%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP124-6.004 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 0.19s 0.45s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP124-6.004 : TPTP v9.0.0. Released v1.2.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.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 15:46:03 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.45 % SZS status Unsatisfiable
% 0.19/0.45 % SZS output start Proof
% 0.19/0.45 tff(product1_type, type, (
% 0.19/0.45 product1: ( $i * $i * $i ) > $o)).
% 0.19/0.45 tff(e_2_type, type, (
% 0.19/0.45 e_2: $i)).
% 0.19/0.45 tff(e_1_type, type, (
% 0.19/0.45 e_1: $i)).
% 0.19/0.45 tff(e_4_type, type, (
% 0.19/0.45 e_4: $i)).
% 0.19/0.45 tff(e_3_type, type, (
% 0.19/0.45 e_3: $i)).
% 0.19/0.45 tff(equalish_type, type, (
% 0.19/0.45 equalish: ( $i * $i ) > $o)).
% 0.19/0.45 tff(product2_type, type, (
% 0.19/0.45 product2: ( $i * $i * $i ) > $o)).
% 0.19/0.45 tff(group_element_type, type, (
% 0.19/0.45 group_element: $i > $o)).
% 0.19/0.45 tff(1,assumption,(~product1(e_2, e_2, e_2)), introduced(assumption)).
% 0.19/0.45 tff(2,plain,
% 0.19/0.45 (^[X: $i] : refl(product1(X, X, X) <=> product1(X, X, X))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(3,plain,
% 0.19/0.45 (![X: $i] : product1(X, X, X) <=> ![X: $i] : product1(X, X, X)),
% 0.19/0.45 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.45 tff(4,plain,
% 0.19/0.45 (![X: $i] : product1(X, X, X) <=> ![X: $i] : product1(X, X, X)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(5,axiom,(![X: $i] : product1(X, X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product1_idempotence')).
% 0.19/0.45 tff(6,plain,
% 0.19/0.45 (![X: $i] : product1(X, X, X)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.45 tff(7,plain,(
% 0.19/0.45 ![X: $i] : product1(X, X, X)),
% 0.19/0.45 inference(skolemize,[status(sab)],[6])).
% 0.19/0.45 tff(8,plain,
% 0.19/0.45 (![X: $i] : product1(X, X, X)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.45 tff(9,plain,
% 0.19/0.45 ((~![X: $i] : product1(X, X, X)) | product1(e_2, e_2, e_2)),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(10,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.19/0.45 tff(11,plain,(product1(e_2, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(12,assumption,(product1(e_3, e_1, e_2)), introduced(assumption)).
% 0.19/0.45 tff(13,plain,
% 0.19/0.45 ((~![X: $i] : product1(X, X, X)) | product1(e_4, e_4, e_4)),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(14,plain,
% 0.19/0.45 (product1(e_4, e_4, e_4)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[13, 8])).
% 0.19/0.45 tff(15,assumption,(product1(e_4, e_1, e_4)), introduced(assumption)).
% 0.19/0.45 tff(16,plain,
% 0.19/0.45 (^[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))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(17,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.45 tff(18,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(19,plain,
% 0.19/0.45 (^[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)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(20,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.45 tff(21,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')).
% 0.19/0.45 tff(22,plain,
% 0.19/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.45 tff(23,plain,
% 0.19/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.19/0.45 tff(24,plain,(
% 0.19/0.45 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[23])).
% 0.19/0.45 tff(25,plain,
% 0.19/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.19/0.45 tff(26,plain,
% 0.19/0.45 ((~equalish(e_1, e_4)) <=> (~equalish(e_1, e_4))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(27,axiom,(~equalish(e_1, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_4')).
% 0.19/0.45 tff(28,plain,
% 0.19/0.45 (~equalish(e_1, e_4)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.45 tff(29,plain,
% 0.19/0.45 (((~![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)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(30,plain,
% 0.19/0.45 ((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)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(31,plain,
% 0.19/0.45 (((~![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))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[30])).
% 0.19/0.45 tff(32,plain,
% 0.19/0.45 (((~![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)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[31, 29])).
% 0.19/0.45 tff(33,plain,
% 0.19/0.45 ((~![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)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(34,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_1, e_4) | (~product1(e_4, e_1, e_4)) | (~product1(e_4, e_4, e_4))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.19/0.45 tff(35,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[34, 28, 25, 15, 14])).
% 0.19/0.45 tff(36,plain,(~product1(e_4, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(37,assumption,(product1(e_2, e_1, e_2)), introduced(assumption)).
% 0.19/0.45 tff(38,plain,
% 0.19/0.45 (^[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))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(39,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[38])).
% 0.19/0.45 tff(40,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(41,plain,
% 0.19/0.45 (^[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)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(42,plain,
% 0.19/0.46 (![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)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[41])).
% 0.19/0.46 tff(43,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')).
% 0.19/0.46 tff(44,plain,
% 0.19/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.19/0.46 tff(45,plain,
% 0.19/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.19/0.46 tff(46,plain,(
% 0.19/0.46 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[45])).
% 0.19/0.46 tff(47,plain,
% 0.19/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.19/0.46 tff(48,plain,
% 0.19/0.46 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(49,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.19/0.46 tff(50,plain,
% 0.19/0.46 (~equalish(e_2, e_3)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.46 tff(51,plain,
% 0.19/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_3) | (~product1(e_2, 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_2, e_3) | (~product1(e_2, e_1, e_2)) | (~product1(e_3, e_1, e_2)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(52,plain,
% 0.19/0.46 ((equalish(e_2, e_3) | (~product1(e_3, e_1, e_2)) | (~product1(e_2, e_1, e_2))) <=> (equalish(e_2, e_3) | (~product1(e_2, e_1, e_2)) | (~product1(e_3, e_1, e_2)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(53,plain,
% 0.19/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_3) | (~product1(e_3, e_1, e_2)) | (~product1(e_2, 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_2, e_3) | (~product1(e_2, e_1, e_2)) | (~product1(e_3, e_1, e_2))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[52])).
% 0.19/0.46 tff(54,plain,
% 0.19/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_3) | (~product1(e_3, e_1, e_2)) | (~product1(e_2, 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_2, e_3) | (~product1(e_2, e_1, e_2)) | (~product1(e_3, e_1, e_2)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[53, 51])).
% 0.19/0.46 tff(55,plain,
% 0.19/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_3) | (~product1(e_3, e_1, e_2)) | (~product1(e_2, e_1, e_2)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(56,plain,
% 0.19/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_3) | (~product1(e_2, e_1, e_2)) | (~product1(e_3, e_1, e_2))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.19/0.46 tff(57,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[56, 50, 47, 37, 12])).
% 0.19/0.46 tff(58,plain,((~product1(e_2, e_1, e_2)) | (~product1(e_3, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(59,plain,
% 0.19/0.46 (~product1(e_2, e_1, e_2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[58, 12])).
% 0.19/0.46 tff(60,assumption,(product2(e_1, e_1, e_3)), introduced(assumption)).
% 0.19/0.46 tff(61,plain,
% 0.19/0.46 (^[X: $i] : refl(product2(X, X, X) <=> product2(X, X, X))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(62,plain,
% 0.19/0.46 (![X: $i] : product2(X, X, X) <=> ![X: $i] : product2(X, X, X)),
% 0.19/0.46 inference(quant_intro,[status(thm)],[61])).
% 0.19/0.46 tff(63,plain,
% 0.19/0.46 (![X: $i] : product2(X, X, X) <=> ![X: $i] : product2(X, X, X)),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(64,axiom,(![X: $i] : product2(X, X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product2_idempotence')).
% 0.19/0.46 tff(65,plain,
% 0.19/0.46 (![X: $i] : product2(X, X, X)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.19/0.46 tff(66,plain,(
% 0.19/0.46 ![X: $i] : product2(X, X, X)),
% 0.19/0.46 inference(skolemize,[status(sab)],[65])).
% 0.19/0.46 tff(67,plain,
% 0.19/0.46 (![X: $i] : product2(X, X, X)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.19/0.46 tff(68,plain,
% 0.19/0.46 ((~![X: $i] : product2(X, X, X)) | product2(e_1, e_1, e_1)),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(69,plain,
% 0.19/0.46 (product2(e_1, e_1, e_1)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.19/0.46 tff(70,plain,
% 0.19/0.46 (^[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))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(71,plain,
% 0.19/0.46 (![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)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[70])).
% 0.19/0.46 tff(72,plain,
% 0.19/0.46 (![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)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(73,plain,
% 0.19/0.46 (^[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)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(74,plain,
% 0.19/0.46 (![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)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[73])).
% 0.19/0.46 tff(75,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')).
% 0.19/0.46 tff(76,plain,
% 0.19/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.19/0.46 tff(77,plain,
% 0.19/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.19/0.46 tff(78,plain,(
% 0.19/0.46 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[77])).
% 0.19/0.46 tff(79,plain,
% 0.19/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[78, 71])).
% 0.19/0.46 tff(80,plain,
% 0.19/0.46 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(81,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.19/0.46 tff(82,plain,
% 0.19/0.46 (~equalish(e_3, e_1)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.19/0.46 tff(83,plain,
% 0.19/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | (equalish(e_3, e_1) | (~product2(e_1, e_1, e_1)) | (~product2(e_1, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | equalish(e_3, e_1) | (~product2(e_1, e_1, e_1)) | (~product2(e_1, e_1, e_3)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(84,plain,
% 0.19/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | (equalish(e_3, e_1) | (~product2(e_1, e_1, e_1)) | (~product2(e_1, e_1, e_3)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(85,plain,
% 0.19/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | equalish(e_3, e_1) | (~product2(e_1, e_1, e_1)) | (~product2(e_1, e_1, e_3))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.19/0.46 tff(86,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[85, 82, 79, 69, 60])).
% 0.19/0.46 tff(87,plain,(~product2(e_1, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(88,assumption,(product1(e_2, e_3, e_1)), introduced(assumption)).
% 0.19/0.46 tff(89,plain,
% 0.19/0.46 (^[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))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(90,plain,
% 0.19/0.46 (![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)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[89])).
% 0.19/0.46 tff(91,plain,
% 0.19/0.46 (![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)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(92,plain,
% 0.19/0.46 (^[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))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(93,plain,
% 0.19/0.46 (![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)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[92])).
% 0.19/0.46 tff(94,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')).
% 0.19/0.46 tff(95,plain,
% 0.19/0.46 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.19/0.46 tff(96,plain,
% 0.19/0.46 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.19/0.46 tff(97,plain,(
% 0.19/0.46 ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[96])).
% 0.19/0.46 tff(98,plain,
% 0.19/0.46 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.19/0.46 tff(99,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_2, e_3, e_1)) | (~product1(e_3, e_1, e_2)) | product2(e_1, e_1, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_2, e_3, e_1)) | (~product1(e_3, e_1, e_2)) | product2(e_1, e_1, e_3))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(100,plain,
% 0.19/0.46 (((~product1(e_2, e_3, e_1)) | product2(e_1, e_1, e_3) | (~product1(e_3, e_1, e_2))) <=> ((~product1(e_2, e_3, e_1)) | (~product1(e_3, e_1, e_2)) | product2(e_1, e_1, e_3))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(101,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_2, e_3, e_1)) | product2(e_1, e_1, e_3) | (~product1(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_2, e_3, e_1)) | (~product1(e_3, e_1, e_2)) | product2(e_1, e_1, e_3)))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[100])).
% 0.19/0.47 tff(102,plain,
% 0.19/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_2, e_3, e_1)) | product2(e_1, e_1, e_3) | (~product1(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_2, e_3, e_1)) | (~product1(e_3, e_1, e_2)) | product2(e_1, e_1, e_3))),
% 0.19/0.47 inference(transitivity,[status(thm)],[101, 99])).
% 0.19/0.47 tff(103,plain,
% 0.19/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_2, e_3, e_1)) | product2(e_1, e_1, e_3) | (~product1(e_3, e_1, e_2)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(104,plain,
% 0.19/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_2, e_3, e_1)) | (~product1(e_3, e_1, e_2)) | product2(e_1, e_1, e_3)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.19/0.47 tff(105,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[104, 98, 12, 88, 87])).
% 0.19/0.47 tff(106,plain,((~product1(e_2, e_3, e_1)) | (~product1(e_3, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(107,plain,
% 0.19/0.47 (~product1(e_2, e_3, e_1)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[106, 12])).
% 0.19/0.47 tff(108,assumption,(product1(e_2, e_3, e_2)), introduced(assumption)).
% 0.19/0.47 tff(109,plain,
% 0.19/0.47 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(110,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.19/0.47 tff(111,plain,
% 0.19/0.47 (~equalish(e_3, e_2)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.19/0.47 tff(112,plain,
% 0.19/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_3, e_2) | (~product1(e_2, e_3, e_2)) | (~product1(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_3, e_2) | (~product1(e_2, e_3, e_2)) | (~product1(e_2, e_2, e_2)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(113,plain,
% 0.19/0.47 ((equalish(e_3, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_2, e_3, e_2))) <=> (equalish(e_3, e_2) | (~product1(e_2, e_3, e_2)) | (~product1(e_2, e_2, e_2)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(114,plain,
% 0.19/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_3, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_2, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_3, e_2) | (~product1(e_2, e_3, e_2)) | (~product1(e_2, e_2, e_2))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[113])).
% 0.19/0.47 tff(115,plain,
% 0.19/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_3, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_2, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_3, e_2) | (~product1(e_2, e_3, e_2)) | (~product1(e_2, e_2, e_2)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[114, 112])).
% 0.19/0.47 tff(116,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_3, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_2, e_3, e_2)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(117,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_3, e_2) | (~product1(e_2, e_3, e_2)) | (~product1(e_2, e_2, e_2))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.19/0.47 tff(118,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[117, 111, 25, 108, 11])).
% 0.19/0.47 tff(119,plain,(~product1(e_2, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(120,assumption,(product1(e_2, e_3, e_3)), introduced(assumption)).
% 0.19/0.47 tff(121,plain,
% 0.19/0.47 ((~![X: $i] : product1(X, X, X)) | product1(e_3, e_3, e_3)),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(122,plain,
% 0.19/0.47 (product1(e_3, e_3, e_3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[121, 8])).
% 0.19/0.47 tff(123,plain,
% 0.19/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_2, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_2, e_3, e_3)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(124,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_2, e_3, e_3)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(125,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_2, e_3, e_3))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.19/0.47 tff(126,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[125, 50, 47, 122, 120])).
% 0.19/0.47 tff(127,plain,(~product1(e_2, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(128,plain,
% 0.19/0.47 (^[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))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(129,plain,
% 0.19/0.47 (![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))) <=> ![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)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[128])).
% 0.19/0.47 tff(130,plain,
% 0.19/0.47 (![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))) <=> ![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)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(131,plain,
% 0.19/0.47 (^[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)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(132,plain,
% 0.19/0.47 (![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)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[131])).
% 0.19/0.47 tff(133,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')).
% 0.19/0.47 tff(134,plain,
% 0.19/0.47 (![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)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.19/0.47 tff(135,plain,
% 0.19/0.47 (![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)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[134, 130])).
% 0.19/0.47 tff(136,plain,(
% 0.19/0.47 ![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)))),
% 0.19/0.47 inference(skolemize,[status(sab)],[135])).
% 0.19/0.47 tff(137,plain,
% 0.19/0.47 (![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)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[136, 129])).
% 0.19/0.47 tff(138,plain,
% 0.19/0.47 (group_element(e_3) <=> group_element(e_3)),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(139,axiom,(group_element(e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_3')).
% 0.19/0.47 tff(140,plain,
% 0.19/0.47 (group_element(e_3)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.19/0.47 tff(141,plain,
% 0.19/0.47 (group_element(e_2) <=> group_element(e_2)),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(142,axiom,(group_element(e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_2')).
% 0.19/0.47 tff(143,plain,
% 0.19/0.47 (group_element(e_2)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.19/0.47 tff(144,plain,
% 0.19/0.47 (((~![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)))) | ((~group_element(e_2)) | (~group_element(e_3)) | product1(e_2, e_3, e_1) | product1(e_2, e_3, e_4) | product1(e_2, e_3, e_3) | product1(e_2, e_3, 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_3)) | product1(e_2, e_3, e_1) | product1(e_2, e_3, e_4) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_2))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(145,plain,
% 0.19/0.47 ((product1(e_2, e_3, e_4) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_2))) <=> ((~group_element(e_2)) | (~group_element(e_3)) | product1(e_2, e_3, e_1) | product1(e_2, e_3, e_4) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_2))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(146,plain,
% 0.19/0.47 (((~![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_2, e_3, e_4) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_1) | (~group_element(e_3)) | (~group_element(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_3)) | product1(e_2, e_3, e_1) | product1(e_2, e_3, e_4) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_2)))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[145])).
% 0.19/0.48 tff(147,plain,
% 0.19/0.48 (((~![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_2, e_3, e_4) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_1) | (~group_element(e_3)) | (~group_element(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_3)) | product1(e_2, e_3, e_1) | product1(e_2, e_3, e_4) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_2))),
% 0.19/0.48 inference(transitivity,[status(thm)],[146, 144])).
% 0.19/0.48 tff(148,plain,
% 0.19/0.48 ((~![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_2, e_3, e_4) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_2)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(149,plain,
% 0.19/0.48 ((~![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_3)) | product1(e_2, e_3, e_1) | product1(e_2, e_3, e_4) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_2)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.19/0.48 tff(150,plain,
% 0.19/0.48 (product1(e_2, e_3, e_1) | product1(e_2, e_3, e_4) | product1(e_2, e_3, e_2)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[149, 143, 140, 137, 127])).
% 0.19/0.48 tff(151,plain,
% 0.19/0.48 (product1(e_2, e_3, e_1) | product1(e_2, e_3, e_4)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[150, 119])).
% 0.19/0.48 tff(152,plain,
% 0.19/0.48 (product1(e_2, e_3, e_4)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[151, 107])).
% 0.19/0.48 tff(153,assumption,(product1(e_2, e_3, e_4)), introduced(assumption)).
% 0.19/0.48 tff(154,assumption,(product1(e_2, e_1, e_4)), introduced(assumption)).
% 0.19/0.48 tff(155,plain,
% 0.19/0.48 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(156,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.19/0.48 tff(157,plain,
% 0.19/0.48 (~equalish(e_1, e_3)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.19/0.48 tff(158,plain,
% 0.19/0.48 (((~![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_2, e_1, e_4)) | (~product1(e_2, e_3, 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_3) | (~product1(e_2, e_1, e_4)) | (~product1(e_2, e_3, e_4)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(159,plain,
% 0.19/0.48 ((equalish(e_1, e_3) | (~product1(e_2, e_3, e_4)) | (~product1(e_2, e_1, e_4))) <=> (equalish(e_1, e_3) | (~product1(e_2, e_1, e_4)) | (~product1(e_2, e_3, e_4)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(160,plain,
% 0.19/0.48 (((~![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_2, e_3, e_4)) | (~product1(e_2, 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_3) | (~product1(e_2, e_1, e_4)) | (~product1(e_2, e_3, e_4))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[159])).
% 0.19/0.48 tff(161,plain,
% 0.19/0.48 (((~![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_2, e_3, e_4)) | (~product1(e_2, 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_3) | (~product1(e_2, e_1, e_4)) | (~product1(e_2, e_3, e_4)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[160, 158])).
% 0.19/0.48 tff(162,plain,
% 0.19/0.48 ((~![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_2, e_3, e_4)) | (~product1(e_2, e_1, e_4)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(163,plain,
% 0.19/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_1, e_3) | (~product1(e_2, e_1, e_4)) | (~product1(e_2, e_3, e_4))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.19/0.48 tff(164,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[163, 157, 25, 154, 153])).
% 0.19/0.48 tff(165,plain,((~product1(e_2, e_1, e_4)) | (~product1(e_2, e_3, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(166,plain,
% 0.19/0.48 (~product1(e_2, e_1, e_4)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[165, 152])).
% 0.19/0.48 tff(167,assumption,(~product1(e_1, e_1, e_1)), introduced(assumption)).
% 0.19/0.48 tff(168,plain,
% 0.19/0.48 ((~![X: $i] : product1(X, X, X)) | product1(e_1, e_1, e_1)),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(169,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[168, 8, 167])).
% 0.19/0.48 tff(170,plain,(product1(e_1, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(171,assumption,(product1(e_2, e_1, e_1)), introduced(assumption)).
% 0.19/0.48 tff(172,plain,
% 0.19/0.48 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(173,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.19/0.48 tff(174,plain,
% 0.19/0.48 (~equalish(e_2, e_1)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.19/0.48 tff(175,plain,
% 0.19/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_2, 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_2, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_2, e_1, e_1)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(176,plain,
% 0.19/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_2, e_1, e_1)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(177,plain,
% 0.19/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_2, e_1, e_1))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.19/0.48 tff(178,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[177, 174, 47, 171, 170])).
% 0.19/0.48 tff(179,plain,(~product1(e_2, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(180,plain,
% 0.19/0.48 (group_element(e_1) <=> group_element(e_1)),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(181,axiom,(group_element(e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_1')).
% 0.19/0.48 tff(182,plain,
% 0.19/0.48 (group_element(e_1)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.19/0.48 tff(183,plain,
% 0.19/0.48 (((~![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_2, e_1, e_2) | product1(e_2, e_1, e_4) | product1(e_2, e_1, e_3) | product1(e_2, 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)))) | (~group_element(e_2)) | (~group_element(e_1)) | product1(e_2, e_1, e_2) | product1(e_2, e_1, e_4) | product1(e_2, e_1, e_3) | product1(e_2, e_1, e_1))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(184,plain,
% 0.19/0.48 ((product1(e_2, e_1, e_4) | product1(e_2, e_1, e_3) | product1(e_2, e_1, e_2) | product1(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2))) <=> ((~group_element(e_2)) | (~group_element(e_1)) | product1(e_2, e_1, e_2) | product1(e_2, e_1, e_4) | product1(e_2, e_1, e_3) | product1(e_2, e_1, e_1))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(185,plain,
% 0.19/0.48 (((~![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_2, e_1, e_4) | product1(e_2, e_1, e_3) | product1(e_2, e_1, e_2) | product1(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(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_2, e_1, e_2) | product1(e_2, e_1, e_4) | product1(e_2, e_1, e_3) | product1(e_2, e_1, e_1)))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[184])).
% 0.19/0.48 tff(186,plain,
% 0.19/0.48 (((~![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_2, e_1, e_4) | product1(e_2, e_1, e_3) | product1(e_2, e_1, e_2) | product1(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(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_2, e_1, e_2) | product1(e_2, e_1, e_4) | product1(e_2, e_1, e_3) | product1(e_2, e_1, e_1))),
% 0.19/0.48 inference(transitivity,[status(thm)],[185, 183])).
% 0.19/0.48 tff(187,plain,
% 0.19/0.48 ((~![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_2, e_1, e_4) | product1(e_2, e_1, e_3) | product1(e_2, e_1, e_2) | product1(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(188,plain,
% 0.19/0.48 ((~![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_2, e_1, e_2) | product1(e_2, e_1, e_4) | product1(e_2, e_1, e_3) | product1(e_2, e_1, e_1)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.19/0.48 tff(189,plain,
% 0.19/0.48 (product1(e_2, e_1, e_2) | product1(e_2, e_1, e_4) | product1(e_2, e_1, e_3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[188, 182, 143, 137, 179])).
% 0.19/0.48 tff(190,plain,
% 0.19/0.48 (product1(e_2, e_1, e_3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[189, 166, 59])).
% 0.19/0.48 tff(191,assumption,(product1(e_2, e_1, e_3)), introduced(assumption)).
% 0.19/0.48 tff(192,assumption,(product1(e_4, e_1, e_3)), introduced(assumption)).
% 0.19/0.48 tff(193,plain,
% 0.19/0.48 ((~equalish(e_4, e_2)) <=> (~equalish(e_4, e_2))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(194,axiom,(~equalish(e_4, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_2')).
% 0.19/0.48 tff(195,plain,
% 0.19/0.48 (~equalish(e_4, e_2)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.19/0.48 tff(196,plain,
% 0.19/0.48 (((~![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_4, e_1, e_3)) | (~product1(e_2, e_1, e_3)))) <=> ((~![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_4, e_1, e_3)) | (~product1(e_2, e_1, e_3)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(197,plain,
% 0.19/0.48 ((equalish(e_4, e_2) | (~product1(e_2, e_1, e_3)) | (~product1(e_4, e_1, e_3))) <=> (equalish(e_4, e_2) | (~product1(e_4, e_1, e_3)) | (~product1(e_2, e_1, e_3)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(198,plain,
% 0.19/0.48 (((~![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_1, e_3)) | (~product1(e_4, e_1, e_3)))) <=> ((~![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_4, e_1, e_3)) | (~product1(e_2, e_1, e_3))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[197])).
% 0.19/0.49 tff(199,plain,
% 0.19/0.49 (((~![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_1, e_3)) | (~product1(e_4, e_1, e_3)))) <=> ((~![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_4, e_1, e_3)) | (~product1(e_2, e_1, e_3)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[198, 196])).
% 0.19/0.49 tff(200,plain,
% 0.19/0.49 ((~![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_1, e_3)) | (~product1(e_4, e_1, e_3)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(201,plain,
% 0.19/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_4, e_2) | (~product1(e_4, e_1, e_3)) | (~product1(e_2, e_1, e_3))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.19/0.49 tff(202,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[201, 195, 47, 192, 191])).
% 0.19/0.49 tff(203,plain,((~product1(e_4, e_1, e_3)) | (~product1(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(204,plain,
% 0.19/0.49 (~product1(e_4, e_1, e_3)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[203, 190])).
% 0.19/0.49 tff(205,assumption,(product1(e_4, e_1, e_1)), introduced(assumption)).
% 0.19/0.49 tff(206,plain,
% 0.19/0.49 ((~equalish(e_4, e_1)) <=> (~equalish(e_4, e_1))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(207,axiom,(~equalish(e_4, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_1')).
% 0.19/0.49 tff(208,plain,
% 0.19/0.49 (~equalish(e_4, e_1)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.19/0.49 tff(209,plain,
% 0.19/0.49 (((~![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)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(210,plain,
% 0.19/0.49 ((~![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)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(211,plain,
% 0.19/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_4, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_4, e_1, e_1))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.19/0.49 tff(212,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[211, 208, 47, 170, 205])).
% 0.19/0.49 tff(213,plain,(~product1(e_4, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(214,plain,
% 0.19/0.49 (group_element(e_4) <=> group_element(e_4)),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(215,axiom,(group_element(e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_4')).
% 0.19/0.49 tff(216,plain,
% 0.19/0.49 (group_element(e_4)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.19/0.49 tff(217,plain,
% 0.19/0.49 (((~![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_1)) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_4) | product1(e_4, e_1, e_1) | product1(e_4, e_1, 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_1)) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_4) | product1(e_4, e_1, e_1) | product1(e_4, e_1, e_3))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(218,plain,
% 0.19/0.49 ((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))) <=> ((~group_element(e_4)) | (~group_element(e_1)) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_4) | product1(e_4, e_1, e_1) | product1(e_4, e_1, e_3))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(219,plain,
% 0.19/0.49 (((~![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)))) | ((~group_element(e_4)) | (~group_element(e_1)) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_4) | product1(e_4, e_1, e_1) | product1(e_4, e_1, e_3)))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[218])).
% 0.19/0.49 tff(220,plain,
% 0.19/0.49 (((~![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)))) | (~group_element(e_4)) | (~group_element(e_1)) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_4) | product1(e_4, e_1, e_1) | product1(e_4, e_1, e_3))),
% 0.19/0.49 inference(transitivity,[status(thm)],[219, 217])).
% 0.19/0.49 tff(221,plain,
% 0.19/0.49 ((~![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)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(222,plain,
% 0.19/0.49 ((~![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_1)) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_4) | product1(e_4, e_1, e_1) | product1(e_4, e_1, e_3)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.19/0.49 tff(223,plain,
% 0.19/0.49 (product1(e_4, e_1, e_2) | product1(e_4, e_1, e_4) | product1(e_4, e_1, e_1) | product1(e_4, e_1, e_3)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[222, 182, 216, 137])).
% 0.19/0.49 tff(224,plain,
% 0.19/0.49 (product1(e_4, e_1, e_2) | product1(e_4, e_1, e_4) | product1(e_4, e_1, e_3)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[223, 213])).
% 0.19/0.49 tff(225,plain,
% 0.19/0.49 (product1(e_4, e_1, e_2)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[224, 204, 36])).
% 0.19/0.49 tff(226,plain,
% 0.19/0.49 ((~equalish(e_3, e_4)) <=> (~equalish(e_3, e_4))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(227,axiom,(~equalish(e_3, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_4')).
% 0.19/0.49 tff(228,plain,
% 0.19/0.49 (~equalish(e_3, e_4)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.19/0.49 tff(229,plain,
% 0.19/0.49 (((~![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_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_3, e_4) | (~product1(e_4, e_1, e_2)) | (~product1(e_3, e_1, e_2)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(230,plain,
% 0.19/0.49 ((~![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_1, e_2)) | (~product1(e_3, e_1, e_2)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(231,plain,
% 0.19/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_3, e_4) | (~product1(e_4, e_1, e_2)) | (~product1(e_3, e_1, e_2))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.19/0.49 tff(232,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[231, 228, 47, 225, 12])).
% 0.19/0.49 tff(233,plain,(~product1(e_3, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(234,assumption,(product1(e_3, e_1, e_1)), introduced(assumption)).
% 0.19/0.49 tff(235,plain,
% 0.19/0.49 (((~![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_3, e_1, e_1)) | (~product1(e_1, 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_3, e_1, e_1)) | (~product1(e_1, e_1, e_1)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(236,plain,
% 0.19/0.49 ((equalish(e_3, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_3, e_1, e_1))) <=> (equalish(e_3, e_1) | (~product1(e_3, e_1, e_1)) | (~product1(e_1, e_1, e_1)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(237,plain,
% 0.19/0.49 (((~![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_3, e_1, e_1)) | (~product1(e_1, e_1, e_1))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[236])).
% 0.19/0.49 tff(238,plain,
% 0.19/0.49 (((~![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_3, e_1, e_1)) | (~product1(e_1, e_1, e_1)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[237, 235])).
% 0.19/0.49 tff(239,plain,
% 0.19/0.49 ((~![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)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(240,plain,
% 0.19/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_3, e_1) | (~product1(e_3, e_1, e_1)) | (~product1(e_1, e_1, e_1))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.19/0.49 tff(241,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[240, 82, 47, 170, 234])).
% 0.19/0.49 tff(242,plain,(~product1(e_3, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(243,assumption,(product1(e_3, e_1, e_3)), introduced(assumption)).
% 0.19/0.49 tff(244,plain,
% 0.19/0.49 (((~![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_3, e_3)) | (~product1(e_3, e_1, e_3)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(245,plain,
% 0.19/0.49 ((~![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)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(246,plain,
% 0.19/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_1, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_3, e_1, e_3))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.19/0.49 tff(247,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[246, 157, 25, 122, 243])).
% 0.19/0.49 tff(248,plain,(~product1(e_3, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(249,plain,
% 0.19/0.49 (((~![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_1)) | (~group_element(e_3)) | product1(e_3, e_1, e_4) | product1(e_3, e_1, e_1) | product1(e_3, e_1, e_3) | product1(e_3, e_1, 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_1)) | (~group_element(e_3)) | product1(e_3, e_1, e_4) | product1(e_3, e_1, e_1) | product1(e_3, e_1, e_3) | product1(e_3, e_1, e_2))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(250,plain,
% 0.19/0.50 ((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))) <=> ((~group_element(e_1)) | (~group_element(e_3)) | product1(e_3, e_1, e_4) | product1(e_3, e_1, e_1) | product1(e_3, e_1, e_3) | product1(e_3, e_1, e_2))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(251,plain,
% 0.19/0.50 (((~![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)))) | ((~group_element(e_1)) | (~group_element(e_3)) | product1(e_3, e_1, e_4) | product1(e_3, e_1, e_1) | product1(e_3, e_1, e_3) | product1(e_3, e_1, e_2)))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[250])).
% 0.19/0.50 tff(252,plain,
% 0.19/0.50 (((~![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)))) | (~group_element(e_1)) | (~group_element(e_3)) | product1(e_3, e_1, e_4) | product1(e_3, e_1, e_1) | product1(e_3, e_1, e_3) | product1(e_3, e_1, e_2))),
% 0.19/0.50 inference(transitivity,[status(thm)],[251, 249])).
% 0.19/0.50 tff(253,plain,
% 0.19/0.50 ((~![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)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(254,plain,
% 0.19/0.50 ((~![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_1)) | (~group_element(e_3)) | product1(e_3, e_1, e_4) | product1(e_3, e_1, e_1) | product1(e_3, e_1, e_3) | product1(e_3, e_1, e_2)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[253, 252])).
% 0.19/0.50 tff(255,plain,
% 0.19/0.50 (product1(e_3, e_1, e_4) | product1(e_3, e_1, e_1) | product1(e_3, e_1, e_2)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[254, 182, 140, 137, 248])).
% 0.19/0.50 tff(256,plain,
% 0.19/0.50 (product1(e_3, e_1, e_4) | product1(e_3, e_1, e_2)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[255, 242])).
% 0.19/0.50 tff(257,plain,
% 0.19/0.50 (product1(e_3, e_1, e_4)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[256, 233])).
% 0.19/0.50 tff(258,assumption,(product1(e_3, e_1, e_4)), introduced(assumption)).
% 0.19/0.50 tff(259,plain,
% 0.19/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_3) | (~product1(e_2, e_1, e_4)) | (~product1(e_3, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_3) | (~product1(e_2, e_1, e_4)) | (~product1(e_3, e_1, e_4)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(260,plain,
% 0.19/0.50 ((equalish(e_2, e_3) | (~product1(e_3, e_1, e_4)) | (~product1(e_2, e_1, e_4))) <=> (equalish(e_2, e_3) | (~product1(e_2, e_1, e_4)) | (~product1(e_3, e_1, e_4)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(261,plain,
% 0.19/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_3) | (~product1(e_3, e_1, e_4)) | (~product1(e_2, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_3) | (~product1(e_2, e_1, e_4)) | (~product1(e_3, e_1, e_4))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[260])).
% 0.19/0.50 tff(262,plain,
% 0.19/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_3) | (~product1(e_3, e_1, e_4)) | (~product1(e_2, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_3) | (~product1(e_2, e_1, e_4)) | (~product1(e_3, e_1, e_4)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[261, 259])).
% 0.19/0.50 tff(263,plain,
% 0.19/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_3) | (~product1(e_3, e_1, e_4)) | (~product1(e_2, e_1, e_4)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(264,plain,
% 0.19/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_3) | (~product1(e_2, e_1, e_4)) | (~product1(e_3, e_1, e_4))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.19/0.50 tff(265,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[264, 50, 47, 154, 258])).
% 0.19/0.50 tff(266,plain,((~product1(e_2, e_1, e_4)) | (~product1(e_3, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(267,plain,
% 0.19/0.50 (~product1(e_2, e_1, e_4)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[266, 257])).
% 0.19/0.50 tff(268,assumption,(product1(e_4, e_3, e_4)), introduced(assumption)).
% 0.19/0.50 tff(269,plain,
% 0.19/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_3, e_4) | (~product1(e_4, e_3, 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_3, e_4) | (~product1(e_4, e_3, e_4)) | (~product1(e_4, e_4, e_4)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(270,plain,
% 0.19/0.50 ((equalish(e_3, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_4, e_3, e_4))) <=> (equalish(e_3, e_4) | (~product1(e_4, e_3, e_4)) | (~product1(e_4, e_4, e_4)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(271,plain,
% 0.19/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_3, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_4, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_3, e_4) | (~product1(e_4, e_3, e_4)) | (~product1(e_4, e_4, e_4))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[270])).
% 0.19/0.50 tff(272,plain,
% 0.19/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_3, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_4, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_3, e_4) | (~product1(e_4, e_3, e_4)) | (~product1(e_4, e_4, e_4)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[271, 269])).
% 0.19/0.50 tff(273,plain,
% 0.19/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_3, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_4, e_3, e_4)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(274,plain,
% 0.19/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_3, e_4) | (~product1(e_4, e_3, e_4)) | (~product1(e_4, e_4, e_4))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.19/0.50 tff(275,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[274, 228, 25, 268, 14])).
% 0.19/0.50 tff(276,plain,(~product1(e_4, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(277,assumption,(~product2(e_1, e_1, e_3)), introduced(assumption)).
% 0.19/0.50 tff(278,assumption,(product1(e_4, e_3, e_1)), introduced(assumption)).
% 0.19/0.50 tff(279,plain,
% 0.19/0.50 (((~![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_4)) | (~product1(e_4, e_3, e_1)) | product2(e_1, e_1, e_3))) <=> ((~![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_4)) | (~product1(e_4, e_3, e_1)) | product2(e_1, e_1, e_3))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(280,plain,
% 0.19/0.50 (((~product1(e_4, e_3, e_1)) | product2(e_1, e_1, e_3) | (~product1(e_3, e_1, e_4))) <=> ((~product1(e_3, e_1, e_4)) | (~product1(e_4, e_3, e_1)) | product2(e_1, e_1, e_3))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(281,plain,
% 0.19/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_4, e_3, e_1)) | product2(e_1, e_1, e_3) | (~product1(e_3, e_1, e_4)))) <=> ((~![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_4)) | (~product1(e_4, e_3, e_1)) | product2(e_1, e_1, e_3)))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[280])).
% 0.19/0.50 tff(282,plain,
% 0.19/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_4, e_3, e_1)) | product2(e_1, e_1, e_3) | (~product1(e_3, e_1, e_4)))) <=> ((~![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_4)) | (~product1(e_4, e_3, e_1)) | product2(e_1, e_1, e_3))),
% 0.19/0.50 inference(transitivity,[status(thm)],[281, 279])).
% 0.19/0.50 tff(283,plain,
% 0.19/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_4, e_3, e_1)) | product2(e_1, e_1, e_3) | (~product1(e_3, e_1, e_4)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(284,plain,
% 0.19/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_3, e_1, e_4)) | (~product1(e_4, e_3, e_1)) | product2(e_1, e_1, e_3)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[283, 282])).
% 0.19/0.50 tff(285,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[284, 98, 258, 278, 277])).
% 0.19/0.50 tff(286,plain,(product2(e_1, e_1, e_3) | (~product1(e_3, e_1, e_4)) | (~product1(e_4, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(287,plain,
% 0.19/0.50 ((~product1(e_3, e_1, e_4)) | (~product1(e_4, e_3, e_1))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[286, 87])).
% 0.19/0.50 tff(288,plain,
% 0.19/0.50 (~product1(e_4, e_3, e_1)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[287, 257])).
% 0.19/0.50 tff(289,assumption,(product1(e_4, e_3, e_3)), introduced(assumption)).
% 0.19/0.50 tff(290,plain,
% 0.19/0.50 ((~equalish(e_4, e_3)) <=> (~equalish(e_4, e_3))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(291,axiom,(~equalish(e_4, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_3')).
% 0.19/0.50 tff(292,plain,
% 0.19/0.50 (~equalish(e_4, e_3)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.19/0.50 tff(293,plain,
% 0.19/0.50 (((~![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_3, e_3)) | (~product1(e_4, e_3, e_3)))) <=> ((~![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_3, e_3)) | (~product1(e_4, e_3, e_3)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(294,plain,
% 0.19/0.50 ((~![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_3, e_3)) | (~product1(e_4, e_3, e_3)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(295,plain,
% 0.19/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_4, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_4, e_3, e_3))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[294, 293])).
% 0.19/0.50 tff(296,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[295, 292, 47, 122, 289])).
% 0.19/0.50 tff(297,plain,(~product1(e_4, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(298,plain,
% 0.19/0.50 (((~![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_3)) | product1(e_4, e_3, e_1) | product1(e_4, e_3, e_4) | product1(e_4, e_3, e_3) | product1(e_4, e_3, 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_4)) | (~group_element(e_3)) | product1(e_4, e_3, e_1) | product1(e_4, e_3, e_4) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_2))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(299,plain,
% 0.19/0.50 ((product1(e_4, e_3, e_4) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_2) | product1(e_4, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_4))) <=> ((~group_element(e_4)) | (~group_element(e_3)) | product1(e_4, e_3, e_1) | product1(e_4, e_3, e_4) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_2))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(300,plain,
% 0.19/0.50 (((~![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_3, e_4) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_2) | product1(e_4, e_3, e_1) | (~group_element(e_3)) | (~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_3)) | product1(e_4, e_3, e_1) | product1(e_4, e_3, e_4) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_2)))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[299])).
% 0.19/0.50 tff(301,plain,
% 0.19/0.50 (((~![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_3, e_4) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_2) | product1(e_4, e_3, e_1) | (~group_element(e_3)) | (~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_3)) | product1(e_4, e_3, e_1) | product1(e_4, e_3, e_4) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_2))),
% 0.19/0.50 inference(transitivity,[status(thm)],[300, 298])).
% 0.19/0.50 tff(302,plain,
% 0.19/0.50 ((~![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_3, e_4) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_2) | product1(e_4, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_4)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(303,plain,
% 0.19/0.50 ((~![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_3)) | product1(e_4, e_3, e_1) | product1(e_4, e_3, e_4) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_2)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[302, 301])).
% 0.19/0.50 tff(304,plain,
% 0.19/0.50 (product1(e_4, e_3, e_1) | product1(e_4, e_3, e_4) | product1(e_4, e_3, e_2)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[303, 140, 216, 137, 297])).
% 0.19/0.50 tff(305,plain,
% 0.19/0.50 (product1(e_4, e_3, e_2)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[304, 288, 276])).
% 0.19/0.50 tff(306,assumption,(product1(e_4, e_3, e_2)), introduced(assumption)).
% 0.19/0.50 tff(307,assumption,(product1(e_4, e_1, e_2)), introduced(assumption)).
% 0.19/0.50 tff(308,plain,
% 0.19/0.50 (((~![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_4, e_1, e_2)) | (~product1(e_4, e_3, e_2)))) <=> ((~![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_4, e_1, e_2)) | (~product1(e_4, e_3, e_2)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(309,plain,
% 0.19/0.50 ((equalish(e_1, e_3) | (~product1(e_4, e_3, e_2)) | (~product1(e_4, e_1, e_2))) <=> (equalish(e_1, e_3) | (~product1(e_4, e_1, e_2)) | (~product1(e_4, e_3, e_2)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(310,plain,
% 0.19/0.50 (((~![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_4, e_3, e_2)) | (~product1(e_4, e_1, e_2)))) <=> ((~![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_4, e_1, e_2)) | (~product1(e_4, e_3, e_2))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[309])).
% 0.19/0.50 tff(311,plain,
% 0.19/0.50 (((~![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_4, e_3, e_2)) | (~product1(e_4, e_1, e_2)))) <=> ((~![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_4, e_1, e_2)) | (~product1(e_4, e_3, e_2)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[310, 308])).
% 0.19/0.50 tff(312,plain,
% 0.19/0.50 ((~![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_4, e_3, e_2)) | (~product1(e_4, e_1, e_2)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(313,plain,
% 0.19/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_1, e_3) | (~product1(e_4, e_1, e_2)) | (~product1(e_4, e_3, e_2))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.19/0.50 tff(314,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[313, 157, 25, 307, 306])).
% 0.19/0.50 tff(315,plain,((~product1(e_4, e_1, e_2)) | (~product1(e_4, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(316,plain,
% 0.19/0.50 (~product1(e_4, e_1, e_2)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[315, 305])).
% 0.19/0.50 tff(317,plain,
% 0.19/0.50 (product1(e_4, e_1, e_3)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[224, 316, 36])).
% 0.19/0.50 tff(318,plain,
% 0.19/0.50 (~product1(e_2, e_1, e_3)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[203, 317])).
% 0.19/0.50 tff(319,plain,
% 0.19/0.50 (product1(e_2, e_1, e_2)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[189, 318, 267])).
% 0.19/0.50 tff(320,plain,
% 0.19/0.50 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(321,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.19/0.50 tff(322,plain,
% 0.19/0.50 (~equalish(e_1, e_2)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[321, 320])).
% 0.19/0.50 tff(323,plain,
% 0.19/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_1, e_2) | (~product1(e_2, e_1, e_2)) | (~product1(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_1, e_2) | (~product1(e_2, e_1, e_2)) | (~product1(e_2, e_2, e_2)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(324,plain,
% 0.19/0.50 ((equalish(e_1, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_2, e_1, e_2))) <=> (equalish(e_1, e_2) | (~product1(e_2, e_1, e_2)) | (~product1(e_2, e_2, e_2)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(325,plain,
% 0.19/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_1, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_2, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_1, e_2) | (~product1(e_2, e_1, e_2)) | (~product1(e_2, e_2, e_2))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[324])).
% 0.19/0.50 tff(326,plain,
% 0.19/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_1, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_2, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_1, e_2) | (~product1(e_2, e_1, e_2)) | (~product1(e_2, e_2, e_2)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[325, 323])).
% 0.19/0.50 tff(327,plain,
% 0.19/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_1, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_2, e_1, e_2)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(328,plain,
% 0.19/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_1, e_2) | (~product1(e_2, e_1, e_2)) | (~product1(e_2, e_2, e_2))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[327, 326])).
% 0.19/0.51 tff(329,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[328, 322, 25, 319, 11])).
% 0.19/0.51 % SZS output end Proof
% 0.19/0.51 % E exiting
%------------------------------------------------------------------------------