%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP025-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:06:52 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.36s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP025-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.10/0.31 % Computer : n006.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Thu Jun 19 15:27:35 EDT 2025
% 0.10/0.32 % CPUTime :
% 0.18/0.36 % SZS status Unsatisfiable
% 0.18/0.36 % SZS output start Proof
% 0.18/0.36 tff(product_type, type, (
% 0.18/0.36 product: ( $i * $i * $i * $i ) > $o)).
% 0.18/0.36 tff(d_type, type, (
% 0.18/0.36 d: $i)).
% 0.18/0.36 tff(c_type, type, (
% 0.18/0.36 c: $i)).
% 0.18/0.36 tff(g2_type, type, (
% 0.18/0.36 g2: $i)).
% 0.18/0.36 tff(an_isomorphism_type, type, (
% 0.18/0.36 an_isomorphism: $i > $i)).
% 0.18/0.36 tff(d3_type, type, (
% 0.18/0.36 d3: $i)).
% 0.18/0.36 tff(d2_type, type, (
% 0.18/0.36 d2: $i)).
% 0.18/0.36 tff(d1_type, type, (
% 0.18/0.36 d1: $i)).
% 0.18/0.36 tff(b_type, type, (
% 0.18/0.36 b: $i)).
% 0.18/0.36 tff(a_type, type, (
% 0.18/0.36 a: $i)).
% 0.18/0.36 tff(g1_type, type, (
% 0.18/0.36 g1: $i)).
% 0.18/0.36 tff(group_member_type, type, (
% 0.18/0.36 group_member: ( $i * $i ) > $o)).
% 0.18/0.36 tff(1,assumption,(d2 = b), introduced(assumption)).
% 0.18/0.36 tff(2,plain,
% 0.18/0.36 (b = d2),
% 0.18/0.36 inference(symmetry,[status(thm)],[1])).
% 0.18/0.36 tff(3,assumption,(d1 = a), introduced(assumption)).
% 0.18/0.36 tff(4,assumption,(d2 = a), introduced(assumption)).
% 0.18/0.36 tff(5,plain,
% 0.18/0.36 (a = d2),
% 0.18/0.36 inference(symmetry,[status(thm)],[4])).
% 0.18/0.36 tff(6,plain,
% 0.18/0.36 (a = d1),
% 0.18/0.36 inference(symmetry,[status(thm)],[3])).
% 0.18/0.36 tff(7,plain,
% 0.18/0.36 (product(g1, a, a, d3) <=> product(g1, d1, d2, d3)),
% 0.18/0.36 inference(monotonicity,[status(thm)],[6, 5])).
% 0.18/0.36 tff(8,plain,
% 0.18/0.36 (product(g1, d1, d2, d3) <=> product(g1, a, a, d3)),
% 0.18/0.36 inference(symmetry,[status(thm)],[7])).
% 0.18/0.36 tff(9,plain,
% 0.18/0.36 (product(g1, d1, d2, d3) <=> product(g1, d1, d2, d3)),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(10,axiom,(product(g1, d1, d2, d3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_times_d2_is_d3')).
% 0.18/0.36 tff(11,plain,
% 0.18/0.36 (product(g1, d1, d2, d3)),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.18/0.36 tff(12,plain,
% 0.18/0.36 (product(g1, a, a, d3)),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[11, 8])).
% 0.18/0.36 tff(13,plain,
% 0.18/0.36 (product(g1, a, a, a) <=> product(g1, a, a, a)),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(14,axiom,(product(g1, a, a, a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_times_a_is_a')).
% 0.18/0.36 tff(15,plain,
% 0.18/0.36 (product(g1, a, a, a)),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.18/0.36 tff(16,plain,
% 0.18/0.36 (^[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))))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(17,plain,
% 0.18/0.36 (![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)))),
% 0.18/0.36 inference(quant_intro,[status(thm)],[16])).
% 0.18/0.36 tff(18,plain,
% 0.18/0.36 (![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)))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(19,plain,
% 0.18/0.36 (^[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))))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(20,plain,
% 0.18/0.36 (![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)))),
% 0.18/0.36 inference(quant_intro,[status(thm)],[19])).
% 0.18/0.36 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/sandbox2/benchmark/Axioms/GRP006-0.ax','total_function2')).
% 0.18/0.36 tff(22,plain,
% 0.18/0.36 (![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.18/0.36 tff(23,plain,
% 0.18/0.36 (![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.18/0.36 tff(24,plain,(
% 0.18/0.36 ![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))),
% 0.18/0.36 inference(skolemize,[status(sab)],[23])).
% 0.18/0.36 tff(25,plain,
% 0.18/0.36 (![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.18/0.36 tff(26,plain,
% 0.18/0.36 (((~![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, a)) | (~product(g1, a, a, d3)))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(27,plain,
% 0.18/0.36 ((~![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)))),
% 0.18/0.36 inference(quant_inst,[status(thm)],[])).
% 0.18/0.36 tff(28,plain,
% 0.18/0.36 ((~![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))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.18/0.36 tff(29,plain,
% 0.18/0.36 ((a = d3) | (~product(g1, a, a, d3))),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[28, 25, 15])).
% 0.18/0.36 tff(30,plain,
% 0.18/0.36 (a = d3),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[29, 12])).
% 0.18/0.36 tff(31,plain,
% 0.18/0.36 (d3 = a),
% 0.18/0.36 inference(symmetry,[status(thm)],[30])).
% 0.18/0.36 tff(32,plain,
% 0.18/0.36 (an_isomorphism(d3) = an_isomorphism(a)),
% 0.18/0.36 inference(monotonicity,[status(thm)],[31])).
% 0.18/0.36 tff(33,plain,
% 0.18/0.36 (an_isomorphism(a) = an_isomorphism(d3)),
% 0.18/0.36 inference(symmetry,[status(thm)],[32])).
% 0.18/0.36 tff(34,plain,
% 0.18/0.36 ((an_isomorphism(a) = c) <=> (an_isomorphism(a) = c)),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(35,axiom,(an_isomorphism(a) = c), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_maps_to_c')).
% 0.18/0.36 tff(36,plain,
% 0.18/0.36 (an_isomorphism(a) = c),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.18/0.36 tff(37,plain,
% 0.18/0.36 (c = an_isomorphism(a)),
% 0.18/0.36 inference(symmetry,[status(thm)],[36])).
% 0.18/0.36 tff(38,plain,
% 0.18/0.36 (c = an_isomorphism(d3)),
% 0.18/0.36 inference(transitivity,[status(thm)],[37, 33])).
% 0.18/0.36 tff(39,plain,
% 0.18/0.36 (an_isomorphism(d2) = an_isomorphism(a)),
% 0.18/0.36 inference(monotonicity,[status(thm)],[4])).
% 0.18/0.36 tff(40,plain,
% 0.18/0.36 (an_isomorphism(a) = an_isomorphism(d2)),
% 0.18/0.36 inference(symmetry,[status(thm)],[39])).
% 0.18/0.36 tff(41,plain,
% 0.18/0.36 (c = an_isomorphism(d2)),
% 0.18/0.36 inference(transitivity,[status(thm)],[37, 40])).
% 0.18/0.36 tff(42,plain,
% 0.18/0.36 (an_isomorphism(d1) = an_isomorphism(a)),
% 0.18/0.36 inference(monotonicity,[status(thm)],[3])).
% 0.18/0.36 tff(43,plain,
% 0.18/0.36 (an_isomorphism(a) = an_isomorphism(d1)),
% 0.18/0.36 inference(symmetry,[status(thm)],[42])).
% 0.18/0.36 tff(44,plain,
% 0.18/0.36 (c = an_isomorphism(d1)),
% 0.18/0.36 inference(transitivity,[status(thm)],[37, 43])).
% 0.18/0.36 tff(45,plain,
% 0.18/0.36 (product(g2, c, c, c) <=> product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3))),
% 0.18/0.36 inference(monotonicity,[status(thm)],[44, 41, 38])).
% 0.18/0.36 tff(46,plain,
% 0.18/0.36 (product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3)) <=> product(g2, c, c, c)),
% 0.18/0.36 inference(symmetry,[status(thm)],[45])).
% 0.18/0.36 tff(47,plain,
% 0.18/0.36 ((~product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3))) <=> (~product(g2, c, c, c))),
% 0.18/0.36 inference(monotonicity,[status(thm)],[46])).
% 0.18/0.36 tff(48,plain,
% 0.18/0.36 ((~product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3))) <=> (~product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3)))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(49,axiom,(~product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_product_holds_in_group2')).
% 0.18/0.36 tff(50,plain,
% 0.18/0.36 (~product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.18/0.36 tff(51,plain,
% 0.18/0.36 (~product(g2, c, c, c)),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[50, 47])).
% 0.18/0.36 tff(52,plain,
% 0.18/0.36 (product(g2, c, c, c) <=> product(g2, c, c, c)),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(53,axiom,(product(g2, c, c, c)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_times_c_is_c')).
% 0.18/0.36 tff(54,plain,
% 0.18/0.36 (product(g2, c, c, c)),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.18/0.36 tff(55,plain,
% 0.18/0.36 ($false),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[54, 51])).
% 0.18/0.36 tff(56,plain,((~(d2 = a)) | (~(d1 = a))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.37 tff(57,plain,
% 0.18/0.37 (~(d2 = a)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[56, 3])).
% 0.18/0.37 tff(58,plain,
% 0.18/0.37 (group_member(d2, g1) <=> group_member(d2, g1)),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(59,axiom,(group_member(d2, g1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_member_of_group1')).
% 0.18/0.37 tff(60,plain,
% 0.18/0.37 (group_member(d2, g1)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.18/0.37 tff(61,plain,
% 0.18/0.37 (^[X: $i] : refl(((X = b) | (X = a) | (~group_member(X, g1))) <=> ((X = b) | (X = a) | (~group_member(X, g1))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(62,plain,
% 0.18/0.37 (![X: $i] : ((X = b) | (X = a) | (~group_member(X, g1))) <=> ![X: $i] : ((X = b) | (X = a) | (~group_member(X, g1)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[61])).
% 0.18/0.37 tff(63,plain,
% 0.18/0.37 (![X: $i] : ((X = b) | (X = a) | (~group_member(X, g1))) <=> ![X: $i] : ((X = b) | (X = a) | (~group_member(X, g1)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(64,plain,
% 0.18/0.37 (^[X: $i] : rewrite((((~group_member(X, g1)) | (X = a)) | (X = b)) <=> ((X = b) | (X = a) | (~group_member(X, g1))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(65,plain,
% 0.18/0.37 (![X: $i] : (((~group_member(X, g1)) | (X = a)) | (X = b)) <=> ![X: $i] : ((X = b) | (X = a) | (~group_member(X, g1)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[64])).
% 0.18/0.37 tff(66,axiom,(![X: $i] : (((~group_member(X, g1)) | (X = a)) | (X = b))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_and_b_only_members_of_group1')).
% 0.18/0.37 tff(67,plain,
% 0.18/0.37 (![X: $i] : ((X = b) | (X = a) | (~group_member(X, g1)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.18/0.37 tff(68,plain,
% 0.18/0.37 (![X: $i] : ((X = b) | (X = a) | (~group_member(X, g1)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.18/0.37 tff(69,plain,(
% 0.18/0.37 ![X: $i] : ((X = b) | (X = a) | (~group_member(X, g1)))),
% 0.18/0.37 inference(skolemize,[status(sab)],[68])).
% 0.18/0.37 tff(70,plain,
% 0.18/0.37 (![X: $i] : ((X = b) | (X = a) | (~group_member(X, g1)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.18/0.37 tff(71,plain,
% 0.18/0.37 (((~![X: $i] : ((X = b) | (X = a) | (~group_member(X, g1)))) | ((d2 = b) | (d2 = a) | (~group_member(d2, g1)))) <=> ((~![X: $i] : ((X = b) | (X = a) | (~group_member(X, g1)))) | (d2 = b) | (d2 = a) | (~group_member(d2, g1)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(72,plain,
% 0.18/0.37 ((~![X: $i] : ((X = b) | (X = a) | (~group_member(X, g1)))) | ((d2 = b) | (d2 = a) | (~group_member(d2, g1)))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(73,plain,
% 0.18/0.37 ((~![X: $i] : ((X = b) | (X = a) | (~group_member(X, g1)))) | (d2 = b) | (d2 = a) | (~group_member(d2, g1))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.18/0.37 tff(74,plain,
% 0.18/0.37 ((d2 = b) | (d2 = a)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[73, 70, 60])).
% 0.18/0.37 tff(75,plain,
% 0.18/0.37 (d2 = b),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[74, 57])).
% 0.18/0.37 tff(76,plain,
% 0.18/0.37 (b = d2),
% 0.18/0.37 inference(symmetry,[status(thm)],[75])).
% 0.18/0.37 tff(77,plain,
% 0.18/0.37 (product(g1, a, b, d3) <=> product(g1, d1, d2, d3)),
% 0.18/0.37 inference(monotonicity,[status(thm)],[6, 76])).
% 0.18/0.37 tff(78,plain,
% 0.18/0.37 (product(g1, d1, d2, d3) <=> product(g1, a, b, d3)),
% 0.18/0.37 inference(symmetry,[status(thm)],[77])).
% 0.18/0.37 tff(79,plain,
% 0.18/0.37 (product(g1, a, b, d3)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[11, 78])).
% 0.18/0.37 tff(80,plain,
% 0.18/0.37 (product(g1, a, b, b) <=> product(g1, a, b, b)),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(81,axiom,(product(g1, a, b, b)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_times_b_is_b')).
% 0.18/0.37 tff(82,plain,
% 0.18/0.37 (product(g1, a, b, b)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.18/0.37 tff(83,plain,
% 0.18/0.37 (((~![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, b, d3)) | (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)))) | (~product(g1, a, b, d3)) | (b = d3) | (~product(g1, a, b, b)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(84,plain,
% 0.18/0.37 (((b = d3) | (~product(g1, a, b, b)) | (~product(g1, a, b, d3))) <=> ((~product(g1, a, b, d3)) | (b = d3) | (~product(g1, a, b, b)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(85,plain,
% 0.18/0.37 (((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((b = d3) | (~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)))) | ((~product(g1, a, b, d3)) | (b = d3) | (~product(g1, a, b, b))))),
% 0.18/0.37 inference(monotonicity,[status(thm)],[84])).
% 0.18/0.37 tff(86,plain,
% 0.18/0.37 (((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((b = d3) | (~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)))) | (~product(g1, a, b, d3)) | (b = d3) | (~product(g1, a, b, b)))),
% 0.18/0.37 inference(transitivity,[status(thm)],[85, 83])).
% 0.18/0.37 tff(87,plain,
% 0.18/0.37 ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((b = d3) | (~product(g1, a, b, b)) | (~product(g1, a, b, d3)))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(88,plain,
% 0.18/0.37 ((~![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, b, d3)) | (b = d3) | (~product(g1, a, b, b))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.18/0.37 tff(89,plain,
% 0.18/0.37 ((~product(g1, a, b, d3)) | (b = d3)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[88, 25, 82])).
% 0.18/0.37 tff(90,plain,
% 0.18/0.37 (b = d3),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[89, 79])).
% 0.18/0.37 tff(91,plain,
% 0.18/0.37 (d3 = b),
% 0.18/0.37 inference(symmetry,[status(thm)],[90])).
% 0.18/0.37 tff(92,plain,
% 0.18/0.37 (an_isomorphism(d3) = an_isomorphism(b)),
% 0.18/0.37 inference(monotonicity,[status(thm)],[91])).
% 0.18/0.37 tff(93,plain,
% 0.18/0.37 (an_isomorphism(b) = an_isomorphism(d3)),
% 0.18/0.37 inference(symmetry,[status(thm)],[92])).
% 0.18/0.37 tff(94,plain,
% 0.18/0.37 ((an_isomorphism(b) = d) <=> (an_isomorphism(b) = d)),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(95,axiom,(an_isomorphism(b) = d), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b_maps_to_d')).
% 0.18/0.37 tff(96,plain,
% 0.18/0.37 (an_isomorphism(b) = d),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.18/0.37 tff(97,plain,
% 0.18/0.37 (d = an_isomorphism(b)),
% 0.18/0.37 inference(symmetry,[status(thm)],[96])).
% 0.18/0.37 tff(98,plain,
% 0.18/0.37 (d = an_isomorphism(d3)),
% 0.18/0.37 inference(transitivity,[status(thm)],[97, 93])).
% 0.18/0.37 tff(99,plain,
% 0.18/0.37 (an_isomorphism(d2) = an_isomorphism(b)),
% 0.18/0.37 inference(monotonicity,[status(thm)],[75])).
% 0.18/0.37 tff(100,plain,
% 0.18/0.37 (an_isomorphism(b) = an_isomorphism(d2)),
% 0.18/0.37 inference(symmetry,[status(thm)],[99])).
% 0.18/0.37 tff(101,plain,
% 0.18/0.37 (d = an_isomorphism(d2)),
% 0.18/0.37 inference(transitivity,[status(thm)],[97, 100])).
% 0.18/0.37 tff(102,plain,
% 0.18/0.37 (product(g2, c, d, d) <=> product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3))),
% 0.18/0.37 inference(monotonicity,[status(thm)],[44, 101, 98])).
% 0.18/0.37 tff(103,plain,
% 0.18/0.37 (product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3)) <=> product(g2, c, d, d)),
% 0.18/0.37 inference(symmetry,[status(thm)],[102])).
% 0.18/0.37 tff(104,plain,
% 0.18/0.37 ((~product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3))) <=> (~product(g2, c, d, d))),
% 0.18/0.37 inference(monotonicity,[status(thm)],[103])).
% 0.18/0.37 tff(105,plain,
% 0.18/0.37 (~product(g2, c, d, d)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[50, 104])).
% 0.18/0.37 tff(106,plain,
% 0.18/0.37 (product(g2, c, d, d) <=> product(g2, c, d, d)),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(107,axiom,(product(g2, c, d, d)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_times_d_is_d')).
% 0.18/0.37 tff(108,plain,
% 0.18/0.37 (product(g2, c, d, d)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.18/0.37 tff(109,plain,
% 0.18/0.37 ($false),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[108, 105])).
% 0.18/0.37 tff(110,plain,(~(d1 = a)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.37 tff(111,plain,
% 0.18/0.37 (group_member(d1, g1) <=> group_member(d1, g1)),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(112,axiom,(group_member(d1, g1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_member_of_group1')).
% 0.18/0.37 tff(113,plain,
% 0.18/0.37 (group_member(d1, g1)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.18/0.37 tff(114,plain,
% 0.18/0.37 (((~![X: $i] : ((X = b) | (X = a) | (~group_member(X, g1)))) | ((d1 = b) | (d1 = a) | (~group_member(d1, g1)))) <=> ((~![X: $i] : ((X = b) | (X = a) | (~group_member(X, g1)))) | (d1 = b) | (d1 = a) | (~group_member(d1, g1)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(115,plain,
% 0.18/0.37 ((~![X: $i] : ((X = b) | (X = a) | (~group_member(X, g1)))) | ((d1 = b) | (d1 = a) | (~group_member(d1, g1)))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(116,plain,
% 0.18/0.37 ((~![X: $i] : ((X = b) | (X = a) | (~group_member(X, g1)))) | (d1 = b) | (d1 = a) | (~group_member(d1, g1))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.18/0.37 tff(117,plain,
% 0.18/0.37 ((d1 = b) | (d1 = a)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[116, 70, 113])).
% 0.18/0.37 tff(118,plain,
% 0.18/0.37 (d1 = b),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[117, 110])).
% 0.18/0.37 tff(119,plain,
% 0.18/0.37 (b = d1),
% 0.18/0.37 inference(symmetry,[status(thm)],[118])).
% 0.18/0.37 tff(120,plain,
% 0.18/0.37 (product(g1, b, b, d3) <=> product(g1, d1, d2, d3)),
% 0.18/0.37 inference(monotonicity,[status(thm)],[119, 2])).
% 0.18/0.37 tff(121,plain,
% 0.18/0.37 (product(g1, d1, d2, d3) <=> product(g1, b, b, d3)),
% 0.18/0.37 inference(symmetry,[status(thm)],[120])).
% 0.18/0.37 tff(122,plain,
% 0.18/0.37 (product(g1, b, b, d3)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[11, 121])).
% 0.18/0.37 tff(123,plain,
% 0.18/0.37 (product(g1, b, b, a) <=> product(g1, b, b, a)),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(124,axiom,(product(g1, b, b, a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b_times_b_is_a')).
% 0.18/0.37 tff(125,plain,
% 0.18/0.37 (product(g1, b, b, a)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.18/0.37 tff(126,plain,
% 0.18/0.37 (((~![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, b, d3)) | (~product(g1, b, b, 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, b, b, d3)) | (~product(g1, b, b, a)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(127,plain,
% 0.18/0.37 (((a = d3) | (~product(g1, b, b, a)) | (~product(g1, b, b, d3))) <=> ((a = d3) | (~product(g1, b, b, d3)) | (~product(g1, b, b, a)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(128,plain,
% 0.18/0.37 (((~![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, b, a)) | (~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)))) | ((a = d3) | (~product(g1, b, b, d3)) | (~product(g1, b, b, a))))),
% 0.18/0.37 inference(monotonicity,[status(thm)],[127])).
% 0.18/0.37 tff(129,plain,
% 0.18/0.37 (((~![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, b, a)) | (~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)))) | (a = d3) | (~product(g1, b, b, d3)) | (~product(g1, b, b, a)))),
% 0.18/0.37 inference(transitivity,[status(thm)],[128, 126])).
% 0.18/0.37 tff(130,plain,
% 0.18/0.37 ((~![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, b, a)) | (~product(g1, b, b, d3)))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(131,plain,
% 0.18/0.37 ((~![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, b, d3)) | (~product(g1, b, b, a))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.18/0.37 tff(132,plain,
% 0.18/0.37 ((a = d3) | (~product(g1, b, b, d3))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[131, 25, 125])).
% 0.18/0.37 tff(133,plain,
% 0.18/0.37 (a = d3),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[132, 122])).
% 0.18/0.37 tff(134,plain,
% 0.18/0.37 (d3 = a),
% 0.18/0.37 inference(symmetry,[status(thm)],[133])).
% 0.18/0.37 tff(135,plain,
% 0.18/0.37 (an_isomorphism(d3) = an_isomorphism(a)),
% 0.18/0.37 inference(monotonicity,[status(thm)],[134])).
% 0.18/0.37 tff(136,plain,
% 0.18/0.37 (an_isomorphism(a) = an_isomorphism(d3)),
% 0.18/0.37 inference(symmetry,[status(thm)],[135])).
% 0.18/0.37 tff(137,plain,
% 0.18/0.37 (c = an_isomorphism(d3)),
% 0.18/0.38 inference(transitivity,[status(thm)],[37, 136])).
% 0.18/0.38 tff(138,plain,
% 0.18/0.38 (an_isomorphism(d2) = an_isomorphism(b)),
% 0.18/0.38 inference(monotonicity,[status(thm)],[1])).
% 0.18/0.38 tff(139,plain,
% 0.18/0.38 (an_isomorphism(b) = an_isomorphism(d2)),
% 0.18/0.38 inference(symmetry,[status(thm)],[138])).
% 0.18/0.38 tff(140,plain,
% 0.18/0.38 (d = an_isomorphism(d2)),
% 0.18/0.38 inference(transitivity,[status(thm)],[97, 139])).
% 0.18/0.38 tff(141,plain,
% 0.18/0.38 (an_isomorphism(d1) = an_isomorphism(b)),
% 0.18/0.38 inference(monotonicity,[status(thm)],[118])).
% 0.18/0.38 tff(142,plain,
% 0.18/0.38 (an_isomorphism(b) = an_isomorphism(d1)),
% 0.18/0.38 inference(symmetry,[status(thm)],[141])).
% 0.18/0.38 tff(143,plain,
% 0.18/0.38 (d = an_isomorphism(d1)),
% 0.18/0.38 inference(transitivity,[status(thm)],[97, 142])).
% 0.18/0.38 tff(144,plain,
% 0.18/0.38 (product(g2, d, d, c) <=> product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[143, 140, 137])).
% 0.18/0.38 tff(145,plain,
% 0.18/0.38 (product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3)) <=> product(g2, d, d, c)),
% 0.18/0.38 inference(symmetry,[status(thm)],[144])).
% 0.18/0.38 tff(146,plain,
% 0.18/0.38 ((~product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3))) <=> (~product(g2, d, d, c))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[145])).
% 0.18/0.38 tff(147,plain,
% 0.18/0.38 (~product(g2, d, d, c)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[50, 146])).
% 0.18/0.38 tff(148,plain,
% 0.18/0.38 (product(g2, d, d, c) <=> product(g2, d, d, c)),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(149,axiom,(product(g2, d, d, c)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d_times_d_is_c')).
% 0.18/0.38 tff(150,plain,
% 0.18/0.38 (product(g2, d, d, c)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.18/0.38 tff(151,plain,
% 0.18/0.38 ($false),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[150, 147])).
% 0.18/0.38 tff(152,plain,(~(d2 = b)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.38 tff(153,plain,
% 0.18/0.38 (d2 = a),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[74, 152])).
% 0.18/0.38 tff(154,plain,
% 0.18/0.38 (a = d2),
% 0.18/0.38 inference(symmetry,[status(thm)],[153])).
% 0.18/0.38 tff(155,plain,
% 0.18/0.38 (product(g1, b, a, d3) <=> product(g1, d1, d2, d3)),
% 0.18/0.38 inference(monotonicity,[status(thm)],[119, 154])).
% 0.18/0.38 tff(156,plain,
% 0.18/0.38 (product(g1, d1, d2, d3) <=> product(g1, b, a, d3)),
% 0.18/0.38 inference(symmetry,[status(thm)],[155])).
% 0.18/0.38 tff(157,plain,
% 0.18/0.38 (product(g1, b, a, d3)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[11, 156])).
% 0.18/0.38 tff(158,plain,
% 0.18/0.38 (product(g1, b, a, b) <=> product(g1, b, a, b)),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(159,axiom,(product(g1, b, a, b)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b_times_a_is_b')).
% 0.18/0.38 tff(160,plain,
% 0.18/0.38 (product(g1, b, a, b)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.18/0.38 tff(161,plain,
% 0.18/0.38 (((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((b = d3) | (~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)))) | (b = d3) | (~product(g1, b, a, d3)) | (~product(g1, b, a, b)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(162,plain,
% 0.18/0.38 (((b = d3) | (~product(g1, b, a, b)) | (~product(g1, b, a, d3))) <=> ((b = d3) | (~product(g1, b, a, d3)) | (~product(g1, b, a, b)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(163,plain,
% 0.18/0.38 (((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((b = d3) | (~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)))) | ((b = d3) | (~product(g1, b, a, d3)) | (~product(g1, b, a, b))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[162])).
% 0.18/0.38 tff(164,plain,
% 0.18/0.38 (((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((b = d3) | (~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)))) | (b = d3) | (~product(g1, b, a, d3)) | (~product(g1, b, a, b)))),
% 0.18/0.38 inference(transitivity,[status(thm)],[163, 161])).
% 0.18/0.38 tff(165,plain,
% 0.18/0.38 ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | ((b = d3) | (~product(g1, b, a, b)) | (~product(g1, b, a, d3)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(166,plain,
% 0.18/0.38 ((~![Xg: $i, W: $i, Z: $i, Y: $i, X: $i] : ((W = Z) | (~product(Xg, X, Y, W)) | (~product(Xg, X, Y, Z)))) | (b = d3) | (~product(g1, b, a, d3)) | (~product(g1, b, a, b))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.18/0.38 tff(167,plain,
% 0.18/0.38 ((b = d3) | (~product(g1, b, a, d3))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[166, 25, 160])).
% 0.18/0.38 tff(168,plain,
% 0.18/0.38 (b = d3),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[167, 157])).
% 0.18/0.38 tff(169,plain,
% 0.18/0.38 (d3 = b),
% 0.18/0.38 inference(symmetry,[status(thm)],[168])).
% 0.18/0.38 tff(170,plain,
% 0.18/0.38 (an_isomorphism(d3) = an_isomorphism(b)),
% 0.18/0.38 inference(monotonicity,[status(thm)],[169])).
% 0.18/0.38 tff(171,plain,
% 0.18/0.38 (an_isomorphism(b) = an_isomorphism(d3)),
% 0.18/0.38 inference(symmetry,[status(thm)],[170])).
% 0.18/0.38 tff(172,plain,
% 0.18/0.38 (d = an_isomorphism(d3)),
% 0.18/0.38 inference(transitivity,[status(thm)],[97, 171])).
% 0.18/0.38 tff(173,plain,
% 0.18/0.38 (an_isomorphism(d2) = an_isomorphism(a)),
% 0.18/0.38 inference(monotonicity,[status(thm)],[153])).
% 0.18/0.38 tff(174,plain,
% 0.18/0.38 (an_isomorphism(a) = an_isomorphism(d2)),
% 0.18/0.38 inference(symmetry,[status(thm)],[173])).
% 0.18/0.38 tff(175,plain,
% 0.18/0.38 (c = an_isomorphism(d2)),
% 0.18/0.38 inference(transitivity,[status(thm)],[37, 174])).
% 0.18/0.38 tff(176,plain,
% 0.18/0.38 (product(g2, d, c, d) <=> product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[143, 175, 172])).
% 0.18/0.38 tff(177,plain,
% 0.18/0.38 (product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3)) <=> product(g2, d, c, d)),
% 0.18/0.38 inference(symmetry,[status(thm)],[176])).
% 0.18/0.38 tff(178,plain,
% 0.18/0.38 ((~product(g2, an_isomorphism(d1), an_isomorphism(d2), an_isomorphism(d3))) <=> (~product(g2, d, c, d))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[177])).
% 0.18/0.38 tff(179,plain,
% 0.18/0.38 (~product(g2, d, c, d)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[50, 178])).
% 0.18/0.38 tff(180,plain,
% 0.18/0.38 (product(g2, d, c, d) <=> product(g2, d, c, d)),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(181,axiom,(product(g2, d, c, d)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d_times_c_is_d')).
% 0.18/0.38 tff(182,plain,
% 0.18/0.38 (product(g2, d, c, d)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.18/0.38 tff(183,plain,
% 0.18/0.38 ($false),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[182, 179])).
% 0.18/0.38 % SZS output end Proof
% 0.18/0.38 % E exiting
%------------------------------------------------------------------------------