%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP125-4.003 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:07:06 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP125-4.003 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n010.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 15:44:11 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.37 % SZS status Unsatisfiable
% 0.20/0.37 % SZS output start Proof
% 0.20/0.37 tff(product_type, type, (
% 0.20/0.37 product: ( $i * $i * $i ) > $o)).
% 0.20/0.37 tff(e_3_type, type, (
% 0.20/0.37 e_3: $i)).
% 0.20/0.37 tff(e_1_type, type, (
% 0.20/0.37 e_1: $i)).
% 0.20/0.37 tff(e_2_type, type, (
% 0.20/0.37 e_2: $i)).
% 0.20/0.37 tff(equalish_type, type, (
% 0.20/0.37 equalish: ( $i * $i ) > $o)).
% 0.20/0.37 tff(group_element_type, type, (
% 0.20/0.37 group_element: $i > $o)).
% 0.20/0.37 tff(1,assumption,(product(e_1, e_2, e_2)), introduced(assumption)).
% 0.20/0.37 tff(2,assumption,(~product(e_2, e_2, e_2)), introduced(assumption)).
% 0.20/0.37 tff(3,plain,
% 0.20/0.37 (^[X: $i] : refl(product(X, X, X) <=> product(X, X, X))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(4,plain,
% 0.20/0.37 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.20/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.37 tff(5,plain,
% 0.20/0.37 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(6,axiom,(![X: $i] : product(X, X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_idempotence')).
% 0.20/0.37 tff(7,plain,
% 0.20/0.37 (![X: $i] : product(X, X, X)),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.37 tff(8,plain,(
% 0.20/0.37 ![X: $i] : product(X, X, X)),
% 0.20/0.37 inference(skolemize,[status(sab)],[7])).
% 0.20/0.37 tff(9,plain,
% 0.20/0.37 (![X: $i] : product(X, X, X)),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.20/0.37 tff(10,plain,
% 0.20/0.37 ((~![X: $i] : product(X, X, X)) | product(e_2, e_2, e_2)),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(11,plain,
% 0.20/0.37 ($false),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[10, 9, 2])).
% 0.20/0.37 tff(12,plain,(product(e_2, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.37 tff(13,plain,
% 0.20/0.37 (^[W: $i, Z: $i, Y: $i, X: $i] : refl(((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X))) <=> ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(14,plain,
% 0.20/0.37 (![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.37 tff(15,plain,
% 0.20/0.37 (![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(16,plain,
% 0.20/0.37 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(W, Y, X)) | (~product(Z, Y, X))) <=> ((~product(W, Y, X)) | (~product(Z, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)))), rewrite((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(17,plain,
% 0.20/0.37 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[16])).
% 0.20/0.37 tff(18,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_left_cancellation')).
% 0.20/0.37 tff(19,plain,
% 0.20/0.37 (![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.20/0.37 tff(20,plain,
% 0.20/0.37 (![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.20/0.37 tff(21,plain,(
% 0.20/0.37 ![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))),
% 0.20/0.37 inference(skolemize,[status(sab)],[20])).
% 0.20/0.37 tff(22,plain,
% 0.20/0.37 (![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.20/0.37 tff(23,plain,
% 0.20/0.37 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(24,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.20/0.37 tff(25,plain,
% 0.20/0.37 (~equalish(e_2, e_1)),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.37 tff(26,plain,
% 0.20/0.37 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | (equalish(e_2, e_1) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(27,plain,
% 0.20/0.37 (((~product(e_2, e_2, e_2)) | equalish(e_2, e_1) | (~product(e_1, e_2, e_2))) <=> (equalish(e_2, e_1) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(28,plain,
% 0.20/0.37 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | ((~product(e_2, e_2, e_2)) | equalish(e_2, e_1) | (~product(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | (equalish(e_2, e_1) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2))))),
% 0.20/0.37 inference(monotonicity,[status(thm)],[27])).
% 0.20/0.37 tff(29,plain,
% 0.20/0.37 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | ((~product(e_2, e_2, e_2)) | equalish(e_2, e_1) | (~product(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.37 inference(transitivity,[status(thm)],[28, 26])).
% 0.20/0.37 tff(30,plain,
% 0.20/0.37 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | ((~product(e_2, e_2, e_2)) | equalish(e_2, e_1) | (~product(e_1, e_2, e_2)))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(31,plain,
% 0.20/0.37 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.20/0.37 tff(32,plain,
% 0.20/0.37 ($false),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[31, 25, 22, 12, 1])).
% 0.20/0.37 tff(33,plain,(~product(e_1, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.37 tff(34,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.20/0.37 tff(35,plain,
% 0.20/0.37 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl(((~product(Y, X, Z2)) | (~product(Z1, Z2, X)) | product(X, Y, Z1)) <=> ((~product(Y, X, Z2)) | (~product(Z1, Z2, X)) | product(X, Y, Z1)))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(36,plain,
% 0.20/0.37 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, X)) | product(X, Y, Z1)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, X)) | product(X, Y, Z1))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.37 tff(37,plain,
% 0.20/0.37 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, X)) | product(X, Y, Z1)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, X)) | product(X, Y, Z1))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(38,plain,
% 0.20/0.37 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : trans(monotonicity(rewrite((product(X, Y, Z1) | (~product(Z1, Z2, X))) <=> ((~product(Z1, Z2, X)) | product(X, Y, Z1))), (((product(X, Y, Z1) | (~product(Z1, Z2, X))) | (~product(Y, X, Z2))) <=> (((~product(Z1, Z2, X)) | product(X, Y, Z1)) | (~product(Y, X, Z2))))), rewrite((((~product(Z1, Z2, X)) | product(X, Y, Z1)) | (~product(Y, X, Z2))) <=> ((~product(Y, X, Z2)) | (~product(Z1, Z2, X)) | product(X, Y, Z1))), (((product(X, Y, Z1) | (~product(Z1, Z2, X))) | (~product(Y, X, Z2))) <=> ((~product(Y, X, Z2)) | (~product(Z1, Z2, X)) | product(X, Y, Z1))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(39,plain,
% 0.20/0.37 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((product(X, Y, Z1) | (~product(Z1, Z2, X))) | (~product(Y, X, Z2))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, X)) | product(X, Y, Z1))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.38 tff(40,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : ((product(X, Y, Z1) | (~product(Z1, Z2, X))) | (~product(Y, X, Z2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qg3_1')).
% 0.20/0.38 tff(41,plain,
% 0.20/0.38 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, X)) | product(X, Y, Z1))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.38 tff(42,plain,
% 0.20/0.38 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, X)) | product(X, Y, Z1))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.20/0.38 tff(43,plain,(
% 0.20/0.38 ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, X)) | product(X, Y, Z1))),
% 0.20/0.38 inference(skolemize,[status(sab)],[42])).
% 0.20/0.38 tff(44,plain,
% 0.20/0.38 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, X)) | product(X, Y, Z1))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.20/0.38 tff(45,plain,
% 0.20/0.38 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, X)) | product(X, Y, Z1))) | (product(e_1, e_2, e_2) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, X)) | product(X, Y, Z1))) | product(e_1, e_2, e_2) | (~product(e_2, e_1, e_1)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(46,plain,
% 0.20/0.38 (((~product(e_2, e_1, e_1)) | (~product(e_2, e_1, e_1)) | product(e_1, e_2, e_2)) <=> (product(e_1, e_2, e_2) | (~product(e_2, e_1, e_1)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(47,plain,
% 0.20/0.38 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, X)) | product(X, Y, Z1))) | ((~product(e_2, e_1, e_1)) | (~product(e_2, e_1, e_1)) | product(e_1, e_2, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, X)) | product(X, Y, Z1))) | (product(e_1, e_2, e_2) | (~product(e_2, e_1, e_1))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[46])).
% 0.20/0.38 tff(48,plain,
% 0.20/0.38 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, X)) | product(X, Y, Z1))) | ((~product(e_2, e_1, e_1)) | (~product(e_2, e_1, e_1)) | product(e_1, e_2, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, X)) | product(X, Y, Z1))) | product(e_1, e_2, e_2) | (~product(e_2, e_1, e_1)))),
% 0.20/0.38 inference(transitivity,[status(thm)],[47, 45])).
% 0.20/0.38 tff(49,plain,
% 0.20/0.38 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, X)) | product(X, Y, Z1))) | ((~product(e_2, e_1, e_1)) | (~product(e_2, e_1, e_1)) | product(e_1, e_2, e_2))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(50,plain,
% 0.20/0.38 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, X)) | product(X, Y, Z1))) | product(e_1, e_2, e_2) | (~product(e_2, e_1, e_1))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.20/0.38 tff(51,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[50, 44, 34, 33])).
% 0.20/0.38 tff(52,plain,(~product(e_2, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(53,plain,
% 0.20/0.38 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl((product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1))) <=> (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(54,plain,
% 0.20/0.38 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[53])).
% 0.20/0.38 tff(55,plain,
% 0.20/0.38 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(56,plain,
% 0.20/0.38 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : trans(monotonicity(rewrite((product(Y, X, Z2) | (~product(Z1, Z2, X))) <=> (product(Y, X, Z2) | (~product(Z1, Z2, X)))), (((product(Y, X, Z2) | (~product(Z1, Z2, X))) | (~product(X, Y, Z1))) <=> ((product(Y, X, Z2) | (~product(Z1, Z2, X))) | (~product(X, Y, Z1))))), rewrite(((product(Y, X, Z2) | (~product(Z1, Z2, X))) | (~product(X, Y, Z1))) <=> (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))), (((product(Y, X, Z2) | (~product(Z1, Z2, X))) | (~product(X, Y, Z1))) <=> (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(57,plain,
% 0.20/0.38 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((product(Y, X, Z2) | (~product(Z1, Z2, X))) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[56])).
% 0.20/0.38 tff(58,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : ((product(Y, X, Z2) | (~product(Z1, Z2, X))) | (~product(X, Y, Z1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qg3_2')).
% 0.20/0.38 tff(59,plain,
% 0.20/0.38 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.38 tff(60,plain,
% 0.20/0.38 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.20/0.38 tff(61,plain,(
% 0.20/0.38 ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[60])).
% 0.20/0.38 tff(62,plain,
% 0.20/0.38 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.20/0.38 tff(63,plain,
% 0.20/0.38 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_2, e_2)) | product(e_1, e_2, e_2) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))) | (~product(e_2, e_2, e_2)) | product(e_1, e_2, e_2) | (~product(e_2, e_1, e_2)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(64,plain,
% 0.20/0.38 ((product(e_1, e_2, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2))) <=> ((~product(e_2, e_2, e_2)) | product(e_1, e_2, e_2) | (~product(e_2, e_1, e_2)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(65,plain,
% 0.20/0.38 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_2, e_2)) | product(e_1, e_2, e_2) | (~product(e_2, e_1, e_2))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[64])).
% 0.20/0.38 tff(66,plain,
% 0.20/0.38 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))) | (~product(e_2, e_2, e_2)) | product(e_1, e_2, e_2) | (~product(e_2, e_1, e_2)))),
% 0.20/0.38 inference(transitivity,[status(thm)],[65, 63])).
% 0.20/0.38 tff(67,plain,
% 0.20/0.38 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(68,plain,
% 0.20/0.38 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, X)) | (~product(X, Y, Z1)))) | (~product(e_2, e_2, e_2)) | product(e_1, e_2, e_2) | (~product(e_2, e_1, e_2))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.20/0.38 tff(69,plain,
% 0.20/0.38 (~product(e_2, e_1, e_2)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[68, 62, 12, 33])).
% 0.20/0.38 tff(70,plain,
% 0.20/0.38 (^[Y: $i, X: $i] : refl(((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(71,plain,
% 0.20/0.38 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[70])).
% 0.20/0.38 tff(72,plain,
% 0.20/0.38 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(73,plain,
% 0.20/0.38 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_1))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> (((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_1)) | product(X, Y, e_2)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1)))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> (((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1)) | product(X, Y, e_3)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1)) | product(X, Y, e_3)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(74,plain,
% 0.20/0.38 (![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[73])).
% 0.20/0.38 tff(75,axiom,(![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_total_function1')).
% 0.20/0.38 tff(76,plain,
% 0.20/0.38 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.20/0.38 tff(77,plain,
% 0.20/0.38 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.20/0.38 tff(78,plain,(
% 0.20/0.38 ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.20/0.38 inference(skolemize,[status(sab)],[77])).
% 0.20/0.38 tff(79,plain,
% 0.20/0.38 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[78, 71])).
% 0.20/0.38 tff(80,plain,
% 0.20/0.38 (group_element(e_2) <=> group_element(e_2)),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(81,axiom,(group_element(e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_2')).
% 0.20/0.38 tff(82,plain,
% 0.20/0.38 (group_element(e_2)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.20/0.38 tff(83,plain,
% 0.20/0.38 (group_element(e_1) <=> group_element(e_1)),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(84,axiom,(group_element(e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_1')).
% 0.20/0.38 tff(85,plain,
% 0.20/0.38 (group_element(e_1)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.20/0.38 tff(86,plain,
% 0.20/0.38 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (product(e_2, e_1, e_2) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_2, e_1, e_2) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_3))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(87,plain,
% 0.20/0.39 (((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1)) <=> (product(e_2, e_1, e_2) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_3))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(88,plain,
% 0.20/0.39 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (product(e_2, e_1, e_2) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_3)))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[87])).
% 0.20/0.39 tff(89,plain,
% 0.20/0.39 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_2, e_1, e_2) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_3))),
% 0.20/0.39 inference(transitivity,[status(thm)],[88, 86])).
% 0.20/0.39 tff(90,plain,
% 0.20/0.39 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(91,plain,
% 0.20/0.39 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_2, e_1, e_2) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_3)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.20/0.39 tff(92,plain,
% 0.20/0.39 (product(e_2, e_1, e_1) | product(e_2, e_1, e_3)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[91, 85, 82, 79, 69])).
% 0.20/0.39 tff(93,plain,
% 0.20/0.39 (product(e_2, e_1, e_3)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[92, 52])).
% 0.20/0.39 tff(94,plain,
% 0.20/0.39 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W))) <=> (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(95,plain,
% 0.20/0.39 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[94])).
% 0.20/0.39 tff(96,plain,
% 0.20/0.39 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(97,plain,
% 0.20/0.39 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(X, Y, W)) | (~product(X, Y, Z))) <=> ((~product(X, Y, Z)) | (~product(X, Y, W)))), ((((~product(X, Y, W)) | (~product(X, Y, Z))) | equalish(W, Z)) <=> (((~product(X, Y, Z)) | (~product(X, Y, W))) | equalish(W, Z)))), rewrite((((~product(X, Y, Z)) | (~product(X, Y, W))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))), ((((~product(X, Y, W)) | (~product(X, Y, Z))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(98,plain,
% 0.20/0.39 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, Y, W)) | (~product(X, Y, Z))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[97])).
% 0.20/0.39 tff(99,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, Y, W)) | (~product(X, Y, Z))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_total_function2')).
% 0.20/0.39 tff(100,plain,
% 0.20/0.39 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.39 tff(101,plain,
% 0.20/0.39 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.20/0.39 tff(102,plain,(
% 0.20/0.39 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[101])).
% 0.20/0.39 tff(103,plain,
% 0.20/0.39 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.20/0.39 tff(104,plain,
% 0.20/0.39 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(105,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.20/0.39 tff(106,plain,
% 0.20/0.39 (~equalish(e_1, e_2)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.39 tff(107,plain,
% 0.20/0.39 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_2, e_1)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(108,plain,
% 0.20/0.39 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_2, e_1)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(109,plain,
% 0.20/0.39 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_2, e_1))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.20/0.39 tff(110,plain,
% 0.20/0.39 ((~product(e_2, e_2, e_2)) | (~product(e_2, e_2, e_1))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[109, 106, 103])).
% 0.20/0.39 tff(111,plain,
% 0.20/0.39 (~product(e_2, e_2, e_1)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[110, 12])).
% 0.20/0.39 tff(112,plain,
% 0.20/0.39 (^[Y: $i, X: $i] : refl(((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(113,plain,
% 0.20/0.39 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[112])).
% 0.20/0.39 tff(114,plain,
% 0.20/0.39 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(115,plain,
% 0.20/0.39 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_1, Y))), (((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) <=> (((~group_element(Y)) | (~group_element(X)) | product(X, e_1, Y)) | product(X, e_2, Y)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product(X, e_1, Y)) | product(X, e_2, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_2, Y) | product(X, e_1, Y))), (((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_2, Y) | product(X, e_1, Y)))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) | product(X, e_3, Y)) <=> (((~group_element(Y)) | (~group_element(X)) | product(X, e_2, Y) | product(X, e_1, Y)) | product(X, e_3, Y)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product(X, e_2, Y) | product(X, e_1, Y)) | product(X, e_3, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) | product(X, e_3, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(116,plain,
% 0.20/0.39 (![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) | product(X, e_3, Y)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[115])).
% 0.20/0.39 tff(117,axiom,(![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) | product(X, e_3, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','column_surjectivity')).
% 0.20/0.39 tff(118,plain,
% 0.20/0.39 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.20/0.39 tff(119,plain,
% 0.20/0.39 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.20/0.39 tff(120,plain,(
% 0.20/0.39 ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.20/0.39 inference(skolemize,[status(sab)],[119])).
% 0.20/0.39 tff(121,plain,
% 0.20/0.39 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.20/0.39 tff(122,plain,
% 0.20/0.39 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_2, e_1) | product(e_2, e_1, e_1) | product(e_2, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_2, e_1) | product(e_2, e_1, e_1) | product(e_2, e_3, e_1))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(123,plain,
% 0.20/0.39 (((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_3, e_1) | product(e_2, e_2, e_1) | product(e_2, e_1, e_1)) <=> ((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_2, e_1) | product(e_2, e_1, e_1) | product(e_2, e_3, e_1))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(124,plain,
% 0.20/0.39 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_3, e_1) | product(e_2, e_2, e_1) | product(e_2, e_1, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_2, e_1) | product(e_2, e_1, e_1) | product(e_2, e_3, e_1)))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[123])).
% 0.20/0.39 tff(125,plain,
% 0.20/0.39 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_3, e_1) | product(e_2, e_2, e_1) | product(e_2, e_1, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_2, e_1) | product(e_2, e_1, e_1) | product(e_2, e_3, e_1))),
% 0.20/0.40 inference(transitivity,[status(thm)],[124, 122])).
% 0.20/0.40 tff(126,plain,
% 0.20/0.40 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_3, e_1) | product(e_2, e_2, e_1) | product(e_2, e_1, e_1))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(127,plain,
% 0.20/0.40 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_2, e_1) | product(e_2, e_1, e_1) | product(e_2, e_3, e_1)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.20/0.40 tff(128,plain,
% 0.20/0.40 (product(e_2, e_1, e_1) | product(e_2, e_3, e_1)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[127, 121, 85, 82, 111])).
% 0.20/0.40 tff(129,plain,
% 0.20/0.40 (product(e_2, e_3, e_1)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[128, 52])).
% 0.20/0.40 tff(130,plain,
% 0.20/0.40 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, X)) | product(X, Y, Z1))) | ((~product(e_2, e_1, e_3)) | (~product(e_2, e_3, e_1)) | product(e_1, e_2, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, X)) | product(X, Y, Z1))) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_3, e_1)) | product(e_1, e_2, e_2))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(131,plain,
% 0.20/0.40 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, X)) | product(X, Y, Z1))) | ((~product(e_2, e_1, e_3)) | (~product(e_2, e_3, e_1)) | product(e_1, e_2, e_2))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(132,plain,
% 0.20/0.40 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, X)) | product(X, Y, Z1))) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_3, e_1)) | product(e_1, e_2, e_2)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.20/0.40 tff(133,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[132, 44, 129, 33, 93])).
% 0.20/0.40 % SZS output end Proof
% 0.20/0.40 % E exiting
%------------------------------------------------------------------------------