%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP124-7.004 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:07:05 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP124-7.004 : TPTP v9.0.0. Released v1.2.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 15:42:39 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.41 % SZS status Unsatisfiable
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(product1_type, type, (
% 0.20/0.41 product1: ( $i * $i * $i ) > $o)).
% 0.20/0.41 tff(e_4_type, type, (
% 0.20/0.41 e_4: $i)).
% 0.20/0.41 tff(e_2_type, type, (
% 0.20/0.41 e_2: $i)).
% 0.20/0.41 tff(e_1_type, type, (
% 0.20/0.41 e_1: $i)).
% 0.20/0.41 tff(e_3_type, type, (
% 0.20/0.41 e_3: $i)).
% 0.20/0.41 tff(equalish_type, type, (
% 0.20/0.41 equalish: ( $i * $i ) > $o)).
% 0.20/0.41 tff(group_element_type, type, (
% 0.20/0.41 group_element: $i > $o)).
% 0.20/0.41 tff(product2_type, type, (
% 0.20/0.41 product2: ( $i * $i * $i ) > $o)).
% 0.20/0.41 tff(1,assumption,(~product1(e_2, e_2, e_2)), introduced(assumption)).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 (^[X: $i] : refl(product1(X, X, X) <=> product1(X, X, X))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 (![X: $i] : product1(X, X, X) <=> ![X: $i] : product1(X, X, X)),
% 0.20/0.41 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.41 tff(4,plain,
% 0.20/0.41 (![X: $i] : product1(X, X, X) <=> ![X: $i] : product1(X, X, X)),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(5,axiom,(![X: $i] : product1(X, X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product1_idempotence')).
% 0.20/0.41 tff(6,plain,
% 0.20/0.41 (![X: $i] : product1(X, X, X)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.41 tff(7,plain,(
% 0.20/0.41 ![X: $i] : product1(X, X, X)),
% 0.20/0.41 inference(skolemize,[status(sab)],[6])).
% 0.20/0.41 tff(8,plain,
% 0.20/0.41 (![X: $i] : product1(X, X, X)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.41 tff(9,plain,
% 0.20/0.41 ((~![X: $i] : product1(X, X, X)) | product1(e_2, e_2, e_2)),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.41 tff(11,plain,(product1(e_2, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(12,assumption,(product1(e_3, e_2, e_2)), introduced(assumption)).
% 0.20/0.41 tff(13,plain,
% 0.20/0.41 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X))) <=> (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.41 tff(15,plain,
% 0.20/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(16,plain,
% 0.20/0.41 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product1(W, Y, X)) | (~product1(Z, Y, X))) <=> ((~product1(Z, Y, X)) | (~product1(W, Y, X)))), ((((~product1(W, Y, X)) | (~product1(Z, Y, X))) | equalish(W, Z)) <=> (((~product1(Z, Y, X)) | (~product1(W, Y, X))) | equalish(W, Z)))), rewrite((((~product1(Z, Y, X)) | (~product1(W, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))), ((((~product1(W, Y, X)) | (~product1(Z, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(17,plain,
% 0.20/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product1(W, Y, X)) | (~product1(Z, Y, X))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[16])).
% 0.20/0.41 tff(18,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product1(W, Y, X)) | (~product1(Z, Y, X))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product1_left_cancellation')).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.20/0.41 tff(20,plain,
% 0.20/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.20/0.41 tff(21,plain,(
% 0.20/0.41 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[20])).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(24,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (~equalish(e_3, e_2)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_2) | (~product1(e_3, e_2, e_2)) | (~product1(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_3, e_2) | (~product1(e_3, e_2, e_2)) | (~product1(e_2, e_2, e_2)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(27,plain,
% 0.20/0.42 ((equalish(e_3, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_3, e_2, e_2))) <=> (equalish(e_3, e_2) | (~product1(e_3, e_2, e_2)) | (~product1(e_2, e_2, e_2)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_3, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_2) | (~product1(e_3, e_2, e_2)) | (~product1(e_2, e_2, e_2))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[27])).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_3, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_3, e_2) | (~product1(e_3, e_2, e_2)) | (~product1(e_2, e_2, e_2)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[28, 26])).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_3, e_2, e_2)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_3, e_2) | (~product1(e_3, e_2, e_2)) | (~product1(e_2, e_2, e_2))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[31, 25, 22, 12, 11])).
% 0.20/0.42 tff(33,plain,(~product1(e_3, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(34,assumption,(~product1(e_4, e_4, e_4)), introduced(assumption)).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 ((~![X: $i] : product1(X, X, X)) | product1(e_4, e_4, e_4)),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[35, 8, 34])).
% 0.20/0.42 tff(37,plain,(product1(e_4, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(38,assumption,(product1(e_4, e_1, e_4)), introduced(assumption)).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y))) <=> (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(40,plain,
% 0.20/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[39])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product1(X, W, Y)) | (~product1(X, Z, Y))) <=> ((~product1(X, Z, Y)) | (~product1(X, W, Y)))), ((((~product1(X, W, Y)) | (~product1(X, Z, Y))) | equalish(W, Z)) <=> (((~product1(X, Z, Y)) | (~product1(X, W, Y))) | equalish(W, Z)))), rewrite((((~product1(X, Z, Y)) | (~product1(X, W, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))), ((((~product1(X, W, Y)) | (~product1(X, Z, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product1(X, W, Y)) | (~product1(X, Z, Y))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[42])).
% 0.20/0.42 tff(44,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product1(X, W, Y)) | (~product1(X, Z, Y))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product1_right_cancellation')).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.20/0.42 tff(47,plain,(
% 0.20/0.42 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[46])).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.20/0.42 tff(49,plain,
% 0.20/0.42 ((~equalish(e_1, e_4)) <=> (~equalish(e_1, e_4))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(50,axiom,(~equalish(e_1, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_4')).
% 0.20/0.42 tff(51,plain,
% 0.20/0.42 (~equalish(e_1, e_4)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.42 tff(52,plain,
% 0.20/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_1, e_4) | (~product1(e_4, e_1, e_4)) | (~product1(e_4, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_1, e_4) | (~product1(e_4, e_1, e_4)) | (~product1(e_4, e_4, e_4)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(53,plain,
% 0.20/0.42 ((equalish(e_1, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_4, e_1, e_4))) <=> (equalish(e_1, e_4) | (~product1(e_4, e_1, e_4)) | (~product1(e_4, e_4, e_4)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(54,plain,
% 0.20/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_1, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_4, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_1, e_4) | (~product1(e_4, e_1, e_4)) | (~product1(e_4, e_4, e_4))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[53])).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_1, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_4, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_1, e_4) | (~product1(e_4, e_1, e_4)) | (~product1(e_4, e_4, e_4)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[54, 52])).
% 0.20/0.42 tff(56,plain,
% 0.20/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_1, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_4, e_1, e_4)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(57,plain,
% 0.20/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_1, e_4) | (~product1(e_4, e_1, e_4)) | (~product1(e_4, e_4, e_4))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[57, 51, 48, 38, 37])).
% 0.20/0.42 tff(59,plain,(~product1(e_4, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(60,assumption,(product1(e_3, e_1, e_2)), introduced(assumption)).
% 0.20/0.42 tff(61,assumption,(product1(e_4, e_1, e_2)), introduced(assumption)).
% 0.20/0.42 tff(62,plain,
% 0.20/0.42 ((~equalish(e_4, e_3)) <=> (~equalish(e_4, e_3))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(63,axiom,(~equalish(e_4, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_3')).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 (~equalish(e_4, e_3)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.42 tff(65,plain,
% 0.20/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_4, e_3) | (~product1(e_4, e_1, e_2)) | (~product1(e_3, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_4, e_3) | (~product1(e_4, e_1, e_2)) | (~product1(e_3, e_1, e_2)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(66,plain,
% 0.20/0.42 ((equalish(e_4, e_3) | (~product1(e_3, e_1, e_2)) | (~product1(e_4, e_1, e_2))) <=> (equalish(e_4, e_3) | (~product1(e_4, e_1, e_2)) | (~product1(e_3, e_1, e_2)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(67,plain,
% 0.20/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_4, e_3) | (~product1(e_3, e_1, e_2)) | (~product1(e_4, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_4, e_3) | (~product1(e_4, e_1, e_2)) | (~product1(e_3, e_1, e_2))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[66])).
% 0.20/0.42 tff(68,plain,
% 0.20/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_4, e_3) | (~product1(e_3, e_1, e_2)) | (~product1(e_4, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_4, e_3) | (~product1(e_4, e_1, e_2)) | (~product1(e_3, e_1, e_2)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[67, 65])).
% 0.20/0.42 tff(69,plain,
% 0.20/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_4, e_3) | (~product1(e_3, e_1, e_2)) | (~product1(e_4, e_1, e_2)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(70,plain,
% 0.20/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_4, e_3) | (~product1(e_4, e_1, e_2)) | (~product1(e_3, e_1, e_2))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.42 tff(71,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[70, 64, 22, 60, 61])).
% 0.20/0.42 tff(72,plain,((~product1(e_4, e_1, e_2)) | (~product1(e_3, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(73,plain,
% 0.20/0.42 (~product1(e_4, e_1, e_2)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[72, 60])).
% 0.20/0.42 tff(74,assumption,(product1(e_4, e_1, e_1)), introduced(assumption)).
% 0.20/0.42 tff(75,plain,
% 0.20/0.42 ((~![X: $i] : product1(X, X, X)) | product1(e_1, e_1, e_1)),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(76,plain,
% 0.20/0.42 (product1(e_1, e_1, e_1)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[75, 8])).
% 0.20/0.42 tff(77,plain,
% 0.20/0.42 ((~equalish(e_4, e_1)) <=> (~equalish(e_4, e_1))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(78,axiom,(~equalish(e_4, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_1')).
% 0.20/0.42 tff(79,plain,
% 0.20/0.42 (~equalish(e_4, e_1)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.42 tff(80,plain,
% 0.20/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_4, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_4, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_4, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_4, e_1, e_1)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(81,plain,
% 0.20/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_4, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_4, e_1, e_1)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(82,plain,
% 0.20/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_4, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_4, e_1, e_1))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.20/0.43 tff(83,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[82, 79, 22, 76, 74])).
% 0.20/0.43 tff(84,plain,(~product1(e_4, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(85,plain,
% 0.20/0.43 (^[Y: $i, X: $i] : refl((product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(86,plain,
% 0.20/0.43 (![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[85])).
% 0.20/0.43 tff(87,plain,
% 0.20/0.43 (![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(88,plain,
% 0.20/0.43 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) <=> (product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) <=> ((product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product1(X, Y, e_2)))), rewrite(((product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product1(X, Y, e_2)) <=> (product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) <=> (product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))), ((((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) | product1(X, Y, e_3)) <=> ((product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product1(X, Y, e_3)))), rewrite(((product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product1(X, Y, e_3)) <=> (product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), ((((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) | product1(X, Y, e_3)) <=> (product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))), (((((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) | product1(X, Y, e_3)) | product1(X, Y, e_4)) <=> ((product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product1(X, Y, e_4)))), rewrite(((product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product1(X, Y, e_4)) <=> (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) | product1(X, Y, e_3)) | product1(X, Y, e_4)) <=> (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(89,plain,
% 0.20/0.43 (![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) | product1(X, Y, e_3)) | product1(X, Y, e_4)) <=> ![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[88])).
% 0.20/0.43 tff(90,axiom,(![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) | product1(X, Y, e_3)) | product1(X, Y, e_4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product1_total_function1')).
% 0.20/0.43 tff(91,plain,
% 0.20/0.43 (![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.20/0.43 tff(92,plain,
% 0.20/0.43 (![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.20/0.43 tff(93,plain,(
% 0.20/0.43 ![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[92])).
% 0.20/0.43 tff(94,plain,
% 0.20/0.43 (![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.20/0.43 tff(95,plain,
% 0.20/0.43 (group_element(e_4) <=> group_element(e_4)),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(96,axiom,(group_element(e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_4')).
% 0.20/0.43 tff(97,plain,
% 0.20/0.43 (group_element(e_4)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.20/0.43 tff(98,plain,
% 0.20/0.43 (group_element(e_1) <=> group_element(e_1)),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(99,axiom,(group_element(e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_1')).
% 0.20/0.43 tff(100,plain,
% 0.20/0.43 (group_element(e_1)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.43 tff(101,plain,
% 0.20/0.43 (((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product1(e_4, e_1, e_3) | product1(e_4, e_1, e_4) | (~group_element(e_4)) | (~group_element(e_1)) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_1))) <=> ((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product1(e_4, e_1, e_3) | product1(e_4, e_1, e_4) | (~group_element(e_4)) | (~group_element(e_1)) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_1))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(102,plain,
% 0.20/0.43 ((product1(e_4, e_1, e_4) | product1(e_4, e_1, e_3) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_4))) <=> (product1(e_4, e_1, e_3) | product1(e_4, e_1, e_4) | (~group_element(e_4)) | (~group_element(e_1)) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_1))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(103,plain,
% 0.20/0.43 (((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product1(e_4, e_1, e_4) | product1(e_4, e_1, e_3) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product1(e_4, e_1, e_3) | product1(e_4, e_1, e_4) | (~group_element(e_4)) | (~group_element(e_1)) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_1)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[102])).
% 0.20/0.43 tff(104,plain,
% 0.20/0.43 (((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product1(e_4, e_1, e_4) | product1(e_4, e_1, e_3) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product1(e_4, e_1, e_3) | product1(e_4, e_1, e_4) | (~group_element(e_4)) | (~group_element(e_1)) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_1))),
% 0.20/0.43 inference(transitivity,[status(thm)],[103, 101])).
% 0.20/0.43 tff(105,plain,
% 0.20/0.43 ((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product1(e_4, e_1, e_4) | product1(e_4, e_1, e_3) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_4)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(106,plain,
% 0.20/0.43 ((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product1(e_4, e_1, e_3) | product1(e_4, e_1, e_4) | (~group_element(e_4)) | (~group_element(e_1)) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_1)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.43 tff(107,plain,
% 0.20/0.43 (product1(e_4, e_1, e_3) | product1(e_4, e_1, e_4) | product1(e_4, e_1, e_2)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[106, 100, 97, 94, 84])).
% 0.20/0.43 tff(108,plain,
% 0.20/0.43 (product1(e_4, e_1, e_3)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[107, 73, 59])).
% 0.20/0.43 tff(109,assumption,(product1(e_4, e_2, e_3)), introduced(assumption)).
% 0.20/0.43 tff(110,assumption,(product1(e_4, e_1, e_3)), introduced(assumption)).
% 0.20/0.43 tff(111,plain,
% 0.20/0.43 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(112,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.20/0.43 tff(113,plain,
% 0.20/0.43 (~equalish(e_2, e_1)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.20/0.43 tff(114,plain,
% 0.20/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_1) | (~product1(e_4, e_1, e_3)) | (~product1(e_4, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_2, e_1) | (~product1(e_4, e_1, e_3)) | (~product1(e_4, e_2, e_3)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(115,plain,
% 0.20/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_1) | (~product1(e_4, e_1, e_3)) | (~product1(e_4, e_2, e_3)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(116,plain,
% 0.20/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_2, e_1) | (~product1(e_4, e_1, e_3)) | (~product1(e_4, e_2, e_3))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.20/0.43 tff(117,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[116, 113, 48, 110, 109])).
% 0.20/0.43 tff(118,plain,((~product1(e_4, e_2, e_3)) | (~product1(e_4, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(119,plain,
% 0.20/0.43 (~product1(e_4, e_2, e_3)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[118, 108])).
% 0.20/0.43 tff(120,assumption,(product1(e_4, e_2, e_2)), introduced(assumption)).
% 0.20/0.43 tff(121,plain,
% 0.20/0.43 ((~equalish(e_4, e_2)) <=> (~equalish(e_4, e_2))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(122,axiom,(~equalish(e_4, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_2')).
% 0.20/0.43 tff(123,plain,
% 0.20/0.43 (~equalish(e_4, e_2)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.20/0.43 tff(124,plain,
% 0.20/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_4, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_4, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_4, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_4, e_2, e_2)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(125,plain,
% 0.20/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_4, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_4, e_2, e_2)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(126,plain,
% 0.20/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_4, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_4, e_2, e_2))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.20/0.44 tff(127,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[126, 123, 22, 11, 120])).
% 0.20/0.44 tff(128,plain,(~product1(e_4, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(129,assumption,(product2(e_4, e_2, e_4)), introduced(assumption)).
% 0.20/0.44 tff(130,plain,
% 0.20/0.44 (^[X: $i] : refl(product2(X, X, X) <=> product2(X, X, X))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(131,plain,
% 0.20/0.44 (![X: $i] : product2(X, X, X) <=> ![X: $i] : product2(X, X, X)),
% 0.20/0.44 inference(quant_intro,[status(thm)],[130])).
% 0.20/0.44 tff(132,plain,
% 0.20/0.44 (![X: $i] : product2(X, X, X) <=> ![X: $i] : product2(X, X, X)),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(133,axiom,(![X: $i] : product2(X, X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product2_idempotence')).
% 0.20/0.44 tff(134,plain,
% 0.20/0.44 (![X: $i] : product2(X, X, X)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.20/0.44 tff(135,plain,(
% 0.20/0.44 ![X: $i] : product2(X, X, X)),
% 0.20/0.44 inference(skolemize,[status(sab)],[134])).
% 0.20/0.44 tff(136,plain,
% 0.20/0.44 (![X: $i] : product2(X, X, X)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[135, 131])).
% 0.20/0.44 tff(137,plain,
% 0.20/0.44 ((~![X: $i] : product2(X, X, X)) | product2(e_4, e_4, e_4)),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(138,plain,
% 0.20/0.44 (product2(e_4, e_4, e_4)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.20/0.44 tff(139,plain,
% 0.20/0.44 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y))) <=> (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(140,plain,
% 0.20/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[139])).
% 0.20/0.44 tff(141,plain,
% 0.20/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(142,plain,
% 0.20/0.44 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product2(X, W, Y)) | (~product2(X, Z, Y))) <=> ((~product2(X, Z, Y)) | (~product2(X, W, Y)))), ((((~product2(X, W, Y)) | (~product2(X, Z, Y))) | equalish(W, Z)) <=> (((~product2(X, Z, Y)) | (~product2(X, W, Y))) | equalish(W, Z)))), rewrite((((~product2(X, Z, Y)) | (~product2(X, W, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))), ((((~product2(X, W, Y)) | (~product2(X, Z, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(143,plain,
% 0.20/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product2(X, W, Y)) | (~product2(X, Z, Y))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[142])).
% 0.20/0.44 tff(144,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product2(X, W, Y)) | (~product2(X, Z, Y))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product2_right_cancellation')).
% 0.20/0.44 tff(145,plain,
% 0.20/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.20/0.44 tff(146,plain,
% 0.20/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[145, 141])).
% 0.20/0.44 tff(147,plain,(
% 0.20/0.44 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[146])).
% 0.20/0.44 tff(148,plain,
% 0.20/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[147, 140])).
% 0.20/0.44 tff(149,plain,
% 0.20/0.44 ((~equalish(e_2, e_4)) <=> (~equalish(e_2, e_4))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(150,axiom,(~equalish(e_2, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_4')).
% 0.20/0.44 tff(151,plain,
% 0.20/0.44 (~equalish(e_2, e_4)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.20/0.44 tff(152,plain,
% 0.20/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_2, e_4) | (~product2(e_4, e_4, e_4)) | (~product2(e_4, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_2, e_4) | (~product2(e_4, e_4, e_4)) | (~product2(e_4, e_2, e_4)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(153,plain,
% 0.20/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_2, e_4) | (~product2(e_4, e_4, e_4)) | (~product2(e_4, e_2, e_4)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(154,plain,
% 0.20/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_2, e_4) | (~product2(e_4, e_4, e_4)) | (~product2(e_4, e_2, e_4))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.20/0.44 tff(155,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[154, 151, 148, 138, 129])).
% 0.20/0.44 tff(156,plain,(~product2(e_4, e_2, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(157,plain,
% 0.20/0.44 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl(((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1))) <=> ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(158,plain,
% 0.20/0.44 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[157])).
% 0.20/0.44 tff(159,plain,
% 0.20/0.44 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(160,plain,
% 0.20/0.44 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : rewrite((((~product1(X, Y, Z1)) | (~product1(Z1, X, Z2))) | product2(Z2, Y, X)) <=> ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(161,plain,
% 0.20/0.44 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product1(X, Y, Z1)) | (~product1(Z1, X, Z2))) | product2(Z2, Y, X)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[160])).
% 0.20/0.44 tff(162,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product1(X, Y, Z1)) | (~product1(Z1, X, Z2))) | product2(Z2, Y, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qg2a')).
% 0.20/0.44 tff(163,plain,
% 0.20/0.44 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.20/0.44 tff(164,plain,
% 0.20/0.44 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[163, 159])).
% 0.20/0.44 tff(165,plain,(
% 0.20/0.44 ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[164])).
% 0.20/0.44 tff(166,plain,
% 0.20/0.44 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[165, 158])).
% 0.20/0.44 tff(167,plain,
% 0.20/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_4, e_4, e_4)) | product2(e_4, e_2, e_4) | (~product1(e_4, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_4, e_4, e_4)) | product2(e_4, e_2, e_4) | (~product1(e_4, e_2, e_4)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(168,plain,
% 0.20/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_4, e_4, e_4)) | product2(e_4, e_2, e_4) | (~product1(e_4, e_2, e_4)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(169,plain,
% 0.20/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_4, e_4, e_4)) | product2(e_4, e_2, e_4) | (~product1(e_4, e_2, e_4))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.20/0.44 tff(170,plain,
% 0.20/0.44 (~product1(e_4, e_2, e_4)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[169, 166, 37, 156])).
% 0.20/0.44 tff(171,plain,
% 0.20/0.44 (group_element(e_2) <=> group_element(e_2)),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(172,axiom,(group_element(e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_2')).
% 0.20/0.44 tff(173,plain,
% 0.20/0.44 (group_element(e_2)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.20/0.44 tff(174,plain,
% 0.20/0.44 (((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_4)) | (~group_element(e_2)) | product1(e_4, e_2, e_2) | product1(e_4, e_2, e_1) | product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3))) <=> ((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | (~group_element(e_2)) | product1(e_4, e_2, e_2) | product1(e_4, e_2, e_1) | product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(175,plain,
% 0.20/0.44 ((product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3) | product1(e_4, e_2, e_2) | product1(e_4, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_4))) <=> ((~group_element(e_4)) | (~group_element(e_2)) | product1(e_4, e_2, e_2) | product1(e_4, e_2, e_1) | product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(176,plain,
% 0.20/0.44 (((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3) | product1(e_4, e_2, e_2) | product1(e_4, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_4)) | (~group_element(e_2)) | product1(e_4, e_2, e_2) | product1(e_4, e_2, e_1) | product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[175])).
% 0.20/0.44 tff(177,plain,
% 0.20/0.44 (((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3) | product1(e_4, e_2, e_2) | product1(e_4, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | (~group_element(e_2)) | product1(e_4, e_2, e_2) | product1(e_4, e_2, e_1) | product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3))),
% 0.20/0.44 inference(transitivity,[status(thm)],[176, 174])).
% 0.20/0.44 tff(178,plain,
% 0.20/0.44 ((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3) | product1(e_4, e_2, e_2) | product1(e_4, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_4)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(179,plain,
% 0.20/0.44 ((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | (~group_element(e_2)) | product1(e_4, e_2, e_2) | product1(e_4, e_2, e_1) | product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.20/0.44 tff(180,plain,
% 0.20/0.44 (product1(e_4, e_2, e_2) | product1(e_4, e_2, e_1) | product1(e_4, e_2, e_3)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[179, 173, 97, 94, 170])).
% 0.20/0.45 tff(181,plain,
% 0.20/0.45 (product1(e_4, e_2, e_1) | product1(e_4, e_2, e_3)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[180, 128])).
% 0.20/0.45 tff(182,plain,
% 0.20/0.45 (product1(e_4, e_2, e_1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[181, 119])).
% 0.20/0.45 tff(183,assumption,(product1(e_3, e_2, e_1)), introduced(assumption)).
% 0.20/0.45 tff(184,assumption,(product1(e_4, e_2, e_1)), introduced(assumption)).
% 0.20/0.45 tff(185,plain,
% 0.20/0.45 ((~equalish(e_3, e_4)) <=> (~equalish(e_3, e_4))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(186,axiom,(~equalish(e_3, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_4')).
% 0.20/0.45 tff(187,plain,
% 0.20/0.45 (~equalish(e_3, e_4)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.20/0.45 tff(188,plain,
% 0.20/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_4) | (~product1(e_3, e_2, e_1)) | (~product1(e_4, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_3, e_4) | (~product1(e_3, e_2, e_1)) | (~product1(e_4, e_2, e_1)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(189,plain,
% 0.20/0.45 ((equalish(e_3, e_4) | (~product1(e_4, e_2, e_1)) | (~product1(e_3, e_2, e_1))) <=> (equalish(e_3, e_4) | (~product1(e_3, e_2, e_1)) | (~product1(e_4, e_2, e_1)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(190,plain,
% 0.20/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_4) | (~product1(e_4, e_2, e_1)) | (~product1(e_3, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_4) | (~product1(e_3, e_2, e_1)) | (~product1(e_4, e_2, e_1))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[189])).
% 0.20/0.45 tff(191,plain,
% 0.20/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_4) | (~product1(e_4, e_2, e_1)) | (~product1(e_3, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_3, e_4) | (~product1(e_3, e_2, e_1)) | (~product1(e_4, e_2, e_1)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[190, 188])).
% 0.20/0.45 tff(192,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_4) | (~product1(e_4, e_2, e_1)) | (~product1(e_3, e_2, e_1)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(193,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_3, e_4) | (~product1(e_3, e_2, e_1)) | (~product1(e_4, e_2, e_1))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.20/0.45 tff(194,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[193, 187, 22, 184, 183])).
% 0.20/0.45 tff(195,plain,((~product1(e_3, e_2, e_1)) | (~product1(e_4, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(196,plain,
% 0.20/0.45 (~product1(e_3, e_2, e_1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[195, 182])).
% 0.20/0.45 tff(197,assumption,(product1(e_3, e_2, e_3)), introduced(assumption)).
% 0.20/0.45 tff(198,plain,
% 0.20/0.45 ((~![X: $i] : product1(X, X, X)) | product1(e_3, e_3, e_3)),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(199,plain,
% 0.20/0.45 (product1(e_3, e_3, e_3)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[198, 8])).
% 0.20/0.45 tff(200,plain,
% 0.20/0.45 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(201,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.20/0.45 tff(202,plain,
% 0.20/0.45 (~equalish(e_2, e_3)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.20/0.45 tff(203,plain,
% 0.20/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_3, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_3, e_2, e_3)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(204,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_3, e_2, e_3)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(205,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_3, e_2, e_3))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.20/0.45 tff(206,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[205, 202, 48, 199, 197])).
% 0.20/0.45 tff(207,plain,(~product1(e_3, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(208,plain,
% 0.20/0.45 (group_element(e_3) <=> group_element(e_3)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(209,axiom,(group_element(e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_3')).
% 0.20/0.45 tff(210,plain,
% 0.20/0.45 (group_element(e_3)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.20/0.45 tff(211,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product1(e_3, e_2, e_2) | (~group_element(e_3)) | (~group_element(e_2)) | product1(e_3, e_2, e_3) | product1(e_3, e_2, e_1) | product1(e_3, e_2, e_4))) <=> ((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product1(e_3, e_2, e_2) | (~group_element(e_3)) | (~group_element(e_2)) | product1(e_3, e_2, e_3) | product1(e_3, e_2, e_1) | product1(e_3, e_2, e_4))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(212,plain,
% 0.20/0.45 ((product1(e_3, e_2, e_4) | product1(e_3, e_2, e_3) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3))) <=> (product1(e_3, e_2, e_2) | (~group_element(e_3)) | (~group_element(e_2)) | product1(e_3, e_2, e_3) | product1(e_3, e_2, e_1) | product1(e_3, e_2, e_4))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(213,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product1(e_3, e_2, e_4) | product1(e_3, e_2, e_3) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product1(e_3, e_2, e_2) | (~group_element(e_3)) | (~group_element(e_2)) | product1(e_3, e_2, e_3) | product1(e_3, e_2, e_1) | product1(e_3, e_2, e_4)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[212])).
% 0.20/0.45 tff(214,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product1(e_3, e_2, e_4) | product1(e_3, e_2, e_3) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product1(e_3, e_2, e_2) | (~group_element(e_3)) | (~group_element(e_2)) | product1(e_3, e_2, e_3) | product1(e_3, e_2, e_1) | product1(e_3, e_2, e_4))),
% 0.20/0.45 inference(transitivity,[status(thm)],[213, 211])).
% 0.20/0.45 tff(215,plain,
% 0.20/0.45 ((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product1(e_3, e_2, e_4) | product1(e_3, e_2, e_3) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(216,plain,
% 0.20/0.45 ((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product1(e_3, e_2, e_2) | (~group_element(e_3)) | (~group_element(e_2)) | product1(e_3, e_2, e_3) | product1(e_3, e_2, e_1) | product1(e_3, e_2, e_4)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.20/0.45 tff(217,plain,
% 0.20/0.45 (product1(e_3, e_2, e_2) | product1(e_3, e_2, e_1) | product1(e_3, e_2, e_4)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[216, 173, 210, 94, 207])).
% 0.20/0.45 tff(218,plain,
% 0.20/0.45 (product1(e_3, e_2, e_4)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[217, 196, 33])).
% 0.20/0.45 tff(219,assumption,(product1(e_3, e_2, e_4)), introduced(assumption)).
% 0.20/0.45 tff(220,assumption,(product1(e_1, e_2, e_4)), introduced(assumption)).
% 0.20/0.45 tff(221,plain,
% 0.20/0.45 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(222,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.20/0.45 tff(223,plain,
% 0.20/0.45 (~equalish(e_3, e_1)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.20/0.45 tff(224,plain,
% 0.20/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_1) | (~product1(e_1, e_2, e_4)) | (~product1(e_3, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_3, e_1) | (~product1(e_1, e_2, e_4)) | (~product1(e_3, e_2, e_4)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(225,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_1) | (~product1(e_1, e_2, e_4)) | (~product1(e_3, e_2, e_4)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(226,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_3, e_1) | (~product1(e_1, e_2, e_4)) | (~product1(e_3, e_2, e_4))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.20/0.45 tff(227,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[226, 223, 22, 220, 219])).
% 0.20/0.45 tff(228,plain,((~product1(e_3, e_2, e_4)) | (~product1(e_1, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(229,plain,
% 0.20/0.46 (~product1(e_1, e_2, e_4)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[228, 218])).
% 0.20/0.46 tff(230,assumption,(product1(e_1, e_2, e_2)), introduced(assumption)).
% 0.20/0.46 tff(231,plain,
% 0.20/0.46 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(232,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.20/0.46 tff(233,plain,
% 0.20/0.46 (~equalish(e_1, e_2)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.20/0.46 tff(234,plain,
% 0.20/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_1, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_1, e_2, e_2)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(235,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_1, e_2, e_2)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(236,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_1, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_1, e_2, e_2))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.20/0.46 tff(237,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[236, 233, 22, 230, 11])).
% 0.20/0.46 tff(238,plain,(~product1(e_1, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(239,assumption,(product1(e_1, e_2, e_1)), introduced(assumption)).
% 0.20/0.46 tff(240,plain,
% 0.20/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_2, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_2, e_1)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(241,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_2, e_1)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(242,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_2, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_2, e_1))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.20/0.46 tff(243,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[242, 113, 48, 76, 239])).
% 0.20/0.46 tff(244,plain,(~product1(e_1, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(245,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | (~group_element(e_1)) | product1(e_1, e_2, e_3) | product1(e_1, e_2, e_4) | product1(e_1, e_2, e_1) | product1(e_1, e_2, e_2))) <=> ((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | (~group_element(e_1)) | product1(e_1, e_2, e_3) | product1(e_1, e_2, e_4) | product1(e_1, e_2, e_1) | product1(e_1, e_2, e_2))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(246,plain,
% 0.20/0.46 ((product1(e_1, e_2, e_4) | product1(e_1, e_2, e_3) | product1(e_1, e_2, e_2) | product1(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1))) <=> ((~group_element(e_2)) | (~group_element(e_1)) | product1(e_1, e_2, e_3) | product1(e_1, e_2, e_4) | product1(e_1, e_2, e_1) | product1(e_1, e_2, e_2))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(247,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product1(e_1, e_2, e_4) | product1(e_1, e_2, e_3) | product1(e_1, e_2, e_2) | product1(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | (~group_element(e_1)) | product1(e_1, e_2, e_3) | product1(e_1, e_2, e_4) | product1(e_1, e_2, e_1) | product1(e_1, e_2, e_2)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[246])).
% 0.20/0.46 tff(248,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product1(e_1, e_2, e_4) | product1(e_1, e_2, e_3) | product1(e_1, e_2, e_2) | product1(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | (~group_element(e_1)) | product1(e_1, e_2, e_3) | product1(e_1, e_2, e_4) | product1(e_1, e_2, e_1) | product1(e_1, e_2, e_2))),
% 0.20/0.46 inference(transitivity,[status(thm)],[247, 245])).
% 0.20/0.46 tff(249,plain,
% 0.20/0.46 ((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product1(e_1, e_2, e_4) | product1(e_1, e_2, e_3) | product1(e_1, e_2, e_2) | product1(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(250,plain,
% 0.20/0.46 ((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | (~group_element(e_1)) | product1(e_1, e_2, e_3) | product1(e_1, e_2, e_4) | product1(e_1, e_2, e_1) | product1(e_1, e_2, e_2)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.20/0.46 tff(251,plain,
% 0.20/0.46 (product1(e_1, e_2, e_3) | product1(e_1, e_2, e_4) | product1(e_1, e_2, e_2)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[250, 100, 173, 94, 244])).
% 0.20/0.46 tff(252,plain,
% 0.20/0.46 (product1(e_1, e_2, e_3) | product1(e_1, e_2, e_4)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[251, 238])).
% 0.20/0.46 tff(253,plain,
% 0.20/0.46 (product1(e_1, e_2, e_3)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[252, 229])).
% 0.20/0.46 tff(254,assumption,(product2(e_2, e_2, e_1)), introduced(assumption)).
% 0.20/0.46 tff(255,assumption,(~product2(e_2, e_2, e_2)), introduced(assumption)).
% 0.20/0.46 tff(256,plain,
% 0.20/0.46 ((~![X: $i] : product2(X, X, X)) | product2(e_2, e_2, e_2)),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(257,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[256, 136, 255])).
% 0.20/0.46 tff(258,plain,(product2(e_2, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(259,plain,
% 0.20/0.46 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W))) <=> (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(260,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[259])).
% 0.20/0.46 tff(261,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(262,plain,
% 0.20/0.46 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product2(X, Y, W)) | (~product2(X, Y, Z))) <=> ((~product2(X, Y, Z)) | (~product2(X, Y, W)))), ((((~product2(X, Y, W)) | (~product2(X, Y, Z))) | equalish(W, Z)) <=> (((~product2(X, Y, Z)) | (~product2(X, Y, W))) | equalish(W, Z)))), rewrite((((~product2(X, Y, Z)) | (~product2(X, Y, W))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))), ((((~product2(X, Y, W)) | (~product2(X, Y, Z))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(263,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product2(X, Y, W)) | (~product2(X, Y, Z))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[262])).
% 0.20/0.46 tff(264,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product2(X, Y, W)) | (~product2(X, Y, Z))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product2_total_function2')).
% 0.20/0.46 tff(265,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.20/0.46 tff(266,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[265, 261])).
% 0.20/0.46 tff(267,plain,(
% 0.20/0.46 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[266])).
% 0.20/0.46 tff(268,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[267, 260])).
% 0.20/0.46 tff(269,plain,
% 0.20/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | (equalish(e_1, e_2) | (~product2(e_2, e_2, e_1)) | (~product2(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | equalish(e_1, e_2) | (~product2(e_2, e_2, e_1)) | (~product2(e_2, e_2, e_2)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(270,plain,
% 0.20/0.46 ((equalish(e_1, e_2) | (~product2(e_2, e_2, e_2)) | (~product2(e_2, e_2, e_1))) <=> (equalish(e_1, e_2) | (~product2(e_2, e_2, e_1)) | (~product2(e_2, e_2, e_2)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(271,plain,
% 0.20/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | (equalish(e_1, e_2) | (~product2(e_2, e_2, e_2)) | (~product2(e_2, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | (equalish(e_1, e_2) | (~product2(e_2, e_2, e_1)) | (~product2(e_2, e_2, e_2))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[270])).
% 0.20/0.46 tff(272,plain,
% 0.20/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | (equalish(e_1, e_2) | (~product2(e_2, e_2, e_2)) | (~product2(e_2, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | equalish(e_1, e_2) | (~product2(e_2, e_2, e_1)) | (~product2(e_2, e_2, e_2)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[271, 269])).
% 0.20/0.46 tff(273,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | (equalish(e_1, e_2) | (~product2(e_2, e_2, e_2)) | (~product2(e_2, e_2, e_1)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(274,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | equalish(e_1, e_2) | (~product2(e_2, e_2, e_1)) | (~product2(e_2, e_2, e_2))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.20/0.46 tff(275,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[274, 233, 268, 258, 254])).
% 0.20/0.46 tff(276,plain,(~product2(e_2, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(277,plain,
% 0.20/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (product2(e_2, e_2, e_1) | (~product1(e_3, e_1, e_2)) | (~product1(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | product2(e_2, e_2, e_1) | (~product1(e_3, e_1, e_2)) | (~product1(e_1, e_2, e_3)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(278,plain,
% 0.20/0.46 (((~product1(e_3, e_1, e_2)) | product2(e_2, e_2, e_1) | (~product1(e_1, e_2, e_3))) <=> (product2(e_2, e_2, e_1) | (~product1(e_3, e_1, e_2)) | (~product1(e_1, e_2, e_3)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(279,plain,
% 0.20/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_3, e_1, e_2)) | product2(e_2, e_2, e_1) | (~product1(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (product2(e_2, e_2, e_1) | (~product1(e_3, e_1, e_2)) | (~product1(e_1, e_2, e_3))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[278])).
% 0.20/0.46 tff(280,plain,
% 0.20/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_3, e_1, e_2)) | product2(e_2, e_2, e_1) | (~product1(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | product2(e_2, e_2, e_1) | (~product1(e_3, e_1, e_2)) | (~product1(e_1, e_2, e_3)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[279, 277])).
% 0.20/0.46 tff(281,plain,
% 0.20/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_3, e_1, e_2)) | product2(e_2, e_2, e_1) | (~product1(e_1, e_2, e_3)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(282,plain,
% 0.20/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | product2(e_2, e_2, e_1) | (~product1(e_3, e_1, e_2)) | (~product1(e_1, e_2, e_3))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.20/0.46 tff(283,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[282, 166, 60, 276, 253])).
% 0.20/0.46 tff(284,plain,(~product1(e_3, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(285,assumption,(product1(e_3, e_1, e_1)), introduced(assumption)).
% 0.20/0.46 tff(286,plain,
% 0.20/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_3, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_3, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_3, e_1, e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(287,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_3, e_1, e_1)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(288,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_3, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_3, e_1, e_1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.20/0.47 tff(289,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[288, 223, 22, 285, 76])).
% 0.20/0.47 tff(290,plain,(~product1(e_3, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(291,assumption,(product1(e_3, e_1, e_3)), introduced(assumption)).
% 0.20/0.47 tff(292,plain,
% 0.20/0.47 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(293,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.20/0.47 tff(294,plain,
% 0.20/0.47 (~equalish(e_1, e_3)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[293, 292])).
% 0.20/0.47 tff(295,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_1, e_3) | (~product1(e_3, e_1, e_3)) | (~product1(e_3, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_1, e_3) | (~product1(e_3, e_1, e_3)) | (~product1(e_3, e_3, e_3)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(296,plain,
% 0.20/0.47 ((equalish(e_1, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_3, e_1, e_3))) <=> (equalish(e_1, e_3) | (~product1(e_3, e_1, e_3)) | (~product1(e_3, e_3, e_3)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(297,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_1, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_3, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_1, e_3) | (~product1(e_3, e_1, e_3)) | (~product1(e_3, e_3, e_3))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[296])).
% 0.20/0.47 tff(298,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_1, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_3, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_1, e_3) | (~product1(e_3, e_1, e_3)) | (~product1(e_3, e_3, e_3)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[297, 295])).
% 0.20/0.47 tff(299,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_1, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_3, e_1, e_3)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(300,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_1, e_3) | (~product1(e_3, e_1, e_3)) | (~product1(e_3, e_3, e_3))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[299, 298])).
% 0.20/0.47 tff(301,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[300, 294, 48, 291, 199])).
% 0.20/0.47 tff(302,plain,(~product1(e_3, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(303,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product1(e_3, e_1, e_3) | (~group_element(e_3)) | product1(e_3, e_1, e_1) | product1(e_3, e_1, e_2) | product1(e_3, e_1, e_4) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product1(e_3, e_1, e_3) | (~group_element(e_3)) | product1(e_3, e_1, e_1) | product1(e_3, e_1, e_2) | product1(e_3, e_1, e_4) | (~group_element(e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(304,plain,
% 0.20/0.47 ((product1(e_3, e_1, e_4) | product1(e_3, e_1, e_3) | product1(e_3, e_1, e_2) | product1(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3))) <=> (product1(e_3, e_1, e_3) | (~group_element(e_3)) | product1(e_3, e_1, e_1) | product1(e_3, e_1, e_2) | product1(e_3, e_1, e_4) | (~group_element(e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(305,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product1(e_3, e_1, e_4) | product1(e_3, e_1, e_3) | product1(e_3, e_1, e_2) | product1(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product1(e_3, e_1, e_3) | (~group_element(e_3)) | product1(e_3, e_1, e_1) | product1(e_3, e_1, e_2) | product1(e_3, e_1, e_4) | (~group_element(e_1))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[304])).
% 0.20/0.47 tff(306,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product1(e_3, e_1, e_4) | product1(e_3, e_1, e_3) | product1(e_3, e_1, e_2) | product1(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product1(e_3, e_1, e_3) | (~group_element(e_3)) | product1(e_3, e_1, e_1) | product1(e_3, e_1, e_2) | product1(e_3, e_1, e_4) | (~group_element(e_1)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[305, 303])).
% 0.20/0.47 tff(307,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product1(e_3, e_1, e_4) | product1(e_3, e_1, e_3) | product1(e_3, e_1, e_2) | product1(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(308,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : (product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product1(e_3, e_1, e_3) | (~group_element(e_3)) | product1(e_3, e_1, e_1) | product1(e_3, e_1, e_2) | product1(e_3, e_1, e_4) | (~group_element(e_1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.20/0.47 tff(309,plain,
% 0.20/0.47 (product1(e_3, e_1, e_3) | product1(e_3, e_1, e_1) | product1(e_3, e_1, e_2) | product1(e_3, e_1, e_4)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[308, 100, 210, 94])).
% 0.20/0.47 tff(310,plain,
% 0.20/0.47 (product1(e_3, e_1, e_1) | product1(e_3, e_1, e_2) | product1(e_3, e_1, e_4)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[309, 302])).
% 0.20/0.47 tff(311,plain,
% 0.20/0.47 (product1(e_3, e_1, e_2) | product1(e_3, e_1, e_4)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[310, 290])).
% 0.20/0.47 tff(312,plain,
% 0.20/0.47 (product1(e_3, e_1, e_4)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[311, 284])).
% 0.20/0.47 tff(313,assumption,(product1(e_3, e_1, e_4)), introduced(assumption)).
% 0.20/0.47 tff(314,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_1) | (~product1(e_3, e_1, e_4)) | (~product1(e_3, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_2, e_1) | (~product1(e_3, e_1, e_4)) | (~product1(e_3, e_2, e_4)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(315,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_1) | (~product1(e_3, e_1, e_4)) | (~product1(e_3, e_2, e_4)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(316,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_2, e_1) | (~product1(e_3, e_1, e_4)) | (~product1(e_3, e_2, e_4))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[315, 314])).
% 0.20/0.47 tff(317,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[316, 113, 48, 313, 219])).
% 0.20/0.47 tff(318,plain,((~product1(e_3, e_2, e_4)) | (~product1(e_3, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(319,plain,
% 0.20/0.47 (~product1(e_3, e_2, e_4)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[318, 312])).
% 0.20/0.47 tff(320,plain,
% 0.20/0.47 (product1(e_3, e_2, e_1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[217, 319, 33])).
% 0.20/0.47 tff(321,plain,
% 0.20/0.47 (~product1(e_4, e_2, e_1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[195, 320])).
% 0.20/0.47 tff(322,plain,
% 0.20/0.47 (product1(e_4, e_2, e_3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[181, 321])).
% 0.20/0.47 tff(323,assumption,(product1(e_1, e_2, e_3)), introduced(assumption)).
% 0.20/0.47 tff(324,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_4) | (~product1(e_1, e_2, e_3)) | (~product1(e_4, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_1, e_4) | (~product1(e_1, e_2, e_3)) | (~product1(e_4, e_2, e_3)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(325,plain,
% 0.20/0.47 ((equalish(e_1, e_4) | (~product1(e_4, e_2, e_3)) | (~product1(e_1, e_2, e_3))) <=> (equalish(e_1, e_4) | (~product1(e_1, e_2, e_3)) | (~product1(e_4, e_2, e_3)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(326,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_4) | (~product1(e_4, e_2, e_3)) | (~product1(e_1, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_4) | (~product1(e_1, e_2, e_3)) | (~product1(e_4, e_2, e_3))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[325])).
% 0.20/0.47 tff(327,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_4) | (~product1(e_4, e_2, e_3)) | (~product1(e_1, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_1, e_4) | (~product1(e_1, e_2, e_3)) | (~product1(e_4, e_2, e_3)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[326, 324])).
% 0.20/0.47 tff(328,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_4) | (~product1(e_4, e_2, e_3)) | (~product1(e_1, e_2, e_3)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(329,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_1, e_4) | (~product1(e_1, e_2, e_3)) | (~product1(e_4, e_2, e_3))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[328, 327])).
% 0.20/0.47 tff(330,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[329, 51, 22, 323, 109])).
% 0.20/0.47 tff(331,plain,((~product1(e_1, e_2, e_3)) | (~product1(e_4, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(332,plain,
% 0.20/0.47 (~product1(e_1, e_2, e_3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[331, 322])).
% 0.20/0.47 tff(333,plain,
% 0.20/0.47 (product1(e_1, e_2, e_4)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[252, 332])).
% 0.20/0.47 tff(334,plain,
% 0.20/0.47 (~product1(e_4, e_1, e_3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[118, 322])).
% 0.20/0.47 tff(335,plain,
% 0.20/0.47 (product1(e_4, e_1, e_2)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[107, 334, 59])).
% 0.20/0.47 tff(336,assumption,(~product2(e_2, e_2, e_1)), introduced(assumption)).
% 0.20/0.47 tff(337,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_4, e_1, e_2)) | product2(e_2, e_2, e_1) | (~product1(e_1, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_4, e_1, e_2)) | product2(e_2, e_2, e_1) | (~product1(e_1, e_2, e_4)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(338,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_4, e_1, e_2)) | product2(e_2, e_2, e_1) | (~product1(e_1, e_2, e_4)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(339,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_4, e_1, e_2)) | product2(e_2, e_2, e_1) | (~product1(e_1, e_2, e_4))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[338, 337])).
% 0.20/0.47 tff(340,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[339, 166, 336, 61, 220])).
% 0.20/0.47 tff(341,plain,(product2(e_2, e_2, e_1) | (~product1(e_4, e_1, e_2)) | (~product1(e_1, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(342,plain,
% 0.20/0.47 ((~product1(e_4, e_1, e_2)) | (~product1(e_1, e_2, e_4))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[341, 276])).
% 0.20/0.47 tff(343,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[342, 335, 333])).
% 0.20/0.47 % SZS output end Proof
% 0.32/0.47 % E exiting
%------------------------------------------------------------------------------