%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP124-3.004 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:07:04 AM UTC 2025
% Result : Unsatisfiable 0.22s 0.50s
% Output : Proof 0.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP124-3.004 : TPTP v9.0.0. Released v1.2.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Jun 19 15:41:55 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.22/0.50 % SZS status Unsatisfiable
% 0.22/0.50 % SZS output start Proof
% 0.22/0.50 tff(product_type, type, (
% 0.22/0.50 product: ( $i * $i * $i ) > $o)).
% 0.22/0.50 tff(e_3_type, type, (
% 0.22/0.50 e_3: $i)).
% 0.22/0.50 tff(e_2_type, type, (
% 0.22/0.50 e_2: $i)).
% 0.22/0.50 tff(e_4_type, type, (
% 0.22/0.50 e_4: $i)).
% 0.22/0.50 tff(e_1_type, type, (
% 0.22/0.50 e_1: $i)).
% 0.22/0.50 tff(equalish_type, type, (
% 0.22/0.50 equalish: ( $i * $i ) > $o)).
% 0.22/0.50 tff(cycle_type, type, (
% 0.22/0.50 cycle: ( $i * $i ) > $o)).
% 0.22/0.50 tff(e_0_type, type, (
% 0.22/0.50 e_0: $i)).
% 0.22/0.50 tff(greater_type, type, (
% 0.22/0.50 greater: ( $i * $i ) > $o)).
% 0.22/0.50 tff(group_element_type, type, (
% 0.22/0.50 group_element: $i > $o)).
% 0.22/0.50 tff(next_type, type, (
% 0.22/0.50 next: ( $i * $i ) > $o)).
% 0.22/0.50 tff(1,assumption,(product(e_1, e_4, e_1)), introduced(assumption)).
% 0.22/0.50 tff(2,assumption,(~product(e_1, e_1, e_1)), introduced(assumption)).
% 0.22/0.50 tff(3,plain,
% 0.22/0.50 (^[X: $i] : refl(product(X, X, X) <=> product(X, X, X))),
% 0.22/0.50 inference(bind,[status(th)],[])).
% 0.22/0.50 tff(4,plain,
% 0.22/0.50 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.22/0.50 inference(quant_intro,[status(thm)],[3])).
% 0.22/0.50 tff(5,plain,
% 0.22/0.50 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(6,axiom,(![X: $i] : product(X, X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_idempotence')).
% 0.22/0.50 tff(7,plain,
% 0.22/0.50 (![X: $i] : product(X, X, X)),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.22/0.50 tff(8,plain,(
% 0.22/0.50 ![X: $i] : product(X, X, X)),
% 0.22/0.50 inference(skolemize,[status(sab)],[7])).
% 0.22/0.50 tff(9,plain,
% 0.22/0.50 (![X: $i] : product(X, X, X)),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.22/0.50 tff(10,plain,
% 0.22/0.50 ((~![X: $i] : product(X, X, X)) | product(e_1, e_1, e_1)),
% 0.22/0.50 inference(quant_inst,[status(thm)],[])).
% 0.22/0.50 tff(11,plain,
% 0.22/0.50 ($false),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[10, 9, 2])).
% 0.22/0.50 tff(12,plain,(product(e_1, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.50 tff(13,plain,
% 0.22/0.50 (^[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))))),
% 0.22/0.50 inference(bind,[status(th)],[])).
% 0.22/0.50 tff(14,plain,
% 0.22/0.50 (![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)))),
% 0.22/0.50 inference(quant_intro,[status(thm)],[13])).
% 0.22/0.50 tff(15,plain,
% 0.22/0.50 (![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)))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(16,plain,
% 0.22/0.50 (^[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)))))),
% 0.22/0.50 inference(bind,[status(th)],[])).
% 0.22/0.50 tff(17,plain,
% 0.22/0.50 (![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)))),
% 0.22/0.50 inference(quant_intro,[status(thm)],[16])).
% 0.22/0.50 tff(18,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')).
% 0.22/0.50 tff(19,plain,
% 0.22/0.50 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.22/0.50 tff(20,plain,
% 0.22/0.50 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.22/0.50 tff(21,plain,(
% 0.22/0.50 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.22/0.50 inference(skolemize,[status(sab)],[20])).
% 0.22/0.50 tff(22,plain,
% 0.22/0.50 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.22/0.50 tff(23,plain,
% 0.22/0.50 ((~equalish(e_4, e_1)) <=> (~equalish(e_4, e_1))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(24,axiom,(~equalish(e_4, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_1')).
% 0.22/0.50 tff(25,plain,
% 0.22/0.50 (~equalish(e_4, e_1)),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.22/0.50 tff(26,plain,
% 0.22/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_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)))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(27,plain,
% 0.22/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1)))),
% 0.22/0.50 inference(quant_inst,[status(thm)],[])).
% 0.22/0.50 tff(28,plain,
% 0.22/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.22/0.50 tff(29,plain,
% 0.22/0.50 ($false),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[28, 25, 22, 12, 1])).
% 0.22/0.50 tff(30,plain,(~product(e_1, e_4, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.50 tff(31,plain,
% 0.22/0.50 ((~![X: $i] : product(X, X, X)) | product(e_3, e_3, e_3)),
% 0.22/0.50 inference(quant_inst,[status(thm)],[])).
% 0.22/0.50 tff(32,plain,
% 0.22/0.50 (product(e_3, e_3, e_3)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[31, 9])).
% 0.22/0.50 tff(33,assumption,(product(e_3, e_1, e_3)), introduced(assumption)).
% 0.22/0.50 tff(34,plain,
% 0.22/0.50 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(35,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.22/0.50 tff(36,plain,
% 0.22/0.50 (~equalish(e_1, e_3)),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.22/0.50 tff(37,plain,
% 0.22/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_3, e_1, 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_1, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(38,plain,
% 0.22/0.50 ((equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3))) <=> (equalish(e_1, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(39,plain,
% 0.22/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_3))))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[38])).
% 0.22/0.50 tff(40,plain,
% 0.22/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.22/0.50 inference(transitivity,[status(thm)],[39, 37])).
% 0.22/0.50 tff(41,plain,
% 0.22/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.22/0.50 inference(quant_inst,[status(thm)],[])).
% 0.22/0.50 tff(42,plain,
% 0.22/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_3))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.22/0.50 tff(43,plain,
% 0.22/0.50 ($false),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[42, 36, 22, 33, 32])).
% 0.22/0.50 tff(44,plain,(~product(e_3, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.50 tff(45,assumption,(product(e_3, e_1, e_2)), introduced(assumption)).
% 0.22/0.50 tff(46,assumption,(product(e_2, e_1, e_2)), introduced(assumption)).
% 0.22/0.50 tff(47,plain,
% 0.22/0.50 (^[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))))),
% 0.22/0.50 inference(bind,[status(th)],[])).
% 0.22/0.50 tff(48,plain,
% 0.22/0.50 (![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)))),
% 0.22/0.50 inference(quant_intro,[status(thm)],[47])).
% 0.22/0.50 tff(49,plain,
% 0.22/0.50 (![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)))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(50,plain,
% 0.22/0.50 (^[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)))))),
% 0.22/0.50 inference(bind,[status(th)],[])).
% 0.22/0.50 tff(51,plain,
% 0.22/0.50 (![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)))),
% 0.22/0.50 inference(quant_intro,[status(thm)],[50])).
% 0.22/0.50 tff(52,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')).
% 0.22/0.50 tff(53,plain,
% 0.22/0.50 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.22/0.50 tff(54,plain,
% 0.22/0.50 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.22/0.50 tff(55,plain,(
% 0.22/0.50 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.22/0.50 inference(skolemize,[status(sab)],[54])).
% 0.22/0.50 tff(56,plain,
% 0.22/0.50 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.22/0.50 tff(57,plain,
% 0.22/0.50 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(58,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.22/0.50 tff(59,plain,
% 0.22/0.50 (~equalish(e_3, e_2)),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.22/0.50 tff(60,plain,
% 0.22/0.50 (((~![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_2)) | (~product(e_3, 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_3, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(61,plain,
% 0.22/0.50 ((~![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_2)) | (~product(e_3, e_1, e_2)))),
% 0.22/0.50 inference(quant_inst,[status(thm)],[])).
% 0.22/0.50 tff(62,plain,
% 0.22/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_1, e_2))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.22/0.50 tff(63,plain,
% 0.22/0.50 ($false),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[62, 59, 56, 46, 45])).
% 0.22/0.50 tff(64,plain,((~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.50 tff(65,plain,
% 0.22/0.50 (~product(e_2, e_1, e_2)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[64, 45])).
% 0.22/0.50 tff(66,assumption,(~product(e_2, e_1, e_2)), introduced(assumption)).
% 0.22/0.50 tff(67,assumption,(cycle(e_2, e_0)), introduced(assumption)).
% 0.22/0.50 tff(68,plain,
% 0.22/0.50 (^[Y: $i, X: $i] : refl(((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0))) <=> ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0))))),
% 0.22/0.50 inference(bind,[status(th)],[])).
% 0.22/0.50 tff(69,plain,
% 0.22/0.50 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0))) <=> ![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.22/0.50 inference(quant_intro,[status(thm)],[68])).
% 0.22/0.50 tff(70,plain,
% 0.22/0.50 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0))) <=> ![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(71,plain,
% 0.22/0.50 (^[Y: $i, X: $i] : rewrite((((~cycle(X, e_0)) | (~product(X, e_1, Y))) | (~greater(Y, X))) <=> ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0))))),
% 0.22/0.50 inference(bind,[status(th)],[])).
% 0.22/0.50 tff(72,plain,
% 0.22/0.50 (![Y: $i, X: $i] : (((~cycle(X, e_0)) | (~product(X, e_1, Y))) | (~greater(Y, X))) <=> ![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.22/0.50 inference(quant_intro,[status(thm)],[71])).
% 0.22/0.50 tff(73,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')).
% 0.22/0.50 tff(74,plain,
% 0.22/0.50 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.22/0.50 tff(75,plain,
% 0.22/0.50 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.22/0.50 tff(76,plain,(
% 0.22/0.50 ![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.22/0.50 inference(skolemize,[status(sab)],[75])).
% 0.22/0.50 tff(77,plain,
% 0.22/0.50 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.22/0.50 tff(78,plain,
% 0.22/0.50 (greater(e_3, e_2) <=> greater(e_3, e_2)),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(79,axiom,(greater(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_greater_e_2')).
% 0.22/0.50 tff(80,plain,
% 0.22/0.50 (greater(e_3, e_2)),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.22/0.50 tff(81,plain,
% 0.22/0.50 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(82,plain,
% 0.22/0.50 (((~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)) | (~cycle(e_2, e_0))) <=> ((~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(83,plain,
% 0.22/0.50 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3))))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[82])).
% 0.22/0.50 tff(84,plain,
% 0.22/0.50 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.22/0.50 inference(transitivity,[status(thm)],[83, 81])).
% 0.22/0.50 tff(85,plain,
% 0.22/0.50 ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)) | (~cycle(e_2, e_0)))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(86,plain,
% 0.22/0.51 ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.22/0.51 tff(87,plain,
% 0.22/0.51 ((~cycle(e_2, e_0)) | (~product(e_2, e_1, e_3))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[86, 80, 77])).
% 0.22/0.51 tff(88,plain,
% 0.22/0.51 (~product(e_2, e_1, e_3)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[87, 67])).
% 0.22/0.51 tff(89,plain,
% 0.22/0.51 (greater(e_4, e_2) <=> greater(e_4, e_2)),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(90,axiom,(greater(e_4, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_greater_e_2')).
% 0.22/0.51 tff(91,plain,
% 0.22/0.51 (greater(e_4, e_2)),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.22/0.51 tff(92,plain,
% 0.22/0.51 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(93,plain,
% 0.22/0.51 (((~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)) | (~cycle(e_2, e_0))) <=> ((~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(94,plain,
% 0.22/0.51 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4))))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[93])).
% 0.22/0.51 tff(95,plain,
% 0.22/0.51 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)))),
% 0.22/0.51 inference(transitivity,[status(thm)],[94, 92])).
% 0.22/0.51 tff(96,plain,
% 0.22/0.51 ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)) | (~cycle(e_2, e_0)))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(97,plain,
% 0.22/0.51 ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.22/0.51 tff(98,plain,
% 0.22/0.51 ((~cycle(e_2, e_0)) | (~product(e_2, e_1, e_4))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[97, 91, 77])).
% 0.22/0.51 tff(99,plain,
% 0.22/0.51 (~product(e_2, e_1, e_4)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[98, 67])).
% 0.22/0.51 tff(100,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.22/0.51 tff(101,plain,
% 0.22/0.51 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(102,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.22/0.51 tff(103,plain,
% 0.22/0.51 (~equalish(e_2, e_1)),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.22/0.51 tff(104,plain,
% 0.22/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_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)))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(105,plain,
% 0.22/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(106,plain,
% 0.22/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.22/0.51 tff(107,plain,
% 0.22/0.51 ($false),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[106, 103, 56, 12, 100])).
% 0.22/0.51 tff(108,plain,(~product(e_2, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.51 tff(109,plain,
% 0.22/0.51 (^[Y: $i, X: $i] : refl(((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) <=> ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))))),
% 0.22/0.51 inference(bind,[status(th)],[])).
% 0.22/0.51 tff(110,plain,
% 0.22/0.51 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) <=> ![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.22/0.51 inference(quant_intro,[status(thm)],[109])).
% 0.22/0.51 tff(111,plain,
% 0.22/0.51 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) <=> ![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(112,plain,
% 0.22/0.51 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) <=> ((~group_element(X)) | product(X, Y, e_1) | (~group_element(Y)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> (((~group_element(X)) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_2)))), rewrite((((~group_element(X)) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_2)) <=> ((~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> ((~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> (((~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_3)))), rewrite((((~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_3)) <=> ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))))), (((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> (((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_4)))), rewrite((((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_4)) <=> ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))), (((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))))),
% 0.22/0.51 inference(bind,[status(th)],[])).
% 0.22/0.51 tff(113,plain,
% 0.22/0.51 (![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> ![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.22/0.51 inference(quant_intro,[status(thm)],[112])).
% 0.22/0.51 tff(114,axiom,(![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_total_function1')).
% 0.22/0.51 tff(115,plain,
% 0.22/0.51 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.22/0.51 tff(116,plain,
% 0.22/0.51 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[115, 111])).
% 0.22/0.51 tff(117,plain,(
% 0.22/0.51 ![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.22/0.51 inference(skolemize,[status(sab)],[116])).
% 0.22/0.51 tff(118,plain,
% 0.22/0.51 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[117, 110])).
% 0.22/0.51 tff(119,plain,
% 0.22/0.51 (group_element(e_2) <=> group_element(e_2)),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(120,axiom,(group_element(e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_2')).
% 0.22/0.51 tff(121,plain,
% 0.22/0.51 (group_element(e_2)),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.22/0.51 tff(122,plain,
% 0.22/0.51 (group_element(e_1) <=> group_element(e_1)),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(123,axiom,(group_element(e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_1')).
% 0.22/0.51 tff(124,plain,
% 0.22/0.51 (group_element(e_1)),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.22/0.51 tff(125,plain,
% 0.22/0.51 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(126,plain,
% 0.22/0.51 (((~group_element(e_2)) | product(e_2, e_1, e_4) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1))) <=> ((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(127,plain,
% 0.22/0.51 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_2, e_1, e_4) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1)))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[126])).
% 0.22/0.51 tff(128,plain,
% 0.22/0.51 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_2, e_1, e_4) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1))),
% 0.22/0.51 inference(transitivity,[status(thm)],[127, 125])).
% 0.22/0.51 tff(129,plain,
% 0.22/0.51 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_2, e_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)))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(130,plain,
% 0.22/0.51 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1)),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.22/0.51 tff(131,plain,
% 0.22/0.51 (product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_2)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[130, 124, 121, 118, 108])).
% 0.22/0.51 tff(132,plain,
% 0.22/0.51 ($false),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[131, 99, 88, 66])).
% 0.22/0.51 tff(133,plain,((~cycle(e_2, e_0)) | product(e_2, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.51 tff(134,plain,
% 0.22/0.51 (~cycle(e_2, e_0)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[133, 65])).
% 0.22/0.51 tff(135,assumption,(cycle(e_2, e_1)), introduced(assumption)).
% 0.22/0.51 tff(136,assumption,(~cycle(e_3, e_3)), introduced(assumption)).
% 0.22/0.51 tff(137,assumption,(cycle(e_3, e_2)), introduced(assumption)).
% 0.22/0.51 tff(138,plain,
% 0.22/0.51 (^[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))))),
% 0.22/0.51 inference(bind,[status(th)],[])).
% 0.22/0.51 tff(139,plain,
% 0.22/0.51 (![W: $i, Z: $i, Y: $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)))),
% 0.22/0.51 inference(quant_intro,[status(thm)],[138])).
% 0.22/0.51 tff(140,plain,
% 0.22/0.51 (![W: $i, Z: $i, Y: $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)))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(141,plain,
% 0.22/0.51 (^[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)))))),
% 0.22/0.51 inference(bind,[status(th)],[])).
% 0.22/0.51 tff(142,plain,
% 0.22/0.51 (![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)))),
% 0.22/0.51 inference(quant_intro,[status(thm)],[141])).
% 0.22/0.51 tff(143,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')).
% 0.22/0.51 tff(144,plain,
% 0.22/0.51 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.22/0.51 tff(145,plain,
% 0.22/0.51 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[144, 140])).
% 0.22/0.51 tff(146,plain,(
% 0.22/0.51 ![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.22/0.51 inference(skolemize,[status(sab)],[145])).
% 0.22/0.51 tff(147,plain,
% 0.22/0.51 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[146, 139])).
% 0.22/0.51 tff(148,plain,
% 0.22/0.51 (cycle(e_4, e_0) <=> cycle(e_4, e_0)),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(149,axiom,(cycle(e_4, e_0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cycle3')).
% 0.22/0.51 tff(150,plain,
% 0.22/0.51 (cycle(e_4, e_0)),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.22/0.51 tff(151,plain,
% 0.22/0.51 (greater(e_2, e_0) <=> greater(e_2, e_0)),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(152,axiom,(greater(e_2, e_0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_greater_e_0')).
% 0.22/0.51 tff(153,plain,
% 0.22/0.51 (greater(e_2, e_0)),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.22/0.51 tff(154,plain,
% 0.22/0.51 (next(e_3, e_4) <=> next(e_3, e_4)),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(155,axiom,(next(e_3, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_then_e_4')).
% 0.22/0.51 tff(156,plain,
% 0.22/0.51 (next(e_3, e_4)),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.22/0.51 tff(157,plain,
% 0.22/0.51 (next(e_0, e_1) <=> next(e_0, e_1)),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(158,axiom,(next(e_0, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_0_then_e_1')).
% 0.22/0.51 tff(159,plain,
% 0.22/0.51 (next(e_0, e_1)),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.22/0.51 tff(160,plain,
% 0.22/0.51 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_2, e_1) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~next(e_0, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_1) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~next(e_0, e_1)))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(161,plain,
% 0.22/0.51 (((~cycle(e_3, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0))) <=> (equalish(e_2, e_1) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~next(e_0, e_1)))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(162,plain,
% 0.22/0.52 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_3, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_2, e_1) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~next(e_0, e_1))))),
% 0.22/0.52 inference(monotonicity,[status(thm)],[161])).
% 0.22/0.52 tff(163,plain,
% 0.22/0.52 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_3, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_1) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~next(e_0, e_1)))),
% 0.22/0.52 inference(transitivity,[status(thm)],[162, 160])).
% 0.22/0.52 tff(164,plain,
% 0.22/0.52 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_3, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)))),
% 0.22/0.52 inference(quant_inst,[status(thm)],[])).
% 0.22/0.52 tff(165,plain,
% 0.22/0.52 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_1) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~next(e_0, e_1))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.22/0.52 tff(166,plain,
% 0.22/0.52 ($false),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[165, 159, 156, 153, 150, 147, 103, 137])).
% 0.22/0.52 tff(167,plain,(~cycle(e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.52 tff(168,plain,
% 0.22/0.52 (^[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))))),
% 0.22/0.52 inference(bind,[status(th)],[])).
% 0.22/0.52 tff(169,plain,
% 0.22/0.52 (![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)))),
% 0.22/0.52 inference(quant_intro,[status(thm)],[168])).
% 0.22/0.52 tff(170,plain,
% 0.22/0.52 (![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)))),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(171,plain,
% 0.22/0.52 (^[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)))))),
% 0.22/0.52 inference(bind,[status(th)],[])).
% 0.22/0.52 tff(172,plain,
% 0.22/0.52 (![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)))),
% 0.22/0.52 inference(quant_intro,[status(thm)],[171])).
% 0.22/0.52 tff(173,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')).
% 0.22/0.52 tff(174,plain,
% 0.22/0.52 (![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)))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.22/0.52 tff(175,plain,
% 0.22/0.52 (![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)))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[174, 170])).
% 0.22/0.52 tff(176,plain,(
% 0.22/0.52 ![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)))),
% 0.22/0.52 inference(skolemize,[status(sab)],[175])).
% 0.22/0.52 tff(177,plain,
% 0.22/0.52 (![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)))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[176, 169])).
% 0.22/0.52 tff(178,plain,
% 0.22/0.52 (greater(e_1, e_0) <=> greater(e_1, e_0)),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(179,axiom,(greater(e_1, e_0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_greater_e_0')).
% 0.22/0.52 tff(180,plain,
% 0.22/0.52 (greater(e_1, e_0)),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.22/0.52 tff(181,plain,
% 0.22/0.52 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_4, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_1)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_4, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_1)))),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(182,plain,
% 0.22/0.52 (((~greater(e_1, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_1))) <=> ((~cycle(e_4, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_1)))),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(183,plain,
% 0.22/0.52 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_1, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_1)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_4, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_1))))),
% 0.22/0.52 inference(monotonicity,[status(thm)],[182])).
% 0.22/0.52 tff(184,plain,
% 0.22/0.52 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_1, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_1)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_4, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_1)))),
% 0.22/0.52 inference(transitivity,[status(thm)],[183, 181])).
% 0.22/0.52 tff(185,plain,
% 0.22/0.52 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_1, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_1)))),
% 0.22/0.52 inference(quant_inst,[status(thm)],[])).
% 0.22/0.52 tff(186,plain,
% 0.22/0.52 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_4, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_1))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.22/0.52 tff(187,plain,
% 0.22/0.52 ((~cycle(e_3, e_0)) | (~cycle(e_2, e_1))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[186, 156, 180, 80, 150, 177])).
% 0.22/0.52 tff(188,plain,
% 0.22/0.52 (~cycle(e_3, e_0)),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[187, 135])).
% 0.22/0.52 tff(189,plain,
% 0.22/0.52 (group_element(e_3) <=> group_element(e_3)),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(190,axiom,(group_element(e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_3')).
% 0.22/0.52 tff(191,plain,
% 0.22/0.52 (group_element(e_3)),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.22/0.52 tff(192,plain,
% 0.22/0.52 (^[X: $i] : refl((cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) <=> (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))))),
% 0.22/0.52 inference(bind,[status(th)],[])).
% 0.22/0.52 tff(193,plain,
% 0.22/0.52 (![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) <=> ![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.22/0.52 inference(quant_intro,[status(thm)],[192])).
% 0.22/0.52 tff(194,plain,
% 0.22/0.52 (![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) <=> ![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(195,plain,
% 0.22/0.52 (^[X: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) <=> (cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))), (((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) <=> ((cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) | cycle(X, e_2)))), rewrite(((cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) | cycle(X, e_2)) <=> (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))), (((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) <=> (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))))), ((((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) | cycle(X, e_3)) <=> ((cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) | cycle(X, e_3)))), rewrite(((cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) | cycle(X, e_3)) <=> (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))), ((((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) | cycle(X, e_3)) <=> (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))))),
% 0.37/0.52 inference(bind,[status(th)],[])).
% 0.37/0.52 tff(196,plain,
% 0.37/0.52 (![X: $i] : (((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) | cycle(X, e_3)) <=> ![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.37/0.52 inference(quant_intro,[status(thm)],[195])).
% 0.37/0.52 tff(197,axiom,(![X: $i] : (((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) | cycle(X, e_3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cycle2')).
% 0.37/0.52 tff(198,plain,
% 0.37/0.52 (![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.37/0.52 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.37/0.52 tff(199,plain,
% 0.37/0.52 (![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.37/0.52 inference(modus_ponens,[status(thm)],[198, 194])).
% 0.37/0.52 tff(200,plain,(
% 0.37/0.52 ![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.37/0.52 inference(skolemize,[status(sab)],[199])).
% 0.37/0.52 tff(201,plain,
% 0.37/0.52 (![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.37/0.52 inference(modus_ponens,[status(thm)],[200, 193])).
% 0.37/0.52 tff(202,plain,
% 0.37/0.52 (((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0) | (~group_element(e_3)))) <=> ((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0) | (~group_element(e_3)))),
% 0.37/0.52 inference(rewrite,[status(thm)],[])).
% 0.37/0.52 tff(203,plain,
% 0.37/0.52 ((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0) | (~group_element(e_3)))),
% 0.37/0.52 inference(quant_inst,[status(thm)],[])).
% 0.37/0.52 tff(204,plain,
% 0.37/0.52 ((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0) | (~group_element(e_3))),
% 0.37/0.52 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.37/0.52 tff(205,plain,
% 0.37/0.52 (cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0)),
% 0.37/0.52 inference(unit_resolution,[status(thm)],[204, 201, 191])).
% 0.37/0.52 tff(206,plain,
% 0.37/0.52 (cycle(e_3, e_1)),
% 0.37/0.52 inference(unit_resolution,[status(thm)],[205, 188, 167, 136])).
% 0.37/0.52 tff(207,plain,
% 0.37/0.52 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.37/0.52 inference(rewrite,[status(thm)],[])).
% 0.37/0.52 tff(208,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.37/0.52 tff(209,plain,
% 0.37/0.52 (~equalish(e_1, e_2)),
% 0.37/0.52 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.37/0.52 tff(210,plain,
% 0.37/0.52 (next(e_2, e_3) <=> next(e_2, e_3)),
% 0.37/0.52 inference(rewrite,[status(thm)],[])).
% 0.37/0.52 tff(211,axiom,(next(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_then_e_3')).
% 0.37/0.52 tff(212,plain,
% 0.37/0.52 (next(e_2, e_3)),
% 0.37/0.52 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.37/0.52 tff(213,plain,
% 0.37/0.52 (next(e_1, e_2) <=> next(e_1, e_2)),
% 0.37/0.52 inference(rewrite,[status(thm)],[])).
% 0.37/0.52 tff(214,axiom,(next(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_then_e_2')).
% 0.37/0.52 tff(215,plain,
% 0.37/0.52 (next(e_1, e_2)),
% 0.37/0.52 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.37/0.52 tff(216,plain,
% 0.37/0.52 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_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)))),
% 0.37/0.52 inference(rewrite,[status(thm)],[])).
% 0.37/0.52 tff(217,plain,
% 0.37/0.52 (((~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)))),
% 0.37/0.52 inference(rewrite,[status(thm)],[])).
% 0.37/0.52 tff(218,plain,
% 0.37/0.52 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_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))))),
% 0.37/0.52 inference(monotonicity,[status(thm)],[217])).
% 0.37/0.52 tff(219,plain,
% 0.37/0.52 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_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)))),
% 0.37/0.52 inference(transitivity,[status(thm)],[218, 216])).
% 0.37/0.52 tff(220,plain,
% 0.37/0.52 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_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)))),
% 0.37/0.52 inference(quant_inst,[status(thm)],[])).
% 0.37/0.52 tff(221,plain,
% 0.37/0.52 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_1, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_1))),
% 0.37/0.52 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.37/0.52 tff(222,plain,
% 0.37/0.52 ($false),
% 0.37/0.52 inference(unit_resolution,[status(thm)],[221, 215, 212, 180, 147, 209, 135, 206])).
% 0.37/0.52 tff(223,plain,((~cycle(e_2, e_1)) | cycle(e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.37/0.52 tff(224,plain,
% 0.37/0.52 (cycle(e_3, e_3)),
% 0.37/0.52 inference(unit_resolution,[status(thm)],[223, 135])).
% 0.37/0.52 tff(225,plain,
% 0.37/0.52 ((~equalish(e_1, e_4)) <=> (~equalish(e_1, e_4))),
% 0.37/0.52 inference(rewrite,[status(thm)],[])).
% 0.37/0.52 tff(226,axiom,(~equalish(e_1, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_4')).
% 0.37/0.52 tff(227,plain,
% 0.37/0.52 (~equalish(e_1, e_4)),
% 0.37/0.52 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.37/0.52 tff(228,plain,
% 0.37/0.52 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_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)))),
% 0.37/0.52 inference(rewrite,[status(thm)],[])).
% 0.37/0.52 tff(229,plain,
% 0.37/0.52 (((~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)))),
% 0.37/0.53 inference(rewrite,[status(thm)],[])).
% 0.37/0.53 tff(230,plain,
% 0.37/0.53 (((~![W: $i, Z: $i, Y: $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))))),
% 0.37/0.53 inference(monotonicity,[status(thm)],[229])).
% 0.37/0.53 tff(231,plain,
% 0.37/0.53 (((~![W: $i, Z: $i, Y: $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)))),
% 0.37/0.53 inference(transitivity,[status(thm)],[230, 228])).
% 0.37/0.53 tff(232,plain,
% 0.37/0.53 ((~![W: $i, Z: $i, Y: $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)))),
% 0.37/0.53 inference(quant_inst,[status(thm)],[])).
% 0.37/0.53 tff(233,plain,
% 0.37/0.53 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_1, e_4) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~next(e_3, e_4)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_3))),
% 0.37/0.53 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.37/0.53 tff(234,plain,
% 0.37/0.53 ($false),
% 0.37/0.53 inference(unit_resolution,[status(thm)],[233, 212, 156, 180, 147, 227, 135, 224])).
% 0.37/0.53 tff(235,plain,(~cycle(e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.37/0.53 tff(236,assumption,(~cycle(e_2, e_1)), introduced(assumption)).
% 0.37/0.53 tff(237,assumption,(~cycle(e_2, e_0)), introduced(assumption)).
% 0.37/0.53 tff(238,assumption,(cycle(e_3, e_0)), introduced(assumption)).
% 0.37/0.53 tff(239,plain,
% 0.37/0.53 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2)))),
% 0.37/0.53 inference(rewrite,[status(thm)],[])).
% 0.37/0.53 tff(240,plain,
% 0.37/0.53 (((~greater(e_2, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_2))) <=> ((~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2)))),
% 0.37/0.53 inference(rewrite,[status(thm)],[])).
% 0.37/0.53 tff(241,plain,
% 0.37/0.53 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_2, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_2)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2))))),
% 0.37/0.53 inference(monotonicity,[status(thm)],[240])).
% 0.37/0.53 tff(242,plain,
% 0.37/0.53 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_2, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_2)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2)))),
% 0.37/0.53 inference(transitivity,[status(thm)],[241, 239])).
% 0.37/0.53 tff(243,plain,
% 0.37/0.53 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_2, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_2)))),
% 0.37/0.53 inference(quant_inst,[status(thm)],[])).
% 0.37/0.53 tff(244,plain,
% 0.37/0.53 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2))),
% 0.37/0.53 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.37/0.53 tff(245,plain,
% 0.37/0.53 ((~cycle(e_3, e_0)) | (~cycle(e_2, e_2))),
% 0.37/0.53 inference(unit_resolution,[status(thm)],[244, 156, 153, 80, 150, 177])).
% 0.37/0.53 tff(246,plain,
% 0.37/0.53 (~cycle(e_2, e_2)),
% 0.37/0.53 inference(unit_resolution,[status(thm)],[245, 238])).
% 0.37/0.53 tff(247,plain,
% 0.37/0.53 (greater(e_3, e_0) <=> greater(e_3, e_0)),
% 0.37/0.53 inference(rewrite,[status(thm)],[])).
% 0.37/0.53 tff(248,axiom,(greater(e_3, e_0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_greater_e_0')).
% 0.37/0.53 tff(249,plain,
% 0.37/0.53 (greater(e_3, e_0)),
% 0.37/0.53 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.37/0.53 tff(250,plain,
% 0.37/0.53 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3)))),
% 0.37/0.53 inference(rewrite,[status(thm)],[])).
% 0.37/0.53 tff(251,plain,
% 0.37/0.53 (((~greater(e_3, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_3))) <=> ((~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3)))),
% 0.37/0.53 inference(rewrite,[status(thm)],[])).
% 0.37/0.53 tff(252,plain,
% 0.37/0.53 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_3, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_3)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3))))),
% 0.37/0.53 inference(monotonicity,[status(thm)],[251])).
% 0.37/0.53 tff(253,plain,
% 0.37/0.53 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_3, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_3)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3)))),
% 0.37/0.53 inference(transitivity,[status(thm)],[252, 250])).
% 0.37/0.53 tff(254,plain,
% 0.37/0.53 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_3, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_3)))),
% 0.37/0.53 inference(quant_inst,[status(thm)],[])).
% 0.37/0.53 tff(255,plain,
% 0.37/0.53 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3))),
% 0.37/0.53 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.37/0.53 tff(256,plain,
% 0.37/0.53 ((~cycle(e_3, e_0)) | (~cycle(e_2, e_3))),
% 0.37/0.53 inference(unit_resolution,[status(thm)],[255, 156, 249, 80, 150, 177])).
% 0.37/0.53 tff(257,plain,
% 0.37/0.53 (~cycle(e_2, e_3)),
% 0.37/0.53 inference(unit_resolution,[status(thm)],[256, 238])).
% 0.37/0.53 tff(258,plain,
% 0.37/0.53 (((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0) | (~group_element(e_2)))) <=> ((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0) | (~group_element(e_2)))),
% 0.37/0.53 inference(rewrite,[status(thm)],[])).
% 0.37/0.53 tff(259,plain,
% 0.37/0.53 ((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0) | (~group_element(e_2)))),
% 0.37/0.53 inference(quant_inst,[status(thm)],[])).
% 0.37/0.53 tff(260,plain,
% 0.37/0.53 ((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0) | (~group_element(e_2))),
% 0.37/0.53 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.37/0.53 tff(261,plain,
% 0.37/0.53 (cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0)),
% 0.37/0.53 inference(unit_resolution,[status(thm)],[260, 201, 121])).
% 0.37/0.53 tff(262,plain,
% 0.37/0.53 ($false),
% 0.37/0.53 inference(unit_resolution,[status(thm)],[261, 257, 246, 237, 236])).
% 0.37/0.53 tff(263,plain,((~cycle(e_3, e_0)) | cycle(e_2, e_0) | cycle(e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.37/0.53 tff(264,plain,
% 0.37/0.53 ((~cycle(e_3, e_0)) | cycle(e_2, e_0)),
% 0.37/0.53 inference(unit_resolution,[status(thm)],[263, 235])).
% 0.37/0.53 tff(265,plain,
% 0.37/0.53 (~cycle(e_3, e_0)),
% 0.37/0.53 inference(unit_resolution,[status(thm)],[264, 134])).
% 0.37/0.53 tff(266,assumption,(cycle(e_3, e_1)), introduced(assumption)).
% 0.37/0.53 tff(267,plain,
% 0.37/0.53 ((~equalish(e_2, e_4)) <=> (~equalish(e_2, e_4))),
% 0.37/0.53 inference(rewrite,[status(thm)],[])).
% 0.37/0.53 tff(268,axiom,(~equalish(e_2, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_4')).
% 0.37/0.53 tff(269,plain,
% 0.37/0.53 (~equalish(e_2, e_4)),
% 0.37/0.53 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.37/0.53 tff(270,plain,
% 0.37/0.53 (^[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))))),
% 0.37/0.53 inference(bind,[status(th)],[])).
% 0.37/0.53 tff(271,plain,
% 0.37/0.53 (![Z: $i, 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)))),
% 0.37/0.53 inference(quant_intro,[status(thm)],[270])).
% 0.37/0.53 tff(272,plain,
% 0.37/0.53 (![Z: $i, 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)))),
% 0.37/0.53 inference(rewrite,[status(thm)],[])).
% 0.37/0.53 tff(273,plain,
% 0.37/0.53 (^[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)))))),
% 0.37/0.53 inference(bind,[status(th)],[])).
% 0.37/0.53 tff(274,plain,
% 0.37/0.53 (![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)))),
% 0.37/0.53 inference(quant_intro,[status(thm)],[273])).
% 0.37/0.53 tff(275,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')).
% 0.37/0.53 tff(276,plain,
% 0.37/0.53 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.37/0.53 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.37/0.53 tff(277,plain,
% 0.37/0.53 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.37/0.53 inference(modus_ponens,[status(thm)],[276, 272])).
% 0.37/0.53 tff(278,plain,(
% 0.37/0.53 ![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.37/0.53 inference(skolemize,[status(sab)],[277])).
% 0.37/0.53 tff(279,plain,
% 0.37/0.53 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.37/0.53 inference(modus_ponens,[status(thm)],[278, 271])).
% 0.37/0.53 tff(280,plain,
% 0.37/0.53 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_2, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_2)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_2)))),
% 0.37/0.53 inference(rewrite,[status(thm)],[])).
% 0.37/0.53 tff(281,plain,
% 0.37/0.53 (((~greater(e_1, e_0)) | (~cycle(e_3, e_1)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2))) <=> (equalish(e_2, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_2)))),
% 0.37/0.53 inference(rewrite,[status(thm)],[])).
% 0.37/0.53 tff(282,plain,
% 0.37/0.53 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_3, e_1)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_2, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_2))))),
% 0.37/0.53 inference(monotonicity,[status(thm)],[281])).
% 0.37/0.53 tff(283,plain,
% 0.37/0.53 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_3, e_1)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_2)))),
% 0.37/0.53 inference(transitivity,[status(thm)],[282, 280])).
% 0.37/0.53 tff(284,plain,
% 0.37/0.53 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_3, e_1)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2)))),
% 0.37/0.53 inference(quant_inst,[status(thm)],[])).
% 0.37/0.53 tff(285,plain,
% 0.37/0.53 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_2))),
% 0.37/0.53 inference(modus_ponens,[status(thm)],[284, 283])).
% 0.37/0.53 tff(286,plain,
% 0.37/0.53 ($false),
% 0.37/0.53 inference(unit_resolution,[status(thm)],[285, 156, 180, 279, 269, 266, 45])).
% 0.37/0.53 tff(287,plain,((~cycle(e_3, e_1)) | (~product(e_3, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.53 tff(288,plain,
% 0.37/0.53 (~cycle(e_3, e_1)),
% 0.37/0.53 inference(unit_resolution,[status(thm)],[287, 45])).
% 0.37/0.53 tff(289,plain,
% 0.37/0.53 (cycle(e_3, e_3) | cycle(e_3, e_1) | cycle(e_3, e_0)),
% 0.37/0.53 inference(unit_resolution,[status(thm)],[205, 167])).
% 0.37/0.53 tff(290,plain,
% 0.37/0.53 (cycle(e_3, e_3)),
% 0.37/0.53 inference(unit_resolution,[status(thm)],[289, 288, 265])).
% 0.37/0.53 tff(291,plain,
% 0.37/0.53 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_2, e_4) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~product(e_3, e_1, e_2)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_4) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.37/0.53 inference(rewrite,[status(thm)],[])).
% 0.37/0.53 tff(292,plain,
% 0.37/0.53 (((~greater(e_3, e_0)) | (~cycle(e_3, e_3)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2))) <=> (equalish(e_2, e_4) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.37/0.53 inference(rewrite,[status(thm)],[])).
% 0.37/0.53 tff(293,plain,
% 0.37/0.53 (((~![Z: $i, 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_3, e_3)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_2, e_4) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~product(e_3, e_1, e_2))))),
% 0.37/0.53 inference(monotonicity,[status(thm)],[292])).
% 0.37/0.53 tff(294,plain,
% 0.37/0.53 (((~![Z: $i, 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_3, e_3)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_4) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.37/0.53 inference(transitivity,[status(thm)],[293, 291])).
% 0.37/0.53 tff(295,plain,
% 0.37/0.53 ((~![Z: $i, 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_3, e_3)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2)))),
% 0.37/0.53 inference(quant_inst,[status(thm)],[])).
% 0.37/0.53 tff(296,plain,
% 0.37/0.53 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_4) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~product(e_3, e_1, e_2))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.37/0.54 tff(297,plain,
% 0.37/0.54 ($false),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[296, 156, 249, 279, 269, 290, 45])).
% 0.37/0.54 tff(298,plain,(~product(e_3, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.37/0.54 tff(299,assumption,(product(e_3, e_1, e_1)), introduced(assumption)).
% 0.37/0.54 tff(300,plain,
% 0.37/0.54 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(301,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.37/0.54 tff(302,plain,
% 0.37/0.54 (~equalish(e_3, e_1)),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.37/0.54 tff(303,plain,
% 0.37/0.54 (((~![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)))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(304,plain,
% 0.37/0.54 ((~![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)))),
% 0.37/0.54 inference(quant_inst,[status(thm)],[])).
% 0.37/0.54 tff(305,plain,
% 0.37/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.37/0.54 tff(306,plain,
% 0.37/0.54 ($false),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[305, 302, 56, 12, 299])).
% 0.37/0.54 tff(307,plain,(~product(e_3, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.37/0.54 tff(308,plain,
% 0.37/0.54 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(309,plain,
% 0.37/0.54 (((~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1))) <=> ((~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1))),
% 0.37/0.54 inference(rewrite,[status(thm)],[])).
% 0.37/0.54 tff(310,plain,
% 0.37/0.54 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1)))),
% 0.37/0.54 inference(monotonicity,[status(thm)],[309])).
% 0.37/0.54 tff(311,plain,
% 0.37/0.54 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1))),
% 0.39/0.54 inference(transitivity,[status(thm)],[310, 308])).
% 0.39/0.54 tff(312,plain,
% 0.39/0.54 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)))),
% 0.39/0.54 inference(quant_inst,[status(thm)],[])).
% 0.39/0.54 tff(313,plain,
% 0.39/0.54 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1)),
% 0.39/0.54 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.39/0.54 tff(314,plain,
% 0.39/0.54 (product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2)),
% 0.39/0.54 inference(unit_resolution,[status(thm)],[313, 124, 191, 118, 307])).
% 0.39/0.54 tff(315,plain,
% 0.39/0.54 (product(e_3, e_1, e_4)),
% 0.39/0.54 inference(unit_resolution,[status(thm)],[314, 298, 44])).
% 0.39/0.54 tff(316,assumption,(product(e_1, e_4, e_3)), introduced(assumption)).
% 0.39/0.54 tff(317,assumption,(product(e_3, e_1, e_4)), introduced(assumption)).
% 0.39/0.54 tff(318,plain,
% 0.39/0.54 (^[Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : refl(((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2)) <=> ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2)))),
% 0.39/0.54 inference(bind,[status(th)],[])).
% 0.39/0.54 tff(319,plain,
% 0.39/0.54 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2)) <=> ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.39/0.54 inference(quant_intro,[status(thm)],[318])).
% 0.39/0.54 tff(320,plain,
% 0.39/0.54 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2)) <=> ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.39/0.54 inference(rewrite,[status(thm)],[])).
% 0.39/0.54 tff(321,plain,
% 0.39/0.54 (^[Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) <=> ((~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))), (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) <=> (((~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | (~product(Z2, X2, Y2))))), rewrite((((~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | (~product(Z2, X2, Y2))) <=> ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))), (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) <=> ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))))), ((((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) | equalish(Y1, Y2)) <=> (((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | equalish(Y1, Y2)))), rewrite((((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | equalish(Y1, Y2)) <=> ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))), ((((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) | equalish(Y1, Y2)) <=> ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))))),
% 0.39/0.54 inference(bind,[status(th)],[])).
% 0.39/0.54 tff(322,plain,
% 0.39/0.54 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) | equalish(Y1, Y2)) <=> ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.39/0.54 inference(quant_intro,[status(thm)],[321])).
% 0.39/0.54 tff(323,axiom,(![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) | equalish(Y1, Y2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qg2_2')).
% 0.39/0.54 tff(324,plain,
% 0.39/0.54 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.39/0.54 inference(modus_ponens,[status(thm)],[323, 322])).
% 0.39/0.54 tff(325,plain,
% 0.39/0.54 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.39/0.54 inference(modus_ponens,[status(thm)],[324, 320])).
% 0.39/0.54 tff(326,plain,(
% 0.39/0.54 ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.39/0.54 inference(skolemize,[status(sab)],[325])).
% 0.39/0.54 tff(327,plain,
% 0.39/0.54 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.39/0.54 inference(modus_ponens,[status(thm)],[326, 319])).
% 0.39/0.54 tff(328,plain,
% 0.39/0.54 ((~equalish(e_4, e_3)) <=> (~equalish(e_4, e_3))),
% 0.39/0.54 inference(rewrite,[status(thm)],[])).
% 0.39/0.54 tff(329,axiom,(~equalish(e_4, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_3')).
% 0.39/0.54 tff(330,plain,
% 0.39/0.54 (~equalish(e_4, e_3)),
% 0.39/0.54 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.39/0.54 tff(331,plain,
% 0.39/0.54 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_4, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_4, e_3)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_4, e_3)))),
% 0.39/0.54 inference(rewrite,[status(thm)],[])).
% 0.39/0.54 tff(332,plain,
% 0.39/0.54 (((~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_4, e_3)) | equalish(e_4, e_3)) <=> (equalish(e_4, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_4, e_3)))),
% 0.39/0.54 inference(rewrite,[status(thm)],[])).
% 0.39/0.54 tff(333,plain,
% 0.39/0.54 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_4, e_3)) | equalish(e_4, e_3))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_4, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_4, e_3))))),
% 0.39/0.54 inference(monotonicity,[status(thm)],[332])).
% 0.39/0.54 tff(334,plain,
% 0.39/0.54 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_4, e_3)) | equalish(e_4, e_3))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_4, e_3)))),
% 0.39/0.54 inference(transitivity,[status(thm)],[333, 331])).
% 0.39/0.54 tff(335,plain,
% 0.39/0.54 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_4, e_3)) | equalish(e_4, e_3))),
% 0.39/0.54 inference(quant_inst,[status(thm)],[])).
% 0.39/0.54 tff(336,plain,
% 0.39/0.54 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_4, e_3))),
% 0.39/0.54 inference(modus_ponens,[status(thm)],[335, 334])).
% 0.39/0.54 tff(337,plain,
% 0.39/0.54 ($false),
% 0.39/0.54 inference(unit_resolution,[status(thm)],[336, 330, 327, 317, 32, 316])).
% 0.39/0.54 tff(338,plain,((~product(e_3, e_1, e_4)) | (~product(e_1, e_4, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.54 tff(339,plain,
% 0.39/0.54 (~product(e_1, e_4, e_3)),
% 0.39/0.54 inference(unit_resolution,[status(thm)],[338, 315])).
% 0.39/0.54 tff(340,assumption,(product(e_1, e_4, e_4)), introduced(assumption)).
% 0.39/0.54 tff(341,plain,
% 0.39/0.54 ((~![X: $i] : product(X, X, X)) | product(e_4, e_4, e_4)),
% 0.39/0.54 inference(quant_inst,[status(thm)],[])).
% 0.39/0.54 tff(342,plain,
% 0.39/0.54 (product(e_4, e_4, e_4)),
% 0.39/0.54 inference(unit_resolution,[status(thm)],[341, 9])).
% 0.39/0.54 tff(343,plain,
% 0.39/0.54 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_1, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_1, e_4, e_4)))),
% 0.39/0.54 inference(rewrite,[status(thm)],[])).
% 0.39/0.54 tff(344,plain,
% 0.39/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_1, e_4, e_4)))),
% 0.39/0.54 inference(quant_inst,[status(thm)],[])).
% 0.39/0.54 tff(345,plain,
% 0.39/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_1, e_4, e_4))),
% 0.39/0.54 inference(modus_ponens,[status(thm)],[344, 343])).
% 0.39/0.54 tff(346,plain,
% 0.39/0.54 ($false),
% 0.39/0.54 inference(unit_resolution,[status(thm)],[345, 227, 56, 342, 340])).
% 0.39/0.54 tff(347,plain,(~product(e_1, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.39/0.54 tff(348,plain,
% 0.39/0.54 (group_element(e_4) <=> group_element(e_4)),
% 0.39/0.54 inference(rewrite,[status(thm)],[])).
% 0.39/0.54 tff(349,axiom,(group_element(e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_4')).
% 0.39/0.54 tff(350,plain,
% 0.39/0.54 (group_element(e_4)),
% 0.39/0.54 inference(modus_ponens,[status(thm)],[349, 348])).
% 0.39/0.54 tff(351,plain,
% 0.39/0.54 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_4)) | product(e_1, e_4, e_2) | product(e_1, e_4, e_3) | product(e_1, e_4, e_1) | product(e_1, e_4, e_4))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_4)) | product(e_1, e_4, e_2) | product(e_1, e_4, e_3) | product(e_1, e_4, e_1) | product(e_1, e_4, e_4))),
% 0.39/0.54 inference(rewrite,[status(thm)],[])).
% 0.39/0.54 tff(352,plain,
% 0.39/0.54 (((~group_element(e_1)) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4))) <=> ((~group_element(e_1)) | (~group_element(e_4)) | product(e_1, e_4, e_2) | product(e_1, e_4, e_3) | product(e_1, e_4, e_1) | product(e_1, e_4, e_4))),
% 0.39/0.54 inference(rewrite,[status(thm)],[])).
% 0.39/0.54 tff(353,plain,
% 0.39/0.54 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_4)) | product(e_1, e_4, e_2) | product(e_1, e_4, e_3) | product(e_1, e_4, e_1) | product(e_1, e_4, e_4)))),
% 0.39/0.54 inference(monotonicity,[status(thm)],[352])).
% 0.39/0.54 tff(354,plain,
% 0.39/0.54 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_4)) | product(e_1, e_4, e_2) | product(e_1, e_4, e_3) | product(e_1, e_4, e_1) | product(e_1, e_4, e_4))),
% 0.39/0.54 inference(transitivity,[status(thm)],[353, 351])).
% 0.39/0.54 tff(355,plain,
% 0.39/0.54 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4)))),
% 0.39/0.54 inference(quant_inst,[status(thm)],[])).
% 0.39/0.54 tff(356,plain,
% 0.39/0.54 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_4)) | product(e_1, e_4, e_2) | product(e_1, e_4, e_3) | product(e_1, e_4, e_1) | product(e_1, e_4, e_4)),
% 0.39/0.54 inference(modus_ponens,[status(thm)],[355, 354])).
% 0.39/0.54 tff(357,plain,
% 0.39/0.54 (product(e_1, e_4, e_2) | product(e_1, e_4, e_3) | product(e_1, e_4, e_1)),
% 0.39/0.54 inference(unit_resolution,[status(thm)],[356, 124, 350, 118, 347])).
% 0.39/0.54 tff(358,plain,
% 0.39/0.54 (product(e_1, e_4, e_2)),
% 0.39/0.54 inference(unit_resolution,[status(thm)],[357, 339, 30])).
% 0.39/0.54 tff(359,assumption,(product(e_1, e_3, e_2)), introduced(assumption)).
% 0.39/0.54 tff(360,assumption,(product(e_1, e_4, e_2)), introduced(assumption)).
% 0.39/0.54 tff(361,plain,
% 0.39/0.54 ((~equalish(e_3, e_4)) <=> (~equalish(e_3, e_4))),
% 0.39/0.54 inference(rewrite,[status(thm)],[])).
% 0.39/0.54 tff(362,axiom,(~equalish(e_3, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_4')).
% 0.39/0.54 tff(363,plain,
% 0.39/0.54 (~equalish(e_3, e_4)),
% 0.39/0.54 inference(modus_ponens,[status(thm)],[362, 361])).
% 0.39/0.54 tff(364,plain,
% 0.39/0.54 (((~![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_1, e_4, e_2)) | (~product(e_1, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_1, e_4, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.39/0.54 inference(rewrite,[status(thm)],[])).
% 0.39/0.54 tff(365,plain,
% 0.39/0.54 ((~![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_1, e_4, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.39/0.54 inference(quant_inst,[status(thm)],[])).
% 0.39/0.54 tff(366,plain,
% 0.39/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_1, e_4, e_2)) | (~product(e_1, e_3, e_2))),
% 0.39/0.54 inference(modus_ponens,[status(thm)],[365, 364])).
% 0.39/0.54 tff(367,plain,
% 0.39/0.54 ($false),
% 0.39/0.54 inference(unit_resolution,[status(thm)],[366, 363, 22, 360, 359])).
% 0.39/0.54 tff(368,plain,((~product(e_1, e_3, e_2)) | (~product(e_1, e_4, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.54 tff(369,plain,
% 0.39/0.54 (~product(e_1, e_3, e_2)),
% 0.39/0.54 inference(unit_resolution,[status(thm)],[368, 358])).
% 0.39/0.55 tff(370,assumption,(product(e_1, e_3, e_3)), introduced(assumption)).
% 0.39/0.55 tff(371,plain,
% 0.39/0.55 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(372,plain,
% 0.39/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.39/0.55 inference(quant_inst,[status(thm)],[])).
% 0.39/0.55 tff(373,plain,
% 0.39/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[372, 371])).
% 0.39/0.55 tff(374,plain,
% 0.39/0.55 ($false),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[373, 36, 56, 32, 370])).
% 0.39/0.55 tff(375,plain,(~product(e_1, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.39/0.55 tff(376,assumption,(product(e_1, e_3, e_1)), introduced(assumption)).
% 0.39/0.55 tff(377,plain,
% 0.39/0.55 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(378,plain,
% 0.39/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.39/0.55 inference(quant_inst,[status(thm)],[])).
% 0.39/0.55 tff(379,plain,
% 0.39/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[378, 377])).
% 0.39/0.55 tff(380,plain,
% 0.39/0.55 ($false),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[379, 302, 22, 12, 376])).
% 0.39/0.55 tff(381,plain,(~product(e_1, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.39/0.55 tff(382,plain,
% 0.39/0.55 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_4) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_4) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(383,plain,
% 0.39/0.55 (((~group_element(e_1)) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3))) <=> ((~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_4) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(384,plain,
% 0.39/0.55 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_4) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1)))),
% 0.39/0.55 inference(monotonicity,[status(thm)],[383])).
% 0.39/0.55 tff(385,plain,
% 0.39/0.55 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_4) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1))),
% 0.39/0.55 inference(transitivity,[status(thm)],[384, 382])).
% 0.39/0.55 tff(386,plain,
% 0.39/0.55 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)))),
% 0.39/0.55 inference(quant_inst,[status(thm)],[])).
% 0.39/0.55 tff(387,plain,
% 0.39/0.55 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_4) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1)),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[386, 385])).
% 0.39/0.55 tff(388,plain,
% 0.39/0.55 (product(e_1, e_3, e_3) | product(e_1, e_3, e_4) | product(e_1, e_3, e_2)),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[387, 124, 191, 118, 381])).
% 0.39/0.55 tff(389,plain,
% 0.39/0.55 (product(e_1, e_3, e_4) | product(e_1, e_3, e_2)),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[388, 375])).
% 0.39/0.55 tff(390,plain,
% 0.39/0.55 (product(e_1, e_3, e_4)),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[389, 369])).
% 0.39/0.55 tff(391,assumption,(product(e_3, e_4, e_3)), introduced(assumption)).
% 0.39/0.55 tff(392,plain,
% 0.39/0.55 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3)))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(393,plain,
% 0.39/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3)))),
% 0.39/0.55 inference(quant_inst,[status(thm)],[])).
% 0.39/0.55 tff(394,plain,
% 0.39/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[393, 392])).
% 0.39/0.55 tff(395,plain,
% 0.39/0.55 ($false),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[394, 330, 22, 32, 391])).
% 0.39/0.55 tff(396,plain,(~product(e_3, e_4, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.39/0.55 tff(397,assumption,(product(e_1, e_3, e_4)), introduced(assumption)).
% 0.39/0.55 tff(398,plain,
% 0.39/0.55 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_4, e_1)) | (~product(e_1, e_3, e_4)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_4, e_1)) | (~product(e_1, e_3, e_4)))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(399,plain,
% 0.39/0.55 (((~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_4, e_1)) | equalish(e_4, e_1)) <=> (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_4, e_1)) | (~product(e_1, e_3, e_4)))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(400,plain,
% 0.39/0.55 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_4, e_1)) | equalish(e_4, e_1))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_4, e_1)) | (~product(e_1, e_3, e_4))))),
% 0.39/0.55 inference(monotonicity,[status(thm)],[399])).
% 0.39/0.55 tff(401,plain,
% 0.39/0.55 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_4, e_1)) | equalish(e_4, e_1))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_4, e_1)) | (~product(e_1, e_3, e_4)))),
% 0.39/0.55 inference(transitivity,[status(thm)],[400, 398])).
% 0.39/0.55 tff(402,plain,
% 0.39/0.55 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_4, e_1)) | equalish(e_4, e_1))),
% 0.39/0.55 inference(quant_inst,[status(thm)],[])).
% 0.39/0.55 tff(403,plain,
% 0.39/0.55 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_4, e_1)) | (~product(e_1, e_3, e_4))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[402, 401])).
% 0.39/0.55 tff(404,plain,
% 0.39/0.55 (~product(e_3, e_4, e_1)),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[403, 25, 327, 12, 397])).
% 0.39/0.55 tff(405,assumption,(product(e_4, e_2, e_2)), introduced(assumption)).
% 0.39/0.55 tff(406,plain,
% 0.39/0.55 ((~equalish(e_4, e_2)) <=> (~equalish(e_4, e_2))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(407,axiom,(~equalish(e_4, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_2')).
% 0.39/0.55 tff(408,plain,
% 0.39/0.55 (~equalish(e_4, e_2)),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[407, 406])).
% 0.39/0.55 tff(409,plain,
% 0.39/0.55 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_4, e_2) | (~product(e_3, e_4, e_2)) | (~product(e_1, e_4, e_2)) | (~product(e_1, e_3, e_4)) | (~product(e_4, e_2, e_2)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_2) | (~product(e_3, e_4, e_2)) | (~product(e_1, e_4, e_2)) | (~product(e_1, e_3, e_4)) | (~product(e_4, e_2, e_2)))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(410,plain,
% 0.39/0.55 (((~product(e_1, e_4, e_2)) | (~product(e_1, e_3, e_4)) | (~product(e_4, e_2, e_2)) | (~product(e_3, e_4, e_2)) | equalish(e_4, e_2)) <=> (equalish(e_4, e_2) | (~product(e_3, e_4, e_2)) | (~product(e_1, e_4, e_2)) | (~product(e_1, e_3, e_4)) | (~product(e_4, e_2, e_2)))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(411,plain,
% 0.39/0.55 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_4, e_2)) | (~product(e_1, e_3, e_4)) | (~product(e_4, e_2, e_2)) | (~product(e_3, e_4, e_2)) | equalish(e_4, e_2))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_4, e_2) | (~product(e_3, e_4, e_2)) | (~product(e_1, e_4, e_2)) | (~product(e_1, e_3, e_4)) | (~product(e_4, e_2, e_2))))),
% 0.39/0.55 inference(monotonicity,[status(thm)],[410])).
% 0.39/0.55 tff(412,plain,
% 0.39/0.55 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_4, e_2)) | (~product(e_1, e_3, e_4)) | (~product(e_4, e_2, e_2)) | (~product(e_3, e_4, e_2)) | equalish(e_4, e_2))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_2) | (~product(e_3, e_4, e_2)) | (~product(e_1, e_4, e_2)) | (~product(e_1, e_3, e_4)) | (~product(e_4, e_2, e_2)))),
% 0.39/0.55 inference(transitivity,[status(thm)],[411, 409])).
% 0.39/0.55 tff(413,plain,
% 0.39/0.55 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_4, e_2)) | (~product(e_1, e_3, e_4)) | (~product(e_4, e_2, e_2)) | (~product(e_3, e_4, e_2)) | equalish(e_4, e_2))),
% 0.39/0.55 inference(quant_inst,[status(thm)],[])).
% 0.39/0.55 tff(414,plain,
% 0.39/0.55 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_2) | (~product(e_3, e_4, e_2)) | (~product(e_1, e_4, e_2)) | (~product(e_1, e_3, e_4)) | (~product(e_4, e_2, e_2))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[413, 412])).
% 0.39/0.55 tff(415,plain,
% 0.39/0.55 (~product(e_3, e_4, e_2)),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[414, 408, 327, 405, 360, 397])).
% 0.39/0.55 tff(416,assumption,(product(e_3, e_4, e_4)), introduced(assumption)).
% 0.39/0.55 tff(417,plain,
% 0.39/0.55 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_4, 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_4) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_4, e_4)))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(418,plain,
% 0.39/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_4, e_4)))),
% 0.39/0.55 inference(quant_inst,[status(thm)],[])).
% 0.39/0.55 tff(419,plain,
% 0.39/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_4, e_4))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[418, 417])).
% 0.39/0.55 tff(420,plain,
% 0.39/0.55 ($false),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[419, 363, 56, 342, 416])).
% 0.39/0.55 tff(421,plain,(~product(e_3, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.39/0.55 tff(422,plain,
% 0.39/0.55 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | (~group_element(e_4)) | product(e_3, e_4, e_4) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | product(e_3, e_4, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_3, e_4, e_4) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | product(e_3, e_4, e_3))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(423,plain,
% 0.39/0.55 (((~group_element(e_3)) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | (~group_element(e_4))) <=> ((~group_element(e_3)) | (~group_element(e_4)) | product(e_3, e_4, e_4) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | product(e_3, e_4, e_3))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(424,plain,
% 0.39/0.55 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | (~group_element(e_4)) | product(e_3, e_4, e_4) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | product(e_3, e_4, e_3)))),
% 0.39/0.56 inference(monotonicity,[status(thm)],[423])).
% 0.39/0.56 tff(425,plain,
% 0.39/0.56 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_3, e_4, e_4) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | product(e_3, e_4, e_3))),
% 0.39/0.56 inference(transitivity,[status(thm)],[424, 422])).
% 0.39/0.56 tff(426,plain,
% 0.39/0.56 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | (~group_element(e_4)))),
% 0.39/0.56 inference(quant_inst,[status(thm)],[])).
% 0.39/0.56 tff(427,plain,
% 0.39/0.56 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_3, e_4, e_4) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | product(e_3, e_4, e_3)),
% 0.39/0.56 inference(modus_ponens,[status(thm)],[426, 425])).
% 0.39/0.56 tff(428,plain,
% 0.39/0.56 (product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | product(e_3, e_4, e_3)),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[427, 191, 350, 118, 421])).
% 0.39/0.56 tff(429,plain,
% 0.39/0.56 ($false),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[428, 415, 404, 396])).
% 0.39/0.56 tff(430,plain,((~product(e_1, e_3, e_4)) | (~product(e_4, e_2, e_2)) | (~product(e_1, e_4, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.56 tff(431,plain,
% 0.39/0.56 (~product(e_4, e_2, e_2)),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[430, 390, 358])).
% 0.39/0.56 tff(432,plain,
% 0.39/0.56 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_1)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_1)))),
% 0.39/0.56 inference(rewrite,[status(thm)],[])).
% 0.39/0.56 tff(433,plain,
% 0.39/0.56 (((~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_2)) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_2, e_1)) | equalish(e_2, e_1)) <=> (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_1)))),
% 0.39/0.56 inference(rewrite,[status(thm)],[])).
% 0.39/0.56 tff(434,plain,
% 0.39/0.56 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_2)) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_2, e_1)) | equalish(e_2, e_1))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_1))))),
% 0.39/0.56 inference(monotonicity,[status(thm)],[433])).
% 0.39/0.56 tff(435,plain,
% 0.39/0.56 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_2)) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_2, e_1)) | equalish(e_2, e_1))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_1)))),
% 0.39/0.56 inference(transitivity,[status(thm)],[434, 432])).
% 0.39/0.56 tff(436,plain,
% 0.39/0.56 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_2)) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_2, e_1)) | equalish(e_2, e_1))),
% 0.39/0.56 inference(quant_inst,[status(thm)],[])).
% 0.39/0.56 tff(437,plain,
% 0.39/0.56 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_1))),
% 0.39/0.56 inference(modus_ponens,[status(thm)],[436, 435])).
% 0.39/0.56 tff(438,plain,
% 0.39/0.56 (~product(e_4, e_2, e_1)),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[437, 103, 327, 12, 358])).
% 0.39/0.56 tff(439,assumption,(product(e_4, e_2, e_4)), introduced(assumption)).
% 0.39/0.56 tff(440,plain,
% 0.39/0.56 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4)))),
% 0.39/0.56 inference(rewrite,[status(thm)],[])).
% 0.39/0.56 tff(441,plain,
% 0.39/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4)))),
% 0.39/0.56 inference(quant_inst,[status(thm)],[])).
% 0.39/0.56 tff(442,plain,
% 0.39/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4))),
% 0.39/0.56 inference(modus_ponens,[status(thm)],[441, 440])).
% 0.39/0.56 tff(443,plain,
% 0.39/0.56 ($false),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[442, 269, 22, 342, 439])).
% 0.39/0.56 tff(444,plain,(~product(e_4, e_2, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.39/0.56 tff(445,plain,
% 0.39/0.56 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | (~group_element(e_4)) | product(e_4, e_2, e_2) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_2)) | (~group_element(e_4)) | product(e_4, e_2, e_2) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_1))),
% 0.39/0.56 inference(rewrite,[status(thm)],[])).
% 0.39/0.56 tff(446,plain,
% 0.39/0.56 (((~group_element(e_4)) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | (~group_element(e_2))) <=> ((~group_element(e_2)) | (~group_element(e_4)) | product(e_4, e_2, e_2) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_1))),
% 0.39/0.56 inference(rewrite,[status(thm)],[])).
% 0.39/0.56 tff(447,plain,
% 0.39/0.56 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_4)) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | (~group_element(e_4)) | product(e_4, e_2, e_2) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_1)))),
% 0.39/0.56 inference(monotonicity,[status(thm)],[446])).
% 0.39/0.56 tff(448,plain,
% 0.39/0.56 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_4)) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_2)) | (~group_element(e_4)) | product(e_4, e_2, e_2) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_1))),
% 0.39/0.56 inference(transitivity,[status(thm)],[447, 445])).
% 0.39/0.56 tff(449,plain,
% 0.39/0.56 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_4)) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | (~group_element(e_2)))),
% 0.39/0.56 inference(quant_inst,[status(thm)],[])).
% 0.39/0.56 tff(450,plain,
% 0.39/0.56 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_2)) | (~group_element(e_4)) | product(e_4, e_2, e_2) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_1)),
% 0.39/0.56 inference(modus_ponens,[status(thm)],[449, 448])).
% 0.39/0.56 tff(451,plain,
% 0.39/0.56 (product(e_4, e_2, e_2) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_1)),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[450, 121, 350, 118])).
% 0.39/0.56 tff(452,plain,
% 0.39/0.56 (product(e_4, e_2, e_2) | product(e_4, e_2, e_3) | product(e_4, e_2, e_1)),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[451, 444])).
% 0.39/0.56 tff(453,plain,
% 0.39/0.56 (product(e_4, e_2, e_3)),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[452, 438, 431])).
% 0.39/0.56 tff(454,plain,
% 0.39/0.56 (~product(e_3, e_4, e_1)),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[403, 25, 327, 12, 390])).
% 0.39/0.56 tff(455,plain,
% 0.39/0.56 (product(e_3, e_4, e_2) | product(e_3, e_4, e_1)),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[428, 396])).
% 0.39/0.56 tff(456,plain,
% 0.39/0.56 (product(e_3, e_4, e_2)),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[455, 454])).
% 0.39/0.56 tff(457,assumption,(product(e_3, e_4, e_2)), introduced(assumption)).
% 0.39/0.56 tff(458,assumption,(product(e_4, e_2, e_3)), introduced(assumption)).
% 0.39/0.56 tff(459,plain,
% 0.39/0.56 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.39/0.56 inference(rewrite,[status(thm)],[])).
% 0.39/0.56 tff(460,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.39/0.56 tff(461,plain,
% 0.39/0.56 (~equalish(e_2, e_3)),
% 0.39/0.56 inference(modus_ponens,[status(thm)],[460, 459])).
% 0.39/0.56 tff(462,plain,
% 0.39/0.56 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_2, e_3)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_2, e_3)))),
% 0.39/0.56 inference(rewrite,[status(thm)],[])).
% 0.39/0.56 tff(463,plain,
% 0.39/0.56 (((~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_2)) | (~product(e_3, e_3, e_3)) | (~product(e_4, e_2, e_3)) | equalish(e_2, e_3)) <=> (equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_2, e_3)))),
% 0.39/0.56 inference(rewrite,[status(thm)],[])).
% 0.39/0.56 tff(464,plain,
% 0.39/0.56 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_2)) | (~product(e_3, e_3, e_3)) | (~product(e_4, e_2, e_3)) | equalish(e_2, e_3))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_2, e_3))))),
% 0.39/0.56 inference(monotonicity,[status(thm)],[463])).
% 0.39/0.56 tff(465,plain,
% 0.39/0.56 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_2)) | (~product(e_3, e_3, e_3)) | (~product(e_4, e_2, e_3)) | equalish(e_2, e_3))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_2, e_3)))),
% 0.39/0.56 inference(transitivity,[status(thm)],[464, 462])).
% 0.39/0.56 tff(466,plain,
% 0.39/0.56 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_2)) | (~product(e_3, e_3, e_3)) | (~product(e_4, e_2, e_3)) | equalish(e_2, e_3))),
% 0.39/0.56 inference(quant_inst,[status(thm)],[])).
% 0.39/0.56 tff(467,plain,
% 0.39/0.56 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_2, e_3))),
% 0.39/0.56 inference(modus_ponens,[status(thm)],[466, 465])).
% 0.39/0.56 tff(468,plain,
% 0.39/0.56 ($false),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[467, 461, 327, 32, 458, 457])).
% 0.39/0.56 tff(469,plain,((~product(e_3, e_4, e_2)) | (~product(e_4, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.56 tff(470,plain,
% 0.39/0.56 ($false),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[469, 456, 453])).
% 0.39/0.56 % SZS output end Proof
% 0.39/0.57 % E exiting
%------------------------------------------------------------------------------