TSTP Solution File: GRP704+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP704+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 : Fri Sep 16 22:29:34 EDT 2022
% Result : Theorem 0.21s 0.49s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP704+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 31 20:02:32 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.49 % SZS status Theorem
% 0.21/0.49 % SZS output start Proof
% 0.21/0.49 tff(mult_type, type, (
% 0.21/0.49 mult: ( $i * $i ) > $i)).
% 0.21/0.49 tff(tptp_fun_X5_0_type, type, (
% 0.21/0.49 tptp_fun_X5_0: $i)).
% 0.21/0.49 tff(op_f_type, type, (
% 0.21/0.49 op_f: $i)).
% 0.21/0.49 tff(tptp_fun_X4_1_type, type, (
% 0.21/0.49 tptp_fun_X4_1: $i)).
% 0.21/0.49 tff(op_c_type, type, (
% 0.21/0.49 op_c: $i)).
% 0.21/0.49 tff(ld_type, type, (
% 0.21/0.49 ld: ( $i * $i ) > $i)).
% 0.21/0.49 tff(unit_type, type, (
% 0.21/0.49 unit: $i)).
% 0.21/0.49 tff(op_d_type, type, (
% 0.21/0.49 op_d: $i)).
% 0.21/0.49 tff(1,plain,
% 0.21/0.49 (^[B: $i, A: $i] : refl((op_f = mult(A, mult(B, ld(mult(A, B), op_c)))) <=> (op_f = mult(A, mult(B, ld(mult(A, B), op_c)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(2,plain,
% 0.21/0.49 (![B: $i, A: $i] : (op_f = mult(A, mult(B, ld(mult(A, B), op_c)))) <=> ![B: $i, A: $i] : (op_f = mult(A, mult(B, ld(mult(A, B), op_c))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.49 tff(3,plain,
% 0.21/0.49 (![B: $i, A: $i] : (op_f = mult(A, mult(B, ld(mult(A, B), op_c)))) <=> ![B: $i, A: $i] : (op_f = mult(A, mult(B, ld(mult(A, B), op_c))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(4,axiom,(![B: $i, A: $i] : (op_f = mult(A, mult(B, ld(mult(A, B), op_c))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f13')).
% 0.21/0.49 tff(5,plain,
% 0.21/0.49 (![B: $i, A: $i] : (op_f = mult(A, mult(B, ld(mult(A, B), op_c))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.49 tff(6,plain,(
% 0.21/0.49 ![B: $i, A: $i] : (op_f = mult(A, mult(B, ld(mult(A, B), op_c))))),
% 0.21/0.49 inference(skolemize,[status(sab)],[5])).
% 0.21/0.49 tff(7,plain,
% 0.21/0.49 (![B: $i, A: $i] : (op_f = mult(A, mult(B, ld(mult(A, B), op_c))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.49 tff(8,plain,
% 0.21/0.49 ((~![B: $i, A: $i] : (op_f = mult(A, mult(B, ld(mult(A, B), op_c))))) | (op_f = mult(unit, mult(unit, ld(mult(unit, unit), op_c))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(9,plain,
% 0.21/0.49 (op_f = mult(unit, mult(unit, ld(mult(unit, unit), op_c)))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.49 tff(10,plain,
% 0.21/0.49 (mult(unit, mult(unit, ld(mult(unit, unit), op_c))) = op_f),
% 0.21/0.49 inference(symmetry,[status(thm)],[9])).
% 0.21/0.49 tff(11,plain,
% 0.21/0.49 (^[A: $i] : refl((mult(unit, A) = A) <=> (mult(unit, A) = A))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(12,plain,
% 0.21/0.49 (![A: $i] : (mult(unit, A) = A) <=> ![A: $i] : (mult(unit, A) = A)),
% 0.21/0.49 inference(quant_intro,[status(thm)],[11])).
% 0.21/0.49 tff(13,plain,
% 0.21/0.49 (![A: $i] : (mult(unit, A) = A) <=> ![A: $i] : (mult(unit, A) = A)),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(14,axiom,(![A: $i] : (mult(unit, A) = A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f06')).
% 0.21/0.49 tff(15,plain,
% 0.21/0.49 (![A: $i] : (mult(unit, A) = A)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.21/0.49 tff(16,plain,(
% 0.21/0.49 ![A: $i] : (mult(unit, A) = A)),
% 0.21/0.49 inference(skolemize,[status(sab)],[15])).
% 0.21/0.49 tff(17,plain,
% 0.21/0.49 (![A: $i] : (mult(unit, A) = A)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.21/0.49 tff(18,plain,
% 0.21/0.49 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, op_c) = op_c)),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(19,plain,
% 0.21/0.49 (mult(unit, op_c) = op_c),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.21/0.49 tff(20,plain,
% 0.21/0.49 (^[B: $i, A: $i] : refl((ld(A, mult(A, B)) = B) <=> (ld(A, mult(A, B)) = B))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(21,plain,
% 0.21/0.49 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B) <=> ![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 0.21/0.49 inference(quant_intro,[status(thm)],[20])).
% 0.21/0.49 tff(22,plain,
% 0.21/0.49 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B) <=> ![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(23,axiom,(![B: $i, A: $i] : (ld(A, mult(A, B)) = B)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f02')).
% 0.21/0.49 tff(24,plain,
% 0.21/0.49 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.21/0.49 tff(25,plain,(
% 0.21/0.49 ![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 0.21/0.49 inference(skolemize,[status(sab)],[24])).
% 0.21/0.49 tff(26,plain,
% 0.21/0.49 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.21/0.49 tff(27,plain,
% 0.21/0.49 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(unit, mult(unit, op_c)) = op_c)),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(28,plain,
% 0.21/0.49 (ld(unit, mult(unit, op_c)) = op_c),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.21/0.49 tff(29,plain,
% 0.21/0.49 (op_c = mult(unit, op_c)),
% 0.21/0.49 inference(symmetry,[status(thm)],[19])).
% 0.21/0.49 tff(30,plain,
% 0.21/0.49 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, unit) = unit)),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(31,plain,
% 0.21/0.49 (mult(unit, unit) = unit),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[30, 17])).
% 0.21/0.49 tff(32,plain,
% 0.21/0.49 (ld(mult(unit, unit), op_c) = ld(unit, mult(unit, op_c))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[31, 29])).
% 0.21/0.49 tff(33,plain,
% 0.21/0.49 (ld(mult(unit, unit), op_c) = op_c),
% 0.21/0.49 inference(transitivity,[status(thm)],[32, 28])).
% 0.21/0.49 tff(34,plain,
% 0.21/0.49 (mult(unit, ld(mult(unit, unit), op_c)) = mult(unit, op_c)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[33])).
% 0.21/0.49 tff(35,plain,
% 0.21/0.49 (mult(unit, ld(mult(unit, unit), op_c)) = op_c),
% 0.21/0.49 inference(transitivity,[status(thm)],[34, 19])).
% 0.21/0.49 tff(36,plain,
% 0.21/0.49 (mult(unit, mult(unit, ld(mult(unit, unit), op_c))) = mult(unit, op_c)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[35])).
% 0.21/0.49 tff(37,plain,
% 0.21/0.49 (mult(unit, op_c) = mult(unit, mult(unit, ld(mult(unit, unit), op_c)))),
% 0.21/0.49 inference(symmetry,[status(thm)],[36])).
% 0.21/0.49 tff(38,plain,
% 0.21/0.49 (op_c = op_f),
% 0.21/0.49 inference(transitivity,[status(thm)],[29, 37, 10])).
% 0.21/0.49 tff(39,plain,
% 0.21/0.49 (mult(X4!1, op_c) = mult(X4!1, op_f)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[38])).
% 0.21/0.49 tff(40,plain,
% 0.21/0.49 (mult(X4!1, op_f) = mult(X4!1, op_c)),
% 0.21/0.49 inference(symmetry,[status(thm)],[39])).
% 0.21/0.49 tff(41,plain,
% 0.21/0.49 (mult(mult(X4!1, op_f), X5!0) = mult(mult(X4!1, op_c), X5!0)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[40])).
% 0.21/0.49 tff(42,plain,
% 0.21/0.49 (mult(mult(X4!1, op_c), X5!0) = mult(mult(X4!1, op_f), X5!0)),
% 0.21/0.49 inference(symmetry,[status(thm)],[41])).
% 0.21/0.49 tff(43,plain,
% 0.21/0.49 (^[B: $i, A: $i] : refl((mult(A, mult(op_c, B)) = mult(mult(A, op_c), B)) <=> (mult(A, mult(op_c, B)) = mult(mult(A, op_c), B)))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(44,plain,
% 0.21/0.49 (![B: $i, A: $i] : (mult(A, mult(op_c, B)) = mult(mult(A, op_c), B)) <=> ![B: $i, A: $i] : (mult(A, mult(op_c, B)) = mult(mult(A, op_c), B))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[43])).
% 0.21/0.49 tff(45,plain,
% 0.21/0.49 (![B: $i, A: $i] : (mult(A, mult(op_c, B)) = mult(mult(A, op_c), B)) <=> ![B: $i, A: $i] : (mult(A, mult(op_c, B)) = mult(mult(A, op_c), B))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(46,axiom,(![B: $i, A: $i] : (mult(A, mult(op_c, B)) = mult(mult(A, op_c), B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f10')).
% 0.21/0.49 tff(47,plain,
% 0.21/0.49 (![B: $i, A: $i] : (mult(A, mult(op_c, B)) = mult(mult(A, op_c), B))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.21/0.49 tff(48,plain,(
% 0.21/0.49 ![B: $i, A: $i] : (mult(A, mult(op_c, B)) = mult(mult(A, op_c), B))),
% 0.21/0.49 inference(skolemize,[status(sab)],[47])).
% 0.21/0.49 tff(49,plain,
% 0.21/0.49 (![B: $i, A: $i] : (mult(A, mult(op_c, B)) = mult(mult(A, op_c), B))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.21/0.49 tff(50,plain,
% 0.21/0.49 ((~![B: $i, A: $i] : (mult(A, mult(op_c, B)) = mult(mult(A, op_c), B))) | (mult(X4!1, mult(op_c, X5!0)) = mult(mult(X4!1, op_c), X5!0))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(51,plain,
% 0.21/0.49 (mult(X4!1, mult(op_c, X5!0)) = mult(mult(X4!1, op_c), X5!0)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.21/0.49 tff(52,plain,
% 0.21/0.49 (^[A: $i] : refl((op_d = ld(A, mult(op_c, A))) <=> (op_d = ld(A, mult(op_c, A))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(53,plain,
% 0.21/0.49 (![A: $i] : (op_d = ld(A, mult(op_c, A))) <=> ![A: $i] : (op_d = ld(A, mult(op_c, A)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[52])).
% 0.21/0.49 tff(54,plain,
% 0.21/0.49 (![A: $i] : (op_d = ld(A, mult(op_c, A))) <=> ![A: $i] : (op_d = ld(A, mult(op_c, A)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(55,axiom,(![A: $i] : (op_d = ld(A, mult(op_c, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f11')).
% 0.21/0.49 tff(56,plain,
% 0.21/0.49 (![A: $i] : (op_d = ld(A, mult(op_c, A)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.21/0.49 tff(57,plain,(
% 0.21/0.49 ![A: $i] : (op_d = ld(A, mult(op_c, A)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[56])).
% 0.21/0.49 tff(58,plain,
% 0.21/0.49 (![A: $i] : (op_d = ld(A, mult(op_c, A)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.21/0.49 tff(59,plain,
% 0.21/0.49 ((~![A: $i] : (op_d = ld(A, mult(op_c, A)))) | (op_d = ld(X5!0, mult(op_c, X5!0)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(60,plain,
% 0.21/0.49 (op_d = ld(X5!0, mult(op_c, X5!0))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.21/0.49 tff(61,plain,
% 0.21/0.49 ((~![A: $i] : (op_d = ld(A, mult(op_c, A)))) | (op_d = ld(unit, mult(op_c, unit)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(62,plain,
% 0.21/0.49 (op_d = ld(unit, mult(op_c, unit))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[61, 58])).
% 0.21/0.49 tff(63,plain,
% 0.21/0.49 (ld(unit, mult(op_c, unit)) = op_d),
% 0.21/0.49 inference(symmetry,[status(thm)],[62])).
% 0.21/0.49 tff(64,plain,
% 0.21/0.49 (^[A: $i] : refl((mult(A, unit) = A) <=> (mult(A, unit) = A))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(65,plain,
% 0.21/0.49 (![A: $i] : (mult(A, unit) = A) <=> ![A: $i] : (mult(A, unit) = A)),
% 0.21/0.49 inference(quant_intro,[status(thm)],[64])).
% 0.21/0.49 tff(66,plain,
% 0.21/0.49 (![A: $i] : (mult(A, unit) = A) <=> ![A: $i] : (mult(A, unit) = A)),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(67,axiom,(![A: $i] : (mult(A, unit) = A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f05')).
% 0.21/0.49 tff(68,plain,
% 0.21/0.49 (![A: $i] : (mult(A, unit) = A)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.21/0.49 tff(69,plain,(
% 0.21/0.49 ![A: $i] : (mult(A, unit) = A)),
% 0.21/0.49 inference(skolemize,[status(sab)],[68])).
% 0.21/0.49 tff(70,plain,
% 0.21/0.49 (![A: $i] : (mult(A, unit) = A)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.21/0.49 tff(71,plain,
% 0.21/0.49 ((~![A: $i] : (mult(A, unit) = A)) | (mult(op_c, unit) = op_c)),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(72,plain,
% 0.21/0.49 (mult(op_c, unit) = op_c),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.21/0.49 tff(73,plain,
% 0.21/0.49 (mult(op_c, unit) = mult(unit, op_c)),
% 0.21/0.49 inference(transitivity,[status(thm)],[72, 29])).
% 0.21/0.49 tff(74,plain,
% 0.21/0.49 (ld(unit, mult(op_c, unit)) = ld(unit, mult(unit, op_c))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[73])).
% 0.21/0.49 tff(75,plain,
% 0.21/0.49 (ld(unit, mult(unit, op_c)) = ld(unit, mult(op_c, unit))),
% 0.21/0.49 inference(symmetry,[status(thm)],[74])).
% 0.21/0.49 tff(76,plain,
% 0.21/0.49 (op_c = ld(unit, mult(unit, op_c))),
% 0.21/0.49 inference(symmetry,[status(thm)],[28])).
% 0.21/0.49 tff(77,plain,
% 0.21/0.49 (op_f = ld(X5!0, mult(op_c, X5!0))),
% 0.21/0.49 inference(transitivity,[status(thm)],[9, 36, 19, 76, 75, 63, 60])).
% 0.21/0.49 tff(78,plain,
% 0.21/0.49 (mult(X5!0, op_f) = mult(X5!0, ld(X5!0, mult(op_c, X5!0)))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[77])).
% 0.21/0.49 tff(79,plain,
% 0.21/0.49 (mult(X5!0, ld(X5!0, mult(op_c, X5!0))) = mult(X5!0, op_f)),
% 0.21/0.49 inference(symmetry,[status(thm)],[78])).
% 0.21/0.49 tff(80,plain,
% 0.21/0.49 (^[B: $i, A: $i] : refl((mult(A, ld(A, B)) = B) <=> (mult(A, ld(A, B)) = B))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(81,plain,
% 0.21/0.49 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B) <=> ![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 0.21/0.49 inference(quant_intro,[status(thm)],[80])).
% 0.21/0.49 tff(82,plain,
% 0.21/0.49 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B) <=> ![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(83,axiom,(![B: $i, A: $i] : (mult(A, ld(A, B)) = B)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f01')).
% 0.21/0.49 tff(84,plain,
% 0.21/0.49 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.21/0.49 tff(85,plain,(
% 0.21/0.49 ![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 0.21/0.49 inference(skolemize,[status(sab)],[84])).
% 0.21/0.49 tff(86,plain,
% 0.21/0.49 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.21/0.49 tff(87,plain,
% 0.21/0.49 ((~![B: $i, A: $i] : (mult(A, ld(A, B)) = B)) | (mult(X5!0, ld(X5!0, mult(op_c, X5!0))) = mult(op_c, X5!0))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(88,plain,
% 0.21/0.49 (mult(X5!0, ld(X5!0, mult(op_c, X5!0))) = mult(op_c, X5!0)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.21/0.49 tff(89,plain,
% 0.21/0.49 (mult(op_c, X5!0) = mult(X5!0, ld(X5!0, mult(op_c, X5!0)))),
% 0.21/0.49 inference(symmetry,[status(thm)],[88])).
% 0.21/0.49 tff(90,plain,
% 0.21/0.49 (mult(op_c, X5!0) = mult(X5!0, op_f)),
% 0.21/0.49 inference(transitivity,[status(thm)],[89, 79])).
% 0.21/0.49 tff(91,plain,
% 0.21/0.49 (mult(X4!1, mult(op_c, X5!0)) = mult(X4!1, mult(X5!0, op_f))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[90])).
% 0.21/0.49 tff(92,plain,
% 0.21/0.49 (mult(X4!1, mult(X5!0, op_f)) = mult(X4!1, mult(op_c, X5!0))),
% 0.21/0.49 inference(symmetry,[status(thm)],[91])).
% 0.21/0.49 tff(93,plain,
% 0.21/0.49 (op_f = op_c),
% 0.21/0.49 inference(transitivity,[status(thm)],[9, 36, 19])).
% 0.21/0.49 tff(94,plain,
% 0.21/0.49 (mult(op_f, X5!0) = mult(op_c, X5!0)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[93])).
% 0.21/0.49 tff(95,plain,
% 0.21/0.49 (mult(op_c, X5!0) = mult(op_f, X5!0)),
% 0.21/0.49 inference(symmetry,[status(thm)],[94])).
% 0.21/0.49 tff(96,plain,
% 0.21/0.49 (mult(X5!0, op_f) = mult(op_f, X5!0)),
% 0.21/0.49 inference(transitivity,[status(thm)],[78, 88, 95])).
% 0.21/0.49 tff(97,plain,
% 0.21/0.49 (mult(X4!1, mult(X5!0, op_f)) = mult(X4!1, mult(op_f, X5!0))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[96])).
% 0.21/0.49 tff(98,plain,
% 0.21/0.49 (mult(X4!1, mult(op_f, X5!0)) = mult(X4!1, mult(X5!0, op_f))),
% 0.21/0.49 inference(symmetry,[status(thm)],[97])).
% 0.21/0.49 tff(99,plain,
% 0.21/0.49 (mult(X4!1, mult(op_f, X5!0)) = mult(mult(X4!1, op_f), X5!0)),
% 0.21/0.49 inference(transitivity,[status(thm)],[98, 92, 51, 42])).
% 0.21/0.49 tff(100,plain,
% 0.21/0.49 (mult(mult(X4!1, X5!0), op_f) = mult(mult(X4!1, X5!0), op_c)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[93])).
% 0.21/0.49 tff(101,plain,
% 0.21/0.49 (mult(mult(X4!1, X5!0), op_c) = mult(mult(X4!1, X5!0), op_f)),
% 0.21/0.49 inference(symmetry,[status(thm)],[100])).
% 0.21/0.49 tff(102,plain,
% 0.21/0.49 (^[B: $i, A: $i] : refl((mult(A, mult(B, op_c)) = mult(mult(A, B), op_c)) <=> (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c)))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(103,plain,
% 0.21/0.49 (![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c)) <=> ![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[102])).
% 0.21/0.49 tff(104,plain,
% 0.21/0.49 (![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c)) <=> ![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(105,axiom,(![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f09')).
% 0.21/0.49 tff(106,plain,
% 0.21/0.49 (![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.21/0.49 tff(107,plain,(
% 0.21/0.49 ![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c))),
% 0.21/0.49 inference(skolemize,[status(sab)],[106])).
% 0.21/0.49 tff(108,plain,
% 0.21/0.49 (![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.21/0.49 tff(109,plain,
% 0.21/0.49 ((~![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c))) | (mult(X4!1, mult(X5!0, op_c)) = mult(mult(X4!1, X5!0), op_c))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(110,plain,
% 0.21/0.49 (mult(X4!1, mult(X5!0, op_c)) = mult(mult(X4!1, X5!0), op_c)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.21/0.49 tff(111,plain,
% 0.21/0.49 (op_c = ld(X5!0, mult(op_c, X5!0))),
% 0.21/0.49 inference(transitivity,[status(thm)],[76, 75, 63, 60])).
% 0.21/0.49 tff(112,plain,
% 0.21/0.49 (mult(X5!0, op_c) = mult(X5!0, ld(X5!0, mult(op_c, X5!0)))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[111])).
% 0.21/0.49 tff(113,plain,
% 0.21/0.49 (mult(X5!0, op_c) = mult(X5!0, op_f)),
% 0.21/0.49 inference(transitivity,[status(thm)],[112, 79])).
% 0.21/0.49 tff(114,plain,
% 0.21/0.49 (mult(X4!1, mult(X5!0, op_c)) = mult(X4!1, mult(X5!0, op_f))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[113])).
% 0.21/0.49 tff(115,plain,
% 0.21/0.49 (mult(X4!1, mult(X5!0, op_f)) = mult(X4!1, mult(X5!0, op_c))),
% 0.21/0.49 inference(symmetry,[status(thm)],[114])).
% 0.21/0.49 tff(116,plain,
% 0.21/0.49 (mult(X4!1, mult(X5!0, op_f)) = mult(mult(X4!1, X5!0), op_f)),
% 0.21/0.49 inference(transitivity,[status(thm)],[115, 110, 101])).
% 0.21/0.49 tff(117,plain,
% 0.21/0.49 ((~![A: $i] : (op_d = ld(A, mult(op_c, A)))) | (op_d = ld(X4!1, mult(op_c, X4!1)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(118,plain,
% 0.21/0.49 (op_d = ld(X4!1, mult(op_c, X4!1))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[117, 58])).
% 0.21/0.49 tff(119,plain,
% 0.21/0.49 (ld(X4!1, mult(op_c, X4!1)) = op_d),
% 0.21/0.49 inference(symmetry,[status(thm)],[118])).
% 0.21/0.49 tff(120,plain,
% 0.21/0.49 (ld(X4!1, mult(op_c, X4!1)) = op_c),
% 0.21/0.49 inference(transitivity,[status(thm)],[119, 62, 74, 28])).
% 0.21/0.49 tff(121,plain,
% 0.21/0.49 (mult(X4!1, ld(X4!1, mult(op_c, X4!1))) = mult(X4!1, op_c)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[120])).
% 0.21/0.50 tff(122,plain,
% 0.21/0.50 ((~![B: $i, A: $i] : (mult(A, ld(A, B)) = B)) | (mult(X4!1, ld(X4!1, mult(op_c, X4!1))) = mult(op_c, X4!1))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(123,plain,
% 0.21/0.50 (mult(X4!1, ld(X4!1, mult(op_c, X4!1))) = mult(op_c, X4!1)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[122, 86])).
% 0.21/0.50 tff(124,plain,
% 0.21/0.50 (mult(op_c, X4!1) = mult(X4!1, ld(X4!1, mult(op_c, X4!1)))),
% 0.21/0.50 inference(symmetry,[status(thm)],[123])).
% 0.21/0.50 tff(125,plain,
% 0.21/0.50 (mult(op_f, X4!1) = mult(op_c, X4!1)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[93])).
% 0.21/0.50 tff(126,plain,
% 0.21/0.50 (mult(op_f, X4!1) = mult(X4!1, op_f)),
% 0.21/0.50 inference(transitivity,[status(thm)],[125, 124, 121, 39])).
% 0.21/0.50 tff(127,plain,
% 0.21/0.50 (mult(mult(op_f, X4!1), X5!0) = mult(mult(X4!1, op_f), X5!0)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[126])).
% 0.21/0.50 tff(128,plain,
% 0.21/0.50 (mult(mult(X4!1, op_f), X5!0) = mult(mult(op_f, X4!1), X5!0)),
% 0.21/0.50 inference(symmetry,[status(thm)],[127])).
% 0.21/0.50 tff(129,plain,
% 0.21/0.50 (mult(op_c, X4!1) = mult(X4!1, op_f)),
% 0.21/0.50 inference(transitivity,[status(thm)],[124, 121, 39])).
% 0.21/0.50 tff(130,plain,
% 0.21/0.50 (mult(mult(op_c, X4!1), X5!0) = mult(mult(X4!1, op_f), X5!0)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[129])).
% 0.21/0.50 tff(131,plain,
% 0.21/0.50 (^[B: $i, A: $i] : refl((mult(op_c, mult(A, B)) = mult(mult(op_c, A), B)) <=> (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B)))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(132,plain,
% 0.21/0.50 (![B: $i, A: $i] : (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B)) <=> ![B: $i, A: $i] : (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[131])).
% 0.21/0.50 tff(133,plain,
% 0.21/0.50 (![B: $i, A: $i] : (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B)) <=> ![B: $i, A: $i] : (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(134,axiom,(![B: $i, A: $i] : (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f08')).
% 0.21/0.50 tff(135,plain,
% 0.21/0.50 (![B: $i, A: $i] : (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.21/0.50 tff(136,plain,(
% 0.21/0.50 ![B: $i, A: $i] : (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B))),
% 0.21/0.50 inference(skolemize,[status(sab)],[135])).
% 0.21/0.50 tff(137,plain,
% 0.21/0.50 (![B: $i, A: $i] : (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.21/0.50 tff(138,plain,
% 0.21/0.50 ((~![B: $i, A: $i] : (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B))) | (mult(op_c, mult(X4!1, X5!0)) = mult(mult(op_c, X4!1), X5!0))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(139,plain,
% 0.21/0.50 (mult(op_c, mult(X4!1, X5!0)) = mult(mult(op_c, X4!1), X5!0)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.21/0.50 tff(140,plain,
% 0.21/0.50 (mult(op_f, mult(X4!1, X5!0)) = mult(op_c, mult(X4!1, X5!0))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[93])).
% 0.21/0.50 tff(141,plain,
% 0.21/0.50 (mult(op_f, mult(X4!1, X5!0)) = mult(mult(op_f, X4!1), X5!0)),
% 0.21/0.50 inference(transitivity,[status(thm)],[140, 139, 130, 128])).
% 0.21/0.50 tff(142,plain,
% 0.21/0.50 ((~(~((~(mult(op_f, mult(X4!1, X5!0)) = mult(mult(op_f, X4!1), X5!0))) | (~(mult(X4!1, mult(X5!0, op_f)) = mult(mult(X4!1, X5!0), op_f))) | (~(mult(X4!1, mult(op_f, X5!0)) = mult(mult(X4!1, op_f), X5!0)))))) <=> ((~(mult(op_f, mult(X4!1, X5!0)) = mult(mult(op_f, X4!1), X5!0))) | (~(mult(X4!1, mult(X5!0, op_f)) = mult(mult(X4!1, X5!0), op_f))) | (~(mult(X4!1, mult(op_f, X5!0)) = mult(mult(X4!1, op_f), X5!0))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(143,plain,
% 0.21/0.50 (((mult(op_f, mult(X4!1, X5!0)) = mult(mult(op_f, X4!1), X5!0)) & (mult(X4!1, mult(X5!0, op_f)) = mult(mult(X4!1, X5!0), op_f)) & (mult(X4!1, mult(op_f, X5!0)) = mult(mult(X4!1, op_f), X5!0))) <=> (~((~(mult(op_f, mult(X4!1, X5!0)) = mult(mult(op_f, X4!1), X5!0))) | (~(mult(X4!1, mult(X5!0, op_f)) = mult(mult(X4!1, X5!0), op_f))) | (~(mult(X4!1, mult(op_f, X5!0)) = mult(mult(X4!1, op_f), X5!0)))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(144,plain,
% 0.21/0.50 ((~((mult(op_f, mult(X4!1, X5!0)) = mult(mult(op_f, X4!1), X5!0)) & (mult(X4!1, mult(X5!0, op_f)) = mult(mult(X4!1, X5!0), op_f)) & (mult(X4!1, mult(op_f, X5!0)) = mult(mult(X4!1, op_f), X5!0)))) <=> (~(~((~(mult(op_f, mult(X4!1, X5!0)) = mult(mult(op_f, X4!1), X5!0))) | (~(mult(X4!1, mult(X5!0, op_f)) = mult(mult(X4!1, X5!0), op_f))) | (~(mult(X4!1, mult(op_f, X5!0)) = mult(mult(X4!1, op_f), X5!0))))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[143])).
% 0.21/0.50 tff(145,plain,
% 0.21/0.50 ((~((mult(op_f, mult(X4!1, X5!0)) = mult(mult(op_f, X4!1), X5!0)) & (mult(X4!1, mult(X5!0, op_f)) = mult(mult(X4!1, X5!0), op_f)) & (mult(X4!1, mult(op_f, X5!0)) = mult(mult(X4!1, op_f), X5!0)))) <=> ((~(mult(op_f, mult(X4!1, X5!0)) = mult(mult(op_f, X4!1), X5!0))) | (~(mult(X4!1, mult(X5!0, op_f)) = mult(mult(X4!1, X5!0), op_f))) | (~(mult(X4!1, mult(op_f, X5!0)) = mult(mult(X4!1, op_f), X5!0))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[144, 142])).
% 0.21/0.50 tff(146,plain,
% 0.21/0.50 ((~![X4: $i, X5: $i] : ((mult(op_f, mult(X4, X5)) = mult(mult(op_f, X4), X5)) & (mult(X4, mult(X5, op_f)) = mult(mult(X4, X5), op_f)) & (mult(X4, mult(op_f, X5)) = mult(mult(X4, op_f), X5)))) <=> (~![X4: $i, X5: $i] : ((mult(op_f, mult(X4, X5)) = mult(mult(op_f, X4), X5)) & (mult(X4, mult(X5, op_f)) = mult(mult(X4, X5), op_f)) & (mult(X4, mult(op_f, X5)) = mult(mult(X4, op_f), X5))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(147,plain,
% 0.21/0.50 ((~![X4: $i, X5: $i] : (((mult(op_f, mult(X4, X5)) = mult(mult(op_f, X4), X5)) & (mult(X4, mult(X5, op_f)) = mult(mult(X4, X5), op_f))) & (mult(X4, mult(op_f, X5)) = mult(mult(X4, op_f), X5)))) <=> (~![X4: $i, X5: $i] : ((mult(op_f, mult(X4, X5)) = mult(mult(op_f, X4), X5)) & (mult(X4, mult(X5, op_f)) = mult(mult(X4, X5), op_f)) & (mult(X4, mult(op_f, X5)) = mult(mult(X4, op_f), X5))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(148,axiom,(~![X4: $i, X5: $i] : (((mult(op_f, mult(X4, X5)) = mult(mult(op_f, X4), X5)) & (mult(X4, mult(X5, op_f)) = mult(mult(X4, X5), op_f))) & (mult(X4, mult(op_f, X5)) = mult(mult(X4, op_f), X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 0.21/0.50 tff(149,plain,
% 0.21/0.50 (~![X4: $i, X5: $i] : ((mult(op_f, mult(X4, X5)) = mult(mult(op_f, X4), X5)) & (mult(X4, mult(X5, op_f)) = mult(mult(X4, X5), op_f)) & (mult(X4, mult(op_f, X5)) = mult(mult(X4, op_f), X5)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.21/0.50 tff(150,plain,
% 0.21/0.50 (~![X4: $i, X5: $i] : ((mult(op_f, mult(X4, X5)) = mult(mult(op_f, X4), X5)) & (mult(X4, mult(X5, op_f)) = mult(mult(X4, X5), op_f)) & (mult(X4, mult(op_f, X5)) = mult(mult(X4, op_f), X5)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[149, 146])).
% 0.21/0.50 tff(151,plain,
% 0.21/0.50 (~![X4: $i, X5: $i] : ((mult(op_f, mult(X4, X5)) = mult(mult(op_f, X4), X5)) & (mult(X4, mult(X5, op_f)) = mult(mult(X4, X5), op_f)) & (mult(X4, mult(op_f, X5)) = mult(mult(X4, op_f), X5)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[150, 146])).
% 0.21/0.50 tff(152,plain,
% 0.21/0.50 (~![X4: $i, X5: $i] : ((mult(op_f, mult(X4, X5)) = mult(mult(op_f, X4), X5)) & (mult(X4, mult(X5, op_f)) = mult(mult(X4, X5), op_f)) & (mult(X4, mult(op_f, X5)) = mult(mult(X4, op_f), X5)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[151, 146])).
% 0.21/0.50 tff(153,plain,
% 0.21/0.50 (~![X4: $i, X5: $i] : ((mult(op_f, mult(X4, X5)) = mult(mult(op_f, X4), X5)) & (mult(X4, mult(X5, op_f)) = mult(mult(X4, X5), op_f)) & (mult(X4, mult(op_f, X5)) = mult(mult(X4, op_f), X5)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[152, 146])).
% 0.21/0.50 tff(154,plain,
% 0.21/0.50 (~![X4: $i, X5: $i] : ((mult(op_f, mult(X4, X5)) = mult(mult(op_f, X4), X5)) & (mult(X4, mult(X5, op_f)) = mult(mult(X4, X5), op_f)) & (mult(X4, mult(op_f, X5)) = mult(mult(X4, op_f), X5)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[153, 146])).
% 0.21/0.50 tff(155,plain,
% 0.21/0.50 (~![X4: $i, X5: $i] : ((mult(op_f, mult(X4, X5)) = mult(mult(op_f, X4), X5)) & (mult(X4, mult(X5, op_f)) = mult(mult(X4, X5), op_f)) & (mult(X4, mult(op_f, X5)) = mult(mult(X4, op_f), X5)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[154, 146])).
% 0.21/0.50 tff(156,plain,(
% 0.21/0.50 ~((mult(op_f, mult(X4!1, X5!0)) = mult(mult(op_f, X4!1), X5!0)) & (mult(X4!1, mult(X5!0, op_f)) = mult(mult(X4!1, X5!0), op_f)) & (mult(X4!1, mult(op_f, X5!0)) = mult(mult(X4!1, op_f), X5!0)))),
% 0.21/0.50 inference(skolemize,[status(sab)],[155])).
% 0.21/0.50 tff(157,plain,
% 0.21/0.50 ((~(mult(op_f, mult(X4!1, X5!0)) = mult(mult(op_f, X4!1), X5!0))) | (~(mult(X4!1, mult(X5!0, op_f)) = mult(mult(X4!1, X5!0), op_f))) | (~(mult(X4!1, mult(op_f, X5!0)) = mult(mult(X4!1, op_f), X5!0)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[156, 145])).
% 0.21/0.50 tff(158,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[157, 141, 116, 99])).
% 0.21/0.50 % SZS output end Proof
%------------------------------------------------------------------------------