%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP126-4.004 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:07:07 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP126-4.004 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.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 15:44:41 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.41 % SZS status Unsatisfiable
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(product_type, type, (
% 0.19/0.41 product: ( $i * $i * $i ) > $o)).
% 0.19/0.41 tff(e_3_type, type, (
% 0.19/0.41 e_3: $i)).
% 0.19/0.41 tff(e_2_type, type, (
% 0.19/0.41 e_2: $i)).
% 0.19/0.41 tff(e_4_type, type, (
% 0.19/0.41 e_4: $i)).
% 0.19/0.41 tff(e_1_type, type, (
% 0.19/0.41 e_1: $i)).
% 0.19/0.41 tff(equalish_type, type, (
% 0.19/0.41 equalish: ( $i * $i ) > $o)).
% 0.19/0.41 tff(group_element_type, type, (
% 0.19/0.41 group_element: $i > $o)).
% 0.19/0.41 tff(1,assumption,(~product(e_3, e_3, e_3)), introduced(assumption)).
% 0.19/0.41 tff(2,plain,
% 0.19/0.41 (^[X: $i] : refl(product(X, X, X) <=> product(X, X, X))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(3,plain,
% 0.19/0.41 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.19/0.41 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.41 tff(4,plain,
% 0.19/0.41 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(5,axiom,(![X: $i] : product(X, X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_idempotence')).
% 0.19/0.41 tff(6,plain,
% 0.19/0.41 (![X: $i] : product(X, X, X)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.41 tff(7,plain,(
% 0.19/0.41 ![X: $i] : product(X, X, X)),
% 0.19/0.41 inference(skolemize,[status(sab)],[6])).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 (![X: $i] : product(X, X, X)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.41 tff(9,plain,
% 0.19/0.41 ((~![X: $i] : product(X, X, X)) | product(e_3, e_3, e_3)),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.19/0.41 tff(11,plain,(product(e_3, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(12,assumption,(~product(e_3, e_3, e_2)), introduced(assumption)).
% 0.19/0.41 tff(13,assumption,(product(e_1, e_1, e_3)), introduced(assumption)).
% 0.19/0.41 tff(14,assumption,(product(e_1, e_3, e_3)), introduced(assumption)).
% 0.19/0.41 tff(15,plain,
% 0.19/0.41 (^[W: $i, Z: $i, Y: $i, X: $i] : refl(((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X))) <=> ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(W, Y, X)) | (~product(Z, Y, X))) <=> ((~product(W, Y, X)) | (~product(Z, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)))), rewrite((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[18])).
% 0.19/0.41 tff(20,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_left_cancellation')).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.19/0.41 tff(22,plain,
% 0.19/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.19/0.41 tff(23,plain,(
% 0.19/0.41 ![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[22])).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(26,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 (~equalish(e_3, e_1)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | (equalish(e_3, e_1) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | equalish(e_3, e_1) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 (((~product(e_3, e_3, e_3)) | equalish(e_3, e_1) | (~product(e_1, e_3, e_3))) <=> (equalish(e_3, e_1) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | ((~product(e_3, e_3, e_3)) | equalish(e_3, e_1) | (~product(e_1, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | (equalish(e_3, e_1) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[29])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | ((~product(e_3, e_3, e_3)) | equalish(e_3, e_1) | (~product(e_1, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | equalish(e_3, e_1) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[30, 28])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | ((~product(e_3, e_3, e_3)) | equalish(e_3, e_1) | (~product(e_1, e_3, e_3)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | equalish(e_3, e_1) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[33, 27, 24, 11, 14])).
% 0.19/0.41 tff(35,plain,(~product(e_1, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl(((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))) <=> ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[36])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : rewrite((((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, Y)) <=> ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, Y)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[39])).
% 0.19/0.41 tff(41,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qg4')).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.19/0.42 tff(43,plain,
% 0.19/0.42 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.19/0.42 tff(44,plain,(
% 0.19/0.42 ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[43])).
% 0.19/0.42 tff(45,plain,
% 0.19/0.42 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.19/0.42 tff(46,plain,
% 0.19/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | product(e_1, e_3, e_3) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_3)) | product(e_1, e_3, e_3) | (~product(e_3, e_3, e_1)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(47,plain,
% 0.19/0.42 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | product(e_1, e_3, e_3) | (~product(e_3, e_3, e_1)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(48,plain,
% 0.19/0.42 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_3)) | product(e_1, e_3, e_3) | (~product(e_3, e_3, e_1))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.19/0.42 tff(49,plain,
% 0.19/0.42 (~product(e_3, e_3, e_1)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[48, 45, 11, 35])).
% 0.19/0.42 tff(50,plain,
% 0.19/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_1, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_1) | (~product(e_1, e_1, e_3)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(51,plain,
% 0.19/0.42 (((~product(e_1, e_1, e_3)) | product(e_3, e_3, e_1) | (~product(e_1, e_1, e_3))) <=> (product(e_3, e_3, e_1) | (~product(e_1, e_1, e_3)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(52,plain,
% 0.19/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_3)) | product(e_3, e_3, e_1) | (~product(e_1, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_1, e_1, e_3))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[51])).
% 0.19/0.42 tff(53,plain,
% 0.19/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_3)) | product(e_3, e_3, e_1) | (~product(e_1, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_1) | (~product(e_1, e_1, e_3)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[52, 50])).
% 0.19/0.42 tff(54,plain,
% 0.19/0.42 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_3)) | product(e_3, e_3, e_1) | (~product(e_1, e_1, e_3)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(55,plain,
% 0.19/0.42 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_1) | (~product(e_1, e_1, e_3))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.42 tff(56,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[55, 45, 49, 13])).
% 0.19/0.42 tff(57,plain,(~product(e_1, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(58,assumption,(~product(e_4, e_2, e_3)), introduced(assumption)).
% 0.19/0.42 tff(59,assumption,(product(e_3, e_4, e_3)), introduced(assumption)).
% 0.19/0.42 tff(60,plain,
% 0.19/0.42 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(61,plain,
% 0.19/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[60])).
% 0.19/0.42 tff(62,plain,
% 0.19/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(63,plain,
% 0.19/0.42 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(X, W, Y)) | (~product(X, Z, Y))) <=> ((~product(X, Z, Y)) | (~product(X, W, Y)))), ((((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> (((~product(X, Z, Y)) | (~product(X, W, Y))) | equalish(W, Z)))), rewrite((((~product(X, Z, Y)) | (~product(X, W, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))), ((((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(64,plain,
% 0.19/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[63])).
% 0.19/0.42 tff(65,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_right_cancellation')).
% 0.19/0.42 tff(66,plain,
% 0.19/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.19/0.42 tff(67,plain,
% 0.19/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.19/0.42 tff(68,plain,(
% 0.19/0.42 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[67])).
% 0.19/0.42 tff(69,plain,
% 0.19/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.19/0.42 tff(70,plain,
% 0.19/0.42 ((~equalish(e_4, e_3)) <=> (~equalish(e_4, e_3))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(71,axiom,(~equalish(e_4, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_3')).
% 0.19/0.42 tff(72,plain,
% 0.19/0.42 (~equalish(e_4, e_3)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.19/0.42 tff(73,plain,
% 0.19/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(74,plain,
% 0.19/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(75,plain,
% 0.19/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.19/0.42 tff(76,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[75, 72, 69, 11, 59])).
% 0.19/0.42 tff(77,plain,(~product(e_3, e_4, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(78,plain,
% 0.19/0.42 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl((product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1))) <=> (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(79,plain,
% 0.19/0.42 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[78])).
% 0.19/0.42 tff(80,plain,
% 0.19/0.42 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : trans(monotonicity(rewrite((product(Y, X, Z2) | (~product(Z1, Z2, Y))) <=> (product(Y, X, Z2) | (~product(Z1, Z2, Y)))), (((product(Y, X, Z2) | (~product(Z1, Z2, Y))) | (~product(X, Y, Z1))) <=> ((product(Y, X, Z2) | (~product(Z1, Z2, Y))) | (~product(X, Y, Z1))))), rewrite(((product(Y, X, Z2) | (~product(Z1, Z2, Y))) | (~product(X, Y, Z1))) <=> (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))), (((product(Y, X, Z2) | (~product(Z1, Z2, Y))) | (~product(X, Y, Z1))) <=> (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(82,plain,
% 0.19/0.42 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((product(Y, X, Z2) | (~product(Z1, Z2, Y))) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[81])).
% 0.19/0.42 tff(83,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : ((product(Y, X, Z2) | (~product(Z1, Z2, Y))) | (~product(X, Y, Z1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qg4_2')).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.19/0.42 tff(85,plain,
% 0.19/0.42 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.19/0.42 tff(86,plain,(
% 0.19/0.42 ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[85])).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.19/0.42 tff(88,plain,
% 0.19/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (product(e_3, e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_4, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | product(e_3, e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_4, e_3, e_3)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(89,plain,
% 0.19/0.42 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (product(e_3, e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_4, e_3, e_3)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(90,plain,
% 0.19/0.42 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | product(e_3, e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_4, e_3, e_3))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 (~product(e_4, e_3, e_3)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[90, 87, 11, 77])).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | product(e_4, e_3, e_3) | (~product(e_3, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_3)) | product(e_4, e_3, e_3) | (~product(e_3, e_3, e_4)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(93,plain,
% 0.19/0.42 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | product(e_4, e_3, e_3) | (~product(e_3, e_3, e_4)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(94,plain,
% 0.19/0.42 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_3)) | product(e_4, e_3, e_3) | (~product(e_3, e_3, e_4))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.19/0.42 tff(95,plain,
% 0.19/0.42 (~product(e_3, e_3, e_4)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[94, 45, 11, 91])).
% 0.19/0.42 tff(96,assumption,(~product(e_3, e_3, e_4)), introduced(assumption)).
% 0.19/0.42 tff(97,assumption,(product(e_4, e_4, e_3)), introduced(assumption)).
% 0.19/0.42 tff(98,plain,
% 0.19/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_4) | (~product(e_4, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_4) | (~product(e_4, e_4, e_3)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(99,plain,
% 0.19/0.42 (((~product(e_4, e_4, e_3)) | product(e_3, e_3, e_4) | (~product(e_4, e_4, e_3))) <=> (product(e_3, e_3, e_4) | (~product(e_4, e_4, e_3)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(100,plain,
% 0.19/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_4, e_3)) | product(e_3, e_3, e_4) | (~product(e_4, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_4) | (~product(e_4, e_4, e_3))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[99])).
% 0.19/0.42 tff(101,plain,
% 0.19/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_4, e_3)) | product(e_3, e_3, e_4) | (~product(e_4, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_4) | (~product(e_4, e_4, e_3)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[100, 98])).
% 0.19/0.42 tff(102,plain,
% 0.19/0.42 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_4, e_3)) | product(e_3, e_3, e_4) | (~product(e_4, e_4, e_3)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(103,plain,
% 0.19/0.42 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_4) | (~product(e_4, e_4, e_3))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.19/0.42 tff(104,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[103, 45, 97, 96])).
% 0.19/0.42 tff(105,plain,((~product(e_4, e_4, e_3)) | product(e_3, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(106,plain,
% 0.19/0.42 (~product(e_4, e_4, e_3)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[105, 95])).
% 0.19/0.42 tff(107,plain,
% 0.19/0.42 (group_element(e_4) <=> group_element(e_4)),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(108,axiom,(group_element(e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_4')).
% 0.19/0.42 tff(109,plain,
% 0.19/0.42 (group_element(e_4)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.19/0.42 tff(110,plain,
% 0.19/0.42 (group_element(e_3) <=> group_element(e_3)),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(111,axiom,(group_element(e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_3')).
% 0.19/0.42 tff(112,plain,
% 0.19/0.42 (group_element(e_3)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.19/0.42 tff(113,plain,
% 0.19/0.42 (^[Y: $i, X: $i] : refl(((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(114,plain,
% 0.19/0.42 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[113])).
% 0.19/0.42 tff(115,plain,
% 0.19/0.42 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(116,plain,
% 0.19/0.43 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_1, Y))), (((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) <=> (((~group_element(Y)) | (~group_element(X)) | product(X, e_1, Y)) | product(X, e_2, Y)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product(X, e_1, Y)) | product(X, e_2, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_2, Y) | product(X, e_1, Y))), (((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_2, Y) | product(X, e_1, Y)))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) | product(X, e_3, Y)) <=> (((~group_element(Y)) | (~group_element(X)) | product(X, e_2, Y) | product(X, e_1, Y)) | product(X, e_3, Y)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product(X, e_2, Y) | product(X, e_1, Y)) | product(X, e_3, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) | product(X, e_3, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)))), (((((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) | product(X, e_3, Y)) | product(X, e_4, Y)) <=> (((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)) | product(X, e_4, Y)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)) | product(X, e_4, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))), (((((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) | product(X, e_3, Y)) | product(X, e_4, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(117,plain,
% 0.19/0.43 (![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) | product(X, e_3, Y)) | product(X, e_4, Y)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[116])).
% 0.19/0.43 tff(118,axiom,(![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) | product(X, e_3, Y)) | product(X, e_4, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','column_surjectivity')).
% 0.19/0.43 tff(119,plain,
% 0.19/0.43 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.19/0.43 tff(120,plain,
% 0.19/0.43 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.19/0.43 tff(121,plain,(
% 0.19/0.43 ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.19/0.43 inference(skolemize,[status(sab)],[120])).
% 0.19/0.43 tff(122,plain,
% 0.19/0.43 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[121, 114])).
% 0.19/0.43 tff(123,plain,
% 0.19/0.43 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_4)) | (~group_element(e_3)) | product(e_4, e_4, e_3) | product(e_4, e_1, e_3) | product(e_4, e_3, e_3) | product(e_4, e_2, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_4)) | (~group_element(e_3)) | product(e_4, e_4, e_3) | product(e_4, e_1, e_3) | product(e_4, e_3, e_3) | product(e_4, e_2, e_3))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(124,plain,
% 0.19/0.43 (((~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_4, e_3) | product(e_4, e_3, e_3) | product(e_4, e_2, e_3) | product(e_4, e_1, e_3)) <=> ((~group_element(e_4)) | (~group_element(e_3)) | product(e_4, e_4, e_3) | product(e_4, e_1, e_3) | product(e_4, e_3, e_3) | product(e_4, e_2, e_3))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(125,plain,
% 0.19/0.43 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_4, e_3) | product(e_4, e_3, e_3) | product(e_4, e_2, e_3) | product(e_4, e_1, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_4)) | (~group_element(e_3)) | product(e_4, e_4, e_3) | product(e_4, e_1, e_3) | product(e_4, e_3, e_3) | product(e_4, e_2, e_3)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[124])).
% 0.19/0.43 tff(126,plain,
% 0.19/0.43 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_4, e_3) | product(e_4, e_3, e_3) | product(e_4, e_2, e_3) | product(e_4, e_1, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_4)) | (~group_element(e_3)) | product(e_4, e_4, e_3) | product(e_4, e_1, e_3) | product(e_4, e_3, e_3) | product(e_4, e_2, e_3))),
% 0.19/0.43 inference(transitivity,[status(thm)],[125, 123])).
% 0.19/0.43 tff(127,plain,
% 0.19/0.43 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_4, e_3) | product(e_4, e_3, e_3) | product(e_4, e_2, e_3) | product(e_4, e_1, e_3))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(128,plain,
% 0.19/0.43 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_4)) | (~group_element(e_3)) | product(e_4, e_4, e_3) | product(e_4, e_1, e_3) | product(e_4, e_3, e_3) | product(e_4, e_2, e_3)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.19/0.43 tff(129,plain,
% 0.19/0.43 (product(e_4, e_4, e_3) | product(e_4, e_1, e_3) | product(e_4, e_2, e_3)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[128, 122, 112, 109, 91])).
% 0.19/0.43 tff(130,plain,
% 0.19/0.43 (product(e_4, e_1, e_3) | product(e_4, e_2, e_3)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[129, 106])).
% 0.19/0.43 tff(131,plain,
% 0.19/0.43 (product(e_4, e_1, e_3)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[130, 58])).
% 0.19/0.43 tff(132,plain,
% 0.19/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_4) | (~product(e_4, e_1, e_3)) | (~product(e_1, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_4) | (~product(e_4, e_1, e_3)) | (~product(e_1, e_4, e_3)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(133,plain,
% 0.19/0.43 (((~product(e_4, e_1, e_3)) | product(e_3, e_3, e_4) | (~product(e_1, e_4, e_3))) <=> (product(e_3, e_3, e_4) | (~product(e_4, e_1, e_3)) | (~product(e_1, e_4, e_3)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(134,plain,
% 0.19/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_1, e_3)) | product(e_3, e_3, e_4) | (~product(e_1, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_4) | (~product(e_4, e_1, e_3)) | (~product(e_1, e_4, e_3))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[133])).
% 0.19/0.44 tff(135,plain,
% 0.19/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_1, e_3)) | product(e_3, e_3, e_4) | (~product(e_1, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_4) | (~product(e_4, e_1, e_3)) | (~product(e_1, e_4, e_3)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[134, 132])).
% 0.19/0.44 tff(136,plain,
% 0.19/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_1, e_3)) | product(e_3, e_3, e_4) | (~product(e_1, e_4, e_3)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(137,plain,
% 0.19/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_4) | (~product(e_4, e_1, e_3)) | (~product(e_1, e_4, e_3))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.19/0.44 tff(138,plain,
% 0.19/0.44 (~product(e_1, e_4, e_3)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[137, 45, 95, 131])).
% 0.19/0.44 tff(139,plain,
% 0.19/0.44 (group_element(e_1) <=> group_element(e_1)),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(140,axiom,(group_element(e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_1')).
% 0.19/0.44 tff(141,plain,
% 0.19/0.44 (group_element(e_1)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.19/0.44 tff(142,plain,
% 0.19/0.44 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_3)) | (~group_element(e_1)) | product(e_1, e_3, e_3) | product(e_1, e_1, e_3) | product(e_1, e_2, e_3) | product(e_1, e_4, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_3)) | (~group_element(e_1)) | product(e_1, e_3, e_3) | product(e_1, e_1, e_3) | product(e_1, e_2, e_3) | product(e_1, e_4, e_3))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(143,plain,
% 0.19/0.44 (((~group_element(e_3)) | (~group_element(e_1)) | product(e_1, e_4, e_3) | product(e_1, e_3, e_3) | product(e_1, e_2, e_3) | product(e_1, e_1, e_3)) <=> ((~group_element(e_3)) | (~group_element(e_1)) | product(e_1, e_3, e_3) | product(e_1, e_1, e_3) | product(e_1, e_2, e_3) | product(e_1, e_4, e_3))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(144,plain,
% 0.19/0.44 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_3)) | (~group_element(e_1)) | product(e_1, e_4, e_3) | product(e_1, e_3, e_3) | product(e_1, e_2, e_3) | product(e_1, e_1, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_3)) | (~group_element(e_1)) | product(e_1, e_3, e_3) | product(e_1, e_1, e_3) | product(e_1, e_2, e_3) | product(e_1, e_4, e_3)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[143])).
% 0.19/0.44 tff(145,plain,
% 0.19/0.44 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_3)) | (~group_element(e_1)) | product(e_1, e_4, e_3) | product(e_1, e_3, e_3) | product(e_1, e_2, e_3) | product(e_1, e_1, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_3)) | (~group_element(e_1)) | product(e_1, e_3, e_3) | product(e_1, e_1, e_3) | product(e_1, e_2, e_3) | product(e_1, e_4, e_3))),
% 0.19/0.44 inference(transitivity,[status(thm)],[144, 142])).
% 0.19/0.44 tff(146,plain,
% 0.19/0.44 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_3)) | (~group_element(e_1)) | product(e_1, e_4, e_3) | product(e_1, e_3, e_3) | product(e_1, e_2, e_3) | product(e_1, e_1, e_3))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(147,plain,
% 0.19/0.44 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_3)) | (~group_element(e_1)) | product(e_1, e_3, e_3) | product(e_1, e_1, e_3) | product(e_1, e_2, e_3) | product(e_1, e_4, e_3)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.19/0.44 tff(148,plain,
% 0.19/0.44 (product(e_1, e_1, e_3) | product(e_1, e_2, e_3) | product(e_1, e_4, e_3)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[147, 122, 141, 112, 35])).
% 0.19/0.44 tff(149,plain,
% 0.19/0.44 (product(e_1, e_2, e_3)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[148, 138, 57])).
% 0.19/0.44 tff(150,assumption,(product(e_1, e_2, e_1)), introduced(assumption)).
% 0.19/0.44 tff(151,assumption,(~product(e_1, e_1, e_1)), introduced(assumption)).
% 0.19/0.44 tff(152,plain,
% 0.19/0.44 ((~![X: $i] : product(X, X, X)) | product(e_1, e_1, e_1)),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(153,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[152, 8, 151])).
% 0.19/0.44 tff(154,plain,(product(e_1, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(155,plain,
% 0.19/0.44 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(156,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.19/0.44 tff(157,plain,
% 0.19/0.44 (~equalish(e_2, e_1)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.19/0.44 tff(158,plain,
% 0.19/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(159,plain,
% 0.19/0.44 ((equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1))) <=> (equalish(e_2, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(160,plain,
% 0.19/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_1))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[159])).
% 0.19/0.44 tff(161,plain,
% 0.19/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[160, 158])).
% 0.19/0.44 tff(162,plain,
% 0.19/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(163,plain,
% 0.19/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_1))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.19/0.44 tff(164,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[163, 157, 69, 154, 150])).
% 0.19/0.44 tff(165,plain,(~product(e_1, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(166,plain,
% 0.19/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | product(e_1, e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(167,plain,
% 0.19/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(168,plain,
% 0.19/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | product(e_1, e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.19/0.44 tff(169,plain,
% 0.19/0.44 (~product(e_2, e_1, e_1)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[168, 87, 154, 165])).
% 0.19/0.44 tff(170,assumption,(product(e_1, e_2, e_3)), introduced(assumption)).
% 0.19/0.44 tff(171,assumption,(product(e_3, e_1, e_2)), introduced(assumption)).
% 0.19/0.44 tff(172,plain,
% 0.19/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_2, e_3)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(173,plain,
% 0.19/0.44 ((product(e_2, e_1, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_2, e_3))) <=> ((~product(e_3, e_1, e_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_2, e_3)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(174,plain,
% 0.19/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_2, e_3))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[173])).
% 0.19/0.44 tff(175,plain,
% 0.19/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_2, e_3)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[174, 172])).
% 0.19/0.44 tff(176,plain,
% 0.19/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_2, e_3)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(177,plain,
% 0.19/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_2, e_3))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.19/0.44 tff(178,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[177, 87, 171, 170, 169])).
% 0.19/0.44 tff(179,plain,((~product(e_3, e_1, e_2)) | (~product(e_1, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(180,plain,
% 0.19/0.44 (~product(e_3, e_1, e_2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[179, 149])).
% 0.19/0.44 tff(181,assumption,(~product(e_2, e_2, e_2)), introduced(assumption)).
% 0.19/0.44 tff(182,plain,
% 0.19/0.44 ((~![X: $i] : product(X, X, X)) | product(e_2, e_2, e_2)),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(183,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[182, 8, 181])).
% 0.19/0.44 tff(184,plain,(product(e_2, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(185,assumption,(product(e_3, e_2, e_2)), introduced(assumption)).
% 0.19/0.45 tff(186,plain,
% 0.19/0.45 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(187,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.19/0.45 tff(188,plain,
% 0.19/0.45 (~equalish(e_2, e_3)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.19/0.45 tff(189,plain,
% 0.19/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(190,plain,
% 0.19/0.45 (((~product(e_2, e_2, e_2)) | equalish(e_2, e_3) | (~product(e_3, e_2, e_2))) <=> (equalish(e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(191,plain,
% 0.19/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | ((~product(e_2, e_2, e_2)) | equalish(e_2, e_3) | (~product(e_3, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[190])).
% 0.19/0.45 tff(192,plain,
% 0.19/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | ((~product(e_2, e_2, e_2)) | equalish(e_2, e_3) | (~product(e_3, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[191, 189])).
% 0.19/0.45 tff(193,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | ((~product(e_2, e_2, e_2)) | equalish(e_2, e_3) | (~product(e_3, e_2, e_2)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(194,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.19/0.45 tff(195,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[194, 188, 24, 185, 184])).
% 0.19/0.45 tff(196,plain,(~product(e_3, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(197,plain,
% 0.19/0.45 (group_element(e_2) <=> group_element(e_2)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(198,axiom,(group_element(e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_2')).
% 0.19/0.45 tff(199,plain,
% 0.19/0.45 (group_element(e_2)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.19/0.45 tff(200,plain,
% 0.19/0.45 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (product(e_3, e_4, e_2) | product(e_3, e_3, e_2) | product(e_3, e_2, e_2) | (~group_element(e_2)) | product(e_3, e_1, e_2) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | product(e_3, e_4, e_2) | product(e_3, e_3, e_2) | product(e_3, e_2, e_2) | (~group_element(e_2)) | product(e_3, e_1, e_2) | (~group_element(e_3)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(201,plain,
% 0.19/0.45 (((~group_element(e_2)) | (~group_element(e_3)) | product(e_3, e_4, e_2) | product(e_3, e_3, e_2) | product(e_3, e_2, e_2) | product(e_3, e_1, e_2)) <=> (product(e_3, e_4, e_2) | product(e_3, e_3, e_2) | product(e_3, e_2, e_2) | (~group_element(e_2)) | product(e_3, e_1, e_2) | (~group_element(e_3)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(202,plain,
% 0.19/0.45 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_2)) | (~group_element(e_3)) | product(e_3, e_4, e_2) | product(e_3, e_3, e_2) | product(e_3, e_2, e_2) | product(e_3, e_1, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (product(e_3, e_4, e_2) | product(e_3, e_3, e_2) | product(e_3, e_2, e_2) | (~group_element(e_2)) | product(e_3, e_1, e_2) | (~group_element(e_3))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[201])).
% 0.19/0.45 tff(203,plain,
% 0.19/0.45 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_2)) | (~group_element(e_3)) | product(e_3, e_4, e_2) | product(e_3, e_3, e_2) | product(e_3, e_2, e_2) | product(e_3, e_1, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | product(e_3, e_4, e_2) | product(e_3, e_3, e_2) | product(e_3, e_2, e_2) | (~group_element(e_2)) | product(e_3, e_1, e_2) | (~group_element(e_3)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[202, 200])).
% 0.19/0.45 tff(204,plain,
% 0.19/0.45 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_2)) | (~group_element(e_3)) | product(e_3, e_4, e_2) | product(e_3, e_3, e_2) | product(e_3, e_2, e_2) | product(e_3, e_1, e_2))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(205,plain,
% 0.19/0.45 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | product(e_3, e_4, e_2) | product(e_3, e_3, e_2) | product(e_3, e_2, e_2) | (~group_element(e_2)) | product(e_3, e_1, e_2) | (~group_element(e_3))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.19/0.45 tff(206,plain,
% 0.19/0.45 (product(e_3, e_4, e_2) | product(e_3, e_3, e_2) | product(e_3, e_1, e_2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[205, 122, 199, 112, 196])).
% 0.19/0.45 tff(207,plain,
% 0.19/0.45 (product(e_3, e_4, e_2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[206, 180, 12])).
% 0.19/0.45 tff(208,assumption,(product(e_2, e_3, e_4)), introduced(assumption)).
% 0.19/0.45 tff(209,assumption,(product(e_3, e_4, e_2)), introduced(assumption)).
% 0.19/0.45 tff(210,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_4, e_2)) | (~product(e_2, e_3, e_4)) | product(e_4, e_3, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (~product(e_3, e_4, e_2)) | (~product(e_2, e_3, e_4)) | product(e_4, e_3, e_3))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(211,plain,
% 0.19/0.45 ((product(e_4, e_3, e_3) | (~product(e_2, e_3, e_4)) | (~product(e_3, e_4, e_2))) <=> ((~product(e_3, e_4, e_2)) | (~product(e_2, e_3, e_4)) | product(e_4, e_3, e_3))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(212,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (product(e_4, e_3, e_3) | (~product(e_2, e_3, e_4)) | (~product(e_3, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_4, e_2)) | (~product(e_2, e_3, e_4)) | product(e_4, e_3, e_3)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[211])).
% 0.19/0.45 tff(213,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (product(e_4, e_3, e_3) | (~product(e_2, e_3, e_4)) | (~product(e_3, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (~product(e_3, e_4, e_2)) | (~product(e_2, e_3, e_4)) | product(e_4, e_3, e_3))),
% 0.19/0.45 inference(transitivity,[status(thm)],[212, 210])).
% 0.19/0.45 tff(214,plain,
% 0.19/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (product(e_4, e_3, e_3) | (~product(e_2, e_3, e_4)) | (~product(e_3, e_4, e_2)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(215,plain,
% 0.19/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (~product(e_3, e_4, e_2)) | (~product(e_2, e_3, e_4)) | product(e_4, e_3, e_3)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.19/0.45 tff(216,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[215, 87, 209, 91, 208])).
% 0.19/0.45 tff(217,plain,((~product(e_2, e_3, e_4)) | (~product(e_3, e_4, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(218,plain,
% 0.19/0.45 (~product(e_2, e_3, e_4)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[217, 207])).
% 0.19/0.45 tff(219,assumption,(product(e_2, e_1, e_2)), introduced(assumption)).
% 0.19/0.45 tff(220,plain,
% 0.19/0.45 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(221,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.19/0.45 tff(222,plain,
% 0.19/0.45 (~equalish(e_1, e_2)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.19/0.45 tff(223,plain,
% 0.19/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(224,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(225,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.19/0.45 tff(226,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[225, 222, 69, 184, 219])).
% 0.19/0.45 tff(227,plain,(~product(e_2, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(228,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_1, e_1)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(229,plain,
% 0.19/0.45 (((~product(e_1, e_1, e_1)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_2))) <=> (product(e_2, e_1, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_1, e_1)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(230,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_1)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_1, e_1))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[229])).
% 0.19/0.45 tff(231,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_1)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_1, e_1)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[230, 228])).
% 0.19/0.45 tff(232,plain,
% 0.19/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_1)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_2)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(233,plain,
% 0.19/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_1, e_1))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.19/0.46 tff(234,plain,
% 0.19/0.46 (~product(e_1, e_1, e_2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[233, 45, 154, 169])).
% 0.19/0.46 tff(235,plain,
% 0.19/0.46 (^[Y: $i, X: $i] : refl((product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) <=> (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(236,plain,
% 0.19/0.46 (![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[235])).
% 0.19/0.46 tff(237,plain,
% 0.19/0.46 (![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(238,plain,
% 0.19/0.46 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) <=> (product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) <=> ((product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) | product(e_2, X, Y)))), rewrite(((product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) | product(e_2, X, Y)) <=> (product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) <=> (product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))))), ((((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) | product(e_3, X, Y)) <=> ((product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) | product(e_3, X, Y)))), rewrite(((product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) | product(e_3, X, Y)) <=> (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))), ((((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) | product(e_3, X, Y)) <=> (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))))), (((((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) | product(e_3, X, Y)) | product(e_4, X, Y)) <=> ((product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) | product(e_4, X, Y)))), rewrite(((product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) | product(e_4, X, Y)) <=> (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))), (((((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) | product(e_3, X, Y)) | product(e_4, X, Y)) <=> (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(239,plain,
% 0.19/0.46 (![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) | product(e_3, X, Y)) | product(e_4, X, Y)) <=> ![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[238])).
% 0.19/0.46 tff(240,axiom,(![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) | product(e_3, X, Y)) | product(e_4, X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','row_surjectivity')).
% 0.19/0.46 tff(241,plain,
% 0.19/0.46 (![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.19/0.46 tff(242,plain,
% 0.19/0.46 (![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[241, 237])).
% 0.19/0.46 tff(243,plain,(
% 0.19/0.46 ![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[242])).
% 0.19/0.46 tff(244,plain,
% 0.19/0.46 (![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[243, 236])).
% 0.19/0.46 tff(245,plain,
% 0.19/0.46 (((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | product(e_3, e_1, e_2) | (~group_element(e_1)) | product(e_4, e_1, e_2) | product(e_2, e_1, e_2) | product(e_1, e_1, e_2))) <=> ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_3, e_1, e_2) | (~group_element(e_1)) | product(e_4, e_1, e_2) | product(e_2, e_1, e_2) | product(e_1, e_1, e_2))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(246,plain,
% 0.19/0.46 ((product(e_4, e_1, e_2) | product(e_3, e_1, e_2) | product(e_2, e_1, e_2) | product(e_1, e_1, e_2) | (~group_element(e_2)) | (~group_element(e_1))) <=> ((~group_element(e_2)) | product(e_3, e_1, e_2) | (~group_element(e_1)) | product(e_4, e_1, e_2) | product(e_2, e_1, e_2) | product(e_1, e_1, e_2))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(247,plain,
% 0.19/0.46 (((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_1, e_2) | product(e_3, e_1, e_2) | product(e_2, e_1, e_2) | product(e_1, e_1, e_2) | (~group_element(e_2)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | product(e_3, e_1, e_2) | (~group_element(e_1)) | product(e_4, e_1, e_2) | product(e_2, e_1, e_2) | product(e_1, e_1, e_2)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[246])).
% 0.19/0.46 tff(248,plain,
% 0.19/0.46 (((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_1, e_2) | product(e_3, e_1, e_2) | product(e_2, e_1, e_2) | product(e_1, e_1, e_2) | (~group_element(e_2)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_3, e_1, e_2) | (~group_element(e_1)) | product(e_4, e_1, e_2) | product(e_2, e_1, e_2) | product(e_1, e_1, e_2))),
% 0.19/0.46 inference(transitivity,[status(thm)],[247, 245])).
% 0.19/0.46 tff(249,plain,
% 0.19/0.46 ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_1, e_2) | product(e_3, e_1, e_2) | product(e_2, e_1, e_2) | product(e_1, e_1, e_2) | (~group_element(e_2)) | (~group_element(e_1)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(250,plain,
% 0.19/0.46 ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_3, e_1, e_2) | (~group_element(e_1)) | product(e_4, e_1, e_2) | product(e_2, e_1, e_2) | product(e_1, e_1, e_2)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.19/0.46 tff(251,plain,
% 0.19/0.46 (product(e_3, e_1, e_2) | product(e_4, e_1, e_2) | product(e_2, e_1, e_2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[250, 244, 141, 199, 234])).
% 0.19/0.46 tff(252,plain,
% 0.19/0.46 (product(e_3, e_1, e_2) | product(e_4, e_1, e_2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[251, 227])).
% 0.19/0.46 tff(253,plain,
% 0.19/0.46 (product(e_4, e_1, e_2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[252, 180])).
% 0.19/0.46 tff(254,assumption,(product(e_4, e_1, e_2)), introduced(assumption)).
% 0.19/0.46 tff(255,assumption,(product(e_4, e_3, e_2)), introduced(assumption)).
% 0.19/0.46 tff(256,plain,
% 0.19/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_1, e_2)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(257,plain,
% 0.19/0.46 ((equalish(e_3, e_1) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_3, e_2))) <=> (equalish(e_3, e_1) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_1, e_2)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(258,plain,
% 0.19/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_1, e_2))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[257])).
% 0.19/0.46 tff(259,plain,
% 0.19/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_1, e_2)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[258, 256])).
% 0.19/0.46 tff(260,plain,
% 0.19/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_3, e_2)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(261,plain,
% 0.19/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_1, e_2))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.19/0.46 tff(262,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[261, 27, 69, 255, 254])).
% 0.19/0.46 tff(263,plain,((~product(e_4, e_3, e_2)) | (~product(e_4, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(264,plain,
% 0.19/0.46 (~product(e_4, e_3, e_2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[263, 253])).
% 0.19/0.46 tff(265,assumption,(product(e_2, e_3, e_2)), introduced(assumption)).
% 0.19/0.46 tff(266,plain,
% 0.19/0.46 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(267,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.19/0.46 tff(268,plain,
% 0.19/0.46 (~equalish(e_3, e_2)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.19/0.46 tff(269,plain,
% 0.19/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(270,plain,
% 0.19/0.46 ((equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_3, e_2))) <=> (equalish(e_3, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(271,plain,
% 0.19/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_2, e_2))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[270])).
% 0.19/0.47 tff(272,plain,
% 0.19/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[271, 269])).
% 0.19/0.47 tff(273,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_3, e_2)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(274,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_2, e_2))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.19/0.47 tff(275,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[274, 268, 69, 184, 265])).
% 0.19/0.47 tff(276,plain,(~product(e_2, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(277,plain,
% 0.19/0.47 (((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_3, e_2) | (~group_element(e_2)) | (~group_element(e_3)) | product(e_4, e_3, e_2) | product(e_2, e_3, e_2) | product(e_1, e_3, e_2))) <=> ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_3, e_2) | (~group_element(e_2)) | (~group_element(e_3)) | product(e_4, e_3, e_2) | product(e_2, e_3, e_2) | product(e_1, e_3, e_2))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(278,plain,
% 0.19/0.47 ((product(e_4, e_3, e_2) | product(e_3, e_3, e_2) | product(e_2, e_3, e_2) | product(e_1, e_3, e_2) | (~group_element(e_2)) | (~group_element(e_3))) <=> (product(e_3, e_3, e_2) | (~group_element(e_2)) | (~group_element(e_3)) | product(e_4, e_3, e_2) | product(e_2, e_3, e_2) | product(e_1, e_3, e_2))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(279,plain,
% 0.19/0.47 (((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_3, e_2) | product(e_3, e_3, e_2) | product(e_2, e_3, e_2) | product(e_1, e_3, e_2) | (~group_element(e_2)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_3, e_2) | (~group_element(e_2)) | (~group_element(e_3)) | product(e_4, e_3, e_2) | product(e_2, e_3, e_2) | product(e_1, e_3, e_2)))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[278])).
% 0.19/0.47 tff(280,plain,
% 0.19/0.47 (((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_3, e_2) | product(e_3, e_3, e_2) | product(e_2, e_3, e_2) | product(e_1, e_3, e_2) | (~group_element(e_2)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_3, e_2) | (~group_element(e_2)) | (~group_element(e_3)) | product(e_4, e_3, e_2) | product(e_2, e_3, e_2) | product(e_1, e_3, e_2))),
% 0.19/0.47 inference(transitivity,[status(thm)],[279, 277])).
% 0.19/0.47 tff(281,plain,
% 0.19/0.47 ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_3, e_2) | product(e_3, e_3, e_2) | product(e_2, e_3, e_2) | product(e_1, e_3, e_2) | (~group_element(e_2)) | (~group_element(e_3)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(282,plain,
% 0.19/0.47 ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_3, e_2) | (~group_element(e_2)) | (~group_element(e_3)) | product(e_4, e_3, e_2) | product(e_2, e_3, e_2) | product(e_1, e_3, e_2)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.19/0.47 tff(283,plain,
% 0.19/0.47 (product(e_3, e_3, e_2) | product(e_4, e_3, e_2) | product(e_1, e_3, e_2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[282, 244, 199, 112, 276])).
% 0.19/0.47 tff(284,plain,
% 0.19/0.47 (product(e_1, e_3, e_2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[283, 264, 12])).
% 0.19/0.47 tff(285,assumption,(product(e_1, e_3, e_4)), introduced(assumption)).
% 0.19/0.47 tff(286,assumption,(product(e_1, e_3, e_2)), introduced(assumption)).
% 0.19/0.47 tff(287,plain,
% 0.19/0.47 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W))) <=> (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(288,plain,
% 0.19/0.47 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[287])).
% 0.19/0.47 tff(289,plain,
% 0.19/0.47 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(290,plain,
% 0.19/0.47 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(X, Y, W)) | (~product(X, Y, Z))) <=> ((~product(X, Y, Z)) | (~product(X, Y, W)))), ((((~product(X, Y, W)) | (~product(X, Y, Z))) | equalish(W, Z)) <=> (((~product(X, Y, Z)) | (~product(X, Y, W))) | equalish(W, Z)))), rewrite((((~product(X, Y, Z)) | (~product(X, Y, W))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))), ((((~product(X, Y, W)) | (~product(X, Y, Z))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(291,plain,
% 0.19/0.47 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, Y, W)) | (~product(X, Y, Z))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[290])).
% 0.19/0.47 tff(292,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, Y, W)) | (~product(X, Y, Z))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_total_function2')).
% 0.19/0.47 tff(293,plain,
% 0.19/0.47 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.19/0.47 tff(294,plain,
% 0.19/0.47 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[293, 289])).
% 0.19/0.47 tff(295,plain,(
% 0.19/0.47 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.19/0.47 inference(skolemize,[status(sab)],[294])).
% 0.19/0.47 tff(296,plain,
% 0.19/0.47 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[295, 288])).
% 0.19/0.47 tff(297,plain,
% 0.19/0.47 ((~equalish(e_2, e_4)) <=> (~equalish(e_2, e_4))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(298,axiom,(~equalish(e_2, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_4')).
% 0.19/0.47 tff(299,plain,
% 0.19/0.47 (~equalish(e_2, e_4)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.19/0.47 tff(300,plain,
% 0.19/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_4) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_2, e_4) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_3, e_4)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(301,plain,
% 0.19/0.47 ((equalish(e_2, e_4) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_3, e_2))) <=> (equalish(e_2, e_4) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_3, e_4)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(302,plain,
% 0.19/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_4) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_4) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_3, e_4))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[301])).
% 0.19/0.47 tff(303,plain,
% 0.19/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_4) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_2, e_4) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_3, e_4)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[302, 300])).
% 0.19/0.47 tff(304,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_4) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_3, e_2)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(305,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_2, e_4) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_3, e_4))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.19/0.47 tff(306,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[305, 299, 296, 286, 285])).
% 0.19/0.47 tff(307,plain,((~product(e_1, e_3, e_2)) | (~product(e_1, e_3, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(308,plain,
% 0.19/0.47 (~product(e_1, e_3, e_4)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[307, 284])).
% 0.19/0.47 tff(309,plain,
% 0.19/0.47 (((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_4)) | (~group_element(e_3)) | product(e_3, e_3, e_4) | product(e_2, e_3, e_4) | product(e_4, e_3, e_4) | product(e_1, e_3, e_4))) <=> ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | (~group_element(e_3)) | product(e_3, e_3, e_4) | product(e_2, e_3, e_4) | product(e_4, e_3, e_4) | product(e_1, e_3, e_4))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(310,plain,
% 0.19/0.47 ((product(e_4, e_3, e_4) | product(e_3, e_3, e_4) | product(e_2, e_3, e_4) | product(e_1, e_3, e_4) | (~group_element(e_4)) | (~group_element(e_3))) <=> ((~group_element(e_4)) | (~group_element(e_3)) | product(e_3, e_3, e_4) | product(e_2, e_3, e_4) | product(e_4, e_3, e_4) | product(e_1, e_3, e_4))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(311,plain,
% 0.19/0.47 (((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_3, e_4) | product(e_3, e_3, e_4) | product(e_2, e_3, e_4) | product(e_1, e_3, e_4) | (~group_element(e_4)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_4)) | (~group_element(e_3)) | product(e_3, e_3, e_4) | product(e_2, e_3, e_4) | product(e_4, e_3, e_4) | product(e_1, e_3, e_4)))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[310])).
% 0.19/0.47 tff(312,plain,
% 0.19/0.47 (((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_3, e_4) | product(e_3, e_3, e_4) | product(e_2, e_3, e_4) | product(e_1, e_3, e_4) | (~group_element(e_4)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | (~group_element(e_3)) | product(e_3, e_3, e_4) | product(e_2, e_3, e_4) | product(e_4, e_3, e_4) | product(e_1, e_3, e_4))),
% 0.19/0.48 inference(transitivity,[status(thm)],[311, 309])).
% 0.19/0.48 tff(313,plain,
% 0.19/0.48 ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_3, e_4) | product(e_3, e_3, e_4) | product(e_2, e_3, e_4) | product(e_1, e_3, e_4) | (~group_element(e_4)) | (~group_element(e_3)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(314,plain,
% 0.19/0.48 ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | (~group_element(e_3)) | product(e_3, e_3, e_4) | product(e_2, e_3, e_4) | product(e_4, e_3, e_4) | product(e_1, e_3, e_4)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[313, 312])).
% 0.19/0.48 tff(315,plain,
% 0.19/0.48 (product(e_2, e_3, e_4) | product(e_4, e_3, e_4) | product(e_1, e_3, e_4)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[314, 244, 112, 109, 95])).
% 0.19/0.48 tff(316,plain,
% 0.19/0.48 (product(e_4, e_3, e_4)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[315, 308, 218])).
% 0.19/0.48 tff(317,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_4, e_2)) | product(e_4, e_2, e_3) | (~product(e_4, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_4, e_2)) | product(e_4, e_2, e_3) | (~product(e_4, e_3, e_4)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(318,plain,
% 0.19/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_4, e_2)) | product(e_4, e_2, e_3) | (~product(e_4, e_3, e_4)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(319,plain,
% 0.19/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_4, e_2)) | product(e_4, e_2, e_3) | (~product(e_4, e_3, e_4))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[318, 317])).
% 0.19/0.48 tff(320,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[319, 45, 207, 58, 316])).
% 0.19/0.48 tff(321,plain,(product(e_4, e_2, e_3) | product(e_3, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(322,plain,
% 0.19/0.48 (product(e_4, e_2, e_3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[321, 12])).
% 0.19/0.48 tff(323,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_4) | (~product(e_2, e_4, e_3)) | (~product(e_4, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_4) | (~product(e_2, e_4, e_3)) | (~product(e_4, e_2, e_3)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(324,plain,
% 0.19/0.48 (((~product(e_4, e_2, e_3)) | product(e_3, e_3, e_4) | (~product(e_2, e_4, e_3))) <=> (product(e_3, e_3, e_4) | (~product(e_2, e_4, e_3)) | (~product(e_4, e_2, e_3)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(325,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_3)) | product(e_3, e_3, e_4) | (~product(e_2, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_4) | (~product(e_2, e_4, e_3)) | (~product(e_4, e_2, e_3))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[324])).
% 0.19/0.48 tff(326,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_3)) | product(e_3, e_3, e_4) | (~product(e_2, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_4) | (~product(e_2, e_4, e_3)) | (~product(e_4, e_2, e_3)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[325, 323])).
% 0.19/0.48 tff(327,plain,
% 0.19/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_3)) | product(e_3, e_3, e_4) | (~product(e_2, e_4, e_3)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(328,plain,
% 0.19/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_4) | (~product(e_2, e_4, e_3)) | (~product(e_4, e_2, e_3))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[327, 326])).
% 0.19/0.48 tff(329,plain,
% 0.19/0.48 (~product(e_2, e_4, e_3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[328, 45, 95, 322])).
% 0.19/0.48 tff(330,assumption,(~product(e_2, e_4, e_3)), introduced(assumption)).
% 0.19/0.48 tff(331,plain,
% 0.19/0.48 (((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_4, e_3) | (~group_element(e_4)) | (~group_element(e_3)) | product(e_4, e_4, e_3) | product(e_2, e_4, e_3) | product(e_1, e_4, e_3))) <=> ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_4, e_3) | (~group_element(e_4)) | (~group_element(e_3)) | product(e_4, e_4, e_3) | product(e_2, e_4, e_3) | product(e_1, e_4, e_3))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(332,plain,
% 0.19/0.48 ((product(e_4, e_4, e_3) | product(e_3, e_4, e_3) | product(e_2, e_4, e_3) | product(e_1, e_4, e_3) | (~group_element(e_3)) | (~group_element(e_4))) <=> (product(e_3, e_4, e_3) | (~group_element(e_4)) | (~group_element(e_3)) | product(e_4, e_4, e_3) | product(e_2, e_4, e_3) | product(e_1, e_4, e_3))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(333,plain,
% 0.19/0.48 (((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_4, e_3) | product(e_3, e_4, e_3) | product(e_2, e_4, e_3) | product(e_1, e_4, e_3) | (~group_element(e_3)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_4, e_3) | (~group_element(e_4)) | (~group_element(e_3)) | product(e_4, e_4, e_3) | product(e_2, e_4, e_3) | product(e_1, e_4, e_3)))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[332])).
% 0.19/0.48 tff(334,plain,
% 0.19/0.48 (((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_4, e_3) | product(e_3, e_4, e_3) | product(e_2, e_4, e_3) | product(e_1, e_4, e_3) | (~group_element(e_3)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_4, e_3) | (~group_element(e_4)) | (~group_element(e_3)) | product(e_4, e_4, e_3) | product(e_2, e_4, e_3) | product(e_1, e_4, e_3))),
% 0.19/0.48 inference(transitivity,[status(thm)],[333, 331])).
% 0.19/0.48 tff(335,plain,
% 0.19/0.48 ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_4, e_3) | product(e_3, e_4, e_3) | product(e_2, e_4, e_3) | product(e_1, e_4, e_3) | (~group_element(e_3)) | (~group_element(e_4)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(336,plain,
% 0.19/0.48 ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_4, e_3) | (~group_element(e_4)) | (~group_element(e_3)) | product(e_4, e_4, e_3) | product(e_2, e_4, e_3) | product(e_1, e_4, e_3)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[335, 334])).
% 0.19/0.48 tff(337,plain,
% 0.19/0.48 (product(e_4, e_4, e_3) | product(e_2, e_4, e_3) | product(e_1, e_4, e_3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[336, 244, 112, 109, 77])).
% 0.19/0.48 tff(338,plain,
% 0.19/0.48 (product(e_2, e_4, e_3) | product(e_1, e_4, e_3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[337, 106])).
% 0.19/0.48 tff(339,plain,
% 0.19/0.48 (product(e_1, e_4, e_3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[338, 330])).
% 0.19/0.48 tff(340,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_4) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_4) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_4, e_3)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(341,plain,
% 0.19/0.48 ((product(e_3, e_3, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_3, e_1))) <=> (product(e_3, e_3, e_4) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_4, e_3)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(342,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_4) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_4, e_3))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[341])).
% 0.19/0.48 tff(343,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_4) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_4, e_3)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[342, 340])).
% 0.19/0.48 tff(344,plain,
% 0.19/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_3, e_1)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(345,plain,
% 0.19/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_4) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_4, e_3))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[344, 343])).
% 0.19/0.48 tff(346,plain,
% 0.19/0.48 (~product(e_3, e_3, e_1)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[345, 87, 95, 339])).
% 0.19/0.48 tff(347,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_4, e_1, e_3)) | (~product(e_1, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_1) | (~product(e_4, e_1, e_3)) | (~product(e_1, e_4, e_3)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(348,plain,
% 0.19/0.48 (((~product(e_1, e_4, e_3)) | product(e_3, e_3, e_1) | (~product(e_4, e_1, e_3))) <=> (product(e_3, e_3, e_1) | (~product(e_4, e_1, e_3)) | (~product(e_1, e_4, e_3)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(349,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_4, e_3)) | product(e_3, e_3, e_1) | (~product(e_4, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_4, e_1, e_3)) | (~product(e_1, e_4, e_3))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[348])).
% 0.19/0.48 tff(350,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_4, e_3)) | product(e_3, e_3, e_1) | (~product(e_4, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_1) | (~product(e_4, e_1, e_3)) | (~product(e_1, e_4, e_3)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[349, 347])).
% 0.19/0.48 tff(351,plain,
% 0.19/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_4, e_3)) | product(e_3, e_3, e_1) | (~product(e_4, e_1, e_3)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(352,plain,
% 0.19/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_1) | (~product(e_4, e_1, e_3)) | (~product(e_1, e_4, e_3))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[351, 350])).
% 0.19/0.48 tff(353,plain,
% 0.19/0.48 (~product(e_4, e_1, e_3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[352, 45, 339, 346])).
% 0.19/0.48 tff(354,plain,
% 0.19/0.48 (product(e_4, e_2, e_3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[130, 353])).
% 0.19/0.48 tff(355,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (product(e_3, e_2, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_4, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | product(e_3, e_2, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_4, e_2, e_3)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(356,plain,
% 0.19/0.48 ((product(e_3, e_2, e_2) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_3, e_4))) <=> (product(e_3, e_2, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_4, e_2, e_3)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(357,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (product(e_3, e_2, e_2) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (product(e_3, e_2, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_4, e_2, e_3))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[356])).
% 0.19/0.48 tff(358,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (product(e_3, e_2, e_2) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | product(e_3, e_2, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_4, e_2, e_3)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[357, 355])).
% 0.19/0.48 tff(359,plain,
% 0.19/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (product(e_3, e_2, e_2) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_3, e_4)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(360,plain,
% 0.19/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | product(e_3, e_2, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_4, e_2, e_3))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[359, 358])).
% 0.19/0.48 tff(361,plain,
% 0.19/0.48 (~product(e_2, e_3, e_4)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[360, 87, 196, 354])).
% 0.19/0.48 tff(362,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_4, e_2)) | product(e_2, e_3, e_4) | (~product(e_3, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (~product(e_3, e_4, e_2)) | product(e_2, e_3, e_4) | (~product(e_3, e_2, e_3)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(363,plain,
% 0.19/0.48 ((product(e_2, e_3, e_4) | (~product(e_3, e_4, e_2)) | (~product(e_3, e_2, e_3))) <=> ((~product(e_3, e_4, e_2)) | product(e_2, e_3, e_4) | (~product(e_3, e_2, e_3)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(364,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_4) | (~product(e_3, e_4, e_2)) | (~product(e_3, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_4, e_2)) | product(e_2, e_3, e_4) | (~product(e_3, e_2, e_3))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[363])).
% 0.19/0.48 tff(365,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_4) | (~product(e_3, e_4, e_2)) | (~product(e_3, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (~product(e_3, e_4, e_2)) | product(e_2, e_3, e_4) | (~product(e_3, e_2, e_3)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[364, 362])).
% 0.19/0.49 tff(366,plain,
% 0.19/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_4) | (~product(e_3, e_4, e_2)) | (~product(e_3, e_2, e_3)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(367,plain,
% 0.19/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (~product(e_3, e_4, e_2)) | product(e_2, e_3, e_4) | (~product(e_3, e_2, e_3))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[366, 365])).
% 0.19/0.49 tff(368,plain,
% 0.19/0.49 (~product(e_3, e_2, e_3)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[367, 87, 209, 361])).
% 0.19/0.49 tff(369,plain,
% 0.19/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (product(e_3, e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | product(e_3, e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_3, e_3)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(370,plain,
% 0.19/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (product(e_3, e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_3, e_3)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(371,plain,
% 0.19/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | product(e_3, e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_3, e_3))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[370, 369])).
% 0.19/0.49 tff(372,plain,
% 0.19/0.49 (~product(e_2, e_3, e_3)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[371, 87, 11, 368])).
% 0.19/0.49 tff(373,assumption,(product(e_2, e_2, e_3)), introduced(assumption)).
% 0.19/0.49 tff(374,plain,
% 0.19/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_2) | (~product(e_2, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_2) | (~product(e_2, e_2, e_3)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(375,plain,
% 0.19/0.49 (((~product(e_2, e_2, e_3)) | product(e_3, e_3, e_2) | (~product(e_2, e_2, e_3))) <=> (product(e_3, e_3, e_2) | (~product(e_2, e_2, e_3)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(376,plain,
% 0.19/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_2, e_3)) | product(e_3, e_3, e_2) | (~product(e_2, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_2) | (~product(e_2, e_2, e_3))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[375])).
% 0.19/0.49 tff(377,plain,
% 0.19/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_2, e_3)) | product(e_3, e_3, e_2) | (~product(e_2, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_2) | (~product(e_2, e_2, e_3)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[376, 374])).
% 0.19/0.49 tff(378,plain,
% 0.19/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_2, e_3)) | product(e_3, e_3, e_2) | (~product(e_2, e_2, e_3)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(379,plain,
% 0.19/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_2) | (~product(e_2, e_2, e_3))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[378, 377])).
% 0.19/0.49 tff(380,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[379, 45, 12, 373])).
% 0.19/0.49 tff(381,plain,((~product(e_2, e_2, e_3)) | product(e_3, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(382,plain,
% 0.19/0.49 (~product(e_2, e_2, e_3)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[381, 12])).
% 0.19/0.49 tff(383,plain,
% 0.19/0.49 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_2)) | (~group_element(e_3)) | product(e_2, e_1, e_3) | product(e_2, e_3, e_3) | product(e_2, e_2, e_3) | product(e_2, e_4, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_2)) | (~group_element(e_3)) | product(e_2, e_1, e_3) | product(e_2, e_3, e_3) | product(e_2, e_2, e_3) | product(e_2, e_4, e_3))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(384,plain,
% 0.19/0.49 (((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_4, e_3) | product(e_2, e_3, e_3) | product(e_2, e_2, e_3) | product(e_2, e_1, e_3)) <=> ((~group_element(e_2)) | (~group_element(e_3)) | product(e_2, e_1, e_3) | product(e_2, e_3, e_3) | product(e_2, e_2, e_3) | product(e_2, e_4, e_3))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(385,plain,
% 0.19/0.49 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_4, e_3) | product(e_2, e_3, e_3) | product(e_2, e_2, e_3) | product(e_2, e_1, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_2)) | (~group_element(e_3)) | product(e_2, e_1, e_3) | product(e_2, e_3, e_3) | product(e_2, e_2, e_3) | product(e_2, e_4, e_3)))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[384])).
% 0.19/0.49 tff(386,plain,
% 0.19/0.49 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_4, e_3) | product(e_2, e_3, e_3) | product(e_2, e_2, e_3) | product(e_2, e_1, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_2)) | (~group_element(e_3)) | product(e_2, e_1, e_3) | product(e_2, e_3, e_3) | product(e_2, e_2, e_3) | product(e_2, e_4, e_3))),
% 0.19/0.49 inference(transitivity,[status(thm)],[385, 383])).
% 0.19/0.49 tff(387,plain,
% 0.19/0.49 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_4, e_3) | product(e_2, e_3, e_3) | product(e_2, e_2, e_3) | product(e_2, e_1, e_3))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(388,plain,
% 0.19/0.49 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_2)) | (~group_element(e_3)) | product(e_2, e_1, e_3) | product(e_2, e_3, e_3) | product(e_2, e_2, e_3) | product(e_2, e_4, e_3)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[387, 386])).
% 0.19/0.49 tff(389,plain,
% 0.19/0.49 (product(e_2, e_1, e_3) | product(e_2, e_3, e_3)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[388, 122, 199, 112, 330, 382])).
% 0.19/0.49 tff(390,plain,
% 0.19/0.49 (product(e_2, e_1, e_3)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[389, 372])).
% 0.19/0.49 tff(391,plain,
% 0.19/0.49 (^[Y: $i, X: $i] : refl(((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(392,plain,
% 0.19/0.49 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[391])).
% 0.19/0.49 tff(393,plain,
% 0.19/0.49 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(394,plain,
% 0.19/0.49 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_1))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> (((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_1)) | product(X, Y, e_2)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1)))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> (((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1)) | product(X, Y, e_3)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1)) | product(X, Y, e_3)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)))), (((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> (((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)) | product(X, Y, e_4)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)) | product(X, Y, e_4)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))), (((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(395,plain,
% 0.19/0.49 (![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[394])).
% 0.19/0.49 tff(396,axiom,(![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_total_function1')).
% 0.19/0.49 tff(397,plain,
% 0.19/0.49 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[396, 395])).
% 0.19/0.49 tff(398,plain,
% 0.19/0.49 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[397, 393])).
% 0.19/0.49 tff(399,plain,(
% 0.19/0.49 ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.19/0.49 inference(skolemize,[status(sab)],[398])).
% 0.19/0.49 tff(400,plain,
% 0.19/0.49 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[399, 392])).
% 0.19/0.49 tff(401,plain,
% 0.19/0.49 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_3)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_4) | product(e_2, e_3, e_3) | product(e_2, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (~group_element(e_2)) | (~group_element(e_3)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_4) | product(e_2, e_3, e_3) | product(e_2, e_3, e_1))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(402,plain,
% 0.19/0.49 (((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_3, e_4) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1)) <=> ((~group_element(e_2)) | (~group_element(e_3)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_4) | product(e_2, e_3, e_3) | product(e_2, e_3, e_1))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(403,plain,
% 0.19/0.49 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_3, e_4) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_3)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_4) | product(e_2, e_3, e_3) | product(e_2, e_3, e_1)))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[402])).
% 0.19/0.49 tff(404,plain,
% 0.19/0.49 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_3, e_4) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (~group_element(e_2)) | (~group_element(e_3)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_4) | product(e_2, e_3, e_3) | product(e_2, e_3, e_1))),
% 0.19/0.49 inference(transitivity,[status(thm)],[403, 401])).
% 0.19/0.49 tff(405,plain,
% 0.19/0.49 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_3, e_4) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(406,plain,
% 0.19/0.49 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (~group_element(e_2)) | (~group_element(e_3)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_4) | product(e_2, e_3, e_3) | product(e_2, e_3, e_1)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[405, 404])).
% 0.19/0.49 tff(407,plain,
% 0.19/0.49 (product(e_2, e_3, e_4) | product(e_2, e_3, e_3) | product(e_2, e_3, e_1)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[406, 199, 112, 400, 276])).
% 0.19/0.49 tff(408,plain,
% 0.19/0.49 (product(e_2, e_3, e_1)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[407, 372, 361])).
% 0.19/0.49 tff(409,plain,
% 0.19/0.49 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl(((~product(Y, X, Z2)) | (~product(Z1, Z2, Y)) | product(X, Y, Z1)) <=> ((~product(Y, X, Z2)) | (~product(Z1, Z2, Y)) | product(X, Y, Z1)))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(410,plain,
% 0.19/0.49 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, Y)) | product(X, Y, Z1)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, Y)) | product(X, Y, Z1))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[409])).
% 0.19/0.49 tff(411,plain,
% 0.19/0.49 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, Y)) | product(X, Y, Z1)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, Y)) | product(X, Y, Z1))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(412,plain,
% 0.19/0.49 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : trans(monotonicity(rewrite((product(X, Y, Z1) | (~product(Z1, Z2, Y))) <=> ((~product(Z1, Z2, Y)) | product(X, Y, Z1))), (((product(X, Y, Z1) | (~product(Z1, Z2, Y))) | (~product(Y, X, Z2))) <=> (((~product(Z1, Z2, Y)) | product(X, Y, Z1)) | (~product(Y, X, Z2))))), rewrite((((~product(Z1, Z2, Y)) | product(X, Y, Z1)) | (~product(Y, X, Z2))) <=> ((~product(Y, X, Z2)) | (~product(Z1, Z2, Y)) | product(X, Y, Z1))), (((product(X, Y, Z1) | (~product(Z1, Z2, Y))) | (~product(Y, X, Z2))) <=> ((~product(Y, X, Z2)) | (~product(Z1, Z2, Y)) | product(X, Y, Z1))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(413,plain,
% 0.19/0.49 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((product(X, Y, Z1) | (~product(Z1, Z2, Y))) | (~product(Y, X, Z2))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, Y)) | product(X, Y, Z1))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[412])).
% 0.19/0.49 tff(414,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : ((product(X, Y, Z1) | (~product(Z1, Z2, Y))) | (~product(Y, X, Z2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qg4_1')).
% 0.19/0.49 tff(415,plain,
% 0.19/0.49 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, Y)) | product(X, Y, Z1))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[414, 413])).
% 0.19/0.49 tff(416,plain,
% 0.19/0.49 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, Y)) | product(X, Y, Z1))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[415, 411])).
% 0.19/0.49 tff(417,plain,(
% 0.19/0.49 ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, Y)) | product(X, Y, Z1))),
% 0.19/0.49 inference(skolemize,[status(sab)],[416])).
% 0.19/0.49 tff(418,plain,
% 0.19/0.49 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, Y)) | product(X, Y, Z1))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[417, 410])).
% 0.19/0.49 tff(419,plain,
% 0.19/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, Y)) | product(X, Y, Z1))) | ((~product(e_1, e_4, e_3)) | (~product(e_2, e_3, e_1)) | product(e_4, e_1, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, Y)) | product(X, Y, Z1))) | (~product(e_1, e_4, e_3)) | (~product(e_2, e_3, e_1)) | product(e_4, e_1, e_2))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(420,plain,
% 0.19/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, Y)) | product(X, Y, Z1))) | ((~product(e_1, e_4, e_3)) | (~product(e_2, e_3, e_1)) | product(e_4, e_1, e_2))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(421,plain,
% 0.19/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, Y)) | product(X, Y, Z1))) | (~product(e_1, e_4, e_3)) | (~product(e_2, e_3, e_1)) | product(e_4, e_1, e_2)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[420, 419])).
% 0.19/0.49 tff(422,plain,
% 0.19/0.49 (product(e_4, e_1, e_2)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[421, 418, 339, 408])).
% 0.19/0.49 tff(423,plain,
% 0.19/0.49 (~product(e_4, e_3, e_2)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[263, 422])).
% 0.19/0.49 tff(424,plain,
% 0.19/0.49 (product(e_1, e_3, e_2)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[283, 423, 12])).
% 0.19/0.49 tff(425,plain,
% 0.19/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, Y)) | product(X, Y, Z1))) | ((~product(e_1, e_3, e_2)) | product(e_1, e_2, e_1) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, Y)) | product(X, Y, Z1))) | (~product(e_1, e_3, e_2)) | product(e_1, e_2, e_1) | (~product(e_2, e_1, e_3)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(426,plain,
% 0.19/0.49 (((~product(e_2, e_1, e_3)) | (~product(e_1, e_3, e_2)) | product(e_1, e_2, e_1)) <=> ((~product(e_1, e_3, e_2)) | product(e_1, e_2, e_1) | (~product(e_2, e_1, e_3)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(427,plain,
% 0.19/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, Y)) | product(X, Y, Z1))) | ((~product(e_2, e_1, e_3)) | (~product(e_1, e_3, e_2)) | product(e_1, e_2, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, Y)) | product(X, Y, Z1))) | ((~product(e_1, e_3, e_2)) | product(e_1, e_2, e_1) | (~product(e_2, e_1, e_3))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[426])).
% 0.19/0.50 tff(428,plain,
% 0.19/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, Y)) | product(X, Y, Z1))) | ((~product(e_2, e_1, e_3)) | (~product(e_1, e_3, e_2)) | product(e_1, e_2, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, Y)) | product(X, Y, Z1))) | (~product(e_1, e_3, e_2)) | product(e_1, e_2, e_1) | (~product(e_2, e_1, e_3)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[427, 425])).
% 0.19/0.50 tff(429,plain,
% 0.19/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, Y)) | product(X, Y, Z1))) | ((~product(e_2, e_1, e_3)) | (~product(e_1, e_3, e_2)) | product(e_1, e_2, e_1))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(430,plain,
% 0.19/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, Y)) | product(X, Y, Z1))) | (~product(e_1, e_3, e_2)) | product(e_1, e_2, e_1) | (~product(e_2, e_1, e_3))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[429, 428])).
% 0.19/0.50 tff(431,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[430, 418, 424, 165, 390])).
% 0.19/0.50 tff(432,plain,(product(e_2, e_4, e_3) | product(e_3, e_3, e_2) | (~product(e_3, e_4, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(433,plain,
% 0.19/0.50 (~product(e_3, e_4, e_2)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[432, 329, 12])).
% 0.19/0.50 tff(434,plain,
% 0.19/0.50 (product(e_1, e_4, e_3)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[338, 329])).
% 0.19/0.50 tff(435,assumption,(product(e_1, e_4, e_3)), introduced(assumption)).
% 0.19/0.50 tff(436,plain,
% 0.19/0.50 (~product(e_3, e_3, e_1)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[345, 87, 95, 435])).
% 0.19/0.50 tff(437,plain,
% 0.19/0.50 (~product(e_4, e_1, e_3)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[352, 45, 435, 436])).
% 0.19/0.50 tff(438,plain,
% 0.19/0.50 (product(e_4, e_2, e_3)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[130, 437])).
% 0.19/0.50 tff(439,plain,
% 0.19/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, Y)) | product(X, Y, Z1))) | ((~product(e_3, e_1, e_2)) | (~product(e_4, e_2, e_3)) | product(e_1, e_3, e_4))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, Y)) | product(X, Y, Z1))) | (~product(e_3, e_1, e_2)) | (~product(e_4, e_2, e_3)) | product(e_1, e_3, e_4))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(440,plain,
% 0.19/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, Y)) | product(X, Y, Z1))) | ((~product(e_3, e_1, e_2)) | (~product(e_4, e_2, e_3)) | product(e_1, e_3, e_4))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(441,plain,
% 0.19/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | (~product(Z1, Z2, Y)) | product(X, Y, Z1))) | (~product(e_3, e_1, e_2)) | (~product(e_4, e_2, e_3)) | product(e_1, e_3, e_4)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[440, 439])).
% 0.19/0.50 tff(442,plain,
% 0.19/0.50 (product(e_1, e_3, e_4)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[441, 418, 171, 438])).
% 0.19/0.50 tff(443,plain,
% 0.19/0.50 (~product(e_1, e_3, e_2)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[307, 442])).
% 0.19/0.50 tff(444,plain,
% 0.19/0.50 (product(e_4, e_3, e_2)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[283, 443, 12])).
% 0.19/0.50 tff(445,assumption,(product(e_4, e_2, e_3)), introduced(assumption)).
% 0.19/0.50 tff(446,assumption,(~product(e_2, e_4, e_1)), introduced(assumption)).
% 0.19/0.50 tff(447,plain,
% 0.19/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (product(e_2, e_4, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_4, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | product(e_2, e_4, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_4, e_2, e_3)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(448,plain,
% 0.19/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | (product(e_2, e_4, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_4, e_2, e_3)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(449,plain,
% 0.19/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Y, X, Z2) | (~product(Z1, Z2, Y)) | (~product(X, Y, Z1)))) | product(e_2, e_4, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_4, e_2, e_3))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[448, 447])).
% 0.19/0.50 tff(450,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[449, 87, 446, 171, 445])).
% 0.19/0.50 tff(451,plain,((~product(e_3, e_1, e_2)) | product(e_2, e_4, e_1) | (~product(e_4, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(452,plain,
% 0.19/0.50 (product(e_2, e_4, e_1)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[451, 438, 171])).
% 0.19/0.50 tff(453,plain,
% 0.19/0.50 ((~equalish(e_4, e_2)) <=> (~equalish(e_4, e_2))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(454,axiom,(~equalish(e_4, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_2')).
% 0.19/0.50 tff(455,plain,
% 0.19/0.50 (~equalish(e_4, e_2)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[454, 453])).
% 0.19/0.50 tff(456,plain,
% 0.19/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | (equalish(e_4, e_2) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | equalish(e_4, e_2) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_4, e_1)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(457,plain,
% 0.19/0.50 (((~product(e_4, e_4, e_1)) | equalish(e_4, e_2) | (~product(e_2, e_4, e_1))) <=> (equalish(e_4, e_2) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_4, e_1)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(458,plain,
% 0.19/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | ((~product(e_4, e_4, e_1)) | equalish(e_4, e_2) | (~product(e_2, e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | (equalish(e_4, e_2) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_4, e_1))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[457])).
% 0.19/0.50 tff(459,plain,
% 0.19/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | ((~product(e_4, e_4, e_1)) | equalish(e_4, e_2) | (~product(e_2, e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | equalish(e_4, e_2) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_4, e_1)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[458, 456])).
% 0.19/0.50 tff(460,plain,
% 0.19/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | ((~product(e_4, e_4, e_1)) | equalish(e_4, e_2) | (~product(e_2, e_4, e_1)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(461,plain,
% 0.19/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~product(W, Y, X)) | equalish(W, Z) | (~product(Z, Y, X)))) | equalish(e_4, e_2) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_4, e_1))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[460, 459])).
% 0.19/0.50 tff(462,plain,
% 0.19/0.50 ((~product(e_2, e_4, e_1)) | (~product(e_4, e_4, e_1))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[461, 455, 24])).
% 0.19/0.50 tff(463,plain,
% 0.19/0.50 (~product(e_4, e_4, e_1)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[462, 452])).
% 0.19/0.50 tff(464,plain,
% 0.19/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_1)) | product(e_1, e_1, e_2) | (~product(e_4, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_2, e_4, e_1)) | product(e_1, e_1, e_2) | (~product(e_4, e_2, e_1)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(465,plain,
% 0.19/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_1)) | product(e_1, e_1, e_2) | (~product(e_4, e_2, e_1)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(466,plain,
% 0.19/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_2, e_4, e_1)) | product(e_1, e_1, e_2) | (~product(e_4, e_2, e_1))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[465, 464])).
% 0.19/0.50 tff(467,plain,
% 0.19/0.50 (~product(e_4, e_2, e_1)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[466, 45, 452, 234])).
% 0.19/0.50 tff(468,plain,
% 0.19/0.50 (~product(e_1, e_2, e_3)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[177, 87, 171, 169])).
% 0.19/0.50 tff(469,plain,
% 0.19/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_2)) | product(e_1, e_2, e_3) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_1, e_2, e_3) | (~product(e_1, e_3, e_1)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(470,plain,
% 0.19/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_2)) | product(e_1, e_2, e_3) | (~product(e_1, e_3, e_1)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(471,plain,
% 0.19/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_1, e_2, e_3) | (~product(e_1, e_3, e_1))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[470, 469])).
% 0.19/0.50 tff(472,plain,
% 0.19/0.50 (~product(e_1, e_3, e_1)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[471, 45, 171, 468])).
% 0.19/0.50 tff(473,plain,
% 0.19/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_1) | (~product(e_1, e_4, e_3)) | (~product(e_4, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_1) | (~product(e_1, e_4, e_3)) | (~product(e_4, e_1, e_1)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(474,plain,
% 0.19/0.50 (((~product(e_1, e_4, e_3)) | product(e_1, e_3, e_1) | (~product(e_4, e_1, e_1))) <=> (product(e_1, e_3, e_1) | (~product(e_1, e_4, e_3)) | (~product(e_4, e_1, e_1)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(475,plain,
% 0.19/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_4, e_3)) | product(e_1, e_3, e_1) | (~product(e_4, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_1) | (~product(e_1, e_4, e_3)) | (~product(e_4, e_1, e_1))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[474])).
% 0.19/0.50 tff(476,plain,
% 0.19/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_4, e_3)) | product(e_1, e_3, e_1) | (~product(e_4, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_1) | (~product(e_1, e_4, e_3)) | (~product(e_4, e_1, e_1)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[475, 473])).
% 0.19/0.50 tff(477,plain,
% 0.19/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_4, e_3)) | product(e_1, e_3, e_1) | (~product(e_4, e_1, e_1)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(478,plain,
% 0.19/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_1) | (~product(e_1, e_4, e_3)) | (~product(e_4, e_1, e_1))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[477, 476])).
% 0.19/0.50 tff(479,plain,
% 0.19/0.50 (~product(e_4, e_1, e_1)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[478, 45, 435, 472])).
% 0.19/0.50 tff(480,plain,
% 0.19/0.50 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (product(e_4, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_1)) | product(e_4, e_3, e_1) | product(e_4, e_2, e_1) | product(e_4, e_1, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | product(e_4, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_1)) | product(e_4, e_3, e_1) | product(e_4, e_2, e_1) | product(e_4, e_1, e_1))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(481,plain,
% 0.19/0.50 (((~group_element(e_1)) | (~group_element(e_4)) | product(e_4, e_4, e_1) | product(e_4, e_3, e_1) | product(e_4, e_2, e_1) | product(e_4, e_1, e_1)) <=> (product(e_4, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_1)) | product(e_4, e_3, e_1) | product(e_4, e_2, e_1) | product(e_4, e_1, e_1))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(482,plain,
% 0.19/0.50 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_1)) | (~group_element(e_4)) | product(e_4, e_4, e_1) | product(e_4, e_3, e_1) | product(e_4, e_2, e_1) | product(e_4, e_1, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (product(e_4, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_1)) | product(e_4, e_3, e_1) | product(e_4, e_2, e_1) | product(e_4, e_1, e_1)))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[481])).
% 0.19/0.50 tff(483,plain,
% 0.19/0.50 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_1)) | (~group_element(e_4)) | product(e_4, e_4, e_1) | product(e_4, e_3, e_1) | product(e_4, e_2, e_1) | product(e_4, e_1, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | product(e_4, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_1)) | product(e_4, e_3, e_1) | product(e_4, e_2, e_1) | product(e_4, e_1, e_1))),
% 0.19/0.50 inference(transitivity,[status(thm)],[482, 480])).
% 0.19/0.50 tff(484,plain,
% 0.19/0.50 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_1)) | (~group_element(e_4)) | product(e_4, e_4, e_1) | product(e_4, e_3, e_1) | product(e_4, e_2, e_1) | product(e_4, e_1, e_1))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(485,plain,
% 0.19/0.50 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | product(e_4, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_1)) | product(e_4, e_3, e_1) | product(e_4, e_2, e_1) | product(e_4, e_1, e_1)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[484, 483])).
% 0.19/0.50 tff(486,plain,
% 0.19/0.50 (product(e_4, e_4, e_1) | product(e_4, e_3, e_1) | product(e_4, e_2, e_1)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[485, 122, 141, 109, 479])).
% 0.19/0.50 tff(487,plain,
% 0.19/0.50 (product(e_4, e_3, e_1)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[486, 467, 463])).
% 0.19/0.50 tff(488,plain,
% 0.19/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_1, e_2) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_1, e_2) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_3, e_1)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(489,plain,
% 0.19/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_1, e_2) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_3, e_1)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(490,plain,
% 0.19/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_1, e_2) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_3, e_1))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[489, 488])).
% 0.19/0.51 tff(491,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[490, 222, 296, 487, 444])).
% 0.19/0.51 tff(492,plain,((~product(e_1, e_4, e_3)) | product(e_3, e_3, e_2) | (~product(e_3, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.51 tff(493,plain,
% 0.19/0.51 (~product(e_3, e_1, e_2)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[492, 434, 12])).
% 0.19/0.51 tff(494,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[206, 493, 433, 12])).
% 0.19/0.51 tff(495,plain,(product(e_3, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.51 tff(496,plain,
% 0.19/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_2, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_3, e_3)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(497,plain,
% 0.19/0.51 ((equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_2))) <=> (equalish(e_2, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_3, e_3)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(498,plain,
% 0.19/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_3, e_3))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[497])).
% 0.19/0.51 tff(499,plain,
% 0.19/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_2, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_3, e_3)))),
% 0.19/0.51 inference(transitivity,[status(thm)],[498, 496])).
% 0.19/0.51 tff(500,plain,
% 0.19/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_2)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(501,plain,
% 0.19/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_2, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_3, e_3))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[500, 499])).
% 0.19/0.51 tff(502,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[501, 188, 296, 495, 11])).
% 0.19/0.51 % SZS output end Proof
% 0.19/0.51 % E exiting
%------------------------------------------------------------------------------