TSTP Solution File: GRP702+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP702+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 22:29:32 EDT 2022
% Result : Theorem 2.68s 1.94s
% Output : Proof 2.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP702+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 20:24:31 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 2.68/1.94 % SZS status Theorem
% 2.68/1.94 % SZS output start Proof
% 2.68/1.94 tff(mult_type, type, (
% 2.68/1.94 mult: ( $i * $i ) > $i)).
% 2.68/1.94 tff(tptp_fun_X1_0_type, type, (
% 2.68/1.94 tptp_fun_X1_0: $i)).
% 2.68/1.94 tff(tptp_fun_X0_1_type, type, (
% 2.68/1.94 tptp_fun_X0_1: $i)).
% 2.68/1.94 tff(op_d_type, type, (
% 2.68/1.94 op_d: $i)).
% 2.68/1.94 tff(op_c_type, type, (
% 2.68/1.94 op_c: $i)).
% 2.68/1.94 tff(ld_type, type, (
% 2.68/1.94 ld: ( $i * $i ) > $i)).
% 2.68/1.94 tff(unit_type, type, (
% 2.68/1.94 unit: $i)).
% 2.68/1.94 tff(1,plain,
% 2.68/1.94 (^[A: $i] : refl((op_d = ld(A, mult(op_c, A))) <=> (op_d = ld(A, mult(op_c, A))))),
% 2.68/1.94 inference(bind,[status(th)],[])).
% 2.68/1.94 tff(2,plain,
% 2.68/1.94 (![A: $i] : (op_d = ld(A, mult(op_c, A))) <=> ![A: $i] : (op_d = ld(A, mult(op_c, A)))),
% 2.68/1.94 inference(quant_intro,[status(thm)],[1])).
% 2.68/1.94 tff(3,plain,
% 2.68/1.94 (![A: $i] : (op_d = ld(A, mult(op_c, A))) <=> ![A: $i] : (op_d = ld(A, mult(op_c, A)))),
% 2.68/1.94 inference(rewrite,[status(thm)],[])).
% 2.68/1.94 tff(4,axiom,(![A: $i] : (op_d = ld(A, mult(op_c, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f11')).
% 2.68/1.94 tff(5,plain,
% 2.68/1.94 (![A: $i] : (op_d = ld(A, mult(op_c, A)))),
% 2.68/1.94 inference(modus_ponens,[status(thm)],[4, 3])).
% 2.68/1.94 tff(6,plain,(
% 2.68/1.94 ![A: $i] : (op_d = ld(A, mult(op_c, A)))),
% 2.68/1.94 inference(skolemize,[status(sab)],[5])).
% 2.68/1.94 tff(7,plain,
% 2.68/1.94 (![A: $i] : (op_d = ld(A, mult(op_c, A)))),
% 2.68/1.94 inference(modus_ponens,[status(thm)],[6, 2])).
% 2.68/1.94 tff(8,plain,
% 2.68/1.94 ((~![A: $i] : (op_d = ld(A, mult(op_c, A)))) | (op_d = ld(unit, mult(op_c, unit)))),
% 2.68/1.94 inference(quant_inst,[status(thm)],[])).
% 2.68/1.94 tff(9,plain,
% 2.68/1.94 (op_d = ld(unit, mult(op_c, unit))),
% 2.68/1.94 inference(unit_resolution,[status(thm)],[8, 7])).
% 2.68/1.94 tff(10,plain,
% 2.68/1.94 (ld(unit, mult(op_c, unit)) = op_d),
% 2.68/1.94 inference(symmetry,[status(thm)],[9])).
% 2.68/1.94 tff(11,plain,
% 2.68/1.94 (^[A: $i] : refl((mult(unit, A) = A) <=> (mult(unit, A) = A))),
% 2.68/1.94 inference(bind,[status(th)],[])).
% 2.68/1.94 tff(12,plain,
% 2.68/1.94 (![A: $i] : (mult(unit, A) = A) <=> ![A: $i] : (mult(unit, A) = A)),
% 2.68/1.94 inference(quant_intro,[status(thm)],[11])).
% 2.68/1.94 tff(13,plain,
% 2.68/1.94 (![A: $i] : (mult(unit, A) = A) <=> ![A: $i] : (mult(unit, A) = A)),
% 2.68/1.94 inference(rewrite,[status(thm)],[])).
% 2.68/1.94 tff(14,axiom,(![A: $i] : (mult(unit, A) = A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f06')).
% 2.68/1.94 tff(15,plain,
% 2.68/1.94 (![A: $i] : (mult(unit, A) = A)),
% 2.68/1.94 inference(modus_ponens,[status(thm)],[14, 13])).
% 2.68/1.94 tff(16,plain,(
% 2.68/1.94 ![A: $i] : (mult(unit, A) = A)),
% 2.68/1.94 inference(skolemize,[status(sab)],[15])).
% 2.68/1.94 tff(17,plain,
% 2.68/1.94 (![A: $i] : (mult(unit, A) = A)),
% 2.68/1.94 inference(modus_ponens,[status(thm)],[16, 12])).
% 2.68/1.94 tff(18,plain,
% 2.68/1.94 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, op_c) = op_c)),
% 2.68/1.94 inference(quant_inst,[status(thm)],[])).
% 2.68/1.94 tff(19,plain,
% 2.68/1.94 (mult(unit, op_c) = op_c),
% 2.68/1.94 inference(unit_resolution,[status(thm)],[18, 17])).
% 2.68/1.94 tff(20,plain,
% 2.68/1.94 (op_c = mult(unit, op_c)),
% 2.68/1.94 inference(symmetry,[status(thm)],[19])).
% 2.68/1.94 tff(21,plain,
% 2.68/1.94 (^[A: $i] : refl((mult(A, unit) = A) <=> (mult(A, unit) = A))),
% 2.68/1.94 inference(bind,[status(th)],[])).
% 2.68/1.94 tff(22,plain,
% 2.68/1.94 (![A: $i] : (mult(A, unit) = A) <=> ![A: $i] : (mult(A, unit) = A)),
% 2.68/1.94 inference(quant_intro,[status(thm)],[21])).
% 2.68/1.94 tff(23,plain,
% 2.68/1.94 (![A: $i] : (mult(A, unit) = A) <=> ![A: $i] : (mult(A, unit) = A)),
% 2.68/1.94 inference(rewrite,[status(thm)],[])).
% 2.68/1.94 tff(24,axiom,(![A: $i] : (mult(A, unit) = A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f05')).
% 2.68/1.94 tff(25,plain,
% 2.68/1.94 (![A: $i] : (mult(A, unit) = A)),
% 2.68/1.94 inference(modus_ponens,[status(thm)],[24, 23])).
% 2.68/1.94 tff(26,plain,(
% 2.68/1.94 ![A: $i] : (mult(A, unit) = A)),
% 2.68/1.94 inference(skolemize,[status(sab)],[25])).
% 2.68/1.94 tff(27,plain,
% 2.68/1.94 (![A: $i] : (mult(A, unit) = A)),
% 2.68/1.94 inference(modus_ponens,[status(thm)],[26, 22])).
% 2.68/1.94 tff(28,plain,
% 2.68/1.94 ((~![A: $i] : (mult(A, unit) = A)) | (mult(op_c, unit) = op_c)),
% 2.68/1.94 inference(quant_inst,[status(thm)],[])).
% 2.68/1.94 tff(29,plain,
% 2.68/1.94 (mult(op_c, unit) = op_c),
% 2.68/1.94 inference(unit_resolution,[status(thm)],[28, 27])).
% 2.68/1.94 tff(30,plain,
% 2.68/1.94 (mult(op_c, unit) = mult(unit, op_c)),
% 2.68/1.94 inference(transitivity,[status(thm)],[29, 20])).
% 2.68/1.94 tff(31,plain,
% 2.68/1.94 (ld(unit, mult(op_c, unit)) = ld(unit, mult(unit, op_c))),
% 2.68/1.94 inference(monotonicity,[status(thm)],[30])).
% 2.68/1.94 tff(32,plain,
% 2.68/1.94 (ld(unit, mult(unit, op_c)) = ld(unit, mult(op_c, unit))),
% 2.68/1.94 inference(symmetry,[status(thm)],[31])).
% 2.68/1.95 tff(33,plain,
% 2.68/1.95 (^[B: $i, A: $i] : refl((ld(A, mult(A, B)) = B) <=> (ld(A, mult(A, B)) = B))),
% 2.68/1.95 inference(bind,[status(th)],[])).
% 2.68/1.95 tff(34,plain,
% 2.68/1.95 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B) <=> ![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 2.68/1.95 inference(quant_intro,[status(thm)],[33])).
% 2.68/1.95 tff(35,plain,
% 2.68/1.95 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B) <=> ![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 2.68/1.95 inference(rewrite,[status(thm)],[])).
% 2.68/1.95 tff(36,axiom,(![B: $i, A: $i] : (ld(A, mult(A, B)) = B)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f02')).
% 2.68/1.95 tff(37,plain,
% 2.68/1.95 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 2.68/1.95 inference(modus_ponens,[status(thm)],[36, 35])).
% 2.68/1.95 tff(38,plain,(
% 2.68/1.95 ![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 2.68/1.95 inference(skolemize,[status(sab)],[37])).
% 2.68/1.95 tff(39,plain,
% 2.68/1.95 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 2.68/1.95 inference(modus_ponens,[status(thm)],[38, 34])).
% 2.68/1.95 tff(40,plain,
% 2.68/1.95 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(unit, mult(unit, op_c)) = op_c)),
% 2.68/1.95 inference(quant_inst,[status(thm)],[])).
% 2.68/1.95 tff(41,plain,
% 2.68/1.95 (ld(unit, mult(unit, op_c)) = op_c),
% 2.68/1.95 inference(unit_resolution,[status(thm)],[40, 39])).
% 2.68/1.95 tff(42,plain,
% 2.68/1.95 (op_c = ld(unit, mult(unit, op_c))),
% 2.68/1.95 inference(symmetry,[status(thm)],[41])).
% 2.68/1.95 tff(43,plain,
% 2.68/1.95 (op_c = op_d),
% 2.68/1.95 inference(transitivity,[status(thm)],[42, 32, 10])).
% 2.68/1.95 tff(44,plain,
% 2.68/1.95 (mult(op_c, X0!1) = mult(op_d, X0!1)),
% 2.68/1.95 inference(monotonicity,[status(thm)],[43])).
% 2.68/1.95 tff(45,plain,
% 2.68/1.95 (mult(op_d, X0!1) = mult(op_c, X0!1)),
% 2.68/1.95 inference(symmetry,[status(thm)],[44])).
% 2.68/1.95 tff(46,plain,
% 2.68/1.95 (mult(mult(op_d, X0!1), X1!0) = mult(mult(op_c, X0!1), X1!0)),
% 2.68/1.95 inference(monotonicity,[status(thm)],[45])).
% 2.68/1.95 tff(47,plain,
% 2.68/1.95 (mult(mult(op_c, X0!1), X1!0) = mult(mult(op_d, X0!1), X1!0)),
% 2.68/1.95 inference(symmetry,[status(thm)],[46])).
% 2.68/1.95 tff(48,plain,
% 2.68/1.95 (^[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)))),
% 2.68/1.95 inference(bind,[status(th)],[])).
% 2.68/1.95 tff(49,plain,
% 2.68/1.95 (![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))),
% 2.68/1.95 inference(quant_intro,[status(thm)],[48])).
% 2.68/1.95 tff(50,plain,
% 2.68/1.95 (![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))),
% 2.68/1.95 inference(rewrite,[status(thm)],[])).
% 2.68/1.95 tff(51,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')).
% 2.68/1.95 tff(52,plain,
% 2.68/1.95 (![B: $i, A: $i] : (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B))),
% 2.68/1.95 inference(modus_ponens,[status(thm)],[51, 50])).
% 2.68/1.95 tff(53,plain,(
% 2.68/1.95 ![B: $i, A: $i] : (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B))),
% 2.68/1.95 inference(skolemize,[status(sab)],[52])).
% 2.68/1.95 tff(54,plain,
% 2.68/1.95 (![B: $i, A: $i] : (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B))),
% 2.68/1.95 inference(modus_ponens,[status(thm)],[53, 49])).
% 2.68/1.95 tff(55,plain,
% 2.68/1.95 ((~![B: $i, A: $i] : (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B))) | (mult(op_c, mult(X0!1, X1!0)) = mult(mult(op_c, X0!1), X1!0))),
% 2.68/1.95 inference(quant_inst,[status(thm)],[])).
% 2.68/1.95 tff(56,plain,
% 2.68/1.95 (mult(op_c, mult(X0!1, X1!0)) = mult(mult(op_c, X0!1), X1!0)),
% 2.68/1.95 inference(unit_resolution,[status(thm)],[55, 54])).
% 2.68/1.95 tff(57,plain,
% 2.68/1.95 (op_d = op_c),
% 2.68/1.95 inference(transitivity,[status(thm)],[9, 31, 41])).
% 2.68/1.95 tff(58,plain,
% 2.68/1.95 (mult(op_d, mult(X0!1, X1!0)) = mult(op_c, mult(X0!1, X1!0))),
% 2.68/1.95 inference(monotonicity,[status(thm)],[57])).
% 2.68/1.95 tff(59,plain,
% 2.68/1.95 (mult(op_d, mult(X0!1, X1!0)) = mult(mult(op_d, X0!1), X1!0)),
% 2.68/1.95 inference(transitivity,[status(thm)],[58, 56, 47])).
% 2.68/1.95 tff(60,plain,
% 2.68/1.95 (mult(X0!1, op_c) = mult(X0!1, op_d)),
% 2.68/1.95 inference(monotonicity,[status(thm)],[43])).
% 2.68/1.95 tff(61,plain,
% 2.68/1.95 (mult(X0!1, op_d) = mult(X0!1, op_c)),
% 2.68/1.95 inference(symmetry,[status(thm)],[60])).
% 2.68/1.95 tff(62,plain,
% 2.68/1.95 (mult(mult(X0!1, op_d), X1!0) = mult(mult(X0!1, op_c), X1!0)),
% 2.68/1.95 inference(monotonicity,[status(thm)],[61])).
% 2.68/1.95 tff(63,plain,
% 2.68/1.95 (mult(mult(X0!1, op_c), X1!0) = mult(mult(X0!1, op_d), X1!0)),
% 2.68/1.95 inference(symmetry,[status(thm)],[62])).
% 2.68/1.95 tff(64,plain,
% 2.68/1.95 (^[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)))),
% 2.68/1.95 inference(bind,[status(th)],[])).
% 2.68/1.95 tff(65,plain,
% 2.68/1.95 (![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))),
% 2.68/1.95 inference(quant_intro,[status(thm)],[64])).
% 2.68/1.95 tff(66,plain,
% 2.68/1.95 (![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))),
% 2.68/1.95 inference(rewrite,[status(thm)],[])).
% 2.68/1.95 tff(67,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')).
% 2.68/1.95 tff(68,plain,
% 2.68/1.95 (![B: $i, A: $i] : (mult(A, mult(op_c, B)) = mult(mult(A, op_c), B))),
% 2.68/1.95 inference(modus_ponens,[status(thm)],[67, 66])).
% 2.68/1.95 tff(69,plain,(
% 2.68/1.95 ![B: $i, A: $i] : (mult(A, mult(op_c, B)) = mult(mult(A, op_c), B))),
% 2.68/1.95 inference(skolemize,[status(sab)],[68])).
% 2.68/1.95 tff(70,plain,
% 2.68/1.95 (![B: $i, A: $i] : (mult(A, mult(op_c, B)) = mult(mult(A, op_c), B))),
% 2.68/1.95 inference(modus_ponens,[status(thm)],[69, 65])).
% 2.68/1.95 tff(71,plain,
% 2.68/1.95 ((~![B: $i, A: $i] : (mult(A, mult(op_c, B)) = mult(mult(A, op_c), B))) | (mult(X0!1, mult(op_c, X1!0)) = mult(mult(X0!1, op_c), X1!0))),
% 2.68/1.95 inference(quant_inst,[status(thm)],[])).
% 2.68/1.95 tff(72,plain,
% 2.68/1.95 (mult(X0!1, mult(op_c, X1!0)) = mult(mult(X0!1, op_c), X1!0)),
% 2.68/1.95 inference(unit_resolution,[status(thm)],[71, 70])).
% 2.68/1.95 tff(73,plain,
% 2.68/1.95 ((~![A: $i] : (op_d = ld(A, mult(op_c, A)))) | (op_d = ld(X1!0, mult(op_c, X1!0)))),
% 2.68/1.95 inference(quant_inst,[status(thm)],[])).
% 2.68/1.95 tff(74,plain,
% 2.68/1.95 (op_d = ld(X1!0, mult(op_c, X1!0))),
% 2.68/1.95 inference(unit_resolution,[status(thm)],[73, 7])).
% 2.68/1.95 tff(75,plain,
% 2.68/1.95 (mult(X1!0, op_d) = mult(X1!0, ld(X1!0, mult(op_c, X1!0)))),
% 2.68/1.95 inference(monotonicity,[status(thm)],[74])).
% 2.68/1.95 tff(76,plain,
% 2.68/1.95 (mult(X1!0, ld(X1!0, mult(op_c, X1!0))) = mult(X1!0, op_d)),
% 2.68/1.95 inference(symmetry,[status(thm)],[75])).
% 2.68/1.95 tff(77,plain,
% 2.68/1.95 (^[B: $i, A: $i] : refl((mult(A, ld(A, B)) = B) <=> (mult(A, ld(A, B)) = B))),
% 2.68/1.95 inference(bind,[status(th)],[])).
% 2.68/1.95 tff(78,plain,
% 2.68/1.95 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B) <=> ![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 2.68/1.95 inference(quant_intro,[status(thm)],[77])).
% 2.68/1.95 tff(79,plain,
% 2.68/1.95 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B) <=> ![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 2.68/1.95 inference(rewrite,[status(thm)],[])).
% 2.68/1.95 tff(80,axiom,(![B: $i, A: $i] : (mult(A, ld(A, B)) = B)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f01')).
% 2.68/1.95 tff(81,plain,
% 2.68/1.95 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 2.68/1.95 inference(modus_ponens,[status(thm)],[80, 79])).
% 2.68/1.95 tff(82,plain,(
% 2.68/1.95 ![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 2.68/1.95 inference(skolemize,[status(sab)],[81])).
% 2.68/1.95 tff(83,plain,
% 2.68/1.95 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 2.68/1.95 inference(modus_ponens,[status(thm)],[82, 78])).
% 2.68/1.95 tff(84,plain,
% 2.68/1.95 ((~![B: $i, A: $i] : (mult(A, ld(A, B)) = B)) | (mult(X1!0, ld(X1!0, mult(op_c, X1!0))) = mult(op_c, X1!0))),
% 2.68/1.95 inference(quant_inst,[status(thm)],[])).
% 2.68/1.95 tff(85,plain,
% 2.68/1.95 (mult(X1!0, ld(X1!0, mult(op_c, X1!0))) = mult(op_c, X1!0)),
% 2.68/1.95 inference(unit_resolution,[status(thm)],[84, 83])).
% 2.68/1.95 tff(86,plain,
% 2.68/1.95 (mult(op_c, X1!0) = mult(X1!0, ld(X1!0, mult(op_c, X1!0)))),
% 2.68/1.95 inference(symmetry,[status(thm)],[85])).
% 2.68/1.95 tff(87,plain,
% 2.68/1.95 (mult(op_c, X1!0) = mult(X1!0, op_d)),
% 2.68/1.95 inference(transitivity,[status(thm)],[86, 76])).
% 2.68/1.95 tff(88,plain,
% 2.68/1.95 (mult(X0!1, mult(op_c, X1!0)) = mult(X0!1, mult(X1!0, op_d))),
% 2.68/1.95 inference(monotonicity,[status(thm)],[87])).
% 2.68/1.95 tff(89,plain,
% 2.68/1.95 (mult(X0!1, mult(X1!0, op_d)) = mult(X0!1, mult(op_c, X1!0))),
% 2.68/1.95 inference(symmetry,[status(thm)],[88])).
% 2.68/1.95 tff(90,plain,
% 2.68/1.95 (mult(op_d, X1!0) = mult(op_c, X1!0)),
% 2.68/1.95 inference(monotonicity,[status(thm)],[57])).
% 2.68/1.95 tff(91,plain,
% 2.68/1.95 (mult(op_c, X1!0) = mult(op_d, X1!0)),
% 2.68/1.95 inference(symmetry,[status(thm)],[90])).
% 2.68/1.95 tff(92,plain,
% 2.68/1.95 (mult(X1!0, op_d) = mult(op_d, X1!0)),
% 2.68/1.95 inference(transitivity,[status(thm)],[75, 85, 91])).
% 2.68/1.95 tff(93,plain,
% 2.68/1.95 (mult(X0!1, mult(X1!0, op_d)) = mult(X0!1, mult(op_d, X1!0))),
% 2.68/1.95 inference(monotonicity,[status(thm)],[92])).
% 2.68/1.95 tff(94,plain,
% 2.68/1.95 (mult(X0!1, mult(op_d, X1!0)) = mult(X0!1, mult(X1!0, op_d))),
% 2.68/1.95 inference(symmetry,[status(thm)],[93])).
% 2.68/1.95 tff(95,plain,
% 2.68/1.95 (mult(X0!1, mult(op_d, X1!0)) = mult(mult(X0!1, op_d), X1!0)),
% 2.68/1.95 inference(transitivity,[status(thm)],[94, 89, 72, 63])).
% 2.68/1.95 tff(96,plain,
% 2.68/1.95 (mult(mult(X0!1, X1!0), op_d) = mult(mult(X0!1, X1!0), op_c)),
% 2.68/1.95 inference(monotonicity,[status(thm)],[57])).
% 2.68/1.95 tff(97,plain,
% 2.68/1.95 (mult(mult(X0!1, X1!0), op_c) = mult(mult(X0!1, X1!0), op_d)),
% 2.68/1.95 inference(symmetry,[status(thm)],[96])).
% 2.68/1.95 tff(98,plain,
% 2.68/1.95 (^[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)))),
% 2.68/1.95 inference(bind,[status(th)],[])).
% 2.68/1.95 tff(99,plain,
% 2.68/1.95 (![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))),
% 2.68/1.95 inference(quant_intro,[status(thm)],[98])).
% 2.68/1.95 tff(100,plain,
% 2.68/1.95 (![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))),
% 2.68/1.95 inference(rewrite,[status(thm)],[])).
% 2.68/1.95 tff(101,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')).
% 2.68/1.95 tff(102,plain,
% 2.68/1.95 (![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c))),
% 2.68/1.95 inference(modus_ponens,[status(thm)],[101, 100])).
% 2.68/1.95 tff(103,plain,(
% 2.68/1.95 ![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c))),
% 2.68/1.95 inference(skolemize,[status(sab)],[102])).
% 2.68/1.95 tff(104,plain,
% 2.68/1.95 (![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c))),
% 2.68/1.95 inference(modus_ponens,[status(thm)],[103, 99])).
% 2.68/1.95 tff(105,plain,
% 2.68/1.95 ((~![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c))) | (mult(X0!1, mult(X1!0, op_c)) = mult(mult(X0!1, X1!0), op_c))),
% 2.68/1.95 inference(quant_inst,[status(thm)],[])).
% 2.68/1.95 tff(106,plain,
% 2.68/1.95 (mult(X0!1, mult(X1!0, op_c)) = mult(mult(X0!1, X1!0), op_c)),
% 2.68/1.95 inference(unit_resolution,[status(thm)],[105, 104])).
% 2.68/1.95 tff(107,plain,
% 2.68/1.95 (mult(X1!0, op_c) = mult(X1!0, op_d)),
% 2.68/1.95 inference(monotonicity,[status(thm)],[43])).
% 2.68/1.95 tff(108,plain,
% 2.68/1.95 (mult(X0!1, mult(X1!0, op_c)) = mult(X0!1, mult(X1!0, op_d))),
% 2.68/1.95 inference(monotonicity,[status(thm)],[107])).
% 2.68/1.95 tff(109,plain,
% 2.68/1.95 (mult(X0!1, mult(X1!0, op_d)) = mult(X0!1, mult(X1!0, op_c))),
% 2.68/1.95 inference(symmetry,[status(thm)],[108])).
% 2.68/1.95 tff(110,plain,
% 2.68/1.95 (mult(X0!1, mult(X1!0, op_d)) = mult(mult(X0!1, X1!0), op_d)),
% 2.68/1.95 inference(transitivity,[status(thm)],[109, 106, 97])).
% 2.68/1.95 tff(111,plain,
% 2.68/1.95 ((~(~((~(mult(op_d, mult(X0!1, X1!0)) = mult(mult(op_d, X0!1), X1!0))) | (~(mult(X0!1, mult(X1!0, op_d)) = mult(mult(X0!1, X1!0), op_d))) | (~(mult(X0!1, mult(op_d, X1!0)) = mult(mult(X0!1, op_d), X1!0)))))) <=> ((~(mult(op_d, mult(X0!1, X1!0)) = mult(mult(op_d, X0!1), X1!0))) | (~(mult(X0!1, mult(X1!0, op_d)) = mult(mult(X0!1, X1!0), op_d))) | (~(mult(X0!1, mult(op_d, X1!0)) = mult(mult(X0!1, op_d), X1!0))))),
% 2.68/1.95 inference(rewrite,[status(thm)],[])).
% 2.68/1.95 tff(112,plain,
% 2.68/1.95 (((mult(op_d, mult(X0!1, X1!0)) = mult(mult(op_d, X0!1), X1!0)) & (mult(X0!1, mult(X1!0, op_d)) = mult(mult(X0!1, X1!0), op_d)) & (mult(X0!1, mult(op_d, X1!0)) = mult(mult(X0!1, op_d), X1!0))) <=> (~((~(mult(op_d, mult(X0!1, X1!0)) = mult(mult(op_d, X0!1), X1!0))) | (~(mult(X0!1, mult(X1!0, op_d)) = mult(mult(X0!1, X1!0), op_d))) | (~(mult(X0!1, mult(op_d, X1!0)) = mult(mult(X0!1, op_d), X1!0)))))),
% 2.68/1.95 inference(rewrite,[status(thm)],[])).
% 2.68/1.95 tff(113,plain,
% 2.68/1.95 ((~((mult(op_d, mult(X0!1, X1!0)) = mult(mult(op_d, X0!1), X1!0)) & (mult(X0!1, mult(X1!0, op_d)) = mult(mult(X0!1, X1!0), op_d)) & (mult(X0!1, mult(op_d, X1!0)) = mult(mult(X0!1, op_d), X1!0)))) <=> (~(~((~(mult(op_d, mult(X0!1, X1!0)) = mult(mult(op_d, X0!1), X1!0))) | (~(mult(X0!1, mult(X1!0, op_d)) = mult(mult(X0!1, X1!0), op_d))) | (~(mult(X0!1, mult(op_d, X1!0)) = mult(mult(X0!1, op_d), X1!0))))))),
% 2.68/1.95 inference(monotonicity,[status(thm)],[112])).
% 2.68/1.95 tff(114,plain,
% 2.68/1.95 ((~((mult(op_d, mult(X0!1, X1!0)) = mult(mult(op_d, X0!1), X1!0)) & (mult(X0!1, mult(X1!0, op_d)) = mult(mult(X0!1, X1!0), op_d)) & (mult(X0!1, mult(op_d, X1!0)) = mult(mult(X0!1, op_d), X1!0)))) <=> ((~(mult(op_d, mult(X0!1, X1!0)) = mult(mult(op_d, X0!1), X1!0))) | (~(mult(X0!1, mult(X1!0, op_d)) = mult(mult(X0!1, X1!0), op_d))) | (~(mult(X0!1, mult(op_d, X1!0)) = mult(mult(X0!1, op_d), X1!0))))),
% 2.68/1.95 inference(transitivity,[status(thm)],[113, 111])).
% 2.68/1.95 tff(115,plain,
% 2.68/1.95 ((~![X0: $i, X1: $i] : ((mult(op_d, mult(X0, X1)) = mult(mult(op_d, X0), X1)) & (mult(X0, mult(X1, op_d)) = mult(mult(X0, X1), op_d)) & (mult(X0, mult(op_d, X1)) = mult(mult(X0, op_d), X1)))) <=> (~![X0: $i, X1: $i] : ((mult(op_d, mult(X0, X1)) = mult(mult(op_d, X0), X1)) & (mult(X0, mult(X1, op_d)) = mult(mult(X0, X1), op_d)) & (mult(X0, mult(op_d, X1)) = mult(mult(X0, op_d), X1))))),
% 2.68/1.95 inference(rewrite,[status(thm)],[])).
% 2.68/1.95 tff(116,plain,
% 2.68/1.95 ((~![X0: $i, X1: $i] : (((mult(op_d, mult(X0, X1)) = mult(mult(op_d, X0), X1)) & (mult(X0, mult(X1, op_d)) = mult(mult(X0, X1), op_d))) & (mult(X0, mult(op_d, X1)) = mult(mult(X0, op_d), X1)))) <=> (~![X0: $i, X1: $i] : ((mult(op_d, mult(X0, X1)) = mult(mult(op_d, X0), X1)) & (mult(X0, mult(X1, op_d)) = mult(mult(X0, X1), op_d)) & (mult(X0, mult(op_d, X1)) = mult(mult(X0, op_d), X1))))),
% 2.68/1.95 inference(rewrite,[status(thm)],[])).
% 2.68/1.95 tff(117,axiom,(~![X0: $i, X1: $i] : (((mult(op_d, mult(X0, X1)) = mult(mult(op_d, X0), X1)) & (mult(X0, mult(X1, op_d)) = mult(mult(X0, X1), op_d))) & (mult(X0, mult(op_d, X1)) = mult(mult(X0, op_d), X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 2.68/1.95 tff(118,plain,
% 2.68/1.95 (~![X0: $i, X1: $i] : ((mult(op_d, mult(X0, X1)) = mult(mult(op_d, X0), X1)) & (mult(X0, mult(X1, op_d)) = mult(mult(X0, X1), op_d)) & (mult(X0, mult(op_d, X1)) = mult(mult(X0, op_d), X1)))),
% 2.68/1.95 inference(modus_ponens,[status(thm)],[117, 116])).
% 2.68/1.95 tff(119,plain,
% 2.68/1.95 (~![X0: $i, X1: $i] : ((mult(op_d, mult(X0, X1)) = mult(mult(op_d, X0), X1)) & (mult(X0, mult(X1, op_d)) = mult(mult(X0, X1), op_d)) & (mult(X0, mult(op_d, X1)) = mult(mult(X0, op_d), X1)))),
% 2.68/1.95 inference(modus_ponens,[status(thm)],[118, 115])).
% 2.68/1.95 tff(120,plain,
% 2.68/1.95 (~![X0: $i, X1: $i] : ((mult(op_d, mult(X0, X1)) = mult(mult(op_d, X0), X1)) & (mult(X0, mult(X1, op_d)) = mult(mult(X0, X1), op_d)) & (mult(X0, mult(op_d, X1)) = mult(mult(X0, op_d), X1)))),
% 2.68/1.95 inference(modus_ponens,[status(thm)],[119, 115])).
% 2.68/1.95 tff(121,plain,
% 2.68/1.95 (~![X0: $i, X1: $i] : ((mult(op_d, mult(X0, X1)) = mult(mult(op_d, X0), X1)) & (mult(X0, mult(X1, op_d)) = mult(mult(X0, X1), op_d)) & (mult(X0, mult(op_d, X1)) = mult(mult(X0, op_d), X1)))),
% 2.68/1.95 inference(modus_ponens,[status(thm)],[120, 115])).
% 2.68/1.95 tff(122,plain,
% 2.68/1.95 (~![X0: $i, X1: $i] : ((mult(op_d, mult(X0, X1)) = mult(mult(op_d, X0), X1)) & (mult(X0, mult(X1, op_d)) = mult(mult(X0, X1), op_d)) & (mult(X0, mult(op_d, X1)) = mult(mult(X0, op_d), X1)))),
% 2.68/1.95 inference(modus_ponens,[status(thm)],[121, 115])).
% 2.68/1.95 tff(123,plain,
% 2.68/1.95 (~![X0: $i, X1: $i] : ((mult(op_d, mult(X0, X1)) = mult(mult(op_d, X0), X1)) & (mult(X0, mult(X1, op_d)) = mult(mult(X0, X1), op_d)) & (mult(X0, mult(op_d, X1)) = mult(mult(X0, op_d), X1)))),
% 2.68/1.95 inference(modus_ponens,[status(thm)],[122, 115])).
% 2.68/1.95 tff(124,plain,
% 2.68/1.95 (~![X0: $i, X1: $i] : ((mult(op_d, mult(X0, X1)) = mult(mult(op_d, X0), X1)) & (mult(X0, mult(X1, op_d)) = mult(mult(X0, X1), op_d)) & (mult(X0, mult(op_d, X1)) = mult(mult(X0, op_d), X1)))),
% 2.68/1.95 inference(modus_ponens,[status(thm)],[123, 115])).
% 2.68/1.95 tff(125,plain,(
% 2.68/1.95 ~((mult(op_d, mult(X0!1, X1!0)) = mult(mult(op_d, X0!1), X1!0)) & (mult(X0!1, mult(X1!0, op_d)) = mult(mult(X0!1, X1!0), op_d)) & (mult(X0!1, mult(op_d, X1!0)) = mult(mult(X0!1, op_d), X1!0)))),
% 2.68/1.95 inference(skolemize,[status(sab)],[124])).
% 2.68/1.95 tff(126,plain,
% 2.68/1.95 ((~(mult(op_d, mult(X0!1, X1!0)) = mult(mult(op_d, X0!1), X1!0))) | (~(mult(X0!1, mult(X1!0, op_d)) = mult(mult(X0!1, X1!0), op_d))) | (~(mult(X0!1, mult(op_d, X1!0)) = mult(mult(X0!1, op_d), X1!0)))),
% 2.68/1.95 inference(modus_ponens,[status(thm)],[125, 114])).
% 2.68/1.95 tff(127,plain,
% 2.68/1.95 (~(mult(op_d, mult(X0!1, X1!0)) = mult(mult(op_d, X0!1), X1!0))),
% 2.68/1.95 inference(unit_resolution,[status(thm)],[126, 110, 95])).
% 2.68/1.95 tff(128,plain,
% 2.68/1.95 ($false),
% 2.68/1.95 inference(unit_resolution,[status(thm)],[127, 59])).
% 2.68/1.95 % SZS output end Proof
%------------------------------------------------------------------------------