%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP129-3.004 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:07:10 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.48s
% Output : Proof 0.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GRP129-3.004 : TPTP v9.0.0. Released v1.2.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 15:43:53 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.48 % SZS status Unsatisfiable
% 0.20/0.48 % SZS output start Proof
% 0.20/0.48 tff(product_type, type, (
% 0.20/0.48 product: ( $i * $i * $i ) > $o)).
% 0.20/0.48 tff(e_2_type, type, (
% 0.20/0.48 e_2: $i)).
% 0.20/0.48 tff(e_3_type, type, (
% 0.20/0.48 e_3: $i)).
% 0.20/0.48 tff(e_1_type, type, (
% 0.20/0.48 e_1: $i)).
% 0.20/0.48 tff(e_4_type, type, (
% 0.20/0.48 e_4: $i)).
% 0.20/0.48 tff(equalish_type, type, (
% 0.20/0.48 equalish: ( $i * $i ) > $o)).
% 0.20/0.48 tff(cycle_type, type, (
% 0.20/0.48 cycle: ( $i * $i ) > $o)).
% 0.20/0.48 tff(e_0_type, type, (
% 0.20/0.48 e_0: $i)).
% 0.20/0.48 tff(next_type, type, (
% 0.20/0.48 next: ( $i * $i ) > $o)).
% 0.20/0.48 tff(greater_type, type, (
% 0.20/0.48 greater: ( $i * $i ) > $o)).
% 0.20/0.48 tff(group_element_type, type, (
% 0.20/0.48 group_element: $i > $o)).
% 0.20/0.48 tff(1,assumption,(product(e_2, e_1, e_2)), introduced(assumption)).
% 0.20/0.48 tff(2,assumption,(product(e_1, e_2, e_3)), introduced(assumption)).
% 0.20/0.48 tff(3,assumption,(product(e_2, e_2, e_3)), introduced(assumption)).
% 0.20/0.48 tff(4,plain,
% 0.20/0.48 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(5,plain,
% 0.20/0.48 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.48 tff(6,plain,
% 0.20/0.48 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(7,plain,
% 0.20/0.48 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(W, Y, X)) | (~product(Z, Y, X))) <=> ((~product(Z, Y, X)) | (~product(W, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> (((~product(Z, Y, X)) | (~product(W, Y, X))) | equalish(W, Z)))), rewrite((((~product(Z, Y, X)) | (~product(W, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(8,plain,
% 0.20/0.48 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[7])).
% 0.20/0.48 tff(9,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_left_cancellation')).
% 0.20/0.48 tff(10,plain,
% 0.20/0.48 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.20/0.48 tff(11,plain,
% 0.20/0.48 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.20/0.48 tff(12,plain,(
% 0.20/0.48 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[11])).
% 0.20/0.48 tff(13,plain,
% 0.20/0.48 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.20/0.48 tff(14,plain,
% 0.20/0.48 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(15,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.20/0.48 tff(16,plain,
% 0.20/0.48 (~equalish(e_2, e_1)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.48 tff(17,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_2, e_3)))) <=> ((~![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_2, e_3)) | (~product(e_2, e_2, e_3)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(18,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_2, e_3)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(19,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_2, e_3))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.20/0.48 tff(20,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[19, 16, 13, 2, 3])).
% 0.20/0.48 tff(21,plain,((~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(22,plain,
% 0.20/0.48 (~product(e_2, e_2, e_3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[21, 2])).
% 0.20/0.48 tff(23,plain,
% 0.20/0.48 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl((product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1))) <=> (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(24,plain,
% 0.20/0.48 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[23])).
% 0.20/0.48 tff(25,plain,
% 0.20/0.48 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(26,plain,
% 0.20/0.48 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : trans(monotonicity(rewrite(((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) <=> ((~product(X, Z1, Z2)) | (~product(Y, X, Z1)))), ((((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) | product(Z1, Y, Z2)) <=> (((~product(X, Z1, Z2)) | (~product(Y, X, Z1))) | product(Z1, Y, Z2)))), rewrite((((~product(X, Z1, Z2)) | (~product(Y, X, Z1))) | product(Z1, Y, Z2)) <=> (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))), ((((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) | product(Z1, Y, Z2)) <=> (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(27,plain,
% 0.20/0.48 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) | product(Z1, Y, Z2)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[26])).
% 0.20/0.48 tff(28,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) | product(Z1, Y, Z2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qg3')).
% 0.20/0.48 tff(29,plain,
% 0.20/0.48 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.48 tff(30,plain,
% 0.20/0.48 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.20/0.48 tff(31,plain,(
% 0.20/0.48 ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[30])).
% 0.20/0.48 tff(32,plain,
% 0.20/0.48 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.20/0.48 tff(33,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(34,plain,
% 0.20/0.48 ((product(e_2, e_2, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2))) <=> (product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(35,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[34])).
% 0.20/0.48 tff(36,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[35, 33])).
% 0.20/0.48 tff(37,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(38,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.48 tff(39,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[38, 32, 1, 2, 22])).
% 0.20/0.48 tff(40,plain,((~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(41,plain,
% 0.20/0.48 (~product(e_1, e_2, e_3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[40, 1])).
% 0.20/0.48 tff(42,assumption,(product(e_1, e_2, e_2)), introduced(assumption)).
% 0.20/0.48 tff(43,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(44,plain,
% 0.20/0.48 ((product(e_2, e_2, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_1, e_2))) <=> (product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(45,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_2))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[44])).
% 0.20/0.48 tff(46,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[45, 43])).
% 0.20/0.48 tff(47,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(48,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_2))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.48 tff(49,plain,
% 0.20/0.48 (product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_2))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[48, 32])).
% 0.20/0.48 tff(50,plain,
% 0.20/0.48 (product(e_2, e_2, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[49, 42, 1])).
% 0.20/0.48 tff(51,plain,
% 0.20/0.48 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(52,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.20/0.48 tff(53,plain,
% 0.20/0.48 (~equalish(e_1, e_2)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.48 tff(54,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(55,plain,
% 0.20/0.48 ((equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2))) <=> (equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(56,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[55])).
% 0.20/0.48 tff(57,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[56, 54])).
% 0.20/0.48 tff(58,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(59,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.48 tff(60,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[59, 53, 13, 50, 42])).
% 0.20/0.48 tff(61,plain,((~product(e_1, e_2, e_2)) | (~product(e_2, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(62,plain,
% 0.20/0.48 (~product(e_1, e_2, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[61, 1])).
% 0.20/0.48 tff(63,assumption,(~cycle(e_1, e_0)), introduced(assumption)).
% 0.20/0.48 tff(64,assumption,(~product(e_1, e_1, e_2)), introduced(assumption)).
% 0.20/0.48 tff(65,assumption,(cycle(e_3, e_3)), introduced(assumption)).
% 0.20/0.48 tff(66,plain,
% 0.20/0.48 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(67,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.20/0.48 tff(68,plain,
% 0.20/0.48 (~equalish(e_3, e_1)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.20/0.48 tff(69,plain,
% 0.20/0.48 (^[W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : refl(((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) <=> ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(70,plain,
% 0.20/0.48 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) <=> ![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[69])).
% 0.20/0.48 tff(71,plain,
% 0.20/0.48 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) <=> ![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(72,plain,
% 0.20/0.49 (^[W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) <=> ((~cycle(X, Y)) | (~next(X, W)) | (~cycle(W, Z)))), (((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) <=> (((~cycle(X, Y)) | (~next(X, W)) | (~cycle(W, Z))) | (~greater(Y, e_0))))), rewrite((((~cycle(X, Y)) | (~next(X, W)) | (~cycle(W, Z))) | (~greater(Y, e_0))) <=> ((~cycle(X, Y)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))), (((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) <=> ((~cycle(X, Y)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))))), ((((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) | (~next(Z, Z1))) <=> (((~cycle(X, Y)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) | (~next(Z, Z1))))), rewrite((((~cycle(X, Y)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) | (~next(Z, Z1))) <=> ((~cycle(X, Y)) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))), ((((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) | (~next(Z, Z1))) <=> ((~cycle(X, Y)) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))))), (((((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) | (~next(Z, Z1))) | equalish(Y, Z1)) <=> (((~cycle(X, Y)) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) | equalish(Y, Z1)))), rewrite((((~cycle(X, Y)) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) | equalish(Y, Z1)) <=> ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))), (((((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) | (~next(Z, Z1))) | equalish(Y, Z1)) <=> ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(73,plain,
% 0.20/0.49 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) | (~next(Z, Z1))) | equalish(Y, Z1)) <=> ![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[72])).
% 0.20/0.49 tff(74,axiom,(![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) | (~next(Z, Z1))) | equalish(Y, Z1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cycle4')).
% 0.20/0.49 tff(75,plain,
% 0.20/0.49 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.49 tff(76,plain,
% 0.20/0.49 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.20/0.49 tff(77,plain,(
% 0.20/0.49 ![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[76])).
% 0.20/0.49 tff(78,plain,
% 0.20/0.49 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.20/0.49 tff(79,plain,
% 0.20/0.49 (cycle(e_4, e_0) <=> cycle(e_4, e_0)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(80,axiom,(cycle(e_4, e_0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cycle3')).
% 0.20/0.49 tff(81,plain,
% 0.20/0.49 (cycle(e_4, e_0)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.20/0.49 tff(82,plain,
% 0.20/0.49 (greater(e_3, e_0) <=> greater(e_3, e_0)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(83,axiom,(greater(e_3, e_0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_greater_e_0')).
% 0.20/0.49 tff(84,plain,
% 0.20/0.49 (greater(e_3, e_0)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.20/0.49 tff(85,plain,
% 0.20/0.49 (next(e_3, e_4) <=> next(e_3, e_4)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(86,axiom,(next(e_3, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_then_e_4')).
% 0.20/0.49 tff(87,plain,
% 0.20/0.49 (next(e_3, e_4)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.49 tff(88,plain,
% 0.20/0.49 (next(e_0, e_1) <=> next(e_0, e_1)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(89,axiom,(next(e_0, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_0_then_e_1')).
% 0.20/0.49 tff(90,plain,
% 0.20/0.49 (next(e_0, e_1)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.20/0.49 tff(91,plain,
% 0.20/0.49 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_3, e_1) | (~cycle(e_4, e_0)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~next(e_0, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_1) | (~cycle(e_4, e_0)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~next(e_0, e_1)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(92,plain,
% 0.20/0.49 (((~cycle(e_3, e_3)) | equalish(e_3, e_1) | (~next(e_0, e_1)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0))) <=> (equalish(e_3, e_1) | (~cycle(e_4, e_0)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~next(e_0, e_1)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(93,plain,
% 0.20/0.49 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_3, e_3)) | equalish(e_3, e_1) | (~next(e_0, e_1)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_3, e_1) | (~cycle(e_4, e_0)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~next(e_0, e_1))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[92])).
% 0.20/0.49 tff(94,plain,
% 0.20/0.49 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_3, e_3)) | equalish(e_3, e_1) | (~next(e_0, e_1)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_1) | (~cycle(e_4, e_0)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~next(e_0, e_1)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[93, 91])).
% 0.20/0.49 tff(95,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_3, e_3)) | equalish(e_3, e_1) | (~next(e_0, e_1)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(96,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_1) | (~cycle(e_4, e_0)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~next(e_0, e_1))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.20/0.49 tff(97,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[96, 90, 87, 84, 81, 78, 68, 65])).
% 0.20/0.49 tff(98,plain,(~cycle(e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(99,assumption,(product(e_1, e_1, e_4)), introduced(assumption)).
% 0.20/0.49 tff(100,plain,
% 0.20/0.49 (^[Y: $i, X: $i] : refl(((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0))) <=> ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(101,plain,
% 0.20/0.49 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0))) <=> ![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[100])).
% 0.20/0.49 tff(102,plain,
% 0.20/0.49 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0))) <=> ![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(103,plain,
% 0.20/0.49 (^[Y: $i, X: $i] : rewrite((((~cycle(X, e_0)) | (~product(X, e_1, Y))) | (~greater(Y, X))) <=> ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(104,plain,
% 0.20/0.49 (![Y: $i, X: $i] : (((~cycle(X, e_0)) | (~product(X, e_1, Y))) | (~greater(Y, X))) <=> ![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[103])).
% 0.20/0.49 tff(105,axiom,(![Y: $i, X: $i] : (((~cycle(X, e_0)) | (~product(X, e_1, Y))) | (~greater(Y, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cycle6')).
% 0.20/0.49 tff(106,plain,
% 0.20/0.49 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.49 tff(107,plain,
% 0.20/0.49 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.20/0.49 tff(108,plain,(
% 0.20/0.49 ![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[107])).
% 0.20/0.49 tff(109,plain,
% 0.20/0.49 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[108, 101])).
% 0.20/0.49 tff(110,plain,
% 0.20/0.49 (greater(e_4, e_1) <=> greater(e_4, e_1)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(111,axiom,(greater(e_4, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_greater_e_1')).
% 0.20/0.49 tff(112,plain,
% 0.20/0.49 (greater(e_4, e_1)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.20/0.49 tff(113,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~cycle(e_1, e_0)) | (~greater(e_4, e_1)) | (~product(e_1, e_1, e_4)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_4, e_1)) | (~product(e_1, e_1, e_4)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(114,plain,
% 0.20/0.49 (((~greater(e_4, e_1)) | (~product(e_1, e_1, e_4)) | (~cycle(e_1, e_0))) <=> ((~cycle(e_1, e_0)) | (~greater(e_4, e_1)) | (~product(e_1, e_1, e_4)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(115,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_4, e_1)) | (~product(e_1, e_1, e_4)) | (~cycle(e_1, e_0)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~cycle(e_1, e_0)) | (~greater(e_4, e_1)) | (~product(e_1, e_1, e_4))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[114])).
% 0.20/0.49 tff(116,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_4, e_1)) | (~product(e_1, e_1, e_4)) | (~cycle(e_1, e_0)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_4, e_1)) | (~product(e_1, e_1, e_4)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[115, 113])).
% 0.20/0.49 tff(117,plain,
% 0.20/0.49 ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_4, e_1)) | (~product(e_1, e_1, e_4)) | (~cycle(e_1, e_0)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(118,plain,
% 0.20/0.49 ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_4, e_1)) | (~product(e_1, e_1, e_4))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.20/0.49 tff(119,plain,
% 0.20/0.49 ((~cycle(e_1, e_0)) | (~product(e_1, e_1, e_4))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[118, 112, 109])).
% 0.20/0.49 tff(120,plain,
% 0.20/0.49 (~cycle(e_1, e_0)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[119, 99])).
% 0.20/0.49 tff(121,assumption,(cycle(e_3, e_0)), introduced(assumption)).
% 0.20/0.49 tff(122,plain,
% 0.20/0.49 (^[W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : refl(((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) <=> ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(123,plain,
% 0.20/0.49 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) <=> ![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[122])).
% 0.20/0.49 tff(124,plain,
% 0.20/0.49 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) <=> ![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(125,plain,
% 0.20/0.49 (^[W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) <=> ((~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))), (((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) <=> (((~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~next(Y, W))))), rewrite((((~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~next(Y, W))) <=> ((~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))), (((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) <=> ((~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))))), ((((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) | (~greater(Y, X))) <=> (((~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~greater(Y, X))))), rewrite((((~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~greater(Y, X))) <=> ((~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))), ((((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) | (~greater(Y, X))) <=> ((~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))))), (((((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) | (~greater(Y, X))) | (~greater(Z1, Z2))) <=> (((~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~greater(Z1, Z2))))), rewrite((((~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~greater(Z1, Z2))) <=> ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))), (((((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) | (~greater(Y, X))) | (~greater(Z1, Z2))) <=> ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(126,plain,
% 0.20/0.49 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) | (~greater(Y, X))) | (~greater(Z1, Z2))) <=> ![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[125])).
% 0.20/0.49 tff(127,axiom,(![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) | (~greater(Y, X))) | (~greater(Z1, Z2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cycle5')).
% 0.20/0.49 tff(128,plain,
% 0.20/0.49 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.20/0.49 tff(129,plain,
% 0.20/0.49 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.20/0.49 tff(130,plain,(
% 0.20/0.49 ![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[129])).
% 0.20/0.49 tff(131,plain,
% 0.20/0.49 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[130, 123])).
% 0.20/0.49 tff(132,plain,
% 0.20/0.49 (greater(e_3, e_1) <=> greater(e_3, e_1)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(133,axiom,(greater(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_greater_e_1')).
% 0.20/0.49 tff(134,plain,
% 0.20/0.49 (greater(e_3, e_1)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.20/0.49 tff(135,plain,
% 0.20/0.49 (greater(e_1, e_0) <=> greater(e_1, e_0)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(136,axiom,(greater(e_1, e_0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_greater_e_0')).
% 0.20/0.49 tff(137,plain,
% 0.20/0.49 (greater(e_1, e_0)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.20/0.49 tff(138,plain,
% 0.20/0.49 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_4, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_1)) | (~greater(e_3, 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)) | (~cycle(e_1, e_1)) | (~greater(e_3, e_1)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(139,plain,
% 0.20/0.49 (((~greater(e_1, e_0)) | (~greater(e_3, e_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_1, e_1))) <=> ((~cycle(e_4, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_1)) | (~greater(e_3, e_1)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(140,plain,
% 0.20/0.49 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_1, e_0)) | (~greater(e_3, e_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_1, 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)) | (~cycle(e_1, e_1)) | (~greater(e_3, e_1))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[139])).
% 0.20/0.49 tff(141,plain,
% 0.20/0.49 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_1, e_0)) | (~greater(e_3, e_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_1, 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)) | (~cycle(e_1, e_1)) | (~greater(e_3, e_1)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[140, 138])).
% 0.20/0.49 tff(142,plain,
% 0.20/0.49 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_1, e_0)) | (~greater(e_3, e_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_1, e_1)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(143,plain,
% 0.20/0.49 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_4, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_1)) | (~greater(e_3, e_1))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.20/0.49 tff(144,plain,
% 0.20/0.50 ((~cycle(e_3, e_0)) | (~cycle(e_1, e_1))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[143, 87, 137, 134, 81, 131])).
% 0.20/0.50 tff(145,plain,
% 0.20/0.50 (~cycle(e_1, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[144, 121])).
% 0.20/0.50 tff(146,plain,
% 0.20/0.50 (greater(e_2, e_0) <=> greater(e_2, e_0)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(147,axiom,(greater(e_2, e_0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_greater_e_0')).
% 0.20/0.50 tff(148,plain,
% 0.20/0.50 (greater(e_2, e_0)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.20/0.50 tff(149,plain,
% 0.20/0.50 (((~![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_1)) | (~cycle(e_1, e_2)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_2)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(150,plain,
% 0.20/0.50 (((~greater(e_2, e_0)) | (~greater(e_3, e_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_1, 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_1)) | (~cycle(e_1, e_2)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(151,plain,
% 0.20/0.50 (((~![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_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_1, e_2)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_2))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[150])).
% 0.20/0.50 tff(152,plain,
% 0.20/0.50 (((~![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_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_1, e_2)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_2)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[151, 149])).
% 0.20/0.50 tff(153,plain,
% 0.20/0.50 ((~![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_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_1, e_2)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(154,plain,
% 0.20/0.50 ((~![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_1)) | (~cycle(e_1, e_2))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.20/0.50 tff(155,plain,
% 0.20/0.50 ((~cycle(e_3, e_0)) | (~cycle(e_1, e_2))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[154, 87, 148, 134, 81, 131])).
% 0.20/0.50 tff(156,plain,
% 0.20/0.50 (~cycle(e_1, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[155, 121])).
% 0.20/0.50 tff(157,plain,
% 0.20/0.50 (((~![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_1)) | (~cycle(e_1, e_3)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_3)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(158,plain,
% 0.20/0.50 (((~greater(e_3, e_0)) | (~greater(e_3, e_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_1, 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_1)) | (~cycle(e_1, e_3)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(159,plain,
% 0.20/0.50 (((~![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_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_1, e_3)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_3))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[158])).
% 0.20/0.50 tff(160,plain,
% 0.20/0.50 (((~![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_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_1, e_3)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_3)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[159, 157])).
% 0.20/0.50 tff(161,plain,
% 0.20/0.50 ((~![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_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_1, e_3)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(162,plain,
% 0.20/0.50 ((~![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_1)) | (~cycle(e_1, e_3))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.20/0.50 tff(163,plain,
% 0.20/0.50 ((~cycle(e_3, e_0)) | (~cycle(e_1, e_3))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[162, 87, 84, 134, 81, 131])).
% 0.20/0.50 tff(164,plain,
% 0.20/0.50 (~cycle(e_1, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[163, 121])).
% 0.20/0.50 tff(165,plain,
% 0.20/0.50 (group_element(e_1) <=> group_element(e_1)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(166,axiom,(group_element(e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_1')).
% 0.20/0.50 tff(167,plain,
% 0.20/0.50 (group_element(e_1)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.20/0.50 tff(168,plain,
% 0.20/0.50 (^[X: $i] : refl((cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) <=> (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(169,plain,
% 0.20/0.50 (![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) <=> ![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[168])).
% 0.20/0.50 tff(170,plain,
% 0.20/0.50 (![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) <=> ![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(171,plain,
% 0.20/0.50 (^[X: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) <=> (cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))), (((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) <=> ((cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) | cycle(X, e_2)))), rewrite(((cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) | cycle(X, e_2)) <=> (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))), (((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) <=> (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))))), ((((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) | cycle(X, e_3)) <=> ((cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) | cycle(X, e_3)))), rewrite(((cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) | cycle(X, e_3)) <=> (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))), ((((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) | cycle(X, e_3)) <=> (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(172,plain,
% 0.20/0.50 (![X: $i] : (((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) | cycle(X, e_3)) <=> ![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[171])).
% 0.20/0.50 tff(173,axiom,(![X: $i] : (((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) | cycle(X, e_3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cycle2')).
% 0.20/0.50 tff(174,plain,
% 0.20/0.50 (![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.20/0.50 tff(175,plain,
% 0.20/0.50 (![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[174, 170])).
% 0.20/0.50 tff(176,plain,(
% 0.20/0.50 ![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[175])).
% 0.20/0.50 tff(177,plain,
% 0.20/0.50 (![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[176, 169])).
% 0.20/0.50 tff(178,plain,
% 0.20/0.50 (((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_1, e_3) | cycle(e_1, e_2) | cycle(e_1, e_1) | cycle(e_1, e_0) | (~group_element(e_1)))) <=> ((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_1, e_3) | cycle(e_1, e_2) | cycle(e_1, e_1) | cycle(e_1, e_0) | (~group_element(e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(179,plain,
% 0.20/0.50 ((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_1, e_3) | cycle(e_1, e_2) | cycle(e_1, e_1) | cycle(e_1, e_0) | (~group_element(e_1)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(180,plain,
% 0.20/0.50 ((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_1, e_3) | cycle(e_1, e_2) | cycle(e_1, e_1) | cycle(e_1, e_0) | (~group_element(e_1))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.20/0.50 tff(181,plain,
% 0.20/0.50 (cycle(e_1, e_3) | cycle(e_1, e_2) | cycle(e_1, e_1) | cycle(e_1, e_0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[180, 177, 167])).
% 0.20/0.50 tff(182,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[181, 164, 156, 63, 145])).
% 0.20/0.50 tff(183,plain,((~cycle(e_3, e_0)) | cycle(e_1, e_0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(184,plain,
% 0.20/0.50 (~cycle(e_3, e_0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[183, 120])).
% 0.20/0.50 tff(185,assumption,(cycle(e_3, e_2)), introduced(assumption)).
% 0.20/0.50 tff(186,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_2, e_1) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~next(e_0, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_1) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~next(e_0, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(187,plain,
% 0.20/0.50 (((~cycle(e_3, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0))) <=> (equalish(e_2, e_1) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~next(e_0, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(188,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_3, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_2, e_1) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~next(e_0, e_1))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[187])).
% 0.20/0.50 tff(189,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_3, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_1) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~next(e_0, e_1)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[188, 186])).
% 0.20/0.50 tff(190,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_3, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(191,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_1) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~next(e_0, e_1))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.20/0.50 tff(192,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[191, 90, 87, 148, 81, 78, 16, 185])).
% 0.20/0.50 tff(193,plain,(~cycle(e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(194,plain,
% 0.20/0.50 (group_element(e_3) <=> group_element(e_3)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(195,axiom,(group_element(e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_3')).
% 0.20/0.50 tff(196,plain,
% 0.20/0.50 (group_element(e_3)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.20/0.50 tff(197,plain,
% 0.20/0.50 (((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0) | (~group_element(e_3)))) <=> ((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0) | (~group_element(e_3)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(198,plain,
% 0.20/0.50 ((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0) | (~group_element(e_3)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(199,plain,
% 0.20/0.50 ((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0) | (~group_element(e_3))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.20/0.50 tff(200,plain,
% 0.20/0.50 (cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[199, 177, 196])).
% 0.20/0.50 tff(201,plain,
% 0.20/0.50 (cycle(e_3, e_3) | cycle(e_3, e_1) | cycle(e_3, e_0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[200, 193])).
% 0.20/0.50 tff(202,plain,
% 0.20/0.50 (cycle(e_3, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[201, 184, 98])).
% 0.20/0.50 tff(203,plain,
% 0.20/0.50 ((~equalish(e_1, e_4)) <=> (~equalish(e_1, e_4))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(204,axiom,(~equalish(e_1, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_4')).
% 0.20/0.50 tff(205,plain,
% 0.20/0.50 (~equalish(e_1, e_4)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.20/0.50 tff(206,plain,
% 0.20/0.50 (^[Z: $i, Y: $i, X: $i, X1: $i] : refl(((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z))) <=> ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(207,plain,
% 0.20/0.50 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z))) <=> ![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[206])).
% 0.20/0.50 tff(208,plain,
% 0.20/0.50 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z))) <=> ![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(209,plain,
% 0.20/0.50 (^[Z: $i, Y: $i, X: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~cycle(X, Y)) | (~product(X, e_1, Z))) | (~greater(Y, e_0))) <=> ((~greater(Y, e_0)) | (~cycle(X, Y)) | (~product(X, e_1, Z)))), (((((~cycle(X, Y)) | (~product(X, e_1, Z))) | (~greater(Y, e_0))) | (~next(X, X1))) <=> (((~greater(Y, e_0)) | (~cycle(X, Y)) | (~product(X, e_1, Z))) | (~next(X, X1))))), rewrite((((~greater(Y, e_0)) | (~cycle(X, Y)) | (~product(X, e_1, Z))) | (~next(X, X1))) <=> ((~greater(Y, e_0)) | (~cycle(X, Y)) | (~next(X, X1)) | (~product(X, e_1, Z)))), (((((~cycle(X, Y)) | (~product(X, e_1, Z))) | (~greater(Y, e_0))) | (~next(X, X1))) <=> ((~greater(Y, e_0)) | (~cycle(X, Y)) | (~next(X, X1)) | (~product(X, e_1, Z))))), ((((((~cycle(X, Y)) | (~product(X, e_1, Z))) | (~greater(Y, e_0))) | (~next(X, X1))) | equalish(Z, X1)) <=> (((~greater(Y, e_0)) | (~cycle(X, Y)) | (~next(X, X1)) | (~product(X, e_1, Z))) | equalish(Z, X1)))), rewrite((((~greater(Y, e_0)) | (~cycle(X, Y)) | (~next(X, X1)) | (~product(X, e_1, Z))) | equalish(Z, X1)) <=> ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))), ((((((~cycle(X, Y)) | (~product(X, e_1, Z))) | (~greater(Y, e_0))) | (~next(X, X1))) | equalish(Z, X1)) <=> ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(210,plain,
% 0.20/0.50 (![Z: $i, Y: $i, X: $i, X1: $i] : (((((~cycle(X, Y)) | (~product(X, e_1, Z))) | (~greater(Y, e_0))) | (~next(X, X1))) | equalish(Z, X1)) <=> ![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[209])).
% 0.20/0.50 tff(211,axiom,(![Z: $i, Y: $i, X: $i, X1: $i] : (((((~cycle(X, Y)) | (~product(X, e_1, Z))) | (~greater(Y, e_0))) | (~next(X, X1))) | equalish(Z, X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cycle7')).
% 0.20/0.50 tff(212,plain,
% 0.20/0.50 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.20/0.50 tff(213,plain,
% 0.20/0.50 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[212, 208])).
% 0.20/0.51 tff(214,plain,(
% 0.20/0.51 ![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[213])).
% 0.20/0.51 tff(215,plain,
% 0.20/0.51 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[214, 207])).
% 0.20/0.51 tff(216,plain,
% 0.20/0.51 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_1, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_1)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_1, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(217,plain,
% 0.20/0.51 (((~greater(e_1, e_0)) | (~cycle(e_3, e_1)) | equalish(e_1, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_1))) <=> (equalish(e_1, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(218,plain,
% 0.20/0.51 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_3, e_1)) | equalish(e_1, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_1)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_1, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_1))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[217])).
% 0.20/0.51 tff(219,plain,
% 0.20/0.51 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_3, e_1)) | equalish(e_1, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_1)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_1, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[218, 216])).
% 0.20/0.51 tff(220,plain,
% 0.20/0.51 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_3, e_1)) | equalish(e_1, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_1)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(221,plain,
% 0.20/0.51 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_1, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_1))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.20/0.51 tff(222,plain,
% 0.20/0.51 (~product(e_3, e_1, e_1)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[221, 87, 137, 215, 205, 202])).
% 0.20/0.51 tff(223,plain,
% 0.20/0.51 ((~equalish(e_3, e_4)) <=> (~equalish(e_3, e_4))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(224,axiom,(~equalish(e_3, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_4')).
% 0.20/0.51 tff(225,plain,
% 0.20/0.51 (~equalish(e_3, e_4)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.20/0.51 tff(226,plain,
% 0.20/0.51 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_3, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_3)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_3, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_3)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(227,plain,
% 0.20/0.51 (((~greater(e_1, e_0)) | (~cycle(e_3, e_1)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_3))) <=> (equalish(e_3, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_3)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(228,plain,
% 0.20/0.51 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_3, e_1)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_3)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_3, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_3))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[227])).
% 0.20/0.51 tff(229,plain,
% 0.20/0.51 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_3, e_1)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_3)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_3, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_3)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[228, 226])).
% 0.20/0.51 tff(230,plain,
% 0.20/0.51 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_3, e_1)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_3)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(231,plain,
% 0.20/0.51 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_3, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_3))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.20/0.51 tff(232,plain,
% 0.20/0.51 (~product(e_3, e_1, e_3)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[231, 87, 137, 215, 225, 202])).
% 0.20/0.51 tff(233,plain,
% 0.20/0.51 ((~equalish(e_2, e_4)) <=> (~equalish(e_2, e_4))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(234,axiom,(~equalish(e_2, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_4')).
% 0.20/0.51 tff(235,plain,
% 0.20/0.51 (~equalish(e_2, e_4)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.20/0.51 tff(236,plain,
% 0.20/0.51 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_2, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_2)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_2)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(237,plain,
% 0.20/0.51 (((~greater(e_1, e_0)) | (~cycle(e_3, e_1)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2))) <=> (equalish(e_2, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_2)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(238,plain,
% 0.20/0.51 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_3, e_1)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_2, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_2))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[237])).
% 0.20/0.51 tff(239,plain,
% 0.20/0.51 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_3, e_1)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_2)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[238, 236])).
% 0.20/0.51 tff(240,plain,
% 0.20/0.51 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_3, e_1)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(241,plain,
% 0.20/0.51 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_2))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.20/0.51 tff(242,plain,
% 0.20/0.51 (~product(e_3, e_1, e_2)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[241, 87, 137, 215, 235, 202])).
% 0.20/0.51 tff(243,plain,
% 0.20/0.51 (^[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))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(244,plain,
% 0.20/0.51 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) <=> ![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[243])).
% 0.20/0.51 tff(245,plain,
% 0.20/0.51 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) <=> ![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(246,plain,
% 0.20/0.51 (^[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)))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(247,plain,
% 0.20/0.51 (![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)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[246])).
% 0.20/0.51 tff(248,axiom,(![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_total_function1')).
% 0.20/0.51 tff(249,plain,
% 0.20/0.51 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.20/0.51 tff(250,plain,
% 0.20/0.51 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[249, 245])).
% 0.20/0.51 tff(251,plain,(
% 0.20/0.51 ![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[250])).
% 0.20/0.51 tff(252,plain,
% 0.20/0.51 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[251, 244])).
% 0.20/0.51 tff(253,plain,
% 0.20/0.51 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(254,plain,
% 0.20/0.51 (((~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1))) <=> ((~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(255,plain,
% 0.20/0.51 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[254])).
% 0.20/0.51 tff(256,plain,
% 0.20/0.51 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1))),
% 0.20/0.51 inference(transitivity,[status(thm)],[255, 253])).
% 0.20/0.51 tff(257,plain,
% 0.20/0.51 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(258,plain,
% 0.20/0.51 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.20/0.51 tff(259,plain,
% 0.20/0.51 (product(e_3, e_1, e_4)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[258, 167, 196, 252, 242, 232, 222])).
% 0.20/0.51 tff(260,plain,
% 0.20/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_4)) | (~product(e_3, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_4)) | (~product(e_3, e_1, e_4)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(261,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_4)) | (~product(e_3, e_1, e_4)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(262,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_4)) | (~product(e_3, e_1, e_4))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.20/0.51 tff(263,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[262, 68, 13, 99, 259])).
% 0.20/0.51 tff(264,plain,(~product(e_1, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(265,assumption,(~cycle(e_1, e_1)), introduced(assumption)).
% 0.20/0.51 tff(266,assumption,(~product(e_1, e_1, e_4)), introduced(assumption)).
% 0.20/0.51 tff(267,assumption,(cycle(e_1, e_2)), introduced(assumption)).
% 0.20/0.51 tff(268,plain,
% 0.20/0.51 (next(e_1, e_2) <=> next(e_1, e_2)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(269,axiom,(next(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_then_e_2')).
% 0.20/0.51 tff(270,plain,
% 0.20/0.51 (next(e_1, e_2)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.20/0.51 tff(271,plain,
% 0.20/0.51 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~product(e_1, e_1, e_1)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(272,plain,
% 0.20/0.51 (((~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_1))) <=> (equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(273,plain,
% 0.20/0.51 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_1)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~product(e_1, e_1, e_1))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[272])).
% 0.20/0.52 tff(274,plain,
% 0.20/0.52 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_1)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[273, 271])).
% 0.20/0.52 tff(275,plain,
% 0.20/0.52 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(276,plain,
% 0.20/0.52 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~product(e_1, e_1, e_1))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.20/0.52 tff(277,plain,
% 0.20/0.52 (~product(e_1, e_1, e_1)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[276, 270, 148, 215, 53, 267])).
% 0.20/0.52 tff(278,plain,
% 0.20/0.52 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(279,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.20/0.52 tff(280,plain,
% 0.20/0.52 (~equalish(e_3, e_2)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.20/0.52 tff(281,plain,
% 0.20/0.52 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~product(e_1, e_1, e_3)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~product(e_1, e_1, e_3)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(282,plain,
% 0.20/0.52 (((~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3))) <=> (equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~product(e_1, e_1, e_3)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(283,plain,
% 0.20/0.52 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~product(e_1, e_1, e_3))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[282])).
% 0.20/0.52 tff(284,plain,
% 0.20/0.52 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~product(e_1, e_1, e_3)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[283, 281])).
% 0.20/0.52 tff(285,plain,
% 0.20/0.52 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(286,plain,
% 0.20/0.52 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~product(e_1, e_1, e_3))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.20/0.52 tff(287,plain,
% 0.20/0.52 (~product(e_1, e_1, e_3)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[286, 270, 148, 215, 280, 267])).
% 0.20/0.52 tff(288,plain,
% 0.20/0.52 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_1, e_2) | product(e_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, 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)) | product(e_1, e_1, e_2) | product(e_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_1))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(289,plain,
% 0.20/0.52 (((~group_element(e_1)) | product(e_1, e_1, e_4) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1))) <=> ((~group_element(e_1)) | product(e_1, e_1, e_2) | product(e_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_1))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(290,plain,
% 0.20/0.52 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_1, e_4) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_1, e_2) | product(e_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_1)))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[289])).
% 0.20/0.52 tff(291,plain,
% 0.20/0.52 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_1, e_4) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | product(e_1, e_1, e_2) | product(e_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_1))),
% 0.20/0.52 inference(transitivity,[status(thm)],[290, 288])).
% 0.20/0.52 tff(292,plain,
% 0.20/0.52 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_1, e_4) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(293,plain,
% 0.20/0.52 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | product(e_1, e_1, e_2) | product(e_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_1)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.20/0.52 tff(294,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[293, 167, 252, 64, 287, 266, 277])).
% 0.20/0.52 tff(295,plain,((~cycle(e_1, e_2)) | product(e_1, e_1, e_2) | product(e_1, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(296,plain,
% 0.20/0.52 (~cycle(e_1, e_2)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[295, 64, 266])).
% 0.20/0.52 tff(297,plain,
% 0.20/0.52 (cycle(e_1, e_3)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[181, 296, 265, 63])).
% 0.20/0.52 tff(298,plain,
% 0.20/0.52 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | (~product(e_1, e_1, e_1)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | (~product(e_1, e_1, e_1)))),
% 0.36/0.52 inference(rewrite,[status(thm)],[])).
% 0.36/0.52 tff(299,plain,
% 0.36/0.52 (((~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_1))) <=> (equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | (~product(e_1, e_1, e_1)))),
% 0.36/0.52 inference(rewrite,[status(thm)],[])).
% 0.36/0.52 tff(300,plain,
% 0.36/0.52 (((~![Z: $i, 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_1, e_3)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_1)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | (~product(e_1, e_1, e_1))))),
% 0.36/0.52 inference(monotonicity,[status(thm)],[299])).
% 0.36/0.52 tff(301,plain,
% 0.36/0.52 (((~![Z: $i, 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_1, e_3)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_1)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | (~product(e_1, e_1, e_1)))),
% 0.36/0.52 inference(transitivity,[status(thm)],[300, 298])).
% 0.36/0.52 tff(302,plain,
% 0.36/0.52 ((~![Z: $i, 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_1, e_3)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_1)))),
% 0.36/0.52 inference(quant_inst,[status(thm)],[])).
% 0.36/0.52 tff(303,plain,
% 0.36/0.52 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | (~product(e_1, e_1, e_1))),
% 0.36/0.52 inference(modus_ponens,[status(thm)],[302, 301])).
% 0.36/0.52 tff(304,plain,
% 0.36/0.52 (~product(e_1, e_1, e_1)),
% 0.36/0.52 inference(unit_resolution,[status(thm)],[303, 270, 84, 215, 53, 297])).
% 0.36/0.52 tff(305,plain,
% 0.36/0.52 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | (~product(e_1, e_1, e_3)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | (~product(e_1, e_1, e_3)))),
% 0.36/0.52 inference(rewrite,[status(thm)],[])).
% 0.36/0.52 tff(306,plain,
% 0.36/0.52 (((~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3))) <=> (equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | (~product(e_1, e_1, e_3)))),
% 0.36/0.52 inference(rewrite,[status(thm)],[])).
% 0.36/0.52 tff(307,plain,
% 0.36/0.52 (((~![Z: $i, 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_1, e_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | (~product(e_1, e_1, e_3))))),
% 0.36/0.52 inference(monotonicity,[status(thm)],[306])).
% 0.36/0.52 tff(308,plain,
% 0.36/0.52 (((~![Z: $i, 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_1, e_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | (~product(e_1, e_1, e_3)))),
% 0.36/0.52 inference(transitivity,[status(thm)],[307, 305])).
% 0.36/0.52 tff(309,plain,
% 0.36/0.52 ((~![Z: $i, 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_1, e_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))),
% 0.36/0.52 inference(quant_inst,[status(thm)],[])).
% 0.36/0.52 tff(310,plain,
% 0.36/0.52 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | (~product(e_1, e_1, e_3))),
% 0.36/0.52 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.36/0.52 tff(311,plain,
% 0.36/0.52 (~product(e_1, e_1, e_3)),
% 0.36/0.52 inference(unit_resolution,[status(thm)],[310, 270, 84, 215, 280, 297])).
% 0.36/0.52 tff(312,plain,
% 0.36/0.52 ($false),
% 0.36/0.52 inference(unit_resolution,[status(thm)],[293, 167, 252, 64, 311, 266, 304])).
% 0.36/0.52 tff(313,plain,(product(e_1, e_1, e_2) | product(e_1, e_1, e_4) | cycle(e_1, e_1) | cycle(e_1, e_0)), inference(lemma,lemma(discharge,[]))).
% 0.36/0.52 tff(314,plain,
% 0.36/0.52 (product(e_1, e_1, e_2) | cycle(e_1, e_1) | cycle(e_1, e_0)),
% 0.36/0.52 inference(unit_resolution,[status(thm)],[313, 264])).
% 0.36/0.52 tff(315,plain,
% 0.36/0.52 (cycle(e_1, e_1)),
% 0.36/0.52 inference(unit_resolution,[status(thm)],[314, 64, 63])).
% 0.36/0.52 tff(316,plain,
% 0.36/0.52 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_1, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_1)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_1, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.36/0.52 inference(rewrite,[status(thm)],[])).
% 0.36/0.52 tff(317,plain,
% 0.36/0.52 (((~greater(e_1, e_0)) | (~cycle(e_1, e_1)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_1))) <=> (equalish(e_1, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.36/0.52 inference(rewrite,[status(thm)],[])).
% 0.36/0.52 tff(318,plain,
% 0.36/0.52 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_1, e_1)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_1)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_1, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_1))))),
% 0.36/0.52 inference(monotonicity,[status(thm)],[317])).
% 0.36/0.52 tff(319,plain,
% 0.36/0.52 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_1, e_1)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_1)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_1, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.36/0.52 inference(transitivity,[status(thm)],[318, 316])).
% 0.36/0.52 tff(320,plain,
% 0.36/0.52 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_1, e_1)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_1)))),
% 0.36/0.52 inference(quant_inst,[status(thm)],[])).
% 0.36/0.52 tff(321,plain,
% 0.36/0.52 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_1, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_1))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.36/0.53 tff(322,plain,
% 0.36/0.53 (~product(e_1, e_1, e_1)),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[321, 270, 137, 215, 53, 315])).
% 0.36/0.53 tff(323,plain,
% 0.36/0.53 (((~![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_3, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_3)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_3, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_3)))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(324,plain,
% 0.36/0.53 (((~greater(e_1, e_0)) | (~cycle(e_1, e_1)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3))) <=> (equalish(e_3, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_3)))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(325,plain,
% 0.36/0.53 (((~![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_1, e_1)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_3, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_3))))),
% 0.36/0.53 inference(monotonicity,[status(thm)],[324])).
% 0.36/0.53 tff(326,plain,
% 0.36/0.53 (((~![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_1, e_1)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_3, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_3)))),
% 0.36/0.53 inference(transitivity,[status(thm)],[325, 323])).
% 0.36/0.53 tff(327,plain,
% 0.36/0.53 ((~![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_1, e_1)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))),
% 0.36/0.53 inference(quant_inst,[status(thm)],[])).
% 0.36/0.53 tff(328,plain,
% 0.36/0.53 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_3, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_3))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[327, 326])).
% 0.36/0.53 tff(329,plain,
% 0.36/0.53 (~product(e_1, e_1, e_3)),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[328, 270, 137, 215, 280, 315])).
% 0.36/0.53 tff(330,plain,
% 0.36/0.53 (product(e_1, e_1, e_2) | product(e_1, e_1, e_3) | product(e_1, e_1, e_1)),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[293, 167, 252, 264])).
% 0.36/0.53 tff(331,plain,
% 0.36/0.53 ($false),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[330, 329, 322, 64])).
% 0.36/0.53 tff(332,plain,(product(e_1, e_1, e_2) | cycle(e_1, e_0)), inference(lemma,lemma(discharge,[]))).
% 0.36/0.53 tff(333,plain,
% 0.36/0.53 (product(e_1, e_1, e_2)),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[332, 63])).
% 0.36/0.53 tff(334,plain,
% 0.36/0.53 (~cycle(e_3, e_0)),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[183, 63])).
% 0.36/0.53 tff(335,plain,
% 0.36/0.53 (cycle(e_3, e_1) | cycle(e_3, e_0)),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[201, 98])).
% 0.36/0.53 tff(336,plain,
% 0.36/0.53 (cycle(e_3, e_1)),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[335, 334])).
% 0.36/0.53 tff(337,assumption,(cycle(e_3, e_1)), introduced(assumption)).
% 0.36/0.53 tff(338,assumption,(cycle(e_2, e_1)), introduced(assumption)).
% 0.36/0.53 tff(339,plain,
% 0.36/0.53 (next(e_2, e_3) <=> next(e_2, e_3)),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(340,axiom,(next(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_then_e_3')).
% 0.36/0.53 tff(341,plain,
% 0.36/0.53 (next(e_2, e_3)),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[340, 339])).
% 0.36/0.53 tff(342,plain,
% 0.36/0.53 (((~![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_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)))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(343,plain,
% 0.36/0.53 (((~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)))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(344,plain,
% 0.36/0.53 (((~![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_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))))),
% 0.36/0.53 inference(monotonicity,[status(thm)],[343])).
% 0.36/0.53 tff(345,plain,
% 0.36/0.53 (((~![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_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)))),
% 0.36/0.53 inference(transitivity,[status(thm)],[344, 342])).
% 0.36/0.53 tff(346,plain,
% 0.36/0.53 ((~![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_2) | (~next(e_1, e_2)) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_1)))),
% 0.36/0.53 inference(quant_inst,[status(thm)],[])).
% 0.36/0.53 tff(347,plain,
% 0.36/0.53 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_1, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_1))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[346, 345])).
% 0.36/0.53 tff(348,plain,
% 0.36/0.53 ($false),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[347, 270, 341, 137, 78, 53, 338, 337])).
% 0.36/0.53 tff(349,plain,((~cycle(e_2, e_1)) | (~cycle(e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.36/0.53 tff(350,plain,
% 0.36/0.53 (~cycle(e_2, e_1)),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[349, 336])).
% 0.36/0.53 tff(351,plain,
% 0.36/0.53 (~product(e_3, e_1, e_1)),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[221, 87, 137, 215, 205, 336])).
% 0.36/0.53 tff(352,plain,
% 0.36/0.53 (~product(e_3, e_1, e_3)),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[231, 87, 137, 215, 225, 336])).
% 0.36/0.53 tff(353,plain,
% 0.36/0.53 (~product(e_3, e_1, e_2)),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[241, 87, 137, 215, 235, 336])).
% 0.36/0.53 tff(354,plain,
% 0.36/0.53 (product(e_3, e_1, e_4)),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[258, 167, 196, 252, 353, 352, 351])).
% 0.36/0.53 tff(355,assumption,(product(e_3, e_2, e_4)), introduced(assumption)).
% 0.36/0.53 tff(356,assumption,(product(e_3, e_1, e_4)), introduced(assumption)).
% 0.36/0.53 tff(357,plain,
% 0.36/0.53 (^[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))))),
% 0.36/0.53 inference(bind,[status(th)],[])).
% 0.36/0.53 tff(358,plain,
% 0.36/0.53 (![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)))),
% 0.36/0.53 inference(quant_intro,[status(thm)],[357])).
% 0.36/0.53 tff(359,plain,
% 0.36/0.53 (![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)))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(360,plain,
% 0.36/0.53 (^[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)))))),
% 0.36/0.53 inference(bind,[status(th)],[])).
% 0.36/0.53 tff(361,plain,
% 0.36/0.53 (![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)))),
% 0.36/0.53 inference(quant_intro,[status(thm)],[360])).
% 0.36/0.53 tff(362,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')).
% 0.36/0.53 tff(363,plain,
% 0.36/0.53 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[362, 361])).
% 0.36/0.53 tff(364,plain,
% 0.36/0.53 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[363, 359])).
% 0.36/0.53 tff(365,plain,(
% 0.36/0.53 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.36/0.53 inference(skolemize,[status(sab)],[364])).
% 0.36/0.53 tff(366,plain,
% 0.36/0.53 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[365, 358])).
% 0.36/0.53 tff(367,plain,
% 0.36/0.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_3, 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_1) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_2, e_4)))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(368,plain,
% 0.36/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_2, e_4)))),
% 0.36/0.53 inference(quant_inst,[status(thm)],[])).
% 0.36/0.53 tff(369,plain,
% 0.36/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_2, e_4))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[368, 367])).
% 0.36/0.53 tff(370,plain,
% 0.36/0.53 ($false),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[369, 16, 366, 356, 355])).
% 0.36/0.53 tff(371,plain,((~product(e_3, e_2, e_4)) | (~product(e_3, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.36/0.53 tff(372,plain,
% 0.36/0.53 (~product(e_3, e_2, e_4)),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[371, 354])).
% 0.36/0.53 tff(373,plain,
% 0.36/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_1)))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(374,plain,
% 0.36/0.53 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_1)))),
% 0.36/0.53 inference(quant_inst,[status(thm)],[])).
% 0.36/0.53 tff(375,plain,
% 0.36/0.53 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_1))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[374, 373])).
% 0.36/0.53 tff(376,plain,
% 0.36/0.53 (~product(e_1, e_3, e_1)),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[375, 32, 264, 354])).
% 0.36/0.53 tff(377,assumption,(product(e_1, e_1, e_2)), introduced(assumption)).
% 0.36/0.53 tff(378,assumption,(product(e_1, e_3, e_2)), introduced(assumption)).
% 0.36/0.53 tff(379,plain,
% 0.36/0.53 (((~![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_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_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(380,plain,
% 0.36/0.53 ((~![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_2)) | (~product(e_1, e_3, e_2)))),
% 0.36/0.53 inference(quant_inst,[status(thm)],[])).
% 0.36/0.53 tff(381,plain,
% 0.36/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_3, e_2))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[380, 379])).
% 0.36/0.53 tff(382,plain,
% 0.36/0.53 ($false),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[381, 68, 366, 377, 378])).
% 0.36/0.53 tff(383,plain,((~product(e_1, e_3, e_2)) | (~product(e_1, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.36/0.53 tff(384,plain,
% 0.36/0.53 (~product(e_1, e_3, e_2)),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[383, 377])).
% 0.36/0.53 tff(385,assumption,(~product(e_3, e_2, e_4)), introduced(assumption)).
% 0.36/0.53 tff(386,assumption,(cycle(e_2, e_2)), introduced(assumption)).
% 0.36/0.53 tff(387,plain,
% 0.36/0.53 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(388,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.36/0.53 tff(389,plain,
% 0.36/0.53 (~equalish(e_1, e_3)),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[388, 387])).
% 0.36/0.53 tff(390,plain,
% 0.36/0.53 (((~![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_1, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_1)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_1, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_1)))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(391,plain,
% 0.36/0.53 (((~greater(e_2, e_0)) | (~cycle(e_2, e_2)) | equalish(e_1, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_1))) <=> (equalish(e_1, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_1)))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(392,plain,
% 0.36/0.53 (((~![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_2, e_0)) | (~cycle(e_2, e_2)) | equalish(e_1, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_1)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_1, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_1))))),
% 0.36/0.53 inference(monotonicity,[status(thm)],[391])).
% 0.36/0.53 tff(393,plain,
% 0.36/0.53 (((~![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_2, e_0)) | (~cycle(e_2, e_2)) | equalish(e_1, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_1)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_1, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_1)))),
% 0.36/0.54 inference(transitivity,[status(thm)],[392, 390])).
% 0.36/0.54 tff(394,plain,
% 0.36/0.54 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_2, e_2)) | equalish(e_1, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_1)))),
% 0.36/0.54 inference(quant_inst,[status(thm)],[])).
% 0.36/0.54 tff(395,plain,
% 0.36/0.54 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_1, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_1))),
% 0.36/0.54 inference(modus_ponens,[status(thm)],[394, 393])).
% 0.36/0.54 tff(396,plain,
% 0.36/0.54 (~product(e_2, e_1, e_1)),
% 0.36/0.54 inference(unit_resolution,[status(thm)],[395, 341, 148, 215, 389, 386])).
% 0.36/0.54 tff(397,plain,
% 0.36/0.54 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.36/0.54 inference(rewrite,[status(thm)],[])).
% 0.36/0.54 tff(398,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.36/0.54 tff(399,plain,
% 0.36/0.54 (~equalish(e_2, e_3)),
% 0.36/0.54 inference(modus_ponens,[status(thm)],[398, 397])).
% 0.36/0.54 tff(400,plain,
% 0.36/0.54 (((~![Z: $i, 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_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, 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_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.36/0.54 inference(rewrite,[status(thm)],[])).
% 0.36/0.54 tff(401,plain,
% 0.36/0.54 (((~greater(e_2, e_0)) | (~cycle(e_2, e_2)) | equalish(e_2, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_2))) <=> (equalish(e_2, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.36/0.54 inference(rewrite,[status(thm)],[])).
% 0.36/0.54 tff(402,plain,
% 0.36/0.54 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_2, e_2)) | equalish(e_2, e_3) | (~next(e_2, e_3)) | (~product(e_2, 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_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_2))))),
% 0.36/0.54 inference(monotonicity,[status(thm)],[401])).
% 0.36/0.54 tff(403,plain,
% 0.36/0.54 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_2, e_2)) | equalish(e_2, e_3) | (~next(e_2, e_3)) | (~product(e_2, 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_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.36/0.54 inference(transitivity,[status(thm)],[402, 400])).
% 0.36/0.54 tff(404,plain,
% 0.36/0.54 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_2, e_2)) | equalish(e_2, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_2)))),
% 0.36/0.54 inference(quant_inst,[status(thm)],[])).
% 0.36/0.54 tff(405,plain,
% 0.36/0.54 ((~![Z: $i, 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_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_2))),
% 0.36/0.54 inference(modus_ponens,[status(thm)],[404, 403])).
% 0.36/0.54 tff(406,plain,
% 0.36/0.54 (~product(e_2, e_1, e_2)),
% 0.36/0.54 inference(unit_resolution,[status(thm)],[405, 341, 148, 215, 399, 386])).
% 0.36/0.54 tff(407,plain,
% 0.36/0.54 ((~equalish(e_4, e_3)) <=> (~equalish(e_4, e_3))),
% 0.36/0.54 inference(rewrite,[status(thm)],[])).
% 0.36/0.54 tff(408,axiom,(~equalish(e_4, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_3')).
% 0.36/0.54 tff(409,plain,
% 0.36/0.54 (~equalish(e_4, e_3)),
% 0.36/0.54 inference(modus_ponens,[status(thm)],[408, 407])).
% 0.36/0.54 tff(410,plain,
% 0.36/0.54 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_4, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_4)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_4)))),
% 0.36/0.54 inference(rewrite,[status(thm)],[])).
% 0.36/0.54 tff(411,plain,
% 0.36/0.54 (((~greater(e_2, e_0)) | (~cycle(e_2, e_2)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4))) <=> (equalish(e_4, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_4)))),
% 0.36/0.54 inference(rewrite,[status(thm)],[])).
% 0.36/0.54 tff(412,plain,
% 0.36/0.54 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_2, e_2)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_4, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_4))))),
% 0.36/0.54 inference(monotonicity,[status(thm)],[411])).
% 0.36/0.54 tff(413,plain,
% 0.36/0.54 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_2, e_2)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_4)))),
% 0.36/0.54 inference(transitivity,[status(thm)],[412, 410])).
% 0.36/0.54 tff(414,plain,
% 0.36/0.54 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_2, e_2)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.36/0.54 inference(quant_inst,[status(thm)],[])).
% 0.36/0.54 tff(415,plain,
% 0.36/0.54 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_4))),
% 0.36/0.54 inference(modus_ponens,[status(thm)],[414, 413])).
% 0.36/0.54 tff(416,plain,
% 0.36/0.54 (~product(e_2, e_1, e_4)),
% 0.36/0.54 inference(unit_resolution,[status(thm)],[415, 341, 148, 215, 409, 386])).
% 0.36/0.54 tff(417,plain,
% 0.36/0.54 (group_element(e_2) <=> group_element(e_2)),
% 0.36/0.54 inference(rewrite,[status(thm)],[])).
% 0.36/0.54 tff(418,axiom,(group_element(e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_2')).
% 0.36/0.54 tff(419,plain,
% 0.36/0.54 (group_element(e_2)),
% 0.36/0.54 inference(modus_ponens,[status(thm)],[418, 417])).
% 0.36/0.54 tff(420,plain,
% 0.36/0.54 (((~![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_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))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(421,plain,
% 0.38/0.54 (((~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))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(422,plain,
% 0.38/0.54 (((~![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_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)))),
% 0.38/0.54 inference(monotonicity,[status(thm)],[421])).
% 0.38/0.54 tff(423,plain,
% 0.38/0.54 (((~![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_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))),
% 0.38/0.54 inference(transitivity,[status(thm)],[422, 420])).
% 0.38/0.54 tff(424,plain,
% 0.38/0.54 ((~![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_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)))),
% 0.38/0.54 inference(quant_inst,[status(thm)],[])).
% 0.38/0.54 tff(425,plain,
% 0.38/0.54 ((~![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_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)),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[424, 423])).
% 0.38/0.54 tff(426,plain,
% 0.38/0.54 (product(e_2, e_1, e_3)),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[425, 167, 419, 252, 416, 406, 396])).
% 0.38/0.54 tff(427,plain,
% 0.38/0.54 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_3, e_2, e_4) | (~product(e_1, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_4) | (~product(e_1, e_3, e_4)))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(428,plain,
% 0.38/0.54 ((product(e_3, e_2, e_4) | (~product(e_1, e_3, e_4)) | (~product(e_2, e_1, e_3))) <=> ((~product(e_2, e_1, e_3)) | product(e_3, e_2, e_4) | (~product(e_1, e_3, e_4)))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(429,plain,
% 0.38/0.54 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_4) | (~product(e_1, e_3, e_4)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_3, e_2, e_4) | (~product(e_1, e_3, e_4))))),
% 0.38/0.54 inference(monotonicity,[status(thm)],[428])).
% 0.38/0.54 tff(430,plain,
% 0.38/0.54 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_4) | (~product(e_1, e_3, e_4)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_4) | (~product(e_1, e_3, e_4)))),
% 0.38/0.54 inference(transitivity,[status(thm)],[429, 427])).
% 0.38/0.54 tff(431,plain,
% 0.38/0.54 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_4) | (~product(e_1, e_3, e_4)) | (~product(e_2, e_1, e_3)))),
% 0.38/0.54 inference(quant_inst,[status(thm)],[])).
% 0.38/0.54 tff(432,plain,
% 0.38/0.54 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_4) | (~product(e_1, e_3, e_4))),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[431, 430])).
% 0.38/0.54 tff(433,plain,
% 0.38/0.54 ((~product(e_2, e_1, e_3)) | product(e_3, e_2, e_4) | (~product(e_1, e_3, e_4))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[432, 32])).
% 0.38/0.54 tff(434,plain,
% 0.38/0.54 (~product(e_1, e_3, e_4)),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[433, 426, 385])).
% 0.38/0.54 tff(435,assumption,(~product(e_1, e_3, e_1)), introduced(assumption)).
% 0.38/0.54 tff(436,plain,
% 0.38/0.54 (((~![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_1, e_3, e_1) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_1) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(437,plain,
% 0.38/0.54 (((~group_element(e_1)) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3))) <=> ((~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_1) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(438,plain,
% 0.38/0.54 (((~![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_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_1) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2)))),
% 0.38/0.54 inference(monotonicity,[status(thm)],[437])).
% 0.38/0.54 tff(439,plain,
% 0.38/0.54 (((~![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_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_1) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2))),
% 0.38/0.54 inference(transitivity,[status(thm)],[438, 436])).
% 0.38/0.54 tff(440,plain,
% 0.38/0.54 ((~![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_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)))),
% 0.38/0.54 inference(quant_inst,[status(thm)],[])).
% 0.38/0.54 tff(441,plain,
% 0.38/0.54 ((~![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_1, e_3, e_1) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2)),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[440, 439])).
% 0.38/0.55 tff(442,plain,
% 0.38/0.55 (product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2)),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[441, 167, 196, 252, 435])).
% 0.38/0.55 tff(443,plain,
% 0.38/0.55 (product(e_1, e_3, e_3)),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[442, 434, 384])).
% 0.38/0.55 tff(444,assumption,(~product(e_3, e_1, e_3)), introduced(assumption)).
% 0.38/0.55 tff(445,assumption,(~product(e_2, e_1, e_2)), introduced(assumption)).
% 0.38/0.55 tff(446,plain,
% 0.38/0.55 (product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_1)),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[425, 167, 419, 252, 445])).
% 0.38/0.55 tff(447,plain,
% 0.38/0.55 (product(e_2, e_1, e_3)),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[446, 416, 396])).
% 0.38/0.55 tff(448,assumption,(~product(e_1, e_1, e_3)), introduced(assumption)).
% 0.38/0.55 tff(449,plain,
% 0.38/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_1)))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(450,plain,
% 0.38/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_1)))),
% 0.38/0.55 inference(quant_inst,[status(thm)],[])).
% 0.38/0.55 tff(451,plain,
% 0.38/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_1))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[450, 449])).
% 0.38/0.55 tff(452,plain,
% 0.38/0.55 (~product(e_1, e_2, e_1)),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[451, 32, 448, 447])).
% 0.38/0.55 tff(453,plain,
% 0.38/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_1, e_2)) | product(e_2, e_1, e_2) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_2) | (~product(e_1, e_2, e_2)))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(454,plain,
% 0.38/0.55 ((product(e_2, e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_1, e_2))) <=> ((~product(e_1, e_1, e_2)) | product(e_2, e_1, e_2) | (~product(e_1, e_2, e_2)))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(455,plain,
% 0.38/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_1, e_2)) | product(e_2, e_1, e_2) | (~product(e_1, e_2, e_2))))),
% 0.38/0.55 inference(monotonicity,[status(thm)],[454])).
% 0.38/0.55 tff(456,plain,
% 0.38/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_2) | (~product(e_1, e_2, e_2)))),
% 0.38/0.55 inference(transitivity,[status(thm)],[455, 453])).
% 0.38/0.55 tff(457,plain,
% 0.38/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_1, e_2)))),
% 0.38/0.55 inference(quant_inst,[status(thm)],[])).
% 0.38/0.55 tff(458,plain,
% 0.38/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_2) | (~product(e_1, e_2, e_2))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[457, 456])).
% 0.38/0.55 tff(459,plain,
% 0.38/0.55 ($false),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[458, 32, 377, 445, 42])).
% 0.38/0.55 tff(460,plain,((~product(e_1, e_2, e_2)) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.38/0.55 tff(461,plain,
% 0.38/0.55 (~product(e_1, e_2, e_2)),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[460, 445, 377])).
% 0.38/0.55 tff(462,assumption,(product(e_1, e_2, e_4)), introduced(assumption)).
% 0.38/0.55 tff(463,assumption,(~product(e_2, e_1, e_4)), introduced(assumption)).
% 0.38/0.55 tff(464,plain,
% 0.38/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_1, e_2)) | product(e_2, e_1, e_4) | (~product(e_1, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_4) | (~product(e_1, e_2, e_4)))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(465,plain,
% 0.38/0.55 ((product(e_2, e_1, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_1, e_2))) <=> ((~product(e_1, e_1, e_2)) | product(e_2, e_1, e_4) | (~product(e_1, e_2, e_4)))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(466,plain,
% 0.38/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_1, e_2)) | product(e_2, e_1, e_4) | (~product(e_1, e_2, e_4))))),
% 0.38/0.55 inference(monotonicity,[status(thm)],[465])).
% 0.38/0.55 tff(467,plain,
% 0.38/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_4) | (~product(e_1, e_2, e_4)))),
% 0.38/0.55 inference(transitivity,[status(thm)],[466, 464])).
% 0.38/0.55 tff(468,plain,
% 0.38/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_1, e_2)))),
% 0.38/0.55 inference(quant_inst,[status(thm)],[])).
% 0.38/0.55 tff(469,plain,
% 0.38/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_4) | (~product(e_1, e_2, e_4))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[468, 467])).
% 0.38/0.55 tff(470,plain,
% 0.38/0.55 ($false),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[469, 32, 377, 463, 462])).
% 0.38/0.55 tff(471,plain,((~product(e_1, e_2, e_4)) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.38/0.55 tff(472,plain,
% 0.38/0.55 (~product(e_1, e_2, e_4)),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[471, 416, 377])).
% 0.38/0.55 tff(473,plain,
% 0.38/0.55 (~product(e_1, e_3, e_4)),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[433, 447, 385])).
% 0.38/0.55 tff(474,plain,
% 0.38/0.55 (product(e_1, e_3, e_3)),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[442, 473, 384])).
% 0.38/0.55 tff(475,assumption,(product(e_1, e_3, e_3)), introduced(assumption)).
% 0.38/0.55 tff(476,plain,
% 0.38/0.55 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(477,plain,
% 0.38/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.38/0.55 inference(quant_inst,[status(thm)],[])).
% 0.38/0.55 tff(478,plain,
% 0.38/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_2, e_3))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[477, 476])).
% 0.38/0.55 tff(479,plain,
% 0.38/0.55 ($false),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[478, 399, 366, 475, 2])).
% 0.38/0.55 tff(480,plain,((~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.55 tff(481,plain,
% 0.38/0.55 (~product(e_1, e_2, e_3)),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[480, 474])).
% 0.38/0.55 tff(482,plain,
% 0.38/0.55 (((~![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_2)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(483,plain,
% 0.38/0.55 (((~group_element(e_1)) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2))) <=> ((~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(484,plain,
% 0.38/0.55 (((~![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_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2)))),
% 0.38/0.55 inference(monotonicity,[status(thm)],[483])).
% 0.38/0.55 tff(485,plain,
% 0.38/0.55 (((~![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_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2))),
% 0.38/0.55 inference(transitivity,[status(thm)],[484, 482])).
% 0.38/0.55 tff(486,plain,
% 0.38/0.55 ((~![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_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)))),
% 0.38/0.55 inference(quant_inst,[status(thm)],[])).
% 0.38/0.55 tff(487,plain,
% 0.38/0.55 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2)),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[486, 485])).
% 0.38/0.55 tff(488,plain,
% 0.38/0.55 ($false),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[487, 167, 419, 252, 481, 472, 461, 452])).
% 0.38/0.55 tff(489,plain,((~cycle(e_2, e_2)) | product(e_1, e_1, e_3) | product(e_1, e_3, e_1) | product(e_3, e_2, e_4) | product(e_2, e_1, e_2) | (~product(e_1, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.55 tff(490,plain,
% 0.38/0.55 (product(e_1, e_1, e_3)),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[489, 406, 435, 385, 386, 377])).
% 0.38/0.55 tff(491,plain,
% 0.38/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_1, e_3)) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_1, e_3)) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_3)))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(492,plain,
% 0.38/0.55 ((product(e_3, e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_1, e_3))) <=> ((~product(e_1, e_1, e_3)) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_3)))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(493,plain,
% 0.38/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_1, e_3)) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_3))))),
% 0.38/0.55 inference(monotonicity,[status(thm)],[492])).
% 0.38/0.55 tff(494,plain,
% 0.38/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_1, e_3)) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_3)))),
% 0.38/0.55 inference(transitivity,[status(thm)],[493, 491])).
% 0.38/0.55 tff(495,plain,
% 0.38/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_1, e_3)))),
% 0.38/0.55 inference(quant_inst,[status(thm)],[])).
% 0.38/0.55 tff(496,plain,
% 0.38/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_1, e_3)) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_3))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[495, 494])).
% 0.38/0.55 tff(497,plain,
% 0.38/0.55 ($false),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[496, 32, 490, 444, 443])).
% 0.38/0.55 tff(498,plain,((~cycle(e_2, e_2)) | product(e_3, e_1, e_3) | product(e_1, e_3, e_1) | product(e_3, e_2, e_4) | (~product(e_1, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.55 tff(499,plain,
% 0.38/0.55 (~cycle(e_2, e_2)),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[498, 352, 376, 372, 333])).
% 0.38/0.55 tff(500,assumption,(~cycle(e_2, e_2)), introduced(assumption)).
% 0.38/0.55 tff(501,plain,
% 0.38/0.55 (~cycle(e_2, e_1)),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[349, 337])).
% 0.38/0.55 tff(502,assumption,(cycle(e_1, e_3)), introduced(assumption)).
% 0.38/0.55 tff(503,plain,
% 0.38/0.55 (greater(e_2, e_1) <=> greater(e_2, e_1)),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(504,axiom,(greater(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_greater_e_1')).
% 0.38/0.55 tff(505,plain,
% 0.38/0.55 (greater(e_2, e_1)),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[504, 503])).
% 0.38/0.55 tff(506,plain,
% 0.38/0.55 (((~![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_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_3)) | (~cycle(e_3, 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_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_3)) | (~cycle(e_3, e_1)))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(507,plain,
% 0.38/0.55 (((~greater(e_3, e_1)) | (~greater(e_2, e_1)) | (~next(e_2, e_3)) | (~cycle(e_3, e_1)) | (~cycle(e_2, e_0)) | (~cycle(e_1, e_3))) <=> ((~cycle(e_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_3)) | (~cycle(e_3, e_1)))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(508,plain,
% 0.38/0.55 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_3, e_1)) | (~greater(e_2, e_1)) | (~next(e_2, e_3)) | (~cycle(e_3, e_1)) | (~cycle(e_2, e_0)) | (~cycle(e_1, e_3)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_3)) | (~cycle(e_3, e_1))))),
% 0.38/0.55 inference(monotonicity,[status(thm)],[507])).
% 0.38/0.55 tff(509,plain,
% 0.38/0.55 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_3, e_1)) | (~greater(e_2, e_1)) | (~next(e_2, e_3)) | (~cycle(e_3, e_1)) | (~cycle(e_2, e_0)) | (~cycle(e_1, e_3)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_3)) | (~cycle(e_3, e_1)))),
% 0.38/0.55 inference(transitivity,[status(thm)],[508, 506])).
% 0.38/0.55 tff(510,plain,
% 0.38/0.55 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_3, e_1)) | (~greater(e_2, e_1)) | (~next(e_2, e_3)) | (~cycle(e_3, e_1)) | (~cycle(e_2, e_0)) | (~cycle(e_1, e_3)))),
% 0.38/0.55 inference(quant_inst,[status(thm)],[])).
% 0.38/0.55 tff(511,plain,
% 0.38/0.55 ((~![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_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_3)) | (~cycle(e_3, e_1))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[510, 509])).
% 0.38/0.55 tff(512,plain,
% 0.38/0.55 ((~cycle(e_2, e_0)) | (~cycle(e_1, e_3)) | (~cycle(e_3, e_1))),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[511, 341, 505, 134, 131])).
% 0.38/0.55 tff(513,plain,
% 0.38/0.55 (~cycle(e_2, e_0)),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[512, 502, 337])).
% 0.38/0.55 tff(514,plain,
% 0.38/0.55 (((~![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)))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(515,plain,
% 0.38/0.55 ((~![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)))),
% 0.38/0.55 inference(quant_inst,[status(thm)],[])).
% 0.38/0.55 tff(516,plain,
% 0.38/0.55 ((~![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))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[515, 514])).
% 0.38/0.55 tff(517,plain,
% 0.38/0.55 (cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0)),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[516, 177, 419])).
% 0.38/0.55 tff(518,plain,
% 0.38/0.55 (cycle(e_2, e_3)),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[517, 513, 500, 501])).
% 0.38/0.55 tff(519,plain,
% 0.38/0.55 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_3, e_4) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_3)) | (~cycle(e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_4) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_3)) | (~cycle(e_2, e_3)))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(520,plain,
% 0.38/0.55 (((~cycle(e_1, e_3)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~greater(e_3, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_3))) <=> (equalish(e_3, e_4) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_3)) | (~cycle(e_2, e_3)))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(521,plain,
% 0.38/0.56 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_1, e_3)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~greater(e_3, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_3, e_4) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_3)) | (~cycle(e_2, e_3))))),
% 0.38/0.56 inference(monotonicity,[status(thm)],[520])).
% 0.38/0.56 tff(522,plain,
% 0.38/0.56 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_1, e_3)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~greater(e_3, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_4) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_3)) | (~cycle(e_2, e_3)))),
% 0.38/0.56 inference(transitivity,[status(thm)],[521, 519])).
% 0.38/0.56 tff(523,plain,
% 0.38/0.56 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_1, e_3)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~greater(e_3, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_3)))),
% 0.38/0.56 inference(quant_inst,[status(thm)],[])).
% 0.38/0.56 tff(524,plain,
% 0.38/0.56 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_4) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_3)) | (~cycle(e_2, e_3))),
% 0.38/0.56 inference(modus_ponens,[status(thm)],[523, 522])).
% 0.38/0.56 tff(525,plain,
% 0.38/0.56 ($false),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[524, 270, 87, 84, 78, 225, 502, 518])).
% 0.38/0.56 tff(526,plain,((~cycle(e_1, e_3)) | cycle(e_2, e_2) | (~cycle(e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.56 tff(527,plain,
% 0.38/0.56 (~cycle(e_1, e_3)),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[526, 500, 336])).
% 0.38/0.56 tff(528,plain,
% 0.38/0.56 (cycle(e_1, e_2)),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[181, 527, 63, 265])).
% 0.38/0.56 tff(529,plain,
% 0.38/0.56 (((~![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_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_2)) | (~cycle(e_3, 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_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_2)) | (~cycle(e_3, e_1)))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(530,plain,
% 0.38/0.56 (((~greater(e_2, e_1)) | (~greater(e_2, e_1)) | (~next(e_2, e_3)) | (~cycle(e_3, e_1)) | (~cycle(e_2, e_0)) | (~cycle(e_1, e_2))) <=> ((~cycle(e_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_2)) | (~cycle(e_3, e_1)))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(531,plain,
% 0.38/0.56 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_2, e_1)) | (~greater(e_2, e_1)) | (~next(e_2, e_3)) | (~cycle(e_3, e_1)) | (~cycle(e_2, e_0)) | (~cycle(e_1, e_2)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_2)) | (~cycle(e_3, e_1))))),
% 0.38/0.56 inference(monotonicity,[status(thm)],[530])).
% 0.38/0.56 tff(532,plain,
% 0.38/0.56 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_2, e_1)) | (~greater(e_2, e_1)) | (~next(e_2, e_3)) | (~cycle(e_3, e_1)) | (~cycle(e_2, e_0)) | (~cycle(e_1, e_2)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_2)) | (~cycle(e_3, e_1)))),
% 0.38/0.56 inference(transitivity,[status(thm)],[531, 529])).
% 0.38/0.56 tff(533,plain,
% 0.38/0.56 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_2, e_1)) | (~greater(e_2, e_1)) | (~next(e_2, e_3)) | (~cycle(e_3, e_1)) | (~cycle(e_2, e_0)) | (~cycle(e_1, e_2)))),
% 0.38/0.56 inference(quant_inst,[status(thm)],[])).
% 0.38/0.56 tff(534,plain,
% 0.38/0.56 ((~![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_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_2)) | (~cycle(e_3, e_1))),
% 0.38/0.56 inference(modus_ponens,[status(thm)],[533, 532])).
% 0.38/0.56 tff(535,plain,
% 0.38/0.56 ((~cycle(e_2, e_0)) | (~cycle(e_1, e_2)) | (~cycle(e_3, e_1))),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[534, 341, 505, 131])).
% 0.38/0.56 tff(536,plain,
% 0.38/0.56 (~cycle(e_2, e_0)),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[535, 528, 336])).
% 0.38/0.56 tff(537,plain,
% 0.38/0.56 (cycle(e_2, e_3)),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[517, 536, 500, 350])).
% 0.38/0.56 tff(538,plain,
% 0.38/0.56 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_2, e_4) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_2)) | (~cycle(e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_4) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_2)) | (~cycle(e_2, e_3)))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(539,plain,
% 0.38/0.56 (((~cycle(e_1, e_2)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~greater(e_2, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_3))) <=> (equalish(e_2, e_4) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_2)) | (~cycle(e_2, e_3)))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(540,plain,
% 0.38/0.56 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_1, e_2)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~greater(e_2, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_2, e_4) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_2)) | (~cycle(e_2, e_3))))),
% 0.38/0.56 inference(monotonicity,[status(thm)],[539])).
% 0.38/0.56 tff(541,plain,
% 0.38/0.56 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_1, e_2)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~greater(e_2, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_4) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_2)) | (~cycle(e_2, e_3)))),
% 0.38/0.56 inference(transitivity,[status(thm)],[540, 538])).
% 0.38/0.56 tff(542,plain,
% 0.38/0.56 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_1, e_2)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~greater(e_2, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_3)))),
% 0.38/0.56 inference(quant_inst,[status(thm)],[])).
% 0.38/0.56 tff(543,plain,
% 0.38/0.56 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_4) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_2)) | (~cycle(e_2, e_3))),
% 0.38/0.56 inference(modus_ponens,[status(thm)],[542, 541])).
% 0.38/0.56 tff(544,plain,
% 0.38/0.56 ($false),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[543, 270, 87, 148, 78, 235, 528, 537])).
% 0.38/0.56 tff(545,plain,(cycle(e_2, e_2) | cycle(e_1, e_0) | cycle(e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.38/0.56 tff(546,plain,
% 0.38/0.56 (cycle(e_1, e_1)),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[545, 499, 63])).
% 0.38/0.56 tff(547,plain,
% 0.38/0.56 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_1, e_4) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_1, e_4) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_3)))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(548,plain,
% 0.38/0.56 (((~cycle(e_1, e_1)) | equalish(e_1, e_4) | (~next(e_3, e_4)) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_3))) <=> (equalish(e_1, e_4) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_3)))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(549,plain,
% 0.38/0.56 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_1, e_1)) | equalish(e_1, e_4) | (~next(e_3, e_4)) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_1, e_4) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_3))))),
% 0.38/0.56 inference(monotonicity,[status(thm)],[548])).
% 0.38/0.56 tff(550,plain,
% 0.38/0.56 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_1, e_1)) | equalish(e_1, e_4) | (~next(e_3, e_4)) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_1, e_4) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_3)))),
% 0.38/0.56 inference(transitivity,[status(thm)],[549, 547])).
% 0.38/0.56 tff(551,plain,
% 0.38/0.56 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_1, e_1)) | equalish(e_1, e_4) | (~next(e_3, e_4)) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_3)))),
% 0.38/0.56 inference(quant_inst,[status(thm)],[])).
% 0.38/0.56 tff(552,plain,
% 0.38/0.56 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_1, e_4) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_3))),
% 0.38/0.56 inference(modus_ponens,[status(thm)],[551, 550])).
% 0.38/0.56 tff(553,plain,
% 0.38/0.56 (~cycle(e_2, e_3)),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[552, 270, 87, 137, 78, 205, 546])).
% 0.38/0.56 tff(554,plain,
% 0.38/0.56 (cycle(e_2, e_0)),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[517, 553, 499, 350])).
% 0.38/0.56 tff(555,plain,
% 0.38/0.56 (greater(e_4, e_2) <=> greater(e_4, e_2)),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(556,axiom,(greater(e_4, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_greater_e_2')).
% 0.38/0.56 tff(557,plain,
% 0.38/0.56 (greater(e_4, e_2)),
% 0.38/0.56 inference(modus_ponens,[status(thm)],[556, 555])).
% 0.38/0.56 tff(558,plain,
% 0.38/0.56 (((~![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)))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(559,plain,
% 0.38/0.56 (((~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)))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(560,plain,
% 0.38/0.56 (((~![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))))),
% 0.38/0.56 inference(monotonicity,[status(thm)],[559])).
% 0.38/0.56 tff(561,plain,
% 0.38/0.56 (((~![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)))),
% 0.38/0.56 inference(transitivity,[status(thm)],[560, 558])).
% 0.38/0.56 tff(562,plain,
% 0.38/0.56 ((~![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)))),
% 0.38/0.56 inference(quant_inst,[status(thm)],[])).
% 0.38/0.56 tff(563,plain,
% 0.38/0.56 ((~![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))),
% 0.38/0.56 inference(modus_ponens,[status(thm)],[562, 561])).
% 0.38/0.56 tff(564,plain,
% 0.38/0.56 ((~cycle(e_2, e_0)) | (~product(e_2, e_1, e_4))),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[563, 557, 109])).
% 0.38/0.56 tff(565,plain,
% 0.38/0.56 (~product(e_2, e_1, e_4)),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[564, 554])).
% 0.38/0.56 tff(566,plain,
% 0.38/0.56 (greater(e_3, e_2) <=> greater(e_3, e_2)),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(567,axiom,(greater(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_greater_e_2')).
% 0.38/0.56 tff(568,plain,
% 0.38/0.56 (greater(e_3, e_2)),
% 0.38/0.56 inference(modus_ponens,[status(thm)],[567, 566])).
% 0.38/0.56 tff(569,plain,
% 0.38/0.56 (((~![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)))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(570,plain,
% 0.38/0.56 (((~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)))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(571,plain,
% 0.38/0.56 (((~![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))))),
% 0.38/0.56 inference(monotonicity,[status(thm)],[570])).
% 0.38/0.56 tff(572,plain,
% 0.38/0.56 (((~![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)))),
% 0.38/0.56 inference(transitivity,[status(thm)],[571, 569])).
% 0.38/0.56 tff(573,plain,
% 0.38/0.56 ((~![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)))),
% 0.38/0.57 inference(quant_inst,[status(thm)],[])).
% 0.38/0.57 tff(574,plain,
% 0.38/0.57 ((~![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))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[573, 572])).
% 0.38/0.57 tff(575,plain,
% 0.38/0.57 ((~cycle(e_2, e_0)) | (~product(e_2, e_1, e_3))),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[574, 568, 109])).
% 0.38/0.57 tff(576,plain,
% 0.38/0.57 (~product(e_2, e_1, e_3)),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[575, 554])).
% 0.38/0.57 tff(577,plain,
% 0.38/0.57 (~product(e_1, e_1, e_1)),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[321, 270, 137, 215, 53, 546])).
% 0.38/0.57 tff(578,plain,
% 0.38/0.57 (~product(e_1, e_2, e_4)),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[471, 463, 377])).
% 0.38/0.57 tff(579,assumption,(~product(e_2, e_1, e_3)), introduced(assumption)).
% 0.38/0.57 tff(580,plain,
% 0.38/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_1, e_2)) | product(e_2, e_1, e_3) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_3) | (~product(e_1, e_2, e_3)))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(581,plain,
% 0.38/0.57 ((product(e_2, e_1, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_1, e_2))) <=> ((~product(e_1, e_1, e_2)) | product(e_2, e_1, e_3) | (~product(e_1, e_2, e_3)))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(582,plain,
% 0.38/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_1, e_2)) | product(e_2, e_1, e_3) | (~product(e_1, e_2, e_3))))),
% 0.38/0.57 inference(monotonicity,[status(thm)],[581])).
% 0.38/0.57 tff(583,plain,
% 0.38/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_3) | (~product(e_1, e_2, e_3)))),
% 0.38/0.57 inference(transitivity,[status(thm)],[582, 580])).
% 0.38/0.57 tff(584,plain,
% 0.38/0.57 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_1, e_2)))),
% 0.38/0.57 inference(quant_inst,[status(thm)],[])).
% 0.38/0.57 tff(585,plain,
% 0.38/0.57 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_3) | (~product(e_1, e_2, e_3))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[584, 583])).
% 0.38/0.57 tff(586,plain,
% 0.38/0.57 ($false),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[585, 32, 377, 579, 2])).
% 0.38/0.57 tff(587,plain,((~product(e_1, e_2, e_3)) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.38/0.57 tff(588,plain,
% 0.38/0.57 (~product(e_1, e_2, e_3)),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[587, 377, 579])).
% 0.38/0.57 tff(589,plain,
% 0.38/0.57 (product(e_1, e_2, e_1) | product(e_1, e_2, e_2)),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[487, 167, 419, 252, 588, 578])).
% 0.38/0.57 tff(590,plain,
% 0.38/0.57 (product(e_1, e_2, e_1)),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[589, 461])).
% 0.38/0.57 tff(591,assumption,(~product(e_1, e_1, e_1)), introduced(assumption)).
% 0.38/0.57 tff(592,plain,
% 0.38/0.57 (product(e_2, e_1, e_2) | product(e_2, e_1, e_1)),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[425, 167, 419, 252, 579, 463])).
% 0.38/0.57 tff(593,plain,
% 0.38/0.57 (product(e_2, e_1, e_1)),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[592, 445])).
% 0.38/0.57 tff(594,plain,
% 0.38/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(595,plain,
% 0.38/0.57 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.38/0.57 inference(quant_inst,[status(thm)],[])).
% 0.38/0.57 tff(596,plain,
% 0.38/0.57 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_2, e_1))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[595, 594])).
% 0.38/0.57 tff(597,plain,
% 0.38/0.57 ($false),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[596, 32, 593, 591, 590])).
% 0.38/0.57 tff(598,plain,(product(e_2, e_1, e_2) | product(e_1, e_1, e_1) | product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | (~product(e_1, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.57 tff(599,plain,
% 0.38/0.57 (product(e_2, e_1, e_2)),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[598, 577, 576, 565, 333])).
% 0.38/0.57 tff(600,plain,
% 0.38/0.57 (((~![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_2)) | (~product(e_2, 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_2, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(601,plain,
% 0.38/0.57 ((~![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_2)) | (~product(e_2, e_1, e_2)))),
% 0.38/0.57 inference(quant_inst,[status(thm)],[])).
% 0.38/0.57 tff(602,plain,
% 0.38/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_2))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[601, 600])).
% 0.38/0.57 tff(603,plain,
% 0.38/0.57 ($false),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[602, 16, 13, 333, 599])).
% 0.38/0.57 tff(604,plain,(cycle(e_1, e_0)), inference(lemma,lemma(discharge,[]))).
% 0.38/0.57 tff(605,plain,
% 0.38/0.57 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~cycle(e_1, e_0)) | (~greater(e_2, e_1)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_2, e_1)) | (~product(e_1, e_1, e_2)))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(606,plain,
% 0.38/0.57 (((~greater(e_2, e_1)) | (~product(e_1, e_1, e_2)) | (~cycle(e_1, e_0))) <=> ((~cycle(e_1, e_0)) | (~greater(e_2, e_1)) | (~product(e_1, e_1, e_2)))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(607,plain,
% 0.38/0.57 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_2, e_1)) | (~product(e_1, e_1, e_2)) | (~cycle(e_1, e_0)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~cycle(e_1, e_0)) | (~greater(e_2, e_1)) | (~product(e_1, e_1, e_2))))),
% 0.38/0.57 inference(monotonicity,[status(thm)],[606])).
% 0.38/0.57 tff(608,plain,
% 0.38/0.57 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_2, e_1)) | (~product(e_1, e_1, e_2)) | (~cycle(e_1, e_0)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_2, e_1)) | (~product(e_1, e_1, e_2)))),
% 0.38/0.57 inference(transitivity,[status(thm)],[607, 605])).
% 0.38/0.57 tff(609,plain,
% 0.38/0.57 ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_2, e_1)) | (~product(e_1, e_1, e_2)) | (~cycle(e_1, e_0)))),
% 0.38/0.57 inference(quant_inst,[status(thm)],[])).
% 0.38/0.57 tff(610,plain,
% 0.38/0.57 ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_2, e_1)) | (~product(e_1, e_1, e_2))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[609, 608])).
% 0.38/0.57 tff(611,plain,
% 0.38/0.57 ((~cycle(e_1, e_0)) | (~product(e_1, e_1, e_2))),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[610, 505, 109])).
% 0.38/0.57 tff(612,plain,
% 0.38/0.57 (~product(e_1, e_1, e_2)),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[611, 604])).
% 0.38/0.57 tff(613,plain,
% 0.38/0.57 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~cycle(e_1, e_0)) | (~greater(e_3, e_1)) | (~product(e_1, e_1, e_3)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_3, e_1)) | (~product(e_1, e_1, e_3)))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(614,plain,
% 0.38/0.57 (((~greater(e_3, e_1)) | (~product(e_1, e_1, e_3)) | (~cycle(e_1, e_0))) <=> ((~cycle(e_1, e_0)) | (~greater(e_3, e_1)) | (~product(e_1, e_1, e_3)))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(615,plain,
% 0.38/0.57 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_3, e_1)) | (~product(e_1, e_1, e_3)) | (~cycle(e_1, e_0)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~cycle(e_1, e_0)) | (~greater(e_3, e_1)) | (~product(e_1, e_1, e_3))))),
% 0.38/0.57 inference(monotonicity,[status(thm)],[614])).
% 0.38/0.57 tff(616,plain,
% 0.38/0.57 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_3, e_1)) | (~product(e_1, e_1, e_3)) | (~cycle(e_1, e_0)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_3, e_1)) | (~product(e_1, e_1, e_3)))),
% 0.38/0.57 inference(transitivity,[status(thm)],[615, 613])).
% 0.38/0.57 tff(617,plain,
% 0.38/0.57 ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_3, e_1)) | (~product(e_1, e_1, e_3)) | (~cycle(e_1, e_0)))),
% 0.38/0.57 inference(quant_inst,[status(thm)],[])).
% 0.38/0.57 tff(618,plain,
% 0.38/0.57 ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_3, e_1)) | (~product(e_1, e_1, e_3))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[617, 616])).
% 0.38/0.57 tff(619,plain,
% 0.38/0.57 ((~cycle(e_1, e_0)) | (~product(e_1, e_1, e_3))),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[618, 134, 109])).
% 0.38/0.57 tff(620,plain,
% 0.38/0.57 (~product(e_1, e_1, e_3)),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[619, 604])).
% 0.38/0.57 tff(621,plain,
% 0.38/0.57 (product(e_1, e_1, e_1)),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[330, 620, 612])).
% 0.38/0.57 tff(622,assumption,(product(e_1, e_2, e_1)), introduced(assumption)).
% 0.38/0.57 tff(623,assumption,(product(e_1, e_1, e_1)), introduced(assumption)).
% 0.38/0.57 tff(624,plain,
% 0.38/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(625,plain,
% 0.38/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.38/0.57 inference(quant_inst,[status(thm)],[])).
% 0.38/0.57 tff(626,plain,
% 0.38/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[625, 624])).
% 0.38/0.57 tff(627,plain,
% 0.38/0.57 ($false),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[626, 16, 366, 623, 622])).
% 0.38/0.57 tff(628,plain,((~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.57 tff(629,plain,
% 0.38/0.57 (~product(e_1, e_2, e_1)),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[628, 621])).
% 0.38/0.57 tff(630,plain,
% 0.38/0.57 (product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2)),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[487, 167, 419, 252, 629])).
% 0.38/0.57 tff(631,plain,
% 0.38/0.57 (product(e_1, e_2, e_4)),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[630, 62, 41])).
% 0.38/0.57 tff(632,assumption,(product(e_2, e_2, e_4)), introduced(assumption)).
% 0.38/0.57 tff(633,plain,
% 0.38/0.57 (((~![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_2, e_4)) | (~product(e_2, e_2, e_4)))) <=> ((~![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_2, e_4)) | (~product(e_2, e_2, e_4)))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(634,plain,
% 0.38/0.57 ((~![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_2, e_4)) | (~product(e_2, e_2, e_4)))),
% 0.38/0.57 inference(quant_inst,[status(thm)],[])).
% 0.38/0.57 tff(635,plain,
% 0.38/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_2, e_4))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[634, 633])).
% 0.38/0.57 tff(636,plain,
% 0.38/0.57 ($false),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[635, 16, 13, 462, 632])).
% 0.38/0.57 tff(637,plain,((~product(e_2, e_2, e_4)) | (~product(e_1, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.57 tff(638,plain,
% 0.38/0.57 (~product(e_2, e_2, e_4)),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[637, 631])).
% 0.38/0.57 tff(639,plain,
% 0.38/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_4) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_2, e_4) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_4)))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(640,plain,
% 0.38/0.57 ((product(e_2, e_2, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_1, e_2))) <=> (product(e_2, e_2, e_4) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_4)))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(641,plain,
% 0.38/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_4) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_4))))),
% 0.38/0.57 inference(monotonicity,[status(thm)],[640])).
% 0.38/0.57 tff(642,plain,
% 0.38/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_2, e_4) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_4)))),
% 0.38/0.57 inference(transitivity,[status(thm)],[641, 639])).
% 0.38/0.57 tff(643,plain,
% 0.38/0.57 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_1, e_2)))),
% 0.38/0.57 inference(quant_inst,[status(thm)],[])).
% 0.38/0.57 tff(644,plain,
% 0.38/0.57 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_2, e_4) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_4))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[643, 642])).
% 0.38/0.57 tff(645,plain,
% 0.38/0.57 ($false),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[644, 32, 1, 631, 638])).
% 0.38/0.57 tff(646,plain,(~product(e_2, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.38/0.57 tff(647,assumption,(product(e_3, e_2, e_2)), introduced(assumption)).
% 0.38/0.57 tff(648,assumption,(product(e_3, e_3, e_4)), introduced(assumption)).
% 0.38/0.57 tff(649,assumption,(product(e_3, e_1, e_1)), introduced(assumption)).
% 0.38/0.57 tff(650,plain,
% 0.38/0.57 (((~![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)))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(651,plain,
% 0.38/0.57 ((~![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)))),
% 0.38/0.57 inference(quant_inst,[status(thm)],[])).
% 0.38/0.57 tff(652,plain,
% 0.38/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[651, 650])).
% 0.38/0.57 tff(653,plain,
% 0.38/0.57 ($false),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[652, 68, 13, 623, 649])).
% 0.38/0.57 tff(654,plain,((~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.57 tff(655,plain,
% 0.38/0.57 (~product(e_3, e_1, e_1)),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[654, 621])).
% 0.38/0.57 tff(656,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.38/0.57 tff(657,plain,
% 0.38/0.57 (((~![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)))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(658,plain,
% 0.38/0.58 ((~![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)))),
% 0.38/0.58 inference(quant_inst,[status(thm)],[])).
% 0.38/0.58 tff(659,plain,
% 0.38/0.58 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1))),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[658, 657])).
% 0.38/0.58 tff(660,plain,
% 0.38/0.58 ($false),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[659, 16, 13, 623, 656])).
% 0.38/0.58 tff(661,plain,((~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.58 tff(662,plain,
% 0.38/0.58 (~product(e_2, e_1, e_1)),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[661, 621])).
% 0.38/0.58 tff(663,assumption,(product(e_2, e_1, e_4)), introduced(assumption)).
% 0.38/0.58 tff(664,assumption,(cycle(e_2, e_3)), introduced(assumption)).
% 0.38/0.58 tff(665,plain,
% 0.38/0.58 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_4)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(666,plain,
% 0.38/0.58 (((~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4))) <=> (equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(667,plain,
% 0.38/0.58 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_4))))),
% 0.38/0.58 inference(monotonicity,[status(thm)],[666])).
% 0.38/0.58 tff(668,plain,
% 0.38/0.58 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.38/0.58 inference(transitivity,[status(thm)],[667, 665])).
% 0.38/0.58 tff(669,plain,
% 0.38/0.58 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.38/0.58 inference(quant_inst,[status(thm)],[])).
% 0.38/0.58 tff(670,plain,
% 0.38/0.58 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_4))),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[669, 668])).
% 0.38/0.58 tff(671,plain,
% 0.38/0.58 ($false),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[670, 341, 84, 215, 409, 664, 663])).
% 0.38/0.58 tff(672,plain,((~cycle(e_2, e_3)) | (~product(e_2, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.58 tff(673,plain,
% 0.38/0.58 (~cycle(e_2, e_3)),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[672, 663])).
% 0.38/0.58 tff(674,plain,
% 0.38/0.58 (~cycle(e_2, e_0)),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[564, 663])).
% 0.38/0.58 tff(675,assumption,(~cycle(e_2, e_3)), introduced(assumption)).
% 0.38/0.58 tff(676,assumption,(~cycle(e_2, e_0)), introduced(assumption)).
% 0.38/0.58 tff(677,plain,
% 0.38/0.58 (cycle(e_2, e_1)),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[517, 500, 676, 675])).
% 0.38/0.58 tff(678,plain,
% 0.38/0.58 (((~![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)))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(679,plain,
% 0.38/0.58 (((~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)))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(680,plain,
% 0.38/0.58 (((~![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))))),
% 0.38/0.58 inference(monotonicity,[status(thm)],[679])).
% 0.38/0.58 tff(681,plain,
% 0.38/0.58 (((~![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)))),
% 0.38/0.58 inference(transitivity,[status(thm)],[680, 678])).
% 0.38/0.58 tff(682,plain,
% 0.38/0.58 ((~![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)))),
% 0.38/0.58 inference(quant_inst,[status(thm)],[])).
% 0.38/0.58 tff(683,plain,
% 0.38/0.58 ((~![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))),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[682, 681])).
% 0.38/0.58 tff(684,plain,
% 0.38/0.58 ((~cycle(e_3, e_0)) | (~cycle(e_2, e_1))),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[683, 87, 137, 568, 81, 131])).
% 0.38/0.58 tff(685,plain,
% 0.38/0.58 (~cycle(e_2, e_1)),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[684, 121])).
% 0.38/0.58 tff(686,plain,
% 0.38/0.58 (((~![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)))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(687,plain,
% 0.38/0.58 (((~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)))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(688,plain,
% 0.38/0.58 (((~![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))))),
% 0.38/0.58 inference(monotonicity,[status(thm)],[687])).
% 0.38/0.58 tff(689,plain,
% 0.38/0.58 (((~![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)))),
% 0.38/0.58 inference(transitivity,[status(thm)],[688, 686])).
% 0.38/0.58 tff(690,plain,
% 0.38/0.58 ((~![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)))),
% 0.38/0.58 inference(quant_inst,[status(thm)],[])).
% 0.38/0.58 tff(691,plain,
% 0.38/0.58 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3))),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[690, 689])).
% 0.38/0.58 tff(692,plain,
% 0.38/0.58 ((~cycle(e_3, e_0)) | (~cycle(e_2, e_3))),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[691, 87, 84, 568, 81, 131])).
% 0.38/0.58 tff(693,plain,
% 0.38/0.58 (~cycle(e_2, e_3)),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[692, 121])).
% 0.38/0.58 tff(694,plain,
% 0.38/0.58 ($false),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[517, 693, 685, 676, 500])).
% 0.38/0.58 tff(695,plain,((~cycle(e_3, e_0)) | cycle(e_2, e_0) | cycle(e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.38/0.58 tff(696,plain,
% 0.38/0.58 (~cycle(e_3, e_0)),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[695, 500, 676])).
% 0.38/0.58 tff(697,plain,
% 0.38/0.58 (cycle(e_3, e_1)),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[335, 696])).
% 0.38/0.58 tff(698,plain,
% 0.38/0.58 ($false),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[349, 697, 677])).
% 0.38/0.58 tff(699,plain,(cycle(e_2, e_2) | cycle(e_2, e_0) | cycle(e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.38/0.58 tff(700,plain,
% 0.38/0.58 (cycle(e_2, e_2)),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[699, 674, 673])).
% 0.38/0.58 tff(701,plain,
% 0.38/0.58 ($false),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[415, 341, 148, 215, 409, 700, 663])).
% 0.38/0.58 tff(702,plain,(~product(e_2, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.38/0.58 tff(703,plain,
% 0.38/0.58 (product(e_2, e_1, e_3) | product(e_2, e_1, e_2)),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[425, 167, 419, 252, 702, 662])).
% 0.38/0.58 tff(704,plain,
% 0.38/0.58 (product(e_2, e_1, e_3)),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[703, 646])).
% 0.38/0.58 tff(705,plain,
% 0.38/0.58 (~cycle(e_2, e_0)),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[575, 704])).
% 0.38/0.58 tff(706,plain,
% 0.38/0.58 ((~cycle(e_3, e_0)) | cycle(e_2, e_2)),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[695, 705])).
% 0.38/0.58 tff(707,plain,
% 0.38/0.58 (~cycle(e_3, e_0)),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[706, 500])).
% 0.38/0.58 tff(708,plain,
% 0.38/0.58 (cycle(e_3, e_1)),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[335, 707])).
% 0.38/0.58 tff(709,plain,
% 0.38/0.58 (cycle(e_2, e_2) | cycle(e_2, e_3)),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[699, 705])).
% 0.38/0.58 tff(710,plain,
% 0.38/0.58 (cycle(e_2, e_3)),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[709, 500])).
% 0.38/0.58 tff(711,plain,
% 0.38/0.58 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_3, e_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_1)))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(712,plain,
% 0.38/0.58 (((~cycle(e_2, e_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_1))) <=> (equalish(e_3, e_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_1)))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(713,plain,
% 0.38/0.58 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_2, e_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_3, e_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_1))))),
% 0.38/0.58 inference(monotonicity,[status(thm)],[712])).
% 0.38/0.58 tff(714,plain,
% 0.38/0.58 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_2, e_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_1)))),
% 0.38/0.58 inference(transitivity,[status(thm)],[713, 711])).
% 0.38/0.58 tff(715,plain,
% 0.38/0.58 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_2, e_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_1)))),
% 0.38/0.58 inference(quant_inst,[status(thm)],[])).
% 0.38/0.58 tff(716,plain,
% 0.38/0.58 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_1))),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[715, 714])).
% 0.38/0.58 tff(717,plain,
% 0.38/0.58 ($false),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[716, 270, 341, 84, 78, 280, 710, 708])).
% 0.38/0.58 tff(718,plain,(cycle(e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.38/0.58 tff(719,plain,
% 0.38/0.58 (((~![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)))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(720,plain,
% 0.38/0.58 (((~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)))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(721,plain,
% 0.38/0.58 (((~![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))))),
% 0.38/0.58 inference(monotonicity,[status(thm)],[720])).
% 0.38/0.58 tff(722,plain,
% 0.38/0.58 (((~![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)))),
% 0.38/0.58 inference(transitivity,[status(thm)],[721, 719])).
% 0.38/0.58 tff(723,plain,
% 0.38/0.58 ((~![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)))),
% 0.38/0.58 inference(quant_inst,[status(thm)],[])).
% 0.38/0.58 tff(724,plain,
% 0.38/0.58 ((~![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))),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[723, 722])).
% 0.38/0.58 tff(725,plain,
% 0.38/0.58 ((~cycle(e_3, e_0)) | (~cycle(e_2, e_2))),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[724, 87, 148, 568, 81, 131])).
% 0.38/0.58 tff(726,plain,
% 0.38/0.58 (~cycle(e_3, e_0)),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[725, 718])).
% 0.38/0.58 tff(727,plain,
% 0.38/0.58 (cycle(e_3, e_1)),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[335, 726])).
% 0.38/0.58 tff(728,plain,
% 0.38/0.58 (~product(e_3, e_1, e_3)),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[231, 87, 137, 215, 225, 727])).
% 0.38/0.58 tff(729,plain,
% 0.38/0.58 (~product(e_3, e_1, e_2)),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[241, 87, 137, 215, 235, 727])).
% 0.38/0.59 tff(730,plain,
% 0.38/0.59 (product(e_3, e_1, e_4)),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[258, 167, 196, 252, 729, 728, 655])).
% 0.38/0.59 tff(731,plain,
% 0.38/0.59 (((~![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_3, e_1, e_4)) | (~product(e_3, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_3, e_4)))),
% 0.38/0.59 inference(rewrite,[status(thm)],[])).
% 0.38/0.59 tff(732,plain,
% 0.38/0.59 ((~![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_3, e_1, e_4)) | (~product(e_3, e_3, e_4)))),
% 0.38/0.59 inference(quant_inst,[status(thm)],[])).
% 0.38/0.59 tff(733,plain,
% 0.38/0.59 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_3, e_4))),
% 0.38/0.59 inference(modus_ponens,[status(thm)],[732, 731])).
% 0.38/0.59 tff(734,plain,
% 0.38/0.59 ($false),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[733, 68, 366, 730, 648])).
% 0.38/0.59 tff(735,plain,(~product(e_3, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.38/0.59 tff(736,assumption,(product(e_3, e_3, e_2)), introduced(assumption)).
% 0.38/0.59 tff(737,plain,
% 0.38/0.59 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_2) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_2)))),
% 0.38/0.59 inference(rewrite,[status(thm)],[])).
% 0.38/0.59 tff(738,plain,
% 0.38/0.59 ((product(e_3, e_1, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_3, e_3))) <=> (product(e_3, e_1, e_2) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_2)))),
% 0.38/0.59 inference(rewrite,[status(thm)],[])).
% 0.38/0.59 tff(739,plain,
% 0.38/0.59 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_2))))),
% 0.38/0.59 inference(monotonicity,[status(thm)],[738])).
% 0.38/0.59 tff(740,plain,
% 0.38/0.59 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_2) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_2)))),
% 0.38/0.59 inference(transitivity,[status(thm)],[739, 737])).
% 0.38/0.59 tff(741,plain,
% 0.38/0.59 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_3, e_3)))),
% 0.38/0.59 inference(quant_inst,[status(thm)],[])).
% 0.38/0.59 tff(742,plain,
% 0.38/0.59 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_2) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_2))),
% 0.38/0.59 inference(modus_ponens,[status(thm)],[741, 740])).
% 0.38/0.59 tff(743,plain,
% 0.38/0.59 ($false),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[742, 32, 729, 475, 736])).
% 0.38/0.59 tff(744,plain,((~product(e_3, e_3, e_2)) | (~product(e_1, e_3, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.59 tff(745,plain,
% 0.38/0.59 (~product(e_3, e_3, e_2)),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[744, 475])).
% 0.38/0.59 tff(746,plain,
% 0.38/0.59 (~product(e_3, e_2, e_4)),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[371, 730])).
% 0.38/0.59 tff(747,plain,
% 0.38/0.59 (product(e_3, e_2, e_4) | (~product(e_1, e_3, e_4))),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[433, 704])).
% 0.38/0.59 tff(748,plain,
% 0.38/0.59 (~product(e_1, e_3, e_4)),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[747, 746])).
% 0.38/0.59 tff(749,plain,
% 0.38/0.59 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_1, e_4)) | (~product(e_3, e_3, e_1)) | product(e_1, e_3, e_4))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_3, e_1)) | product(e_1, e_3, e_4))),
% 0.38/0.59 inference(rewrite,[status(thm)],[])).
% 0.38/0.59 tff(750,plain,
% 0.38/0.59 ((product(e_1, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_3, e_1))) <=> ((~product(e_3, e_1, e_4)) | (~product(e_3, e_3, e_1)) | product(e_1, e_3, e_4))),
% 0.38/0.59 inference(rewrite,[status(thm)],[])).
% 0.38/0.59 tff(751,plain,
% 0.38/0.59 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_1, e_4)) | (~product(e_3, e_3, e_1)) | product(e_1, e_3, e_4)))),
% 0.38/0.59 inference(monotonicity,[status(thm)],[750])).
% 0.38/0.59 tff(752,plain,
% 0.38/0.59 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_3, e_1)) | product(e_1, e_3, e_4))),
% 0.38/0.59 inference(transitivity,[status(thm)],[751, 749])).
% 0.38/0.59 tff(753,plain,
% 0.38/0.59 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_3, e_1)))),
% 0.38/0.59 inference(quant_inst,[status(thm)],[])).
% 0.38/0.59 tff(754,plain,
% 0.38/0.59 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_3, e_1)) | product(e_1, e_3, e_4)),
% 0.38/0.59 inference(modus_ponens,[status(thm)],[753, 752])).
% 0.38/0.59 tff(755,plain,
% 0.38/0.59 (~product(e_3, e_3, e_1)),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[754, 32, 730, 748])).
% 0.38/0.59 tff(756,plain,
% 0.38/0.59 (((~![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_3, e_2) | product(e_3, e_3, e_4) | product(e_3, e_3, e_3) | product(e_3, 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_3)) | product(e_3, e_3, e_2) | product(e_3, e_3, e_4) | product(e_3, e_3, e_3) | product(e_3, e_3, e_1))),
% 0.38/0.59 inference(rewrite,[status(thm)],[])).
% 0.38/0.59 tff(757,plain,
% 0.38/0.59 (((~group_element(e_3)) | product(e_3, e_3, e_4) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3))) <=> ((~group_element(e_3)) | product(e_3, e_3, e_2) | product(e_3, e_3, e_4) | product(e_3, e_3, e_3) | product(e_3, e_3, e_1))),
% 0.38/0.59 inference(rewrite,[status(thm)],[])).
% 0.38/0.59 tff(758,plain,
% 0.38/0.59 (((~![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_3, e_4) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_3, e_2) | product(e_3, e_3, e_4) | product(e_3, e_3, e_3) | product(e_3, e_3, e_1)))),
% 0.38/0.59 inference(monotonicity,[status(thm)],[757])).
% 0.38/0.59 tff(759,plain,
% 0.38/0.59 (((~![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_3, e_4) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_3)) | product(e_3, e_3, e_2) | product(e_3, e_3, e_4) | product(e_3, e_3, e_3) | product(e_3, e_3, e_1))),
% 0.38/0.59 inference(transitivity,[status(thm)],[758, 756])).
% 0.38/0.59 tff(760,plain,
% 0.38/0.59 ((~![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_3, e_4) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)))),
% 0.38/0.59 inference(quant_inst,[status(thm)],[])).
% 0.38/0.59 tff(761,plain,
% 0.38/0.59 ((~![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_3, e_2) | product(e_3, e_3, e_4) | product(e_3, e_3, e_3) | product(e_3, e_3, e_1)),
% 0.38/0.59 inference(modus_ponens,[status(thm)],[760, 759])).
% 0.38/0.59 tff(762,plain,
% 0.38/0.59 (product(e_3, e_3, e_2) | product(e_3, e_3, e_4) | product(e_3, e_3, e_3)),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[761, 196, 252, 755])).
% 0.38/0.59 tff(763,plain,
% 0.38/0.59 (product(e_3, e_3, e_3)),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[762, 745, 735])).
% 0.38/0.59 tff(764,plain,
% 0.38/0.59 (((~![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_1, e_3, e_3)) | (~product(e_3, 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_1, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.38/0.59 inference(rewrite,[status(thm)],[])).
% 0.38/0.59 tff(765,plain,
% 0.38/0.59 ((equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3))) <=> (equalish(e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.38/0.59 inference(rewrite,[status(thm)],[])).
% 0.38/0.59 tff(766,plain,
% 0.38/0.59 (((~![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_1, e_3, e_3)) | (~product(e_3, e_3, e_3))))),
% 0.38/0.59 inference(monotonicity,[status(thm)],[765])).
% 0.38/0.59 tff(767,plain,
% 0.38/0.59 (((~![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_1, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.38/0.59 inference(transitivity,[status(thm)],[766, 764])).
% 0.38/0.59 tff(768,plain,
% 0.38/0.59 ((~![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)))),
% 0.38/0.59 inference(quant_inst,[status(thm)],[])).
% 0.38/0.59 tff(769,plain,
% 0.38/0.59 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3))),
% 0.38/0.59 inference(modus_ponens,[status(thm)],[768, 767])).
% 0.38/0.59 tff(770,plain,
% 0.38/0.59 ($false),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[769, 389, 13, 475, 763])).
% 0.38/0.59 tff(771,plain,(~product(e_1, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.38/0.59 tff(772,assumption,(product(e_1, e_3, e_1)), introduced(assumption)).
% 0.38/0.59 tff(773,plain,
% 0.38/0.59 (((~![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)))),
% 0.38/0.59 inference(rewrite,[status(thm)],[])).
% 0.38/0.59 tff(774,plain,
% 0.38/0.59 ((~![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)))),
% 0.38/0.59 inference(quant_inst,[status(thm)],[])).
% 0.38/0.59 tff(775,plain,
% 0.38/0.59 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1))),
% 0.38/0.59 inference(modus_ponens,[status(thm)],[774, 773])).
% 0.38/0.59 tff(776,plain,
% 0.38/0.59 ($false),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[775, 68, 366, 623, 772])).
% 0.38/0.59 tff(777,plain,((~product(e_1, e_3, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.59 tff(778,plain,
% 0.38/0.59 (~product(e_1, e_3, e_1)),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[777, 621])).
% 0.38/0.59 tff(779,plain,
% 0.38/0.59 (product(e_1, e_3, e_3) | product(e_1, e_3, e_2)),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[441, 167, 196, 252, 748, 778])).
% 0.38/0.59 tff(780,plain,
% 0.38/0.59 (product(e_1, e_3, e_2)),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[779, 771])).
% 0.38/0.59 tff(781,plain,
% 0.38/0.59 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.38/0.59 inference(rewrite,[status(thm)],[])).
% 0.38/0.59 tff(782,plain,
% 0.38/0.59 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.38/0.59 inference(quant_inst,[status(thm)],[])).
% 0.38/0.59 tff(783,plain,
% 0.38/0.59 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_1, e_3, e_2))),
% 0.38/0.59 inference(modus_ponens,[status(thm)],[782, 781])).
% 0.38/0.59 tff(784,plain,
% 0.38/0.59 ($false),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[783, 32, 780, 647, 646])).
% 0.38/0.59 tff(785,plain,(~product(e_3, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.38/0.59 tff(786,plain,
% 0.38/0.59 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_3, e_2, e_2) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_2) | (~product(e_1, e_3, e_2)))),
% 0.38/0.59 inference(rewrite,[status(thm)],[])).
% 0.38/0.59 tff(787,plain,
% 0.38/0.59 ((product(e_3, e_2, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_3))) <=> ((~product(e_2, e_1, e_3)) | product(e_3, e_2, e_2) | (~product(e_1, e_3, e_2)))),
% 0.38/0.59 inference(rewrite,[status(thm)],[])).
% 0.38/0.59 tff(788,plain,
% 0.38/0.59 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_3, e_2, e_2) | (~product(e_1, e_3, e_2))))),
% 0.38/0.59 inference(monotonicity,[status(thm)],[787])).
% 0.38/0.59 tff(789,plain,
% 0.38/0.59 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_2) | (~product(e_1, e_3, e_2)))),
% 0.38/0.59 inference(transitivity,[status(thm)],[788, 786])).
% 0.38/0.59 tff(790,plain,
% 0.38/0.59 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.38/0.59 inference(quant_inst,[status(thm)],[])).
% 0.38/0.59 tff(791,plain,
% 0.38/0.59 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_2) | (~product(e_1, e_3, e_2))),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[790, 789])).
% 0.38/0.60 tff(792,plain,
% 0.38/0.60 ($false),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[791, 32, 704, 780, 785])).
% 0.38/0.60 % SZS output end Proof
% 0.38/0.60 % E exiting
%------------------------------------------------------------------------------