%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP128-3.005 : 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 05:07:09 AM UTC 2025
% Result : Unsatisfiable 0.41s 0.59s
% Output : Proof 0.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP128-3.005 : TPTP v9.0.0. Released v1.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 15:47:33 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.41/0.59 % SZS status Unsatisfiable
% 0.41/0.59 % SZS output start Proof
% 0.41/0.59 tff(product_type, type, (
% 0.41/0.59 product: ( $i * $i * $i ) > $o)).
% 0.41/0.59 tff(e_5_type, type, (
% 0.41/0.59 e_5: $i)).
% 0.41/0.59 tff(e_3_type, type, (
% 0.41/0.59 e_3: $i)).
% 0.41/0.59 tff(e_1_type, type, (
% 0.41/0.59 e_1: $i)).
% 0.41/0.59 tff(e_4_type, type, (
% 0.41/0.59 e_4: $i)).
% 0.41/0.59 tff(cycle_type, type, (
% 0.41/0.59 cycle: ( $i * $i ) > $o)).
% 0.41/0.59 tff(e_0_type, type, (
% 0.41/0.59 e_0: $i)).
% 0.41/0.59 tff(e_2_type, type, (
% 0.41/0.59 e_2: $i)).
% 0.41/0.59 tff(next_type, type, (
% 0.41/0.59 next: ( $i * $i ) > $o)).
% 0.41/0.59 tff(greater_type, type, (
% 0.41/0.59 greater: ( $i * $i ) > $o)).
% 0.41/0.59 tff(equalish_type, type, (
% 0.41/0.59 equalish: ( $i * $i ) > $o)).
% 0.41/0.59 tff(group_element_type, type, (
% 0.41/0.59 group_element: $i > $o)).
% 0.41/0.59 tff(1,assumption,(cycle(e_2, e_2)), introduced(assumption)).
% 0.41/0.59 tff(2,plain,
% 0.41/0.59 (^[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))))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(3,plain,
% 0.41/0.59 (![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)))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[2])).
% 0.41/0.59 tff(4,plain,
% 0.41/0.59 (![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)))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(5,plain,
% 0.41/0.59 (^[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)))))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(6,plain,
% 0.41/0.59 (![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)))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[5])).
% 0.41/0.59 tff(7,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')).
% 0.41/0.59 tff(8,plain,
% 0.41/0.59 (![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)))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.41/0.59 tff(9,plain,
% 0.41/0.59 (![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)))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.41/0.59 tff(10,plain,(
% 0.41/0.59 ![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)))),
% 0.41/0.59 inference(skolemize,[status(sab)],[9])).
% 0.41/0.59 tff(11,plain,
% 0.41/0.59 (![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)))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.41/0.59 tff(12,plain,
% 0.41/0.59 (cycle(e_5, e_0) <=> cycle(e_5, e_0)),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(13,axiom,(cycle(e_5, e_0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cycle3')).
% 0.41/0.59 tff(14,plain,
% 0.41/0.59 (cycle(e_5, e_0)),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.41/0.59 tff(15,plain,
% 0.41/0.59 (greater(e_4, e_2) <=> greater(e_4, e_2)),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(16,axiom,(greater(e_4, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_greater_e_2')).
% 0.41/0.59 tff(17,plain,
% 0.41/0.59 (greater(e_4, e_2)),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.41/0.59 tff(18,plain,
% 0.41/0.59 (greater(e_2, e_0) <=> greater(e_2, e_0)),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(19,axiom,(greater(e_2, e_0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_greater_e_0')).
% 0.41/0.59 tff(20,plain,
% 0.41/0.59 (greater(e_2, e_0)),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.41/0.59 tff(21,plain,
% 0.41/0.59 (next(e_4, e_5) <=> next(e_4, e_5)),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(22,axiom,(next(e_4, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_then_e_5')).
% 0.41/0.59 tff(23,plain,
% 0.41/0.59 (next(e_4, e_5)),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.41/0.59 tff(24,plain,
% 0.41/0.59 (((~![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_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, 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_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_2)))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(25,plain,
% 0.41/0.59 (((~greater(e_2, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_2))) <=> ((~cycle(e_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_2)))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(26,plain,
% 0.41/0.59 (((~![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_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, 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_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_2))))),
% 0.41/0.59 inference(monotonicity,[status(thm)],[25])).
% 0.41/0.59 tff(27,plain,
% 0.41/0.59 (((~![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_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, 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_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_2)))),
% 0.41/0.59 inference(transitivity,[status(thm)],[26, 24])).
% 0.41/0.59 tff(28,plain,
% 0.41/0.59 ((~![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_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_2)))),
% 0.41/0.59 inference(quant_inst,[status(thm)],[])).
% 0.41/0.59 tff(29,plain,
% 0.41/0.59 ((~![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_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_2))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.41/0.59 tff(30,plain,
% 0.41/0.59 ((~cycle(e_4, e_0)) | (~cycle(e_2, e_2))),
% 0.41/0.59 inference(unit_resolution,[status(thm)],[29, 23, 20, 17, 14, 11])).
% 0.41/0.59 tff(31,plain,
% 0.41/0.59 (~cycle(e_4, e_0)),
% 0.41/0.59 inference(unit_resolution,[status(thm)],[30, 1])).
% 0.41/0.59 tff(32,assumption,(cycle(e_4, e_3)), introduced(assumption)).
% 0.41/0.59 tff(33,plain,
% 0.41/0.59 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(34,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.41/0.59 tff(35,plain,
% 0.41/0.59 (~equalish(e_3, e_1)),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.41/0.59 tff(36,plain,
% 0.41/0.59 (^[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))))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(37,plain,
% 0.41/0.59 (![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)))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[36])).
% 0.41/0.59 tff(38,plain,
% 0.41/0.59 (![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)))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(39,plain,
% 0.41/0.59 (^[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)))))),
% 0.41/0.60 inference(bind,[status(th)],[])).
% 0.41/0.60 tff(40,plain,
% 0.41/0.60 (![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)))),
% 0.41/0.60 inference(quant_intro,[status(thm)],[39])).
% 0.41/0.60 tff(41,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')).
% 0.41/0.60 tff(42,plain,
% 0.41/0.60 (![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)))),
% 0.41/0.60 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.41/0.60 tff(43,plain,
% 0.41/0.60 (![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)))),
% 0.41/0.60 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.41/0.60 tff(44,plain,(
% 0.41/0.60 ![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)))),
% 0.41/0.60 inference(skolemize,[status(sab)],[43])).
% 0.41/0.60 tff(45,plain,
% 0.41/0.60 (![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)))),
% 0.41/0.60 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.41/0.60 tff(46,plain,
% 0.41/0.60 (greater(e_3, e_0) <=> greater(e_3, e_0)),
% 0.41/0.60 inference(rewrite,[status(thm)],[])).
% 0.41/0.60 tff(47,axiom,(greater(e_3, e_0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_greater_e_0')).
% 0.41/0.60 tff(48,plain,
% 0.41/0.60 (greater(e_3, e_0)),
% 0.41/0.60 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.41/0.60 tff(49,plain,
% 0.41/0.60 (next(e_0, e_1) <=> next(e_0, e_1)),
% 0.41/0.60 inference(rewrite,[status(thm)],[])).
% 0.41/0.60 tff(50,axiom,(next(e_0, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_0_then_e_1')).
% 0.41/0.60 tff(51,plain,
% 0.41/0.60 (next(e_0, e_1)),
% 0.41/0.60 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.41/0.60 tff(52,plain,
% 0.41/0.60 (((~![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_5, e_0)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, 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_5, e_0)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_3)) | (~next(e_0, e_1)))),
% 0.41/0.60 inference(rewrite,[status(thm)],[])).
% 0.41/0.60 tff(53,plain,
% 0.41/0.60 (((~cycle(e_4, e_3)) | equalish(e_3, e_1) | (~next(e_0, e_1)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0))) <=> (equalish(e_3, e_1) | (~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_3)) | (~next(e_0, e_1)))),
% 0.41/0.60 inference(rewrite,[status(thm)],[])).
% 0.41/0.60 tff(54,plain,
% 0.41/0.60 (((~![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_4, e_3)) | equalish(e_3, e_1) | (~next(e_0, e_1)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, 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_5, e_0)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_3)) | (~next(e_0, e_1))))),
% 0.41/0.60 inference(monotonicity,[status(thm)],[53])).
% 0.41/0.60 tff(55,plain,
% 0.41/0.60 (((~![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_4, e_3)) | equalish(e_3, e_1) | (~next(e_0, e_1)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, 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_5, e_0)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_3)) | (~next(e_0, e_1)))),
% 0.41/0.60 inference(transitivity,[status(thm)],[54, 52])).
% 0.41/0.60 tff(56,plain,
% 0.41/0.60 ((~![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_4, e_3)) | equalish(e_3, e_1) | (~next(e_0, e_1)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)))),
% 0.41/0.60 inference(quant_inst,[status(thm)],[])).
% 0.41/0.60 tff(57,plain,
% 0.41/0.60 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_1) | (~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_3)) | (~next(e_0, e_1))),
% 0.41/0.60 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.41/0.60 tff(58,plain,
% 0.41/0.60 ($false),
% 0.41/0.60 inference(unit_resolution,[status(thm)],[57, 51, 23, 48, 14, 45, 35, 32])).
% 0.41/0.60 tff(59,plain,(~cycle(e_4, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.41/0.60 tff(60,assumption,(cycle(e_4, e_2)), introduced(assumption)).
% 0.41/0.60 tff(61,plain,
% 0.41/0.60 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.41/0.60 inference(rewrite,[status(thm)],[])).
% 0.41/0.60 tff(62,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.41/0.60 tff(63,plain,
% 0.41/0.60 (~equalish(e_2, e_1)),
% 0.41/0.60 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.41/0.60 tff(64,plain,
% 0.41/0.60 (((~![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_5, e_0)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, 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_5, e_0)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_2)) | (~next(e_0, e_1)))),
% 0.41/0.60 inference(rewrite,[status(thm)],[])).
% 0.41/0.60 tff(65,plain,
% 0.41/0.60 (((~cycle(e_4, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0))) <=> (equalish(e_2, e_1) | (~cycle(e_5, e_0)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_2)) | (~next(e_0, e_1)))),
% 0.41/0.60 inference(rewrite,[status(thm)],[])).
% 0.41/0.60 tff(66,plain,
% 0.41/0.60 (((~![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_4, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, 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_5, e_0)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_2)) | (~next(e_0, e_1))))),
% 0.41/0.60 inference(monotonicity,[status(thm)],[65])).
% 0.41/0.60 tff(67,plain,
% 0.41/0.60 (((~![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_4, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, 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_5, e_0)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_2)) | (~next(e_0, e_1)))),
% 0.41/0.60 inference(transitivity,[status(thm)],[66, 64])).
% 0.41/0.60 tff(68,plain,
% 0.41/0.60 ((~![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_4, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)))),
% 0.41/0.60 inference(quant_inst,[status(thm)],[])).
% 0.41/0.60 tff(69,plain,
% 0.41/0.60 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_1) | (~cycle(e_5, e_0)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_2)) | (~next(e_0, e_1))),
% 0.41/0.60 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.41/0.60 tff(70,plain,
% 0.41/0.60 ($false),
% 0.41/0.60 inference(unit_resolution,[status(thm)],[69, 51, 23, 20, 14, 45, 63, 60])).
% 0.41/0.60 tff(71,plain,(~cycle(e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.41/0.60 tff(72,assumption,(cycle(e_4, e_4)), introduced(assumption)).
% 0.41/0.60 tff(73,plain,
% 0.41/0.60 ((~equalish(e_4, e_1)) <=> (~equalish(e_4, e_1))),
% 0.41/0.60 inference(rewrite,[status(thm)],[])).
% 0.41/0.60 tff(74,axiom,(~equalish(e_4, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_1')).
% 0.41/0.60 tff(75,plain,
% 0.41/0.60 (~equalish(e_4, e_1)),
% 0.41/0.60 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.41/0.60 tff(76,plain,
% 0.41/0.60 (greater(e_4, e_0) <=> greater(e_4, e_0)),
% 0.41/0.60 inference(rewrite,[status(thm)],[])).
% 0.41/0.60 tff(77,axiom,(greater(e_4, e_0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_greater_e_0')).
% 0.41/0.60 tff(78,plain,
% 0.41/0.60 (greater(e_4, e_0)),
% 0.41/0.60 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.41/0.60 tff(79,plain,
% 0.41/0.60 (((~![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_4, e_1) | (~cycle(e_5, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_4)) | (~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_4, e_1) | (~cycle(e_5, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_4)) | (~next(e_0, e_1)))),
% 0.41/0.60 inference(rewrite,[status(thm)],[])).
% 0.41/0.60 tff(80,plain,
% 0.41/0.60 (((~cycle(e_4, e_4)) | equalish(e_4, e_1) | (~next(e_0, e_1)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0))) <=> (equalish(e_4, e_1) | (~cycle(e_5, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_4)) | (~next(e_0, e_1)))),
% 0.41/0.60 inference(rewrite,[status(thm)],[])).
% 0.41/0.60 tff(81,plain,
% 0.41/0.60 (((~![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_4, e_4)) | equalish(e_4, e_1) | (~next(e_0, e_1)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, 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_4, e_1) | (~cycle(e_5, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_4)) | (~next(e_0, e_1))))),
% 0.41/0.60 inference(monotonicity,[status(thm)],[80])).
% 0.41/0.60 tff(82,plain,
% 0.41/0.60 (((~![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_4, e_4)) | equalish(e_4, e_1) | (~next(e_0, e_1)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, 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_4, e_1) | (~cycle(e_5, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_4)) | (~next(e_0, e_1)))),
% 0.41/0.60 inference(transitivity,[status(thm)],[81, 79])).
% 0.41/0.60 tff(83,plain,
% 0.41/0.60 ((~![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_4, e_4)) | equalish(e_4, e_1) | (~next(e_0, e_1)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)))),
% 0.41/0.60 inference(quant_inst,[status(thm)],[])).
% 0.41/0.60 tff(84,plain,
% 0.41/0.60 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_4, e_1) | (~cycle(e_5, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_4)) | (~next(e_0, e_1))),
% 0.41/0.60 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.41/0.60 tff(85,plain,
% 0.41/0.60 ($false),
% 0.41/0.60 inference(unit_resolution,[status(thm)],[84, 51, 23, 78, 14, 45, 75, 72])).
% 0.41/0.60 tff(86,plain,(~cycle(e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.41/0.60 tff(87,plain,
% 0.41/0.60 (group_element(e_4) <=> group_element(e_4)),
% 0.41/0.60 inference(rewrite,[status(thm)],[])).
% 0.41/0.60 tff(88,axiom,(group_element(e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_4')).
% 0.41/0.60 tff(89,plain,
% 0.41/0.60 (group_element(e_4)),
% 0.41/0.60 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.41/0.60 tff(90,plain,
% 0.41/0.60 (^[X: $i] : refl((cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) <=> (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))))),
% 0.41/0.60 inference(bind,[status(th)],[])).
% 0.41/0.60 tff(91,plain,
% 0.41/0.60 (![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) <=> ![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.41/0.60 inference(quant_intro,[status(thm)],[90])).
% 0.41/0.60 tff(92,plain,
% 0.41/0.60 (![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) <=> ![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.41/0.60 inference(rewrite,[status(thm)],[])).
% 0.41/0.60 tff(93,plain,
% 0.41/0.60 (^[X: $i] : trans(monotonicity(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))))), (((((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) | cycle(X, e_3)) | cycle(X, e_4)) <=> ((cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) | cycle(X, e_4)))), rewrite(((cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) | cycle(X, e_4)) <=> (cycle(X, e_4) | 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_4)) <=> (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))))),
% 0.41/0.60 inference(bind,[status(th)],[])).
% 0.41/0.60 tff(94,plain,
% 0.43/0.60 (![X: $i] : ((((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) | cycle(X, e_3)) | cycle(X, e_4)) <=> ![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.43/0.60 inference(quant_intro,[status(thm)],[93])).
% 0.43/0.60 tff(95,axiom,(![X: $i] : ((((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) | cycle(X, e_3)) | cycle(X, e_4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cycle2')).
% 0.43/0.60 tff(96,plain,
% 0.43/0.60 (![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.43/0.60 tff(97,plain,
% 0.43/0.60 (![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.43/0.60 tff(98,plain,(
% 0.43/0.60 ![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.43/0.60 inference(skolemize,[status(sab)],[97])).
% 0.43/0.60 tff(99,plain,
% 0.43/0.60 (![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.43/0.60 tff(100,plain,
% 0.43/0.60 (((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_4, e_4) | cycle(e_4, e_3) | cycle(e_4, e_2) | cycle(e_4, e_1) | cycle(e_4, e_0) | (~group_element(e_4)))) <=> ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_4, e_4) | cycle(e_4, e_3) | cycle(e_4, e_2) | cycle(e_4, e_1) | cycle(e_4, e_0) | (~group_element(e_4)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(101,plain,
% 0.43/0.60 ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_4, e_4) | cycle(e_4, e_3) | cycle(e_4, e_2) | cycle(e_4, e_1) | cycle(e_4, e_0) | (~group_element(e_4)))),
% 0.43/0.60 inference(quant_inst,[status(thm)],[])).
% 0.43/0.60 tff(102,plain,
% 0.43/0.60 ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_4, e_4) | cycle(e_4, e_3) | cycle(e_4, e_2) | cycle(e_4, e_1) | cycle(e_4, e_0) | (~group_element(e_4))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.43/0.60 tff(103,plain,
% 0.43/0.60 (cycle(e_4, e_4) | cycle(e_4, e_3) | cycle(e_4, e_2) | cycle(e_4, e_1) | cycle(e_4, e_0)),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[102, 99, 89])).
% 0.43/0.60 tff(104,plain,
% 0.43/0.60 (cycle(e_4, e_3) | cycle(e_4, e_1) | cycle(e_4, e_0)),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[103, 86, 71])).
% 0.43/0.60 tff(105,plain,
% 0.43/0.60 (cycle(e_4, e_1) | cycle(e_4, e_0)),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[104, 59])).
% 0.43/0.60 tff(106,plain,
% 0.43/0.60 (cycle(e_4, e_1)),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[105, 31])).
% 0.43/0.60 tff(107,plain,
% 0.43/0.60 ((~equalish(e_2, e_4)) <=> (~equalish(e_2, e_4))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(108,axiom,(~equalish(e_2, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_4')).
% 0.43/0.60 tff(109,plain,
% 0.43/0.60 (~equalish(e_2, e_4)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.43/0.60 tff(110,plain,
% 0.43/0.60 (next(e_3, e_4) <=> next(e_3, e_4)),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(111,axiom,(next(e_3, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_then_e_4')).
% 0.43/0.60 tff(112,plain,
% 0.43/0.60 (next(e_3, e_4)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.43/0.60 tff(113,plain,
% 0.43/0.60 (next(e_2, e_3) <=> next(e_2, e_3)),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(114,axiom,(next(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_then_e_3')).
% 0.43/0.60 tff(115,plain,
% 0.43/0.60 (next(e_2, e_3)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.43/0.60 tff(116,plain,
% 0.43/0.60 (((~![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_4) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~next(e_3, e_4)) | (~cycle(e_2, e_2)) | (~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_2, e_4) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~next(e_3, e_4)) | (~cycle(e_2, e_2)) | (~cycle(e_3, e_3)))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(117,plain,
% 0.43/0.61 (((~cycle(e_2, e_2)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_3))) <=> (equalish(e_2, e_4) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~next(e_3, e_4)) | (~cycle(e_2, e_2)) | (~cycle(e_3, e_3)))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(118,plain,
% 0.43/0.61 (((~![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_2)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~greater(e_2, 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_2, e_4) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~next(e_3, e_4)) | (~cycle(e_2, e_2)) | (~cycle(e_3, e_3))))),
% 0.43/0.61 inference(monotonicity,[status(thm)],[117])).
% 0.43/0.61 tff(119,plain,
% 0.43/0.61 (((~![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_2)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~greater(e_2, 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_2, e_4) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~next(e_3, e_4)) | (~cycle(e_2, e_2)) | (~cycle(e_3, e_3)))),
% 0.43/0.61 inference(transitivity,[status(thm)],[118, 116])).
% 0.43/0.61 tff(120,plain,
% 0.43/0.61 ((~![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_2)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_3)))),
% 0.43/0.61 inference(quant_inst,[status(thm)],[])).
% 0.43/0.61 tff(121,plain,
% 0.43/0.61 ((~![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_4) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~next(e_3, e_4)) | (~cycle(e_2, e_2)) | (~cycle(e_3, e_3))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.43/0.61 tff(122,plain,
% 0.43/0.61 (~cycle(e_3, e_3)),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[121, 115, 112, 20, 45, 109, 1])).
% 0.43/0.61 tff(123,plain,
% 0.43/0.61 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(124,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.43/0.61 tff(125,plain,
% 0.43/0.61 (~equalish(e_2, e_3)),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.43/0.61 tff(126,plain,
% 0.43/0.61 (((~![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_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~cycle(e_3, e_2)))) <=> ((~![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_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~cycle(e_3, e_2)))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(127,plain,
% 0.43/0.61 (((~cycle(e_2, e_2)) | equalish(e_2, e_3) | (~next(e_2, e_3)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2))) <=> (equalish(e_2, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~cycle(e_3, e_2)))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(128,plain,
% 0.43/0.61 (((~![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_2)) | equalish(e_2, e_3) | (~next(e_2, e_3)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2)))) <=> ((~![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_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~cycle(e_3, e_2))))),
% 0.43/0.61 inference(monotonicity,[status(thm)],[127])).
% 0.43/0.61 tff(129,plain,
% 0.43/0.61 (((~![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_2)) | equalish(e_2, e_3) | (~next(e_2, e_3)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2)))) <=> ((~![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_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~cycle(e_3, e_2)))),
% 0.43/0.61 inference(transitivity,[status(thm)],[128, 126])).
% 0.43/0.61 tff(130,plain,
% 0.43/0.61 ((~![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_2)) | equalish(e_2, e_3) | (~next(e_2, e_3)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2)))),
% 0.43/0.61 inference(quant_inst,[status(thm)],[])).
% 0.43/0.61 tff(131,plain,
% 0.43/0.61 ((~![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_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~cycle(e_3, e_2))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.43/0.61 tff(132,plain,
% 0.43/0.61 (~cycle(e_3, e_2)),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[131, 115, 20, 45, 125, 1])).
% 0.43/0.61 tff(133,plain,
% 0.43/0.61 (greater(e_3, e_2) <=> greater(e_3, e_2)),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(134,axiom,(greater(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_greater_e_2')).
% 0.43/0.61 tff(135,plain,
% 0.43/0.61 (greater(e_3, e_2)),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.43/0.61 tff(136,plain,
% 0.43/0.61 (greater(e_2, e_1) <=> greater(e_2, e_1)),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(137,axiom,(greater(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_greater_e_1')).
% 0.43/0.61 tff(138,plain,
% 0.43/0.61 (greater(e_2, e_1)),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.43/0.61 tff(139,plain,
% 0.43/0.61 (((~![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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_2, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2)) | (~cycle(e_4, 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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_2, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2)) | (~cycle(e_4, e_1)))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(140,plain,
% 0.43/0.61 (((~greater(e_2, e_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_2))) <=> ((~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_2, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2)) | (~cycle(e_4, e_1)))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(141,plain,
% 0.43/0.61 (((~![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_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_2, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2)) | (~cycle(e_4, e_1))))),
% 0.43/0.61 inference(monotonicity,[status(thm)],[140])).
% 0.43/0.61 tff(142,plain,
% 0.43/0.61 (((~![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_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_2, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2)) | (~cycle(e_4, e_1)))),
% 0.43/0.61 inference(transitivity,[status(thm)],[141, 139])).
% 0.43/0.61 tff(143,plain,
% 0.43/0.61 ((~![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_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_2)))),
% 0.43/0.61 inference(quant_inst,[status(thm)],[])).
% 0.43/0.61 tff(144,plain,
% 0.43/0.61 ((~![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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_2, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2)) | (~cycle(e_4, e_1))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.43/0.61 tff(145,plain,
% 0.43/0.61 ((~cycle(e_3, e_0)) | (~cycle(e_2, e_2)) | (~cycle(e_4, e_1))),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[144, 112, 138, 135, 11])).
% 0.43/0.61 tff(146,plain,
% 0.43/0.61 (~cycle(e_3, e_0)),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[145, 106, 1])).
% 0.43/0.61 tff(147,plain,
% 0.43/0.61 ((~equalish(e_2, e_5)) <=> (~equalish(e_2, e_5))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(148,axiom,(~equalish(e_2, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_5')).
% 0.43/0.61 tff(149,plain,
% 0.43/0.61 (~equalish(e_2, e_5)),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.43/0.61 tff(150,plain,
% 0.43/0.61 (((~![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_5) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~next(e_4, e_5)) | (~cycle(e_2, e_2)) | (~cycle(e_3, e_4)))) <=> ((~![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_5) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~next(e_4, e_5)) | (~cycle(e_2, e_2)) | (~cycle(e_3, e_4)))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(151,plain,
% 0.43/0.61 (((~cycle(e_2, e_2)) | equalish(e_2, e_5) | (~next(e_4, e_5)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_4))) <=> (equalish(e_2, e_5) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~next(e_4, e_5)) | (~cycle(e_2, e_2)) | (~cycle(e_3, e_4)))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(152,plain,
% 0.43/0.61 (((~![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_2)) | equalish(e_2, e_5) | (~next(e_4, e_5)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_4)))) <=> ((~![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_5) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~next(e_4, e_5)) | (~cycle(e_2, e_2)) | (~cycle(e_3, e_4))))),
% 0.43/0.61 inference(monotonicity,[status(thm)],[151])).
% 0.43/0.61 tff(153,plain,
% 0.43/0.61 (((~![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_2)) | equalish(e_2, e_5) | (~next(e_4, e_5)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_4)))) <=> ((~![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_5) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~next(e_4, e_5)) | (~cycle(e_2, e_2)) | (~cycle(e_3, e_4)))),
% 0.43/0.61 inference(transitivity,[status(thm)],[152, 150])).
% 0.43/0.61 tff(154,plain,
% 0.43/0.61 ((~![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_2)) | equalish(e_2, e_5) | (~next(e_4, e_5)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_4)))),
% 0.43/0.61 inference(quant_inst,[status(thm)],[])).
% 0.43/0.61 tff(155,plain,
% 0.43/0.61 ((~![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_5) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~next(e_4, e_5)) | (~cycle(e_2, e_2)) | (~cycle(e_3, e_4))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.43/0.61 tff(156,plain,
% 0.43/0.61 (~cycle(e_3, e_4)),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[155, 115, 23, 20, 45, 149, 1])).
% 0.43/0.61 tff(157,plain,
% 0.43/0.61 (group_element(e_3) <=> group_element(e_3)),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(158,axiom,(group_element(e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_3')).
% 0.43/0.61 tff(159,plain,
% 0.43/0.61 (group_element(e_3)),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.43/0.61 tff(160,plain,
% 0.43/0.61 (((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_3, e_4) | 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_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_3, e_4) | cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0) | (~group_element(e_3)))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(161,plain,
% 0.43/0.61 ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_3, e_4) | cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0) | (~group_element(e_3)))),
% 0.43/0.61 inference(quant_inst,[status(thm)],[])).
% 0.43/0.61 tff(162,plain,
% 0.43/0.61 ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_3, e_4) | cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0) | (~group_element(e_3))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.43/0.61 tff(163,plain,
% 0.43/0.61 (cycle(e_3, e_4) | cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0)),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[162, 99, 159])).
% 0.43/0.61 tff(164,plain,
% 0.43/0.61 (cycle(e_3, e_1)),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[163, 156, 146, 132, 122])).
% 0.43/0.61 tff(165,plain,
% 0.43/0.61 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(166,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.43/0.61 tff(167,plain,
% 0.43/0.61 (~equalish(e_1, e_2)),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.43/0.61 tff(168,plain,
% 0.43/0.61 (greater(e_1, e_0) <=> greater(e_1, e_0)),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(169,axiom,(greater(e_1, e_0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_greater_e_0')).
% 0.43/0.61 tff(170,plain,
% 0.43/0.61 (greater(e_1, e_0)),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.43/0.61 tff(171,plain,
% 0.43/0.61 (next(e_1, e_2) <=> next(e_1, e_2)),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(172,axiom,(next(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_then_e_2')).
% 0.43/0.61 tff(173,plain,
% 0.43/0.61 (next(e_1, e_2)),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.43/0.61 tff(174,plain,
% 0.43/0.61 (((~![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_3, e_4)) | (~cycle(e_3, e_1)) | (~cycle(e_4, 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_3, e_4)) | (~cycle(e_3, e_1)) | (~cycle(e_4, e_1)))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(175,plain,
% 0.43/0.62 (((~cycle(e_3, e_1)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1))) <=> (equalish(e_1, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~cycle(e_4, e_1)))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(176,plain,
% 0.43/0.62 (((~![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_1)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, 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_3, e_4)) | (~cycle(e_3, e_1)) | (~cycle(e_4, e_1))))),
% 0.43/0.62 inference(monotonicity,[status(thm)],[175])).
% 0.43/0.62 tff(177,plain,
% 0.43/0.62 (((~![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_1)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, 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_3, e_4)) | (~cycle(e_3, e_1)) | (~cycle(e_4, e_1)))),
% 0.43/0.62 inference(transitivity,[status(thm)],[176, 174])).
% 0.43/0.62 tff(178,plain,
% 0.43/0.62 ((~![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_1)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)))),
% 0.43/0.62 inference(quant_inst,[status(thm)],[])).
% 0.43/0.62 tff(179,plain,
% 0.43/0.62 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_1, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~cycle(e_4, e_1))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.43/0.62 tff(180,plain,
% 0.43/0.62 ($false),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[179, 173, 112, 170, 45, 167, 164, 106])).
% 0.43/0.62 tff(181,plain,(~cycle(e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.43/0.62 tff(182,assumption,(cycle(e_2, e_4)), introduced(assumption)).
% 0.43/0.62 tff(183,plain,
% 0.43/0.62 (((~![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_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_4)))) <=> ((~![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_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_4)))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(184,plain,
% 0.43/0.62 (((~greater(e_4, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_4))) <=> ((~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_4)))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(185,plain,
% 0.43/0.62 (((~![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_4, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_4)))) <=> ((~![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_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_4))))),
% 0.43/0.62 inference(monotonicity,[status(thm)],[184])).
% 0.43/0.62 tff(186,plain,
% 0.43/0.62 (((~![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_4, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_4)))) <=> ((~![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_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_4)))),
% 0.43/0.62 inference(transitivity,[status(thm)],[185, 183])).
% 0.43/0.62 tff(187,plain,
% 0.43/0.62 ((~![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_4, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_4)))),
% 0.43/0.62 inference(quant_inst,[status(thm)],[])).
% 0.43/0.62 tff(188,plain,
% 0.43/0.62 ((~![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_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_4))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.43/0.62 tff(189,plain,
% 0.43/0.62 ((~cycle(e_4, e_0)) | (~cycle(e_2, e_4))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[188, 23, 78, 17, 14, 11])).
% 0.43/0.62 tff(190,plain,
% 0.43/0.62 (~cycle(e_4, e_0)),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[189, 182])).
% 0.43/0.62 tff(191,plain,
% 0.43/0.62 (cycle(e_4, e_1)),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[104, 190, 59])).
% 0.43/0.62 tff(192,plain,
% 0.43/0.62 ((~equalish(e_4, e_3)) <=> (~equalish(e_4, e_3))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(193,axiom,(~equalish(e_4, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_3')).
% 0.43/0.62 tff(194,plain,
% 0.43/0.62 (~equalish(e_4, e_3)),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.43/0.62 tff(195,plain,
% 0.43/0.62 (((~![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_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_2)) | (~cycle(e_2, e_4)))) <=> ((~![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_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_2)) | (~cycle(e_2, e_4)))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(196,plain,
% 0.43/0.62 (((~cycle(e_2, e_4)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2))) <=> (equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_2)) | (~cycle(e_2, e_4)))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(197,plain,
% 0.43/0.62 (((~![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_4)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2)))) <=> ((~![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_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_2)) | (~cycle(e_2, e_4))))),
% 0.43/0.62 inference(monotonicity,[status(thm)],[196])).
% 0.43/0.62 tff(198,plain,
% 0.43/0.62 (((~![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_4)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2)))) <=> ((~![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_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_2)) | (~cycle(e_2, e_4)))),
% 0.43/0.62 inference(transitivity,[status(thm)],[197, 195])).
% 0.43/0.62 tff(199,plain,
% 0.43/0.62 ((~![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_4)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2)))),
% 0.43/0.62 inference(quant_inst,[status(thm)],[])).
% 0.43/0.62 tff(200,plain,
% 0.43/0.62 ((~![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_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_2)) | (~cycle(e_2, e_4))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.43/0.62 tff(201,plain,
% 0.43/0.62 (~cycle(e_3, e_2)),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[200, 115, 78, 45, 194, 182])).
% 0.43/0.62 tff(202,plain,
% 0.43/0.62 ((~equalish(e_4, e_2)) <=> (~equalish(e_4, e_2))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(203,axiom,(~equalish(e_4, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_2')).
% 0.43/0.62 tff(204,plain,
% 0.43/0.62 (~equalish(e_4, e_2)),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.43/0.62 tff(205,plain,
% 0.43/0.62 (((~![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_4, e_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_1)) | (~cycle(e_2, e_4)))) <=> ((~![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_4, e_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_1)) | (~cycle(e_2, e_4)))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(206,plain,
% 0.43/0.62 (((~cycle(e_2, e_4)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_1))) <=> (equalish(e_4, e_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_1)) | (~cycle(e_2, e_4)))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(207,plain,
% 0.43/0.62 (((~![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_4)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~greater(e_4, 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_4, e_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_1)) | (~cycle(e_2, e_4))))),
% 0.43/0.62 inference(monotonicity,[status(thm)],[206])).
% 0.43/0.62 tff(208,plain,
% 0.43/0.62 (((~![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_4)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~greater(e_4, 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_4, e_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_1)) | (~cycle(e_2, e_4)))),
% 0.43/0.62 inference(transitivity,[status(thm)],[207, 205])).
% 0.43/0.62 tff(209,plain,
% 0.43/0.62 ((~![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_4)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_1)))),
% 0.43/0.62 inference(quant_inst,[status(thm)],[])).
% 0.43/0.62 tff(210,plain,
% 0.43/0.62 ((~![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_4, e_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_1)) | (~cycle(e_2, e_4))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.43/0.62 tff(211,plain,
% 0.43/0.62 (~cycle(e_3, e_1)),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[210, 173, 115, 78, 45, 204, 182])).
% 0.43/0.62 tff(212,plain,
% 0.43/0.62 (greater(e_4, e_1) <=> greater(e_4, e_1)),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(213,axiom,(greater(e_4, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_greater_e_1')).
% 0.43/0.62 tff(214,plain,
% 0.43/0.62 (greater(e_4, e_1)),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.43/0.62 tff(215,plain,
% 0.43/0.62 (((~![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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_4, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_4)) | (~cycle(e_4, 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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_4, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_4)) | (~cycle(e_4, e_1)))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(216,plain,
% 0.43/0.62 (((~greater(e_4, e_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_4))) <=> ((~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_4, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_4)) | (~cycle(e_4, e_1)))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(217,plain,
% 0.43/0.62 (((~![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_4, e_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_4)))) <=> ((~![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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_4, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_4)) | (~cycle(e_4, e_1))))),
% 0.45/0.62 inference(monotonicity,[status(thm)],[216])).
% 0.45/0.62 tff(218,plain,
% 0.45/0.62 (((~![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_4, e_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_4)))) <=> ((~![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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_4, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_4)) | (~cycle(e_4, e_1)))),
% 0.45/0.62 inference(transitivity,[status(thm)],[217, 215])).
% 0.45/0.62 tff(219,plain,
% 0.45/0.62 ((~![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_4, e_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_4)))),
% 0.45/0.62 inference(quant_inst,[status(thm)],[])).
% 0.45/0.62 tff(220,plain,
% 0.45/0.62 ((~![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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_4, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_4)) | (~cycle(e_4, e_1))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.45/0.62 tff(221,plain,
% 0.45/0.62 ((~cycle(e_3, e_0)) | (~cycle(e_2, e_4)) | (~cycle(e_4, e_1))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[220, 112, 214, 135, 11])).
% 0.45/0.62 tff(222,plain,
% 0.45/0.62 (~cycle(e_3, e_0)),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[221, 191, 182])).
% 0.45/0.62 tff(223,plain,
% 0.45/0.62 ((~equalish(e_4, e_5)) <=> (~equalish(e_4, e_5))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(224,axiom,(~equalish(e_4, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_5')).
% 0.45/0.62 tff(225,plain,
% 0.45/0.62 (~equalish(e_4, e_5)),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.45/0.63 tff(226,plain,
% 0.45/0.63 (((~![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_4, e_5) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_4)) | (~cycle(e_3, e_4)))) <=> ((~![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_4, e_5) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_4)) | (~cycle(e_3, e_4)))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(227,plain,
% 0.45/0.63 (((~cycle(e_2, e_4)) | equalish(e_4, e_5) | (~next(e_4, e_5)) | (~greater(e_4, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_4))) <=> (equalish(e_4, e_5) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_4)) | (~cycle(e_3, e_4)))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(228,plain,
% 0.45/0.63 (((~![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_4)) | equalish(e_4, e_5) | (~next(e_4, e_5)) | (~greater(e_4, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_4)))) <=> ((~![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_4, e_5) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_4)) | (~cycle(e_3, e_4))))),
% 0.45/0.63 inference(monotonicity,[status(thm)],[227])).
% 0.45/0.63 tff(229,plain,
% 0.45/0.63 (((~![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_4)) | equalish(e_4, e_5) | (~next(e_4, e_5)) | (~greater(e_4, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_4)))) <=> ((~![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_4, e_5) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_4)) | (~cycle(e_3, e_4)))),
% 0.45/0.63 inference(transitivity,[status(thm)],[228, 226])).
% 0.45/0.63 tff(230,plain,
% 0.45/0.63 ((~![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_4)) | equalish(e_4, e_5) | (~next(e_4, e_5)) | (~greater(e_4, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_4)))),
% 0.45/0.63 inference(quant_inst,[status(thm)],[])).
% 0.45/0.63 tff(231,plain,
% 0.45/0.63 ((~![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_4, e_5) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_4)) | (~cycle(e_3, e_4))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.45/0.63 tff(232,plain,
% 0.45/0.63 (~cycle(e_3, e_4)),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[231, 115, 23, 78, 45, 225, 182])).
% 0.45/0.63 tff(233,plain,
% 0.45/0.63 (cycle(e_3, e_3)),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[163, 232, 222, 211, 201])).
% 0.45/0.63 tff(234,plain,
% 0.45/0.63 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(235,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.45/0.63 tff(236,plain,
% 0.45/0.63 (~equalish(e_3, e_2)),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.45/0.63 tff(237,plain,
% 0.45/0.63 (((~![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_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~cycle(e_4, 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_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~cycle(e_4, e_1)))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(238,plain,
% 0.45/0.63 (((~cycle(e_3, e_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1))) <=> (equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~cycle(e_4, e_1)))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(239,plain,
% 0.45/0.63 (((~![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_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, 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_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~cycle(e_4, e_1))))),
% 0.45/0.63 inference(monotonicity,[status(thm)],[238])).
% 0.45/0.63 tff(240,plain,
% 0.45/0.63 (((~![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_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, 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_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~cycle(e_4, e_1)))),
% 0.45/0.63 inference(transitivity,[status(thm)],[239, 237])).
% 0.45/0.63 tff(241,plain,
% 0.45/0.63 ((~![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_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)))),
% 0.45/0.63 inference(quant_inst,[status(thm)],[])).
% 0.45/0.63 tff(242,plain,
% 0.45/0.63 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~cycle(e_4, e_1))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.45/0.63 tff(243,plain,
% 0.45/0.63 ($false),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[242, 173, 112, 48, 45, 236, 233, 191])).
% 0.45/0.63 tff(244,plain,(~cycle(e_2, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.45/0.63 tff(245,assumption,(~product(e_2, e_1, e_3)), introduced(assumption)).
% 0.45/0.63 tff(246,assumption,(product(e_2, e_1, e_5)), introduced(assumption)).
% 0.45/0.63 tff(247,plain,
% 0.45/0.63 ((~equalish(e_5, e_3)) <=> (~equalish(e_5, e_3))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(248,axiom,(~equalish(e_5, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_is_not_e_3')).
% 0.45/0.63 tff(249,plain,
% 0.45/0.63 (~equalish(e_5, e_3)),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.45/0.63 tff(250,plain,
% 0.45/0.63 (^[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))))),
% 0.45/0.63 inference(bind,[status(th)],[])).
% 0.45/0.63 tff(251,plain,
% 0.45/0.63 (![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)))),
% 0.45/0.63 inference(quant_intro,[status(thm)],[250])).
% 0.45/0.63 tff(252,plain,
% 0.45/0.63 (![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)))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(253,plain,
% 0.45/0.63 (^[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)))))),
% 0.45/0.63 inference(bind,[status(th)],[])).
% 0.45/0.63 tff(254,plain,
% 0.45/0.63 (![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)))),
% 0.45/0.63 inference(quant_intro,[status(thm)],[253])).
% 0.45/0.63 tff(255,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')).
% 0.45/0.63 tff(256,plain,
% 0.45/0.63 (![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)))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.45/0.63 tff(257,plain,
% 0.45/0.63 (![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)))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[256, 252])).
% 0.45/0.63 tff(258,plain,(
% 0.45/0.63 ![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)))),
% 0.45/0.63 inference(skolemize,[status(sab)],[257])).
% 0.45/0.63 tff(259,plain,
% 0.45/0.63 (![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)))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[258, 251])).
% 0.45/0.63 tff(260,plain,
% 0.45/0.63 (((~![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_5, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_5)))) <=> ((~![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_5, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_5)))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(261,plain,
% 0.45/0.63 (((~greater(e_2, e_0)) | (~cycle(e_2, e_2)) | equalish(e_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5))) <=> (equalish(e_5, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_5)))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(262,plain,
% 0.45/0.63 (((~![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_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))) <=> ((~![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_5, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_5))))),
% 0.45/0.63 inference(monotonicity,[status(thm)],[261])).
% 0.45/0.63 tff(263,plain,
% 0.45/0.63 (((~![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_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))) <=> ((~![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_5, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_5)))),
% 0.45/0.63 inference(transitivity,[status(thm)],[262, 260])).
% 0.45/0.63 tff(264,plain,
% 0.45/0.63 ((~![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_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))),
% 0.45/0.63 inference(quant_inst,[status(thm)],[])).
% 0.45/0.63 tff(265,plain,
% 0.45/0.63 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_5, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_5))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.45/0.63 tff(266,plain,
% 0.45/0.63 ($false),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[265, 115, 20, 259, 249, 1, 246])).
% 0.45/0.63 tff(267,plain,((~cycle(e_2, e_2)) | (~product(e_2, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.45/0.63 tff(268,plain,
% 0.45/0.63 (~cycle(e_2, e_2)),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[267, 246])).
% 0.45/0.63 tff(269,plain,
% 0.45/0.63 (^[Y: $i, X: $i] : refl(((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0))) <=> ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0))))),
% 0.45/0.63 inference(bind,[status(th)],[])).
% 0.45/0.63 tff(270,plain,
% 0.45/0.63 (![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0))) <=> ![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))),
% 0.45/0.63 inference(quant_intro,[status(thm)],[269])).
% 0.45/0.63 tff(271,plain,
% 0.45/0.63 (![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0))) <=> ![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(272,plain,
% 0.45/0.63 (^[Y: $i, X: $i] : rewrite((((~cycle(X, e_0)) | (~product(X, e_1, Y))) | (~greater(Y, X))) <=> ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0))))),
% 0.45/0.63 inference(bind,[status(th)],[])).
% 0.45/0.63 tff(273,plain,
% 0.45/0.63 (![Y: $i, X: $i] : (((~cycle(X, e_0)) | (~product(X, e_1, Y))) | (~greater(Y, X))) <=> ![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))),
% 0.45/0.63 inference(quant_intro,[status(thm)],[272])).
% 0.45/0.63 tff(274,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')).
% 0.45/0.63 tff(275,plain,
% 0.45/0.63 (![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.45/0.63 tff(276,plain,
% 0.45/0.63 (![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[275, 271])).
% 0.45/0.63 tff(277,plain,(
% 0.45/0.63 ![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))),
% 0.45/0.63 inference(skolemize,[status(sab)],[276])).
% 0.45/0.63 tff(278,plain,
% 0.45/0.63 (![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[277, 270])).
% 0.45/0.63 tff(279,plain,
% 0.45/0.63 (greater(e_5, e_2) <=> greater(e_5, e_2)),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(280,axiom,(greater(e_5, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_greater_e_2')).
% 0.45/0.63 tff(281,plain,
% 0.45/0.63 (greater(e_5, e_2)),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.45/0.63 tff(282,plain,
% 0.45/0.63 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_2, e_0)) | (~greater(e_5, e_2)) | (~product(e_2, e_1, e_5)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_5, e_2)) | (~product(e_2, e_1, e_5)))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(283,plain,
% 0.45/0.63 (((~product(e_2, e_1, e_5)) | (~greater(e_5, e_2)) | (~cycle(e_2, e_0))) <=> ((~cycle(e_2, e_0)) | (~greater(e_5, e_2)) | (~product(e_2, e_1, e_5)))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(284,plain,
% 0.45/0.63 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_5)) | (~greater(e_5, e_2)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_2, e_0)) | (~greater(e_5, e_2)) | (~product(e_2, e_1, e_5))))),
% 0.45/0.63 inference(monotonicity,[status(thm)],[283])).
% 0.45/0.63 tff(285,plain,
% 0.45/0.63 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_5)) | (~greater(e_5, e_2)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_5, e_2)) | (~product(e_2, e_1, e_5)))),
% 0.45/0.63 inference(transitivity,[status(thm)],[284, 282])).
% 0.45/0.63 tff(286,plain,
% 0.45/0.63 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_5)) | (~greater(e_5, e_2)) | (~cycle(e_2, e_0)))),
% 0.45/0.63 inference(quant_inst,[status(thm)],[])).
% 0.45/0.63 tff(287,plain,
% 0.45/0.63 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_5, e_2)) | (~product(e_2, e_1, e_5))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.45/0.63 tff(288,plain,
% 0.45/0.63 ((~cycle(e_2, e_0)) | (~product(e_2, e_1, e_5))),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[287, 281, 278])).
% 0.45/0.63 tff(289,plain,
% 0.45/0.63 (~cycle(e_2, e_0)),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[288, 246])).
% 0.45/0.63 tff(290,assumption,(~cycle(e_2, e_3)), introduced(assumption)).
% 0.45/0.63 tff(291,plain,
% 0.45/0.63 (((~![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_5, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | (~product(e_2, e_1, e_5)))) <=> ((~![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_5, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | (~product(e_2, e_1, e_5)))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(292,plain,
% 0.45/0.63 (((~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | equalish(e_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5))) <=> (equalish(e_5, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | (~product(e_2, e_1, e_5)))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(293,plain,
% 0.45/0.63 (((~![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_4, e_0)) | (~cycle(e_2, e_4)) | equalish(e_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))) <=> ((~![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_5, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | (~product(e_2, e_1, e_5))))),
% 0.45/0.63 inference(monotonicity,[status(thm)],[292])).
% 0.45/0.63 tff(294,plain,
% 0.45/0.63 (((~![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_4, e_0)) | (~cycle(e_2, e_4)) | equalish(e_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))) <=> ((~![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_5, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | (~product(e_2, e_1, e_5)))),
% 0.45/0.63 inference(transitivity,[status(thm)],[293, 291])).
% 0.45/0.63 tff(295,plain,
% 0.45/0.63 ((~![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_4, e_0)) | (~cycle(e_2, e_4)) | equalish(e_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))),
% 0.45/0.63 inference(quant_inst,[status(thm)],[])).
% 0.45/0.64 tff(296,plain,
% 0.45/0.64 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_5, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | (~product(e_2, e_1, e_5))),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.45/0.64 tff(297,plain,
% 0.45/0.64 ($false),
% 0.45/0.64 inference(unit_resolution,[status(thm)],[296, 115, 78, 259, 249, 182, 246])).
% 0.45/0.64 tff(298,plain,((~cycle(e_2, e_4)) | (~product(e_2, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.45/0.64 tff(299,plain,
% 0.45/0.64 (~cycle(e_2, e_4)),
% 0.45/0.64 inference(unit_resolution,[status(thm)],[298, 246])).
% 0.45/0.64 tff(300,plain,
% 0.45/0.64 (group_element(e_2) <=> group_element(e_2)),
% 0.45/0.64 inference(rewrite,[status(thm)],[])).
% 0.45/0.64 tff(301,axiom,(group_element(e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_2')).
% 0.45/0.64 tff(302,plain,
% 0.45/0.64 (group_element(e_2)),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.45/0.64 tff(303,plain,
% 0.45/0.64 (((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_2, e_4) | 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_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_2, e_4) | cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0) | (~group_element(e_2)))),
% 0.45/0.64 inference(rewrite,[status(thm)],[])).
% 0.45/0.64 tff(304,plain,
% 0.45/0.64 ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_2, e_4) | cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0) | (~group_element(e_2)))),
% 0.45/0.64 inference(quant_inst,[status(thm)],[])).
% 0.45/0.64 tff(305,plain,
% 0.45/0.64 ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_2, e_4) | cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0) | (~group_element(e_2))),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.45/0.64 tff(306,plain,
% 0.45/0.64 (cycle(e_2, e_4) | cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0)),
% 0.45/0.64 inference(unit_resolution,[status(thm)],[305, 99, 302])).
% 0.45/0.64 tff(307,plain,
% 0.45/0.64 (cycle(e_2, e_1)),
% 0.45/0.64 inference(unit_resolution,[status(thm)],[306, 299, 290, 289, 268])).
% 0.45/0.64 tff(308,plain,
% 0.45/0.64 (((~![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_5, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_5)))) <=> ((~![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_5, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_5)))),
% 0.45/0.64 inference(rewrite,[status(thm)],[])).
% 0.45/0.64 tff(309,plain,
% 0.45/0.64 (((~greater(e_1, e_0)) | (~cycle(e_2, e_1)) | equalish(e_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5))) <=> (equalish(e_5, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_5)))),
% 0.45/0.64 inference(rewrite,[status(thm)],[])).
% 0.45/0.64 tff(310,plain,
% 0.45/0.64 (((~![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_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))) <=> ((~![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_5, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_5))))),
% 0.45/0.64 inference(monotonicity,[status(thm)],[309])).
% 0.45/0.64 tff(311,plain,
% 0.45/0.64 (((~![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_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))) <=> ((~![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_5, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_5)))),
% 0.45/0.64 inference(transitivity,[status(thm)],[310, 308])).
% 0.45/0.64 tff(312,plain,
% 0.45/0.64 ((~![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_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))),
% 0.45/0.64 inference(quant_inst,[status(thm)],[])).
% 0.45/0.64 tff(313,plain,
% 0.45/0.64 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_5, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_5))),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.45/0.64 tff(314,plain,
% 0.45/0.64 ($false),
% 0.45/0.64 inference(unit_resolution,[status(thm)],[313, 115, 170, 259, 249, 307, 246])).
% 0.45/0.64 tff(315,plain,((~product(e_2, e_1, e_5)) | cycle(e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.45/0.64 tff(316,plain,
% 0.45/0.64 (cycle(e_2, e_3)),
% 0.45/0.64 inference(unit_resolution,[status(thm)],[315, 246])).
% 0.45/0.64 tff(317,plain,
% 0.45/0.64 (((~![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_5, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_5)))) <=> ((~![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_5, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_5)))),
% 0.45/0.64 inference(rewrite,[status(thm)],[])).
% 0.45/0.64 tff(318,plain,
% 0.45/0.64 (((~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | equalish(e_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5))) <=> (equalish(e_5, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_5)))),
% 0.45/0.64 inference(rewrite,[status(thm)],[])).
% 0.45/0.64 tff(319,plain,
% 0.45/0.64 (((~![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_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))) <=> ((~![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_5, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_5))))),
% 0.45/0.64 inference(monotonicity,[status(thm)],[318])).
% 0.45/0.64 tff(320,plain,
% 0.45/0.64 (((~![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_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))) <=> ((~![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_5, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_5)))),
% 0.45/0.64 inference(transitivity,[status(thm)],[319, 317])).
% 0.45/0.64 tff(321,plain,
% 0.45/0.64 ((~![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_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))),
% 0.45/0.64 inference(quant_inst,[status(thm)],[])).
% 0.45/0.64 tff(322,plain,
% 0.45/0.64 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_5, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_5))),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[321, 320])).
% 0.45/0.64 tff(323,plain,
% 0.45/0.64 ($false),
% 0.45/0.64 inference(unit_resolution,[status(thm)],[322, 115, 48, 259, 249, 316, 246])).
% 0.45/0.64 tff(324,plain,(~product(e_2, e_1, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.45/0.64 tff(325,assumption,(~cycle(e_2, e_2)), introduced(assumption)).
% 0.45/0.64 tff(326,assumption,(product(e_2, e_1, e_4)), introduced(assumption)).
% 0.45/0.64 tff(327,assumption,(~cycle(e_2, e_4)), introduced(assumption)).
% 0.45/0.64 tff(328,plain,
% 0.45/0.64 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~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] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)))),
% 0.45/0.64 inference(rewrite,[status(thm)],[])).
% 0.45/0.64 tff(329,plain,
% 0.45/0.64 (((~product(e_2, e_1, e_4)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_0))) <=> ((~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)))),
% 0.45/0.64 inference(rewrite,[status(thm)],[])).
% 0.45/0.64 tff(330,plain,
% 0.45/0.64 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_4)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4))))),
% 0.45/0.64 inference(monotonicity,[status(thm)],[329])).
% 0.45/0.64 tff(331,plain,
% 0.45/0.64 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_4)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)))),
% 0.45/0.64 inference(transitivity,[status(thm)],[330, 328])).
% 0.45/0.64 tff(332,plain,
% 0.45/0.64 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_4)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_0)))),
% 0.45/0.64 inference(quant_inst,[status(thm)],[])).
% 0.45/0.64 tff(333,plain,
% 0.45/0.64 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4))),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[332, 331])).
% 0.45/0.64 tff(334,plain,
% 0.45/0.64 ((~cycle(e_2, e_0)) | (~product(e_2, e_1, e_4))),
% 0.45/0.64 inference(unit_resolution,[status(thm)],[333, 17, 278])).
% 0.45/0.64 tff(335,plain,
% 0.45/0.64 (~cycle(e_2, e_0)),
% 0.45/0.64 inference(unit_resolution,[status(thm)],[334, 326])).
% 0.45/0.64 tff(336,plain,
% 0.45/0.64 (cycle(e_2, e_1)),
% 0.45/0.64 inference(unit_resolution,[status(thm)],[306, 335, 290, 327, 325])).
% 0.45/0.64 tff(337,plain,
% 0.45/0.64 (((~![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)))),
% 0.45/0.64 inference(rewrite,[status(thm)],[])).
% 0.45/0.64 tff(338,plain,
% 0.45/0.64 (((~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)))),
% 0.45/0.64 inference(rewrite,[status(thm)],[])).
% 0.45/0.64 tff(339,plain,
% 0.45/0.64 (((~![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))))),
% 0.45/0.64 inference(monotonicity,[status(thm)],[338])).
% 0.45/0.64 tff(340,plain,
% 0.45/0.64 (((~![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)))),
% 0.45/0.64 inference(transitivity,[status(thm)],[339, 337])).
% 0.45/0.64 tff(341,plain,
% 0.45/0.64 ((~![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)))),
% 0.45/0.64 inference(quant_inst,[status(thm)],[])).
% 0.45/0.64 tff(342,plain,
% 0.45/0.64 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_4))),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[341, 340])).
% 0.45/0.64 tff(343,plain,
% 0.45/0.64 ($false),
% 0.45/0.64 inference(unit_resolution,[status(thm)],[342, 115, 170, 259, 194, 336, 326])).
% 0.45/0.64 tff(344,plain,((~product(e_2, e_1, e_4)) | cycle(e_2, e_3) | cycle(e_2, e_4) | cycle(e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.45/0.64 tff(345,plain,
% 0.45/0.64 (cycle(e_2, e_3)),
% 0.45/0.64 inference(unit_resolution,[status(thm)],[344, 326, 327, 325])).
% 0.45/0.64 tff(346,plain,
% 0.45/0.64 (((~![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)))),
% 0.45/0.64 inference(rewrite,[status(thm)],[])).
% 0.45/0.64 tff(347,plain,
% 0.45/0.64 (((~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)))),
% 0.45/0.64 inference(rewrite,[status(thm)],[])).
% 0.45/0.64 tff(348,plain,
% 0.45/0.64 (((~![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))))),
% 0.45/0.64 inference(monotonicity,[status(thm)],[347])).
% 0.45/0.64 tff(349,plain,
% 0.45/0.64 (((~![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)))),
% 0.45/0.64 inference(transitivity,[status(thm)],[348, 346])).
% 0.45/0.64 tff(350,plain,
% 0.45/0.64 ((~![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)))),
% 0.45/0.64 inference(quant_inst,[status(thm)],[])).
% 0.45/0.64 tff(351,plain,
% 0.45/0.64 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_4))),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[350, 349])).
% 0.45/0.64 tff(352,plain,
% 0.45/0.64 ($false),
% 0.45/0.64 inference(unit_resolution,[status(thm)],[351, 115, 48, 259, 194, 345, 326])).
% 0.45/0.64 tff(353,plain,((~product(e_2, e_1, e_4)) | cycle(e_2, e_4) | cycle(e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.45/0.65 tff(354,plain,
% 0.45/0.65 (cycle(e_2, e_4)),
% 0.45/0.65 inference(unit_resolution,[status(thm)],[353, 326, 325])).
% 0.45/0.65 tff(355,plain,
% 0.45/0.65 (((~![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_4, e_0)) | (~cycle(e_2, e_4)) | (~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_4, e_0)) | (~cycle(e_2, e_4)) | (~product(e_2, e_1, e_4)))),
% 0.45/0.65 inference(rewrite,[status(thm)],[])).
% 0.45/0.65 tff(356,plain,
% 0.45/0.65 (((~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | 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_4, e_0)) | (~cycle(e_2, e_4)) | (~product(e_2, e_1, e_4)))),
% 0.45/0.65 inference(rewrite,[status(thm)],[])).
% 0.45/0.65 tff(357,plain,
% 0.45/0.65 (((~![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_4, e_0)) | (~cycle(e_2, e_4)) | 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_4, e_0)) | (~cycle(e_2, e_4)) | (~product(e_2, e_1, e_4))))),
% 0.45/0.65 inference(monotonicity,[status(thm)],[356])).
% 0.45/0.65 tff(358,plain,
% 0.45/0.65 (((~![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_4, e_0)) | (~cycle(e_2, e_4)) | 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_4, e_0)) | (~cycle(e_2, e_4)) | (~product(e_2, e_1, e_4)))),
% 0.45/0.65 inference(transitivity,[status(thm)],[357, 355])).
% 0.45/0.65 tff(359,plain,
% 0.45/0.65 ((~![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_4, e_0)) | (~cycle(e_2, e_4)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.45/0.65 inference(quant_inst,[status(thm)],[])).
% 0.45/0.65 tff(360,plain,
% 0.45/0.65 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | (~product(e_2, e_1, e_4))),
% 0.45/0.65 inference(modus_ponens,[status(thm)],[359, 358])).
% 0.45/0.65 tff(361,plain,
% 0.45/0.65 ($false),
% 0.45/0.65 inference(unit_resolution,[status(thm)],[360, 115, 78, 259, 194, 354, 326])).
% 0.45/0.65 tff(362,plain,((~product(e_2, e_1, e_4)) | cycle(e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.45/0.65 tff(363,plain,
% 0.45/0.65 (~product(e_2, e_1, e_4)),
% 0.45/0.65 inference(unit_resolution,[status(thm)],[362, 325])).
% 0.45/0.65 tff(364,assumption,(product(e_2, e_1, e_2)), introduced(assumption)).
% 0.45/0.65 tff(365,plain,
% 0.45/0.65 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl((product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1))) <=> (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1))))),
% 0.45/0.65 inference(bind,[status(th)],[])).
% 0.45/0.65 tff(366,plain,
% 0.45/0.65 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.45/0.65 inference(quant_intro,[status(thm)],[365])).
% 0.45/0.65 tff(367,plain,
% 0.45/0.65 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.45/0.65 inference(rewrite,[status(thm)],[])).
% 0.45/0.65 tff(368,plain,
% 0.45/0.65 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : rewrite((((~product(X, Y, Z1)) | (~product(Z1, Y, Z2))) | product(X, Z1, Z2)) <=> (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1))))),
% 0.45/0.65 inference(bind,[status(th)],[])).
% 0.45/0.65 tff(369,plain,
% 0.45/0.65 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Z1, Y, Z2))) | product(X, Z1, Z2)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.45/0.65 inference(quant_intro,[status(thm)],[368])).
% 0.45/0.65 tff(370,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Z1, Y, Z2))) | product(X, Z1, Z2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qg3')).
% 0.45/0.65 tff(371,plain,
% 0.45/0.65 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.45/0.65 inference(modus_ponens,[status(thm)],[370, 369])).
% 0.45/0.65 tff(372,plain,
% 0.45/0.65 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.45/0.65 inference(modus_ponens,[status(thm)],[371, 367])).
% 0.45/0.65 tff(373,plain,(
% 0.45/0.65 ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.45/0.65 inference(skolemize,[status(sab)],[372])).
% 0.45/0.65 tff(374,plain,
% 0.45/0.65 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.45/0.65 inference(modus_ponens,[status(thm)],[373, 366])).
% 0.45/0.65 tff(375,plain,
% 0.45/0.65 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2)))),
% 0.45/0.65 inference(rewrite,[status(thm)],[])).
% 0.45/0.65 tff(376,plain,
% 0.45/0.65 ((product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_1, e_2))) <=> (product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2)))),
% 0.45/0.65 inference(rewrite,[status(thm)],[])).
% 0.45/0.65 tff(377,plain,
% 0.45/0.65 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2))))),
% 0.45/0.65 inference(monotonicity,[status(thm)],[376])).
% 0.45/0.65 tff(378,plain,
% 0.45/0.65 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2)))),
% 0.45/0.65 inference(transitivity,[status(thm)],[377, 375])).
% 0.45/0.65 tff(379,plain,
% 0.45/0.65 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.45/0.65 inference(quant_inst,[status(thm)],[])).
% 0.45/0.65 tff(380,plain,
% 0.45/0.65 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2))),
% 0.45/0.65 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.45/0.65 tff(381,plain,
% 0.45/0.65 (product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2))),
% 0.45/0.65 inference(unit_resolution,[status(thm)],[380, 374])).
% 0.45/0.65 tff(382,plain,
% 0.45/0.65 (product(e_2, e_2, e_2)),
% 0.45/0.65 inference(unit_resolution,[status(thm)],[381, 364])).
% 0.45/0.65 tff(383,plain,
% 0.45/0.65 (^[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))))),
% 0.45/0.65 inference(bind,[status(th)],[])).
% 0.45/0.65 tff(384,plain,
% 0.45/0.65 (![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)))),
% 0.45/0.65 inference(quant_intro,[status(thm)],[383])).
% 0.45/0.65 tff(385,plain,
% 0.45/0.65 (![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)))),
% 0.45/0.65 inference(rewrite,[status(thm)],[])).
% 0.45/0.65 tff(386,plain,
% 0.45/0.65 (^[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)))))),
% 0.45/0.65 inference(bind,[status(th)],[])).
% 0.45/0.65 tff(387,plain,
% 0.45/0.65 (![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)))),
% 0.45/0.65 inference(quant_intro,[status(thm)],[386])).
% 0.45/0.65 tff(388,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')).
% 0.45/0.65 tff(389,plain,
% 0.45/0.65 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.45/0.65 inference(modus_ponens,[status(thm)],[388, 387])).
% 0.45/0.65 tff(390,plain,
% 0.45/0.65 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.45/0.65 inference(modus_ponens,[status(thm)],[389, 385])).
% 0.45/0.65 tff(391,plain,(
% 0.45/0.65 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.45/0.65 inference(skolemize,[status(sab)],[390])).
% 0.45/0.65 tff(392,plain,
% 0.45/0.65 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.45/0.65 inference(modus_ponens,[status(thm)],[391, 384])).
% 0.45/0.65 tff(393,plain,
% 0.45/0.65 (((~![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_1, e_2)) | (~product(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.45/0.65 inference(rewrite,[status(thm)],[])).
% 0.45/0.65 tff(394,plain,
% 0.45/0.65 ((equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2))) <=> (equalish(e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.45/0.65 inference(rewrite,[status(thm)],[])).
% 0.45/0.65 tff(395,plain,
% 0.45/0.65 (((~![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_1, e_2)) | (~product(e_2, e_2, e_2))))),
% 0.45/0.65 inference(monotonicity,[status(thm)],[394])).
% 0.45/0.65 tff(396,plain,
% 0.45/0.65 (((~![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_1, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.45/0.65 inference(transitivity,[status(thm)],[395, 393])).
% 0.45/0.65 tff(397,plain,
% 0.45/0.65 ((~![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)))),
% 0.45/0.65 inference(quant_inst,[status(thm)],[])).
% 0.45/0.65 tff(398,plain,
% 0.45/0.65 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2))),
% 0.45/0.65 inference(modus_ponens,[status(thm)],[397, 396])).
% 0.45/0.65 tff(399,plain,
% 0.45/0.65 ($false),
% 0.45/0.65 inference(unit_resolution,[status(thm)],[398, 167, 392, 364, 382])).
% 0.45/0.65 tff(400,plain,(~product(e_2, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.45/0.65 tff(401,plain,
% 0.45/0.65 (^[Y: $i, X: $i] : refl(((~group_element(X)) | product(X, Y, e_5) | 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_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))))),
% 0.45/0.65 inference(bind,[status(th)],[])).
% 0.45/0.65 tff(402,plain,
% 0.45/0.65 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.45/0.65 inference(quant_intro,[status(thm)],[401])).
% 0.45/0.65 tff(403,plain,
% 0.45/0.65 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.45/0.65 inference(rewrite,[status(thm)],[])).
% 0.45/0.65 tff(404,plain,
% 0.45/0.65 (^[Y: $i, X: $i] : trans(monotonicity(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))))), ((((((((~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)) | product(X, Y, e_5)) <=> (((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_5)))), rewrite((((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_5)) <=> ((~group_element(X)) | product(X, Y, e_5) | 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)) | product(X, Y, e_5)) <=> ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))))),
% 0.45/0.65 inference(bind,[status(th)],[])).
% 0.45/0.65 tff(405,plain,
% 0.45/0.65 (![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)) | product(X, Y, e_5)) <=> ![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.45/0.65 inference(quant_intro,[status(thm)],[404])).
% 0.45/0.65 tff(406,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)) | product(X, Y, e_5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_total_function1')).
% 0.45/0.65 tff(407,plain,
% 0.45/0.65 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.45/0.65 inference(modus_ponens,[status(thm)],[406, 405])).
% 0.45/0.65 tff(408,plain,
% 0.45/0.65 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.45/0.65 inference(modus_ponens,[status(thm)],[407, 403])).
% 0.45/0.65 tff(409,plain,(
% 0.45/0.65 ![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.45/0.65 inference(skolemize,[status(sab)],[408])).
% 0.45/0.65 tff(410,plain,
% 0.45/0.65 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.45/0.65 inference(modus_ponens,[status(thm)],[409, 402])).
% 0.45/0.65 tff(411,plain,
% 0.45/0.65 (group_element(e_1) <=> group_element(e_1)),
% 0.45/0.65 inference(rewrite,[status(thm)],[])).
% 0.45/0.65 tff(412,axiom,(group_element(e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_1')).
% 0.45/0.65 tff(413,plain,
% 0.45/0.65 (group_element(e_1)),
% 0.45/0.65 inference(modus_ponens,[status(thm)],[412, 411])).
% 0.45/0.65 tff(414,plain,
% 0.45/0.65 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_5) | 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_5) | 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_5) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1))),
% 0.45/0.65 inference(rewrite,[status(thm)],[])).
% 0.45/0.65 tff(415,plain,
% 0.45/0.65 (((~group_element(e_2)) | product(e_2, e_1, e_5) | 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_5) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1))),
% 0.45/0.65 inference(rewrite,[status(thm)],[])).
% 0.45/0.65 tff(416,plain,
% 0.45/0.65 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_5) | 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_5) | 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_5) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1)))),
% 0.45/0.66 inference(monotonicity,[status(thm)],[415])).
% 0.45/0.66 tff(417,plain,
% 0.45/0.66 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_5) | 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_5) | 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_5) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1))),
% 0.45/0.66 inference(transitivity,[status(thm)],[416, 414])).
% 0.45/0.66 tff(418,plain,
% 0.45/0.66 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_5) | 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)))),
% 0.45/0.66 inference(quant_inst,[status(thm)],[])).
% 0.45/0.66 tff(419,plain,
% 0.45/0.66 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_5) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1)),
% 0.45/0.66 inference(modus_ponens,[status(thm)],[418, 417])).
% 0.45/0.66 tff(420,plain,
% 0.45/0.66 (product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_5) | product(e_2, e_1, e_1)),
% 0.45/0.66 inference(unit_resolution,[status(thm)],[419, 413, 302, 410, 400])).
% 0.45/0.66 tff(421,plain,
% 0.45/0.66 (product(e_2, e_1, e_1)),
% 0.45/0.66 inference(unit_resolution,[status(thm)],[420, 363, 324, 245])).
% 0.45/0.66 tff(422,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.45/0.66 tff(423,assumption,(cycle(e_2, e_3)), introduced(assumption)).
% 0.45/0.66 tff(424,plain,
% 0.45/0.66 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.45/0.66 inference(rewrite,[status(thm)],[])).
% 0.45/0.66 tff(425,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.45/0.66 tff(426,plain,
% 0.45/0.66 (~equalish(e_1, e_3)),
% 0.45/0.66 inference(modus_ponens,[status(thm)],[425, 424])).
% 0.45/0.66 tff(427,plain,
% 0.45/0.66 (((~![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_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, 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_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_1)))),
% 0.45/0.66 inference(rewrite,[status(thm)],[])).
% 0.45/0.66 tff(428,plain,
% 0.45/0.66 (((~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | equalish(e_1, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_1))) <=> (equalish(e_1, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_1)))),
% 0.45/0.66 inference(rewrite,[status(thm)],[])).
% 0.45/0.66 tff(429,plain,
% 0.45/0.66 (((~![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_1, e_3) | (~next(e_2, e_3)) | (~product(e_2, 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_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_1))))),
% 0.45/0.66 inference(monotonicity,[status(thm)],[428])).
% 0.45/0.66 tff(430,plain,
% 0.45/0.66 (((~![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_1, e_3) | (~next(e_2, e_3)) | (~product(e_2, 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_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_1)))),
% 0.45/0.66 inference(transitivity,[status(thm)],[429, 427])).
% 0.45/0.66 tff(431,plain,
% 0.45/0.66 ((~![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_1, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_1)))),
% 0.45/0.66 inference(quant_inst,[status(thm)],[])).
% 0.45/0.66 tff(432,plain,
% 0.45/0.66 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_1, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_1))),
% 0.45/0.66 inference(modus_ponens,[status(thm)],[431, 430])).
% 0.45/0.66 tff(433,plain,
% 0.45/0.66 ($false),
% 0.45/0.66 inference(unit_resolution,[status(thm)],[432, 115, 48, 259, 426, 423, 422])).
% 0.45/0.66 tff(434,plain,((~cycle(e_2, e_3)) | (~product(e_2, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.45/0.66 tff(435,plain,
% 0.45/0.66 (~cycle(e_2, e_3)),
% 0.45/0.66 inference(unit_resolution,[status(thm)],[434, 421])).
% 0.45/0.66 tff(436,assumption,(cycle(e_2, e_0)), introduced(assumption)).
% 0.45/0.66 tff(437,assumption,(cycle(e_1, e_2)), introduced(assumption)).
% 0.45/0.66 tff(438,plain,
% 0.45/0.66 (((~![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) | (~next(e_1, e_2)) | (~cycle(e_2, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_1, 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) | (~next(e_1, e_2)) | (~cycle(e_2, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~next(e_0, e_1)))),
% 0.45/0.66 inference(rewrite,[status(thm)],[])).
% 0.45/0.66 tff(439,plain,
% 0.45/0.66 (((~cycle(e_1, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_0))) <=> (equalish(e_2, e_1) | (~next(e_1, e_2)) | (~cycle(e_2, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~next(e_0, e_1)))),
% 0.45/0.66 inference(rewrite,[status(thm)],[])).
% 0.45/0.66 tff(440,plain,
% 0.45/0.66 (((~![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_1, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, 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) | (~next(e_1, e_2)) | (~cycle(e_2, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~next(e_0, e_1))))),
% 0.45/0.66 inference(monotonicity,[status(thm)],[439])).
% 0.45/0.66 tff(441,plain,
% 0.45/0.66 (((~![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_1, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, 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) | (~next(e_1, e_2)) | (~cycle(e_2, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~next(e_0, e_1)))),
% 0.45/0.66 inference(transitivity,[status(thm)],[440, 438])).
% 0.45/0.66 tff(442,plain,
% 0.45/0.66 ((~![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_1, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_0)))),
% 0.45/0.66 inference(quant_inst,[status(thm)],[])).
% 0.45/0.66 tff(443,plain,
% 0.45/0.66 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_1) | (~next(e_1, e_2)) | (~cycle(e_2, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~next(e_0, e_1))),
% 0.45/0.66 inference(modus_ponens,[status(thm)],[442, 441])).
% 0.45/0.66 tff(444,plain,
% 0.45/0.66 ($false),
% 0.45/0.66 inference(unit_resolution,[status(thm)],[443, 51, 173, 20, 45, 63, 437, 436])).
% 0.45/0.66 tff(445,plain,((~cycle(e_1, e_2)) | (~cycle(e_2, e_0))), inference(lemma,lemma(discharge,[]))).
% 0.45/0.66 tff(446,plain,
% 0.45/0.66 (~cycle(e_1, e_2)),
% 0.45/0.66 inference(unit_resolution,[status(thm)],[445, 436])).
% 0.45/0.66 tff(447,assumption,(cycle(e_1, e_3)), introduced(assumption)).
% 0.45/0.66 tff(448,plain,
% 0.45/0.66 (((~![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) | (~next(e_1, e_2)) | (~cycle(e_2, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_1, 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) | (~next(e_1, e_2)) | (~cycle(e_2, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | (~next(e_0, e_1)))),
% 0.45/0.66 inference(rewrite,[status(thm)],[])).
% 0.45/0.66 tff(449,plain,
% 0.45/0.66 (((~cycle(e_1, e_3)) | equalish(e_3, e_1) | (~next(e_0, e_1)) | (~greater(e_3, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_0))) <=> (equalish(e_3, e_1) | (~next(e_1, e_2)) | (~cycle(e_2, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | (~next(e_0, e_1)))),
% 0.45/0.66 inference(rewrite,[status(thm)],[])).
% 0.45/0.66 tff(450,plain,
% 0.45/0.66 (((~![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_1, e_3)) | equalish(e_3, e_1) | (~next(e_0, e_1)) | (~greater(e_3, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, 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) | (~next(e_1, e_2)) | (~cycle(e_2, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | (~next(e_0, e_1))))),
% 0.45/0.66 inference(monotonicity,[status(thm)],[449])).
% 0.45/0.66 tff(451,plain,
% 0.45/0.66 (((~![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_1, e_3)) | equalish(e_3, e_1) | (~next(e_0, e_1)) | (~greater(e_3, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, 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) | (~next(e_1, e_2)) | (~cycle(e_2, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | (~next(e_0, e_1)))),
% 0.45/0.66 inference(transitivity,[status(thm)],[450, 448])).
% 0.45/0.66 tff(452,plain,
% 0.45/0.66 ((~![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_1, e_3)) | equalish(e_3, e_1) | (~next(e_0, e_1)) | (~greater(e_3, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_0)))),
% 0.45/0.66 inference(quant_inst,[status(thm)],[])).
% 0.45/0.66 tff(453,plain,
% 0.45/0.66 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_1) | (~next(e_1, e_2)) | (~cycle(e_2, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | (~next(e_0, e_1))),
% 0.45/0.66 inference(modus_ponens,[status(thm)],[452, 451])).
% 0.45/0.66 tff(454,plain,
% 0.45/0.66 ($false),
% 0.45/0.66 inference(unit_resolution,[status(thm)],[453, 51, 173, 48, 45, 35, 447, 436])).
% 0.45/0.66 tff(455,plain,((~cycle(e_1, e_3)) | (~cycle(e_2, e_0))), inference(lemma,lemma(discharge,[]))).
% 0.45/0.66 tff(456,plain,
% 0.45/0.66 (~cycle(e_1, e_3)),
% 0.45/0.66 inference(unit_resolution,[status(thm)],[455, 436])).
% 0.45/0.66 tff(457,assumption,(~cycle(e_1, e_2)), introduced(assumption)).
% 0.45/0.66 tff(458,assumption,(~cycle(e_1, e_3)), introduced(assumption)).
% 0.45/0.66 tff(459,assumption,(~cycle(e_1, e_4)), introduced(assumption)).
% 0.45/0.66 tff(460,assumption,(product(e_1, e_1, e_4)), introduced(assumption)).
% 0.45/0.66 tff(461,plain,
% 0.45/0.66 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_1, e_0)) | (~greater(e_4, e_1)) | (~product(e_1, e_1, e_4)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_4, e_1)) | (~product(e_1, e_1, e_4)))),
% 0.45/0.66 inference(rewrite,[status(thm)],[])).
% 0.45/0.66 tff(462,plain,
% 0.45/0.66 (((~product(e_1, e_1, e_4)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_0))) <=> ((~cycle(e_1, e_0)) | (~greater(e_4, e_1)) | (~product(e_1, e_1, e_4)))),
% 0.45/0.66 inference(rewrite,[status(thm)],[])).
% 0.45/0.66 tff(463,plain,
% 0.45/0.66 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_1, e_1, e_4)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_1, e_0)) | (~greater(e_4, e_1)) | (~product(e_1, e_1, e_4))))),
% 0.45/0.66 inference(monotonicity,[status(thm)],[462])).
% 0.45/0.66 tff(464,plain,
% 0.45/0.66 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_1, e_1, e_4)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_4, e_1)) | (~product(e_1, e_1, e_4)))),
% 0.45/0.66 inference(transitivity,[status(thm)],[463, 461])).
% 0.45/0.66 tff(465,plain,
% 0.45/0.66 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_1, e_1, e_4)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_0)))),
% 0.45/0.66 inference(quant_inst,[status(thm)],[])).
% 0.45/0.66 tff(466,plain,
% 0.45/0.66 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_4, e_1)) | (~product(e_1, e_1, e_4))),
% 0.45/0.66 inference(modus_ponens,[status(thm)],[465, 464])).
% 0.45/0.66 tff(467,plain,
% 0.45/0.66 ((~cycle(e_1, e_0)) | (~product(e_1, e_1, e_4))),
% 0.45/0.66 inference(unit_resolution,[status(thm)],[466, 214, 278])).
% 0.45/0.66 tff(468,plain,
% 0.45/0.66 (~cycle(e_1, e_0)),
% 0.45/0.66 inference(unit_resolution,[status(thm)],[467, 460])).
% 0.45/0.66 tff(469,plain,
% 0.45/0.66 (((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_1, e_4) | cycle(e_1, e_3) | cycle(e_1, e_2) | cycle(e_1, e_1) | cycle(e_1, e_0) | (~group_element(e_1)))) <=> ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_1, e_4) | cycle(e_1, e_3) | cycle(e_1, e_2) | cycle(e_1, e_1) | cycle(e_1, e_0) | (~group_element(e_1)))),
% 0.45/0.66 inference(rewrite,[status(thm)],[])).
% 0.45/0.66 tff(470,plain,
% 0.45/0.66 ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_1, e_4) | cycle(e_1, e_3) | cycle(e_1, e_2) | cycle(e_1, e_1) | cycle(e_1, e_0) | (~group_element(e_1)))),
% 0.45/0.66 inference(quant_inst,[status(thm)],[])).
% 0.45/0.66 tff(471,plain,
% 0.45/0.66 ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_1, e_4) | cycle(e_1, e_3) | cycle(e_1, e_2) | cycle(e_1, e_1) | cycle(e_1, e_0) | (~group_element(e_1))),
% 0.45/0.66 inference(modus_ponens,[status(thm)],[470, 469])).
% 0.45/0.66 tff(472,plain,
% 0.45/0.66 (cycle(e_1, e_4) | cycle(e_1, e_3) | cycle(e_1, e_2) | cycle(e_1, e_1) | cycle(e_1, e_0)),
% 0.45/0.66 inference(unit_resolution,[status(thm)],[471, 99, 413])).
% 0.45/0.66 tff(473,plain,
% 0.45/0.66 (cycle(e_1, e_1)),
% 0.45/0.66 inference(unit_resolution,[status(thm)],[472, 468, 459, 458, 457])).
% 0.45/0.66 tff(474,plain,
% 0.45/0.66 (((~![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_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, 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_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_4)))),
% 0.45/0.66 inference(rewrite,[status(thm)],[])).
% 0.45/0.66 tff(475,plain,
% 0.45/0.66 (((~greater(e_1, e_0)) | (~cycle(e_1, e_1)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_4))) <=> (equalish(e_4, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_4)))),
% 0.45/0.66 inference(rewrite,[status(thm)],[])).
% 0.45/0.66 tff(476,plain,
% 0.45/0.66 (((~![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_1, e_1)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~product(e_1, 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_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_4))))),
% 0.45/0.66 inference(monotonicity,[status(thm)],[475])).
% 0.45/0.66 tff(477,plain,
% 0.45/0.66 (((~![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_1, e_1)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~product(e_1, 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_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_4)))),
% 0.45/0.66 inference(transitivity,[status(thm)],[476, 474])).
% 0.45/0.66 tff(478,plain,
% 0.45/0.66 ((~![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_1, e_1)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_4)))),
% 0.45/0.66 inference(quant_inst,[status(thm)],[])).
% 0.45/0.66 tff(479,plain,
% 0.45/0.66 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_4))),
% 0.45/0.67 inference(modus_ponens,[status(thm)],[478, 477])).
% 0.45/0.67 tff(480,plain,
% 0.45/0.67 ($false),
% 0.45/0.67 inference(unit_resolution,[status(thm)],[479, 173, 170, 259, 204, 473, 460])).
% 0.45/0.67 tff(481,plain,((~product(e_1, e_1, e_4)) | cycle(e_1, e_4) | cycle(e_1, e_3) | cycle(e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.45/0.67 tff(482,plain,
% 0.45/0.67 (~product(e_1, e_1, e_4)),
% 0.45/0.67 inference(unit_resolution,[status(thm)],[481, 457, 458, 459])).
% 0.45/0.67 tff(483,assumption,(product(e_1, e_1, e_1)), introduced(assumption)).
% 0.45/0.67 tff(484,plain,
% 0.45/0.67 (^[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))))),
% 0.45/0.67 inference(bind,[status(th)],[])).
% 0.45/0.67 tff(485,plain,
% 0.45/0.67 (![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)))),
% 0.45/0.67 inference(quant_intro,[status(thm)],[484])).
% 0.45/0.67 tff(486,plain,
% 0.45/0.67 (![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)))),
% 0.45/0.67 inference(rewrite,[status(thm)],[])).
% 0.45/0.67 tff(487,plain,
% 0.45/0.67 (^[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)))))),
% 0.45/0.67 inference(bind,[status(th)],[])).
% 0.45/0.67 tff(488,plain,
% 0.45/0.67 (![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)))),
% 0.45/0.67 inference(quant_intro,[status(thm)],[487])).
% 0.45/0.67 tff(489,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')).
% 0.45/0.67 tff(490,plain,
% 0.45/0.67 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.45/0.67 inference(modus_ponens,[status(thm)],[489, 488])).
% 0.45/0.67 tff(491,plain,
% 0.45/0.67 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.45/0.67 inference(modus_ponens,[status(thm)],[490, 486])).
% 0.45/0.67 tff(492,plain,(
% 0.45/0.67 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.45/0.67 inference(skolemize,[status(sab)],[491])).
% 0.45/0.67 tff(493,plain,
% 0.45/0.67 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.45/0.67 inference(modus_ponens,[status(thm)],[492, 485])).
% 0.45/0.67 tff(494,plain,
% 0.45/0.67 (((~![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)))),
% 0.45/0.67 inference(rewrite,[status(thm)],[])).
% 0.45/0.67 tff(495,plain,
% 0.45/0.67 ((~![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)))),
% 0.45/0.67 inference(quant_inst,[status(thm)],[])).
% 0.45/0.67 tff(496,plain,
% 0.45/0.67 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1))),
% 0.45/0.67 inference(modus_ponens,[status(thm)],[495, 494])).
% 0.45/0.67 tff(497,plain,
% 0.45/0.67 ($false),
% 0.45/0.67 inference(unit_resolution,[status(thm)],[496, 63, 493, 483, 422])).
% 0.45/0.67 tff(498,plain,((~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.45/0.67 tff(499,plain,
% 0.45/0.67 (~product(e_1, e_1, e_1)),
% 0.45/0.67 inference(unit_resolution,[status(thm)],[498, 422])).
% 0.45/0.67 tff(500,assumption,(cycle(e_1, e_0)), introduced(assumption)).
% 0.45/0.67 tff(501,plain,
% 0.45/0.67 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_1, e_0)) | (~greater(e_2, e_1)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_2, e_1)) | (~product(e_1, e_1, e_2)))),
% 0.45/0.67 inference(rewrite,[status(thm)],[])).
% 0.45/0.67 tff(502,plain,
% 0.45/0.67 (((~product(e_1, e_1, e_2)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_0))) <=> ((~cycle(e_1, e_0)) | (~greater(e_2, e_1)) | (~product(e_1, e_1, e_2)))),
% 0.45/0.67 inference(rewrite,[status(thm)],[])).
% 0.45/0.67 tff(503,plain,
% 0.45/0.67 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_1, e_1, e_2)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_1, e_0)) | (~greater(e_2, e_1)) | (~product(e_1, e_1, e_2))))),
% 0.45/0.67 inference(monotonicity,[status(thm)],[502])).
% 0.45/0.67 tff(504,plain,
% 0.45/0.67 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_1, e_1, e_2)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_2, e_1)) | (~product(e_1, e_1, e_2)))),
% 0.45/0.67 inference(transitivity,[status(thm)],[503, 501])).
% 0.45/0.67 tff(505,plain,
% 0.45/0.67 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_1, e_1, e_2)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_0)))),
% 0.45/0.67 inference(quant_inst,[status(thm)],[])).
% 0.45/0.67 tff(506,plain,
% 0.45/0.67 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_2, e_1)) | (~product(e_1, e_1, e_2))),
% 0.45/0.67 inference(modus_ponens,[status(thm)],[505, 504])).
% 0.45/0.67 tff(507,plain,
% 0.45/0.67 ((~cycle(e_1, e_0)) | (~product(e_1, e_1, e_2))),
% 0.45/0.67 inference(unit_resolution,[status(thm)],[506, 138, 278])).
% 0.45/0.67 tff(508,plain,
% 0.45/0.67 (~product(e_1, e_1, e_2)),
% 0.45/0.67 inference(unit_resolution,[status(thm)],[507, 500])).
% 0.45/0.67 tff(509,assumption,(~product(e_1, e_1, e_1)), introduced(assumption)).
% 0.45/0.67 tff(510,plain,
% 0.45/0.67 (greater(e_3, e_1) <=> greater(e_3, e_1)),
% 0.45/0.67 inference(rewrite,[status(thm)],[])).
% 0.45/0.67 tff(511,axiom,(greater(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_greater_e_1')).
% 0.45/0.67 tff(512,plain,
% 0.45/0.67 (greater(e_3, e_1)),
% 0.45/0.67 inference(modus_ponens,[status(thm)],[511, 510])).
% 0.45/0.67 tff(513,plain,
% 0.45/0.67 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_1, e_0)) | (~greater(e_3, e_1)) | (~product(e_1, e_1, e_3)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_3, e_1)) | (~product(e_1, e_1, e_3)))),
% 0.45/0.67 inference(rewrite,[status(thm)],[])).
% 0.45/0.67 tff(514,plain,
% 0.45/0.67 (((~product(e_1, e_1, e_3)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_0))) <=> ((~cycle(e_1, e_0)) | (~greater(e_3, e_1)) | (~product(e_1, e_1, e_3)))),
% 0.45/0.67 inference(rewrite,[status(thm)],[])).
% 0.45/0.67 tff(515,plain,
% 0.45/0.67 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_1, e_1, e_3)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_1, e_0)) | (~greater(e_3, e_1)) | (~product(e_1, e_1, e_3))))),
% 0.45/0.67 inference(monotonicity,[status(thm)],[514])).
% 0.45/0.67 tff(516,plain,
% 0.45/0.67 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_1, e_1, e_3)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_3, e_1)) | (~product(e_1, e_1, e_3)))),
% 0.45/0.67 inference(transitivity,[status(thm)],[515, 513])).
% 0.45/0.67 tff(517,plain,
% 0.45/0.67 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_1, e_1, e_3)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_0)))),
% 0.45/0.67 inference(quant_inst,[status(thm)],[])).
% 0.45/0.67 tff(518,plain,
% 0.45/0.67 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_3, e_1)) | (~product(e_1, e_1, e_3))),
% 0.45/0.67 inference(modus_ponens,[status(thm)],[517, 516])).
% 0.45/0.67 tff(519,plain,
% 0.45/0.67 ((~cycle(e_1, e_0)) | (~product(e_1, e_1, e_3))),
% 0.45/0.67 inference(unit_resolution,[status(thm)],[518, 512, 278])).
% 0.45/0.67 tff(520,plain,
% 0.45/0.67 (~product(e_1, e_1, e_3)),
% 0.45/0.67 inference(unit_resolution,[status(thm)],[519, 500])).
% 0.45/0.67 tff(521,plain,
% 0.45/0.67 (greater(e_5, e_1) <=> greater(e_5, e_1)),
% 0.45/0.67 inference(rewrite,[status(thm)],[])).
% 0.45/0.67 tff(522,axiom,(greater(e_5, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_greater_e_1')).
% 0.45/0.67 tff(523,plain,
% 0.45/0.67 (greater(e_5, e_1)),
% 0.45/0.67 inference(modus_ponens,[status(thm)],[522, 521])).
% 0.45/0.67 tff(524,plain,
% 0.45/0.67 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_1, e_0)) | (~greater(e_5, e_1)) | (~product(e_1, e_1, e_5)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_5, e_1)) | (~product(e_1, e_1, e_5)))),
% 0.45/0.67 inference(rewrite,[status(thm)],[])).
% 0.45/0.67 tff(525,plain,
% 0.45/0.67 (((~product(e_1, e_1, e_5)) | (~greater(e_5, e_1)) | (~cycle(e_1, e_0))) <=> ((~cycle(e_1, e_0)) | (~greater(e_5, e_1)) | (~product(e_1, e_1, e_5)))),
% 0.45/0.67 inference(rewrite,[status(thm)],[])).
% 0.45/0.67 tff(526,plain,
% 0.45/0.67 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_1, e_1, e_5)) | (~greater(e_5, e_1)) | (~cycle(e_1, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_1, e_0)) | (~greater(e_5, e_1)) | (~product(e_1, e_1, e_5))))),
% 0.45/0.67 inference(monotonicity,[status(thm)],[525])).
% 0.45/0.67 tff(527,plain,
% 0.45/0.67 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_1, e_1, e_5)) | (~greater(e_5, e_1)) | (~cycle(e_1, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_5, e_1)) | (~product(e_1, e_1, e_5)))),
% 0.45/0.67 inference(transitivity,[status(thm)],[526, 524])).
% 0.45/0.67 tff(528,plain,
% 0.45/0.67 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_1, e_1, e_5)) | (~greater(e_5, e_1)) | (~cycle(e_1, e_0)))),
% 0.45/0.67 inference(quant_inst,[status(thm)],[])).
% 0.45/0.67 tff(529,plain,
% 0.45/0.67 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_5, e_1)) | (~product(e_1, e_1, e_5))),
% 0.45/0.67 inference(modus_ponens,[status(thm)],[528, 527])).
% 0.45/0.67 tff(530,plain,
% 0.45/0.67 ((~cycle(e_1, e_0)) | (~product(e_1, e_1, e_5))),
% 0.45/0.67 inference(unit_resolution,[status(thm)],[529, 523, 278])).
% 0.45/0.67 tff(531,plain,
% 0.45/0.67 (~product(e_1, e_1, e_5)),
% 0.45/0.67 inference(unit_resolution,[status(thm)],[530, 500])).
% 0.45/0.67 tff(532,assumption,(~product(e_1, e_1, e_4)), introduced(assumption)).
% 0.45/0.67 tff(533,plain,
% 0.45/0.67 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_1, e_2) | product(e_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_5) | product(e_1, e_1, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_1, e_2) | product(e_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_5) | product(e_1, e_1, e_1))),
% 0.45/0.67 inference(rewrite,[status(thm)],[])).
% 0.45/0.67 tff(534,plain,
% 0.45/0.67 (((~group_element(e_1)) | product(e_1, e_1, e_5) | product(e_1, e_1, e_4) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1))) <=> ((~group_element(e_1)) | product(e_1, e_1, e_2) | product(e_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_5) | product(e_1, e_1, e_1))),
% 0.45/0.67 inference(rewrite,[status(thm)],[])).
% 0.45/0.67 tff(535,plain,
% 0.45/0.67 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_1, e_5) | product(e_1, e_1, e_4) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_1, e_2) | product(e_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_5) | product(e_1, e_1, e_1)))),
% 0.45/0.67 inference(monotonicity,[status(thm)],[534])).
% 0.45/0.67 tff(536,plain,
% 0.45/0.67 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_1, e_5) | product(e_1, e_1, e_4) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_1, e_2) | product(e_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_5) | product(e_1, e_1, e_1))),
% 0.45/0.67 inference(transitivity,[status(thm)],[535, 533])).
% 0.45/0.67 tff(537,plain,
% 0.45/0.67 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_1, e_5) | product(e_1, e_1, e_4) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))),
% 0.45/0.67 inference(quant_inst,[status(thm)],[])).
% 0.45/0.67 tff(538,plain,
% 0.45/0.67 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | product(e_1, e_1, e_2) | product(e_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_5) | product(e_1, e_1, e_1)),
% 0.45/0.67 inference(modus_ponens,[status(thm)],[537, 536])).
% 0.45/0.67 tff(539,plain,
% 0.45/0.67 (product(e_1, e_1, e_2) | product(e_1, e_1, e_3) | product(e_1, e_1, e_5) | product(e_1, e_1, e_1)),
% 0.45/0.67 inference(unit_resolution,[status(thm)],[538, 413, 410, 532])).
% 0.45/0.67 tff(540,plain,
% 0.45/0.67 ($false),
% 0.45/0.67 inference(unit_resolution,[status(thm)],[539, 531, 520, 509, 508])).
% 0.45/0.67 tff(541,plain,((~cycle(e_1, e_0)) | product(e_1, e_1, e_1) | product(e_1, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.45/0.67 tff(542,plain,
% 0.45/0.67 (~cycle(e_1, e_0)),
% 0.45/0.67 inference(unit_resolution,[status(thm)],[541, 499, 482])).
% 0.45/0.67 tff(543,plain,
% 0.45/0.67 (cycle(e_1, e_1)),
% 0.45/0.67 inference(unit_resolution,[status(thm)],[472, 542, 459, 458, 457])).
% 0.45/0.67 tff(544,plain,
% 0.45/0.67 (((~![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_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, 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_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_3)))),
% 0.45/0.67 inference(rewrite,[status(thm)],[])).
% 0.45/0.67 tff(545,plain,
% 0.45/0.67 (((~greater(e_1, e_0)) | (~cycle(e_1, e_1)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3))) <=> (equalish(e_3, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_3)))),
% 0.45/0.67 inference(rewrite,[status(thm)],[])).
% 0.45/0.67 tff(546,plain,
% 0.45/0.67 (((~![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_1, e_1)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~product(e_1, 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_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_3))))),
% 0.45/0.67 inference(monotonicity,[status(thm)],[545])).
% 0.45/0.67 tff(547,plain,
% 0.45/0.67 (((~![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_1, e_1)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~product(e_1, 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_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_3)))),
% 0.45/0.67 inference(transitivity,[status(thm)],[546, 544])).
% 0.45/0.67 tff(548,plain,
% 0.45/0.67 ((~![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_1, e_1)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))),
% 0.45/0.67 inference(quant_inst,[status(thm)],[])).
% 0.45/0.67 tff(549,plain,
% 0.45/0.67 ((~![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_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_3))),
% 0.45/0.67 inference(modus_ponens,[status(thm)],[548, 547])).
% 0.45/0.67 tff(550,plain,
% 0.45/0.67 (~product(e_1, e_1, e_3)),
% 0.45/0.67 inference(unit_resolution,[status(thm)],[549, 173, 170, 259, 236, 543])).
% 0.45/0.67 tff(551,plain,
% 0.45/0.67 ((~equalish(e_5, e_2)) <=> (~equalish(e_5, e_2))),
% 0.45/0.67 inference(rewrite,[status(thm)],[])).
% 0.45/0.67 tff(552,axiom,(~equalish(e_5, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_is_not_e_2')).
% 0.45/0.67 tff(553,plain,
% 0.45/0.68 (~equalish(e_5, e_2)),
% 0.45/0.68 inference(modus_ponens,[status(thm)],[552, 551])).
% 0.45/0.68 tff(554,plain,
% 0.45/0.68 (((~![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_5, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_5)))) <=> ((~![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_5, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_5)))),
% 0.45/0.68 inference(rewrite,[status(thm)],[])).
% 0.45/0.68 tff(555,plain,
% 0.45/0.68 (((~greater(e_1, e_0)) | (~cycle(e_1, e_1)) | equalish(e_5, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_5))) <=> (equalish(e_5, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_5)))),
% 0.45/0.68 inference(rewrite,[status(thm)],[])).
% 0.45/0.68 tff(556,plain,
% 0.45/0.68 (((~![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_1, e_1)) | equalish(e_5, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_5)))) <=> ((~![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_5, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_5))))),
% 0.45/0.68 inference(monotonicity,[status(thm)],[555])).
% 0.45/0.68 tff(557,plain,
% 0.45/0.68 (((~![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_1, e_1)) | equalish(e_5, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_5)))) <=> ((~![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_5, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_5)))),
% 0.45/0.68 inference(transitivity,[status(thm)],[556, 554])).
% 0.45/0.68 tff(558,plain,
% 0.45/0.68 ((~![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_1, e_1)) | equalish(e_5, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_5)))),
% 0.45/0.68 inference(quant_inst,[status(thm)],[])).
% 0.45/0.68 tff(559,plain,
% 0.45/0.68 ((~![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_5, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_5))),
% 0.45/0.68 inference(modus_ponens,[status(thm)],[558, 557])).
% 0.45/0.68 tff(560,plain,
% 0.45/0.68 (~product(e_1, e_1, e_5)),
% 0.45/0.68 inference(unit_resolution,[status(thm)],[559, 173, 170, 259, 553, 543])).
% 0.45/0.68 tff(561,plain,
% 0.45/0.68 (product(e_1, e_1, e_2) | product(e_1, e_1, e_3) | product(e_1, e_1, e_5) | product(e_1, e_1, e_1)),
% 0.45/0.68 inference(unit_resolution,[status(thm)],[538, 413, 410, 482])).
% 0.45/0.68 tff(562,plain,
% 0.45/0.68 (product(e_1, e_1, e_2)),
% 0.45/0.68 inference(unit_resolution,[status(thm)],[561, 560, 499, 550])).
% 0.45/0.68 tff(563,plain,
% 0.45/0.68 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_2)) | product(e_2, e_1, e_2) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_2) | (~product(e_2, e_1, e_1)))),
% 0.45/0.68 inference(rewrite,[status(thm)],[])).
% 0.45/0.68 tff(564,plain,
% 0.45/0.68 ((product(e_2, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1))) <=> ((~product(e_1, e_1, e_2)) | product(e_2, e_1, e_2) | (~product(e_2, e_1, e_1)))),
% 0.45/0.68 inference(rewrite,[status(thm)],[])).
% 0.45/0.68 tff(565,plain,
% 0.45/0.68 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_2)) | product(e_2, e_1, e_2) | (~product(e_2, e_1, e_1))))),
% 0.45/0.68 inference(monotonicity,[status(thm)],[564])).
% 0.45/0.68 tff(566,plain,
% 0.45/0.68 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_2) | (~product(e_2, e_1, e_1)))),
% 0.45/0.68 inference(transitivity,[status(thm)],[565, 563])).
% 0.45/0.68 tff(567,plain,
% 0.45/0.68 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1)))),
% 0.45/0.68 inference(quant_inst,[status(thm)],[])).
% 0.45/0.68 tff(568,plain,
% 0.45/0.68 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_2) | (~product(e_2, e_1, e_1))),
% 0.45/0.68 inference(modus_ponens,[status(thm)],[567, 566])).
% 0.45/0.68 tff(569,plain,
% 0.45/0.68 ($false),
% 0.45/0.68 inference(unit_resolution,[status(thm)],[568, 374, 562, 422, 400])).
% 0.45/0.68 tff(570,plain,((~product(e_2, e_1, e_1)) | cycle(e_1, e_4) | cycle(e_1, e_3) | cycle(e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.45/0.68 tff(571,plain,
% 0.45/0.68 (cycle(e_1, e_4)),
% 0.45/0.68 inference(unit_resolution,[status(thm)],[570, 456, 422, 446])).
% 0.45/0.68 tff(572,plain,
% 0.45/0.68 (((~![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_4, e_1) | (~next(e_1, e_2)) | (~cycle(e_2, e_0)) | (~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | (~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_4, e_1) | (~next(e_1, e_2)) | (~cycle(e_2, e_0)) | (~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | (~next(e_0, e_1)))),
% 0.45/0.68 inference(rewrite,[status(thm)],[])).
% 0.45/0.68 tff(573,plain,
% 0.45/0.68 (((~cycle(e_1, e_4)) | equalish(e_4, e_1) | (~next(e_0, e_1)) | (~greater(e_4, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_0))) <=> (equalish(e_4, e_1) | (~next(e_1, e_2)) | (~cycle(e_2, e_0)) | (~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | (~next(e_0, e_1)))),
% 0.45/0.68 inference(rewrite,[status(thm)],[])).
% 0.45/0.68 tff(574,plain,
% 0.45/0.68 (((~![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_1, e_4)) | equalish(e_4, e_1) | (~next(e_0, e_1)) | (~greater(e_4, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, 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_4, e_1) | (~next(e_1, e_2)) | (~cycle(e_2, e_0)) | (~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | (~next(e_0, e_1))))),
% 0.45/0.68 inference(monotonicity,[status(thm)],[573])).
% 0.45/0.68 tff(575,plain,
% 0.45/0.68 (((~![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_1, e_4)) | equalish(e_4, e_1) | (~next(e_0, e_1)) | (~greater(e_4, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, 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_4, e_1) | (~next(e_1, e_2)) | (~cycle(e_2, e_0)) | (~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | (~next(e_0, e_1)))),
% 0.45/0.68 inference(transitivity,[status(thm)],[574, 572])).
% 0.45/0.68 tff(576,plain,
% 0.45/0.68 ((~![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_1, e_4)) | equalish(e_4, e_1) | (~next(e_0, e_1)) | (~greater(e_4, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_0)))),
% 0.45/0.68 inference(quant_inst,[status(thm)],[])).
% 0.45/0.68 tff(577,plain,
% 0.45/0.68 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_4, e_1) | (~next(e_1, e_2)) | (~cycle(e_2, e_0)) | (~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | (~next(e_0, e_1))),
% 0.45/0.68 inference(modus_ponens,[status(thm)],[576, 575])).
% 0.45/0.68 tff(578,plain,
% 0.45/0.68 ($false),
% 0.45/0.68 inference(unit_resolution,[status(thm)],[577, 51, 173, 78, 45, 75, 571, 436])).
% 0.45/0.68 tff(579,plain,((~cycle(e_2, e_0)) | (~product(e_2, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.45/0.68 tff(580,plain,
% 0.45/0.68 (~cycle(e_2, e_0)),
% 0.45/0.68 inference(unit_resolution,[status(thm)],[579, 422])).
% 0.45/0.68 tff(581,plain,
% 0.45/0.68 (cycle(e_2, e_1)),
% 0.45/0.68 inference(unit_resolution,[status(thm)],[306, 580, 290, 327, 325])).
% 0.45/0.68 tff(582,plain,
% 0.45/0.68 (((~![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_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, 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_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.45/0.68 inference(rewrite,[status(thm)],[])).
% 0.45/0.68 tff(583,plain,
% 0.45/0.68 (((~greater(e_1, e_0)) | (~cycle(e_2, e_1)) | equalish(e_1, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_1))) <=> (equalish(e_1, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.45/0.68 inference(rewrite,[status(thm)],[])).
% 0.45/0.68 tff(584,plain,
% 0.45/0.68 (((~![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_1, e_3) | (~next(e_2, e_3)) | (~product(e_2, 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_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_1))))),
% 0.45/0.68 inference(monotonicity,[status(thm)],[583])).
% 0.45/0.68 tff(585,plain,
% 0.45/0.68 (((~![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_1, e_3) | (~next(e_2, e_3)) | (~product(e_2, 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_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.45/0.68 inference(transitivity,[status(thm)],[584, 582])).
% 0.45/0.68 tff(586,plain,
% 0.45/0.68 ((~![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_1, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_1)))),
% 0.45/0.68 inference(quant_inst,[status(thm)],[])).
% 0.45/0.68 tff(587,plain,
% 0.45/0.68 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_1, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_1))),
% 0.45/0.68 inference(modus_ponens,[status(thm)],[586, 585])).
% 0.45/0.68 tff(588,plain,
% 0.45/0.68 ($false),
% 0.45/0.68 inference(unit_resolution,[status(thm)],[587, 115, 170, 259, 426, 581, 422])).
% 0.45/0.68 tff(589,plain,((~product(e_2, e_1, e_1)) | cycle(e_2, e_3) | cycle(e_2, e_4) | cycle(e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.45/0.68 tff(590,plain,
% 0.45/0.68 (cycle(e_2, e_4)),
% 0.45/0.68 inference(unit_resolution,[status(thm)],[589, 435, 421, 325])).
% 0.45/0.68 tff(591,plain,
% 0.45/0.68 (((~![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_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | (~product(e_2, 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_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | (~product(e_2, e_1, e_1)))),
% 0.45/0.68 inference(rewrite,[status(thm)],[])).
% 0.45/0.68 tff(592,plain,
% 0.45/0.68 (((~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | equalish(e_1, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_1))) <=> (equalish(e_1, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | (~product(e_2, e_1, e_1)))),
% 0.45/0.68 inference(rewrite,[status(thm)],[])).
% 0.45/0.68 tff(593,plain,
% 0.45/0.68 (((~![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_4, e_0)) | (~cycle(e_2, e_4)) | equalish(e_1, e_3) | (~next(e_2, e_3)) | (~product(e_2, 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_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | (~product(e_2, e_1, e_1))))),
% 0.45/0.68 inference(monotonicity,[status(thm)],[592])).
% 0.45/0.68 tff(594,plain,
% 0.45/0.68 (((~![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_4, e_0)) | (~cycle(e_2, e_4)) | equalish(e_1, e_3) | (~next(e_2, e_3)) | (~product(e_2, 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_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | (~product(e_2, e_1, e_1)))),
% 0.45/0.68 inference(transitivity,[status(thm)],[593, 591])).
% 0.45/0.68 tff(595,plain,
% 0.45/0.68 ((~![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_4, e_0)) | (~cycle(e_2, e_4)) | equalish(e_1, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_1)))),
% 0.45/0.68 inference(quant_inst,[status(thm)],[])).
% 0.45/0.68 tff(596,plain,
% 0.45/0.68 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_1, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | (~product(e_2, e_1, e_1))),
% 0.45/0.68 inference(modus_ponens,[status(thm)],[595, 594])).
% 0.45/0.68 tff(597,plain,
% 0.45/0.68 ($false),
% 0.45/0.68 inference(unit_resolution,[status(thm)],[596, 115, 78, 259, 426, 590, 421])).
% 0.45/0.68 tff(598,plain,(cycle(e_2, e_2) | product(e_2, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.45/0.68 tff(599,plain,
% 0.45/0.68 (cycle(e_2, e_2)),
% 0.45/0.68 inference(unit_resolution,[status(thm)],[598, 245])).
% 0.45/0.68 tff(600,assumption,(~product(e_2, e_1, e_1)), introduced(assumption)).
% 0.45/0.68 tff(601,plain,
% 0.45/0.68 (~product(e_2, e_1, e_5)),
% 0.45/0.68 inference(unit_resolution,[status(thm)],[267, 1])).
% 0.45/0.68 tff(602,plain,
% 0.45/0.68 (product(e_2, e_1, e_4)),
% 0.45/0.68 inference(unit_resolution,[status(thm)],[420, 601, 245, 600])).
% 0.45/0.68 tff(603,plain,
% 0.45/0.68 (((~![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)))),
% 0.45/0.68 inference(rewrite,[status(thm)],[])).
% 0.45/0.68 tff(604,plain,
% 0.45/0.68 (((~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)))),
% 0.45/0.68 inference(rewrite,[status(thm)],[])).
% 0.45/0.68 tff(605,plain,
% 0.45/0.68 (((~![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))))),
% 0.45/0.69 inference(monotonicity,[status(thm)],[604])).
% 0.45/0.69 tff(606,plain,
% 0.45/0.69 (((~![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)))),
% 0.45/0.69 inference(transitivity,[status(thm)],[605, 603])).
% 0.45/0.69 tff(607,plain,
% 0.45/0.69 ((~![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)))),
% 0.45/0.69 inference(quant_inst,[status(thm)],[])).
% 0.45/0.69 tff(608,plain,
% 0.45/0.69 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_4))),
% 0.45/0.69 inference(modus_ponens,[status(thm)],[607, 606])).
% 0.45/0.69 tff(609,plain,
% 0.45/0.69 ($false),
% 0.45/0.69 inference(unit_resolution,[status(thm)],[608, 115, 20, 259, 194, 1, 602])).
% 0.45/0.69 tff(610,plain,((~cycle(e_2, e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.45/0.69 tff(611,plain,
% 0.45/0.69 (product(e_2, e_1, e_1)),
% 0.45/0.69 inference(unit_resolution,[status(thm)],[610, 599, 245])).
% 0.45/0.69 tff(612,plain,
% 0.45/0.69 (((~![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_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, 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_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_1)))),
% 0.45/0.69 inference(rewrite,[status(thm)],[])).
% 0.45/0.69 tff(613,plain,
% 0.45/0.69 (((~greater(e_2, e_0)) | (~cycle(e_2, e_2)) | equalish(e_1, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_1))) <=> (equalish(e_1, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_1)))),
% 0.45/0.69 inference(rewrite,[status(thm)],[])).
% 0.45/0.69 tff(614,plain,
% 0.45/0.69 (((~![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_1, e_3) | (~next(e_2, e_3)) | (~product(e_2, 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_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_1))))),
% 0.45/0.69 inference(monotonicity,[status(thm)],[613])).
% 0.45/0.69 tff(615,plain,
% 0.45/0.69 (((~![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_1, e_3) | (~next(e_2, e_3)) | (~product(e_2, 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_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_1)))),
% 0.45/0.69 inference(transitivity,[status(thm)],[614, 612])).
% 0.45/0.69 tff(616,plain,
% 0.45/0.69 ((~![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_1, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_1)))),
% 0.45/0.69 inference(quant_inst,[status(thm)],[])).
% 0.45/0.69 tff(617,plain,
% 0.45/0.69 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_1, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_1))),
% 0.45/0.69 inference(modus_ponens,[status(thm)],[616, 615])).
% 0.45/0.69 tff(618,plain,
% 0.45/0.69 ($false),
% 0.45/0.69 inference(unit_resolution,[status(thm)],[617, 115, 20, 259, 426, 599, 611])).
% 0.45/0.69 tff(619,plain,(product(e_2, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.45/0.69 tff(620,plain,
% 0.45/0.69 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~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] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.45/0.69 inference(rewrite,[status(thm)],[])).
% 0.45/0.69 tff(621,plain,
% 0.45/0.69 (((~product(e_2, e_1, e_3)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_0))) <=> ((~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.45/0.69 inference(rewrite,[status(thm)],[])).
% 0.45/0.69 tff(622,plain,
% 0.45/0.69 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_3)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3))))),
% 0.45/0.69 inference(monotonicity,[status(thm)],[621])).
% 0.45/0.69 tff(623,plain,
% 0.45/0.69 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_3)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.45/0.69 inference(transitivity,[status(thm)],[622, 620])).
% 0.45/0.69 tff(624,plain,
% 0.45/0.69 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_3)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_0)))),
% 0.45/0.69 inference(quant_inst,[status(thm)],[])).
% 0.45/0.69 tff(625,plain,
% 0.45/0.69 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3))),
% 0.45/0.69 inference(modus_ponens,[status(thm)],[624, 623])).
% 0.45/0.69 tff(626,plain,
% 0.45/0.69 ((~cycle(e_2, e_0)) | (~product(e_2, e_1, e_3))),
% 0.45/0.69 inference(unit_resolution,[status(thm)],[625, 135, 278])).
% 0.45/0.69 tff(627,plain,
% 0.45/0.69 (~cycle(e_2, e_0)),
% 0.45/0.69 inference(unit_resolution,[status(thm)],[626, 619])).
% 0.45/0.69 tff(628,plain,
% 0.45/0.69 (cycle(e_2, e_1)),
% 0.45/0.69 inference(unit_resolution,[status(thm)],[306, 327, 627, 290, 325])).
% 0.45/0.69 tff(629,plain,
% 0.45/0.69 (((~![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_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_1)) | (~greater(e_4, 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_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_1)) | (~greater(e_4, e_2)))),
% 0.45/0.69 inference(rewrite,[status(thm)],[])).
% 0.45/0.69 tff(630,plain,
% 0.45/0.69 (((~greater(e_1, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_1))) <=> ((~cycle(e_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_1)) | (~greater(e_4, e_2)))),
% 0.45/0.69 inference(rewrite,[status(thm)],[])).
% 0.45/0.69 tff(631,plain,
% 0.45/0.69 (((~![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_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, 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_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_1)) | (~greater(e_4, e_2))))),
% 0.45/0.69 inference(monotonicity,[status(thm)],[630])).
% 0.45/0.69 tff(632,plain,
% 0.45/0.69 (((~![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_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, 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_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_1)) | (~greater(e_4, e_2)))),
% 0.45/0.69 inference(transitivity,[status(thm)],[631, 629])).
% 0.45/0.69 tff(633,plain,
% 0.45/0.69 ((~![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_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_1)))),
% 0.45/0.69 inference(quant_inst,[status(thm)],[])).
% 0.45/0.69 tff(634,plain,
% 0.45/0.69 ((~![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_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_1)) | (~greater(e_4, e_2))),
% 0.45/0.69 inference(modus_ponens,[status(thm)],[633, 632])).
% 0.45/0.69 tff(635,plain,
% 0.45/0.69 ((~cycle(e_4, e_0)) | (~cycle(e_2, e_1))),
% 0.45/0.69 inference(unit_resolution,[status(thm)],[634, 23, 170, 17, 14, 11])).
% 0.45/0.69 tff(636,plain,
% 0.45/0.69 (~cycle(e_4, e_0)),
% 0.45/0.69 inference(unit_resolution,[status(thm)],[635, 628])).
% 0.45/0.69 tff(637,plain,
% 0.45/0.69 ((~equalish(e_1, e_4)) <=> (~equalish(e_1, e_4))),
% 0.45/0.69 inference(rewrite,[status(thm)],[])).
% 0.45/0.69 tff(638,axiom,(~equalish(e_1, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_4')).
% 0.45/0.69 tff(639,plain,
% 0.45/0.69 (~equalish(e_1, e_4)),
% 0.45/0.69 inference(modus_ponens,[status(thm)],[638, 637])).
% 0.45/0.69 tff(640,plain,
% 0.45/0.69 (((~![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)))),
% 0.45/0.69 inference(rewrite,[status(thm)],[])).
% 0.45/0.69 tff(641,plain,
% 0.45/0.69 (((~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)))),
% 0.45/0.69 inference(rewrite,[status(thm)],[])).
% 0.45/0.69 tff(642,plain,
% 0.45/0.69 (((~![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))))),
% 0.45/0.69 inference(monotonicity,[status(thm)],[641])).
% 0.45/0.69 tff(643,plain,
% 0.45/0.69 (((~![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)))),
% 0.45/0.69 inference(transitivity,[status(thm)],[642, 640])).
% 0.45/0.69 tff(644,plain,
% 0.45/0.69 ((~![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)))),
% 0.45/0.69 inference(quant_inst,[status(thm)],[])).
% 0.45/0.69 tff(645,plain,
% 0.45/0.69 ((~![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))),
% 0.45/0.69 inference(modus_ponens,[status(thm)],[644, 643])).
% 0.45/0.69 tff(646,plain,
% 0.45/0.69 (~cycle(e_3, e_3)),
% 0.45/0.69 inference(unit_resolution,[status(thm)],[645, 115, 112, 170, 45, 639, 628])).
% 0.45/0.69 tff(647,plain,
% 0.45/0.69 (((~![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)))),
% 0.45/0.69 inference(rewrite,[status(thm)],[])).
% 0.45/0.69 tff(648,plain,
% 0.45/0.69 (((~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)))),
% 0.45/0.69 inference(rewrite,[status(thm)],[])).
% 0.45/0.69 tff(649,plain,
% 0.45/0.69 (((~![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))))),
% 0.45/0.69 inference(monotonicity,[status(thm)],[648])).
% 0.45/0.69 tff(650,plain,
% 0.45/0.69 (((~![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)))),
% 0.45/0.69 inference(transitivity,[status(thm)],[649, 647])).
% 0.45/0.69 tff(651,plain,
% 0.45/0.69 ((~![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)))),
% 0.45/0.69 inference(quant_inst,[status(thm)],[])).
% 0.45/0.69 tff(652,plain,
% 0.45/0.69 ((~![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))),
% 0.45/0.69 inference(modus_ponens,[status(thm)],[651, 650])).
% 0.45/0.69 tff(653,plain,
% 0.45/0.69 (~cycle(e_3, e_1)),
% 0.45/0.69 inference(unit_resolution,[status(thm)],[652, 173, 115, 170, 45, 167, 628])).
% 0.45/0.70 tff(654,plain,
% 0.45/0.70 (((~![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_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_2)))) <=> ((~![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_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_2)))),
% 0.45/0.70 inference(rewrite,[status(thm)],[])).
% 0.45/0.70 tff(655,plain,
% 0.45/0.70 (((~cycle(e_2, e_1)) | equalish(e_1, e_3) | (~next(e_2, e_3)) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2))) <=> (equalish(e_1, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_2)))),
% 0.45/0.70 inference(rewrite,[status(thm)],[])).
% 0.45/0.70 tff(656,plain,
% 0.45/0.70 (((~![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_3) | (~next(e_2, e_3)) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2)))) <=> ((~![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_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_2))))),
% 0.45/0.70 inference(monotonicity,[status(thm)],[655])).
% 0.45/0.70 tff(657,plain,
% 0.45/0.70 (((~![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_3) | (~next(e_2, e_3)) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2)))) <=> ((~![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_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_2)))),
% 0.45/0.70 inference(transitivity,[status(thm)],[656, 654])).
% 0.45/0.70 tff(658,plain,
% 0.45/0.70 ((~![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_3) | (~next(e_2, e_3)) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2)))),
% 0.45/0.70 inference(quant_inst,[status(thm)],[])).
% 0.45/0.70 tff(659,plain,
% 0.45/0.70 ((~![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_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_2))),
% 0.45/0.70 inference(modus_ponens,[status(thm)],[658, 657])).
% 0.45/0.70 tff(660,plain,
% 0.45/0.70 (~cycle(e_3, e_2)),
% 0.45/0.70 inference(unit_resolution,[status(thm)],[659, 115, 170, 45, 426, 628])).
% 0.45/0.70 tff(661,plain,
% 0.45/0.70 ((~equalish(e_1, e_5)) <=> (~equalish(e_1, e_5))),
% 0.45/0.70 inference(rewrite,[status(thm)],[])).
% 0.45/0.70 tff(662,axiom,(~equalish(e_1, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_5')).
% 0.45/0.70 tff(663,plain,
% 0.45/0.70 (~equalish(e_1, e_5)),
% 0.45/0.70 inference(modus_ponens,[status(thm)],[662, 661])).
% 0.45/0.70 tff(664,plain,
% 0.45/0.70 (((~![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_5) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~next(e_4, e_5)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_4)))) <=> ((~![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_5) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~next(e_4, e_5)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_4)))),
% 0.45/0.70 inference(rewrite,[status(thm)],[])).
% 0.45/0.70 tff(665,plain,
% 0.45/0.70 (((~cycle(e_2, e_1)) | equalish(e_1, e_5) | (~next(e_4, e_5)) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_4))) <=> (equalish(e_1, e_5) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~next(e_4, e_5)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_4)))),
% 0.45/0.70 inference(rewrite,[status(thm)],[])).
% 0.45/0.70 tff(666,plain,
% 0.45/0.70 (((~![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_5) | (~next(e_4, e_5)) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_4)))) <=> ((~![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_5) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~next(e_4, e_5)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_4))))),
% 0.45/0.70 inference(monotonicity,[status(thm)],[665])).
% 0.45/0.70 tff(667,plain,
% 0.45/0.70 (((~![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_5) | (~next(e_4, e_5)) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_4)))) <=> ((~![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_5) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~next(e_4, e_5)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_4)))),
% 0.45/0.70 inference(transitivity,[status(thm)],[666, 664])).
% 0.45/0.70 tff(668,plain,
% 0.45/0.70 ((~![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_5) | (~next(e_4, e_5)) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_4)))),
% 0.45/0.70 inference(quant_inst,[status(thm)],[])).
% 0.45/0.70 tff(669,plain,
% 0.45/0.70 ((~![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_5) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~next(e_4, e_5)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_4))),
% 0.45/0.70 inference(modus_ponens,[status(thm)],[668, 667])).
% 0.45/0.70 tff(670,plain,
% 0.45/0.70 (~cycle(e_3, e_4)),
% 0.45/0.70 inference(unit_resolution,[status(thm)],[669, 115, 23, 170, 45, 663, 628])).
% 0.45/0.70 tff(671,plain,
% 0.45/0.70 (cycle(e_3, e_0)),
% 0.45/0.70 inference(unit_resolution,[status(thm)],[163, 670, 660, 653, 646])).
% 0.45/0.70 tff(672,assumption,(~cycle(e_4, e_0)), introduced(assumption)).
% 0.45/0.70 tff(673,assumption,(cycle(e_3, e_0)), introduced(assumption)).
% 0.45/0.70 tff(674,assumption,(cycle(e_1, e_4)), introduced(assumption)).
% 0.45/0.70 tff(675,plain,
% 0.45/0.70 (((~![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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_4)) | (~cycle(e_4, 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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_4)) | (~cycle(e_4, e_1)))),
% 0.45/0.70 inference(rewrite,[status(thm)],[])).
% 0.45/0.70 tff(676,plain,
% 0.45/0.70 (((~greater(e_4, e_1)) | (~greater(e_3, e_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_1, e_4))) <=> ((~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_4)) | (~cycle(e_4, e_1)))),
% 0.45/0.70 inference(rewrite,[status(thm)],[])).
% 0.45/0.70 tff(677,plain,
% 0.45/0.70 (((~![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_4, e_1)) | (~greater(e_3, e_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_1, e_4)))) <=> ((~![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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_4)) | (~cycle(e_4, e_1))))),
% 0.45/0.70 inference(monotonicity,[status(thm)],[676])).
% 0.45/0.70 tff(678,plain,
% 0.45/0.70 (((~![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_4, e_1)) | (~greater(e_3, e_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_1, e_4)))) <=> ((~![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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_4)) | (~cycle(e_4, e_1)))),
% 0.45/0.70 inference(transitivity,[status(thm)],[677, 675])).
% 0.45/0.70 tff(679,plain,
% 0.45/0.70 ((~![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_4, e_1)) | (~greater(e_3, e_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_1, e_4)))),
% 0.45/0.70 inference(quant_inst,[status(thm)],[])).
% 0.45/0.70 tff(680,plain,
% 0.45/0.70 ((~![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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_4)) | (~cycle(e_4, e_1))),
% 0.45/0.70 inference(modus_ponens,[status(thm)],[679, 678])).
% 0.45/0.70 tff(681,plain,
% 0.45/0.70 ((~cycle(e_3, e_0)) | (~cycle(e_1, e_4)) | (~cycle(e_4, e_1))),
% 0.45/0.70 inference(unit_resolution,[status(thm)],[680, 112, 512, 214, 11])).
% 0.45/0.70 tff(682,plain,
% 0.45/0.70 (~cycle(e_4, e_1)),
% 0.45/0.70 inference(unit_resolution,[status(thm)],[681, 674, 673])).
% 0.45/0.70 tff(683,plain,
% 0.45/0.70 (greater(e_4, e_3) <=> greater(e_4, e_3)),
% 0.45/0.70 inference(rewrite,[status(thm)],[])).
% 0.45/0.70 tff(684,axiom,(greater(e_4, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_greater_e_3')).
% 0.45/0.70 tff(685,plain,
% 0.45/0.70 (greater(e_4, e_3)),
% 0.45/0.70 inference(modus_ponens,[status(thm)],[684, 683])).
% 0.45/0.70 tff(686,plain,
% 0.45/0.70 (((~![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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_4, e_3)) | (~cycle(e_1, e_4)) | (~cycle(e_4, 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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_4, e_3)) | (~cycle(e_1, e_4)) | (~cycle(e_4, e_3)))),
% 0.45/0.70 inference(rewrite,[status(thm)],[])).
% 0.45/0.70 tff(687,plain,
% 0.45/0.70 (((~greater(e_4, e_3)) | (~greater(e_3, e_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_3)) | (~cycle(e_3, e_0)) | (~cycle(e_1, e_4))) <=> ((~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_4, e_3)) | (~cycle(e_1, e_4)) | (~cycle(e_4, e_3)))),
% 0.45/0.70 inference(rewrite,[status(thm)],[])).
% 0.45/0.70 tff(688,plain,
% 0.45/0.70 (((~![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_4, e_3)) | (~greater(e_3, e_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_3)) | (~cycle(e_3, e_0)) | (~cycle(e_1, e_4)))) <=> ((~![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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_4, e_3)) | (~cycle(e_1, e_4)) | (~cycle(e_4, e_3))))),
% 0.45/0.70 inference(monotonicity,[status(thm)],[687])).
% 0.45/0.70 tff(689,plain,
% 0.45/0.70 (((~![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_4, e_3)) | (~greater(e_3, e_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_3)) | (~cycle(e_3, e_0)) | (~cycle(e_1, e_4)))) <=> ((~![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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_4, e_3)) | (~cycle(e_1, e_4)) | (~cycle(e_4, e_3)))),
% 0.45/0.70 inference(transitivity,[status(thm)],[688, 686])).
% 0.45/0.70 tff(690,plain,
% 0.45/0.70 ((~![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_4, e_3)) | (~greater(e_3, e_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_3)) | (~cycle(e_3, e_0)) | (~cycle(e_1, e_4)))),
% 0.45/0.70 inference(quant_inst,[status(thm)],[])).
% 0.45/0.70 tff(691,plain,
% 0.45/0.70 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_4, e_3)) | (~cycle(e_1, e_4)) | (~cycle(e_4, e_3))),
% 0.45/0.70 inference(modus_ponens,[status(thm)],[690, 689])).
% 0.45/0.70 tff(692,plain,
% 0.45/0.70 ((~cycle(e_3, e_0)) | (~cycle(e_1, e_4)) | (~cycle(e_4, e_3))),
% 0.45/0.70 inference(unit_resolution,[status(thm)],[691, 112, 512, 685, 11])).
% 0.45/0.70 tff(693,plain,
% 0.45/0.70 (~cycle(e_4, e_3)),
% 0.45/0.70 inference(unit_resolution,[status(thm)],[692, 674, 673])).
% 0.45/0.70 tff(694,plain,
% 0.45/0.70 ($false),
% 0.45/0.70 inference(unit_resolution,[status(thm)],[104, 693, 682, 672])).
% 0.45/0.70 tff(695,plain,((~cycle(e_1, e_4)) | cycle(e_4, e_0) | (~cycle(e_3, e_0))), inference(lemma,lemma(discharge,[]))).
% 0.45/0.70 tff(696,plain,
% 0.45/0.70 (~cycle(e_1, e_4)),
% 0.45/0.70 inference(unit_resolution,[status(thm)],[695, 671, 636])).
% 0.45/0.70 tff(697,plain,
% 0.45/0.70 (cycle(e_4, e_1)),
% 0.45/0.70 inference(unit_resolution,[status(thm)],[104, 636, 59])).
% 0.45/0.70 tff(698,plain,
% 0.45/0.70 (((~![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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_2, e_1)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_2)) | (~cycle(e_4, 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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_2, e_1)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_2)) | (~cycle(e_4, e_1)))),
% 0.45/0.70 inference(rewrite,[status(thm)],[])).
% 0.45/0.70 tff(699,plain,
% 0.45/0.70 (((~greater(e_2, e_1)) | (~greater(e_3, e_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_1, e_2))) <=> ((~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_2, e_1)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_2)) | (~cycle(e_4, e_1)))),
% 0.45/0.70 inference(rewrite,[status(thm)],[])).
% 0.45/0.70 tff(700,plain,
% 0.45/0.70 (((~![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_1)) | (~greater(e_3, e_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_1, 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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_2, e_1)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_2)) | (~cycle(e_4, e_1))))),
% 0.45/0.70 inference(monotonicity,[status(thm)],[699])).
% 0.45/0.70 tff(701,plain,
% 0.45/0.70 (((~![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_1)) | (~greater(e_3, e_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_1, 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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_2, e_1)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_2)) | (~cycle(e_4, e_1)))),
% 0.45/0.70 inference(transitivity,[status(thm)],[700, 698])).
% 0.45/0.70 tff(702,plain,
% 0.45/0.70 ((~![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_1)) | (~greater(e_3, e_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_1, e_2)))),
% 0.45/0.71 inference(quant_inst,[status(thm)],[])).
% 0.45/0.71 tff(703,plain,
% 0.45/0.71 ((~![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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_2, e_1)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_2)) | (~cycle(e_4, e_1))),
% 0.45/0.71 inference(modus_ponens,[status(thm)],[702, 701])).
% 0.45/0.71 tff(704,plain,
% 0.45/0.71 ((~cycle(e_3, e_0)) | (~cycle(e_1, e_2)) | (~cycle(e_4, e_1))),
% 0.45/0.71 inference(unit_resolution,[status(thm)],[703, 112, 138, 512, 11])).
% 0.45/0.71 tff(705,plain,
% 0.45/0.71 (~cycle(e_1, e_2)),
% 0.45/0.71 inference(unit_resolution,[status(thm)],[704, 671, 697])).
% 0.45/0.71 tff(706,plain,
% 0.45/0.71 (((~![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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_3)) | (~cycle(e_4, 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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_3)) | (~cycle(e_4, e_1)))),
% 0.45/0.71 inference(rewrite,[status(thm)],[])).
% 0.45/0.71 tff(707,plain,
% 0.45/0.71 (((~greater(e_3, e_1)) | (~greater(e_3, e_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_1, e_3))) <=> ((~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_3)) | (~cycle(e_4, e_1)))),
% 0.45/0.71 inference(rewrite,[status(thm)],[])).
% 0.45/0.71 tff(708,plain,
% 0.45/0.71 (((~![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_1)) | (~greater(e_3, e_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_1, 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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_3)) | (~cycle(e_4, e_1))))),
% 0.45/0.71 inference(monotonicity,[status(thm)],[707])).
% 0.45/0.71 tff(709,plain,
% 0.45/0.71 (((~![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_1)) | (~greater(e_3, e_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_1, 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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_3)) | (~cycle(e_4, e_1)))),
% 0.45/0.71 inference(transitivity,[status(thm)],[708, 706])).
% 0.45/0.71 tff(710,plain,
% 0.45/0.71 ((~![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_1)) | (~greater(e_3, e_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_1, e_3)))),
% 0.45/0.71 inference(quant_inst,[status(thm)],[])).
% 0.45/0.71 tff(711,plain,
% 0.45/0.71 ((~![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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_3)) | (~cycle(e_4, e_1))),
% 0.45/0.71 inference(modus_ponens,[status(thm)],[710, 709])).
% 0.45/0.71 tff(712,plain,
% 0.45/0.71 ((~cycle(e_3, e_0)) | (~cycle(e_1, e_3)) | (~cycle(e_4, e_1))),
% 0.45/0.71 inference(unit_resolution,[status(thm)],[711, 112, 512, 11])).
% 0.45/0.71 tff(713,plain,
% 0.45/0.71 (~cycle(e_1, e_3)),
% 0.45/0.71 inference(unit_resolution,[status(thm)],[712, 671, 697])).
% 0.45/0.71 tff(714,assumption,(~cycle(e_2, e_0)), introduced(assumption)).
% 0.45/0.71 tff(715,plain,
% 0.45/0.71 (cycle(e_2, e_1)),
% 0.45/0.71 inference(unit_resolution,[status(thm)],[306, 290, 714, 327, 325])).
% 0.45/0.71 tff(716,plain,
% 0.45/0.71 (~cycle(e_3, e_2)),
% 0.45/0.71 inference(unit_resolution,[status(thm)],[659, 115, 170, 45, 426, 715])).
% 0.45/0.71 tff(717,plain,
% 0.45/0.71 (~cycle(e_3, e_1)),
% 0.45/0.71 inference(unit_resolution,[status(thm)],[652, 173, 115, 170, 45, 167, 715])).
% 0.45/0.71 tff(718,plain,
% 0.45/0.71 (~cycle(e_3, e_3)),
% 0.45/0.71 inference(unit_resolution,[status(thm)],[645, 115, 112, 170, 45, 639, 715])).
% 0.45/0.71 tff(719,plain,
% 0.45/0.71 (~cycle(e_3, e_4)),
% 0.45/0.71 inference(unit_resolution,[status(thm)],[669, 115, 23, 170, 45, 663, 715])).
% 0.45/0.71 tff(720,plain,
% 0.45/0.71 (cycle(e_3, e_0)),
% 0.45/0.71 inference(unit_resolution,[status(thm)],[163, 719, 718, 717, 716])).
% 0.45/0.71 tff(721,plain,
% 0.45/0.71 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_3, e_0)) | (~greater(e_4, e_3)) | (~product(e_3, e_1, e_4)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_3, e_0)) | (~greater(e_4, e_3)) | (~product(e_3, e_1, e_4)))),
% 0.45/0.71 inference(rewrite,[status(thm)],[])).
% 0.45/0.71 tff(722,plain,
% 0.45/0.71 (((~product(e_3, e_1, e_4)) | (~greater(e_4, e_3)) | (~cycle(e_3, e_0))) <=> ((~cycle(e_3, e_0)) | (~greater(e_4, e_3)) | (~product(e_3, e_1, e_4)))),
% 0.45/0.71 inference(rewrite,[status(thm)],[])).
% 0.45/0.71 tff(723,plain,
% 0.45/0.71 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_3, e_1, e_4)) | (~greater(e_4, e_3)) | (~cycle(e_3, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_3, e_0)) | (~greater(e_4, e_3)) | (~product(e_3, e_1, e_4))))),
% 0.45/0.71 inference(monotonicity,[status(thm)],[722])).
% 0.45/0.71 tff(724,plain,
% 0.45/0.71 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_3, e_1, e_4)) | (~greater(e_4, e_3)) | (~cycle(e_3, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_3, e_0)) | (~greater(e_4, e_3)) | (~product(e_3, e_1, e_4)))),
% 0.45/0.71 inference(transitivity,[status(thm)],[723, 721])).
% 0.45/0.71 tff(725,plain,
% 0.45/0.71 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_3, e_1, e_4)) | (~greater(e_4, e_3)) | (~cycle(e_3, e_0)))),
% 0.45/0.71 inference(quant_inst,[status(thm)],[])).
% 0.45/0.71 tff(726,plain,
% 0.45/0.71 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_3, e_0)) | (~greater(e_4, e_3)) | (~product(e_3, e_1, e_4))),
% 0.45/0.71 inference(modus_ponens,[status(thm)],[725, 724])).
% 0.45/0.71 tff(727,plain,
% 0.45/0.71 ((~cycle(e_3, e_0)) | (~product(e_3, e_1, e_4))),
% 0.45/0.71 inference(unit_resolution,[status(thm)],[726, 685, 278])).
% 0.45/0.71 tff(728,plain,
% 0.45/0.71 (~product(e_3, e_1, e_4)),
% 0.45/0.71 inference(unit_resolution,[status(thm)],[727, 720])).
% 0.45/0.71 tff(729,plain,
% 0.45/0.71 (greater(e_5, e_3) <=> greater(e_5, e_3)),
% 0.45/0.71 inference(rewrite,[status(thm)],[])).
% 0.45/0.71 tff(730,axiom,(greater(e_5, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_greater_e_3')).
% 0.45/0.71 tff(731,plain,
% 0.45/0.71 (greater(e_5, e_3)),
% 0.45/0.71 inference(modus_ponens,[status(thm)],[730, 729])).
% 0.45/0.71 tff(732,plain,
% 0.45/0.71 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_3, e_0)) | (~greater(e_5, e_3)) | (~product(e_3, e_1, e_5)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_3, e_0)) | (~greater(e_5, e_3)) | (~product(e_3, e_1, e_5)))),
% 0.45/0.71 inference(rewrite,[status(thm)],[])).
% 0.45/0.71 tff(733,plain,
% 0.45/0.71 (((~product(e_3, e_1, e_5)) | (~greater(e_5, e_3)) | (~cycle(e_3, e_0))) <=> ((~cycle(e_3, e_0)) | (~greater(e_5, e_3)) | (~product(e_3, e_1, e_5)))),
% 0.45/0.71 inference(rewrite,[status(thm)],[])).
% 0.45/0.71 tff(734,plain,
% 0.45/0.71 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_3, e_1, e_5)) | (~greater(e_5, e_3)) | (~cycle(e_3, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_3, e_0)) | (~greater(e_5, e_3)) | (~product(e_3, e_1, e_5))))),
% 0.45/0.71 inference(monotonicity,[status(thm)],[733])).
% 0.45/0.71 tff(735,plain,
% 0.45/0.71 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_3, e_1, e_5)) | (~greater(e_5, e_3)) | (~cycle(e_3, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_3, e_0)) | (~greater(e_5, e_3)) | (~product(e_3, e_1, e_5)))),
% 0.45/0.71 inference(transitivity,[status(thm)],[734, 732])).
% 0.45/0.71 tff(736,plain,
% 0.45/0.71 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_3, e_1, e_5)) | (~greater(e_5, e_3)) | (~cycle(e_3, e_0)))),
% 0.45/0.71 inference(quant_inst,[status(thm)],[])).
% 0.45/0.71 tff(737,plain,
% 0.45/0.71 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_3, e_0)) | (~greater(e_5, e_3)) | (~product(e_3, e_1, e_5))),
% 0.45/0.71 inference(modus_ponens,[status(thm)],[736, 735])).
% 0.45/0.71 tff(738,plain,
% 0.45/0.71 ((~cycle(e_3, e_0)) | (~product(e_3, e_1, e_5))),
% 0.45/0.71 inference(unit_resolution,[status(thm)],[737, 731, 278])).
% 0.45/0.71 tff(739,plain,
% 0.45/0.71 (~product(e_3, e_1, e_5)),
% 0.45/0.71 inference(unit_resolution,[status(thm)],[738, 720])).
% 0.45/0.71 tff(740,plain,
% 0.45/0.71 (~product(e_2, e_1, e_1)),
% 0.45/0.71 inference(unit_resolution,[status(thm)],[570, 457, 459, 458])).
% 0.45/0.71 tff(741,plain,
% 0.45/0.71 (~product(e_2, e_1, e_5)),
% 0.45/0.71 inference(unit_resolution,[status(thm)],[315, 290])).
% 0.45/0.71 tff(742,assumption,(~product(e_2, e_1, e_5)), introduced(assumption)).
% 0.45/0.71 tff(743,assumption,(cycle(e_1, e_1)), introduced(assumption)).
% 0.45/0.71 tff(744,plain,
% 0.45/0.71 (((~![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_1, e_2)) | (~next(e_3, e_4)) | (~cycle(e_1, e_1)) | (~cycle(e_2, 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_1, e_2)) | (~next(e_3, e_4)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_3)))),
% 0.45/0.71 inference(rewrite,[status(thm)],[])).
% 0.45/0.71 tff(745,plain,
% 0.45/0.71 (((~cycle(e_1, e_1)) | equalish(e_1, e_4) | (~next(e_3, e_4)) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_3))) <=> (equalish(e_1, e_4) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_3)))),
% 0.45/0.71 inference(rewrite,[status(thm)],[])).
% 0.45/0.71 tff(746,plain,
% 0.45/0.71 (((~![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_1, e_1)) | equalish(e_1, e_4) | (~next(e_3, e_4)) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, 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_1, e_2)) | (~next(e_3, e_4)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_3))))),
% 0.45/0.71 inference(monotonicity,[status(thm)],[745])).
% 0.45/0.71 tff(747,plain,
% 0.45/0.71 (((~![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_1, e_1)) | equalish(e_1, e_4) | (~next(e_3, e_4)) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, 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_1, e_2)) | (~next(e_3, e_4)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_3)))),
% 0.45/0.71 inference(transitivity,[status(thm)],[746, 744])).
% 0.45/0.71 tff(748,plain,
% 0.45/0.71 ((~![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_1, e_1)) | equalish(e_1, e_4) | (~next(e_3, e_4)) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_3)))),
% 0.45/0.71 inference(quant_inst,[status(thm)],[])).
% 0.45/0.71 tff(749,plain,
% 0.45/0.71 ((~![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_1, e_2)) | (~next(e_3, e_4)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_3))),
% 0.45/0.71 inference(modus_ponens,[status(thm)],[748, 747])).
% 0.45/0.71 tff(750,plain,
% 0.45/0.71 (~cycle(e_2, e_3)),
% 0.45/0.71 inference(unit_resolution,[status(thm)],[749, 173, 112, 170, 45, 639, 743])).
% 0.45/0.71 tff(751,plain,
% 0.45/0.71 (~product(e_2, e_1, e_4)),
% 0.45/0.71 inference(unit_resolution,[status(thm)],[344, 750, 327, 325])).
% 0.45/0.71 tff(752,plain,
% 0.45/0.71 (((~![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)) | (~cycle(e_1, e_1)) | (~cycle(e_2, 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)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_1)))),
% 0.45/0.71 inference(rewrite,[status(thm)],[])).
% 0.45/0.71 tff(753,plain,
% 0.45/0.71 (((~cycle(e_1, e_1)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_1))) <=> (equalish(e_1, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_1)))),
% 0.45/0.71 inference(rewrite,[status(thm)],[])).
% 0.45/0.71 tff(754,plain,
% 0.45/0.71 (((~![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_1, e_1)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, 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)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_1))))),
% 0.45/0.71 inference(monotonicity,[status(thm)],[753])).
% 0.45/0.71 tff(755,plain,
% 0.45/0.71 (((~![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_1, e_1)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, 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)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_1)))),
% 0.45/0.71 inference(transitivity,[status(thm)],[754, 752])).
% 0.45/0.71 tff(756,plain,
% 0.45/0.71 ((~![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_1, e_1)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_1)))),
% 0.45/0.71 inference(quant_inst,[status(thm)],[])).
% 0.45/0.71 tff(757,plain,
% 0.45/0.71 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_1, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_1))),
% 0.45/0.71 inference(modus_ponens,[status(thm)],[756, 755])).
% 0.45/0.71 tff(758,plain,
% 0.45/0.71 (~cycle(e_2, e_1)),
% 0.45/0.71 inference(unit_resolution,[status(thm)],[757, 173, 170, 45, 167, 743])).
% 0.45/0.71 tff(759,plain,
% 0.45/0.71 (cycle(e_2, e_0)),
% 0.45/0.71 inference(unit_resolution,[status(thm)],[306, 758, 750, 327, 325])).
% 0.45/0.71 tff(760,plain,
% 0.45/0.71 (~product(e_2, e_1, e_3)),
% 0.45/0.71 inference(unit_resolution,[status(thm)],[626, 759])).
% 0.45/0.71 tff(761,plain,
% 0.45/0.71 ($false),
% 0.45/0.71 inference(unit_resolution,[status(thm)],[420, 760, 751, 742, 600])).
% 0.45/0.71 tff(762,plain,((~cycle(e_1, e_1)) | product(e_2, e_1, e_5) | product(e_2, e_1, e_1) | cycle(e_2, e_4) | cycle(e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.45/0.71 tff(763,plain,
% 0.45/0.71 (~cycle(e_1, e_1)),
% 0.45/0.71 inference(unit_resolution,[status(thm)],[762, 741, 740, 327, 325])).
% 0.45/0.71 tff(764,assumption,(~cycle(e_1, e_1)), introduced(assumption)).
% 0.45/0.71 tff(765,plain,
% 0.45/0.71 (cycle(e_1, e_0)),
% 0.45/0.71 inference(unit_resolution,[status(thm)],[472, 459, 764, 458, 457])).
% 0.45/0.71 tff(766,plain,
% 0.45/0.71 (~product(e_1, e_1, e_4)),
% 0.45/0.71 inference(unit_resolution,[status(thm)],[481, 459, 458, 457])).
% 0.45/0.71 tff(767,plain,
% 0.45/0.71 ($false),
% 0.45/0.71 inference(unit_resolution,[status(thm)],[541, 766, 765, 509])).
% 0.54/0.71 tff(768,plain,(cycle(e_1, e_4) | product(e_1, e_1, e_1) | cycle(e_1, e_3) | cycle(e_1, e_2) | cycle(e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.71 tff(769,plain,
% 0.54/0.71 (product(e_1, e_1, e_1)),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[768, 763, 459, 458, 457])).
% 0.54/0.71 tff(770,assumption,(product(e_3, e_1, e_1)), introduced(assumption)).
% 0.54/0.71 tff(771,plain,
% 0.54/0.71 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, 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_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.54/0.71 inference(rewrite,[status(thm)],[])).
% 0.54/0.71 tff(772,plain,
% 0.54/0.71 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.54/0.71 inference(quant_inst,[status(thm)],[])).
% 0.54/0.71 tff(773,plain,
% 0.54/0.71 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1))),
% 0.54/0.71 inference(modus_ponens,[status(thm)],[772, 771])).
% 0.54/0.71 tff(774,plain,
% 0.54/0.71 ($false),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[773, 35, 493, 483, 770])).
% 0.54/0.71 tff(775,plain,((~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.71 tff(776,plain,
% 0.54/0.71 (~product(e_3, e_1, e_1)),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[775, 769])).
% 0.54/0.71 tff(777,assumption,(product(e_3, e_2, e_3)), introduced(assumption)).
% 0.54/0.71 tff(778,plain,
% 0.54/0.71 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_3)) | product(e_3, e_3, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_2, e_3)) | product(e_3, e_3, e_3))),
% 0.54/0.71 inference(rewrite,[status(thm)],[])).
% 0.54/0.71 tff(779,plain,
% 0.54/0.71 ((product(e_3, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_2, e_3))) <=> ((~product(e_3, e_2, e_3)) | product(e_3, e_3, e_3))),
% 0.54/0.71 inference(rewrite,[status(thm)],[])).
% 0.54/0.71 tff(780,plain,
% 0.54/0.71 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_3)) | product(e_3, e_3, e_3)))),
% 0.54/0.71 inference(monotonicity,[status(thm)],[779])).
% 0.54/0.71 tff(781,plain,
% 0.54/0.71 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_2, e_3)) | product(e_3, e_3, e_3))),
% 0.54/0.71 inference(transitivity,[status(thm)],[780, 778])).
% 0.54/0.71 tff(782,plain,
% 0.54/0.71 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.54/0.71 inference(quant_inst,[status(thm)],[])).
% 0.54/0.71 tff(783,plain,
% 0.54/0.71 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_2, e_3)) | product(e_3, e_3, e_3)),
% 0.54/0.71 inference(modus_ponens,[status(thm)],[782, 781])).
% 0.54/0.71 tff(784,plain,
% 0.54/0.71 ((~product(e_3, e_2, e_3)) | product(e_3, e_3, e_3)),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[783, 374])).
% 0.54/0.71 tff(785,plain,
% 0.54/0.71 (product(e_3, e_3, e_3)),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[784, 777])).
% 0.54/0.71 tff(786,plain,
% 0.54/0.71 (((~![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_3, e_2, e_3)) | (~product(e_3, e_3, e_3)))) <=> ((~![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_3, e_2, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(787,plain,
% 0.54/0.72 ((equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3))) <=> (equalish(e_2, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(788,plain,
% 0.54/0.72 (((~![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_3, e_3, e_3)) | (~product(e_3, e_2, e_3)))) <=> ((~![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_3, e_2, e_3)) | (~product(e_3, e_3, e_3))))),
% 0.54/0.72 inference(monotonicity,[status(thm)],[787])).
% 0.54/0.72 tff(789,plain,
% 0.54/0.72 (((~![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_3, e_3, e_3)) | (~product(e_3, e_2, e_3)))) <=> ((~![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_3, e_2, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.54/0.72 inference(transitivity,[status(thm)],[788, 786])).
% 0.54/0.72 tff(790,plain,
% 0.54/0.72 ((~![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_3, e_3, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.54/0.72 inference(quant_inst,[status(thm)],[])).
% 0.54/0.72 tff(791,plain,
% 0.54/0.72 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_3, e_3))),
% 0.54/0.72 inference(modus_ponens,[status(thm)],[790, 789])).
% 0.54/0.72 tff(792,plain,
% 0.54/0.72 ($false),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[791, 125, 392, 777, 785])).
% 0.54/0.72 tff(793,plain,(~product(e_3, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.72 tff(794,plain,
% 0.54/0.72 (~product(e_2, e_1, e_4)),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[353, 325, 327])).
% 0.54/0.72 tff(795,plain,
% 0.54/0.72 (product(e_2, e_1, e_3)),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[420, 741, 740, 794])).
% 0.54/0.72 tff(796,plain,
% 0.54/0.72 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_2)) | product(e_3, e_2, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_2)) | product(e_3, e_2, e_3))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(797,plain,
% 0.54/0.72 ((product(e_3, e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_2))) <=> ((~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_2)) | product(e_3, e_2, e_3))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(798,plain,
% 0.54/0.72 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_2)) | product(e_3, e_2, e_3)))),
% 0.54/0.72 inference(monotonicity,[status(thm)],[797])).
% 0.54/0.72 tff(799,plain,
% 0.54/0.72 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_2)) | product(e_3, e_2, e_3))),
% 0.54/0.72 inference(transitivity,[status(thm)],[798, 796])).
% 0.54/0.72 tff(800,plain,
% 0.54/0.72 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.54/0.72 inference(quant_inst,[status(thm)],[])).
% 0.54/0.72 tff(801,plain,
% 0.54/0.72 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_2)) | product(e_3, e_2, e_3)),
% 0.54/0.72 inference(modus_ponens,[status(thm)],[800, 799])).
% 0.54/0.72 tff(802,plain,
% 0.54/0.72 ((~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_2)) | product(e_3, e_2, e_3)),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[801, 374])).
% 0.54/0.72 tff(803,plain,
% 0.54/0.72 (~product(e_3, e_1, e_2)),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[802, 795, 793])).
% 0.54/0.72 tff(804,assumption,(product(e_3, e_1, e_3)), introduced(assumption)).
% 0.54/0.72 tff(805,assumption,(product(e_2, e_1, e_3)), introduced(assumption)).
% 0.54/0.72 tff(806,plain,
% 0.54/0.72 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(807,plain,
% 0.54/0.72 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.54/0.72 inference(quant_inst,[status(thm)],[])).
% 0.54/0.72 tff(808,plain,
% 0.54/0.72 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3))),
% 0.54/0.72 inference(modus_ponens,[status(thm)],[807, 806])).
% 0.54/0.72 tff(809,plain,
% 0.54/0.72 ($false),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[808, 236, 493, 805, 804])).
% 0.54/0.72 tff(810,plain,((~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.72 tff(811,plain,
% 0.54/0.72 (~product(e_3, e_1, e_3)),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[810, 795])).
% 0.54/0.72 tff(812,plain,
% 0.54/0.72 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_5) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | product(e_3, e_1, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_5) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | product(e_3, e_1, e_3))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(813,plain,
% 0.54/0.72 (((~group_element(e_3)) | product(e_3, e_1, e_5) | 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_5) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | product(e_3, e_1, e_3))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(814,plain,
% 0.54/0.72 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_5) | 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_5) | 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_5) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | product(e_3, e_1, e_3)))),
% 0.54/0.72 inference(monotonicity,[status(thm)],[813])).
% 0.54/0.72 tff(815,plain,
% 0.54/0.72 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_5) | 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_5) | 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_5) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | product(e_3, e_1, e_3))),
% 0.54/0.72 inference(transitivity,[status(thm)],[814, 812])).
% 0.54/0.72 tff(816,plain,
% 0.54/0.72 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_5) | 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)))),
% 0.54/0.72 inference(quant_inst,[status(thm)],[])).
% 0.54/0.72 tff(817,plain,
% 0.54/0.72 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_5) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | product(e_3, e_1, e_3)),
% 0.54/0.72 inference(modus_ponens,[status(thm)],[816, 815])).
% 0.54/0.72 tff(818,plain,
% 0.54/0.72 (product(e_3, e_1, e_4) | product(e_3, e_1, e_5)),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[817, 413, 159, 410, 811, 803, 776])).
% 0.54/0.72 tff(819,plain,
% 0.54/0.72 ($false),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[818, 739, 728])).
% 0.54/0.72 tff(820,plain,(cycle(e_2, e_3) | cycle(e_1, e_4) | cycle(e_1, e_3) | cycle(e_1, e_2) | cycle(e_2, e_4) | cycle(e_2, e_2) | cycle(e_2, e_0)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.72 tff(821,plain,
% 0.54/0.72 ($false),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[820, 713, 705, 327, 290, 325, 696, 627])).
% 0.54/0.72 tff(822,plain,(cycle(e_2, e_4) | cycle(e_2, e_3) | cycle(e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.72 tff(823,plain,
% 0.54/0.72 (cycle(e_2, e_3) | cycle(e_2, e_2)),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[822, 244])).
% 0.54/0.72 tff(824,plain,
% 0.54/0.72 (cycle(e_2, e_3)),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[823, 181])).
% 0.54/0.72 tff(825,plain,
% 0.54/0.72 (((~![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_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, 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_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_3)))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(826,plain,
% 0.54/0.72 (((~greater(e_3, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_3))) <=> ((~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_3)))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(827,plain,
% 0.54/0.72 (((~![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_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, 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_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_3))))),
% 0.54/0.72 inference(monotonicity,[status(thm)],[826])).
% 0.54/0.72 tff(828,plain,
% 0.54/0.72 (((~![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_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, 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_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_3)))),
% 0.54/0.72 inference(transitivity,[status(thm)],[827, 825])).
% 0.54/0.72 tff(829,plain,
% 0.54/0.72 ((~![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_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_3)))),
% 0.54/0.72 inference(quant_inst,[status(thm)],[])).
% 0.54/0.72 tff(830,plain,
% 0.54/0.72 ((~![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_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_3))),
% 0.54/0.72 inference(modus_ponens,[status(thm)],[829, 828])).
% 0.54/0.72 tff(831,plain,
% 0.54/0.72 ((~cycle(e_4, e_0)) | (~cycle(e_2, e_3))),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[830, 23, 48, 17, 14, 11])).
% 0.54/0.72 tff(832,plain,
% 0.54/0.72 (~cycle(e_4, e_0)),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[831, 824])).
% 0.54/0.72 tff(833,plain,
% 0.54/0.72 (cycle(e_4, e_1)),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[105, 832])).
% 0.54/0.72 tff(834,plain,
% 0.54/0.72 (((~![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_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, 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_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_4)))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(835,plain,
% 0.54/0.72 (((~greater(e_1, e_0)) | (~cycle(e_4, e_1)) | equalish(e_4, e_5) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_4))) <=> (equalish(e_4, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_4)))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(836,plain,
% 0.54/0.72 (((~![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_4, e_1)) | equalish(e_4, e_5) | (~next(e_4, e_5)) | (~product(e_4, 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_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_4))))),
% 0.54/0.72 inference(monotonicity,[status(thm)],[835])).
% 0.54/0.72 tff(837,plain,
% 0.54/0.72 (((~![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_4, e_1)) | equalish(e_4, e_5) | (~next(e_4, e_5)) | (~product(e_4, 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_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_4)))),
% 0.54/0.72 inference(transitivity,[status(thm)],[836, 834])).
% 0.54/0.72 tff(838,plain,
% 0.54/0.72 ((~![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_4, e_1)) | equalish(e_4, e_5) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_4)))),
% 0.54/0.72 inference(quant_inst,[status(thm)],[])).
% 0.54/0.72 tff(839,plain,
% 0.54/0.72 ((~![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_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_4))),
% 0.54/0.72 inference(modus_ponens,[status(thm)],[838, 837])).
% 0.54/0.72 tff(840,plain,
% 0.54/0.72 (~product(e_4, e_1, e_4)),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[839, 23, 170, 259, 225, 833])).
% 0.54/0.73 tff(841,plain,
% 0.54/0.73 ((~equalish(e_3, e_5)) <=> (~equalish(e_3, e_5))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(842,axiom,(~equalish(e_3, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_5')).
% 0.54/0.73 tff(843,plain,
% 0.54/0.73 (~equalish(e_3, e_5)),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[842, 841])).
% 0.54/0.73 tff(844,plain,
% 0.54/0.73 (((~![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_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, 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_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_3)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(845,plain,
% 0.54/0.73 (((~greater(e_1, e_0)) | (~cycle(e_4, e_1)) | equalish(e_3, e_5) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_3))) <=> (equalish(e_3, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_3)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(846,plain,
% 0.54/0.73 (((~![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_4, e_1)) | equalish(e_3, e_5) | (~next(e_4, e_5)) | (~product(e_4, 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_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_3))))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[845])).
% 0.54/0.73 tff(847,plain,
% 0.54/0.73 (((~![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_4, e_1)) | equalish(e_3, e_5) | (~next(e_4, e_5)) | (~product(e_4, 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_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_3)))),
% 0.54/0.73 inference(transitivity,[status(thm)],[846, 844])).
% 0.54/0.73 tff(848,plain,
% 0.54/0.73 ((~![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_4, e_1)) | equalish(e_3, e_5) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_3)))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(849,plain,
% 0.54/0.73 ((~![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_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_3))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[848, 847])).
% 0.54/0.73 tff(850,plain,
% 0.54/0.73 (~product(e_4, e_1, e_3)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[849, 23, 170, 259, 843, 833])).
% 0.54/0.73 tff(851,plain,
% 0.54/0.73 (((~![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_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, 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_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_1)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(852,plain,
% 0.54/0.73 (((~greater(e_1, e_0)) | (~cycle(e_4, e_1)) | equalish(e_1, e_5) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_1))) <=> (equalish(e_1, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_1)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(853,plain,
% 0.54/0.73 (((~![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_4, e_1)) | equalish(e_1, e_5) | (~next(e_4, e_5)) | (~product(e_4, 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_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_1))))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[852])).
% 0.54/0.73 tff(854,plain,
% 0.54/0.73 (((~![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_4, e_1)) | equalish(e_1, e_5) | (~next(e_4, e_5)) | (~product(e_4, 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_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_1)))),
% 0.54/0.73 inference(transitivity,[status(thm)],[853, 851])).
% 0.54/0.73 tff(855,plain,
% 0.54/0.73 ((~![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_4, e_1)) | equalish(e_1, e_5) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_1)))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(856,plain,
% 0.54/0.73 ((~![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_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_1))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[855, 854])).
% 0.54/0.73 tff(857,plain,
% 0.54/0.73 (~product(e_4, e_1, e_1)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[856, 23, 170, 259, 663, 833])).
% 0.54/0.73 tff(858,plain,
% 0.54/0.73 (((~![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_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, 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_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_2)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(859,plain,
% 0.54/0.73 (((~greater(e_1, e_0)) | (~cycle(e_4, e_1)) | equalish(e_2, e_5) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_2))) <=> (equalish(e_2, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_2)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(860,plain,
% 0.54/0.73 (((~![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_4, e_1)) | equalish(e_2, e_5) | (~next(e_4, e_5)) | (~product(e_4, 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_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_2))))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[859])).
% 0.54/0.73 tff(861,plain,
% 0.54/0.73 (((~![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_4, e_1)) | equalish(e_2, e_5) | (~next(e_4, e_5)) | (~product(e_4, 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_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_2)))),
% 0.54/0.73 inference(transitivity,[status(thm)],[860, 858])).
% 0.54/0.73 tff(862,plain,
% 0.54/0.73 ((~![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_4, e_1)) | equalish(e_2, e_5) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_2)))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(863,plain,
% 0.54/0.73 ((~![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_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_2))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[862, 861])).
% 0.54/0.73 tff(864,plain,
% 0.54/0.73 (~product(e_4, e_1, e_2)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[863, 23, 170, 259, 149, 833])).
% 0.54/0.73 tff(865,plain,
% 0.54/0.73 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(866,plain,
% 0.54/0.73 (((~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1))) <=> ((~group_element(e_1)) | (~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(867,plain,
% 0.54/0.73 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1)))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[866])).
% 0.54/0.73 tff(868,plain,
% 0.54/0.73 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1))),
% 0.54/0.73 inference(transitivity,[status(thm)],[867, 865])).
% 0.54/0.73 tff(869,plain,
% 0.54/0.73 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(870,plain,
% 0.54/0.73 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1)),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[869, 868])).
% 0.54/0.73 tff(871,plain,
% 0.54/0.73 (product(e_4, e_1, e_5)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[870, 413, 89, 410, 864, 857, 850, 840])).
% 0.54/0.73 tff(872,plain,
% 0.54/0.73 ((~equalish(e_3, e_4)) <=> (~equalish(e_3, e_4))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(873,axiom,(~equalish(e_3, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_4')).
% 0.54/0.73 tff(874,plain,
% 0.54/0.73 (~equalish(e_3, e_4)),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[873, 872])).
% 0.54/0.73 tff(875,plain,
% 0.54/0.73 (((~![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_4) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(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_3, e_4) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_3)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(876,plain,
% 0.54/0.73 (((~cycle(e_2, e_3)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~greater(e_3, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_3))) <=> (equalish(e_3, e_4) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_3)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(877,plain,
% 0.54/0.73 (((~![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_3)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~greater(e_3, 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_3, e_4) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_3))))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[876])).
% 0.54/0.73 tff(878,plain,
% 0.54/0.73 (((~![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_3)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~greater(e_3, 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_3, e_4) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_3)))),
% 0.54/0.73 inference(transitivity,[status(thm)],[877, 875])).
% 0.54/0.73 tff(879,plain,
% 0.54/0.73 ((~![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_3)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~greater(e_3, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_3)))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(880,plain,
% 0.54/0.73 ((~![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_4) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_3))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[879, 878])).
% 0.54/0.73 tff(881,plain,
% 0.54/0.73 (~cycle(e_3, e_3)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[880, 115, 112, 48, 45, 874, 824])).
% 0.54/0.73 tff(882,plain,
% 0.54/0.73 (((~![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_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_3, e_1)) | (~cycle(e_2, 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_3, e_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_3, e_1)) | (~cycle(e_2, e_3)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(883,plain,
% 0.54/0.73 (((~cycle(e_2, e_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_1))) <=> (equalish(e_3, e_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_3, e_1)) | (~cycle(e_2, e_3)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(884,plain,
% 0.54/0.74 (((~![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_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, 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_3, e_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_3, e_1)) | (~cycle(e_2, e_3))))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[883])).
% 0.54/0.74 tff(885,plain,
% 0.54/0.74 (((~![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_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, 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_3, e_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_3, e_1)) | (~cycle(e_2, e_3)))),
% 0.54/0.74 inference(transitivity,[status(thm)],[884, 882])).
% 0.54/0.74 tff(886,plain,
% 0.54/0.74 ((~![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_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_1)))),
% 0.54/0.74 inference(quant_inst,[status(thm)],[])).
% 0.54/0.74 tff(887,plain,
% 0.54/0.74 ((~![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_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_3, e_1)) | (~cycle(e_2, e_3))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[886, 885])).
% 0.54/0.74 tff(888,plain,
% 0.54/0.74 (~cycle(e_3, e_1)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[887, 173, 115, 48, 45, 236, 824])).
% 0.54/0.74 tff(889,plain,
% 0.54/0.74 (((~![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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3)) | (~cycle(e_4, 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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3)) | (~cycle(e_4, e_1)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(890,plain,
% 0.54/0.74 (((~greater(e_3, e_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_3))) <=> ((~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3)) | (~cycle(e_4, e_1)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(891,plain,
% 0.54/0.74 (((~![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_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3)) | (~cycle(e_4, e_1))))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[890])).
% 0.54/0.74 tff(892,plain,
% 0.54/0.74 (((~![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_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3)) | (~cycle(e_4, e_1)))),
% 0.54/0.74 inference(transitivity,[status(thm)],[891, 889])).
% 0.54/0.74 tff(893,plain,
% 0.54/0.74 ((~![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_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_3)))),
% 0.54/0.74 inference(quant_inst,[status(thm)],[])).
% 0.54/0.74 tff(894,plain,
% 0.54/0.74 ((~![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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3)) | (~cycle(e_4, e_1))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[893, 892])).
% 0.54/0.74 tff(895,plain,
% 0.54/0.74 ((~cycle(e_3, e_0)) | (~cycle(e_2, e_3)) | (~cycle(e_4, e_1))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[894, 112, 512, 135, 11])).
% 0.54/0.74 tff(896,plain,
% 0.54/0.74 (~cycle(e_3, e_0)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[895, 833, 824])).
% 0.54/0.74 tff(897,plain,
% 0.54/0.74 (((~![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_5) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_4)))) <=> ((~![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_5) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_4)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(898,plain,
% 0.54/0.74 (((~cycle(e_2, e_3)) | equalish(e_3, e_5) | (~next(e_4, e_5)) | (~greater(e_3, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_4))) <=> (equalish(e_3, e_5) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_4)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(899,plain,
% 0.54/0.74 (((~![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_3)) | equalish(e_3, e_5) | (~next(e_4, e_5)) | (~greater(e_3, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_4)))) <=> ((~![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_5) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_4))))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[898])).
% 0.54/0.74 tff(900,plain,
% 0.54/0.74 (((~![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_3)) | equalish(e_3, e_5) | (~next(e_4, e_5)) | (~greater(e_3, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_4)))) <=> ((~![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_5) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_4)))),
% 0.54/0.74 inference(transitivity,[status(thm)],[899, 897])).
% 0.54/0.74 tff(901,plain,
% 0.54/0.74 ((~![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_3)) | equalish(e_3, e_5) | (~next(e_4, e_5)) | (~greater(e_3, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_4)))),
% 0.54/0.74 inference(quant_inst,[status(thm)],[])).
% 0.54/0.74 tff(902,plain,
% 0.54/0.74 ((~![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_5) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_4))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[901, 900])).
% 0.54/0.74 tff(903,plain,
% 0.54/0.74 (~cycle(e_3, e_4)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[902, 115, 23, 48, 45, 843, 824])).
% 0.54/0.74 tff(904,plain,
% 0.54/0.74 (cycle(e_3, e_2)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[163, 903, 896, 888, 881])).
% 0.54/0.74 tff(905,plain,
% 0.54/0.74 (((~![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_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~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_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_1)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(906,plain,
% 0.54/0.74 (((~greater(e_2, e_0)) | (~cycle(e_3, e_2)) | equalish(e_1, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_1))) <=> (equalish(e_1, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_1)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(907,plain,
% 0.54/0.74 (((~![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_3, e_2)) | 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_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_1))))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[906])).
% 0.54/0.74 tff(908,plain,
% 0.54/0.74 (((~![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_3, e_2)) | 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_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_1)))),
% 0.54/0.74 inference(transitivity,[status(thm)],[907, 905])).
% 0.54/0.74 tff(909,plain,
% 0.54/0.74 ((~![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_3, e_2)) | equalish(e_1, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_1)))),
% 0.54/0.74 inference(quant_inst,[status(thm)],[])).
% 0.54/0.74 tff(910,plain,
% 0.54/0.74 ((~![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_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_1))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[909, 908])).
% 0.54/0.74 tff(911,plain,
% 0.54/0.74 (~product(e_3, e_1, e_1)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[910, 112, 20, 259, 639, 904])).
% 0.54/0.74 tff(912,plain,
% 0.54/0.74 ((~equalish(e_5, e_4)) <=> (~equalish(e_5, e_4))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(913,axiom,(~equalish(e_5, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_is_not_e_4')).
% 0.54/0.74 tff(914,plain,
% 0.54/0.74 (~equalish(e_5, e_4)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[913, 912])).
% 0.54/0.74 tff(915,plain,
% 0.54/0.74 (((~![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_5, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_5)))) <=> ((~![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_5, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_5)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(916,plain,
% 0.54/0.74 (((~greater(e_2, e_0)) | (~cycle(e_3, e_2)) | equalish(e_5, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5))) <=> (equalish(e_5, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_5)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(917,plain,
% 0.54/0.74 (((~![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_3, e_2)) | equalish(e_5, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5)))) <=> ((~![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_5, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_5))))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[916])).
% 0.54/0.74 tff(918,plain,
% 0.54/0.74 (((~![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_3, e_2)) | equalish(e_5, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5)))) <=> ((~![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_5, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_5)))),
% 0.54/0.74 inference(transitivity,[status(thm)],[917, 915])).
% 0.54/0.74 tff(919,plain,
% 0.54/0.74 ((~![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_3, e_2)) | equalish(e_5, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5)))),
% 0.54/0.74 inference(quant_inst,[status(thm)],[])).
% 0.54/0.74 tff(920,plain,
% 0.54/0.74 ((~![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_5, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_5))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[919, 918])).
% 0.54/0.74 tff(921,plain,
% 0.54/0.74 (~product(e_3, e_1, e_5)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[920, 112, 20, 259, 914, 904])).
% 0.54/0.74 tff(922,plain,
% 0.54/0.74 (~product(e_3, e_1, e_2)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[802, 619, 793])).
% 0.54/0.74 tff(923,plain,
% 0.54/0.74 (~product(e_3, e_1, e_3)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[810, 619])).
% 0.54/0.74 tff(924,plain,
% 0.54/0.74 (product(e_3, e_1, e_4) | product(e_3, e_1, e_5) | product(e_3, e_1, e_1)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[817, 413, 159, 410, 923, 922])).
% 0.54/0.74 tff(925,plain,
% 0.54/0.74 (product(e_3, e_1, e_4)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[924, 921, 911])).
% 0.54/0.74 tff(926,assumption,(~product(e_3, e_4, e_5)), introduced(assumption)).
% 0.54/0.74 tff(927,assumption,(product(e_4, e_1, e_5)), introduced(assumption)).
% 0.54/0.74 tff(928,assumption,(product(e_3, e_1, e_4)), introduced(assumption)).
% 0.54/0.74 tff(929,plain,
% 0.54/0.74 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_5)) | product(e_3, e_4, e_5))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_5)) | product(e_3, e_4, e_5))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(930,plain,
% 0.54/0.74 ((product(e_3, e_4, e_5) | (~product(e_4, e_1, e_5)) | (~product(e_3, e_1, e_4))) <=> ((~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_5)) | product(e_3, e_4, e_5))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(931,plain,
% 0.54/0.74 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_4, e_5) | (~product(e_4, e_1, e_5)) | (~product(e_3, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_5)) | product(e_3, e_4, e_5)))),
% 0.54/0.75 inference(monotonicity,[status(thm)],[930])).
% 0.54/0.75 tff(932,plain,
% 0.54/0.75 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_4, e_5) | (~product(e_4, e_1, e_5)) | (~product(e_3, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_5)) | product(e_3, e_4, e_5))),
% 0.54/0.75 inference(transitivity,[status(thm)],[931, 929])).
% 0.54/0.75 tff(933,plain,
% 0.54/0.75 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_4, e_5) | (~product(e_4, e_1, e_5)) | (~product(e_3, e_1, e_4)))),
% 0.54/0.75 inference(quant_inst,[status(thm)],[])).
% 0.54/0.75 tff(934,plain,
% 0.54/0.75 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_5)) | product(e_3, e_4, e_5)),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[933, 932])).
% 0.54/0.75 tff(935,plain,
% 0.54/0.75 ($false),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[934, 374, 928, 927, 926])).
% 0.54/0.75 tff(936,plain,(product(e_3, e_4, e_5) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.75 tff(937,plain,
% 0.54/0.75 (product(e_3, e_4, e_5)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[936, 925, 871])).
% 0.54/0.75 tff(938,plain,
% 0.54/0.75 (~product(e_2, e_1, e_4)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[362, 181])).
% 0.54/0.75 tff(939,plain,
% 0.54/0.75 (~product(e_2, e_1, e_1)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[434, 824])).
% 0.54/0.75 tff(940,plain,
% 0.54/0.75 ((~cycle(e_1, e_1)) | product(e_2, e_1, e_1) | cycle(e_2, e_2)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[762, 324, 244])).
% 0.54/0.75 tff(941,plain,
% 0.54/0.75 (~cycle(e_1, e_1)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[940, 939, 181])).
% 0.54/0.75 tff(942,plain,
% 0.54/0.75 (((~![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_4) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_2)) | (~cycle(e_2, 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_2, e_4) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_2)) | (~cycle(e_2, e_3)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(943,plain,
% 0.54/0.75 (((~cycle(e_1, e_2)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~greater(e_2, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_3))) <=> (equalish(e_2, e_4) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_2)) | (~cycle(e_2, e_3)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(944,plain,
% 0.54/0.75 (((~![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_1, e_2)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~greater(e_2, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, 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_2, e_4) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_2)) | (~cycle(e_2, e_3))))),
% 0.54/0.75 inference(monotonicity,[status(thm)],[943])).
% 0.54/0.75 tff(945,plain,
% 0.54/0.75 (((~![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_1, e_2)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~greater(e_2, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, 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_2, e_4) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_2)) | (~cycle(e_2, e_3)))),
% 0.54/0.75 inference(transitivity,[status(thm)],[944, 942])).
% 0.54/0.75 tff(946,plain,
% 0.54/0.75 ((~![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_1, e_2)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~greater(e_2, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_3)))),
% 0.54/0.75 inference(quant_inst,[status(thm)],[])).
% 0.54/0.75 tff(947,plain,
% 0.54/0.75 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_4) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_2)) | (~cycle(e_2, e_3))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[946, 945])).
% 0.54/0.75 tff(948,plain,
% 0.54/0.75 ($false),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[947, 173, 112, 20, 45, 109, 437, 423])).
% 0.54/0.75 tff(949,plain,((~cycle(e_1, e_2)) | (~cycle(e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.75 tff(950,plain,
% 0.54/0.75 (~cycle(e_1, e_2)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[949, 824])).
% 0.54/0.75 tff(951,plain,
% 0.54/0.75 (((~![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_4) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_3)) | (~cycle(e_2, 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_3, e_4) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_3)) | (~cycle(e_2, e_3)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(952,plain,
% 0.54/0.75 (((~cycle(e_1, e_3)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~greater(e_3, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_3))) <=> (equalish(e_3, e_4) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_3)) | (~cycle(e_2, e_3)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(953,plain,
% 0.54/0.75 (((~![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_1, e_3)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~greater(e_3, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, 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_3, e_4) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_3)) | (~cycle(e_2, e_3))))),
% 0.54/0.75 inference(monotonicity,[status(thm)],[952])).
% 0.54/0.75 tff(954,plain,
% 0.54/0.75 (((~![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_1, e_3)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~greater(e_3, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, 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_3, e_4) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_3)) | (~cycle(e_2, e_3)))),
% 0.54/0.75 inference(transitivity,[status(thm)],[953, 951])).
% 0.54/0.75 tff(955,plain,
% 0.54/0.75 ((~![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_1, e_3)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~greater(e_3, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_3)))),
% 0.54/0.75 inference(quant_inst,[status(thm)],[])).
% 0.54/0.75 tff(956,plain,
% 0.54/0.75 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_4) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_3)) | (~cycle(e_2, e_3))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[955, 954])).
% 0.54/0.75 tff(957,plain,
% 0.54/0.75 ($false),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[956, 173, 112, 48, 45, 874, 447, 423])).
% 0.54/0.75 tff(958,plain,((~cycle(e_1, e_3)) | (~cycle(e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.75 tff(959,plain,
% 0.54/0.75 (~cycle(e_1, e_3)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[958, 824])).
% 0.54/0.75 tff(960,assumption,(product(e_5, e_1, e_5)), introduced(assumption)).
% 0.54/0.75 tff(961,plain,
% 0.54/0.75 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_4) | (~product(e_5, e_1, e_5)) | (~product(e_4, e_1, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_4) | (~product(e_5, e_1, e_5)) | (~product(e_4, e_1, e_5)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(962,plain,
% 0.54/0.75 ((equalish(e_5, e_4) | (~product(e_4, e_1, e_5)) | (~product(e_5, e_1, e_5))) <=> (equalish(e_5, e_4) | (~product(e_5, e_1, e_5)) | (~product(e_4, e_1, e_5)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(963,plain,
% 0.54/0.75 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_4) | (~product(e_4, e_1, e_5)) | (~product(e_5, e_1, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_4) | (~product(e_5, e_1, e_5)) | (~product(e_4, e_1, e_5))))),
% 0.54/0.75 inference(monotonicity,[status(thm)],[962])).
% 0.54/0.75 tff(964,plain,
% 0.54/0.75 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_4) | (~product(e_4, e_1, e_5)) | (~product(e_5, e_1, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_4) | (~product(e_5, e_1, e_5)) | (~product(e_4, e_1, e_5)))),
% 0.54/0.75 inference(transitivity,[status(thm)],[963, 961])).
% 0.54/0.75 tff(965,plain,
% 0.54/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_4) | (~product(e_4, e_1, e_5)) | (~product(e_5, e_1, e_5)))),
% 0.54/0.75 inference(quant_inst,[status(thm)],[])).
% 0.54/0.75 tff(966,plain,
% 0.54/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_4) | (~product(e_5, e_1, e_5)) | (~product(e_4, e_1, e_5))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[965, 964])).
% 0.54/0.75 tff(967,plain,
% 0.54/0.75 ($false),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[966, 914, 493, 960, 927])).
% 0.54/0.75 tff(968,plain,((~product(e_5, e_1, e_5)) | (~product(e_4, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.75 tff(969,plain,
% 0.54/0.75 (~product(e_5, e_1, e_5)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[968, 871])).
% 0.54/0.75 tff(970,assumption,(product(e_5, e_1, e_4)), introduced(assumption)).
% 0.54/0.75 tff(971,plain,
% 0.54/0.75 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_5, e_1, e_4)) | (~product(e_3, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_3) | (~product(e_5, e_1, e_4)) | (~product(e_3, e_1, e_4)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(972,plain,
% 0.54/0.75 ((equalish(e_5, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_5, e_1, e_4))) <=> (equalish(e_5, e_3) | (~product(e_5, e_1, e_4)) | (~product(e_3, e_1, e_4)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(973,plain,
% 0.54/0.75 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_5, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_5, e_1, e_4)) | (~product(e_3, e_1, e_4))))),
% 0.54/0.75 inference(monotonicity,[status(thm)],[972])).
% 0.54/0.75 tff(974,plain,
% 0.54/0.75 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_5, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_3) | (~product(e_5, e_1, e_4)) | (~product(e_3, e_1, e_4)))),
% 0.54/0.75 inference(transitivity,[status(thm)],[973, 971])).
% 0.54/0.75 tff(975,plain,
% 0.54/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_5, e_1, e_4)))),
% 0.54/0.75 inference(quant_inst,[status(thm)],[])).
% 0.54/0.75 tff(976,plain,
% 0.54/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_3) | (~product(e_5, e_1, e_4)) | (~product(e_3, e_1, e_4))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[975, 974])).
% 0.54/0.75 tff(977,plain,
% 0.54/0.75 ($false),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[976, 249, 493, 970, 928])).
% 0.54/0.75 tff(978,plain,((~product(e_5, e_1, e_4)) | (~product(e_3, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.75 tff(979,plain,
% 0.54/0.75 (~product(e_5, e_1, e_4)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[978, 925])).
% 0.54/0.75 tff(980,assumption,(product(e_1, e_1, e_2)), introduced(assumption)).
% 0.54/0.75 tff(981,assumption,(product(e_5, e_1, e_2)), introduced(assumption)).
% 0.54/0.75 tff(982,plain,
% 0.54/0.75 ((~equalish(e_5, e_1)) <=> (~equalish(e_5, e_1))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(983,axiom,(~equalish(e_5, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_is_not_e_1')).
% 0.54/0.75 tff(984,plain,
% 0.54/0.75 (~equalish(e_5, e_1)),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[983, 982])).
% 0.54/0.75 tff(985,plain,
% 0.54/0.75 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_5, e_1, e_2)) | (~product(e_1, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_1) | (~product(e_5, e_1, e_2)) | (~product(e_1, e_1, e_2)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(986,plain,
% 0.54/0.75 ((equalish(e_5, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_5, e_1, e_2))) <=> (equalish(e_5, e_1) | (~product(e_5, e_1, e_2)) | (~product(e_1, e_1, e_2)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(987,plain,
% 0.54/0.75 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_5, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_5, e_1, e_2)) | (~product(e_1, e_1, e_2))))),
% 0.54/0.75 inference(monotonicity,[status(thm)],[986])).
% 0.54/0.75 tff(988,plain,
% 0.54/0.75 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_5, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_1) | (~product(e_5, e_1, e_2)) | (~product(e_1, e_1, e_2)))),
% 0.54/0.75 inference(transitivity,[status(thm)],[987, 985])).
% 0.54/0.75 tff(989,plain,
% 0.54/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_5, e_1, e_2)))),
% 0.54/0.75 inference(quant_inst,[status(thm)],[])).
% 0.54/0.75 tff(990,plain,
% 0.54/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_1) | (~product(e_5, e_1, e_2)) | (~product(e_1, e_1, e_2))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[989, 988])).
% 0.54/0.75 tff(991,plain,
% 0.54/0.75 ($false),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[990, 984, 493, 981, 980])).
% 0.54/0.75 tff(992,plain,((~product(e_5, e_1, e_2)) | (~product(e_1, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.75 tff(993,plain,
% 0.54/0.75 (~product(e_5, e_1, e_2)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[992, 980])).
% 0.54/0.75 tff(994,assumption,(~product(e_5, e_1, e_4)), introduced(assumption)).
% 0.54/0.75 tff(995,assumption,(~product(e_5, e_1, e_5)), introduced(assumption)).
% 0.54/0.75 tff(996,assumption,(product(e_5, e_1, e_3)), introduced(assumption)).
% 0.54/0.75 tff(997,plain,
% 0.54/0.75 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_5, e_1, e_3)) | (~product(e_2, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_2) | (~product(e_5, e_1, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(998,plain,
% 0.54/0.76 ((equalish(e_5, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_5, e_1, e_3))) <=> (equalish(e_5, e_2) | (~product(e_5, e_1, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(999,plain,
% 0.54/0.76 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_5, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_5, e_1, e_3)) | (~product(e_2, e_1, e_3))))),
% 0.54/0.76 inference(monotonicity,[status(thm)],[998])).
% 0.54/0.76 tff(1000,plain,
% 0.54/0.76 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_5, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_2) | (~product(e_5, e_1, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.54/0.76 inference(transitivity,[status(thm)],[999, 997])).
% 0.54/0.76 tff(1001,plain,
% 0.54/0.76 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_5, e_1, e_3)))),
% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(1002,plain,
% 0.54/0.76 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_2) | (~product(e_5, e_1, e_3)) | (~product(e_2, e_1, e_3))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1001, 1000])).
% 0.54/0.76 tff(1003,plain,
% 0.54/0.76 ($false),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[1002, 553, 493, 996, 619])).
% 0.54/0.76 tff(1004,plain,(~product(e_5, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.76 tff(1005,plain,
% 0.54/0.76 (group_element(e_5) <=> group_element(e_5)),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1006,axiom,(group_element(e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_5')).
% 0.54/0.76 tff(1007,plain,
% 0.54/0.76 (group_element(e_5)),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1006, 1005])).
% 0.54/0.76 tff(1008,plain,
% 0.54/0.76 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (product(e_5, e_1, e_1) | product(e_5, e_1, e_2) | product(e_5, e_1, e_3) | product(e_5, e_1, e_4) | product(e_5, e_1, e_5) | (~group_element(e_1)) | (~group_element(e_5)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | product(e_5, e_1, e_1) | product(e_5, e_1, e_2) | product(e_5, e_1, e_3) | product(e_5, e_1, e_4) | product(e_5, e_1, e_5) | (~group_element(e_1)) | (~group_element(e_5)))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1009,plain,
% 0.54/0.76 (((~group_element(e_5)) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | (~group_element(e_1))) <=> (product(e_5, e_1, e_1) | product(e_5, e_1, e_2) | product(e_5, e_1, e_3) | product(e_5, e_1, e_4) | product(e_5, e_1, e_5) | (~group_element(e_1)) | (~group_element(e_5)))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1010,plain,
% 0.54/0.76 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_5)) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (product(e_5, e_1, e_1) | product(e_5, e_1, e_2) | product(e_5, e_1, e_3) | product(e_5, e_1, e_4) | product(e_5, e_1, e_5) | (~group_element(e_1)) | (~group_element(e_5))))),
% 0.54/0.76 inference(monotonicity,[status(thm)],[1009])).
% 0.54/0.76 tff(1011,plain,
% 0.54/0.76 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_5)) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | product(e_5, e_1, e_1) | product(e_5, e_1, e_2) | product(e_5, e_1, e_3) | product(e_5, e_1, e_4) | product(e_5, e_1, e_5) | (~group_element(e_1)) | (~group_element(e_5)))),
% 0.54/0.76 inference(transitivity,[status(thm)],[1010, 1008])).
% 0.54/0.76 tff(1012,plain,
% 0.54/0.76 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_5)) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | (~group_element(e_1)))),
% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(1013,plain,
% 0.54/0.76 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | product(e_5, e_1, e_1) | product(e_5, e_1, e_2) | product(e_5, e_1, e_3) | product(e_5, e_1, e_4) | product(e_5, e_1, e_5) | (~group_element(e_1)) | (~group_element(e_5))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1012, 1011])).
% 0.54/0.76 tff(1014,plain,
% 0.54/0.76 (product(e_5, e_1, e_1) | product(e_5, e_1, e_2) | product(e_5, e_1, e_3) | product(e_5, e_1, e_4) | product(e_5, e_1, e_5)),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[1013, 413, 1007, 410])).
% 0.54/0.76 tff(1015,plain,
% 0.54/0.76 (product(e_5, e_1, e_1)),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[1014, 993, 1004, 995, 994])).
% 0.54/0.76 tff(1016,plain,
% 0.54/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_5, e_1, e_1)) | product(e_5, e_1, e_2) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_5, e_1, e_1)) | product(e_5, e_1, e_2) | (~product(e_1, e_1, e_2)))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1017,plain,
% 0.54/0.76 ((product(e_5, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_5, e_1, e_1))) <=> ((~product(e_5, e_1, e_1)) | product(e_5, e_1, e_2) | (~product(e_1, e_1, e_2)))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1018,plain,
% 0.54/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_5, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_5, e_1, e_1)) | product(e_5, e_1, e_2) | (~product(e_1, e_1, e_2))))),
% 0.54/0.76 inference(monotonicity,[status(thm)],[1017])).
% 0.54/0.76 tff(1019,plain,
% 0.54/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_5, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_5, e_1, e_1)) | product(e_5, e_1, e_2) | (~product(e_1, e_1, e_2)))),
% 0.54/0.76 inference(transitivity,[status(thm)],[1018, 1016])).
% 0.54/0.76 tff(1020,plain,
% 0.54/0.76 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_5, e_1, e_1)))),
% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(1021,plain,
% 0.54/0.76 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_5, e_1, e_1)) | product(e_5, e_1, e_2) | (~product(e_1, e_1, e_2))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1020, 1019])).
% 0.54/0.76 tff(1022,plain,
% 0.54/0.76 ($false),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[1021, 374, 1015, 993, 980])).
% 0.54/0.76 tff(1023,plain,((~product(e_1, e_1, e_2)) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.76 tff(1024,plain,
% 0.54/0.76 (~product(e_1, e_1, e_2)),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[1023, 979, 969])).
% 0.54/0.76 tff(1025,assumption,(~product(e_1, e_1, e_2)), introduced(assumption)).
% 0.54/0.76 tff(1026,plain,
% 0.54/0.76 (((~![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_5, e_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | (~product(e_1, e_1, e_5)))) <=> ((~![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_5, e_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | (~product(e_1, e_1, e_5)))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1027,plain,
% 0.54/0.76 (((~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | equalish(e_5, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_5))) <=> (equalish(e_5, e_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | (~product(e_1, e_1, e_5)))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1028,plain,
% 0.54/0.76 (((~![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_4, e_0)) | (~cycle(e_1, e_4)) | equalish(e_5, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_5)))) <=> ((~![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_5, e_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | (~product(e_1, e_1, e_5))))),
% 0.54/0.76 inference(monotonicity,[status(thm)],[1027])).
% 0.54/0.76 tff(1029,plain,
% 0.54/0.76 (((~![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_4, e_0)) | (~cycle(e_1, e_4)) | equalish(e_5, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_5)))) <=> ((~![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_5, e_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | (~product(e_1, e_1, e_5)))),
% 0.54/0.76 inference(transitivity,[status(thm)],[1028, 1026])).
% 0.54/0.76 tff(1030,plain,
% 0.54/0.76 ((~![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_4, e_0)) | (~cycle(e_1, e_4)) | equalish(e_5, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_5)))),
% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(1031,plain,
% 0.54/0.76 ((~![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_5, e_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | (~product(e_1, e_1, e_5))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1030, 1029])).
% 0.54/0.76 tff(1032,plain,
% 0.54/0.76 (~product(e_1, e_1, e_5)),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[1031, 173, 78, 259, 553, 674])).
% 0.54/0.76 tff(1033,plain,
% 0.54/0.76 (((~![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_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | (~product(e_1, 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_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | (~product(e_1, e_1, e_3)))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1034,plain,
% 0.54/0.76 (((~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3))) <=> (equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | (~product(e_1, e_1, e_3)))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1035,plain,
% 0.54/0.76 (((~![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_4, e_0)) | (~cycle(e_1, e_4)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~product(e_1, 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_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | (~product(e_1, e_1, e_3))))),
% 0.54/0.76 inference(monotonicity,[status(thm)],[1034])).
% 0.54/0.76 tff(1036,plain,
% 0.54/0.76 (((~![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_4, e_0)) | (~cycle(e_1, e_4)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~product(e_1, 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_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | (~product(e_1, e_1, e_3)))),
% 0.54/0.76 inference(transitivity,[status(thm)],[1035, 1033])).
% 0.54/0.76 tff(1037,plain,
% 0.54/0.76 ((~![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_4, e_0)) | (~cycle(e_1, e_4)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))),
% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(1038,plain,
% 0.54/0.76 ((~![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_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | (~product(e_1, e_1, e_3))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1037, 1036])).
% 0.54/0.76 tff(1039,plain,
% 0.54/0.76 (~product(e_1, e_1, e_3)),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[1038, 173, 78, 259, 236, 674])).
% 0.54/0.76 tff(1040,plain,
% 0.54/0.76 (((~![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_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | (~product(e_1, 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_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | (~product(e_1, e_1, e_4)))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1041,plain,
% 0.54/0.76 (((~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_4))) <=> (equalish(e_4, e_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | (~product(e_1, e_1, e_4)))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1042,plain,
% 0.54/0.76 (((~![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_4, e_0)) | (~cycle(e_1, e_4)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~product(e_1, 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_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | (~product(e_1, e_1, e_4))))),
% 0.54/0.76 inference(monotonicity,[status(thm)],[1041])).
% 0.54/0.76 tff(1043,plain,
% 0.54/0.76 (((~![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_4, e_0)) | (~cycle(e_1, e_4)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~product(e_1, 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_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | (~product(e_1, e_1, e_4)))),
% 0.54/0.76 inference(transitivity,[status(thm)],[1042, 1040])).
% 0.54/0.76 tff(1044,plain,
% 0.54/0.76 ((~![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_4, e_0)) | (~cycle(e_1, e_4)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_4)))),
% 0.54/0.77 inference(quant_inst,[status(thm)],[])).
% 0.54/0.77 tff(1045,plain,
% 0.54/0.77 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | (~product(e_1, e_1, e_4))),
% 0.54/0.77 inference(modus_ponens,[status(thm)],[1044, 1043])).
% 0.54/0.77 tff(1046,plain,
% 0.54/0.77 (~product(e_1, e_1, e_4)),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[1045, 173, 78, 259, 204, 674])).
% 0.54/0.77 tff(1047,plain,
% 0.54/0.77 (product(e_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_5) | product(e_1, e_1, e_1)),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[538, 413, 410, 1025])).
% 0.54/0.77 tff(1048,plain,
% 0.54/0.77 ($false),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[1047, 1046, 1039, 1032, 509])).
% 0.54/0.77 tff(1049,plain,((~cycle(e_1, e_4)) | product(e_1, e_1, e_1) | product(e_1, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.77 tff(1050,plain,
% 0.54/0.77 (~cycle(e_1, e_4)),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[1049, 509, 1025])).
% 0.54/0.77 tff(1051,plain,
% 0.54/0.77 ($false),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[768, 1050, 509, 764, 458, 457])).
% 0.54/0.77 tff(1052,plain,(product(e_1, e_1, e_1) | cycle(e_1, e_1) | cycle(e_1, e_3) | cycle(e_1, e_2) | product(e_1, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.77 tff(1053,plain,
% 0.54/0.77 (product(e_1, e_1, e_1)),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[1052, 1024, 959, 950, 941])).
% 0.54/0.77 tff(1054,assumption,(product(e_1, e_4, e_1)), introduced(assumption)).
% 0.54/0.77 tff(1055,plain,
% 0.54/0.77 (((~![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_1, e_1, e_1)) | (~product(e_1, e_4, e_1)))) <=> ((~![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_1, e_1, e_1)) | (~product(e_1, e_4, e_1)))),
% 0.54/0.77 inference(rewrite,[status(thm)],[])).
% 0.54/0.77 tff(1056,plain,
% 0.54/0.77 ((~![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_1, e_1, e_1)) | (~product(e_1, e_4, e_1)))),
% 0.54/0.77 inference(quant_inst,[status(thm)],[])).
% 0.54/0.77 tff(1057,plain,
% 0.54/0.77 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1))),
% 0.54/0.77 inference(modus_ponens,[status(thm)],[1056, 1055])).
% 0.54/0.77 tff(1058,plain,
% 0.54/0.77 ($false),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[1057, 75, 392, 483, 1054])).
% 0.54/0.77 tff(1059,plain,((~product(e_1, e_4, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.77 tff(1060,plain,
% 0.54/0.77 (~product(e_1, e_4, e_1)),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[1059, 1053])).
% 0.54/0.77 tff(1061,assumption,(~product(e_2, e_3, e_4)), introduced(assumption)).
% 0.54/0.77 tff(1062,plain,
% 0.54/0.77 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_4)) | product(e_2, e_3, e_4))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_4)) | product(e_2, e_3, e_4))),
% 0.54/0.77 inference(rewrite,[status(thm)],[])).
% 0.54/0.77 tff(1063,plain,
% 0.54/0.77 ((product(e_2, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_2, e_1, e_3))) <=> ((~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_4)) | product(e_2, e_3, e_4))),
% 0.54/0.77 inference(rewrite,[status(thm)],[])).
% 0.54/0.77 tff(1064,plain,
% 0.54/0.77 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_4)) | product(e_2, e_3, e_4)))),
% 0.54/0.77 inference(monotonicity,[status(thm)],[1063])).
% 0.54/0.77 tff(1065,plain,
% 0.54/0.77 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_4)) | product(e_2, e_3, e_4))),
% 0.54/0.77 inference(transitivity,[status(thm)],[1064, 1062])).
% 0.54/0.77 tff(1066,plain,
% 0.54/0.77 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_2, e_1, e_3)))),
% 0.54/0.77 inference(quant_inst,[status(thm)],[])).
% 0.54/0.77 tff(1067,plain,
% 0.54/0.77 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_4)) | product(e_2, e_3, e_4)),
% 0.54/0.77 inference(modus_ponens,[status(thm)],[1066, 1065])).
% 0.54/0.77 tff(1068,plain,
% 0.54/0.77 ($false),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[1067, 374, 619, 928, 1061])).
% 0.54/0.77 tff(1069,plain,(product(e_2, e_3, e_4) | (~product(e_3, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.77 tff(1070,plain,
% 0.54/0.77 (product(e_2, e_3, e_4)),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[1069, 925])).
% 0.54/0.77 tff(1071,assumption,(product(e_2, e_4, e_4)), introduced(assumption)).
% 0.54/0.77 tff(1072,assumption,(product(e_2, e_3, e_4)), introduced(assumption)).
% 0.54/0.77 tff(1073,plain,
% 0.54/0.77 (((~![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_2, e_4, e_4)) | (~product(e_2, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_2, e_4, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.54/0.77 inference(rewrite,[status(thm)],[])).
% 0.54/0.77 tff(1074,plain,
% 0.54/0.77 ((equalish(e_4, e_3) | (~product(e_2, e_3, e_4)) | (~product(e_2, e_4, e_4))) <=> (equalish(e_4, e_3) | (~product(e_2, e_4, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.54/0.77 inference(rewrite,[status(thm)],[])).
% 0.54/0.77 tff(1075,plain,
% 0.54/0.77 (((~![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_2, e_3, e_4)) | (~product(e_2, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_2, e_4, e_4)) | (~product(e_2, e_3, e_4))))),
% 0.54/0.77 inference(monotonicity,[status(thm)],[1074])).
% 0.54/0.77 tff(1076,plain,
% 0.54/0.77 (((~![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_2, e_3, e_4)) | (~product(e_2, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_2, e_4, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.54/0.77 inference(transitivity,[status(thm)],[1075, 1073])).
% 0.54/0.77 tff(1077,plain,
% 0.54/0.77 ((~![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_2, e_3, e_4)) | (~product(e_2, e_4, e_4)))),
% 0.54/0.77 inference(quant_inst,[status(thm)],[])).
% 0.54/0.77 tff(1078,plain,
% 0.54/0.77 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_2, e_4, e_4)) | (~product(e_2, e_3, e_4))),
% 0.54/0.77 inference(modus_ponens,[status(thm)],[1077, 1076])).
% 0.54/0.77 tff(1079,plain,
% 0.54/0.77 ($false),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[1078, 194, 392, 1072, 1071])).
% 0.54/0.77 tff(1080,plain,((~product(e_2, e_4, e_4)) | (~product(e_2, e_3, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.77 tff(1081,plain,
% 0.54/0.77 (~product(e_2, e_4, e_4)),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[1080, 1070])).
% 0.54/0.77 tff(1082,assumption,(product(e_3, e_4, e_5)), introduced(assumption)).
% 0.54/0.77 tff(1083,assumption,(product(e_2, e_4, e_5)), introduced(assumption)).
% 0.54/0.77 tff(1084,plain,
% 0.54/0.77 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_4, e_5)) | (~product(e_2, e_4, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_4, e_5)) | (~product(e_2, e_4, e_5)))),
% 0.54/0.77 inference(rewrite,[status(thm)],[])).
% 0.54/0.77 tff(1085,plain,
% 0.54/0.77 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_4, e_5)) | (~product(e_2, e_4, e_5)))),
% 0.54/0.77 inference(quant_inst,[status(thm)],[])).
% 0.54/0.77 tff(1086,plain,
% 0.54/0.77 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_4, e_5)) | (~product(e_2, e_4, e_5))),
% 0.54/0.77 inference(modus_ponens,[status(thm)],[1085, 1084])).
% 0.54/0.77 tff(1087,plain,
% 0.54/0.77 ($false),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[1086, 125, 493, 1083, 1082])).
% 0.54/0.77 tff(1088,plain,((~product(e_2, e_4, e_5)) | (~product(e_3, e_4, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.77 tff(1089,plain,
% 0.54/0.77 (~product(e_2, e_4, e_5)),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[1088, 937])).
% 0.54/0.77 tff(1090,assumption,(product(e_2, e_4, e_2)), introduced(assumption)).
% 0.54/0.77 tff(1091,plain,
% 0.54/0.77 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_2) | (~product(e_2, e_4, e_2)))),
% 0.54/0.77 inference(rewrite,[status(thm)],[])).
% 0.54/0.77 tff(1092,plain,
% 0.54/0.77 ((product(e_2, e_2, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_2, e_4, e_2))) <=> (product(e_2, e_2, e_2) | (~product(e_2, e_4, e_2)))),
% 0.54/0.77 inference(rewrite,[status(thm)],[])).
% 0.54/0.77 tff(1093,plain,
% 0.54/0.77 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_2, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_4, e_2))))),
% 0.54/0.77 inference(monotonicity,[status(thm)],[1092])).
% 0.54/0.77 tff(1094,plain,
% 0.54/0.77 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_2, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_2) | (~product(e_2, e_4, e_2)))),
% 0.54/0.77 inference(transitivity,[status(thm)],[1093, 1091])).
% 0.54/0.77 tff(1095,plain,
% 0.54/0.77 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_2, e_4, e_2)))),
% 0.54/0.77 inference(quant_inst,[status(thm)],[])).
% 0.54/0.77 tff(1096,plain,
% 0.54/0.77 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_2) | (~product(e_2, e_4, e_2))),
% 0.54/0.77 inference(modus_ponens,[status(thm)],[1095, 1094])).
% 0.54/0.77 tff(1097,plain,
% 0.54/0.77 (product(e_2, e_2, e_2) | (~product(e_2, e_4, e_2))),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[1096, 374])).
% 0.54/0.77 tff(1098,plain,
% 0.54/0.77 (product(e_2, e_2, e_2)),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[1097, 1090])).
% 0.54/0.77 tff(1099,assumption,(product(e_2, e_2, e_2)), introduced(assumption)).
% 0.54/0.77 tff(1100,plain,
% 0.54/0.77 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2)))),
% 0.54/0.77 inference(rewrite,[status(thm)],[])).
% 0.54/0.77 tff(1101,plain,
% 0.54/0.77 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2)))),
% 0.54/0.77 inference(quant_inst,[status(thm)],[])).
% 0.54/0.77 tff(1102,plain,
% 0.54/0.77 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2))),
% 0.54/0.77 inference(modus_ponens,[status(thm)],[1101, 1100])).
% 0.54/0.77 tff(1103,plain,
% 0.54/0.77 ($false),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[1102, 204, 392, 1099, 1090])).
% 0.54/0.77 tff(1104,plain,((~product(e_2, e_4, e_2)) | (~product(e_2, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.77 tff(1105,plain,
% 0.54/0.77 ($false),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[1104, 1098, 1090])).
% 0.54/0.77 tff(1106,plain,(~product(e_2, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.77 tff(1107,assumption,(product(e_2, e_4, e_3)), introduced(assumption)).
% 0.54/0.77 tff(1108,plain,
% 0.54/0.77 (((~![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)))),
% 0.54/0.77 inference(rewrite,[status(thm)],[])).
% 0.54/0.77 tff(1109,plain,
% 0.54/0.77 ((~![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)))),
% 0.54/0.77 inference(quant_inst,[status(thm)],[])).
% 0.54/0.77 tff(1110,plain,
% 0.54/0.77 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3))),
% 0.54/0.77 inference(modus_ponens,[status(thm)],[1109, 1108])).
% 0.54/0.77 tff(1111,plain,
% 0.54/0.77 ($false),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[1110, 75, 392, 805, 1107])).
% 0.54/0.77 tff(1112,plain,((~product(e_2, e_4, e_3)) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.77 tff(1113,plain,
% 0.54/0.77 (~product(e_2, e_4, e_3)),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[1112, 619])).
% 0.54/0.77 tff(1114,plain,
% 0.54/0.77 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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)) | (~group_element(e_4)) | product(e_2, e_4, e_3) | product(e_2, e_4, e_1) | product(e_2, e_4, e_5) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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)) | (~group_element(e_4)) | product(e_2, e_4, e_3) | product(e_2, e_4, e_1) | product(e_2, e_4, e_5) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2))),
% 0.54/0.77 inference(rewrite,[status(thm)],[])).
% 0.54/0.77 tff(1115,plain,
% 0.54/0.77 (((~group_element(e_2)) | product(e_2, e_4, e_5) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4))) <=> ((~group_element(e_2)) | (~group_element(e_4)) | product(e_2, e_4, e_3) | product(e_2, e_4, e_1) | product(e_2, e_4, e_5) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2))),
% 0.54/0.77 inference(rewrite,[status(thm)],[])).
% 0.54/0.77 tff(1116,plain,
% 0.54/0.77 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_2, e_4, e_5) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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)) | (~group_element(e_4)) | product(e_2, e_4, e_3) | product(e_2, e_4, e_1) | product(e_2, e_4, e_5) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2)))),
% 0.54/0.77 inference(monotonicity,[status(thm)],[1115])).
% 0.54/0.77 tff(1117,plain,
% 0.54/0.77 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_2, e_4, e_5) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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)) | (~group_element(e_4)) | product(e_2, e_4, e_3) | product(e_2, e_4, e_1) | product(e_2, e_4, e_5) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2))),
% 0.54/0.77 inference(transitivity,[status(thm)],[1116, 1114])).
% 0.54/0.77 tff(1118,plain,
% 0.54/0.77 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_2, e_4, e_5) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)))),
% 0.54/0.77 inference(quant_inst,[status(thm)],[])).
% 0.54/0.77 tff(1119,plain,
% 0.54/0.77 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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)) | (~group_element(e_4)) | product(e_2, e_4, e_3) | product(e_2, e_4, e_1) | product(e_2, e_4, e_5) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2)),
% 0.54/0.78 inference(modus_ponens,[status(thm)],[1118, 1117])).
% 0.54/0.78 tff(1120,plain,
% 0.54/0.78 (product(e_2, e_4, e_3) | product(e_2, e_4, e_1) | product(e_2, e_4, e_5) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2)),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[1119, 302, 89, 410])).
% 0.54/0.78 tff(1121,plain,
% 0.54/0.78 (product(e_2, e_4, e_1) | product(e_2, e_4, e_5) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2)),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[1120, 1113])).
% 0.54/0.78 tff(1122,plain,
% 0.54/0.78 (product(e_2, e_4, e_1) | product(e_2, e_4, e_5) | product(e_2, e_4, e_4)),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[1121, 1106])).
% 0.54/0.78 tff(1123,plain,
% 0.54/0.78 (product(e_2, e_4, e_1)),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[1122, 1089, 1081])).
% 0.54/0.78 tff(1124,assumption,(product(e_2, e_4, e_1)), introduced(assumption)).
% 0.54/0.78 tff(1125,assumption,(product(e_1, e_4, e_5)), introduced(assumption)).
% 0.54/0.78 tff(1126,plain,
% 0.54/0.78 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_5) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_5)))),
% 0.54/0.78 inference(rewrite,[status(thm)],[])).
% 0.54/0.78 tff(1127,plain,
% 0.54/0.78 ((product(e_2, e_1, e_5) | (~product(e_1, e_4, e_5)) | (~product(e_2, e_4, e_1))) <=> (product(e_2, e_1, e_5) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_5)))),
% 0.54/0.78 inference(rewrite,[status(thm)],[])).
% 0.54/0.78 tff(1128,plain,
% 0.54/0.78 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_1, e_4, e_5)) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_5))))),
% 0.54/0.78 inference(monotonicity,[status(thm)],[1127])).
% 0.54/0.78 tff(1129,plain,
% 0.54/0.78 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_1, e_4, e_5)) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_5) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_5)))),
% 0.54/0.78 inference(transitivity,[status(thm)],[1128, 1126])).
% 0.54/0.78 tff(1130,plain,
% 0.54/0.78 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_1, e_4, e_5)) | (~product(e_2, e_4, e_1)))),
% 0.54/0.78 inference(quant_inst,[status(thm)],[])).
% 0.54/0.78 tff(1131,plain,
% 0.54/0.78 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_5) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_5))),
% 0.54/0.78 inference(modus_ponens,[status(thm)],[1130, 1129])).
% 0.54/0.78 tff(1132,plain,
% 0.54/0.78 ($false),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[1131, 374, 324, 1124, 1125])).
% 0.54/0.78 tff(1133,plain,((~product(e_1, e_4, e_5)) | (~product(e_2, e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.78 tff(1134,plain,
% 0.54/0.78 (~product(e_1, e_4, e_5)),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[1133, 1124])).
% 0.54/0.78 tff(1135,assumption,(~product(e_1, e_4, e_3)), introduced(assumption)).
% 0.54/0.78 tff(1136,assumption,(~product(e_1, e_4, e_1)), introduced(assumption)).
% 0.54/0.78 tff(1137,assumption,(product(e_1, e_4, e_2)), introduced(assumption)).
% 0.54/0.78 tff(1138,plain,
% 0.54/0.78 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_2) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_2)))),
% 0.54/0.78 inference(rewrite,[status(thm)],[])).
% 0.54/0.78 tff(1139,plain,
% 0.54/0.78 ((product(e_2, e_1, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_2, e_4, e_1))) <=> (product(e_2, e_1, e_2) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_2)))),
% 0.54/0.78 inference(rewrite,[status(thm)],[])).
% 0.54/0.78 tff(1140,plain,
% 0.54/0.78 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_2))))),
% 0.54/0.78 inference(monotonicity,[status(thm)],[1139])).
% 0.54/0.78 tff(1141,plain,
% 0.54/0.78 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_2) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_2)))),
% 0.54/0.78 inference(transitivity,[status(thm)],[1140, 1138])).
% 0.54/0.78 tff(1142,plain,
% 0.54/0.78 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_2, e_4, e_1)))),
% 0.54/0.78 inference(quant_inst,[status(thm)],[])).
% 0.54/0.78 tff(1143,plain,
% 0.54/0.78 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_2) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_2))),
% 0.54/0.78 inference(modus_ponens,[status(thm)],[1142, 1141])).
% 0.54/0.78 tff(1144,plain,
% 0.54/0.78 ($false),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[1143, 374, 400, 1124, 1137])).
% 0.54/0.78 tff(1145,plain,((~product(e_1, e_4, e_2)) | (~product(e_2, e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.78 tff(1146,plain,
% 0.54/0.78 (~product(e_1, e_4, e_2)),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[1145, 1124])).
% 0.54/0.78 tff(1147,plain,
% 0.54/0.78 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_4)) | product(e_1, e_4, e_3) | product(e_1, e_4, e_4) | product(e_1, e_4, e_2) | product(e_1, e_4, e_5) | product(e_1, e_4, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_4)) | product(e_1, e_4, e_3) | product(e_1, e_4, e_4) | product(e_1, e_4, e_2) | product(e_1, e_4, e_5) | product(e_1, e_4, e_1))),
% 0.54/0.78 inference(rewrite,[status(thm)],[])).
% 0.54/0.78 tff(1148,plain,
% 0.54/0.78 (((~group_element(e_1)) | product(e_1, e_4, e_5) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4))) <=> ((~group_element(e_1)) | (~group_element(e_4)) | product(e_1, e_4, e_3) | product(e_1, e_4, e_4) | product(e_1, e_4, e_2) | product(e_1, e_4, e_5) | product(e_1, e_4, e_1))),
% 0.54/0.78 inference(rewrite,[status(thm)],[])).
% 0.54/0.78 tff(1149,plain,
% 0.54/0.78 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_4, e_5) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_4)) | product(e_1, e_4, e_3) | product(e_1, e_4, e_4) | product(e_1, e_4, e_2) | product(e_1, e_4, e_5) | product(e_1, e_4, e_1)))),
% 0.54/0.78 inference(monotonicity,[status(thm)],[1148])).
% 0.54/0.78 tff(1150,plain,
% 0.54/0.78 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_4, e_5) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_4)) | product(e_1, e_4, e_3) | product(e_1, e_4, e_4) | product(e_1, e_4, e_2) | product(e_1, e_4, e_5) | product(e_1, e_4, e_1))),
% 0.54/0.78 inference(transitivity,[status(thm)],[1149, 1147])).
% 0.54/0.78 tff(1151,plain,
% 0.54/0.78 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_4, e_5) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4)))),
% 0.54/0.78 inference(quant_inst,[status(thm)],[])).
% 0.54/0.78 tff(1152,plain,
% 0.54/0.78 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_4)) | product(e_1, e_4, e_3) | product(e_1, e_4, e_4) | product(e_1, e_4, e_2) | product(e_1, e_4, e_5) | product(e_1, e_4, e_1)),
% 0.54/0.78 inference(modus_ponens,[status(thm)],[1151, 1150])).
% 0.54/0.78 tff(1153,plain,
% 0.54/0.78 (product(e_1, e_4, e_3) | product(e_1, e_4, e_4) | product(e_1, e_4, e_2) | product(e_1, e_4, e_5) | product(e_1, e_4, e_1)),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[1152, 413, 89, 410])).
% 0.54/0.78 tff(1154,plain,
% 0.54/0.78 (product(e_1, e_4, e_4)),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[1153, 1146, 1136, 1135, 1134])).
% 0.54/0.78 tff(1155,assumption,(~product(e_2, e_1, e_4)), introduced(assumption)).
% 0.54/0.78 tff(1156,plain,
% 0.54/0.78 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_4) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_4)))),
% 0.54/0.78 inference(rewrite,[status(thm)],[])).
% 0.54/0.78 tff(1157,plain,
% 0.54/0.78 ((product(e_2, e_1, e_4) | (~product(e_1, e_4, e_4)) | (~product(e_2, e_4, e_1))) <=> (product(e_2, e_1, e_4) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_4)))),
% 0.54/0.78 inference(rewrite,[status(thm)],[])).
% 0.54/0.78 tff(1158,plain,
% 0.54/0.78 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_4, e_4)) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_4))))),
% 0.54/0.78 inference(monotonicity,[status(thm)],[1157])).
% 0.54/0.78 tff(1159,plain,
% 0.54/0.78 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_4, e_4)) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_4) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_4)))),
% 0.54/0.78 inference(transitivity,[status(thm)],[1158, 1156])).
% 0.54/0.78 tff(1160,plain,
% 0.54/0.78 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_4, e_4)) | (~product(e_2, e_4, e_1)))),
% 0.54/0.78 inference(quant_inst,[status(thm)],[])).
% 0.54/0.78 tff(1161,plain,
% 0.54/0.78 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_4) | (~product(e_2, e_4, e_1)) | (~product(e_1, e_4, e_4))),
% 0.54/0.78 inference(modus_ponens,[status(thm)],[1160, 1159])).
% 0.54/0.78 tff(1162,plain,
% 0.54/0.78 ($false),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[1161, 374, 1155, 1124, 1154])).
% 0.54/0.78 tff(1163,plain,((~product(e_2, e_4, e_1)) | product(e_2, e_1, e_4) | product(e_1, e_4, e_1) | product(e_1, e_4, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.78 tff(1164,plain,
% 0.54/0.78 (product(e_1, e_4, e_3)),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[1163, 1123, 1060, 938])).
% 0.54/0.78 tff(1165,plain,
% 0.54/0.78 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_5) | (~product(e_3, e_4, e_5)) | (~product(e_1, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_5) | (~product(e_3, e_4, e_5)) | (~product(e_1, e_4, e_3)))),
% 0.54/0.78 inference(rewrite,[status(thm)],[])).
% 0.54/0.78 tff(1166,plain,
% 0.54/0.78 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_5) | (~product(e_3, e_4, e_5)) | (~product(e_1, e_4, e_3)))),
% 0.54/0.78 inference(quant_inst,[status(thm)],[])).
% 0.54/0.78 tff(1167,plain,
% 0.54/0.78 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_5) | (~product(e_3, e_4, e_5)) | (~product(e_1, e_4, e_3))),
% 0.54/0.78 inference(modus_ponens,[status(thm)],[1166, 1165])).
% 0.54/0.78 tff(1168,plain,
% 0.54/0.78 (product(e_1, e_3, e_5) | (~product(e_3, e_4, e_5)) | (~product(e_1, e_4, e_3))),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[1167, 374])).
% 0.54/0.78 tff(1169,plain,
% 0.54/0.78 (product(e_1, e_3, e_5)),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[1168, 1164, 937])).
% 0.54/0.78 tff(1170,assumption,(product(e_3, e_3, e_4)), introduced(assumption)).
% 0.54/0.78 tff(1171,plain,
% 0.54/0.78 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_3, e_3, e_4)) | (~product(e_2, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_3, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.54/0.78 inference(rewrite,[status(thm)],[])).
% 0.54/0.78 tff(1172,plain,
% 0.54/0.78 ((equalish(e_3, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_3, e_3, e_4))) <=> (equalish(e_3, e_2) | (~product(e_3, e_3, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.54/0.78 inference(rewrite,[status(thm)],[])).
% 0.54/0.78 tff(1173,plain,
% 0.54/0.78 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_3, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_3, e_3, e_4)) | (~product(e_2, e_3, e_4))))),
% 0.54/0.78 inference(monotonicity,[status(thm)],[1172])).
% 0.54/0.78 tff(1174,plain,
% 0.54/0.78 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_3, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_3, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.54/0.78 inference(transitivity,[status(thm)],[1173, 1171])).
% 0.54/0.78 tff(1175,plain,
% 0.54/0.78 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_3, e_3, e_4)))),
% 0.54/0.78 inference(quant_inst,[status(thm)],[])).
% 0.54/0.78 tff(1176,plain,
% 0.54/0.78 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_3, e_4)) | (~product(e_2, e_3, e_4))),
% 0.54/0.78 inference(modus_ponens,[status(thm)],[1175, 1174])).
% 0.54/0.78 tff(1177,plain,
% 0.54/0.78 ($false),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[1176, 236, 493, 1072, 1170])).
% 0.54/0.78 tff(1178,plain,((~product(e_3, e_3, e_4)) | (~product(e_2, e_3, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.78 tff(1179,plain,
% 0.54/0.78 (~product(e_3, e_3, e_4)),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[1178, 1070])).
% 0.54/0.78 tff(1180,assumption,(product(e_3, e_3, e_5)), introduced(assumption)).
% 0.54/0.78 tff(1181,plain,
% 0.54/0.78 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_4) | (~product(e_3, e_4, e_5)) | (~product(e_3, e_3, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_3, e_4, e_5)) | (~product(e_3, e_3, e_5)))),
% 0.54/0.78 inference(rewrite,[status(thm)],[])).
% 0.54/0.78 tff(1182,plain,
% 0.54/0.78 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_4) | (~product(e_3, e_4, e_5)) | (~product(e_3, e_3, e_5)))),
% 0.54/0.78 inference(quant_inst,[status(thm)],[])).
% 0.54/0.78 tff(1183,plain,
% 0.54/0.78 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_3, e_4, e_5)) | (~product(e_3, e_3, e_5))),
% 0.54/0.78 inference(modus_ponens,[status(thm)],[1182, 1181])).
% 0.54/0.78 tff(1184,plain,
% 0.54/0.78 ($false),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[1183, 874, 392, 1180, 1082])).
% 0.54/0.78 tff(1185,plain,((~product(e_3, e_3, e_5)) | (~product(e_3, e_4, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.78 tff(1186,plain,
% 0.54/0.78 (~product(e_3, e_3, e_5)),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[1185, 937])).
% 0.54/0.78 tff(1187,assumption,(product(e_5, e_1, e_1)), introduced(assumption)).
% 0.54/0.78 tff(1188,plain,
% 0.54/0.78 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_5, e_1, e_1)) | (~product(e_1, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_1) | (~product(e_5, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.54/0.78 inference(rewrite,[status(thm)],[])).
% 0.54/0.78 tff(1189,plain,
% 0.54/0.78 ((equalish(e_5, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_5, e_1, e_1))) <=> (equalish(e_5, e_1) | (~product(e_5, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.54/0.78 inference(rewrite,[status(thm)],[])).
% 0.54/0.78 tff(1190,plain,
% 0.54/0.78 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_5, 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_5, e_1) | (~product(e_5, e_1, e_1)) | (~product(e_1, e_1, e_1))))),
% 0.54/0.78 inference(monotonicity,[status(thm)],[1189])).
% 0.54/0.78 tff(1191,plain,
% 0.54/0.78 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_5, 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_5, e_1) | (~product(e_5, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.54/0.78 inference(transitivity,[status(thm)],[1190, 1188])).
% 0.54/0.78 tff(1192,plain,
% 0.54/0.78 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_5, e_1, e_1)))),
% 0.54/0.78 inference(quant_inst,[status(thm)],[])).
% 0.54/0.78 tff(1193,plain,
% 0.61/0.79 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_1) | (~product(e_5, e_1, e_1)) | (~product(e_1, e_1, e_1))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[1192, 1191])).
% 0.61/0.79 tff(1194,plain,
% 0.61/0.79 ($false),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[1193, 984, 493, 1187, 483])).
% 0.61/0.79 tff(1195,plain,((~product(e_5, e_1, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.61/0.79 tff(1196,plain,
% 0.61/0.79 (~product(e_5, e_1, e_1)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[1195, 1053])).
% 0.61/0.79 tff(1197,plain,
% 0.61/0.79 (product(e_5, e_1, e_1) | product(e_5, e_1, e_2) | product(e_5, e_1, e_4) | product(e_5, e_1, e_5)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[1014, 1004])).
% 0.61/0.79 tff(1198,plain,
% 0.61/0.79 (product(e_5, e_1, e_2)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[1197, 1196, 969, 979])).
% 0.61/0.79 tff(1199,assumption,(product(e_5, e_3, e_2)), introduced(assumption)).
% 0.61/0.79 tff(1200,plain,
% 0.61/0.79 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_5, e_1, e_2)) | (~product(e_5, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_5, e_1, e_2)) | (~product(e_5, e_3, e_2)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(1201,plain,
% 0.61/0.79 ((equalish(e_1, e_3) | (~product(e_5, e_3, e_2)) | (~product(e_5, e_1, e_2))) <=> (equalish(e_1, e_3) | (~product(e_5, e_1, e_2)) | (~product(e_5, e_3, e_2)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(1202,plain,
% 0.61/0.79 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_5, e_3, e_2)) | (~product(e_5, 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_3) | (~product(e_5, e_1, e_2)) | (~product(e_5, e_3, e_2))))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[1201])).
% 0.61/0.79 tff(1203,plain,
% 0.61/0.79 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_5, e_3, e_2)) | (~product(e_5, 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_3) | (~product(e_5, e_1, e_2)) | (~product(e_5, e_3, e_2)))),
% 0.61/0.79 inference(transitivity,[status(thm)],[1202, 1200])).
% 0.61/0.79 tff(1204,plain,
% 0.61/0.79 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_5, e_3, e_2)) | (~product(e_5, e_1, e_2)))),
% 0.61/0.79 inference(quant_inst,[status(thm)],[])).
% 0.61/0.79 tff(1205,plain,
% 0.61/0.79 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_5, e_1, e_2)) | (~product(e_5, e_3, e_2))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[1204, 1203])).
% 0.61/0.79 tff(1206,plain,
% 0.61/0.79 ($false),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[1205, 426, 392, 981, 1199])).
% 0.61/0.79 tff(1207,plain,((~product(e_5, e_1, e_2)) | (~product(e_5, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.61/0.79 tff(1208,plain,
% 0.61/0.79 (~product(e_5, e_3, e_2)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[1207, 1198])).
% 0.61/0.79 tff(1209,assumption,(product(e_5, e_3, e_4)), introduced(assumption)).
% 0.61/0.79 tff(1210,plain,
% 0.61/0.79 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_5, e_3, e_4)) | (~product(e_2, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_2) | (~product(e_5, e_3, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(1211,plain,
% 0.61/0.79 ((equalish(e_5, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_5, e_3, e_4))) <=> (equalish(e_5, e_2) | (~product(e_5, e_3, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(1212,plain,
% 0.61/0.79 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_5, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_5, e_3, e_4)) | (~product(e_2, e_3, e_4))))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[1211])).
% 0.61/0.79 tff(1213,plain,
% 0.61/0.79 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_5, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_2) | (~product(e_5, e_3, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.61/0.79 inference(transitivity,[status(thm)],[1212, 1210])).
% 0.61/0.79 tff(1214,plain,
% 0.61/0.79 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_5, e_3, e_4)))),
% 0.61/0.79 inference(quant_inst,[status(thm)],[])).
% 0.61/0.79 tff(1215,plain,
% 0.61/0.79 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_2) | (~product(e_5, e_3, e_4)) | (~product(e_2, e_3, e_4))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[1214, 1213])).
% 0.61/0.79 tff(1216,plain,
% 0.61/0.79 ($false),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[1215, 553, 493, 1209, 1072])).
% 0.61/0.79 tff(1217,plain,((~product(e_5, e_3, e_4)) | (~product(e_2, e_3, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.61/0.79 tff(1218,plain,
% 0.61/0.79 (~product(e_5, e_3, e_4)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[1217, 1070])).
% 0.61/0.79 tff(1219,assumption,(product(e_1, e_3, e_5)), introduced(assumption)).
% 0.61/0.79 tff(1220,assumption,(product(e_5, e_3, e_1)), introduced(assumption)).
% 0.61/0.79 tff(1221,plain,
% 0.61/0.79 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_1, e_5) | (~product(e_1, e_3, e_5)) | (~product(e_5, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_1, e_5) | (~product(e_1, e_3, e_5)) | (~product(e_5, e_3, e_1)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(1222,plain,
% 0.61/0.79 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_1, e_5) | (~product(e_1, e_3, e_5)) | (~product(e_5, e_3, e_1)))),
% 0.61/0.79 inference(quant_inst,[status(thm)],[])).
% 0.61/0.79 tff(1223,plain,
% 0.61/0.79 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_1, e_5) | (~product(e_1, e_3, e_5)) | (~product(e_5, e_3, e_1))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[1222, 1221])).
% 0.61/0.79 tff(1224,plain,
% 0.61/0.79 ($false),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[1223, 374, 995, 1220, 1219])).
% 0.61/0.79 tff(1225,plain,((~product(e_1, e_3, e_5)) | product(e_5, e_1, e_5) | (~product(e_5, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.61/0.79 tff(1226,plain,
% 0.61/0.79 (~product(e_5, e_3, e_1)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[1225, 1169, 969])).
% 0.61/0.79 tff(1227,assumption,(product(e_5, e_3, e_5)), introduced(assumption)).
% 0.61/0.79 tff(1228,plain,
% 0.61/0.79 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_5, e_3, e_5)) | product(e_5, e_5, e_5))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_5, e_3, e_5)) | product(e_5, e_5, e_5))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(1229,plain,
% 0.61/0.79 ((product(e_5, e_5, e_5) | (~product(e_5, e_3, e_5)) | (~product(e_5, e_3, e_5))) <=> ((~product(e_5, e_3, e_5)) | product(e_5, e_5, e_5))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(1230,plain,
% 0.61/0.79 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_5, e_5) | (~product(e_5, e_3, e_5)) | (~product(e_5, e_3, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_5, e_3, e_5)) | product(e_5, e_5, e_5)))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[1229])).
% 0.61/0.79 tff(1231,plain,
% 0.61/0.79 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_5, e_5) | (~product(e_5, e_3, e_5)) | (~product(e_5, e_3, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_5, e_3, e_5)) | product(e_5, e_5, e_5))),
% 0.61/0.79 inference(transitivity,[status(thm)],[1230, 1228])).
% 0.61/0.79 tff(1232,plain,
% 0.61/0.79 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_5, e_5) | (~product(e_5, e_3, e_5)) | (~product(e_5, e_3, e_5)))),
% 0.61/0.79 inference(quant_inst,[status(thm)],[])).
% 0.61/0.79 tff(1233,plain,
% 0.61/0.79 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_5, e_3, e_5)) | product(e_5, e_5, e_5)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[1232, 1231])).
% 0.61/0.79 tff(1234,plain,
% 0.61/0.79 ((~product(e_5, e_3, e_5)) | product(e_5, e_5, e_5)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[1233, 374])).
% 0.61/0.79 tff(1235,plain,
% 0.61/0.79 (product(e_5, e_5, e_5)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[1234, 1227])).
% 0.61/0.79 tff(1236,plain,
% 0.61/0.79 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_5, e_3, e_5)) | (~product(e_5, e_5, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_5) | (~product(e_5, e_3, e_5)) | (~product(e_5, e_5, e_5)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(1237,plain,
% 0.61/0.79 ((equalish(e_3, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_3, e_5))) <=> (equalish(e_3, e_5) | (~product(e_5, e_3, e_5)) | (~product(e_5, e_5, e_5)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(1238,plain,
% 0.61/0.79 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_3, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_5, e_3, e_5)) | (~product(e_5, e_5, e_5))))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[1237])).
% 0.61/0.79 tff(1239,plain,
% 0.61/0.79 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_3, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_5) | (~product(e_5, e_3, e_5)) | (~product(e_5, e_5, e_5)))),
% 0.61/0.79 inference(transitivity,[status(thm)],[1238, 1236])).
% 0.61/0.79 tff(1240,plain,
% 0.61/0.79 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_3, e_5)))),
% 0.61/0.79 inference(quant_inst,[status(thm)],[])).
% 0.61/0.79 tff(1241,plain,
% 0.61/0.79 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_5) | (~product(e_5, e_3, e_5)) | (~product(e_5, e_5, e_5))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[1240, 1239])).
% 0.61/0.79 tff(1242,plain,
% 0.61/0.79 ($false),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[1241, 843, 392, 1227, 1235])).
% 0.61/0.79 tff(1243,plain,(~product(e_5, e_3, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.61/0.79 tff(1244,plain,
% 0.61/0.79 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_5, e_3, e_1) | (~group_element(e_5)) | product(e_5, e_3, e_2) | product(e_5, e_3, e_4) | product(e_5, e_3, e_5) | product(e_5, e_3, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_5, e_3, e_1) | (~group_element(e_5)) | product(e_5, e_3, e_2) | product(e_5, e_3, e_4) | product(e_5, e_3, e_5) | product(e_5, e_3, e_3))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(1245,plain,
% 0.61/0.79 (((~group_element(e_5)) | product(e_5, e_3, e_5) | product(e_5, e_3, e_4) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_1) | (~group_element(e_3))) <=> ((~group_element(e_3)) | product(e_5, e_3, e_1) | (~group_element(e_5)) | product(e_5, e_3, e_2) | product(e_5, e_3, e_4) | product(e_5, e_3, e_5) | product(e_5, e_3, e_3))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(1246,plain,
% 0.61/0.79 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_5)) | product(e_5, e_3, e_5) | product(e_5, e_3, e_4) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_1) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_5, e_3, e_1) | (~group_element(e_5)) | product(e_5, e_3, e_2) | product(e_5, e_3, e_4) | product(e_5, e_3, e_5) | product(e_5, e_3, e_3)))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[1245])).
% 0.61/0.79 tff(1247,plain,
% 0.61/0.79 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_5)) | product(e_5, e_3, e_5) | product(e_5, e_3, e_4) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_1) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_5, e_3, e_1) | (~group_element(e_5)) | product(e_5, e_3, e_2) | product(e_5, e_3, e_4) | product(e_5, e_3, e_5) | product(e_5, e_3, e_3))),
% 0.61/0.79 inference(transitivity,[status(thm)],[1246, 1244])).
% 0.61/0.79 tff(1248,plain,
% 0.61/0.79 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_5)) | product(e_5, e_3, e_5) | product(e_5, e_3, e_4) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_1) | (~group_element(e_3)))),
% 0.61/0.79 inference(quant_inst,[status(thm)],[])).
% 0.61/0.79 tff(1249,plain,
% 0.61/0.79 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_5, e_3, e_1) | (~group_element(e_5)) | product(e_5, e_3, e_2) | product(e_5, e_3, e_4) | product(e_5, e_3, e_5) | product(e_5, e_3, e_3)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[1248, 1247])).
% 0.61/0.79 tff(1250,plain,
% 0.61/0.79 (product(e_5, e_3, e_1) | product(e_5, e_3, e_2) | product(e_5, e_3, e_4) | product(e_5, e_3, e_5) | product(e_5, e_3, e_3)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[1249, 159, 1007, 410])).
% 0.61/0.79 tff(1251,plain,
% 0.61/0.79 (product(e_5, e_3, e_1) | product(e_5, e_3, e_2) | product(e_5, e_3, e_4) | product(e_5, e_3, e_3)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[1250, 1243])).
% 0.61/0.79 tff(1252,plain,
% 0.61/0.79 (product(e_5, e_3, e_3)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[1251, 1226, 1218, 1208])).
% 0.61/0.79 tff(1253,plain,
% 0.61/0.79 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_3, e_2) | (~product(e_5, e_3, e_3)) | (~product(e_3, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_3, e_2) | (~product(e_5, e_3, e_3)) | (~product(e_3, e_3, e_2)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(1254,plain,
% 0.61/0.79 ((product(e_5, e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_5, e_3, e_3))) <=> (product(e_5, e_3, e_2) | (~product(e_5, e_3, e_3)) | (~product(e_3, e_3, e_2)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(1255,plain,
% 0.61/0.79 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_5, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_3, e_2) | (~product(e_5, e_3, e_3)) | (~product(e_3, e_3, e_2))))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[1254])).
% 0.61/0.80 tff(1256,plain,
% 0.61/0.80 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_5, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_3, e_2) | (~product(e_5, e_3, e_3)) | (~product(e_3, e_3, e_2)))),
% 0.61/0.80 inference(transitivity,[status(thm)],[1255, 1253])).
% 0.61/0.80 tff(1257,plain,
% 0.61/0.80 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_5, e_3, e_3)))),
% 0.61/0.80 inference(quant_inst,[status(thm)],[])).
% 0.61/0.80 tff(1258,plain,
% 0.61/0.80 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_3, e_2) | (~product(e_5, e_3, e_3)) | (~product(e_3, e_3, e_2))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[1257, 1256])).
% 0.61/0.80 tff(1259,plain,
% 0.61/0.80 (product(e_5, e_3, e_2) | (~product(e_5, e_3, e_3)) | (~product(e_3, e_3, e_2))),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[1258, 374])).
% 0.61/0.80 tff(1260,plain,
% 0.61/0.80 (~product(e_3, e_3, e_2)),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[1259, 1252, 1208])).
% 0.61/0.80 tff(1261,assumption,(product(e_3, e_3, e_3)), introduced(assumption)).
% 0.61/0.80 tff(1262,assumption,(product(e_5, e_3, e_3)), introduced(assumption)).
% 0.61/0.80 tff(1263,plain,
% 0.61/0.80 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_5, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_5, e_3, e_3)))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(1264,plain,
% 0.61/0.80 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_5, e_3, e_3)))),
% 0.61/0.80 inference(quant_inst,[status(thm)],[])).
% 0.61/0.80 tff(1265,plain,
% 0.61/0.80 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_5, e_3, e_3))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[1264, 1263])).
% 0.61/0.80 tff(1266,plain,
% 0.61/0.80 ($false),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[1265, 249, 493, 1262, 1261])).
% 0.61/0.80 tff(1267,plain,((~product(e_5, e_3, e_3)) | (~product(e_3, e_3, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.61/0.80 tff(1268,plain,
% 0.61/0.80 (~product(e_3, e_3, e_3)),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[1267, 1252])).
% 0.61/0.80 tff(1269,plain,
% 0.61/0.80 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_5) | product(e_3, e_3, e_4) | product(e_3, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_5) | product(e_3, e_3, e_4) | product(e_3, e_3, e_1))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(1270,plain,
% 0.61/0.80 (((~group_element(e_3)) | product(e_3, e_3, e_5) | product(e_3, e_3, e_4) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3))) <=> ((~group_element(e_3)) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_5) | product(e_3, e_3, e_4) | product(e_3, e_3, e_1))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(1271,plain,
% 0.61/0.80 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_3, e_5) | product(e_3, e_3, e_4) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_5) | product(e_3, e_3, e_4) | product(e_3, e_3, e_1)))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[1270])).
% 0.61/0.80 tff(1272,plain,
% 0.61/0.80 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_3, e_5) | product(e_3, e_3, e_4) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_5) | product(e_3, e_3, e_4) | product(e_3, e_3, e_1))),
% 0.61/0.80 inference(transitivity,[status(thm)],[1271, 1269])).
% 0.61/0.80 tff(1273,plain,
% 0.61/0.80 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_3, e_5) | product(e_3, e_3, e_4) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)))),
% 0.61/0.80 inference(quant_inst,[status(thm)],[])).
% 0.61/0.80 tff(1274,plain,
% 0.61/0.80 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | 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_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_5) | product(e_3, e_3, e_4) | product(e_3, e_3, e_1)),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[1273, 1272])).
% 0.61/0.80 tff(1275,plain,
% 0.61/0.80 (product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_5) | product(e_3, e_3, e_4) | product(e_3, e_3, e_1)),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[1274, 159, 410])).
% 0.61/0.80 tff(1276,plain,
% 0.61/0.80 (product(e_3, e_3, e_1)),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[1275, 1268, 1260, 1186, 1179])).
% 0.61/0.80 tff(1277,plain,
% 0.61/0.80 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_5) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_5)))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(1278,plain,
% 0.61/0.80 ((product(e_3, e_1, e_5) | (~product(e_1, e_3, e_5)) | (~product(e_3, e_3, e_1))) <=> (product(e_3, e_1, e_5) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_5)))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(1279,plain,
% 0.61/0.80 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_1, e_3, e_5)) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_5))))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[1278])).
% 0.61/0.80 tff(1280,plain,
% 0.61/0.80 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_1, e_3, e_5)) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_5) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_5)))),
% 0.61/0.80 inference(transitivity,[status(thm)],[1279, 1277])).
% 0.61/0.80 tff(1281,plain,
% 0.61/0.80 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_1, e_3, e_5)) | (~product(e_3, e_3, e_1)))),
% 0.61/0.80 inference(quant_inst,[status(thm)],[])).
% 0.61/0.80 tff(1282,plain,
% 0.61/0.80 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_5) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_5))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[1281, 1280])).
% 0.61/0.80 tff(1283,plain,
% 0.61/0.80 ($false),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[1282, 374, 921, 1276, 1169])).
% 0.61/0.80 % SZS output end Proof
% 0.61/0.80 % E exiting
%------------------------------------------------------------------------------