%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP126-3.004 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:07:07 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP126-3.004 : TPTP v9.0.0. Released v1.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 15:47:03 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.46 % SZS status Unsatisfiable
% 0.20/0.46 % SZS output start Proof
% 0.20/0.46 tff(cycle_type, type, (
% 0.20/0.46 cycle: ( $i * $i ) > $o)).
% 0.20/0.46 tff(e_3_type, type, (
% 0.20/0.46 e_3: $i)).
% 0.20/0.46 tff(e_0_type, type, (
% 0.20/0.46 e_0: $i)).
% 0.20/0.46 tff(e_1_type, type, (
% 0.20/0.46 e_1: $i)).
% 0.20/0.46 tff(e_2_type, type, (
% 0.20/0.46 e_2: $i)).
% 0.20/0.46 tff(next_type, type, (
% 0.20/0.46 next: ( $i * $i ) > $o)).
% 0.20/0.46 tff(greater_type, type, (
% 0.20/0.46 greater: ( $i * $i ) > $o)).
% 0.20/0.46 tff(e_4_type, type, (
% 0.20/0.46 e_4: $i)).
% 0.20/0.46 tff(equalish_type, type, (
% 0.20/0.46 equalish: ( $i * $i ) > $o)).
% 0.20/0.46 tff(group_element_type, type, (
% 0.20/0.46 group_element: $i > $o)).
% 0.20/0.46 tff(product_type, type, (
% 0.20/0.46 product: ( $i * $i * $i ) > $o)).
% 0.20/0.46 tff(1,assumption,(cycle(e_2, e_1)), introduced(assumption)).
% 0.20/0.46 tff(2,assumption,(~cycle(e_3, e_3)), introduced(assumption)).
% 0.20/0.46 tff(3,plain,
% 0.20/0.46 (^[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))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(4,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))) <=> ![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)],[3])).
% 0.20/0.46 tff(5,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))) <=> ![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(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(6,plain,
% 0.20/0.46 (^[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)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(7,plain,
% 0.20/0.46 (![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)],[6])).
% 0.20/0.46 tff(8,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/sandbox2/benchmark/theBenchmark.p','cycle5')).
% 0.20/0.46 tff(9,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)],[8, 7])).
% 0.20/0.46 tff(10,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)],[9, 5])).
% 0.20/0.46 tff(11,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)],[10])).
% 0.20/0.46 tff(12,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)],[11, 4])).
% 0.20/0.46 tff(13,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(14,axiom,(cycle(e_4, e_0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cycle3')).
% 0.20/0.46 tff(15,plain,
% 0.20/0.46 (cycle(e_4, e_0)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.20/0.46 tff(16,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(17,axiom,(greater(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_greater_e_2')).
% 0.20/0.46 tff(18,plain,
% 0.20/0.46 (greater(e_3, e_2)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.20/0.46 tff(19,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(20,axiom,(greater(e_1, e_0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_greater_e_0')).
% 0.20/0.46 tff(21,plain,
% 0.20/0.46 (greater(e_1, e_0)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.46 tff(22,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(23,axiom,(next(e_3, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_then_e_4')).
% 0.20/0.46 tff(24,plain,
% 0.20/0.46 (next(e_3, e_4)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.46 tff(25,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(26,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(27,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)],[26])).
% 0.20/0.46 tff(28,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)],[27, 25])).
% 0.20/0.46 tff(29,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(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)))) | (~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)],[29, 28])).
% 0.20/0.46 tff(31,plain,
% 0.20/0.46 ((~cycle(e_3, e_0)) | (~cycle(e_2, e_1))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[30, 24, 21, 18, 15, 12])).
% 0.20/0.46 tff(32,plain,
% 0.20/0.46 (~cycle(e_3, e_0)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[31, 1])).
% 0.20/0.46 tff(33,assumption,(cycle(e_3, e_2)), introduced(assumption)).
% 0.20/0.46 tff(34,plain,
% 0.20/0.46 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(35,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.20/0.46 tff(36,plain,
% 0.20/0.46 (~equalish(e_2, e_1)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.46 tff(37,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(38,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)],[37])).
% 0.20/0.46 tff(39,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(40,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(41,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)],[40])).
% 0.20/0.47 tff(42,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/sandbox2/benchmark/theBenchmark.p','cycle4')).
% 0.20/0.47 tff(43,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)],[42, 41])).
% 0.20/0.47 tff(44,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)],[43, 39])).
% 0.20/0.47 tff(45,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)],[44])).
% 0.20/0.47 tff(46,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)],[45, 38])).
% 0.20/0.47 tff(47,plain,
% 0.20/0.47 (greater(e_2, e_0) <=> greater(e_2, e_0)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(48,axiom,(greater(e_2, e_0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_greater_e_0')).
% 0.20/0.47 tff(49,plain,
% 0.20/0.47 (greater(e_2, e_0)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.20/0.47 tff(50,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(51,axiom,(next(e_0, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_0_then_e_1')).
% 0.20/0.47 tff(52,plain,
% 0.20/0.47 (next(e_0, e_1)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.47 tff(53,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(54,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(55,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)],[54])).
% 0.20/0.47 tff(56,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)],[55, 53])).
% 0.20/0.47 tff(57,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(58,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_1) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~next(e_0, e_1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.20/0.47 tff(59,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[58, 52, 24, 49, 15, 46, 36, 33])).
% 0.20/0.47 tff(60,plain,(~cycle(e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(61,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(62,axiom,(group_element(e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_3')).
% 0.20/0.47 tff(63,plain,
% 0.20/0.47 (group_element(e_3)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.47 tff(64,plain,
% 0.20/0.47 (^[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))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(65,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))) <=> ![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[64])).
% 0.20/0.47 tff(66,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))) <=> ![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(67,plain,
% 0.20/0.47 (^[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)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(68,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[67])).
% 0.20/0.47 tff(69,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/sandbox2/benchmark/theBenchmark.p','cycle2')).
% 0.20/0.47 tff(70,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)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.47 tff(71,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)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.20/0.47 tff(72,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)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[71])).
% 0.20/0.47 tff(73,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)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.20/0.47 tff(74,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(75,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(76,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)],[75, 74])).
% 0.20/0.47 tff(77,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)],[76, 73, 63])).
% 0.20/0.47 tff(78,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)],[77, 60])).
% 0.20/0.47 tff(79,plain,
% 0.20/0.47 (cycle(e_3, e_1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[78, 32, 2])).
% 0.20/0.47 tff(80,plain,
% 0.20/0.47 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(81,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.20/0.47 tff(82,plain,
% 0.20/0.47 (~equalish(e_1, e_2)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.20/0.47 tff(83,plain,
% 0.20/0.47 (next(e_2, e_3) <=> next(e_2, e_3)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(84,axiom,(next(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_then_e_3')).
% 0.20/0.47 tff(85,plain,
% 0.20/0.47 (next(e_2, e_3)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.20/0.47 tff(86,plain,
% 0.20/0.47 (next(e_1, e_2) <=> next(e_1, e_2)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(87,axiom,(next(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_then_e_2')).
% 0.20/0.47 tff(88,plain,
% 0.20/0.47 (next(e_1, e_2)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.20/0.47 tff(89,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_1, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~cycle(e_3, 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_1, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(90,plain,
% 0.20/0.47 (((~cycle(e_2, e_1)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_1))) <=> (equalish(e_1, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(91,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_2, e_1)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, 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_1, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_1))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[90])).
% 0.20/0.47 tff(92,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_2, e_1)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, 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_1, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_1)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[91, 89])).
% 0.20/0.47 tff(93,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_2, e_1)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_1)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(94,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_1, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.20/0.47 tff(95,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[94, 88, 85, 21, 46, 82, 1, 79])).
% 0.20/0.47 tff(96,plain,((~cycle(e_2, e_1)) | cycle(e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(97,plain,
% 0.20/0.47 (cycle(e_3, e_3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[96, 1])).
% 0.20/0.47 tff(98,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(99,axiom,(~equalish(e_1, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_4')).
% 0.20/0.47 tff(100,plain,
% 0.20/0.47 (~equalish(e_1, e_4)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.47 tff(101,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_1, e_4) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~next(e_3, e_4)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_3)))) <=> ((~![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_1, e_4) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~next(e_3, e_4)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_3)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(102,plain,
% 0.20/0.47 (((~cycle(e_2, e_1)) | equalish(e_1, e_4) | (~next(e_3, e_4)) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_3))) <=> (equalish(e_1, e_4) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~next(e_3, e_4)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_3)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(103,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_2, e_1)) | equalish(e_1, e_4) | (~next(e_3, e_4)) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_3)))) <=> ((~![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_1, e_4) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~next(e_3, e_4)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_3))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[102])).
% 0.20/0.47 tff(104,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_2, e_1)) | equalish(e_1, e_4) | (~next(e_3, e_4)) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_3)))) <=> ((~![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_1, e_4) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~next(e_3, e_4)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_3)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[103, 101])).
% 0.20/0.47 tff(105,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_2, e_1)) | equalish(e_1, e_4) | (~next(e_3, e_4)) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_3)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(106,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_1, e_4) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~next(e_3, e_4)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_3))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.47 tff(107,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[106, 85, 24, 21, 46, 100, 1, 97])).
% 0.20/0.47 tff(108,plain,(~cycle(e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(109,assumption,(~cycle(e_2, e_1)), introduced(assumption)).
% 0.20/0.47 tff(110,assumption,(cycle(e_2, e_0)), introduced(assumption)).
% 0.20/0.47 tff(111,plain,
% 0.20/0.47 (^[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))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(112,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[111])).
% 0.20/0.47 tff(113,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(114,plain,
% 0.20/0.47 (^[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))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(115,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[114])).
% 0.20/0.47 tff(116,axiom,(![Y: $i, X: $i] : (((~cycle(X, e_0)) | (~product(X, e_1, Y))) | (~greater(Y, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cycle6')).
% 0.20/0.47 tff(117,plain,
% 0.20/0.47 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.20/0.47 tff(118,plain,
% 0.20/0.47 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[117, 113])).
% 0.20/0.47 tff(119,plain,(
% 0.20/0.47 ![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[118])).
% 0.20/0.47 tff(120,plain,
% 0.20/0.47 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[119, 112])).
% 0.20/0.47 tff(121,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(122,plain,
% 0.20/0.48 (((~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)) | (~cycle(e_2, e_0))) <=> ((~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(123,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)) | (~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_3, e_2)) | (~product(e_2, e_1, e_3))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[122])).
% 0.20/0.48 tff(124,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)) | (~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_3, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[123, 121])).
% 0.20/0.48 tff(125,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)) | (~cycle(e_2, e_0)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(126,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.20/0.48 tff(127,plain,
% 0.20/0.48 ((~cycle(e_2, e_0)) | (~product(e_2, e_1, e_3))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[126, 18, 120])).
% 0.20/0.48 tff(128,plain,
% 0.20/0.48 (~product(e_2, e_1, e_3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[127, 110])).
% 0.20/0.48 tff(129,plain,
% 0.20/0.48 (greater(e_4, e_2) <=> greater(e_4, e_2)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(130,axiom,(greater(e_4, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_greater_e_2')).
% 0.20/0.48 tff(131,plain,
% 0.20/0.48 (greater(e_4, e_2)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.20/0.48 tff(132,plain,
% 0.20/0.48 (((~![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)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(133,plain,
% 0.20/0.48 (((~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)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(134,plain,
% 0.20/0.48 (((~![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))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[133])).
% 0.20/0.48 tff(135,plain,
% 0.20/0.48 (((~![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)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[134, 132])).
% 0.20/0.48 tff(136,plain,
% 0.20/0.48 ((~![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)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(137,plain,
% 0.20/0.48 ((~![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))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.20/0.48 tff(138,plain,
% 0.20/0.48 ((~cycle(e_2, e_0)) | (~product(e_2, e_1, e_4))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[137, 131, 120])).
% 0.20/0.48 tff(139,plain,
% 0.20/0.48 (~product(e_2, e_1, e_4)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[138, 110])).
% 0.20/0.48 tff(140,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.20/0.48 tff(141,assumption,(~product(e_1, e_1, e_1)), introduced(assumption)).
% 0.20/0.48 tff(142,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(143,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)],[142])).
% 0.20/0.48 tff(144,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(145,axiom,(![X: $i] : product(X, X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_idempotence')).
% 0.20/0.48 tff(146,plain,
% 0.20/0.48 (![X: $i] : product(X, X, X)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.20/0.48 tff(147,plain,(
% 0.20/0.48 ![X: $i] : product(X, X, X)),
% 0.20/0.48 inference(skolemize,[status(sab)],[146])).
% 0.20/0.48 tff(148,plain,
% 0.20/0.48 (![X: $i] : product(X, X, X)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[147, 143])).
% 0.20/0.48 tff(149,plain,
% 0.20/0.48 ((~![X: $i] : product(X, X, X)) | product(e_1, e_1, e_1)),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(150,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[149, 148, 141])).
% 0.20/0.48 tff(151,plain,(product(e_1, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(152,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(153,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)],[152])).
% 0.20/0.48 tff(154,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(155,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(156,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)],[155])).
% 0.20/0.48 tff(157,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_left_cancellation')).
% 0.20/0.48 tff(158,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)],[157, 156])).
% 0.20/0.48 tff(159,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)],[158, 154])).
% 0.20/0.48 tff(160,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)],[159])).
% 0.20/0.48 tff(161,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)],[160, 153])).
% 0.20/0.48 tff(162,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_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)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(163,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_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(164,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.20/0.48 tff(165,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[164, 36, 161, 151, 140])).
% 0.20/0.48 tff(166,plain,(~product(e_2, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(167,plain,
% 0.20/0.48 ((~![X: $i] : product(X, X, X)) | product(e_2, e_2, e_2)),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(168,plain,
% 0.20/0.48 (product(e_2, e_2, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[167, 148])).
% 0.20/0.48 tff(169,assumption,(product(e_2, e_1, e_2)), introduced(assumption)).
% 0.20/0.48 tff(170,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(171,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)],[170])).
% 0.20/0.48 tff(172,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(173,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(174,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)],[173])).
% 0.20/0.48 tff(175,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_right_cancellation')).
% 0.20/0.48 tff(176,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)],[175, 174])).
% 0.20/0.48 tff(177,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)],[176, 172])).
% 0.20/0.48 tff(178,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)],[177])).
% 0.20/0.48 tff(179,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)],[178, 171])).
% 0.20/0.48 tff(180,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_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(181,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_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(182,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.20/0.48 tff(183,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[182, 82, 179, 169, 168])).
% 0.20/0.48 tff(184,plain,(~product(e_2, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(185,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(186,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)],[185])).
% 0.20/0.48 tff(187,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(188,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(189,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)],[188])).
% 0.20/0.48 tff(190,axiom,(![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_total_function1')).
% 0.20/0.48 tff(191,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)],[190, 189])).
% 0.20/0.48 tff(192,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)],[191, 187])).
% 0.20/0.48 tff(193,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)],[192])).
% 0.20/0.48 tff(194,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)],[193, 186])).
% 0.20/0.48 tff(195,plain,
% 0.20/0.48 (group_element(e_2) <=> group_element(e_2)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(196,axiom,(group_element(e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_2')).
% 0.20/0.48 tff(197,plain,
% 0.20/0.48 (group_element(e_2)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.20/0.48 tff(198,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(199,axiom,(group_element(e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_1')).
% 0.20/0.48 tff(200,plain,
% 0.20/0.48 (group_element(e_1)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.20/0.48 tff(201,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_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))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(202,plain,
% 0.20/0.48 (((~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))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 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)))) | ((~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)))),
% 0.20/0.48 inference(monotonicity,[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)))) | ((~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))),
% 0.20/0.48 inference(transitivity,[status(thm)],[203, 201])).
% 0.20/0.48 tff(205,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_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)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(206,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.20/0.48 tff(207,plain,
% 0.20/0.48 (product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_1)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[206, 200, 197, 194, 184])).
% 0.20/0.48 tff(208,plain,
% 0.20/0.48 (product(e_2, e_1, e_3) | product(e_2, e_1, e_4)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[207, 166])).
% 0.20/0.48 tff(209,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[208, 139, 128])).
% 0.20/0.48 tff(210,plain,(~cycle(e_2, e_0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(211,assumption,(cycle(e_3, e_0)), introduced(assumption)).
% 0.20/0.48 tff(212,plain,
% 0.20/0.48 (((~![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)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(213,plain,
% 0.20/0.48 (((~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)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(214,plain,
% 0.20/0.48 (((~![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))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[213])).
% 0.20/0.48 tff(215,plain,
% 0.20/0.48 (((~![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)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[214, 212])).
% 0.20/0.49 tff(216,plain,
% 0.20/0.49 ((~![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)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(217,plain,
% 0.20/0.49 ((~![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))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.20/0.49 tff(218,plain,
% 0.20/0.49 ((~cycle(e_3, e_0)) | (~cycle(e_2, e_2))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[217, 24, 49, 18, 15, 12])).
% 0.20/0.49 tff(219,plain,
% 0.20/0.49 (~cycle(e_2, e_2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[218, 211])).
% 0.20/0.49 tff(220,plain,
% 0.20/0.49 (greater(e_3, e_0) <=> greater(e_3, e_0)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(221,axiom,(greater(e_3, e_0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_greater_e_0')).
% 0.20/0.49 tff(222,plain,
% 0.20/0.49 (greater(e_3, e_0)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.20/0.49 tff(223,plain,
% 0.20/0.49 (((~![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)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(224,plain,
% 0.20/0.49 (((~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)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(225,plain,
% 0.20/0.49 (((~![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))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[224])).
% 0.20/0.49 tff(226,plain,
% 0.20/0.49 (((~![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)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[225, 223])).
% 0.20/0.49 tff(227,plain,
% 0.20/0.49 ((~![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)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(228,plain,
% 0.20/0.49 ((~![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))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.20/0.49 tff(229,plain,
% 0.20/0.49 ((~cycle(e_3, e_0)) | (~cycle(e_2, e_3))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[228, 24, 222, 18, 15, 12])).
% 0.20/0.49 tff(230,plain,
% 0.20/0.49 (~cycle(e_2, e_3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[229, 211])).
% 0.20/0.49 tff(231,plain,
% 0.20/0.49 (((~![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)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(232,plain,
% 0.20/0.49 ((~![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)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(233,plain,
% 0.20/0.49 ((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0) | (~group_element(e_2))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.20/0.49 tff(234,plain,
% 0.20/0.49 (cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[233, 73, 197])).
% 0.20/0.49 tff(235,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[234, 230, 219, 210, 109])).
% 0.20/0.49 tff(236,plain,((~cycle(e_3, e_0)) | cycle(e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(237,plain,
% 0.20/0.49 (~cycle(e_3, e_0)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[236, 108])).
% 0.20/0.49 tff(238,assumption,(product(e_3, e_4, e_3)), introduced(assumption)).
% 0.20/0.49 tff(239,plain,
% 0.20/0.49 ((~![X: $i] : product(X, X, X)) | product(e_3, e_3, e_3)),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(240,plain,
% 0.20/0.49 (product(e_3, e_3, e_3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[239, 148])).
% 0.20/0.49 tff(241,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(242,axiom,(~equalish(e_4, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_3')).
% 0.20/0.49 tff(243,plain,
% 0.20/0.49 (~equalish(e_4, e_3)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.20/0.49 tff(244,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_3, e_3, e_3)) | (~product(e_3, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(245,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_3, e_3, e_3)) | (~product(e_3, e_4, e_3)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(246,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.20/0.49 tff(247,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[246, 243, 179, 240, 238])).
% 0.20/0.49 tff(248,plain,(~product(e_3, e_4, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(249,assumption,(cycle(e_3, e_1)), introduced(assumption)).
% 0.20/0.49 tff(250,plain,
% 0.20/0.49 ((~equalish(e_3, e_4)) <=> (~equalish(e_3, e_4))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(251,axiom,(~equalish(e_3, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_4')).
% 0.20/0.49 tff(252,plain,
% 0.20/0.49 (~equalish(e_3, e_4)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.20/0.49 tff(253,plain,
% 0.20/0.49 (^[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))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(254,plain,
% 0.20/0.49 (![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)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[253])).
% 0.20/0.49 tff(255,plain,
% 0.20/0.49 (![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)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(256,plain,
% 0.20/0.49 (^[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)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(257,plain,
% 0.20/0.49 (![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)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[256])).
% 0.20/0.49 tff(258,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/sandbox2/benchmark/theBenchmark.p','cycle7')).
% 0.20/0.49 tff(259,plain,
% 0.20/0.49 (![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)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.20/0.49 tff(260,plain,
% 0.20/0.49 (![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)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[259, 255])).
% 0.20/0.49 tff(261,plain,(
% 0.20/0.49 ![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)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[260])).
% 0.20/0.49 tff(262,plain,
% 0.20/0.49 (![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)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[261, 254])).
% 0.20/0.49 tff(263,plain,
% 0.20/0.49 (((~![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_3, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_3)))) <=> ((~![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_3, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_3)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(264,plain,
% 0.20/0.49 (((~greater(e_1, e_0)) | (~cycle(e_3, e_1)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_3))) <=> (equalish(e_3, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_3)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(265,plain,
% 0.20/0.49 (((~![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_3, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_3)))) <=> ((~![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_3, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_3))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[264])).
% 0.20/0.49 tff(266,plain,
% 0.20/0.49 (((~![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_3, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_3)))) <=> ((~![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_3, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_3)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[265, 263])).
% 0.20/0.49 tff(267,plain,
% 0.20/0.49 ((~![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_3, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_3)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(268,plain,
% 0.20/0.49 ((~![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_3, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_3))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.20/0.49 tff(269,plain,
% 0.20/0.49 (~product(e_3, e_1, e_3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[268, 24, 21, 262, 252, 249])).
% 0.20/0.49 tff(270,plain,
% 0.20/0.49 (((~![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)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(271,plain,
% 0.20/0.49 (((~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)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(272,plain,
% 0.20/0.49 (((~![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))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[271])).
% 0.20/0.49 tff(273,plain,
% 0.20/0.49 (((~![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)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[272, 270])).
% 0.20/0.50 tff(274,plain,
% 0.20/0.50 ((~![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)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(275,plain,
% 0.20/0.50 ((~![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))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.20/0.50 tff(276,plain,
% 0.20/0.50 (~product(e_3, e_1, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[275, 24, 21, 262, 100, 249])).
% 0.20/0.50 tff(277,plain,
% 0.20/0.50 ((~equalish(e_2, e_4)) <=> (~equalish(e_2, e_4))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(278,axiom,(~equalish(e_2, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_4')).
% 0.20/0.50 tff(279,plain,
% 0.20/0.50 (~equalish(e_2, e_4)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.20/0.50 tff(280,plain,
% 0.20/0.50 (((~![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)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(281,plain,
% 0.20/0.50 (((~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)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(282,plain,
% 0.20/0.50 (((~![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))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[281])).
% 0.20/0.50 tff(283,plain,
% 0.20/0.50 (((~![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)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[282, 280])).
% 0.20/0.50 tff(284,plain,
% 0.20/0.50 ((~![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)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(285,plain,
% 0.20/0.50 ((~![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))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[284, 283])).
% 0.20/0.50 tff(286,plain,
% 0.20/0.50 (~product(e_3, e_1, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[285, 24, 21, 262, 279, 249])).
% 0.20/0.50 tff(287,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)) | (~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))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(288,plain,
% 0.20/0.50 (((~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))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(289,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_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)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[288])).
% 0.20/0.50 tff(290,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_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))),
% 0.20/0.50 inference(transitivity,[status(thm)],[289, 287])).
% 0.20/0.50 tff(291,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_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)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(292,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)) | (~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)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.20/0.50 tff(293,plain,
% 0.20/0.50 (product(e_3, e_1, e_4)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[292, 200, 63, 194, 286, 276, 269])).
% 0.20/0.50 tff(294,plain,
% 0.20/0.50 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl(((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))) <=> ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(295,plain,
% 0.20/0.50 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[294])).
% 0.20/0.50 tff(296,plain,
% 0.20/0.50 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(297,plain,
% 0.20/0.50 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : rewrite((((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, Y)) <=> ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(298,plain,
% 0.20/0.50 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, Y)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[297])).
% 0.20/0.50 tff(299,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qg4')).
% 0.20/0.50 tff(300,plain,
% 0.20/0.50 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[299, 298])).
% 0.20/0.50 tff(301,plain,
% 0.20/0.50 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[300, 296])).
% 0.20/0.50 tff(302,plain,(
% 0.20/0.50 ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[301])).
% 0.20/0.50 tff(303,plain,
% 0.20/0.50 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[302, 295])).
% 0.20/0.50 tff(304,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_3, e_4, e_3) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | product(e_3, e_4, e_3) | (~product(e_1, e_3, e_3)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(305,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_3, e_4, e_3) | (~product(e_1, e_3, e_3)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(306,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | product(e_3, e_4, e_3) | (~product(e_1, e_3, e_3))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[305, 304])).
% 0.20/0.50 tff(307,plain,
% 0.20/0.50 (~product(e_1, e_3, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[306, 303, 293, 248])).
% 0.20/0.50 tff(308,assumption,(product(e_2, e_4, e_3)), introduced(assumption)).
% 0.20/0.50 tff(309,assumption,(product(e_2, e_1, e_4)), introduced(assumption)).
% 0.20/0.50 tff(310,assumption,(cycle(e_2, e_2)), introduced(assumption)).
% 0.20/0.50 tff(311,plain,
% 0.20/0.50 (((~![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_4, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_4)))) <=> ((~![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_4, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_4)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(312,plain,
% 0.20/0.50 (((~greater(e_2, e_0)) | (~cycle(e_2, e_2)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4))) <=> (equalish(e_4, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_4)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(313,plain,
% 0.20/0.50 (((~![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_2, e_0)) | (~cycle(e_2, e_2)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))) <=> ((~![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_4, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_4))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[312])).
% 0.20/0.50 tff(314,plain,
% 0.20/0.50 (((~![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_2, e_0)) | (~cycle(e_2, e_2)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))) <=> ((~![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_4, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_4)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[313, 311])).
% 0.20/0.50 tff(315,plain,
% 0.20/0.50 ((~![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_2, e_0)) | (~cycle(e_2, e_2)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(316,plain,
% 0.20/0.50 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_4))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[315, 314])).
% 0.20/0.50 tff(317,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[316, 85, 49, 262, 243, 310, 309])).
% 0.20/0.50 tff(318,plain,((~cycle(e_2, e_2)) | (~product(e_2, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(319,plain,
% 0.20/0.50 (~cycle(e_2, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[318, 309])).
% 0.20/0.50 tff(320,assumption,(cycle(e_2, e_3)), introduced(assumption)).
% 0.20/0.50 tff(321,plain,
% 0.20/0.50 (((~![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_4, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_4)))) <=> ((~![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_4, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(322,plain,
% 0.20/0.50 (((~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4))) <=> (equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(323,plain,
% 0.20/0.50 (((~![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_3, e_0)) | (~cycle(e_2, e_3)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))) <=> ((~![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_4, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_4))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[322])).
% 0.20/0.50 tff(324,plain,
% 0.20/0.50 (((~![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_3, e_0)) | (~cycle(e_2, e_3)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))) <=> ((~![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_4, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[323, 321])).
% 0.20/0.50 tff(325,plain,
% 0.20/0.50 ((~![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_3, e_0)) | (~cycle(e_2, e_3)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(326,plain,
% 0.20/0.50 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_4))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[325, 324])).
% 0.20/0.50 tff(327,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[326, 85, 222, 262, 243, 320, 309])).
% 0.20/0.50 tff(328,plain,((~cycle(e_2, e_3)) | (~product(e_2, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(329,plain,
% 0.20/0.50 (~cycle(e_2, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[328, 309])).
% 0.20/0.50 tff(330,plain,
% 0.20/0.50 (cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[234, 210])).
% 0.20/0.50 tff(331,plain,
% 0.20/0.50 (cycle(e_2, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[330, 329, 319])).
% 0.20/0.50 tff(332,plain,
% 0.20/0.50 (((~![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_4, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_4)))) <=> ((~![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_4, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_4)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(333,plain,
% 0.20/0.50 (((~greater(e_1, e_0)) | (~cycle(e_2, e_1)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4))) <=> (equalish(e_4, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_4)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(334,plain,
% 0.20/0.50 (((~![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_2, e_1)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))) <=> ((~![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_4, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_4))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[333])).
% 0.20/0.50 tff(335,plain,
% 0.20/0.50 (((~![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_2, e_1)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))) <=> ((~![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_4, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_4)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[334, 332])).
% 0.20/0.50 tff(336,plain,
% 0.20/0.50 ((~![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_2, e_1)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(337,plain,
% 0.20/0.50 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_4))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[336, 335])).
% 0.20/0.50 tff(338,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[337, 85, 21, 262, 243, 331, 309])).
% 0.20/0.50 tff(339,plain,(~product(e_2, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(340,plain,
% 0.20/0.50 (product(e_2, e_1, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[208, 339])).
% 0.20/0.50 tff(341,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(342,axiom,(~equalish(e_4, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_1')).
% 0.20/0.50 tff(343,plain,
% 0.20/0.50 (~equalish(e_4, e_1)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[342, 341])).
% 0.20/0.50 tff(344,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)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(345,plain,
% 0.20/0.51 ((~![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)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(346,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.20/0.51 tff(347,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[346, 343, 179, 340, 308])).
% 0.20/0.51 tff(348,plain,(~product(e_2, e_4, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(349,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_2)) | product(e_2, e_4, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_2)) | product(e_2, e_4, e_3))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(350,plain,
% 0.20/0.51 (((~product(e_3, e_1, e_4)) | product(e_2, e_4, e_3) | (~product(e_1, e_3, e_2))) <=> ((~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_2)) | product(e_2, e_4, e_3))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(351,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_2, e_4, e_3) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_2)) | product(e_2, e_4, e_3)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[350])).
% 0.20/0.51 tff(352,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_2, e_4, e_3) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_2)) | product(e_2, e_4, e_3))),
% 0.20/0.51 inference(transitivity,[status(thm)],[351, 349])).
% 0.20/0.51 tff(353,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_2, e_4, e_3) | (~product(e_1, e_3, e_2)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(354,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_2)) | product(e_2, e_4, e_3)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[353, 352])).
% 0.20/0.51 tff(355,plain,
% 0.20/0.51 (~product(e_1, e_3, e_2)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[354, 303, 293, 348])).
% 0.20/0.51 tff(356,assumption,(product(e_1, e_3, e_1)), introduced(assumption)).
% 0.20/0.51 tff(357,plain,
% 0.20/0.51 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(358,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.20/0.51 tff(359,plain,
% 0.20/0.51 (~equalish(e_3, e_1)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[358, 357])).
% 0.20/0.51 tff(360,plain,
% 0.20/0.51 (((~![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)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(361,plain,
% 0.20/0.51 ((~![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)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(362,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[361, 360])).
% 0.20/0.51 tff(363,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[362, 359, 179, 151, 356])).
% 0.20/0.51 tff(364,plain,(~product(e_1, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(365,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_1)) | (~group_element(e_3)) | product(e_1, e_3, e_1) | product(e_1, e_3, e_2) | product(e_1, e_3, e_4) | product(e_1, e_3, 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_2) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(366,plain,
% 0.20/0.51 (((~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_2) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(367,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_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_2) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[366])).
% 0.20/0.51 tff(368,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_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_2) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3))),
% 0.20/0.51 inference(transitivity,[status(thm)],[367, 365])).
% 0.20/0.51 tff(369,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_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)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(370,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_1)) | (~group_element(e_3)) | product(e_1, e_3, e_1) | product(e_1, e_3, e_2) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[369, 368])).
% 0.20/0.51 tff(371,plain,
% 0.20/0.51 (product(e_1, e_3, e_2) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[370, 200, 63, 194, 364])).
% 0.20/0.51 tff(372,plain,
% 0.20/0.51 (product(e_1, e_3, e_4)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[371, 355, 307])).
% 0.20/0.51 tff(373,assumption,(~product(e_3, e_1, e_1)), introduced(assumption)).
% 0.20/0.51 tff(374,assumption,(product(e_1, e_2, e_1)), introduced(assumption)).
% 0.20/0.51 tff(375,assumption,(product(e_2, e_1, e_3)), introduced(assumption)).
% 0.20/0.51 tff(376,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_3, e_1, e_1) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_3, e_1, e_1) | (~product(e_1, e_2, e_1)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(377,plain,
% 0.20/0.51 (((~product(e_1, e_2, e_1)) | product(e_3, e_1, e_1) | (~product(e_2, e_1, e_3))) <=> ((~product(e_2, e_1, e_3)) | product(e_3, e_1, e_1) | (~product(e_1, e_2, e_1)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(378,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_1)) | product(e_3, e_1, e_1) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_3, e_1, e_1) | (~product(e_1, e_2, e_1))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[377])).
% 0.20/0.51 tff(379,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_1)) | product(e_3, e_1, e_1) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_3, e_1, e_1) | (~product(e_1, e_2, e_1)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[378, 376])).
% 0.20/0.51 tff(380,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_1)) | product(e_3, e_1, e_1) | (~product(e_2, e_1, e_3)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(381,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_3, e_1, e_1) | (~product(e_1, e_2, e_1))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[380, 379])).
% 0.20/0.51 tff(382,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[381, 303, 375, 374, 373])).
% 0.20/0.51 tff(383,plain,((~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_3)) | product(e_3, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(384,plain,
% 0.20/0.51 (~product(e_1, e_2, e_1)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[383, 276, 340])).
% 0.20/0.51 tff(385,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_1)) | product(e_1, e_3, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_1)) | product(e_1, e_3, e_3))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(386,plain,
% 0.20/0.51 (((~product(e_3, e_3, e_3)) | product(e_1, e_3, e_3) | (~product(e_3, e_3, e_1))) <=> ((~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_1)) | product(e_1, e_3, e_3))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(387,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | product(e_1, e_3, e_3) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_1)) | product(e_1, e_3, e_3)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[386])).
% 0.20/0.51 tff(388,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | product(e_1, e_3, e_3) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_1)) | product(e_1, e_3, e_3))),
% 0.20/0.51 inference(transitivity,[status(thm)],[387, 385])).
% 0.20/0.51 tff(389,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | product(e_1, e_3, e_3) | (~product(e_3, e_3, e_1)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(390,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_1)) | product(e_1, e_3, e_3)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[389, 388])).
% 0.20/0.51 tff(391,plain,
% 0.20/0.51 (~product(e_3, e_3, e_1)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[390, 303, 240, 307])).
% 0.20/0.51 tff(392,assumption,(product(e_1, e_2, e_3)), introduced(assumption)).
% 0.20/0.51 tff(393,assumption,(~product(e_3, e_3, e_1)), introduced(assumption)).
% 0.20/0.51 tff(394,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_3, e_3, e_1) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_3, e_3, e_1) | (~product(e_1, e_2, e_3)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(395,plain,
% 0.20/0.51 (((~product(e_1, e_2, e_3)) | product(e_3, e_3, e_1) | (~product(e_2, e_1, e_3))) <=> ((~product(e_2, e_1, e_3)) | product(e_3, e_3, e_1) | (~product(e_1, e_2, e_3)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(396,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_3, e_3, e_1) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_3, e_3, e_1) | (~product(e_1, e_2, e_3))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[395])).
% 0.20/0.51 tff(397,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_3, e_3, e_1) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_3, e_3, e_1) | (~product(e_1, e_2, e_3)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[396, 394])).
% 0.20/0.51 tff(398,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_3, e_3, e_1) | (~product(e_2, e_1, e_3)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(399,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_3, e_3, e_1) | (~product(e_1, e_2, e_3))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[398, 397])).
% 0.20/0.51 tff(400,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[399, 303, 340, 393, 392])).
% 0.20/0.51 tff(401,plain,((~product(e_1, e_2, e_3)) | product(e_3, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(402,plain,
% 0.20/0.51 (~product(e_1, e_2, e_3)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[401, 391])).
% 0.20/0.51 tff(403,assumption,(product(e_1, e_2, e_2)), introduced(assumption)).
% 0.20/0.51 tff(404,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_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(405,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_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(406,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[405, 404])).
% 0.20/0.52 tff(407,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[406, 82, 161, 168, 403])).
% 0.20/0.52 tff(408,plain,(~product(e_1, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(409,plain,
% 0.20/0.52 (((~![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_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_1) | product(e_1, e_2, 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_2)) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_1) | product(e_1, e_2, e_2))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(410,plain,
% 0.20/0.52 (((~group_element(e_1)) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2))) <=> ((~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_1) | product(e_1, e_2, e_2))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(411,plain,
% 0.20/0.52 (((~![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_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(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_2)) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_1) | product(e_1, e_2, e_2)))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[410])).
% 0.20/0.52 tff(412,plain,
% 0.20/0.52 (((~![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_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(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_2)) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_1) | product(e_1, e_2, e_2))),
% 0.20/0.52 inference(transitivity,[status(thm)],[411, 409])).
% 0.20/0.52 tff(413,plain,
% 0.20/0.52 ((~![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_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(414,plain,
% 0.20/0.52 ((~![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_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_1) | product(e_1, e_2, e_2)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[413, 412])).
% 0.20/0.52 tff(415,plain,
% 0.20/0.52 (product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_1)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[414, 200, 197, 194, 408])).
% 0.20/0.52 tff(416,plain,
% 0.20/0.52 (product(e_1, e_2, e_4)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[415, 402, 384])).
% 0.20/0.52 tff(417,plain,
% 0.20/0.52 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(418,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.20/0.52 tff(419,plain,
% 0.20/0.52 (~equalish(e_2, e_3)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[418, 417])).
% 0.20/0.52 tff(420,plain,
% 0.20/0.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_2, e_4)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(421,plain,
% 0.20/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_2, e_4)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(422,plain,
% 0.20/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_2, e_4))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[421, 420])).
% 0.20/0.52 tff(423,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[422, 419, 179, 416, 372])).
% 0.20/0.52 tff(424,plain,(~cycle(e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(425,plain,
% 0.20/0.52 (cycle(e_3, e_3)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[78, 424, 237])).
% 0.20/0.52 tff(426,plain,
% 0.20/0.52 (((~![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)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(427,plain,
% 0.20/0.52 (((~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)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(428,plain,
% 0.20/0.52 (((~![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))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[427])).
% 0.20/0.52 tff(429,plain,
% 0.20/0.52 (((~![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)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[428, 426])).
% 0.20/0.52 tff(430,plain,
% 0.20/0.52 ((~![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)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(431,plain,
% 0.20/0.52 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_1) | (~cycle(e_4, e_0)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~next(e_0, e_1))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[430, 429])).
% 0.20/0.52 tff(432,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[431, 52, 24, 222, 15, 46, 359, 425])).
% 0.20/0.52 % SZS output end Proof
% 0.20/0.52 % E exiting
%------------------------------------------------------------------------------