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 1 * (e ^^^ ( ~~~d ||| (e &&& f))) - 5 * ((d &&& e) ^^^ (e ||| ~~~f)) + 5 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 11 * ( ~~~e ||| ~~~(d ^^^ f)) - 7 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 2 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 1 * (f ^^^ (d &&& ( ~~~e ||| f))) + 1 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 7 * ((d &&& f) ^^^ (e ||| f)) + 7 * ((d &&& f) ||| (e &&& ~~~f)) + 11 * ~~~(e ||| ~~~f) + 4 * (f ^^^ ( ~~~d &&& (e ||| f))) - 11 * d - 3 * (d ^^^ (e ^^^ f)) - 6 * (d &&& ~~~f) - 1 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 2 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 1 * (e &&& ~~~(d &&& ~~~f)) + 1 * ( ~~~d ||| (e ||| f)) - 5 * ((d &&& e) ||| (e ^^^ f)) - 2 * (e ^^^ ( ~~~d &&& (e ||| f))) - 6 * ( ~~~d &&& (e ||| f)) - 2 * (e ||| ~~~(d ||| f)) - 6 * (e ^^^ ( ~~~d ||| (e ||| f))) + 2 * (e ^^^ (d ||| ( ~~~e ||| f))) + 2 * (e ^^^ ~~~(d ||| ~~~f)) + 1 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 4 * ~~~(d &&& f) - 7 * (f &&& (d ||| e)) + 18 * ~~~(d ||| (e ||| f)) + 46 * ~~~(d ||| ( ~~~e ||| f)) + 38 * ~~~( ~~~d ||| (e ||| f)) - 8 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 9 * ( ~~~d &&& ( ~~~e &&& f)) + 52 * ( ~~~d &&& (e &&& f)) + 44 * (d &&& (e &&& f)) = - 14 * (d &&& ( ~~~e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2437 (x y : BitVec w) : +theorem e_2437 : - 5 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 2 * ~~~(e ^^^ f) + 1 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * (e &&& f) - 5 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 2 * (d ||| ( ~~~e ||| f)) - 7 * (e ^^^ ~~~(d ||| f)) - 11 * ~~~(d ^^^ ( ~~~e ||| f)) - 3 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 2 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 6 * (d ^^^ f) + 4 * (e ^^^ (d ||| f)) - 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 11 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 6 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 3 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 2 * (e ^^^ (d ||| ( ~~~e &&& f))) - 5 * ((d &&& e) ^^^ (e ||| ~~~f)) + 1 * (e ^^^ (d ||| (e ^^^ f))) + 4 * ((d ^^^ e) ||| (d ^^^ f)) + 4 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 3 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 3 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 7 * (f ^^^ (d &&& ( ~~~e ||| f))) + 5 * ( ~~~d &&& (e ||| f)) - 2 * (e ||| ~~~f) + 2 * (e ^^^ (d &&& ~~~f)) + 1 * ~~~(d ||| (e ^^^ f)) + 5 * (d &&& ~~~f) + 7 * (f &&& (d ||| ~~~e)) - 5 * ((d ||| e) &&& (e ^^^ f)) - 2 * (d &&& ( ~~~e ||| f)) - 11 * (e ^^^ ~~~(d ||| ~~~f)) + 7 * ~~~( ~~~d ||| (e &&& f)) - 6 * (f ^^^ (d &&& e)) + 1 * (e ^^^ ( ~~~d &&& (e ||| f))) - 5 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 4 * (f ||| (d &&& ~~~e)) + 11 * ~~~(d ^^^ (e &&& f)) + 2 * (e ||| (d &&& ~~~f)) + 2 * (e ^^^ (d ||| ( ~~~e ||| f))) - 1 * (e ^^^ ~~~(d ||| (e &&& f))) - 2 * ~~~(d ^^^ f) + 1 * (e ^^^ ( ~~~d ||| (e &&& f))) - 1 * (d ^^^ (e ||| f)) + 5 * (f &&& (d ||| e)) + 2 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 2 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 7 * (e &&& (d ||| ~~~f)) - 2 * (e ||| ~~~(d ^^^ f)) + 1 * ((d &&& e) ||| ~~~(e ||| f)) - 7 * (e ||| (d ^^^ f)) + 1 * (d &&& e) + 1 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 1 * (e ^^^ f) + 4 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 2 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 7 * ~~~(d &&& ~~~e) - 7 * (e ^^^ ~~~(d &&& ~~~f)) - 11 * ~~~(d &&& (e ||| f)) - 11 * (e ^^^ ~~~(d &&& (e ||| f))) - 2 * (d ||| ( ~~~e &&& f)) - 3 * (f &&& ~~~(d &&& e)) + 7 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 1 * ~~~( ~~~d &&& (e ^^^ f)) + 1 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 1 * (f ^^^ ~~~(d &&& ~~~e)) + 5 * (f ||| ~~~(d ||| e)) + 19 * ~~~(d ||| (e ||| f)) + 13 * ~~~(d ||| ( ~~~e ||| f)) + 24 * ~~~( ~~~d ||| (e ||| f)) + 7 * ( ~~~d &&& ( ~~~e &&& f)) + 2 * ( ~~~d &&& (e &&& f)) - 16 * (d &&& ( ~~~e &&& f)) + 15 * (d &&& (e &&& f)) = - 28 * ~~~( ~~~d ||| ( ~~~e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2438 (x y : BitVec w) : +theorem e_2438 : 11 * (f ||| ~~~(d ^^^ e)) + 3 * ~~~(e &&& ~~~f) + 4 * (f ^^^ ~~~(d ||| (e &&& f))) - 3 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 11 * (d ||| f) - 2 * (e ^^^ (d ||| ~~~f)) - 1 * ( ~~~f ||| ~~~(d ^^^ e)) + 1 * (f &&& ~~~(d ^^^ e)) + 4 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 2 * ((d ||| ~~~e) &&& (e ^^^ f)) - 11 * ((d ||| e) &&& (e ^^^ f)) - 1 * (d ||| ~~~f) - 1 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 6 * (f ^^^ (d &&& e)) - 5 * (e ^^^ (d &&& ( ~~~e ||| f))) + 5 * ((d ||| e) &&& ~~~(e ^^^ f)) - 6 * ~~~( ~~~d ||| (e &&& f)) - 6 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 2 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 1 * ~~~(d ^^^ ( ~~~e ||| f)) + 4 * (d &&& (e ||| f)) - 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 2 * ~~~(d ^^^ f) + 5 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 5 * ~~~(e ||| f) + 1 * (d ||| ~~~e) + 5 * ( ~~~d ||| (e ||| f)) + 1 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 1 * (e ^^^ (d &&& f)) + 2 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 1 * (e ^^^ (d ||| (e ||| f))) + 3 * ( ~~~d ||| (e &&& f)) - 1 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 6 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 1 * (d &&& ~~~f) - 7 * ( ~~~e &&& (d ^^^ f)) + 2 * (f ^^^ ~~~(d ||| ~~~e)) + 11 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 11 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 2 * (d &&& f) + 7 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 5 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 11 * f - 11 * (d &&& e) - 5 * (f ^^^ ( ~~~d ||| (e ||| f))) + 4 * (e ||| ~~~f) + 1 * (e ^^^ ~~~(d ||| (e &&& f))) - 7 * ( ~~~d &&& (e ||| f)) - 7 * ( ~~~e ||| (d ^^^ f)) + 3 * (e ^^^ ~~~(d &&& ~~~f)) - 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 4 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 1 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 7 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 2 * (f ^^^ ~~~(d &&& (e ||| f))) - 5 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 1 * ( ~~~d ||| (e ^^^ f)) + 11 * ((d &&& f) ||| (e &&& ~~~f)) - 6 * (d ||| e) - 1 * (e &&& (d ^^^ f)) - 5 * (f ^^^ (d &&& ~~~e)) + 7 * ~~~(d ^^^ (e ||| f)) + 1 * (d ||| ( ~~~e ||| f)) - 3 * (f ^^^ (d ||| ( ~~~e ||| f))) - 1 * (d ||| (e ^^^ f)) - 3 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 1 * (f ^^^ ~~~(d &&& (e &&& f))) - 26 * ~~~(d ||| (e ||| f)) - 6 * ~~~(d ||| ( ~~~e ||| f)) + 40 * ~~~( ~~~d ||| (e ||| f)) + 48 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 16 * ( ~~~d &&& ( ~~~e &&& f)) - 6 * ( ~~~d &&& (e &&& f)) + 4 * (d &&& ( ~~~e &&& f)) - 55 * (d &&& (e &&& f)) = 2 * (f ^^^ ~~~(d &&& ~~~e)) - 1 * (e ^^^ ( ~~~d ||| (e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2439 (x y : BitVec w) : +theorem e_2439 : - 3 * (e ^^^ ~~~(d &&& f)) + 2 * (e &&& ~~~(d &&& ~~~f)) + 3 * (e ^^^ (d ||| (e ||| f))) + 11 * (f ||| (d &&& e)) + 1 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 11 * ~~~( ~~~d &&& (e &&& f)) + 11 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 5 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 1 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 3 * (d ^^^ f) - 3 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 1 * ((d &&& e) ||| (e ^^^ f)) - 1 * (f ^^^ ~~~(d ||| e)) + 2 * ~~~(d &&& e) + 3 * (f ^^^ (d &&& ( ~~~e ||| f))) - 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 2 * (d ||| ( ~~~e ||| f)) + 4 * ( ~~~d &&& ( ~~~e ||| f)) - 6 * ((d &&& e) ||| ~~~(e ||| f)) + 1 * (f ^^^ (d &&& (e ||| f))) - 1 * (e ^^^ (d ||| ~~~f)) + 1 * (f ||| ~~~(d ||| e)) - 1 * (e ^^^ ~~~(d ||| f)) - 2 * ~~~(d ||| (e ^^^ f)) - 1 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 3 * (e ^^^ ~~~(d ||| (e &&& f))) - 7 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 3 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 5 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 3 * (f ^^^ ~~~(d ||| ~~~e)) + 1 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 2 * (f &&& ~~~(d &&& e)) + 11 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 2 * (f &&& (d ||| ~~~e)) - 2 * (f ^^^ ( ~~~d &&& (e ||| f))) + 7 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 5 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 1 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 5 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 7 * (d ^^^ (e ||| f)) - 1 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 2 * ~~~(d &&& ( ~~~e &&& f)) - 7 * ((e &&& f) ||| (d &&& (e ||| f))) + 2 * ~~~(d ||| f) - 2 * ~~~(d ^^^ (e ^^^ f)) - 5 * ( ~~~f &&& (d ^^^ e)) - 11 * (e ||| (d &&& f)) + 4 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 11 * (d ||| e) - 2 * (f &&& ~~~(d &&& ~~~e)) + 2 * (e ^^^ (d &&& (e ||| f))) + 1 * ((d &&& f) ||| (e &&& ~~~f)) - 2 * (e &&& (d ||| f)) - 1 * (f ^^^ ( ~~~d ||| (e ||| f))) - 2 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 2 * ~~~( ~~~d &&& (e ||| f)) + 7 * (f ^^^ (d &&& e)) + 7 * (f ^^^ ~~~(d &&& e)) - 11 * ~~~(d &&& ~~~e) + 2 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 1 * (e ^^^ ~~~(d &&& ~~~f)) + 1 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 3 * (f ^^^ ~~~(d &&& (e &&& f))) + 1 * (f ^^^ (d ||| ( ~~~e &&& f))) - 6 * ((d &&& ~~~e) ||| (e ^^^ f)) + 7 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 2 * (e &&& (d ^^^ f)) + 6 * ~~~(d ||| (e ||| f)) + 67 * ~~~(d ||| ( ~~~e ||| f)) + 21 * ~~~( ~~~d ||| (e ||| f)) + 32 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 4 * ( ~~~d &&& ( ~~~e &&& f)) - 9 * ( ~~~d &&& (e &&& f)) + 10 * (d &&& ( ~~~e &&& f)) + 39 * (d &&& (e &&& f)) = 1 * ( ~~~d ||| (e &&& f)) + 5 * (e ||| ~~~f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2440 (x y : BitVec w) : +theorem e_2440 : - 6 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 5 * (f ^^^ ( ~~~d ||| (e ||| f))) + 5 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 11 * (f &&& (d ^^^ e)) + 7 * (e &&& (d ||| ~~~f)) + 5 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 2 * ((d &&& e) ||| ~~~(e ^^^ f)) - 7 * (e ^^^ ~~~(d ||| f)) - 11 * (d ^^^ (e &&& f)) - 11 * ~~~( ~~~d &&& (e ^^^ f)) - 6 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 2 * ((d &&& f) ^^^ (e ||| f)) - 6 * ~~~( ~~~d &&& (e ||| f)) - 7 * (f ^^^ (d ||| (e &&& f))) + 2 * (d ^^^ (e ||| f)) + 3 * ((d ^^^ e) &&& (d ^^^ f)) - 6 * (f ^^^ (d ||| e)) + 5 * ( ~~~f &&& (d ^^^ e)) - 6 * ((d ||| ~~~e) &&& (e ^^^ f)) + 11 * (f ^^^ ( ~~~d &&& (e ||| f))) - 7 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 2 * (f ^^^ ~~~(d ||| (e &&& f))) + 11 * (d &&& ( ~~~e ||| f)) + 2 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 2 * ~~~(d ^^^ (e ||| f)) - 2 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 1 * ( ~~~d ||| ( ~~~e &&& f)) + 1 * (d &&& (e ||| f)) + 1 * ~~~(e ||| ~~~f) - 3 * (d &&& ~~~f) + 3 * ~~~(d &&& (e ||| f)) - 1 * (e ^^^ ( ~~~d ||| (e &&& f))) - 5 * ( ~~~f ||| ~~~(d ^^^ e)) - 5 * ((e &&& f) ||| (d &&& (e ||| f))) - 7 * ~~~(d &&& ~~~f) - 6 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 1 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 7 * (d ||| e) + 7 * ((d ||| e) &&& (e ^^^ f)) - 7 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 4 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 11 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 7 * (f ||| (d ^^^ e)) + 11 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 1 * ~~~(d ||| ( ~~~e &&& f)) - 5 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 2 * ~~~(d ^^^ (e ^^^ f)) + 4 * ~~~(d ||| e) + 1 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 3 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * ~~~(d &&& ~~~e) + 2 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 1 * (f &&& ~~~(d &&& e)) - 1 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 1 * (e &&& ~~~(d &&& ~~~f)) + 2 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * (f ^^^ ~~~(d ||| e)) + 3 * ~~~(d ||| (e &&& f)) - 1 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 5 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 1 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 4 * ( ~~~f &&& ~~~(d ^^^ e)) + 1 * ( ~~~d ||| (e ^^^ f)) - 2 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 2 * (d ^^^ f) - 2 * (e ^^^ (d ||| ( ~~~e ||| f))) + 11 * (e ||| (d &&& ~~~f)) + 1 * (f ^^^ (d ||| ( ~~~e &&& f))) + 18 * ~~~(d ||| (e ||| f)) - 32 * ~~~(d ||| ( ~~~e ||| f)) + 17 * ~~~( ~~~d ||| (e ||| f)) + 26 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 26 * ( ~~~d &&& ( ~~~e &&& f)) + 18 * ( ~~~d &&& (e &&& f)) + 10 * (d &&& ( ~~~e &&& f)) + 16 * (d &&& (e &&& f)) = - 5 * ((d &&& e) ||| ~~~(e ||| ~~~f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2441 (x y : BitVec w) : +theorem e_2441 : 2 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 11 * (f &&& (d ||| e)) + 4 * (e ^^^ (d &&& (e ^^^ f))) - 11 * (f ||| (d ^^^ e)) - 7 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 2 * (f ^^^ (d ||| ~~~e)) - 6 * (e ||| f) - 5 * (e ^^^ (d &&& (e ||| f))) + 7 * (e &&& ~~~(d ^^^ f)) - 7 * (e ^^^ ~~~(d ||| (e &&& f))) + 2 * ~~~(d ||| f) - 1 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 2 * (f &&& ~~~(d &&& e)) - 1 * (d ||| ~~~f) + 1 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 3 * (e &&& (d ^^^ f)) - 2 * (f ||| (d &&& ~~~e)) - 2 * ((d &&& f) ^^^ (e ||| f)) - 1 * (f ^^^ (d ||| ( ~~~e ||| f))) - 11 * (f &&& ~~~(d &&& ~~~e)) + 2 * (f ^^^ (d &&& ~~~e)) - 2 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 1 * (d ^^^ e) - 1 * ( ~~~d &&& (e ||| f)) + 1 * (e ^^^ ~~~(d &&& (e ||| f))) + 4 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 1 * (d &&& ~~~e) + 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 7 * (e ^^^ (d &&& ~~~f)) - 2 * (d &&& ~~~f) - 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 11 * ~~~(d &&& ~~~d) - 5 * (e ^^^ ( ~~~d ||| (e &&& f))) - 11 * ( ~~~e &&& (d ^^^ f)) - 2 * (e ||| (d &&& ~~~f)) + 7 * (e ^^^ (d &&& ( ~~~e ||| f))) + 1 * e + 1 * ( ~~~f &&& ~~~(d ^^^ e)) + 1 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 3 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 1 * ((d ^^^ e) ||| ~~~(d ^^^ f)) + 1 * (e ||| (d ^^^ f)) + 2 * ( ~~~e ||| ~~~(d ^^^ f)) + 1 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 1 * ~~~(d &&& ~~~f) + 1 * (f ^^^ ~~~(d &&& e)) - 2 * ( ~~~f &&& (d ^^^ e)) - 1 * ~~~(d &&& f) - 2 * (d &&& f) - 11 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 6 * ( ~~~e ||| (d ^^^ f)) + 11 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 5 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 2 * ~~~(e ||| ~~~f) + 4 * ((d ^^^ e) ||| (d ^^^ f)) - 3 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (e &&& (d ||| f)) + 4 * ~~~(d ||| (e ^^^ f)) + 11 * (e ||| ~~~f) - 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 4 * (f ||| ~~~(d ||| ~~~e)) + 1 * ~~~(d ^^^ ( ~~~e &&& f)) - 5 * (f ^^^ ~~~(d ||| ~~~e)) - 3 * (e ^^^ f) - 1 * (d ||| f) - 11 * (e &&& f) + 2 * f - 1 * ( ~~~d ||| (e &&& f)) + 12 * ~~~(d ||| (e ||| f)) - 1 * ~~~(d ||| ( ~~~e ||| f)) + 15 * ~~~( ~~~d ||| (e ||| f)) + 35 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 66 * ( ~~~d &&& ( ~~~e &&& f)) + 6 * ( ~~~d &&& (e &&& f)) + 10 * (d &&& ( ~~~e &&& f)) + 17 * (d &&& (e &&& f)) = 1 * ~~~e := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2442 (x y : BitVec w) : +theorem e_2442 : - 1 * (f ^^^ (d &&& e)) + 4 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 11 * ~~~( ~~~d &&& (e ^^^ f)) + 11 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 5 * (d ||| f) - 2 * (e ^^^ (d ||| ~~~f)) - 1 * (e ^^^ ~~~(d ||| f)) + 1 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 7 * (f ^^^ (d ||| ~~~e)) + 2 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 5 * ~~~(d ||| ~~~f) - 3 * (d &&& ~~~f) - 5 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 7 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 1 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 2 * ~~~(d &&& ~~~f) - 2 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 6 * (d &&& ~~~e) - 7 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 1 * ~~~e - 2 * (d ^^^ ( ~~~e &&& f)) - 11 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 3 * (f ^^^ ( ~~~d ||| (e &&& f))) - 6 * (f ^^^ ~~~(d ||| ~~~e)) - 2 * (e ^^^ (d &&& ~~~f)) - 7 * (e ||| ~~~f) - 2 * ( ~~~d &&& (e ||| f)) + 1 * (f ^^^ (d ||| (e ||| f))) + 7 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 2 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 1 * ~~~(e &&& f) - 2 * (d &&& (e ||| f)) + 4 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 11 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 3 * ((d &&& e) ||| ~~~(e ^^^ f)) + 11 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 6 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 2 * ((d ||| ~~~e) &&& (e ^^^ f)) - 2 * ~~~(d &&& ~~~d) + 5 * ~~~(d &&& e) + 2 * (d &&& f) + 2 * (d &&& ( ~~~e ||| f)) - 1 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 7 * (e ^^^ (d &&& f)) + 7 * (e ^^^ ( ~~~d ||| (e &&& f))) - 6 * (d &&& (e ^^^ f)) + 3 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 1 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 5 * (f ^^^ ( ~~~d &&& (e ||| f))) + 7 * ~~~(d &&& (e &&& f)) - 11 * ~~~(e ||| f) + 4 * ~~~(d &&& (e ||| f)) - 3 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 3 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 11 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 11 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 1 * ~~~(d &&& (e ^^^ f)) + 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 2 * (d ^^^ e) + 2 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 5 * (e ^^^ ~~~(d &&& f)) + 3 * (e ^^^ ~~~(d ||| (e &&& f))) - 1 * ~~~(d ||| f) - 2 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * (e ||| ~~~(d ||| ~~~f)) - 1 * (f ||| ~~~(d ||| e)) - 36 * ~~~(d ||| (e ||| f)) - 30 * ~~~(d ||| ( ~~~e ||| f)) - 46 * ~~~( ~~~d ||| (e ||| f)) - 24 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 40 * ( ~~~d &&& ( ~~~e &&& f)) - 40 * ( ~~~d &&& (e &&& f)) - 27 * (d &&& ( ~~~e &&& f)) - 32 * (d &&& (e &&& f)) = - 4 * ~~~(d &&& ( ~~~e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2443 (x y : BitVec w) : +theorem e_2443 : - 2 * (e ^^^ (d &&& ( ~~~e ||| f))) + 2 * (d &&& (e ^^^ f)) + 3 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 6 * (f ||| ~~~(d ||| e)) - 1 * (d ||| ( ~~~e ||| f)) + 7 * (d ^^^ (e ||| f)) - 1 * ~~~(d &&& (e ^^^ f)) + 11 * (e &&& ~~~(d &&& ~~~f)) + 1 * (e ||| f) - 11 * ((d &&& f) ^^^ (e ||| f)) + 7 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 2 * (e ^^^ (d ||| (e &&& f))) - 6 * (d ||| ~~~f) + 11 * ~~~d - 5 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 5 * (e &&& ~~~f) - 1 * ~~~(e ||| f) + 5 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 1 * ( ~~~d &&& (e ^^^ f)) + 1 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (f ||| ~~~(d ||| ~~~e)) + 1 * (f &&& ~~~(d &&& e)) + 1 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 1 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 2 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 1 * (f ^^^ ~~~(d ||| (e &&& f))) + 2 * ( ~~~e ||| ~~~(d ^^^ f)) + 4 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 6 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 3 * (e &&& ~~~(d ^^^ f)) + 2 * (f ^^^ (d ||| (e ||| f))) - 11 * ( ~~~f ||| (d ^^^ e)) + 3 * ~~~( ~~~d &&& (e ||| f)) + 1 * ~~~(d ^^^ (e ||| f)) + 1 * (d &&& ~~~f) + 1 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 2 * ( ~~~e &&& ~~~(d ^^^ f)) + 4 * (d ^^^ f) - 11 * (f ^^^ ~~~(d ||| ~~~e)) - 1 * ~~~(d ||| e) - 1 * (d &&& ( ~~~e ||| f)) + 1 * ((d ^^^ e) ||| (d ^^^ f)) - 3 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 2 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 2 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 3 * (e &&& ~~~(d &&& f)) + 1 * ~~~(d ^^^ e) + 11 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 1 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 1 * (e ||| ~~~(d ^^^ f)) + 1 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 1 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 3 * (e ^^^ ~~~(d &&& ~~~f)) + 7 * ~~~(d ^^^ ( ~~~e &&& f)) + 2 * (d ||| f) - 5 * (e ||| (d &&& f)) - 5 * e + 1 * ~~~(d ^^^ (e ^^^ f)) - 7 * ~~~(d &&& f) - 3 * (e ||| (d ^^^ f)) - 1 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 11 * ( ~~~e &&& (d ^^^ f)) + 2 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 2 * (e ^^^ (d ||| (e ^^^ f))) + 7 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 6 * (f ^^^ ~~~(d &&& ~~~e)) + 11 * ~~~( ~~~d ||| (e &&& f)) + 4 * ~~~(d ||| (e ||| f)) + 22 * ~~~(d ||| ( ~~~e ||| f)) - 34 * ~~~( ~~~d ||| (e ||| f)) + 23 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 31 * ( ~~~d &&& ( ~~~e &&& f)) - 3 * ( ~~~d &&& (e &&& f)) + 29 * (d &&& ( ~~~e &&& f)) - 5 * (d &&& (e &&& f)) = - 3 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2444 (x y : BitVec w) : +theorem e_2444 : - 6 * ~~~(d ||| f) - 6 * (e &&& ~~~(d &&& f)) + 7 * ((d ||| e) &&& (e ^^^ f)) - 2 * (e &&& ~~~(d &&& ~~~f)) - 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 2 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 7 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 2 * (f ^^^ (d ||| ( ~~~e &&& f))) - 6 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 2 * (e ^^^ (d &&& (e ^^^ f))) - 5 * ( ~~~d ||| ( ~~~e &&& f)) + 4 * ((d ||| e) &&& ~~~(e ^^^ f)) - 1 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 1 * (e ^^^ ~~~(d ||| f)) + 5 * ~~~(d &&& f) - 1 * ( ~~~f &&& (d ^^^ e)) + 5 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 1 * (e ^^^ (d ||| f)) + 11 * (f ^^^ ~~~(d ||| e)) - 3 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 11 * ( ~~~d ||| ( ~~~e ||| f)) + 1 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 1 * ~~~(d &&& ~~~e) + 1 * (e ^^^ (d &&& (e ||| f))) + 11 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 2 * ( ~~~e &&& (d ^^^ f)) - 7 * (f ||| ~~~(d ||| ~~~e)) + 1 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 7 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 2 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 1 * (e ^^^ (d ||| (e ||| f))) + 4 * (f ^^^ (d ||| (e &&& f))) - 2 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 4 * ~~~( ~~~d ||| (e &&& f)) - 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 5 * (f ||| ~~~(d ^^^ e)) - 3 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 3 * f - 1 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 1 * (e &&& (d ||| ~~~f)) + 3 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 3 * ~~~(d ^^^ (e ^^^ f)) + 7 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 1 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 2 * (f ^^^ (d ||| ( ~~~e ||| f))) - 11 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 3 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 11 * (d ^^^ (e &&& f)) - 5 * (e ^^^ (d &&& f)) + 1 * (d ||| f) - 11 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 6 * ~~~(d &&& (e ^^^ f)) - 6 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 3 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 2 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 4 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 1 * ~~~(d &&& e) + 5 * e - 5 * d - 2 * (f ^^^ (d &&& ~~~e)) - 3 * ~~~(d ^^^ (e &&& f)) + 2 * (e ^^^ ( ~~~d ||| (e ||| f))) - 1 * (d ^^^ ( ~~~e &&& f)) + 11 * ~~~(d ^^^ f) + 1 * (e ^^^ (d &&& ( ~~~e ||| f))) - 2 * ( ~~~d &&& (e ^^^ f)) - 5 * (f ||| (d &&& ~~~e)) + 5 * (e &&& ~~~(d ^^^ f)) - 5 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 18 * ~~~(d ||| (e ||| f)) + 19 * ~~~(d ||| ( ~~~e ||| f)) + 18 * ~~~( ~~~d ||| (e ||| f)) + 29 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 40 * ( ~~~d &&& ( ~~~e &&& f)) + 18 * ( ~~~d &&& (e &&& f)) + 4 * (d &&& ( ~~~e &&& f)) + 3 * (d &&& (e &&& f)) = - 2 * (f &&& (d ||| ~~~e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2445 (x y : BitVec w) : +theorem e_2445 : 2 * (f ^^^ ~~~(d ||| e)) + 2 * (d &&& ~~~f) + 11 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 7 * (d &&& (e ||| f)) - 7 * (e &&& ~~~f) + 11 * ~~~e - 7 * ~~~(d ^^^ (e &&& f)) + 3 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 1 * ( ~~~d ||| (e &&& f)) + 1 * ~~~(d ||| f) + 4 * ((d ^^^ e) ||| (d ^^^ f)) - 3 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 3 * ( ~~~d ||| (e ||| f)) + 3 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 1 * ((d &&& f) ||| ~~~(e ||| f)) - 2 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * (f ^^^ ~~~(d &&& e)) - 5 * (e ^^^ ~~~(d ||| (e &&& f))) + 1 * ~~~f - 1 * (e ^^^ (d ||| ( ~~~e &&& f))) + 2 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 2 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 5 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 3 * (f ||| (d &&& e)) + 11 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 11 * (e ^^^ ~~~(d ||| f)) - 2 * (f ||| ~~~(d ^^^ e)) - 5 * ~~~(d &&& (e &&& f)) - 1 * (f &&& ~~~(d &&& e)) + 11 * e - 6 * (f ||| (d ^^^ e)) + 4 * ~~~(d ||| ~~~f) + 2 * ~~~( ~~~d &&& (e &&& f)) - 3 * (e ||| ~~~(d ^^^ f)) + 4 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 1 * ( ~~~f ||| ~~~(d ^^^ e)) + 1 * ( ~~~e &&& (d ^^^ f)) - 3 * ~~~(e ^^^ f) + 5 * ( ~~~e ||| ~~~(d ^^^ f)) + 2 * (e ^^^ (d ||| f)) - 2 * (e ||| ~~~(d ||| f)) + 5 * (f &&& (d ||| ~~~e)) - 1 * ~~~( ~~~d ||| (e &&& f)) - 2 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 7 * (f ^^^ ( ~~~d ||| (e &&& f))) - 3 * (e ^^^ ~~~(d &&& ~~~f)) + 7 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 2 * ((d &&& f) ||| (e &&& ~~~f)) + 1 * ~~~( ~~~d &&& (e ||| f)) - 7 * (d ||| (e &&& f)) - 11 * (d &&& e) - 6 * (e ^^^ ~~~(d ||| ~~~f)) - 6 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 11 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 5 * ( ~~~e &&& ~~~(d ^^^ f)) + 1 * ~~~(d &&& (e ||| f)) + 1 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 1 * (e ^^^ ( ~~~d ||| (e ||| f))) + 2 * (e ^^^ ~~~(d &&& (e &&& f))) + 2 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 1 * (d ^^^ (e &&& f)) + 5 * (f ^^^ ~~~(d &&& (e ||| f))) - 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 3 * (f ^^^ ( ~~~d &&& (e ||| f))) - 2 * (d ||| ~~~e) - 1 * (d ^^^ e) - 1 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 2 * (e ^^^ ( ~~~d ||| (e &&& f))) - 6 * ~~~( ~~~d &&& (e ^^^ f)) + 1 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 4 * ~~~(d ||| (e ||| f)) - 26 * ~~~(d ||| ( ~~~e ||| f)) - 6 * ~~~( ~~~d ||| (e ||| f)) + 54 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 32 * ( ~~~d &&& (e &&& f)) - 20 * (d &&& ( ~~~e &&& f)) + 41 * (d &&& (e &&& f)) = 5 * ( ~~~d &&& ( ~~~e &&& f)) - 3 * (e &&& ~~~(d &&& ~~~f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2446 (x y : BitVec w) : +theorem e_2446 : 1 * ( ~~~e &&& ~~~(d ^^^ f)) - 2 * (f ||| ~~~(d ||| ~~~e)) - 1 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 2 * (e ^^^ f) + 1 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 5 * (e ||| (d &&& f)) - 7 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 1 * ((d &&& e) ||| ~~~(e ||| f)) - 2 * ( ~~~d ||| (e &&& f)) + 2 * (f ^^^ (d &&& ~~~e)) + 4 * (d ||| (e ^^^ f)) + 1 * (d ||| ~~~f) + 7 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 3 * ( ~~~d &&& ( ~~~e ||| f)) - 3 * ~~~(e &&& f) + 11 * ~~~(d &&& e) - 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 5 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * ((d &&& e) ||| (e ^^^ f)) - 2 * (e &&& (d ^^^ f)) + 2 * (e ||| (d ^^^ f)) - 6 * ~~~(e ||| ~~~f) - 7 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 7 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 7 * ~~~(d ^^^ ( ~~~e &&& f)) + 3 * (f ^^^ (d ||| (e &&& f))) + 5 * (e ||| f) + 1 * ( ~~~f &&& ~~~(d ^^^ e)) + 1 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 2 * (e ^^^ ( ~~~d ||| (e &&& f))) + 11 * (d ||| f) - 6 * (e ^^^ (d ||| f)) - 11 * ~~~(d ^^^ (e &&& f)) + 11 * ((d &&& f) ||| (e &&& ~~~f)) - 11 * (e &&& ~~~(d &&& f)) - 2 * (f ^^^ ( ~~~d &&& (e ||| f))) - 1 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 3 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 1 * ~~~(d ||| e) - 7 * ~~~e + 5 * (e ^^^ ~~~(d ||| ~~~f)) - 2 * (e ^^^ (d ||| (e &&& f))) + 3 * (f &&& ~~~(d &&& e)) - 5 * ~~~(d ^^^ e) + 2 * (f ||| (d ^^^ e)) + 1 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 11 * ~~~(d ||| ~~~f) - 7 * (e ||| ~~~(d ^^^ f)) + 1 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 11 * (e ^^^ (d &&& (e ^^^ f))) - 5 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 3 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 11 * ~~~(d ||| (e &&& f)) - 3 * (e ^^^ (d ||| ( ~~~e ||| f))) + 2 * (f &&& ~~~(d &&& ~~~e)) - 1 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 1 * ~~~f - 1 * ( ~~~d ||| (e ||| f)) + 11 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * ~~~( ~~~d &&& (e ||| f)) + 1 * ( ~~~d &&& (e ^^^ f)) - 1 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 2 * (e ^^^ (d ||| ~~~f)) - 1 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 11 * ~~~(e ^^^ f) - 6 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 5 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 2 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 39 * ~~~(d ||| (e ||| f)) + 29 * ~~~(d ||| ( ~~~e ||| f)) - 4 * ~~~( ~~~d ||| (e ||| f)) - 3 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 20 * ( ~~~d &&& ( ~~~e &&& f)) + 5 * ( ~~~d &&& (e &&& f)) + 3 * (d &&& ( ~~~e &&& f)) + 22 * (d &&& (e &&& f)) = - 2 * ~~~d + 1 * (e ||| (d &&& ~~~f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2447 (x y : BitVec w) : +theorem e_2447 : - 1 * (e ^^^ ~~~(d &&& (e &&& f))) + 3 * ((d ^^^ e) &&& (d ^^^ f)) - 1 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 6 * (e ||| ~~~(d ||| f)) - 6 * (f ^^^ (d ||| ( ~~~e &&& f))) + 1 * ~~~(d &&& ( ~~~e &&& f)) + 2 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 3 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 2 * (e ||| (d &&& ~~~f)) + 4 * (f ^^^ ( ~~~d ||| (e ||| f))) - 2 * (f ^^^ (d ||| (e &&& f))) + 5 * (f ^^^ (d &&& (e ||| f))) + 11 * (f ^^^ ~~~(d ||| e)) + 3 * (f ^^^ ~~~(d &&& e)) - 5 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 11 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 2 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 1 * ~~~(d ^^^ (e ^^^ f)) + 1 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 1 * ~~~(d ||| (e ^^^ f)) - 1 * (d ^^^ e) + 2 * (f ^^^ (d &&& ~~~e)) - 11 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (f &&& (d ||| ~~~e)) - 5 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 2 * ( ~~~d &&& (e ^^^ f)) + 7 * (f ^^^ (d ||| ( ~~~e ||| f))) + 1 * ~~~(d ^^^ (e &&& f)) - 1 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 2 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 11 * ((d &&& f) ||| ~~~(e ||| f)) - 5 * (f &&& (d ^^^ e)) + 1 * (e ^^^ (d ||| ( ~~~e &&& f))) - 1 * (e ^^^ ( ~~~d &&& (e ||| f))) + 3 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 3 * ~~~(e ||| ~~~f) - 2 * ((d &&& ~~~e) ||| (e ^^^ f)) - 7 * ( ~~~d ||| (e ^^^ f)) - 2 * (f ^^^ (d ||| (e ||| f))) + 4 * ( ~~~d &&& (e ||| f)) + 1 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 6 * (d ||| f) - 2 * (e ^^^ (d ||| f)) + 1 * (f ||| ~~~(d ^^^ e)) + 3 * (e &&& ~~~(d ^^^ f)) + 2 * (f ^^^ ~~~(d &&& (e ||| f))) - 5 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 4 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 6 * (d ^^^ ( ~~~e &&& f)) - 11 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 1 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 11 * (e ^^^ (d &&& (e ^^^ f))) - 2 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 1 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 5 * (e ||| (d ^^^ f)) + 2 * ~~~( ~~~d &&& (e ||| f)) + 7 * e - 1 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 11 * ~~~(d ^^^ (e ||| f)) - 3 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 3 * ( ~~~d &&& ( ~~~e ||| f)) + 3 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 1 * ~~~(d ||| ( ~~~e &&& f)) + 11 * (d ||| ( ~~~e &&& f)) - 3 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * (d &&& f) + 5 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 19 * ~~~(d ||| (e ||| f)) - 2 * ~~~(d ||| ( ~~~e ||| f)) + 4 * ~~~( ~~~d ||| (e ||| f)) + 8 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 14 * ( ~~~d &&& ( ~~~e &&& f)) + 15 * ( ~~~d &&& (e &&& f)) - 20 * (d &&& ( ~~~e &&& f)) - 30 * (d &&& (e &&& f)) = - 5 * (e &&& ~~~(d &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2448 (x y : BitVec w) : +theorem e_2448 : - 2 * ~~~(d ^^^ e) - 1 * (f ^^^ ~~~(d &&& (e &&& f))) + 11 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 7 * (d ^^^ f) + 2 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * ~~~(d ||| ( ~~~e &&& f)) - 11 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 5 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 2 * (e &&& (d ^^^ f)) + 5 * ~~~(d ^^^ ( ~~~e &&& f)) + 2 * ~~~(d &&& (e ||| f)) + 1 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 5 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * (f ^^^ ~~~(d &&& (e ||| f))) - 2 * (e &&& f) - 2 * ((d ^^^ e) &&& (d ^^^ f)) + 1 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 1 * ~~~(d ^^^ f) - 6 * (f ^^^ ~~~(d ||| e)) - 1 * (d &&& ~~~e) - 2 * ~~~(d &&& ( ~~~e &&& f)) - 1 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 2 * ( ~~~e ||| ~~~(d ^^^ f)) + 7 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 11 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 11 * ~~~(d ^^^ (e ^^^ f)) - 6 * ( ~~~f &&& (d ^^^ e)) + 5 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 6 * (d ||| ( ~~~e &&& f)) + 7 * (e ^^^ (d ||| ( ~~~e ||| f))) - 2 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 6 * ((d ^^^ e) ||| (d ^^^ f)) + 4 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 3 * (e ^^^ ~~~(d ||| f)) - 3 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 7 * (f ^^^ (d &&& ( ~~~e ||| f))) + 4 * (d ||| ~~~f) - 3 * ((d ||| e) &&& ~~~(e ^^^ f)) - 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 11 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 7 * (f &&& ~~~(d ^^^ e)) - 1 * ((d &&& f) ^^^ (e ||| f)) + 1 * (f ^^^ ~~~(d &&& e)) + 1 * ( ~~~d ||| (e &&& f)) - 2 * ~~~( ~~~d &&& (e ||| f)) - 1 * ((d &&& e) ^^^ (e ||| ~~~f)) + 7 * ( ~~~d &&& (e ||| f)) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 1 * (e ||| ~~~(d ^^^ f)) - 1 * ((d ||| ~~~e) &&& (e ^^^ f)) + 3 * ~~~(d &&& ~~~d) - 3 * ~~~( ~~~d ||| (e &&& f)) - 2 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 1 * (f ^^^ ~~~(d &&& ~~~e)) + 3 * (e ||| ~~~(d ||| f)) - 5 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 2 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 2 * (f ||| ~~~(d ^^^ e)) - 3 * (d ||| (e &&& f)) + 11 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 11 * (e ^^^ (d &&& f)) + 4 * (f ^^^ ~~~(d ||| (e &&& f))) + 7 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 1 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 3 * ((e &&& f) ||| (d &&& (e ||| f))) + 1 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 2 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 1 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 27 * ~~~(d ||| (e ||| f)) - 68 * ~~~(d ||| ( ~~~e ||| f)) - 21 * ~~~( ~~~d ||| (e ||| f)) - 37 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 6 * ( ~~~d &&& ( ~~~e &&& f)) - 33 * ( ~~~d &&& (e &&& f)) - 8 * (d &&& ( ~~~e &&& f)) + 3 * (d &&& (e &&& f)) = - 1 * (e ^^^ ( ~~~d &&& (e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2449 (x y : BitVec w) : +theorem e_2449 : - 1 * (e ^^^ ~~~(d &&& (e ||| f))) - 5 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 5 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 1 * ( ~~~d ||| (e ||| f)) + 1 * ( ~~~e ||| ~~~(d ^^^ f)) + 5 * (e &&& ~~~(d &&& ~~~f)) + 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 2 * (e &&& (d ^^^ f)) + 1 * ( ~~~d ||| (e &&& f)) - 1 * (d ||| e) - 11 * (d &&& f) - 1 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 1 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 3 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 2 * ~~~f + 11 * ~~~(d &&& f) + 5 * ((d &&& f) ||| (e &&& ~~~f)) + 4 * (e ^^^ ~~~(d ||| ~~~f)) + 5 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 7 * (d ^^^ (e &&& f)) + 11 * (e ^^^ ~~~(d &&& f)) - 7 * (e ^^^ (d ||| (e ||| f))) + 2 * (d &&& ~~~f) + 4 * ~~~( ~~~d ||| (e ^^^ f)) + 11 * (d ^^^ f) - 1 * (e &&& (d ||| ~~~f)) + 3 * ~~~( ~~~d &&& (e ^^^ f)) - 11 * (e ^^^ ~~~(d ||| f)) - 1 * (d ||| (e ||| f)) - 1 * (e ^^^ ~~~(d &&& (e &&& f))) - 1 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 1 * e + 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * (d ^^^ (e ||| f)) + 2 * (e ||| (d &&& f)) + 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 4 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 7 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 2 * (d ^^^ (e ^^^ f)) + 2 * ((d ^^^ e) &&& (d ^^^ f)) - 1 * (f ^^^ (d ||| (e &&& f))) + 7 * ((d &&& e) ||| ~~~(e ^^^ f)) + 5 * (e ^^^ ( ~~~d &&& (e ||| f))) - 3 * ~~~(e ^^^ f) - 6 * (e ^^^ ( ~~~d ||| (e &&& f))) - 6 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 7 * (d ||| ( ~~~e ||| f)) - 6 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 1 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 3 * (e ||| ~~~(d ||| f)) + 5 * (f ||| (d &&& ~~~e)) - 6 * (e ||| f) - 6 * ~~~(d ||| f) + 4 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 11 * (d &&& (e ||| f)) - 11 * (d ^^^ ( ~~~e &&& f)) - 7 * (d &&& ( ~~~e ||| f)) - 7 * (f &&& ~~~(d &&& e)) - 2 * ( ~~~d ||| ( ~~~e ||| f)) + 1 * ( ~~~f &&& ~~~(d ^^^ e)) - 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 7 * ((d &&& e) ||| (e ^^^ f)) + 7 * (d ^^^ ( ~~~e ||| f)) + 2 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 2 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 1 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 7 * (f ^^^ ~~~(d &&& (e ||| f))) - 5 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 7 * ~~~(d ||| (e ||| f)) - 7 * ~~~(d ||| ( ~~~e ||| f)) - 4 * ~~~( ~~~d ||| (e ||| f)) + 18 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 6 * ( ~~~d &&& ( ~~~e &&& f)) - 7 * ( ~~~d &&& (e &&& f)) + 41 * (d &&& ( ~~~e &&& f)) + 8 * (d &&& (e &&& f)) = 3 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 11 * ~~~( ~~~d ||| (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2450 (x y : BitVec w) : +theorem e_2450 : - 1 * (e &&& (d ^^^ f)) - 1 * (f ^^^ (d ||| e)) + 1 * ( ~~~e ||| (d ^^^ f)) + 5 * (e &&& (d ||| ~~~f)) - 11 * ~~~(d ^^^ f) - 3 * ((d &&& e) ^^^ (e ||| ~~~f)) + 3 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 3 * ( ~~~d ||| (e &&& f)) + 5 * (f ||| ~~~(d ||| e)) + 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 11 * ( ~~~d ||| (e ||| f)) - 6 * (e ^^^ ~~~(d ||| f)) + 11 * ~~~( ~~~d &&& (e ||| f)) - 5 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 6 * (e ||| ~~~(d ^^^ f)) + 1 * (f ||| (d ^^^ e)) + 4 * (f ^^^ (d ||| ( ~~~e ||| f))) + 2 * (e &&& (d ||| f)) + 1 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 5 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 4 * (e ||| ~~~(d ||| ~~~f)) - 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 3 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 2 * (e ||| ~~~f) + 3 * ~~~(d ||| ~~~f) - 1 * (f ^^^ (d ||| (e &&& f))) - 7 * (d ^^^ (e &&& f)) + 2 * ((d &&& e) ||| (e ^^^ f)) + 7 * (e ^^^ ~~~(d &&& (e &&& f))) + 11 * ((d &&& e) ||| ~~~(e ^^^ f)) + 2 * (d ||| f) - 11 * ((d ^^^ e) ||| (d ^^^ f)) - 1 * (f ^^^ (d &&& ( ~~~e ||| f))) + 11 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 1 * (e ^^^ (d &&& ( ~~~e ||| f))) + 5 * ( ~~~f ||| ~~~(d ^^^ e)) - 2 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 2 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 2 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 7 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 1 * (d ||| ( ~~~e &&& f)) + 1 * (d ||| ~~~f) - 11 * (e ^^^ ~~~(d ||| (e &&& f))) + 1 * (e ^^^ (d ||| (e ||| f))) - 6 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 1 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 2 * f + 2 * (f &&& (d ^^^ e)) + 7 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 5 * ~~~(d ^^^ (e &&& f)) - 2 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 2 * ~~~(e &&& f) - 1 * ~~~(d &&& ( ~~~e ||| f)) - 7 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 2 * ~~~d - 1 * ((d &&& e) ||| ~~~(e ||| f)) - 1 * (d &&& (e ^^^ f)) - 7 * (d &&& ~~~e) + 1 * ( ~~~e &&& ~~~(d ^^^ f)) + 4 * (e ^^^ (d ||| f)) - 6 * ~~~(d ||| ( ~~~e &&& f)) - 5 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 5 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 2 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 3 * (d ||| ~~~e) + 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 7 * ( ~~~d &&& (e ||| f)) - 11 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 21 * ~~~(d ||| (e ||| f)) - 3 * ~~~(d ||| ( ~~~e ||| f)) - 16 * ~~~( ~~~d ||| (e ||| f)) + 4 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 46 * ( ~~~d &&& ( ~~~e &&& f)) + 11 * ( ~~~d &&& (e &&& f)) - 10 * (d &&& ( ~~~e &&& f)) - 29 * (d &&& (e &&& f)) = - 4 * ((d ||| ~~~e) &&& (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2451 (x y : BitVec w) : +theorem e_2451 : - 1 * (e ^^^ ~~~(d &&& (e ||| f))) + 3 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 7 * ~~~(d ||| ( ~~~e &&& f)) + 4 * ( ~~~e &&& (d ^^^ f)) - 6 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 2 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 6 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 1 * ((e &&& f) ||| (d &&& (e ||| f))) - 2 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 5 * (f ||| ~~~(d ||| ~~~e)) - 3 * (e ^^^ ~~~(d ||| (e &&& f))) + 3 * ((d ||| e) &&& (e ^^^ f)) + 5 * ( ~~~d ||| ( ~~~e &&& f)) - 3 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 1 * (f ||| (d ^^^ e)) - 5 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 11 * ( ~~~e &&& ~~~(d ^^^ f)) - 7 * (f ^^^ ( ~~~d ||| (e &&& f))) + 5 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 1 * (e ||| ~~~(d ||| f)) + 1 * (e ||| (d &&& ~~~f)) + 1 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 1 * (e ^^^ ( ~~~d &&& (e ||| f))) + 4 * (d &&& e) - 1 * ~~~(d ||| f) + 1 * (e ^^^ (d &&& (e ||| f))) + 3 * ((d ||| ~~~e) &&& (e ^^^ f)) - 3 * (e ^^^ f) - 2 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 1 * (d ^^^ f) - 2 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 11 * (e ^^^ (d ||| (e &&& f))) + 7 * (e ||| f) + 11 * ( ~~~d ||| (e ^^^ f)) - 6 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 6 * ~~~(d ^^^ ( ~~~e ||| f)) + 2 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 1 * (f ^^^ ~~~(d ||| ~~~e)) - 1 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 2 * ( ~~~f ||| ~~~(d ^^^ e)) - 2 * ~~~(d ^^^ f) + 1 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 7 * ( ~~~d &&& (e ^^^ f)) - 11 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 3 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 5 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 3 * (e ^^^ (d &&& (e ^^^ f))) - 2 * f - 5 * (e ^^^ (d ||| f)) + 1 * ( ~~~d &&& ( ~~~e ||| f)) - 1 * (e &&& ~~~(d &&& ~~~f)) + 7 * (d ^^^ ( ~~~e &&& f)) - 11 * (f ^^^ (d ||| (e &&& f))) + 4 * ( ~~~e ||| (d ^^^ f)) - 5 * ~~~(d ^^^ (e &&& f)) + 1 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 3 * (e ||| (d ^^^ f)) - 3 * (d ||| e) + 7 * ~~~(e &&& ~~~f) + 2 * (e ^^^ ~~~(d &&& f)) + 11 * (d ||| (e ||| f)) - 7 * ( ~~~d &&& (e ||| f)) + 2 * (f ^^^ (d ||| ( ~~~e &&& f))) - 3 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 1 * ( ~~~e ||| ~~~(d ^^^ f)) + 7 * (e ^^^ (d ||| (e ||| f))) + 2 * e - 1 * (f &&& ~~~(d &&& e)) + 1 * (e ^^^ ~~~(d &&& (e &&& f))) + 19 * ~~~(d ||| (e ||| f)) + 21 * ~~~(d ||| ( ~~~e ||| f)) - 15 * ~~~( ~~~d ||| (e ||| f)) - 27 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 7 * ( ~~~d &&& ( ~~~e &&& f)) - 51 * ( ~~~d &&& (e &&& f)) - 44 * (d &&& (e &&& f)) = - 11 * (d ||| (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2452 (x y : BitVec w) : +theorem e_2452 : 7 * (d ^^^ ( ~~~e &&& f)) - 7 * ~~~f + 2 * (d ||| (e ||| f)) + 1 * (d ||| (e ^^^ f)) - 1 * (f ||| (d &&& e)) + 2 * (f ^^^ (d ||| ~~~e)) - 3 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 1 * (d ^^^ (e &&& f)) + 3 * (e ||| ~~~(d ||| f)) + 4 * (e &&& f) + 3 * (f &&& (d ||| e)) - 1 * (e ^^^ ~~~(d &&& f)) + 5 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 11 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 1 * (e &&& (d ^^^ f)) + 3 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 11 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 11 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (e ^^^ (d &&& (e ||| f))) - 7 * ( ~~~d &&& (e ^^^ f)) - 2 * ((d &&& f) ^^^ (e ||| f)) + 11 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * ~~~(d ^^^ e) - 5 * ( ~~~e ||| (d ^^^ f)) - 2 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 1 * (e ||| ~~~(d ||| ~~~f)) - 1 * ~~~(d &&& ~~~d) - 2 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 1 * ~~~(d &&& (e ||| f)) - 2 * ~~~(d ||| (e &&& f)) + 4 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 1 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 5 * f - 6 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 11 * (d &&& ~~~e) + 2 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 1 * ~~~(e ^^^ f) - 1 * ~~~(e &&& f) - 3 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 2 * ~~~(d ||| (e ^^^ f)) - 11 * (f ||| ~~~(d ||| ~~~e)) + 11 * (f ||| (d ^^^ e)) + 1 * ~~~(d &&& ~~~e) + 2 * ~~~(d &&& ( ~~~e &&& f)) - 5 * (d ||| e) - 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 5 * (f ^^^ ~~~(d &&& ~~~e)) - 3 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 11 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 2 * (f ^^^ (d ||| ( ~~~e &&& f))) - 6 * (e &&& ~~~(d &&& f)) + 1 * (e &&& (d ||| ~~~f)) - 1 * ~~~(d &&& e) + 1 * ~~~(d ^^^ f) + 4 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 2 * ((d ||| e) &&& (e ^^^ f)) + 7 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 7 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 3 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 5 * (e &&& ~~~(d &&& ~~~f)) + 5 * (f ^^^ (d &&& (e ||| f))) + 4 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 7 * ~~~(d &&& ~~~f) - 6 * (f ^^^ (d ||| e)) - 1 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 1 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 2 * (d ^^^ ( ~~~e ||| f)) - 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 4 * (e ^^^ (d ||| f)) - 15 * ~~~(d ||| (e ||| f)) + 7 * ~~~(d ||| ( ~~~e ||| f)) + 1 * ~~~( ~~~d ||| (e ||| f)) + 23 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 12 * ( ~~~d &&& ( ~~~e &&& f)) - 39 * ( ~~~d &&& (e &&& f)) - 18 * (d &&& ( ~~~e &&& f)) - 32 * (d &&& (e &&& f)) = - 11 * ( ~~~(d &&& e) &&& (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2453 (x y : BitVec w) : +theorem e_2453 : - 3 * ~~~(d ^^^ f) - 1 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 7 * (d ||| ~~~e) + 11 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 3 * (d ^^^ (e ^^^ f)) + 3 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 1 * (e ^^^ ( ~~~d ||| (e ||| f))) - 2 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * ~~~(e ||| ~~~f) + 2 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 5 * (e ^^^ (d &&& (e ||| f))) - 6 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 5 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 3 * (e ||| f) + 1 * ~~~( ~~~d ||| (e ^^^ f)) + 5 * (e ^^^ (d ||| (e ||| f))) - 2 * ~~~(d ^^^ e) + 1 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 1 * ~~~( ~~~d ||| (e &&& f)) + 2 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 7 * ( ~~~e ||| (d ^^^ f)) + 4 * (e &&& (d ^^^ f)) - 1 * ~~~(d &&& ~~~e) + 5 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 1 * (f ||| (d &&& ~~~e)) - 1 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 1 * d - 1 * (f ^^^ (d ||| ~~~e)) + 7 * (f &&& (d ||| e)) - 11 * ~~~(d ||| ~~~f) - 1 * (d &&& ~~~e) + 5 * (e ||| (d &&& ~~~f)) - 1 * ~~~(e &&& f) - 1 * ((d ^^^ e) ||| (d ^^^ f)) - 5 * ~~~e + 11 * ~~~(d &&& f) - 1 * (f ^^^ ~~~(d ||| ~~~e)) + 4 * (e ^^^ ~~~(d ||| (e &&& f))) + 2 * (f ^^^ (d &&& e)) - 1 * (d ^^^ e) - 3 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * (f &&& (d ||| ~~~e)) - 6 * (d ^^^ ( ~~~e &&& f)) - 1 * ((d &&& e) ||| ~~~(e ^^^ f)) - 11 * (e ||| ~~~(d ||| ~~~f)) - 1 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 2 * (d ||| (e ^^^ f)) + 2 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 3 * (f ^^^ ( ~~~d ||| (e ||| f))) - 7 * (d ^^^ (e ||| f)) + 3 * (f ^^^ ~~~(d &&& e)) - 1 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 6 * (d ^^^ f) - 1 * (f ^^^ (d ||| ( ~~~e &&& f))) + 7 * (d &&& ~~~f) - 2 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 1 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 7 * (e ^^^ (d ||| ~~~f)) - 6 * (d ||| f) + 11 * (e ^^^ (d ||| f)) - 2 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 2 * (e ^^^ ~~~(d &&& f)) - 5 * (f ^^^ (d &&& (e ||| f))) + 1 * ~~~(d ^^^ (e ^^^ f)) - 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * (e ||| ~~~(d ||| f)) + 2 * ( ~~~d ||| ( ~~~e &&& f)) - 2 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 4 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 5 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 10 * ~~~(d ||| (e ||| f)) - 17 * ~~~(d ||| ( ~~~e ||| f)) - 1 * ~~~( ~~~d ||| (e ||| f)) + 22 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 18 * ( ~~~d &&& ( ~~~e &&& f)) + 24 * ( ~~~d &&& (e &&& f)) + 5 * (d &&& ( ~~~e &&& f)) - 12 * (d &&& (e &&& f)) = 2 * ( ~~~d &&& (e ^^^ f)) - 1 * ~~~(d &&& ~~~d) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2454 (x y : BitVec w) : +theorem e_2454 : 2 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 1 * (f &&& ~~~(d &&& ~~~e)) - 2 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 6 * ( ~~~d ||| (e ||| f)) + 2 * (f ^^^ (d ||| ( ~~~e &&& f))) + 11 * (d ||| ( ~~~e &&& f)) - 2 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 6 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 5 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 1 * ( ~~~d ||| (e ^^^ f)) - 6 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 7 * (e ||| ~~~(d ||| ~~~f)) + 1 * (f ^^^ (d &&& e)) + 2 * ~~~(d &&& (e ^^^ f)) + 7 * (e ^^^ (d ||| ( ~~~e ||| f))) + 4 * ~~~(d ^^^ e) - 7 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 3 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 1 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 11 * ((d ^^^ e) ||| (d ^^^ f)) - 11 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 1 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 3 * ~~~(d &&& ~~~f) + 11 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 1 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 5 * (f ^^^ (d ||| ( ~~~e ||| f))) - 6 * ((d ||| ~~~e) &&& (e ^^^ f)) - 1 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 3 * ~~~(d &&& (e ||| f)) + 1 * (e ^^^ (d ||| ( ~~~e &&& f))) + 1 * ( ~~~d ||| (e &&& f)) + 1 * (f ^^^ ( ~~~d ||| (e ||| f))) + 1 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 11 * ~~~(d ||| (e &&& f)) - 1 * (d &&& e) - 3 * (d ||| f) - 7 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 11 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 4 * (e &&& ~~~(d ^^^ f)) - 1 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 5 * ~~~(d ^^^ (e &&& f)) + 7 * ~~~( ~~~d &&& (e &&& f)) + 4 * (e &&& (d ||| f)) - 3 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 2 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 11 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 1 * (d ||| ~~~f) - 7 * ~~~(d ^^^ ( ~~~e &&& f)) - 2 * ((d ||| e) &&& ~~~(e ^^^ f)) - 7 * (f ^^^ ~~~(d ||| (e &&& f))) - 7 * ~~~(e ^^^ f) + 7 * (e &&& (d ||| ~~~f)) + 11 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 2 * (e ||| ~~~f) + 5 * (f ^^^ (d &&& ~~~e)) + 4 * ~~~(d ||| ( ~~~e &&& f)) + 11 * (f ^^^ (d ||| (e &&& f))) + 5 * (e ^^^ (d &&& f)) + 2 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 3 * ((d &&& f) ||| ~~~(e ||| f)) - 5 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 2 * (e ^^^ ( ~~~d &&& (e ||| f))) - 2 * ( ~~~f &&& (d ^^^ e)) - 1 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 2 * ~~~(d ||| f) - 2 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 7 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 1 * ~~~(e ||| f) + 2 * (e ^^^ (d ||| f)) - 2 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 2 * (e ||| (d ^^^ f)) - 12 * ~~~(d ||| (e ||| f)) - 36 * ~~~(d ||| ( ~~~e ||| f)) - 39 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 17 * ( ~~~d &&& ( ~~~e &&& f)) + 9 * ( ~~~d &&& (e &&& f)) - 17 * (d &&& ( ~~~e &&& f)) - 16 * (d &&& (e &&& f)) = 23 * ~~~( ~~~d ||| (e ||| f)) + 5 * (e &&& f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2455 (x y : BitVec w) : +theorem e_2455 : 2 * ~~~(d ^^^ e) - 2 * (e ||| (d ^^^ f)) + 5 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * ((d &&& f) ||| (e &&& ~~~f)) - 6 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 3 * (f ^^^ ( ~~~d ||| (e ||| f))) + 3 * ~~~( ~~~d &&& (e ^^^ f)) - 1 * (e &&& ~~~(d ^^^ f)) - 3 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 11 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 5 * ((d &&& e) ^^^ (e ||| ~~~f)) - 1 * ( ~~~e &&& (d ^^^ f)) + 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 1 * ~~~(d ^^^ (e ^^^ f)) + 11 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 1 * ~~~( ~~~d &&& (e ||| f)) + 2 * (f &&& ~~~(d &&& ~~~e)) - 1 * (f ^^^ (d ||| ~~~e)) - 1 * ~~~(d &&& ( ~~~e ||| f)) + 2 * ~~~(d &&& (e &&& f)) - 1 * (f ^^^ ~~~(d ||| ~~~e)) - 7 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 6 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 3 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 11 * (d ||| ~~~f) - 3 * (e &&& ~~~(d &&& f)) - 11 * (f ^^^ (d ||| ( ~~~e &&& f))) - 1 * (f ^^^ (d &&& ~~~e)) - 5 * ((d ^^^ e) &&& (d ^^^ f)) + 2 * ~~~(d ^^^ f) + 7 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 11 * (f &&& (d ||| e)) + 4 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 2 * ~~~(d &&& ( ~~~e &&& f)) + 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 2 * (d ||| (e &&& f)) - 1 * ( ~~~e &&& ~~~(d ^^^ f)) - 5 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 6 * ~~~(d &&& ~~~f) + 2 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 1 * ( ~~~f &&& ~~~(d ^^^ e)) + 2 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 11 * (d ^^^ (e ||| f)) - 1 * (e &&& (d ^^^ f)) - 2 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 4 * ( ~~~e ||| (d ^^^ f)) - 7 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 5 * (e ^^^ (d &&& (e ||| f))) - 2 * (e &&& (d ||| f)) - 5 * (e ||| ~~~(d ^^^ f)) - 1 * (d ||| ~~~e) + 4 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 7 * ~~~(d ||| ( ~~~e &&& f)) + 11 * (d ^^^ (e ^^^ f)) - 1 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 7 * (e ^^^ (d ||| (e &&& f))) - 6 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 5 * ~~~(d ||| (e ^^^ f)) + 5 * (e ^^^ (d &&& ~~~f)) - 7 * (f ^^^ ~~~(d &&& ~~~e)) + 1 * (f &&& ~~~(d &&& e)) + 3 * (e ^^^ (d ||| (e ||| f))) + 5 * ((d &&& ~~~e) ||| (e ^^^ f)) + 11 * (f ^^^ (d ||| (e ||| f))) + 2 * (d &&& f) - 1 * ( ~~~f ||| ~~~(d ^^^ e)) + 4 * ~~~(e &&& ~~~f) - 2 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 7 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 3 * ( ~~~d &&& (e ||| f)) + 20 * ~~~(d ||| (e ||| f)) - 11 * ~~~(d ||| ( ~~~e ||| f)) - 10 * ~~~( ~~~d ||| (e ||| f)) + 17 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 37 * ( ~~~d &&& ( ~~~e &&& f)) + 40 * ( ~~~d &&& (e &&& f)) + 50 * (d &&& ( ~~~e &&& f)) + 21 * (d &&& (e &&& f)) = - 3 * ((d &&& f) ||| ~~~(e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2456 (x y : BitVec w) : +theorem e_2456 : 7 * (e ||| ~~~f) + 1 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 7 * (e &&& ~~~(d &&& f)) + 11 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 3 * (d &&& f) - 7 * ( ~~~d ||| (e &&& f)) + 2 * ((d &&& ~~~e) ||| (e ^^^ f)) + 2 * ~~~(e ||| ~~~f) - 2 * ~~~(d ^^^ e) - 7 * (d &&& ( ~~~e ||| f)) - 5 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 2 * (d ||| ( ~~~e ||| f)) - 3 * (d &&& ~~~f) - 2 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 5 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 6 * (e ^^^ (d ||| (e &&& f))) - 1 * (f ||| ~~~(d ^^^ e)) - 1 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 7 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 2 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * ((e &&& f) ||| (d &&& (e ||| f))) + 7 * (f ^^^ ( ~~~d ||| (e ||| f))) - 1 * f - 5 * ((d &&& e) ^^^ (e ||| ~~~f)) - 3 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 2 * ~~~(d &&& ( ~~~e ||| f)) + 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 6 * ((d &&& e) ^^^ (e ||| f)) + 2 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 3 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 1 * (e &&& ~~~f) + 2 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 5 * ~~~(d &&& (e &&& f)) + 2 * (f ^^^ ~~~(d &&& ~~~e)) + 3 * (e ^^^ ~~~(d ||| f)) + 3 * ((d &&& e) ||| ~~~(e ||| f)) - 6 * (d ^^^ ( ~~~e &&& f)) - 5 * (e ^^^ ~~~(d &&& (e &&& f))) + 3 * ~~~d + 3 * ((d &&& f) ||| ~~~(e ||| f)) + 5 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * ~~~(e &&& f) + 1 * ~~~(d &&& ~~~e) + 4 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 11 * ~~~(d ^^^ (e ^^^ f)) - 3 * ( ~~~d ||| ( ~~~e ||| f)) + 11 * ~~~f - 11 * (e &&& f) - 1 * ~~~(e ^^^ f) - 1 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * (f ^^^ (d ||| ( ~~~e ||| f))) - 2 * (f ||| (d &&& ~~~e)) - 3 * (f &&& ~~~(d ^^^ e)) + 1 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 1 * ~~~(d ||| ( ~~~e &&& f)) + 1 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 3 * (d ||| (e ^^^ f)) - 7 * (e ^^^ (d &&& (e ^^^ f))) + 1 * (f ^^^ (d ||| ( ~~~e &&& f))) + 2 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 1 * (e &&& ~~~(d ^^^ f)) + 1 * (e ^^^ (d ||| ( ~~~e &&& f))) - 3 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 2 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 5 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 3 * (f ^^^ (d ||| (e ||| f))) - 11 * (d ||| (e &&& f)) - 7 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 1 * (f ^^^ (d ||| (e &&& f))) - 2 * (f ^^^ (d &&& (e ||| f))) - 11 * (d ^^^ ( ~~~e ||| f)) - 26 * ~~~(d ||| (e ||| f)) + 1 * ~~~(d ||| ( ~~~e ||| f)) - 58 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 36 * ( ~~~d &&& ( ~~~e &&& f)) + 37 * ( ~~~d &&& (e &&& f)) + 21 * (d &&& ( ~~~e &&& f)) + 31 * (d &&& (e &&& f)) = 2 * ~~~( ~~~d ||| (e ||| f)) - 5 * (e ^^^ ( ~~~d &&& (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2457 (x y : BitVec w) : +theorem e_2457 : - 1 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 2 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 6 * (d &&& ( ~~~e ||| f)) + 1 * (f &&& (d ||| ~~~e)) + 4 * (e ^^^ f) - 1 * (f &&& (d ||| e)) - 1 * ~~~(d ^^^ (e ^^^ f)) - 3 * ~~~(d ||| f) - 2 * (f ^^^ (d &&& (e ||| f))) - 1 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 2 * (e ^^^ ~~~(d ||| ~~~f)) - 1 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 4 * (e ^^^ (d &&& ( ~~~e ||| f))) + 5 * ( ~~~f &&& (d ^^^ e)) - 1 * ~~~(d ||| ( ~~~e &&& f)) - 2 * f - 5 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * (f &&& ~~~(d &&& ~~~e)) + 5 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 7 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 7 * ~~~(d &&& ~~~f) - 1 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 7 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 7 * (f ^^^ ~~~(d &&& ~~~e)) - 11 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 2 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 1 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 5 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 5 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 3 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 11 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 6 * ~~~(d ||| (e &&& f)) - 7 * ((d ^^^ e) ||| ~~~(d ^^^ f)) + 11 * (e ^^^ (d ||| (e &&& f))) + 5 * ~~~(e ||| ~~~f) - 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 7 * ((d ||| ~~~e) &&& (e ^^^ f)) + 4 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 2 * ~~~(d &&& (e &&& f)) - 7 * (d ||| ~~~f) - 6 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 11 * e + 4 * ~~~(d ^^^ (e ||| f)) + 2 * (e ^^^ ~~~(d &&& (e &&& f))) + 3 * (e ||| ~~~(d ||| f)) + 1 * (f ||| (d &&& e)) - 1 * (e ^^^ ( ~~~d &&& (e ||| f))) + 1 * ( ~~~d &&& (e ^^^ f)) + 3 * ~~~(e &&& ~~~f) - 2 * ( ~~~f &&& ~~~(d ^^^ e)) + 5 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 3 * ((d ^^^ e) ||| (d ^^^ f)) - 5 * (f ^^^ ~~~(d ||| ~~~e)) + 4 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 3 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 1 * ~~~e - 7 * (d &&& f) + 1 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 1 * (e ^^^ (d &&& (e ||| f))) + 1 * ~~~(d ^^^ f) + 1 * (d &&& e) - 2 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 2 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 2 * (d ||| e) - 11 * (d &&& (e ||| f)) + 3 * ((e &&& f) ||| (d &&& (e ||| f))) + 11 * ((d ^^^ e) &&& (d ^^^ f)) + 2 * d - 1 * ~~~(d ^^^ ( ~~~e ||| f)) + 31 * ~~~(d ||| (e ||| f)) + 15 * ~~~(d ||| ( ~~~e ||| f)) + 15 * ~~~( ~~~d ||| (e ||| f)) - 2 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 4 * ( ~~~d &&& ( ~~~e &&& f)) - 3 * ( ~~~d &&& (e &&& f)) + 14 * (d &&& ( ~~~e &&& f)) + 41 * (d &&& (e &&& f)) = 7 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2458 (x y : BitVec w) : +theorem e_2458 : 1 * (e ^^^ (d ||| (e ||| f))) + 2 * ~~~(d ||| e) + 1 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 11 * d - 3 * ~~~(e ||| ~~~f) - 7 * (f ^^^ ( ~~~d ||| (e ||| f))) - 2 * (e &&& (d ||| ~~~f)) + 1 * ~~~(d ^^^ (e &&& f)) - 3 * ( ~~~f &&& ~~~(d ^^^ e)) + 2 * (f &&& ~~~(d ^^^ e)) - 1 * (e ^^^ (d &&& ~~~f)) - 6 * (f ^^^ ~~~(d &&& (e ||| f))) + 4 * ((d ^^^ e) ||| (d ^^^ f)) + 4 * (f &&& (d ||| ~~~e)) - 2 * (d &&& (e ||| f)) + 5 * (e ^^^ (d &&& (e ^^^ f))) - 6 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 6 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 3 * (e &&& ~~~f) - 1 * (e ||| (d &&& ~~~f)) + 11 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 2 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 1 * ( ~~~e &&& ~~~(d ^^^ f)) + 11 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 2 * ~~~(d &&& (e ||| f)) - 1 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 6 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 1 * ~~~(e &&& ~~~f) + 1 * (d ||| (e ^^^ f)) - 2 * (f ||| ~~~(d ||| e)) + 4 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 11 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 3 * (f ^^^ ~~~(d ||| (e &&& f))) + 1 * (e ^^^ ~~~(d ||| (e &&& f))) - 11 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 7 * ~~~( ~~~d ||| (e ^^^ f)) - 5 * ((d ||| e) &&& (e ^^^ f)) + 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 3 * (f ^^^ (d ||| e)) + 3 * ~~~( ~~~d ||| (e &&& f)) - 1 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 11 * (f ^^^ (d &&& ~~~e)) - 7 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 5 * (d &&& f) + 2 * (f ^^^ (d &&& e)) - 2 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 1 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 2 * (d &&& (e ^^^ f)) - 6 * (e ||| f) + 2 * (f ^^^ (d &&& ( ~~~e ||| f))) + 1 * e + 1 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 5 * ~~~(d ^^^ (e ||| f)) - 7 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 2 * (e ^^^ (d ||| f)) - 6 * ~~~f - 2 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 7 * ~~~(d ||| ~~~f) + 11 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 11 * ~~~(d ^^^ f) + 5 * ( ~~~d ||| (e ^^^ f)) - 1 * ~~~(e ^^^ f) + 5 * ((d ||| e) &&& ~~~(e ^^^ f)) + 2 * (f ^^^ ~~~(d ||| e)) + 4 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 1 * (f ^^^ ( ~~~d &&& (e ||| f))) - 7 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * ~~~(d ||| ~~~e) + 3 * (e &&& ~~~(d ^^^ f)) + 7 * ~~~(d ||| (e ||| f)) + 41 * ~~~(d ||| ( ~~~e ||| f)) + 12 * ~~~( ~~~d ||| (e ||| f)) + 23 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 21 * ( ~~~d &&& ( ~~~e &&& f)) + 4 * (d &&& ( ~~~e &&& f)) + 27 * (d &&& (e &&& f)) = 17 * ( ~~~d &&& (e &&& f)) - 11 * (e ^^^ ~~~(d &&& (e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2459 (x y : BitVec w) : +theorem e_2459 : - 7 * ((d &&& f) ||| (e &&& ~~~f)) - 2 * ~~~(d &&& ~~~e) - 6 * (e ^^^ (d &&& ~~~f)) + 4 * (d &&& e) - 2 * ~~~(d ||| ~~~e) + 4 * ( ~~~f &&& ~~~(d ^^^ e)) + 11 * ~~~(d ^^^ (e &&& f)) - 1 * (d &&& f) + 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 3 * ~~~(d ||| f) - 11 * (e ^^^ (d &&& (e ^^^ f))) - 1 * ~~~(d &&& ( ~~~e ||| f)) + 2 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 11 * ~~~(d &&& ~~~f) - 1 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 7 * (e &&& (d ||| ~~~f)) - 3 * (f ||| (d &&& e)) + 2 * ~~~(e ||| f) - 11 * (e ||| (d ^^^ f)) - 3 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 7 * (e ^^^ ( ~~~d ||| (e &&& f))) - 1 * (d ||| (e ||| f)) + 11 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 2 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 1 * ( ~~~e &&& ~~~(d ^^^ f)) - 2 * ( ~~~d ||| (e ||| f)) - 1 * ((d &&& f) ^^^ (e ||| f)) + 2 * (d ^^^ (e &&& f)) - 1 * ~~~(d ^^^ e) - 2 * (f ^^^ (d ||| (e ||| f))) + 1 * (e ^^^ ~~~(d ||| (e &&& f))) + 4 * ~~~(d &&& (e &&& f)) - 5 * ~~~(d ^^^ ( ~~~e &&& f)) + 3 * (e ^^^ ~~~(d &&& (e &&& f))) - 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 7 * (d ||| ~~~e) - 1 * ~~~( ~~~d &&& (e ||| f)) - 7 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 2 * (e ^^^ (d ||| (e &&& f))) + 2 * (d ||| (e ^^^ f)) - 1 * ((d ||| ~~~e) &&& (e ^^^ f)) + 1 * (f ^^^ ( ~~~d ||| (e ||| f))) - 6 * ( ~~~f &&& (d ^^^ e)) + 1 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 11 * (f ^^^ (d ||| ( ~~~e &&& f))) + 5 * ~~~(d ||| e) + 5 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 5 * (f ^^^ ~~~(d ||| e)) + 11 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 11 * (e ^^^ (d ||| (e ^^^ f))) - 2 * (e ||| ~~~f) + 4 * d - 6 * ((d ^^^ e) &&& (d ^^^ f)) + 2 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 1 * ((d ^^^ e) ||| (d ^^^ f)) - 11 * (e ||| ~~~(d ||| f)) + 1 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 1 * ~~~(d &&& e) + 5 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 2 * (d &&& (e ||| f)) + 5 * e - 6 * (e ^^^ (d &&& ( ~~~e ||| f))) - 5 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 2 * ( ~~~d &&& (e ||| f)) + 1 * (e ^^^ (d ||| f)) + 7 * (d ^^^ (e ^^^ f)) - 1 * ~~~(d ||| (e &&& f)) - 5 * ~~~( ~~~d ||| (e ^^^ f)) + 2 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 1 * ~~~(e ||| ~~~f) + 7 * ~~~(d ||| (e ||| f)) + 54 * ~~~(d ||| ( ~~~e ||| f)) + 2 * ~~~( ~~~d ||| (e ||| f)) + 20 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 13 * ( ~~~d &&& ( ~~~e &&& f)) + 40 * ( ~~~d &&& (e &&& f)) + 1 * (d &&& ( ~~~e &&& f)) + 24 * (d &&& (e &&& f)) = - 11 * (e &&& (d ^^^ f)) + 6 * ~~~d := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2460 (x y : BitVec w) : +theorem e_2460 : 4 * (d ||| (e ||| f)) + 4 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 6 * (d &&& (e ||| f)) + 7 * (f ||| (d &&& ~~~e)) - 3 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 2 * (d &&& ~~~e) - 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 11 * (e &&& ~~~f) + 11 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 2 * (f ^^^ ~~~(d &&& (e &&& f))) - 7 * ~~~f + 11 * (e ^^^ ( ~~~d ||| (e &&& f))) + 1 * (f ^^^ ~~~(d ||| (e &&& f))) + 5 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 7 * (f &&& ~~~(d ^^^ e)) + 4 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 2 * ((d &&& f) ||| (e &&& ~~~f)) + 7 * ((d &&& f) ||| ~~~(e ||| f)) + 1 * f - 1 * (d ||| ~~~e) - 1 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 2 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 2 * (f ^^^ ~~~(d ||| e)) - 6 * ~~~(d ^^^ f) - 1 * (e &&& ~~~(d &&& f)) - 2 * (e ^^^ (d &&& ( ~~~e ||| f))) - 7 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 7 * (f ^^^ ~~~(d &&& (e ||| f))) + 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 2 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 5 * ~~~(e &&& ~~~f) + 1 * (e ||| ~~~(d ||| ~~~f)) + 5 * (f ^^^ ~~~(d &&& ~~~e)) - 7 * (f ^^^ ~~~(d &&& e)) - 1 * ~~~(d &&& (e ^^^ f)) - 1 * (e ||| ~~~(d ^^^ f)) + 2 * (f &&& (d ^^^ e)) + 1 * (e ^^^ (d ||| (e ^^^ f))) + 2 * ~~~e - 5 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 1 * (f ^^^ ~~~(d ||| ~~~e)) + 1 * (e ^^^ ~~~(d &&& (e &&& f))) - 3 * (e ^^^ (d ||| (e &&& f))) + 11 * ((d &&& e) ||| ~~~(e ^^^ f)) + 1 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 3 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * ~~~(e &&& f) - 1 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 1 * ((d &&& e) ||| ~~~(e ||| f)) + 5 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * (f ||| ~~~(d ^^^ e)) + 1 * ((e &&& f) ||| (d &&& (e ||| f))) - 11 * ~~~( ~~~d &&& (e ||| f)) + 1 * (f ^^^ (d ||| (e &&& f))) + 2 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 11 * ( ~~~d ||| ( ~~~e &&& f)) + 4 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 11 * ~~~(d ^^^ (e &&& f)) - 2 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 4 * (f ^^^ (d &&& e)) - 1 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 1 * ( ~~~f &&& (d ^^^ e)) + 3 * ~~~(d &&& ( ~~~e &&& f)) - 1 * ~~~( ~~~d ||| (e ^^^ f)) - 2 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * ~~~( ~~~d ||| (e &&& f)) + 2 * (e ^^^ ~~~(d &&& f)) + 11 * (f ||| ~~~(d ||| e)) + 7 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * ( ~~~f ||| (d ^^^ e)) - 3 * ~~~(d ^^^ (e ^^^ f)) - 26 * ~~~(d ||| (e ||| f)) + 34 * ~~~(d ||| ( ~~~e ||| f)) - 10 * ~~~( ~~~d ||| (e ||| f)) - 32 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 51 * ( ~~~d &&& ( ~~~e &&& f)) - 60 * ( ~~~d &&& (e &&& f)) - 21 * (d &&& (e &&& f)) = 15 * (d &&& ( ~~~e &&& f)) - 5 * ( ~~~e ||| (d ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2461 (x y : BitVec w) : +theorem e_2461 : 4 * ~~~(e &&& ~~~f) + 3 * ((d &&& e) ^^^ (e ||| ~~~f)) + 3 * (d ||| (e ^^^ f)) - 3 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 1 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 1 * (e ^^^ (d ||| (e &&& f))) + 2 * (e ^^^ ~~~(d &&& ~~~f)) - 7 * (f ^^^ ~~~(d ||| (e &&& f))) + 1 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 11 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 3 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 1 * ( ~~~d &&& (e ||| f)) - 1 * (d &&& e) - 2 * (f ^^^ (d &&& e)) - 5 * (d ||| ( ~~~e &&& f)) + 5 * ~~~( ~~~d ||| (e ^^^ f)) - 3 * (e ^^^ (d &&& (e ||| f))) + 5 * ~~~f - 1 * ( ~~~f &&& ~~~(d ^^^ e)) - 6 * ~~~(e ^^^ f) + 3 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 1 * (f ^^^ ( ~~~d ||| (e ||| f))) - 6 * ( ~~~e ||| (d ^^^ f)) + 1 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 5 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 1 * (e ||| ~~~(d ||| f)) + 1 * ~~~(d &&& ~~~d) - 3 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 7 * (f ||| ~~~(d ^^^ e)) - 2 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 5 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 7 * (e ||| f) - 11 * (f ^^^ ~~~(d ||| ~~~e)) - 1 * ( ~~~d ||| ( ~~~e ||| f)) + 1 * (d &&& f) + 2 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 1 * ~~~( ~~~d &&& (e ||| f)) + 7 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 5 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 2 * ~~~(d ^^^ ( ~~~e ||| f)) + 7 * (d &&& ~~~e) + 1 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 1 * (f ||| ~~~(d ||| ~~~e)) + 4 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 5 * ~~~(d &&& ~~~e) + 11 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 1 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 2 * ((d &&& f) ||| (e &&& ~~~f)) + 2 * (e ^^^ ~~~(d ||| f)) + 2 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 2 * ((d ||| e) &&& ~~~(e ^^^ f)) - 5 * ((d &&& e) ^^^ (e ||| f)) - 3 * (e &&& (d ||| ~~~f)) - 1 * ~~~(d &&& (e ||| f)) + 4 * ~~~(d &&& ( ~~~e ||| f)) - 2 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * ~~~(d ||| e) - 5 * (f &&& (d ^^^ e)) + 1 * ~~~(d &&& e) + 2 * (d ||| (e ||| f)) + 5 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 1 * (e &&& (d ^^^ f)) - 1 * (d &&& (e ||| f)) + 1 * ~~~(d ^^^ (e &&& f)) + 11 * (f ^^^ (d &&& (e ||| f))) - 11 * (e ^^^ ~~~(d &&& (e ||| f))) + 2 * (e ^^^ ~~~(d ||| ~~~f)) + 1 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 7 * (f ||| ~~~(d ||| e)) - 40 * ~~~(d ||| (e ||| f)) - 25 * ~~~(d ||| ( ~~~e ||| f)) - 6 * ~~~( ~~~d ||| (e ||| f)) - 30 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 7 * ( ~~~d &&& ( ~~~e &&& f)) + 11 * ( ~~~d &&& (e &&& f)) + 18 * (d &&& ( ~~~e &&& f)) + 15 * (d &&& (e &&& f)) = 7 * ((e &&& f) ||| (d &&& (e ||| f))) - 1 * d := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2462 (x y : BitVec w) : +theorem e_2462 : 1 * ( ~~~d ||| ( ~~~e ||| f)) + 7 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * (e &&& ~~~f) - 1 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 11 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 1 * (e ^^^ ~~~(d ||| f)) - 3 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 1 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 2 * ~~~( ~~~d ||| (e ^^^ f)) + 4 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 7 * (f &&& ~~~(d &&& e)) - 11 * (f ||| ~~~(d ^^^ e)) + 2 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 3 * (e ^^^ ( ~~~d &&& (e ||| f))) + 4 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 5 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 5 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 3 * ((d &&& f) ||| (e &&& ~~~f)) + 11 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 2 * ( ~~~d ||| (e ^^^ f)) - 7 * (f ^^^ ~~~(d ||| ~~~e)) + 7 * (f ^^^ (d &&& ( ~~~e ||| f))) + 1 * ((d &&& e) ||| ~~~(e ||| f)) - 7 * (f ||| (d &&& ~~~e)) - 2 * (e ^^^ ~~~(d &&& (e ||| f))) + 1 * (e &&& f) + 7 * (f ^^^ (d &&& (e ||| f))) - 6 * (d ||| ( ~~~e ||| f)) + 7 * (d ^^^ ( ~~~e &&& f)) - 5 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 7 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 2 * (f ^^^ ~~~(d &&& (e ||| f))) + 2 * (e ^^^ (d ||| ( ~~~e ||| f))) - 1 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 7 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 11 * (e ^^^ ( ~~~d ||| (e &&& f))) - 1 * (f ^^^ ~~~(d ||| (e &&& f))) + 4 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 3 * ~~~(e ||| ~~~f) + 1 * (f ^^^ (d ||| ( ~~~e ||| f))) - 3 * (f ^^^ (d &&& ~~~e)) - 7 * (e ^^^ (d &&& (e ||| f))) + 1 * ((d ||| e) &&& ~~~(e ^^^ f)) + 1 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 1 * e + 1 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * ~~~(e &&& f) - 1 * ~~~(d &&& ~~~f) - 1 * ( ~~~d &&& ( ~~~e ||| f)) + 7 * ~~~(d &&& f) + 5 * (e ^^^ (d ||| (e &&& f))) + 1 * (e ^^^ ( ~~~d ||| (e ||| f))) - 6 * ~~~(d &&& ~~~d) + 1 * (e &&& ~~~(d &&& f)) + 1 * ~~~(d &&& (e ||| f)) + 5 * (e &&& ~~~(d &&& ~~~f)) - 1 * (f ^^^ (d ||| e)) + 11 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 2 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 2 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * (e ^^^ (d ||| (e ^^^ f))) + 11 * (d &&& e) - 1 * (d ^^^ ( ~~~e ||| f)) - 3 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 5 * (f ||| ~~~(d ||| ~~~e)) - 1 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 5 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 11 * (e ^^^ (d ||| (e ||| f))) + 16 * ~~~(d ||| (e ||| f)) - 4 * ~~~(d ||| ( ~~~e ||| f)) - 1 * ~~~( ~~~d ||| (e ||| f)) - 29 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 30 * ( ~~~d &&& ( ~~~e &&& f)) + 12 * ( ~~~d &&& (e &&& f)) + 3 * (d &&& ( ~~~e &&& f)) + 18 * (d &&& (e &&& f)) = 6 * (e ||| ~~~(d ||| ~~~f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2463 (x y : BitVec w) : +theorem e_2463 : - 1 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 1 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 5 * d + 1 * ~~~(e ||| ~~~f) + 2 * (d &&& f) - 2 * ( ~~~d ||| (e ||| f)) - 2 * (e ^^^ (d ||| ~~~f)) - 6 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 2 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * ((d ||| e) &&& ~~~(e ^^^ f)) - 6 * ((d &&& e) ||| (e ^^^ f)) - 3 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 1 * (f ||| ~~~(d ||| e)) - 6 * ~~~(d &&& (e ^^^ f)) - 11 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 11 * (d ||| (e &&& f)) + 1 * (f ^^^ ( ~~~d &&& (e ||| f))) + 11 * (f ^^^ (d &&& (e ||| f))) + 5 * ( ~~~f &&& (d ^^^ e)) + 1 * ( ~~~d ||| (e &&& f)) + 7 * (d ^^^ ( ~~~e &&& f)) + 1 * ((d ^^^ e) &&& (d ^^^ f)) + 2 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 1 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 6 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 5 * f - 1 * (f ^^^ ~~~(d &&& (e ||| f))) - 2 * ~~~(d &&& f) + 7 * (f &&& ~~~(d &&& e)) - 11 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 1 * (f ^^^ ( ~~~d ||| (e &&& f))) - 3 * (f ^^^ ~~~(d ||| e)) + 5 * ~~~(d &&& (e ||| f)) - 3 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 7 * (e ||| (d &&& f)) - 5 * ( ~~~f ||| (d ^^^ e)) - 2 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 1 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 5 * (f ^^^ (d ||| ( ~~~e &&& f))) - 5 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 1 * ((d &&& f) ||| ~~~(e ||| f)) + 11 * (d &&& ~~~e) - 3 * (d ||| f) - 7 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 7 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 3 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 2 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 1 * (e ^^^ (d &&& (e ^^^ f))) + 1 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 3 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 1 * (f ^^^ ~~~(d ||| ~~~e)) + 2 * (d ||| ( ~~~e &&& f)) - 1 * (f &&& (d ||| ~~~e)) + 7 * ( ~~~d ||| ( ~~~e &&& f)) + 3 * ~~~(d ^^^ ( ~~~e ||| f)) - 1 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 11 * (e ||| ~~~(d ||| ~~~f)) + 2 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 7 * (f ^^^ (d ||| (e ||| f))) + 1 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 2 * ~~~(d &&& ~~~d) + 2 * (e ^^^ (d &&& (e ||| f))) - 2 * (f ||| (d &&& e)) + 1 * (e ^^^ (d ||| ( ~~~e &&& f))) + 4 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 3 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 11 * (d &&& (e ^^^ f)) + 3 * e - 7 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 2 * (e ^^^ ~~~(d &&& f)) + 4 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 44 * ~~~(d ||| (e ||| f)) + 25 * ~~~(d ||| ( ~~~e ||| f)) + 24 * ~~~( ~~~d ||| (e ||| f)) + 45 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 12 * ( ~~~d &&& ( ~~~e &&& f)) + 44 * ( ~~~d &&& (e &&& f)) + 21 * (d &&& ( ~~~e &&& f)) + 62 * (d &&& (e &&& f)) = - 1 * (f ||| (d ^^^ e)) + 7 * (d ||| ( ~~~e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2464 (x y : BitVec w) : +theorem e_2464 : 3 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 7 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 6 * (f ^^^ (d &&& e)) - 7 * (d ^^^ ( ~~~e &&& f)) - 1 * (e ||| ~~~f) + 11 * (f ^^^ (d &&& (e ||| f))) - 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 1 * ( ~~~e ||| (d ^^^ f)) - 3 * (e ^^^ f) - 2 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 1 * ((d &&& f) ||| (e &&& ~~~f)) + 1 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 5 * ( ~~~e &&& (d ^^^ f)) + 1 * ~~~(d &&& ( ~~~e ||| f)) + 2 * (e &&& ~~~f) + 1 * (e ^^^ (d ||| (e ^^^ f))) - 6 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 6 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 1 * (e ||| ~~~(d ||| ~~~f)) - 1 * ( ~~~d ||| ( ~~~e ||| f)) + 5 * ( ~~~f &&& (d ^^^ e)) - 1 * (e ^^^ (d ||| (e ||| f))) + 5 * (d ^^^ (e ||| f)) + 1 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 3 * ((d ^^^ e) &&& (d ^^^ f)) - 1 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 4 * ~~~( ~~~d &&& (e ^^^ f)) + 4 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 2 * (f ^^^ (d &&& ~~~e)) + 3 * ((d &&& e) ||| ~~~(e ||| f)) + 2 * (f ^^^ (d ||| ( ~~~e &&& f))) + 1 * (e ^^^ ~~~(d &&& (e ||| f))) - 1 * (f ^^^ (d ||| (e ||| f))) + 2 * (f &&& (d ^^^ e)) - 11 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 3 * ~~~(d &&& (e ^^^ f)) - 11 * (f ^^^ ~~~(d &&& e)) - 1 * (d ^^^ e) - 7 * ((d &&& ~~~e) ||| (e ^^^ f)) - 7 * (d &&& e) - 2 * ~~~(d &&& (e ||| f)) + 5 * (f ^^^ ( ~~~d ||| (e ||| f))) + 7 * (d ||| e) - 2 * (f &&& ~~~(d &&& ~~~e)) - 1 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 2 * (f ||| (d ^^^ e)) + 1 * (f ^^^ (d &&& ( ~~~e ||| f))) - 2 * (d ||| ( ~~~e &&& f)) + 2 * ((d ^^^ e) ||| ~~~(d ^^^ f)) + 11 * (d ^^^ f) + 5 * ~~~( ~~~d &&& (e ||| f)) - 1 * ~~~(d &&& f) - 3 * (f ||| (d &&& ~~~e)) + 1 * (d &&& (e ||| f)) + 11 * (e ^^^ (d &&& ~~~f)) - 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 5 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 2 * (e ^^^ (d &&& (e ^^^ f))) + 4 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 1 * ~~~(d &&& e) - 5 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 11 * ( ~~~d ||| (e ||| f)) + 2 * ( ~~~d ||| (e ^^^ f)) - 3 * ~~~( ~~~d ||| (e &&& f)) + 2 * (f ^^^ ~~~(d ||| e)) + 4 * ((e &&& f) ||| (d &&& (e ||| f))) + 1 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 3 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 1 * ~~~(e &&& ~~~f) - 1 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 28 * ~~~(d ||| (e ||| f)) + 14 * ~~~(d ||| ( ~~~e ||| f)) - 10 * ~~~( ~~~d ||| (e ||| f)) - 10 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 23 * ( ~~~d &&& ( ~~~e &&& f)) - 18 * ( ~~~d &&& (e &&& f)) + 14 * (d &&& ( ~~~e &&& f)) + 32 * (d &&& (e &&& f)) = - 7 * ((d ||| e) &&& (e ^^^ f)) + 1 * (f ^^^ ( ~~~d ||| (e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2465 (x y : BitVec w) : +theorem e_2465 : - 3 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 4 * ~~~( ~~~d &&& (e &&& f)) + 1 * e - 3 * (e ||| (d ^^^ f)) - 2 * ~~~(d &&& ~~~f) - 5 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 1 * (e ||| ~~~(d ^^^ f)) + 2 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 6 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 11 * ((d ||| ~~~e) &&& (e ^^^ f)) - 11 * ~~~(d ^^^ e) - 1 * ( ~~~d ||| ( ~~~e ||| f)) - 2 * (e &&& (d ||| ~~~f)) + 2 * (d ||| (e ||| f)) - 1 * (e ^^^ ( ~~~d ||| (e ||| f))) + 1 * ( ~~~f &&& ~~~(d ^^^ e)) + 2 * (f ^^^ ( ~~~d ||| (e ||| f))) + 1 * ~~~(e &&& f) + 3 * ~~~(d &&& ~~~e) + 2 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 1 * (d ||| ~~~f) - 5 * (e ||| (d &&& f)) + 2 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 2 * (f ||| (d &&& ~~~e)) - 5 * (e ^^^ (d ||| ( ~~~e ||| f))) - 2 * (f ^^^ ~~~(d &&& ~~~e)) - 1 * ~~~(d &&& (e ||| f)) - 1 * (d ^^^ (e ||| f)) - 3 * ( ~~~d &&& (e ^^^ f)) + 1 * (e ^^^ ~~~(d &&& ~~~f)) + 3 * ((d &&& e) ||| ~~~(e ||| f)) - 6 * (e ^^^ ~~~(d &&& f)) + 7 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 2 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 5 * (f ^^^ ~~~(d &&& e)) - 6 * ((d &&& e) ^^^ (e ||| f)) - 11 * (e ^^^ f) - 6 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 4 * ~~~(d ||| ~~~f) + 4 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 1 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 1 * (e &&& (d ^^^ f)) + 1 * ( ~~~d ||| (e &&& f)) + 1 * (e ||| f) + 5 * (f ^^^ (d &&& ( ~~~e ||| f))) + 3 * (d ^^^ (e &&& f)) - 6 * (e ^^^ ~~~(d &&& (e ||| f))) + 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 4 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 7 * (e ||| ~~~(d ||| f)) - 1 * (d ||| ( ~~~e ||| f)) + 5 * (e ^^^ (d ||| f)) - 3 * (d ^^^ f) + 1 * ~~~(d ^^^ ( ~~~e &&& f)) + 11 * ~~~(d &&& f) + 5 * ~~~(d &&& (e &&& f)) - 1 * (d ||| (e &&& f)) + 1 * (d &&& (e ^^^ f)) - 11 * (e ^^^ (d &&& ~~~f)) - 2 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 3 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 2 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 1 * (e ^^^ ~~~(d &&& (e &&& f))) + 7 * ( ~~~e &&& (d ^^^ f)) + 3 * ~~~(d ^^^ ( ~~~e ||| f)) - 3 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 1 * (e ^^^ ~~~(d ||| ~~~f)) + 1 * ( ~~~f ||| (d ^^^ e)) - 1 * ((d &&& f) ||| (e &&& ~~~f)) + 4 * ((d &&& e) ^^^ (e ||| ~~~f)) + 1 * (e ^^^ (d ||| (e &&& f))) + 11 * ~~~(d ||| (e ||| f)) + 1 * ~~~(d ||| ( ~~~e ||| f)) - 25 * ~~~( ~~~d ||| (e ||| f)) + 11 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 28 * ( ~~~d &&& ( ~~~e &&& f)) - 7 * ( ~~~d &&& (e &&& f)) + 33 * (d &&& ( ~~~e &&& f)) + 20 * (d &&& (e &&& f)) = 6 * (d ^^^ e) + 7 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2466 (x y : BitVec w) : +theorem e_2466 : 3 * ~~~(d &&& (e &&& f)) - 6 * ~~~f - 1 * (e ^^^ (d &&& (e ||| f))) - 2 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 7 * (e ||| ~~~f) - 11 * ~~~(e &&& f) + 2 * (e &&& ~~~f) + 5 * (f ^^^ (d &&& ( ~~~e ||| f))) + 11 * (e ||| f) - 1 * (e ^^^ (d ||| (e ^^^ f))) + 1 * ~~~(d ^^^ f) - 1 * (d &&& (e ^^^ f)) - 2 * ((d ||| e) &&& ~~~(e ^^^ f)) + 4 * (f ^^^ (d ||| ( ~~~e &&& f))) - 11 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 7 * (f ^^^ ~~~(d &&& e)) + 1 * ~~~(e &&& ~~~f) - 1 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 11 * (e ^^^ ( ~~~d ||| (e ||| f))) - 7 * (e ||| (d &&& f)) - 2 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 1 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 4 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 3 * (d ^^^ ( ~~~e ||| f)) + 11 * (e &&& ~~~(d &&& ~~~f)) + 3 * ((e &&& f) ||| (d &&& (e ||| f))) + 5 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 2 * ( ~~~d ||| (e &&& f)) - 1 * ~~~(d ^^^ (e &&& f)) - 6 * ((d &&& e) ^^^ (e ||| f)) + 1 * ~~~e + 1 * (e ^^^ f) - 3 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 1 * ~~~(d &&& ( ~~~e ||| f)) - 3 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 11 * ((d &&& f) ||| ~~~(e ||| f)) + 4 * (e ^^^ (d ||| ( ~~~e &&& f))) - 1 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 5 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 5 * f - 7 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 2 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 5 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 4 * ((d ||| ~~~e) &&& (e ^^^ f)) + 4 * (e ||| (d &&& ~~~f)) + 1 * (f ||| (d ^^^ e)) - 2 * ~~~(d &&& (e ^^^ f)) + 2 * d - 1 * (e &&& (d ||| f)) + 2 * (f ||| (d &&& e)) - 6 * ~~~(d ||| (e ^^^ f)) + 1 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 2 * (e ^^^ ( ~~~d ||| (e &&& f))) + 2 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 3 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 7 * (f &&& ~~~(d ^^^ e)) + 2 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 1 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 6 * ~~~(d &&& ~~~f) + 7 * (e &&& (d ||| ~~~f)) + 2 * (e ||| ~~~(d ^^^ f)) - 3 * (f ||| ~~~(d ||| ~~~e)) - 11 * (e ^^^ ~~~(d &&& (e &&& f))) + 3 * ((d ^^^ e) &&& (d ^^^ f)) - 1 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 1 * ((d ^^^ e) ||| (d ^^^ f)) - 1 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 2 * (d ^^^ (e ^^^ f)) + 57 * ~~~(d ||| (e ||| f)) + 4 * ~~~(d ||| ( ~~~e ||| f)) + 9 * ~~~( ~~~d ||| (e ||| f)) - 12 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 28 * ( ~~~d &&& ( ~~~e &&& f)) + 6 * ( ~~~d &&& (e &&& f)) + 23 * (d &&& ( ~~~e &&& f)) - 18 * (d &&& (e &&& f)) = - 1 * ((d &&& e) ||| ~~~(e ||| f)) - 1 * (e ^^^ (d &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2467 (x y : BitVec w) : +theorem e_2467 : 1 * ( ~~~d ||| (e &&& f)) + 1 * (e ^^^ ( ~~~d &&& (e ||| f))) + 3 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 4 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * (e ||| ~~~(d ^^^ f)) + 1 * ( ~~~e ||| ~~~(d ^^^ f)) - 6 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 1 * ~~~(d &&& (e &&& f)) + 11 * (f ^^^ ~~~(d &&& (e &&& f))) - 3 * ~~~(e &&& ~~~f) + 4 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 7 * (f ||| ~~~(d ||| e)) + 2 * ((d &&& ~~~e) ||| (e ^^^ f)) - 5 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 1 * ( ~~~f ||| ~~~(d ^^^ e)) - 11 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 1 * (e ^^^ (d &&& (e ||| f))) - 3 * ~~~(d ||| (e ^^^ f)) + 3 * ~~~(d &&& ~~~f) - 11 * (e ^^^ (d &&& ( ~~~e ||| f))) - 1 * (f ^^^ (d &&& ~~~e)) - 7 * ~~~(d ||| e) + 2 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 1 * ~~~(d ||| ~~~f) + 3 * (d ||| f) + 7 * (e ^^^ ~~~(d &&& (e &&& f))) - 7 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 1 * ( ~~~d &&& (e ||| f)) + 1 * (f ||| (d &&& ~~~e)) + 5 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 2 * ((d &&& e) ||| ~~~(e ||| f)) - 11 * (d ||| ~~~e) + 4 * (d ^^^ (e &&& f)) + 2 * (e ^^^ ~~~(d ||| (e &&& f))) + 11 * (f ^^^ (d ||| ~~~e)) + 1 * e - 7 * f - 2 * (e ^^^ ~~~(d &&& (e ||| f))) - 1 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 1 * ((d &&& e) ||| ~~~(e ^^^ f)) + 2 * (f ^^^ ( ~~~d ||| (e &&& f))) + 7 * (e ||| (d &&& ~~~f)) + 3 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 11 * (f &&& (d ||| e)) + 2 * (e ||| ~~~(d ||| ~~~f)) - 6 * (e &&& ~~~f) - 3 * ~~~(d &&& f) - 2 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 7 * (e ^^^ (d ||| (e &&& f))) + 5 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 3 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 1 * ~~~(d &&& (e ^^^ f)) + 11 * ~~~(d &&& ~~~e) + 5 * (e ^^^ (d ||| (e ^^^ f))) - 2 * ((d ||| e) &&& (e ^^^ f)) - 1 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * (e ^^^ ~~~(d ||| f)) - 1 * (f &&& ~~~(d ^^^ e)) + 4 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 1 * (f ^^^ ~~~(d &&& e)) - 2 * ~~~( ~~~d ||| (e ^^^ f)) - 3 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 11 * (d ^^^ (e ||| f)) + 2 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 2 * (d ^^^ ( ~~~e ||| f)) - 1 * (d &&& ( ~~~e ||| f)) - 2 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 4 * ((d &&& f) ||| (e &&& ~~~f)) + 1 * (e ^^^ (d ||| ( ~~~e ||| f))) + 4 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 16 * ~~~(d ||| (e ||| f)) - 19 * ~~~(d ||| ( ~~~e ||| f)) - 28 * ~~~( ~~~d ||| (e ||| f)) - 15 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 19 * ( ~~~d &&& ( ~~~e &&& f)) - 50 * ( ~~~d &&& (e &&& f)) - 10 * (d &&& ( ~~~e &&& f)) - 54 * (d &&& (e &&& f)) = 7 * (e ^^^ (d ||| ( ~~~e &&& f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2468 (x y : BitVec w) : +theorem e_2468 : 1 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 2 * ~~~(e ^^^ f) + 3 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 5 * ( ~~~d ||| ( ~~~e ||| f)) - 1 * ~~~( ~~~d ||| (e ^^^ f)) - 7 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 2 * ~~~(d ^^^ e) + 5 * (e &&& (d ^^^ f)) + 2 * (e &&& ~~~(d &&& ~~~f)) + 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 1 * (e ||| f) - 5 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 2 * ~~~(d ^^^ (e ||| f)) + 4 * ~~~(d ||| (e ^^^ f)) - 2 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 11 * ~~~(d &&& ~~~d) + 2 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 5 * (e ^^^ (d &&& f)) + 1 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 1 * ((d &&& e) ||| (e ^^^ f)) + 5 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 1 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 11 * (f ^^^ ~~~(d &&& (e &&& f))) - 6 * (d &&& f) + 7 * (f ^^^ (d ||| ( ~~~e &&& f))) + 7 * (d ||| (e &&& f)) + 3 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 6 * (f ^^^ ~~~(d &&& (e ||| f))) - 1 * ((d &&& ~~~e) ||| (e ^^^ f)) - 6 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 1 * (e ^^^ f) + 11 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 6 * (d ||| ( ~~~e ||| f)) - 2 * ~~~(d ||| ~~~f) + 5 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 5 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 3 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 3 * ( ~~~e ||| (d ^^^ f)) + 7 * (e ^^^ ~~~(d &&& f)) + 11 * (d &&& ~~~e) - 1 * ( ~~~e &&& (d ^^^ f)) + 1 * ((d &&& e) ||| ~~~(e ||| f)) - 1 * (e ^^^ ( ~~~d ||| (e ||| f))) - 2 * (e ^^^ ~~~(d ||| (e &&& f))) + 4 * (e ^^^ (d ||| ( ~~~e &&& f))) + 7 * ( ~~~f &&& (d ^^^ e)) - 6 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 4 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 3 * (d ||| (e ^^^ f)) + 2 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 1 * ((d &&& f) ||| ~~~(e ||| f)) - 11 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 2 * (e ||| (d &&& f)) + 4 * (e ^^^ (d ||| (e ||| f))) - 3 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 2 * ~~~(d ^^^ ( ~~~e &&& f)) + 1 * (e ^^^ ~~~(d &&& (e ||| f))) - 11 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 4 * (f ^^^ ( ~~~d ||| (e ||| f))) + 2 * (d ||| (e ||| f)) + 2 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 1 * (e ^^^ (d &&& ( ~~~e ||| f))) - 1 * (e ||| ~~~(d ||| f)) - 2 * ((d ||| ~~~e) &&& (e ^^^ f)) + 7 * (f ^^^ (d ||| e)) + 2 * ( ~~~d &&& ( ~~~e ||| f)) + 2 * (e ^^^ (d &&& (e ^^^ f))) + 3 * ~~~(d &&& ~~~f) + 2 * ~~~( ~~~d &&& (e ^^^ f)) - 6 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 22 * ~~~(d ||| (e ||| f)) - 24 * ~~~(d ||| ( ~~~e ||| f)) - 27 * ~~~( ~~~d ||| (e ||| f)) - 43 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 27 * ( ~~~d &&& ( ~~~e &&& f)) - 17 * ( ~~~d &&& (e &&& f)) + 1 * (d &&& ( ~~~e &&& f)) + 29 * (d &&& (e &&& f)) = 3 * (f ^^^ (d &&& ~~~e)) + 1 * ( ~~~f ||| (d ^^^ e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2469 (x y : BitVec w) : +theorem e_2469 : 1 * (d ||| ~~~f) - 1 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 1 * ~~~(d ^^^ ( ~~~e &&& f)) + 7 * (e &&& ~~~(d &&& ~~~f)) - 2 * (f &&& (d ^^^ e)) + 5 * (d ||| (e ||| f)) - 1 * ((d &&& e) ||| ~~~(e ||| f)) - 2 * (e &&& (d ||| f)) + 2 * (e ^^^ ~~~(d &&& (e &&& f))) - 5 * ~~~( ~~~d &&& (e ^^^ f)) - 3 * (e ^^^ ~~~(d &&& (e ||| f))) + 7 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 4 * ( ~~~e ||| ~~~(d ^^^ f)) + 2 * (f ||| ~~~(d ||| ~~~e)) - 11 * (f ^^^ (d ||| ( ~~~e &&& f))) - 6 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 3 * ((d &&& e) ^^^ (e ||| ~~~f)) - 11 * (f ||| (d &&& e)) + 1 * (f ^^^ ~~~(d &&& ~~~e)) - 11 * (d ||| ( ~~~e ||| f)) - 1 * ~~~(d &&& ( ~~~e ||| f)) - 6 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 1 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 5 * (f ||| ~~~(d ||| e)) + 3 * ((d &&& e) ||| ~~~(e ^^^ f)) + 3 * (d &&& (e ^^^ f)) - 7 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 3 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 1 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 1 * (e ||| ~~~(d ||| f)) - 7 * (d ^^^ (e &&& f)) - 2 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 1 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * (f ^^^ ( ~~~d ||| (e ||| f))) + 4 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 1 * (e &&& (d ||| ~~~f)) + 1 * ~~~(d ^^^ ( ~~~e ||| f)) + 1 * ((d &&& f) ||| (e &&& ~~~f)) + 4 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 2 * ~~~(d &&& ( ~~~e &&& f)) - 1 * ( ~~~f ||| ~~~(d ^^^ e)) + 2 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 6 * ~~~(d &&& (e ||| f)) + 2 * ~~~(d ||| e) + 2 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 3 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 7 * (f ^^^ (d ||| (e ||| f))) - 2 * (e ^^^ (d &&& (e ^^^ f))) + 3 * ~~~d + 11 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 2 * ( ~~~d ||| (e ||| f)) + 5 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 5 * ~~~(d ||| ~~~e) - 2 * ~~~e - 3 * (f ^^^ ~~~(d &&& (e ||| f))) + 4 * (e ^^^ ~~~(d &&& ~~~f)) - 6 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 1 * (d ||| e) + 4 * ~~~(d &&& ~~~d) - 7 * (e ^^^ ~~~(d &&& f)) + 4 * (e ^^^ ( ~~~d &&& (e ||| f))) - 3 * (e ^^^ (d ||| (e ^^^ f))) + 1 * ~~~(d ^^^ f) - 7 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 5 * (f ^^^ (d ||| ~~~e)) - 1 * (d ^^^ f) - 1 * (d ^^^ ( ~~~e &&& f)) + 7 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 3 * (e ^^^ ( ~~~d ||| (e &&& f))) - 2 * (d &&& ( ~~~e ||| f)) + 22 * ~~~(d ||| (e ||| f)) + 2 * ~~~(d ||| ( ~~~e ||| f)) + 59 * ~~~( ~~~d ||| (e ||| f)) + 20 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 18 * ( ~~~d &&& ( ~~~e &&& f)) + 40 * ( ~~~d &&& (e &&& f)) + 1 * (d &&& ( ~~~e &&& f)) + 3 * (d &&& (e &&& f)) = - 1 * ((d ^^^ e) &&& (d ^^^ f)) - 2 * (e &&& ~~~(d ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2470 (x y : BitVec w) : +theorem e_2470 : - 1 * ( ~~~e &&& ~~~(d ^^^ f)) - 3 * f - 1 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 4 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 7 * ~~~(e &&& f) - 1 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 1 * (e ||| f) - 2 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 1 * ~~~(d &&& ( ~~~e &&& f)) + 2 * (e ^^^ ~~~(d ||| (e &&& f))) + 4 * ~~~f + 3 * (e ||| (d &&& ~~~f)) + 1 * ~~~(d &&& ~~~e) - 7 * (d ^^^ (e ^^^ f)) + 3 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 1 * ( ~~~d ||| (e &&& f)) - 3 * (f ^^^ ( ~~~d ||| (e &&& f))) - 6 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 2 * ((d &&& e) ^^^ (e ||| ~~~f)) - 11 * (d &&& (e ^^^ f)) + 5 * ((d ||| ~~~e) &&& (e ^^^ f)) - 1 * (d ||| ( ~~~e ||| f)) + 11 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 2 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 3 * (f ^^^ (d &&& ( ~~~e ||| f))) + 3 * (e ^^^ ~~~(d &&& (e ||| f))) - 2 * ~~~(e &&& ~~~f) - 11 * (e ^^^ ~~~(d &&& ~~~f)) + 2 * ~~~( ~~~d ||| (e &&& f)) + 4 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 11 * (f ^^^ ( ~~~d ||| (e ||| f))) + 11 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 7 * ~~~e + 4 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 5 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 11 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 4 * (d ^^^ ( ~~~e &&& f)) - 1 * (d ||| f) + 5 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 2 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 2 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 5 * (e &&& ~~~(d &&& f)) + 2 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 5 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 3 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 1 * (e ^^^ ~~~(d &&& f)) - 11 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 1 * ( ~~~d ||| ( ~~~e ||| f)) + 1 * ~~~(d ^^^ ( ~~~e ||| f)) - 11 * ((d &&& f) ||| ~~~(e ||| f)) - 5 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 1 * e - 3 * ~~~(d &&& ~~~d) + 5 * (f ^^^ (d ||| ( ~~~e &&& f))) - 1 * (e ^^^ ~~~(d &&& (e &&& f))) - 5 * (d ^^^ f) + 7 * (f &&& (d ||| e)) + 1 * ( ~~~d &&& (e ^^^ f)) + 1 * (e ^^^ (d &&& (e ||| f))) + 11 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 11 * (f ^^^ ~~~(d ||| (e &&& f))) + 7 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 1 * (e &&& ~~~(d &&& ~~~f)) + 1 * ( ~~~d ||| (e ||| f)) - 1 * ~~~(d &&& ~~~f) - 2 * (e &&& ~~~(d ^^^ f)) - 6 * (e ^^^ (d ||| (e &&& f))) - 1 * ~~~(d ||| f) + 3 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 11 * ((d &&& e) ||| (e ^^^ f)) + 8 * ~~~(d ||| (e ||| f)) - 35 * ~~~(d ||| ( ~~~e ||| f)) + 5 * ~~~( ~~~d ||| (e ||| f)) - 75 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 13 * ( ~~~d &&& ( ~~~e &&& f)) - 11 * ( ~~~d &&& (e &&& f)) + 31 * (d &&& ( ~~~e &&& f)) - 47 * (d &&& (e &&& f)) = - 1 * (f ^^^ (d ||| e)) - 5 * ((e &&& f) ||| (d &&& (e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2471 (x y : BitVec w) : +theorem e_2471 : 1 * (d &&& (e ||| f)) - 2 * ( ~~~d ||| (e ||| f)) + 3 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 1 * ~~~(d &&& ~~~f) + 3 * (f ^^^ (d ||| ~~~e)) - 1 * (e &&& ~~~(d ^^^ f)) + 2 * (e ^^^ ~~~(d &&& (e &&& f))) + 1 * ~~~(d ||| ~~~e) - 5 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * ~~~(d &&& ~~~e) - 6 * (e ^^^ ~~~(d &&& ~~~f)) + 7 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 3 * (e &&& f) + 3 * (f ^^^ ~~~(d ||| e)) - 1 * (e ^^^ ~~~(d ||| (e &&& f))) + 1 * ~~~( ~~~d &&& (e ^^^ f)) + 11 * (e ^^^ (d &&& ~~~f)) - 2 * (d &&& ~~~f) + 3 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 2 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 7 * (f ^^^ (d ||| (e ||| f))) - 7 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 4 * (e ^^^ (d ||| ~~~f)) + 1 * (e &&& ~~~(d &&& ~~~f)) + 1 * (f ^^^ (d ||| (e &&& f))) - 2 * ( ~~~d ||| (e &&& f)) + 4 * ( ~~~d ||| (e ^^^ f)) - 1 * d + 1 * ~~~(d ^^^ (e ^^^ f)) - 6 * ~~~(d &&& (e ^^^ f)) + 1 * (e ||| ~~~f) + 2 * (d ||| ~~~e) + 4 * ((e &&& f) ||| (d &&& (e ||| f))) - 11 * ~~~(d ^^^ (e ||| f)) - 1 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 1 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 1 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 11 * ~~~(e &&& ~~~f) - 1 * ~~~(e ||| ~~~f) + 5 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 2 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * (e ||| ~~~(d ||| ~~~f)) + 1 * ~~~( ~~~d &&& (e ||| f)) + 11 * (e ^^^ ~~~(d &&& f)) + 4 * ((d &&& f) ^^^ (e ||| f)) - 3 * ~~~(d ||| e) - 2 * (d &&& ( ~~~e ||| f)) + 3 * e - 11 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 6 * ~~~(d ^^^ f) + 1 * (e ^^^ (d &&& f)) - 2 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 2 * ( ~~~d &&& (e ^^^ f)) - 2 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 6 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 1 * ~~~(d &&& ( ~~~e &&& f)) + 7 * f - 2 * (f ^^^ ~~~(d &&& ~~~e)) - 3 * (e ^^^ ( ~~~d ||| (e &&& f))) - 11 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 7 * ((d &&& ~~~e) ||| (e ^^^ f)) + 2 * ~~~(d ^^^ ( ~~~e &&& f)) - 5 * (f ||| ~~~(d ||| e)) - 2 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 1 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 5 * (e ^^^ (d ||| (e ^^^ f))) - 11 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 7 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 7 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 5 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 2 * (d ||| f) + 22 * ~~~(d ||| (e ||| f)) + 6 * ~~~(d ||| ( ~~~e ||| f)) - 13 * ~~~( ~~~d ||| (e ||| f)) + 37 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 14 * ( ~~~d &&& ( ~~~e &&& f)) - 36 * ( ~~~d &&& (e &&& f)) + 51 * (d &&& ( ~~~e &&& f)) - 36 * (d &&& (e &&& f)) = 3 * (e ^^^ ~~~(d ||| ~~~f)) - 1 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2472 (x y : BitVec w) : +theorem e_2472 : - 2 * ~~~(d ^^^ ( ~~~e &&& f)) + 5 * (f ||| ~~~(d ^^^ e)) + 1 * ~~~(d ^^^ (e ^^^ f)) + 2 * (f ^^^ (d ||| ~~~e)) - 1 * (e &&& ~~~(d &&& f)) - 5 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 1 * (e ^^^ ~~~(d &&& ~~~f)) + 1 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 1 * ( ~~~d ||| (e ^^^ f)) - 1 * (e ^^^ (d ||| ( ~~~e ||| f))) - 1 * (f &&& ~~~(d ^^^ e)) - 3 * (d ^^^ e) + 2 * ~~~d - 2 * ~~~(d ^^^ ( ~~~e ||| f)) + 5 * ( ~~~e &&& ~~~(d ^^^ f)) + 2 * ( ~~~d ||| ( ~~~e &&& f)) - 1 * ( ~~~f &&& (d ^^^ e)) - 1 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 6 * ((d &&& e) ||| ~~~(e ||| f)) - 6 * (d ^^^ ( ~~~e &&& f)) - 7 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 5 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 7 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 6 * (e ^^^ (d ||| (e &&& f))) + 7 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 1 * (f ^^^ ~~~(d &&& e)) - 7 * (e ||| f) + 4 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 1 * (f ^^^ (d ||| ( ~~~e ||| f))) + 1 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 11 * (e ^^^ ( ~~~d ||| (e &&& f))) - 2 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 5 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 4 * (e ^^^ ~~~(d ||| ~~~f)) + 1 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 5 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 1 * (f ^^^ (d ||| e)) + 3 * ~~~(d &&& (e ^^^ f)) + 3 * (f &&& ~~~(d &&& e)) - 3 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 11 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 2 * (e ||| (d ^^^ f)) + 11 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 1 * ~~~( ~~~d &&& (e ^^^ f)) - 1 * e + 11 * ~~~(d &&& ~~~f) - 2 * (f ^^^ ( ~~~d ||| (e &&& f))) + 3 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 5 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 11 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * (e ||| ~~~(d ||| f)) + 1 * (d &&& f) + 1 * ( ~~~e ||| ~~~(d ^^^ f)) - 3 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 2 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * (e ^^^ ~~~(d &&& f)) - 2 * ~~~(d ||| f) + 3 * (f ^^^ (d ||| (e ||| f))) + 4 * ~~~(d ^^^ (e ||| f)) + 1 * ( ~~~f ||| (d ^^^ e)) - 5 * ((d &&& e) ^^^ (e ||| f)) - 11 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 4 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 2 * ((d &&& f) ||| (e &&& ~~~f)) - 3 * f + 2 * (e ^^^ f) + 7 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 5 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 3 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 3 * (e &&& ~~~(d &&& ~~~f)) - 29 * ~~~(d ||| (e ||| f)) - 10 * ~~~(d ||| ( ~~~e ||| f)) - 3 * ~~~( ~~~d ||| (e ||| f)) + 6 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 47 * ( ~~~d &&& ( ~~~e &&& f)) - 19 * ( ~~~d &&& (e &&& f)) - 11 * (d &&& ( ~~~e &&& f)) - 8 * (d &&& (e &&& f)) = - 5 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2473 (x y : BitVec w) : +theorem e_2473 : 1 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 11 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 1 * ~~~(d &&& f) + 7 * (d &&& f) + 1 * ( ~~~d ||| (e ||| f)) + 2 * ( ~~~d &&& ( ~~~e ||| f)) + 1 * (e ^^^ (d &&& f)) + 5 * (d ^^^ (e ||| f)) - 6 * (e ||| ~~~(d ^^^ f)) + 1 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 2 * (d ||| ~~~f) + 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 7 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 2 * (e ^^^ ( ~~~d ||| (e ||| f))) + 2 * (f ^^^ (d ||| ( ~~~e ||| f))) + 11 * (d ^^^ (e ^^^ f)) - 3 * (f ^^^ ( ~~~d ||| (e ||| f))) - 1 * ((d &&& f) ||| (e &&& ~~~f)) - 5 * ( ~~~e &&& (d ^^^ f)) - 5 * ~~~(d ^^^ (e &&& f)) - 1 * (e ^^^ ~~~(d ||| ~~~f)) + 2 * ((d &&& e) ||| ~~~(e ||| f)) + 1 * (f &&& ~~~(d &&& e)) - 7 * (d &&& ( ~~~e ||| f)) + 2 * f - 2 * ~~~(d ||| ~~~f) - 2 * ( ~~~d ||| (e &&& f)) - 6 * (d &&& ~~~f) - 3 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 11 * (f ^^^ ( ~~~d ||| (e &&& f))) - 3 * (e &&& (d ||| ~~~f)) + 7 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * (f ^^^ ~~~(d &&& ~~~e)) + 4 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 2 * (f ||| (d &&& e)) + 2 * (f ||| ~~~(d ||| ~~~e)) - 1 * (f ^^^ (d &&& ( ~~~e ||| f))) + 1 * (d ^^^ (e &&& f)) - 11 * ~~~(d ^^^ (e ||| f)) - 2 * (e ^^^ (d ||| (e ||| f))) + 3 * (e ||| (d &&& ~~~f)) - 2 * ( ~~~f &&& ~~~(d ^^^ e)) + 3 * (f ^^^ ~~~(d &&& (e &&& f))) + 1 * (e ||| (d ^^^ f)) + 7 * (f ||| (d ^^^ e)) - 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 2 * ~~~(d ||| e) + 11 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 4 * (d ||| (e ||| f)) - 11 * (f ||| ~~~(d ||| e)) - 7 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 1 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 1 * ((d &&& ~~~e) ||| (e ^^^ f)) - 1 * ~~~(d ^^^ f) - 7 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 5 * (f ^^^ ~~~(d &&& e)) - 2 * ((d &&& e) ^^^ (e ||| f)) - 11 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 1 * ~~~(e &&& f) + 11 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 11 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 5 * ~~~(d ||| (e &&& f)) - 5 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 5 * ( ~~~d ||| (e ^^^ f)) - 1 * (e ||| f) - 1 * ~~~(e ||| ~~~f) - 1 * ~~~(d &&& (e ^^^ f)) + 1 * (d ||| ( ~~~e ||| f)) + 3 * ((e &&& f) ||| (d &&& (e ||| f))) + 5 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 1 * (d &&& ~~~e) + 45 * ~~~(d ||| (e ||| f)) + 33 * ~~~(d ||| ( ~~~e ||| f)) + 1 * ~~~( ~~~d ||| (e ||| f)) + 45 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 3 * ( ~~~d &&& (e &&& f)) + 12 * (d &&& ( ~~~e &&& f)) + 9 * (d &&& (e &&& f)) = 2 * (f ^^^ (d ||| (e ||| f))) + 5 * (e ||| ~~~f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2474 (x y : BitVec w) : +theorem e_2474 : - 2 * ~~~(d ^^^ (e &&& f)) + 5 * (e ^^^ ~~~(d &&& (e &&& f))) + 3 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 5 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 1 * (f ^^^ ( ~~~d ||| (e &&& f))) + 4 * ((d ||| ~~~e) &&& (e ^^^ f)) - 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 6 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * ((d &&& e) ||| ~~~(e ^^^ f)) - 7 * (e &&& (d ||| f)) - 2 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * (d ||| (e ^^^ f)) - 5 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 2 * (e ||| (d &&& ~~~f)) + 1 * (d ^^^ (e ||| f)) - 7 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 5 * (f ^^^ ~~~(d ||| e)) + 2 * (f ^^^ ~~~(d ||| ~~~e)) + 3 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 5 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 2 * (f ^^^ (d ||| (e &&& f))) - 1 * ( ~~~d ||| ( ~~~e ||| f)) - 5 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 1 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 7 * (d &&& (e ^^^ f)) - 6 * (e ||| ~~~f) + 4 * d + 2 * (e ^^^ (d ||| f)) - 2 * (f ^^^ (d ||| (e ||| f))) + 1 * ( ~~~d &&& (e ^^^ f)) - 3 * (d &&& (e ||| f)) + 1 * (d ||| e) + 3 * (d ^^^ e) - 1 * (e &&& (d ^^^ f)) - 5 * ( ~~~e &&& (d ^^^ f)) + 1 * (e ^^^ (d &&& ~~~f)) - 2 * ((d &&& e) ^^^ (e ||| ~~~f)) + 2 * ~~~(d ^^^ ( ~~~e &&& f)) + 2 * (e ^^^ (d ||| (e &&& f))) + 2 * (f ^^^ (d &&& ( ~~~e ||| f))) + 2 * ~~~(d ^^^ (e ^^^ f)) - 5 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 2 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 11 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 3 * (e ^^^ (d &&& ( ~~~e ||| f))) - 7 * (d ^^^ ( ~~~e &&& f)) + 5 * ~~~(d ||| (e &&& f)) + 3 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 7 * ~~~( ~~~d &&& (e ||| f)) + 4 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 1 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 4 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 7 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 1 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 6 * (f ||| (d &&& e)) + 11 * ( ~~~f &&& (d ^^^ e)) + 3 * ( ~~~e ||| ~~~(d ^^^ f)) + 1 * ((d &&& e) ||| ~~~(e ||| f)) + 5 * (e ||| ~~~(d ||| ~~~f)) + 2 * ~~~(e ^^^ f) + 11 * ( ~~~d ||| ( ~~~e &&& f)) - 11 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 2 * ~~~(d ||| (e ^^^ f)) - 11 * (d ||| (e ||| f)) + 11 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 1 * ((d ^^^ e) ||| (d ^^^ f)) + 1 * ( ~~~f &&& ~~~(d ^^^ e)) - 11 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 2 * (f ^^^ ~~~(d &&& (e &&& f))) + 2 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 11 * (e ^^^ (d ||| (e ||| f))) - 3 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 2 * ~~~(d ^^^ ( ~~~e ||| f)) + 3 * ~~~(d ||| ( ~~~e ||| f)) + 17 * ~~~( ~~~d ||| (e ||| f)) + 52 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 10 * ( ~~~d &&& ( ~~~e &&& f)) + 50 * ( ~~~d &&& (e &&& f)) - 20 * (d &&& ( ~~~e &&& f)) + 40 * (d &&& (e &&& f)) = - 1 * (f ^^^ (d &&& e)) + 1 * (d ||| ( ~~~e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2475 (x y : BitVec w) : +theorem e_2475 : - 2 * ( ~~~e &&& (d ^^^ f)) - 3 * (f ^^^ (d ||| ~~~e)) - 6 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 6 * (e &&& ~~~(d &&& f)) + 3 * ~~~( ~~~d &&& (e ||| f)) - 11 * (e ^^^ ~~~(d &&& ~~~f)) + 11 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 6 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 4 * (f ||| ~~~(d ^^^ e)) - 5 * (f &&& ~~~(d &&& ~~~e)) + 4 * ~~~(d ^^^ ( ~~~e &&& f)) - 2 * (e &&& ~~~(d ^^^ f)) - 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 1 * (f ||| (d &&& ~~~e)) - 1 * (e ^^^ ( ~~~d ||| (e ||| f))) + 11 * ((e &&& f) ||| (d &&& (e ||| f))) + 1 * ~~~(e &&& ~~~f) + 5 * ~~~(e ||| f) - 1 * (f ^^^ (d ||| (e ||| f))) - 2 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 3 * (f ^^^ ~~~(d &&& (e ||| f))) + 1 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 11 * (d &&& (e ^^^ f)) + 2 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 2 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 2 * (f ^^^ (d ||| ( ~~~e &&& f))) - 2 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 5 * (d &&& ~~~f) - 1 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 3 * ~~~(d ||| (e &&& f)) + 4 * ~~~(d ^^^ (e &&& f)) + 2 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 7 * (e &&& f) - 7 * ~~~(d ^^^ e) + 1 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 1 * ~~~(d &&& e) - 1 * ~~~(d &&& (e ^^^ f)) + 3 * (f ^^^ (d ||| e)) - 5 * (f ^^^ ~~~(d &&& (e &&& f))) + 1 * (e ^^^ ~~~(d ||| ~~~f)) - 7 * ( ~~~d &&& (e ^^^ f)) + 11 * (f ^^^ (d ||| ( ~~~e ||| f))) - 2 * ( ~~~d ||| (e &&& f)) - 11 * ((d &&& ~~~e) ||| (e ^^^ f)) + 7 * (e ||| ~~~(d ||| f)) - 1 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 7 * ((d ^^^ e) ||| ~~~(d ^^^ f)) + 1 * (f ^^^ ( ~~~d ||| (e &&& f))) - 5 * ~~~e + 2 * ( ~~~d &&& ( ~~~e ||| f)) + 2 * (e ^^^ ( ~~~d &&& (e ||| f))) + 11 * (f ^^^ (d &&& (e ||| f))) + 1 * ~~~(d &&& ( ~~~e ||| f)) + 7 * (e ||| ~~~(d ||| ~~~f)) + 5 * ((d ||| e) &&& ~~~(e ^^^ f)) - 5 * (e ||| ~~~(d ^^^ f)) + 5 * ~~~(d ||| f) - 2 * (f ^^^ ~~~(d &&& ~~~e)) - 1 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 1 * f - 3 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 3 * (e ^^^ (d &&& (e ^^^ f))) - 7 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 1 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 1 * ~~~( ~~~d ||| (e &&& f)) + 2 * ~~~(d &&& ~~~d) - 1 * (e ^^^ (d ||| ( ~~~e ||| f))) + 1 * ((d ^^^ e) ||| (d ^^^ f)) + 1 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 1 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 6 * (e ||| (d &&& f)) - 6 * (d ^^^ ( ~~~e &&& f)) - 7 * ~~~(d ||| (e ||| f)) + 3 * ~~~(d ||| ( ~~~e ||| f)) + 27 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 47 * ( ~~~d &&& ( ~~~e &&& f)) - 25 * ( ~~~d &&& (e &&& f)) + 39 * (d &&& ( ~~~e &&& f)) + 17 * (d &&& (e &&& f)) = - 23 * ~~~( ~~~d ||| (e ||| f)) + 7 * (d ||| ~~~f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2476 (x y : BitVec w) : +theorem e_2476 : 3 * (e ^^^ ~~~(d &&& (e &&& f))) + 11 * (d ||| ~~~f) + 2 * (f ^^^ ~~~(d &&& (e &&& f))) - 7 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 11 * ((d ^^^ e) ||| (d ^^^ f)) - 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 1 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 7 * (e ^^^ (d ||| f)) - 11 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 1 * ( ~~~d ||| (e ^^^ f)) + 2 * (f ||| ~~~(d ||| e)) - 5 * ~~~( ~~~d &&& (e &&& f)) + 1 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 5 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 4 * (f ^^^ ~~~(d &&& ~~~e)) + 5 * ~~~(d ||| e) - 1 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 6 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 2 * (d ||| e) + 3 * ((e &&& f) ||| (d &&& (e ||| f))) + 7 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 3 * (d &&& ( ~~~e ||| f)) + 1 * ( ~~~e &&& ~~~(d ^^^ f)) - 1 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 7 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 2 * (e &&& ~~~(d &&& f)) - 1 * ( ~~~e &&& (d ^^^ f)) - 11 * (e ^^^ ( ~~~d &&& (e ||| f))) + 3 * (f ^^^ (d ||| (e &&& f))) + 5 * ~~~(d ||| (e ^^^ f)) + 3 * ~~~(d ^^^ (e ||| f)) + 1 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * (e ^^^ (d ||| (e ^^^ f))) - 2 * (e ||| ~~~(d ||| ~~~f)) + 1 * ((d ||| e) &&& (e ^^^ f)) - 2 * (d &&& (e ^^^ f)) + 2 * (f ^^^ ( ~~~d ||| (e ||| f))) + 4 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 2 * (e &&& (d ||| f)) - 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 1 * (e ^^^ (d &&& ~~~f)) - 5 * (e ^^^ f) - 2 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 11 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 1 * ~~~(d ^^^ ( ~~~e ||| f)) - 1 * ( ~~~e ||| ~~~(d ^^^ f)) + 1 * (f &&& ~~~(d ^^^ e)) - 2 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 1 * (e ^^^ ~~~(d ||| ~~~f)) - 11 * (d &&& e) - 6 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 1 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 3 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 3 * (f ^^^ ~~~(d ||| (e &&& f))) + 5 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 5 * ~~~( ~~~d ||| (e &&& f)) - 1 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 3 * ~~~( ~~~d &&& (e ||| f)) + 2 * ((d &&& f) ||| (e &&& ~~~f)) - 11 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 11 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 1 * ~~~(d &&& ~~~d) - 3 * (e ^^^ (d ||| ( ~~~e &&& f))) + 7 * ~~~(d &&& e) + 1 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 1 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 2 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 7 * (e &&& ~~~f) - 6 * (f ^^^ (d &&& ( ~~~e ||| f))) - 6 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 64 * ~~~(d ||| (e ||| f)) - 14 * ~~~(d ||| ( ~~~e ||| f)) + 31 * ~~~( ~~~d ||| (e ||| f)) + 55 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 29 * ( ~~~d &&& ( ~~~e &&& f)) + 43 * ( ~~~d &&& (e &&& f)) + 11 * (d &&& ( ~~~e &&& f)) + 35 * (d &&& (e &&& f)) = 1 * (e ||| (d &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2477 (x y : BitVec w) : +theorem e_2477 : - 6 * (e &&& f) + 3 * ~~~(d ^^^ ( ~~~e &&& f)) + 1 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 2 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 7 * ~~~(d &&& ~~~f) - 7 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 1 * (f ^^^ (d ||| (e &&& f))) + 11 * (e ||| ~~~f) + 11 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * ((e &&& f) ||| (d &&& (e ||| f))) + 4 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 2 * (f ^^^ ~~~(d &&& (e &&& f))) + 2 * (f ^^^ ~~~(d &&& e)) - 1 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 3 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 6 * ( ~~~d &&& (e ||| f)) - 2 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 11 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 2 * (e &&& (d ||| ~~~f)) + 2 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 3 * (d ^^^ (e &&& f)) + 7 * (f &&& (d ||| e)) + 4 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 6 * (d ^^^ ( ~~~e ||| f)) + 4 * (e &&& (d ^^^ f)) - 11 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 2 * ( ~~~e ||| ~~~(d ^^^ f)) - 11 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 1 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 2 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 2 * (f ^^^ (d ||| (e ||| f))) - 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 11 * ( ~~~d ||| ( ~~~e &&& f)) - 7 * (f &&& ~~~(d &&& ~~~e)) + 5 * (d ||| (e &&& f)) + 2 * e - 1 * ~~~(e ||| ~~~f) + 1 * ~~~(e ||| f) + 5 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 1 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 1 * ((d &&& e) ^^^ (e ||| f)) - 11 * ~~~(e ^^^ f) - 1 * (d ||| e) + 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 3 * (d &&& (e ^^^ f)) - 2 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 3 * (f ^^^ ~~~(d ||| ~~~e)) + 1 * (f ^^^ (d &&& ~~~e)) - 6 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 6 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * ~~~f - 2 * (f ||| ~~~(d ^^^ e)) - 11 * ((d &&& e) ||| ~~~(e ^^^ f)) + 4 * ( ~~~e &&& (d ^^^ f)) + 2 * ((d ||| e) &&& ~~~(e ^^^ f)) + 5 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 4 * (f ^^^ (d ||| ( ~~~e ||| f))) + 11 * ~~~(d ^^^ (e ^^^ f)) - 2 * ~~~(d &&& ~~~e) - 3 * (e ^^^ ( ~~~d ||| (e ||| f))) + 11 * (e ^^^ (d &&& ~~~f)) + 1 * (e ^^^ (d &&& f)) - 3 * (e ||| ~~~(d ^^^ f)) + 3 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 7 * (e ^^^ (d ||| ~~~f)) - 7 * ~~~(d ^^^ e) + 7 * (d ||| ( ~~~e ||| f)) - 1 * ((d ^^^ e) ||| (d ^^^ f)) - 7 * ~~~(d ||| ( ~~~e &&& f)) - 1 * (d ||| (e ||| f)) + 1 * (d ||| f) + 1 * ~~~(e &&& ~~~f) - 2 * ~~~(d ||| (e ||| f)) - 29 * ~~~(d ||| ( ~~~e ||| f)) - 63 * ~~~( ~~~d ||| (e ||| f)) - 15 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 22 * ( ~~~d &&& ( ~~~e &&& f)) - 12 * ( ~~~d &&& (e &&& f)) - 42 * (d &&& ( ~~~e &&& f)) = - 1 * ~~~(d ^^^ (e ||| f)) - 4 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2478 (x y : BitVec w) : +theorem e_2478 : - 5 * ~~~(d ||| (e ^^^ f)) + 2 * ~~~(d &&& e) - 2 * ~~~(d ^^^ f) - 7 * (d ||| f) - 6 * (d ^^^ e) - 7 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 1 * (d &&& ( ~~~e ||| f)) + 1 * (e ^^^ (d ||| f)) - 2 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 5 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 1 * (e &&& (d ||| ~~~f)) + 4 * (f &&& ~~~(d ^^^ e)) - 7 * ((d &&& e) ||| ~~~(e ||| f)) + 2 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 3 * ( ~~~f ||| (d ^^^ e)) - 1 * ( ~~~f &&& ~~~(d ^^^ e)) - 1 * (e ^^^ (d ||| (e &&& f))) + 1 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 3 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 1 * (e ^^^ (d &&& ~~~f)) + 1 * (f &&& (d ^^^ e)) - 3 * (d ||| ~~~f) - 1 * (e ^^^ ( ~~~d ||| (e &&& f))) + 7 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 3 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 1 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 2 * (e ^^^ ( ~~~d ||| (e ||| f))) + 1 * (d ||| (e ^^^ f)) + 1 * (e ^^^ (d ||| (e ^^^ f))) + 2 * (e ||| (d ^^^ f)) + 3 * (f ^^^ ~~~(d ||| e)) - 5 * (e &&& (d ^^^ f)) + 5 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * ~~~(d ||| ~~~e) + 1 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 1 * (d &&& e) - 2 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 5 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 4 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 2 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 2 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 1 * (e ||| (d &&& f)) + 11 * (f ^^^ ~~~(d &&& (e ||| f))) + 5 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 3 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 3 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 6 * (f &&& (d ||| ~~~e)) - 5 * ((d ^^^ e) ||| ~~~(d ^^^ f)) + 2 * ~~~(d &&& (e ^^^ f)) - 1 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 2 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 1 * ~~~(d &&& f) + 2 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 11 * (e ||| ~~~(d ||| ~~~f)) - 1 * ((d ||| ~~~e) &&& (e ^^^ f)) + 5 * (d &&& ~~~e) + 1 * (d &&& (e ||| f)) + 3 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 1 * ( ~~~d &&& (e ^^^ f)) - 1 * ~~~(d ||| f) - 1 * ~~~( ~~~d ||| (e &&& f)) - 2 * ~~~(d &&& ~~~d) + 2 * (f ||| (d ^^^ e)) - 6 * (f ^^^ ( ~~~d ||| (e &&& f))) - 11 * (e &&& ~~~(d &&& f)) - 7 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 7 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 11 * (f ^^^ ( ~~~d ||| (e ||| f))) + 1 * e + 7 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 8 * ~~~(d ||| (e ||| f)) + 31 * ~~~(d ||| ( ~~~e ||| f)) - 34 * ~~~( ~~~d ||| (e ||| f)) + 33 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 17 * ( ~~~d &&& ( ~~~e &&& f)) + 18 * ( ~~~d &&& (e &&& f)) - 15 * (d &&& ( ~~~e &&& f)) + 32 * (d &&& (e &&& f)) = - 5 * ( ~~~f &&& (d ^^^ e)) - 11 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2479 (x y : BitVec w) : +theorem e_2479 : - 5 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 11 * (e ^^^ ~~~(d &&& (e &&& f))) - 11 * ~~~( ~~~d &&& (e ^^^ f)) - 1 * (f &&& ~~~(d &&& e)) + 1 * (e ^^^ ~~~(d &&& (e ||| f))) + 2 * (f ^^^ ~~~(d &&& ~~~e)) - 2 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 5 * (e &&& (d ^^^ f)) + 7 * (e ^^^ (d ||| (e ^^^ f))) + 2 * ((e &&& f) ||| (d &&& (e ||| f))) - 1 * ( ~~~d ||| (e ||| f)) + 11 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 2 * (e ||| ~~~f) - 1 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 1 * (d ||| f) - 7 * ( ~~~d ||| ( ~~~e ||| f)) - 1 * (e ^^^ ~~~(d &&& ~~~f)) + 11 * (f ^^^ (d &&& (e ||| f))) + 4 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 3 * (f ^^^ (d &&& ~~~e)) - 1 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 4 * ~~~(d ||| (e &&& f)) - 1 * (d ^^^ e) - 11 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 2 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 11 * ~~~(d ||| f) + 3 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 2 * (f ^^^ ~~~(d ||| (e &&& f))) + 2 * ~~~(d ^^^ ( ~~~e &&& f)) + 11 * (d ^^^ (e &&& f)) + 2 * ~~~( ~~~d &&& (e &&& f)) + 1 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 7 * (f ^^^ ~~~(d ||| ~~~e)) + 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 4 * ( ~~~e ||| (d ^^^ f)) - 6 * ((d &&& e) ||| ~~~(e ||| f)) - 5 * ((d &&& f) ||| (e &&& ~~~f)) + 4 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 1 * ~~~(d ||| ~~~e) - 1 * ((d &&& f) ||| ~~~(e ||| f)) - 5 * (d ^^^ ( ~~~e &&& f)) - 3 * ~~~(d ||| ( ~~~e &&& f)) + 1 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 1 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 1 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 11 * (e ^^^ (d &&& ~~~f)) + 2 * ((d ||| e) &&& (e ^^^ f)) - 7 * (d &&& ( ~~~e ||| f)) - 1 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 3 * (e ||| ~~~(d ^^^ f)) - 6 * (e ||| ~~~(d ||| ~~~f)) - 6 * (f ^^^ (d ||| ( ~~~e ||| f))) - 1 * d - 3 * (d ||| (e &&& f)) - 3 * (e ^^^ (d ||| ( ~~~e ||| f))) - 6 * (d ^^^ (e ^^^ f)) - 5 * ( ~~~d ||| ( ~~~e &&& f)) - 1 * ( ~~~d ||| (e ^^^ f)) + 1 * (e ^^^ ~~~(d &&& f)) + 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 7 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 5 * ( ~~~f &&& ~~~(d ^^^ e)) + 11 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 1 * (d ||| ( ~~~e &&& f)) + 3 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 2 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 2 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 11 * ~~~(d &&& (e ^^^ f)) + 2 * e - 1 * (e ||| f) - 2 * ~~~(d ^^^ f) + 7 * (e ||| (d &&& f)) + 5 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 41 * ~~~(d ||| (e ||| f)) + 6 * ~~~(d ||| ( ~~~e ||| f)) - 18 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 11 * ( ~~~d &&& ( ~~~e &&& f)) - 34 * ( ~~~d &&& (e &&& f)) - 15 * (d &&& ( ~~~e &&& f)) + 43 * (d &&& (e &&& f)) = 21 * ~~~( ~~~d ||| (e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2480 (x y : BitVec w) : +theorem e_2480 : 5 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 3 * (e ^^^ (d &&& ~~~f)) + 5 * (e ||| ~~~(d ||| ~~~f)) - 2 * ~~~(d &&& ( ~~~e &&& f)) + 2 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 5 * (f ^^^ (d &&& ~~~e)) + 5 * ((d &&& e) ^^^ (e ||| f)) - 5 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 7 * (e &&& (d ||| ~~~f)) + 7 * (f ^^^ ~~~(d &&& ~~~e)) + 11 * ~~~e - 3 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 2 * (d ||| (e ||| f)) + 7 * (e ||| f) + 1 * (f ^^^ (d ||| e)) - 1 * (d &&& ~~~e) + 7 * ( ~~~d &&& ( ~~~e ||| f)) + 11 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 2 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 6 * (e ^^^ ~~~(d &&& ~~~f)) - 11 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 7 * (e ^^^ ~~~(d &&& f)) - 5 * (d ||| (e &&& f)) - 2 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 7 * ~~~(d ^^^ e) + 1 * (e ^^^ (d ||| ~~~f)) + 11 * ((d ||| e) &&& (e ^^^ f)) - 2 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 5 * (f &&& (d ||| ~~~e)) + 1 * (e &&& ~~~(d &&& ~~~f)) - 11 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 1 * ( ~~~d &&& (e ^^^ f)) + 1 * (e ^^^ (d &&& (e ^^^ f))) + 3 * ~~~(d &&& f) - 6 * ~~~(e ||| f) - 5 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 11 * (f ^^^ (d ||| (e &&& f))) - 7 * ((d &&& f) ||| (e &&& ~~~f)) - 6 * ( ~~~d ||| (e ||| f)) - 1 * ~~~(d &&& ~~~d) + 4 * ~~~(d ^^^ ( ~~~e ||| f)) + 1 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * ~~~(d &&& (e ^^^ f)) + 5 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 2 * (f ^^^ (d ||| (e ||| f))) + 2 * (e &&& (d ^^^ f)) + 2 * (e ||| ~~~(d ||| f)) - 3 * (d &&& e) + 1 * (e ||| ~~~(d ^^^ f)) + 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 1 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) - 7 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 11 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 3 * (d ^^^ (e ||| f)) - 3 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 5 * ~~~(d ||| ~~~e) - 11 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 2 * ~~~(d &&& (e &&& f)) - 3 * (f ^^^ ~~~(d &&& (e &&& f))) - 2 * f - 1 * ~~~(d &&& (e ||| f)) - 7 * (e ^^^ (d ||| (e &&& f))) + 5 * ((d ||| ~~~e) &&& (e ^^^ f)) + 1 * (f ||| (d &&& ~~~e)) + 1 * ((e &&& f) ||| (d &&& (e ||| f))) - 11 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 2 * (d ^^^ ( ~~~e ||| f)) + 3 * (f &&& ~~~(d ^^^ e)) - 5 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * (d &&& (e ^^^ f)) + 4 * (f ^^^ ~~~(d &&& e)) + 18 * ~~~(d ||| (e ||| f)) + 21 * ~~~(d ||| ( ~~~e ||| f)) + 49 * ~~~( ~~~d ||| (e ||| f)) + 27 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 10 * ( ~~~d &&& ( ~~~e &&& f)) - 38 * ( ~~~d &&& (e &&& f)) - 3 * (d &&& ( ~~~e &&& f)) + 4 * (d &&& (e &&& f)) = - 4 * (d ^^^ e) + 1 * ( ~~~d ||| (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2481 (x y : BitVec w) : +theorem e_2481 : 1 * (f ^^^ (d &&& ~~~e)) - 1 * (d ||| e) + 4 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 3 * (d &&& f) + 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * ( ~~~d ||| ( ~~~e ||| f)) - 2 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 7 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 2 * (e ||| f) + 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 2 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 3 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 2 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * (e ^^^ (d ||| (e &&& f))) - 2 * ~~~( ~~~d &&& (e ||| f)) + 11 * ((d ||| e) &&& ~~~(e ^^^ f)) - 11 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 6 * (f &&& ~~~(d &&& ~~~e)) - 7 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 1 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 11 * (f ^^^ (d ||| (e ||| f))) + 2 * ~~~(d &&& (e ^^^ f)) - 1 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 4 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 1 * ( ~~~e &&& (d ^^^ f)) - 7 * (f ^^^ (d ||| ~~~e)) - 3 * (e ||| ~~~(d ||| f)) - 7 * ~~~(d ^^^ (e &&& f)) - 11 * ~~~(e ||| f) - 1 * (f &&& (d ||| ~~~e)) + 5 * (f &&& (d ||| e)) + 5 * d - 2 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 3 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 1 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 2 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 1 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 1 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 1 * (d ^^^ (e &&& f)) + 2 * ~~~(d ^^^ (e ||| f)) + 2 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 11 * ((d &&& f) ^^^ (e ||| f)) + 4 * ( ~~~d &&& (e ||| f)) - 5 * (f &&& ~~~(d ^^^ e)) + 1 * ~~~(d &&& ( ~~~e &&& f)) - 5 * (e ^^^ f) + 1 * (f &&& (d ^^^ e)) + 7 * ~~~( ~~~d ||| (e &&& f)) - 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 3 * (d ||| ( ~~~e ||| f)) - 7 * ~~~(d ||| ~~~e) + 3 * (d ||| ~~~f) - 7 * (e &&& f) - 1 * (f ^^^ ( ~~~d &&& (e ||| f))) - 2 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 11 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 1 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 11 * ~~~d + 1 * ((d &&& ~~~e) ||| (e ^^^ f)) + 11 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 6 * ((d &&& e) ||| ~~~(e ||| f)) - 1 * ~~~(d ||| ( ~~~e &&& f)) + 1 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 11 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 2 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 6 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 7 * (e ^^^ (d ||| ( ~~~e ||| f))) - 3 * ~~~( ~~~d &&& (e ^^^ f)) + 1 * (f ^^^ (d &&& (e ||| f))) + 5 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 6 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 5 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 39 * ~~~(d ||| (e ||| f)) + 22 * ~~~(d ||| ( ~~~e ||| f)) - 26 * ~~~( ~~~d ||| (e ||| f)) - 3 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 21 * ( ~~~d &&& ( ~~~e &&& f)) + 41 * ( ~~~d &&& (e &&& f)) - 1 * (d &&& ( ~~~e &&& f)) + 10 * (d &&& (e &&& f)) = 1 * ( ~~~d ||| (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2482 (x y : BitVec w) : +theorem e_2482 : 1 * (e ^^^ ~~~(d &&& (e ||| f))) + 7 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 1 * (e ||| ~~~(d ||| f)) + 11 * ((d &&& e) ||| ~~~(e ^^^ f)) - 5 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 3 * (e &&& (d ||| f)) + 1 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 3 * (d ^^^ (e ||| f)) - 1 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 1 * ( ~~~d &&& (e ^^^ f)) + 2 * (e ^^^ ~~~(d &&& f)) + 2 * ~~~(d &&& (e ^^^ f)) + 5 * (f ||| ~~~(d ||| ~~~e)) + 2 * (d ||| (e ^^^ f)) - 1 * (e ^^^ ( ~~~d &&& (e ||| f))) + 7 * ((d &&& f) ||| (e &&& ~~~f)) - 2 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 1 * ( ~~~d ||| (e ||| f)) - 1 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 7 * ~~~( ~~~d &&& (e ||| f)) + 2 * (d ||| (e ||| f)) - 1 * ( ~~~e &&& (d ^^^ f)) + 2 * ~~~(d &&& ~~~d) + 1 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 11 * ((d &&& e) ^^^ (e ||| f)) - 1 * (e &&& ~~~f) - 2 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 5 * (f &&& ~~~(d &&& e)) - 3 * ((d &&& e) ||| ~~~(e ||| f)) - 3 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 4 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 1 * (f ^^^ (d &&& e)) - 7 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) + 7 * ((d &&& ~~~e) ||| (e ^^^ f)) - 6 * ~~~(d &&& f) + 2 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 5 * (d &&& ~~~e) - 5 * (e ^^^ (d &&& (e ||| f))) - 7 * (e &&& ~~~(d &&& ~~~f)) + 1 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 1 * (e ^^^ ( ~~~d ||| (e ||| f))) - 2 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 5 * ~~~(d ^^^ (e ^^^ f)) + 1 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 3 * (d &&& (e ||| f)) - 11 * ~~~(d ^^^ (e &&& f)) - 3 * (e ^^^ ~~~(d ||| (e &&& f))) + 11 * (e ^^^ f) - 1 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 7 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 1 * (d ||| f) + 4 * (e ||| ~~~(d ^^^ f)) - 2 * (f ^^^ ( ~~~d ||| (e &&& f))) - 2 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * (e ^^^ ~~~(d &&& (e &&& f))) - 5 * (e &&& f) + 1 * (f ^^^ (d ||| e)) + 1 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 5 * ~~~(d ||| ( ~~~e &&& f)) + 5 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 7 * (e ^^^ ~~~(d ||| ~~~f)) - 7 * f + 2 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 6 * ( ~~~f ||| ~~~(d ^^^ e)) + 4 * ( ~~~d ||| ( ~~~e &&& f)) - 3 * ((d &&& e) ||| (e ^^^ f)) + 4 * (e ^^^ (d ||| ( ~~~e &&& f))) + 1 * ~~~(d &&& ( ~~~e ||| f)) - 7 * (d ||| ~~~f) - 1 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 1 * (e ||| f) + 1 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 2 * ~~~( ~~~d &&& (e ^^^ f)) - 3 * ~~~(d ||| (e ||| f)) - 24 * ~~~(d ||| ( ~~~e ||| f)) - 23 * ~~~( ~~~d ||| (e ||| f)) - 66 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 15 * ( ~~~d &&& ( ~~~e &&& f)) - 29 * ( ~~~d &&& (e &&& f)) - 67 * (d &&& ( ~~~e &&& f)) - 3 * (d &&& (e &&& f)) = - 4 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 11 * ( ~~~d ||| (e ^^^ f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2483 (x y : BitVec w) : +theorem e_2483 : 1 * (d &&& ( ~~~e ||| f)) + 2 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 5 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 6 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 2 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 3 * (e ^^^ ( ~~~d ||| (e ||| f))) - 1 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 2 * (d ||| ~~~e) - 5 * (e ||| (d &&& f)) + 1 * (e ^^^ ( ~~~d &&& (e ^^^ f))) - 1 * (e ^^^ (d ||| f)) + 3 * (d ||| (e ^^^ f)) + 4 * (e ^^^ ~~~(d &&& (e &&& f))) - 6 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * (f ^^^ (d ||| ( ~~~e &&& f))) - 11 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 1 * ( ~~~f &&& ~~~(d ^^^ e)) - 5 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 1 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 7 * (f ^^^ ( ~~~d ||| (e ||| f))) - 1 * (e &&& (d ^^^ f)) + 3 * (e ||| (d ^^^ f)) + 1 * (d ||| ( ~~~e ||| f)) + 2 * ~~~d - 1 * ((d &&& f) ^^^ (e ||| f)) - 2 * (e ^^^ (d ||| (e ||| f))) - 1 * (f ^^^ ~~~(d &&& e)) - 7 * ~~~(d ||| f) - 2 * ~~~(d &&& ~~~d) + 1 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 2 * (f ||| (d ^^^ e)) + 7 * (e ^^^ (d &&& (e ^^^ f))) + 11 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 3 * ~~~(d ||| ( ~~~e &&& f)) + 7 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * ((d &&& f) ||| (e &&& ~~~f)) - 3 * (f ||| ~~~(d ||| ~~~e)) - 2 * (d ^^^ (e ^^^ f)) - 6 * ~~~(d ||| (e &&& f)) - 1 * (e ^^^ (d &&& ( ~~~e ||| f))) - 2 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 2 * (d &&& e) - 1 * (f ^^^ (d &&& ~~~e)) + 5 * (f ^^^ (d ||| (e &&& f))) - 11 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 11 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 2 * (d ^^^ f) - 1 * (f ||| (d &&& e)) - 1 * (e ^^^ (d ||| (e &&& f))) + 1 * ~~~(d ^^^ (e ^^^ f)) + 2 * ~~~( ~~~d ||| (e &&& f)) - 7 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 4 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 11 * (f ||| (d &&& ~~~e)) + 5 * (e ^^^ ~~~(d &&& ~~~f)) - 6 * (e ^^^ (d ||| (e ^^^ f))) + 5 * (f &&& (d ^^^ e)) + 4 * (f ^^^ ~~~(d &&& ~~~e)) + 1 * ~~~(d ||| (e ^^^ f)) + 11 * (e ||| f) - 1 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) + 4 * (e &&& ~~~(d ^^^ f)) + 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * ( ~~~e &&& ~~~(d ^^^ f)) - 1 * ~~~(d &&& ~~~e) + 1 * (f &&& (d ||| e)) + 3 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 3 * ((e &&& f) ||| (d &&& (e ||| f))) - 1 * (e &&& ~~~f) + 11 * (e ^^^ ( ~~~d &&& (e ||| f))) + 7 * (f ^^^ ~~~(d ||| e)) + 9 * ~~~(d ||| (e ||| f)) + 7 * ~~~(d ||| ( ~~~e ||| f)) + 11 * ~~~( ~~~d ||| (e ||| f)) - 13 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 3 * ( ~~~d &&& ( ~~~e &&& f)) + 9 * ( ~~~d &&& (e &&& f)) - 8 * (d &&& ( ~~~e &&& f)) - 32 * (d &&& (e &&& f)) = - 11 * ~~~(d ^^^ f) - 1 * (d ||| ~~~f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2484 (x y : BitVec w) : +theorem e_2484 : 11 * ~~~(e ||| f) + 1 * (e ^^^ ~~~(d ||| ~~~f)) + 2 * (e &&& (d ^^^ f)) + 11 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 1 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) - 2 * (f ^^^ ( ~~~d &&& (e ||| f))) + 2 * ~~~(d &&& ~~~d) + 5 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 11 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 2 * ( ~~~f &&& ~~~(d ^^^ e)) - 3 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 11 * (d ||| ~~~f) - 7 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 11 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 6 * ( ~~~d ||| (e ^^^ f)) + 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) - 3 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 1 * (f ^^^ (d ||| (e &&& f))) - 3 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 5 * (d ^^^ f) + 4 * (f ^^^ (d ||| e)) - 7 * (f ^^^ (d &&& e)) + 3 * (d &&& ~~~f) + 11 * (d &&& (e ||| f)) + 7 * (e ||| ~~~(d ||| ~~~f)) - 5 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 3 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 2 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 4 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 2 * (f ||| ~~~(d ^^^ e)) - 5 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 1 * ~~~(d &&& ( ~~~e &&& f)) - 6 * (e ||| (d ^^^ f)) + 5 * (d &&& ( ~~~e ||| f)) - 1 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) - 11 * ~~~(d ||| ~~~e) + 5 * (e ||| f) + 2 * (d ||| (e &&& f)) + 4 * (e ||| (d &&& ~~~f)) - 2 * ( ~~~f ||| ~~~(d ^^^ e)) + 2 * (e ^^^ (d ||| f)) + 1 * ~~~( ~~~d ||| (e &&& f)) + 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 1 * (d ^^^ ( ~~~e &&& f)) - 7 * (e ^^^ (d &&& ~~~f)) + 7 * ~~~(d ^^^ (e ||| f)) - 2 * (f ^^^ (d ||| (e ||| f))) - 5 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 6 * ~~~(d &&& f) - 1 * (f ^^^ ~~~(d ||| e)) + 3 * (e &&& ~~~f) - 3 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) - 2 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 4 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * ( ~~~f ||| (d ^^^ e)) + 1 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 1 * (e ^^^ (d ||| (e ^^^ f))) - 7 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 1 * (e ^^^ (d ||| (e &&& f))) - 1 * ((d &&& f) ^^^ (e ||| f)) - 1 * ( ~~~(d ||| e) ||| (e ^^^ f)) - 6 * ~~~( ~~~d &&& (e ||| f)) + 5 * (e ^^^ (d ||| ~~~f)) + 4 * ((d &&& e) ||| ~~~(e ||| f)) + 1 * e - 5 * ( ~~~e ||| (d ^^^ f)) + 1 * d - 2 * (d ||| ( ~~~e ||| f)) - 7 * (d &&& ~~~e) + 1 * (d ^^^ e) - 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 11 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 17 * ~~~(d ||| (e ||| f)) + 19 * ~~~(d ||| ( ~~~e ||| f)) - 12 * ~~~( ~~~d ||| (e ||| f)) - 5 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 32 * ( ~~~d &&& ( ~~~e &&& f)) + 36 * ( ~~~d &&& (e &&& f)) - 6 * (d &&& ( ~~~e &&& f)) - 17 * (d &&& (e &&& f)) = - 2 * (e &&& ~~~(d &&& ~~~f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2485 (x y : BitVec w) : +theorem e_2485 : - 1 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 1 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 7 * ( ~~~d ||| ( ~~~e ||| f)) + 1 * (e &&& (d ^^^ f)) + 7 * (d &&& e) + 11 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 2 * ((d &&& e) ||| ~~~(e ^^^ f)) - 1 * (e &&& (d ||| ~~~f)) - 5 * ( ~~~d ||| (e ^^^ f)) - 11 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 6 * (f ^^^ (d &&& ( ~~~e ||| f))) - 1 * ((d &&& e) ||| (e ^^^ f)) + 1 * (e ^^^ (d ||| ( ~~~e &&& f))) + 3 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 1 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 3 * (f ^^^ ~~~(d &&& e)) + 2 * ~~~( ~~~d &&& (e &&& f)) + 11 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 7 * (f ^^^ (d ||| ( ~~~e ||| f))) + 3 * (d &&& ~~~e) - 1 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 5 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 11 * (e ||| ~~~(d ||| f)) + 1 * (d ||| (e &&& f)) + 3 * (d ^^^ f) + 2 * (f &&& (d ||| ~~~e)) - 2 * (f ^^^ (d ||| e)) + 4 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 3 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 2 * (f ||| ~~~(d ||| e)) + 5 * (f ||| ~~~(d ||| ~~~e)) - 1 * (e ||| ~~~f) + 1 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 4 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 1 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 1 * (f ^^^ (d ||| ( ~~~e &&& f))) + 1 * (d ^^^ (e ^^^ f)) + 7 * (e ^^^ (d ||| ~~~f)) - 7 * ( ~~~(d &&& e) &&& (e ^^^ f)) - 3 * (d &&& f) - 1 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 7 * ~~~(d &&& (e ||| f)) - 7 * ( ~~~d &&& (e ^^^ f)) + 3 * ~~~(d &&& ~~~d) - 7 * (e &&& ~~~(d &&& ~~~f)) - 1 * (e ^^^ (d ||| ( ~~~e ||| f))) - 6 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 2 * (e ||| (d &&& ~~~f)) + 5 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 2 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 1 * (f ^^^ (d &&& (e ||| f))) + 3 * ~~~(d ^^^ (e &&& f)) - 3 * (f &&& ~~~(d &&& ~~~e)) + 2 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 3 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 5 * ~~~( ~~~d &&& (e ||| f)) - 1 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 2 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 3 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 11 * (f ^^^ ~~~(d ||| ~~~e)) - 11 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 2 * (d &&& (e ^^^ f)) + 2 * (e ||| (d &&& f)) + 1 * (f ^^^ ~~~(d &&& (e &&& f))) - 6 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 1 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 2 * ( ~~~d ||| (e ||| f)) - 7 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 6 * (f ||| (d ^^^ e)) - 11 * (e ^^^ (d ||| (e ^^^ f))) - 6 * ~~~(d ||| (e ||| f)) + 27 * ~~~(d ||| ( ~~~e ||| f)) + 12 * ~~~( ~~~d ||| (e ||| f)) - 2 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 21 * ( ~~~d &&& ( ~~~e &&& f)) - 9 * ( ~~~d &&& (e &&& f)) + 7 * (d &&& ( ~~~e &&& f)) + 31 * (d &&& (e &&& f)) = 5 * ~~~(e &&& ~~~f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2486 (x y : BitVec w) : +theorem e_2486 : 4 * ~~~(d &&& ~~~e) - 3 * ~~~(d ||| ( ~~~e &&& f)) + 5 * (f &&& ~~~(d &&& ~~~e)) - 7 * (d ||| ( ~~~e &&& f)) - 3 * ~~~( ~~~d &&& (e ||| f)) + 3 * (e ||| ~~~(d ||| f)) - 2 * ~~~( ~~~d &&& (e &&& f)) - 1 * f - 2 * ~~~(d &&& ~~~f) + 2 * ( ~~~d &&& (e ||| f)) + 1 * (f ||| (d &&& e)) - 1 * ~~~(d &&& (e ^^^ f)) - 3 * ( ~~~d ||| ( ~~~e ||| f)) + 7 * (f ^^^ (d &&& (e ||| f))) - 2 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 11 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 5 * (d ^^^ ( ~~~e ||| f)) - 1 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 2 * (e ^^^ (d ||| (e &&& f))) + 4 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 2 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 11 * (e ||| (d &&& f)) + 1 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) + 2 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 2 * ~~~(e ^^^ f) - 2 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 6 * (d ^^^ (e ^^^ f)) + 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 7 * ((d &&& e) ^^^ (e ||| f)) + 4 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 2 * ((d &&& f) ||| (e &&& ~~~f)) + 7 * (d ^^^ (e ||| f)) - 2 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 2 * (d &&& f) + 11 * ( ~~~d ||| ( ~~~e &&& f)) - 5 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 5 * (e ^^^ ~~~(d ||| f)) + 3 * (e &&& ~~~(d &&& ~~~f)) + 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 1 * (e &&& (d ||| f)) - 5 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * ~~~d + 1 * (e &&& ~~~f) + 3 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) + 4 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 4 * (e ||| (d &&& ~~~f)) - 1 * (d ^^^ e) + 2 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * (f ^^^ (d &&& ( ~~~e ||| f))) - 1 * (e ^^^ f) - 2 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 11 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) - 2 * (f ^^^ ~~~(d &&& e)) + 5 * (d ||| (e &&& f)) - 2 * (e ^^^ (d ||| ( ~~~e &&& f))) - 5 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 2 * (f ^^^ ~~~(d &&& (e ||| f))) - 3 * (d ||| ~~~f) + 1 * (f ^^^ (d ||| ( ~~~e ||| f))) + 1 * (f ||| ~~~(d ||| ~~~e)) + 3 * ( ~~~f &&& ~~~(d ^^^ e)) + 1 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 11 * (e ^^^ (d &&& f)) + 7 * (f ^^^ ( ~~~d &&& (e ||| f))) - 7 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 7 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 11 * (e ^^^ (d ||| ( ~~~e ||| f))) - 6 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 11 * ((d ||| e) &&& ~~~(e ^^^ f)) - 6 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 11 * (f ^^^ ~~~(d ||| e)) + 38 * ~~~(d ||| (e ||| f)) - 3 * ~~~(d ||| ( ~~~e ||| f)) + 30 * ~~~( ~~~d ||| (e ||| f)) - 25 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 17 * ( ~~~d &&& ( ~~~e &&& f)) - 7 * ( ~~~d &&& (e &&& f)) + 18 * (d &&& ( ~~~e &&& f)) + 43 * (d &&& (e &&& f)) = 7 * ~~~(d ^^^ ( ~~~e ||| f)) + 1 * (e ^^^ ~~~(d &&& ~~~f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2487 (x y : BitVec w) : +theorem e_2487 : - 11 * (e ^^^ (d &&& (e ^^^ f))) + 7 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 11 * (d ||| ( ~~~e &&& f)) - 2 * (d ||| (e &&& f)) + 2 * (e &&& (d ^^^ f)) + 4 * (f ^^^ ~~~(d &&& e)) + 1 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 11 * (e ||| (d &&& ~~~f)) + 5 * ( ~~~d ||| (e &&& f)) + 1 * (d &&& e) + 7 * (e ^^^ ~~~(d &&& f)) - 1 * (d ^^^ f) + 2 * (d &&& ( ~~~e ||| f)) - 7 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 7 * (f ^^^ ~~~(d &&& (e &&& f))) - 1 * (f ^^^ ( ~~~d ||| (e ||| f))) - 2 * ~~~(d ||| f) - 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 2 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 5 * (e ^^^ (d &&& f)) - 1 * (f ^^^ ~~~(d &&& ~~~e)) + 11 * ~~~(d ^^^ ( ~~~e &&& f)) - 7 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 2 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 1 * (e &&& f) + 1 * (f ^^^ (d ||| ( ~~~e &&& f))) + 2 * (e ^^^ ( ~~~d &&& (e ||| f))) + 1 * (f ||| ~~~(d ||| ~~~e)) - 2 * ~~~(e ||| ~~~f) - 2 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 1 * (f &&& ~~~(d &&& e)) - 1 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 3 * ~~~(d ^^^ (e &&& f)) + 4 * e - 1 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 1 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * (f ^^^ (d ||| ( ~~~e ||| f))) - 1 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 7 * ~~~(d &&& e) + 1 * ~~~(d ^^^ f) + 5 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 1 * (e ||| (d ^^^ f)) - 2 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * ~~~(d &&& (e ||| f)) + 11 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 7 * (e &&& ~~~(d ^^^ f)) + 5 * (e ^^^ (d &&& ( ~~~e ||| f))) + 11 * ~~~(d &&& ( ~~~e ||| f)) + 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 5 * (e ^^^ (d ||| f)) - 2 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 3 * ~~~(d &&& f) + 2 * (d ||| f) - 1 * ~~~( ~~~d &&& (e &&& f)) + 11 * ~~~(d ||| ( ~~~e &&& f)) - 6 * (f ^^^ (d ||| ~~~e)) + 5 * (f ^^^ (d &&& ~~~e)) - 5 * ~~~(d &&& ( ~~~e &&& f)) - 1 * (e ^^^ ~~~(d &&& (e ||| f))) + 5 * ~~~( ~~~d ||| (e ^^^ f)) - 1 * ((d ^^^ e) ||| ~~~(d ^^^ f)) + 7 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 1 * (e ^^^ (d &&& (e ||| f))) - 3 * (d ^^^ (e ^^^ f)) + 1 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 5 * ((d ^^^ e) &&& (d ^^^ f)) - 6 * ~~~( ~~~d ||| (e &&& f)) - 1 * ((d ||| e) &&& (e ^^^ f)) + 3 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 2 * (f ^^^ ~~~(d ||| (e &&& f))) + 3 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 3 * ( ~~~f &&& (d ^^^ e)) - 3 * ((d &&& f) ^^^ (e ||| f)) - 62 * ~~~(d ||| (e ||| f)) + 5 * ~~~(d ||| ( ~~~e ||| f)) - 10 * ~~~( ~~~d ||| (e ||| f)) - 4 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 30 * ( ~~~d &&& ( ~~~e &&& f)) - 35 * ( ~~~d &&& (e &&& f)) - 2 * (d &&& ( ~~~e &&& f)) - 34 * (d &&& (e &&& f)) = - 4 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2488 (x y : BitVec w) : +theorem e_2488 : 2 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 1 * (e ^^^ ~~~(d &&& ~~~f)) - 5 * ((d &&& f) ||| ~~~(e ||| f)) - 5 * ~~~(d ^^^ (e &&& f)) + 1 * ~~~(d ||| (e &&& f)) - 1 * ( ~~~d ||| (e ^^^ f)) + 1 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 11 * (e ^^^ ~~~(d &&& f)) - 1 * ((d ||| ~~~e) &&& (e ^^^ f)) + 2 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) + 3 * (d &&& ~~~f) + 2 * ((d &&& e) ^^^ (e ||| f)) - 3 * (e ^^^ (d ||| ~~~f)) + 1 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 5 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 7 * (f ^^^ (d &&& e)) + 11 * ( ~~~e ||| ~~~(d ^^^ f)) - 5 * ( ~~~d &&& ( ~~~e ||| f)) + 2 * ~~~(d ^^^ (e ^^^ f)) - 11 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 11 * (e &&& ~~~(d &&& ~~~f)) + 5 * ( ~~~e ||| (d ^^^ f)) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 3 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 5 * ((e &&& f) ||| (d &&& (e ||| f))) + 1 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (d &&& (e ^^^ f)) - 11 * (d ^^^ ( ~~~e &&& f)) + 2 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 5 * e - 11 * (e ^^^ ( ~~~d ||| (e ||| f))) + 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 11 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 2 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 5 * (e ^^^ ~~~(d ||| (e &&& f))) - 1 * (f ^^^ (d ||| e)) + 4 * (d ||| (e &&& f)) - 1 * ( ~~~e &&& (d ^^^ f)) - 1 * ( ~~~d &&& (e ^^^ f)) + 4 * ~~~d - 7 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * ~~~e + 1 * ~~~(e ^^^ f) + 5 * f - 1 * (e ^^^ ( ~~~d ||| (e &&& f))) + 1 * (f ^^^ ~~~(d ||| e)) - 11 * ~~~f - 6 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 5 * (f ^^^ ~~~(d &&& (e &&& f))) + 2 * ( ~~~e &&& ~~~(d ^^^ f)) - 1 * ~~~(d &&& (e &&& f)) + 2 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) + 3 * ~~~(d ^^^ ( ~~~e &&& f)) + 1 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) - 2 * (e ||| (d ^^^ f)) + 2 * ~~~(e ||| f) + 3 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 2 * (f ||| ~~~(d ^^^ e)) - 3 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 7 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 1 * (f ^^^ (d &&& (e ||| f))) - 3 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 2 * (e ||| f) + 7 * (d ||| f) - 2 * ~~~(e &&& ~~~f) - 1 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 7 * ~~~(d &&& ~~~e) - 6 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 4 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 2 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 4 * ( ~~~f &&& (d ^^^ e)) - 5 * ~~~(d &&& (e ||| f)) - 1 * ~~~(d ^^^ e) + 30 * ~~~(d ||| (e ||| f)) - 12 * ~~~(d ||| ( ~~~e ||| f)) + 30 * ~~~( ~~~d ||| (e ||| f)) - 12 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 15 * ( ~~~d &&& ( ~~~e &&& f)) - 14 * ( ~~~d &&& (e &&& f)) + 19 * (d &&& ( ~~~e &&& f)) + 7 * (d &&& (e &&& f)) = 1 * d + 7 * ( ~~~d ||| (e &&& f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2489 (x y : BitVec w) : +theorem e_2489 : 2 * (f ^^^ ~~~(d ||| ~~~e)) - 1 * ~~~( ~~~d ||| (e ^^^ f)) + 5 * ~~~(e &&& f) + 7 * ( ~~~d &&& (e ^^^ f)) - 5 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 1 * ~~~( ~~~d &&& (e &&& f)) - 1 * (e ^^^ ~~~(d &&& f)) + 7 * (e &&& ~~~(d ^^^ f)) - 7 * (e &&& (d ^^^ f)) - 1 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 1 * (d ||| e) + 11 * (e ^^^ (d ||| ( ~~~e ||| f))) - 1 * ~~~(e ^^^ f) - 1 * (e &&& (d ||| ~~~f)) - 7 * (e ^^^ ~~~(d ||| (e ^^^ f))) + 3 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) + 2 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 4 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) - 6 * ((d &&& e) ||| ~~~(e ||| f)) - 2 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 1 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 1 * (e ^^^ f) + 1 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 1 * (e ^^^ ( ~~~d ||| (e &&& f))) - 7 * ~~~(d ^^^ ( ~~~e &&& f)) - 2 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 2 * ( ~~~e &&& (d ^^^ f)) - 6 * (f ^^^ (d ||| ( ~~~e ||| f))) + 5 * (d &&& ~~~e) + 7 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 2 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 2 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 2 * ~~~(d ||| ~~~e) + 1 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * ~~~(d &&& (e ||| f)) + 1 * ((d &&& f) ||| (e &&& ~~~f)) + 5 * ( ~~~d ||| ( ~~~e &&& f)) + 4 * ~~~(d ||| ( ~~~e &&& f)) + 3 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 1 * d - 11 * (d ^^^ (e ||| f)) + 2 * (f ^^^ (d &&& (e ||| f))) + 2 * ((d &&& e) ^^^ (e ||| f)) + 5 * (f ^^^ ( ~~~d ||| (e ||| f))) + 1 * (f ^^^ (d ||| ~~~e)) - 6 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 4 * (f ^^^ ~~~(d &&& e)) - 3 * (f ^^^ (d &&& ( ~~~e ||| f))) - 7 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) + 3 * (d ||| (e ||| f)) - 7 * (f ^^^ (d &&& e)) + 3 * ~~~(d ^^^ f) - 2 * ( ~~~f ||| (d ^^^ e)) - 1 * ~~~(d ||| f) + 11 * ((d ^^^ e) &&& (d ^^^ f)) + 2 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 11 * ~~~(d ^^^ (e ||| f)) - 2 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 11 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 2 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 3 * (f ^^^ ( ~~~d &&& (e ||| f))) - 1 * ~~~(e ||| ~~~f) - 3 * (f &&& (d ||| e)) - 5 * ~~~d - 7 * ~~~(d &&& ~~~e) + 4 * (f ||| (d ^^^ e)) - 11 * f - 3 * (e ^^^ (d ||| ~~~f)) - 5 * ~~~f - 3 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * (f ^^^ (d ||| (e ||| f))) - 11 * (e ^^^ ~~~(d &&& ~~~f)) + 1 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 14 * ~~~(d ||| (e ||| f)) - 22 * ~~~(d ||| ( ~~~e ||| f)) - 26 * ~~~( ~~~d ||| (e ||| f)) + 16 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 19 * ( ~~~d &&& ( ~~~e &&& f)) + 11 * ( ~~~d &&& (e &&& f)) - 5 * (d &&& ( ~~~e &&& f)) + 8 * (d &&& (e &&& f)) = - 2 * ( ~~~d ||| ( ~~~e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2490 (x y : BitVec w) : +theorem e_2490 : - 3 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 11 * (d ^^^ e) + 3 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 3 * (f &&& ~~~(d ^^^ e)) + 5 * (f ^^^ ~~~(d ||| ~~~e)) + 2 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) + 1 * (d ^^^ (e ||| f)) + 7 * (e ^^^ (d &&& (e ||| f))) + 5 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 5 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) - 1 * ((d ^^^ e) &&& ~~~(d ^^^ f)) + 7 * ((d &&& e) ^^^ (e ||| ~~~f)) + 3 * ( ~~~d ||| ( ~~~e &&& f)) - 11 * ((d ^^^ e) ||| (d ^^^ f)) + 1 * ( ~~~e ||| (d ^^^ f)) - 3 * (f ^^^ (d ||| (e &&& f))) + 2 * (d &&& e) - 5 * (e ||| f) - 2 * ~~~(d ^^^ (e ^^^ f)) + 1 * ( ~~~d ||| ( ~~~e ||| f)) - 11 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * (e ||| (d &&& f)) - 7 * ((d ^^^ e) ||| ~~~(d ^^^ f)) + 7 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 7 * ((d ||| e) &&& ~~~(e ^^^ f)) - 1 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 2 * (f &&& ~~~(d &&& e)) - 2 * ~~~(d &&& ~~~e) + 5 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 1 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 2 * (e ^^^ (d &&& ~~~f)) - 6 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 5 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 2 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 11 * ~~~e + 2 * (e ^^^ f) - 2 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 1 * (d &&& ~~~f) + 5 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 1 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 2 * (e ^^^ (d ||| ~~~f)) - 1 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * (e ^^^ (d ||| ( ~~~e &&& f))) + 2 * ~~~(d ^^^ (e &&& f)) - 5 * ~~~f + 1 * f + 3 * (d ||| (e &&& f)) + 4 * (f ^^^ ( ~~~d ||| (e &&& f))) - 2 * ~~~(d &&& e) + 4 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 2 * (f ^^^ ~~~(d &&& (e &&& f))) - 3 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 7 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 7 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 1 * (e &&& (d ^^^ f)) + 2 * (f ^^^ (d &&& (e ||| f))) + 2 * ( ~~~f &&& (d ^^^ e)) - 3 * (e ^^^ (d &&& (e ^^^ f))) - 1 * ((d ||| ~~~e) &&& (e ^^^ f)) + 4 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 11 * ~~~(e &&& f) + 11 * ~~~(d &&& (e ^^^ f)) + 2 * (f ^^^ ( ~~~d &&& (e ||| f))) + 4 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 7 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 7 * (d ||| e) - 1 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) + 1 * (d ||| ( ~~~e ||| f)) - 1 * ((e &&& f) ||| ( ~~~d &&& (e ||| f))) - 2 * (e ^^^ (d &&& ( ~~~e ||| f))) - 7 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) + 1 * (f ||| ~~~(d ^^^ e)) - 7 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 7 * ( ~~~e &&& (d ^^^ f)) + 7 * ~~~(d &&& f) - 14 * ~~~(d ||| (e ||| f)) - 20 * ~~~(d ||| ( ~~~e ||| f)) - 12 * ~~~( ~~~d ||| (e ||| f)) + 11 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 1 * ( ~~~d &&& (e &&& f)) + 22 * (d &&& ( ~~~e &&& f)) - 23 * (d &&& (e &&& f)) = - 1 * ( ~~~f ||| ~~~(d ^^^ e)) - 1 * ~~~(e ||| ~~~f) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2491 (x y : BitVec w) : +theorem e_2491 : - 7 * (e ^^^ (d ||| ~~~f)) + 5 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 11 * (f ^^^ ~~~(d &&& (e ||| f))) + 1 * (d &&& ~~~e) + 2 * (e ^^^ ~~~(d &&& (e &&& f))) + 3 * ((d ||| e) &&& (e ^^^ f)) - 11 * ~~~( ~~~d &&& (e &&& f)) - 1 * (d ^^^ (e ^^^ f)) + 1 * (e ||| ~~~f) - 2 * ( ~~~f ||| ~~~(d ^^^ e)) - 1 * (f ^^^ (d &&& e)) + 4 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 2 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 6 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 5 * (f ||| ~~~(d ^^^ e)) + 4 * ~~~( ~~~d &&& (e ||| f)) - 11 * (f ^^^ (d ||| ( ~~~e ||| f))) - 5 * ((e &&& f) ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 6 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 1 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 6 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 1 * (d ^^^ (e ||| f)) + 2 * ~~~f + 5 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 1 * (e &&& (d ^^^ f)) + 3 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 2 * (e ||| f) - 11 * (e ^^^ ~~~(d &&& f)) + 1 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) + 5 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) - 3 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 1 * (e ||| ~~~(d ||| ~~~f)) + 1 * (f ||| (d ^^^ e)) + 1 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 2 * (f ||| ~~~(d ||| ~~~e)) + 5 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 2 * ( ~~~f &&& (d ^^^ e)) + 4 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 11 * ~~~(d ^^^ (e ||| f)) + 1 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 7 * ((d ^^^ e) &&& (d ^^^ f)) - 2 * ( ~~~e ||| (d ^^^ f)) - 2 * (d ^^^ (e &&& f)) + 1 * (e &&& ~~~f) + 1 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 6 * ((d &&& f) ^^^ (e ||| f)) + 2 * d + 1 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 7 * f + 2 * ~~~(d ^^^ (e &&& f)) + 5 * (e &&& ~~~(d ^^^ f)) + 1 * ~~~(d &&& (e ||| f)) - 11 * ~~~e - 7 * (d ||| (e &&& f)) + 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 1 * (d &&& ( ~~~e ||| f)) - 1 * ( ~~~(d ||| e) ||| ~~~(e ^^^ f)) - 11 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) - 1 * ~~~(d &&& ~~~f) - 7 * ((d ^^^ e) ||| (d ^^^ f)) - 1 * (d ||| (e ^^^ f)) - 2 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 7 * (e ^^^ (d &&& (e ||| f))) - 2 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) - 6 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 1 * (f ^^^ (d ||| ( ~~~e &&& f))) + 11 * (e &&& (d ||| ~~~f)) - 2 * ( ~~~(d ^^^ e) ||| ~~~(d ^^^ f)) + 1 * (d ||| ~~~e) + 5 * (e ^^^ (d &&& ( ~~~e ||| f))) + 3 * (f ^^^ (d ||| (e ||| f))) - 2 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * (f ^^^ (d ||| (e &&& f))) - 1 * ~~~(d &&& (e ^^^ f)) + 47 * ~~~(d ||| (e ||| f)) - 26 * ~~~(d ||| ( ~~~e ||| f)) + 58 * ~~~( ~~~d ||| (e ||| f)) + 28 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 62 * ( ~~~d &&& ( ~~~e &&& f)) + 52 * ( ~~~d &&& (e &&& f)) + 24 * (d &&& ( ~~~e &&& f)) + 24 * (d &&& (e &&& f)) = 11 * ~~~(d &&& ~~~e) + 3 * (f ||| (d &&& ~~~e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2492 (x y : BitVec w) : +theorem e_2492 : - 1 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 5 * ((d &&& e) ||| ~~~(e ||| f)) + 2 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 11 * (d &&& e) - 1 * (e ^^^ (d ||| (e &&& f))) - 2 * ((d ^^^ e) &&& (d ^^^ f)) - 1 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 3 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 3 * (f ^^^ ~~~(d &&& (e ||| f))) + 5 * (f ^^^ ~~~(d &&& (e &&& f))) - 6 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 4 * (e ^^^ (d &&& f)) + 4 * ~~~( ~~~d &&& (e ||| f)) + 3 * d - 11 * (e ^^^ (d ||| (e ^^^ f))) - 11 * (e ^^^ (d &&& ~~~f)) + 2 * (d &&& ~~~f) - 3 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) - 1 * (e ||| (d &&& f)) - 1 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 6 * ((d ||| e) &&& ~~~(e ^^^ f)) + 2 * (d &&& (e ||| f)) + 3 * (d ^^^ ( ~~~e ||| f)) - 7 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 3 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) - 5 * ((d &&& e) ^^^ (e ||| ~~~f)) + 4 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 11 * (e &&& f) - 7 * ( ~~~d ||| (e ^^^ f)) - 1 * ((d ^^^ e) ||| (d ^^^ f)) + 11 * (e ||| ~~~(d ||| f)) + 1 * ~~~(e ||| ~~~f) - 2 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 2 * (e ^^^ ( ~~~d ||| (e &&& f))) - 11 * ( ~~~d ||| ( ~~~e ||| f)) + 2 * ((d &&& f) ||| (e &&& ~~~f)) - 11 * ~~~(d ^^^ f) + 1 * ~~~(d &&& e) + 7 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 6 * (e ^^^ ~~~(d &&& (e ||| f))) - 5 * (f &&& ~~~(d &&& ~~~e)) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 1 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) - 5 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 5 * (f ||| (d ^^^ e)) - 2 * (f ^^^ (d ||| ( ~~~e &&& f))) - 2 * ~~~(d &&& (e ^^^ f)) + 1 * ~~~(d &&& f) + 5 * (f ^^^ (d &&& e)) - 2 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * (e ^^^ (d ||| f)) - 3 * (f ||| (d &&& e)) - 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 2 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) + 2 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 11 * ~~~(d ||| ~~~e) - 1 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 11 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 1 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) + 7 * ( ~~~d &&& (e ^^^ f)) + 1 * (d ||| e) + 7 * ( ~~~e &&& ~~~(d ^^^ f)) - 5 * (f ^^^ (d ||| (e ||| f))) + 2 * ~~~(e &&& ~~~f) + 4 * (e ^^^ ~~~(d ||| (e &&& f))) + 1 * (e ||| f) + 11 * (d ^^^ (e ||| f)) + 1 * ~~~(d ^^^ (e &&& f)) + 4 * (f ^^^ ~~~(d ||| e)) - 2 * ~~~(d &&& ( ~~~e ||| f)) + 11 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 7 * (d ||| ( ~~~e ||| f)) + 1 * (e ||| (d &&& ~~~f)) + 7 * ~~~(d ||| (e ||| f)) + 17 * ~~~(d ||| ( ~~~e ||| f)) + 44 * ~~~( ~~~d ||| (e ||| f)) - 41 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 13 * ( ~~~d &&& ( ~~~e &&& f)) + 42 * ( ~~~d &&& (e &&& f)) + 20 * (d &&& ( ~~~e &&& f)) + 29 * (d &&& (e &&& f)) = 5 * (e ^^^ ( ~~~d &&& (e ||| f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2493 (x y : BitVec w) : +theorem e_2493 : - 3 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 1 * (d ^^^ ( ~~~e ||| f)) + 4 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 7 * ~~~(d &&& e) - 1 * ((d ||| e) &&& (e ^^^ f)) + 4 * (f &&& ~~~(d ^^^ e)) - 2 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 11 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 7 * ((d &&& e) ^^^ (e ||| ~~~f)) + 2 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 11 * (e ^^^ (d ||| ~~~f)) + 2 * (f ^^^ ~~~(d ||| (e &&& f))) + 1 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) - 2 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 4 * ~~~(d ^^^ ( ~~~e &&& f)) - 11 * (f &&& (d ^^^ e)) + 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 5 * (f ^^^ (d ||| ( ~~~e &&& f))) - 3 * (d ||| e) + 3 * ((d ^^^ e) ||| ~~~(d ^^^ f)) + 1 * ((d ||| ~~~e) &&& (e ^^^ f)) + 2 * ((d &&& ~~~e) ||| (e ^^^ f)) + 11 * ~~~(d ^^^ (e &&& f)) - 5 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 1 * (e &&& ~~~(d &&& f)) + 1 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 1 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) - 2 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 2 * (f ||| ~~~(d ||| e)) - 6 * (d ||| (e ^^^ f)) - 7 * ( ~~~d ||| (e &&& f)) + 2 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 4 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 1 * (e ^^^ ~~~( ~~~d &&& (e &&& f))) - 6 * ~~~(d &&& (e ||| f)) + 11 * ~~~f + 4 * (d ^^^ ( ~~~e &&& f)) - 6 * (d ^^^ (e ||| f)) - 1 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) + 2 * ~~~(d &&& (e ^^^ f)) + 3 * (e ||| (d &&& ~~~f)) - 11 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 1 * (d &&& ( ~~~e ||| f)) - 11 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 5 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 3 * (d ||| ( ~~~e ||| f)) - 1 * ~~~(d ^^^ (e ^^^ f)) + 1 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) + 5 * ( ~~~f &&& ~~~(d ^^^ e)) + 5 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 5 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 3 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 11 * ~~~(d &&& ~~~f) + 1 * ~~~(e ||| ~~~f) - 1 * (e ^^^ (d &&& (e ^^^ f))) + 1 * (e ^^^ ~~~(d ||| ~~~f)) + 3 * (f ^^^ ~~~(d ||| ~~~e)) - 5 * (f ^^^ ( ~~~d ||| (e ||| f))) - 5 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 2 * (d &&& e) + 1 * (f ^^^ (d ||| (e ||| f))) + 2 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 5 * ((e &&& f) ||| (d &&& (e ||| f))) - 3 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 5 * (e ^^^ (d &&& ~~~f)) - 7 * (d ||| (e &&& f)) - 6 * ( ~~~d ||| (e ||| f)) - 2 * (e ^^^ ~~~(d &&& (e &&& f))) - 1 * (f &&& (d ||| e)) + 5 * ~~~(d ||| (e &&& f)) - 5 * (e ^^^ (d &&& ( ~~~e ||| f))) + 1 * (e ||| ~~~(d ||| ~~~f)) - 1 * (d ^^^ f) - 1 * ( ~~~f ||| ~~~(d ^^^ e)) + 15 * ~~~(d ||| (e ||| f)) + 50 * ~~~(d ||| ( ~~~e ||| f)) + 63 * ~~~( ~~~d ||| (e ||| f)) + 33 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 3 * ( ~~~d &&& ( ~~~e &&& f)) + 46 * ( ~~~d &&& (e &&& f)) + 55 * (d &&& ( ~~~e &&& f)) + 1 * (d &&& (e &&& f)) = 2 * (d &&& (e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2494 (x y : BitVec w) : +theorem e_2494 : - 6 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) - 2 * (f ^^^ (d ||| ( ~~~e ||| f))) - 3 * (e ^^^ ( ~~~d &&& (e ||| f))) - 6 * ~~~(d &&& ~~~e) + 1 * ~~~(d ^^^ f) + 7 * (d ^^^ (e ||| f)) - 3 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 1 * (f ^^^ ( ~~~d ||| (e ||| f))) - 5 * (d &&& ( ~~~e ||| f)) - 2 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) + 4 * ~~~(d ||| f) + 7 * (f &&& ~~~(d ^^^ e)) - 7 * (e &&& ~~~(d ^^^ f)) - 11 * ((d &&& f) ||| (e &&& ~~~f)) + 1 * ( ~~~e ||| ~~~(d ^^^ f)) - 1 * (e &&& ~~~(d &&& f)) - 1 * (e ^^^ ~~~(d &&& f)) - 5 * ((d &&& e) ||| ~~~(e ||| ~~~f)) + 2 * (e ^^^ (d ||| (e ||| f))) + 2 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 11 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 1 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * (d ^^^ (e &&& f)) - 5 * (f ||| ~~~(d ||| e)) + 11 * (e ||| ~~~(d ||| ~~~f)) + 2 * (e ||| ~~~(d ^^^ f)) + 4 * (f ||| (d &&& ~~~e)) - 6 * (f ^^^ (d ||| ~~~e)) + 2 * (d ||| (e ^^^ f)) - 7 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 2 * ~~~(d &&& ~~~f) + 3 * (f ^^^ ~~~( ~~~d ||| (e &&& f))) + 4 * ~~~d - 3 * (f ||| (d ^^^ e)) + 11 * ((d ^^^ e) &&& (d ^^^ f)) + 2 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 7 * (f ^^^ (d ||| (e ||| f))) + 3 * (d ||| f) + 2 * ~~~(d ||| (e &&& f)) - 2 * ((d &&& f) ||| ~~~(e ||| f)) + 1 * (e &&& f) - 7 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 2 * ((d ||| ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 4 * ((d ||| e) &&& ~~~(e ^^^ f)) + 2 * (e ^^^ ~~~(d ||| f)) - 1 * ~~~(d &&& f) - 1 * ((d &&& ~~~e) ||| (d ^^^ (e ^^^ f))) + 1 * ( ~~~d ||| (e ||| f)) + 1 * ~~~(d ||| ~~~f) + 1 * (e ^^^ ~~~(d &&& (e &&& f))) - 2 * (d ^^^ ( ~~~e ||| f)) - 5 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) + 1 * ( ~~~d ||| ( ~~~e ||| f)) - 5 * ~~~f + 5 * ~~~(d ^^^ ( ~~~e &&& f)) + 5 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 2 * (d ^^^ ( ~~~e &&& f)) - 1 * ~~~(e &&& f) + 3 * (e ^^^ (d &&& f)) - 1 * (d ||| (e &&& f)) - 7 * ((d &&& e) ||| (e ^^^ f)) + 5 * (e ^^^ (d ||| (e &&& f))) - 2 * (f ^^^ (d &&& (e ||| f))) - 6 * ((d ||| e) &&& (e ^^^ f)) + 7 * (e ^^^ ~~~(d &&& (e ^^^ f))) - 7 * (f ||| ~~~(d ||| ~~~e)) - 11 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * (f ^^^ ~~~(d &&& (e ||| f))) + 1 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 5 * (f ^^^ ~~~(d ||| (e &&& f))) - 1 * (e ^^^ (d &&& ~~~f)) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 11 * e + 1 * ~~~(d ^^^ (e &&& f)) + 3 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) + 41 * ~~~(d ||| (e ||| f)) + 32 * ~~~(d ||| ( ~~~e ||| f)) + 30 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 12 * ( ~~~d &&& ( ~~~e &&& f)) - 7 * ( ~~~d &&& (e &&& f)) + 62 * (d &&& ( ~~~e &&& f)) + 35 * (d &&& (e &&& f)) = - 1 * (f &&& (d ^^^ e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2495 (x y : BitVec w) : +theorem e_2495 : 5 * (e ||| f) + 11 * ((d &&& e) ^^^ (e ||| ~~~f)) + 4 * (d ^^^ (e &&& f)) + 2 * ( ~~~e ||| (d ^^^ f)) - 1 * (e ^^^ (d ||| ( ~~~e &&& f))) + 4 * ~~~(d ||| f) - 1 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 1 * (d ||| ( ~~~e &&& f)) - 11 * ( ~~~f ||| ~~~(d ^^^ e)) + 1 * ~~~f - 1 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 5 * ((d &&& ~~~e) ||| (e ^^^ f)) + 3 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 2 * (e ^^^ ( ~~~d &&& (e ||| f))) + 7 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) + 4 * (e ^^^ (d &&& (e ^^^ f))) - 2 * (d ^^^ (e ||| f)) - 6 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) - 1 * ( ~~~f &&& ~~~(d ^^^ e)) + 1 * (d &&& ~~~f) - 5 * (e ||| ~~~(d ||| f)) + 1 * (e ^^^ ~~~( ~~~d ||| (e &&& f))) + 2 * ~~~(d ^^^ e) + 2 * (e ^^^ ~~~(d ||| ~~~f)) + 1 * (e &&& (d ||| ~~~f)) + 7 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 1 * (e ||| ~~~f) + 4 * ( ~~~d ||| (e ^^^ f)) - 11 * (e &&& ~~~(d ^^^ f)) - 1 * (d ||| (e &&& f)) + 1 * ( ~~~d ||| (e ||| f)) - 6 * ~~~(d &&& f) + 2 * ((e &&& ~~~f) ||| ~~~( ~~~d ||| ( ~~~e &&& f))) + 1 * (e ||| (d &&& f)) - 6 * (e &&& ~~~(d &&& f)) + 5 * ( ~~~d &&& (e ||| f)) + 5 * ~~~(e &&& ~~~f) + 7 * (d ||| (e ^^^ f)) - 2 * (d &&& (e ||| f)) + 1 * (e ^^^ ( ~~~d ||| (e &&& f))) - 2 * ((d ||| e) &&& (e ^^^ f)) - 1 * (f ^^^ (d &&& (e ||| f))) - 3 * (e &&& f) - 1 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 11 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) - 1 * ~~~( ~~~d &&& (e ||| f)) - 11 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) + 4 * ((d &&& f) ||| ~~~(e ||| f)) - 7 * ( ~~~e ||| ~~~(d ^^^ f)) - 2 * (e ^^^ ( ~~~d ||| (e ^^^ f))) + 2 * ((d ^^^ e) &&& (d ^^^ f)) + 7 * ( ~~~d &&& (e ^^^ f)) - 2 * (d ^^^ ( ~~~e ||| f)) + 7 * ((d &&& e) ||| ~~~(e ||| f)) - 2 * ~~~(d &&& (e ^^^ f)) + 1 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 11 * ((e &&& f) ||| (d &&& (e ||| f))) + 3 * ((d &&& f) ^^^ ~~~(e &&& ~~~f)) - 3 * ~~~( ~~~d &&& (e &&& f)) + 1 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 2 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 3 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 1 * (e ||| ~~~(d ^^^ f)) - 6 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 1 * (e ^^^ ~~~(d &&& (e &&& f))) + 2 * ~~~(d ^^^ ( ~~~e ||| f)) + 1 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (f &&& (d ||| e)) - 5 * ~~~(d &&& e) - 7 * (e ^^^ (d ||| ~~~f)) - 1 * (d ^^^ f) - 1 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) - 2 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 7 * ( ~~~e &&& ~~~(d ^^^ f)) + 24 * ~~~(d ||| (e ||| f)) + 6 * ~~~(d ||| ( ~~~e ||| f)) + 22 * ~~~( ~~~d ||| (e ||| f)) + 24 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 8 * ( ~~~d &&& ( ~~~e &&& f)) + 25 * ( ~~~d &&& (e &&& f)) + 20 * (d &&& ( ~~~e &&& f)) + 53 * (d &&& (e &&& f)) = - 1 * ~~~(d &&& ~~~f) + 2 * (f &&& (d ||| ~~~e)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2496 (x y : BitVec w) : +theorem e_2496 : 2 * ((d &&& e) ||| (d ^^^ (e ^^^ f))) - 3 * (f ||| (d &&& ~~~e)) - 2 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 5 * ( ~~~d ||| (e ||| f)) + 11 * (e ^^^ (d &&& f)) - 2 * (f ^^^ ( ~~~d &&& (e ||| f))) - 11 * ( ~~~d ||| (e ^^^ f)) - 6 * ( ~~~f &&& (d ^^^ e)) - 2 * (e ||| ~~~f) - 5 * ( ~~~d ||| ( ~~~e &&& f)) + 3 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) - 1 * (e ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 1 * ~~~(d &&& ~~~e) - 1 * ( ~~~(d ||| ~~~e) ||| ~~~(e ^^^ f)) + 2 * (f &&& ~~~(d ^^^ e)) + 1 * (e &&& (d ||| f)) - 1 * ( ~~~d ||| ( ~~~e ||| f)) - 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 1 * (e ^^^ (d ||| ~~~f)) - 6 * (f &&& (d ||| e)) + 7 * (e ^^^ (d &&& ( ~~~e ||| f))) + 1 * (e ^^^ ( ~~~d &&& (e ||| f))) + 4 * ((d &&& e) ^^^ ~~~(d ^^^ (e &&& f))) + 7 * (e ||| (d &&& f)) + 2 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 1 * (e ^^^ ~~~(d &&& (e &&& f))) + 1 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 2 * (f ^^^ (d ||| (e &&& f))) + 5 * (e ^^^ ~~~(d &&& (e ||| f))) + 1 * (f ^^^ ( ~~~d ||| (e ||| f))) + 3 * (d ||| e) + 1 * (e &&& ~~~f) - 3 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) - 7 * ((d ||| e) &&& ~~~(e ^^^ f)) + 1 * ( ~~~d &&& (e ^^^ f)) - 1 * (d &&& ~~~e) - 1 * (d ^^^ (e ^^^ f)) + 7 * (d ||| (e ||| f)) + 2 * ( ~~~(d ^^^ e) ||| (d ^^^ f)) - 2 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 3 * ~~~( ~~~d ||| (e ^^^ f)) + 3 * (f ||| (d &&& e)) - 1 * ((d &&& ~~~e) ||| (e ^^^ f)) + 7 * (d ^^^ f) - 1 * (e ^^^ ( ~~~d ||| (e &&& f))) - 5 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 1 * (e ||| ~~~(d ||| ~~~f)) + 5 * ~~~(d ^^^ e) - 6 * ~~~f + 1 * ( ~~~(d &&& ~~~e) &&& ~~~(e ^^^ f)) + 1 * (f ^^^ ~~~(d ||| ~~~e)) - 2 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) - 6 * (d ||| ( ~~~e &&& f)) + 7 * (d ^^^ (e ||| f)) + 2 * (e ^^^ (d ||| ( ~~~e ||| f))) - 5 * ((d &&& e) ||| (e ^^^ f)) + 7 * (e &&& f) + 1 * (f ^^^ (d &&& e)) + 3 * ((d ||| e) &&& (e ^^^ f)) + 4 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 7 * ~~~(e ^^^ f) + 3 * ~~~(d ||| (e ^^^ f)) - 6 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 7 * ( ~~~d &&& ( ~~~e ||| f)) - 6 * (f ^^^ (d &&& ~~~e)) - 3 * (f ^^^ ( ~~~d ||| (e &&& f))) + 2 * (d ||| ( ~~~e ||| f)) + 5 * ~~~(d ||| e) - 2 * (f ^^^ (d ||| ( ~~~e ||| f))) + 1 * ((d &&& f) ||| ~~~(e ||| f)) + 1 * ((d &&& e) ^^^ (d ^^^ ( ~~~e ||| f))) - 2 * (d ^^^ ( ~~~e ||| f)) - 11 * ((d ||| ~~~e) &&& (e ^^^ f)) - 2 * ( ~~~d &&& (e ||| f)) + 13 * ~~~(d ||| (e ||| f)) + 2 * ~~~(d ||| ( ~~~e ||| f)) + 20 * ~~~( ~~~d ||| (e ||| f)) - 3 * ( ~~~d &&& ( ~~~e &&& f)) - 9 * ( ~~~d &&& (e &&& f)) + 18 * (d &&& ( ~~~e &&& f)) + 17 * (d &&& (e &&& f)) = 18 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 2 * ((d &&& f) ^^^ (e ||| f)) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2497 (x y : BitVec w) : +theorem e_2497 : 3 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) + 1 * (d ^^^ ( ~~~e &&& f)) - 1 * (d ||| ~~~f) - 6 * (e ^^^ ~~~(d &&& ( ~~~e ||| f))) + 1 * ~~~( ~~~d &&& ( ~~~e ||| f)) + 2 * (e ^^^ f) - 5 * ~~~(e ||| ~~~f) + 3 * ~~~f - 11 * (d &&& e) - 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) + 4 * ((e &&& f) ^^^ ~~~(d &&& (e ^^^ f))) - 1 * (f ||| ~~~(d ||| ~~~e)) - 11 * (f ^^^ ( ~~~d ||| (e ||| f))) - 2 * (f ||| ~~~(d ||| e)) + 3 * (e &&& ~~~(d &&& ~~~f)) - 2 * ~~~(d ^^^ (e ^^^ f)) + 1 * (f ^^^ ( ~~~d ||| (e &&& f))) + 5 * ((d &&& e) ^^^ (e ||| ~~~f)) - 1 * (e ^^^ ~~~(d &&& (e ||| f))) - 1 * ~~~(d &&& (e ||| f)) - 7 * ~~~(d ^^^ e) + 4 * ( ~~~(d ||| ~~~e) ||| (e ^^^ f)) + 4 * (e ^^^ ( ~~~d ||| (e &&& f))) - 2 * (e ||| ~~~(d ||| ~~~f)) - 3 * (d ||| f) + 11 * ~~~( ~~~d &&& (e ^^^ f)) - 5 * (e ^^^ (d ||| f)) + 3 * ((d &&& e) ||| ~~~(d ^^^ (e ^^^ f))) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 2 * ~~~(d ||| ~~~f) + 5 * (d &&& ~~~e) - 5 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 7 * ~~~(d ||| (e ^^^ f)) - 1 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * (e ^^^ (d ||| (e &&& f))) - 1 * ( ~~~d &&& ( ~~~e ||| f)) + 1 * (f ^^^ (d ||| (e &&& f))) + 1 * ((d ||| ~~~e) &&& (e ^^^ f)) - 6 * ( ~~~e &&& (d ^^^ f)) - 3 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 1 * ((d ||| e) &&& ~~~(e ^^^ f)) + 2 * (f ^^^ ~~~(d &&& ~~~e)) + 11 * (f ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 7 * ( ~~~(d &&& e) &&& (e ^^^ f)) + 5 * (e ^^^ (d ||| ( ~~~e ||| f))) - 1 * (f ^^^ ~~~( ~~~d &&& (e &&& f))) - 11 * (e ^^^ (d &&& (e ||| f))) - 7 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 2 * ~~~d - 5 * ( ~~~(d ^^^ e) &&& ~~~(d ^^^ f)) - 5 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) - 7 * ((d &&& e) ||| (e ^^^ f)) - 1 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) + 2 * ((d &&& f) ||| ~~~(e ||| f)) + 3 * (e ||| ~~~(d ||| f)) + 3 * (e ||| (d &&& f)) + 1 * (e ^^^ ( ~~~d &&& (e ||| f))) + 1 * ( ~~~(d &&& ~~~e) &&& ~~~(d ^^^ (e ^^^ f))) + 7 * (e ^^^ (d ||| (e ^^^ f))) - 6 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 1 * (f &&& ~~~(d ^^^ e)) + 5 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 2 * (d &&& ( ~~~e ||| f)) - 7 * e - 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 11 * ((d ||| ~~~e) &&& ~~~(e ^^^ f)) + 3 * ~~~(d &&& ~~~e) + 5 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 4 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) - 2 * ~~~(d ^^^ ( ~~~e &&& f)) - 1 * ((d &&& f) ^^^ ~~~(d ^^^ ( ~~~e &&& f))) - 1 * ((d &&& e) ||| ~~~(e ^^^ f)) + 1 * (f &&& ~~~(d &&& e)) + 1 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 2 * ~~~(d ^^^ (e &&& f)) - 36 * ~~~(d ||| (e ||| f)) + 16 * ~~~(d ||| ( ~~~e ||| f)) - 36 * ~~~( ~~~d ||| (e ||| f)) + 1 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 13 * ( ~~~d &&& ( ~~~e &&& f)) + 4 * (d &&& ( ~~~e &&& f)) + 16 * (d &&& (e &&& f)) = - 7 * ~~~(d ||| ~~~e) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2498 (x y : BitVec w) : +theorem e_2498 : 1 * (e ^^^ ( ~~~d ||| (e &&& f))) - 3 * ((d ||| e) &&& ~~~(d ^^^ (e ^^^ f))) - 1 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 5 * ~~~(d ||| ~~~e) - 1 * ~~~(e &&& f) + 3 * ~~~( ~~~d ||| ( ~~~e &&& f)) + 2 * (e ^^^ (d ||| ( ~~~e ||| f))) + 1 * ~~~(d &&& ~~~d) - 11 * (e ^^^ (d ||| (e &&& f))) - 5 * (e ||| (d &&& f)) + 1 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) + 2 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) - 7 * (f ^^^ ~~~(d ||| (e &&& f))) + 7 * (f ^^^ (d &&& e)) - 5 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 11 * (e ||| ~~~(d ||| ~~~f)) - 7 * ( ~~~d &&& (e ||| f)) + 2 * ~~~( ~~~d &&& ( ~~~e &&& f)) + 1 * d + 11 * ( ~~~f ||| ~~~(d ^^^ e)) - 1 * ( ~~~(d ^^^ e) &&& (d ^^^ f)) + 1 * (f ^^^ ( ~~~d ||| (e &&& f))) - 3 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 4 * (e ^^^ ~~~( ~~~d &&& ( ~~~e &&& f))) - 6 * ((d &&& e) ^^^ (e ||| ~~~f)) - 1 * ( ~~~e &&& ~~~(d ^^^ f)) + 7 * (e ||| ~~~(d ^^^ f)) + 4 * (e ||| f) + 7 * ~~~(d &&& f) + 3 * ~~~(d ^^^ (e ^^^ f)) - 6 * (f ^^^ ~~~(d ||| ~~~e)) + 1 * (f ^^^ ( ~~~d ||| ( ~~~e &&& f))) + 1 * ( ~~~d &&& (e ^^^ f)) - 2 * ((e &&& f) ||| (d &&& (e ||| f))) - 11 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) + 2 * ( ~~~d ||| ( ~~~e &&& f)) + 5 * ((d &&& f) ^^^ (e ||| f)) - 6 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 7 * (e ^^^ ~~~(d &&& (e ||| f))) - 11 * ( ~~~e ||| (d ^^^ f)) - 2 * (f ^^^ ~~~(d &&& ~~~e)) + 1 * ~~~( ~~~d ||| (e &&& f)) - 2 * ~~~f + 1 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 2 * ( ~~~(d ||| e) ||| ~~~(d ^^^ (e ^^^ f))) - 2 * ~~~(d &&& ( ~~~e &&& f)) - 5 * ((d ||| e) &&& ~~~(e ^^^ f)) - 2 * (d ||| (e &&& f)) + 2 * (e ^^^ ~~~(d &&& ( ~~~e &&& f))) + 1 * ( ~~~(d &&& e) &&& ~~~(e ^^^ f)) + 4 * ((d ^^^ e) &&& (d ^^^ f)) + 11 * ~~~( ~~~d &&& (e ^^^ f)) + 2 * (e ^^^ ~~~(d ||| (e ^^^ f))) - 1 * (f ^^^ (d &&& (e ||| f))) + 2 * (d ^^^ (e ^^^ f)) + 5 * ( ~~~e &&& (d ^^^ f)) - 7 * (d ||| ~~~e) + 11 * (f ^^^ (d ||| ( ~~~e ||| f))) - 2 * ((d &&& e) ||| ~~~(e ^^^ f)) + 5 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 4 * ( ~~~d ||| (e ^^^ f)) + 2 * (f &&& (d ^^^ e)) - 1 * (f ||| (d ^^^ e)) - 1 * (d ^^^ e) - 5 * ((d &&& e) ^^^ (e ||| f)) - 2 * ~~~(d &&& (e ^^^ f)) + 1 * ~~~( ~~~d ||| (e ^^^ f)) - 6 * (e &&& (d ^^^ f)) - 1 * (e ^^^ ~~~(d &&& ~~~f)) - 1 * ~~~(d ^^^ (e ||| f)) - 1 * (f ||| (d &&& ~~~e)) + 2 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) - 3 * (e ^^^ (d &&& (e ||| f))) + 3 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) - 20 * ~~~(d ||| (e ||| f)) + 9 * ~~~(d ||| ( ~~~e ||| f)) - 18 * ~~~( ~~~d ||| (e ||| f)) - 38 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 22 * ( ~~~d &&& ( ~~~e &&& f)) + 13 * ( ~~~d &&& (e &&& f)) + 42 * (d &&& ( ~~~e &&& f)) - 5 * (d &&& (e &&& f)) = 1 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 5 * f := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2499 (x y : BitVec w) : +theorem e_2499 : - 11 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 2 * (d &&& e) + 1 * (f ||| ~~~(d ^^^ e)) - 1 * ~~~(d ^^^ ( ~~~e ||| f)) + 1 * ~~~(d ^^^ e) - 5 * ((d ||| e) &&& (d ^^^ (e ^^^ f))) + 5 * ~~~f - 5 * (d ^^^ (e ^^^ f)) + 1 * ((d &&& f) ^^^ ~~~(d ^^^ (e &&& f))) + 3 * ( ~~~d &&& (e ^^^ f)) - 1 * (e ^^^ ( ~~~d ||| ( ~~~e ||| f))) - 1 * (e ^^^ ( ~~~d &&& (e ||| f))) + 4 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) - 2 * (e ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 11 * (f ^^^ (d ||| ( ~~~e ||| f))) - 11 * d - 1 * (e ^^^ ~~~(d ||| ~~~f)) - 5 * ~~~( ~~~d &&& (e ||| f)) + 2 * ((d &&& e) ||| ~~~(e ||| ~~~f)) - 1 * (d &&& f) + 5 * (e ^^^ ( ~~~d &&& (e ^^^ f))) + 11 * ((d &&& ~~~e) ||| (e ^^^ f)) - 7 * ~~~( ~~~d &&& (e ^^^ f)) + 5 * (e ^^^ (d &&& (e ^^^ f))) - 3 * ~~~( ~~~d &&& (e &&& f)) + 2 * (e ^^^ ~~~(d &&& (e ||| f))) + 2 * (f ^^^ (d ||| (e ||| f))) + 2 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 1 * (e ^^^ ~~~(d ||| ( ~~~e &&& f))) - 6 * ~~~(e &&& f) + 1 * (d ||| ( ~~~e &&& f)) - 1 * ~~~(e ||| f) + 2 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) + 11 * ~~~(d &&& (e &&& f)) - 3 * (f ^^^ ~~~(d ||| e)) - 11 * ((d ^^^ e) &&& ~~~(d ^^^ f)) - 2 * (f ^^^ ~~~(d &&& ( ~~~e ||| f))) - 2 * ((d &&& f) ^^^ (d ^^^ ( ~~~e &&& f))) + 7 * ( ~~~d &&& ( ~~~e ||| f)) - 1 * ~~~(d &&& ~~~f) + 7 * ((d &&& e) ^^^ ~~~(d ^^^ ( ~~~e ||| f))) - 1 * (e ^^^ ~~~(d &&& (e ^^^ f))) + 11 * ( ~~~(d ||| ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) + 11 * ~~~(d &&& f) - 5 * ((d &&& e) ||| ~~~(e ^^^ f)) + 11 * (e ||| ~~~(d ||| ~~~f)) + 1 * ~~~(d ||| ~~~f) + 5 * ( ~~~(d ||| e) ||| (e ^^^ f)) + 4 * ~~~(e ^^^ f) - 3 * (d ||| f) - 2 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 1 * (d ||| ~~~e) - 2 * ((d ^^^ e) ||| (d ^^^ f)) - 7 * (f ^^^ ~~~(d &&& e)) + 1 * (e ^^^ ~~~(d &&& ~~~f)) - 3 * (e ^^^ (d ||| (e &&& f))) + 1 * ((d &&& e) ||| ~~~(e ||| f)) - 1 * ~~~( ~~~d ||| (e ^^^ f)) + 1 * (f ^^^ ( ~~~d &&& (e ||| f))) + 3 * ( ~~~(d &&& e) &&& ~~~(d ^^^ (e ^^^ f))) - 11 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) + 5 * (e ^^^ ~~~(d &&& (e &&& f))) - 6 * (f ^^^ (d ||| e)) + 7 * ((d &&& f) ^^^ (d ^^^ (e &&& f))) - 7 * (e ||| (d &&& ~~~f)) + 7 * (e &&& ~~~f) + 3 * (d ||| ( ~~~e ||| f)) - 1 * ~~~(d ||| (e ^^^ f)) - 2 * (e ^^^ (d &&& ~~~f)) + 3 * ~~~(d &&& ~~~d) + 3 * ((d &&& e) ||| (e ^^^ f)) - 1 * (f ^^^ ~~~(d ||| ( ~~~e &&& f))) - 7 * ((d &&& e) ^^^ (d ^^^ (e &&& f))) + 4 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 6 * ~~~(d &&& ~~~e) - 13 * ~~~(d ||| (e ||| f)) - 19 * ~~~(d ||| ( ~~~e ||| f)) + 49 * ~~~( ~~~d ||| (e ||| f)) - 19 * ~~~( ~~~d ||| ( ~~~e ||| f)) - 30 * ( ~~~d &&& ( ~~~e &&& f)) - 23 * ( ~~~d &&& (e &&& f)) + 31 * (d &&& (e &&& f)) = 3 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 6 * ( ~~~(d &&& e) &&& (d ^^^ (e ^^^ f))) := by - bv_automata_circuit (config := { backend := .cadical }) + bv_mba -theorem e_2500 (x y : BitVec w) : +theorem e_2500 : 7 * ( ~~~f ||| (d ^^^ e)) - 6 * ( ~~~(d &&& ~~~e) &&& (e ^^^ f)) - 11 * ( ~~~(d &&& ~~~e) &&& (d ^^^ (e ^^^ f))) - 1 * (f ^^^ ~~~( ~~~d &&& (e ||| f))) + 3 * ((e &&& ~~~f) ||| ~~~(d ||| ( ~~~e &&& f))) - 3 * (f ||| ~~~(d ||| ~~~e)) + 1 * ~~~(e ^^^ f) + 1 * ~~~(d &&& (e ||| f)) + 5 * ( ~~~(d ||| ~~~e) ||| (d ^^^ (e ^^^ f))) + 1 * (e ^^^ ~~~(d ||| (e &&& f))) + 1 * ~~~(d ||| ( ~~~e &&& f)) - 1 * ( ~~~d ||| (e ^^^ f)) + 4 * (e ^^^ ~~~( ~~~d &&& (e ||| f))) + 3 * ((d &&& ~~~e) ||| ~~~(e ^^^ f)) + 4 * (f ^^^ ( ~~~d ||| ( ~~~e ||| f))) + 4 * ((e &&& ~~~f) ^^^ (d ||| (e ^^^ f))) + 7 * ((d &&& ~~~e) ||| (e ^^^ f)) + 2 * ((d ||| e) &&& (e ^^^ f)) + 3 * (e ^^^ ~~~( ~~~d ||| (e ^^^ f))) - 6 * (e ^^^ ~~~(d &&& f)) - 1 * (e ^^^ ( ~~~d ||| (e ||| f))) + 5 * (f ^^^ (d &&& (e ||| f))) + 4 * ((d &&& f) ^^^ (e ||| f)) + 1 * (e &&& (d ||| ~~~f)) - 2 * ~~~(d &&& ~~~e) + 7 * (f ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 3 * ((d &&& e) ||| ~~~(e ^^^ f)) - 1 * ~~~( ~~~d &&& ( ~~~e ||| f)) - 5 * (f ^^^ ( ~~~d ||| (e &&& f))) - 1 * (d ||| (e ||| f)) + 5 * (d &&& ~~~f) + 7 * (f ||| (d &&& e)) - 1 * ( ~~~d &&& (e ||| f)) + 1 * ( ~~~(d ||| e) ||| (d ^^^ (e ^^^ f))) + 7 * (e ^^^ ~~~( ~~~d &&& (e ^^^ f))) + 1 * ((d ||| ~~~e) &&& (d ^^^ (e ^^^ f))) + 11 * ~~~(d ||| (e ^^^ f)) + 4 * (e ^^^ (d &&& (e ^^^ f))) - 1 * ( ~~~d ||| ( ~~~e ||| f)) + 5 * ((d &&& ~~~e) ||| ~~~(d ^^^ (e ^^^ f))) - 11 * (e ^^^ ( ~~~d ||| (e ^^^ f))) - 1 * (d &&& (e ||| f)) - 1 * (f ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 3 * (e ^^^ ( ~~~d &&& (e ||| f))) + 7 * (e ^^^ (d &&& ~~~f)) + 1 * ~~~( ~~~d &&& ( ~~~e &&& f)) - 1 * (e ^^^ (d ||| (e &&& f))) + 1 * (e ^^^ (d &&& ( ~~~e ||| f))) - 1 * (f ^^^ ( ~~~d &&& ( ~~~e ||| f))) - 1 * (d ||| ( ~~~e &&& f)) - 6 * (e ^^^ ~~~(d ||| ~~~f)) + 3 * ~~~(d ||| f) + 4 * (e ||| ~~~(d ^^^ f)) - 2 * ~~~(d &&& ( ~~~e ||| f)) - 6 * f - 1 * (e ||| ~~~(d ||| ~~~f)) + 5 * ((d ^^^ e) ||| ~~~(d ^^^ f)) - 2 * (f ^^^ ( ~~~d ||| (e ||| f))) + 5 * (f ^^^ ~~~(d ||| ~~~e)) - 11 * (e ||| (d &&& ~~~f)) + 11 * ~~~(d &&& (e &&& f)) - 3 * (e ^^^ ~~~( ~~~d &&& ( ~~~e ||| f))) - 5 * ((d &&& e) ||| (e ^^^ f)) + 1 * ((e &&& ~~~f) ^^^ ( ~~~d ||| (e ^^^ f))) - 3 * (f ^^^ ~~~(d &&& ( ~~~e &&& f))) - 1 * ~~~(d &&& ( ~~~e &&& f)) + 4 * ~~~( ~~~d &&& (e &&& f)) - 6 * ((d ||| e) &&& ~~~(e ^^^ f)) - 11 * ( ~~~e &&& (d ^^^ f)) - 7 * (f &&& (d ||| ~~~e)) + 5 * (d &&& ( ~~~e ||| f)) + 11 * ~~~(e ||| f) - 7 * (f ^^^ ~~~(d &&& e)) + 1 * ((d ^^^ e) &&& (d ^^^ f)) - 39 * ~~~(d ||| (e ||| f)) - 29 * ~~~(d ||| ( ~~~e ||| f)) - 54 * ~~~( ~~~d ||| (e ||| f)) - 32 * ~~~( ~~~d ||| ( ~~~e ||| f)) + 19 * ( ~~~d &&& ( ~~~e &&& f)) - 60 * ( ~~~d &&& (e &&& f)) - 31 * (d &&& ( ~~~e &&& f)) + 33 * (d &&& (e &&& f)) = - 1 * (e ^^^ ~~~( ~~~d ||| ( ~~~e &&& f))) + 3 * ~~~(d ^^^ f) := by b v_automata_circuit (config := { backend := .cadical }) diff --git a/SSA/Projects/InstCombine/TacticAuto.lean b/SSA/Projects/InstCombine/TacticAuto.lean index baa56ebdd..8286c5e36 100644 --- a/SSA/Projects/InstCombine/TacticAuto.lean +++ b/SSA/Projects/InstCombine/TacticAuto.lean @@ -5,6 +5,7 @@ import Mathlib.Tactic.Ring import SSA.Projects.InstCombine.ForLean import SSA.Projects.InstCombine.LLVM.EDSL import SSA.Experimental.Bits.Fast.Reflect +import SSA.Experimental.Bits.Fast.MBA import SSA.Experimental.Bits.FastCopy.Reflect import SSA.Experimental.Bits.AutoStructs.Tactic import SSA.Experimental.Bits.AutoStructs.ForLean @@ -316,7 +317,8 @@ macro "bv_bench": tactic => "bv_auto" : (bv_auto; done), "bv_automata_circuit_prop" : (bool_to_prop; bv_automata_circuit; done), "bv_automata_circuit" : (bv_automata_circuit; done), - "bv_normalize_automata_circuit" : ((try (solve | bv_normalize)); (try bv_automata_circuit); done) + "bv_normalize_automata_circuit" : ((try (solve | bv_normalize)); (try bv_automata_circuit); done), + "bv_mba" : ((try (solve | bv_normalize)); (try bv_mba); done) ] try bv_auto try sorry