%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP125-3.005 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:07:06 AM UTC 2025
% Result : Unsatisfiable 0.40s 0.61s
% Output : Proof 0.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP125-3.005 : TPTP v9.0.0. Released v1.2.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 15:46:33 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.40/0.61 % SZS status Unsatisfiable
% 0.40/0.61 % SZS output start Proof
% 0.40/0.61 tff(product_type, type, (
% 0.40/0.61 product: ( $i * $i * $i ) > $o)).
% 0.40/0.61 tff(e_2_type, type, (
% 0.40/0.61 e_2: $i)).
% 0.40/0.61 tff(e_1_type, type, (
% 0.40/0.61 e_1: $i)).
% 0.40/0.61 tff(e_4_type, type, (
% 0.40/0.61 e_4: $i)).
% 0.40/0.61 tff(e_5_type, type, (
% 0.40/0.61 e_5: $i)).
% 0.40/0.61 tff(e_3_type, type, (
% 0.40/0.61 e_3: $i)).
% 0.40/0.61 tff(equalish_type, type, (
% 0.40/0.61 equalish: ( $i * $i ) > $o)).
% 0.40/0.61 tff(cycle_type, type, (
% 0.40/0.61 cycle: ( $i * $i ) > $o)).
% 0.40/0.61 tff(next_type, type, (
% 0.40/0.61 next: ( $i * $i ) > $o)).
% 0.40/0.61 tff(greater_type, type, (
% 0.40/0.61 greater: ( $i * $i ) > $o)).
% 0.40/0.61 tff(e_0_type, type, (
% 0.40/0.61 e_0: $i)).
% 0.40/0.61 tff(group_element_type, type, (
% 0.40/0.61 group_element: $i > $o)).
% 0.40/0.61 tff(1,assumption,(product(e_3, e_2, e_5)), introduced(assumption)).
% 0.40/0.61 tff(2,assumption,(product(e_1, e_2, e_5)), introduced(assumption)).
% 0.40/0.61 tff(3,plain,
% 0.40/0.61 (^[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))))),
% 0.40/0.61 inference(bind,[status(th)],[])).
% 0.40/0.61 tff(4,plain,
% 0.40/0.61 (![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)))),
% 0.40/0.61 inference(quant_intro,[status(thm)],[3])).
% 0.40/0.61 tff(5,plain,
% 0.40/0.61 (![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)))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(6,plain,
% 0.40/0.61 (^[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)))))),
% 0.40/0.61 inference(bind,[status(th)],[])).
% 0.40/0.61 tff(7,plain,
% 0.40/0.61 (![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)))),
% 0.40/0.61 inference(quant_intro,[status(thm)],[6])).
% 0.40/0.61 tff(8,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')).
% 0.40/0.61 tff(9,plain,
% 0.40/0.61 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.40/0.61 tff(10,plain,
% 0.40/0.61 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.40/0.61 tff(11,plain,(
% 0.40/0.61 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.40/0.61 inference(skolemize,[status(sab)],[10])).
% 0.40/0.61 tff(12,plain,
% 0.40/0.61 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.40/0.61 tff(13,plain,
% 0.40/0.61 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(14,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.40/0.61 tff(15,plain,
% 0.40/0.61 (~equalish(e_3, e_1)),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.40/0.61 tff(16,plain,
% 0.40/0.61 (((~![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_2, e_5)) | (~product(e_3, e_2, e_5)))) <=> ((~![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_2, e_5)) | (~product(e_3, e_2, e_5)))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(17,plain,
% 0.40/0.61 ((~![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_2, e_5)) | (~product(e_3, e_2, e_5)))),
% 0.40/0.61 inference(quant_inst,[status(thm)],[])).
% 0.40/0.61 tff(18,plain,
% 0.40/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_2, e_5)) | (~product(e_3, e_2, e_5))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.40/0.61 tff(19,plain,
% 0.40/0.61 ($false),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[18, 15, 12, 2, 1])).
% 0.40/0.61 tff(20,plain,((~product(e_3, e_2, e_5)) | (~product(e_1, e_2, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.61 tff(21,plain,
% 0.40/0.61 (~product(e_1, e_2, e_5)),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[20, 1])).
% 0.40/0.61 tff(22,assumption,(product(e_1, e_2, e_1)), introduced(assumption)).
% 0.40/0.61 tff(23,assumption,(~product(e_1, e_1, e_1)), introduced(assumption)).
% 0.40/0.61 tff(24,plain,
% 0.40/0.61 (^[X: $i] : refl(product(X, X, X) <=> product(X, X, X))),
% 0.40/0.61 inference(bind,[status(th)],[])).
% 0.40/0.61 tff(25,plain,
% 0.40/0.61 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.40/0.61 inference(quant_intro,[status(thm)],[24])).
% 0.40/0.61 tff(26,plain,
% 0.40/0.61 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(27,axiom,(![X: $i] : product(X, X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_idempotence')).
% 0.40/0.61 tff(28,plain,
% 0.40/0.61 (![X: $i] : product(X, X, X)),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.40/0.61 tff(29,plain,(
% 0.40/0.61 ![X: $i] : product(X, X, X)),
% 0.40/0.61 inference(skolemize,[status(sab)],[28])).
% 0.40/0.61 tff(30,plain,
% 0.40/0.61 (![X: $i] : product(X, X, X)),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.40/0.61 tff(31,plain,
% 0.40/0.61 ((~![X: $i] : product(X, X, X)) | product(e_1, e_1, e_1)),
% 0.40/0.61 inference(quant_inst,[status(thm)],[])).
% 0.40/0.61 tff(32,plain,
% 0.40/0.61 ($false),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[31, 30, 23])).
% 0.40/0.61 tff(33,plain,(product(e_1, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.61 tff(34,plain,
% 0.40/0.61 (^[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))))),
% 0.40/0.61 inference(bind,[status(th)],[])).
% 0.40/0.61 tff(35,plain,
% 0.40/0.61 (![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)))),
% 0.40/0.61 inference(quant_intro,[status(thm)],[34])).
% 0.40/0.61 tff(36,plain,
% 0.40/0.61 (![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)))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(37,plain,
% 0.40/0.61 (^[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)))))),
% 0.40/0.61 inference(bind,[status(th)],[])).
% 0.40/0.61 tff(38,plain,
% 0.40/0.61 (![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)))),
% 0.40/0.61 inference(quant_intro,[status(thm)],[37])).
% 0.40/0.61 tff(39,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')).
% 0.40/0.61 tff(40,plain,
% 0.40/0.61 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.40/0.61 tff(41,plain,
% 0.40/0.61 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.40/0.61 tff(42,plain,(
% 0.40/0.61 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.40/0.61 inference(skolemize,[status(sab)],[41])).
% 0.40/0.61 tff(43,plain,
% 0.40/0.61 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.40/0.61 tff(44,plain,
% 0.40/0.61 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(45,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.40/0.61 tff(46,plain,
% 0.40/0.61 (~equalish(e_2, e_1)),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.40/0.61 tff(47,plain,
% 0.40/0.61 (((~![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)))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(48,plain,
% 0.40/0.61 ((~![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)))),
% 0.40/0.61 inference(quant_inst,[status(thm)],[])).
% 0.40/0.61 tff(49,plain,
% 0.40/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.40/0.61 tff(50,plain,
% 0.40/0.61 ($false),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[49, 46, 43, 33, 22])).
% 0.40/0.61 tff(51,plain,(~product(e_1, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.61 tff(52,plain,
% 0.40/0.61 ((~![X: $i] : product(X, X, X)) | product(e_3, e_3, e_3)),
% 0.40/0.61 inference(quant_inst,[status(thm)],[])).
% 0.40/0.61 tff(53,plain,
% 0.40/0.61 (product(e_3, e_3, e_3)),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[52, 30])).
% 0.40/0.61 tff(54,assumption,(product(e_2, e_3, e_3)), introduced(assumption)).
% 0.40/0.61 tff(55,plain,
% 0.40/0.61 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(56,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.40/0.61 tff(57,plain,
% 0.40/0.61 (~equalish(e_2, e_3)),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.40/0.61 tff(58,plain,
% 0.40/0.61 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_2, 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_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_3, e_3)))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(59,plain,
% 0.40/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_3, e_3)))),
% 0.40/0.61 inference(quant_inst,[status(thm)],[])).
% 0.40/0.61 tff(60,plain,
% 0.40/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_3, e_3))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.40/0.61 tff(61,plain,
% 0.40/0.61 ($false),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[60, 57, 12, 54, 53])).
% 0.40/0.61 tff(62,plain,(~product(e_2, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.61 tff(63,plain,
% 0.40/0.61 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl(((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1))) <=> ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1))))),
% 0.40/0.61 inference(bind,[status(th)],[])).
% 0.40/0.61 tff(64,plain,
% 0.40/0.61 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.40/0.61 inference(quant_intro,[status(thm)],[63])).
% 0.40/0.61 tff(65,plain,
% 0.40/0.61 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(66,plain,
% 0.40/0.61 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : rewrite((((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, X)) <=> ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1))))),
% 0.40/0.61 inference(bind,[status(th)],[])).
% 0.40/0.61 tff(67,plain,
% 0.40/0.61 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, X)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.40/0.61 inference(quant_intro,[status(thm)],[66])).
% 0.40/0.61 tff(68,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qg3')).
% 0.40/0.61 tff(69,plain,
% 0.40/0.61 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.40/0.61 tff(70,plain,
% 0.40/0.61 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.40/0.61 tff(71,plain,(
% 0.40/0.61 ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.40/0.61 inference(skolemize,[status(sab)],[70])).
% 0.40/0.61 tff(72,plain,
% 0.40/0.61 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.40/0.61 tff(73,plain,
% 0.40/0.61 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_2)))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(74,plain,
% 0.40/0.61 (((~product(e_3, e_3, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_3, e_2))) <=> (product(e_2, e_3, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_2)))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(75,plain,
% 0.40/0.61 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_2))))),
% 0.40/0.61 inference(monotonicity,[status(thm)],[74])).
% 0.40/0.61 tff(76,plain,
% 0.40/0.61 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_2)))),
% 0.40/0.61 inference(transitivity,[status(thm)],[75, 73])).
% 0.40/0.61 tff(77,plain,
% 0.40/0.61 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_3, e_2)))),
% 0.40/0.61 inference(quant_inst,[status(thm)],[])).
% 0.40/0.61 tff(78,plain,
% 0.40/0.61 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_2))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.40/0.61 tff(79,plain,
% 0.40/0.61 (~product(e_3, e_3, e_2)),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[78, 72, 62, 53])).
% 0.40/0.61 tff(80,assumption,(product(e_2, e_1, e_5)), introduced(assumption)).
% 0.40/0.61 tff(81,assumption,(cycle(e_2, e_1)), introduced(assumption)).
% 0.40/0.61 tff(82,plain,
% 0.40/0.61 ((~equalish(e_5, e_3)) <=> (~equalish(e_5, e_3))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(83,axiom,(~equalish(e_5, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_is_not_e_3')).
% 0.40/0.61 tff(84,plain,
% 0.40/0.61 (~equalish(e_5, e_3)),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.40/0.61 tff(85,plain,
% 0.40/0.61 (^[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))))),
% 0.40/0.62 inference(bind,[status(th)],[])).
% 0.40/0.62 tff(86,plain,
% 0.40/0.62 (![Z: $i, 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)))),
% 0.40/0.62 inference(quant_intro,[status(thm)],[85])).
% 0.40/0.62 tff(87,plain,
% 0.40/0.62 (![Z: $i, 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)))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(88,plain,
% 0.40/0.62 (^[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)))))),
% 0.40/0.62 inference(bind,[status(th)],[])).
% 0.40/0.62 tff(89,plain,
% 0.40/0.62 (![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)))),
% 0.40/0.62 inference(quant_intro,[status(thm)],[88])).
% 0.40/0.62 tff(90,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')).
% 0.40/0.62 tff(91,plain,
% 0.40/0.62 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.40/0.62 tff(92,plain,
% 0.40/0.62 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.40/0.62 tff(93,plain,(
% 0.40/0.62 ![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.40/0.62 inference(skolemize,[status(sab)],[92])).
% 0.40/0.62 tff(94,plain,
% 0.40/0.62 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.40/0.62 tff(95,plain,
% 0.40/0.62 (greater(e_1, e_0) <=> greater(e_1, e_0)),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(96,axiom,(greater(e_1, e_0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_greater_e_0')).
% 0.40/0.62 tff(97,plain,
% 0.40/0.62 (greater(e_1, e_0)),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.40/0.62 tff(98,plain,
% 0.40/0.62 (next(e_2, e_3) <=> next(e_2, e_3)),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(99,axiom,(next(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_then_e_3')).
% 0.40/0.62 tff(100,plain,
% 0.40/0.62 (next(e_2, e_3)),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.40/0.62 tff(101,plain,
% 0.40/0.62 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_5, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_5)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_5, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_5)))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(102,plain,
% 0.40/0.62 (((~greater(e_1, e_0)) | (~cycle(e_2, e_1)) | equalish(e_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5))) <=> (equalish(e_5, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_5)))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(103,plain,
% 0.40/0.62 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_2, e_1)) | equalish(e_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_5, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_5))))),
% 0.40/0.62 inference(monotonicity,[status(thm)],[102])).
% 0.40/0.62 tff(104,plain,
% 0.40/0.62 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_2, e_1)) | equalish(e_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_5, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_5)))),
% 0.40/0.62 inference(transitivity,[status(thm)],[103, 101])).
% 0.40/0.62 tff(105,plain,
% 0.40/0.62 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_2, e_1)) | equalish(e_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(106,plain,
% 0.40/0.62 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_5, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_5))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.40/0.62 tff(107,plain,
% 0.40/0.62 ($false),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[106, 100, 97, 94, 84, 81, 80])).
% 0.40/0.62 tff(108,plain,((~cycle(e_2, e_1)) | (~product(e_2, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.62 tff(109,plain,
% 0.40/0.62 (~cycle(e_2, e_1)),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[108, 80])).
% 0.40/0.62 tff(110,assumption,(cycle(e_2, e_3)), introduced(assumption)).
% 0.40/0.62 tff(111,plain,
% 0.40/0.62 (greater(e_3, e_0) <=> greater(e_3, e_0)),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(112,axiom,(greater(e_3, e_0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_greater_e_0')).
% 0.40/0.62 tff(113,plain,
% 0.40/0.62 (greater(e_3, e_0)),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.40/0.62 tff(114,plain,
% 0.40/0.62 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_5, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_5)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_5, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_5)))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(115,plain,
% 0.40/0.62 (((~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | equalish(e_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5))) <=> (equalish(e_5, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_5)))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(116,plain,
% 0.40/0.62 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | equalish(e_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_5, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_5))))),
% 0.40/0.62 inference(monotonicity,[status(thm)],[115])).
% 0.40/0.62 tff(117,plain,
% 0.40/0.62 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | equalish(e_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_5, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_5)))),
% 0.40/0.62 inference(transitivity,[status(thm)],[116, 114])).
% 0.40/0.62 tff(118,plain,
% 0.40/0.62 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | equalish(e_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(119,plain,
% 0.40/0.62 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_5, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_5))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.40/0.62 tff(120,plain,
% 0.40/0.62 ($false),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[119, 100, 113, 94, 84, 110, 80])).
% 0.40/0.62 tff(121,plain,((~cycle(e_2, e_3)) | (~product(e_2, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.62 tff(122,plain,
% 0.40/0.62 (~cycle(e_2, e_3)),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[121, 80])).
% 0.40/0.62 tff(123,assumption,(cycle(e_2, e_2)), introduced(assumption)).
% 0.40/0.62 tff(124,plain,
% 0.40/0.62 (greater(e_2, e_0) <=> greater(e_2, e_0)),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(125,axiom,(greater(e_2, e_0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_greater_e_0')).
% 0.40/0.62 tff(126,plain,
% 0.40/0.62 (greater(e_2, e_0)),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.40/0.62 tff(127,plain,
% 0.40/0.62 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_5, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_5)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_5, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_5)))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(128,plain,
% 0.40/0.62 (((~greater(e_2, e_0)) | (~cycle(e_2, e_2)) | equalish(e_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5))) <=> (equalish(e_5, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_5)))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(129,plain,
% 0.40/0.62 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_2, e_2)) | equalish(e_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_5, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_5))))),
% 0.40/0.62 inference(monotonicity,[status(thm)],[128])).
% 0.40/0.62 tff(130,plain,
% 0.40/0.62 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_2, e_2)) | equalish(e_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_5, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_5)))),
% 0.40/0.62 inference(transitivity,[status(thm)],[129, 127])).
% 0.40/0.62 tff(131,plain,
% 0.40/0.62 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_2, e_2)) | equalish(e_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(132,plain,
% 0.40/0.62 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_5, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_5))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.40/0.62 tff(133,plain,
% 0.40/0.62 ($false),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[132, 100, 126, 94, 84, 123, 80])).
% 0.40/0.62 tff(134,plain,((~cycle(e_2, e_2)) | (~product(e_2, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.62 tff(135,plain,
% 0.40/0.62 (~cycle(e_2, e_2)),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[134, 80])).
% 0.40/0.62 tff(136,plain,
% 0.40/0.62 ((~![X: $i] : product(X, X, X)) | product(e_2, e_2, e_2)),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(137,plain,
% 0.40/0.62 (product(e_2, e_2, e_2)),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[136, 30])).
% 0.40/0.62 tff(138,assumption,(product(e_2, e_1, e_2)), introduced(assumption)).
% 0.40/0.62 tff(139,plain,
% 0.40/0.62 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(140,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.40/0.62 tff(141,plain,
% 0.40/0.62 (~equalish(e_1, e_2)),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.40/0.62 tff(142,plain,
% 0.40/0.62 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(143,plain,
% 0.40/0.62 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(144,plain,
% 0.40/0.62 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.40/0.62 tff(145,plain,
% 0.40/0.62 ($false),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[144, 141, 43, 138, 137])).
% 0.40/0.62 tff(146,plain,(~product(e_2, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.62 tff(147,assumption,(cycle(e_2, e_0)), introduced(assumption)).
% 0.40/0.62 tff(148,plain,
% 0.40/0.62 (^[Y: $i, X: $i] : refl(((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0))) <=> ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0))))),
% 0.40/0.62 inference(bind,[status(th)],[])).
% 0.40/0.62 tff(149,plain,
% 0.40/0.62 (![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0))) <=> ![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))),
% 0.40/0.62 inference(quant_intro,[status(thm)],[148])).
% 0.40/0.62 tff(150,plain,
% 0.40/0.62 (![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0))) <=> ![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(151,plain,
% 0.40/0.62 (^[Y: $i, X: $i] : rewrite((((~cycle(X, e_0)) | (~product(X, e_1, Y))) | (~greater(Y, X))) <=> ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0))))),
% 0.40/0.62 inference(bind,[status(th)],[])).
% 0.40/0.62 tff(152,plain,
% 0.40/0.62 (![Y: $i, X: $i] : (((~cycle(X, e_0)) | (~product(X, e_1, Y))) | (~greater(Y, X))) <=> ![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))),
% 0.40/0.62 inference(quant_intro,[status(thm)],[151])).
% 0.40/0.62 tff(153,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')).
% 0.40/0.62 tff(154,plain,
% 0.40/0.62 (![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.40/0.62 tff(155,plain,
% 0.40/0.62 (![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[154, 150])).
% 0.40/0.62 tff(156,plain,(
% 0.40/0.62 ![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))),
% 0.40/0.62 inference(skolemize,[status(sab)],[155])).
% 0.40/0.62 tff(157,plain,
% 0.40/0.62 (![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[156, 149])).
% 0.40/0.62 tff(158,plain,
% 0.40/0.62 (greater(e_3, e_2) <=> greater(e_3, e_2)),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(159,axiom,(greater(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_greater_e_2')).
% 0.40/0.62 tff(160,plain,
% 0.40/0.62 (greater(e_3, e_2)),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.40/0.62 tff(161,plain,
% 0.40/0.62 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(162,plain,
% 0.40/0.62 (((~product(e_2, e_1, e_3)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_0))) <=> ((~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(163,plain,
% 0.40/0.62 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_3)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3))))),
% 0.40/0.62 inference(monotonicity,[status(thm)],[162])).
% 0.40/0.62 tff(164,plain,
% 0.40/0.62 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_3)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.40/0.62 inference(transitivity,[status(thm)],[163, 161])).
% 0.40/0.62 tff(165,plain,
% 0.40/0.62 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_3)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_0)))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(166,plain,
% 0.40/0.62 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.40/0.62 tff(167,plain,
% 0.40/0.62 ((~cycle(e_2, e_0)) | (~product(e_2, e_1, e_3))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[166, 160, 157])).
% 0.40/0.62 tff(168,plain,
% 0.40/0.62 (~product(e_2, e_1, e_3)),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[167, 147])).
% 0.40/0.62 tff(169,plain,
% 0.40/0.62 (greater(e_5, e_2) <=> greater(e_5, e_2)),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(170,axiom,(greater(e_5, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_greater_e_2')).
% 0.40/0.62 tff(171,plain,
% 0.40/0.62 (greater(e_5, e_2)),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.40/0.62 tff(172,plain,
% 0.40/0.62 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_2, e_0)) | (~greater(e_5, e_2)) | (~product(e_2, e_1, e_5)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_5, e_2)) | (~product(e_2, e_1, e_5)))),
% 0.40/0.63 inference(rewrite,[status(thm)],[])).
% 0.40/0.63 tff(173,plain,
% 0.40/0.63 (((~product(e_2, e_1, e_5)) | (~greater(e_5, e_2)) | (~cycle(e_2, e_0))) <=> ((~cycle(e_2, e_0)) | (~greater(e_5, e_2)) | (~product(e_2, e_1, e_5)))),
% 0.40/0.63 inference(rewrite,[status(thm)],[])).
% 0.40/0.63 tff(174,plain,
% 0.40/0.63 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_5)) | (~greater(e_5, e_2)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_2, e_0)) | (~greater(e_5, e_2)) | (~product(e_2, e_1, e_5))))),
% 0.40/0.63 inference(monotonicity,[status(thm)],[173])).
% 0.40/0.63 tff(175,plain,
% 0.40/0.63 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_5)) | (~greater(e_5, e_2)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_5, e_2)) | (~product(e_2, e_1, e_5)))),
% 0.40/0.63 inference(transitivity,[status(thm)],[174, 172])).
% 0.40/0.63 tff(176,plain,
% 0.40/0.63 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_5)) | (~greater(e_5, e_2)) | (~cycle(e_2, e_0)))),
% 0.40/0.63 inference(quant_inst,[status(thm)],[])).
% 0.40/0.63 tff(177,plain,
% 0.40/0.63 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_5, e_2)) | (~product(e_2, e_1, e_5))),
% 0.40/0.63 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.40/0.63 tff(178,plain,
% 0.40/0.63 ((~cycle(e_2, e_0)) | (~product(e_2, e_1, e_5))),
% 0.40/0.63 inference(unit_resolution,[status(thm)],[177, 171, 157])).
% 0.40/0.63 tff(179,plain,
% 0.40/0.63 (~product(e_2, e_1, e_5)),
% 0.40/0.63 inference(unit_resolution,[status(thm)],[178, 147])).
% 0.40/0.63 tff(180,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.40/0.63 tff(181,assumption,(product(e_1, e_1, e_1)), introduced(assumption)).
% 0.40/0.63 tff(182,plain,
% 0.40/0.63 (((~![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)))),
% 0.40/0.63 inference(rewrite,[status(thm)],[])).
% 0.40/0.63 tff(183,plain,
% 0.40/0.63 ((~![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)))),
% 0.40/0.63 inference(quant_inst,[status(thm)],[])).
% 0.40/0.63 tff(184,plain,
% 0.40/0.63 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1))),
% 0.40/0.63 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.40/0.63 tff(185,plain,
% 0.40/0.63 ($false),
% 0.40/0.63 inference(unit_resolution,[status(thm)],[184, 46, 12, 181, 180])).
% 0.40/0.63 tff(186,plain,((~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.63 tff(187,plain,
% 0.40/0.63 (~product(e_2, e_1, e_1)),
% 0.40/0.63 inference(unit_resolution,[status(thm)],[186, 33])).
% 0.40/0.63 tff(188,assumption,(product(e_2, e_1, e_4)), introduced(assumption)).
% 0.40/0.63 tff(189,plain,
% 0.40/0.63 ((~equalish(e_4, e_3)) <=> (~equalish(e_4, e_3))),
% 0.40/0.63 inference(rewrite,[status(thm)],[])).
% 0.40/0.63 tff(190,axiom,(~equalish(e_4, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_3')).
% 0.40/0.63 tff(191,plain,
% 0.40/0.63 (~equalish(e_4, e_3)),
% 0.40/0.63 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.40/0.63 tff(192,plain,
% 0.40/0.63 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_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)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(193,plain,
% 0.47/0.63 (((~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)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(194,plain,
% 0.47/0.63 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_2, e_2)) | equalish(e_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))))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[193])).
% 0.47/0.63 tff(195,plain,
% 0.47/0.63 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_2, e_2)) | equalish(e_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)))),
% 0.47/0.63 inference(transitivity,[status(thm)],[194, 192])).
% 0.47/0.63 tff(196,plain,
% 0.47/0.63 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_2, e_2)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(197,plain,
% 0.47/0.63 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_4))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.47/0.63 tff(198,plain,
% 0.47/0.63 ($false),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[197, 100, 126, 94, 191, 123, 188])).
% 0.47/0.63 tff(199,plain,((~cycle(e_2, e_2)) | (~product(e_2, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.63 tff(200,plain,
% 0.47/0.63 (~cycle(e_2, e_2)),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[199, 188])).
% 0.47/0.63 tff(201,plain,
% 0.47/0.63 (greater(e_4, e_2) <=> greater(e_4, e_2)),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(202,axiom,(greater(e_4, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_greater_e_2')).
% 0.47/0.63 tff(203,plain,
% 0.47/0.63 (greater(e_4, e_2)),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.47/0.63 tff(204,plain,
% 0.47/0.63 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(205,plain,
% 0.47/0.63 (((~product(e_2, e_1, e_4)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_0))) <=> ((~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(206,plain,
% 0.47/0.63 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_4)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4))))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[205])).
% 0.47/0.63 tff(207,plain,
% 0.47/0.63 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_4)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)))),
% 0.47/0.63 inference(transitivity,[status(thm)],[206, 204])).
% 0.47/0.63 tff(208,plain,
% 0.47/0.63 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_4)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_0)))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(209,plain,
% 0.47/0.63 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.47/0.63 tff(210,plain,
% 0.47/0.63 ((~cycle(e_2, e_0)) | (~product(e_2, e_1, e_4))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[209, 203, 157])).
% 0.47/0.63 tff(211,plain,
% 0.47/0.63 (~cycle(e_2, e_0)),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[210, 188])).
% 0.47/0.63 tff(212,plain,
% 0.47/0.63 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_4, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_4)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_4)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(213,plain,
% 0.47/0.63 (((~greater(e_1, e_0)) | (~cycle(e_2, e_1)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4))) <=> (equalish(e_4, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_4)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(214,plain,
% 0.47/0.63 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_2, e_1)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_4, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_4))))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[213])).
% 0.47/0.63 tff(215,plain,
% 0.47/0.63 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_2, e_1)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_4)))),
% 0.47/0.63 inference(transitivity,[status(thm)],[214, 212])).
% 0.47/0.63 tff(216,plain,
% 0.47/0.63 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_2, e_1)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(217,plain,
% 0.47/0.63 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_4))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.47/0.63 tff(218,plain,
% 0.47/0.63 ($false),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[217, 100, 97, 94, 191, 81, 188])).
% 0.47/0.63 tff(219,plain,((~cycle(e_2, e_1)) | (~product(e_2, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.63 tff(220,plain,
% 0.47/0.63 (~cycle(e_2, e_1)),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[219, 188])).
% 0.47/0.63 tff(221,assumption,(cycle(e_2, e_4)), introduced(assumption)).
% 0.47/0.63 tff(222,plain,
% 0.47/0.63 (greater(e_4, e_0) <=> greater(e_4, e_0)),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(223,axiom,(greater(e_4, e_0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_greater_e_0')).
% 0.47/0.63 tff(224,plain,
% 0.47/0.63 (greater(e_4, e_0)),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.47/0.63 tff(225,plain,
% 0.47/0.63 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | (~product(e_2, e_1, e_4)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | (~product(e_2, e_1, e_4)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(226,plain,
% 0.47/0.63 (((~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4))) <=> (equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | (~product(e_2, e_1, e_4)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(227,plain,
% 0.47/0.63 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | (~product(e_2, e_1, e_4))))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[226])).
% 0.47/0.63 tff(228,plain,
% 0.47/0.63 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | (~product(e_2, e_1, e_4)))),
% 0.47/0.63 inference(transitivity,[status(thm)],[227, 225])).
% 0.47/0.63 tff(229,plain,
% 0.47/0.63 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(230,plain,
% 0.47/0.63 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | (~product(e_2, e_1, e_4))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.47/0.63 tff(231,plain,
% 0.47/0.63 ($false),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[230, 100, 224, 94, 191, 221, 188])).
% 0.47/0.63 tff(232,plain,((~cycle(e_2, e_4)) | (~product(e_2, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.63 tff(233,plain,
% 0.47/0.63 (~cycle(e_2, e_4)),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[232, 188])).
% 0.47/0.63 tff(234,plain,
% 0.47/0.63 (group_element(e_2) <=> group_element(e_2)),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(235,axiom,(group_element(e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_2')).
% 0.47/0.63 tff(236,plain,
% 0.47/0.63 (group_element(e_2)),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.47/0.63 tff(237,plain,
% 0.47/0.63 (^[X: $i] : refl((cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) <=> (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))))),
% 0.47/0.63 inference(bind,[status(th)],[])).
% 0.47/0.63 tff(238,plain,
% 0.47/0.63 (![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) <=> ![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.47/0.63 inference(quant_intro,[status(thm)],[237])).
% 0.47/0.63 tff(239,plain,
% 0.47/0.63 (![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) <=> ![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(240,plain,
% 0.47/0.64 (^[X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) <=> (cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))), (((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) <=> ((cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) | cycle(X, e_2)))), rewrite(((cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) | cycle(X, e_2)) <=> (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))), (((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) <=> (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))))), ((((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) | cycle(X, e_3)) <=> ((cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) | cycle(X, e_3)))), rewrite(((cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) | cycle(X, e_3)) <=> (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))), ((((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) | cycle(X, e_3)) <=> (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))))), (((((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) | cycle(X, e_3)) | cycle(X, e_4)) <=> ((cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) | cycle(X, e_4)))), rewrite(((cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) | cycle(X, e_4)) <=> (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))), (((((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) | cycle(X, e_3)) | cycle(X, e_4)) <=> (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(241,plain,
% 0.47/0.64 (![X: $i] : ((((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) | cycle(X, e_3)) | cycle(X, e_4)) <=> ![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[240])).
% 0.47/0.64 tff(242,axiom,(![X: $i] : ((((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) | cycle(X, e_3)) | cycle(X, e_4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cycle2')).
% 0.47/0.64 tff(243,plain,
% 0.47/0.64 (![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.47/0.64 tff(244,plain,
% 0.47/0.64 (![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[243, 239])).
% 0.47/0.64 tff(245,plain,(
% 0.47/0.64 ![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.47/0.64 inference(skolemize,[status(sab)],[244])).
% 0.47/0.64 tff(246,plain,
% 0.47/0.64 (![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[245, 238])).
% 0.47/0.64 tff(247,plain,
% 0.47/0.64 (((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_2, e_4) | cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0) | (~group_element(e_2)))) <=> ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_2, e_4) | cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0) | (~group_element(e_2)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(248,plain,
% 0.47/0.64 ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_2, e_4) | cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0) | (~group_element(e_2)))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(249,plain,
% 0.47/0.64 ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_2, e_4) | cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0) | (~group_element(e_2))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.47/0.64 tff(250,plain,
% 0.47/0.64 (cycle(e_2, e_4) | cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[249, 246, 236])).
% 0.47/0.64 tff(251,plain,
% 0.47/0.64 (cycle(e_2, e_3)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[250, 233, 220, 211, 200])).
% 0.47/0.64 tff(252,plain,
% 0.47/0.64 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_4)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(253,plain,
% 0.47/0.64 (((~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4))) <=> (equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(254,plain,
% 0.47/0.64 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_4))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[253])).
% 0.47/0.64 tff(255,plain,
% 0.47/0.64 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.47/0.64 inference(transitivity,[status(thm)],[254, 252])).
% 0.47/0.64 tff(256,plain,
% 0.47/0.64 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(257,plain,
% 0.47/0.64 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_4))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.47/0.64 tff(258,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[257, 100, 113, 94, 191, 251, 188])).
% 0.47/0.64 tff(259,plain,(~product(e_2, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(260,plain,
% 0.47/0.64 (^[Y: $i, X: $i] : refl(((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) <=> ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(261,plain,
% 0.47/0.64 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) <=> ![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[260])).
% 0.47/0.64 tff(262,plain,
% 0.47/0.64 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) <=> ![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(263,plain,
% 0.47/0.64 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) <=> ((~group_element(X)) | product(X, Y, e_1) | (~group_element(Y)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> (((~group_element(X)) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_2)))), rewrite((((~group_element(X)) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_2)) <=> ((~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> ((~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> (((~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_3)))), rewrite((((~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_3)) <=> ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))))), (((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> (((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_4)))), rewrite((((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_4)) <=> ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))), (((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))))), ((((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) | product(X, Y, e_5)) <=> (((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_5)))), rewrite((((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_5)) <=> ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))), ((((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) | product(X, Y, e_5)) <=> ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(264,plain,
% 0.47/0.64 (![Y: $i, X: $i] : (((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) | product(X, Y, e_5)) <=> ![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[263])).
% 0.47/0.64 tff(265,axiom,(![Y: $i, X: $i] : (((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) | product(X, Y, e_5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_total_function1')).
% 0.47/0.64 tff(266,plain,
% 0.47/0.64 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.47/0.64 tff(267,plain,
% 0.47/0.64 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[266, 262])).
% 0.47/0.64 tff(268,plain,(
% 0.47/0.64 ![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.47/0.64 inference(skolemize,[status(sab)],[267])).
% 0.47/0.64 tff(269,plain,
% 0.47/0.64 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[268, 261])).
% 0.47/0.64 tff(270,plain,
% 0.47/0.64 (group_element(e_1) <=> group_element(e_1)),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(271,axiom,(group_element(e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_1')).
% 0.47/0.64 tff(272,plain,
% 0.47/0.64 (group_element(e_1)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.47/0.64 tff(273,plain,
% 0.47/0.64 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_5) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_5) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(274,plain,
% 0.47/0.64 (((~group_element(e_2)) | product(e_2, e_1, e_5) | product(e_2, e_1, e_4) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1))) <=> ((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_5) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(275,plain,
% 0.47/0.64 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_2, e_1, e_5) | product(e_2, e_1, e_4) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_5) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1)))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[274])).
% 0.47/0.64 tff(276,plain,
% 0.47/0.64 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_2, e_1, e_5) | product(e_2, e_1, e_4) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_5) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1))),
% 0.47/0.64 inference(transitivity,[status(thm)],[275, 273])).
% 0.47/0.64 tff(277,plain,
% 0.47/0.64 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_2, e_1, e_5) | product(e_2, e_1, e_4) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(278,plain,
% 0.47/0.64 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_5) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.47/0.64 tff(279,plain,
% 0.47/0.64 (product(e_2, e_1, e_3) | product(e_2, e_1, e_5) | product(e_2, e_1, e_2)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[278, 272, 236, 269, 259, 187])).
% 0.47/0.64 tff(280,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[279, 179, 168, 146])).
% 0.47/0.64 tff(281,plain,(~cycle(e_2, e_0)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(282,plain,
% 0.47/0.64 (cycle(e_2, e_4) | cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[250, 281])).
% 0.47/0.64 tff(283,plain,
% 0.47/0.64 (cycle(e_2, e_4)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[282, 135, 122, 109])).
% 0.47/0.64 tff(284,plain,
% 0.47/0.64 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_5, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | (~product(e_2, e_1, e_5)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_5, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | (~product(e_2, e_1, e_5)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(285,plain,
% 0.47/0.64 (((~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | equalish(e_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5))) <=> (equalish(e_5, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | (~product(e_2, e_1, e_5)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(286,plain,
% 0.47/0.64 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | equalish(e_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_5, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | (~product(e_2, e_1, e_5))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[285])).
% 0.47/0.64 tff(287,plain,
% 0.47/0.64 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | equalish(e_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_5, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | (~product(e_2, e_1, e_5)))),
% 0.47/0.64 inference(transitivity,[status(thm)],[286, 284])).
% 0.47/0.64 tff(288,plain,
% 0.47/0.64 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | equalish(e_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(289,plain,
% 0.47/0.65 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_5, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | (~product(e_2, e_1, e_5))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[288, 287])).
% 0.47/0.65 tff(290,plain,
% 0.47/0.65 ($false),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[289, 100, 224, 94, 84, 283, 80])).
% 0.47/0.65 tff(291,plain,(~product(e_2, e_1, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.65 tff(292,plain,
% 0.47/0.65 (product(e_2, e_1, e_3) | product(e_2, e_1, e_5)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[279, 146])).
% 0.47/0.65 tff(293,plain,
% 0.47/0.65 (product(e_2, e_1, e_3)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[292, 291])).
% 0.47/0.65 tff(294,assumption,(~product(e_3, e_3, e_2)), introduced(assumption)).
% 0.47/0.65 tff(295,assumption,(product(e_1, e_2, e_3)), introduced(assumption)).
% 0.47/0.65 tff(296,assumption,(product(e_2, e_1, e_3)), introduced(assumption)).
% 0.47/0.65 tff(297,plain,
% 0.47/0.65 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_3, e_3, e_2) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_3, e_3, e_2) | (~product(e_1, e_2, e_3)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(298,plain,
% 0.47/0.65 (((~product(e_1, e_2, e_3)) | product(e_3, e_3, e_2) | (~product(e_2, e_1, e_3))) <=> ((~product(e_2, e_1, e_3)) | product(e_3, e_3, e_2) | (~product(e_1, e_2, e_3)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(299,plain,
% 0.47/0.65 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_3, e_3, e_2) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_3, e_3, e_2) | (~product(e_1, e_2, e_3))))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[298])).
% 0.47/0.65 tff(300,plain,
% 0.47/0.65 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_3, e_3, e_2) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_3, e_3, e_2) | (~product(e_1, e_2, e_3)))),
% 0.47/0.65 inference(transitivity,[status(thm)],[299, 297])).
% 0.47/0.65 tff(301,plain,
% 0.47/0.65 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_3, e_3, e_2) | (~product(e_2, e_1, e_3)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(302,plain,
% 0.47/0.65 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_3, e_3, e_2) | (~product(e_1, e_2, e_3))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.47/0.65 tff(303,plain,
% 0.47/0.65 ($false),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[302, 72, 296, 295, 294])).
% 0.47/0.65 tff(304,plain,((~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_3)) | product(e_3, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.65 tff(305,plain,
% 0.47/0.65 ((~product(e_1, e_2, e_3)) | product(e_3, e_3, e_2)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[304, 293])).
% 0.47/0.65 tff(306,plain,
% 0.47/0.65 (~product(e_1, e_2, e_3)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[305, 79])).
% 0.47/0.65 tff(307,assumption,(product(e_1, e_2, e_2)), introduced(assumption)).
% 0.47/0.65 tff(308,plain,
% 0.47/0.65 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(309,plain,
% 0.47/0.65 ((~![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)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(310,plain,
% 0.47/0.65 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.47/0.65 tff(311,plain,
% 0.47/0.65 ($false),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[310, 141, 12, 137, 307])).
% 0.47/0.65 tff(312,plain,(~product(e_1, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.65 tff(313,plain,
% 0.47/0.65 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_5) | product(e_1, e_2, e_3) | product(e_1, e_2, e_4) | product(e_1, e_2, e_1) | product(e_1, e_2, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_5) | product(e_1, e_2, e_3) | product(e_1, e_2, e_4) | product(e_1, e_2, e_1) | product(e_1, e_2, e_2))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(314,plain,
% 0.47/0.65 (((~group_element(e_1)) | product(e_1, e_2, e_5) | 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_5) | product(e_1, e_2, e_3) | product(e_1, e_2, e_4) | product(e_1, e_2, e_1) | product(e_1, e_2, e_2))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(315,plain,
% 0.47/0.65 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_2, e_5) | 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_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_5) | product(e_1, e_2, e_3) | product(e_1, e_2, e_4) | product(e_1, e_2, e_1) | product(e_1, e_2, e_2)))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[314])).
% 0.47/0.65 tff(316,plain,
% 0.47/0.65 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_2, e_5) | 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_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_5) | product(e_1, e_2, e_3) | product(e_1, e_2, e_4) | product(e_1, e_2, e_1) | product(e_1, e_2, e_2))),
% 0.47/0.65 inference(transitivity,[status(thm)],[315, 313])).
% 0.47/0.65 tff(317,plain,
% 0.47/0.65 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_2, e_5) | 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)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(318,plain,
% 0.47/0.65 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_5) | product(e_1, e_2, e_3) | product(e_1, e_2, e_4) | product(e_1, e_2, e_1) | product(e_1, e_2, e_2)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[317, 316])).
% 0.47/0.65 tff(319,plain,
% 0.47/0.65 (product(e_1, e_2, e_5) | product(e_1, e_2, e_3) | product(e_1, e_2, e_4) | product(e_1, e_2, e_1)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[318, 272, 236, 269, 312])).
% 0.47/0.65 tff(320,plain,
% 0.47/0.65 (product(e_1, e_2, e_5) | product(e_1, e_2, e_4)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[319, 306, 51])).
% 0.47/0.65 tff(321,plain,
% 0.47/0.65 (product(e_1, e_2, e_4)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[320, 21])).
% 0.47/0.65 tff(322,assumption,(product(e_5, e_4, e_3)), introduced(assumption)).
% 0.47/0.65 tff(323,assumption,(product(e_3, e_1, e_5)), introduced(assumption)).
% 0.47/0.65 tff(324,assumption,(cycle(e_3, e_4)), introduced(assumption)).
% 0.47/0.65 tff(325,plain,
% 0.47/0.65 ((~equalish(e_5, e_4)) <=> (~equalish(e_5, e_4))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(326,axiom,(~equalish(e_5, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_is_not_e_4')).
% 0.47/0.65 tff(327,plain,
% 0.47/0.65 (~equalish(e_5, e_4)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[326, 325])).
% 0.47/0.65 tff(328,plain,
% 0.47/0.65 (next(e_3, e_4) <=> next(e_3, e_4)),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(329,axiom,(next(e_3, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_then_e_4')).
% 0.47/0.65 tff(330,plain,
% 0.47/0.65 (next(e_3, e_4)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.47/0.65 tff(331,plain,
% 0.47/0.65 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_5, e_4) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | (~product(e_3, e_1, e_5)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_5, e_4) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | (~product(e_3, e_1, e_5)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(332,plain,
% 0.47/0.65 (((~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | equalish(e_5, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5))) <=> (equalish(e_5, e_4) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | (~product(e_3, e_1, e_5)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(333,plain,
% 0.47/0.65 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | equalish(e_5, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_5, e_4) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | (~product(e_3, e_1, e_5))))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[332])).
% 0.47/0.65 tff(334,plain,
% 0.47/0.65 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | equalish(e_5, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_5, e_4) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | (~product(e_3, e_1, e_5)))),
% 0.47/0.65 inference(transitivity,[status(thm)],[333, 331])).
% 0.47/0.65 tff(335,plain,
% 0.47/0.65 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | equalish(e_5, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(336,plain,
% 0.47/0.65 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_5, e_4) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | (~product(e_3, e_1, e_5))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[335, 334])).
% 0.47/0.65 tff(337,plain,
% 0.47/0.65 ($false),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[336, 330, 224, 94, 327, 324, 323])).
% 0.47/0.65 tff(338,plain,((~cycle(e_3, e_4)) | (~product(e_3, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.65 tff(339,plain,
% 0.47/0.65 (~cycle(e_3, e_4)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[338, 323])).
% 0.47/0.65 tff(340,plain,
% 0.47/0.65 (greater(e_5, e_3) <=> greater(e_5, e_3)),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(341,axiom,(greater(e_5, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_greater_e_3')).
% 0.47/0.65 tff(342,plain,
% 0.47/0.65 (greater(e_5, e_3)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[341, 340])).
% 0.47/0.65 tff(343,plain,
% 0.47/0.65 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_3, e_0)) | (~greater(e_5, e_3)) | (~product(e_3, e_1, e_5)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_3, e_0)) | (~greater(e_5, e_3)) | (~product(e_3, e_1, e_5)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(344,plain,
% 0.47/0.65 (((~product(e_3, e_1, e_5)) | (~greater(e_5, e_3)) | (~cycle(e_3, e_0))) <=> ((~cycle(e_3, e_0)) | (~greater(e_5, e_3)) | (~product(e_3, e_1, e_5)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(345,plain,
% 0.47/0.65 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_3, e_1, e_5)) | (~greater(e_5, e_3)) | (~cycle(e_3, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_3, e_0)) | (~greater(e_5, e_3)) | (~product(e_3, e_1, e_5))))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[344])).
% 0.47/0.65 tff(346,plain,
% 0.47/0.65 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_3, e_1, e_5)) | (~greater(e_5, e_3)) | (~cycle(e_3, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_3, e_0)) | (~greater(e_5, e_3)) | (~product(e_3, e_1, e_5)))),
% 0.47/0.65 inference(transitivity,[status(thm)],[345, 343])).
% 0.47/0.65 tff(347,plain,
% 0.47/0.65 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_3, e_1, e_5)) | (~greater(e_5, e_3)) | (~cycle(e_3, e_0)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(348,plain,
% 0.47/0.65 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_3, e_0)) | (~greater(e_5, e_3)) | (~product(e_3, e_1, e_5))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[347, 346])).
% 0.47/0.65 tff(349,plain,
% 0.47/0.65 ((~cycle(e_3, e_0)) | (~product(e_3, e_1, e_5))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[348, 342, 157])).
% 0.47/0.65 tff(350,plain,
% 0.47/0.65 (~cycle(e_3, e_0)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[349, 323])).
% 0.47/0.65 tff(351,assumption,(cycle(e_3, e_2)), introduced(assumption)).
% 0.47/0.65 tff(352,plain,
% 0.47/0.65 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_5, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_5)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_5, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_5)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(353,plain,
% 0.47/0.65 (((~greater(e_2, e_0)) | (~cycle(e_3, e_2)) | equalish(e_5, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5))) <=> (equalish(e_5, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_5)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(354,plain,
% 0.47/0.65 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_3, e_2)) | equalish(e_5, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_5, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_5))))),
% 0.47/0.66 inference(monotonicity,[status(thm)],[353])).
% 0.47/0.66 tff(355,plain,
% 0.47/0.66 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_3, e_2)) | equalish(e_5, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_5, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_5)))),
% 0.47/0.66 inference(transitivity,[status(thm)],[354, 352])).
% 0.47/0.66 tff(356,plain,
% 0.47/0.66 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_3, e_2)) | equalish(e_5, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5)))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(357,plain,
% 0.47/0.66 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_5, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_5))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[356, 355])).
% 0.47/0.66 tff(358,plain,
% 0.47/0.66 ($false),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[357, 330, 126, 94, 327, 351, 323])).
% 0.47/0.66 tff(359,plain,((~cycle(e_3, e_2)) | (~product(e_3, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.66 tff(360,plain,
% 0.47/0.66 (~cycle(e_3, e_2)),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[359, 323])).
% 0.47/0.66 tff(361,assumption,(cycle(e_3, e_3)), introduced(assumption)).
% 0.47/0.66 tff(362,plain,
% 0.47/0.66 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_5, e_4) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~product(e_3, e_1, e_5)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_5, e_4) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~product(e_3, e_1, e_5)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(363,plain,
% 0.47/0.66 (((~greater(e_3, e_0)) | (~cycle(e_3, e_3)) | equalish(e_5, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5))) <=> (equalish(e_5, e_4) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~product(e_3, e_1, e_5)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(364,plain,
% 0.47/0.66 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_3, e_0)) | (~cycle(e_3, e_3)) | equalish(e_5, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_5, e_4) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~product(e_3, e_1, e_5))))),
% 0.47/0.66 inference(monotonicity,[status(thm)],[363])).
% 0.47/0.66 tff(365,plain,
% 0.47/0.66 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_3, e_0)) | (~cycle(e_3, e_3)) | equalish(e_5, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_5, e_4) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~product(e_3, e_1, e_5)))),
% 0.47/0.66 inference(transitivity,[status(thm)],[364, 362])).
% 0.47/0.66 tff(366,plain,
% 0.47/0.66 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_3, e_0)) | (~cycle(e_3, e_3)) | equalish(e_5, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5)))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(367,plain,
% 0.47/0.66 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_5, e_4) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~product(e_3, e_1, e_5))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[366, 365])).
% 0.47/0.66 tff(368,plain,
% 0.47/0.66 ($false),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[367, 330, 113, 94, 327, 361, 323])).
% 0.47/0.66 tff(369,plain,((~cycle(e_3, e_3)) | (~product(e_3, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.66 tff(370,plain,
% 0.47/0.66 (~cycle(e_3, e_3)),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[369, 323])).
% 0.47/0.66 tff(371,plain,
% 0.47/0.66 (group_element(e_3) <=> group_element(e_3)),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(372,axiom,(group_element(e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_3')).
% 0.47/0.66 tff(373,plain,
% 0.47/0.66 (group_element(e_3)),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[372, 371])).
% 0.47/0.66 tff(374,plain,
% 0.47/0.66 (((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_3, e_4) | cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0) | (~group_element(e_3)))) <=> ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_3, e_4) | cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0) | (~group_element(e_3)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(375,plain,
% 0.47/0.66 ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_3, e_4) | cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0) | (~group_element(e_3)))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(376,plain,
% 0.47/0.66 ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_3, e_4) | cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0) | (~group_element(e_3))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[375, 374])).
% 0.47/0.66 tff(377,plain,
% 0.47/0.66 (cycle(e_3, e_4) | cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0)),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[376, 246, 373])).
% 0.47/0.66 tff(378,plain,
% 0.47/0.66 (cycle(e_3, e_1)),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[377, 370, 360, 350, 339])).
% 0.47/0.66 tff(379,plain,
% 0.47/0.66 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_5, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_5)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_5, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_5)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(380,plain,
% 0.47/0.66 (((~greater(e_1, e_0)) | (~cycle(e_3, e_1)) | equalish(e_5, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5))) <=> (equalish(e_5, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_5)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(381,plain,
% 0.47/0.66 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_3, e_1)) | equalish(e_5, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_5, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_5))))),
% 0.47/0.66 inference(monotonicity,[status(thm)],[380])).
% 0.47/0.66 tff(382,plain,
% 0.47/0.66 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_3, e_1)) | equalish(e_5, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_5, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_5)))),
% 0.50/0.66 inference(transitivity,[status(thm)],[381, 379])).
% 0.50/0.66 tff(383,plain,
% 0.50/0.66 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_3, e_1)) | equalish(e_5, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5)))),
% 0.50/0.66 inference(quant_inst,[status(thm)],[])).
% 0.50/0.66 tff(384,plain,
% 0.50/0.66 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_5, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_5))),
% 0.50/0.66 inference(modus_ponens,[status(thm)],[383, 382])).
% 0.50/0.66 tff(385,plain,
% 0.50/0.66 ($false),
% 0.50/0.66 inference(unit_resolution,[status(thm)],[384, 330, 97, 94, 327, 378, 323])).
% 0.50/0.66 tff(386,plain,(~product(e_3, e_1, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.50/0.66 tff(387,assumption,(~product(e_3, e_1, e_5)), introduced(assumption)).
% 0.50/0.66 tff(388,assumption,(product(e_4, e_5, e_1)), introduced(assumption)).
% 0.50/0.66 tff(389,plain,
% 0.50/0.66 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_4, e_5, e_1)) | (~product(e_5, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_5) | (~product(e_4, e_5, e_1)) | (~product(e_5, e_4, e_3)))),
% 0.50/0.66 inference(rewrite,[status(thm)],[])).
% 0.50/0.66 tff(390,plain,
% 0.50/0.66 (((~product(e_4, e_5, e_1)) | product(e_3, e_1, e_5) | (~product(e_5, e_4, e_3))) <=> (product(e_3, e_1, e_5) | (~product(e_4, e_5, e_1)) | (~product(e_5, e_4, e_3)))),
% 0.50/0.66 inference(rewrite,[status(thm)],[])).
% 0.50/0.66 tff(391,plain,
% 0.50/0.66 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_5, e_1)) | product(e_3, e_1, e_5) | (~product(e_5, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_4, e_5, e_1)) | (~product(e_5, e_4, e_3))))),
% 0.50/0.66 inference(monotonicity,[status(thm)],[390])).
% 0.50/0.66 tff(392,plain,
% 0.50/0.66 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_5, e_1)) | product(e_3, e_1, e_5) | (~product(e_5, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_5) | (~product(e_4, e_5, e_1)) | (~product(e_5, e_4, e_3)))),
% 0.50/0.66 inference(transitivity,[status(thm)],[391, 389])).
% 0.50/0.66 tff(393,plain,
% 0.50/0.66 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_5, e_1)) | product(e_3, e_1, e_5) | (~product(e_5, e_4, e_3)))),
% 0.50/0.66 inference(quant_inst,[status(thm)],[])).
% 0.50/0.66 tff(394,plain,
% 0.50/0.66 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_5) | (~product(e_4, e_5, e_1)) | (~product(e_5, e_4, e_3))),
% 0.50/0.66 inference(modus_ponens,[status(thm)],[393, 392])).
% 0.50/0.66 tff(395,plain,
% 0.50/0.66 ($false),
% 0.50/0.66 inference(unit_resolution,[status(thm)],[394, 72, 387, 322, 388])).
% 0.50/0.66 tff(396,plain,((~product(e_4, e_5, e_1)) | product(e_3, e_1, e_5) | (~product(e_5, e_4, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.50/0.66 tff(397,plain,
% 0.50/0.66 (~product(e_4, e_5, e_1)),
% 0.50/0.66 inference(unit_resolution,[status(thm)],[396, 322, 387])).
% 0.50/0.66 tff(398,assumption,(~product(e_2, e_3, e_4)), introduced(assumption)).
% 0.50/0.66 tff(399,plain,
% 0.50/0.66 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_4) | (~product(e_4, e_5, e_2)) | (~product(e_5, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_4) | (~product(e_4, e_5, e_2)) | (~product(e_5, e_4, e_3)))),
% 0.50/0.66 inference(rewrite,[status(thm)],[])).
% 0.50/0.66 tff(400,plain,
% 0.50/0.66 (((~product(e_5, e_4, e_3)) | product(e_2, e_3, e_4) | (~product(e_4, e_5, e_2))) <=> (product(e_2, e_3, e_4) | (~product(e_4, e_5, e_2)) | (~product(e_5, e_4, e_3)))),
% 0.50/0.66 inference(rewrite,[status(thm)],[])).
% 0.50/0.66 tff(401,plain,
% 0.50/0.66 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_4, e_3)) | product(e_2, e_3, e_4) | (~product(e_4, e_5, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_4) | (~product(e_4, e_5, e_2)) | (~product(e_5, e_4, e_3))))),
% 0.50/0.66 inference(monotonicity,[status(thm)],[400])).
% 0.50/0.66 tff(402,plain,
% 0.50/0.66 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_4, e_3)) | product(e_2, e_3, e_4) | (~product(e_4, e_5, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_4) | (~product(e_4, e_5, e_2)) | (~product(e_5, e_4, e_3)))),
% 0.50/0.66 inference(transitivity,[status(thm)],[401, 399])).
% 0.50/0.66 tff(403,plain,
% 0.50/0.66 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_4, e_3)) | product(e_2, e_3, e_4) | (~product(e_4, e_5, e_2)))),
% 0.50/0.66 inference(quant_inst,[status(thm)],[])).
% 0.50/0.66 tff(404,plain,
% 0.50/0.66 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_4) | (~product(e_4, e_5, e_2)) | (~product(e_5, e_4, e_3))),
% 0.50/0.66 inference(modus_ponens,[status(thm)],[403, 402])).
% 0.50/0.66 tff(405,plain,
% 0.50/0.66 (~product(e_4, e_5, e_2)),
% 0.50/0.66 inference(unit_resolution,[status(thm)],[404, 72, 398, 322])).
% 0.50/0.66 tff(406,assumption,(product(e_4, e_5, e_4)), introduced(assumption)).
% 0.50/0.66 tff(407,plain,
% 0.50/0.66 ((~![X: $i] : product(X, X, X)) | product(e_4, e_4, e_4)),
% 0.50/0.66 inference(quant_inst,[status(thm)],[])).
% 0.50/0.66 tff(408,plain,
% 0.50/0.66 (product(e_4, e_4, e_4)),
% 0.50/0.66 inference(unit_resolution,[status(thm)],[407, 30])).
% 0.50/0.66 tff(409,plain,
% 0.50/0.66 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_5, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_5, e_4)))),
% 0.50/0.66 inference(rewrite,[status(thm)],[])).
% 0.50/0.66 tff(410,plain,
% 0.50/0.66 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_5, e_4)))),
% 0.50/0.66 inference(quant_inst,[status(thm)],[])).
% 0.50/0.66 tff(411,plain,
% 0.50/0.66 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_5, e_4))),
% 0.50/0.66 inference(modus_ponens,[status(thm)],[410, 409])).
% 0.50/0.66 tff(412,plain,
% 0.50/0.66 ($false),
% 0.50/0.66 inference(unit_resolution,[status(thm)],[411, 327, 43, 408, 406])).
% 0.50/0.66 tff(413,plain,(~product(e_4, e_5, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.50/0.66 tff(414,assumption,(product(e_4, e_5, e_5)), introduced(assumption)).
% 0.50/0.66 tff(415,plain,
% 0.50/0.66 ((~![X: $i] : product(X, X, X)) | product(e_5, e_5, e_5)),
% 0.50/0.66 inference(quant_inst,[status(thm)],[])).
% 0.50/0.66 tff(416,plain,
% 0.50/0.66 (product(e_5, e_5, e_5)),
% 0.50/0.66 inference(unit_resolution,[status(thm)],[415, 30])).
% 0.50/0.66 tff(417,plain,
% 0.50/0.66 ((~equalish(e_4, e_5)) <=> (~equalish(e_4, e_5))),
% 0.50/0.66 inference(rewrite,[status(thm)],[])).
% 0.50/0.66 tff(418,axiom,(~equalish(e_4, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_5')).
% 0.50/0.66 tff(419,plain,
% 0.50/0.66 (~equalish(e_4, e_5)),
% 0.50/0.66 inference(modus_ponens,[status(thm)],[418, 417])).
% 0.50/0.66 tff(420,plain,
% 0.50/0.66 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_4, e_5, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_4, e_5, e_5)))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(421,plain,
% 0.50/0.67 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_4, e_5, e_5)))),
% 0.50/0.67 inference(quant_inst,[status(thm)],[])).
% 0.50/0.67 tff(422,plain,
% 0.50/0.67 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_4, e_5, e_5))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[421, 420])).
% 0.50/0.67 tff(423,plain,
% 0.50/0.67 ($false),
% 0.50/0.67 inference(unit_resolution,[status(thm)],[422, 419, 12, 416, 414])).
% 0.50/0.67 tff(424,plain,(~product(e_4, e_5, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.50/0.67 tff(425,plain,
% 0.50/0.67 (group_element(e_5) <=> group_element(e_5)),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(426,axiom,(group_element(e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_5')).
% 0.50/0.67 tff(427,plain,
% 0.50/0.67 (group_element(e_5)),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[426, 425])).
% 0.50/0.67 tff(428,plain,
% 0.50/0.67 (group_element(e_4) <=> group_element(e_4)),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(429,axiom,(group_element(e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_4')).
% 0.50/0.67 tff(430,plain,
% 0.50/0.67 (group_element(e_4)),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[429, 428])).
% 0.50/0.67 tff(431,plain,
% 0.50/0.67 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_4)) | (~group_element(e_5)) | product(e_4, e_5, e_2) | product(e_4, e_5, e_4) | product(e_4, e_5, e_1) | product(e_4, e_5, e_3) | product(e_4, e_5, e_5))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_4)) | (~group_element(e_5)) | product(e_4, e_5, e_2) | product(e_4, e_5, e_4) | product(e_4, e_5, e_1) | product(e_4, e_5, e_3) | product(e_4, e_5, e_5))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(432,plain,
% 0.50/0.67 (((~group_element(e_4)) | product(e_4, e_5, e_5) | product(e_4, e_5, e_4) | product(e_4, e_5, e_3) | product(e_4, e_5, e_2) | product(e_4, e_5, e_1) | (~group_element(e_5))) <=> ((~group_element(e_4)) | (~group_element(e_5)) | product(e_4, e_5, e_2) | product(e_4, e_5, e_4) | product(e_4, e_5, e_1) | product(e_4, e_5, e_3) | product(e_4, e_5, e_5))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(433,plain,
% 0.50/0.67 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_4)) | product(e_4, e_5, e_5) | product(e_4, e_5, e_4) | product(e_4, e_5, e_3) | product(e_4, e_5, e_2) | product(e_4, e_5, e_1) | (~group_element(e_5)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_4)) | (~group_element(e_5)) | product(e_4, e_5, e_2) | product(e_4, e_5, e_4) | product(e_4, e_5, e_1) | product(e_4, e_5, e_3) | product(e_4, e_5, e_5)))),
% 0.50/0.67 inference(monotonicity,[status(thm)],[432])).
% 0.50/0.67 tff(434,plain,
% 0.50/0.67 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_4)) | product(e_4, e_5, e_5) | product(e_4, e_5, e_4) | product(e_4, e_5, e_3) | product(e_4, e_5, e_2) | product(e_4, e_5, e_1) | (~group_element(e_5)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_4)) | (~group_element(e_5)) | product(e_4, e_5, e_2) | product(e_4, e_5, e_4) | product(e_4, e_5, e_1) | product(e_4, e_5, e_3) | product(e_4, e_5, e_5))),
% 0.50/0.67 inference(transitivity,[status(thm)],[433, 431])).
% 0.50/0.67 tff(435,plain,
% 0.50/0.67 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_4)) | product(e_4, e_5, e_5) | product(e_4, e_5, e_4) | product(e_4, e_5, e_3) | product(e_4, e_5, e_2) | product(e_4, e_5, e_1) | (~group_element(e_5)))),
% 0.50/0.67 inference(quant_inst,[status(thm)],[])).
% 0.50/0.67 tff(436,plain,
% 0.50/0.67 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_4)) | (~group_element(e_5)) | product(e_4, e_5, e_2) | product(e_4, e_5, e_4) | product(e_4, e_5, e_1) | product(e_4, e_5, e_3) | product(e_4, e_5, e_5)),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[435, 434])).
% 0.50/0.67 tff(437,plain,
% 0.50/0.67 (product(e_4, e_5, e_2) | product(e_4, e_5, e_4) | product(e_4, e_5, e_1) | product(e_4, e_5, e_3)),
% 0.50/0.67 inference(unit_resolution,[status(thm)],[436, 430, 427, 269, 424])).
% 0.50/0.67 tff(438,plain,
% 0.50/0.67 (product(e_4, e_5, e_2) | product(e_4, e_5, e_1) | product(e_4, e_5, e_3)),
% 0.50/0.67 inference(unit_resolution,[status(thm)],[437, 413])).
% 0.50/0.67 tff(439,plain,
% 0.50/0.67 (product(e_4, e_5, e_3)),
% 0.50/0.67 inference(unit_resolution,[status(thm)],[438, 405, 397])).
% 0.50/0.67 tff(440,assumption,(product(e_5, e_3, e_3)), introduced(assumption)).
% 0.50/0.67 tff(441,plain,
% 0.50/0.67 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_5, e_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_5, e_3) | (~product(e_5, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(442,plain,
% 0.50/0.67 ((equalish(e_5, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_5, e_3, e_3))) <=> (equalish(e_5, e_3) | (~product(e_5, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(443,plain,
% 0.50/0.67 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_5, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_5, e_3, e_3)) | (~product(e_3, e_3, e_3))))),
% 0.50/0.67 inference(monotonicity,[status(thm)],[442])).
% 0.50/0.67 tff(444,plain,
% 0.50/0.67 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_5, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_3) | (~product(e_5, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.50/0.67 inference(transitivity,[status(thm)],[443, 441])).
% 0.50/0.67 tff(445,plain,
% 0.50/0.67 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_5, e_3, e_3)))),
% 0.50/0.67 inference(quant_inst,[status(thm)],[])).
% 0.50/0.67 tff(446,plain,
% 0.50/0.67 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_3) | (~product(e_5, e_3, e_3)) | (~product(e_3, e_3, e_3))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[445, 444])).
% 0.50/0.67 tff(447,plain,
% 0.50/0.67 ($false),
% 0.50/0.67 inference(unit_resolution,[status(thm)],[446, 84, 12, 440, 53])).
% 0.50/0.67 tff(448,plain,(~product(e_5, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.50/0.67 tff(449,plain,
% 0.50/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_5, e_3, e_3) | (~product(e_3, e_3, e_5)) | (~product(e_3, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_5, e_3, e_3) | (~product(e_3, e_3, e_5)) | (~product(e_3, e_3, e_3)))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(450,plain,
% 0.50/0.67 (((~product(e_3, e_3, e_3)) | product(e_5, e_3, e_3) | (~product(e_3, e_3, e_5))) <=> (product(e_5, e_3, e_3) | (~product(e_3, e_3, e_5)) | (~product(e_3, e_3, e_3)))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(451,plain,
% 0.50/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | product(e_5, e_3, e_3) | (~product(e_3, e_3, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_5, e_3, e_3) | (~product(e_3, e_3, e_5)) | (~product(e_3, e_3, e_3))))),
% 0.50/0.67 inference(monotonicity,[status(thm)],[450])).
% 0.50/0.67 tff(452,plain,
% 0.50/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | product(e_5, e_3, e_3) | (~product(e_3, e_3, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_5, e_3, e_3) | (~product(e_3, e_3, e_5)) | (~product(e_3, e_3, e_3)))),
% 0.50/0.67 inference(transitivity,[status(thm)],[451, 449])).
% 0.50/0.67 tff(453,plain,
% 0.50/0.67 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | product(e_5, e_3, e_3) | (~product(e_3, e_3, e_5)))),
% 0.50/0.67 inference(quant_inst,[status(thm)],[])).
% 0.50/0.67 tff(454,plain,
% 0.50/0.67 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_5, e_3, e_3) | (~product(e_3, e_3, e_5)) | (~product(e_3, e_3, e_3))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[453, 452])).
% 0.50/0.67 tff(455,plain,
% 0.50/0.67 (~product(e_3, e_3, e_5)),
% 0.50/0.67 inference(unit_resolution,[status(thm)],[454, 72, 448, 53])).
% 0.50/0.67 tff(456,plain,
% 0.50/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_5) | (~product(e_4, e_5, e_3)) | (~product(e_5, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_5) | (~product(e_4, e_5, e_3)) | (~product(e_5, e_4, e_3)))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(457,plain,
% 0.50/0.67 (((~product(e_4, e_5, e_3)) | product(e_3, e_3, e_5) | (~product(e_5, e_4, e_3))) <=> (product(e_3, e_3, e_5) | (~product(e_4, e_5, e_3)) | (~product(e_5, e_4, e_3)))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(458,plain,
% 0.50/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_5, e_3)) | product(e_3, e_3, e_5) | (~product(e_5, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_5) | (~product(e_4, e_5, e_3)) | (~product(e_5, e_4, e_3))))),
% 0.50/0.67 inference(monotonicity,[status(thm)],[457])).
% 0.50/0.67 tff(459,plain,
% 0.50/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_5, e_3)) | product(e_3, e_3, e_5) | (~product(e_5, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_5) | (~product(e_4, e_5, e_3)) | (~product(e_5, e_4, e_3)))),
% 0.50/0.67 inference(transitivity,[status(thm)],[458, 456])).
% 0.50/0.67 tff(460,plain,
% 0.50/0.67 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_5, e_3)) | product(e_3, e_3, e_5) | (~product(e_5, e_4, e_3)))),
% 0.50/0.67 inference(quant_inst,[status(thm)],[])).
% 0.50/0.67 tff(461,plain,
% 0.50/0.67 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_5) | (~product(e_4, e_5, e_3)) | (~product(e_5, e_4, e_3))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[460, 459])).
% 0.50/0.67 tff(462,plain,
% 0.50/0.67 ($false),
% 0.50/0.67 inference(unit_resolution,[status(thm)],[461, 72, 322, 455, 439])).
% 0.50/0.67 tff(463,plain,((~product(e_5, e_4, e_3)) | product(e_2, e_3, e_4) | product(e_3, e_1, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.50/0.67 tff(464,plain,
% 0.50/0.67 ((~product(e_5, e_4, e_3)) | product(e_2, e_3, e_4)),
% 0.50/0.67 inference(unit_resolution,[status(thm)],[463, 386])).
% 0.50/0.67 tff(465,plain,
% 0.50/0.67 (product(e_2, e_3, e_4)),
% 0.50/0.67 inference(unit_resolution,[status(thm)],[464, 322])).
% 0.50/0.67 tff(466,assumption,(product(e_3, e_2, e_4)), introduced(assumption)).
% 0.50/0.67 tff(467,assumption,(product(e_3, e_4, e_4)), introduced(assumption)).
% 0.50/0.67 tff(468,plain,
% 0.50/0.67 ((~equalish(e_3, e_4)) <=> (~equalish(e_3, e_4))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(469,axiom,(~equalish(e_3, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_4')).
% 0.50/0.67 tff(470,plain,
% 0.50/0.67 (~equalish(e_3, e_4)),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[469, 468])).
% 0.50/0.67 tff(471,plain,
% 0.50/0.67 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_4, e_4)))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(472,plain,
% 0.50/0.67 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_4, e_4)))),
% 0.50/0.67 inference(quant_inst,[status(thm)],[])).
% 0.50/0.67 tff(473,plain,
% 0.50/0.67 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_4, e_4))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[472, 471])).
% 0.50/0.67 tff(474,plain,
% 0.50/0.67 ($false),
% 0.50/0.67 inference(unit_resolution,[status(thm)],[473, 470, 12, 467, 408])).
% 0.50/0.67 tff(475,plain,(~product(e_3, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.50/0.67 tff(476,plain,
% 0.50/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_4, e_3)) | (~product(e_4, e_4, e_4)) | product(e_3, e_4, e_4))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_4, e_4, e_3)) | (~product(e_4, e_4, e_4)) | product(e_3, e_4, e_4))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(477,plain,
% 0.50/0.67 (((~product(e_4, e_4, e_4)) | product(e_3, e_4, e_4) | (~product(e_4, e_4, e_3))) <=> ((~product(e_4, e_4, e_3)) | (~product(e_4, e_4, e_4)) | product(e_3, e_4, e_4))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(478,plain,
% 0.50/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_4, e_4)) | product(e_3, e_4, e_4) | (~product(e_4, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_4, e_3)) | (~product(e_4, e_4, e_4)) | product(e_3, e_4, e_4)))),
% 0.50/0.67 inference(monotonicity,[status(thm)],[477])).
% 0.50/0.67 tff(479,plain,
% 0.50/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_4, e_4)) | product(e_3, e_4, e_4) | (~product(e_4, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_4, e_4, e_3)) | (~product(e_4, e_4, e_4)) | product(e_3, e_4, e_4))),
% 0.50/0.67 inference(transitivity,[status(thm)],[478, 476])).
% 0.50/0.67 tff(480,plain,
% 0.50/0.67 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_4, e_4)) | product(e_3, e_4, e_4) | (~product(e_4, e_4, e_3)))),
% 0.50/0.67 inference(quant_inst,[status(thm)],[])).
% 0.50/0.67 tff(481,plain,
% 0.50/0.67 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_4, e_4, e_3)) | (~product(e_4, e_4, e_4)) | product(e_3, e_4, e_4)),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[480, 479])).
% 0.50/0.67 tff(482,plain,
% 0.50/0.67 (~product(e_4, e_4, e_3)),
% 0.50/0.67 inference(unit_resolution,[status(thm)],[481, 72, 475, 408])).
% 0.50/0.67 tff(483,assumption,(product(e_2, e_3, e_4)), introduced(assumption)).
% 0.50/0.67 tff(484,plain,
% 0.50/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_4, e_4, e_3) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_4, e_4, e_3) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(485,plain,
% 0.50/0.68 (((~product(e_2, e_3, e_4)) | product(e_4, e_4, e_3) | (~product(e_3, e_2, e_4))) <=> (product(e_4, e_4, e_3) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(486,plain,
% 0.50/0.68 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_4)) | product(e_4, e_4, e_3) | (~product(e_3, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_4, e_4, e_3) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_4))))),
% 0.50/0.68 inference(monotonicity,[status(thm)],[485])).
% 0.50/0.68 tff(487,plain,
% 0.50/0.68 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_4)) | product(e_4, e_4, e_3) | (~product(e_3, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_4, e_4, e_3) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.50/0.68 inference(transitivity,[status(thm)],[486, 484])).
% 0.50/0.68 tff(488,plain,
% 0.50/0.68 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_4)) | product(e_4, e_4, e_3) | (~product(e_3, e_2, e_4)))),
% 0.50/0.68 inference(quant_inst,[status(thm)],[])).
% 0.50/0.68 tff(489,plain,
% 0.50/0.68 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_4, e_4, e_3) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_4))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[488, 487])).
% 0.50/0.68 tff(490,plain,
% 0.50/0.68 ($false),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[489, 72, 483, 482, 466])).
% 0.50/0.68 tff(491,plain,((~product(e_2, e_3, e_4)) | (~product(e_3, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.50/0.68 tff(492,plain,
% 0.50/0.68 (~product(e_3, e_2, e_4)),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[491, 465])).
% 0.50/0.68 tff(493,assumption,(product(e_5, e_4, e_2)), introduced(assumption)).
% 0.50/0.68 tff(494,plain,
% 0.50/0.68 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_5, e_4, e_2)) | (~product(e_4, e_5, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_5) | (~product(e_5, e_4, e_2)) | (~product(e_4, e_5, e_1)))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(495,plain,
% 0.50/0.68 (((~product(e_4, e_5, e_1)) | product(e_2, e_1, e_5) | (~product(e_5, e_4, e_2))) <=> (product(e_2, e_1, e_5) | (~product(e_5, e_4, e_2)) | (~product(e_4, e_5, e_1)))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(496,plain,
% 0.50/0.68 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_5, e_1)) | product(e_2, e_1, e_5) | (~product(e_5, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_5, e_4, e_2)) | (~product(e_4, e_5, e_1))))),
% 0.50/0.68 inference(monotonicity,[status(thm)],[495])).
% 0.50/0.68 tff(497,plain,
% 0.50/0.68 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_5, e_1)) | product(e_2, e_1, e_5) | (~product(e_5, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_5) | (~product(e_5, e_4, e_2)) | (~product(e_4, e_5, e_1)))),
% 0.50/0.68 inference(transitivity,[status(thm)],[496, 494])).
% 0.50/0.68 tff(498,plain,
% 0.50/0.68 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_5, e_1)) | product(e_2, e_1, e_5) | (~product(e_5, e_4, e_2)))),
% 0.50/0.68 inference(quant_inst,[status(thm)],[])).
% 0.50/0.68 tff(499,plain,
% 0.50/0.68 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_5) | (~product(e_5, e_4, e_2)) | (~product(e_4, e_5, e_1))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[498, 497])).
% 0.50/0.68 tff(500,plain,
% 0.50/0.68 ($false),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[499, 72, 291, 493, 388])).
% 0.50/0.68 tff(501,plain,((~product(e_4, e_5, e_1)) | (~product(e_5, e_4, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.50/0.68 tff(502,plain,
% 0.50/0.68 (~product(e_5, e_4, e_2)),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[501, 388])).
% 0.50/0.68 tff(503,assumption,(~product(e_5, e_4, e_2)), introduced(assumption)).
% 0.50/0.68 tff(504,plain,
% 0.50/0.68 ((~product(e_4, e_5, e_1)) | (~product(e_5, e_4, e_3))),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[396, 386])).
% 0.50/0.68 tff(505,plain,
% 0.50/0.68 (~product(e_5, e_4, e_3)),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[504, 388])).
% 0.50/0.68 tff(506,assumption,(product(e_1, e_4, e_1)), introduced(assumption)).
% 0.50/0.68 tff(507,plain,
% 0.50/0.68 ((~equalish(e_4, e_1)) <=> (~equalish(e_4, e_1))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(508,axiom,(~equalish(e_4, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_1')).
% 0.50/0.68 tff(509,plain,
% 0.50/0.68 (~equalish(e_4, e_1)),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[508, 507])).
% 0.50/0.68 tff(510,plain,
% 0.50/0.68 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1)))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(511,plain,
% 0.50/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1)))),
% 0.50/0.68 inference(quant_inst,[status(thm)],[])).
% 0.50/0.68 tff(512,plain,
% 0.50/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[511, 510])).
% 0.50/0.68 tff(513,plain,
% 0.50/0.68 ($false),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[512, 509, 43, 33, 506])).
% 0.50/0.68 tff(514,plain,(~product(e_1, e_4, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.50/0.68 tff(515,assumption,(product(e_1, e_1, e_4)), introduced(assumption)).
% 0.50/0.68 tff(516,plain,
% 0.50/0.68 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_4)) | (~product(e_1, e_1, e_1)) | product(e_1, e_4, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_4)) | (~product(e_1, e_1, e_1)) | product(e_1, e_4, e_1))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(517,plain,
% 0.50/0.68 (((~product(e_1, e_1, e_4)) | product(e_1, e_4, e_1) | (~product(e_1, e_1, e_1))) <=> ((~product(e_1, e_1, e_4)) | (~product(e_1, e_1, e_1)) | product(e_1, e_4, e_1))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(518,plain,
% 0.50/0.68 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_4)) | product(e_1, e_4, e_1) | (~product(e_1, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_4)) | (~product(e_1, e_1, e_1)) | product(e_1, e_4, e_1)))),
% 0.50/0.68 inference(monotonicity,[status(thm)],[517])).
% 0.50/0.68 tff(519,plain,
% 0.50/0.68 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_4)) | product(e_1, e_4, e_1) | (~product(e_1, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_4)) | (~product(e_1, e_1, e_1)) | product(e_1, e_4, e_1))),
% 0.50/0.68 inference(transitivity,[status(thm)],[518, 516])).
% 0.50/0.68 tff(520,plain,
% 0.50/0.68 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_4)) | product(e_1, e_4, e_1) | (~product(e_1, e_1, e_1)))),
% 0.50/0.68 inference(quant_inst,[status(thm)],[])).
% 0.50/0.68 tff(521,plain,
% 0.50/0.68 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_4)) | (~product(e_1, e_1, e_1)) | product(e_1, e_4, e_1)),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[520, 519])).
% 0.50/0.68 tff(522,plain,
% 0.50/0.68 ($false),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[521, 72, 515, 33, 514])).
% 0.50/0.68 tff(523,plain,(~product(e_1, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.50/0.68 tff(524,assumption,(product(e_5, e_4, e_1)), introduced(assumption)).
% 0.50/0.68 tff(525,assumption,(~product(e_1, e_1, e_4)), introduced(assumption)).
% 0.50/0.68 tff(526,plain,
% 0.50/0.68 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_4) | (~product(e_5, e_4, e_1)) | (~product(e_4, e_5, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_4) | (~product(e_5, e_4, e_1)) | (~product(e_4, e_5, e_1)))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(527,plain,
% 0.50/0.68 (((~product(e_5, e_4, e_1)) | product(e_1, e_1, e_4) | (~product(e_4, e_5, e_1))) <=> (product(e_1, e_1, e_4) | (~product(e_5, e_4, e_1)) | (~product(e_4, e_5, e_1)))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(528,plain,
% 0.50/0.68 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_4, e_1)) | product(e_1, e_1, e_4) | (~product(e_4, e_5, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_4) | (~product(e_5, e_4, e_1)) | (~product(e_4, e_5, e_1))))),
% 0.50/0.68 inference(monotonicity,[status(thm)],[527])).
% 0.50/0.68 tff(529,plain,
% 0.50/0.68 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_4, e_1)) | product(e_1, e_1, e_4) | (~product(e_4, e_5, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_4) | (~product(e_5, e_4, e_1)) | (~product(e_4, e_5, e_1)))),
% 0.50/0.68 inference(transitivity,[status(thm)],[528, 526])).
% 0.50/0.68 tff(530,plain,
% 0.50/0.68 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_4, e_1)) | product(e_1, e_1, e_4) | (~product(e_4, e_5, e_1)))),
% 0.50/0.68 inference(quant_inst,[status(thm)],[])).
% 0.50/0.68 tff(531,plain,
% 0.50/0.68 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_4) | (~product(e_5, e_4, e_1)) | (~product(e_4, e_5, e_1))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[530, 529])).
% 0.50/0.68 tff(532,plain,
% 0.50/0.68 ($false),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[531, 72, 525, 524, 388])).
% 0.50/0.68 tff(533,plain,(product(e_1, e_1, e_4) | (~product(e_5, e_4, e_1)) | (~product(e_4, e_5, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.50/0.68 tff(534,plain,
% 0.50/0.68 ((~product(e_5, e_4, e_1)) | (~product(e_4, e_5, e_1))),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[533, 523])).
% 0.50/0.68 tff(535,plain,
% 0.50/0.68 (~product(e_5, e_4, e_1)),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[534, 388])).
% 0.50/0.68 tff(536,assumption,(product(e_5, e_4, e_4)), introduced(assumption)).
% 0.50/0.68 tff(537,plain,
% 0.50/0.68 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_5, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_5, e_4, e_4)))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(538,plain,
% 0.50/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_5, e_4, e_4)))),
% 0.50/0.68 inference(quant_inst,[status(thm)],[])).
% 0.50/0.68 tff(539,plain,
% 0.50/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_5, e_4, e_4))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[538, 537])).
% 0.50/0.68 tff(540,plain,
% 0.50/0.68 ($false),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[539, 327, 12, 536, 408])).
% 0.50/0.68 tff(541,plain,(~product(e_5, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.50/0.68 tff(542,assumption,(product(e_5, e_4, e_5)), introduced(assumption)).
% 0.50/0.68 tff(543,plain,
% 0.50/0.68 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_4, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_4, e_5)))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(544,plain,
% 0.50/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_4, e_5)))),
% 0.50/0.68 inference(quant_inst,[status(thm)],[])).
% 0.50/0.68 tff(545,plain,
% 0.50/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_4, e_5))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[544, 543])).
% 0.50/0.68 tff(546,plain,
% 0.50/0.68 ($false),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[545, 419, 43, 416, 542])).
% 0.50/0.68 tff(547,plain,(~product(e_5, e_4, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.50/0.68 tff(548,plain,
% 0.50/0.68 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_4)) | (~group_element(e_5)) | product(e_5, e_4, e_2) | product(e_5, e_4, e_5) | product(e_5, e_4, e_4) | product(e_5, e_4, e_1) | product(e_5, e_4, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_4)) | (~group_element(e_5)) | product(e_5, e_4, e_2) | product(e_5, e_4, e_5) | product(e_5, e_4, e_4) | product(e_5, e_4, e_1) | product(e_5, e_4, e_3))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(549,plain,
% 0.50/0.68 (((~group_element(e_5)) | product(e_5, e_4, e_5) | product(e_5, e_4, e_4) | product(e_5, e_4, e_3) | product(e_5, e_4, e_2) | product(e_5, e_4, e_1) | (~group_element(e_4))) <=> ((~group_element(e_4)) | (~group_element(e_5)) | product(e_5, e_4, e_2) | product(e_5, e_4, e_5) | product(e_5, e_4, e_4) | product(e_5, e_4, e_1) | product(e_5, e_4, e_3))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(550,plain,
% 0.50/0.68 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_5)) | product(e_5, e_4, e_5) | product(e_5, e_4, e_4) | product(e_5, e_4, e_3) | product(e_5, e_4, e_2) | product(e_5, e_4, e_1) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_4)) | (~group_element(e_5)) | product(e_5, e_4, e_2) | product(e_5, e_4, e_5) | product(e_5, e_4, e_4) | product(e_5, e_4, e_1) | product(e_5, e_4, e_3)))),
% 0.50/0.68 inference(monotonicity,[status(thm)],[549])).
% 0.50/0.68 tff(551,plain,
% 0.50/0.68 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_5)) | product(e_5, e_4, e_5) | product(e_5, e_4, e_4) | product(e_5, e_4, e_3) | product(e_5, e_4, e_2) | product(e_5, e_4, e_1) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_4)) | (~group_element(e_5)) | product(e_5, e_4, e_2) | product(e_5, e_4, e_5) | product(e_5, e_4, e_4) | product(e_5, e_4, e_1) | product(e_5, e_4, e_3))),
% 0.50/0.68 inference(transitivity,[status(thm)],[550, 548])).
% 0.50/0.68 tff(552,plain,
% 0.50/0.68 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_5)) | product(e_5, e_4, e_5) | product(e_5, e_4, e_4) | product(e_5, e_4, e_3) | product(e_5, e_4, e_2) | product(e_5, e_4, e_1) | (~group_element(e_4)))),
% 0.50/0.68 inference(quant_inst,[status(thm)],[])).
% 0.50/0.68 tff(553,plain,
% 0.50/0.68 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_4)) | (~group_element(e_5)) | product(e_5, e_4, e_2) | product(e_5, e_4, e_5) | product(e_5, e_4, e_4) | product(e_5, e_4, e_1) | product(e_5, e_4, e_3)),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[552, 551])).
% 0.50/0.68 tff(554,plain,
% 0.50/0.68 (product(e_5, e_4, e_2) | product(e_5, e_4, e_5) | product(e_5, e_4, e_4) | product(e_5, e_4, e_1) | product(e_5, e_4, e_3)),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[553, 430, 427, 269])).
% 0.50/0.68 tff(555,plain,
% 0.50/0.68 (product(e_5, e_4, e_2) | product(e_5, e_4, e_1) | product(e_5, e_4, e_3)),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[554, 547, 541])).
% 0.50/0.68 tff(556,plain,
% 0.50/0.68 ($false),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[555, 535, 505, 503])).
% 0.50/0.68 tff(557,plain,((~product(e_4, e_5, e_1)) | product(e_5, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.50/0.68 tff(558,plain,
% 0.50/0.68 ($false),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[557, 502, 388])).
% 0.50/0.68 tff(559,plain,(~product(e_4, e_5, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.50/0.68 tff(560,assumption,(product(e_4, e_5, e_3)), introduced(assumption)).
% 0.50/0.68 tff(561,plain,
% 0.50/0.68 ($false),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[461, 72, 322, 455, 560])).
% 0.50/0.68 tff(562,plain,((~product(e_4, e_5, e_3)) | (~product(e_5, e_4, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.50/0.68 tff(563,plain,
% 0.50/0.68 (~product(e_4, e_5, e_3)),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[562, 322])).
% 0.50/0.68 tff(564,plain,
% 0.50/0.68 (product(e_4, e_5, e_2)),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[438, 563, 559])).
% 0.50/0.68 tff(565,assumption,(product(e_3, e_5, e_2)), introduced(assumption)).
% 0.50/0.68 tff(566,assumption,(product(e_4, e_5, e_2)), introduced(assumption)).
% 0.50/0.68 tff(567,plain,
% 0.50/0.68 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_4, e_5, e_2)) | (~product(e_3, e_5, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_4) | (~product(e_4, e_5, e_2)) | (~product(e_3, e_5, e_2)))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(568,plain,
% 0.50/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_4, e_5, e_2)) | (~product(e_3, e_5, e_2)))),
% 0.50/0.68 inference(quant_inst,[status(thm)],[])).
% 0.50/0.68 tff(569,plain,
% 0.50/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_4) | (~product(e_4, e_5, e_2)) | (~product(e_3, e_5, e_2))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[568, 567])).
% 0.50/0.68 tff(570,plain,
% 0.50/0.68 ($false),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[569, 470, 12, 566, 565])).
% 0.50/0.68 tff(571,plain,((~product(e_3, e_5, e_2)) | (~product(e_4, e_5, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.50/0.68 tff(572,plain,
% 0.50/0.68 (~product(e_3, e_5, e_2)),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[571, 564])).
% 0.50/0.68 tff(573,assumption,(~product(e_3, e_5, e_2)), introduced(assumption)).
% 0.50/0.68 tff(574,plain,
% 0.50/0.68 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_5)) | product(e_3, e_5, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_5)) | product(e_3, e_5, e_2))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(575,plain,
% 0.50/0.69 (((~product(e_1, e_2, e_5)) | product(e_3, e_5, e_2) | (~product(e_2, e_1, e_3))) <=> ((~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_5)) | product(e_3, e_5, e_2))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(576,plain,
% 0.50/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_5)) | product(e_3, e_5, e_2) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_5)) | product(e_3, e_5, e_2)))),
% 0.50/0.69 inference(monotonicity,[status(thm)],[575])).
% 0.50/0.69 tff(577,plain,
% 0.50/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_5)) | product(e_3, e_5, e_2) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_5)) | product(e_3, e_5, e_2))),
% 0.50/0.69 inference(transitivity,[status(thm)],[576, 574])).
% 0.50/0.69 tff(578,plain,
% 0.50/0.69 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_5)) | product(e_3, e_5, e_2) | (~product(e_2, e_1, e_3)))),
% 0.50/0.69 inference(quant_inst,[status(thm)],[])).
% 0.50/0.69 tff(579,plain,
% 0.50/0.69 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_5)) | product(e_3, e_5, e_2)),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[578, 577])).
% 0.50/0.69 tff(580,plain,
% 0.50/0.69 ($false),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[579, 72, 293, 2, 573])).
% 0.50/0.69 tff(581,plain,(product(e_3, e_5, e_2) | (~product(e_1, e_2, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.50/0.69 tff(582,plain,
% 0.50/0.69 (~product(e_1, e_2, e_5)),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[581, 572])).
% 0.50/0.69 tff(583,plain,
% 0.50/0.69 (product(e_1, e_2, e_4)),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[320, 582])).
% 0.50/0.69 tff(584,assumption,(~product(e_4, e_3, e_1)), introduced(assumption)).
% 0.50/0.69 tff(585,assumption,(product(e_1, e_2, e_4)), introduced(assumption)).
% 0.50/0.69 tff(586,plain,
% 0.50/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_4)) | product(e_4, e_3, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_4)) | product(e_4, e_3, e_1))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(587,plain,
% 0.50/0.69 (((~product(e_2, e_1, e_3)) | product(e_4, e_3, e_1) | (~product(e_1, e_2, e_4))) <=> ((~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_4)) | product(e_4, e_3, e_1))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(588,plain,
% 0.50/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_4, e_3, e_1) | (~product(e_1, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_4)) | product(e_4, e_3, e_1)))),
% 0.50/0.69 inference(monotonicity,[status(thm)],[587])).
% 0.50/0.69 tff(589,plain,
% 0.50/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_4, e_3, e_1) | (~product(e_1, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_4)) | product(e_4, e_3, e_1))),
% 0.50/0.69 inference(transitivity,[status(thm)],[588, 586])).
% 0.50/0.69 tff(590,plain,
% 0.50/0.69 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_4, e_3, e_1) | (~product(e_1, e_2, e_4)))),
% 0.50/0.69 inference(quant_inst,[status(thm)],[])).
% 0.50/0.69 tff(591,plain,
% 0.50/0.69 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_4)) | product(e_4, e_3, e_1)),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[590, 589])).
% 0.50/0.69 tff(592,plain,
% 0.50/0.69 ($false),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[591, 72, 293, 585, 584])).
% 0.50/0.69 tff(593,plain,(product(e_4, e_3, e_1) | (~product(e_1, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.50/0.69 tff(594,plain,
% 0.50/0.69 (product(e_4, e_3, e_1)),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[593, 583])).
% 0.50/0.69 tff(595,assumption,(product(e_4, e_3, e_1)), introduced(assumption)).
% 0.50/0.69 tff(596,assumption,(product(e_3, e_4, e_1)), introduced(assumption)).
% 0.50/0.69 tff(597,assumption,(product(e_4, e_1, e_1)), introduced(assumption)).
% 0.50/0.69 tff(598,plain,
% 0.50/0.69 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1)))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(599,plain,
% 0.50/0.69 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1)))),
% 0.50/0.69 inference(quant_inst,[status(thm)],[])).
% 0.50/0.69 tff(600,plain,
% 0.50/0.69 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[599, 598])).
% 0.50/0.69 tff(601,plain,
% 0.50/0.69 ($false),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[600, 509, 12, 181, 597])).
% 0.50/0.69 tff(602,plain,((~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.50/0.69 tff(603,plain,
% 0.50/0.69 (~product(e_4, e_1, e_1)),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[602, 33])).
% 0.50/0.69 tff(604,plain,
% 0.50/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_4)) | product(e_4, e_1, e_1) | (~product(e_1, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_4)) | product(e_4, e_1, e_1) | (~product(e_1, e_1, e_1)))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(605,plain,
% 0.50/0.69 (((~product(e_1, e_1, e_1)) | product(e_4, e_1, e_1) | (~product(e_1, e_1, e_4))) <=> ((~product(e_1, e_1, e_4)) | product(e_4, e_1, e_1) | (~product(e_1, e_1, e_1)))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(606,plain,
% 0.50/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_1)) | product(e_4, e_1, e_1) | (~product(e_1, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_4)) | product(e_4, e_1, e_1) | (~product(e_1, e_1, e_1))))),
% 0.50/0.69 inference(monotonicity,[status(thm)],[605])).
% 0.50/0.69 tff(607,plain,
% 0.50/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_1)) | product(e_4, e_1, e_1) | (~product(e_1, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_4)) | product(e_4, e_1, e_1) | (~product(e_1, e_1, e_1)))),
% 0.50/0.69 inference(transitivity,[status(thm)],[606, 604])).
% 0.50/0.69 tff(608,plain,
% 0.50/0.69 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_1)) | product(e_4, e_1, e_1) | (~product(e_1, e_1, e_4)))),
% 0.50/0.69 inference(quant_inst,[status(thm)],[])).
% 0.50/0.69 tff(609,plain,
% 0.50/0.69 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_4)) | product(e_4, e_1, e_1) | (~product(e_1, e_1, e_1))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[608, 607])).
% 0.50/0.69 tff(610,plain,
% 0.50/0.69 (~product(e_1, e_1, e_4)),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[609, 72, 33, 603])).
% 0.50/0.69 tff(611,plain,
% 0.50/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_3, e_1)))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(612,plain,
% 0.50/0.69 (((~product(e_3, e_4, e_1)) | product(e_1, e_1, e_4) | (~product(e_4, e_3, e_1))) <=> (product(e_1, e_1, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_3, e_1)))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(613,plain,
% 0.50/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_4, e_1)) | product(e_1, e_1, e_4) | (~product(e_4, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_3, e_1))))),
% 0.50/0.69 inference(monotonicity,[status(thm)],[612])).
% 0.50/0.69 tff(614,plain,
% 0.50/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_4, e_1)) | product(e_1, e_1, e_4) | (~product(e_4, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_3, e_1)))),
% 0.50/0.69 inference(transitivity,[status(thm)],[613, 611])).
% 0.50/0.69 tff(615,plain,
% 0.50/0.69 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_4, e_1)) | product(e_1, e_1, e_4) | (~product(e_4, e_3, e_1)))),
% 0.50/0.69 inference(quant_inst,[status(thm)],[])).
% 0.50/0.69 tff(616,plain,
% 0.50/0.69 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_3, e_1))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[615, 614])).
% 0.50/0.69 tff(617,plain,
% 0.50/0.69 ($false),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[616, 72, 610, 596, 595])).
% 0.50/0.69 tff(618,plain,((~product(e_3, e_4, e_1)) | (~product(e_4, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.50/0.69 tff(619,plain,
% 0.50/0.69 (~product(e_3, e_4, e_1)),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[618, 594])).
% 0.50/0.69 tff(620,assumption,(product(e_1, e_4, e_3)), introduced(assumption)).
% 0.50/0.69 tff(621,plain,
% 0.50/0.69 ((~equalish(e_5, e_1)) <=> (~equalish(e_5, e_1))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(622,axiom,(~equalish(e_5, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_is_not_e_1')).
% 0.50/0.69 tff(623,plain,
% 0.50/0.69 (~equalish(e_5, e_1)),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[622, 621])).
% 0.50/0.69 tff(624,plain,
% 0.50/0.69 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_1, e_4, e_3)) | (~product(e_5, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_1) | (~product(e_1, e_4, e_3)) | (~product(e_5, e_4, e_3)))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(625,plain,
% 0.50/0.69 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_1, e_4, e_3)) | (~product(e_5, e_4, e_3)))),
% 0.50/0.69 inference(quant_inst,[status(thm)],[])).
% 0.50/0.69 tff(626,plain,
% 0.50/0.69 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_1) | (~product(e_1, e_4, e_3)) | (~product(e_5, e_4, e_3))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[625, 624])).
% 0.50/0.69 tff(627,plain,
% 0.50/0.69 ($false),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[626, 623, 12, 322, 620])).
% 0.50/0.69 tff(628,plain,((~product(e_5, e_4, e_3)) | (~product(e_1, e_4, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.50/0.69 tff(629,plain,
% 0.50/0.69 (~product(e_1, e_4, e_3)),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[628, 322])).
% 0.50/0.69 tff(630,assumption,(product(e_4, e_1, e_2)), introduced(assumption)).
% 0.50/0.69 tff(631,plain,
% 0.50/0.69 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_1) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_5, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_1) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_5, e_2)))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(632,plain,
% 0.50/0.69 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_1) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_5, e_2)))),
% 0.50/0.69 inference(quant_inst,[status(thm)],[])).
% 0.50/0.69 tff(633,plain,
% 0.50/0.69 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_1) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_5, e_2))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[632, 631])).
% 0.50/0.69 tff(634,plain,
% 0.50/0.69 ($false),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[633, 623, 43, 630, 566])).
% 0.50/0.69 tff(635,plain,((~product(e_4, e_5, e_2)) | (~product(e_4, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.50/0.69 tff(636,plain,
% 0.50/0.69 (~product(e_4, e_1, e_2)),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[635, 564])).
% 0.50/0.69 tff(637,assumption,(product(e_4, e_1, e_4)), introduced(assumption)).
% 0.50/0.69 tff(638,plain,
% 0.50/0.69 ((~equalish(e_1, e_4)) <=> (~equalish(e_1, e_4))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(639,axiom,(~equalish(e_1, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_4')).
% 0.50/0.69 tff(640,plain,
% 0.50/0.69 (~equalish(e_1, e_4)),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[639, 638])).
% 0.50/0.69 tff(641,plain,
% 0.50/0.69 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(642,plain,
% 0.50/0.69 ((equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4))) <=> (equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(643,plain,
% 0.50/0.69 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4))))),
% 0.50/0.69 inference(monotonicity,[status(thm)],[642])).
% 0.50/0.69 tff(644,plain,
% 0.50/0.69 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.50/0.69 inference(transitivity,[status(thm)],[643, 641])).
% 0.50/0.69 tff(645,plain,
% 0.50/0.69 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4)))),
% 0.50/0.69 inference(quant_inst,[status(thm)],[])).
% 0.50/0.69 tff(646,plain,
% 0.50/0.69 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[645, 644])).
% 0.50/0.69 tff(647,plain,
% 0.50/0.69 ($false),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[646, 640, 43, 408, 637])).
% 0.50/0.69 tff(648,plain,(~product(e_4, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.50/0.69 tff(649,assumption,(product(e_4, e_1, e_3)), introduced(assumption)).
% 0.50/0.70 tff(650,plain,
% 0.50/0.70 ((~equalish(e_4, e_2)) <=> (~equalish(e_4, e_2))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(651,axiom,(~equalish(e_4, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_2')).
% 0.50/0.70 tff(652,plain,
% 0.50/0.70 (~equalish(e_4, e_2)),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[651, 650])).
% 0.50/0.70 tff(653,plain,
% 0.50/0.70 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_4, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_4, e_1, e_3)))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(654,plain,
% 0.50/0.70 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_4, e_1, e_3)))),
% 0.50/0.70 inference(quant_inst,[status(thm)],[])).
% 0.50/0.70 tff(655,plain,
% 0.50/0.70 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_4, e_1, e_3))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[654, 653])).
% 0.50/0.70 tff(656,plain,
% 0.50/0.70 ($false),
% 0.50/0.70 inference(unit_resolution,[status(thm)],[655, 652, 12, 293, 649])).
% 0.50/0.70 tff(657,plain,(~product(e_4, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.50/0.70 tff(658,plain,
% 0.50/0.70 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(659,plain,
% 0.50/0.70 (((~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1))) <=> ((~group_element(e_1)) | (~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(660,plain,
% 0.50/0.70 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1)))),
% 0.50/0.70 inference(monotonicity,[status(thm)],[659])).
% 0.50/0.70 tff(661,plain,
% 0.50/0.70 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1))),
% 0.50/0.70 inference(transitivity,[status(thm)],[660, 658])).
% 0.50/0.70 tff(662,plain,
% 0.50/0.70 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)))),
% 0.50/0.70 inference(quant_inst,[status(thm)],[])).
% 0.50/0.70 tff(663,plain,
% 0.50/0.70 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1)),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[662, 661])).
% 0.50/0.70 tff(664,plain,
% 0.50/0.70 (product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_2)),
% 0.50/0.70 inference(unit_resolution,[status(thm)],[663, 272, 430, 269, 603, 657])).
% 0.50/0.70 tff(665,plain,
% 0.50/0.70 (product(e_4, e_1, e_5) | product(e_4, e_1, e_2)),
% 0.50/0.70 inference(unit_resolution,[status(thm)],[664, 648])).
% 0.50/0.70 tff(666,plain,
% 0.50/0.70 (product(e_4, e_1, e_5)),
% 0.50/0.70 inference(unit_resolution,[status(thm)],[665, 636])).
% 0.50/0.70 tff(667,plain,
% 0.50/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_5, e_5)) | (~product(e_5, e_5, e_4)) | product(e_4, e_5, e_5))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_5, e_4)) | product(e_4, e_5, e_5))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(668,plain,
% 0.50/0.70 (((~product(e_5, e_5, e_5)) | product(e_4, e_5, e_5) | (~product(e_5, e_5, e_4))) <=> ((~product(e_5, e_5, e_5)) | (~product(e_5, e_5, e_4)) | product(e_4, e_5, e_5))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(669,plain,
% 0.50/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_5, e_5)) | product(e_4, e_5, e_5) | (~product(e_5, e_5, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_5, e_5)) | (~product(e_5, e_5, e_4)) | product(e_4, e_5, e_5)))),
% 0.50/0.70 inference(monotonicity,[status(thm)],[668])).
% 0.50/0.70 tff(670,plain,
% 0.50/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_5, e_5)) | product(e_4, e_5, e_5) | (~product(e_5, e_5, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_5, e_4)) | product(e_4, e_5, e_5))),
% 0.50/0.70 inference(transitivity,[status(thm)],[669, 667])).
% 0.50/0.70 tff(671,plain,
% 0.50/0.70 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_5, e_5)) | product(e_4, e_5, e_5) | (~product(e_5, e_5, e_4)))),
% 0.50/0.70 inference(quant_inst,[status(thm)],[])).
% 0.50/0.70 tff(672,plain,
% 0.50/0.70 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_5, e_4)) | product(e_4, e_5, e_5)),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[671, 670])).
% 0.50/0.70 tff(673,plain,
% 0.50/0.70 (~product(e_5, e_5, e_4)),
% 0.50/0.70 inference(unit_resolution,[status(thm)],[672, 72, 416, 424])).
% 0.50/0.70 tff(674,assumption,(product(e_1, e_4, e_5)), introduced(assumption)).
% 0.50/0.70 tff(675,assumption,(product(e_4, e_1, e_5)), introduced(assumption)).
% 0.50/0.70 tff(676,plain,
% 0.50/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_1, e_5)) | product(e_5, e_5, e_4) | (~product(e_1, e_4, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_4, e_1, e_5)) | product(e_5, e_5, e_4) | (~product(e_1, e_4, e_5)))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(677,plain,
% 0.50/0.70 (((~product(e_1, e_4, e_5)) | product(e_5, e_5, e_4) | (~product(e_4, e_1, e_5))) <=> ((~product(e_4, e_1, e_5)) | product(e_5, e_5, e_4) | (~product(e_1, e_4, e_5)))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(678,plain,
% 0.50/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_4, e_5)) | product(e_5, e_5, e_4) | (~product(e_4, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_1, e_5)) | product(e_5, e_5, e_4) | (~product(e_1, e_4, e_5))))),
% 0.50/0.70 inference(monotonicity,[status(thm)],[677])).
% 0.50/0.70 tff(679,plain,
% 0.50/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_4, e_5)) | product(e_5, e_5, e_4) | (~product(e_4, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_4, e_1, e_5)) | product(e_5, e_5, e_4) | (~product(e_1, e_4, e_5)))),
% 0.50/0.70 inference(transitivity,[status(thm)],[678, 676])).
% 0.50/0.70 tff(680,plain,
% 0.50/0.70 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_4, e_5)) | product(e_5, e_5, e_4) | (~product(e_4, e_1, e_5)))),
% 0.50/0.70 inference(quant_inst,[status(thm)],[])).
% 0.50/0.70 tff(681,plain,
% 0.50/0.70 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_4, e_1, e_5)) | product(e_5, e_5, e_4) | (~product(e_1, e_4, e_5))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[680, 679])).
% 0.50/0.70 tff(682,plain,
% 0.50/0.70 ($false),
% 0.50/0.70 inference(unit_resolution,[status(thm)],[681, 72, 675, 674, 673])).
% 0.50/0.70 tff(683,plain,((~product(e_1, e_4, e_5)) | (~product(e_4, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.50/0.70 tff(684,plain,
% 0.50/0.70 (~product(e_1, e_4, e_5)),
% 0.50/0.70 inference(unit_resolution,[status(thm)],[683, 666])).
% 0.50/0.70 tff(685,assumption,(product(e_1, e_4, e_4)), introduced(assumption)).
% 0.50/0.70 tff(686,plain,
% 0.50/0.70 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_1, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_1, e_4, e_4)))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(687,plain,
% 0.50/0.70 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_1, e_4, e_4)))),
% 0.50/0.70 inference(quant_inst,[status(thm)],[])).
% 0.50/0.70 tff(688,plain,
% 0.50/0.70 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_1, e_4, e_4))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[687, 686])).
% 0.50/0.70 tff(689,plain,
% 0.50/0.70 ($false),
% 0.50/0.70 inference(unit_resolution,[status(thm)],[688, 640, 12, 685, 408])).
% 0.50/0.70 tff(690,plain,(~product(e_1, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.50/0.70 tff(691,plain,
% 0.50/0.70 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_4)) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | product(e_1, e_4, e_4) | product(e_1, e_4, e_5) | product(e_1, e_4, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_4)) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | product(e_1, e_4, e_4) | product(e_1, e_4, e_5) | product(e_1, e_4, e_3))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(692,plain,
% 0.50/0.70 (((~group_element(e_1)) | product(e_1, e_4, e_5) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4))) <=> ((~group_element(e_1)) | (~group_element(e_4)) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | product(e_1, e_4, e_4) | product(e_1, e_4, e_5) | product(e_1, e_4, e_3))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(693,plain,
% 0.50/0.70 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_4, e_5) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_4)) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | product(e_1, e_4, e_4) | product(e_1, e_4, e_5) | product(e_1, e_4, e_3)))),
% 0.50/0.70 inference(monotonicity,[status(thm)],[692])).
% 0.50/0.70 tff(694,plain,
% 0.50/0.70 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_4, e_5) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_4)) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | product(e_1, e_4, e_4) | product(e_1, e_4, e_5) | product(e_1, e_4, e_3))),
% 0.50/0.70 inference(transitivity,[status(thm)],[693, 691])).
% 0.50/0.70 tff(695,plain,
% 0.50/0.70 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_4, e_5) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4)))),
% 0.50/0.70 inference(quant_inst,[status(thm)],[])).
% 0.50/0.70 tff(696,plain,
% 0.50/0.70 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_4)) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | product(e_1, e_4, e_4) | product(e_1, e_4, e_5) | product(e_1, e_4, e_3)),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[695, 694])).
% 0.50/0.70 tff(697,plain,
% 0.50/0.70 (product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | product(e_1, e_4, e_4) | product(e_1, e_4, e_5) | product(e_1, e_4, e_3)),
% 0.50/0.70 inference(unit_resolution,[status(thm)],[696, 272, 430, 269])).
% 0.50/0.70 tff(698,plain,
% 0.50/0.70 (product(e_1, e_4, e_2) | product(e_1, e_4, e_4) | product(e_1, e_4, e_5) | product(e_1, e_4, e_3)),
% 0.50/0.70 inference(unit_resolution,[status(thm)],[697, 514])).
% 0.50/0.70 tff(699,plain,
% 0.50/0.70 (product(e_1, e_4, e_2) | product(e_1, e_4, e_5) | product(e_1, e_4, e_3)),
% 0.50/0.70 inference(unit_resolution,[status(thm)],[698, 690])).
% 0.50/0.70 tff(700,plain,
% 0.50/0.70 (product(e_1, e_4, e_2)),
% 0.50/0.70 inference(unit_resolution,[status(thm)],[699, 684, 629])).
% 0.50/0.70 tff(701,assumption,(product(e_3, e_4, e_2)), introduced(assumption)).
% 0.50/0.70 tff(702,assumption,(product(e_1, e_4, e_2)), introduced(assumption)).
% 0.50/0.70 tff(703,plain,
% 0.50/0.70 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(704,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.50/0.70 tff(705,plain,
% 0.50/0.70 (~equalish(e_1, e_3)),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[704, 703])).
% 0.50/0.70 tff(706,plain,
% 0.50/0.70 (((~![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_4, e_2)) | (~product(e_3, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_4, e_2)) | (~product(e_3, e_4, e_2)))),
% 0.50/0.71 inference(rewrite,[status(thm)],[])).
% 0.50/0.71 tff(707,plain,
% 0.50/0.71 ((equalish(e_1, e_3) | (~product(e_3, e_4, e_2)) | (~product(e_1, e_4, e_2))) <=> (equalish(e_1, e_3) | (~product(e_1, e_4, e_2)) | (~product(e_3, e_4, e_2)))),
% 0.50/0.71 inference(rewrite,[status(thm)],[])).
% 0.50/0.71 tff(708,plain,
% 0.50/0.71 (((~![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_4, e_2)) | (~product(e_1, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_1, e_4, e_2)) | (~product(e_3, e_4, e_2))))),
% 0.50/0.71 inference(monotonicity,[status(thm)],[707])).
% 0.50/0.71 tff(709,plain,
% 0.50/0.71 (((~![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_4, e_2)) | (~product(e_1, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_4, e_2)) | (~product(e_3, e_4, e_2)))),
% 0.50/0.71 inference(transitivity,[status(thm)],[708, 706])).
% 0.50/0.71 tff(710,plain,
% 0.50/0.71 ((~![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_4, e_2)) | (~product(e_1, e_4, e_2)))),
% 0.50/0.71 inference(quant_inst,[status(thm)],[])).
% 0.50/0.71 tff(711,plain,
% 0.50/0.71 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_4, e_2)) | (~product(e_3, e_4, e_2))),
% 0.50/0.71 inference(modus_ponens,[status(thm)],[710, 709])).
% 0.50/0.71 tff(712,plain,
% 0.50/0.71 ($false),
% 0.50/0.71 inference(unit_resolution,[status(thm)],[711, 705, 12, 702, 701])).
% 0.50/0.71 tff(713,plain,((~product(e_1, e_4, e_2)) | (~product(e_3, e_4, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.50/0.71 tff(714,plain,
% 0.50/0.71 (~product(e_3, e_4, e_2)),
% 0.50/0.71 inference(unit_resolution,[status(thm)],[713, 700])).
% 0.50/0.71 tff(715,assumption,(product(e_3, e_4, e_3)), introduced(assumption)).
% 0.50/0.71 tff(716,plain,
% 0.50/0.71 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_3, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.50/0.71 inference(rewrite,[status(thm)],[])).
% 0.50/0.71 tff(717,plain,
% 0.50/0.71 ((equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3))) <=> (equalish(e_4, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.50/0.71 inference(rewrite,[status(thm)],[])).
% 0.50/0.71 tff(718,plain,
% 0.50/0.71 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_3, e_3, e_3))))),
% 0.50/0.71 inference(monotonicity,[status(thm)],[717])).
% 0.50/0.71 tff(719,plain,
% 0.50/0.71 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.50/0.71 inference(transitivity,[status(thm)],[718, 716])).
% 0.50/0.71 tff(720,plain,
% 0.50/0.71 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3)))),
% 0.50/0.71 inference(quant_inst,[status(thm)],[])).
% 0.50/0.71 tff(721,plain,
% 0.50/0.71 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_3, e_3, e_3))),
% 0.50/0.71 inference(modus_ponens,[status(thm)],[720, 719])).
% 0.50/0.71 tff(722,plain,
% 0.50/0.71 ($false),
% 0.50/0.71 inference(unit_resolution,[status(thm)],[721, 191, 43, 715, 53])).
% 0.50/0.71 tff(723,plain,(~product(e_3, e_4, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.50/0.71 tff(724,plain,
% 0.50/0.71 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | (~group_element(e_4)) | product(e_3, e_4, e_1) | product(e_3, e_4, e_5) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_4))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_3, e_4, e_1) | product(e_3, e_4, e_5) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_4))),
% 0.50/0.71 inference(rewrite,[status(thm)],[])).
% 0.50/0.71 tff(725,plain,
% 0.50/0.71 (((~group_element(e_3)) | product(e_3, e_4, e_5) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | (~group_element(e_4))) <=> ((~group_element(e_3)) | (~group_element(e_4)) | product(e_3, e_4, e_1) | product(e_3, e_4, e_5) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_4))),
% 0.50/0.71 inference(rewrite,[status(thm)],[])).
% 0.50/0.71 tff(726,plain,
% 0.50/0.71 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_4, e_5) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | (~group_element(e_4)) | product(e_3, e_4, e_1) | product(e_3, e_4, e_5) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_4)))),
% 0.50/0.71 inference(monotonicity,[status(thm)],[725])).
% 0.50/0.71 tff(727,plain,
% 0.50/0.71 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_4, e_5) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_3, e_4, e_1) | product(e_3, e_4, e_5) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_4))),
% 0.50/0.71 inference(transitivity,[status(thm)],[726, 724])).
% 0.50/0.71 tff(728,plain,
% 0.50/0.71 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_4, e_5) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | (~group_element(e_4)))),
% 0.50/0.71 inference(quant_inst,[status(thm)],[])).
% 0.50/0.71 tff(729,plain,
% 0.50/0.71 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_3, e_4, e_1) | product(e_3, e_4, e_5) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_4)),
% 0.50/0.71 inference(modus_ponens,[status(thm)],[728, 727])).
% 0.50/0.71 tff(730,plain,
% 0.50/0.71 (product(e_3, e_4, e_1) | product(e_3, e_4, e_5) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_4)),
% 0.50/0.71 inference(unit_resolution,[status(thm)],[729, 373, 430, 269])).
% 0.50/0.71 tff(731,plain,
% 0.50/0.71 (product(e_3, e_4, e_1) | product(e_3, e_4, e_5) | product(e_3, e_4, e_2)),
% 0.50/0.71 inference(unit_resolution,[status(thm)],[730, 475, 723])).
% 0.50/0.71 tff(732,plain,
% 0.50/0.71 (product(e_3, e_4, e_5)),
% 0.50/0.71 inference(unit_resolution,[status(thm)],[731, 714, 619])).
% 0.50/0.71 tff(733,assumption,(product(e_3, e_4, e_5)), introduced(assumption)).
% 0.50/0.71 tff(734,plain,
% 0.50/0.71 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_3, e_4, e_5)) | (~product(e_3, e_2, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_2) | (~product(e_3, e_4, e_5)) | (~product(e_3, e_2, e_5)))),
% 0.50/0.71 inference(rewrite,[status(thm)],[])).
% 0.50/0.71 tff(735,plain,
% 0.50/0.71 ((equalish(e_4, e_2) | (~product(e_3, e_2, e_5)) | (~product(e_3, e_4, e_5))) <=> (equalish(e_4, e_2) | (~product(e_3, e_4, e_5)) | (~product(e_3, e_2, e_5)))),
% 0.50/0.71 inference(rewrite,[status(thm)],[])).
% 0.50/0.71 tff(736,plain,
% 0.50/0.71 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_3, e_2, e_5)) | (~product(e_3, e_4, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_3, e_4, e_5)) | (~product(e_3, e_2, e_5))))),
% 0.50/0.71 inference(monotonicity,[status(thm)],[735])).
% 0.50/0.71 tff(737,plain,
% 0.50/0.71 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_3, e_2, e_5)) | (~product(e_3, e_4, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_2) | (~product(e_3, e_4, e_5)) | (~product(e_3, e_2, e_5)))),
% 0.50/0.71 inference(transitivity,[status(thm)],[736, 734])).
% 0.50/0.71 tff(738,plain,
% 0.50/0.71 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_3, e_2, e_5)) | (~product(e_3, e_4, e_5)))),
% 0.50/0.71 inference(quant_inst,[status(thm)],[])).
% 0.50/0.71 tff(739,plain,
% 0.50/0.71 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_2) | (~product(e_3, e_4, e_5)) | (~product(e_3, e_2, e_5))),
% 0.50/0.71 inference(modus_ponens,[status(thm)],[738, 737])).
% 0.50/0.71 tff(740,plain,
% 0.50/0.71 ($false),
% 0.50/0.71 inference(unit_resolution,[status(thm)],[739, 652, 43, 733, 1])).
% 0.50/0.71 tff(741,plain,((~product(e_3, e_4, e_5)) | (~product(e_3, e_2, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.50/0.71 tff(742,plain,
% 0.50/0.71 (~product(e_3, e_2, e_5)),
% 0.50/0.71 inference(unit_resolution,[status(thm)],[741, 732])).
% 0.50/0.71 tff(743,assumption,(product(e_3, e_2, e_3)), introduced(assumption)).
% 0.50/0.71 tff(744,plain,
% 0.50/0.71 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.50/0.71 inference(rewrite,[status(thm)],[])).
% 0.50/0.71 tff(745,plain,
% 0.50/0.71 ((equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3))) <=> (equalish(e_2, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.50/0.71 inference(rewrite,[status(thm)],[])).
% 0.50/0.71 tff(746,plain,
% 0.50/0.71 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_3, e_3))))),
% 0.50/0.71 inference(monotonicity,[status(thm)],[745])).
% 0.50/0.71 tff(747,plain,
% 0.50/0.71 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.50/0.71 inference(transitivity,[status(thm)],[746, 744])).
% 0.50/0.71 tff(748,plain,
% 0.50/0.71 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.50/0.71 inference(quant_inst,[status(thm)],[])).
% 0.50/0.71 tff(749,plain,
% 0.50/0.71 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_3, e_3))),
% 0.50/0.71 inference(modus_ponens,[status(thm)],[748, 747])).
% 0.50/0.71 tff(750,plain,
% 0.50/0.71 ($false),
% 0.50/0.71 inference(unit_resolution,[status(thm)],[749, 57, 43, 53, 743])).
% 0.50/0.71 tff(751,plain,(~product(e_3, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.50/0.71 tff(752,assumption,(product(e_3, e_2, e_2)), introduced(assumption)).
% 0.50/0.71 tff(753,plain,
% 0.50/0.71 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.50/0.71 inference(rewrite,[status(thm)],[])).
% 0.50/0.71 tff(754,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.50/0.71 tff(755,plain,
% 0.50/0.71 (~equalish(e_3, e_2)),
% 0.50/0.71 inference(modus_ponens,[status(thm)],[754, 753])).
% 0.50/0.71 tff(756,plain,
% 0.50/0.71 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, 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_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.50/0.71 inference(rewrite,[status(thm)],[])).
% 0.50/0.71 tff(757,plain,
% 0.50/0.71 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.50/0.71 inference(quant_inst,[status(thm)],[])).
% 0.50/0.71 tff(758,plain,
% 0.50/0.71 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2))),
% 0.50/0.71 inference(modus_ponens,[status(thm)],[757, 756])).
% 0.50/0.71 tff(759,plain,
% 0.50/0.71 ($false),
% 0.50/0.71 inference(unit_resolution,[status(thm)],[758, 755, 12, 137, 752])).
% 0.50/0.71 tff(760,plain,(~product(e_3, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.50/0.71 tff(761,plain,
% 0.50/0.71 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | (~group_element(e_3)) | product(e_3, e_2, e_4) | product(e_3, e_2, e_5) | product(e_3, e_2, e_1) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_2)) | (~group_element(e_3)) | product(e_3, e_2, e_4) | product(e_3, e_2, e_5) | product(e_3, e_2, e_1) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2))),
% 0.50/0.71 inference(rewrite,[status(thm)],[])).
% 0.50/0.71 tff(762,plain,
% 0.50/0.71 (((~group_element(e_3)) | product(e_3, e_2, e_5) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2))) <=> ((~group_element(e_2)) | (~group_element(e_3)) | product(e_3, e_2, e_4) | product(e_3, e_2, e_5) | product(e_3, e_2, e_1) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2))),
% 0.50/0.71 inference(rewrite,[status(thm)],[])).
% 0.50/0.71 tff(763,plain,
% 0.50/0.71 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_2, e_5) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | (~group_element(e_3)) | product(e_3, e_2, e_4) | product(e_3, e_2, e_5) | product(e_3, e_2, e_1) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2)))),
% 0.50/0.71 inference(monotonicity,[status(thm)],[762])).
% 0.50/0.71 tff(764,plain,
% 0.50/0.71 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_2, e_5) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_2)) | (~group_element(e_3)) | product(e_3, e_2, e_4) | product(e_3, e_2, e_5) | product(e_3, e_2, e_1) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2))),
% 0.50/0.72 inference(transitivity,[status(thm)],[763, 761])).
% 0.50/0.72 tff(765,plain,
% 0.50/0.72 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_2, e_5) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)))),
% 0.50/0.72 inference(quant_inst,[status(thm)],[])).
% 0.50/0.72 tff(766,plain,
% 0.50/0.72 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_2)) | (~group_element(e_3)) | product(e_3, e_2, e_4) | product(e_3, e_2, e_5) | product(e_3, e_2, e_1) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2)),
% 0.50/0.72 inference(modus_ponens,[status(thm)],[765, 764])).
% 0.50/0.72 tff(767,plain,
% 0.50/0.72 (product(e_3, e_2, e_4) | product(e_3, e_2, e_5) | product(e_3, e_2, e_1) | product(e_3, e_2, e_3)),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[766, 236, 373, 269, 760])).
% 0.50/0.72 tff(768,plain,
% 0.50/0.72 (product(e_3, e_2, e_4) | product(e_3, e_2, e_5) | product(e_3, e_2, e_1)),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[767, 751])).
% 0.50/0.72 tff(769,plain,
% 0.50/0.72 (product(e_3, e_2, e_1)),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[768, 742, 492])).
% 0.50/0.72 tff(770,plain,
% 0.50/0.72 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_4)))),
% 0.50/0.72 inference(rewrite,[status(thm)],[])).
% 0.50/0.72 tff(771,plain,
% 0.50/0.72 (((~product(e_3, e_2, e_1)) | product(e_4, e_1, e_2) | (~product(e_2, e_3, e_4))) <=> (product(e_4, e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_4)))),
% 0.50/0.72 inference(rewrite,[status(thm)],[])).
% 0.50/0.72 tff(772,plain,
% 0.50/0.72 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_1)) | product(e_4, e_1, e_2) | (~product(e_2, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_4))))),
% 0.50/0.72 inference(monotonicity,[status(thm)],[771])).
% 0.50/0.72 tff(773,plain,
% 0.50/0.72 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_1)) | product(e_4, e_1, e_2) | (~product(e_2, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_4)))),
% 0.50/0.72 inference(transitivity,[status(thm)],[772, 770])).
% 0.50/0.72 tff(774,plain,
% 0.50/0.72 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_1)) | product(e_4, e_1, e_2) | (~product(e_2, e_3, e_4)))),
% 0.50/0.72 inference(quant_inst,[status(thm)],[])).
% 0.50/0.72 tff(775,plain,
% 0.50/0.72 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_4))),
% 0.50/0.72 inference(modus_ponens,[status(thm)],[774, 773])).
% 0.50/0.72 tff(776,plain,
% 0.50/0.72 ($false),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[775, 72, 636, 465, 769])).
% 0.50/0.72 tff(777,plain,(~product(e_5, e_4, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.50/0.72 tff(778,plain,
% 0.50/0.72 (~product(e_3, e_4, e_5)),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[741, 1])).
% 0.50/0.72 tff(779,assumption,(~product(e_5, e_4, e_3)), introduced(assumption)).
% 0.50/0.72 tff(780,assumption,(~product(e_3, e_4, e_5)), introduced(assumption)).
% 0.50/0.72 tff(781,plain,
% 0.50/0.72 (~product(e_3, e_4, e_1)),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[618, 595])).
% 0.50/0.72 tff(782,plain,
% 0.50/0.72 (product(e_3, e_4, e_2)),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[731, 781, 780])).
% 0.50/0.72 tff(783,plain,
% 0.50/0.72 ((~equalish(e_3, e_5)) <=> (~equalish(e_3, e_5))),
% 0.50/0.72 inference(rewrite,[status(thm)],[])).
% 0.50/0.72 tff(784,axiom,(~equalish(e_3, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_5')).
% 0.50/0.72 tff(785,plain,
% 0.50/0.72 (~equalish(e_3, e_5)),
% 0.50/0.72 inference(modus_ponens,[status(thm)],[784, 783])).
% 0.50/0.72 tff(786,plain,
% 0.50/0.72 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_5) | (~product(e_5, e_4, e_2)) | (~product(e_3, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_5) | (~product(e_5, e_4, e_2)) | (~product(e_3, e_4, e_2)))),
% 0.50/0.72 inference(rewrite,[status(thm)],[])).
% 0.50/0.72 tff(787,plain,
% 0.50/0.72 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_5) | (~product(e_5, e_4, e_2)) | (~product(e_3, e_4, e_2)))),
% 0.50/0.72 inference(quant_inst,[status(thm)],[])).
% 0.50/0.72 tff(788,plain,
% 0.50/0.72 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_5) | (~product(e_5, e_4, e_2)) | (~product(e_3, e_4, e_2))),
% 0.50/0.72 inference(modus_ponens,[status(thm)],[787, 786])).
% 0.50/0.72 tff(789,plain,
% 0.50/0.72 ($false),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[788, 785, 12, 493, 701])).
% 0.50/0.72 tff(790,plain,((~product(e_3, e_4, e_2)) | (~product(e_5, e_4, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.50/0.72 tff(791,plain,
% 0.50/0.72 (~product(e_5, e_4, e_2)),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[790, 782])).
% 0.50/0.72 tff(792,plain,
% 0.50/0.72 (product(e_5, e_4, e_1)),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[555, 791, 779])).
% 0.50/0.72 tff(793,plain,
% 0.50/0.72 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_5, e_4, e_1)) | (~product(e_4, e_5, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_4) | (~product(e_5, e_4, e_1)) | (~product(e_4, e_5, e_2)))),
% 0.50/0.72 inference(rewrite,[status(thm)],[])).
% 0.50/0.72 tff(794,plain,
% 0.50/0.72 (((~product(e_5, e_4, e_1)) | product(e_2, e_1, e_4) | (~product(e_4, e_5, e_2))) <=> (product(e_2, e_1, e_4) | (~product(e_5, e_4, e_1)) | (~product(e_4, e_5, e_2)))),
% 0.50/0.72 inference(rewrite,[status(thm)],[])).
% 0.50/0.72 tff(795,plain,
% 0.50/0.72 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_4, e_1)) | product(e_2, e_1, e_4) | (~product(e_4, e_5, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_5, e_4, e_1)) | (~product(e_4, e_5, e_2))))),
% 0.50/0.72 inference(monotonicity,[status(thm)],[794])).
% 0.50/0.72 tff(796,plain,
% 0.50/0.72 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_4, e_1)) | product(e_2, e_1, e_4) | (~product(e_4, e_5, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_4) | (~product(e_5, e_4, e_1)) | (~product(e_4, e_5, e_2)))),
% 0.50/0.72 inference(transitivity,[status(thm)],[795, 793])).
% 0.50/0.72 tff(797,plain,
% 0.50/0.72 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_4, e_1)) | product(e_2, e_1, e_4) | (~product(e_4, e_5, e_2)))),
% 0.50/0.72 inference(quant_inst,[status(thm)],[])).
% 0.50/0.72 tff(798,plain,
% 0.50/0.72 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_4) | (~product(e_5, e_4, e_1)) | (~product(e_4, e_5, e_2))),
% 0.50/0.72 inference(modus_ponens,[status(thm)],[797, 796])).
% 0.50/0.72 tff(799,plain,
% 0.50/0.72 (~product(e_4, e_5, e_2)),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[798, 72, 259, 792])).
% 0.50/0.72 tff(800,assumption,(product(e_5, e_5, e_3)), introduced(assumption)).
% 0.50/0.72 tff(801,plain,
% 0.50/0.72 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_5) | (~product(e_5, e_5, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_5) | (~product(e_5, e_5, e_3)))),
% 0.50/0.72 inference(rewrite,[status(thm)],[])).
% 0.50/0.72 tff(802,plain,
% 0.50/0.72 (((~product(e_5, e_5, e_3)) | product(e_3, e_3, e_5) | (~product(e_5, e_5, e_3))) <=> (product(e_3, e_3, e_5) | (~product(e_5, e_5, e_3)))),
% 0.50/0.72 inference(rewrite,[status(thm)],[])).
% 0.50/0.72 tff(803,plain,
% 0.50/0.72 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_5, e_3)) | product(e_3, e_3, e_5) | (~product(e_5, e_5, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_5) | (~product(e_5, e_5, e_3))))),
% 0.50/0.72 inference(monotonicity,[status(thm)],[802])).
% 0.50/0.72 tff(804,plain,
% 0.50/0.72 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_5, e_3)) | product(e_3, e_3, e_5) | (~product(e_5, e_5, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_5) | (~product(e_5, e_5, e_3)))),
% 0.50/0.72 inference(transitivity,[status(thm)],[803, 801])).
% 0.50/0.72 tff(805,plain,
% 0.50/0.72 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_5, e_3)) | product(e_3, e_3, e_5) | (~product(e_5, e_5, e_3)))),
% 0.50/0.72 inference(quant_inst,[status(thm)],[])).
% 0.50/0.72 tff(806,plain,
% 0.50/0.72 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_5) | (~product(e_5, e_5, e_3))),
% 0.50/0.72 inference(modus_ponens,[status(thm)],[805, 804])).
% 0.50/0.72 tff(807,plain,
% 0.50/0.72 ($false),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[806, 72, 455, 800])).
% 0.50/0.72 tff(808,plain,(~product(e_5, e_5, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.50/0.72 tff(809,assumption,(~product(e_5, e_5, e_3)), introduced(assumption)).
% 0.50/0.72 tff(810,assumption,(product(e_2, e_3, e_5)), introduced(assumption)).
% 0.50/0.72 tff(811,plain,
% 0.50/0.72 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_5)) | product(e_5, e_5, e_3) | (~product(e_2, e_3, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_2, e_5)) | product(e_5, e_5, e_3) | (~product(e_2, e_3, e_5)))),
% 0.50/0.72 inference(rewrite,[status(thm)],[])).
% 0.50/0.72 tff(812,plain,
% 0.50/0.72 (((~product(e_2, e_3, e_5)) | product(e_5, e_5, e_3) | (~product(e_3, e_2, e_5))) <=> ((~product(e_3, e_2, e_5)) | product(e_5, e_5, e_3) | (~product(e_2, e_3, e_5)))),
% 0.50/0.72 inference(rewrite,[status(thm)],[])).
% 0.50/0.72 tff(813,plain,
% 0.50/0.72 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_5)) | product(e_5, e_5, e_3) | (~product(e_3, e_2, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_5)) | product(e_5, e_5, e_3) | (~product(e_2, e_3, e_5))))),
% 0.50/0.72 inference(monotonicity,[status(thm)],[812])).
% 0.50/0.72 tff(814,plain,
% 0.50/0.72 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_5)) | product(e_5, e_5, e_3) | (~product(e_3, e_2, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_2, e_5)) | product(e_5, e_5, e_3) | (~product(e_2, e_3, e_5)))),
% 0.50/0.72 inference(transitivity,[status(thm)],[813, 811])).
% 0.50/0.72 tff(815,plain,
% 0.50/0.72 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_5)) | product(e_5, e_5, e_3) | (~product(e_3, e_2, e_5)))),
% 0.50/0.72 inference(quant_inst,[status(thm)],[])).
% 0.50/0.72 tff(816,plain,
% 0.50/0.72 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_2, e_5)) | product(e_5, e_5, e_3) | (~product(e_2, e_3, e_5))),
% 0.50/0.72 inference(modus_ponens,[status(thm)],[815, 814])).
% 0.50/0.72 tff(817,plain,
% 0.50/0.72 ($false),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[816, 72, 810, 1, 809])).
% 0.50/0.72 tff(818,plain,(product(e_5, e_5, e_3) | (~product(e_2, e_3, e_5)) | (~product(e_3, e_2, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.50/0.72 tff(819,plain,
% 0.50/0.72 (~product(e_2, e_3, e_5)),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[818, 1, 808])).
% 0.50/0.72 tff(820,assumption,(product(e_2, e_3, e_1)), introduced(assumption)).
% 0.50/0.72 tff(821,plain,
% 0.50/0.72 ((~equalish(e_2, e_4)) <=> (~equalish(e_2, e_4))),
% 0.50/0.72 inference(rewrite,[status(thm)],[])).
% 0.50/0.72 tff(822,axiom,(~equalish(e_2, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_4')).
% 0.50/0.72 tff(823,plain,
% 0.50/0.72 (~equalish(e_2, e_4)),
% 0.50/0.72 inference(modus_ponens,[status(thm)],[822, 821])).
% 0.50/0.72 tff(824,plain,
% 0.50/0.72 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_4, e_3, e_1)) | (~product(e_2, e_3, 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_4) | (~product(e_4, e_3, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.50/0.72 inference(rewrite,[status(thm)],[])).
% 0.50/0.72 tff(825,plain,
% 0.50/0.72 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_4, e_3, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.50/0.72 inference(quant_inst,[status(thm)],[])).
% 0.50/0.72 tff(826,plain,
% 0.50/0.72 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_4) | (~product(e_4, e_3, e_1)) | (~product(e_2, e_3, e_1))),
% 0.50/0.72 inference(modus_ponens,[status(thm)],[825, 824])).
% 0.50/0.72 tff(827,plain,
% 0.50/0.72 ($false),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[826, 823, 12, 820, 595])).
% 0.50/0.72 tff(828,plain,((~product(e_2, e_3, e_1)) | (~product(e_4, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.50/0.72 tff(829,plain,
% 0.50/0.72 (~product(e_2, e_3, e_1)),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[828, 595])).
% 0.50/0.72 tff(830,assumption,(product(e_2, e_3, e_2)), introduced(assumption)).
% 0.50/0.72 tff(831,plain,
% 0.50/0.72 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, 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_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_3, e_2)))),
% 0.50/0.72 inference(rewrite,[status(thm)],[])).
% 0.50/0.72 tff(832,plain,
% 0.50/0.72 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_3, e_2)))),
% 0.50/0.72 inference(quant_inst,[status(thm)],[])).
% 0.50/0.72 tff(833,plain,
% 0.50/0.72 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_3, e_2))),
% 0.50/0.72 inference(modus_ponens,[status(thm)],[832, 831])).
% 0.50/0.72 tff(834,plain,
% 0.50/0.72 ($false),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[833, 755, 43, 830, 137])).
% 0.50/0.72 tff(835,plain,(~product(e_2, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.50/0.72 tff(836,plain,
% 0.50/0.72 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | (~group_element(e_3)) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | product(e_2, e_3, e_4) | product(e_2, e_3, e_5))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_2)) | (~group_element(e_3)) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | product(e_2, e_3, e_4) | product(e_2, e_3, e_5))),
% 0.50/0.72 inference(rewrite,[status(thm)],[])).
% 0.50/0.72 tff(837,plain,
% 0.50/0.72 (((~group_element(e_2)) | product(e_2, e_3, e_5) | product(e_2, e_3, e_4) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3))) <=> ((~group_element(e_2)) | (~group_element(e_3)) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | product(e_2, e_3, e_4) | product(e_2, e_3, e_5))),
% 0.50/0.72 inference(rewrite,[status(thm)],[])).
% 0.50/0.72 tff(838,plain,
% 0.50/0.72 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_2, e_3, e_5) | product(e_2, e_3, e_4) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | (~group_element(e_3)) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | product(e_2, e_3, e_4) | product(e_2, e_3, e_5)))),
% 0.50/0.72 inference(monotonicity,[status(thm)],[837])).
% 0.50/0.72 tff(839,plain,
% 0.50/0.72 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_2, e_3, e_5) | product(e_2, e_3, e_4) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_2)) | (~group_element(e_3)) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | product(e_2, e_3, e_4) | product(e_2, e_3, e_5))),
% 0.50/0.72 inference(transitivity,[status(thm)],[838, 836])).
% 0.50/0.72 tff(840,plain,
% 0.50/0.72 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_2, e_3, e_5) | product(e_2, e_3, e_4) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)))),
% 0.50/0.72 inference(quant_inst,[status(thm)],[])).
% 0.50/0.72 tff(841,plain,
% 0.50/0.72 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_2)) | (~group_element(e_3)) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | product(e_2, e_3, e_4) | product(e_2, e_3, e_5)),
% 0.50/0.72 inference(modus_ponens,[status(thm)],[840, 839])).
% 0.50/0.72 tff(842,plain,
% 0.50/0.72 (product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | product(e_2, e_3, e_4) | product(e_2, e_3, e_5)),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[841, 236, 373, 269])).
% 0.50/0.72 tff(843,plain,
% 0.50/0.72 (product(e_2, e_3, e_3) | product(e_2, e_3, e_1) | product(e_2, e_3, e_4) | product(e_2, e_3, e_5)),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[842, 835])).
% 0.50/0.72 tff(844,plain,
% 0.50/0.72 (product(e_2, e_3, e_4)),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[843, 829, 62, 819])).
% 0.50/0.72 tff(845,plain,
% 0.50/0.72 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_4, e_5, e_2) | (~product(e_3, e_2, e_5)) | (~product(e_2, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_4, e_5, e_2) | (~product(e_3, e_2, e_5)) | (~product(e_2, e_3, e_4)))),
% 0.50/0.73 inference(rewrite,[status(thm)],[])).
% 0.50/0.73 tff(846,plain,
% 0.50/0.73 (((~product(e_3, e_2, e_5)) | product(e_4, e_5, e_2) | (~product(e_2, e_3, e_4))) <=> (product(e_4, e_5, e_2) | (~product(e_3, e_2, e_5)) | (~product(e_2, e_3, e_4)))),
% 0.50/0.73 inference(rewrite,[status(thm)],[])).
% 0.50/0.73 tff(847,plain,
% 0.50/0.73 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_5)) | product(e_4, e_5, e_2) | (~product(e_2, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_4, e_5, e_2) | (~product(e_3, e_2, e_5)) | (~product(e_2, e_3, e_4))))),
% 0.50/0.73 inference(monotonicity,[status(thm)],[846])).
% 0.50/0.73 tff(848,plain,
% 0.50/0.73 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_5)) | product(e_4, e_5, e_2) | (~product(e_2, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_4, e_5, e_2) | (~product(e_3, e_2, e_5)) | (~product(e_2, e_3, e_4)))),
% 0.50/0.73 inference(transitivity,[status(thm)],[847, 845])).
% 0.50/0.73 tff(849,plain,
% 0.50/0.73 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_5)) | product(e_4, e_5, e_2) | (~product(e_2, e_3, e_4)))),
% 0.50/0.73 inference(quant_inst,[status(thm)],[])).
% 0.50/0.73 tff(850,plain,
% 0.50/0.73 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_4, e_5, e_2) | (~product(e_3, e_2, e_5)) | (~product(e_2, e_3, e_4))),
% 0.50/0.73 inference(modus_ponens,[status(thm)],[849, 848])).
% 0.50/0.73 tff(851,plain,
% 0.50/0.73 ($false),
% 0.50/0.73 inference(unit_resolution,[status(thm)],[850, 72, 844, 1, 799])).
% 0.50/0.73 tff(852,plain,((~product(e_4, e_3, e_1)) | (~product(e_3, e_2, e_5)) | product(e_5, e_4, e_3) | product(e_3, e_4, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.50/0.73 tff(853,plain,
% 0.50/0.73 (~product(e_4, e_3, e_1)),
% 0.50/0.73 inference(unit_resolution,[status(thm)],[852, 778, 777, 1])).
% 0.50/0.73 tff(854,plain,
% 0.50/0.73 ($false),
% 0.50/0.73 inference(unit_resolution,[status(thm)],[593, 853, 321])).
% 0.50/0.73 tff(855,plain,(~product(e_3, e_2, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.50/0.73 tff(856,plain,
% 0.50/0.73 (~product(e_3, e_5, e_2)),
% 0.50/0.73 inference(unit_resolution,[status(thm)],[571, 566])).
% 0.50/0.73 tff(857,plain,
% 0.50/0.73 (~product(e_1, e_2, e_5)),
% 0.50/0.73 inference(unit_resolution,[status(thm)],[581, 856])).
% 0.50/0.73 tff(858,plain,
% 0.50/0.73 (product(e_1, e_2, e_4)),
% 0.50/0.73 inference(unit_resolution,[status(thm)],[320, 857])).
% 0.50/0.73 tff(859,plain,
% 0.50/0.73 (((~![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_2, e_4)) | (~product(e_3, 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_3, e_1) | (~product(e_1, e_2, e_4)) | (~product(e_3, e_2, e_4)))),
% 0.50/0.73 inference(rewrite,[status(thm)],[])).
% 0.50/0.73 tff(860,plain,
% 0.50/0.73 ((~![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_2, e_4)) | (~product(e_3, e_2, e_4)))),
% 0.57/0.73 inference(quant_inst,[status(thm)],[])).
% 0.57/0.73 tff(861,plain,
% 0.57/0.73 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_2, e_4)) | (~product(e_3, e_2, e_4))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[860, 859])).
% 0.57/0.73 tff(862,plain,
% 0.57/0.73 ($false),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[861, 15, 12, 585, 466])).
% 0.57/0.73 tff(863,plain,((~product(e_3, e_2, e_4)) | (~product(e_1, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.73 tff(864,plain,
% 0.57/0.73 (~product(e_3, e_2, e_4)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[863, 858])).
% 0.57/0.73 tff(865,plain,
% 0.57/0.73 (~product(e_4, e_1, e_2)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[635, 566])).
% 0.57/0.73 tff(866,plain,
% 0.57/0.73 (product(e_4, e_1, e_5)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[665, 865])).
% 0.57/0.73 tff(867,plain,
% 0.57/0.73 (~product(e_1, e_4, e_5)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[683, 866])).
% 0.57/0.73 tff(868,plain,
% 0.57/0.73 ($false),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[798, 72, 259, 524, 566])).
% 0.57/0.73 tff(869,plain,((~product(e_5, e_4, e_1)) | (~product(e_4, e_5, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.73 tff(870,plain,
% 0.57/0.73 (~product(e_5, e_4, e_1)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[869, 566])).
% 0.57/0.73 tff(871,plain,
% 0.57/0.73 (product(e_5, e_4, e_2)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[555, 870, 779])).
% 0.57/0.73 tff(872,assumption,(~product(e_3, e_5, e_1)), introduced(assumption)).
% 0.57/0.73 tff(873,assumption,(~product(e_1, e_4, e_5)), introduced(assumption)).
% 0.57/0.73 tff(874,plain,
% 0.57/0.73 ((~equalish(e_1, e_5)) <=> (~equalish(e_1, e_5))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(875,axiom,(~equalish(e_1, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_5')).
% 0.57/0.73 tff(876,plain,
% 0.57/0.73 (~equalish(e_1, e_5)),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[875, 874])).
% 0.57/0.73 tff(877,plain,
% 0.57/0.73 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_5) | (~product(e_1, e_4, e_2)) | (~product(e_5, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_5) | (~product(e_1, e_4, e_2)) | (~product(e_5, e_4, e_2)))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(878,plain,
% 0.57/0.73 ((equalish(e_1, e_5) | (~product(e_5, e_4, e_2)) | (~product(e_1, e_4, e_2))) <=> (equalish(e_1, e_5) | (~product(e_1, e_4, e_2)) | (~product(e_5, e_4, e_2)))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(879,plain,
% 0.57/0.73 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_5) | (~product(e_5, e_4, e_2)) | (~product(e_1, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_5) | (~product(e_1, e_4, e_2)) | (~product(e_5, e_4, e_2))))),
% 0.57/0.73 inference(monotonicity,[status(thm)],[878])).
% 0.57/0.73 tff(880,plain,
% 0.57/0.73 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_5) | (~product(e_5, e_4, e_2)) | (~product(e_1, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_5) | (~product(e_1, e_4, e_2)) | (~product(e_5, e_4, e_2)))),
% 0.57/0.73 inference(transitivity,[status(thm)],[879, 877])).
% 0.57/0.73 tff(881,plain,
% 0.57/0.73 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_5) | (~product(e_5, e_4, e_2)) | (~product(e_1, e_4, e_2)))),
% 0.57/0.73 inference(quant_inst,[status(thm)],[])).
% 0.57/0.73 tff(882,plain,
% 0.57/0.73 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_5) | (~product(e_1, e_4, e_2)) | (~product(e_5, e_4, e_2))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[881, 880])).
% 0.57/0.73 tff(883,plain,
% 0.57/0.73 ($false),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[882, 876, 12, 493, 702])).
% 0.57/0.73 tff(884,plain,((~product(e_1, e_4, e_2)) | (~product(e_5, e_4, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.73 tff(885,plain,
% 0.57/0.73 (~product(e_1, e_4, e_2)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[884, 493])).
% 0.57/0.73 tff(886,plain,
% 0.57/0.73 (product(e_1, e_4, e_3)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[699, 885, 873])).
% 0.57/0.73 tff(887,plain,
% 0.57/0.73 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_1, e_5)) | product(e_3, e_5, e_1) | (~product(e_1, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_4, e_1, e_5)) | product(e_3, e_5, e_1) | (~product(e_1, e_4, e_3)))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(888,plain,
% 0.57/0.73 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_1, e_5)) | product(e_3, e_5, e_1) | (~product(e_1, e_4, e_3)))),
% 0.57/0.73 inference(quant_inst,[status(thm)],[])).
% 0.57/0.73 tff(889,plain,
% 0.57/0.73 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_4, e_1, e_5)) | product(e_3, e_5, e_1) | (~product(e_1, e_4, e_3))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[888, 887])).
% 0.57/0.73 tff(890,plain,
% 0.57/0.73 ($false),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[889, 72, 675, 620, 872])).
% 0.57/0.73 tff(891,plain,((~product(e_1, e_4, e_3)) | (~product(e_4, e_1, e_5)) | product(e_3, e_5, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.57/0.73 tff(892,plain,
% 0.57/0.73 (~product(e_4, e_1, e_5)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[891, 886, 872])).
% 0.57/0.73 tff(893,plain,
% 0.57/0.73 (~product(e_4, e_5, e_1)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[501, 493])).
% 0.57/0.73 tff(894,assumption,(~product(e_3, e_2, e_4)), introduced(assumption)).
% 0.57/0.73 tff(895,plain,
% 0.57/0.73 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_3, e_2, e_4) | (~product(e_5, e_4, e_2)) | (~product(e_4, e_5, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_2, e_4) | (~product(e_5, e_4, e_2)) | (~product(e_4, e_5, e_3)))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(896,plain,
% 0.57/0.73 (((~product(e_5, e_4, e_2)) | product(e_3, e_2, e_4) | (~product(e_4, e_5, e_3))) <=> (product(e_3, e_2, e_4) | (~product(e_5, e_4, e_2)) | (~product(e_4, e_5, e_3)))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(897,plain,
% 0.57/0.73 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_4, e_2)) | product(e_3, e_2, e_4) | (~product(e_4, e_5, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_3, e_2, e_4) | (~product(e_5, e_4, e_2)) | (~product(e_4, e_5, e_3))))),
% 0.57/0.73 inference(monotonicity,[status(thm)],[896])).
% 0.57/0.73 tff(898,plain,
% 0.57/0.73 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_4, e_2)) | product(e_3, e_2, e_4) | (~product(e_4, e_5, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_2, e_4) | (~product(e_5, e_4, e_2)) | (~product(e_4, e_5, e_3)))),
% 0.57/0.73 inference(transitivity,[status(thm)],[897, 895])).
% 0.57/0.73 tff(899,plain,
% 0.57/0.73 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_4, e_2)) | product(e_3, e_2, e_4) | (~product(e_4, e_5, e_3)))),
% 0.57/0.73 inference(quant_inst,[status(thm)],[])).
% 0.57/0.73 tff(900,plain,
% 0.57/0.73 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_2, e_4) | (~product(e_5, e_4, e_2)) | (~product(e_4, e_5, e_3))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[899, 898])).
% 0.57/0.73 tff(901,plain,
% 0.57/0.73 ($false),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[900, 72, 493, 894, 560])).
% 0.57/0.73 tff(902,plain,(product(e_3, e_2, e_4) | (~product(e_5, e_4, e_2)) | (~product(e_4, e_5, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.73 tff(903,plain,
% 0.57/0.73 (~product(e_4, e_5, e_3)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[902, 493, 894])).
% 0.57/0.73 tff(904,plain,
% 0.57/0.73 (product(e_4, e_5, e_2)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[438, 903, 893])).
% 0.57/0.73 tff(905,plain,
% 0.57/0.73 (~product(e_4, e_1, e_2)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[635, 904])).
% 0.57/0.73 tff(906,plain,
% 0.57/0.73 ($false),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[665, 905, 892])).
% 0.57/0.73 tff(907,plain,((~product(e_5, e_4, e_2)) | product(e_3, e_5, e_1) | product(e_1, e_4, e_5) | product(e_3, e_2, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.57/0.73 tff(908,plain,
% 0.57/0.73 (product(e_3, e_5, e_1)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[907, 871, 867, 864])).
% 0.57/0.73 tff(909,assumption,(product(e_3, e_5, e_1)), introduced(assumption)).
% 0.57/0.73 tff(910,assumption,(product(e_3, e_2, e_1)), introduced(assumption)).
% 0.57/0.73 tff(911,plain,
% 0.57/0.73 ((~equalish(e_5, e_2)) <=> (~equalish(e_5, e_2))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(912,axiom,(~equalish(e_5, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_is_not_e_2')).
% 0.57/0.73 tff(913,plain,
% 0.57/0.73 (~equalish(e_5, e_2)),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[912, 911])).
% 0.57/0.73 tff(914,plain,
% 0.57/0.73 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_3, e_5, e_1)) | (~product(e_3, 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_5, e_2) | (~product(e_3, e_5, e_1)) | (~product(e_3, e_2, e_1)))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(915,plain,
% 0.57/0.73 ((equalish(e_5, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_5, e_1))) <=> (equalish(e_5, e_2) | (~product(e_3, e_5, e_1)) | (~product(e_3, e_2, e_1)))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(916,plain,
% 0.57/0.73 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_5, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_3, e_5, e_1)) | (~product(e_3, e_2, e_1))))),
% 0.57/0.73 inference(monotonicity,[status(thm)],[915])).
% 0.57/0.73 tff(917,plain,
% 0.57/0.73 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_5, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_2) | (~product(e_3, e_5, e_1)) | (~product(e_3, e_2, e_1)))),
% 0.57/0.73 inference(transitivity,[status(thm)],[916, 914])).
% 0.57/0.73 tff(918,plain,
% 0.57/0.73 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_5, e_1)))),
% 0.57/0.73 inference(quant_inst,[status(thm)],[])).
% 0.57/0.73 tff(919,plain,
% 0.57/0.73 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_2) | (~product(e_3, e_5, e_1)) | (~product(e_3, e_2, e_1))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[918, 917])).
% 0.57/0.73 tff(920,plain,
% 0.57/0.73 ($false),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[919, 913, 43, 910, 909])).
% 0.57/0.73 tff(921,plain,((~product(e_3, e_5, e_1)) | (~product(e_3, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.73 tff(922,plain,
% 0.57/0.73 (~product(e_3, e_2, e_1)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[921, 908])).
% 0.57/0.73 tff(923,plain,
% 0.57/0.73 (product(e_4, e_3, e_1)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[593, 858])).
% 0.57/0.73 tff(924,plain,
% 0.57/0.73 (~product(e_3, e_4, e_1)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[618, 923])).
% 0.57/0.73 tff(925,plain,
% 0.57/0.73 (~product(e_3, e_4, e_2)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[790, 871])).
% 0.57/0.73 tff(926,plain,
% 0.57/0.73 (product(e_3, e_4, e_5)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[731, 925, 924])).
% 0.57/0.73 tff(927,plain,
% 0.57/0.73 (~product(e_3, e_2, e_5)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[741, 926])).
% 0.57/0.73 tff(928,plain,
% 0.57/0.73 ($false),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[768, 927, 922, 864])).
% 0.57/0.73 tff(929,plain,((~product(e_4, e_5, e_2)) | product(e_5, e_4, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.57/0.73 tff(930,plain,
% 0.57/0.73 (~product(e_4, e_5, e_2)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[929, 777])).
% 0.57/0.73 tff(931,plain,
% 0.57/0.73 (product(e_4, e_5, e_3)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[438, 930, 559])).
% 0.57/0.73 tff(932,assumption,(~product(e_3, e_2, e_5)), introduced(assumption)).
% 0.57/0.73 tff(933,assumption,(product(e_3, e_1, e_4)), introduced(assumption)).
% 0.57/0.73 tff(934,plain,
% 0.57/0.73 (((~![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)))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(935,plain,
% 0.57/0.73 ((~![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)))),
% 0.57/0.74 inference(quant_inst,[status(thm)],[])).
% 0.57/0.74 tff(936,plain,
% 0.57/0.74 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_2, e_4))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[935, 934])).
% 0.57/0.74 tff(937,plain,
% 0.57/0.74 ($false),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[936, 46, 43, 933, 466])).
% 0.57/0.74 tff(938,plain,((~product(e_3, e_2, e_4)) | (~product(e_3, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.74 tff(939,plain,
% 0.57/0.74 (~product(e_3, e_1, e_4)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[938, 466])).
% 0.57/0.74 tff(940,plain,
% 0.57/0.74 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_3, e_3)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(941,plain,
% 0.57/0.74 (((~product(e_3, e_4, e_1)) | product(e_3, e_1, e_4) | (~product(e_4, e_3, e_3))) <=> (product(e_3, e_1, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_3, e_3)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(942,plain,
% 0.57/0.74 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_4, e_1)) | product(e_3, e_1, e_4) | (~product(e_4, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_3, e_3))))),
% 0.57/0.74 inference(monotonicity,[status(thm)],[941])).
% 0.57/0.74 tff(943,plain,
% 0.57/0.74 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_4, e_1)) | product(e_3, e_1, e_4) | (~product(e_4, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_3, e_3)))),
% 0.57/0.74 inference(transitivity,[status(thm)],[942, 940])).
% 0.57/0.74 tff(944,plain,
% 0.57/0.74 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_4, e_1)) | product(e_3, e_1, e_4) | (~product(e_4, e_3, e_3)))),
% 0.57/0.74 inference(quant_inst,[status(thm)],[])).
% 0.57/0.74 tff(945,plain,
% 0.57/0.74 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_3, e_3))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[944, 943])).
% 0.57/0.74 tff(946,plain,
% 0.57/0.74 (~product(e_4, e_3, e_3)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[945, 72, 939, 596])).
% 0.57/0.74 tff(947,plain,
% 0.57/0.74 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_3, e_4)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(948,plain,
% 0.57/0.74 (((~product(e_3, e_4, e_1)) | product(e_4, e_1, e_4) | (~product(e_4, e_3, e_4))) <=> (product(e_4, e_1, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_3, e_4)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(949,plain,
% 0.57/0.74 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_4, e_1)) | product(e_4, e_1, e_4) | (~product(e_4, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_3, e_4))))),
% 0.57/0.74 inference(monotonicity,[status(thm)],[948])).
% 0.57/0.74 tff(950,plain,
% 0.57/0.74 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_4, e_1)) | product(e_4, e_1, e_4) | (~product(e_4, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_3, e_4)))),
% 0.57/0.74 inference(transitivity,[status(thm)],[949, 947])).
% 0.57/0.74 tff(951,plain,
% 0.57/0.74 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_4, e_1)) | product(e_4, e_1, e_4) | (~product(e_4, e_3, e_4)))),
% 0.57/0.74 inference(quant_inst,[status(thm)],[])).
% 0.57/0.74 tff(952,plain,
% 0.57/0.74 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_3, e_4))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[951, 950])).
% 0.57/0.74 tff(953,plain,
% 0.57/0.74 (~product(e_4, e_3, e_4)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[952, 72, 596, 648])).
% 0.57/0.74 tff(954,plain,
% 0.57/0.74 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_4, e_3, e_2)) | (~product(e_3, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_4) | (~product(e_4, e_3, e_2)) | (~product(e_3, e_4, e_1)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(955,plain,
% 0.57/0.74 (((~product(e_3, e_4, e_1)) | product(e_2, e_1, e_4) | (~product(e_4, e_3, e_2))) <=> (product(e_2, e_1, e_4) | (~product(e_4, e_3, e_2)) | (~product(e_3, e_4, e_1)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(956,plain,
% 0.57/0.74 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_4, e_1)) | product(e_2, e_1, e_4) | (~product(e_4, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_4, e_3, e_2)) | (~product(e_3, e_4, e_1))))),
% 0.57/0.74 inference(monotonicity,[status(thm)],[955])).
% 0.57/0.74 tff(957,plain,
% 0.57/0.74 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_4, e_1)) | product(e_2, e_1, e_4) | (~product(e_4, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_4) | (~product(e_4, e_3, e_2)) | (~product(e_3, e_4, e_1)))),
% 0.57/0.74 inference(transitivity,[status(thm)],[956, 954])).
% 0.57/0.74 tff(958,plain,
% 0.57/0.74 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_4, e_1)) | product(e_2, e_1, e_4) | (~product(e_4, e_3, e_2)))),
% 0.57/0.74 inference(quant_inst,[status(thm)],[])).
% 0.57/0.74 tff(959,plain,
% 0.57/0.74 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_4) | (~product(e_4, e_3, e_2)) | (~product(e_3, e_4, e_1))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[958, 957])).
% 0.57/0.74 tff(960,plain,
% 0.57/0.74 (~product(e_4, e_3, e_2)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[959, 72, 259, 596])).
% 0.57/0.74 tff(961,plain,
% 0.57/0.74 (~product(e_4, e_3, e_1)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[618, 596])).
% 0.57/0.74 tff(962,plain,
% 0.57/0.74 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_4) | product(e_4, e_3, e_1) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_5))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_4) | product(e_4, e_3, e_1) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_5))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(963,plain,
% 0.57/0.74 (((~group_element(e_4)) | product(e_4, e_3, e_5) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1) | (~group_element(e_3))) <=> ((~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_4) | product(e_4, e_3, e_1) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_5))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(964,plain,
% 0.57/0.74 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_4)) | product(e_4, e_3, e_5) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_4) | product(e_4, e_3, e_1) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_5)))),
% 0.57/0.74 inference(monotonicity,[status(thm)],[963])).
% 0.57/0.74 tff(965,plain,
% 0.57/0.74 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_4)) | product(e_4, e_3, e_5) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_4) | product(e_4, e_3, e_1) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_5))),
% 0.57/0.74 inference(transitivity,[status(thm)],[964, 962])).
% 0.57/0.74 tff(966,plain,
% 0.57/0.74 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_4)) | product(e_4, e_3, e_5) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1) | (~group_element(e_3)))),
% 0.57/0.74 inference(quant_inst,[status(thm)],[])).
% 0.57/0.74 tff(967,plain,
% 0.57/0.74 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_4) | product(e_4, e_3, e_1) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_5)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[966, 965])).
% 0.57/0.74 tff(968,plain,
% 0.57/0.74 (product(e_4, e_3, e_3) | product(e_4, e_3, e_5)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[967, 373, 430, 269, 961, 960, 953])).
% 0.57/0.74 tff(969,plain,
% 0.57/0.74 (product(e_4, e_3, e_5)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[968, 946])).
% 0.57/0.74 tff(970,plain,
% 0.57/0.74 (~product(e_2, e_3, e_4)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[491, 466])).
% 0.57/0.74 tff(971,plain,
% 0.57/0.74 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_3) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_3) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_1)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(972,plain,
% 0.57/0.74 (((~product(e_2, e_3, e_1)) | product(e_4, e_1, e_3) | (~product(e_3, e_2, e_4))) <=> (product(e_4, e_1, e_3) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_1)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(973,plain,
% 0.57/0.74 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_1)) | product(e_4, e_1, e_3) | (~product(e_3, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_3) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_1))))),
% 0.57/0.74 inference(monotonicity,[status(thm)],[972])).
% 0.57/0.74 tff(974,plain,
% 0.57/0.74 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_1)) | product(e_4, e_1, e_3) | (~product(e_3, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_3) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_1)))),
% 0.57/0.74 inference(transitivity,[status(thm)],[973, 971])).
% 0.57/0.74 tff(975,plain,
% 0.57/0.74 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_1)) | product(e_4, e_1, e_3) | (~product(e_3, e_2, e_4)))),
% 0.57/0.74 inference(quant_inst,[status(thm)],[])).
% 0.57/0.74 tff(976,plain,
% 0.57/0.74 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_3) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_1))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[975, 974])).
% 0.57/0.74 tff(977,plain,
% 0.57/0.74 ($false),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[976, 72, 820, 466, 657])).
% 0.57/0.74 tff(978,plain,((~product(e_2, e_3, e_1)) | (~product(e_3, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.74 tff(979,plain,
% 0.57/0.74 (~product(e_2, e_3, e_1)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[978, 466])).
% 0.57/0.74 tff(980,plain,
% 0.57/0.74 (product(e_2, e_3, e_5)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[843, 979, 62, 970])).
% 0.57/0.74 tff(981,plain,
% 0.57/0.74 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_4, e_3, e_5)) | (~product(e_2, e_3, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_4, e_3, e_5)) | (~product(e_2, e_3, e_5)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(982,plain,
% 0.57/0.74 ((equalish(e_4, e_2) | (~product(e_2, e_3, e_5)) | (~product(e_4, e_3, e_5))) <=> (equalish(e_4, e_2) | (~product(e_4, e_3, e_5)) | (~product(e_2, e_3, e_5)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(983,plain,
% 0.57/0.74 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_2, e_3, e_5)) | (~product(e_4, e_3, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_4, e_3, e_5)) | (~product(e_2, e_3, e_5))))),
% 0.57/0.74 inference(monotonicity,[status(thm)],[982])).
% 0.57/0.74 tff(984,plain,
% 0.57/0.74 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_2, e_3, e_5)) | (~product(e_4, e_3, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_4, e_3, e_5)) | (~product(e_2, e_3, e_5)))),
% 0.57/0.74 inference(transitivity,[status(thm)],[983, 981])).
% 0.57/0.74 tff(985,plain,
% 0.57/0.74 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_2, e_3, e_5)) | (~product(e_4, e_3, e_5)))),
% 0.57/0.74 inference(quant_inst,[status(thm)],[])).
% 0.57/0.74 tff(986,plain,
% 0.57/0.74 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_4, e_3, e_5)) | (~product(e_2, e_3, e_5))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[985, 984])).
% 0.57/0.74 tff(987,plain,
% 0.57/0.74 ($false),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[986, 652, 12, 980, 969])).
% 0.57/0.74 tff(988,plain,((~product(e_3, e_2, e_4)) | (~product(e_3, e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.74 tff(989,plain,
% 0.57/0.74 (~product(e_3, e_2, e_4)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[988, 596])).
% 0.57/0.74 tff(990,plain,
% 0.57/0.74 (product(e_3, e_2, e_1)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[768, 989, 932])).
% 0.57/0.74 tff(991,plain,
% 0.57/0.74 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_3, 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_4) | (~product(e_3, e_4, e_1)) | (~product(e_3, e_2, e_1)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(992,plain,
% 0.57/0.74 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_3, e_2, e_1)))),
% 0.57/0.74 inference(quant_inst,[status(thm)],[])).
% 0.57/0.74 tff(993,plain,
% 0.57/0.74 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_3, e_2, e_1))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[992, 991])).
% 0.57/0.74 tff(994,plain,
% 0.57/0.74 ($false),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[993, 823, 43, 596, 990])).
% 0.57/0.74 tff(995,plain,((~product(e_3, e_4, e_1)) | product(e_3, e_2, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.57/0.74 tff(996,plain,
% 0.57/0.74 (~product(e_3, e_4, e_1)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[995, 855])).
% 0.57/0.74 tff(997,plain,
% 0.57/0.74 (~product(e_1, e_2, e_4)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[593, 584])).
% 0.57/0.74 tff(998,plain,
% 0.57/0.74 (product(e_1, e_2, e_5)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[320, 997])).
% 0.57/0.74 tff(999,plain,
% 0.57/0.74 (product(e_3, e_5, e_2)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[581, 998])).
% 0.57/0.74 tff(1000,plain,
% 0.57/0.74 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_4) | (~product(e_3, e_4, e_2)) | (~product(e_3, e_5, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_4) | (~product(e_3, e_4, e_2)) | (~product(e_3, e_5, e_2)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(1001,plain,
% 0.57/0.74 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_4) | (~product(e_3, e_4, e_2)) | (~product(e_3, e_5, e_2)))),
% 0.57/0.74 inference(quant_inst,[status(thm)],[])).
% 0.57/0.74 tff(1002,plain,
% 0.57/0.74 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_4) | (~product(e_3, e_4, e_2)) | (~product(e_3, e_5, e_2))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[1001, 1000])).
% 0.57/0.74 tff(1003,plain,
% 0.57/0.74 ($false),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1002, 327, 43, 701, 565])).
% 0.57/0.74 tff(1004,plain,((~product(e_3, e_5, e_2)) | (~product(e_3, e_4, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.74 tff(1005,plain,
% 0.57/0.74 (~product(e_3, e_4, e_2)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1004, 999])).
% 0.57/0.74 tff(1006,plain,
% 0.57/0.74 (product(e_3, e_4, e_5)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[731, 1005, 996])).
% 0.57/0.74 tff(1007,plain,
% 0.57/0.74 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_4, e_5)) | product(e_4, e_5, e_4) | (~product(e_4, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_4, e_5)) | product(e_4, e_5, e_4) | (~product(e_4, e_3, e_4)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(1008,plain,
% 0.57/0.74 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_4, e_5)) | product(e_4, e_5, e_4) | (~product(e_4, e_3, e_4)))),
% 0.57/0.74 inference(quant_inst,[status(thm)],[])).
% 0.57/0.74 tff(1009,plain,
% 0.57/0.74 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_4, e_5)) | product(e_4, e_5, e_4) | (~product(e_4, e_3, e_4))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[1008, 1007])).
% 0.57/0.74 tff(1010,plain,
% 0.57/0.74 (~product(e_4, e_3, e_4)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[1009, 72, 1006, 413])).
% 0.57/0.74 tff(1011,plain,
% 0.57/0.74 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_5, e_5, e_4) | (~product(e_3, e_4, e_5)) | (~product(e_4, e_3, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_5, e_5, e_4) | (~product(e_3, e_4, e_5)) | (~product(e_4, e_3, e_5)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(1012,plain,
% 0.57/0.75 (((~product(e_3, e_4, e_5)) | product(e_5, e_5, e_4) | (~product(e_4, e_3, e_5))) <=> (product(e_5, e_5, e_4) | (~product(e_3, e_4, e_5)) | (~product(e_4, e_3, e_5)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(1013,plain,
% 0.57/0.75 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_4, e_5)) | product(e_5, e_5, e_4) | (~product(e_4, e_3, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_5, e_5, e_4) | (~product(e_3, e_4, e_5)) | (~product(e_4, e_3, e_5))))),
% 0.57/0.75 inference(monotonicity,[status(thm)],[1012])).
% 0.57/0.75 tff(1014,plain,
% 0.57/0.75 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_4, e_5)) | product(e_5, e_5, e_4) | (~product(e_4, e_3, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_5, e_5, e_4) | (~product(e_3, e_4, e_5)) | (~product(e_4, e_3, e_5)))),
% 0.57/0.75 inference(transitivity,[status(thm)],[1013, 1011])).
% 0.57/0.75 tff(1015,plain,
% 0.57/0.75 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_4, e_5)) | product(e_5, e_5, e_4) | (~product(e_4, e_3, e_5)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(1016,plain,
% 0.57/0.75 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_5, e_5, e_4) | (~product(e_3, e_4, e_5)) | (~product(e_4, e_3, e_5))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[1015, 1014])).
% 0.57/0.75 tff(1017,plain,
% 0.57/0.75 (~product(e_4, e_3, e_5)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[1016, 72, 1006, 673])).
% 0.57/0.75 tff(1018,assumption,(product(e_4, e_3, e_3)), introduced(assumption)).
% 0.57/0.75 tff(1019,plain,
% 0.57/0.75 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_5, e_3, e_3) | (~product(e_3, e_4, e_5)) | (~product(e_4, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_5, e_3, e_3) | (~product(e_3, e_4, e_5)) | (~product(e_4, e_3, e_3)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(1020,plain,
% 0.57/0.75 (((~product(e_4, e_3, e_3)) | product(e_5, e_3, e_3) | (~product(e_3, e_4, e_5))) <=> (product(e_5, e_3, e_3) | (~product(e_3, e_4, e_5)) | (~product(e_4, e_3, e_3)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(1021,plain,
% 0.57/0.75 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_3, e_3)) | product(e_5, e_3, e_3) | (~product(e_3, e_4, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_5, e_3, e_3) | (~product(e_3, e_4, e_5)) | (~product(e_4, e_3, e_3))))),
% 0.57/0.75 inference(monotonicity,[status(thm)],[1020])).
% 0.57/0.75 tff(1022,plain,
% 0.57/0.75 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_3, e_3)) | product(e_5, e_3, e_3) | (~product(e_3, e_4, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_5, e_3, e_3) | (~product(e_3, e_4, e_5)) | (~product(e_4, e_3, e_3)))),
% 0.57/0.75 inference(transitivity,[status(thm)],[1021, 1019])).
% 0.57/0.75 tff(1023,plain,
% 0.57/0.75 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_3, e_3)) | product(e_5, e_3, e_3) | (~product(e_3, e_4, e_5)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(1024,plain,
% 0.57/0.75 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_5, e_3, e_3) | (~product(e_3, e_4, e_5)) | (~product(e_4, e_3, e_3))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[1023, 1022])).
% 0.57/0.75 tff(1025,plain,
% 0.57/0.75 ($false),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[1024, 72, 448, 733, 1018])).
% 0.57/0.75 tff(1026,plain,((~product(e_4, e_3, e_3)) | (~product(e_3, e_4, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.75 tff(1027,plain,
% 0.57/0.75 (~product(e_4, e_3, e_3)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[1026, 1006])).
% 0.57/0.75 tff(1028,plain,
% 0.57/0.75 (product(e_4, e_3, e_2)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[967, 373, 430, 269, 584, 1027, 1017, 1010])).
% 0.57/0.75 tff(1029,assumption,(product(e_4, e_3, e_2)), introduced(assumption)).
% 0.57/0.75 tff(1030,plain,
% 0.57/0.75 (((~![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_4, e_1, e_2)) | (~product(e_4, 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_4, e_1, e_2)) | (~product(e_4, e_3, e_2)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(1031,plain,
% 0.57/0.75 ((~![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_4, e_1, e_2)) | (~product(e_4, e_3, e_2)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(1032,plain,
% 0.57/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_3, e_2))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[1031, 1030])).
% 0.57/0.75 tff(1033,plain,
% 0.57/0.75 ($false),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[1032, 15, 43, 630, 1029])).
% 0.57/0.75 tff(1034,plain,((~product(e_4, e_3, e_2)) | (~product(e_4, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.75 tff(1035,plain,
% 0.57/0.75 (~product(e_4, e_1, e_2)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[1034, 1028])).
% 0.57/0.75 tff(1036,plain,
% 0.57/0.75 (product(e_4, e_1, e_5)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[665, 1035])).
% 0.57/0.75 tff(1037,plain,
% 0.57/0.75 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_1, e_2, e_5)) | (~product(e_1, e_4, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_1, e_2, e_5)) | (~product(e_1, e_4, e_5)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(1038,plain,
% 0.57/0.75 ((equalish(e_2, e_4) | (~product(e_1, e_4, e_5)) | (~product(e_1, e_2, e_5))) <=> (equalish(e_2, e_4) | (~product(e_1, e_2, e_5)) | (~product(e_1, e_4, e_5)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(1039,plain,
% 0.57/0.75 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_1, e_4, e_5)) | (~product(e_1, e_2, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_1, e_2, e_5)) | (~product(e_1, e_4, e_5))))),
% 0.57/0.75 inference(monotonicity,[status(thm)],[1038])).
% 0.57/0.75 tff(1040,plain,
% 0.57/0.75 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_1, e_4, e_5)) | (~product(e_1, e_2, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_1, e_2, e_5)) | (~product(e_1, e_4, e_5)))),
% 0.57/0.75 inference(transitivity,[status(thm)],[1039, 1037])).
% 0.57/0.75 tff(1041,plain,
% 0.57/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_1, e_4, e_5)) | (~product(e_1, e_2, e_5)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(1042,plain,
% 0.57/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_1, e_2, e_5)) | (~product(e_1, e_4, e_5))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[1041, 1040])).
% 0.57/0.75 tff(1043,plain,
% 0.57/0.75 ($false),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[1042, 823, 43, 674, 2])).
% 0.57/0.75 tff(1044,plain,((~product(e_1, e_2, e_5)) | (~product(e_1, e_4, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.75 tff(1045,plain,
% 0.57/0.75 (~product(e_1, e_4, e_5)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[1044, 998])).
% 0.57/0.75 tff(1046,assumption,(~product(e_4, e_1, e_2)), introduced(assumption)).
% 0.57/0.75 tff(1047,assumption,(~product(e_3, e_1, e_2)), introduced(assumption)).
% 0.57/0.75 tff(1048,assumption,(product(e_3, e_1, e_3)), introduced(assumption)).
% 0.57/0.75 tff(1049,plain,
% 0.57/0.75 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(1050,plain,
% 0.57/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(1051,plain,
% 0.57/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[1050, 1049])).
% 0.57/0.75 tff(1052,plain,
% 0.57/0.75 ($false),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[1051, 755, 12, 296, 1048])).
% 0.57/0.75 tff(1053,plain,((~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.75 tff(1054,plain,
% 0.57/0.75 (~product(e_3, e_1, e_3)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[1053, 293])).
% 0.57/0.75 tff(1055,assumption,(product(e_3, e_1, e_1)), introduced(assumption)).
% 0.57/0.75 tff(1056,plain,
% 0.57/0.75 (((~![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)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(1057,plain,
% 0.57/0.75 ((~![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)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(1058,plain,
% 0.57/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[1057, 1056])).
% 0.57/0.75 tff(1059,plain,
% 0.57/0.75 ($false),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[1058, 15, 12, 181, 1055])).
% 0.57/0.75 tff(1060,plain,((~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.75 tff(1061,plain,
% 0.57/0.75 (~product(e_3, e_1, e_1)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[1060, 33])).
% 0.57/0.75 tff(1062,plain,
% 0.57/0.75 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_5) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | product(e_3, e_1, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_5) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | product(e_3, e_1, e_3))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(1063,plain,
% 0.57/0.75 (((~group_element(e_3)) | product(e_3, e_1, e_5) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1))) <=> ((~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_5) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | product(e_3, e_1, e_3))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(1064,plain,
% 0.57/0.75 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_1, e_5) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_5) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | product(e_3, e_1, e_3)))),
% 0.57/0.75 inference(monotonicity,[status(thm)],[1063])).
% 0.57/0.75 tff(1065,plain,
% 0.57/0.75 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_1, e_5) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_5) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | product(e_3, e_1, e_3))),
% 0.57/0.75 inference(transitivity,[status(thm)],[1064, 1062])).
% 0.57/0.75 tff(1066,plain,
% 0.57/0.75 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_1, e_5) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(1067,plain,
% 0.57/0.75 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_5) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | product(e_3, e_1, e_3)),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[1066, 1065])).
% 0.57/0.75 tff(1068,plain,
% 0.57/0.75 (product(e_3, e_1, e_4) | product(e_3, e_1, e_2)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[1067, 272, 373, 269, 387, 1061, 1054])).
% 0.57/0.75 tff(1069,plain,
% 0.57/0.75 (product(e_3, e_1, e_4)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[1068, 1047])).
% 0.57/0.75 tff(1070,plain,
% 0.57/0.75 (~product(e_3, e_2, e_4)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[938, 1069])).
% 0.57/0.75 tff(1071,plain,
% 0.57/0.75 (product(e_3, e_2, e_1)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[768, 1070, 932])).
% 0.57/0.75 tff(1072,plain,
% 0.57/0.75 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_4)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(1073,plain,
% 0.57/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_4)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(1074,plain,
% 0.57/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_4))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[1073, 1072])).
% 0.57/0.75 tff(1075,plain,
% 0.57/0.75 ($false),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[1074, 191, 12, 933, 637])).
% 0.57/0.75 tff(1076,plain,((~product(e_4, e_1, e_4)) | (~product(e_3, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.75 tff(1077,plain,
% 0.57/0.75 (~product(e_4, e_1, e_4)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[1076, 1069])).
% 0.57/0.76 tff(1078,plain,
% 0.57/0.76 (product(e_4, e_1, e_5)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[664, 1077, 1046])).
% 0.57/0.76 tff(1079,plain,
% 0.57/0.76 (~product(e_2, e_3, e_4)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[775, 72, 1046, 910])).
% 0.57/0.76 tff(1080,plain,
% 0.57/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_2) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_2, e_1)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(1081,plain,
% 0.57/0.76 (((~product(e_3, e_2, e_1)) | product(e_3, e_1, e_2) | (~product(e_2, e_3, e_3))) <=> (product(e_3, e_1, e_2) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_2, e_1)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(1082,plain,
% 0.57/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_1)) | product(e_3, e_1, e_2) | (~product(e_2, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_2, e_1))))),
% 0.57/0.76 inference(monotonicity,[status(thm)],[1081])).
% 0.57/0.76 tff(1083,plain,
% 0.57/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_1)) | product(e_3, e_1, e_2) | (~product(e_2, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_2) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_2, e_1)))),
% 0.57/0.76 inference(transitivity,[status(thm)],[1082, 1080])).
% 0.57/0.76 tff(1084,plain,
% 0.57/0.76 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_1)) | product(e_3, e_1, e_2) | (~product(e_2, e_3, e_3)))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(1085,plain,
% 0.57/0.76 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_2) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_2, e_1))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[1084, 1083])).
% 0.57/0.76 tff(1086,plain,
% 0.57/0.76 (~product(e_2, e_3, e_3)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[1085, 72, 1047, 910])).
% 0.57/0.76 tff(1087,plain,
% 0.57/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_1)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(1088,plain,
% 0.57/0.76 (((~product(e_1, e_1, e_1)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_2))) <=> ((~product(e_1, e_1, e_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_1)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(1089,plain,
% 0.57/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_1)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_1))))),
% 0.57/0.76 inference(monotonicity,[status(thm)],[1088])).
% 0.57/0.76 tff(1090,plain,
% 0.57/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_1)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_1)))),
% 0.57/0.76 inference(transitivity,[status(thm)],[1089, 1087])).
% 0.57/0.76 tff(1091,plain,
% 0.57/0.76 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_1)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_2)))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(1092,plain,
% 0.57/0.76 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_1))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[1091, 1090])).
% 0.57/0.76 tff(1093,plain,
% 0.57/0.76 (~product(e_1, e_1, e_2)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[1092, 72, 187, 33])).
% 0.57/0.76 tff(1094,plain,
% 0.57/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(1095,plain,
% 0.57/0.76 (((~product(e_3, e_2, e_1)) | product(e_1, e_1, e_2) | (~product(e_2, e_3, e_1))) <=> (product(e_1, e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(1096,plain,
% 0.57/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_1)) | product(e_1, e_1, e_2) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1))))),
% 0.57/0.76 inference(monotonicity,[status(thm)],[1095])).
% 0.57/0.76 tff(1097,plain,
% 0.57/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_1)) | product(e_1, e_1, e_2) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.57/0.76 inference(transitivity,[status(thm)],[1096, 1094])).
% 0.57/0.76 tff(1098,plain,
% 0.57/0.76 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_1)) | product(e_1, e_1, e_2) | (~product(e_2, e_3, e_1)))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(1099,plain,
% 0.57/0.76 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[1098, 1097])).
% 0.57/0.76 tff(1100,plain,
% 0.57/0.76 (~product(e_2, e_3, e_1)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[1099, 72, 1093, 910])).
% 0.57/0.76 tff(1101,plain,
% 0.57/0.76 (product(e_2, e_3, e_5)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[843, 1100, 1086, 1079])).
% 0.57/0.76 tff(1102,assumption,(product(e_1, e_3, e_5)), introduced(assumption)).
% 0.57/0.76 tff(1103,plain,
% 0.57/0.76 (((~![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_3, e_5)) | (~product(e_1, e_3, e_5)))) <=> ((~![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_3, e_5)) | (~product(e_1, e_3, e_5)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(1104,plain,
% 0.57/0.76 ((~![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_3, e_5)) | (~product(e_1, e_3, e_5)))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(1105,plain,
% 0.57/0.76 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_3, e_5)) | (~product(e_1, e_3, e_5))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[1104, 1103])).
% 0.57/0.76 tff(1106,plain,
% 0.57/0.76 ($false),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[1105, 141, 12, 810, 1102])).
% 0.57/0.76 tff(1107,plain,((~product(e_1, e_3, e_5)) | (~product(e_2, e_3, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.76 tff(1108,plain,
% 0.57/0.76 (~product(e_1, e_3, e_5)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[1107, 1101])).
% 0.57/0.76 tff(1109,plain,
% 0.57/0.76 (~product(e_1, e_4, e_5)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[683, 675])).
% 0.57/0.76 tff(1110,plain,
% 0.57/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_1, e_5)) | product(e_5, e_4, e_4) | (~product(e_1, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_4, e_1, e_5)) | product(e_5, e_4, e_4) | (~product(e_1, e_4, e_4)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(1111,plain,
% 0.57/0.76 (((~product(e_1, e_4, e_4)) | product(e_5, e_4, e_4) | (~product(e_4, e_1, e_5))) <=> ((~product(e_4, e_1, e_5)) | product(e_5, e_4, e_4) | (~product(e_1, e_4, e_4)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(1112,plain,
% 0.57/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_4, e_4)) | product(e_5, e_4, e_4) | (~product(e_4, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_1, e_5)) | product(e_5, e_4, e_4) | (~product(e_1, e_4, e_4))))),
% 0.57/0.76 inference(monotonicity,[status(thm)],[1111])).
% 0.57/0.76 tff(1113,plain,
% 0.57/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_4, e_4)) | product(e_5, e_4, e_4) | (~product(e_4, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_4, e_1, e_5)) | product(e_5, e_4, e_4) | (~product(e_1, e_4, e_4)))),
% 0.57/0.76 inference(transitivity,[status(thm)],[1112, 1110])).
% 0.57/0.76 tff(1114,plain,
% 0.57/0.76 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_4, e_4)) | product(e_5, e_4, e_4) | (~product(e_4, e_1, e_5)))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(1115,plain,
% 0.57/0.76 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_4, e_1, e_5)) | product(e_5, e_4, e_4) | (~product(e_1, e_4, e_4))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[1114, 1113])).
% 0.57/0.76 tff(1116,plain,
% 0.57/0.76 ($false),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[1115, 72, 675, 541, 685])).
% 0.57/0.76 tff(1117,plain,((~product(e_1, e_4, e_4)) | (~product(e_4, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.76 tff(1118,plain,
% 0.57/0.76 (~product(e_1, e_4, e_4)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[1117, 675])).
% 0.57/0.76 tff(1119,plain,
% 0.57/0.76 (~product(e_3, e_5, e_1)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[921, 910])).
% 0.57/0.76 tff(1120,plain,
% 0.57/0.76 (~product(e_1, e_4, e_3)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[891, 1119, 675])).
% 0.57/0.76 tff(1121,plain,
% 0.57/0.76 (product(e_1, e_4, e_2)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[698, 1120, 1118, 1109])).
% 0.57/0.76 tff(1122,plain,
% 0.57/0.76 (~product(e_5, e_4, e_2)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[884, 1121])).
% 0.57/0.76 tff(1123,plain,
% 0.57/0.76 (~product(e_5, e_4, e_3)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[463, 1079, 387])).
% 0.57/0.76 tff(1124,plain,
% 0.57/0.76 (product(e_5, e_4, e_1)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[555, 1123, 1122])).
% 0.57/0.76 tff(1125,plain,
% 0.57/0.76 (~product(e_4, e_5, e_1)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[531, 72, 610, 1124])).
% 0.57/0.76 tff(1126,plain,
% 0.57/0.76 (~product(e_4, e_5, e_2)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[798, 72, 259, 1124])).
% 0.57/0.76 tff(1127,plain,
% 0.57/0.76 (product(e_4, e_5, e_3)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[438, 1126, 1125])).
% 0.57/0.76 tff(1128,plain,
% 0.57/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_4, e_1)) | (~product(e_4, e_5, e_3)) | product(e_1, e_3, e_5))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_5, e_4, e_1)) | (~product(e_4, e_5, e_3)) | product(e_1, e_3, e_5))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(1129,plain,
% 0.60/0.76 (((~product(e_4, e_5, e_3)) | product(e_1, e_3, e_5) | (~product(e_5, e_4, e_1))) <=> ((~product(e_5, e_4, e_1)) | (~product(e_4, e_5, e_3)) | product(e_1, e_3, e_5))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(1130,plain,
% 0.60/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_5, e_3)) | product(e_1, e_3, e_5) | (~product(e_5, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_4, e_1)) | (~product(e_4, e_5, e_3)) | product(e_1, e_3, e_5)))),
% 0.60/0.76 inference(monotonicity,[status(thm)],[1129])).
% 0.60/0.76 tff(1131,plain,
% 0.60/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_5, e_3)) | product(e_1, e_3, e_5) | (~product(e_5, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_5, e_4, e_1)) | (~product(e_4, e_5, e_3)) | product(e_1, e_3, e_5))),
% 0.60/0.76 inference(transitivity,[status(thm)],[1130, 1128])).
% 0.60/0.76 tff(1132,plain,
% 0.60/0.76 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_5, e_3)) | product(e_1, e_3, e_5) | (~product(e_5, e_4, e_1)))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(1133,plain,
% 0.60/0.76 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_5, e_4, e_1)) | (~product(e_4, e_5, e_3)) | product(e_1, e_3, e_5)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[1132, 1131])).
% 0.60/0.76 tff(1134,plain,
% 0.60/0.76 ($false),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[1133, 72, 1124, 1127, 1108])).
% 0.60/0.76 tff(1135,plain,((~product(e_3, e_2, e_1)) | product(e_3, e_1, e_5) | (~product(e_4, e_1, e_5)) | product(e_3, e_1, e_2) | product(e_4, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.76 tff(1136,plain,
% 0.60/0.76 ($false),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[1135, 1078, 1071, 387, 1047, 1046])).
% 0.60/0.76 tff(1137,plain,(product(e_3, e_1, e_2) | product(e_3, e_1, e_5) | product(e_4, e_1, e_2) | product(e_3, e_2, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.76 tff(1138,plain,
% 0.60/0.76 (product(e_3, e_1, e_2) | product(e_4, e_1, e_2) | product(e_3, e_2, e_5)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[1137, 386])).
% 0.60/0.76 tff(1139,plain,
% 0.60/0.76 (product(e_3, e_1, e_2)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[1138, 1035, 855])).
% 0.60/0.76 tff(1140,assumption,(cycle(e_4, e_3)), introduced(assumption)).
% 0.60/0.76 tff(1141,plain,
% 0.60/0.76 (^[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))))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(1142,plain,
% 0.60/0.76 (![W: $i, Z: $i, Y: $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)))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[1141])).
% 0.60/0.76 tff(1143,plain,
% 0.60/0.76 (![W: $i, Z: $i, Y: $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)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(1144,plain,
% 0.60/0.76 (^[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)))))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(1145,plain,
% 0.60/0.76 (![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)))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[1144])).
% 0.60/0.76 tff(1146,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')).
% 0.60/0.76 tff(1147,plain,
% 0.60/0.76 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[1146, 1145])).
% 0.60/0.76 tff(1148,plain,
% 0.60/0.76 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[1147, 1143])).
% 0.60/0.76 tff(1149,plain,(
% 0.60/0.76 ![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.60/0.76 inference(skolemize,[status(sab)],[1148])).
% 0.60/0.76 tff(1150,plain,
% 0.60/0.76 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[1149, 1142])).
% 0.60/0.76 tff(1151,plain,
% 0.60/0.76 (cycle(e_5, e_0) <=> cycle(e_5, e_0)),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(1152,axiom,(cycle(e_5, e_0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cycle3')).
% 0.60/0.76 tff(1153,plain,
% 0.60/0.76 (cycle(e_5, e_0)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[1152, 1151])).
% 0.60/0.76 tff(1154,plain,
% 0.60/0.76 (next(e_4, e_5) <=> next(e_4, e_5)),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(1155,axiom,(next(e_4, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_then_e_5')).
% 0.60/0.76 tff(1156,plain,
% 0.60/0.76 (next(e_4, e_5)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[1155, 1154])).
% 0.60/0.76 tff(1157,plain,
% 0.60/0.76 (next(e_0, e_1) <=> next(e_0, e_1)),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(1158,axiom,(next(e_0, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_0_then_e_1')).
% 0.60/0.76 tff(1159,plain,
% 0.60/0.76 (next(e_0, e_1)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[1158, 1157])).
% 0.60/0.76 tff(1160,plain,
% 0.60/0.76 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_3, e_1) | (~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_3)) | (~next(e_0, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_1) | (~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_3)) | (~next(e_0, e_1)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1161,plain,
% 0.60/0.77 (((~cycle(e_4, e_3)) | equalish(e_3, e_1) | (~next(e_0, e_1)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0))) <=> (equalish(e_3, e_1) | (~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_3)) | (~next(e_0, e_1)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1162,plain,
% 0.60/0.77 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_4, e_3)) | equalish(e_3, e_1) | (~next(e_0, e_1)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_3, e_1) | (~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_3)) | (~next(e_0, e_1))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[1161])).
% 0.60/0.77 tff(1163,plain,
% 0.60/0.77 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_4, e_3)) | equalish(e_3, e_1) | (~next(e_0, e_1)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_1) | (~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_3)) | (~next(e_0, e_1)))),
% 0.60/0.77 inference(transitivity,[status(thm)],[1162, 1160])).
% 0.60/0.77 tff(1164,plain,
% 0.60/0.77 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_4, e_3)) | equalish(e_3, e_1) | (~next(e_0, e_1)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(1165,plain,
% 0.60/0.77 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_1) | (~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_3)) | (~next(e_0, e_1))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1164, 1163])).
% 0.60/0.77 tff(1166,plain,
% 0.60/0.77 ($false),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1165, 1159, 1156, 113, 1153, 1150, 15, 1140])).
% 0.60/0.77 tff(1167,plain,(~cycle(e_4, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.77 tff(1168,plain,
% 0.60/0.77 (greater(e_5, e_4) <=> greater(e_5, e_4)),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1169,axiom,(greater(e_5, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_greater_e_4')).
% 0.60/0.77 tff(1170,plain,
% 0.60/0.77 (greater(e_5, e_4)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1169, 1168])).
% 0.60/0.77 tff(1171,plain,
% 0.60/0.77 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_4, e_0)) | (~greater(e_5, e_4)) | (~product(e_4, e_1, e_5)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_4, e_0)) | (~greater(e_5, e_4)) | (~product(e_4, e_1, e_5)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1172,plain,
% 0.60/0.77 (((~product(e_4, e_1, e_5)) | (~greater(e_5, e_4)) | (~cycle(e_4, e_0))) <=> ((~cycle(e_4, e_0)) | (~greater(e_5, e_4)) | (~product(e_4, e_1, e_5)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1173,plain,
% 0.60/0.77 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_4, e_1, e_5)) | (~greater(e_5, e_4)) | (~cycle(e_4, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_4, e_0)) | (~greater(e_5, e_4)) | (~product(e_4, e_1, e_5))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[1172])).
% 0.60/0.77 tff(1174,plain,
% 0.60/0.77 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_4, e_1, e_5)) | (~greater(e_5, e_4)) | (~cycle(e_4, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_4, e_0)) | (~greater(e_5, e_4)) | (~product(e_4, e_1, e_5)))),
% 0.60/0.77 inference(transitivity,[status(thm)],[1173, 1171])).
% 0.60/0.77 tff(1175,plain,
% 0.60/0.77 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_4, e_1, e_5)) | (~greater(e_5, e_4)) | (~cycle(e_4, e_0)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(1176,plain,
% 0.60/0.77 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_4, e_0)) | (~greater(e_5, e_4)) | (~product(e_4, e_1, e_5))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1175, 1174])).
% 0.60/0.77 tff(1177,plain,
% 0.60/0.77 ((~cycle(e_4, e_0)) | (~product(e_4, e_1, e_5))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1176, 1170, 157])).
% 0.60/0.77 tff(1178,plain,
% 0.60/0.77 (~cycle(e_4, e_0)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1177, 1036])).
% 0.60/0.77 tff(1179,assumption,(cycle(e_4, e_2)), introduced(assumption)).
% 0.60/0.77 tff(1180,plain,
% 0.60/0.77 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_2, e_1) | (~cycle(e_5, e_0)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_2)) | (~next(e_0, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_1) | (~cycle(e_5, e_0)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_2)) | (~next(e_0, e_1)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1181,plain,
% 0.60/0.77 (((~cycle(e_4, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0))) <=> (equalish(e_2, e_1) | (~cycle(e_5, e_0)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_2)) | (~next(e_0, e_1)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1182,plain,
% 0.60/0.77 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_4, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_2, e_1) | (~cycle(e_5, e_0)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_2)) | (~next(e_0, e_1))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[1181])).
% 0.60/0.77 tff(1183,plain,
% 0.60/0.77 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_4, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_1) | (~cycle(e_5, e_0)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_2)) | (~next(e_0, e_1)))),
% 0.60/0.77 inference(transitivity,[status(thm)],[1182, 1180])).
% 0.60/0.77 tff(1184,plain,
% 0.60/0.77 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_4, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(1185,plain,
% 0.60/0.77 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_1) | (~cycle(e_5, e_0)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_2)) | (~next(e_0, e_1))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1184, 1183])).
% 0.60/0.77 tff(1186,plain,
% 0.60/0.77 ($false),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1185, 1159, 1156, 126, 1153, 1150, 46, 1179])).
% 0.60/0.77 tff(1187,plain,(~cycle(e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.77 tff(1188,assumption,(cycle(e_4, e_4)), introduced(assumption)).
% 0.60/0.77 tff(1189,plain,
% 0.60/0.77 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_4, e_1) | (~cycle(e_5, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_4)) | (~next(e_0, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_4, e_1) | (~cycle(e_5, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_4)) | (~next(e_0, e_1)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1190,plain,
% 0.60/0.77 (((~cycle(e_4, e_4)) | equalish(e_4, e_1) | (~next(e_0, e_1)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0))) <=> (equalish(e_4, e_1) | (~cycle(e_5, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_4)) | (~next(e_0, e_1)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1191,plain,
% 0.60/0.77 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_4, e_4)) | equalish(e_4, e_1) | (~next(e_0, e_1)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_4, e_1) | (~cycle(e_5, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_4)) | (~next(e_0, e_1))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[1190])).
% 0.60/0.77 tff(1192,plain,
% 0.60/0.77 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_4, e_4)) | equalish(e_4, e_1) | (~next(e_0, e_1)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_4, e_1) | (~cycle(e_5, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_4)) | (~next(e_0, e_1)))),
% 0.60/0.77 inference(transitivity,[status(thm)],[1191, 1189])).
% 0.60/0.77 tff(1193,plain,
% 0.60/0.77 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_4, e_4)) | equalish(e_4, e_1) | (~next(e_0, e_1)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(1194,plain,
% 0.60/0.77 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_4, e_1) | (~cycle(e_5, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_4)) | (~next(e_0, e_1))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1193, 1192])).
% 0.60/0.77 tff(1195,plain,
% 0.60/0.77 ($false),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1194, 1159, 1156, 224, 1153, 1150, 509, 1188])).
% 0.60/0.77 tff(1196,plain,(~cycle(e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.77 tff(1197,plain,
% 0.60/0.77 (((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_4, e_4) | cycle(e_4, e_3) | cycle(e_4, e_2) | cycle(e_4, e_1) | cycle(e_4, e_0) | (~group_element(e_4)))) <=> ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_4, e_4) | cycle(e_4, e_3) | cycle(e_4, e_2) | cycle(e_4, e_1) | cycle(e_4, e_0) | (~group_element(e_4)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1198,plain,
% 0.60/0.77 ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_4, e_4) | cycle(e_4, e_3) | cycle(e_4, e_2) | cycle(e_4, e_1) | cycle(e_4, e_0) | (~group_element(e_4)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(1199,plain,
% 0.60/0.77 ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_4, e_4) | cycle(e_4, e_3) | cycle(e_4, e_2) | cycle(e_4, e_1) | cycle(e_4, e_0) | (~group_element(e_4))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1198, 1197])).
% 0.60/0.77 tff(1200,plain,
% 0.60/0.77 (cycle(e_4, e_4) | cycle(e_4, e_3) | cycle(e_4, e_2) | cycle(e_4, e_1) | cycle(e_4, e_0)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1199, 246, 430])).
% 0.60/0.77 tff(1201,plain,
% 0.60/0.77 (cycle(e_4, e_3) | cycle(e_4, e_1) | cycle(e_4, e_0)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1200, 1196, 1187])).
% 0.60/0.77 tff(1202,plain,
% 0.60/0.77 (cycle(e_4, e_1)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1201, 1178, 1167])).
% 0.60/0.77 tff(1203,assumption,(cycle(e_4, e_1)), introduced(assumption)).
% 0.60/0.77 tff(1204,plain,
% 0.60/0.77 (next(e_1, e_2) <=> next(e_1, e_2)),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1205,axiom,(next(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_then_e_2')).
% 0.60/0.77 tff(1206,plain,
% 0.60/0.77 (next(e_1, e_2)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1205, 1204])).
% 0.60/0.77 tff(1207,plain,
% 0.60/0.77 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_4, e_2) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | (~cycle(e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | (~cycle(e_4, e_1)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1208,plain,
% 0.60/0.77 (((~cycle(e_3, e_4)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1))) <=> (equalish(e_4, e_2) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | (~cycle(e_4, e_1)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1209,plain,
% 0.60/0.77 (((~![W: $i, Z: $i, Y: $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_4)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_4, e_2) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | (~cycle(e_4, e_1))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[1208])).
% 0.60/0.77 tff(1210,plain,
% 0.60/0.77 (((~![W: $i, Z: $i, Y: $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_4)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | (~cycle(e_4, e_1)))),
% 0.60/0.77 inference(transitivity,[status(thm)],[1209, 1207])).
% 0.60/0.77 tff(1211,plain,
% 0.60/0.77 ((~![W: $i, Z: $i, Y: $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_4)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(1212,plain,
% 0.60/0.77 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | (~cycle(e_4, e_1))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1211, 1210])).
% 0.60/0.78 tff(1213,plain,
% 0.60/0.78 ($false),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1212, 1206, 330, 224, 1150, 652, 324, 1203])).
% 0.60/0.78 tff(1214,plain,((~cycle(e_3, e_4)) | (~cycle(e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.78 tff(1215,plain,
% 0.60/0.78 (~cycle(e_3, e_4)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1214, 1202])).
% 0.60/0.78 tff(1216,assumption,(product(e_3, e_1, e_2)), introduced(assumption)).
% 0.60/0.78 tff(1217,assumption,(~cycle(e_3, e_4)), introduced(assumption)).
% 0.60/0.78 tff(1218,assumption,(cycle(e_3, e_1)), introduced(assumption)).
% 0.60/0.78 tff(1219,plain,
% 0.60/0.78 (((~![Z: $i, 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)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1220,plain,
% 0.60/0.78 (((~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)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1221,plain,
% 0.60/0.78 (((~![Z: $i, 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))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[1220])).
% 0.60/0.78 tff(1222,plain,
% 0.60/0.78 (((~![Z: $i, 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)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[1221, 1219])).
% 0.60/0.78 tff(1223,plain,
% 0.60/0.78 ((~![Z: $i, 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)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(1224,plain,
% 0.60/0.78 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_2))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1223, 1222])).
% 0.60/0.78 tff(1225,plain,
% 0.60/0.78 ($false),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1224, 330, 97, 94, 823, 1218, 1216])).
% 0.60/0.78 tff(1226,plain,((~cycle(e_3, e_1)) | (~product(e_3, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.78 tff(1227,plain,
% 0.60/0.78 (~cycle(e_3, e_1)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1226, 1216])).
% 0.60/0.78 tff(1228,assumption,(~cycle(e_3, e_0)), introduced(assumption)).
% 0.60/0.78 tff(1229,plain,
% 0.60/0.78 (((~![Z: $i, 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_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~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_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1230,plain,
% 0.60/0.78 (((~greater(e_2, e_0)) | (~cycle(e_3, e_2)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2))) <=> (equalish(e_2, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1231,plain,
% 0.60/0.78 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_3, e_2)) | equalish(e_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_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_2))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[1230])).
% 0.60/0.78 tff(1232,plain,
% 0.60/0.78 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_3, e_2)) | equalish(e_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_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[1231, 1229])).
% 0.60/0.78 tff(1233,plain,
% 0.60/0.78 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_3, e_2)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(1234,plain,
% 0.60/0.78 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_2))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1233, 1232])).
% 0.60/0.78 tff(1235,plain,
% 0.60/0.78 ($false),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1234, 330, 126, 94, 823, 351, 1216])).
% 0.60/0.78 tff(1236,plain,((~cycle(e_3, e_2)) | (~product(e_3, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.78 tff(1237,plain,
% 0.60/0.78 (~cycle(e_3, e_2)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1236, 1216])).
% 0.60/0.78 tff(1238,plain,
% 0.60/0.78 (cycle(e_3, e_3)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[377, 1237, 1228, 1227, 1217])).
% 0.60/0.78 tff(1239,plain,
% 0.60/0.78 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_2, e_4) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~product(e_3, e_1, e_2)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_4) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1240,plain,
% 0.60/0.78 (((~greater(e_3, e_0)) | (~cycle(e_3, e_3)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2))) <=> (equalish(e_2, e_4) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1241,plain,
% 0.60/0.78 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_3, e_0)) | (~cycle(e_3, e_3)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_2, e_4) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~product(e_3, e_1, e_2))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[1240])).
% 0.60/0.78 tff(1242,plain,
% 0.60/0.78 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_3, e_0)) | (~cycle(e_3, e_3)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_4) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[1241, 1239])).
% 0.60/0.78 tff(1243,plain,
% 0.60/0.78 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_3, e_0)) | (~cycle(e_3, e_3)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(1244,plain,
% 0.60/0.78 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_4) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~product(e_3, e_1, e_2))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1243, 1242])).
% 0.60/0.78 tff(1245,plain,
% 0.60/0.78 ($false),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1244, 330, 113, 94, 823, 1238, 1216])).
% 0.60/0.78 tff(1246,plain,((~product(e_3, e_1, e_2)) | cycle(e_3, e_0) | cycle(e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.78 tff(1247,plain,
% 0.60/0.78 (cycle(e_3, e_0)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1246, 1215, 1139])).
% 0.60/0.78 tff(1248,plain,
% 0.60/0.78 (greater(e_4, e_3) <=> greater(e_4, e_3)),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1249,axiom,(greater(e_4, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_greater_e_3')).
% 0.60/0.78 tff(1250,plain,
% 0.60/0.78 (greater(e_4, e_3)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1249, 1248])).
% 0.60/0.78 tff(1251,plain,
% 0.60/0.78 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_3, e_0)) | (~greater(e_4, e_3)) | (~product(e_3, e_1, e_4)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_3, e_0)) | (~greater(e_4, e_3)) | (~product(e_3, e_1, e_4)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1252,plain,
% 0.60/0.78 (((~product(e_3, e_1, e_4)) | (~greater(e_4, e_3)) | (~cycle(e_3, e_0))) <=> ((~cycle(e_3, e_0)) | (~greater(e_4, e_3)) | (~product(e_3, e_1, e_4)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1253,plain,
% 0.60/0.78 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_3, e_1, e_4)) | (~greater(e_4, e_3)) | (~cycle(e_3, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_3, e_0)) | (~greater(e_4, e_3)) | (~product(e_3, e_1, e_4))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[1252])).
% 0.60/0.78 tff(1254,plain,
% 0.60/0.78 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_3, e_1, e_4)) | (~greater(e_4, e_3)) | (~cycle(e_3, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_3, e_0)) | (~greater(e_4, e_3)) | (~product(e_3, e_1, e_4)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[1253, 1251])).
% 0.60/0.78 tff(1255,plain,
% 0.60/0.78 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_3, e_1, e_4)) | (~greater(e_4, e_3)) | (~cycle(e_3, e_0)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(1256,plain,
% 0.60/0.78 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_3, e_0)) | (~greater(e_4, e_3)) | (~product(e_3, e_1, e_4))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1255, 1254])).
% 0.60/0.78 tff(1257,plain,
% 0.60/0.78 ((~cycle(e_3, e_0)) | (~product(e_3, e_1, e_4))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1256, 1250, 157])).
% 0.60/0.78 tff(1258,plain,
% 0.60/0.78 (~product(e_3, e_1, e_4)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1257, 1247])).
% 0.60/0.78 tff(1259,assumption,(~product(e_3, e_1, e_4)), introduced(assumption)).
% 0.60/0.78 tff(1260,plain,
% 0.60/0.78 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_4) | (~product(e_5, e_4, e_1)) | (~product(e_4, e_5, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_4) | (~product(e_5, e_4, e_1)) | (~product(e_4, e_5, e_3)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1261,plain,
% 0.60/0.78 (((~product(e_5, e_4, e_1)) | product(e_3, e_1, e_4) | (~product(e_4, e_5, e_3))) <=> (product(e_3, e_1, e_4) | (~product(e_5, e_4, e_1)) | (~product(e_4, e_5, e_3)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1262,plain,
% 0.60/0.78 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_4, e_1)) | product(e_3, e_1, e_4) | (~product(e_4, e_5, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_4) | (~product(e_5, e_4, e_1)) | (~product(e_4, e_5, e_3))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[1261])).
% 0.60/0.78 tff(1263,plain,
% 0.60/0.78 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_4, e_1)) | product(e_3, e_1, e_4) | (~product(e_4, e_5, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_4) | (~product(e_5, e_4, e_1)) | (~product(e_4, e_5, e_3)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[1262, 1260])).
% 0.60/0.78 tff(1264,plain,
% 0.60/0.78 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_4, e_1)) | product(e_3, e_1, e_4) | (~product(e_4, e_5, e_3)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(1265,plain,
% 0.60/0.78 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_4) | (~product(e_5, e_4, e_1)) | (~product(e_4, e_5, e_3))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1264, 1263])).
% 0.60/0.78 tff(1266,plain,
% 0.60/0.78 ($false),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1265, 72, 1259, 524, 560])).
% 0.60/0.78 tff(1267,plain,(product(e_3, e_1, e_4) | (~product(e_5, e_4, e_1)) | (~product(e_4, e_5, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.78 tff(1268,plain,
% 0.60/0.78 (~product(e_5, e_4, e_1)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1267, 1258, 931])).
% 0.60/0.78 tff(1269,plain,
% 0.60/0.78 (product(e_5, e_4, e_2)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[555, 1268, 777])).
% 0.60/0.78 tff(1270,plain,
% 0.60/0.78 (~product(e_1, e_4, e_2)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[884, 1269])).
% 0.60/0.78 tff(1271,plain,
% 0.60/0.78 (product(e_1, e_4, e_3)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[699, 1270, 1045])).
% 0.60/0.78 tff(1272,plain,
% 0.60/0.78 (product(e_3, e_5, e_1)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[891, 1271, 1036])).
% 0.60/0.78 tff(1273,assumption,(~product(e_5, e_3, e_1)), introduced(assumption)).
% 0.60/0.78 tff(1274,plain,
% 0.60/0.78 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_5, e_3, e_1) | (~product(e_1, e_2, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_5, e_3, e_1) | (~product(e_1, e_2, e_5)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1275,plain,
% 0.60/0.78 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_5, e_3, e_1) | (~product(e_1, e_2, e_5)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(1276,plain,
% 0.60/0.78 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_5, e_3, e_1) | (~product(e_1, e_2, e_5))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1275, 1274])).
% 0.60/0.78 tff(1277,plain,
% 0.60/0.78 ($false),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1276, 72, 293, 1273, 2])).
% 0.60/0.79 tff(1278,plain,(product(e_5, e_3, e_1) | (~product(e_1, e_2, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.79 tff(1279,plain,
% 0.60/0.79 (product(e_5, e_3, e_1)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1278, 998])).
% 0.60/0.79 tff(1280,plain,
% 0.60/0.79 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_3)) | (~product(e_1, e_1, e_1)) | product(e_3, e_1, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_3)) | (~product(e_1, e_1, e_1)) | product(e_3, e_1, e_1))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1281,plain,
% 0.60/0.79 (((~product(e_1, e_1, e_1)) | product(e_3, e_1, e_1) | (~product(e_1, e_1, e_3))) <=> ((~product(e_1, e_1, e_3)) | (~product(e_1, e_1, e_1)) | product(e_3, e_1, e_1))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1282,plain,
% 0.60/0.79 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_1)) | product(e_3, e_1, e_1) | (~product(e_1, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_3)) | (~product(e_1, e_1, e_1)) | product(e_3, e_1, e_1)))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[1281])).
% 0.60/0.79 tff(1283,plain,
% 0.60/0.79 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_1)) | product(e_3, e_1, e_1) | (~product(e_1, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_3)) | (~product(e_1, e_1, e_1)) | product(e_3, e_1, e_1))),
% 0.60/0.79 inference(transitivity,[status(thm)],[1282, 1280])).
% 0.60/0.79 tff(1284,plain,
% 0.60/0.79 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_1)) | product(e_3, e_1, e_1) | (~product(e_1, e_1, e_3)))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(1285,plain,
% 0.60/0.79 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_3)) | (~product(e_1, e_1, e_1)) | product(e_3, e_1, e_1)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1284, 1283])).
% 0.60/0.79 tff(1286,plain,
% 0.60/0.79 (~product(e_1, e_1, e_3)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1285, 72, 33, 1061])).
% 0.60/0.79 tff(1287,plain,
% 0.60/0.79 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_5, e_3, e_1)) | (~product(e_3, e_5, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_3) | (~product(e_5, e_3, e_1)) | (~product(e_3, e_5, e_1)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1288,plain,
% 0.60/0.79 (((~product(e_5, e_3, e_1)) | product(e_1, e_1, e_3) | (~product(e_3, e_5, e_1))) <=> (product(e_1, e_1, e_3) | (~product(e_5, e_3, e_1)) | (~product(e_3, e_5, e_1)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1289,plain,
% 0.60/0.79 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_3, e_1)) | product(e_1, e_1, e_3) | (~product(e_3, e_5, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_5, e_3, e_1)) | (~product(e_3, e_5, e_1))))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[1288])).
% 0.60/0.79 tff(1290,plain,
% 0.60/0.79 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_3, e_1)) | product(e_1, e_1, e_3) | (~product(e_3, e_5, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_3) | (~product(e_5, e_3, e_1)) | (~product(e_3, e_5, e_1)))),
% 0.60/0.79 inference(transitivity,[status(thm)],[1289, 1287])).
% 0.60/0.79 tff(1291,plain,
% 0.60/0.79 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_3, e_1)) | product(e_1, e_1, e_3) | (~product(e_3, e_5, e_1)))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(1292,plain,
% 0.60/0.79 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_3) | (~product(e_5, e_3, e_1)) | (~product(e_3, e_5, e_1))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1291, 1290])).
% 0.60/0.79 tff(1293,plain,
% 0.60/0.79 ($false),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1292, 72, 1286, 1279, 1272])).
% 0.60/0.79 tff(1294,plain,(product(e_4, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.79 tff(1295,assumption,(product(e_5, e_3, e_1)), introduced(assumption)).
% 0.60/0.79 tff(1296,plain,
% 0.60/0.79 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_4) | (~product(e_5, e_3, e_1)) | (~product(e_4, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_4) | (~product(e_5, e_3, e_1)) | (~product(e_4, e_3, e_1)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1297,plain,
% 0.60/0.79 ((equalish(e_5, e_4) | (~product(e_4, e_3, e_1)) | (~product(e_5, e_3, e_1))) <=> (equalish(e_5, e_4) | (~product(e_5, e_3, e_1)) | (~product(e_4, e_3, e_1)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1298,plain,
% 0.60/0.79 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_4) | (~product(e_4, e_3, e_1)) | (~product(e_5, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_4) | (~product(e_5, e_3, e_1)) | (~product(e_4, e_3, e_1))))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[1297])).
% 0.60/0.79 tff(1299,plain,
% 0.60/0.79 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_4) | (~product(e_4, e_3, e_1)) | (~product(e_5, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_4) | (~product(e_5, e_3, e_1)) | (~product(e_4, e_3, e_1)))),
% 0.60/0.79 inference(transitivity,[status(thm)],[1298, 1296])).
% 0.60/0.79 tff(1300,plain,
% 0.60/0.79 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_4) | (~product(e_4, e_3, e_1)) | (~product(e_5, e_3, e_1)))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(1301,plain,
% 0.60/0.79 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_4) | (~product(e_5, e_3, e_1)) | (~product(e_4, e_3, e_1))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1300, 1299])).
% 0.60/0.79 tff(1302,plain,
% 0.60/0.79 ($false),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1301, 327, 12, 1295, 595])).
% 0.60/0.79 tff(1303,plain,((~product(e_5, e_3, e_1)) | (~product(e_4, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.79 tff(1304,plain,
% 0.60/0.79 (~product(e_5, e_3, e_1)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1303, 1294])).
% 0.60/0.79 tff(1305,plain,
% 0.60/0.79 (~product(e_1, e_2, e_5)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1278, 1304])).
% 0.60/0.79 tff(1306,plain,
% 0.60/0.79 (product(e_1, e_2, e_4)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[320, 1305])).
% 0.60/0.79 tff(1307,plain,
% 0.60/0.79 (~product(e_3, e_2, e_4)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[863, 1306])).
% 0.60/0.79 tff(1308,plain,
% 0.60/0.79 (~product(e_5, e_4, e_2)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[902, 1307, 931])).
% 0.60/0.79 tff(1309,plain,
% 0.60/0.79 (product(e_5, e_4, e_1)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[555, 1308, 777])).
% 0.60/0.79 tff(1310,plain,
% 0.60/0.79 (product(e_3, e_1, e_4)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1267, 1309, 931])).
% 0.60/0.79 tff(1311,plain,
% 0.60/0.79 (~cycle(e_3, e_0)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1257, 1310])).
% 0.60/0.79 tff(1312,assumption,(cycle(e_4, e_0)), introduced(assumption)).
% 0.60/0.79 tff(1313,plain,
% 0.60/0.79 (^[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))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(1314,plain,
% 0.60/0.79 (![W: $i, Y: $i, Z1: $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)))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[1313])).
% 0.60/0.79 tff(1315,plain,
% 0.60/0.79 (![W: $i, Y: $i, Z1: $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)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1316,plain,
% 0.60/0.79 (^[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)))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(1317,plain,
% 0.60/0.79 (![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)))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[1316])).
% 0.60/0.79 tff(1318,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')).
% 0.60/0.79 tff(1319,plain,
% 0.60/0.79 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1318, 1317])).
% 0.60/0.79 tff(1320,plain,
% 0.60/0.79 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1319, 1315])).
% 0.60/0.79 tff(1321,plain,(
% 0.60/0.79 ![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.60/0.79 inference(skolemize,[status(sab)],[1320])).
% 0.60/0.79 tff(1322,plain,
% 0.60/0.79 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1321, 1314])).
% 0.60/0.79 tff(1323,plain,
% 0.60/0.79 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_1)) | (~greater(e_4, e_2)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_1)) | (~greater(e_4, e_2)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1324,plain,
% 0.60/0.79 (((~greater(e_1, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_1))) <=> ((~cycle(e_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_1)) | (~greater(e_4, e_2)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1325,plain,
% 0.60/0.79 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_1, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_1)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_1)) | (~greater(e_4, e_2))))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[1324])).
% 0.60/0.79 tff(1326,plain,
% 0.60/0.79 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_1, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_1)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_1)) | (~greater(e_4, e_2)))),
% 0.60/0.79 inference(transitivity,[status(thm)],[1325, 1323])).
% 0.60/0.79 tff(1327,plain,
% 0.60/0.79 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_1, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_1)))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(1328,plain,
% 0.60/0.79 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_1)) | (~greater(e_4, e_2))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1327, 1326])).
% 0.60/0.79 tff(1329,plain,
% 0.60/0.79 ((~cycle(e_4, e_0)) | (~cycle(e_2, e_1))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1328, 1156, 97, 203, 1153, 1322])).
% 0.60/0.79 tff(1330,plain,
% 0.60/0.79 (~cycle(e_2, e_1)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1329, 1312])).
% 0.60/0.79 tff(1331,plain,
% 0.60/0.79 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_2)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_2)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1332,plain,
% 0.60/0.79 (((~greater(e_2, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_2))) <=> ((~cycle(e_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_2)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1333,plain,
% 0.60/0.79 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_2, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_2)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_2))))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[1332])).
% 0.60/0.79 tff(1334,plain,
% 0.60/0.79 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_2, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_2)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_2)))),
% 0.60/0.79 inference(transitivity,[status(thm)],[1333, 1331])).
% 0.60/0.79 tff(1335,plain,
% 0.60/0.79 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_2, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_2)))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(1336,plain,
% 0.60/0.79 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_2))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1335, 1334])).
% 0.60/0.79 tff(1337,plain,
% 0.60/0.79 ((~cycle(e_4, e_0)) | (~cycle(e_2, e_2))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1336, 1156, 126, 203, 1153, 1322])).
% 0.60/0.79 tff(1338,plain,
% 0.60/0.79 (~cycle(e_2, e_2)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1337, 1312])).
% 0.60/0.79 tff(1339,plain,
% 0.60/0.79 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_3, e_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_3, e_1)) | (~cycle(e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_3, e_1)) | (~cycle(e_2, e_3)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1340,plain,
% 0.60/0.79 (((~cycle(e_2, e_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_1))) <=> (equalish(e_3, e_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_3, e_1)) | (~cycle(e_2, e_3)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1341,plain,
% 0.60/0.79 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_2, e_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_3, e_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_3, e_1)) | (~cycle(e_2, e_3))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[1340])).
% 0.60/0.80 tff(1342,plain,
% 0.60/0.80 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_2, e_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_3, e_1)) | (~cycle(e_2, e_3)))),
% 0.60/0.80 inference(transitivity,[status(thm)],[1341, 1339])).
% 0.60/0.80 tff(1343,plain,
% 0.60/0.80 ((~![W: $i, Z: $i, Y: $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)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(1344,plain,
% 0.60/0.80 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_3, e_1)) | (~cycle(e_2, e_3))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[1343, 1342])).
% 0.60/0.80 tff(1345,plain,
% 0.60/0.80 (~cycle(e_3, e_1)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1344, 1206, 100, 113, 1150, 755, 110])).
% 0.60/0.80 tff(1346,plain,
% 0.60/0.80 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_3, e_1) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~next(e_0, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_1) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~next(e_0, e_1)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1347,plain,
% 0.60/0.80 (((~cycle(e_2, e_3)) | equalish(e_3, e_1) | (~next(e_0, e_1)) | (~greater(e_3, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0))) <=> (equalish(e_3, e_1) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~next(e_0, e_1)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1348,plain,
% 0.60/0.80 (((~![W: $i, Z: $i, Y: $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_1) | (~next(e_0, e_1)) | (~greater(e_3, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_3, e_1) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~next(e_0, e_1))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[1347])).
% 0.60/0.80 tff(1349,plain,
% 0.60/0.80 (((~![W: $i, Z: $i, Y: $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_1) | (~next(e_0, e_1)) | (~greater(e_3, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_1) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~next(e_0, e_1)))),
% 0.60/0.80 inference(transitivity,[status(thm)],[1348, 1346])).
% 0.60/0.80 tff(1350,plain,
% 0.60/0.80 ((~![W: $i, Z: $i, Y: $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_1) | (~next(e_0, e_1)) | (~greater(e_3, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(1351,plain,
% 0.60/0.80 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_1) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~next(e_0, e_1))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[1350, 1349])).
% 0.60/0.80 tff(1352,plain,
% 0.60/0.80 (~cycle(e_3, e_0)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1351, 1159, 100, 113, 1150, 15, 110])).
% 0.60/0.80 tff(1353,plain,
% 0.60/0.80 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_3, e_5) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_5) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_4)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1354,plain,
% 0.60/0.80 (((~cycle(e_2, e_3)) | equalish(e_3, e_5) | (~next(e_4, e_5)) | (~greater(e_3, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_4))) <=> (equalish(e_3, e_5) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_4)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1355,plain,
% 0.60/0.80 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_2, e_3)) | equalish(e_3, e_5) | (~next(e_4, e_5)) | (~greater(e_3, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_3, e_5) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_4))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[1354])).
% 0.60/0.80 tff(1356,plain,
% 0.60/0.80 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_2, e_3)) | equalish(e_3, e_5) | (~next(e_4, e_5)) | (~greater(e_3, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_5) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_4)))),
% 0.60/0.80 inference(transitivity,[status(thm)],[1355, 1353])).
% 0.60/0.80 tff(1357,plain,
% 0.60/0.80 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_2, e_3)) | equalish(e_3, e_5) | (~next(e_4, e_5)) | (~greater(e_3, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_4)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(1358,plain,
% 0.60/0.80 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_5) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_4))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[1357, 1356])).
% 0.60/0.80 tff(1359,plain,
% 0.60/0.80 (~cycle(e_3, e_4)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1358, 100, 1156, 113, 1150, 785, 110])).
% 0.60/0.80 tff(1360,plain,
% 0.60/0.80 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_3, e_4) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_4) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_3)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1361,plain,
% 0.60/0.80 (((~cycle(e_2, e_3)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~greater(e_3, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_3))) <=> (equalish(e_3, e_4) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_3)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1362,plain,
% 0.60/0.80 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_2, e_3)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~greater(e_3, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_3, e_4) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_3))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[1361])).
% 0.60/0.80 tff(1363,plain,
% 0.60/0.80 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_2, e_3)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~greater(e_3, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_4) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_3)))),
% 0.60/0.80 inference(transitivity,[status(thm)],[1362, 1360])).
% 0.60/0.80 tff(1364,plain,
% 0.60/0.80 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_2, e_3)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~greater(e_3, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_3)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(1365,plain,
% 0.60/0.80 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_4) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_3))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[1364, 1363])).
% 0.60/0.80 tff(1366,plain,
% 0.60/0.80 (~cycle(e_3, e_3)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1365, 100, 330, 113, 1150, 470, 110])).
% 0.60/0.80 tff(1367,plain,
% 0.60/0.80 (cycle(e_3, e_2)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[377, 1366, 1359, 1352, 1345])).
% 0.60/0.80 tff(1368,plain,
% 0.60/0.80 (~product(e_3, e_1, e_5)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[357, 330, 126, 94, 327, 1367])).
% 0.60/0.80 tff(1369,plain,
% 0.60/0.80 (((~![Z: $i, 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_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~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_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_3)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1370,plain,
% 0.60/0.80 (((~greater(e_2, e_0)) | (~cycle(e_3, e_2)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_3))) <=> (equalish(e_3, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_3)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1371,plain,
% 0.60/0.80 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_3, e_2)) | equalish(e_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_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_3))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[1370])).
% 0.60/0.80 tff(1372,plain,
% 0.60/0.80 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_3, e_2)) | equalish(e_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_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_3)))),
% 0.60/0.80 inference(transitivity,[status(thm)],[1371, 1369])).
% 0.60/0.80 tff(1373,plain,
% 0.60/0.80 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_3, e_2)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_3)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(1374,plain,
% 0.60/0.80 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_3, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_3))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[1373, 1372])).
% 0.60/0.80 tff(1375,plain,
% 0.60/0.80 (~product(e_3, e_1, e_3)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1374, 330, 126, 94, 470, 351])).
% 0.60/0.80 tff(1376,plain,
% 0.60/0.80 (~product(e_3, e_1, e_2)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1234, 330, 126, 94, 823, 351])).
% 0.60/0.80 tff(1377,plain,
% 0.60/0.80 ($false),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1067, 272, 373, 269, 1259, 387, 1376, 1061, 1375])).
% 0.60/0.80 tff(1378,plain,((~cycle(e_3, e_2)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.80 tff(1379,plain,
% 0.60/0.80 (product(e_3, e_1, e_4)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1378, 1368, 1367])).
% 0.60/0.80 tff(1380,plain,
% 0.60/0.80 (~product(e_3, e_2, e_4)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[938, 1379])).
% 0.60/0.80 tff(1381,plain,
% 0.60/0.80 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_3)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_3)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1382,plain,
% 0.60/0.80 (((~greater(e_3, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_3))) <=> ((~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_3)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1383,plain,
% 0.60/0.80 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_3, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_3)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_3))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[1382])).
% 0.60/0.80 tff(1384,plain,
% 0.60/0.80 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_3, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_3)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_3)))),
% 0.60/0.80 inference(transitivity,[status(thm)],[1383, 1381])).
% 0.60/0.80 tff(1385,plain,
% 0.60/0.80 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_3, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_3)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(1386,plain,
% 0.60/0.80 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_3))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[1385, 1384])).
% 0.60/0.80 tff(1387,plain,
% 0.60/0.80 ((~cycle(e_4, e_0)) | (~cycle(e_2, e_3))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1386, 1156, 113, 203, 1153, 1322])).
% 0.60/0.80 tff(1388,plain,
% 0.60/0.80 (~cycle(e_4, e_0)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1387, 110])).
% 0.60/0.80 tff(1389,plain,
% 0.60/0.80 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_2, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~cycle(e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~cycle(e_4, e_3)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1390,plain,
% 0.60/0.80 (((~cycle(e_3, e_2)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_3))) <=> (equalish(e_2, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~cycle(e_4, e_3)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1391,plain,
% 0.60/0.80 (((~![W: $i, Z: $i, Y: $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_4) | (~next(e_3, e_4)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_2, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~cycle(e_4, e_3))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[1390])).
% 0.60/0.80 tff(1392,plain,
% 0.60/0.80 (((~![W: $i, Z: $i, Y: $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_4) | (~next(e_3, e_4)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~cycle(e_4, e_3)))),
% 0.60/0.80 inference(transitivity,[status(thm)],[1391, 1389])).
% 0.60/0.80 tff(1393,plain,
% 0.60/0.80 ((~![W: $i, Z: $i, Y: $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_4) | (~next(e_3, e_4)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_3)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(1394,plain,
% 0.60/0.80 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~cycle(e_4, e_3))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[1393, 1392])).
% 0.60/0.81 tff(1395,plain,
% 0.60/0.81 (~cycle(e_4, e_3)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1394, 330, 126, 1150, 823, 1367])).
% 0.60/0.81 tff(1396,plain,
% 0.60/0.81 (cycle(e_4, e_1)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1201, 1395, 1388])).
% 0.60/0.81 tff(1397,plain,
% 0.60/0.81 ((~equalish(e_2, e_5)) <=> (~equalish(e_2, e_5))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1398,axiom,(~equalish(e_2, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_5')).
% 0.60/0.81 tff(1399,plain,
% 0.60/0.81 (~equalish(e_2, e_5)),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[1398, 1397])).
% 0.60/0.81 tff(1400,plain,
% 0.60/0.81 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_2, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_2)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_2)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1401,plain,
% 0.60/0.81 (((~greater(e_1, e_0)) | (~cycle(e_4, e_1)) | equalish(e_2, e_5) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_2))) <=> (equalish(e_2, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_2)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1402,plain,
% 0.60/0.81 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_4, e_1)) | equalish(e_2, e_5) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_2)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_2, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_2))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[1401])).
% 0.60/0.81 tff(1403,plain,
% 0.60/0.81 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_4, e_1)) | equalish(e_2, e_5) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_2)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_2)))),
% 0.60/0.81 inference(transitivity,[status(thm)],[1402, 1400])).
% 0.60/0.81 tff(1404,plain,
% 0.60/0.81 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_4, e_1)) | equalish(e_2, e_5) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_2)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(1405,plain,
% 0.60/0.81 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_2))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[1404, 1403])).
% 0.60/0.81 tff(1406,plain,
% 0.60/0.81 (~product(e_4, e_1, e_2)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1405, 1156, 97, 94, 1399, 1396])).
% 0.60/0.81 tff(1407,plain,
% 0.60/0.81 (~product(e_3, e_1, e_2)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1234, 330, 126, 94, 823, 1367])).
% 0.60/0.81 tff(1408,plain,
% 0.60/0.81 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_4, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_4)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_4)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1409,plain,
% 0.60/0.81 (((~greater(e_1, e_0)) | (~cycle(e_4, e_1)) | equalish(e_4, e_5) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_4))) <=> (equalish(e_4, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_4)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1410,plain,
% 0.60/0.81 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_4, e_1)) | equalish(e_4, e_5) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_4)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_4, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_4))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[1409])).
% 0.60/0.81 tff(1411,plain,
% 0.60/0.81 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_4, e_1)) | equalish(e_4, e_5) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_4)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_4)))),
% 0.60/0.81 inference(transitivity,[status(thm)],[1410, 1408])).
% 0.60/0.81 tff(1412,plain,
% 0.60/0.81 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_4, e_1)) | equalish(e_4, e_5) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_4)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(1413,plain,
% 0.60/0.81 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_4))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[1412, 1411])).
% 0.60/0.81 tff(1414,plain,
% 0.60/0.81 (~product(e_4, e_1, e_4)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1413, 1156, 97, 94, 419, 1396])).
% 0.60/0.81 tff(1415,plain,
% 0.60/0.81 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_3, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_3)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_3, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_3)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1416,plain,
% 0.60/0.81 (((~greater(e_1, e_0)) | (~cycle(e_4, e_1)) | equalish(e_3, e_5) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_3))) <=> (equalish(e_3, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_3)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1417,plain,
% 0.60/0.81 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_4, e_1)) | equalish(e_3, e_5) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_3)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_3, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_3))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[1416])).
% 0.60/0.81 tff(1418,plain,
% 0.60/0.81 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_4, e_1)) | equalish(e_3, e_5) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_3)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_3, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_3)))),
% 0.60/0.81 inference(transitivity,[status(thm)],[1417, 1415])).
% 0.60/0.81 tff(1419,plain,
% 0.60/0.81 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_4, e_1)) | equalish(e_3, e_5) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_3)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(1420,plain,
% 0.60/0.81 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_3, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_3))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[1419, 1418])).
% 0.60/0.81 tff(1421,plain,
% 0.60/0.81 (~product(e_4, e_1, e_3)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1420, 1156, 97, 94, 785, 1396])).
% 0.60/0.81 tff(1422,plain,
% 0.60/0.81 (product(e_4, e_1, e_5)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[663, 272, 430, 269, 1406, 603, 1421, 1414])).
% 0.60/0.81 tff(1423,plain,
% 0.60/0.81 (~product(e_3, e_2, e_1)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1135, 1368, 1422, 1407, 1406])).
% 0.60/0.81 tff(1424,plain,
% 0.60/0.81 (product(e_3, e_2, e_5)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[768, 1423, 1380])).
% 0.60/0.81 tff(1425,plain,
% 0.60/0.81 (~product(e_3, e_4, e_5)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[741, 1424])).
% 0.60/0.81 tff(1426,plain,
% 0.60/0.81 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_1, e_4, e_1) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | product(e_1, e_4, e_1) | (~product(e_1, e_3, e_1)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1427,plain,
% 0.60/0.81 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_1, e_4, e_1) | (~product(e_1, e_3, e_1)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(1428,plain,
% 0.60/0.81 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | product(e_1, e_4, e_1) | (~product(e_1, e_3, e_1))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[1427, 1426])).
% 0.60/0.81 tff(1429,plain,
% 0.60/0.81 (~product(e_1, e_3, e_1)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1428, 72, 1379, 514])).
% 0.60/0.81 tff(1430,plain,
% 0.60/0.81 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_1)) | product(e_1, e_3, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_1)) | product(e_1, e_3, e_1))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1431,plain,
% 0.60/0.81 (((~product(e_2, e_1, e_3)) | product(e_1, e_3, e_1) | (~product(e_1, e_2, e_1))) <=> ((~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_1)) | product(e_1, e_3, e_1))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1432,plain,
% 0.60/0.81 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_1, e_3, e_1) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_1)) | product(e_1, e_3, e_1)))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[1431])).
% 0.60/0.81 tff(1433,plain,
% 0.60/0.81 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_1, e_3, e_1) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_1)) | product(e_1, e_3, e_1))),
% 0.60/0.81 inference(transitivity,[status(thm)],[1432, 1430])).
% 0.60/0.81 tff(1434,plain,
% 0.60/0.81 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_1, e_3, e_1) | (~product(e_1, e_2, e_1)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(1435,plain,
% 0.60/0.81 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_1)) | product(e_1, e_3, e_1)),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[1434, 1433])).
% 0.60/0.81 tff(1436,plain,
% 0.60/0.81 (~product(e_1, e_2, e_1)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1435, 72, 293, 1429])).
% 0.60/0.81 tff(1437,plain,
% 0.60/0.81 (~product(e_1, e_2, e_5)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[20, 1424])).
% 0.60/0.81 tff(1438,plain,
% 0.60/0.81 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_5, e_3, e_3) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_2, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_5, e_3, e_3) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_2, e_5)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1439,plain,
% 0.60/0.81 (((~product(e_2, e_3, e_3)) | product(e_5, e_3, e_3) | (~product(e_3, e_2, e_5))) <=> (product(e_5, e_3, e_3) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_2, e_5)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1440,plain,
% 0.60/0.81 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_3)) | product(e_5, e_3, e_3) | (~product(e_3, e_2, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_5, e_3, e_3) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_2, e_5))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[1439])).
% 0.60/0.81 tff(1441,plain,
% 0.60/0.81 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_3)) | product(e_5, e_3, e_3) | (~product(e_3, e_2, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_5, e_3, e_3) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_2, e_5)))),
% 0.60/0.81 inference(transitivity,[status(thm)],[1440, 1438])).
% 0.60/0.81 tff(1442,plain,
% 0.60/0.81 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_3)) | product(e_5, e_3, e_3) | (~product(e_3, e_2, e_5)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(1443,plain,
% 0.60/0.81 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_5, e_3, e_3) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_2, e_5))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[1442, 1441])).
% 0.60/0.81 tff(1444,plain,
% 0.60/0.81 ($false),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1443, 72, 448, 54, 1])).
% 0.60/0.81 tff(1445,plain,((~product(e_2, e_3, e_3)) | (~product(e_3, e_2, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.81 tff(1446,plain,
% 0.60/0.81 (~product(e_2, e_3, e_3)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1445, 1424])).
% 0.60/0.81 tff(1447,plain,
% 0.60/0.81 (~product(e_3, e_3, e_2)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[78, 72, 1446, 53])).
% 0.60/0.81 tff(1448,plain,
% 0.60/0.81 (~product(e_1, e_2, e_3)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[305, 1447])).
% 0.60/0.81 tff(1449,plain,
% 0.60/0.81 (product(e_1, e_2, e_4)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[319, 1448, 1437, 1436])).
% 0.60/0.81 tff(1450,plain,
% 0.60/0.81 (product(e_4, e_3, e_1)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[593, 1449])).
% 0.60/0.81 tff(1451,plain,
% 0.60/0.81 (~product(e_3, e_4, e_1)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[618, 1450])).
% 0.60/0.81 tff(1452,plain,
% 0.60/0.81 (product(e_3, e_4, e_2)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[731, 1451, 1425])).
% 0.60/0.81 tff(1453,plain,
% 0.60/0.81 (~product(e_5, e_4, e_2)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[790, 1452])).
% 0.60/0.81 tff(1454,plain,
% 0.60/0.81 (~product(e_1, e_4, e_5)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[683, 1422])).
% 0.60/0.81 tff(1455,plain,
% 0.60/0.81 (~product(e_1, e_4, e_4)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1117, 1422])).
% 0.60/0.81 tff(1456,plain,
% 0.60/0.81 (~product(e_1, e_4, e_2)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[713, 1452])).
% 0.60/0.81 tff(1457,plain,
% 0.60/0.81 (product(e_1, e_4, e_3)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[698, 1456, 1455, 1454])).
% 0.60/0.81 tff(1458,plain,
% 0.60/0.81 (~product(e_5, e_4, e_3)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[628, 1457])).
% 0.60/0.81 tff(1459,plain,
% 0.60/0.81 (product(e_5, e_4, e_1)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[555, 1458, 1453])).
% 0.60/0.81 tff(1460,plain,
% 0.60/0.81 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_4) | (~product(e_5, e_4, e_1)) | (~product(e_5, 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_4) | (~product(e_5, e_4, e_1)) | (~product(e_5, e_3, e_1)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1461,plain,
% 0.60/0.81 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_4) | (~product(e_5, e_4, e_1)) | (~product(e_5, e_3, e_1)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(1462,plain,
% 0.60/0.81 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_5, e_4, e_1)) | (~product(e_5, e_3, e_1))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[1461, 1460])).
% 0.60/0.81 tff(1463,plain,
% 0.60/0.81 ($false),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1462, 470, 43, 1295, 524])).
% 0.60/0.81 tff(1464,plain,((~product(e_5, e_3, e_1)) | (~product(e_5, e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.81 tff(1465,plain,
% 0.60/0.81 (~product(e_5, e_3, e_1)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1464, 1459])).
% 0.60/0.81 tff(1466,plain,
% 0.60/0.81 (~product(e_2, e_3, e_1)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[828, 1450])).
% 0.60/0.81 tff(1467,plain,
% 0.60/0.81 (~product(e_4, e_5, e_2)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[798, 72, 259, 1459])).
% 0.60/0.81 tff(1468,plain,
% 0.60/0.81 (~product(e_2, e_3, e_4)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[850, 72, 1424, 1467])).
% 0.60/0.81 tff(1469,plain,
% 0.60/0.81 (product(e_2, e_3, e_5)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[843, 1468, 1446, 1466])).
% 0.60/0.81 tff(1470,assumption,(product(e_5, e_3, e_5)), introduced(assumption)).
% 0.60/0.81 tff(1471,plain,
% 0.60/0.81 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_3, e_5)) | (~product(e_5, e_3, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_2) | (~product(e_2, e_3, e_5)) | (~product(e_5, e_3, e_5)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1472,plain,
% 0.60/0.81 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_3, e_5)) | (~product(e_5, e_3, e_5)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(1473,plain,
% 0.60/0.81 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_2) | (~product(e_2, e_3, e_5)) | (~product(e_5, e_3, e_5))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[1472, 1471])).
% 0.60/0.81 tff(1474,plain,
% 0.60/0.81 ($false),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1473, 913, 12, 1470, 810])).
% 0.60/0.81 tff(1475,plain,((~product(e_5, e_3, e_5)) | (~product(e_2, e_3, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.81 tff(1476,plain,
% 0.60/0.81 (~product(e_5, e_3, e_5)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1475, 1469])).
% 0.60/0.81 tff(1477,plain,
% 0.60/0.81 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_3)) | product(e_3, e_4, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_3)) | product(e_3, e_4, e_1))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1478,plain,
% 0.60/0.81 (((~product(e_3, e_1, e_4)) | product(e_3, e_4, e_1) | (~product(e_1, e_3, e_3))) <=> ((~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_3)) | product(e_3, e_4, e_1))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1479,plain,
% 0.60/0.81 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_3, e_4, e_1) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_3)) | product(e_3, e_4, e_1)))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[1478])).
% 0.60/0.81 tff(1480,plain,
% 0.60/0.81 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_3, e_4, e_1) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_3)) | product(e_3, e_4, e_1))),
% 0.60/0.81 inference(transitivity,[status(thm)],[1479, 1477])).
% 0.60/0.81 tff(1481,plain,
% 0.60/0.81 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_3, e_4, e_1) | (~product(e_1, e_3, e_3)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(1482,plain,
% 0.60/0.81 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_3)) | product(e_3, e_4, e_1)),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[1481, 1480])).
% 0.60/0.81 tff(1483,plain,
% 0.60/0.81 (~product(e_1, e_3, e_3)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1482, 72, 1379, 1451])).
% 0.60/0.81 tff(1484,assumption,(product(e_1, e_3, e_4)), introduced(assumption)).
% 0.60/0.81 tff(1485,plain,
% 0.60/0.81 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_4, e_4, e_3) | (~product(e_1, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | product(e_4, e_4, e_3) | (~product(e_1, e_3, e_4)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1486,plain,
% 0.60/0.81 (((~product(e_1, e_3, e_4)) | product(e_4, e_4, e_3) | (~product(e_3, e_1, e_4))) <=> ((~product(e_3, e_1, e_4)) | product(e_4, e_4, e_3) | (~product(e_1, e_3, e_4)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1487,plain,
% 0.60/0.81 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_4)) | product(e_4, e_4, e_3) | (~product(e_3, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_4, e_4, e_3) | (~product(e_1, e_3, e_4))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[1486])).
% 0.60/0.81 tff(1488,plain,
% 0.60/0.81 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_4)) | product(e_4, e_4, e_3) | (~product(e_3, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | product(e_4, e_4, e_3) | (~product(e_1, e_3, e_4)))),
% 0.60/0.81 inference(transitivity,[status(thm)],[1487, 1485])).
% 0.60/0.81 tff(1489,plain,
% 0.60/0.81 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_4)) | product(e_4, e_4, e_3) | (~product(e_3, e_1, e_4)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(1490,plain,
% 0.60/0.81 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | product(e_4, e_4, e_3) | (~product(e_1, e_3, e_4))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[1489, 1488])).
% 0.60/0.81 tff(1491,plain,
% 0.60/0.81 ($false),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1490, 72, 933, 482, 1484])).
% 0.60/0.81 tff(1492,plain,((~product(e_1, e_3, e_4)) | (~product(e_3, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.81 tff(1493,plain,
% 0.60/0.81 (~product(e_1, e_3, e_4)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1492, 1379])).
% 0.60/0.82 tff(1494,plain,
% 0.60/0.82 (~product(e_1, e_3, e_5)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1107, 1469])).
% 0.60/0.82 tff(1495,plain,
% 0.60/0.82 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | product(e_1, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | product(e_1, e_3, e_1))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(1496,plain,
% 0.60/0.82 (((~group_element(e_1)) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3))) <=> ((~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | product(e_1, e_3, e_1))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(1497,plain,
% 0.60/0.82 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_3, e_5) | 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_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | product(e_1, e_3, e_1)))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[1496])).
% 0.60/0.82 tff(1498,plain,
% 0.60/0.82 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_3, e_5) | 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_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | product(e_1, e_3, e_1))),
% 0.60/0.82 inference(transitivity,[status(thm)],[1497, 1495])).
% 0.60/0.82 tff(1499,plain,
% 0.60/0.82 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_3, e_5) | 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)))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(1500,plain,
% 0.60/0.82 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | product(e_1, e_3, e_1)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[1499, 1498])).
% 0.60/0.82 tff(1501,plain,
% 0.60/0.82 (product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1500, 272, 373, 269, 1429])).
% 0.60/0.82 tff(1502,plain,
% 0.60/0.82 (product(e_1, e_3, e_2)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1501, 1494, 1493, 1483])).
% 0.60/0.82 tff(1503,assumption,(product(e_1, e_3, e_2)), introduced(assumption)).
% 0.60/0.82 tff(1504,assumption,(product(e_5, e_3, e_2)), introduced(assumption)).
% 0.60/0.82 tff(1505,plain,
% 0.60/0.82 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_5, e_3, e_2)) | (~product(e_1, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_1) | (~product(e_5, e_3, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(1506,plain,
% 0.60/0.82 ((equalish(e_5, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_5, e_3, e_2))) <=> (equalish(e_5, e_1) | (~product(e_5, e_3, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(1507,plain,
% 0.60/0.82 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_5, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_5, e_3, e_2)) | (~product(e_1, e_3, e_2))))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[1506])).
% 0.60/0.82 tff(1508,plain,
% 0.60/0.82 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_5, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_1) | (~product(e_5, e_3, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.60/0.82 inference(transitivity,[status(thm)],[1507, 1505])).
% 0.60/0.82 tff(1509,plain,
% 0.60/0.82 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_5, e_3, e_2)))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(1510,plain,
% 0.60/0.82 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_1) | (~product(e_5, e_3, e_2)) | (~product(e_1, e_3, e_2))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[1509, 1508])).
% 0.60/0.82 tff(1511,plain,
% 0.60/0.82 ($false),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1510, 623, 12, 1504, 1503])).
% 0.60/0.82 tff(1512,plain,((~product(e_5, e_3, e_2)) | (~product(e_1, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.82 tff(1513,plain,
% 0.60/0.82 (~product(e_5, e_3, e_2)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1512, 1502])).
% 0.60/0.82 tff(1514,plain,
% 0.60/0.82 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_5, e_3, e_1) | (~group_element(e_5)) | product(e_5, e_3, e_2) | product(e_5, e_3, e_4) | product(e_5, e_3, e_5) | product(e_5, e_3, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_3)) | product(e_5, e_3, e_1) | (~group_element(e_5)) | product(e_5, e_3, e_2) | product(e_5, e_3, e_4) | product(e_5, e_3, e_5) | product(e_5, e_3, e_3))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(1515,plain,
% 0.60/0.82 (((~group_element(e_5)) | product(e_5, e_3, e_5) | product(e_5, e_3, e_4) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_1) | (~group_element(e_3))) <=> ((~group_element(e_3)) | product(e_5, e_3, e_1) | (~group_element(e_5)) | product(e_5, e_3, e_2) | product(e_5, e_3, e_4) | product(e_5, e_3, e_5) | product(e_5, e_3, e_3))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(1516,plain,
% 0.60/0.82 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_5)) | product(e_5, e_3, e_5) | product(e_5, e_3, e_4) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_1) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_5, e_3, e_1) | (~group_element(e_5)) | product(e_5, e_3, e_2) | product(e_5, e_3, e_4) | product(e_5, e_3, e_5) | product(e_5, e_3, e_3)))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[1515])).
% 0.60/0.82 tff(1517,plain,
% 0.60/0.82 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_5)) | product(e_5, e_3, e_5) | product(e_5, e_3, e_4) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_1) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_3)) | product(e_5, e_3, e_1) | (~group_element(e_5)) | product(e_5, e_3, e_2) | product(e_5, e_3, e_4) | product(e_5, e_3, e_5) | product(e_5, e_3, e_3))),
% 0.60/0.82 inference(transitivity,[status(thm)],[1516, 1514])).
% 0.60/0.82 tff(1518,plain,
% 0.60/0.82 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_5)) | product(e_5, e_3, e_5) | product(e_5, e_3, e_4) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_1) | (~group_element(e_3)))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(1519,plain,
% 0.60/0.82 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_3)) | product(e_5, e_3, e_1) | (~group_element(e_5)) | product(e_5, e_3, e_2) | product(e_5, e_3, e_4) | product(e_5, e_3, e_5) | product(e_5, e_3, e_3)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[1518, 1517])).
% 0.60/0.82 tff(1520,plain,
% 0.60/0.82 (product(e_5, e_3, e_1) | product(e_5, e_3, e_2) | product(e_5, e_3, e_4) | product(e_5, e_3, e_5) | product(e_5, e_3, e_3)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1519, 373, 427, 269])).
% 0.60/0.82 tff(1521,plain,
% 0.60/0.82 (product(e_5, e_3, e_1) | product(e_5, e_3, e_2) | product(e_5, e_3, e_4) | product(e_5, e_3, e_5)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1520, 448])).
% 0.60/0.82 tff(1522,plain,
% 0.60/0.82 (product(e_5, e_3, e_4)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1521, 1513, 1476, 1465])).
% 0.60/0.82 tff(1523,assumption,(product(e_3, e_5, e_5)), introduced(assumption)).
% 0.60/0.82 tff(1524,assumption,(product(e_5, e_3, e_4)), introduced(assumption)).
% 0.60/0.82 tff(1525,plain,
% 0.60/0.82 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_5, e_5)) | product(e_4, e_5, e_5) | (~product(e_5, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_5, e_5)) | product(e_4, e_5, e_5) | (~product(e_5, e_3, e_4)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(1526,plain,
% 0.60/0.82 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_5, e_5)) | product(e_4, e_5, e_5) | (~product(e_5, e_3, e_4)))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(1527,plain,
% 0.60/0.82 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_5, e_5)) | product(e_4, e_5, e_5) | (~product(e_5, e_3, e_4))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[1526, 1525])).
% 0.60/0.82 tff(1528,plain,
% 0.60/0.82 ($false),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1527, 72, 1524, 424, 1523])).
% 0.60/0.82 tff(1529,plain,((~product(e_3, e_5, e_5)) | (~product(e_5, e_3, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.82 tff(1530,plain,
% 0.60/0.82 (~product(e_3, e_5, e_5)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1529, 1522])).
% 0.60/0.82 tff(1531,plain,
% 0.60/0.82 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_5, e_5)) | product(e_3, e_5, e_5) | (~product(e_5, e_5, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_5, e_5, e_5)) | product(e_3, e_5, e_5) | (~product(e_5, e_5, e_3)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(1532,plain,
% 0.60/0.82 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_5, e_5)) | product(e_3, e_5, e_5) | (~product(e_5, e_5, e_3)))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(1533,plain,
% 0.60/0.82 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_5, e_5, e_5)) | product(e_3, e_5, e_5) | (~product(e_5, e_5, e_3))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[1532, 1531])).
% 0.60/0.82 tff(1534,plain,
% 0.60/0.82 (~product(e_5, e_5, e_3)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1533, 72, 416, 1530])).
% 0.60/0.82 tff(1535,plain,
% 0.60/0.82 ($false),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[816, 72, 1469, 1424, 1534])).
% 0.60/0.82 tff(1536,plain,(~cycle(e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.82 tff(1537,plain,
% 0.60/0.82 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_4)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_4)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(1538,plain,
% 0.60/0.82 (((~greater(e_4, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_4))) <=> ((~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_4)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(1539,plain,
% 0.60/0.82 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_4, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_4)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_4))))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[1538])).
% 0.60/0.82 tff(1540,plain,
% 0.60/0.82 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_4, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_4)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_4)))),
% 0.60/0.82 inference(transitivity,[status(thm)],[1539, 1537])).
% 0.60/0.82 tff(1541,plain,
% 0.60/0.82 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_4, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_4)))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(1542,plain,
% 0.60/0.82 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_4))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[1541, 1540])).
% 0.60/0.82 tff(1543,plain,
% 0.60/0.82 ((~cycle(e_4, e_0)) | (~cycle(e_2, e_4))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1542, 1156, 224, 203, 1153, 1322])).
% 0.60/0.82 tff(1544,plain,
% 0.60/0.82 (~cycle(e_4, e_0)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1543, 221])).
% 0.60/0.82 tff(1545,plain,
% 0.60/0.82 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_4, e_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_1)) | (~cycle(e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_1)) | (~cycle(e_2, e_4)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(1546,plain,
% 0.60/0.82 (((~cycle(e_2, e_4)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_1))) <=> (equalish(e_4, e_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_1)) | (~cycle(e_2, e_4)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(1547,plain,
% 0.60/0.82 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_2, e_4)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_4, e_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_1)) | (~cycle(e_2, e_4))))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[1546])).
% 0.60/0.82 tff(1548,plain,
% 0.60/0.82 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_2, e_4)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_1)) | (~cycle(e_2, e_4)))),
% 0.60/0.82 inference(transitivity,[status(thm)],[1547, 1545])).
% 0.60/0.82 tff(1549,plain,
% 0.60/0.82 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_2, e_4)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_1)))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(1550,plain,
% 0.60/0.82 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_1)) | (~cycle(e_2, e_4))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[1549, 1548])).
% 0.60/0.82 tff(1551,plain,
% 0.60/0.82 (~cycle(e_3, e_1)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1550, 1206, 100, 224, 1150, 652, 221])).
% 0.60/0.82 tff(1552,plain,
% 0.60/0.82 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_4, e_1) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)) | (~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | (~next(e_0, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_4, e_1) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)) | (~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | (~next(e_0, e_1)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(1553,plain,
% 0.60/0.82 (((~cycle(e_2, e_4)) | equalish(e_4, e_1) | (~next(e_0, e_1)) | (~greater(e_4, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0))) <=> (equalish(e_4, e_1) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)) | (~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | (~next(e_0, e_1)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(1554,plain,
% 0.60/0.83 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_2, e_4)) | equalish(e_4, e_1) | (~next(e_0, e_1)) | (~greater(e_4, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_4, e_1) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)) | (~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | (~next(e_0, e_1))))),
% 0.60/0.83 inference(monotonicity,[status(thm)],[1553])).
% 0.60/0.83 tff(1555,plain,
% 0.60/0.83 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_2, e_4)) | equalish(e_4, e_1) | (~next(e_0, e_1)) | (~greater(e_4, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_4, e_1) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)) | (~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | (~next(e_0, e_1)))),
% 0.60/0.83 inference(transitivity,[status(thm)],[1554, 1552])).
% 0.60/0.83 tff(1556,plain,
% 0.60/0.83 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_2, e_4)) | equalish(e_4, e_1) | (~next(e_0, e_1)) | (~greater(e_4, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)))),
% 0.60/0.83 inference(quant_inst,[status(thm)],[])).
% 0.60/0.83 tff(1557,plain,
% 0.60/0.83 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_4, e_1) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)) | (~greater(e_4, e_0)) | (~cycle(e_2, e_4)) | (~next(e_0, e_1))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[1556, 1555])).
% 0.60/0.83 tff(1558,plain,
% 0.60/0.83 (~cycle(e_3, e_0)),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[1557, 1159, 100, 224, 1150, 509, 221])).
% 0.60/0.83 tff(1559,plain,
% 0.60/0.83 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_4, e_5) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_4)) | (~cycle(e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_4, e_5) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_4)) | (~cycle(e_3, e_4)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(1560,plain,
% 0.60/0.83 (((~cycle(e_2, e_4)) | equalish(e_4, e_5) | (~next(e_4, e_5)) | (~greater(e_4, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_4))) <=> (equalish(e_4, e_5) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_4)) | (~cycle(e_3, e_4)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(1561,plain,
% 0.60/0.83 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_2, e_4)) | equalish(e_4, e_5) | (~next(e_4, e_5)) | (~greater(e_4, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_4, e_5) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_4)) | (~cycle(e_3, e_4))))),
% 0.60/0.83 inference(monotonicity,[status(thm)],[1560])).
% 0.60/0.83 tff(1562,plain,
% 0.60/0.83 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_2, e_4)) | equalish(e_4, e_5) | (~next(e_4, e_5)) | (~greater(e_4, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_4, e_5) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_4)) | (~cycle(e_3, e_4)))),
% 0.60/0.83 inference(transitivity,[status(thm)],[1561, 1559])).
% 0.60/0.83 tff(1563,plain,
% 0.60/0.83 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_2, e_4)) | equalish(e_4, e_5) | (~next(e_4, e_5)) | (~greater(e_4, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_4)))),
% 0.60/0.83 inference(quant_inst,[status(thm)],[])).
% 0.60/0.83 tff(1564,plain,
% 0.60/0.83 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_4, e_5) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_4)) | (~cycle(e_3, e_4))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[1563, 1562])).
% 0.60/0.83 tff(1565,plain,
% 0.60/0.83 (~cycle(e_3, e_4)),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[1564, 100, 1156, 224, 1150, 419, 221])).
% 0.60/0.83 tff(1566,plain,
% 0.60/0.83 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_2)) | (~cycle(e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_2)) | (~cycle(e_2, e_4)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(1567,plain,
% 0.60/0.83 (((~cycle(e_2, e_4)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2))) <=> (equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_2)) | (~cycle(e_2, e_4)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(1568,plain,
% 0.60/0.83 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_2, e_4)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_2)) | (~cycle(e_2, e_4))))),
% 0.60/0.83 inference(monotonicity,[status(thm)],[1567])).
% 0.60/0.83 tff(1569,plain,
% 0.60/0.83 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_2, e_4)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_2)) | (~cycle(e_2, e_4)))),
% 0.60/0.83 inference(transitivity,[status(thm)],[1568, 1566])).
% 0.60/0.83 tff(1570,plain,
% 0.60/0.83 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_2, e_4)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2)))),
% 0.60/0.83 inference(quant_inst,[status(thm)],[])).
% 0.60/0.83 tff(1571,plain,
% 0.60/0.83 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_2)) | (~cycle(e_2, e_4))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[1570, 1569])).
% 0.60/0.83 tff(1572,plain,
% 0.60/0.83 (~cycle(e_3, e_2)),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[1571, 100, 224, 1150, 191, 221])).
% 0.60/0.83 tff(1573,plain,
% 0.60/0.83 (cycle(e_3, e_3)),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[377, 1572, 1565, 1558, 1551])).
% 0.60/0.83 tff(1574,plain,
% 0.60/0.83 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~cycle(e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~cycle(e_4, e_1)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(1575,plain,
% 0.60/0.83 (((~cycle(e_3, e_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1))) <=> (equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~cycle(e_4, e_1)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(1576,plain,
% 0.60/0.83 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_3, e_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~cycle(e_4, e_1))))),
% 0.60/0.83 inference(monotonicity,[status(thm)],[1575])).
% 0.60/0.83 tff(1577,plain,
% 0.60/0.83 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_3, e_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~cycle(e_4, e_1)))),
% 0.60/0.83 inference(transitivity,[status(thm)],[1576, 1574])).
% 0.60/0.83 tff(1578,plain,
% 0.60/0.83 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_3, e_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)))),
% 0.60/0.83 inference(quant_inst,[status(thm)],[])).
% 0.60/0.83 tff(1579,plain,
% 0.60/0.83 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~cycle(e_4, e_1))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[1578, 1577])).
% 0.60/0.83 tff(1580,plain,
% 0.60/0.83 (~cycle(e_4, e_1)),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[1579, 1206, 330, 113, 1150, 755, 1573])).
% 0.60/0.83 tff(1581,plain,
% 0.60/0.83 (((~![W: $i, Z: $i, Y: $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) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~cycle(e_4, 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) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~cycle(e_4, e_3)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(1582,plain,
% 0.60/0.83 (((~cycle(e_3, e_3)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_3))) <=> (equalish(e_3, e_4) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~cycle(e_4, e_3)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(1583,plain,
% 0.60/0.83 (((~![W: $i, Z: $i, Y: $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_4) | (~next(e_3, e_4)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, 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) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~cycle(e_4, e_3))))),
% 0.67/0.83 inference(monotonicity,[status(thm)],[1582])).
% 0.67/0.83 tff(1584,plain,
% 0.67/0.83 (((~![W: $i, Z: $i, Y: $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_4) | (~next(e_3, e_4)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, 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) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~cycle(e_4, e_3)))),
% 0.67/0.83 inference(transitivity,[status(thm)],[1583, 1581])).
% 0.67/0.83 tff(1585,plain,
% 0.67/0.83 ((~![W: $i, Z: $i, Y: $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_4) | (~next(e_3, e_4)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_3)))),
% 0.67/0.83 inference(quant_inst,[status(thm)],[])).
% 0.67/0.83 tff(1586,plain,
% 0.67/0.83 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_4) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~cycle(e_4, e_3))),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[1585, 1584])).
% 0.67/0.83 tff(1587,plain,
% 0.67/0.83 (~cycle(e_4, e_3)),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[1586, 330, 113, 1150, 470, 1573])).
% 0.67/0.83 tff(1588,plain,
% 0.67/0.83 ($false),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[1201, 1587, 1580, 1544])).
% 0.67/0.83 tff(1589,plain,(~cycle(e_2, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.83 tff(1590,plain,
% 0.67/0.83 (cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1)),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[282, 1589])).
% 0.67/0.83 tff(1591,plain,
% 0.67/0.83 (cycle(e_2, e_2) | cycle(e_2, e_1)),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[1590, 1536])).
% 0.67/0.83 tff(1592,plain,
% 0.67/0.83 ($false),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[1591, 1338, 1330])).
% 0.67/0.83 tff(1593,plain,(~cycle(e_4, e_0)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.83 tff(1594,plain,
% 0.67/0.83 (cycle(e_4, e_1)),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[1201, 1593, 1167])).
% 0.67/0.83 tff(1595,plain,
% 0.67/0.83 (~cycle(e_3, e_4)),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[1214, 1594])).
% 0.67/0.83 tff(1596,plain,
% 0.67/0.83 (~product(e_3, e_1, e_2)),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[1246, 1595, 1311])).
% 0.67/0.83 tff(1597,plain,
% 0.67/0.83 (product(e_4, e_1, e_2)),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[1138, 1596, 855])).
% 0.67/0.83 tff(1598,plain,
% 0.67/0.83 ($false),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[1405, 1156, 97, 94, 1399, 1594, 1597])).
% 0.67/0.83 % SZS output end Proof
% 0.67/0.83 % E exiting
%------------------------------------------------------------------------------