TSTP Solution File: GRP026-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP026-1 : TPTP v8.1.0. Bugfixed v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 22:25:30 EDT 2022
% Result : Unsatisfiable 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP026-1 : TPTP v8.1.0. Bugfixed v2.0.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 31 14:06:57 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.20/0.40 % SZS status Unsatisfiable
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(product_type, type, (
% 0.20/0.40 product: ( $i * $i * $i * $i ) > $o)).
% 0.20/0.40 tff(an_isomorphism_type, type, (
% 0.20/0.40 an_isomorphism: $i > $i)).
% 0.20/0.40 tff(d3_type, type, (
% 0.20/0.40 d3: $i)).
% 0.20/0.40 tff(d2_type, type, (
% 0.20/0.40 d2: $i)).
% 0.20/0.40 tff(d1_type, type, (
% 0.20/0.40 d1: $i)).
% 0.20/0.40 tff(g2_type, type, (
% 0.20/0.40 g2: $i)).
% 0.20/0.40 tff(b_type, type, (
% 0.20/0.40 b: $i)).
% 0.20/0.40 tff(c_type, type, (
% 0.20/0.40 c: $i)).
% 0.20/0.40 tff(a_type, type, (
% 0.20/0.40 a: $i)).
% 0.20/0.40 tff(g1_type, type, (
% 0.20/0.40 g1: $i)).
% 0.20/0.40 tff(h_type, type, (
% 0.20/0.40 h: $i)).
% 0.20/0.40 tff(f_type, type, (
% 0.20/0.40 f: $i)).
% 0.20/0.40 tff(group_member_type, type, (
% 0.20/0.40 group_member: ( $i * $i ) > $o)).
% 0.20/0.40 tff(g_type, type, (
% 0.20/0.40 g: $i)).
% 0.20/0.40 tff(1,assumption,(d2 = b), introduced(assumption)).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (b = d2),
% 0.20/0.40 inference(symmetry,[status(thm)],[1])).
% 0.20/0.40 tff(3,assumption,(d1 = a), introduced(assumption)).
% 0.20/0.40 tff(4,assumption,(d2 = c), introduced(assumption)).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (c = d2),
% 0.20/0.40 inference(symmetry,[status(thm)],[4])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 (a = d1),
% 0.20/0.40 inference(symmetry,[status(thm)],[3])).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 (product(g1, a, c, d3) <=> product(g1, d1, d2, d3)),
% 0.20/0.40 inference(monotonicity,[status(thm)],[6, 5])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (product(g1, d1, d2, d3) <=> product(g1, a, c, d3)),
% 0.20/0.40 inference(symmetry,[status(thm)],[7])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (product(g1, d1, d2, d3) <=> product(g1, d1, d2, d3)),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(10,axiom,(product(g1, d1, d2, d3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_times_d2_is_d3')).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (product(g1, d1, d2, d3)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (product(g1, a, c, d3)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[11, 8])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (product(g1, a, c, c) <=> product(g1, a, c, c)),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(14,axiom,(product(g1, a, c, c)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a_times_c_is_c')).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (product(g1, a, c, c)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 (^[Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : refl(((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z))) <=> ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z))) <=> ![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[16])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z))) <=> ![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (^[Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : rewrite((((~product(Xg, X, Y, Z)) | (~product(Xg, X, Y, W))) | (W = Z)) <=> ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 (![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : (((~product(Xg, X, Y, Z)) | (~product(Xg, X, Y, W))) | (W = Z)) <=> ![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.40 tff(21,axiom,(![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : (((~product(Xg, X, Y, Z)) | (~product(Xg, X, Y, W))) | (W = Z))), file('/export/starexec/sandbox/benchmark/Axioms/GRP006-0.ax','total_function2')).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 (![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.20/0.40 tff(24,plain,(
% 0.20/0.40 ![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[23])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 (![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 (((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((~product(g1, a, c, d3)) | (c = d3) | (~product(g1, a, c, c)))) <=> ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | (~product(g1, a, c, d3)) | (c = d3) | (~product(g1, a, c, c)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 (((c = d3) | (~product(g1, a, c, c)) | (~product(g1, a, c, d3))) <=> ((~product(g1, a, c, d3)) | (c = d3) | (~product(g1, a, c, c)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 (((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((c = d3) | (~product(g1, a, c, c)) | (~product(g1, a, c, d3)))) <=> ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((~product(g1, a, c, d3)) | (c = d3) | (~product(g1, a, c, c))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[27])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((c = d3) | (~product(g1, a, c, c)) | (~product(g1, a, c, d3)))) <=> ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | (~product(g1, a, c, d3)) | (c = d3) | (~product(g1, a, c, c)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[28, 26])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((c = d3) | (~product(g1, a, c, c)) | (~product(g1, a, c, d3)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | (~product(g1, a, c, d3)) | (c = d3) | (~product(g1, a, c, c))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 ((~product(g1, a, c, d3)) | (c = d3)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[31, 25, 15])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 (c = d3),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[32, 12])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 (d3 = c),
% 0.20/0.41 inference(symmetry,[status(thm)],[33])).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 (an_isomorphism(d3) = an_isomorphism(c)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[34])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 (an_isomorphism(c) = an_isomorphism(d3)),
% 0.20/0.41 inference(symmetry,[status(thm)],[35])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 (an_isomorphism(d2) = an_isomorphism(c)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[4])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 (an_isomorphism(c) = an_isomorphism(d2)),
% 0.20/0.41 inference(symmetry,[status(thm)],[37])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (an_isomorphism(d1) = an_isomorphism(a)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[3])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 (an_isomorphism(a) = an_isomorphism(d1)),
% 0.20/0.41 inference(symmetry,[status(thm)],[39])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 (product(g2, an_isomorphism(a), an_isomorphism(c), an_isomorphism(c)) <=> product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[40, 38, 36])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 (product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3)) <=> product(g2, an_isomorphism(a), an_isomorphism(c), an_isomorphism(c))),
% 0.20/0.41 inference(symmetry,[status(thm)],[41])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 ((~product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3))) <=> (~product(g2, an_isomorphism(a), an_isomorphism(c), an_isomorphism(c)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[42])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 ((~product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3))) <=> (~product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(45,axiom,(~product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_product_holds_in_group2')).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 (~product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 (~product(g2, an_isomorphism(a), an_isomorphism(c), an_isomorphism(c))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[46, 43])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 (product(g2, f, h, h) <=> product(g2, an_isomorphism(a), an_isomorphism(c), an_isomorphism(c))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 (product(g2, f, h, h) <=> product(g2, f, h, h)),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(50,axiom,(product(g2, f, h, h)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f_times_h_is_h')).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (product(g2, f, h, h)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 (product(g2, an_isomorphism(a), an_isomorphism(c), an_isomorphism(c))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[51, 48])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[52, 47])).
% 0.20/0.41 tff(54,plain,((~(d2 = c)) | (~(d1 = a))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 (~(d2 = c)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[54, 3])).
% 0.20/0.41 tff(56,assumption,(d2 = a), introduced(assumption)).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 (a = d2),
% 0.20/0.41 inference(symmetry,[status(thm)],[56])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 (product(g1, a, a, d3) <=> product(g1, d1, d2, d3)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[6, 57])).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 (product(g1, d1, d2, d3) <=> product(g1, a, a, d3)),
% 0.20/0.41 inference(symmetry,[status(thm)],[58])).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 (product(g1, a, a, d3)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[11, 59])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 (product(g1, a, a, a) <=> product(g1, a, a, a)),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(62,axiom,(product(g1, a, a, a)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a_times_a_is_a')).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 (product(g1, a, a, a)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.41 tff(64,plain,
% 0.20/0.41 (((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((a = d3) | (~product(g1, a, a, d3)) | (~product(g1, a, a, a)))) <=> ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | (a = d3) | (~product(g1, a, a, d3)) | (~product(g1, a, a, a)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 (((a = d3) | (~product(g1, a, a, a)) | (~product(g1, a, a, d3))) <=> ((a = d3) | (~product(g1, a, a, d3)) | (~product(g1, a, a, a)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 (((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((a = d3) | (~product(g1, a, a, a)) | (~product(g1, a, a, d3)))) <=> ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((a = d3) | (~product(g1, a, a, d3)) | (~product(g1, a, a, a))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[65])).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 (((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((a = d3) | (~product(g1, a, a, a)) | (~product(g1, a, a, d3)))) <=> ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | (a = d3) | (~product(g1, a, a, d3)) | (~product(g1, a, a, a)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[66, 64])).
% 0.20/0.41 tff(68,plain,
% 0.20/0.41 ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((a = d3) | (~product(g1, a, a, a)) | (~product(g1, a, a, d3)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(69,plain,
% 0.20/0.41 ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | (a = d3) | (~product(g1, a, a, d3)) | (~product(g1, a, a, a))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 ((a = d3) | (~product(g1, a, a, d3))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[69, 25, 63])).
% 0.20/0.41 tff(71,plain,
% 0.20/0.41 (a = d3),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[70, 60])).
% 0.20/0.41 tff(72,plain,
% 0.20/0.41 (d3 = a),
% 0.20/0.41 inference(symmetry,[status(thm)],[71])).
% 0.20/0.41 tff(73,plain,
% 0.20/0.41 (an_isomorphism(d3) = an_isomorphism(a)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[72])).
% 0.20/0.42 tff(74,plain,
% 0.20/0.42 (an_isomorphism(a) = an_isomorphism(d3)),
% 0.20/0.42 inference(symmetry,[status(thm)],[73])).
% 0.20/0.42 tff(75,plain,
% 0.20/0.42 (an_isomorphism(d2) = an_isomorphism(a)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[56])).
% 0.20/0.42 tff(76,plain,
% 0.20/0.42 (an_isomorphism(a) = an_isomorphism(d2)),
% 0.20/0.42 inference(symmetry,[status(thm)],[75])).
% 0.20/0.42 tff(77,plain,
% 0.20/0.42 (product(g2, an_isomorphism(a), an_isomorphism(a), an_isomorphism(a)) <=> product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[40, 76, 74])).
% 0.20/0.42 tff(78,plain,
% 0.20/0.42 (product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3)) <=> product(g2, an_isomorphism(a), an_isomorphism(a), an_isomorphism(a))),
% 0.20/0.42 inference(symmetry,[status(thm)],[77])).
% 0.20/0.42 tff(79,plain,
% 0.20/0.42 ((~product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3))) <=> (~product(g2, an_isomorphism(a), an_isomorphism(a), an_isomorphism(a)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[78])).
% 0.20/0.42 tff(80,plain,
% 0.20/0.42 (~product(g2, an_isomorphism(a), an_isomorphism(a), an_isomorphism(a))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[46, 79])).
% 0.20/0.42 tff(81,plain,
% 0.20/0.42 (product(g2, f, f, f) <=> product(g2, an_isomorphism(a), an_isomorphism(a), an_isomorphism(a))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(82,plain,
% 0.20/0.42 (product(g2, f, f, f) <=> product(g2, f, f, f)),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(83,axiom,(product(g2, f, f, f)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f_times_f_is_f')).
% 0.20/0.42 tff(84,plain,
% 0.20/0.42 (product(g2, f, f, f)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.20/0.42 tff(85,plain,
% 0.20/0.42 (product(g2, an_isomorphism(a), an_isomorphism(a), an_isomorphism(a))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[84, 81])).
% 0.20/0.42 tff(86,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[85, 80])).
% 0.20/0.42 tff(87,plain,((~(d2 = a)) | (~(d1 = a))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(88,plain,
% 0.20/0.42 (~(d2 = a)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[87, 3])).
% 0.20/0.42 tff(89,plain,
% 0.20/0.42 (group_member(d2, g1) <=> group_member(d2, g1)),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(90,axiom,(group_member(d2, g1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_in_group1')).
% 0.20/0.42 tff(91,plain,
% 0.20/0.42 (group_member(d2, g1)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.20/0.42 tff(92,plain,
% 0.20/0.42 (^[X: $i] : refl(((X = c) | (X = b) | (X = a) | (~group_member(X, g1))) <=> ((X = c) | (X = b) | (X = a) | (~group_member(X, g1))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(93,plain,
% 0.20/0.42 (![X: $i] : ((X = c) | (X = b) | (X = a) | (~group_member(X, g1))) <=> ![X: $i] : ((X = c) | (X = b) | (X = a) | (~group_member(X, g1)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[92])).
% 0.20/0.42 tff(94,plain,
% 0.20/0.42 (![X: $i] : ((X = c) | (X = b) | (X = a) | (~group_member(X, g1))) <=> ![X: $i] : ((X = c) | (X = b) | (X = a) | (~group_member(X, g1)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(95,plain,
% 0.20/0.42 (^[X: $i] : trans(monotonicity(rewrite((((~group_member(X, g1)) | (X = a)) | (X = b)) <=> ((X = b) | (X = a) | (~group_member(X, g1)))), (((((~group_member(X, g1)) | (X = a)) | (X = b)) | (X = c)) <=> (((X = b) | (X = a) | (~group_member(X, g1))) | (X = c)))), rewrite((((X = b) | (X = a) | (~group_member(X, g1))) | (X = c)) <=> ((X = c) | (X = b) | (X = a) | (~group_member(X, g1)))), (((((~group_member(X, g1)) | (X = a)) | (X = b)) | (X = c)) <=> ((X = c) | (X = b) | (X = a) | (~group_member(X, g1)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(96,plain,
% 0.20/0.42 (![X: $i] : ((((~group_member(X, g1)) | (X = a)) | (X = b)) | (X = c)) <=> ![X: $i] : ((X = c) | (X = b) | (X = a) | (~group_member(X, g1)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[95])).
% 0.20/0.42 tff(97,axiom,(![X: $i] : ((((~group_member(X, g1)) | (X = a)) | (X = b)) | (X = c))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','all_of_group1')).
% 0.20/0.42 tff(98,plain,
% 0.20/0.42 (![X: $i] : ((X = c) | (X = b) | (X = a) | (~group_member(X, g1)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.20/0.42 tff(99,plain,
% 0.20/0.42 (![X: $i] : ((X = c) | (X = b) | (X = a) | (~group_member(X, g1)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.20/0.42 tff(100,plain,(
% 0.20/0.42 ![X: $i] : ((X = c) | (X = b) | (X = a) | (~group_member(X, g1)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[99])).
% 0.20/0.42 tff(101,plain,
% 0.20/0.42 (![X: $i] : ((X = c) | (X = b) | (X = a) | (~group_member(X, g1)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[100, 93])).
% 0.20/0.42 tff(102,plain,
% 0.20/0.42 (((~![X: $i] : ((X = c) | (X = b) | (X = a) | (~group_member(X, g1)))) | ((d2 = c) | (d2 = b) | (d2 = a) | (~group_member(d2, g1)))) <=> ((~![X: $i] : ((X = c) | (X = b) | (X = a) | (~group_member(X, g1)))) | (d2 = c) | (d2 = b) | (d2 = a) | (~group_member(d2, g1)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(103,plain,
% 0.20/0.42 ((~![X: $i] : ((X = c) | (X = b) | (X = a) | (~group_member(X, g1)))) | ((d2 = c) | (d2 = b) | (d2 = a) | (~group_member(d2, g1)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(104,plain,
% 0.20/0.42 ((~![X: $i] : ((X = c) | (X = b) | (X = a) | (~group_member(X, g1)))) | (d2 = c) | (d2 = b) | (d2 = a) | (~group_member(d2, g1))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.20/0.42 tff(105,plain,
% 0.20/0.42 ((d2 = c) | (d2 = b) | (d2 = a)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[104, 101, 91])).
% 0.20/0.42 tff(106,plain,
% 0.20/0.42 (d2 = b),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[105, 88, 55])).
% 0.20/0.42 tff(107,plain,
% 0.20/0.42 (product(g1, a, b, d3) <=> product(g1, d1, d2, d3)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[6, 2])).
% 0.20/0.42 tff(108,plain,
% 0.20/0.42 (product(g1, d1, d2, d3) <=> product(g1, a, b, d3)),
% 0.20/0.42 inference(symmetry,[status(thm)],[107])).
% 0.20/0.42 tff(109,plain,
% 0.20/0.42 (product(g1, a, b, d3)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[11, 108])).
% 0.20/0.42 tff(110,assumption,(~(d3 = b)), introduced(assumption)).
% 0.20/0.42 tff(111,plain,
% 0.20/0.42 (product(g1, a, b, b) <=> product(g1, a, b, b)),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(112,axiom,(product(g1, a, b, b)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a_times_b_is_b')).
% 0.20/0.42 tff(113,plain,
% 0.20/0.42 (product(g1, a, b, b)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.20/0.42 tff(114,plain,
% 0.20/0.42 (((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((d3 = b) | (~product(g1, a, b, b)) | (~product(g1, a, b, d3)))) <=> ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | (d3 = b) | (~product(g1, a, b, b)) | (~product(g1, a, b, d3)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(115,plain,
% 0.20/0.42 (((d3 = b) | (~product(g1, a, b, d3)) | (~product(g1, a, b, b))) <=> ((d3 = b) | (~product(g1, a, b, b)) | (~product(g1, a, b, d3)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(116,plain,
% 0.20/0.42 (((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((d3 = b) | (~product(g1, a, b, d3)) | (~product(g1, a, b, b)))) <=> ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((d3 = b) | (~product(g1, a, b, b)) | (~product(g1, a, b, d3))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[115])).
% 0.20/0.42 tff(117,plain,
% 0.20/0.42 (((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((d3 = b) | (~product(g1, a, b, d3)) | (~product(g1, a, b, b)))) <=> ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | (d3 = b) | (~product(g1, a, b, b)) | (~product(g1, a, b, d3)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[116, 114])).
% 0.20/0.42 tff(118,plain,
% 0.20/0.42 ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((d3 = b) | (~product(g1, a, b, d3)) | (~product(g1, a, b, b)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(119,plain,
% 0.20/0.42 ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | (d3 = b) | (~product(g1, a, b, b)) | (~product(g1, a, b, d3))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.20/0.42 tff(120,plain,
% 0.20/0.42 (~product(g1, a, b, d3)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[119, 25, 113, 110])).
% 0.20/0.42 tff(121,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[120, 109])).
% 0.20/0.42 tff(122,plain,((~(d2 = b)) | (~(d1 = a)) | (d3 = b)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(123,plain,
% 0.20/0.42 (d3 = b),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[122, 106, 3])).
% 0.20/0.42 tff(124,plain,
% 0.20/0.42 (an_isomorphism(d3) = an_isomorphism(b)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[123])).
% 0.20/0.42 tff(125,plain,
% 0.20/0.42 (an_isomorphism(d2) = an_isomorphism(b)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[106])).
% 0.20/0.42 tff(126,plain,
% 0.20/0.42 (product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3)) <=> product(g2, an_isomorphism(a), an_isomorphism(b), an_isomorphism(b))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[39, 125, 124])).
% 0.20/0.42 tff(127,plain,
% 0.20/0.42 (product(g2, an_isomorphism(a), an_isomorphism(b), an_isomorphism(b)) <=> product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3))),
% 0.20/0.42 inference(symmetry,[status(thm)],[126])).
% 0.20/0.42 tff(128,plain,
% 0.20/0.42 (product(g2, f, g, g) <=> product(g2, an_isomorphism(a), an_isomorphism(b), an_isomorphism(b))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(129,plain,
% 0.20/0.42 (product(g2, f, g, g) <=> product(g2, f, g, g)),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(130,axiom,(product(g2, f, g, g)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f_times_g_is_g')).
% 0.20/0.42 tff(131,plain,
% 0.20/0.42 (product(g2, f, g, g)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.20/0.42 tff(132,plain,
% 0.20/0.42 (product(g2, an_isomorphism(a), an_isomorphism(b), an_isomorphism(b))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[131, 128])).
% 0.20/0.42 tff(133,plain,
% 0.20/0.42 (product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[132, 127])).
% 0.20/0.42 tff(134,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[46, 133])).
% 0.20/0.42 tff(135,plain,(~(d1 = a)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(136,assumption,(~(d1 = c)), introduced(assumption)).
% 0.20/0.42 tff(137,assumption,(~(d1 = a)), introduced(assumption)).
% 0.20/0.42 tff(138,plain,
% 0.20/0.42 (group_member(d1, g1) <=> group_member(d1, g1)),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(139,axiom,(group_member(d1, g1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_in_group1')).
% 0.20/0.42 tff(140,plain,
% 0.20/0.42 (group_member(d1, g1)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.20/0.42 tff(141,plain,
% 0.20/0.42 (((~![X: $i] : ((X = c) | (X = b) | (X = a) | (~group_member(X, g1)))) | ((d1 = c) | (d1 = b) | (d1 = a) | (~group_member(d1, g1)))) <=> ((~![X: $i] : ((X = c) | (X = b) | (X = a) | (~group_member(X, g1)))) | (d1 = c) | (d1 = b) | (d1 = a) | (~group_member(d1, g1)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(142,plain,
% 0.20/0.42 ((~![X: $i] : ((X = c) | (X = b) | (X = a) | (~group_member(X, g1)))) | ((d1 = c) | (d1 = b) | (d1 = a) | (~group_member(d1, g1)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(143,plain,
% 0.20/0.42 ((~![X: $i] : ((X = c) | (X = b) | (X = a) | (~group_member(X, g1)))) | (d1 = c) | (d1 = b) | (d1 = a) | (~group_member(d1, g1))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.20/0.42 tff(144,plain,
% 0.20/0.42 ((d1 = c) | (d1 = b) | (d1 = a)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[143, 101, 140])).
% 0.20/0.42 tff(145,plain,
% 0.20/0.42 (d1 = b),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[144, 137, 136])).
% 0.20/0.42 tff(146,assumption,(d1 = b), introduced(assumption)).
% 0.20/0.42 tff(147,plain,
% 0.20/0.42 (b = d1),
% 0.20/0.42 inference(symmetry,[status(thm)],[146])).
% 0.20/0.42 tff(148,plain,
% 0.20/0.42 (product(g1, b, b, d3) <=> product(g1, d1, d2, d3)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[147, 2])).
% 0.20/0.42 tff(149,plain,
% 0.20/0.42 (product(g1, d1, d2, d3) <=> product(g1, b, b, d3)),
% 0.20/0.42 inference(symmetry,[status(thm)],[148])).
% 0.20/0.42 tff(150,plain,
% 0.20/0.42 (product(g1, b, b, d3)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[11, 149])).
% 0.20/0.42 tff(151,plain,
% 0.20/0.42 (product(g1, b, b, c) <=> product(g1, b, b, c)),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(152,axiom,(product(g1, b, b, c)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','b_times_b_is_c')).
% 0.20/0.42 tff(153,plain,
% 0.20/0.42 (product(g1, b, b, c)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.20/0.42 tff(154,plain,
% 0.20/0.42 (((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((~product(g1, b, b, c)) | (c = d3) | (~product(g1, b, b, d3)))) <=> ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | (~product(g1, b, b, c)) | (c = d3) | (~product(g1, b, b, d3)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(155,plain,
% 0.20/0.43 (((c = d3) | (~product(g1, b, b, c)) | (~product(g1, b, b, d3))) <=> ((~product(g1, b, b, c)) | (c = d3) | (~product(g1, b, b, d3)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(156,plain,
% 0.20/0.43 (((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((c = d3) | (~product(g1, b, b, c)) | (~product(g1, b, b, d3)))) <=> ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((~product(g1, b, b, c)) | (c = d3) | (~product(g1, b, b, d3))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[155])).
% 0.20/0.43 tff(157,plain,
% 0.20/0.43 (((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((c = d3) | (~product(g1, b, b, c)) | (~product(g1, b, b, d3)))) <=> ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | (~product(g1, b, b, c)) | (c = d3) | (~product(g1, b, b, d3)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[156, 154])).
% 0.20/0.43 tff(158,plain,
% 0.20/0.43 ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((c = d3) | (~product(g1, b, b, c)) | (~product(g1, b, b, d3)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(159,plain,
% 0.20/0.43 ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | (~product(g1, b, b, c)) | (c = d3) | (~product(g1, b, b, d3))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.20/0.43 tff(160,plain,
% 0.20/0.43 ((c = d3) | (~product(g1, b, b, d3))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[159, 25, 153])).
% 0.20/0.43 tff(161,plain,
% 0.20/0.43 (c = d3),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[160, 150])).
% 0.20/0.43 tff(162,plain,
% 0.20/0.43 (an_isomorphism(c) = an_isomorphism(d3)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[161])).
% 0.20/0.43 tff(163,plain,
% 0.20/0.43 (an_isomorphism(d2) = an_isomorphism(b)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[1])).
% 0.20/0.43 tff(164,plain,
% 0.20/0.43 (an_isomorphism(b) = an_isomorphism(d2)),
% 0.20/0.43 inference(symmetry,[status(thm)],[163])).
% 0.20/0.43 tff(165,plain,
% 0.20/0.43 (an_isomorphism(d1) = an_isomorphism(b)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[146])).
% 0.20/0.43 tff(166,plain,
% 0.20/0.43 (an_isomorphism(b) = an_isomorphism(d1)),
% 0.20/0.43 inference(symmetry,[status(thm)],[165])).
% 0.20/0.43 tff(167,plain,
% 0.20/0.43 (product(g2, an_isomorphism(b), an_isomorphism(b), an_isomorphism(c)) <=> product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[166, 164, 162])).
% 0.20/0.43 tff(168,plain,
% 0.20/0.43 (product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3)) <=> product(g2, an_isomorphism(b), an_isomorphism(b), an_isomorphism(c))),
% 0.20/0.43 inference(symmetry,[status(thm)],[167])).
% 0.20/0.43 tff(169,plain,
% 0.20/0.43 ((~product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3))) <=> (~product(g2, an_isomorphism(b), an_isomorphism(b), an_isomorphism(c)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[168])).
% 0.20/0.43 tff(170,plain,
% 0.20/0.43 (~product(g2, an_isomorphism(b), an_isomorphism(b), an_isomorphism(c))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[46, 169])).
% 0.20/0.43 tff(171,plain,
% 0.20/0.43 (product(g2, g, g, h) <=> product(g2, an_isomorphism(b), an_isomorphism(b), an_isomorphism(c))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(172,plain,
% 0.20/0.43 (product(g2, g, g, h) <=> product(g2, g, g, h)),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(173,axiom,(product(g2, g, g, h)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','g_times_g_is_h')).
% 0.20/0.43 tff(174,plain,
% 0.20/0.43 (product(g2, g, g, h)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.20/0.43 tff(175,plain,
% 0.20/0.43 (product(g2, an_isomorphism(b), an_isomorphism(b), an_isomorphism(c))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[174, 171])).
% 0.20/0.43 tff(176,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[175, 170])).
% 0.20/0.43 tff(177,plain,((~(d2 = b)) | (~(d1 = b))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(178,plain,
% 0.20/0.43 (~(d2 = b)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[177, 145])).
% 0.20/0.43 tff(179,assumption,(product(g1, b, a, a)), introduced(assumption)).
% 0.20/0.43 tff(180,plain,
% 0.20/0.43 ((b = a) <=> (d1 = a)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[147])).
% 0.20/0.43 tff(181,plain,
% 0.20/0.43 ((d1 = a) <=> (b = a)),
% 0.20/0.43 inference(symmetry,[status(thm)],[180])).
% 0.20/0.43 tff(182,plain,
% 0.20/0.43 ((~(d1 = a)) <=> (~(b = a))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[181])).
% 0.20/0.43 tff(183,plain,
% 0.20/0.43 (~(b = a)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[137, 182])).
% 0.20/0.43 tff(184,plain,
% 0.20/0.43 (product(g1, b, a, b) <=> product(g1, b, a, b)),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(185,axiom,(product(g1, b, a, b)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','b_times_a_is_b')).
% 0.20/0.43 tff(186,plain,
% 0.20/0.43 (product(g1, b, a, b)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.20/0.43 tff(187,plain,
% 0.20/0.43 (((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((~product(g1, b, a, a)) | (b = a) | (~product(g1, b, a, b)))) <=> ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | (~product(g1, b, a, a)) | (b = a) | (~product(g1, b, a, b)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(188,plain,
% 0.20/0.43 (((b = a) | (~product(g1, b, a, b)) | (~product(g1, b, a, a))) <=> ((~product(g1, b, a, a)) | (b = a) | (~product(g1, b, a, b)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(189,plain,
% 0.20/0.43 (((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((b = a) | (~product(g1, b, a, b)) | (~product(g1, b, a, a)))) <=> ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((~product(g1, b, a, a)) | (b = a) | (~product(g1, b, a, b))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[188])).
% 0.20/0.43 tff(190,plain,
% 0.20/0.43 (((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((b = a) | (~product(g1, b, a, b)) | (~product(g1, b, a, a)))) <=> ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | (~product(g1, b, a, a)) | (b = a) | (~product(g1, b, a, b)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[189, 187])).
% 0.20/0.43 tff(191,plain,
% 0.20/0.43 ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((b = a) | (~product(g1, b, a, b)) | (~product(g1, b, a, a)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(192,plain,
% 0.20/0.43 ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | (~product(g1, b, a, a)) | (b = a) | (~product(g1, b, a, b))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.20/0.43 tff(193,plain,
% 0.20/0.43 ((~product(g1, b, a, a)) | (b = a)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[192, 25, 186])).
% 0.20/0.43 tff(194,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[193, 183, 179])).
% 0.20/0.43 tff(195,plain,((~product(g1, b, a, a)) | (d1 = a) | (~(d1 = b))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(196,plain,
% 0.20/0.43 (~product(g1, b, a, a)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[195, 137, 145])).
% 0.20/0.43 tff(197,assumption,(d3 = b), introduced(assumption)).
% 0.20/0.43 tff(198,plain,
% 0.20/0.43 (an_isomorphism(d3) = an_isomorphism(b)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[197])).
% 0.20/0.43 tff(199,plain,
% 0.20/0.43 (product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3)) <=> product(g2, an_isomorphism(b), an_isomorphism(a), an_isomorphism(b))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[165, 75, 198])).
% 0.20/0.43 tff(200,plain,
% 0.20/0.43 (product(g2, an_isomorphism(b), an_isomorphism(a), an_isomorphism(b)) <=> product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3))),
% 0.20/0.43 inference(symmetry,[status(thm)],[199])).
% 0.20/0.43 tff(201,plain,
% 0.20/0.43 (product(g2, g, f, g) <=> product(g2, an_isomorphism(b), an_isomorphism(a), an_isomorphism(b))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(202,plain,
% 0.20/0.43 (product(g2, g, f, g) <=> product(g2, g, f, g)),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(203,axiom,(product(g2, g, f, g)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','g_times_f_is_g')).
% 0.20/0.44 tff(204,plain,
% 0.20/0.44 (product(g2, g, f, g)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.20/0.44 tff(205,plain,
% 0.20/0.44 (product(g2, an_isomorphism(b), an_isomorphism(a), an_isomorphism(b))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[204, 201])).
% 0.20/0.44 tff(206,plain,
% 0.20/0.44 (product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[205, 200])).
% 0.20/0.44 tff(207,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[46, 206])).
% 0.20/0.44 tff(208,plain,((~(d2 = a)) | (~(d3 = b)) | (~(d1 = b))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(209,plain,
% 0.20/0.44 (~(d2 = a)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[208, 197, 146])).
% 0.20/0.44 tff(210,assumption,(~product(g1, b, a, a)), introduced(assumption)).
% 0.20/0.44 tff(211,plain,
% 0.20/0.44 (b = d3),
% 0.20/0.44 inference(symmetry,[status(thm)],[197])).
% 0.20/0.44 tff(212,plain,
% 0.20/0.44 (product(g1, b, c, b) <=> product(g1, d1, d2, d3)),
% 0.20/0.44 inference(monotonicity,[status(thm)],[147, 5, 211])).
% 0.20/0.44 tff(213,plain,
% 0.20/0.44 (product(g1, d1, d2, d3) <=> product(g1, b, c, b)),
% 0.20/0.44 inference(symmetry,[status(thm)],[212])).
% 0.20/0.44 tff(214,plain,
% 0.20/0.44 (product(g1, b, c, b)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[11, 213])).
% 0.20/0.44 tff(215,plain,
% 0.20/0.44 (product(g1, b, c, a) <=> product(g1, b, c, a)),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(216,axiom,(product(g1, b, c, a)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','b_times_c_is_a')).
% 0.20/0.44 tff(217,plain,
% 0.20/0.44 (product(g1, b, c, a)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.20/0.44 tff(218,plain,
% 0.20/0.44 (product(g1, c, a, c) <=> product(g1, c, a, c)),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(219,axiom,(product(g1, c, a, c)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_times_a_is_c')).
% 0.20/0.44 tff(220,plain,
% 0.20/0.44 (product(g1, c, a, c)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.20/0.44 tff(221,plain,
% 0.20/0.44 (^[Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : refl((product(Xg, Xy, Z, Xyz) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)) | (~product(Xg, X, Yz, Xyz))) <=> (product(Xg, Xy, Z, Xyz) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)) | (~product(Xg, X, Yz, Xyz))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(222,plain,
% 0.20/0.44 (![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, Xy, Z, Xyz) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)) | (~product(Xg, X, Yz, Xyz))) <=> ![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, Xy, Z, Xyz) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)) | (~product(Xg, X, Yz, Xyz)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[221])).
% 0.20/0.44 tff(223,plain,
% 0.20/0.44 (![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, Xy, Z, Xyz) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)) | (~product(Xg, X, Yz, Xyz))) <=> ![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, Xy, Z, Xyz) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)) | (~product(Xg, X, Yz, Xyz)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(224,plain,
% 0.20/0.44 (^[Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : trans(monotonicity(rewrite((((~product(Xg, X, Y, Xy)) | (~product(Xg, Y, Z, Yz))) | (~product(Xg, X, Yz, Xyz))) <=> ((~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)) | (~product(Xg, X, Yz, Xyz)))), (((((~product(Xg, X, Y, Xy)) | (~product(Xg, Y, Z, Yz))) | (~product(Xg, X, Yz, Xyz))) | product(Xg, Xy, Z, Xyz)) <=> (((~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)) | (~product(Xg, X, Yz, Xyz))) | product(Xg, Xy, Z, Xyz)))), rewrite((((~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)) | (~product(Xg, X, Yz, Xyz))) | product(Xg, Xy, Z, Xyz)) <=> (product(Xg, Xy, Z, Xyz) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)) | (~product(Xg, X, Yz, Xyz)))), (((((~product(Xg, X, Y, Xy)) | (~product(Xg, Y, Z, Yz))) | (~product(Xg, X, Yz, Xyz))) | product(Xg, Xy, Z, Xyz)) <=> (product(Xg, Xy, Z, Xyz) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)) | (~product(Xg, X, Yz, Xyz)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(225,plain,
% 0.20/0.44 (![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : ((((~product(Xg, X, Y, Xy)) | (~product(Xg, Y, Z, Yz))) | (~product(Xg, X, Yz, Xyz))) | product(Xg, Xy, Z, Xyz)) <=> ![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, Xy, Z, Xyz) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)) | (~product(Xg, X, Yz, Xyz)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[224])).
% 0.20/0.44 tff(226,axiom,(![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : ((((~product(Xg, X, Y, Xy)) | (~product(Xg, Y, Z, Yz))) | (~product(Xg, X, Yz, Xyz))) | product(Xg, Xy, Z, Xyz))), file('/export/starexec/sandbox/benchmark/Axioms/GRP006-0.ax','associativity2')).
% 0.20/0.44 tff(227,plain,
% 0.20/0.44 (![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, Xy, Z, Xyz) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)) | (~product(Xg, X, Yz, Xyz)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.20/0.44 tff(228,plain,
% 0.20/0.44 (![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, Xy, Z, Xyz) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)) | (~product(Xg, X, Yz, Xyz)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[227, 223])).
% 0.20/0.44 tff(229,plain,(
% 0.20/0.44 ![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, Xy, Z, Xyz) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)) | (~product(Xg, X, Yz, Xyz)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[228])).
% 0.20/0.44 tff(230,plain,
% 0.20/0.44 (![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, Xy, Z, Xyz) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)) | (~product(Xg, X, Yz, Xyz)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[229, 222])).
% 0.20/0.44 tff(231,plain,
% 0.20/0.44 (((~![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, Xy, Z, Xyz) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)) | (~product(Xg, X, Yz, Xyz)))) | (product(g1, b, a, a) | (~product(g1, b, c, a)) | (~product(g1, c, a, c)) | (~product(g1, b, c, b)))) <=> ((~![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, Xy, Z, Xyz) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)) | (~product(Xg, X, Yz, Xyz)))) | product(g1, b, a, a) | (~product(g1, b, c, a)) | (~product(g1, c, a, c)) | (~product(g1, b, c, b)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(232,plain,
% 0.20/0.44 ((product(g1, b, a, a) | (~product(g1, c, a, c)) | (~product(g1, b, c, b)) | (~product(g1, b, c, a))) <=> (product(g1, b, a, a) | (~product(g1, b, c, a)) | (~product(g1, c, a, c)) | (~product(g1, b, c, b)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(233,plain,
% 0.20/0.44 (((~![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, Xy, Z, Xyz) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)) | (~product(Xg, X, Yz, Xyz)))) | (product(g1, b, a, a) | (~product(g1, c, a, c)) | (~product(g1, b, c, b)) | (~product(g1, b, c, a)))) <=> ((~![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, Xy, Z, Xyz) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)) | (~product(Xg, X, Yz, Xyz)))) | (product(g1, b, a, a) | (~product(g1, b, c, a)) | (~product(g1, c, a, c)) | (~product(g1, b, c, b))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[232])).
% 0.20/0.44 tff(234,plain,
% 0.20/0.44 (((~![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, Xy, Z, Xyz) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)) | (~product(Xg, X, Yz, Xyz)))) | (product(g1, b, a, a) | (~product(g1, c, a, c)) | (~product(g1, b, c, b)) | (~product(g1, b, c, a)))) <=> ((~![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, Xy, Z, Xyz) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)) | (~product(Xg, X, Yz, Xyz)))) | product(g1, b, a, a) | (~product(g1, b, c, a)) | (~product(g1, c, a, c)) | (~product(g1, b, c, b)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[233, 231])).
% 0.20/0.44 tff(235,plain,
% 0.20/0.44 ((~![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, Xy, Z, Xyz) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)) | (~product(Xg, X, Yz, Xyz)))) | (product(g1, b, a, a) | (~product(g1, c, a, c)) | (~product(g1, b, c, b)) | (~product(g1, b, c, a)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(236,plain,
% 0.20/0.44 ((~![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, Xy, Z, Xyz) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)) | (~product(Xg, X, Yz, Xyz)))) | product(g1, b, a, a) | (~product(g1, b, c, a)) | (~product(g1, c, a, c)) | (~product(g1, b, c, b))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.20/0.44 tff(237,plain,
% 0.20/0.44 (~product(g1, b, c, b)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[236, 230, 220, 217, 210])).
% 0.20/0.44 tff(238,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[237, 214])).
% 0.20/0.44 tff(239,plain,((~(d2 = c)) | (~(d3 = b)) | (~(d1 = b)) | product(g1, b, a, a)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(240,plain,
% 0.20/0.44 (~(d2 = c)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[239, 197, 146, 210])).
% 0.20/0.44 tff(241,plain,
% 0.20/0.44 (d2 = b),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[105, 240, 209])).
% 0.20/0.44 tff(242,plain,
% 0.20/0.44 (product(g1, d1, d2, d3) <=> product(g1, b, b, b)),
% 0.20/0.44 inference(monotonicity,[status(thm)],[146, 241, 197])).
% 0.20/0.44 tff(243,plain,
% 0.20/0.44 (product(g1, b, b, b) <=> product(g1, d1, d2, d3)),
% 0.20/0.44 inference(symmetry,[status(thm)],[242])).
% 0.20/0.44 tff(244,plain,
% 0.20/0.44 ((~product(g1, b, b, b)) <=> (~product(g1, d1, d2, d3))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[243])).
% 0.20/0.44 tff(245,plain,
% 0.20/0.44 (^[Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : refl((product(Xg, X, Yz, Xyz) | (~product(Xg, Xy, Z, Xyz)) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy))) <=> (product(Xg, X, Yz, Xyz) | (~product(Xg, Xy, Z, Xyz)) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(246,plain,
% 0.20/0.44 (![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, X, Yz, Xyz) | (~product(Xg, Xy, Z, Xyz)) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy))) <=> ![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, X, Yz, Xyz) | (~product(Xg, Xy, Z, Xyz)) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[245])).
% 0.20/0.44 tff(247,plain,
% 0.20/0.44 (![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, X, Yz, Xyz) | (~product(Xg, Xy, Z, Xyz)) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy))) <=> ![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, X, Yz, Xyz) | (~product(Xg, Xy, Z, Xyz)) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(248,plain,
% 0.20/0.44 (^[Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : trans(monotonicity(rewrite((((~product(Xg, X, Y, Xy)) | (~product(Xg, Y, Z, Yz))) | (~product(Xg, Xy, Z, Xyz))) <=> ((~product(Xg, Xy, Z, Xyz)) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)))), (((((~product(Xg, X, Y, Xy)) | (~product(Xg, Y, Z, Yz))) | (~product(Xg, Xy, Z, Xyz))) | product(Xg, X, Yz, Xyz)) <=> (((~product(Xg, Xy, Z, Xyz)) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy))) | product(Xg, X, Yz, Xyz)))), rewrite((((~product(Xg, Xy, Z, Xyz)) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy))) | product(Xg, X, Yz, Xyz)) <=> (product(Xg, X, Yz, Xyz) | (~product(Xg, Xy, Z, Xyz)) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)))), (((((~product(Xg, X, Y, Xy)) | (~product(Xg, Y, Z, Yz))) | (~product(Xg, Xy, Z, Xyz))) | product(Xg, X, Yz, Xyz)) <=> (product(Xg, X, Yz, Xyz) | (~product(Xg, Xy, Z, Xyz)) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(249,plain,
% 0.20/0.44 (![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : ((((~product(Xg, X, Y, Xy)) | (~product(Xg, Y, Z, Yz))) | (~product(Xg, Xy, Z, Xyz))) | product(Xg, X, Yz, Xyz)) <=> ![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, X, Yz, Xyz) | (~product(Xg, Xy, Z, Xyz)) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[248])).
% 0.20/0.44 tff(250,axiom,(![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : ((((~product(Xg, X, Y, Xy)) | (~product(Xg, Y, Z, Yz))) | (~product(Xg, Xy, Z, Xyz))) | product(Xg, X, Yz, Xyz))), file('/export/starexec/sandbox/benchmark/Axioms/GRP006-0.ax','associativity1')).
% 0.20/0.45 tff(251,plain,
% 0.20/0.45 (![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, X, Yz, Xyz) | (~product(Xg, Xy, Z, Xyz)) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.20/0.45 tff(252,plain,
% 0.20/0.45 (![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, X, Yz, Xyz) | (~product(Xg, Xy, Z, Xyz)) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[251, 247])).
% 0.20/0.45 tff(253,plain,(
% 0.20/0.45 ![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, X, Yz, Xyz) | (~product(Xg, Xy, Z, Xyz)) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[252])).
% 0.20/0.45 tff(254,plain,
% 0.20/0.45 (![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, X, Yz, Xyz) | (~product(Xg, Xy, Z, Xyz)) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[253, 246])).
% 0.20/0.45 tff(255,plain,
% 0.20/0.45 (((~![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, X, Yz, Xyz) | (~product(Xg, Xy, Z, Xyz)) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)))) | (product(g1, b, a, a) | (~product(g1, b, c, a)) | (~product(g1, b, b, b)))) <=> ((~![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, X, Yz, Xyz) | (~product(Xg, Xy, Z, Xyz)) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)))) | product(g1, b, a, a) | (~product(g1, b, c, a)) | (~product(g1, b, b, b)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(256,plain,
% 0.20/0.45 ((product(g1, b, a, a) | (~product(g1, b, c, a)) | (~product(g1, b, c, a)) | (~product(g1, b, b, b))) <=> (product(g1, b, a, a) | (~product(g1, b, c, a)) | (~product(g1, b, b, b)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(257,plain,
% 0.20/0.45 (((~![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, X, Yz, Xyz) | (~product(Xg, Xy, Z, Xyz)) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)))) | (product(g1, b, a, a) | (~product(g1, b, c, a)) | (~product(g1, b, c, a)) | (~product(g1, b, b, b)))) <=> ((~![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, X, Yz, Xyz) | (~product(Xg, Xy, Z, Xyz)) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)))) | (product(g1, b, a, a) | (~product(g1, b, c, a)) | (~product(g1, b, b, b))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[256])).
% 0.20/0.45 tff(258,plain,
% 0.20/0.45 (((~![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, X, Yz, Xyz) | (~product(Xg, Xy, Z, Xyz)) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)))) | (product(g1, b, a, a) | (~product(g1, b, c, a)) | (~product(g1, b, c, a)) | (~product(g1, b, b, b)))) <=> ((~![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, X, Yz, Xyz) | (~product(Xg, Xy, Z, Xyz)) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)))) | product(g1, b, a, a) | (~product(g1, b, c, a)) | (~product(g1, b, b, b)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[257, 255])).
% 0.20/0.45 tff(259,plain,
% 0.20/0.45 ((~![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, X, Yz, Xyz) | (~product(Xg, Xy, Z, Xyz)) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)))) | (product(g1, b, a, a) | (~product(g1, b, c, a)) | (~product(g1, b, c, a)) | (~product(g1, b, b, b)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(260,plain,
% 0.20/0.45 ((~![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, X, Yz, Xyz) | (~product(Xg, Xy, Z, Xyz)) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)))) | product(g1, b, a, a) | (~product(g1, b, c, a)) | (~product(g1, b, b, b))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.20/0.45 tff(261,plain,
% 0.20/0.45 (~product(g1, b, b, b)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[260, 254, 217, 210])).
% 0.20/0.45 tff(262,plain,
% 0.20/0.45 (~product(g1, d1, d2, d3)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[261, 244])).
% 0.20/0.45 tff(263,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[11, 262])).
% 0.20/0.45 tff(264,plain,((~(d3 = b)) | (~(d1 = b)) | product(g1, b, a, a)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(265,plain,
% 0.20/0.45 (~(d3 = b)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[264, 145, 196])).
% 0.20/0.45 tff(266,plain,
% 0.20/0.45 (product(g1, b, a, d3) <=> product(g1, d1, d2, d3)),
% 0.20/0.45 inference(monotonicity,[status(thm)],[147, 57])).
% 0.20/0.45 tff(267,plain,
% 0.20/0.45 (product(g1, d1, d2, d3) <=> product(g1, b, a, d3)),
% 0.20/0.45 inference(symmetry,[status(thm)],[266])).
% 0.20/0.45 tff(268,plain,
% 0.20/0.45 (product(g1, b, a, d3)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[11, 267])).
% 0.20/0.45 tff(269,plain,
% 0.20/0.45 (((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((d3 = b) | (~product(g1, b, a, b)) | (~product(g1, b, a, d3)))) <=> ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | (d3 = b) | (~product(g1, b, a, b)) | (~product(g1, b, a, d3)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(270,plain,
% 0.20/0.45 (((d3 = b) | (~product(g1, b, a, d3)) | (~product(g1, b, a, b))) <=> ((d3 = b) | (~product(g1, b, a, b)) | (~product(g1, b, a, d3)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(271,plain,
% 0.20/0.45 (((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((d3 = b) | (~product(g1, b, a, d3)) | (~product(g1, b, a, b)))) <=> ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((d3 = b) | (~product(g1, b, a, b)) | (~product(g1, b, a, d3))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[270])).
% 0.20/0.45 tff(272,plain,
% 0.20/0.45 (((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((d3 = b) | (~product(g1, b, a, d3)) | (~product(g1, b, a, b)))) <=> ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | (d3 = b) | (~product(g1, b, a, b)) | (~product(g1, b, a, d3)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[271, 269])).
% 0.20/0.45 tff(273,plain,
% 0.20/0.45 ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((d3 = b) | (~product(g1, b, a, d3)) | (~product(g1, b, a, b)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(274,plain,
% 0.20/0.45 ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | (d3 = b) | (~product(g1, b, a, b)) | (~product(g1, b, a, d3))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.20/0.45 tff(275,plain,
% 0.20/0.45 (~product(g1, b, a, d3)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[274, 25, 186, 110])).
% 0.20/0.45 tff(276,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[275, 268])).
% 0.20/0.45 tff(277,plain,((~(d2 = a)) | (~(d1 = b)) | (d3 = b)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(278,plain,
% 0.20/0.45 (~(d2 = a)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[277, 145, 265])).
% 0.20/0.45 tff(279,plain,
% 0.20/0.45 (d2 = c),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[105, 278, 178])).
% 0.20/0.45 tff(280,plain,
% 0.20/0.45 (c = d2),
% 0.20/0.45 inference(symmetry,[status(thm)],[279])).
% 0.20/0.45 tff(281,plain,
% 0.20/0.45 (b = d1),
% 0.20/0.45 inference(symmetry,[status(thm)],[145])).
% 0.20/0.45 tff(282,plain,
% 0.20/0.45 (product(g1, b, c, d3) <=> product(g1, d1, d2, d3)),
% 0.20/0.45 inference(monotonicity,[status(thm)],[281, 280])).
% 0.20/0.45 tff(283,plain,
% 0.20/0.45 (product(g1, d1, d2, d3) <=> product(g1, b, c, d3)),
% 0.20/0.45 inference(symmetry,[status(thm)],[282])).
% 0.20/0.45 tff(284,plain,
% 0.20/0.45 (product(g1, b, c, d3)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[11, 283])).
% 0.20/0.45 tff(285,plain,
% 0.20/0.45 (((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((~product(g1, b, c, a)) | (a = d3) | (~product(g1, b, c, d3)))) <=> ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | (~product(g1, b, c, a)) | (a = d3) | (~product(g1, b, c, d3)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(286,plain,
% 0.20/0.45 (((a = d3) | (~product(g1, b, c, a)) | (~product(g1, b, c, d3))) <=> ((~product(g1, b, c, a)) | (a = d3) | (~product(g1, b, c, d3)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(287,plain,
% 0.20/0.45 (((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((a = d3) | (~product(g1, b, c, a)) | (~product(g1, b, c, d3)))) <=> ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((~product(g1, b, c, a)) | (a = d3) | (~product(g1, b, c, d3))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[286])).
% 0.20/0.46 tff(288,plain,
% 0.20/0.46 (((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((a = d3) | (~product(g1, b, c, a)) | (~product(g1, b, c, d3)))) <=> ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | (~product(g1, b, c, a)) | (a = d3) | (~product(g1, b, c, d3)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[287, 285])).
% 0.20/0.46 tff(289,plain,
% 0.20/0.46 ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((a = d3) | (~product(g1, b, c, a)) | (~product(g1, b, c, d3)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(290,plain,
% 0.20/0.46 ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | (~product(g1, b, c, a)) | (a = d3) | (~product(g1, b, c, d3))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.20/0.46 tff(291,plain,
% 0.20/0.46 ((a = d3) | (~product(g1, b, c, d3))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[290, 25, 217])).
% 0.20/0.46 tff(292,plain,
% 0.20/0.46 (a = d3),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[291, 284])).
% 0.20/0.46 tff(293,plain,
% 0.20/0.46 (an_isomorphism(a) = an_isomorphism(d3)),
% 0.20/0.46 inference(monotonicity,[status(thm)],[292])).
% 0.20/0.46 tff(294,plain,
% 0.20/0.46 (an_isomorphism(d2) = an_isomorphism(c)),
% 0.20/0.46 inference(monotonicity,[status(thm)],[279])).
% 0.20/0.46 tff(295,plain,
% 0.20/0.46 (an_isomorphism(c) = an_isomorphism(d2)),
% 0.20/0.46 inference(symmetry,[status(thm)],[294])).
% 0.20/0.46 tff(296,plain,
% 0.20/0.46 (an_isomorphism(d1) = an_isomorphism(b)),
% 0.20/0.46 inference(monotonicity,[status(thm)],[145])).
% 0.20/0.46 tff(297,plain,
% 0.20/0.46 (an_isomorphism(b) = an_isomorphism(d1)),
% 0.20/0.46 inference(symmetry,[status(thm)],[296])).
% 0.20/0.46 tff(298,plain,
% 0.20/0.46 (product(g2, an_isomorphism(b), an_isomorphism(c), an_isomorphism(a)) <=> product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[297, 295, 293])).
% 0.20/0.46 tff(299,plain,
% 0.20/0.46 (product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3)) <=> product(g2, an_isomorphism(b), an_isomorphism(c), an_isomorphism(a))),
% 0.20/0.46 inference(symmetry,[status(thm)],[298])).
% 0.20/0.46 tff(300,plain,
% 0.20/0.46 ((~product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3))) <=> (~product(g2, an_isomorphism(b), an_isomorphism(c), an_isomorphism(a)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[299])).
% 0.20/0.46 tff(301,plain,
% 0.20/0.46 (~product(g2, an_isomorphism(b), an_isomorphism(c), an_isomorphism(a))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[46, 300])).
% 0.20/0.46 tff(302,plain,
% 0.20/0.46 (product(g2, g, h, f) <=> product(g2, an_isomorphism(b), an_isomorphism(c), an_isomorphism(a))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(303,plain,
% 0.20/0.46 (product(g2, g, h, f) <=> product(g2, g, h, f)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(304,axiom,(product(g2, g, h, f)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','g_times_h_is_f')).
% 0.20/0.46 tff(305,plain,
% 0.20/0.46 (product(g2, g, h, f)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.20/0.46 tff(306,plain,
% 0.20/0.46 (product(g2, an_isomorphism(b), an_isomorphism(c), an_isomorphism(a))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[305, 302])).
% 0.20/0.46 tff(307,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[306, 301])).
% 0.20/0.46 tff(308,plain,((d1 = a) | (d1 = c)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(309,plain,
% 0.20/0.46 (d1 = c),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[308, 135])).
% 0.20/0.46 tff(310,plain,
% 0.20/0.46 (c = d1),
% 0.20/0.46 inference(symmetry,[status(thm)],[309])).
% 0.20/0.46 tff(311,plain,
% 0.20/0.46 (product(g1, c, b, d3) <=> product(g1, d1, d2, d3)),
% 0.20/0.46 inference(monotonicity,[status(thm)],[310, 2])).
% 0.20/0.46 tff(312,plain,
% 0.20/0.46 (product(g1, d1, d2, d3) <=> product(g1, c, b, d3)),
% 0.20/0.46 inference(symmetry,[status(thm)],[311])).
% 0.20/0.46 tff(313,plain,
% 0.20/0.46 (product(g1, c, b, d3)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[11, 312])).
% 0.20/0.46 tff(314,plain,
% 0.20/0.46 (product(g1, c, b, a) <=> product(g1, c, b, a)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(315,axiom,(product(g1, c, b, a)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_times_b_is_a')).
% 0.20/0.46 tff(316,plain,
% 0.20/0.46 (product(g1, c, b, a)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[315, 314])).
% 0.20/0.46 tff(317,plain,
% 0.20/0.46 (((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((a = d3) | (~product(g1, c, b, a)) | (~product(g1, c, b, d3)))) <=> ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | (a = d3) | (~product(g1, c, b, a)) | (~product(g1, c, b, d3)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(318,plain,
% 0.20/0.46 ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((a = d3) | (~product(g1, c, b, a)) | (~product(g1, c, b, d3)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(319,plain,
% 0.20/0.46 ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | (a = d3) | (~product(g1, c, b, a)) | (~product(g1, c, b, d3))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[318, 317])).
% 0.20/0.46 tff(320,plain,
% 0.20/0.46 ((a = d3) | (~product(g1, c, b, d3))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[319, 25, 316])).
% 0.20/0.46 tff(321,plain,
% 0.20/0.46 (a = d3),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[320, 313])).
% 0.20/0.46 tff(322,plain,
% 0.20/0.46 (an_isomorphism(a) = an_isomorphism(d3)),
% 0.20/0.46 inference(monotonicity,[status(thm)],[321])).
% 0.20/0.46 tff(323,plain,
% 0.20/0.46 (product(g2, an_isomorphism(b), an_isomorphism(c), an_isomorphism(a)) <=> product(g2, an_isomorphism(b), an_isomorphism(c), an_isomorphism(d3))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[322])).
% 0.20/0.46 tff(324,plain,
% 0.20/0.46 (product(g2, an_isomorphism(b), an_isomorphism(c), an_isomorphism(d3)) <=> product(g2, an_isomorphism(b), an_isomorphism(c), an_isomorphism(a))),
% 0.20/0.46 inference(symmetry,[status(thm)],[323])).
% 0.20/0.46 tff(325,plain,
% 0.20/0.46 ((~product(g2, an_isomorphism(b), an_isomorphism(c), an_isomorphism(d3))) <=> (~product(g2, an_isomorphism(b), an_isomorphism(c), an_isomorphism(a)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[324])).
% 0.20/0.46 tff(326,plain,
% 0.20/0.46 (an_isomorphism(d1) = an_isomorphism(c)),
% 0.20/0.46 inference(monotonicity,[status(thm)],[309])).
% 0.20/0.46 tff(327,plain,
% 0.20/0.46 (an_isomorphism(c) = an_isomorphism(d1)),
% 0.20/0.46 inference(symmetry,[status(thm)],[326])).
% 0.20/0.46 tff(328,plain,
% 0.20/0.46 (product(g2, an_isomorphism(c), an_isomorphism(b), an_isomorphism(d3)) <=> product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[327, 164])).
% 0.20/0.46 tff(329,plain,
% 0.20/0.46 (product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3)) <=> product(g2, an_isomorphism(c), an_isomorphism(b), an_isomorphism(d3))),
% 0.20/0.46 inference(symmetry,[status(thm)],[328])).
% 0.20/0.46 tff(330,plain,
% 0.20/0.46 ((~product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3))) <=> (~product(g2, an_isomorphism(c), an_isomorphism(b), an_isomorphism(d3)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[329])).
% 0.20/0.46 tff(331,plain,
% 0.20/0.46 (~product(g2, an_isomorphism(c), an_isomorphism(b), an_isomorphism(d3))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[46, 330])).
% 0.20/0.46 tff(332,plain,
% 0.20/0.46 (((~![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, Xy, Z, Xyz) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)) | (~product(Xg, X, Yz, Xyz)))) | ((~product(g2, an_isomorphism(b), an_isomorphism(b), an_isomorphism(c))) | (~product(g2, an_isomorphism(b), an_isomorphism(c), an_isomorphism(d3))) | product(g2, an_isomorphism(c), an_isomorphism(b), an_isomorphism(d3)))) <=> ((~![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, Xy, Z, Xyz) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)) | (~product(Xg, X, Yz, Xyz)))) | (~product(g2, an_isomorphism(b), an_isomorphism(b), an_isomorphism(c))) | (~product(g2, an_isomorphism(b), an_isomorphism(c), an_isomorphism(d3))) | product(g2, an_isomorphism(c), an_isomorphism(b), an_isomorphism(d3)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(333,plain,
% 0.20/0.46 ((product(g2, an_isomorphism(c), an_isomorphism(b), an_isomorphism(d3)) | (~product(g2, an_isomorphism(b), an_isomorphism(b), an_isomorphism(c))) | (~product(g2, an_isomorphism(b), an_isomorphism(b), an_isomorphism(c))) | (~product(g2, an_isomorphism(b), an_isomorphism(c), an_isomorphism(d3)))) <=> ((~product(g2, an_isomorphism(b), an_isomorphism(b), an_isomorphism(c))) | (~product(g2, an_isomorphism(b), an_isomorphism(c), an_isomorphism(d3))) | product(g2, an_isomorphism(c), an_isomorphism(b), an_isomorphism(d3)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(334,plain,
% 0.20/0.46 (((~![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, Xy, Z, Xyz) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)) | (~product(Xg, X, Yz, Xyz)))) | (product(g2, an_isomorphism(c), an_isomorphism(b), an_isomorphism(d3)) | (~product(g2, an_isomorphism(b), an_isomorphism(b), an_isomorphism(c))) | (~product(g2, an_isomorphism(b), an_isomorphism(b), an_isomorphism(c))) | (~product(g2, an_isomorphism(b), an_isomorphism(c), an_isomorphism(d3))))) <=> ((~![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, Xy, Z, Xyz) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)) | (~product(Xg, X, Yz, Xyz)))) | ((~product(g2, an_isomorphism(b), an_isomorphism(b), an_isomorphism(c))) | (~product(g2, an_isomorphism(b), an_isomorphism(c), an_isomorphism(d3))) | product(g2, an_isomorphism(c), an_isomorphism(b), an_isomorphism(d3))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[333])).
% 0.20/0.46 tff(335,plain,
% 0.20/0.46 (((~![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, Xy, Z, Xyz) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)) | (~product(Xg, X, Yz, Xyz)))) | (product(g2, an_isomorphism(c), an_isomorphism(b), an_isomorphism(d3)) | (~product(g2, an_isomorphism(b), an_isomorphism(b), an_isomorphism(c))) | (~product(g2, an_isomorphism(b), an_isomorphism(b), an_isomorphism(c))) | (~product(g2, an_isomorphism(b), an_isomorphism(c), an_isomorphism(d3))))) <=> ((~![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, Xy, Z, Xyz) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)) | (~product(Xg, X, Yz, Xyz)))) | (~product(g2, an_isomorphism(b), an_isomorphism(b), an_isomorphism(c))) | (~product(g2, an_isomorphism(b), an_isomorphism(c), an_isomorphism(d3))) | product(g2, an_isomorphism(c), an_isomorphism(b), an_isomorphism(d3)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[334, 332])).
% 0.20/0.46 tff(336,plain,
% 0.20/0.46 ((~![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, Xy, Z, Xyz) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)) | (~product(Xg, X, Yz, Xyz)))) | (product(g2, an_isomorphism(c), an_isomorphism(b), an_isomorphism(d3)) | (~product(g2, an_isomorphism(b), an_isomorphism(b), an_isomorphism(c))) | (~product(g2, an_isomorphism(b), an_isomorphism(b), an_isomorphism(c))) | (~product(g2, an_isomorphism(b), an_isomorphism(c), an_isomorphism(d3))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(337,plain,
% 0.20/0.46 ((~![Xy: $i, Xg: $i, Z: $i, Y: $i, Xyz: $i, X: $i, Yz: $i] : (product(Xg, Xy, Z, Xyz) | (~product(Xg, Y, Z, Yz)) | (~product(Xg, X, Y, Xy)) | (~product(Xg, X, Yz, Xyz)))) | (~product(g2, an_isomorphism(b), an_isomorphism(b), an_isomorphism(c))) | (~product(g2, an_isomorphism(b), an_isomorphism(c), an_isomorphism(d3))) | product(g2, an_isomorphism(c), an_isomorphism(b), an_isomorphism(d3))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[336, 335])).
% 0.20/0.46 tff(338,plain,
% 0.20/0.46 ((~product(g2, an_isomorphism(b), an_isomorphism(c), an_isomorphism(d3))) | product(g2, an_isomorphism(c), an_isomorphism(b), an_isomorphism(d3))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[337, 230, 175])).
% 0.20/0.46 tff(339,plain,
% 0.20/0.46 (~product(g2, an_isomorphism(b), an_isomorphism(c), an_isomorphism(d3))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[338, 331])).
% 0.20/0.46 tff(340,plain,
% 0.20/0.46 (~product(g2, an_isomorphism(b), an_isomorphism(c), an_isomorphism(a))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[339, 325])).
% 0.20/0.46 tff(341,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[306, 340])).
% 0.20/0.46 tff(342,plain,(~(d2 = b)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(343,plain,
% 0.20/0.46 (product(g1, c, a, d3) <=> product(g1, d1, d2, d3)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[310, 57])).
% 0.20/0.47 tff(344,plain,
% 0.20/0.47 (product(g1, d1, d2, d3) <=> product(g1, c, a, d3)),
% 0.20/0.47 inference(symmetry,[status(thm)],[343])).
% 0.20/0.47 tff(345,plain,
% 0.20/0.47 (product(g1, c, a, d3)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[11, 344])).
% 0.20/0.47 tff(346,plain,
% 0.20/0.47 (((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((~product(g1, c, a, c)) | (c = d3) | (~product(g1, c, a, d3)))) <=> ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | (~product(g1, c, a, c)) | (c = d3) | (~product(g1, c, a, d3)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(347,plain,
% 0.20/0.47 (((c = d3) | (~product(g1, c, a, c)) | (~product(g1, c, a, d3))) <=> ((~product(g1, c, a, c)) | (c = d3) | (~product(g1, c, a, d3)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(348,plain,
% 0.20/0.47 (((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((c = d3) | (~product(g1, c, a, c)) | (~product(g1, c, a, d3)))) <=> ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((~product(g1, c, a, c)) | (c = d3) | (~product(g1, c, a, d3))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[347])).
% 0.20/0.47 tff(349,plain,
% 0.20/0.47 (((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((c = d3) | (~product(g1, c, a, c)) | (~product(g1, c, a, d3)))) <=> ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | (~product(g1, c, a, c)) | (c = d3) | (~product(g1, c, a, d3)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[348, 346])).
% 0.20/0.47 tff(350,plain,
% 0.20/0.47 ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((c = d3) | (~product(g1, c, a, c)) | (~product(g1, c, a, d3)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(351,plain,
% 0.20/0.47 ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | (~product(g1, c, a, c)) | (c = d3) | (~product(g1, c, a, d3))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[350, 349])).
% 0.20/0.47 tff(352,plain,
% 0.20/0.47 ((c = d3) | (~product(g1, c, a, d3))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[351, 25, 220])).
% 0.20/0.47 tff(353,plain,
% 0.20/0.47 (c = d3),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[352, 345])).
% 0.20/0.47 tff(354,plain,
% 0.20/0.47 (d3 = c),
% 0.20/0.47 inference(symmetry,[status(thm)],[353])).
% 0.20/0.47 tff(355,plain,
% 0.20/0.47 (an_isomorphism(d3) = an_isomorphism(c)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[354])).
% 0.20/0.47 tff(356,plain,
% 0.20/0.47 (an_isomorphism(c) = an_isomorphism(d3)),
% 0.20/0.47 inference(symmetry,[status(thm)],[355])).
% 0.20/0.47 tff(357,plain,
% 0.20/0.47 (product(g2, an_isomorphism(c), an_isomorphism(a), an_isomorphism(c)) <=> product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[327, 76, 356])).
% 0.20/0.47 tff(358,plain,
% 0.20/0.47 (product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3)) <=> product(g2, an_isomorphism(c), an_isomorphism(a), an_isomorphism(c))),
% 0.20/0.47 inference(symmetry,[status(thm)],[357])).
% 0.20/0.47 tff(359,plain,
% 0.20/0.47 ((~product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3))) <=> (~product(g2, an_isomorphism(c), an_isomorphism(a), an_isomorphism(c)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[358])).
% 0.20/0.47 tff(360,plain,
% 0.20/0.47 (~product(g2, an_isomorphism(c), an_isomorphism(a), an_isomorphism(c))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[46, 359])).
% 0.20/0.47 tff(361,plain,
% 0.20/0.47 (product(g2, h, f, h) <=> product(g2, an_isomorphism(c), an_isomorphism(a), an_isomorphism(c))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(362,plain,
% 0.20/0.47 (product(g2, h, f, h) <=> product(g2, h, f, h)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(363,axiom,(product(g2, h, f, h)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','h_times_f_is_h')).
% 0.20/0.47 tff(364,plain,
% 0.20/0.47 (product(g2, h, f, h)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[363, 362])).
% 0.20/0.47 tff(365,plain,
% 0.20/0.47 (product(g2, an_isomorphism(c), an_isomorphism(a), an_isomorphism(c))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[364, 361])).
% 0.20/0.47 tff(366,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[365, 360])).
% 0.20/0.47 tff(367,plain,(~(d2 = a)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(368,plain,
% 0.20/0.47 (d2 = c),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[105, 367, 342])).
% 0.20/0.47 tff(369,plain,
% 0.20/0.47 (product(g1, c, c, d3) <=> product(g1, d1, d2, d3)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[310, 5])).
% 0.20/0.47 tff(370,plain,
% 0.20/0.47 (product(g1, d1, d2, d3) <=> product(g1, c, c, d3)),
% 0.20/0.47 inference(symmetry,[status(thm)],[369])).
% 0.20/0.47 tff(371,plain,
% 0.20/0.47 (product(g1, c, c, d3)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[11, 370])).
% 0.20/0.47 tff(372,plain,
% 0.20/0.47 (product(g1, c, c, b) <=> product(g1, c, c, b)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(373,axiom,(product(g1, c, c, b)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c_times_c_is_b')).
% 0.20/0.47 tff(374,plain,
% 0.20/0.47 (product(g1, c, c, b)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[373, 372])).
% 0.20/0.47 tff(375,plain,
% 0.20/0.47 (((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((d3 = b) | (~product(g1, c, c, b)) | (~product(g1, c, c, d3)))) <=> ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | (d3 = b) | (~product(g1, c, c, b)) | (~product(g1, c, c, d3)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(376,plain,
% 0.20/0.47 (((d3 = b) | (~product(g1, c, c, d3)) | (~product(g1, c, c, b))) <=> ((d3 = b) | (~product(g1, c, c, b)) | (~product(g1, c, c, d3)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(377,plain,
% 0.20/0.47 (((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((d3 = b) | (~product(g1, c, c, d3)) | (~product(g1, c, c, b)))) <=> ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((d3 = b) | (~product(g1, c, c, b)) | (~product(g1, c, c, d3))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[376])).
% 0.20/0.47 tff(378,plain,
% 0.20/0.47 (((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((d3 = b) | (~product(g1, c, c, d3)) | (~product(g1, c, c, b)))) <=> ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | (d3 = b) | (~product(g1, c, c, b)) | (~product(g1, c, c, d3)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[377, 375])).
% 0.20/0.47 tff(379,plain,
% 0.20/0.47 ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((d3 = b) | (~product(g1, c, c, d3)) | (~product(g1, c, c, b)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(380,plain,
% 0.20/0.47 ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | (d3 = b) | (~product(g1, c, c, b)) | (~product(g1, c, c, d3))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.20/0.47 tff(381,plain,
% 0.20/0.47 (~product(g1, c, c, d3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[380, 25, 374, 110])).
% 0.20/0.47 tff(382,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[381, 371])).
% 0.20/0.47 tff(383,plain,((~(d2 = c)) | (d3 = b)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(384,plain,
% 0.20/0.47 (d3 = b),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[383, 368])).
% 0.20/0.47 tff(385,plain,
% 0.20/0.47 (an_isomorphism(d3) = an_isomorphism(b)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[384])).
% 0.20/0.47 tff(386,plain,
% 0.20/0.47 (an_isomorphism(d2) = an_isomorphism(c)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[368])).
% 0.20/0.47 tff(387,plain,
% 0.20/0.47 (product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3)) <=> product(g2, an_isomorphism(c), an_isomorphism(c), an_isomorphism(b))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[326, 386, 385])).
% 0.20/0.47 tff(388,plain,
% 0.20/0.47 (product(g2, an_isomorphism(c), an_isomorphism(c), an_isomorphism(b)) <=> product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3))),
% 0.20/0.47 inference(symmetry,[status(thm)],[387])).
% 0.20/0.47 tff(389,plain,
% 0.20/0.47 (product(g2, h, h, g) <=> product(g2, an_isomorphism(c), an_isomorphism(c), an_isomorphism(b))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(390,plain,
% 0.20/0.47 (product(g2, h, h, g) <=> product(g2, h, h, g)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(391,axiom,(product(g2, h, h, g)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','h_times_h_is_g')).
% 0.20/0.47 tff(392,plain,
% 0.20/0.47 (product(g2, h, h, g)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[391, 390])).
% 0.20/0.47 tff(393,plain,
% 0.20/0.47 (product(g2, an_isomorphism(c), an_isomorphism(c), an_isomorphism(b))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[392, 389])).
% 0.20/0.47 tff(394,plain,
% 0.20/0.47 (product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[393, 388])).
% 0.20/0.47 tff(395,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[46, 394])).
% 0.20/0.47 % SZS output end Proof
%------------------------------------------------------------------------------