%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP665+1 : TPTP v9.0.0. Released v4.0.0.
% 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 05:08:25 AM UTC 2025
% Result : Theorem 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP665+1 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 16:47:53 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(mult_type, type, (
% 0.21/0.39 mult: ( $i * $i ) > $i)).
% 0.21/0.39 tff(op_c_type, type, (
% 0.21/0.39 op_c: $i)).
% 0.21/0.39 tff(tptp_fun_X1_0_type, type, (
% 0.21/0.39 tptp_fun_X1_0: $i)).
% 0.21/0.39 tff(tptp_fun_X0_1_type, type, (
% 0.21/0.39 tptp_fun_X0_1: $i)).
% 0.21/0.39 tff(rd_type, type, (
% 0.21/0.39 rd: ( $i * $i ) > $i)).
% 0.21/0.39 tff(ld_type, type, (
% 0.21/0.39 ld: ( $i * $i ) > $i)).
% 0.21/0.39 tff(1,plain,
% 0.21/0.39 (^[A: $i] : refl((mult(op_c, A) = mult(A, op_c)) <=> (mult(op_c, A) = mult(A, op_c)))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 (![A: $i] : (mult(op_c, A) = mult(A, op_c)) <=> ![A: $i] : (mult(op_c, A) = mult(A, op_c))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.39 tff(3,plain,
% 0.21/0.39 (![A: $i] : (mult(op_c, A) = mult(A, op_c)) <=> ![A: $i] : (mult(op_c, A) = mult(A, op_c))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(4,axiom,(![A: $i] : (mult(op_c, A) = mult(A, op_c))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f09')).
% 0.21/0.39 tff(5,plain,
% 0.21/0.39 (![A: $i] : (mult(op_c, A) = mult(A, op_c))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.39 tff(6,plain,(
% 0.21/0.39 ![A: $i] : (mult(op_c, A) = mult(A, op_c))),
% 0.21/0.39 inference(skolemize,[status(sab)],[5])).
% 0.21/0.39 tff(7,plain,
% 0.21/0.39 (![A: $i] : (mult(op_c, A) = mult(A, op_c))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.39 tff(8,plain,
% 0.21/0.39 ((~![A: $i] : (mult(op_c, A) = mult(A, op_c))) | (mult(op_c, X1!0) = mult(X1!0, op_c))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(9,plain,
% 0.21/0.39 (mult(op_c, X1!0) = mult(X1!0, op_c)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.39 tff(10,plain,
% 0.21/0.39 (mult(X1!0, op_c) = mult(op_c, X1!0)),
% 0.21/0.39 inference(symmetry,[status(thm)],[9])).
% 0.21/0.39 tff(11,plain,
% 0.21/0.39 (mult(X0!1, mult(X1!0, op_c)) = mult(X0!1, mult(op_c, X1!0))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[10])).
% 0.21/0.39 tff(12,plain,
% 0.21/0.39 (mult(X0!1, mult(op_c, X1!0)) = mult(X0!1, mult(X1!0, op_c))),
% 0.21/0.39 inference(symmetry,[status(thm)],[11])).
% 0.21/0.39 tff(13,plain,
% 0.21/0.39 (^[C: $i, B: $i, A: $i] : refl((mult(A, mult(B, C)) = mult(rd(mult(A, B), A), mult(A, C))) <=> (mult(A, mult(B, C)) = mult(rd(mult(A, B), A), mult(A, C))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(14,plain,
% 0.21/0.39 (![C: $i, B: $i, A: $i] : (mult(A, mult(B, C)) = mult(rd(mult(A, B), A), mult(A, C))) <=> ![C: $i, B: $i, A: $i] : (mult(A, mult(B, C)) = mult(rd(mult(A, B), A), mult(A, C)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[13])).
% 0.21/0.39 tff(15,plain,
% 0.21/0.39 (![C: $i, B: $i, A: $i] : (mult(A, mult(B, C)) = mult(rd(mult(A, B), A), mult(A, C))) <=> ![C: $i, B: $i, A: $i] : (mult(A, mult(B, C)) = mult(rd(mult(A, B), A), mult(A, C)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(16,axiom,(![C: $i, B: $i, A: $i] : (mult(A, mult(B, C)) = mult(rd(mult(A, B), A), mult(A, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f07')).
% 0.21/0.39 tff(17,plain,
% 0.21/0.39 (![C: $i, B: $i, A: $i] : (mult(A, mult(B, C)) = mult(rd(mult(A, B), A), mult(A, C)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.21/0.39 tff(18,plain,(
% 0.21/0.39 ![C: $i, B: $i, A: $i] : (mult(A, mult(B, C)) = mult(rd(mult(A, B), A), mult(A, C)))),
% 0.21/0.39 inference(skolemize,[status(sab)],[17])).
% 0.21/0.39 tff(19,plain,
% 0.21/0.39 (![C: $i, B: $i, A: $i] : (mult(A, mult(B, C)) = mult(rd(mult(A, B), A), mult(A, C)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.21/0.39 tff(20,plain,
% 0.21/0.39 ((~![C: $i, B: $i, A: $i] : (mult(A, mult(B, C)) = mult(rd(mult(A, B), A), mult(A, C)))) | (mult(X0!1, mult(op_c, X1!0)) = mult(rd(mult(X0!1, op_c), X0!1), mult(X0!1, X1!0)))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(21,plain,
% 0.21/0.39 (mult(X0!1, mult(op_c, X1!0)) = mult(rd(mult(X0!1, op_c), X0!1), mult(X0!1, X1!0))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.21/0.39 tff(22,plain,
% 0.21/0.39 (mult(rd(mult(X0!1, op_c), X0!1), mult(X0!1, X1!0)) = mult(X0!1, mult(op_c, X1!0))),
% 0.21/0.39 inference(symmetry,[status(thm)],[21])).
% 0.21/0.39 tff(23,plain,
% 0.21/0.39 (^[B: $i, A: $i] : refl((rd(mult(A, B), B) = A) <=> (rd(mult(A, B), B) = A))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(24,plain,
% 0.21/0.39 (![B: $i, A: $i] : (rd(mult(A, B), B) = A) <=> ![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 0.21/0.39 inference(quant_intro,[status(thm)],[23])).
% 0.21/0.39 tff(25,plain,
% 0.21/0.39 (![B: $i, A: $i] : (rd(mult(A, B), B) = A) <=> ![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(26,axiom,(![B: $i, A: $i] : (rd(mult(A, B), B) = A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f04')).
% 0.21/0.39 tff(27,plain,
% 0.21/0.39 (![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.21/0.39 tff(28,plain,(
% 0.21/0.39 ![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 0.21/0.39 inference(skolemize,[status(sab)],[27])).
% 0.21/0.39 tff(29,plain,
% 0.21/0.39 (![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.21/0.39 tff(30,plain,
% 0.21/0.39 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(op_c, X0!1), X0!1) = op_c)),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(31,plain,
% 0.21/0.39 (rd(mult(op_c, X0!1), X0!1) = op_c),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.21/0.39 tff(32,plain,
% 0.21/0.39 ((~![A: $i] : (mult(op_c, A) = mult(A, op_c))) | (mult(op_c, X0!1) = mult(X0!1, op_c))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(33,plain,
% 0.21/0.39 (mult(op_c, X0!1) = mult(X0!1, op_c)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[32, 7])).
% 0.21/0.39 tff(34,plain,
% 0.21/0.39 (mult(X0!1, op_c) = mult(op_c, X0!1)),
% 0.21/0.39 inference(symmetry,[status(thm)],[33])).
% 0.21/0.39 tff(35,plain,
% 0.21/0.39 (rd(mult(X0!1, op_c), X0!1) = rd(mult(op_c, X0!1), X0!1)),
% 0.21/0.39 inference(monotonicity,[status(thm)],[34])).
% 0.21/0.39 tff(36,plain,
% 0.21/0.39 (rd(mult(X0!1, op_c), X0!1) = op_c),
% 0.21/0.39 inference(transitivity,[status(thm)],[35, 31])).
% 0.21/0.39 tff(37,plain,
% 0.21/0.39 (mult(rd(mult(X0!1, op_c), X0!1), mult(X0!1, X1!0)) = mult(op_c, mult(X0!1, X1!0))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[36])).
% 0.21/0.39 tff(38,plain,
% 0.21/0.39 (mult(op_c, mult(X0!1, X1!0)) = mult(rd(mult(X0!1, op_c), X0!1), mult(X0!1, X1!0))),
% 0.21/0.39 inference(symmetry,[status(thm)],[37])).
% 0.21/0.39 tff(39,plain,
% 0.21/0.39 ((~![A: $i] : (mult(op_c, A) = mult(A, op_c))) | (mult(op_c, mult(X0!1, X1!0)) = mult(mult(X0!1, X1!0), op_c))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(40,plain,
% 0.21/0.39 (mult(op_c, mult(X0!1, X1!0)) = mult(mult(X0!1, X1!0), op_c)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[39, 7])).
% 0.21/0.39 tff(41,plain,
% 0.21/0.39 (mult(mult(X0!1, X1!0), op_c) = mult(op_c, mult(X0!1, X1!0))),
% 0.21/0.39 inference(symmetry,[status(thm)],[40])).
% 0.21/0.39 tff(42,plain,
% 0.21/0.39 (mult(mult(X0!1, X1!0), op_c) = mult(X0!1, mult(X1!0, op_c))),
% 0.21/0.39 inference(transitivity,[status(thm)],[41, 38, 22, 12])).
% 0.21/0.39 tff(43,plain,
% 0.21/0.39 (ld(op_c, mult(X1!0, op_c)) = ld(op_c, mult(op_c, X1!0))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[10])).
% 0.21/0.39 tff(44,plain,
% 0.21/0.39 (ld(op_c, mult(op_c, X1!0)) = ld(op_c, mult(X1!0, op_c))),
% 0.21/0.39 inference(symmetry,[status(thm)],[43])).
% 0.21/0.39 tff(45,plain,
% 0.21/0.39 (^[B: $i, A: $i] : refl((ld(A, mult(A, B)) = B) <=> (ld(A, mult(A, B)) = B))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(46,plain,
% 0.21/0.39 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B) <=> ![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 0.21/0.39 inference(quant_intro,[status(thm)],[45])).
% 0.21/0.39 tff(47,plain,
% 0.21/0.39 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B) <=> ![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(48,axiom,(![B: $i, A: $i] : (ld(A, mult(A, B)) = B)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f02')).
% 0.21/0.39 tff(49,plain,
% 0.21/0.39 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.21/0.39 tff(50,plain,(
% 0.21/0.39 ![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 0.21/0.39 inference(skolemize,[status(sab)],[49])).
% 0.21/0.39 tff(51,plain,
% 0.21/0.39 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.21/0.39 tff(52,plain,
% 0.21/0.39 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(op_c, mult(op_c, X1!0)) = X1!0)),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(53,plain,
% 0.21/0.39 (ld(op_c, mult(op_c, X1!0)) = X1!0),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.21/0.39 tff(54,plain,
% 0.21/0.39 (X1!0 = ld(op_c, mult(op_c, X1!0))),
% 0.21/0.39 inference(symmetry,[status(thm)],[53])).
% 0.21/0.39 tff(55,plain,
% 0.21/0.39 (X1!0 = ld(op_c, mult(X1!0, op_c))),
% 0.21/0.39 inference(transitivity,[status(thm)],[54, 44])).
% 0.21/0.39 tff(56,plain,
% 0.21/0.39 (mult(mult(op_c, X0!1), X1!0) = mult(mult(X0!1, op_c), ld(op_c, mult(X1!0, op_c)))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[33, 55])).
% 0.21/0.39 tff(57,plain,
% 0.21/0.39 (mult(mult(X0!1, op_c), ld(op_c, mult(X1!0, op_c))) = mult(mult(op_c, X0!1), X1!0)),
% 0.21/0.39 inference(symmetry,[status(thm)],[56])).
% 0.21/0.39 tff(58,plain,
% 0.21/0.39 (^[C: $i, B: $i, A: $i] : refl((mult(mult(A, B), C) = mult(mult(A, C), ld(C, mult(B, C)))) <=> (mult(mult(A, B), C) = mult(mult(A, C), ld(C, mult(B, C)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(59,plain,
% 0.21/0.39 (![C: $i, B: $i, A: $i] : (mult(mult(A, B), C) = mult(mult(A, C), ld(C, mult(B, C)))) <=> ![C: $i, B: $i, A: $i] : (mult(mult(A, B), C) = mult(mult(A, C), ld(C, mult(B, C))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[58])).
% 0.21/0.39 tff(60,plain,
% 0.21/0.39 (![C: $i, B: $i, A: $i] : (mult(mult(A, B), C) = mult(mult(A, C), ld(C, mult(B, C)))) <=> ![C: $i, B: $i, A: $i] : (mult(mult(A, B), C) = mult(mult(A, C), ld(C, mult(B, C))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(61,axiom,(![C: $i, B: $i, A: $i] : (mult(mult(A, B), C) = mult(mult(A, C), ld(C, mult(B, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f08')).
% 0.21/0.39 tff(62,plain,
% 0.21/0.39 (![C: $i, B: $i, A: $i] : (mult(mult(A, B), C) = mult(mult(A, C), ld(C, mult(B, C))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.21/0.39 tff(63,plain,(
% 0.21/0.39 ![C: $i, B: $i, A: $i] : (mult(mult(A, B), C) = mult(mult(A, C), ld(C, mult(B, C))))),
% 0.21/0.39 inference(skolemize,[status(sab)],[62])).
% 0.21/0.39 tff(64,plain,
% 0.21/0.39 (![C: $i, B: $i, A: $i] : (mult(mult(A, B), C) = mult(mult(A, C), ld(C, mult(B, C))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.21/0.39 tff(65,plain,
% 0.21/0.39 ((~![C: $i, B: $i, A: $i] : (mult(mult(A, B), C) = mult(mult(A, C), ld(C, mult(B, C))))) | (mult(mult(X0!1, X1!0), op_c) = mult(mult(X0!1, op_c), ld(op_c, mult(X1!0, op_c))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(66,plain,
% 0.21/0.39 (mult(mult(X0!1, X1!0), op_c) = mult(mult(X0!1, op_c), ld(op_c, mult(X1!0, op_c)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.21/0.39 tff(67,plain,
% 0.21/0.39 (mult(op_c, mult(X0!1, X1!0)) = mult(mult(op_c, X0!1), X1!0)),
% 0.21/0.39 inference(transitivity,[status(thm)],[40, 66, 57])).
% 0.21/0.39 tff(68,assumption,(~(mult(op_c, mult(X0!1, X1!0)) = mult(mult(op_c, X0!1), X1!0))), introduced(assumption)).
% 0.21/0.39 tff(69,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.21/0.39 tff(70,plain,(mult(op_c, mult(X0!1, X1!0)) = mult(mult(op_c, X0!1), X1!0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.39 tff(71,plain,
% 0.21/0.39 (mult(mult(op_c, X0!1), X1!0) = mult(op_c, mult(X0!1, X1!0))),
% 0.21/0.39 inference(symmetry,[status(thm)],[70])).
% 0.21/0.39 tff(72,plain,
% 0.21/0.39 (mult(mult(X0!1, op_c), X1!0) = mult(mult(op_c, X0!1), X1!0)),
% 0.21/0.39 inference(monotonicity,[status(thm)],[34])).
% 0.21/0.39 tff(73,plain,
% 0.21/0.39 (mult(mult(X0!1, op_c), X1!0) = mult(X0!1, mult(op_c, X1!0))),
% 0.21/0.39 inference(transitivity,[status(thm)],[72, 71, 38, 22])).
% 0.21/0.39 tff(74,plain,
% 0.21/0.39 ((~(~((~(mult(op_c, mult(X0!1, X1!0)) = mult(mult(op_c, X0!1), X1!0))) | (~(mult(mult(X0!1, op_c), X1!0) = mult(X0!1, mult(op_c, X1!0)))) | (~(mult(mult(X0!1, X1!0), op_c) = mult(X0!1, mult(X1!0, op_c))))))) <=> ((~(mult(op_c, mult(X0!1, X1!0)) = mult(mult(op_c, X0!1), X1!0))) | (~(mult(mult(X0!1, op_c), X1!0) = mult(X0!1, mult(op_c, X1!0)))) | (~(mult(mult(X0!1, X1!0), op_c) = mult(X0!1, mult(X1!0, op_c)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(75,plain,
% 0.21/0.39 (((mult(op_c, mult(X0!1, X1!0)) = mult(mult(op_c, X0!1), X1!0)) & (mult(mult(X0!1, op_c), X1!0) = mult(X0!1, mult(op_c, X1!0))) & (mult(mult(X0!1, X1!0), op_c) = mult(X0!1, mult(X1!0, op_c)))) <=> (~((~(mult(op_c, mult(X0!1, X1!0)) = mult(mult(op_c, X0!1), X1!0))) | (~(mult(mult(X0!1, op_c), X1!0) = mult(X0!1, mult(op_c, X1!0)))) | (~(mult(mult(X0!1, X1!0), op_c) = mult(X0!1, mult(X1!0, op_c))))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(76,plain,
% 0.21/0.39 ((~((mult(op_c, mult(X0!1, X1!0)) = mult(mult(op_c, X0!1), X1!0)) & (mult(mult(X0!1, op_c), X1!0) = mult(X0!1, mult(op_c, X1!0))) & (mult(mult(X0!1, X1!0), op_c) = mult(X0!1, mult(X1!0, op_c))))) <=> (~(~((~(mult(op_c, mult(X0!1, X1!0)) = mult(mult(op_c, X0!1), X1!0))) | (~(mult(mult(X0!1, op_c), X1!0) = mult(X0!1, mult(op_c, X1!0)))) | (~(mult(mult(X0!1, X1!0), op_c) = mult(X0!1, mult(X1!0, op_c)))))))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[75])).
% 0.21/0.40 tff(77,plain,
% 0.21/0.40 ((~((mult(op_c, mult(X0!1, X1!0)) = mult(mult(op_c, X0!1), X1!0)) & (mult(mult(X0!1, op_c), X1!0) = mult(X0!1, mult(op_c, X1!0))) & (mult(mult(X0!1, X1!0), op_c) = mult(X0!1, mult(X1!0, op_c))))) <=> ((~(mult(op_c, mult(X0!1, X1!0)) = mult(mult(op_c, X0!1), X1!0))) | (~(mult(mult(X0!1, op_c), X1!0) = mult(X0!1, mult(op_c, X1!0)))) | (~(mult(mult(X0!1, X1!0), op_c) = mult(X0!1, mult(X1!0, op_c)))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[76, 74])).
% 0.21/0.40 tff(78,plain,
% 0.21/0.40 ((~![X0: $i, X1: $i] : ((mult(op_c, mult(X0, X1)) = mult(mult(op_c, X0), X1)) & (mult(mult(X0, op_c), X1) = mult(X0, mult(op_c, X1))) & (mult(mult(X0, X1), op_c) = mult(X0, mult(X1, op_c))))) <=> (~![X0: $i, X1: $i] : ((mult(op_c, mult(X0, X1)) = mult(mult(op_c, X0), X1)) & (mult(mult(X0, op_c), X1) = mult(X0, mult(op_c, X1))) & (mult(mult(X0, X1), op_c) = mult(X0, mult(X1, op_c)))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(79,plain,
% 0.21/0.40 ((~![X0: $i, X1: $i] : (((mult(op_c, mult(X0, X1)) = mult(mult(op_c, X0), X1)) & (mult(mult(X0, op_c), X1) = mult(X0, mult(op_c, X1)))) & (mult(mult(X0, X1), op_c) = mult(X0, mult(X1, op_c))))) <=> (~![X0: $i, X1: $i] : ((mult(op_c, mult(X0, X1)) = mult(mult(op_c, X0), X1)) & (mult(mult(X0, op_c), X1) = mult(X0, mult(op_c, X1))) & (mult(mult(X0, X1), op_c) = mult(X0, mult(X1, op_c)))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(80,axiom,(~![X0: $i, X1: $i] : (((mult(op_c, mult(X0, X1)) = mult(mult(op_c, X0), X1)) & (mult(mult(X0, op_c), X1) = mult(X0, mult(op_c, X1)))) & (mult(mult(X0, X1), op_c) = mult(X0, mult(X1, op_c))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 0.21/0.40 tff(81,plain,
% 0.21/0.40 (~![X0: $i, X1: $i] : ((mult(op_c, mult(X0, X1)) = mult(mult(op_c, X0), X1)) & (mult(mult(X0, op_c), X1) = mult(X0, mult(op_c, X1))) & (mult(mult(X0, X1), op_c) = mult(X0, mult(X1, op_c))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.21/0.40 tff(82,plain,
% 0.21/0.40 (~![X0: $i, X1: $i] : ((mult(op_c, mult(X0, X1)) = mult(mult(op_c, X0), X1)) & (mult(mult(X0, op_c), X1) = mult(X0, mult(op_c, X1))) & (mult(mult(X0, X1), op_c) = mult(X0, mult(X1, op_c))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[81, 78])).
% 0.21/0.40 tff(83,plain,
% 0.21/0.40 (~![X0: $i, X1: $i] : ((mult(op_c, mult(X0, X1)) = mult(mult(op_c, X0), X1)) & (mult(mult(X0, op_c), X1) = mult(X0, mult(op_c, X1))) & (mult(mult(X0, X1), op_c) = mult(X0, mult(X1, op_c))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.21/0.40 tff(84,plain,
% 0.21/0.40 (~![X0: $i, X1: $i] : ((mult(op_c, mult(X0, X1)) = mult(mult(op_c, X0), X1)) & (mult(mult(X0, op_c), X1) = mult(X0, mult(op_c, X1))) & (mult(mult(X0, X1), op_c) = mult(X0, mult(X1, op_c))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[83, 78])).
% 0.21/0.40 tff(85,plain,(
% 0.21/0.40 ~((mult(op_c, mult(X0!1, X1!0)) = mult(mult(op_c, X0!1), X1!0)) & (mult(mult(X0!1, op_c), X1!0) = mult(X0!1, mult(op_c, X1!0))) & (mult(mult(X0!1, X1!0), op_c) = mult(X0!1, mult(X1!0, op_c))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[84])).
% 0.21/0.40 tff(86,plain,
% 0.21/0.40 ((~(mult(op_c, mult(X0!1, X1!0)) = mult(mult(op_c, X0!1), X1!0))) | (~(mult(mult(X0!1, op_c), X1!0) = mult(X0!1, mult(op_c, X1!0)))) | (~(mult(mult(X0!1, X1!0), op_c) = mult(X0!1, mult(X1!0, op_c))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[85, 77])).
% 0.21/0.40 tff(87,plain,
% 0.21/0.40 (~(mult(mult(X0!1, X1!0), op_c) = mult(X0!1, mult(X1!0, op_c)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[86, 73, 70])).
% 0.21/0.40 tff(88,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[87, 42])).
% 0.21/0.40 % SZS output end Proof
% 0.21/0.40 % E exiting
%------------------------------------------------------------------------------