%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP125-2.005 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 0.20s 0.49s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP125-2.005 : TPTP v9.0.0. Released v1.2.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 15:42:54 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.49 % SZS status Unsatisfiable
% 0.20/0.49 % SZS output start Proof
% 0.20/0.49 tff(product_type, type, (
% 0.20/0.49 product: ( $i * $i * $i ) > $o)).
% 0.20/0.49 tff(e_3_type, type, (
% 0.20/0.49 e_3: $i)).
% 0.20/0.49 tff(e_4_type, type, (
% 0.20/0.49 e_4: $i)).
% 0.20/0.49 tff(e_2_type, type, (
% 0.20/0.49 e_2: $i)).
% 0.20/0.49 tff(e_1_type, type, (
% 0.20/0.49 e_1: $i)).
% 0.20/0.49 tff(e_5_type, type, (
% 0.20/0.49 e_5: $i)).
% 0.20/0.49 tff(equalish_type, type, (
% 0.20/0.49 equalish: ( $i * $i ) > $o)).
% 0.20/0.49 tff(next_type, type, (
% 0.20/0.49 next: ( $i * $i ) > $o)).
% 0.20/0.49 tff(greater_type, type, (
% 0.20/0.49 greater: ( $i * $i ) > $o)).
% 0.20/0.49 tff(group_element_type, type, (
% 0.20/0.49 group_element: $i > $o)).
% 0.20/0.49 tff(1,assumption,(~product(e_4, e_2, e_1)), introduced(assumption)).
% 0.20/0.49 tff(2,assumption,(~product(e_1, e_3, e_4)), introduced(assumption)).
% 0.20/0.49 tff(3,assumption,(product(e_1, e_2, e_2)), introduced(assumption)).
% 0.20/0.49 tff(4,plain,
% 0.20/0.49 (^[X: $i] : refl(product(X, X, X) <=> product(X, X, X))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(5,plain,
% 0.20/0.49 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.20/0.49 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.49 tff(6,plain,
% 0.20/0.49 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(7,axiom,(![X: $i] : product(X, X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_idempotence')).
% 0.20/0.49 tff(8,plain,
% 0.20/0.49 (![X: $i] : product(X, X, X)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.20/0.49 tff(9,plain,(
% 0.20/0.49 ![X: $i] : product(X, X, X)),
% 0.20/0.49 inference(skolemize,[status(sab)],[8])).
% 0.20/0.49 tff(10,plain,
% 0.20/0.49 (![X: $i] : product(X, X, X)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.49 tff(11,plain,
% 0.20/0.49 ((~![X: $i] : product(X, X, X)) | product(e_2, e_2, e_2)),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(12,plain,
% 0.20/0.49 (product(e_2, e_2, e_2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.20/0.49 tff(13,plain,
% 0.20/0.49 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(14,plain,
% 0.20/0.49 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.49 tff(15,plain,
% 0.20/0.49 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(16,plain,
% 0.20/0.49 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(W, Y, X)) | (~product(Z, Y, X))) <=> ((~product(Z, Y, X)) | (~product(W, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> (((~product(Z, Y, X)) | (~product(W, Y, X))) | equalish(W, Z)))), rewrite((((~product(Z, Y, X)) | (~product(W, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(17,plain,
% 0.20/0.49 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[16])).
% 0.20/0.49 tff(18,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_left_cancellation')).
% 0.20/0.49 tff(19,plain,
% 0.20/0.49 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.20/0.49 tff(20,plain,
% 0.20/0.49 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.20/0.49 tff(21,plain,(
% 0.20/0.49 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[20])).
% 0.20/0.49 tff(22,plain,
% 0.20/0.49 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.20/0.50 tff(23,plain,
% 0.20/0.50 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(24,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.20/0.50 tff(25,plain,
% 0.20/0.50 (~equalish(e_1, e_2)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.50 tff(26,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(27,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(28,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.50 tff(29,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[28, 25, 22, 12, 3])).
% 0.20/0.50 tff(30,plain,(~product(e_1, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(31,plain,
% 0.20/0.50 (^[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))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(32,plain,
% 0.20/0.50 (![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)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.50 tff(33,plain,
% 0.20/0.50 (![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)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(34,plain,
% 0.20/0.50 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : rewrite((((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, X)) <=> ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(35,plain,
% 0.20/0.50 (![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)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[34])).
% 0.20/0.50 tff(36,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')).
% 0.20/0.50 tff(37,plain,
% 0.20/0.50 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.50 tff(38,plain,
% 0.20/0.50 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.20/0.50 tff(39,plain,(
% 0.20/0.50 ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[38])).
% 0.20/0.50 tff(40,plain,
% 0.20/0.50 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.20/0.50 tff(41,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_2, e_2)) | product(e_1, e_2, e_2) | (~product(e_2, 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_2, e_2)) | product(e_1, e_2, e_2) | (~product(e_2, e_2, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(42,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_2, e_2)) | product(e_1, e_2, e_2) | (~product(e_2, e_2, e_1)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(43,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_2, e_2, e_2)) | product(e_1, e_2, e_2) | (~product(e_2, e_2, e_1))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.50 tff(44,plain,
% 0.20/0.50 (~product(e_2, e_2, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[43, 40, 12, 30])).
% 0.20/0.50 tff(45,assumption,(product(e_2, e_5, e_3)), introduced(assumption)).
% 0.20/0.50 tff(46,assumption,(~product(e_1, e_1, e_1)), introduced(assumption)).
% 0.20/0.50 tff(47,plain,
% 0.20/0.50 ((~![X: $i] : product(X, X, X)) | product(e_1, e_1, e_1)),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(48,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[47, 10, 46])).
% 0.20/0.50 tff(49,plain,(product(e_1, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(50,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.20/0.50 tff(51,assumption,(product(e_1, e_1, e_1)), introduced(assumption)).
% 0.20/0.50 tff(52,plain,
% 0.20/0.50 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(53,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.20/0.50 tff(54,plain,
% 0.20/0.50 (~equalish(e_2, e_1)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.50 tff(55,plain,
% 0.20/0.50 (((~![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_2, e_1, e_1)) | (~product(e_1, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(56,plain,
% 0.20/0.50 ((equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1))) <=> (equalish(e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(57,plain,
% 0.20/0.50 (((~![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_2, e_1, e_1)) | (~product(e_1, e_1, e_1))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[56])).
% 0.20/0.50 tff(58,plain,
% 0.20/0.50 (((~![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_2, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[57, 55])).
% 0.20/0.50 tff(59,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(60,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.50 tff(61,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[60, 54, 22, 51, 50])).
% 0.20/0.50 tff(62,plain,((~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(63,plain,
% 0.20/0.50 (~product(e_2, e_1, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[62, 49])).
% 0.20/0.50 tff(64,assumption,(product(e_2, e_1, e_2)), introduced(assumption)).
% 0.20/0.50 tff(65,plain,
% 0.20/0.50 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(66,plain,
% 0.20/0.50 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[65])).
% 0.20/0.50 tff(67,plain,
% 0.20/0.50 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(68,plain,
% 0.20/0.50 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(X, W, Y)) | (~product(X, Z, Y))) <=> ((~product(X, Z, Y)) | (~product(X, W, Y)))), ((((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> (((~product(X, Z, Y)) | (~product(X, W, Y))) | equalish(W, Z)))), rewrite((((~product(X, Z, Y)) | (~product(X, W, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))), ((((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(69,plain,
% 0.20/0.50 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.50 tff(70,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_right_cancellation')).
% 0.20/0.50 tff(71,plain,
% 0.20/0.50 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.50 tff(72,plain,
% 0.20/0.50 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.20/0.50 tff(73,plain,(
% 0.20/0.50 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[72])).
% 0.20/0.50 tff(74,plain,
% 0.20/0.50 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.20/0.50 tff(75,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(76,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(77,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.50 tff(78,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[77, 25, 74, 64, 12])).
% 0.20/0.50 tff(79,plain,(~product(e_2, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(80,plain,
% 0.20/0.50 (^[Y: $i, X: $i, X1: $i] : refl(((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y))) <=> ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(81,plain,
% 0.20/0.50 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y))) <=> ![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[80])).
% 0.20/0.50 tff(82,plain,
% 0.20/0.50 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y))) <=> ![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(83,plain,
% 0.20/0.50 (^[Y: $i, X: $i, X1: $i] : trans(monotonicity(rewrite(((~product(X, e_1, Y)) | (~next(X, X1))) <=> ((~next(X, X1)) | (~product(X, e_1, Y)))), ((((~product(X, e_1, Y)) | (~next(X, X1))) | (~greater(Y, X1))) <=> (((~next(X, X1)) | (~product(X, e_1, Y))) | (~greater(Y, X1))))), rewrite((((~next(X, X1)) | (~product(X, e_1, Y))) | (~greater(Y, X1))) <=> ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))), ((((~product(X, e_1, Y)) | (~next(X, X1))) | (~greater(Y, X1))) <=> ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(84,plain,
% 0.20/0.50 (![Y: $i, X: $i, X1: $i] : (((~product(X, e_1, Y)) | (~next(X, X1))) | (~greater(Y, X1))) <=> ![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[83])).
% 0.20/0.50 tff(85,axiom,(![Y: $i, X: $i, X1: $i] : (((~product(X, e_1, Y)) | (~next(X, X1))) | (~greater(Y, X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','no_redundancy')).
% 0.20/0.50 tff(86,plain,
% 0.20/0.50 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.50 tff(87,plain,
% 0.20/0.50 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.20/0.50 tff(88,plain,(
% 0.20/0.50 ![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[87])).
% 0.20/0.50 tff(89,plain,
% 0.20/0.50 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.20/0.50 tff(90,plain,
% 0.20/0.50 (greater(e_5, e_3) <=> greater(e_5, e_3)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(91,axiom,(greater(e_5, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_greater_e_3')).
% 0.20/0.50 tff(92,plain,
% 0.20/0.50 (greater(e_5, e_3)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.20/0.50 tff(93,plain,
% 0.20/0.50 (next(e_2, e_3) <=> next(e_2, e_3)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(94,axiom,(next(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_then_e_3')).
% 0.20/0.50 tff(95,plain,
% 0.20/0.50 (next(e_2, e_3)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.50 tff(96,plain,
% 0.20/0.50 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_5, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_5, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(97,plain,
% 0.20/0.50 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_5, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(98,plain,
% 0.20/0.50 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_5, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.20/0.50 tff(99,plain,
% 0.20/0.50 (~product(e_2, e_1, e_5)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[98, 95, 92, 89])).
% 0.20/0.50 tff(100,plain,
% 0.20/0.50 (greater(e_4, e_3) <=> greater(e_4, e_3)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(101,axiom,(greater(e_4, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_greater_e_3')).
% 0.20/0.50 tff(102,plain,
% 0.20/0.50 (greater(e_4, e_3)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.20/0.50 tff(103,plain,
% 0.20/0.50 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_4, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_4, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(104,plain,
% 0.20/0.50 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_4, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(105,plain,
% 0.20/0.50 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_4, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.20/0.50 tff(106,plain,
% 0.20/0.50 (~product(e_2, e_1, e_4)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[105, 95, 102, 89])).
% 0.20/0.50 tff(107,plain,
% 0.20/0.50 (^[Y: $i, X: $i] : refl((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)) | (~group_element(X))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(108,plain,
% 0.20/0.50 (![Y: $i, X: $i] : (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))) <=> ![Y: $i, X: $i] : (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)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[107])).
% 0.20/0.50 tff(109,plain,
% 0.20/0.50 (![Y: $i, X: $i] : (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))) <=> ![Y: $i, X: $i] : (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)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(110,plain,
% 0.20/0.50 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) <=> (product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> ((product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_2)))), rewrite(((product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_2)) <=> (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))), ((((((~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_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_3)))), rewrite(((product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_3)) <=> (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), ((((((~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_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))), (((((((~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_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_4)))), rewrite(((product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_4)) <=> (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((((~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_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))), ((((((((~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)) <=> ((product(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)))), rewrite(((product(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_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(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)) <=> (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)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(111,plain,
% 0.20/0.50 (![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] : (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)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[110])).
% 0.20/0.50 tff(112,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')).
% 0.20/0.50 tff(113,plain,
% 0.20/0.50 (![Y: $i, X: $i] : (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)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.20/0.50 tff(114,plain,
% 0.20/0.50 (![Y: $i, X: $i] : (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)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.20/0.50 tff(115,plain,(
% 0.20/0.50 ![Y: $i, X: $i] : (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)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[114])).
% 0.20/0.50 tff(116,plain,
% 0.20/0.50 (![Y: $i, X: $i] : (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)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[115, 108])).
% 0.20/0.50 tff(117,plain,
% 0.20/0.50 (group_element(e_2) <=> group_element(e_2)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(118,axiom,(group_element(e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_2')).
% 0.20/0.50 tff(119,plain,
% 0.20/0.50 (group_element(e_2)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.20/0.50 tff(120,plain,
% 0.20/0.50 (group_element(e_1) <=> group_element(e_1)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(121,axiom,(group_element(e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_1')).
% 0.20/0.50 tff(122,plain,
% 0.20/0.50 (group_element(e_1)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.20/0.50 tff(123,plain,
% 0.20/0.50 (((~![Y: $i, X: $i] : (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(e_2, e_1, e_4) | product(e_2, e_1, e_5) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (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(e_2, e_1, e_4) | product(e_2, e_1, e_5) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_2)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(124,plain,
% 0.20/0.50 ((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_2))) <=> (product(e_2, e_1, e_4) | product(e_2, e_1, e_5) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_2)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(125,plain,
% 0.20/0.51 (((~![Y: $i, X: $i] : (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(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_2)))) <=> ((~![Y: $i, X: $i] : (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(e_2, e_1, e_4) | product(e_2, e_1, e_5) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_2))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[124])).
% 0.20/0.51 tff(126,plain,
% 0.20/0.51 (((~![Y: $i, X: $i] : (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(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_2)))) <=> ((~![Y: $i, X: $i] : (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(e_2, e_1, e_4) | product(e_2, e_1, e_5) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_2)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[125, 123])).
% 0.20/0.51 tff(127,plain,
% 0.20/0.51 ((~![Y: $i, X: $i] : (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(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_2)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(128,plain,
% 0.20/0.51 ((~![Y: $i, X: $i] : (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(e_2, e_1, e_4) | product(e_2, e_1, e_5) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_2))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.20/0.51 tff(129,plain,
% 0.20/0.51 (product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[128, 122, 119, 116, 106, 99])).
% 0.20/0.51 tff(130,plain,
% 0.20/0.51 (product(e_2, e_1, e_3) | product(e_2, e_1, e_1)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[129, 79])).
% 0.20/0.51 tff(131,plain,
% 0.20/0.51 (product(e_2, e_1, e_3)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[130, 63])).
% 0.20/0.51 tff(132,plain,
% 0.20/0.51 ((~equalish(e_5, e_1)) <=> (~equalish(e_5, e_1))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(133,axiom,(~equalish(e_5, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_is_not_e_1')).
% 0.20/0.51 tff(134,plain,
% 0.20/0.51 (~equalish(e_5, e_1)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.20/0.51 tff(135,plain,
% 0.20/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_5, e_3)))) <=> ((~![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_2, e_1, e_3)) | (~product(e_2, e_5, e_3)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(136,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_5, e_3)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(137,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_5, e_3))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.20/0.51 tff(138,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[137, 134, 74, 131, 45])).
% 0.20/0.51 tff(139,plain,(~product(e_2, e_5, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(140,assumption,(product(e_3, e_1, e_2)), introduced(assumption)).
% 0.20/0.51 tff(141,plain,
% 0.20/0.51 (((~![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_1, e_3, e_5)) | product(e_2, 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_2)) | (~product(e_1, e_3, e_5)) | product(e_2, e_5, e_3))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(142,plain,
% 0.20/0.51 (((~product(e_1, e_3, e_5)) | product(e_2, e_5, e_3) | (~product(e_3, e_1, e_2))) <=> ((~product(e_3, e_1, e_2)) | (~product(e_1, e_3, e_5)) | product(e_2, e_5, e_3))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(143,plain,
% 0.20/0.51 (((~![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_5)) | product(e_2, e_5, e_3) | (~product(e_3, 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_3, e_1, e_2)) | (~product(e_1, e_3, e_5)) | product(e_2, e_5, e_3)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[142])).
% 0.20/0.51 tff(144,plain,
% 0.20/0.51 (((~![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_5)) | product(e_2, e_5, e_3) | (~product(e_3, 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_3, e_1, e_2)) | (~product(e_1, e_3, e_5)) | product(e_2, e_5, e_3))),
% 0.20/0.51 inference(transitivity,[status(thm)],[143, 141])).
% 0.20/0.51 tff(145,plain,
% 0.20/0.51 ((~![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_5)) | product(e_2, e_5, e_3) | (~product(e_3, e_1, e_2)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(146,plain,
% 0.20/0.51 ((~![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_1, e_3, e_5)) | product(e_2, e_5, e_3)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.20/0.51 tff(147,plain,
% 0.20/0.51 ((~product(e_3, e_1, e_2)) | (~product(e_1, e_3, e_5)) | product(e_2, e_5, e_3)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[146, 40])).
% 0.20/0.51 tff(148,plain,
% 0.20/0.51 (~product(e_1, e_3, e_5)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[147, 140, 139])).
% 0.20/0.51 tff(149,assumption,(product(e_1, e_3, e_1)), introduced(assumption)).
% 0.20/0.51 tff(150,plain,
% 0.20/0.51 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(151,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.20/0.51 tff(152,plain,
% 0.20/0.51 (~equalish(e_3, e_1)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.20/0.51 tff(153,plain,
% 0.20/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(154,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(155,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.20/0.51 tff(156,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[155, 152, 74, 51, 149])).
% 0.20/0.51 tff(157,plain,((~product(e_1, e_3, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(158,plain,
% 0.20/0.51 (~product(e_1, e_3, e_1)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[157, 49])).
% 0.20/0.51 tff(159,assumption,(product(e_1, e_3, e_3)), introduced(assumption)).
% 0.20/0.51 tff(160,plain,
% 0.20/0.51 ((~![X: $i] : product(X, X, X)) | product(e_3, e_3, e_3)),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(161,plain,
% 0.20/0.51 (product(e_3, e_3, e_3)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[160, 10])).
% 0.20/0.51 tff(162,plain,
% 0.20/0.51 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(163,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.20/0.51 tff(164,plain,
% 0.20/0.51 (~equalish(e_1, e_3)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.20/0.51 tff(165,plain,
% 0.20/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(166,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(167,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.20/0.51 tff(168,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[167, 164, 22, 161, 159])).
% 0.20/0.51 tff(169,plain,(~product(e_1, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(170,plain,
% 0.20/0.51 (group_element(e_3) <=> group_element(e_3)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(171,axiom,(group_element(e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_3')).
% 0.20/0.51 tff(172,plain,
% 0.20/0.51 (group_element(e_3)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.20/0.51 tff(173,plain,
% 0.20/0.51 (((~![Y: $i, X: $i] : (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(e_1)) | (~group_element(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_3) | product(e_1, e_3, e_1))) <=> ((~![Y: $i, X: $i] : (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(e_1)) | (~group_element(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_3) | product(e_1, e_3, e_1))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(174,plain,
% 0.20/0.51 ((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_1)) | (~group_element(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_3) | product(e_1, e_3, e_1))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(175,plain,
% 0.20/0.51 (((~![Y: $i, X: $i] : (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(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)))) <=> ((~![Y: $i, X: $i] : (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(e_1)) | (~group_element(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_3) | product(e_1, e_3, e_1)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[174])).
% 0.20/0.51 tff(176,plain,
% 0.20/0.51 (((~![Y: $i, X: $i] : (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(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)))) <=> ((~![Y: $i, X: $i] : (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(e_1)) | (~group_element(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_3) | product(e_1, e_3, e_1))),
% 0.20/0.51 inference(transitivity,[status(thm)],[175, 173])).
% 0.20/0.51 tff(177,plain,
% 0.20/0.51 ((~![Y: $i, X: $i] : (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(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)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(178,plain,
% 0.20/0.51 ((~![Y: $i, X: $i] : (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(e_1)) | (~group_element(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_3) | product(e_1, e_3, e_1)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.20/0.51 tff(179,plain,
% 0.20/0.51 (product(e_1, e_3, e_2) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[178, 122, 172, 116, 169, 158])).
% 0.20/0.51 tff(180,plain,
% 0.20/0.51 (product(e_1, e_3, e_2)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[179, 148, 2])).
% 0.20/0.51 tff(181,plain,
% 0.20/0.51 (((~![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_2)) | (~product(e_3, e_1, e_2)) | product(e_2, 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_1, e_3, e_2)) | (~product(e_3, e_1, e_2)) | product(e_2, e_2, e_1))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(182,plain,
% 0.20/0.51 (((~product(e_3, e_1, e_2)) | product(e_2, e_2, e_1) | (~product(e_1, e_3, e_2))) <=> ((~product(e_1, e_3, e_2)) | (~product(e_3, e_1, e_2)) | product(e_2, e_2, e_1))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(183,plain,
% 0.20/0.51 (((~![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_2, e_1) | (~product(e_1, 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_1, e_3, e_2)) | (~product(e_3, e_1, e_2)) | product(e_2, e_2, e_1)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[182])).
% 0.20/0.51 tff(184,plain,
% 0.20/0.51 (((~![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_2, e_1) | (~product(e_1, 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_1, e_3, e_2)) | (~product(e_3, e_1, e_2)) | product(e_2, e_2, e_1))),
% 0.20/0.51 inference(transitivity,[status(thm)],[183, 181])).
% 0.20/0.51 tff(185,plain,
% 0.20/0.51 ((~![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_2, e_1) | (~product(e_1, e_3, e_2)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(186,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_1, e_2)) | product(e_2, e_2, e_1)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.20/0.52 tff(187,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[186, 40, 140, 180, 44])).
% 0.20/0.52 tff(188,plain,((~product(e_3, e_1, e_2)) | product(e_1, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(189,plain,
% 0.20/0.52 (~product(e_3, e_1, e_2)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[188, 2])).
% 0.20/0.52 tff(190,assumption,(product(e_3, e_1, e_1)), introduced(assumption)).
% 0.20/0.52 tff(191,plain,
% 0.20/0.52 (((~![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_3, e_1, e_1)) | (~product(e_1, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(192,plain,
% 0.20/0.52 ((equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1))) <=> (equalish(e_3, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(193,plain,
% 0.20/0.52 (((~![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_3, e_1, e_1)) | (~product(e_1, e_1, e_1))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[192])).
% 0.20/0.52 tff(194,plain,
% 0.20/0.52 (((~![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_3, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[193, 191])).
% 0.20/0.52 tff(195,plain,
% 0.20/0.52 ((~![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)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(196,plain,
% 0.20/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.20/0.52 tff(197,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[196, 152, 22, 51, 190])).
% 0.20/0.52 tff(198,plain,((~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(199,plain,
% 0.20/0.52 (~product(e_3, e_1, e_1)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[198, 49])).
% 0.20/0.52 tff(200,assumption,(product(e_3, e_1, e_3)), introduced(assumption)).
% 0.20/0.52 tff(201,plain,
% 0.20/0.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(202,plain,
% 0.20/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(203,plain,
% 0.20/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.20/0.52 tff(204,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[203, 164, 74, 200, 161])).
% 0.20/0.52 tff(205,plain,(~product(e_3, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(206,plain,
% 0.20/0.52 (greater(e_5, e_4) <=> greater(e_5, e_4)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(207,axiom,(greater(e_5, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_greater_e_4')).
% 0.20/0.52 tff(208,plain,
% 0.20/0.52 (greater(e_5, e_4)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.20/0.52 tff(209,plain,
% 0.20/0.52 (next(e_3, e_4) <=> next(e_3, e_4)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(210,axiom,(next(e_3, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_then_e_4')).
% 0.20/0.52 tff(211,plain,
% 0.20/0.52 (next(e_3, e_4)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.20/0.52 tff(212,plain,
% 0.20/0.52 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_5, e_4)) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_5, e_4)) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(213,plain,
% 0.20/0.52 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_5, e_4)) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(214,plain,
% 0.20/0.52 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_5, e_4)) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.20/0.52 tff(215,plain,
% 0.20/0.52 (~product(e_3, e_1, e_5)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[214, 211, 208, 89])).
% 0.20/0.52 tff(216,plain,
% 0.20/0.52 (((~![Y: $i, X: $i] : (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(e_3, e_1, e_5) | (~group_element(e_1)) | 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_3)))) <=> ((~![Y: $i, X: $i] : (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(e_3, e_1, e_5) | (~group_element(e_1)) | 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_3)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(217,plain,
% 0.20/0.52 ((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_3))) <=> (product(e_3, e_1, e_5) | (~group_element(e_1)) | 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_3)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(218,plain,
% 0.20/0.52 (((~![Y: $i, X: $i] : (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(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_3)))) <=> ((~![Y: $i, X: $i] : (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(e_3, e_1, e_5) | (~group_element(e_1)) | 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_3))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[217])).
% 0.20/0.52 tff(219,plain,
% 0.20/0.52 (((~![Y: $i, X: $i] : (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(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_3)))) <=> ((~![Y: $i, X: $i] : (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(e_3, e_1, e_5) | (~group_element(e_1)) | 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_3)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[218, 216])).
% 0.20/0.52 tff(220,plain,
% 0.20/0.52 ((~![Y: $i, X: $i] : (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(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_3)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(221,plain,
% 0.20/0.52 ((~![Y: $i, X: $i] : (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(e_3, e_1, e_5) | (~group_element(e_1)) | 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_3))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.20/0.52 tff(222,plain,
% 0.20/0.52 (product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[221, 122, 172, 116, 215])).
% 0.20/0.52 tff(223,plain,
% 0.20/0.52 (product(e_3, e_1, e_4) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[222, 205])).
% 0.20/0.52 tff(224,plain,
% 0.20/0.52 (product(e_3, e_1, e_4) | product(e_3, e_1, e_2)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[223, 199])).
% 0.20/0.52 tff(225,plain,
% 0.20/0.52 (product(e_3, e_1, e_4)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[224, 189])).
% 0.20/0.52 tff(226,assumption,(product(e_4, e_1, e_4)), introduced(assumption)).
% 0.20/0.52 tff(227,assumption,(product(e_3, e_1, e_4)), introduced(assumption)).
% 0.20/0.52 tff(228,plain,
% 0.20/0.52 ((~equalish(e_4, e_3)) <=> (~equalish(e_4, e_3))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(229,axiom,(~equalish(e_4, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_3')).
% 0.20/0.52 tff(230,plain,
% 0.20/0.52 (~equalish(e_4, e_3)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.20/0.52 tff(231,plain,
% 0.20/0.52 (((~![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_4, e_1, e_4)) | (~product(e_3, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_4, e_1, e_4)) | (~product(e_3, e_1, e_4)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(232,plain,
% 0.20/0.52 ((equalish(e_4, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_4))) <=> (equalish(e_4, e_3) | (~product(e_4, e_1, e_4)) | (~product(e_3, e_1, e_4)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(233,plain,
% 0.20/0.52 (((~![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_4, e_1, e_4)) | (~product(e_3, e_1, e_4))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[232])).
% 0.20/0.52 tff(234,plain,
% 0.20/0.52 (((~![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_4, e_1, e_4)) | (~product(e_3, e_1, e_4)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[233, 231])).
% 0.20/0.52 tff(235,plain,
% 0.20/0.52 ((~![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)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(236,plain,
% 0.20/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_4, e_1, e_4)) | (~product(e_3, e_1, e_4))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.20/0.52 tff(237,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[236, 230, 22, 227, 226])).
% 0.20/0.52 tff(238,plain,((~product(e_4, e_1, e_4)) | (~product(e_3, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(239,plain,
% 0.20/0.52 (~product(e_4, e_1, e_4)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[238, 225])).
% 0.20/0.52 tff(240,assumption,(product(e_5, e_1, e_4)), introduced(assumption)).
% 0.20/0.52 tff(241,plain,
% 0.20/0.52 ((~equalish(e_5, e_3)) <=> (~equalish(e_5, e_3))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(242,axiom,(~equalish(e_5, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_is_not_e_3')).
% 0.20/0.52 tff(243,plain,
% 0.20/0.52 (~equalish(e_5, e_3)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.20/0.52 tff(244,plain,
% 0.20/0.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_5, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_5, e_1, e_4)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(245,plain,
% 0.20/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_5, e_1, e_4)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(246,plain,
% 0.20/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_5, e_1, e_4))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.20/0.52 tff(247,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[246, 243, 22, 227, 240])).
% 0.20/0.52 tff(248,plain,((~product(e_5, e_1, e_4)) | (~product(e_3, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(249,plain,
% 0.20/0.52 (~product(e_5, e_1, e_4)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[248, 225])).
% 0.20/0.52 tff(250,assumption,(product(e_5, e_1, e_3)), introduced(assumption)).
% 0.20/0.52 tff(251,assumption,(product(e_2, e_1, e_3)), introduced(assumption)).
% 0.20/0.52 tff(252,plain,
% 0.20/0.52 ((~equalish(e_5, e_2)) <=> (~equalish(e_5, e_2))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(253,axiom,(~equalish(e_5, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_is_not_e_2')).
% 0.20/0.52 tff(254,plain,
% 0.20/0.52 (~equalish(e_5, e_2)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[253, 252])).
% 0.20/0.52 tff(255,plain,
% 0.20/0.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_5, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_5, e_1, e_3)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(256,plain,
% 0.20/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_5, e_1, e_3)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(257,plain,
% 0.20/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_5, e_1, e_3))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.20/0.52 tff(258,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[257, 254, 22, 251, 250])).
% 0.20/0.52 tff(259,plain,((~product(e_5, e_1, e_3)) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(260,plain,
% 0.20/0.52 (~product(e_5, e_1, e_3)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[259, 131])).
% 0.20/0.52 tff(261,assumption,(product(e_5, e_1, e_1)), introduced(assumption)).
% 0.20/0.52 tff(262,plain,
% 0.20/0.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_5, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_5, e_1, e_1)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(263,plain,
% 0.20/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_5, e_1, e_1)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(264,plain,
% 0.20/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_5, e_1, e_1))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.20/0.52 tff(265,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[264, 134, 22, 51, 261])).
% 0.20/0.52 tff(266,plain,((~product(e_5, e_1, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(267,plain,
% 0.20/0.52 (~product(e_5, e_1, e_1)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[266, 49])).
% 0.20/0.52 tff(268,plain,
% 0.20/0.52 ((~![X: $i] : product(X, X, X)) | product(e_5, e_5, e_5)),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(269,plain,
% 0.20/0.52 (product(e_5, e_5, e_5)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[268, 10])).
% 0.20/0.52 tff(270,assumption,(product(e_5, e_1, e_5)), introduced(assumption)).
% 0.20/0.52 tff(271,plain,
% 0.20/0.52 ((~equalish(e_1, e_5)) <=> (~equalish(e_1, e_5))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(272,axiom,(~equalish(e_1, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_5')).
% 0.20/0.52 tff(273,plain,
% 0.20/0.52 (~equalish(e_1, e_5)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.20/0.52 tff(274,plain,
% 0.20/0.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_1, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_1, e_5)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(275,plain,
% 0.20/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_1, e_5)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(276,plain,
% 0.20/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_1, e_5))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.20/0.52 tff(277,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[276, 273, 74, 270, 269])).
% 0.20/0.52 tff(278,plain,(~product(e_5, e_1, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(279,plain,
% 0.20/0.52 (group_element(e_5) <=> group_element(e_5)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(280,axiom,(group_element(e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_5')).
% 0.20/0.52 tff(281,plain,
% 0.20/0.52 (group_element(e_5)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.20/0.52 tff(282,plain,
% 0.20/0.52 (((~![Y: $i, X: $i] : (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(e_1)) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | (~group_element(e_5)) | product(e_5, e_1, e_3) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4))) <=> ((~![Y: $i, X: $i] : (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(e_1)) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | (~group_element(e_5)) | product(e_5, e_1, e_3) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(283,plain,
% 0.20/0.52 ((product(e_5, e_1, e_5) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_5))) <=> ((~group_element(e_1)) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | (~group_element(e_5)) | product(e_5, e_1, e_3) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(284,plain,
% 0.20/0.52 (((~![Y: $i, X: $i] : (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(e_5, e_1, e_5) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_5)))) <=> ((~![Y: $i, X: $i] : (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(e_1)) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | (~group_element(e_5)) | product(e_5, e_1, e_3) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4)))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[283])).
% 0.20/0.53 tff(285,plain,
% 0.20/0.53 (((~![Y: $i, X: $i] : (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(e_5, e_1, e_5) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_5)))) <=> ((~![Y: $i, X: $i] : (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(e_1)) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | (~group_element(e_5)) | product(e_5, e_1, e_3) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4))),
% 0.20/0.53 inference(transitivity,[status(thm)],[284, 282])).
% 0.20/0.53 tff(286,plain,
% 0.20/0.53 ((~![Y: $i, X: $i] : (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(e_5, e_1, e_5) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_5)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(287,plain,
% 0.20/0.53 ((~![Y: $i, X: $i] : (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(e_1)) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | (~group_element(e_5)) | product(e_5, e_1, e_3) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.20/0.53 tff(288,plain,
% 0.20/0.53 (product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | product(e_5, e_1, e_3) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[287, 122, 281, 116])).
% 0.20/0.53 tff(289,plain,
% 0.20/0.53 (product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | product(e_5, e_1, e_3) | product(e_5, e_1, e_4)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[288, 278])).
% 0.20/0.53 tff(290,plain,
% 0.20/0.53 (product(e_5, e_1, e_2) | product(e_5, e_1, e_4)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[289, 267, 260])).
% 0.20/0.53 tff(291,plain,
% 0.20/0.53 (product(e_5, e_1, e_2)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[290, 249])).
% 0.20/0.53 tff(292,assumption,(product(e_4, e_1, e_2)), introduced(assumption)).
% 0.20/0.53 tff(293,assumption,(product(e_5, e_1, e_2)), introduced(assumption)).
% 0.20/0.53 tff(294,plain,
% 0.20/0.53 ((~equalish(e_4, e_5)) <=> (~equalish(e_4, e_5))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(295,axiom,(~equalish(e_4, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_5')).
% 0.20/0.53 tff(296,plain,
% 0.20/0.53 (~equalish(e_4, e_5)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.20/0.53 tff(297,plain,
% 0.20/0.53 (((~![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_1, e_2)) | (~product(e_4, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_5) | (~product(e_5, e_1, e_2)) | (~product(e_4, e_1, e_2)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(298,plain,
% 0.20/0.53 ((~![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_1, e_2)) | (~product(e_4, e_1, e_2)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(299,plain,
% 0.20/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_5) | (~product(e_5, e_1, e_2)) | (~product(e_4, e_1, e_2))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.20/0.53 tff(300,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[299, 296, 22, 293, 292])).
% 0.20/0.53 tff(301,plain,((~product(e_4, e_1, e_2)) | (~product(e_5, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(302,plain,
% 0.20/0.53 (~product(e_4, e_1, e_2)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[301, 291])).
% 0.20/0.53 tff(303,assumption,(product(e_4, e_1, e_1)), introduced(assumption)).
% 0.20/0.53 tff(304,plain,
% 0.20/0.53 ((~equalish(e_4, e_1)) <=> (~equalish(e_4, e_1))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(305,axiom,(~equalish(e_4, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_1')).
% 0.20/0.53 tff(306,plain,
% 0.20/0.53 (~equalish(e_4, e_1)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[305, 304])).
% 0.20/0.53 tff(307,plain,
% 0.20/0.53 (((~![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)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(308,plain,
% 0.20/0.53 ((~![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)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(309,plain,
% 0.20/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[308, 307])).
% 0.20/0.53 tff(310,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[309, 306, 22, 49, 303])).
% 0.20/0.53 tff(311,plain,(~product(e_4, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(312,assumption,(product(e_4, e_1, e_3)), introduced(assumption)).
% 0.20/0.53 tff(313,plain,
% 0.20/0.53 ((~equalish(e_4, e_2)) <=> (~equalish(e_4, e_2))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(314,axiom,(~equalish(e_4, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_2')).
% 0.20/0.53 tff(315,plain,
% 0.20/0.53 (~equalish(e_4, e_2)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[314, 313])).
% 0.20/0.53 tff(316,plain,
% 0.20/0.53 (((~![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)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(317,plain,
% 0.20/0.53 ((~![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)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(318,plain,
% 0.20/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_4, e_1, e_3))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[317, 316])).
% 0.20/0.53 tff(319,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[318, 315, 22, 251, 312])).
% 0.20/0.53 tff(320,plain,((~product(e_4, e_1, e_3)) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(321,plain,
% 0.20/0.53 (~product(e_4, e_1, e_3)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[320, 131])).
% 0.20/0.53 tff(322,plain,
% 0.20/0.53 (group_element(e_4) <=> group_element(e_4)),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(323,axiom,(group_element(e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_4')).
% 0.20/0.53 tff(324,plain,
% 0.20/0.53 (group_element(e_4)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[323, 322])).
% 0.20/0.53 tff(325,plain,
% 0.20/0.53 (((~![Y: $i, X: $i] : (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(e_1)) | (~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3))) <=> ((~![Y: $i, X: $i] : (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(e_1)) | (~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(326,plain,
% 0.20/0.53 ((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_4))) <=> ((~group_element(e_1)) | (~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(327,plain,
% 0.20/0.53 (((~![Y: $i, X: $i] : (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(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_4)))) <=> ((~![Y: $i, X: $i] : (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(e_1)) | (~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3)))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[326])).
% 0.20/0.53 tff(328,plain,
% 0.20/0.53 (((~![Y: $i, X: $i] : (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(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_4)))) <=> ((~![Y: $i, X: $i] : (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(e_1)) | (~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3))),
% 0.20/0.53 inference(transitivity,[status(thm)],[327, 325])).
% 0.20/0.53 tff(329,plain,
% 0.20/0.53 ((~![Y: $i, X: $i] : (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(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_4)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(330,plain,
% 0.20/0.53 ((~![Y: $i, X: $i] : (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(e_1)) | (~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.20/0.53 tff(331,plain,
% 0.20/0.53 (product(e_4, e_1, e_5) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[330, 122, 324, 116])).
% 0.20/0.53 tff(332,plain,
% 0.20/0.53 (product(e_4, e_1, e_5) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | product(e_4, e_1, e_4)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[331, 321])).
% 0.20/0.53 tff(333,plain,
% 0.20/0.53 (product(e_4, e_1, e_5) | product(e_4, e_1, e_2) | product(e_4, e_1, e_4)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[332, 311])).
% 0.20/0.53 tff(334,plain,
% 0.20/0.53 (product(e_4, e_1, e_5)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[333, 302, 239])).
% 0.20/0.53 tff(335,assumption,(product(e_1, e_5, e_5)), introduced(assumption)).
% 0.20/0.53 tff(336,plain,
% 0.20/0.53 (((~![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_5, e_5)) | (~product(e_1, 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_1, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_1, e_5, e_5)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(337,plain,
% 0.20/0.53 ((~![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_5, e_5)) | (~product(e_1, e_5, e_5)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(338,plain,
% 0.20/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_1, e_5, e_5))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[337, 336])).
% 0.20/0.53 tff(339,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[338, 273, 22, 269, 335])).
% 0.20/0.53 tff(340,plain,(~product(e_1, e_5, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(341,plain,
% 0.20/0.53 (((~![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_1, e_5, e_5) | (~product(e_5, 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_5, e_5, e_5)) | product(e_1, e_5, e_5) | (~product(e_5, e_5, e_1)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(342,plain,
% 0.20/0.53 ((~![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_1, e_5, e_5) | (~product(e_5, e_5, e_1)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(343,plain,
% 0.20/0.53 ((~![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_1, e_5, e_5) | (~product(e_5, e_5, e_1))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[342, 341])).
% 0.20/0.53 tff(344,plain,
% 0.20/0.53 (~product(e_5, e_5, e_1)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[343, 40, 269, 340])).
% 0.20/0.53 tff(345,plain,
% 0.20/0.53 (((~![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_1) | (~product(e_1, e_4, e_5)) | (~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_5, e_5, e_1) | (~product(e_1, e_4, e_5)) | (~product(e_4, e_1, e_5)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(346,plain,
% 0.20/0.53 (((~product(e_4, e_1, e_5)) | product(e_5, e_5, e_1) | (~product(e_1, e_4, e_5))) <=> (product(e_5, e_5, e_1) | (~product(e_1, e_4, e_5)) | (~product(e_4, e_1, e_5)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(347,plain,
% 0.20/0.53 (((~![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_1) | (~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_5, e_5, e_1) | (~product(e_1, e_4, e_5)) | (~product(e_4, e_1, e_5))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[346])).
% 0.20/0.53 tff(348,plain,
% 0.20/0.53 (((~![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_1) | (~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_5, e_5, e_1) | (~product(e_1, e_4, e_5)) | (~product(e_4, e_1, e_5)))),
% 0.20/0.53 inference(transitivity,[status(thm)],[347, 345])).
% 0.20/0.53 tff(349,plain,
% 0.20/0.53 ((~![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_1) | (~product(e_1, e_4, e_5)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(350,plain,
% 0.20/0.53 ((~![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_1) | (~product(e_1, e_4, e_5)) | (~product(e_4, e_1, e_5))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[349, 348])).
% 0.20/0.53 tff(351,plain,
% 0.20/0.53 (~product(e_1, e_4, e_5)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[350, 40, 334, 344])).
% 0.20/0.54 tff(352,plain,
% 0.20/0.54 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_1, e_2)) | product(e_2, e_2, e_1) | (~product(e_1, 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_5, e_1, e_2)) | product(e_2, e_2, e_1) | (~product(e_1, e_5, e_2)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(353,plain,
% 0.20/0.54 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_1, e_2)) | product(e_2, e_2, e_1) | (~product(e_1, e_5, e_2)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(354,plain,
% 0.20/0.54 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_5, e_1, e_2)) | product(e_2, e_2, e_1) | (~product(e_1, e_5, e_2))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[353, 352])).
% 0.20/0.54 tff(355,plain,
% 0.20/0.54 (~product(e_1, e_5, e_2)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[354, 40, 291, 44])).
% 0.20/0.54 tff(356,assumption,(product(e_1, e_2, e_1)), introduced(assumption)).
% 0.20/0.54 tff(357,plain,
% 0.20/0.54 (((~![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)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(358,plain,
% 0.20/0.54 ((~![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)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(359,plain,
% 0.20/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[358, 357])).
% 0.20/0.54 tff(360,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[359, 54, 74, 49, 356])).
% 0.20/0.54 tff(361,plain,(~product(e_1, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(362,plain,
% 0.20/0.54 (((~![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_1) | (~product(e_1, e_5, e_1)) | (~product(e_5, 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_2, e_1) | (~product(e_1, e_5, e_1)) | (~product(e_5, e_1, e_2)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(363,plain,
% 0.20/0.54 (((~product(e_5, e_1, e_2)) | product(e_1, e_2, e_1) | (~product(e_1, e_5, e_1))) <=> (product(e_1, e_2, e_1) | (~product(e_1, e_5, e_1)) | (~product(e_5, e_1, e_2)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(364,plain,
% 0.20/0.54 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_1, e_2)) | product(e_1, e_2, e_1) | (~product(e_1, 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_2, e_1) | (~product(e_1, e_5, e_1)) | (~product(e_5, e_1, e_2))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[363])).
% 0.20/0.54 tff(365,plain,
% 0.20/0.54 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_1, e_2)) | product(e_1, e_2, e_1) | (~product(e_1, 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_2, e_1) | (~product(e_1, e_5, e_1)) | (~product(e_5, e_1, e_2)))),
% 0.20/0.54 inference(transitivity,[status(thm)],[364, 362])).
% 0.20/0.54 tff(366,plain,
% 0.20/0.54 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_5, e_1, e_2)) | product(e_1, e_2, e_1) | (~product(e_1, e_5, e_1)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(367,plain,
% 0.20/0.54 ((~![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_1) | (~product(e_1, e_5, e_1)) | (~product(e_5, e_1, e_2))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[366, 365])).
% 0.20/0.54 tff(368,plain,
% 0.20/0.54 (~product(e_1, e_5, e_1)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[367, 40, 291, 361])).
% 0.20/0.54 tff(369,assumption,(~product(e_1, e_5, e_2)), introduced(assumption)).
% 0.20/0.54 tff(370,assumption,(~product(e_1, e_5, e_1)), introduced(assumption)).
% 0.20/0.54 tff(371,assumption,(product(e_1, e_2, e_4)), introduced(assumption)).
% 0.20/0.54 tff(372,assumption,(product(e_1, e_5, e_4)), introduced(assumption)).
% 0.20/0.54 tff(373,plain,
% 0.20/0.54 (((~![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_1, e_5, e_4)) | (~product(e_1, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_2) | (~product(e_1, e_5, e_4)) | (~product(e_1, e_2, e_4)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(374,plain,
% 0.20/0.54 ((equalish(e_5, e_2) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_5, e_4))) <=> (equalish(e_5, e_2) | (~product(e_1, e_5, e_4)) | (~product(e_1, e_2, e_4)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(375,plain,
% 0.20/0.54 (((~![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_1, e_2, e_4)) | (~product(e_1, 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_2) | (~product(e_1, e_5, e_4)) | (~product(e_1, e_2, e_4))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[374])).
% 0.20/0.54 tff(376,plain,
% 0.20/0.54 (((~![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_1, e_2, e_4)) | (~product(e_1, 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_2) | (~product(e_1, e_5, e_4)) | (~product(e_1, e_2, e_4)))),
% 0.20/0.54 inference(transitivity,[status(thm)],[375, 373])).
% 0.20/0.54 tff(377,plain,
% 0.20/0.54 ((~![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_1, e_2, e_4)) | (~product(e_1, e_5, e_4)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(378,plain,
% 0.20/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_2) | (~product(e_1, e_5, e_4)) | (~product(e_1, e_2, e_4))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[377, 376])).
% 0.20/0.54 tff(379,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[378, 254, 74, 371, 372])).
% 0.20/0.54 tff(380,plain,((~product(e_1, e_5, e_4)) | (~product(e_1, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(381,plain,
% 0.20/0.54 (~product(e_1, e_5, e_4)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[380, 371])).
% 0.20/0.54 tff(382,plain,
% 0.20/0.54 (((~![Y: $i, X: $i] : (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(e_1)) | (~group_element(e_5)) | product(e_1, e_5, e_3) | product(e_1, e_5, e_1) | product(e_1, e_5, e_2) | product(e_1, e_5, e_5) | product(e_1, e_5, e_4))) <=> ((~![Y: $i, X: $i] : (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(e_1)) | (~group_element(e_5)) | product(e_1, e_5, e_3) | product(e_1, e_5, e_1) | product(e_1, e_5, e_2) | product(e_1, e_5, e_5) | product(e_1, e_5, e_4))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(383,plain,
% 0.20/0.54 ((product(e_1, e_5, e_5) | product(e_1, e_5, e_4) | product(e_1, e_5, e_3) | product(e_1, e_5, e_2) | product(e_1, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_1))) <=> ((~group_element(e_1)) | (~group_element(e_5)) | product(e_1, e_5, e_3) | product(e_1, e_5, e_1) | product(e_1, e_5, e_2) | product(e_1, e_5, e_5) | product(e_1, e_5, e_4))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(384,plain,
% 0.20/0.54 (((~![Y: $i, X: $i] : (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(e_1, e_5, e_5) | product(e_1, e_5, e_4) | product(e_1, e_5, e_3) | product(e_1, e_5, e_2) | product(e_1, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (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(e_1)) | (~group_element(e_5)) | product(e_1, e_5, e_3) | product(e_1, e_5, e_1) | product(e_1, e_5, e_2) | product(e_1, e_5, e_5) | product(e_1, e_5, e_4)))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[383])).
% 0.20/0.54 tff(385,plain,
% 0.20/0.54 (((~![Y: $i, X: $i] : (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(e_1, e_5, e_5) | product(e_1, e_5, e_4) | product(e_1, e_5, e_3) | product(e_1, e_5, e_2) | product(e_1, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (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(e_1)) | (~group_element(e_5)) | product(e_1, e_5, e_3) | product(e_1, e_5, e_1) | product(e_1, e_5, e_2) | product(e_1, e_5, e_5) | product(e_1, e_5, e_4))),
% 0.20/0.54 inference(transitivity,[status(thm)],[384, 382])).
% 0.20/0.54 tff(386,plain,
% 0.20/0.54 ((~![Y: $i, X: $i] : (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(e_1, e_5, e_5) | product(e_1, e_5, e_4) | product(e_1, e_5, e_3) | product(e_1, e_5, e_2) | product(e_1, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_1)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(387,plain,
% 0.20/0.54 ((~![Y: $i, X: $i] : (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(e_1)) | (~group_element(e_5)) | product(e_1, e_5, e_3) | product(e_1, e_5, e_1) | product(e_1, e_5, e_2) | product(e_1, e_5, e_5) | product(e_1, e_5, e_4)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[386, 385])).
% 0.20/0.54 tff(388,plain,
% 0.20/0.54 (product(e_1, e_5, e_3) | product(e_1, e_5, e_1) | product(e_1, e_5, e_2) | product(e_1, e_5, e_4)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[387, 122, 281, 116, 340])).
% 0.20/0.54 tff(389,plain,
% 0.20/0.54 (product(e_1, e_5, e_3)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[388, 381, 370, 369])).
% 0.20/0.54 tff(390,assumption,(~product(e_1, e_4, e_5)), introduced(assumption)).
% 0.20/0.54 tff(391,plain,
% 0.20/0.54 (((~![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_3, 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_3)) | (~product(e_1, e_2, e_4)) | product(e_3, e_4, e_2))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(392,plain,
% 0.20/0.54 (((~product(e_1, e_2, e_4)) | product(e_3, e_4, e_2) | (~product(e_2, e_1, e_3))) <=> ((~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_4)) | product(e_3, e_4, e_2))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(393,plain,
% 0.20/0.54 (((~![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_4)) | product(e_3, e_4, 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_4)) | product(e_3, e_4, e_2)))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[392])).
% 0.20/0.54 tff(394,plain,
% 0.20/0.54 (((~![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_4)) | product(e_3, e_4, 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_4)) | product(e_3, e_4, e_2))),
% 0.20/0.54 inference(transitivity,[status(thm)],[393, 391])).
% 0.20/0.54 tff(395,plain,
% 0.20/0.54 ((~![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_4)) | product(e_3, e_4, e_2) | (~product(e_2, e_1, e_3)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(396,plain,
% 0.20/0.54 ((~![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_3, e_4, e_2)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[395, 394])).
% 0.20/0.54 tff(397,plain,
% 0.20/0.54 ((~product(e_1, e_2, e_4)) | product(e_3, e_4, e_2)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[396, 40, 131])).
% 0.20/0.54 tff(398,plain,
% 0.20/0.54 (product(e_3, e_4, e_2)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[397, 371])).
% 0.20/0.54 tff(399,assumption,(product(e_3, e_4, e_2)), introduced(assumption)).
% 0.20/0.54 tff(400,assumption,(product(e_1, e_4, e_2)), introduced(assumption)).
% 0.20/0.54 tff(401,plain,
% 0.20/0.54 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_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_1) | (~product(e_1, e_4, e_2)) | (~product(e_3, e_4, e_2)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(402,plain,
% 0.20/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_4, e_2)) | (~product(e_3, e_4, e_2)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(403,plain,
% 0.20/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_4, e_2)) | (~product(e_3, e_4, e_2))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[402, 401])).
% 0.20/0.54 tff(404,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[403, 152, 22, 400, 399])).
% 0.20/0.54 tff(405,plain,((~product(e_3, e_4, e_2)) | (~product(e_1, e_4, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(406,plain,
% 0.20/0.54 (~product(e_1, e_4, e_2)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[405, 398])).
% 0.20/0.54 tff(407,assumption,(product(e_1, e_4, e_1)), introduced(assumption)).
% 0.20/0.54 tff(408,plain,
% 0.20/0.54 (((~![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)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(409,plain,
% 0.20/0.54 ((~![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)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(410,plain,
% 0.20/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[409, 408])).
% 0.20/0.54 tff(411,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[410, 306, 74, 49, 407])).
% 0.20/0.54 tff(412,plain,(~product(e_1, e_4, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(413,plain,
% 0.20/0.54 ((~![X: $i] : product(X, X, X)) | product(e_4, e_4, e_4)),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(414,plain,
% 0.20/0.54 (product(e_4, e_4, e_4)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[413, 10])).
% 0.20/0.54 tff(415,assumption,(product(e_1, e_4, e_4)), introduced(assumption)).
% 0.20/0.54 tff(416,plain,
% 0.20/0.54 ((~equalish(e_1, e_4)) <=> (~equalish(e_1, e_4))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(417,axiom,(~equalish(e_1, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_4')).
% 0.20/0.54 tff(418,plain,
% 0.20/0.54 (~equalish(e_1, e_4)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[417, 416])).
% 0.20/0.54 tff(419,plain,
% 0.20/0.54 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_1, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_1, e_4, e_4)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(420,plain,
% 0.20/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_1, e_4, e_4)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(421,plain,
% 0.20/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_1, e_4, e_4))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[420, 419])).
% 0.20/0.54 tff(422,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[421, 418, 22, 415, 414])).
% 0.20/0.54 tff(423,plain,(~product(e_1, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(424,plain,
% 0.20/0.54 (((~![Y: $i, X: $i] : (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(e_1)) | (~group_element(e_4)) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_5) | product(e_1, e_4, e_1) | product(e_1, e_4, e_4))) <=> ((~![Y: $i, X: $i] : (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(e_1)) | (~group_element(e_4)) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_5) | product(e_1, e_4, e_1) | product(e_1, e_4, e_4))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(425,plain,
% 0.20/0.54 ((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_1)) | (~group_element(e_4)) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_5) | product(e_1, e_4, e_1) | product(e_1, e_4, e_4))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(426,plain,
% 0.20/0.54 (((~![Y: $i, X: $i] : (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(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)))) <=> ((~![Y: $i, X: $i] : (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(e_1)) | (~group_element(e_4)) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_5) | product(e_1, e_4, e_1) | product(e_1, e_4, e_4)))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[425])).
% 0.20/0.54 tff(427,plain,
% 0.20/0.54 (((~![Y: $i, X: $i] : (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(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)))) <=> ((~![Y: $i, X: $i] : (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(e_1)) | (~group_element(e_4)) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_5) | product(e_1, e_4, e_1) | product(e_1, e_4, e_4))),
% 0.20/0.54 inference(transitivity,[status(thm)],[426, 424])).
% 0.20/0.54 tff(428,plain,
% 0.20/0.54 ((~![Y: $i, X: $i] : (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(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)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(429,plain,
% 0.20/0.55 ((~![Y: $i, X: $i] : (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(e_1)) | (~group_element(e_4)) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_5) | product(e_1, e_4, e_1) | product(e_1, e_4, e_4)),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[428, 427])).
% 0.20/0.55 tff(430,plain,
% 0.20/0.55 (product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_5) | product(e_1, e_4, e_1) | product(e_1, e_4, e_4)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[429, 122, 324, 116])).
% 0.20/0.55 tff(431,plain,
% 0.20/0.55 (product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_5) | product(e_1, e_4, e_1)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[430, 423])).
% 0.20/0.55 tff(432,plain,
% 0.20/0.55 (product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_5)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[431, 412])).
% 0.20/0.55 tff(433,plain,
% 0.20/0.55 (product(e_1, e_4, e_3)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[432, 406, 390])).
% 0.20/0.55 tff(434,plain,
% 0.20/0.55 ((~equalish(e_5, e_4)) <=> (~equalish(e_5, e_4))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(435,axiom,(~equalish(e_5, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_is_not_e_4')).
% 0.20/0.55 tff(436,plain,
% 0.20/0.55 (~equalish(e_5, e_4)),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[435, 434])).
% 0.20/0.55 tff(437,plain,
% 0.20/0.55 (((~![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_1, e_4, e_3)) | (~product(e_1, e_5, e_3)))) <=> ((~![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_1, e_4, e_3)) | (~product(e_1, e_5, e_3)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(438,plain,
% 0.20/0.55 ((~![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_1, e_4, e_3)) | (~product(e_1, e_5, e_3)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(439,plain,
% 0.20/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_1, e_5, e_3))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[438, 437])).
% 0.20/0.55 tff(440,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[439, 436, 74, 433, 389])).
% 0.20/0.55 tff(441,plain,((~product(e_1, e_2, e_4)) | product(e_1, e_5, e_1) | product(e_1, e_5, e_2) | product(e_1, e_4, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(442,plain,
% 0.20/0.55 (~product(e_1, e_2, e_4)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[441, 368, 355, 351])).
% 0.20/0.55 tff(443,plain,
% 0.20/0.55 (((~![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_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_1)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(444,plain,
% 0.20/0.55 (((~product(e_3, e_3, e_3)) | product(e_1, e_3, e_3) | (~product(e_3, e_3, e_1))) <=> (product(e_1, e_3, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_1)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(445,plain,
% 0.20/0.55 (((~![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_1, e_3, e_3) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_1))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[444])).
% 0.20/0.55 tff(446,plain,
% 0.20/0.55 (((~![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_1, e_3, e_3) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_1)))),
% 0.20/0.55 inference(transitivity,[status(thm)],[445, 443])).
% 0.20/0.55 tff(447,plain,
% 0.20/0.55 ((~![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_1, e_3, e_3) | (~product(e_3, e_3, e_1)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(448,plain,
% 0.20/0.55 ((~![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_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_1))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[447, 446])).
% 0.20/0.55 tff(449,plain,
% 0.20/0.55 (~product(e_3, e_3, e_1)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[448, 40, 161, 169])).
% 0.20/0.55 tff(450,plain,
% 0.20/0.55 (((~![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_1) | (~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_1) | (~product(e_1, e_2, e_3)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(451,plain,
% 0.20/0.55 ((~![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_1) | (~product(e_1, e_2, e_3)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(452,plain,
% 0.20/0.55 ((~![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_1) | (~product(e_1, e_2, e_3))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[451, 450])).
% 0.20/0.55 tff(453,plain,
% 0.20/0.55 (~product(e_1, e_2, e_3)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[452, 40, 131, 449])).
% 0.20/0.55 tff(454,plain,
% 0.20/0.55 (((~![Y: $i, X: $i] : (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(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | product(e_1, e_2, e_3) | product(e_1, e_2, e_5) | product(e_1, e_2, e_4))) <=> ((~![Y: $i, X: $i] : (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(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | product(e_1, e_2, e_3) | product(e_1, e_2, e_5) | product(e_1, e_2, e_4))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(455,plain,
% 0.20/0.55 ((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_1)) | (~group_element(e_2)) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | product(e_1, e_2, e_3) | product(e_1, e_2, e_5) | product(e_1, e_2, e_4))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(456,plain,
% 0.20/0.55 (((~![Y: $i, X: $i] : (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(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)))) <=> ((~![Y: $i, X: $i] : (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(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | product(e_1, e_2, e_3) | product(e_1, e_2, e_5) | product(e_1, e_2, e_4)))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[455])).
% 0.20/0.55 tff(457,plain,
% 0.20/0.55 (((~![Y: $i, X: $i] : (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(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)))) <=> ((~![Y: $i, X: $i] : (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(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | product(e_1, e_2, e_3) | product(e_1, e_2, e_5) | product(e_1, e_2, e_4))),
% 0.20/0.55 inference(transitivity,[status(thm)],[456, 454])).
% 0.20/0.55 tff(458,plain,
% 0.20/0.55 ((~![Y: $i, X: $i] : (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(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)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(459,plain,
% 0.20/0.55 ((~![Y: $i, X: $i] : (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(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | product(e_1, e_2, e_3) | product(e_1, e_2, e_5) | product(e_1, e_2, e_4)),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[458, 457])).
% 0.20/0.55 tff(460,plain,
% 0.20/0.55 (product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | product(e_1, e_2, e_5) | product(e_1, e_2, e_4)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[459, 122, 119, 116, 453])).
% 0.20/0.55 tff(461,plain,
% 0.20/0.55 (product(e_1, e_2, e_5) | product(e_1, e_2, e_4)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[460, 30, 361])).
% 0.20/0.55 tff(462,plain,
% 0.20/0.55 (product(e_1, e_2, e_5)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[461, 442])).
% 0.20/0.55 tff(463,assumption,(product(e_1, e_2, e_5)), introduced(assumption)).
% 0.20/0.55 tff(464,assumption,(product(e_1, e_3, e_5)), introduced(assumption)).
% 0.20/0.55 tff(465,plain,
% 0.20/0.55 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(466,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.20/0.55 tff(467,plain,
% 0.20/0.55 (~equalish(e_2, e_3)),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[466, 465])).
% 0.20/0.55 tff(468,plain,
% 0.20/0.55 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_1, e_3, e_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_3) | (~product(e_1, e_3, e_5)) | (~product(e_1, e_2, e_5)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(469,plain,
% 0.20/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_1, e_3, e_5)) | (~product(e_1, e_2, e_5)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(470,plain,
% 0.20/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_1, e_3, e_5)) | (~product(e_1, e_2, e_5))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[469, 468])).
% 0.20/0.55 tff(471,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[470, 467, 74, 464, 463])).
% 0.20/0.55 tff(472,plain,((~product(e_1, e_2, e_5)) | (~product(e_1, e_3, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(473,plain,
% 0.20/0.55 (~product(e_1, e_3, e_5)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[472, 462])).
% 0.20/0.55 tff(474,plain,
% 0.20/0.55 (product(e_1, e_3, e_2)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[179, 473, 2])).
% 0.20/0.55 tff(475,assumption,(product(e_1, e_3, e_2)), introduced(assumption)).
% 0.20/0.55 tff(476,plain,
% 0.20/0.55 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_4, e_2)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(477,plain,
% 0.20/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_4, e_2)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(478,plain,
% 0.20/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_4, e_2))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[477, 476])).
% 0.20/0.55 tff(479,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[478, 230, 74, 400, 475])).
% 0.20/0.55 tff(480,plain,((~product(e_1, e_4, e_2)) | (~product(e_1, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(481,plain,
% 0.20/0.55 (~product(e_1, e_4, e_2)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[480, 474])).
% 0.20/0.55 tff(482,plain,
% 0.20/0.55 (product(e_1, e_4, e_3)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[432, 481, 351])).
% 0.20/0.55 tff(483,plain,
% 0.20/0.55 (((~![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_3)) | (~product(e_4, e_1, e_5)) | 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_4, e_3)) | (~product(e_4, e_1, e_5)) | product(e_3, e_5, e_1))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(484,plain,
% 0.20/0.55 (((~product(e_4, e_1, e_5)) | product(e_3, e_5, e_1) | (~product(e_1, e_4, e_3))) <=> ((~product(e_1, e_4, e_3)) | (~product(e_4, e_1, e_5)) | product(e_3, e_5, e_1))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(485,plain,
% 0.20/0.55 (((~![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_1, e_4, e_3)) | (~product(e_4, e_1, e_5)) | product(e_3, e_5, e_1)))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[484])).
% 0.20/0.55 tff(486,plain,
% 0.20/0.55 (((~![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_1, e_4, e_3)) | (~product(e_4, e_1, e_5)) | product(e_3, e_5, e_1))),
% 0.20/0.55 inference(transitivity,[status(thm)],[485, 483])).
% 0.20/0.55 tff(487,plain,
% 0.20/0.55 ((~![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)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(488,plain,
% 0.20/0.55 ((~![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_3)) | (~product(e_4, e_1, e_5)) | product(e_3, e_5, e_1)),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[487, 486])).
% 0.20/0.55 tff(489,plain,
% 0.20/0.55 ((~product(e_1, e_4, e_3)) | (~product(e_4, e_1, e_5)) | product(e_3, e_5, e_1)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[488, 40])).
% 0.20/0.55 tff(490,plain,
% 0.20/0.55 (product(e_3, e_5, e_1)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[489, 482, 334])).
% 0.20/0.55 tff(491,plain,
% 0.20/0.55 (greater(e_5, e_2) <=> greater(e_5, e_2)),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(492,axiom,(greater(e_5, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_greater_e_2')).
% 0.20/0.55 tff(493,plain,
% 0.20/0.55 (greater(e_5, e_2)),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[492, 491])).
% 0.20/0.55 tff(494,plain,
% 0.20/0.55 (next(e_1, e_2) <=> next(e_1, e_2)),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(495,axiom,(next(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_then_e_2')).
% 0.20/0.55 tff(496,plain,
% 0.20/0.55 (next(e_1, e_2)),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[495, 494])).
% 0.20/0.55 tff(497,plain,
% 0.20/0.55 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_5, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_5)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_5, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_5)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(498,plain,
% 0.20/0.56 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_5, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_5)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(499,plain,
% 0.20/0.56 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_5, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_5))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[498, 497])).
% 0.20/0.56 tff(500,plain,
% 0.20/0.56 (~product(e_1, e_1, e_5)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[499, 496, 493, 89])).
% 0.20/0.56 tff(501,plain,
% 0.20/0.56 (((~![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_5) | (~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_5) | (~product(e_5, e_3, e_1)) | (~product(e_3, e_5, e_1)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(502,plain,
% 0.20/0.56 (((~product(e_3, e_5, e_1)) | product(e_1, e_1, e_5) | (~product(e_5, e_3, e_1))) <=> (product(e_1, e_1, e_5) | (~product(e_5, e_3, e_1)) | (~product(e_3, e_5, e_1)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(503,plain,
% 0.20/0.56 (((~![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_1)) | product(e_1, e_1, e_5) | (~product(e_5, 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_5) | (~product(e_5, e_3, e_1)) | (~product(e_3, e_5, e_1))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[502])).
% 0.20/0.56 tff(504,plain,
% 0.20/0.56 (((~![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_1)) | product(e_1, e_1, e_5) | (~product(e_5, 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_5) | (~product(e_5, e_3, e_1)) | (~product(e_3, e_5, e_1)))),
% 0.20/0.56 inference(transitivity,[status(thm)],[503, 501])).
% 0.20/0.56 tff(505,plain,
% 0.20/0.56 ((~![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_1)) | product(e_1, e_1, e_5) | (~product(e_5, e_3, e_1)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(506,plain,
% 0.20/0.56 ((~![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_5) | (~product(e_5, e_3, e_1)) | (~product(e_3, e_5, e_1))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[505, 504])).
% 0.20/0.56 tff(507,plain,
% 0.20/0.56 (~product(e_5, e_3, e_1)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[506, 40, 500, 490])).
% 0.20/0.56 tff(508,plain,
% 0.20/0.56 (((~![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_5, 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_5)) | product(e_5, e_3, e_1))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(509,plain,
% 0.20/0.56 (((~product(e_2, e_1, e_3)) | product(e_5, e_3, e_1) | (~product(e_1, e_2, e_5))) <=> ((~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_5)) | product(e_5, e_3, e_1))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(510,plain,
% 0.20/0.56 (((~![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_1, e_2, e_5)) | product(e_5, e_3, e_1)))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[509])).
% 0.20/0.56 tff(511,plain,
% 0.20/0.56 (((~![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_1, e_2, e_5)) | product(e_5, e_3, e_1))),
% 0.20/0.56 inference(transitivity,[status(thm)],[510, 508])).
% 0.20/0.56 tff(512,plain,
% 0.20/0.56 ((~![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)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(513,plain,
% 0.20/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_5)) | product(e_5, e_3, e_1)),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[512, 511])).
% 0.20/0.56 tff(514,plain,
% 0.20/0.56 ($false),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[513, 40, 131, 462, 507])).
% 0.20/0.56 tff(515,plain,(product(e_1, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.56 tff(516,plain,
% 0.20/0.56 (((~![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_4, e_4, e_4)) | (~product(e_4, 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_4, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_4, e_1)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(517,plain,
% 0.20/0.56 (((~product(e_4, e_4, e_4)) | product(e_1, e_4, e_4) | (~product(e_4, e_4, e_1))) <=> (product(e_1, e_4, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_4, e_1)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(518,plain,
% 0.20/0.56 (((~![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_1, e_4, e_4) | (~product(e_4, 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_4, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_4, e_1))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[517])).
% 0.20/0.56 tff(519,plain,
% 0.20/0.56 (((~![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_1, e_4, e_4) | (~product(e_4, 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_4, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_4, e_1)))),
% 0.20/0.56 inference(transitivity,[status(thm)],[518, 516])).
% 0.20/0.56 tff(520,plain,
% 0.20/0.56 ((~![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_1, e_4, e_4) | (~product(e_4, e_4, e_1)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(521,plain,
% 0.20/0.56 ((~![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_4, e_4, e_4)) | (~product(e_4, e_4, e_1))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[520, 519])).
% 0.20/0.56 tff(522,plain,
% 0.20/0.56 (~product(e_4, e_4, e_1)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[521, 40, 423, 414])).
% 0.20/0.56 tff(523,assumption,(product(e_1, e_3, e_4)), introduced(assumption)).
% 0.20/0.56 tff(524,plain,
% 0.20/0.56 (((~![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_3, e_1, e_4)) | product(e_4, 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_3, e_4)) | (~product(e_3, e_1, e_4)) | product(e_4, e_4, e_1))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(525,plain,
% 0.20/0.56 (((~product(e_3, e_1, e_4)) | product(e_4, e_4, e_1) | (~product(e_1, e_3, e_4))) <=> ((~product(e_1, e_3, e_4)) | (~product(e_3, e_1, e_4)) | product(e_4, e_4, e_1))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(526,plain,
% 0.20/0.56 (((~![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_1) | (~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_1, e_3, e_4)) | (~product(e_3, e_1, e_4)) | product(e_4, e_4, e_1)))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[525])).
% 0.20/0.56 tff(527,plain,
% 0.20/0.56 (((~![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_1) | (~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_1, e_3, e_4)) | (~product(e_3, e_1, e_4)) | product(e_4, e_4, e_1))),
% 0.20/0.56 inference(transitivity,[status(thm)],[526, 524])).
% 0.20/0.56 tff(528,plain,
% 0.20/0.56 ((~![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_1) | (~product(e_1, e_3, e_4)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(529,plain,
% 0.20/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_4)) | (~product(e_3, e_1, e_4)) | product(e_4, e_4, e_1)),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[528, 527])).
% 0.20/0.56 tff(530,plain,
% 0.20/0.56 ($false),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[529, 40, 227, 523, 522])).
% 0.20/0.56 tff(531,plain,((~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.56 tff(532,plain,
% 0.20/0.56 (~product(e_3, e_1, e_4)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[531, 515])).
% 0.20/0.56 tff(533,plain,
% 0.20/0.56 (product(e_3, e_1, e_2)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[224, 532])).
% 0.20/0.56 tff(534,plain,
% 0.20/0.56 (((~![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_3, e_1, e_2)) | product(e_4, 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_1, e_3, e_4)) | (~product(e_3, e_1, e_2)) | product(e_4, e_2, e_1))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(535,plain,
% 0.20/0.56 (((~product(e_3, e_1, e_2)) | product(e_4, e_2, e_1) | (~product(e_1, e_3, e_4))) <=> ((~product(e_1, e_3, e_4)) | (~product(e_3, e_1, e_2)) | product(e_4, e_2, e_1))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(536,plain,
% 0.20/0.56 (((~![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_4, e_2, e_1) | (~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_1, e_3, e_4)) | (~product(e_3, e_1, e_2)) | product(e_4, e_2, e_1)))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[535])).
% 0.20/0.56 tff(537,plain,
% 0.20/0.56 (((~![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_4, e_2, e_1) | (~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_1, e_3, e_4)) | (~product(e_3, e_1, e_2)) | product(e_4, e_2, e_1))),
% 0.20/0.56 inference(transitivity,[status(thm)],[536, 534])).
% 0.20/0.56 tff(538,plain,
% 0.20/0.56 ((~![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_4, e_2, e_1) | (~product(e_1, e_3, e_4)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(539,plain,
% 0.20/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_4)) | (~product(e_3, e_1, e_2)) | product(e_4, e_2, e_1)),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[538, 537])).
% 0.20/0.56 tff(540,plain,
% 0.20/0.56 ($false),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[539, 40, 533, 515, 1])).
% 0.20/0.56 tff(541,plain,(product(e_4, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.56 tff(542,plain,
% 0.20/0.56 (((~![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_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, 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_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_2)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(543,plain,
% 0.20/0.56 (((~product(e_4, e_2, e_1)) | product(e_2, e_1, e_2) | (~product(e_2, e_4, e_2))) <=> (product(e_2, e_1, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_2)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(544,plain,
% 0.20/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_1)) | product(e_2, e_1, e_2) | (~product(e_2, 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_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_2))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[543])).
% 0.20/0.56 tff(545,plain,
% 0.20/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_1)) | product(e_2, e_1, e_2) | (~product(e_2, 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_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_2)))),
% 0.20/0.56 inference(transitivity,[status(thm)],[544, 542])).
% 0.20/0.56 tff(546,plain,
% 0.20/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_1)) | product(e_2, e_1, e_2) | (~product(e_2, e_4, e_2)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(547,plain,
% 0.20/0.56 ((~![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_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_2))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[546, 545])).
% 0.20/0.56 tff(548,plain,
% 0.20/0.56 (~product(e_2, e_4, e_2)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[547, 40, 79, 541])).
% 0.20/0.56 tff(549,assumption,(product(e_2, e_4, e_4)), introduced(assumption)).
% 0.20/0.56 tff(550,plain,
% 0.20/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_1)) | product(e_1, e_4, e_4) | (~product(e_2, 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_2, e_1)) | product(e_1, e_4, e_4) | (~product(e_2, e_4, e_4)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(551,plain,
% 0.20/0.56 (((~product(e_2, e_4, e_4)) | product(e_1, e_4, e_4) | (~product(e_4, e_2, e_1))) <=> ((~product(e_4, e_2, e_1)) | product(e_1, e_4, e_4) | (~product(e_2, e_4, e_4)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(552,plain,
% 0.20/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_4)) | product(e_1, e_4, e_4) | (~product(e_4, 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_4, e_2, e_1)) | product(e_1, e_4, e_4) | (~product(e_2, e_4, e_4))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[551])).
% 0.20/0.56 tff(553,plain,
% 0.20/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_4)) | product(e_1, e_4, e_4) | (~product(e_4, 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_4, e_2, e_1)) | product(e_1, e_4, e_4) | (~product(e_2, e_4, e_4)))),
% 0.20/0.56 inference(transitivity,[status(thm)],[552, 550])).
% 0.20/0.57 tff(554,plain,
% 0.20/0.57 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_4)) | product(e_1, e_4, e_4) | (~product(e_4, e_2, e_1)))),
% 0.20/0.57 inference(quant_inst,[status(thm)],[])).
% 0.20/0.57 tff(555,plain,
% 0.20/0.57 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_4, e_2, e_1)) | product(e_1, e_4, e_4) | (~product(e_2, e_4, e_4))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[554, 553])).
% 0.20/0.57 tff(556,plain,
% 0.20/0.57 ($false),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[555, 40, 549, 423, 541])).
% 0.20/0.57 tff(557,plain,(~product(e_2, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.57 tff(558,plain,
% 0.20/0.57 ((~equalish(e_3, e_5)) <=> (~equalish(e_3, e_5))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(559,axiom,(~equalish(e_3, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_5')).
% 0.20/0.57 tff(560,plain,
% 0.20/0.57 (~equalish(e_3, e_5)),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[559, 558])).
% 0.20/0.57 tff(561,plain,
% 0.20/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_5) | (~product(e_3, e_1, e_2)) | (~product(e_5, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_5) | (~product(e_3, e_1, e_2)) | (~product(e_5, e_1, e_2)))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(562,plain,
% 0.20/0.57 ((equalish(e_3, e_5) | (~product(e_5, e_1, e_2)) | (~product(e_3, e_1, e_2))) <=> (equalish(e_3, e_5) | (~product(e_3, e_1, e_2)) | (~product(e_5, e_1, e_2)))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(563,plain,
% 0.20/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_5) | (~product(e_5, e_1, e_2)) | (~product(e_3, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_5) | (~product(e_3, e_1, e_2)) | (~product(e_5, e_1, e_2))))),
% 0.20/0.57 inference(monotonicity,[status(thm)],[562])).
% 0.20/0.57 tff(564,plain,
% 0.20/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_5) | (~product(e_5, e_1, e_2)) | (~product(e_3, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_5) | (~product(e_3, e_1, e_2)) | (~product(e_5, e_1, e_2)))),
% 0.20/0.57 inference(transitivity,[status(thm)],[563, 561])).
% 0.20/0.57 tff(565,plain,
% 0.20/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_5) | (~product(e_5, e_1, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.20/0.57 inference(quant_inst,[status(thm)],[])).
% 0.20/0.57 tff(566,plain,
% 0.20/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_5) | (~product(e_3, e_1, e_2)) | (~product(e_5, e_1, e_2))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[565, 564])).
% 0.20/0.57 tff(567,plain,
% 0.20/0.57 ($false),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[566, 560, 22, 140, 293])).
% 0.20/0.57 tff(568,plain,((~product(e_3, e_1, e_2)) | (~product(e_5, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.57 tff(569,plain,
% 0.20/0.57 (~product(e_5, e_1, e_2)),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[568, 533])).
% 0.20/0.57 tff(570,plain,
% 0.20/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_5, e_1, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, 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_1, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_5)))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(571,plain,
% 0.20/0.57 (((~product(e_4, e_2, e_1)) | product(e_5, e_1, e_2) | (~product(e_2, e_4, e_5))) <=> (product(e_5, e_1, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_5)))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(572,plain,
% 0.20/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_1)) | product(e_5, e_1, e_2) | (~product(e_2, 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_1, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_5))))),
% 0.20/0.57 inference(monotonicity,[status(thm)],[571])).
% 0.20/0.57 tff(573,plain,
% 0.20/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_1)) | product(e_5, e_1, e_2) | (~product(e_2, 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_1, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_5)))),
% 0.20/0.57 inference(transitivity,[status(thm)],[572, 570])).
% 0.20/0.57 tff(574,plain,
% 0.20/0.57 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_1)) | product(e_5, e_1, e_2) | (~product(e_2, e_4, e_5)))),
% 0.20/0.57 inference(quant_inst,[status(thm)],[])).
% 0.20/0.57 tff(575,plain,
% 0.20/0.57 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_5, e_1, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_5))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[574, 573])).
% 0.20/0.57 tff(576,plain,
% 0.20/0.57 (~product(e_2, e_4, e_5)),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[575, 40, 569, 541])).
% 0.20/0.57 tff(577,assumption,(product(e_2, e_4, e_1)), introduced(assumption)).
% 0.20/0.57 tff(578,plain,
% 0.20/0.57 (greater(e_4, e_2) <=> greater(e_4, e_2)),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(579,axiom,(greater(e_4, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_greater_e_2')).
% 0.20/0.57 tff(580,plain,
% 0.20/0.57 (greater(e_4, e_2)),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[579, 578])).
% 0.20/0.57 tff(581,plain,
% 0.20/0.57 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_4, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_4)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_4, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_4)))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(582,plain,
% 0.20/0.57 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_4, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_4)))),
% 0.20/0.57 inference(quant_inst,[status(thm)],[])).
% 0.20/0.57 tff(583,plain,
% 0.20/0.57 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_4, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_4))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[582, 581])).
% 0.20/0.57 tff(584,plain,
% 0.20/0.57 (~product(e_1, e_1, e_4)),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[583, 496, 580, 89])).
% 0.20/0.57 tff(585,plain,
% 0.20/0.57 (((~![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_2, e_1)) | (~product(e_2, 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_4, e_2, e_1)) | (~product(e_2, e_4, e_1)))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(586,plain,
% 0.20/0.57 (((~product(e_2, e_4, e_1)) | product(e_1, e_1, e_4) | (~product(e_4, e_2, e_1))) <=> (product(e_1, e_1, e_4) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_1)))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(587,plain,
% 0.20/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_1)) | product(e_1, e_1, e_4) | (~product(e_4, 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_1, e_1, e_4) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_1))))),
% 0.20/0.57 inference(monotonicity,[status(thm)],[586])).
% 0.20/0.57 tff(588,plain,
% 0.20/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_1)) | product(e_1, e_1, e_4) | (~product(e_4, 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_1, e_1, e_4) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_1)))),
% 0.20/0.57 inference(transitivity,[status(thm)],[587, 585])).
% 0.20/0.57 tff(589,plain,
% 0.20/0.57 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_1)) | product(e_1, e_1, e_4) | (~product(e_4, e_2, e_1)))),
% 0.20/0.57 inference(quant_inst,[status(thm)],[])).
% 0.20/0.57 tff(590,plain,
% 0.20/0.57 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_4) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_1))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[589, 588])).
% 0.20/0.57 tff(591,plain,
% 0.20/0.57 ($false),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[590, 40, 584, 577, 541])).
% 0.20/0.57 tff(592,plain,(~product(e_2, e_4, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.57 tff(593,plain,
% 0.20/0.57 (((~![Y: $i, X: $i] : (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(e_2)) | product(e_2, e_4, e_5) | product(e_2, e_4, e_4) | (~group_element(e_4)) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1))) <=> ((~![Y: $i, X: $i] : (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(e_2)) | product(e_2, e_4, e_5) | product(e_2, e_4, e_4) | (~group_element(e_4)) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(594,plain,
% 0.20/0.57 ((product(e_2, e_4, e_5) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_2))) <=> ((~group_element(e_2)) | product(e_2, e_4, e_5) | product(e_2, e_4, e_4) | (~group_element(e_4)) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(595,plain,
% 0.20/0.57 (((~![Y: $i, X: $i] : (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(e_2, e_4, e_5) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (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(e_2)) | product(e_2, e_4, e_5) | product(e_2, e_4, e_4) | (~group_element(e_4)) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1)))),
% 0.20/0.57 inference(monotonicity,[status(thm)],[594])).
% 0.20/0.57 tff(596,plain,
% 0.20/0.57 (((~![Y: $i, X: $i] : (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(e_2, e_4, e_5) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (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(e_2)) | product(e_2, e_4, e_5) | product(e_2, e_4, e_4) | (~group_element(e_4)) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1))),
% 0.20/0.57 inference(transitivity,[status(thm)],[595, 593])).
% 0.20/0.57 tff(597,plain,
% 0.20/0.57 ((~![Y: $i, X: $i] : (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(e_2, e_4, e_5) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_2)))),
% 0.20/0.57 inference(quant_inst,[status(thm)],[])).
% 0.20/0.57 tff(598,plain,
% 0.20/0.57 ((~![Y: $i, X: $i] : (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(e_2)) | product(e_2, e_4, e_5) | product(e_2, e_4, e_4) | (~group_element(e_4)) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1)),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[597, 596])).
% 0.20/0.57 tff(599,plain,
% 0.20/0.57 (product(e_2, e_4, e_5) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1)),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[598, 119, 324, 116])).
% 0.20/0.57 tff(600,plain,
% 0.20/0.57 (product(e_2, e_4, e_3)),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[599, 592, 576, 557, 548])).
% 0.20/0.57 tff(601,plain,
% 0.20/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3)))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(602,plain,
% 0.20/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3)))),
% 0.20/0.57 inference(quant_inst,[status(thm)],[])).
% 0.20/0.57 tff(603,plain,
% 0.20/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[602, 601])).
% 0.20/0.57 tff(604,plain,
% 0.20/0.57 ($false),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[603, 306, 74, 131, 600])).
% 0.20/0.57 % SZS output end Proof
% 0.20/0.57 % E exiting
%------------------------------------------------------------------------------