%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP402-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:07:43 AM UTC 2025
% Result : Unsatisfiable 0.14s 0.40s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : GRP402-1 : TPTP v9.0.0. Released v2.5.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Jun 19 16:01:38 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.40 % SZS status Unsatisfiable
% 0.14/0.40 % SZS output start Proof
% 0.14/0.40 tff(commutator_type, type, (
% 0.14/0.40 commutator: ( $i * $i ) > $i)).
% 0.14/0.40 tff(c_type, type, (
% 0.14/0.40 c: $i)).
% 0.14/0.40 tff(b_type, type, (
% 0.14/0.40 b: $i)).
% 0.14/0.40 tff(a_type, type, (
% 0.14/0.40 a: $i)).
% 0.14/0.40 tff(inj_0_type, type, (
% 0.14/0.40 inj_0: ( $i * $i ) > $i)).
% 0.14/0.40 tff(multiply_type, type, (
% 0.14/0.40 multiply: ( $i * $i ) > $i)).
% 0.14/0.40 tff(inj_1_type, type, (
% 0.14/0.40 inj_1: ( $i * $i ) > $i)).
% 0.14/0.40 tff(1,plain,
% 0.14/0.40 (![B: $i, A: $i, C: $i] : ((~(multiply(A, B) = multiply(C, B))) | (A = C)) <=> ![Xk!0: $i, Xk!1: $i] : (inj_0(Xk!0, multiply(Xk!1, Xk!0)) = Xk!1)),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(2,plain,
% 0.14/0.40 (![B: $i, A: $i, C: $i] : ((~(multiply(A, B) = multiply(C, B))) | (A = C)) <=> ![B: $i, A: $i, C: $i] : ((~(multiply(A, B) = multiply(C, B))) | (A = C))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(3,axiom,(![B: $i, A: $i, C: $i] : ((~(multiply(A, B) = multiply(C, B))) | (A = C))), file('/export/starexec/sandbox2/benchmark/Axioms/GRP008-1.ax','right_cancellation')).
% 0.14/0.40 tff(4,plain,
% 0.14/0.40 (![B: $i, A: $i, C: $i] : ((~(multiply(A, B) = multiply(C, B))) | (A = C))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.14/0.40 tff(5,plain,(
% 0.14/0.40 ![B: $i, A: $i, C: $i] : ((~(multiply(A, B) = multiply(C, B))) | (A = C))),
% 0.14/0.40 inference(skolemize,[status(sab)],[4])).
% 0.14/0.40 tff(6,plain,
% 0.14/0.40 (![Xk!0: $i, Xk!1: $i] : (inj_0(Xk!0, multiply(Xk!1, Xk!0)) = Xk!1)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.14/0.40 tff(7,plain,
% 0.14/0.40 ((~![Xk!0: $i, Xk!1: $i] : (inj_0(Xk!0, multiply(Xk!1, Xk!0)) = Xk!1)) | (inj_0(multiply(a, commutator(a, b)), multiply(commutator(a, commutator(b, c)), multiply(a, commutator(a, b)))) = commutator(a, commutator(b, c)))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(8,plain,
% 0.14/0.40 (inj_0(multiply(a, commutator(a, b)), multiply(commutator(a, commutator(b, c)), multiply(a, commutator(a, b)))) = commutator(a, commutator(b, c))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[7, 6])).
% 0.14/0.40 tff(9,plain,
% 0.14/0.40 (^[Z: $i, Y: $i, X: $i] : refl((multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))) <=> (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(10,plain,
% 0.14/0.40 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[9])).
% 0.14/0.40 tff(11,plain,
% 0.14/0.40 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(12,axiom,(![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GRP008-0.ax','associativity_of_multiply')).
% 0.14/0.40 tff(13,plain,
% 0.14/0.40 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.14/0.40 tff(14,plain,(
% 0.14/0.40 ![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.14/0.40 inference(skolemize,[status(sab)],[13])).
% 0.14/0.40 tff(15,plain,
% 0.14/0.40 (![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.14/0.40 tff(16,plain,
% 0.14/0.40 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(commutator(a, commutator(b, c)), a), commutator(a, b)) = multiply(commutator(a, commutator(b, c)), multiply(a, commutator(a, b))))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(17,plain,
% 0.14/0.40 (multiply(multiply(commutator(a, commutator(b, c)), a), commutator(a, b)) = multiply(commutator(a, commutator(b, c)), multiply(a, commutator(a, b)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.14/0.40 tff(18,plain,
% 0.14/0.40 ((~![Xk!0: $i, Xk!1: $i] : (inj_0(Xk!0, multiply(Xk!1, Xk!0)) = Xk!1)) | (inj_0(commutator(b, c), multiply(a, commutator(b, c))) = a)),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(19,plain,
% 0.14/0.40 (inj_0(commutator(b, c), multiply(a, commutator(b, c))) = a),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[18, 6])).
% 0.14/0.40 tff(20,plain,
% 0.14/0.40 (^[B: $i, A: $i] : refl((multiply(A, B) = multiply(B, multiply(A, commutator(A, B)))) <=> (multiply(A, B) = multiply(B, multiply(A, commutator(A, B)))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(21,plain,
% 0.14/0.40 (![B: $i, A: $i] : (multiply(A, B) = multiply(B, multiply(A, commutator(A, B)))) <=> ![B: $i, A: $i] : (multiply(A, B) = multiply(B, multiply(A, commutator(A, B))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[20])).
% 0.14/0.40 tff(22,plain,
% 0.14/0.40 (![B: $i, A: $i] : (multiply(A, B) = multiply(B, multiply(A, commutator(A, B)))) <=> ![B: $i, A: $i] : (multiply(A, B) = multiply(B, multiply(A, commutator(A, B))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(23,axiom,(![B: $i, A: $i] : (multiply(A, B) = multiply(B, multiply(A, commutator(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutator')).
% 0.14/0.40 tff(24,plain,
% 0.14/0.40 (![B: $i, A: $i] : (multiply(A, B) = multiply(B, multiply(A, commutator(A, B))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.14/0.40 tff(25,plain,(
% 0.14/0.40 ![B: $i, A: $i] : (multiply(A, B) = multiply(B, multiply(A, commutator(A, B))))),
% 0.14/0.40 inference(skolemize,[status(sab)],[24])).
% 0.14/0.40 tff(26,plain,
% 0.14/0.40 (![B: $i, A: $i] : (multiply(A, B) = multiply(B, multiply(A, commutator(A, B))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.14/0.40 tff(27,plain,
% 0.14/0.40 ((~![B: $i, A: $i] : (multiply(A, B) = multiply(B, multiply(A, commutator(A, B))))) | (multiply(a, commutator(b, c)) = multiply(commutator(b, c), multiply(a, commutator(a, commutator(b, c)))))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(28,plain,
% 0.14/0.40 (multiply(a, commutator(b, c)) = multiply(commutator(b, c), multiply(a, commutator(a, commutator(b, c))))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.14/0.40 tff(29,plain,
% 0.14/0.40 (multiply(commutator(b, c), multiply(a, commutator(a, commutator(b, c)))) = multiply(a, commutator(b, c))),
% 0.14/0.40 inference(symmetry,[status(thm)],[28])).
% 0.14/0.40 tff(30,plain,
% 0.14/0.40 (^[B: $i, A: $i, C: $i] : refl((multiply(commutator(A, B), C) = multiply(C, commutator(A, B))) <=> (multiply(commutator(A, B), C) = multiply(C, commutator(A, B))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(31,plain,
% 0.14/0.40 (![B: $i, A: $i, C: $i] : (multiply(commutator(A, B), C) = multiply(C, commutator(A, B))) <=> ![B: $i, A: $i, C: $i] : (multiply(commutator(A, B), C) = multiply(C, commutator(A, B)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[30])).
% 0.14/0.40 tff(32,plain,
% 0.14/0.40 (![B: $i, A: $i, C: $i] : (multiply(commutator(A, B), C) = multiply(C, commutator(A, B))) <=> ![B: $i, A: $i, C: $i] : (multiply(commutator(A, B), C) = multiply(C, commutator(A, B)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(33,axiom,(![B: $i, A: $i, C: $i] : (multiply(commutator(A, B), C) = multiply(C, commutator(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','nilpotency')).
% 0.14/0.40 tff(34,plain,
% 0.14/0.40 (![B: $i, A: $i, C: $i] : (multiply(commutator(A, B), C) = multiply(C, commutator(A, B)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.14/0.40 tff(35,plain,(
% 0.14/0.40 ![B: $i, A: $i, C: $i] : (multiply(commutator(A, B), C) = multiply(C, commutator(A, B)))),
% 0.14/0.40 inference(skolemize,[status(sab)],[34])).
% 0.14/0.40 tff(36,plain,
% 0.14/0.40 (![B: $i, A: $i, C: $i] : (multiply(commutator(A, B), C) = multiply(C, commutator(A, B)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.14/0.40 tff(37,plain,
% 0.14/0.40 ((~![B: $i, A: $i, C: $i] : (multiply(commutator(A, B), C) = multiply(C, commutator(A, B)))) | (multiply(commutator(b, c), multiply(a, commutator(a, commutator(b, c)))) = multiply(multiply(a, commutator(a, commutator(b, c))), commutator(b, c)))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(38,plain,
% 0.14/0.40 (multiply(commutator(b, c), multiply(a, commutator(a, commutator(b, c)))) = multiply(multiply(a, commutator(a, commutator(b, c))), commutator(b, c))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.14/0.40 tff(39,plain,
% 0.14/0.40 (multiply(multiply(a, commutator(a, commutator(b, c))), commutator(b, c)) = multiply(commutator(b, c), multiply(a, commutator(a, commutator(b, c))))),
% 0.14/0.40 inference(symmetry,[status(thm)],[38])).
% 0.14/0.40 tff(40,plain,
% 0.14/0.40 (multiply(multiply(a, commutator(a, commutator(b, c))), commutator(b, c)) = multiply(a, commutator(b, c))),
% 0.14/0.40 inference(transitivity,[status(thm)],[39, 29])).
% 0.14/0.40 tff(41,plain,
% 0.14/0.40 (inj_0(commutator(b, c), multiply(multiply(a, commutator(a, commutator(b, c))), commutator(b, c))) = inj_0(commutator(b, c), multiply(a, commutator(b, c)))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[40])).
% 0.14/0.40 tff(42,plain,
% 0.14/0.40 ((~![Xk!0: $i, Xk!1: $i] : (inj_0(Xk!0, multiply(Xk!1, Xk!0)) = Xk!1)) | (inj_0(commutator(b, c), multiply(multiply(a, commutator(a, commutator(b, c))), commutator(b, c))) = multiply(a, commutator(a, commutator(b, c))))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(43,plain,
% 0.14/0.40 (inj_0(commutator(b, c), multiply(multiply(a, commutator(a, commutator(b, c))), commutator(b, c))) = multiply(a, commutator(a, commutator(b, c)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[42, 6])).
% 0.14/0.40 tff(44,plain,
% 0.14/0.40 (multiply(a, commutator(a, commutator(b, c))) = inj_0(commutator(b, c), multiply(multiply(a, commutator(a, commutator(b, c))), commutator(b, c)))),
% 0.14/0.40 inference(symmetry,[status(thm)],[43])).
% 0.14/0.40 tff(45,plain,
% 0.14/0.40 ((~![B: $i, A: $i, C: $i] : (multiply(commutator(A, B), C) = multiply(C, commutator(A, B)))) | (multiply(commutator(a, commutator(b, c)), a) = multiply(a, commutator(a, commutator(b, c))))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(46,plain,
% 0.14/0.40 (multiply(commutator(a, commutator(b, c)), a) = multiply(a, commutator(a, commutator(b, c)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[45, 36])).
% 0.14/0.40 tff(47,plain,
% 0.14/0.40 (multiply(commutator(a, commutator(b, c)), a) = a),
% 0.14/0.40 inference(transitivity,[status(thm)],[46, 44, 41, 19])).
% 0.14/0.40 tff(48,plain,
% 0.14/0.40 (multiply(multiply(commutator(a, commutator(b, c)), a), commutator(a, b)) = multiply(a, commutator(a, b))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[47])).
% 0.14/0.40 tff(49,plain,
% 0.14/0.40 (multiply(a, commutator(a, b)) = multiply(multiply(commutator(a, commutator(b, c)), a), commutator(a, b))),
% 0.14/0.40 inference(symmetry,[status(thm)],[48])).
% 0.14/0.40 tff(50,plain,
% 0.14/0.40 ((~![B: $i, A: $i, C: $i] : (multiply(commutator(A, B), C) = multiply(C, commutator(A, B)))) | (multiply(commutator(a, b), a) = multiply(a, commutator(a, b)))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(51,plain,
% 0.14/0.40 (multiply(commutator(a, b), a) = multiply(a, commutator(a, b))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[50, 36])).
% 0.14/0.40 tff(52,plain,
% 0.14/0.40 (![B: $i, A: $i, C: $i] : ((~(multiply(A, B) = multiply(A, C))) | (B = C)) <=> ![Xk!0: $i, Xk!1: $i] : (inj_1(Xk!1, multiply(Xk!1, Xk!0)) = Xk!0)),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(53,plain,
% 0.14/0.40 (![B: $i, A: $i, C: $i] : ((~(multiply(A, B) = multiply(A, C))) | (B = C)) <=> ![B: $i, A: $i, C: $i] : ((~(multiply(A, B) = multiply(A, C))) | (B = C))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(54,axiom,(![B: $i, A: $i, C: $i] : ((~(multiply(A, B) = multiply(A, C))) | (B = C))), file('/export/starexec/sandbox2/benchmark/Axioms/GRP008-1.ax','left_cancellation')).
% 0.14/0.40 tff(55,plain,
% 0.14/0.40 (![B: $i, A: $i, C: $i] : ((~(multiply(A, B) = multiply(A, C))) | (B = C))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.14/0.41 tff(56,plain,(
% 0.14/0.41 ![B: $i, A: $i, C: $i] : ((~(multiply(A, B) = multiply(A, C))) | (B = C))),
% 0.14/0.41 inference(skolemize,[status(sab)],[55])).
% 0.14/0.41 tff(57,plain,
% 0.14/0.41 (![Xk!0: $i, Xk!1: $i] : (inj_1(Xk!1, multiply(Xk!1, Xk!0)) = Xk!0)),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.14/0.41 tff(58,plain,
% 0.14/0.41 ((~![Xk!0: $i, Xk!1: $i] : (inj_1(Xk!1, multiply(Xk!1, Xk!0)) = Xk!0)) | (inj_1(c, multiply(c, commutator(a, b))) = commutator(a, b))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(59,plain,
% 0.14/0.41 (inj_1(c, multiply(c, commutator(a, b))) = commutator(a, b)),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.14/0.41 tff(60,plain,
% 0.14/0.41 ((~![B: $i, A: $i, C: $i] : (multiply(commutator(A, B), C) = multiply(C, commutator(A, B)))) | (multiply(commutator(a, b), c) = multiply(c, commutator(a, b)))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(61,plain,
% 0.14/0.41 (multiply(commutator(a, b), c) = multiply(c, commutator(a, b))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[60, 36])).
% 0.14/0.41 tff(62,plain,
% 0.14/0.41 ((~![B: $i, A: $i] : (multiply(A, B) = multiply(B, multiply(A, commutator(A, B))))) | (multiply(commutator(a, b), c) = multiply(c, multiply(commutator(a, b), commutator(commutator(a, b), c))))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(63,plain,
% 0.14/0.41 (multiply(commutator(a, b), c) = multiply(c, multiply(commutator(a, b), commutator(commutator(a, b), c)))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[62, 26])).
% 0.14/0.41 tff(64,plain,
% 0.14/0.41 (multiply(c, multiply(commutator(a, b), commutator(commutator(a, b), c))) = multiply(commutator(a, b), c)),
% 0.14/0.41 inference(symmetry,[status(thm)],[63])).
% 0.14/0.41 tff(65,plain,
% 0.14/0.41 (multiply(c, multiply(commutator(a, b), commutator(commutator(a, b), c))) = multiply(c, commutator(a, b))),
% 0.14/0.41 inference(transitivity,[status(thm)],[64, 61])).
% 0.14/0.41 tff(66,plain,
% 0.14/0.41 (inj_1(c, multiply(c, multiply(commutator(a, b), commutator(commutator(a, b), c)))) = inj_1(c, multiply(c, commutator(a, b)))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[65])).
% 0.14/0.41 tff(67,plain,
% 0.14/0.41 ((~![Xk!0: $i, Xk!1: $i] : (inj_1(Xk!1, multiply(Xk!1, Xk!0)) = Xk!0)) | (inj_1(c, multiply(c, multiply(commutator(a, b), commutator(commutator(a, b), c)))) = multiply(commutator(a, b), commutator(commutator(a, b), c)))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(68,plain,
% 0.14/0.41 (inj_1(c, multiply(c, multiply(commutator(a, b), commutator(commutator(a, b), c)))) = multiply(commutator(a, b), commutator(commutator(a, b), c))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[67, 57])).
% 0.14/0.41 tff(69,plain,
% 0.14/0.41 (multiply(commutator(a, b), commutator(commutator(a, b), c)) = inj_1(c, multiply(c, multiply(commutator(a, b), commutator(commutator(a, b), c))))),
% 0.14/0.41 inference(symmetry,[status(thm)],[68])).
% 0.14/0.41 tff(70,plain,
% 0.14/0.41 (multiply(commutator(a, b), commutator(commutator(a, b), c)) = commutator(a, b)),
% 0.14/0.41 inference(transitivity,[status(thm)],[69, 66, 59])).
% 0.14/0.41 tff(71,plain,
% 0.14/0.41 (multiply(multiply(commutator(a, b), commutator(commutator(a, b), c)), a) = multiply(commutator(a, b), a)),
% 0.14/0.41 inference(monotonicity,[status(thm)],[70])).
% 0.14/0.41 tff(72,plain,
% 0.14/0.41 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(commutator(a, b), commutator(commutator(a, b), c)), a) = multiply(commutator(a, b), multiply(commutator(commutator(a, b), c), a)))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(73,plain,
% 0.14/0.41 (multiply(multiply(commutator(a, b), commutator(commutator(a, b), c)), a) = multiply(commutator(a, b), multiply(commutator(commutator(a, b), c), a))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[72, 15])).
% 0.14/0.41 tff(74,plain,
% 0.14/0.41 (multiply(commutator(a, b), multiply(commutator(commutator(a, b), c), a)) = multiply(multiply(commutator(a, b), commutator(commutator(a, b), c)), a)),
% 0.14/0.41 inference(symmetry,[status(thm)],[73])).
% 0.14/0.41 tff(75,plain,
% 0.14/0.41 ((~![B: $i, A: $i, C: $i] : (multiply(commutator(A, B), C) = multiply(C, commutator(A, B)))) | (multiply(commutator(a, b), multiply(commutator(commutator(a, b), c), a)) = multiply(multiply(commutator(commutator(a, b), c), a), commutator(a, b)))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(76,plain,
% 0.14/0.41 (multiply(commutator(a, b), multiply(commutator(commutator(a, b), c), a)) = multiply(multiply(commutator(commutator(a, b), c), a), commutator(a, b))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[75, 36])).
% 0.14/0.41 tff(77,plain,
% 0.14/0.41 (multiply(multiply(commutator(commutator(a, b), c), a), commutator(a, b)) = multiply(commutator(a, b), multiply(commutator(commutator(a, b), c), a))),
% 0.14/0.41 inference(symmetry,[status(thm)],[76])).
% 0.14/0.41 tff(78,plain,
% 0.14/0.41 ((~![Z: $i, Y: $i, X: $i] : (multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)))) | (multiply(multiply(commutator(commutator(a, b), c), a), commutator(a, b)) = multiply(commutator(commutator(a, b), c), multiply(a, commutator(a, b))))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(79,plain,
% 0.14/0.41 (multiply(multiply(commutator(commutator(a, b), c), a), commutator(a, b)) = multiply(commutator(commutator(a, b), c), multiply(a, commutator(a, b)))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[78, 15])).
% 0.14/0.41 tff(80,plain,
% 0.14/0.41 (multiply(commutator(commutator(a, b), c), multiply(a, commutator(a, b))) = multiply(multiply(commutator(commutator(a, b), c), a), commutator(a, b))),
% 0.22/0.41 inference(symmetry,[status(thm)],[79])).
% 0.22/0.41 tff(81,plain,
% 0.22/0.41 (multiply(commutator(commutator(a, b), c), multiply(a, commutator(a, b))) = multiply(commutator(a, commutator(b, c)), multiply(a, commutator(a, b)))),
% 0.22/0.41 inference(transitivity,[status(thm)],[80, 77, 74, 71, 51, 49, 17])).
% 0.22/0.41 tff(82,plain,
% 0.22/0.41 (inj_0(multiply(a, commutator(a, b)), multiply(commutator(commutator(a, b), c), multiply(a, commutator(a, b)))) = inj_0(multiply(a, commutator(a, b)), multiply(commutator(a, commutator(b, c)), multiply(a, commutator(a, b))))),
% 0.22/0.41 inference(monotonicity,[status(thm)],[81])).
% 0.22/0.41 tff(83,plain,
% 0.22/0.41 ((~![Xk!0: $i, Xk!1: $i] : (inj_0(Xk!0, multiply(Xk!1, Xk!0)) = Xk!1)) | (inj_0(multiply(a, commutator(a, b)), multiply(commutator(commutator(a, b), c), multiply(a, commutator(a, b)))) = commutator(commutator(a, b), c))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(84,plain,
% 0.22/0.41 (inj_0(multiply(a, commutator(a, b)), multiply(commutator(commutator(a, b), c), multiply(a, commutator(a, b)))) = commutator(commutator(a, b), c)),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[83, 6])).
% 0.22/0.41 tff(85,plain,
% 0.22/0.41 (commutator(commutator(a, b), c) = inj_0(multiply(a, commutator(a, b)), multiply(commutator(commutator(a, b), c), multiply(a, commutator(a, b))))),
% 0.22/0.41 inference(symmetry,[status(thm)],[84])).
% 0.22/0.41 tff(86,plain,
% 0.22/0.41 (commutator(commutator(a, b), c) = commutator(a, commutator(b, c))),
% 0.22/0.41 inference(transitivity,[status(thm)],[85, 82, 8])).
% 0.22/0.41 tff(87,plain,
% 0.22/0.41 ((~(commutator(commutator(a, b), c) = commutator(a, commutator(b, c)))) <=> (~(commutator(commutator(a, b), c) = commutator(a, commutator(b, c))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(88,axiom,(~(commutator(commutator(a, b), c) = commutator(a, commutator(b, c)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_commutator_is_associative')).
% 0.22/0.41 tff(89,plain,
% 0.22/0.41 (~(commutator(commutator(a, b), c) = commutator(a, commutator(b, c)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.22/0.41 tff(90,plain,
% 0.22/0.41 ($false),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[89, 86])).
% 0.22/0.41 % SZS output end Proof
% 0.22/0.41 % E exiting
%------------------------------------------------------------------------------