%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP127-3.004 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:07:08 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.45s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP127-3.004 : TPTP v9.0.0. Released v1.2.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n006.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Thu Jun 19 15:42:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.45 % SZS status Unsatisfiable
% 0.20/0.45 % SZS output start Proof
% 0.20/0.45 tff(product_type, type, (
% 0.20/0.45 product: ( $i * $i * $i ) > $o)).
% 0.20/0.45 tff(e_4_type, type, (
% 0.20/0.45 e_4: $i)).
% 0.20/0.45 tff(e_1_type, type, (
% 0.20/0.45 e_1: $i)).
% 0.20/0.45 tff(e_2_type, type, (
% 0.20/0.45 e_2: $i)).
% 0.20/0.45 tff(e_3_type, type, (
% 0.20/0.45 e_3: $i)).
% 0.20/0.45 tff(cycle_type, type, (
% 0.20/0.45 cycle: ( $i * $i ) > $o)).
% 0.20/0.45 tff(e_0_type, type, (
% 0.20/0.45 e_0: $i)).
% 0.20/0.45 tff(greater_type, type, (
% 0.20/0.45 greater: ( $i * $i ) > $o)).
% 0.20/0.45 tff(next_type, type, (
% 0.20/0.45 next: ( $i * $i ) > $o)).
% 0.20/0.45 tff(group_element_type, type, (
% 0.20/0.45 group_element: $i > $o)).
% 0.20/0.45 tff(equalish_type, type, (
% 0.20/0.45 equalish: ( $i * $i ) > $o)).
% 0.20/0.45 tff(1,assumption,(product(e_2, e_1, e_4)), introduced(assumption)).
% 0.20/0.45 tff(2,plain,
% 0.20/0.45 (^[Y: $i, X: $i] : refl(((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0))) <=> ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(3,plain,
% 0.20/0.45 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0))) <=> ![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.45 tff(4,plain,
% 0.20/0.45 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0))) <=> ![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(5,plain,
% 0.20/0.45 (^[Y: $i, X: $i] : rewrite((((~cycle(X, e_0)) | (~product(X, e_1, Y))) | (~greater(Y, X))) <=> ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(6,plain,
% 0.20/0.45 (![Y: $i, X: $i] : (((~cycle(X, e_0)) | (~product(X, e_1, Y))) | (~greater(Y, X))) <=> ![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[5])).
% 0.20/0.45 tff(7,axiom,(![Y: $i, X: $i] : (((~cycle(X, e_0)) | (~product(X, e_1, Y))) | (~greater(Y, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cycle6')).
% 0.20/0.45 tff(8,plain,
% 0.20/0.45 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.20/0.45 tff(9,plain,
% 0.20/0.45 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.20/0.45 tff(10,plain,(
% 0.20/0.45 ![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[9])).
% 0.20/0.45 tff(11,plain,
% 0.20/0.45 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.20/0.45 tff(12,plain,
% 0.20/0.45 (greater(e_4, e_2) <=> greater(e_4, e_2)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(13,axiom,(greater(e_4, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_greater_e_2')).
% 0.20/0.45 tff(14,plain,
% 0.20/0.45 (greater(e_4, e_2)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.45 tff(15,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(16,plain,
% 0.20/0.45 (((~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)) | (~cycle(e_2, e_0))) <=> ((~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(17,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[16])).
% 0.20/0.45 tff(18,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[17, 15])).
% 0.20/0.45 tff(19,plain,
% 0.20/0.45 ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)) | (~cycle(e_2, e_0)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(20,plain,
% 0.20/0.45 ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.20/0.45 tff(21,plain,
% 0.20/0.45 ((~cycle(e_2, e_0)) | (~product(e_2, e_1, e_4))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[20, 14, 11])).
% 0.20/0.45 tff(22,plain,
% 0.20/0.45 (~cycle(e_2, e_0)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[21, 1])).
% 0.20/0.45 tff(23,assumption,(cycle(e_3, e_0)), introduced(assumption)).
% 0.20/0.45 tff(24,plain,
% 0.20/0.45 (^[W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : refl(((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) <=> ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(25,plain,
% 0.20/0.45 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) <=> ![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.45 tff(26,plain,
% 0.20/0.45 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) <=> ![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(27,plain,
% 0.20/0.45 (^[W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) <=> ((~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))), (((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) <=> (((~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~next(Y, W))))), rewrite((((~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~next(Y, W))) <=> ((~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))), (((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) <=> ((~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))))), ((((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) | (~greater(Y, X))) <=> (((~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~greater(Y, X))))), rewrite((((~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~greater(Y, X))) <=> ((~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))), ((((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) | (~greater(Y, X))) <=> ((~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))))), (((((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) | (~greater(Y, X))) | (~greater(Z1, Z2))) <=> (((~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~greater(Z1, Z2))))), rewrite((((~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~greater(Z1, Z2))) <=> ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))), (((((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) | (~greater(Y, X))) | (~greater(Z1, Z2))) <=> ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(28,plain,
% 0.20/0.45 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) | (~greater(Y, X))) | (~greater(Z1, Z2))) <=> ![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.46 tff(29,axiom,(![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) | (~greater(Y, X))) | (~greater(Z1, Z2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cycle5')).
% 0.20/0.46 tff(30,plain,
% 0.20/0.46 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.46 tff(31,plain,
% 0.20/0.46 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.20/0.46 tff(32,plain,(
% 0.20/0.46 ![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[31])).
% 0.20/0.46 tff(33,plain,
% 0.20/0.46 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.20/0.46 tff(34,plain,
% 0.20/0.46 (cycle(e_4, e_0) <=> cycle(e_4, e_0)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(35,axiom,(cycle(e_4, e_0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cycle3')).
% 0.20/0.46 tff(36,plain,
% 0.20/0.46 (cycle(e_4, e_0)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.46 tff(37,plain,
% 0.20/0.46 (greater(e_3, e_2) <=> greater(e_3, e_2)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(38,axiom,(greater(e_3, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_greater_e_2')).
% 0.20/0.46 tff(39,plain,
% 0.20/0.46 (greater(e_3, e_2)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.20/0.46 tff(40,plain,
% 0.20/0.46 (greater(e_3, e_0) <=> greater(e_3, e_0)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(41,axiom,(greater(e_3, e_0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_greater_e_0')).
% 0.20/0.46 tff(42,plain,
% 0.20/0.46 (greater(e_3, e_0)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.46 tff(43,plain,
% 0.20/0.46 (next(e_3, e_4) <=> next(e_3, e_4)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(44,axiom,(next(e_3, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_then_e_4')).
% 0.20/0.46 tff(45,plain,
% 0.20/0.46 (next(e_3, e_4)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.46 tff(46,plain,
% 0.20/0.46 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(47,plain,
% 0.20/0.46 (((~greater(e_3, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_3))) <=> ((~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(48,plain,
% 0.20/0.46 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_3, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_3)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[47])).
% 0.20/0.46 tff(49,plain,
% 0.20/0.46 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_3, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_3)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[48, 46])).
% 0.20/0.46 tff(50,plain,
% 0.20/0.46 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_3, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_3)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(51,plain,
% 0.20/0.46 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.46 tff(52,plain,
% 0.20/0.46 ((~cycle(e_3, e_0)) | (~cycle(e_2, e_3))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[51, 45, 42, 39, 36, 33])).
% 0.20/0.46 tff(53,plain,
% 0.20/0.46 (~cycle(e_2, e_3)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[52, 23])).
% 0.20/0.46 tff(54,assumption,(~cycle(e_2, e_0)), introduced(assumption)).
% 0.20/0.46 tff(55,plain,
% 0.20/0.46 (greater(e_1, e_0) <=> greater(e_1, e_0)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(56,axiom,(greater(e_1, e_0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_greater_e_0')).
% 0.20/0.46 tff(57,plain,
% 0.20/0.46 (greater(e_1, e_0)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.46 tff(58,plain,
% 0.20/0.46 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_4, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_1)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_4, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_1)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(59,plain,
% 0.20/0.46 (((~greater(e_1, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_1))) <=> ((~cycle(e_4, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_1)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(60,plain,
% 0.20/0.46 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_1, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_1)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_4, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_1))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[59])).
% 0.20/0.46 tff(61,plain,
% 0.20/0.46 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_1, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_1)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_4, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_1)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[60, 58])).
% 0.20/0.46 tff(62,plain,
% 0.20/0.46 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_1, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_1)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(63,plain,
% 0.20/0.46 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_4, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_1))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.46 tff(64,plain,
% 0.20/0.46 ((~cycle(e_3, e_0)) | (~cycle(e_2, e_1))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[63, 45, 57, 39, 36, 33])).
% 0.20/0.46 tff(65,plain,
% 0.20/0.46 (~cycle(e_2, e_1)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[64, 23])).
% 0.20/0.46 tff(66,plain,
% 0.20/0.46 (greater(e_2, e_0) <=> greater(e_2, e_0)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(67,axiom,(greater(e_2, e_0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_greater_e_0')).
% 0.20/0.46 tff(68,plain,
% 0.20/0.46 (greater(e_2, e_0)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.20/0.46 tff(69,plain,
% 0.20/0.46 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(70,plain,
% 0.20/0.46 (((~greater(e_2, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_2))) <=> ((~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(71,plain,
% 0.20/0.46 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_2, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_2)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[70])).
% 0.20/0.46 tff(72,plain,
% 0.20/0.46 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_2, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_2)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[71, 69])).
% 0.20/0.46 tff(73,plain,
% 0.20/0.46 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_2, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_2)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(74,plain,
% 0.20/0.46 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.20/0.46 tff(75,plain,
% 0.20/0.46 ((~cycle(e_3, e_0)) | (~cycle(e_2, e_2))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[74, 45, 68, 39, 36, 33])).
% 0.20/0.46 tff(76,plain,
% 0.20/0.46 (~cycle(e_2, e_2)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[75, 23])).
% 0.20/0.46 tff(77,plain,
% 0.20/0.46 (group_element(e_2) <=> group_element(e_2)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(78,axiom,(group_element(e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_2')).
% 0.20/0.46 tff(79,plain,
% 0.20/0.46 (group_element(e_2)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.46 tff(80,plain,
% 0.20/0.46 (^[X: $i] : refl((cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) <=> (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(81,plain,
% 0.20/0.46 (![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) <=> ![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[80])).
% 0.20/0.46 tff(82,plain,
% 0.20/0.46 (![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) <=> ![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(83,plain,
% 0.20/0.46 (^[X: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) <=> (cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))), (((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) <=> ((cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) | cycle(X, e_2)))), rewrite(((cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) | cycle(X, e_2)) <=> (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))), (((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) <=> (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))))), ((((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) | cycle(X, e_3)) <=> ((cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) | cycle(X, e_3)))), rewrite(((cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) | cycle(X, e_3)) <=> (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))), ((((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) | cycle(X, e_3)) <=> (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(84,plain,
% 0.20/0.46 (![X: $i] : (((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) | cycle(X, e_3)) <=> ![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[83])).
% 0.20/0.46 tff(85,axiom,(![X: $i] : (((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) | cycle(X, e_3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cycle2')).
% 0.20/0.46 tff(86,plain,
% 0.20/0.46 (![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.46 tff(87,plain,
% 0.20/0.46 (![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.20/0.46 tff(88,plain,(
% 0.20/0.46 ![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[87])).
% 0.20/0.46 tff(89,plain,
% 0.20/0.46 (![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.20/0.46 tff(90,plain,
% 0.20/0.46 (((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0) | (~group_element(e_2)))) <=> ((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0) | (~group_element(e_2)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(91,plain,
% 0.20/0.46 ((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0) | (~group_element(e_2)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(92,plain,
% 0.20/0.46 ((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0) | (~group_element(e_2))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.20/0.46 tff(93,plain,
% 0.20/0.46 (cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[92, 89, 79])).
% 0.20/0.46 tff(94,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[93, 76, 65, 54, 53])).
% 0.20/0.46 tff(95,plain,((~cycle(e_3, e_0)) | cycle(e_2, e_0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(96,plain,
% 0.20/0.46 (~cycle(e_3, e_0)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[95, 22])).
% 0.20/0.46 tff(97,assumption,(cycle(e_3, e_3)), introduced(assumption)).
% 0.20/0.46 tff(98,plain,
% 0.20/0.46 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(99,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.20/0.46 tff(100,plain,
% 0.20/0.46 (~equalish(e_3, e_1)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.46 tff(101,plain,
% 0.20/0.46 (^[W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : refl(((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) <=> ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(102,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) <=> ![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[101])).
% 0.20/0.46 tff(103,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) <=> ![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(104,plain,
% 0.20/0.46 (^[W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) <=> ((~cycle(X, Y)) | (~next(X, W)) | (~cycle(W, Z)))), (((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) <=> (((~cycle(X, Y)) | (~next(X, W)) | (~cycle(W, Z))) | (~greater(Y, e_0))))), rewrite((((~cycle(X, Y)) | (~next(X, W)) | (~cycle(W, Z))) | (~greater(Y, e_0))) <=> ((~cycle(X, Y)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))), (((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) <=> ((~cycle(X, Y)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))))), ((((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) | (~next(Z, Z1))) <=> (((~cycle(X, Y)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) | (~next(Z, Z1))))), rewrite((((~cycle(X, Y)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) | (~next(Z, Z1))) <=> ((~cycle(X, Y)) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))), ((((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) | (~next(Z, Z1))) <=> ((~cycle(X, Y)) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))))), (((((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) | (~next(Z, Z1))) | equalish(Y, Z1)) <=> (((~cycle(X, Y)) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) | equalish(Y, Z1)))), rewrite((((~cycle(X, Y)) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) | equalish(Y, Z1)) <=> ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))), (((((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) | (~next(Z, Z1))) | equalish(Y, Z1)) <=> ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(105,plain,
% 0.20/0.47 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) | (~next(Z, Z1))) | equalish(Y, Z1)) <=> ![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[104])).
% 0.20/0.47 tff(106,axiom,(![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) | (~next(Z, Z1))) | equalish(Y, Z1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cycle4')).
% 0.20/0.47 tff(107,plain,
% 0.20/0.47 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.20/0.47 tff(108,plain,
% 0.20/0.47 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.20/0.47 tff(109,plain,(
% 0.20/0.47 ![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[108])).
% 0.20/0.47 tff(110,plain,
% 0.20/0.47 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.20/0.47 tff(111,plain,
% 0.20/0.47 (next(e_0, e_1) <=> next(e_0, e_1)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(112,axiom,(next(e_0, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_0_then_e_1')).
% 0.20/0.47 tff(113,plain,
% 0.20/0.47 (next(e_0, e_1)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.20/0.47 tff(114,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_3, e_1) | (~cycle(e_4, e_0)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~next(e_0, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_1) | (~cycle(e_4, e_0)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~next(e_0, e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(115,plain,
% 0.20/0.47 (((~cycle(e_3, e_3)) | equalish(e_3, e_1) | (~next(e_0, e_1)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0))) <=> (equalish(e_3, e_1) | (~cycle(e_4, e_0)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~next(e_0, e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(116,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_3, e_3)) | equalish(e_3, e_1) | (~next(e_0, e_1)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_3, e_1) | (~cycle(e_4, e_0)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~next(e_0, e_1))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[115])).
% 0.20/0.47 tff(117,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_3, e_3)) | equalish(e_3, e_1) | (~next(e_0, e_1)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_1) | (~cycle(e_4, e_0)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~next(e_0, e_1)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[116, 114])).
% 0.20/0.47 tff(118,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_3, e_3)) | equalish(e_3, e_1) | (~next(e_0, e_1)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(119,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_1) | (~cycle(e_4, e_0)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~next(e_0, e_1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.20/0.47 tff(120,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[119, 113, 45, 42, 36, 110, 100, 97])).
% 0.20/0.47 tff(121,plain,(~cycle(e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(122,assumption,(cycle(e_3, e_2)), introduced(assumption)).
% 0.20/0.47 tff(123,plain,
% 0.20/0.47 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(124,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.20/0.47 tff(125,plain,
% 0.20/0.47 (~equalish(e_2, e_1)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.20/0.47 tff(126,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_2, e_1) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~next(e_0, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_1) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~next(e_0, e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(127,plain,
% 0.20/0.47 (((~cycle(e_3, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0))) <=> (equalish(e_2, e_1) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~next(e_0, e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(128,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_3, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_2, e_1) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~next(e_0, e_1))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[127])).
% 0.20/0.47 tff(129,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_3, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_1) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~next(e_0, e_1)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[128, 126])).
% 0.20/0.47 tff(130,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_3, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(131,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_1) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~next(e_0, e_1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.20/0.47 tff(132,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[131, 113, 45, 68, 36, 110, 125, 122])).
% 0.20/0.47 tff(133,plain,(~cycle(e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(134,plain,
% 0.20/0.47 (group_element(e_3) <=> group_element(e_3)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(135,axiom,(group_element(e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_3')).
% 0.20/0.47 tff(136,plain,
% 0.20/0.47 (group_element(e_3)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.20/0.47 tff(137,plain,
% 0.20/0.47 (((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0) | (~group_element(e_3)))) <=> ((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0) | (~group_element(e_3)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(138,plain,
% 0.20/0.47 ((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0) | (~group_element(e_3)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(139,plain,
% 0.20/0.47 ((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0) | (~group_element(e_3))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.20/0.47 tff(140,plain,
% 0.20/0.47 (cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[139, 89, 136])).
% 0.20/0.47 tff(141,plain,
% 0.20/0.47 (cycle(e_3, e_3) | cycle(e_3, e_1) | cycle(e_3, e_0)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[140, 133])).
% 0.20/0.47 tff(142,plain,
% 0.20/0.47 (cycle(e_3, e_1) | cycle(e_3, e_0)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[141, 121])).
% 0.20/0.47 tff(143,plain,
% 0.20/0.47 (cycle(e_3, e_1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[142, 96])).
% 0.20/0.47 tff(144,plain,
% 0.20/0.47 ((~equalish(e_1, e_4)) <=> (~equalish(e_1, e_4))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(145,axiom,(~equalish(e_1, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_4')).
% 0.20/0.47 tff(146,plain,
% 0.20/0.47 (~equalish(e_1, e_4)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.20/0.47 tff(147,plain,
% 0.20/0.47 (^[Z: $i, Y: $i, X: $i, X1: $i] : refl(((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z))) <=> ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(148,plain,
% 0.20/0.47 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z))) <=> ![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[147])).
% 0.20/0.47 tff(149,plain,
% 0.20/0.47 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z))) <=> ![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(150,plain,
% 0.20/0.47 (^[Z: $i, Y: $i, X: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~cycle(X, Y)) | (~product(X, e_1, Z))) | (~greater(Y, e_0))) <=> ((~greater(Y, e_0)) | (~cycle(X, Y)) | (~product(X, e_1, Z)))), (((((~cycle(X, Y)) | (~product(X, e_1, Z))) | (~greater(Y, e_0))) | (~next(X, X1))) <=> (((~greater(Y, e_0)) | (~cycle(X, Y)) | (~product(X, e_1, Z))) | (~next(X, X1))))), rewrite((((~greater(Y, e_0)) | (~cycle(X, Y)) | (~product(X, e_1, Z))) | (~next(X, X1))) <=> ((~greater(Y, e_0)) | (~cycle(X, Y)) | (~next(X, X1)) | (~product(X, e_1, Z)))), (((((~cycle(X, Y)) | (~product(X, e_1, Z))) | (~greater(Y, e_0))) | (~next(X, X1))) <=> ((~greater(Y, e_0)) | (~cycle(X, Y)) | (~next(X, X1)) | (~product(X, e_1, Z))))), ((((((~cycle(X, Y)) | (~product(X, e_1, Z))) | (~greater(Y, e_0))) | (~next(X, X1))) | equalish(Z, X1)) <=> (((~greater(Y, e_0)) | (~cycle(X, Y)) | (~next(X, X1)) | (~product(X, e_1, Z))) | equalish(Z, X1)))), rewrite((((~greater(Y, e_0)) | (~cycle(X, Y)) | (~next(X, X1)) | (~product(X, e_1, Z))) | equalish(Z, X1)) <=> ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))), ((((((~cycle(X, Y)) | (~product(X, e_1, Z))) | (~greater(Y, e_0))) | (~next(X, X1))) | equalish(Z, X1)) <=> ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(151,plain,
% 0.20/0.47 (![Z: $i, Y: $i, X: $i, X1: $i] : (((((~cycle(X, Y)) | (~product(X, e_1, Z))) | (~greater(Y, e_0))) | (~next(X, X1))) | equalish(Z, X1)) <=> ![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[150])).
% 0.20/0.47 tff(152,axiom,(![Z: $i, Y: $i, X: $i, X1: $i] : (((((~cycle(X, Y)) | (~product(X, e_1, Z))) | (~greater(Y, e_0))) | (~next(X, X1))) | equalish(Z, X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cycle7')).
% 0.20/0.47 tff(153,plain,
% 0.20/0.47 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.20/0.47 tff(154,plain,
% 0.20/0.47 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[153, 149])).
% 0.20/0.47 tff(155,plain,(
% 0.20/0.47 ![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[154])).
% 0.20/0.47 tff(156,plain,
% 0.20/0.47 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[155, 148])).
% 0.20/0.47 tff(157,plain,
% 0.20/0.47 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_1, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_1)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_1, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(158,plain,
% 0.20/0.47 (((~greater(e_1, e_0)) | (~cycle(e_3, e_1)) | equalish(e_1, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_1))) <=> (equalish(e_1, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(159,plain,
% 0.20/0.47 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_3, e_1)) | equalish(e_1, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_1)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_1, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_1))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[158])).
% 0.20/0.47 tff(160,plain,
% 0.20/0.47 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_3, e_1)) | equalish(e_1, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_1)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_1, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[159, 157])).
% 0.20/0.47 tff(161,plain,
% 0.20/0.47 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_3, e_1)) | equalish(e_1, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_1)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(162,plain,
% 0.20/0.47 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_1, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.20/0.47 tff(163,plain,
% 0.20/0.47 (~product(e_3, e_1, e_1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[162, 45, 57, 156, 146, 143])).
% 0.20/0.47 tff(164,plain,
% 0.20/0.47 ((~equalish(e_2, e_4)) <=> (~equalish(e_2, e_4))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(165,axiom,(~equalish(e_2, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_4')).
% 0.20/0.47 tff(166,plain,
% 0.20/0.47 (~equalish(e_2, e_4)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.20/0.47 tff(167,plain,
% 0.20/0.47 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_2, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_2)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_2)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(168,plain,
% 0.20/0.47 (((~greater(e_1, e_0)) | (~cycle(e_3, e_1)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2))) <=> (equalish(e_2, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_2)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(169,plain,
% 0.20/0.47 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_3, e_1)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_2, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_2))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[168])).
% 0.20/0.47 tff(170,plain,
% 0.20/0.47 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_3, e_1)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_2)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[169, 167])).
% 0.20/0.47 tff(171,plain,
% 0.20/0.47 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_3, e_1)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(172,plain,
% 0.20/0.47 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_2))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.20/0.48 tff(173,plain,
% 0.20/0.48 (~product(e_3, e_1, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[172, 45, 57, 156, 166, 143])).
% 0.20/0.48 tff(174,assumption,(product(e_3, e_1, e_3)), introduced(assumption)).
% 0.20/0.48 tff(175,plain,
% 0.20/0.48 (^[X: $i] : refl(product(X, X, X) <=> product(X, X, X))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(176,plain,
% 0.20/0.48 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.20/0.48 inference(quant_intro,[status(thm)],[175])).
% 0.20/0.48 tff(177,plain,
% 0.20/0.48 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(178,axiom,(![X: $i] : product(X, X, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_idempotence')).
% 0.20/0.48 tff(179,plain,
% 0.20/0.48 (![X: $i] : product(X, X, X)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.20/0.48 tff(180,plain,(
% 0.20/0.48 ![X: $i] : product(X, X, X)),
% 0.20/0.48 inference(skolemize,[status(sab)],[179])).
% 0.20/0.48 tff(181,plain,
% 0.20/0.48 (![X: $i] : product(X, X, X)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[180, 176])).
% 0.20/0.48 tff(182,plain,
% 0.20/0.48 ((~![X: $i] : product(X, X, X)) | product(e_3, e_3, e_3)),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(183,plain,
% 0.20/0.48 (product(e_3, e_3, e_3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[182, 181])).
% 0.20/0.48 tff(184,plain,
% 0.20/0.48 (^[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))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(185,plain,
% 0.20/0.48 (![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)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[184])).
% 0.20/0.48 tff(186,plain,
% 0.20/0.48 (![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)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(187,plain,
% 0.20/0.48 (^[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)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(188,plain,
% 0.20/0.48 (![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)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[187])).
% 0.20/0.48 tff(189,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_right_cancellation')).
% 0.20/0.48 tff(190,plain,
% 0.20/0.48 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.20/0.48 tff(191,plain,
% 0.20/0.48 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[190, 186])).
% 0.20/0.48 tff(192,plain,(
% 0.20/0.48 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[191])).
% 0.20/0.48 tff(193,plain,
% 0.20/0.48 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[192, 185])).
% 0.20/0.48 tff(194,plain,
% 0.20/0.48 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(195,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.20/0.48 tff(196,plain,
% 0.20/0.48 (~equalish(e_1, e_3)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.20/0.48 tff(197,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(198,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(199,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.20/0.48 tff(200,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[199, 196, 193, 183, 174])).
% 0.20/0.48 tff(201,plain,(~product(e_3, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(202,plain,
% 0.20/0.48 (^[Y: $i, X: $i] : refl(((~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) | (~group_element(Y))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(203,plain,
% 0.20/0.48 (![Y: $i, X: $i] : ((~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))) <=> ![Y: $i, X: $i] : ((~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)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[202])).
% 0.20/0.48 tff(204,plain,
% 0.20/0.48 (![Y: $i, X: $i] : ((~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))) <=> ![Y: $i, X: $i] : ((~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)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(205,plain,
% 0.20/0.48 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) <=> ((~group_element(X)) | product(X, Y, e_1) | (~group_element(Y)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> (((~group_element(X)) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_2)))), rewrite((((~group_element(X)) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_2)) <=> ((~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> ((~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> (((~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_3)))), rewrite((((~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_3)) <=> ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))))), (((((((~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(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_4)))), rewrite((((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_4)) <=> ((~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)) | (~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(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(206,plain,
% 0.20/0.48 (![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(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[205])).
% 0.20/0.48 tff(207,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/sandbox/benchmark/theBenchmark.p','product_total_function1')).
% 0.20/0.48 tff(208,plain,
% 0.20/0.48 (![Y: $i, X: $i] : ((~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)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.20/0.48 tff(209,plain,
% 0.20/0.48 (![Y: $i, X: $i] : ((~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)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[208, 204])).
% 0.20/0.48 tff(210,plain,(
% 0.20/0.48 ![Y: $i, X: $i] : ((~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)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[209])).
% 0.20/0.48 tff(211,plain,
% 0.20/0.48 (![Y: $i, X: $i] : ((~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)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[210, 203])).
% 0.20/0.48 tff(212,plain,
% 0.20/0.48 (group_element(e_1) <=> group_element(e_1)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(213,axiom,(group_element(e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_1')).
% 0.20/0.48 tff(214,plain,
% 0.20/0.48 (group_element(e_1)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.20/0.48 tff(215,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(216,plain,
% 0.20/0.48 (((~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1))) <=> ((~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(217,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : ((~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(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[216])).
% 0.20/0.48 tff(218,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : ((~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(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1))),
% 0.20/0.48 inference(transitivity,[status(thm)],[217, 215])).
% 0.20/0.48 tff(219,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : ((~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(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(220,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.20/0.48 tff(221,plain,
% 0.20/0.48 (product(e_3, e_1, e_4) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[220, 214, 136, 211, 201])).
% 0.20/0.48 tff(222,plain,
% 0.20/0.48 (product(e_3, e_1, e_4)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[221, 173, 163])).
% 0.20/0.48 tff(223,plain,
% 0.20/0.48 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(224,plain,
% 0.20/0.48 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[223])).
% 0.20/0.48 tff(225,plain,
% 0.20/0.48 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(226,plain,
% 0.20/0.48 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(W, Y, X)) | (~product(Z, Y, X))) <=> ((~product(Z, Y, X)) | (~product(W, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> (((~product(Z, Y, X)) | (~product(W, Y, X))) | equalish(W, Z)))), rewrite((((~product(Z, Y, X)) | (~product(W, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(227,plain,
% 0.20/0.48 (![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] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[226])).
% 0.20/0.48 tff(228,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_left_cancellation')).
% 0.20/0.48 tff(229,plain,
% 0.20/0.48 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.20/0.48 tff(230,plain,
% 0.20/0.48 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[229, 225])).
% 0.20/0.48 tff(231,plain,(
% 0.20/0.48 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[230])).
% 0.20/0.48 tff(232,plain,
% 0.20/0.48 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[231, 224])).
% 0.20/0.48 tff(233,plain,
% 0.20/0.48 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(234,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.20/0.48 tff(235,plain,
% 0.20/0.48 (~equalish(e_3, e_2)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.20/0.48 tff(236,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_4)) | (~product(e_3, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_1, e_4)) | (~product(e_3, e_1, e_4)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(237,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_4)) | (~product(e_3, e_1, e_4)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(238,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_1, e_4)) | (~product(e_3, e_1, e_4))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.20/0.48 tff(239,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[238, 235, 232, 1, 222])).
% 0.20/0.48 tff(240,plain,(~product(e_2, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(241,assumption,(~product(e_2, e_1, e_4)), introduced(assumption)).
% 0.20/0.48 tff(242,assumption,(product(e_1, e_3, e_1)), introduced(assumption)).
% 0.20/0.48 tff(243,assumption,(~product(e_1, e_1, e_1)), introduced(assumption)).
% 0.20/0.48 tff(244,plain,
% 0.20/0.48 ((~![X: $i] : product(X, X, X)) | product(e_1, e_1, e_1)),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(245,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[244, 181, 243])).
% 0.20/0.48 tff(246,plain,(product(e_1, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(247,plain,
% 0.20/0.48 (((~![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_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))) <=> ((~![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_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(248,plain,
% 0.20/0.48 ((~![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_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(249,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.20/0.48 tff(250,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[249, 100, 193, 246, 242])).
% 0.20/0.48 tff(251,plain,(~product(e_1, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(252,assumption,(product(e_1, e_3, e_2)), introduced(assumption)).
% 0.20/0.48 tff(253,assumption,(product(e_2, e_1, e_3)), introduced(assumption)).
% 0.20/0.48 tff(254,plain,
% 0.20/0.48 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl((product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1))) <=> (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(255,plain,
% 0.20/0.48 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[254])).
% 0.20/0.48 tff(256,plain,
% 0.20/0.48 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(257,plain,
% 0.20/0.48 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : trans(monotonicity(rewrite(((~product(Y, X, Z1)) | (~product(Z1, Y, Z2))) <=> ((~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))), ((((~product(Y, X, Z1)) | (~product(Z1, Y, Z2))) | product(Z2, Y, X)) <=> (((~product(Z1, Y, Z2)) | (~product(Y, X, Z1))) | product(Z2, Y, X)))), rewrite((((~product(Z1, Y, Z2)) | (~product(Y, X, Z1))) | product(Z2, Y, X)) <=> (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))), ((((~product(Y, X, Z1)) | (~product(Z1, Y, Z2))) | product(Z2, Y, X)) <=> (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(258,plain,
% 0.20/0.48 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(Y, X, Z1)) | (~product(Z1, Y, Z2))) | product(Z2, Y, X)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[257])).
% 0.20/0.48 tff(259,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(Y, X, Z1)) | (~product(Z1, Y, Z2))) | product(Z2, Y, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qg3')).
% 0.20/0.48 tff(260,plain,
% 0.20/0.48 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.20/0.48 tff(261,plain,
% 0.20/0.48 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[260, 256])).
% 0.20/0.48 tff(262,plain,(
% 0.20/0.48 ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[261])).
% 0.20/0.48 tff(263,plain,
% 0.20/0.48 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[262, 255])).
% 0.20/0.48 tff(264,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(265,plain,
% 0.20/0.48 ((product(e_3, e_1, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_3, e_2))) <=> ((~product(e_2, e_1, e_3)) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(266,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_2))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[265])).
% 0.20/0.48 tff(267,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_2)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[266, 264])).
% 0.20/0.48 tff(268,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_3, e_2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(269,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_2))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.20/0.48 tff(270,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[269, 263, 253, 201, 252])).
% 0.20/0.48 tff(271,plain,((~product(e_2, e_1, e_3)) | (~product(e_1, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(272,plain,
% 0.20/0.49 (~product(e_2, e_1, e_3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[271, 252])).
% 0.20/0.49 tff(273,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.20/0.49 tff(274,plain,
% 0.20/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(275,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(276,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.20/0.49 tff(277,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[276, 125, 232, 246, 273])).
% 0.20/0.49 tff(278,plain,(~product(e_2, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(279,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(280,plain,
% 0.20/0.49 (((~group_element(e_2)) | product(e_2, e_1, e_4) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1))) <=> ((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(281,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : ((~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(e_2)) | product(e_2, e_1, e_4) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1)))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[280])).
% 0.20/0.49 tff(282,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : ((~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(e_2)) | product(e_2, e_1, e_4) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1))),
% 0.20/0.49 inference(transitivity,[status(thm)],[281, 279])).
% 0.20/0.49 tff(283,plain,
% 0.20/0.49 ((~![Y: $i, X: $i] : ((~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(e_2)) | product(e_2, e_1, e_4) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(284,plain,
% 0.20/0.49 ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[283, 282])).
% 0.20/0.49 tff(285,plain,
% 0.20/0.49 (product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[284, 214, 79, 211, 278])).
% 0.20/0.49 tff(286,plain,
% 0.20/0.49 (product(e_2, e_1, e_2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[285, 272, 241])).
% 0.20/0.49 tff(287,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(288,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(289,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_3, e_2))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[288, 287])).
% 0.20/0.49 tff(290,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[289, 263, 272, 286, 252])).
% 0.20/0.49 tff(291,plain,((~product(e_1, e_3, e_2)) | product(e_2, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(292,plain,
% 0.20/0.49 (~product(e_1, e_3, e_2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[291, 241])).
% 0.20/0.49 tff(293,assumption,(product(e_1, e_3, e_3)), introduced(assumption)).
% 0.20/0.49 tff(294,plain,
% 0.20/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(295,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(296,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.20/0.49 tff(297,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[296, 196, 232, 183, 293])).
% 0.20/0.49 tff(298,plain,(~product(e_1, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(299,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_1) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_1) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(300,plain,
% 0.20/0.49 (((~group_element(e_1)) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3))) <=> ((~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_1) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(301,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : ((~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(e_1)) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_1) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2)))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[300])).
% 0.20/0.49 tff(302,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : ((~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(e_1)) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_1) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2))),
% 0.20/0.49 inference(transitivity,[status(thm)],[301, 299])).
% 0.20/0.49 tff(303,plain,
% 0.20/0.49 ((~![Y: $i, X: $i] : ((~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(e_1)) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(304,plain,
% 0.20/0.49 ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_1) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[303, 302])).
% 0.20/0.49 tff(305,plain,
% 0.20/0.49 (product(e_1, e_3, e_1) | product(e_1, e_3, e_4) | product(e_1, e_3, e_2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[304, 214, 136, 211, 298])).
% 0.20/0.49 tff(306,plain,
% 0.20/0.49 (product(e_1, e_3, e_4)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[305, 292, 251])).
% 0.20/0.49 tff(307,assumption,(product(e_1, e_3, e_4)), introduced(assumption)).
% 0.20/0.49 tff(308,assumption,(product(e_1, e_1, e_4)), introduced(assumption)).
% 0.20/0.49 tff(309,plain,
% 0.20/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_1, e_1, e_4)) | (~product(e_1, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_1, e_1, e_4)) | (~product(e_1, e_3, e_4)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(310,plain,
% 0.20/0.49 ((equalish(e_1, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_1, e_4))) <=> (equalish(e_1, e_3) | (~product(e_1, e_1, e_4)) | (~product(e_1, e_3, e_4)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(311,plain,
% 0.20/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_1, e_1, e_4)) | (~product(e_1, e_3, e_4))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[310])).
% 0.20/0.49 tff(312,plain,
% 0.20/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_1, e_1, e_4)) | (~product(e_1, e_3, e_4)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[311, 309])).
% 0.20/0.49 tff(313,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_1, e_4)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(314,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_1, e_1, e_4)) | (~product(e_1, e_3, e_4))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[313, 312])).
% 0.20/0.49 tff(315,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[314, 196, 193, 308, 307])).
% 0.20/0.49 tff(316,plain,((~product(e_1, e_1, e_4)) | (~product(e_1, e_3, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(317,plain,
% 0.20/0.49 (~product(e_1, e_1, e_4)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[316, 306])).
% 0.20/0.49 tff(318,assumption,(~product(e_1, e_1, e_4)), introduced(assumption)).
% 0.20/0.49 tff(319,assumption,(~product(e_1, e_4, e_2)), introduced(assumption)).
% 0.20/0.49 tff(320,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_4) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_4) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(321,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_4) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(322,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_4) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[321, 320])).
% 0.20/0.49 tff(323,plain,
% 0.20/0.49 (~product(e_1, e_4, e_1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[322, 263, 318, 246])).
% 0.20/0.49 tff(324,assumption,(product(e_1, e_4, e_4)), introduced(assumption)).
% 0.20/0.49 tff(325,plain,
% 0.20/0.49 ((~equalish(e_4, e_3)) <=> (~equalish(e_4, e_3))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(326,axiom,(~equalish(e_4, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_is_not_e_3')).
% 0.20/0.49 tff(327,plain,
% 0.20/0.49 (~equalish(e_4, e_3)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[326, 325])).
% 0.20/0.49 tff(328,plain,
% 0.20/0.49 (((~![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_1, e_3, e_4)) | (~product(e_1, e_4, e_4)))) <=> ((~![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_1, e_3, e_4)) | (~product(e_1, e_4, e_4)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(329,plain,
% 0.20/0.49 ((~![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_1, e_3, e_4)) | (~product(e_1, e_4, e_4)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(330,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_4, e_4))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.20/0.49 tff(331,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[330, 327, 193, 307, 324])).
% 0.20/0.49 tff(332,plain,((~product(e_1, e_4, e_4)) | (~product(e_1, e_3, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(333,plain,
% 0.20/0.49 (~product(e_1, e_4, e_4)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[332, 306])).
% 0.20/0.49 tff(334,plain,
% 0.20/0.49 (group_element(e_4) <=> group_element(e_4)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(335,axiom,(group_element(e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_4')).
% 0.20/0.49 tff(336,plain,
% 0.20/0.49 (group_element(e_4)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[335, 334])).
% 0.20/0.49 tff(337,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : ((~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(e_1)) | product(e_1, e_4, e_1) | product(e_1, e_4, e_3) | product(e_1, e_4, e_4) | product(e_1, e_4, e_2) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | product(e_1, e_4, e_1) | product(e_1, e_4, e_3) | product(e_1, e_4, e_4) | product(e_1, e_4, e_2) | (~group_element(e_4)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(338,plain,
% 0.20/0.50 (((~group_element(e_1)) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4))) <=> ((~group_element(e_1)) | product(e_1, e_4, e_1) | product(e_1, e_4, e_3) | product(e_1, e_4, e_4) | product(e_1, e_4, e_2) | (~group_element(e_4)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(339,plain,
% 0.20/0.50 (((~![Y: $i, X: $i] : ((~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(e_1)) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | product(e_1, e_4, e_1) | product(e_1, e_4, e_3) | product(e_1, e_4, e_4) | product(e_1, e_4, e_2) | (~group_element(e_4))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[338])).
% 0.20/0.50 tff(340,plain,
% 0.20/0.50 (((~![Y: $i, X: $i] : ((~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(e_1)) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | product(e_1, e_4, e_1) | product(e_1, e_4, e_3) | product(e_1, e_4, e_4) | product(e_1, e_4, e_2) | (~group_element(e_4)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[339, 337])).
% 0.20/0.50 tff(341,plain,
% 0.20/0.50 ((~![Y: $i, X: $i] : ((~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(e_1)) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(342,plain,
% 0.20/0.50 ((~![Y: $i, X: $i] : ((~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(e_1)) | product(e_1, e_4, e_1) | product(e_1, e_4, e_3) | product(e_1, e_4, e_4) | product(e_1, e_4, e_2) | (~group_element(e_4))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[341, 340])).
% 0.20/0.50 tff(343,plain,
% 0.20/0.50 (product(e_1, e_4, e_1) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[342, 214, 336, 211, 333])).
% 0.20/0.50 tff(344,plain,
% 0.20/0.50 (product(e_1, e_4, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[343, 323, 319])).
% 0.20/0.50 tff(345,assumption,(product(e_1, e_4, e_3)), introduced(assumption)).
% 0.20/0.50 tff(346,assumption,(product(e_3, e_1, e_1)), introduced(assumption)).
% 0.20/0.50 tff(347,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_4) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_4) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_4, e_3)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(348,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_4) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_4, e_3)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(349,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_4) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_4, e_3))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[348, 347])).
% 0.20/0.50 tff(350,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[349, 263, 318, 345, 346])).
% 0.20/0.50 tff(351,plain,((~product(e_3, e_1, e_1)) | product(e_1, e_1, e_4) | (~product(e_1, e_4, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(352,plain,
% 0.20/0.50 (~product(e_3, e_1, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[351, 345, 318])).
% 0.20/0.50 tff(353,assumption,(product(e_3, e_1, e_2)), introduced(assumption)).
% 0.20/0.50 tff(354,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(355,plain,
% 0.20/0.50 ((product(e_2, e_1, e_4) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_4, e_3))) <=> (product(e_2, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(356,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_2))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[355])).
% 0.20/0.50 tff(357,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[356, 354])).
% 0.20/0.50 tff(358,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_4, e_3)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(359,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_2))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[358, 357])).
% 0.20/0.50 tff(360,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[359, 263, 241, 345, 353])).
% 0.20/0.50 tff(361,plain,((~product(e_3, e_1, e_2)) | product(e_2, e_1, e_4) | (~product(e_1, e_4, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(362,plain,
% 0.20/0.50 (~product(e_3, e_1, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[361, 345, 241])).
% 0.20/0.50 tff(363,assumption,(~product(e_3, e_1, e_4)), introduced(assumption)).
% 0.20/0.50 tff(364,plain,
% 0.20/0.50 (product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[220, 214, 136, 211, 363])).
% 0.20/0.50 tff(365,plain,
% 0.20/0.50 (product(e_3, e_1, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[364, 362, 352])).
% 0.20/0.50 tff(366,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(367,plain,
% 0.20/0.50 ((product(e_3, e_1, e_4) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_4, e_3))) <=> (product(e_3, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(368,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_4) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_3))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[367])).
% 0.20/0.50 tff(369,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_4) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[368, 366])).
% 0.20/0.50 tff(370,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_4) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_4, e_3)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(371,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_3))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[370, 369])).
% 0.20/0.50 tff(372,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[371, 263, 363, 345, 365])).
% 0.20/0.50 tff(373,plain,((~product(e_1, e_4, e_3)) | product(e_3, e_1, e_4) | product(e_2, e_1, e_4) | product(e_1, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(374,plain,
% 0.20/0.50 (product(e_3, e_1, e_4)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[373, 344, 318, 241])).
% 0.20/0.50 tff(375,assumption,(product(e_3, e_1, e_4)), introduced(assumption)).
% 0.20/0.50 tff(376,assumption,(~product(e_4, e_1, e_4)), introduced(assumption)).
% 0.20/0.50 tff(377,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_4, e_3)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(378,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_4, e_3)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(379,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_4, e_3))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[378, 377])).
% 0.20/0.50 tff(380,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[379, 263, 376, 375, 345])).
% 0.20/0.50 tff(381,plain,(product(e_4, e_1, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_4, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(382,plain,
% 0.20/0.50 (product(e_4, e_1, e_4)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[381, 374, 344])).
% 0.20/0.50 tff(383,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_3) | (~product(e_4, e_1, e_4)) | (~product(e_3, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_4, e_1, e_4)) | (~product(e_3, e_1, e_4)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(384,plain,
% 0.20/0.50 ((equalish(e_4, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_4))) <=> (equalish(e_4, e_3) | (~product(e_4, e_1, e_4)) | (~product(e_3, e_1, e_4)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(385,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_3) | (~product(e_4, e_1, e_4)) | (~product(e_3, e_1, e_4))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[384])).
% 0.20/0.50 tff(386,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_4, e_1, e_4)) | (~product(e_3, e_1, e_4)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[385, 383])).
% 0.20/0.50 tff(387,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_4)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(388,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_4, e_1, e_4)) | (~product(e_3, e_1, e_4))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[387, 386])).
% 0.20/0.50 tff(389,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[388, 327, 232, 382, 374])).
% 0.20/0.50 tff(390,plain,(product(e_1, e_1, e_4) | product(e_2, e_1, e_4) | product(e_1, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(391,plain,
% 0.20/0.50 (product(e_1, e_4, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[390, 317, 241])).
% 0.20/0.50 tff(392,assumption,(product(e_2, e_1, e_2)), introduced(assumption)).
% 0.20/0.50 tff(393,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_4) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_4, e_2)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(394,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_4, e_2)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(395,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_4) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_4, e_2))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[394, 393])).
% 0.20/0.50 tff(396,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[395, 263, 241, 392, 391])).
% 0.20/0.50 tff(397,plain,((~product(e_2, e_1, e_2)) | product(e_2, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(398,plain,
% 0.20/0.50 (~product(e_2, e_1, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[397, 240])).
% 0.20/0.50 tff(399,plain,
% 0.20/0.50 (product(e_2, e_1, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[285, 398, 240])).
% 0.20/0.50 tff(400,assumption,(product(e_2, e_4, e_3)), introduced(assumption)).
% 0.20/0.50 tff(401,plain,
% 0.20/0.50 ((~equalish(e_4, e_1)) <=> (~equalish(e_4, e_1))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(402,axiom,(~equalish(e_4, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_is_not_e_1')).
% 0.20/0.50 tff(403,plain,
% 0.20/0.50 (~equalish(e_4, e_1)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[402, 401])).
% 0.20/0.50 tff(404,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, 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_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(405,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(406,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[405, 404])).
% 0.20/0.50 tff(407,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[406, 403, 193, 253, 400])).
% 0.20/0.50 tff(408,plain,((~product(e_2, e_4, e_3)) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(409,plain,
% 0.20/0.50 (~product(e_2, e_4, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[408, 399])).
% 0.20/0.50 tff(410,plain,
% 0.20/0.50 (~product(e_1, e_3, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[291, 240])).
% 0.20/0.50 tff(411,plain,
% 0.20/0.50 (product(e_1, e_3, e_4) | product(e_1, e_3, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[305, 251])).
% 0.20/0.50 tff(412,plain,
% 0.20/0.50 (product(e_1, e_3, e_4)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[411, 410])).
% 0.20/0.50 tff(413,plain,
% 0.20/0.50 (~product(e_1, e_1, e_4)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[316, 412])).
% 0.20/0.50 tff(414,plain,
% 0.20/0.50 (product(e_1, e_4, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[390, 413, 240])).
% 0.20/0.50 tff(415,assumption,(product(e_1, e_4, e_2)), introduced(assumption)).
% 0.20/0.51 tff(416,assumption,(product(e_2, e_4, e_2)), introduced(assumption)).
% 0.20/0.51 tff(417,plain,
% 0.20/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_4, e_2)) | (~product(e_2, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_4, e_2)) | (~product(e_2, e_4, e_2)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(418,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_4, e_2)) | (~product(e_2, e_4, e_2)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(419,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_4, e_2)) | (~product(e_2, e_4, e_2))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[418, 417])).
% 0.20/0.51 tff(420,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[419, 125, 232, 416, 415])).
% 0.20/0.51 tff(421,plain,((~product(e_2, e_4, e_2)) | (~product(e_1, e_4, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(422,plain,
% 0.20/0.51 (~product(e_2, e_4, e_2)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[421, 414])).
% 0.20/0.51 tff(423,assumption,(product(e_4, e_1, e_3)), introduced(assumption)).
% 0.20/0.51 tff(424,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_1, e_3)) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_1, e_3)) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_4)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(425,plain,
% 0.20/0.51 ((product(e_3, e_1, e_3) | (~product(e_4, e_1, e_3)) | (~product(e_1, e_3, e_4))) <=> ((~product(e_4, e_1, e_3)) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_4)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(426,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_4, e_1, e_3)) | (~product(e_1, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_1, e_3)) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_4))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[425])).
% 0.20/0.51 tff(427,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_4, e_1, e_3)) | (~product(e_1, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_1, e_3)) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_4)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[426, 424])).
% 0.20/0.51 tff(428,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_4, e_1, e_3)) | (~product(e_1, e_3, e_4)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(429,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_1, e_3)) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_4))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[428, 427])).
% 0.20/0.51 tff(430,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[429, 263, 423, 201, 307])).
% 0.20/0.51 tff(431,plain,((~product(e_4, e_1, e_3)) | (~product(e_1, e_3, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(432,plain,
% 0.20/0.51 (~product(e_4, e_1, e_3)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[431, 412])).
% 0.20/0.51 tff(433,assumption,(product(e_4, e_1, e_4)), introduced(assumption)).
% 0.20/0.51 tff(434,assumption,(~product(e_4, e_1, e_3)), introduced(assumption)).
% 0.20/0.51 tff(435,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_3) | (~product(e_4, e_1, e_4)) | (~product(e_1, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_3) | (~product(e_4, e_1, e_4)) | (~product(e_1, e_3, e_4)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(436,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_3) | (~product(e_4, e_1, e_4)) | (~product(e_1, e_3, e_4)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(437,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_3) | (~product(e_4, e_1, e_4)) | (~product(e_1, e_3, e_4))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[436, 435])).
% 0.20/0.51 tff(438,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[437, 263, 434, 433, 307])).
% 0.20/0.51 tff(439,plain,((~product(e_4, e_1, e_4)) | product(e_4, e_1, e_3) | (~product(e_1, e_3, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(440,plain,
% 0.20/0.51 (~product(e_4, e_1, e_4)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[439, 432, 412])).
% 0.20/0.51 tff(441,assumption,(product(e_4, e_1, e_1)), introduced(assumption)).
% 0.20/0.51 tff(442,plain,
% 0.20/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(443,plain,
% 0.20/0.51 ((equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1))) <=> (equalish(e_4, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(444,plain,
% 0.20/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[443])).
% 0.20/0.51 tff(445,plain,
% 0.20/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[444, 442])).
% 0.20/0.51 tff(446,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(447,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[446, 445])).
% 0.20/0.51 tff(448,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[447, 403, 232, 441, 246])).
% 0.20/0.51 tff(449,plain,(~product(e_4, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(450,plain,
% 0.20/0.51 (((~![Y: $i, X: $i] : ((~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)))) | (product(e_4, e_1, e_1) | product(e_4, e_1, e_2) | product(e_4, e_1, e_3) | product(e_4, e_1, e_4) | (~group_element(e_1)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : ((~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)))) | product(e_4, e_1, e_1) | product(e_4, e_1, e_2) | product(e_4, e_1, e_3) | product(e_4, e_1, e_4) | (~group_element(e_1)) | (~group_element(e_4)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(451,plain,
% 0.20/0.51 (((~group_element(e_4)) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1))) <=> (product(e_4, e_1, e_1) | product(e_4, e_1, e_2) | product(e_4, e_1, e_3) | product(e_4, e_1, e_4) | (~group_element(e_1)) | (~group_element(e_4)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(452,plain,
% 0.20/0.51 (((~![Y: $i, X: $i] : ((~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(e_4)) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~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)))) | (product(e_4, e_1, e_1) | product(e_4, e_1, e_2) | product(e_4, e_1, e_3) | product(e_4, e_1, e_4) | (~group_element(e_1)) | (~group_element(e_4))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[451])).
% 0.20/0.51 tff(453,plain,
% 0.20/0.51 (((~![Y: $i, X: $i] : ((~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(e_4)) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~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)))) | product(e_4, e_1, e_1) | product(e_4, e_1, e_2) | product(e_4, e_1, e_3) | product(e_4, e_1, e_4) | (~group_element(e_1)) | (~group_element(e_4)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[452, 450])).
% 0.20/0.51 tff(454,plain,
% 0.20/0.51 ((~![Y: $i, X: $i] : ((~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(e_4)) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(455,plain,
% 0.20/0.51 ((~![Y: $i, X: $i] : ((~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)))) | product(e_4, e_1, e_1) | product(e_4, e_1, e_2) | product(e_4, e_1, e_3) | product(e_4, e_1, e_4) | (~group_element(e_1)) | (~group_element(e_4))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[454, 453])).
% 0.20/0.51 tff(456,plain,
% 0.20/0.51 (product(e_4, e_1, e_2) | product(e_4, e_1, e_3) | product(e_4, e_1, e_4)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[455, 214, 336, 211, 449])).
% 0.20/0.51 tff(457,plain,
% 0.20/0.51 (product(e_4, e_1, e_2)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[456, 440, 432])).
% 0.20/0.51 tff(458,plain,
% 0.20/0.51 (~product(e_1, e_4, e_1)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[322, 263, 413, 246])).
% 0.20/0.51 tff(459,assumption,(~product(e_1, e_4, e_1)), introduced(assumption)).
% 0.20/0.51 tff(460,assumption,(product(e_2, e_4, e_1)), introduced(assumption)).
% 0.20/0.51 tff(461,assumption,(product(e_4, e_1, e_2)), introduced(assumption)).
% 0.20/0.51 tff(462,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_1, e_2)) | product(e_1, e_4, e_1) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_1, e_2)) | product(e_1, e_4, e_1) | (~product(e_2, e_4, e_1)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(463,plain,
% 0.20/0.51 ((product(e_1, e_4, e_1) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_2))) <=> ((~product(e_4, e_1, e_2)) | product(e_1, e_4, e_1) | (~product(e_2, e_4, e_1)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(464,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_4, e_1) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_1, e_2)) | product(e_1, e_4, e_1) | (~product(e_2, e_4, e_1))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[463])).
% 0.20/0.51 tff(465,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_4, e_1) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_1, e_2)) | product(e_1, e_4, e_1) | (~product(e_2, e_4, e_1)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[464, 462])).
% 0.20/0.51 tff(466,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_4, e_1) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_2)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(467,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_1, e_2)) | product(e_1, e_4, e_1) | (~product(e_2, e_4, e_1))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[466, 465])).
% 0.20/0.51 tff(468,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[467, 263, 461, 460, 459])).
% 0.20/0.51 tff(469,plain,((~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_2)) | product(e_1, e_4, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(470,plain,
% 0.20/0.51 (~product(e_2, e_4, e_1)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[469, 458, 457])).
% 0.20/0.51 tff(471,plain,
% 0.20/0.51 (((~![Y: $i, X: $i] : ((~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(e_2)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : ((~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(e_2)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | (~group_element(e_4)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(472,plain,
% 0.20/0.51 (((~group_element(e_2)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4))) <=> ((~group_element(e_2)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | (~group_element(e_4)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(473,plain,
% 0.20/0.51 (((~![Y: $i, X: $i] : ((~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(e_2)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : ((~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(e_2)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | (~group_element(e_4))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[472])).
% 0.20/0.51 tff(474,plain,
% 0.20/0.51 (((~![Y: $i, X: $i] : ((~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(e_2)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : ((~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(e_2)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | (~group_element(e_4)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[473, 471])).
% 0.20/0.51 tff(475,plain,
% 0.20/0.51 ((~![Y: $i, X: $i] : ((~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(e_2)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(476,plain,
% 0.20/0.51 ((~![Y: $i, X: $i] : ((~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(e_2)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | (~group_element(e_4))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[475, 474])).
% 0.20/0.51 tff(477,plain,
% 0.20/0.51 (product(e_2, e_4, e_4) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[476, 79, 336, 211])).
% 0.20/0.51 tff(478,plain,
% 0.20/0.51 (product(e_2, e_4, e_4)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[477, 470, 422, 409])).
% 0.20/0.51 tff(479,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_1, e_2)) | product(e_4, e_4, e_1) | (~product(e_2, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_1, e_2)) | product(e_4, e_4, e_1) | (~product(e_2, e_4, e_4)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(480,plain,
% 0.20/0.51 ((product(e_4, e_4, e_1) | (~product(e_2, e_4, e_4)) | (~product(e_4, e_1, e_2))) <=> ((~product(e_4, e_1, e_2)) | product(e_4, e_4, e_1) | (~product(e_2, e_4, e_4)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(481,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_4, e_1) | (~product(e_2, e_4, e_4)) | (~product(e_4, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_1, e_2)) | product(e_4, e_4, e_1) | (~product(e_2, e_4, e_4))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[480])).
% 0.20/0.51 tff(482,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_4, e_1) | (~product(e_2, e_4, e_4)) | (~product(e_4, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_1, e_2)) | product(e_4, e_4, e_1) | (~product(e_2, e_4, e_4)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[481, 479])).
% 0.20/0.51 tff(483,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_4, e_1) | (~product(e_2, e_4, e_4)) | (~product(e_4, e_1, e_2)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(484,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_1, e_2)) | product(e_4, e_4, e_1) | (~product(e_2, e_4, e_4))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[483, 482])).
% 0.20/0.51 tff(485,plain,
% 0.20/0.51 (product(e_4, e_4, e_1)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[484, 263, 457, 478])).
% 0.20/0.51 tff(486,plain,
% 0.20/0.51 (~product(e_1, e_4, e_4)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[332, 412])).
% 0.20/0.52 tff(487,plain,
% 0.20/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_4, e_4) | (~product(e_4, e_4, e_1)) | (~product(e_4, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_4, e_4) | (~product(e_4, e_4, e_1)) | (~product(e_4, e_4, e_4)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(488,plain,
% 0.20/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_4, e_4) | (~product(e_4, e_4, e_1)) | (~product(e_4, e_4, e_4)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(489,plain,
% 0.20/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_4, e_4) | (~product(e_4, e_4, e_1)) | (~product(e_4, e_4, e_4))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[488, 487])).
% 0.20/0.52 tff(490,plain,
% 0.20/0.52 (~product(e_4, e_4, e_4)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[489, 263, 486, 485])).
% 0.20/0.52 tff(491,plain,
% 0.20/0.52 ((~![X: $i] : product(X, X, X)) | product(e_4, e_4, e_4)),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(492,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[491, 181, 490])).
% 0.20/0.52 % SZS output end Proof
% 0.20/0.52 % E exiting
%------------------------------------------------------------------------------