TSTP Solution File: GRP703+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP703+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 22:29:33 EDT 2022
% Result : Theorem 0.18s 0.46s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP703+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 31 20:16:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.18/0.46 % SZS status Theorem
% 0.18/0.46 % SZS output start Proof
% 0.18/0.46 tff(mult_type, type, (
% 0.18/0.46 mult: ( $i * $i ) > $i)).
% 0.18/0.46 tff(tptp_fun_X3_0_type, type, (
% 0.18/0.46 tptp_fun_X3_0: $i)).
% 0.18/0.46 tff(tptp_fun_X2_1_type, type, (
% 0.18/0.46 tptp_fun_X2_1: $i)).
% 0.18/0.46 tff(op_e_type, type, (
% 0.18/0.46 op_e: $i)).
% 0.18/0.46 tff(op_c_type, type, (
% 0.18/0.46 op_c: $i)).
% 0.18/0.46 tff(unit_type, type, (
% 0.18/0.46 unit: $i)).
% 0.18/0.46 tff(rd_type, type, (
% 0.18/0.46 rd: ( $i * $i ) > $i)).
% 0.18/0.46 tff(ld_type, type, (
% 0.18/0.46 ld: ( $i * $i ) > $i)).
% 0.18/0.46 tff(op_d_type, type, (
% 0.18/0.46 op_d: $i)).
% 0.18/0.46 tff(1,plain,
% 0.18/0.46 (^[B: $i, A: $i] : refl((op_e = mult(mult(rd(op_c, mult(A, B)), B), A)) <=> (op_e = mult(mult(rd(op_c, mult(A, B)), B), A)))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(2,plain,
% 0.18/0.46 (![B: $i, A: $i] : (op_e = mult(mult(rd(op_c, mult(A, B)), B), A)) <=> ![B: $i, A: $i] : (op_e = mult(mult(rd(op_c, mult(A, B)), B), A))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.46 tff(3,plain,
% 0.18/0.46 (![B: $i, A: $i] : (op_e = mult(mult(rd(op_c, mult(A, B)), B), A)) <=> ![B: $i, A: $i] : (op_e = mult(mult(rd(op_c, mult(A, B)), B), A))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(4,axiom,(![B: $i, A: $i] : (op_e = mult(mult(rd(op_c, mult(A, B)), B), A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f12')).
% 0.18/0.47 tff(5,plain,
% 0.18/0.47 (![B: $i, A: $i] : (op_e = mult(mult(rd(op_c, mult(A, B)), B), A))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.18/0.47 tff(6,plain,(
% 0.18/0.47 ![B: $i, A: $i] : (op_e = mult(mult(rd(op_c, mult(A, B)), B), A))),
% 0.18/0.47 inference(skolemize,[status(sab)],[5])).
% 0.18/0.47 tff(7,plain,
% 0.18/0.47 (![B: $i, A: $i] : (op_e = mult(mult(rd(op_c, mult(A, B)), B), A))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.18/0.47 tff(8,plain,
% 0.18/0.47 ((~![B: $i, A: $i] : (op_e = mult(mult(rd(op_c, mult(A, B)), B), A))) | (op_e = mult(mult(rd(op_c, mult(op_c, unit)), unit), op_c))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(9,plain,
% 0.18/0.47 (op_e = mult(mult(rd(op_c, mult(op_c, unit)), unit), op_c)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.18/0.47 tff(10,plain,
% 0.18/0.47 (mult(mult(rd(op_c, mult(op_c, unit)), unit), op_c) = op_e),
% 0.18/0.47 inference(symmetry,[status(thm)],[9])).
% 0.18/0.47 tff(11,plain,
% 0.18/0.47 (^[A: $i] : refl((mult(unit, A) = A) <=> (mult(unit, A) = A))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(12,plain,
% 0.18/0.47 (![A: $i] : (mult(unit, A) = A) <=> ![A: $i] : (mult(unit, A) = A)),
% 0.18/0.47 inference(quant_intro,[status(thm)],[11])).
% 0.18/0.47 tff(13,plain,
% 0.18/0.47 (![A: $i] : (mult(unit, A) = A) <=> ![A: $i] : (mult(unit, A) = A)),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(14,axiom,(![A: $i] : (mult(unit, A) = A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f06')).
% 0.18/0.47 tff(15,plain,
% 0.18/0.47 (![A: $i] : (mult(unit, A) = A)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.18/0.47 tff(16,plain,(
% 0.18/0.47 ![A: $i] : (mult(unit, A) = A)),
% 0.18/0.47 inference(skolemize,[status(sab)],[15])).
% 0.18/0.47 tff(17,plain,
% 0.18/0.47 (![A: $i] : (mult(unit, A) = A)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.18/0.47 tff(18,plain,
% 0.18/0.47 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, unit) = unit)),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(19,plain,
% 0.18/0.47 (mult(unit, unit) = unit),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.18/0.47 tff(20,plain,
% 0.18/0.47 (^[B: $i, A: $i] : refl((rd(mult(A, B), B) = A) <=> (rd(mult(A, B), B) = A))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(21,plain,
% 0.18/0.47 (![B: $i, A: $i] : (rd(mult(A, B), B) = A) <=> ![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 0.18/0.47 inference(quant_intro,[status(thm)],[20])).
% 0.18/0.47 tff(22,plain,
% 0.18/0.47 (![B: $i, A: $i] : (rd(mult(A, B), B) = A) <=> ![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(23,axiom,(![B: $i, A: $i] : (rd(mult(A, B), B) = A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f04')).
% 0.18/0.47 tff(24,plain,
% 0.18/0.47 (![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.18/0.47 tff(25,plain,(
% 0.18/0.47 ![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 0.18/0.47 inference(skolemize,[status(sab)],[24])).
% 0.18/0.47 tff(26,plain,
% 0.18/0.47 (![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.18/0.47 tff(27,plain,
% 0.18/0.47 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(unit, op_c), op_c) = unit)),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(28,plain,
% 0.18/0.47 (rd(mult(unit, op_c), op_c) = unit),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.18/0.47 tff(29,plain,
% 0.18/0.47 (^[A: $i] : refl((mult(A, unit) = A) <=> (mult(A, unit) = A))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(30,plain,
% 0.18/0.47 (![A: $i] : (mult(A, unit) = A) <=> ![A: $i] : (mult(A, unit) = A)),
% 0.18/0.47 inference(quant_intro,[status(thm)],[29])).
% 0.18/0.47 tff(31,plain,
% 0.18/0.47 (![A: $i] : (mult(A, unit) = A) <=> ![A: $i] : (mult(A, unit) = A)),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(32,axiom,(![A: $i] : (mult(A, unit) = A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f05')).
% 0.18/0.47 tff(33,plain,
% 0.18/0.47 (![A: $i] : (mult(A, unit) = A)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.18/0.47 tff(34,plain,(
% 0.18/0.47 ![A: $i] : (mult(A, unit) = A)),
% 0.18/0.47 inference(skolemize,[status(sab)],[33])).
% 0.18/0.47 tff(35,plain,
% 0.18/0.47 (![A: $i] : (mult(A, unit) = A)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.18/0.47 tff(36,plain,
% 0.18/0.47 ((~![A: $i] : (mult(A, unit) = A)) | (mult(op_c, unit) = op_c)),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(37,plain,
% 0.18/0.47 (mult(op_c, unit) = op_c),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.18/0.47 tff(38,plain,
% 0.18/0.47 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, op_c) = op_c)),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(39,plain,
% 0.18/0.47 (mult(unit, op_c) = op_c),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[38, 17])).
% 0.18/0.47 tff(40,plain,
% 0.18/0.47 (op_c = mult(unit, op_c)),
% 0.18/0.47 inference(symmetry,[status(thm)],[39])).
% 0.18/0.47 tff(41,plain,
% 0.18/0.47 (rd(op_c, mult(op_c, unit)) = rd(mult(unit, op_c), op_c)),
% 0.18/0.47 inference(monotonicity,[status(thm)],[40, 37])).
% 0.18/0.47 tff(42,plain,
% 0.18/0.47 (rd(op_c, mult(op_c, unit)) = unit),
% 0.18/0.47 inference(transitivity,[status(thm)],[41, 28])).
% 0.18/0.47 tff(43,plain,
% 0.18/0.47 (mult(rd(op_c, mult(op_c, unit)), unit) = mult(unit, unit)),
% 0.18/0.47 inference(monotonicity,[status(thm)],[42])).
% 0.18/0.47 tff(44,plain,
% 0.18/0.47 (mult(rd(op_c, mult(op_c, unit)), unit) = unit),
% 0.18/0.47 inference(transitivity,[status(thm)],[43, 19])).
% 0.18/0.47 tff(45,plain,
% 0.18/0.47 (mult(mult(rd(op_c, mult(op_c, unit)), unit), op_c) = mult(unit, op_c)),
% 0.18/0.47 inference(monotonicity,[status(thm)],[44])).
% 0.18/0.47 tff(46,plain,
% 0.18/0.47 (mult(unit, op_c) = mult(mult(rd(op_c, mult(op_c, unit)), unit), op_c)),
% 0.18/0.47 inference(symmetry,[status(thm)],[45])).
% 0.18/0.47 tff(47,plain,
% 0.18/0.47 (op_c = op_e),
% 0.18/0.47 inference(transitivity,[status(thm)],[40, 46, 10])).
% 0.18/0.47 tff(48,plain,
% 0.18/0.47 (mult(op_c, X2!1) = mult(op_e, X2!1)),
% 0.18/0.47 inference(monotonicity,[status(thm)],[47])).
% 0.18/0.47 tff(49,plain,
% 0.18/0.47 (mult(op_e, X2!1) = mult(op_c, X2!1)),
% 0.18/0.47 inference(symmetry,[status(thm)],[48])).
% 0.18/0.47 tff(50,plain,
% 0.18/0.47 (mult(mult(op_e, X2!1), X3!0) = mult(mult(op_c, X2!1), X3!0)),
% 0.18/0.47 inference(monotonicity,[status(thm)],[49])).
% 0.18/0.47 tff(51,plain,
% 0.18/0.47 (mult(mult(op_c, X2!1), X3!0) = mult(mult(op_e, X2!1), X3!0)),
% 0.18/0.47 inference(symmetry,[status(thm)],[50])).
% 0.18/0.47 tff(52,plain,
% 0.18/0.47 (^[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)))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(53,plain,
% 0.18/0.47 (![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))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[52])).
% 0.18/0.47 tff(54,plain,
% 0.18/0.47 (![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))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(55,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')).
% 0.18/0.47 tff(56,plain,
% 0.18/0.47 (![B: $i, A: $i] : (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.18/0.47 tff(57,plain,(
% 0.18/0.47 ![B: $i, A: $i] : (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B))),
% 0.18/0.47 inference(skolemize,[status(sab)],[56])).
% 0.18/0.47 tff(58,plain,
% 0.18/0.47 (![B: $i, A: $i] : (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.18/0.47 tff(59,plain,
% 0.18/0.47 ((~![B: $i, A: $i] : (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B))) | (mult(op_c, mult(X2!1, X3!0)) = mult(mult(op_c, X2!1), X3!0))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(60,plain,
% 0.18/0.47 (mult(op_c, mult(X2!1, X3!0)) = mult(mult(op_c, X2!1), X3!0)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.18/0.47 tff(61,plain,
% 0.18/0.47 (op_e = op_c),
% 0.18/0.47 inference(transitivity,[status(thm)],[9, 45, 39])).
% 0.18/0.47 tff(62,plain,
% 0.18/0.47 (mult(op_e, mult(X2!1, X3!0)) = mult(op_c, mult(X2!1, X3!0))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[61])).
% 0.18/0.47 tff(63,plain,
% 0.18/0.47 (mult(op_e, mult(X2!1, X3!0)) = mult(mult(op_e, X2!1), X3!0)),
% 0.18/0.47 inference(transitivity,[status(thm)],[62, 60, 51])).
% 0.18/0.47 tff(64,plain,
% 0.18/0.47 (mult(X2!1, op_e) = mult(X2!1, op_c)),
% 0.18/0.47 inference(monotonicity,[status(thm)],[61])).
% 0.18/0.47 tff(65,plain,
% 0.18/0.47 (mult(mult(X2!1, op_e), X3!0) = mult(mult(X2!1, op_c), X3!0)),
% 0.18/0.47 inference(monotonicity,[status(thm)],[64])).
% 0.18/0.47 tff(66,plain,
% 0.18/0.47 (mult(mult(X2!1, op_c), X3!0) = mult(mult(X2!1, op_e), X3!0)),
% 0.18/0.47 inference(symmetry,[status(thm)],[65])).
% 0.18/0.47 tff(67,plain,
% 0.18/0.47 (^[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)))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(68,plain,
% 0.18/0.47 (![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))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[67])).
% 0.18/0.47 tff(69,plain,
% 0.18/0.47 (![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))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(70,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')).
% 0.18/0.47 tff(71,plain,
% 0.18/0.47 (![B: $i, A: $i] : (mult(A, mult(op_c, B)) = mult(mult(A, op_c), B))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.18/0.47 tff(72,plain,(
% 0.18/0.47 ![B: $i, A: $i] : (mult(A, mult(op_c, B)) = mult(mult(A, op_c), B))),
% 0.18/0.47 inference(skolemize,[status(sab)],[71])).
% 0.18/0.47 tff(73,plain,
% 0.18/0.47 (![B: $i, A: $i] : (mult(A, mult(op_c, B)) = mult(mult(A, op_c), B))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.18/0.47 tff(74,plain,
% 0.18/0.47 ((~![B: $i, A: $i] : (mult(A, mult(op_c, B)) = mult(mult(A, op_c), B))) | (mult(X2!1, mult(op_c, X3!0)) = mult(mult(X2!1, op_c), X3!0))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(75,plain,
% 0.18/0.47 (mult(X2!1, mult(op_c, X3!0)) = mult(mult(X2!1, op_c), X3!0)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.18/0.47 tff(76,plain,
% 0.18/0.47 (mult(op_e, X3!0) = mult(op_c, X3!0)),
% 0.18/0.47 inference(monotonicity,[status(thm)],[61])).
% 0.18/0.47 tff(77,plain,
% 0.18/0.47 (mult(X2!1, mult(op_e, X3!0)) = mult(X2!1, mult(op_c, X3!0))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[76])).
% 0.18/0.47 tff(78,plain,
% 0.18/0.47 (mult(X2!1, mult(op_e, X3!0)) = mult(mult(X2!1, op_e), X3!0)),
% 0.18/0.47 inference(transitivity,[status(thm)],[77, 75, 66])).
% 0.18/0.47 tff(79,plain,
% 0.18/0.47 (mult(mult(X2!1, X3!0), op_e) = mult(mult(X2!1, X3!0), op_c)),
% 0.18/0.47 inference(monotonicity,[status(thm)],[61])).
% 0.18/0.47 tff(80,plain,
% 0.18/0.47 (mult(mult(X2!1, X3!0), op_c) = mult(mult(X2!1, X3!0), op_e)),
% 0.18/0.47 inference(symmetry,[status(thm)],[79])).
% 0.18/0.47 tff(81,plain,
% 0.18/0.47 (^[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)))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(82,plain,
% 0.18/0.47 (![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))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[81])).
% 0.18/0.47 tff(83,plain,
% 0.18/0.47 (![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))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(84,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')).
% 0.18/0.47 tff(85,plain,
% 0.18/0.47 (![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.18/0.47 tff(86,plain,(
% 0.18/0.47 ![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c))),
% 0.18/0.47 inference(skolemize,[status(sab)],[85])).
% 0.18/0.47 tff(87,plain,
% 0.18/0.47 (![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.18/0.47 tff(88,plain,
% 0.18/0.47 ((~![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c))) | (mult(X2!1, mult(X3!0, op_c)) = mult(mult(X2!1, X3!0), op_c))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(89,plain,
% 0.18/0.47 (mult(X2!1, mult(X3!0, op_c)) = mult(mult(X2!1, X3!0), op_c)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.18/0.47 tff(90,plain,
% 0.18/0.47 (^[B: $i, A: $i] : refl((mult(A, ld(A, B)) = B) <=> (mult(A, ld(A, B)) = B))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(91,plain,
% 0.18/0.47 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B) <=> ![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 0.18/0.47 inference(quant_intro,[status(thm)],[90])).
% 0.18/0.47 tff(92,plain,
% 0.18/0.47 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B) <=> ![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(93,axiom,(![B: $i, A: $i] : (mult(A, ld(A, B)) = B)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f01')).
% 0.18/0.47 tff(94,plain,
% 0.18/0.47 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.18/0.47 tff(95,plain,(
% 0.18/0.47 ![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 0.18/0.47 inference(skolemize,[status(sab)],[94])).
% 0.18/0.47 tff(96,plain,
% 0.18/0.47 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.18/0.47 tff(97,plain,
% 0.18/0.47 ((~![B: $i, A: $i] : (mult(A, ld(A, B)) = B)) | (mult(X3!0, ld(X3!0, mult(op_c, X3!0))) = mult(op_c, X3!0))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(98,plain,
% 0.18/0.47 (mult(X3!0, ld(X3!0, mult(op_c, X3!0))) = mult(op_c, X3!0)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.18/0.47 tff(99,plain,
% 0.18/0.47 (^[A: $i] : refl((op_d = ld(A, mult(op_c, A))) <=> (op_d = ld(A, mult(op_c, A))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(100,plain,
% 0.18/0.47 (![A: $i] : (op_d = ld(A, mult(op_c, A))) <=> ![A: $i] : (op_d = ld(A, mult(op_c, A)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[99])).
% 0.18/0.47 tff(101,plain,
% 0.18/0.47 (![A: $i] : (op_d = ld(A, mult(op_c, A))) <=> ![A: $i] : (op_d = ld(A, mult(op_c, A)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(102,axiom,(![A: $i] : (op_d = ld(A, mult(op_c, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f11')).
% 0.18/0.47 tff(103,plain,
% 0.18/0.47 (![A: $i] : (op_d = ld(A, mult(op_c, A)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.18/0.47 tff(104,plain,(
% 0.18/0.47 ![A: $i] : (op_d = ld(A, mult(op_c, A)))),
% 0.18/0.47 inference(skolemize,[status(sab)],[103])).
% 0.18/0.47 tff(105,plain,
% 0.18/0.47 (![A: $i] : (op_d = ld(A, mult(op_c, A)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.18/0.47 tff(106,plain,
% 0.18/0.47 ((~![A: $i] : (op_d = ld(A, mult(op_c, A)))) | (op_d = ld(X3!0, mult(op_c, X3!0)))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(107,plain,
% 0.18/0.47 (op_d = ld(X3!0, mult(op_c, X3!0))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.18/0.47 tff(108,plain,
% 0.18/0.47 ((~![A: $i] : (op_d = ld(A, mult(op_c, A)))) | (op_d = ld(unit, mult(op_c, unit)))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(109,plain,
% 0.18/0.47 (op_d = ld(unit, mult(op_c, unit))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[108, 105])).
% 0.18/0.47 tff(110,plain,
% 0.18/0.47 (ld(unit, mult(op_c, unit)) = op_d),
% 0.18/0.47 inference(symmetry,[status(thm)],[109])).
% 0.18/0.47 tff(111,plain,
% 0.18/0.47 (mult(op_c, unit) = mult(unit, op_c)),
% 0.18/0.47 inference(transitivity,[status(thm)],[37, 40])).
% 0.18/0.47 tff(112,plain,
% 0.18/0.47 (ld(unit, mult(op_c, unit)) = ld(unit, mult(unit, op_c))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[111])).
% 0.18/0.47 tff(113,plain,
% 0.18/0.47 (ld(unit, mult(unit, op_c)) = ld(unit, mult(op_c, unit))),
% 0.18/0.47 inference(symmetry,[status(thm)],[112])).
% 0.18/0.47 tff(114,plain,
% 0.18/0.47 (^[B: $i, A: $i] : refl((ld(A, mult(A, B)) = B) <=> (ld(A, mult(A, B)) = B))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(115,plain,
% 0.18/0.47 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B) <=> ![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 0.18/0.47 inference(quant_intro,[status(thm)],[114])).
% 0.18/0.47 tff(116,plain,
% 0.18/0.47 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B) <=> ![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(117,axiom,(![B: $i, A: $i] : (ld(A, mult(A, B)) = B)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f02')).
% 0.18/0.47 tff(118,plain,
% 0.18/0.47 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.18/0.47 tff(119,plain,(
% 0.18/0.47 ![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 0.18/0.47 inference(skolemize,[status(sab)],[118])).
% 0.18/0.47 tff(120,plain,
% 0.18/0.47 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.18/0.47 tff(121,plain,
% 0.18/0.47 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(unit, mult(unit, op_c)) = op_c)),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(122,plain,
% 0.18/0.47 (ld(unit, mult(unit, op_c)) = op_c),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.18/0.47 tff(123,plain,
% 0.18/0.47 (op_c = ld(unit, mult(unit, op_c))),
% 0.18/0.47 inference(symmetry,[status(thm)],[122])).
% 0.18/0.47 tff(124,plain,
% 0.18/0.47 (op_c = ld(X3!0, mult(op_c, X3!0))),
% 0.18/0.47 inference(transitivity,[status(thm)],[123, 113, 110, 107])).
% 0.18/0.47 tff(125,plain,
% 0.18/0.47 (mult(X3!0, op_c) = mult(X3!0, ld(X3!0, mult(op_c, X3!0)))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[124])).
% 0.18/0.47 tff(126,plain,
% 0.18/0.47 (mult(X3!0, op_c) = mult(op_c, X3!0)),
% 0.18/0.47 inference(transitivity,[status(thm)],[125, 98])).
% 0.18/0.47 tff(127,plain,
% 0.18/0.47 (mult(X2!1, mult(X3!0, op_c)) = mult(X2!1, mult(op_c, X3!0))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[126])).
% 0.18/0.47 tff(128,plain,
% 0.18/0.47 (mult(X2!1, mult(op_c, X3!0)) = mult(X2!1, mult(X3!0, op_c))),
% 0.18/0.47 inference(symmetry,[status(thm)],[127])).
% 0.18/0.47 tff(129,plain,
% 0.18/0.47 (op_e = ld(X3!0, mult(op_c, X3!0))),
% 0.18/0.47 inference(transitivity,[status(thm)],[9, 45, 39, 123, 113, 110, 107])).
% 0.18/0.47 tff(130,plain,
% 0.18/0.47 (mult(X3!0, op_e) = mult(X3!0, ld(X3!0, mult(op_c, X3!0)))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[129])).
% 0.18/0.47 tff(131,plain,
% 0.18/0.47 (mult(X3!0, op_e) = mult(op_c, X3!0)),
% 0.18/0.47 inference(transitivity,[status(thm)],[130, 98])).
% 0.18/0.47 tff(132,plain,
% 0.18/0.47 (mult(X2!1, mult(X3!0, op_e)) = mult(X2!1, mult(op_c, X3!0))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[131])).
% 0.18/0.47 tff(133,plain,
% 0.18/0.47 (mult(X2!1, mult(X3!0, op_e)) = mult(mult(X2!1, X3!0), op_e)),
% 0.18/0.47 inference(transitivity,[status(thm)],[132, 128, 89, 80])).
% 0.18/0.47 tff(134,plain,
% 0.18/0.47 ((~(~((~(mult(op_e, mult(X2!1, X3!0)) = mult(mult(op_e, X2!1), X3!0))) | (~(mult(X2!1, mult(X3!0, op_e)) = mult(mult(X2!1, X3!0), op_e))) | (~(mult(X2!1, mult(op_e, X3!0)) = mult(mult(X2!1, op_e), X3!0)))))) <=> ((~(mult(op_e, mult(X2!1, X3!0)) = mult(mult(op_e, X2!1), X3!0))) | (~(mult(X2!1, mult(X3!0, op_e)) = mult(mult(X2!1, X3!0), op_e))) | (~(mult(X2!1, mult(op_e, X3!0)) = mult(mult(X2!1, op_e), X3!0))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(135,plain,
% 0.18/0.47 (((mult(op_e, mult(X2!1, X3!0)) = mult(mult(op_e, X2!1), X3!0)) & (mult(X2!1, mult(X3!0, op_e)) = mult(mult(X2!1, X3!0), op_e)) & (mult(X2!1, mult(op_e, X3!0)) = mult(mult(X2!1, op_e), X3!0))) <=> (~((~(mult(op_e, mult(X2!1, X3!0)) = mult(mult(op_e, X2!1), X3!0))) | (~(mult(X2!1, mult(X3!0, op_e)) = mult(mult(X2!1, X3!0), op_e))) | (~(mult(X2!1, mult(op_e, X3!0)) = mult(mult(X2!1, op_e), X3!0)))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(136,plain,
% 0.18/0.47 ((~((mult(op_e, mult(X2!1, X3!0)) = mult(mult(op_e, X2!1), X3!0)) & (mult(X2!1, mult(X3!0, op_e)) = mult(mult(X2!1, X3!0), op_e)) & (mult(X2!1, mult(op_e, X3!0)) = mult(mult(X2!1, op_e), X3!0)))) <=> (~(~((~(mult(op_e, mult(X2!1, X3!0)) = mult(mult(op_e, X2!1), X3!0))) | (~(mult(X2!1, mult(X3!0, op_e)) = mult(mult(X2!1, X3!0), op_e))) | (~(mult(X2!1, mult(op_e, X3!0)) = mult(mult(X2!1, op_e), X3!0))))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[135])).
% 0.18/0.47 tff(137,plain,
% 0.18/0.47 ((~((mult(op_e, mult(X2!1, X3!0)) = mult(mult(op_e, X2!1), X3!0)) & (mult(X2!1, mult(X3!0, op_e)) = mult(mult(X2!1, X3!0), op_e)) & (mult(X2!1, mult(op_e, X3!0)) = mult(mult(X2!1, op_e), X3!0)))) <=> ((~(mult(op_e, mult(X2!1, X3!0)) = mult(mult(op_e, X2!1), X3!0))) | (~(mult(X2!1, mult(X3!0, op_e)) = mult(mult(X2!1, X3!0), op_e))) | (~(mult(X2!1, mult(op_e, X3!0)) = mult(mult(X2!1, op_e), X3!0))))),
% 0.18/0.47 inference(transitivity,[status(thm)],[136, 134])).
% 0.18/0.47 tff(138,plain,
% 0.18/0.47 ((~![X2: $i, X3: $i] : ((mult(op_e, mult(X2, X3)) = mult(mult(op_e, X2), X3)) & (mult(X2, mult(X3, op_e)) = mult(mult(X2, X3), op_e)) & (mult(X2, mult(op_e, X3)) = mult(mult(X2, op_e), X3)))) <=> (~![X2: $i, X3: $i] : ((mult(op_e, mult(X2, X3)) = mult(mult(op_e, X2), X3)) & (mult(X2, mult(X3, op_e)) = mult(mult(X2, X3), op_e)) & (mult(X2, mult(op_e, X3)) = mult(mult(X2, op_e), X3))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(139,plain,
% 0.18/0.48 ((~![X2: $i, X3: $i] : (((mult(op_e, mult(X2, X3)) = mult(mult(op_e, X2), X3)) & (mult(X2, mult(X3, op_e)) = mult(mult(X2, X3), op_e))) & (mult(X2, mult(op_e, X3)) = mult(mult(X2, op_e), X3)))) <=> (~![X2: $i, X3: $i] : ((mult(op_e, mult(X2, X3)) = mult(mult(op_e, X2), X3)) & (mult(X2, mult(X3, op_e)) = mult(mult(X2, X3), op_e)) & (mult(X2, mult(op_e, X3)) = mult(mult(X2, op_e), X3))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(140,axiom,(~![X2: $i, X3: $i] : (((mult(op_e, mult(X2, X3)) = mult(mult(op_e, X2), X3)) & (mult(X2, mult(X3, op_e)) = mult(mult(X2, X3), op_e))) & (mult(X2, mult(op_e, X3)) = mult(mult(X2, op_e), X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 0.18/0.48 tff(141,plain,
% 0.18/0.48 (~![X2: $i, X3: $i] : ((mult(op_e, mult(X2, X3)) = mult(mult(op_e, X2), X3)) & (mult(X2, mult(X3, op_e)) = mult(mult(X2, X3), op_e)) & (mult(X2, mult(op_e, X3)) = mult(mult(X2, op_e), X3)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.18/0.48 tff(142,plain,
% 0.18/0.48 (~![X2: $i, X3: $i] : ((mult(op_e, mult(X2, X3)) = mult(mult(op_e, X2), X3)) & (mult(X2, mult(X3, op_e)) = mult(mult(X2, X3), op_e)) & (mult(X2, mult(op_e, X3)) = mult(mult(X2, op_e), X3)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[141, 138])).
% 0.18/0.48 tff(143,plain,
% 0.18/0.48 (~![X2: $i, X3: $i] : ((mult(op_e, mult(X2, X3)) = mult(mult(op_e, X2), X3)) & (mult(X2, mult(X3, op_e)) = mult(mult(X2, X3), op_e)) & (mult(X2, mult(op_e, X3)) = mult(mult(X2, op_e), X3)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[142, 138])).
% 0.18/0.48 tff(144,plain,
% 0.18/0.48 (~![X2: $i, X3: $i] : ((mult(op_e, mult(X2, X3)) = mult(mult(op_e, X2), X3)) & (mult(X2, mult(X3, op_e)) = mult(mult(X2, X3), op_e)) & (mult(X2, mult(op_e, X3)) = mult(mult(X2, op_e), X3)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[143, 138])).
% 0.18/0.48 tff(145,plain,
% 0.18/0.48 (~![X2: $i, X3: $i] : ((mult(op_e, mult(X2, X3)) = mult(mult(op_e, X2), X3)) & (mult(X2, mult(X3, op_e)) = mult(mult(X2, X3), op_e)) & (mult(X2, mult(op_e, X3)) = mult(mult(X2, op_e), X3)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[144, 138])).
% 0.18/0.48 tff(146,plain,
% 0.18/0.48 (~![X2: $i, X3: $i] : ((mult(op_e, mult(X2, X3)) = mult(mult(op_e, X2), X3)) & (mult(X2, mult(X3, op_e)) = mult(mult(X2, X3), op_e)) & (mult(X2, mult(op_e, X3)) = mult(mult(X2, op_e), X3)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[145, 138])).
% 0.18/0.48 tff(147,plain,
% 0.18/0.48 (~![X2: $i, X3: $i] : ((mult(op_e, mult(X2, X3)) = mult(mult(op_e, X2), X3)) & (mult(X2, mult(X3, op_e)) = mult(mult(X2, X3), op_e)) & (mult(X2, mult(op_e, X3)) = mult(mult(X2, op_e), X3)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[146, 138])).
% 0.18/0.48 tff(148,plain,(
% 0.18/0.48 ~((mult(op_e, mult(X2!1, X3!0)) = mult(mult(op_e, X2!1), X3!0)) & (mult(X2!1, mult(X3!0, op_e)) = mult(mult(X2!1, X3!0), op_e)) & (mult(X2!1, mult(op_e, X3!0)) = mult(mult(X2!1, op_e), X3!0)))),
% 0.18/0.48 inference(skolemize,[status(sab)],[147])).
% 0.18/0.48 tff(149,plain,
% 0.18/0.48 ((~(mult(op_e, mult(X2!1, X3!0)) = mult(mult(op_e, X2!1), X3!0))) | (~(mult(X2!1, mult(X3!0, op_e)) = mult(mult(X2!1, X3!0), op_e))) | (~(mult(X2!1, mult(op_e, X3!0)) = mult(mult(X2!1, op_e), X3!0)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[148, 137])).
% 0.18/0.48 tff(150,plain,
% 0.18/0.48 (~(mult(op_e, mult(X2!1, X3!0)) = mult(mult(op_e, X2!1), X3!0))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[149, 133, 78])).
% 0.18/0.48 tff(151,plain,
% 0.18/0.48 ($false),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[150, 63])).
% 0.18/0.48 % SZS output end Proof
%------------------------------------------------------------------------------