%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP127-2.006 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:07:08 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.53s
% Output : Proof 0.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP127-2.006 : TPTP v9.0.0. Released v1.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n010.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 15:44:56 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.53 % SZS status Unsatisfiable
% 0.20/0.53 % SZS output start Proof
% 0.20/0.53 tff(product_type, type, (
% 0.20/0.53 product: ( $i * $i * $i ) > $o)).
% 0.20/0.53 tff(e_1_type, type, (
% 0.20/0.53 e_1: $i)).
% 0.20/0.53 tff(e_3_type, type, (
% 0.20/0.53 e_3: $i)).
% 0.20/0.53 tff(e_2_type, type, (
% 0.20/0.53 e_2: $i)).
% 0.20/0.53 tff(e_5_type, type, (
% 0.20/0.53 e_5: $i)).
% 0.20/0.53 tff(e_4_type, type, (
% 0.20/0.53 e_4: $i)).
% 0.20/0.53 tff(e_6_type, type, (
% 0.20/0.53 e_6: $i)).
% 0.20/0.53 tff(next_type, type, (
% 0.20/0.53 next: ( $i * $i ) > $o)).
% 0.20/0.53 tff(greater_type, type, (
% 0.20/0.53 greater: ( $i * $i ) > $o)).
% 0.20/0.53 tff(equalish_type, type, (
% 0.20/0.53 equalish: ( $i * $i ) > $o)).
% 0.20/0.53 tff(group_element_type, type, (
% 0.20/0.53 group_element: $i > $o)).
% 0.20/0.53 tff(1,assumption,(product(e_5, e_2, e_3)), introduced(assumption)).
% 0.20/0.53 tff(2,assumption,(product(e_3, e_4, e_1)), introduced(assumption)).
% 0.20/0.53 tff(3,assumption,(product(e_4, e_3, e_5)), introduced(assumption)).
% 0.20/0.53 tff(4,assumption,(product(e_1, e_5, e_6)), introduced(assumption)).
% 0.20/0.53 tff(5,assumption,(product(e_6, e_1, e_1)), introduced(assumption)).
% 0.20/0.53 tff(6,plain,
% 0.20/0.53 (^[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))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(7,plain,
% 0.20/0.53 (![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)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.53 tff(8,plain,
% 0.20/0.53 (![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)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(9,plain,
% 0.20/0.53 (^[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)))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(10,plain,
% 0.20/0.53 (![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)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[9])).
% 0.20/0.53 tff(11,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')).
% 0.20/0.53 tff(12,plain,
% 0.20/0.53 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.20/0.53 tff(13,plain,
% 0.20/0.53 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.20/0.53 tff(14,plain,(
% 0.20/0.53 ![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.20/0.53 inference(skolemize,[status(sab)],[13])).
% 0.20/0.53 tff(15,plain,
% 0.20/0.53 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.20/0.53 tff(16,plain,
% 0.20/0.53 (greater(e_5, e_2) <=> greater(e_5, e_2)),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(17,axiom,(greater(e_5, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_greater_e_2')).
% 0.20/0.53 tff(18,plain,
% 0.20/0.53 (greater(e_5, e_2)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.20/0.53 tff(19,plain,
% 0.20/0.53 (next(e_1, e_2) <=> next(e_1, e_2)),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(20,axiom,(next(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_then_e_2')).
% 0.20/0.53 tff(21,plain,
% 0.20/0.53 (next(e_1, e_2)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.53 tff(22,plain,
% 0.20/0.53 (((~![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)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(23,plain,
% 0.20/0.53 ((~![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)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(24,plain,
% 0.20/0.53 ((~![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))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.53 tff(25,plain,
% 0.20/0.53 (~product(e_1, e_1, e_5)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[24, 21, 18, 15])).
% 0.20/0.53 tff(26,plain,
% 0.20/0.53 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl((product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1))) <=> (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(27,plain,
% 0.20/0.53 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[26])).
% 0.20/0.53 tff(28,plain,
% 0.20/0.53 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(29,plain,
% 0.20/0.53 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : trans(monotonicity(rewrite(((~product(Y, X, Z1)) | (~product(Z1, Y, Z2))) <=> ((~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))), ((((~product(Y, X, Z1)) | (~product(Z1, Y, Z2))) | product(Z2, Y, X)) <=> (((~product(Z1, Y, Z2)) | (~product(Y, X, Z1))) | product(Z2, Y, X)))), rewrite((((~product(Z1, Y, Z2)) | (~product(Y, X, Z1))) | product(Z2, Y, X)) <=> (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))), ((((~product(Y, X, Z1)) | (~product(Z1, Y, Z2))) | product(Z2, Y, X)) <=> (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(30,plain,
% 0.20/0.53 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(Y, X, Z1)) | (~product(Z1, Y, Z2))) | product(Z2, Y, X)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[29])).
% 0.20/0.53 tff(31,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(Y, X, Z1)) | (~product(Z1, Y, Z2))) | product(Z2, Y, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qg3')).
% 0.20/0.53 tff(32,plain,
% 0.20/0.53 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.20/0.53 tff(33,plain,
% 0.20/0.53 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.20/0.53 tff(34,plain,(
% 0.20/0.53 ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.53 inference(skolemize,[status(sab)],[33])).
% 0.20/0.53 tff(35,plain,
% 0.20/0.53 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.20/0.53 tff(36,plain,
% 0.20/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_6, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_6, e_1, e_1)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(37,plain,
% 0.20/0.53 ((product(e_1, e_1, e_5) | (~product(e_6, e_1, e_1)) | (~product(e_1, e_5, e_6))) <=> (product(e_1, e_1, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_6, e_1, e_1)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(38,plain,
% 0.20/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_5) | (~product(e_6, e_1, e_1)) | (~product(e_1, e_5, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_6, e_1, e_1))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[37])).
% 0.20/0.54 tff(39,plain,
% 0.20/0.54 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_5) | (~product(e_6, e_1, e_1)) | (~product(e_1, e_5, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_6, e_1, e_1)))),
% 0.20/0.54 inference(transitivity,[status(thm)],[38, 36])).
% 0.20/0.54 tff(40,plain,
% 0.20/0.54 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_5) | (~product(e_6, e_1, e_1)) | (~product(e_1, e_5, e_6)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(41,plain,
% 0.20/0.54 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_6, e_1, e_1))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.54 tff(42,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[41, 35, 25, 4, 5])).
% 0.20/0.54 tff(43,plain,((~product(e_6, e_1, e_1)) | (~product(e_1, e_5, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(44,plain,
% 0.20/0.54 (~product(e_6, e_1, e_1)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[43, 4])).
% 0.20/0.54 tff(45,assumption,(product(e_6, e_1, e_3)), introduced(assumption)).
% 0.20/0.54 tff(46,plain,
% 0.20/0.54 (^[X: $i] : refl(product(X, X, X) <=> product(X, X, X))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(47,plain,
% 0.20/0.54 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.20/0.54 inference(quant_intro,[status(thm)],[46])).
% 0.20/0.54 tff(48,plain,
% 0.20/0.54 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(49,axiom,(![X: $i] : product(X, X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_idempotence')).
% 0.20/0.54 tff(50,plain,
% 0.20/0.54 (![X: $i] : product(X, X, X)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.20/0.54 tff(51,plain,(
% 0.20/0.54 ![X: $i] : product(X, X, X)),
% 0.20/0.54 inference(skolemize,[status(sab)],[50])).
% 0.20/0.54 tff(52,plain,
% 0.20/0.54 (![X: $i] : product(X, X, X)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.20/0.54 tff(53,plain,
% 0.20/0.54 ((~![X: $i] : product(X, X, X)) | product(e_2, e_2, e_2)),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(54,plain,
% 0.20/0.54 (product(e_2, e_2, e_2)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.20/0.54 tff(55,assumption,(product(e_2, e_1, e_2)), introduced(assumption)).
% 0.20/0.54 tff(56,plain,
% 0.20/0.54 (^[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))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(57,plain,
% 0.20/0.54 (![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)))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[56])).
% 0.20/0.54 tff(58,plain,
% 0.20/0.54 (![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)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(59,plain,
% 0.20/0.54 (^[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)))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(60,plain,
% 0.20/0.54 (![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)))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[59])).
% 0.20/0.54 tff(61,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')).
% 0.20/0.54 tff(62,plain,
% 0.20/0.54 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.54 tff(63,plain,
% 0.20/0.54 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.20/0.54 tff(64,plain,(
% 0.20/0.54 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.54 inference(skolemize,[status(sab)],[63])).
% 0.20/0.54 tff(65,plain,
% 0.20/0.54 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.20/0.54 tff(66,plain,
% 0.20/0.54 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(67,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.20/0.54 tff(68,plain,
% 0.20/0.54 (~equalish(e_1, e_2)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.20/0.54 tff(69,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_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(70,plain,
% 0.20/0.54 ((equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2))) <=> (equalish(e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(71,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_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[70])).
% 0.20/0.54 tff(72,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_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.20/0.54 inference(transitivity,[status(thm)],[71, 69])).
% 0.20/0.54 tff(73,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_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(74,plain,
% 0.20/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.20/0.54 tff(75,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[74, 68, 65, 55, 54])).
% 0.20/0.54 tff(76,plain,(~product(e_2, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(77,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.20/0.54 tff(78,assumption,(~product(e_1, e_1, e_1)), introduced(assumption)).
% 0.20/0.54 tff(79,plain,
% 0.20/0.54 ((~![X: $i] : product(X, X, X)) | product(e_1, e_1, e_1)),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(80,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[79, 52, 78])).
% 0.20/0.54 tff(81,plain,(product(e_1, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(82,plain,
% 0.20/0.54 (^[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))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(83,plain,
% 0.20/0.54 (![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)))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[82])).
% 0.20/0.54 tff(84,plain,
% 0.20/0.54 (![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)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(85,plain,
% 0.20/0.54 (^[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)))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(86,plain,
% 0.20/0.54 (![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)))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[85])).
% 0.20/0.54 tff(87,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')).
% 0.20/0.54 tff(88,plain,
% 0.20/0.54 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.20/0.54 tff(89,plain,
% 0.20/0.54 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.20/0.54 tff(90,plain,(
% 0.20/0.54 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.54 inference(skolemize,[status(sab)],[89])).
% 0.20/0.54 tff(91,plain,
% 0.20/0.54 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[90, 83])).
% 0.20/0.54 tff(92,plain,
% 0.20/0.54 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(93,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.20/0.54 tff(94,plain,
% 0.20/0.54 (~equalish(e_2, e_1)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.20/0.54 tff(95,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_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)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(96,plain,
% 0.20/0.54 ((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)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(97,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_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))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[96])).
% 0.20/0.54 tff(98,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_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)))),
% 0.20/0.54 inference(transitivity,[status(thm)],[97, 95])).
% 0.20/0.54 tff(99,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_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(100,plain,
% 0.20/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.54 tff(101,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[100, 94, 91, 81, 77])).
% 0.20/0.54 tff(102,plain,(~product(e_2, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(103,plain,
% 0.20/0.54 (greater(e_6, e_3) <=> greater(e_6, e_3)),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(104,axiom,(greater(e_6, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_6_greater_e_3')).
% 0.20/0.54 tff(105,plain,
% 0.20/0.54 (greater(e_6, e_3)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.20/0.54 tff(106,plain,
% 0.20/0.54 (next(e_2, e_3) <=> next(e_2, e_3)),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(107,axiom,(next(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_then_e_3')).
% 0.20/0.54 tff(108,plain,
% 0.20/0.54 (next(e_2, e_3)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.20/0.54 tff(109,plain,
% 0.20/0.54 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_6, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_6)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_6, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_6)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(110,plain,
% 0.20/0.54 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_6, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_6)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(111,plain,
% 0.20/0.54 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_6, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_6))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.20/0.54 tff(112,plain,
% 0.20/0.54 (~product(e_2, e_1, e_6)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[111, 108, 105, 15])).
% 0.20/0.54 tff(113,plain,
% 0.20/0.54 (greater(e_5, e_3) <=> greater(e_5, e_3)),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(114,axiom,(greater(e_5, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_greater_e_3')).
% 0.20/0.54 tff(115,plain,
% 0.20/0.54 (greater(e_5, e_3)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.20/0.54 tff(116,plain,
% 0.20/0.54 (((~![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)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(117,plain,
% 0.20/0.54 ((~![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)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(118,plain,
% 0.20/0.54 ((~![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))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.20/0.54 tff(119,plain,
% 0.20/0.54 (~product(e_2, e_1, e_5)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[118, 108, 115, 15])).
% 0.20/0.54 tff(120,plain,
% 0.20/0.54 (greater(e_4, e_3) <=> greater(e_4, e_3)),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(121,axiom,(greater(e_4, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_greater_e_3')).
% 0.20/0.54 tff(122,plain,
% 0.20/0.54 (greater(e_4, e_3)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.20/0.54 tff(123,plain,
% 0.20/0.54 (((~![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)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(124,plain,
% 0.20/0.54 ((~![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)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(125,plain,
% 0.20/0.54 ((~![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))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.20/0.54 tff(126,plain,
% 0.20/0.54 (~product(e_2, e_1, e_4)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[125, 108, 122, 15])).
% 0.20/0.54 tff(127,plain,
% 0.20/0.54 (^[Y: $i, X: $i] : refl((product(X, Y, e_6) | product(X, Y, e_5) | product(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_6) | product(X, Y, e_5) | product(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))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(128,plain,
% 0.20/0.54 (![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6) | product(X, Y, e_5) | product(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)))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[127])).
% 0.20/0.54 tff(129,plain,
% 0.20/0.54 (![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6) | product(X, Y, e_5) | product(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)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(130,plain,
% 0.20/0.54 (^[Y: $i, X: $i] : trans(monotonicity(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))))), (((((((((~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_6)) <=> ((product(X, Y, e_5) | product(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_6)))), rewrite(((product(X, Y, e_5) | product(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_6)) <=> (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6)) <=> (product(X, Y, e_6) | product(X, Y, e_5) | product(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)))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(131,plain,
% 0.20/0.54 (![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)) | product(X, Y, e_6)) <=> ![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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)))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[130])).
% 0.20/0.54 tff(132,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)) | product(X, Y, e_6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_total_function1')).
% 0.20/0.54 tff(133,plain,
% 0.20/0.54 (![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.20/0.54 tff(134,plain,
% 0.20/0.54 (![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.20/0.54 tff(135,plain,(
% 0.20/0.54 ![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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)))),
% 0.20/0.54 inference(skolemize,[status(sab)],[134])).
% 0.20/0.55 tff(136,plain,
% 0.20/0.55 (![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[135, 128])).
% 0.20/0.55 tff(137,plain,
% 0.20/0.55 (group_element(e_2) <=> group_element(e_2)),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(138,axiom,(group_element(e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_2')).
% 0.20/0.55 tff(139,plain,
% 0.20/0.55 (group_element(e_2)),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.20/0.55 tff(140,plain,
% 0.20/0.55 (group_element(e_1) <=> group_element(e_1)),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(141,axiom,(group_element(e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_1')).
% 0.20/0.55 tff(142,plain,
% 0.20/0.55 (group_element(e_1)),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.20/0.55 tff(143,plain,
% 0.20/0.55 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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) | product(e_2, e_1, e_6) | (~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_6) | product(X, Y, e_5) | product(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) | product(e_2, e_1, e_6) | (~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)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(144,plain,
% 0.20/0.55 ((product(e_2, e_1, e_6) | 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) | product(e_2, e_1, e_6) | (~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)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(145,plain,
% 0.20/0.55 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6) | 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_6) | product(X, Y, e_5) | product(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) | product(e_2, e_1, e_6) | (~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))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[144])).
% 0.20/0.55 tff(146,plain,
% 0.20/0.55 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6) | 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_6) | product(X, Y, e_5) | product(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) | product(e_2, e_1, e_6) | (~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)))),
% 0.20/0.55 inference(transitivity,[status(thm)],[145, 143])).
% 0.20/0.55 tff(147,plain,
% 0.20/0.55 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6) | 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)))),
% 0.40/0.55 inference(quant_inst,[status(thm)],[])).
% 0.40/0.55 tff(148,plain,
% 0.40/0.55 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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) | product(e_2, e_1, e_6) | (~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))),
% 0.40/0.55 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.40/0.55 tff(149,plain,
% 0.40/0.55 (product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1)),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[148, 142, 139, 136, 126, 119, 112])).
% 0.40/0.55 tff(150,plain,
% 0.40/0.55 (product(e_2, e_1, e_3) | product(e_2, e_1, e_2)),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[149, 102])).
% 0.40/0.55 tff(151,plain,
% 0.40/0.55 (product(e_2, e_1, e_3)),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[150, 76])).
% 0.40/0.55 tff(152,plain,
% 0.40/0.55 ((~equalish(e_6, e_2)) <=> (~equalish(e_6, e_2))),
% 0.40/0.55 inference(rewrite,[status(thm)],[])).
% 0.40/0.55 tff(153,axiom,(~equalish(e_6, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_6_is_not_e_2')).
% 0.40/0.55 tff(154,plain,
% 0.40/0.55 (~equalish(e_6, e_2)),
% 0.40/0.55 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.40/0.55 tff(155,plain,
% 0.40/0.55 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_6, 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_6, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_6, e_1, e_3)))),
% 0.40/0.55 inference(rewrite,[status(thm)],[])).
% 0.40/0.55 tff(156,plain,
% 0.40/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_6, e_1, e_3)))),
% 0.40/0.55 inference(quant_inst,[status(thm)],[])).
% 0.40/0.55 tff(157,plain,
% 0.40/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_6, e_1, e_3))),
% 0.40/0.55 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.40/0.55 tff(158,plain,
% 0.40/0.55 ($false),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[157, 154, 91, 151, 45])).
% 0.40/0.55 tff(159,plain,(~product(e_6, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.55 tff(160,assumption,(product(e_6, e_1, e_4)), introduced(assumption)).
% 0.40/0.55 tff(161,assumption,(~product(e_3, e_1, e_4)), introduced(assumption)).
% 0.40/0.55 tff(162,assumption,(product(e_3, e_1, e_3)), introduced(assumption)).
% 0.40/0.55 tff(163,plain,
% 0.40/0.55 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.40/0.55 inference(rewrite,[status(thm)],[])).
% 0.40/0.55 tff(164,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.40/0.55 tff(165,plain,
% 0.40/0.55 (~equalish(e_3, e_2)),
% 0.40/0.55 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.40/0.55 tff(166,plain,
% 0.40/0.55 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.40/0.55 inference(rewrite,[status(thm)],[])).
% 0.40/0.55 tff(167,plain,
% 0.40/0.55 ((equalish(e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3))) <=> (equalish(e_3, e_2) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.40/0.55 inference(rewrite,[status(thm)],[])).
% 0.40/0.55 tff(168,plain,
% 0.40/0.55 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3))))),
% 0.40/0.55 inference(monotonicity,[status(thm)],[167])).
% 0.40/0.55 tff(169,plain,
% 0.40/0.55 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.40/0.55 inference(transitivity,[status(thm)],[168, 166])).
% 0.40/0.55 tff(170,plain,
% 0.40/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.40/0.55 inference(quant_inst,[status(thm)],[])).
% 0.40/0.55 tff(171,plain,
% 0.40/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3))),
% 0.40/0.55 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.40/0.55 tff(172,plain,
% 0.40/0.55 ($false),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[171, 165, 91, 151, 162])).
% 0.40/0.55 tff(173,plain,(~product(e_3, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.55 tff(174,assumption,(product(e_3, e_1, e_1)), introduced(assumption)).
% 0.40/0.55 tff(175,plain,
% 0.40/0.55 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.40/0.55 inference(rewrite,[status(thm)],[])).
% 0.40/0.55 tff(176,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.40/0.55 tff(177,plain,
% 0.40/0.55 (~equalish(e_3, e_1)),
% 0.40/0.55 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.40/0.55 tff(178,plain,
% 0.40/0.55 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.40/0.55 inference(rewrite,[status(thm)],[])).
% 0.40/0.55 tff(179,plain,
% 0.40/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.40/0.55 inference(quant_inst,[status(thm)],[])).
% 0.40/0.55 tff(180,plain,
% 0.40/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1))),
% 0.40/0.55 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.40/0.55 tff(181,plain,
% 0.40/0.55 ($false),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[180, 177, 91, 81, 174])).
% 0.40/0.55 tff(182,plain,(~product(e_3, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.55 tff(183,plain,
% 0.40/0.55 (greater(e_6, e_4) <=> greater(e_6, e_4)),
% 0.40/0.55 inference(rewrite,[status(thm)],[])).
% 0.40/0.55 tff(184,axiom,(greater(e_6, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_6_greater_e_4')).
% 0.40/0.55 tff(185,plain,
% 0.40/0.55 (greater(e_6, e_4)),
% 0.40/0.55 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.40/0.55 tff(186,plain,
% 0.40/0.55 (next(e_3, e_4) <=> next(e_3, e_4)),
% 0.40/0.55 inference(rewrite,[status(thm)],[])).
% 0.40/0.55 tff(187,axiom,(next(e_3, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_then_e_4')).
% 0.40/0.55 tff(188,plain,
% 0.40/0.55 (next(e_3, e_4)),
% 0.40/0.55 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.40/0.55 tff(189,plain,
% 0.40/0.55 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_6, e_4)) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_6)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_6, e_4)) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_6)))),
% 0.40/0.55 inference(rewrite,[status(thm)],[])).
% 0.40/0.55 tff(190,plain,
% 0.40/0.55 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_6, e_4)) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_6)))),
% 0.40/0.55 inference(quant_inst,[status(thm)],[])).
% 0.40/0.55 tff(191,plain,
% 0.40/0.55 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_6, e_4)) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_6))),
% 0.40/0.55 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.40/0.55 tff(192,plain,
% 0.40/0.55 (~product(e_3, e_1, e_6)),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[191, 188, 185, 15])).
% 0.40/0.55 tff(193,plain,
% 0.40/0.55 (greater(e_5, e_4) <=> greater(e_5, e_4)),
% 0.40/0.55 inference(rewrite,[status(thm)],[])).
% 0.40/0.55 tff(194,axiom,(greater(e_5, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_greater_e_4')).
% 0.40/0.55 tff(195,plain,
% 0.40/0.55 (greater(e_5, e_4)),
% 0.40/0.55 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.40/0.55 tff(196,plain,
% 0.40/0.55 (((~![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)))),
% 0.40/0.55 inference(rewrite,[status(thm)],[])).
% 0.40/0.55 tff(197,plain,
% 0.40/0.55 ((~![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)))),
% 0.40/0.55 inference(quant_inst,[status(thm)],[])).
% 0.40/0.55 tff(198,plain,
% 0.40/0.55 ((~![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))),
% 0.40/0.55 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.40/0.55 tff(199,plain,
% 0.40/0.55 (~product(e_3, e_1, e_5)),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[198, 188, 195, 15])).
% 0.40/0.55 tff(200,plain,
% 0.40/0.55 (group_element(e_3) <=> group_element(e_3)),
% 0.40/0.55 inference(rewrite,[status(thm)],[])).
% 0.40/0.55 tff(201,axiom,(group_element(e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_3')).
% 0.40/0.55 tff(202,plain,
% 0.40/0.55 (group_element(e_3)),
% 0.40/0.55 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.40/0.55 tff(203,plain,
% 0.40/0.55 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6) | (~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_6) | product(X, Y, e_5) | product(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_6) | (~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)))),
% 0.40/0.55 inference(rewrite,[status(thm)],[])).
% 0.40/0.55 tff(204,plain,
% 0.40/0.55 ((product(e_3, e_1, e_6) | 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) | product(e_3, e_1, e_6) | (~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)))),
% 0.40/0.55 inference(rewrite,[status(thm)],[])).
% 0.40/0.55 tff(205,plain,
% 0.40/0.55 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6) | 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_6) | product(X, Y, e_5) | product(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_6) | (~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))))),
% 0.40/0.55 inference(monotonicity,[status(thm)],[204])).
% 0.40/0.55 tff(206,plain,
% 0.40/0.55 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6) | 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_6) | product(X, Y, e_5) | product(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_6) | (~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)))),
% 0.40/0.56 inference(transitivity,[status(thm)],[205, 203])).
% 0.40/0.56 tff(207,plain,
% 0.40/0.56 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6) | 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)))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(208,plain,
% 0.40/0.56 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6) | (~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))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.40/0.56 tff(209,plain,
% 0.40/0.56 (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)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[208, 142, 202, 136, 199, 192])).
% 0.40/0.56 tff(210,plain,
% 0.40/0.56 (product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[209, 182])).
% 0.40/0.56 tff(211,plain,
% 0.40/0.56 (product(e_3, e_1, e_4) | product(e_3, e_1, e_2)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[210, 173])).
% 0.40/0.56 tff(212,plain,
% 0.40/0.56 (product(e_3, e_1, e_2)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[211, 161])).
% 0.40/0.56 tff(213,plain,
% 0.40/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(214,plain,
% 0.40/0.56 ((product(e_2, e_1, e_4) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_4, e_3))) <=> (product(e_2, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(215,plain,
% 0.40/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_2))))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[214])).
% 0.40/0.56 tff(216,plain,
% 0.40/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.40/0.56 inference(transitivity,[status(thm)],[215, 213])).
% 0.40/0.56 tff(217,plain,
% 0.40/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_4, e_3)))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(218,plain,
% 0.40/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_2))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.40/0.56 tff(219,plain,
% 0.40/0.56 (~product(e_1, e_4, e_3)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[218, 35, 126, 212])).
% 0.40/0.56 tff(220,plain,
% 0.40/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_1, e_5, e_3)) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_5) | (~product(e_1, e_5, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(221,plain,
% 0.40/0.56 ((product(e_2, e_1, e_5) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_5, e_3))) <=> (product(e_2, e_1, e_5) | (~product(e_1, e_5, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(222,plain,
% 0.40/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_5, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_1, e_5, e_3)) | (~product(e_3, e_1, e_2))))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[221])).
% 0.40/0.56 tff(223,plain,
% 0.40/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_5, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_5) | (~product(e_1, e_5, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.40/0.56 inference(transitivity,[status(thm)],[222, 220])).
% 0.40/0.56 tff(224,plain,
% 0.40/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_5, e_3)))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(225,plain,
% 0.40/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_5) | (~product(e_1, e_5, e_3)) | (~product(e_3, e_1, e_2))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.40/0.56 tff(226,plain,
% 0.40/0.56 (~product(e_1, e_5, e_3)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[225, 35, 119, 212])).
% 0.40/0.56 tff(227,plain,
% 0.40/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_4) | (~product(e_1, e_4, e_2)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_4) | (~product(e_1, e_4, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(228,plain,
% 0.40/0.56 ((product(e_3, e_1, e_4) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_4, e_2))) <=> (product(e_3, e_1, e_4) | (~product(e_1, e_4, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(229,plain,
% 0.40/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_4) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_4) | (~product(e_1, e_4, e_2)) | (~product(e_2, e_1, e_3))))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[228])).
% 0.40/0.56 tff(230,plain,
% 0.40/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_4) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_4) | (~product(e_1, e_4, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.40/0.56 inference(transitivity,[status(thm)],[229, 227])).
% 0.40/0.56 tff(231,plain,
% 0.40/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_4) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_4, e_2)))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(232,plain,
% 0.40/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_4) | (~product(e_1, e_4, e_2)) | (~product(e_2, e_1, e_3))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.40/0.56 tff(233,plain,
% 0.40/0.56 (~product(e_1, e_4, e_2)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[232, 35, 151, 161])).
% 0.40/0.56 tff(234,assumption,(~product(e_1, e_4, e_2)), introduced(assumption)).
% 0.40/0.56 tff(235,assumption,(product(e_1, e_6, e_3)), introduced(assumption)).
% 0.40/0.56 tff(236,assumption,(product(e_3, e_1, e_4)), introduced(assumption)).
% 0.40/0.56 tff(237,plain,
% 0.40/0.56 (greater(e_6, e_5) <=> greater(e_6, e_5)),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(238,axiom,(greater(e_6, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_6_greater_e_5')).
% 0.40/0.56 tff(239,plain,
% 0.40/0.56 (greater(e_6, e_5)),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.40/0.56 tff(240,plain,
% 0.40/0.56 (next(e_4, e_5) <=> next(e_4, e_5)),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(241,axiom,(next(e_4, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_then_e_5')).
% 0.40/0.56 tff(242,plain,
% 0.40/0.56 (next(e_4, e_5)),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.40/0.56 tff(243,plain,
% 0.40/0.56 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_6, e_5)) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_6)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_6, e_5)) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_6)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(244,plain,
% 0.40/0.56 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_6, e_5)) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_6)))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(245,plain,
% 0.40/0.56 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_6, e_5)) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_6))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.40/0.56 tff(246,plain,
% 0.40/0.56 (~product(e_4, e_1, e_6)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[245, 242, 239, 15])).
% 0.40/0.56 tff(247,plain,
% 0.40/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_6) | (~product(e_1, e_6, e_3)) | (~product(e_3, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_6) | (~product(e_1, e_6, e_3)) | (~product(e_3, e_1, e_4)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(248,plain,
% 0.40/0.56 ((product(e_4, e_1, e_6) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_6, e_3))) <=> (product(e_4, e_1, e_6) | (~product(e_1, e_6, e_3)) | (~product(e_3, e_1, e_4)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(249,plain,
% 0.40/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_6) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_6, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_6) | (~product(e_1, e_6, e_3)) | (~product(e_3, e_1, e_4))))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[248])).
% 0.40/0.56 tff(250,plain,
% 0.40/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_6) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_6, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_6) | (~product(e_1, e_6, e_3)) | (~product(e_3, e_1, e_4)))),
% 0.40/0.56 inference(transitivity,[status(thm)],[249, 247])).
% 0.40/0.56 tff(251,plain,
% 0.40/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_6) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_6, e_3)))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(252,plain,
% 0.40/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_6) | (~product(e_1, e_6, e_3)) | (~product(e_3, e_1, e_4))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.40/0.56 tff(253,plain,
% 0.40/0.56 ($false),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[252, 35, 246, 236, 235])).
% 0.40/0.56 tff(254,plain,((~product(e_3, e_1, e_4)) | (~product(e_1, e_6, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.56 tff(255,plain,
% 0.40/0.56 (~product(e_3, e_1, e_4)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[254, 235])).
% 0.40/0.56 tff(256,assumption,(product(e_3, e_1, e_2)), introduced(assumption)).
% 0.40/0.56 tff(257,plain,
% 0.40/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_6) | (~product(e_1, e_6, e_3)) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_6) | (~product(e_1, e_6, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(258,plain,
% 0.40/0.56 ((product(e_2, e_1, e_6) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_6, e_3))) <=> (product(e_2, e_1, e_6) | (~product(e_1, e_6, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(259,plain,
% 0.40/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_6) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_6, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_6) | (~product(e_1, e_6, e_3)) | (~product(e_3, e_1, e_2))))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[258])).
% 0.40/0.56 tff(260,plain,
% 0.40/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_6) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_6, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_6) | (~product(e_1, e_6, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.40/0.56 inference(transitivity,[status(thm)],[259, 257])).
% 0.40/0.56 tff(261,plain,
% 0.40/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_6) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_6, e_3)))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(262,plain,
% 0.40/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_6) | (~product(e_1, e_6, e_3)) | (~product(e_3, e_1, e_2))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.40/0.56 tff(263,plain,
% 0.40/0.56 ($false),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[262, 35, 112, 256, 235])).
% 0.40/0.56 tff(264,plain,((~product(e_3, e_1, e_2)) | (~product(e_1, e_6, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.56 tff(265,plain,
% 0.40/0.56 (~product(e_3, e_1, e_2)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[264, 235])).
% 0.40/0.56 tff(266,plain,
% 0.40/0.56 (product(e_3, e_1, e_3)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[210, 265, 255])).
% 0.40/0.56 tff(267,plain,
% 0.40/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_6) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_6, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_6) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_6, e_3)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(268,plain,
% 0.40/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_6) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_6, e_3)))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(269,plain,
% 0.40/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_6) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_6, e_3))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.40/0.56 tff(270,plain,
% 0.40/0.56 ($false),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[269, 35, 192, 266, 235])).
% 0.40/0.56 tff(271,plain,(~product(e_1, e_6, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.56 tff(272,assumption,(~product(e_1, e_6, e_4)), introduced(assumption)).
% 0.40/0.56 tff(273,assumption,(product(e_1, e_6, e_2)), introduced(assumption)).
% 0.40/0.56 tff(274,assumption,(~product(e_2, e_1, e_2)), introduced(assumption)).
% 0.40/0.56 tff(275,assumption,(product(e_2, e_1, e_3)), introduced(assumption)).
% 0.40/0.56 tff(276,plain,
% 0.40/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_6) | (~product(e_1, e_6, e_2)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_6) | (~product(e_1, e_6, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(277,plain,
% 0.40/0.56 ((product(e_3, e_1, e_6) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_6, e_2))) <=> (product(e_3, e_1, e_6) | (~product(e_1, e_6, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(278,plain,
% 0.40/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_6) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_6, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_6) | (~product(e_1, e_6, e_2)) | (~product(e_2, e_1, e_3))))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[277])).
% 0.40/0.56 tff(279,plain,
% 0.40/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_6) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_6, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_6) | (~product(e_1, e_6, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.40/0.56 inference(transitivity,[status(thm)],[278, 276])).
% 0.40/0.56 tff(280,plain,
% 0.40/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_6) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_6, e_2)))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(281,plain,
% 0.40/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_6) | (~product(e_1, e_6, e_2)) | (~product(e_2, e_1, e_3))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.40/0.56 tff(282,plain,
% 0.40/0.56 ($false),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[281, 35, 192, 275, 273])).
% 0.40/0.56 tff(283,plain,((~product(e_2, e_1, e_3)) | (~product(e_1, e_6, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.56 tff(284,plain,
% 0.40/0.56 (~product(e_2, e_1, e_3)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[283, 273])).
% 0.40/0.56 tff(285,plain,
% 0.40/0.56 (product(e_2, e_1, e_1)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[149, 284, 274])).
% 0.40/0.56 tff(286,plain,
% 0.40/0.56 (greater(e_6, e_2) <=> greater(e_6, e_2)),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(287,axiom,(greater(e_6, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_6_greater_e_2')).
% 0.40/0.56 tff(288,plain,
% 0.40/0.56 (greater(e_6, e_2)),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.40/0.56 tff(289,plain,
% 0.40/0.56 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_6, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_6)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_6, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_6)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(290,plain,
% 0.40/0.56 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_6, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_6)))),
% 0.42/0.57 inference(quant_inst,[status(thm)],[])).
% 0.42/0.57 tff(291,plain,
% 0.42/0.57 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_6, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_6))),
% 0.42/0.57 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.42/0.57 tff(292,plain,
% 0.42/0.57 (~product(e_1, e_1, e_6)),
% 0.42/0.57 inference(unit_resolution,[status(thm)],[291, 21, 288, 15])).
% 0.42/0.57 tff(293,plain,
% 0.42/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_6) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_6, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_6) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_6, e_2)))),
% 0.42/0.57 inference(rewrite,[status(thm)],[])).
% 0.42/0.57 tff(294,plain,
% 0.42/0.57 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_6) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_6, e_2)))),
% 0.42/0.57 inference(quant_inst,[status(thm)],[])).
% 0.42/0.57 tff(295,plain,
% 0.42/0.57 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_6) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_6, e_2))),
% 0.42/0.57 inference(modus_ponens,[status(thm)],[294, 293])).
% 0.42/0.57 tff(296,plain,
% 0.42/0.57 ($false),
% 0.42/0.57 inference(unit_resolution,[status(thm)],[295, 35, 292, 285, 273])).
% 0.42/0.57 tff(297,plain,((~product(e_1, e_6, e_2)) | product(e_2, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.42/0.57 tff(298,plain,
% 0.42/0.57 (~product(e_1, e_6, e_2)),
% 0.42/0.57 inference(unit_resolution,[status(thm)],[297, 76])).
% 0.42/0.57 tff(299,plain,
% 0.42/0.57 ((~![X: $i] : product(X, X, X)) | product(e_6, e_6, e_6)),
% 0.42/0.57 inference(quant_inst,[status(thm)],[])).
% 0.42/0.57 tff(300,plain,
% 0.42/0.57 (product(e_6, e_6, e_6)),
% 0.42/0.57 inference(unit_resolution,[status(thm)],[299, 52])).
% 0.42/0.57 tff(301,assumption,(product(e_1, e_6, e_6)), introduced(assumption)).
% 0.42/0.57 tff(302,plain,
% 0.42/0.57 ((~equalish(e_1, e_6)) <=> (~equalish(e_1, e_6))),
% 0.42/0.57 inference(rewrite,[status(thm)],[])).
% 0.42/0.57 tff(303,axiom,(~equalish(e_1, e_6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_6')).
% 0.42/0.57 tff(304,plain,
% 0.42/0.57 (~equalish(e_1, e_6)),
% 0.42/0.57 inference(modus_ponens,[status(thm)],[303, 302])).
% 0.42/0.57 tff(305,plain,
% 0.42/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_6) | (~product(e_1, e_6, e_6)) | (~product(e_6, e_6, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_6) | (~product(e_1, e_6, e_6)) | (~product(e_6, e_6, e_6)))),
% 0.42/0.57 inference(rewrite,[status(thm)],[])).
% 0.42/0.57 tff(306,plain,
% 0.42/0.57 ((equalish(e_1, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_1, e_6, e_6))) <=> (equalish(e_1, e_6) | (~product(e_1, e_6, e_6)) | (~product(e_6, e_6, e_6)))),
% 0.42/0.57 inference(rewrite,[status(thm)],[])).
% 0.42/0.57 tff(307,plain,
% 0.42/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_1, e_6, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_6) | (~product(e_1, e_6, e_6)) | (~product(e_6, e_6, e_6))))),
% 0.42/0.57 inference(monotonicity,[status(thm)],[306])).
% 0.42/0.57 tff(308,plain,
% 0.42/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_1, e_6, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_6) | (~product(e_1, e_6, e_6)) | (~product(e_6, e_6, e_6)))),
% 0.42/0.57 inference(transitivity,[status(thm)],[307, 305])).
% 0.42/0.57 tff(309,plain,
% 0.42/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_1, e_6, e_6)))),
% 0.42/0.57 inference(quant_inst,[status(thm)],[])).
% 0.42/0.57 tff(310,plain,
% 0.42/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_6) | (~product(e_1, e_6, e_6)) | (~product(e_6, e_6, e_6))),
% 0.42/0.57 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.42/0.57 tff(311,plain,
% 0.42/0.57 ($false),
% 0.42/0.57 inference(unit_resolution,[status(thm)],[310, 304, 91, 301, 300])).
% 0.42/0.57 tff(312,plain,(~product(e_1, e_6, e_6)), inference(lemma,lemma(discharge,[]))).
% 0.42/0.57 tff(313,plain,
% 0.42/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_6) | (~product(e_1, e_6, e_1)) | (~product(e_1, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_6) | (~product(e_1, e_6, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.42/0.57 inference(rewrite,[status(thm)],[])).
% 0.42/0.57 tff(314,plain,
% 0.42/0.57 ((product(e_1, e_1, e_6) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_6, e_1))) <=> (product(e_1, e_1, e_6) | (~product(e_1, e_6, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.42/0.57 inference(rewrite,[status(thm)],[])).
% 0.42/0.57 tff(315,plain,
% 0.42/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_6) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_6, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_6) | (~product(e_1, e_6, e_1)) | (~product(e_1, e_1, e_1))))),
% 0.42/0.57 inference(monotonicity,[status(thm)],[314])).
% 0.42/0.57 tff(316,plain,
% 0.42/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_6) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_6, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_6) | (~product(e_1, e_6, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.42/0.57 inference(transitivity,[status(thm)],[315, 313])).
% 0.42/0.57 tff(317,plain,
% 0.42/0.57 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_6) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_6, e_1)))),
% 0.42/0.57 inference(quant_inst,[status(thm)],[])).
% 0.42/0.57 tff(318,plain,
% 0.42/0.57 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_6) | (~product(e_1, e_6, e_1)) | (~product(e_1, e_1, e_1))),
% 0.42/0.57 inference(modus_ponens,[status(thm)],[317, 316])).
% 0.42/0.57 tff(319,plain,
% 0.42/0.57 (~product(e_1, e_6, e_1)),
% 0.42/0.57 inference(unit_resolution,[status(thm)],[318, 35, 292, 81])).
% 0.42/0.57 tff(320,plain,
% 0.42/0.57 (group_element(e_6) <=> group_element(e_6)),
% 0.42/0.57 inference(rewrite,[status(thm)],[])).
% 0.42/0.57 tff(321,axiom,(group_element(e_6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_6')).
% 0.42/0.57 tff(322,plain,
% 0.42/0.57 (group_element(e_6)),
% 0.42/0.57 inference(modus_ponens,[status(thm)],[321, 320])).
% 0.42/0.57 tff(323,plain,
% 0.42/0.57 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_1, e_6, e_1) | product(e_1, e_6, e_6) | product(e_1, e_6, e_5) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3) | product(e_1, e_6, e_2) | (~group_element(e_6)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_1, e_6, e_1) | product(e_1, e_6, e_6) | product(e_1, e_6, e_5) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3) | product(e_1, e_6, e_2) | (~group_element(e_6)))),
% 0.42/0.57 inference(rewrite,[status(thm)],[])).
% 0.42/0.57 tff(324,plain,
% 0.42/0.57 ((product(e_1, e_6, e_6) | product(e_1, e_6, e_5) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3) | product(e_1, e_6, e_2) | product(e_1, e_6, e_1) | (~group_element(e_6)) | (~group_element(e_1))) <=> ((~group_element(e_1)) | product(e_1, e_6, e_1) | product(e_1, e_6, e_6) | product(e_1, e_6, e_5) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3) | product(e_1, e_6, e_2) | (~group_element(e_6)))),
% 0.42/0.57 inference(rewrite,[status(thm)],[])).
% 0.42/0.57 tff(325,plain,
% 0.42/0.57 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6, e_6) | product(e_1, e_6, e_5) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3) | product(e_1, e_6, e_2) | product(e_1, e_6, e_1) | (~group_element(e_6)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_1, e_6, e_1) | product(e_1, e_6, e_6) | product(e_1, e_6, e_5) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3) | product(e_1, e_6, e_2) | (~group_element(e_6))))),
% 0.42/0.57 inference(monotonicity,[status(thm)],[324])).
% 0.42/0.57 tff(326,plain,
% 0.42/0.57 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6, e_6) | product(e_1, e_6, e_5) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3) | product(e_1, e_6, e_2) | product(e_1, e_6, e_1) | (~group_element(e_6)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_1, e_6, e_1) | product(e_1, e_6, e_6) | product(e_1, e_6, e_5) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3) | product(e_1, e_6, e_2) | (~group_element(e_6)))),
% 0.42/0.57 inference(transitivity,[status(thm)],[325, 323])).
% 0.42/0.57 tff(327,plain,
% 0.42/0.57 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6, e_6) | product(e_1, e_6, e_5) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3) | product(e_1, e_6, e_2) | product(e_1, e_6, e_1) | (~group_element(e_6)) | (~group_element(e_1)))),
% 0.42/0.57 inference(quant_inst,[status(thm)],[])).
% 0.42/0.57 tff(328,plain,
% 0.42/0.57 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_1, e_6, e_1) | product(e_1, e_6, e_6) | product(e_1, e_6, e_5) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3) | product(e_1, e_6, e_2) | (~group_element(e_6))),
% 0.42/0.57 inference(modus_ponens,[status(thm)],[327, 326])).
% 0.42/0.57 tff(329,plain,
% 0.42/0.57 (product(e_1, e_6, e_6) | product(e_1, e_6, e_5) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3) | product(e_1, e_6, e_2)),
% 0.42/0.57 inference(unit_resolution,[status(thm)],[328, 142, 322, 136, 319])).
% 0.42/0.57 tff(330,plain,
% 0.42/0.57 (product(e_1, e_6, e_5) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3) | product(e_1, e_6, e_2)),
% 0.42/0.57 inference(unit_resolution,[status(thm)],[329, 312])).
% 0.42/0.57 tff(331,plain,
% 0.42/0.57 (product(e_1, e_6, e_5) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3)),
% 0.42/0.57 inference(unit_resolution,[status(thm)],[330, 298])).
% 0.42/0.57 tff(332,plain,
% 0.42/0.57 (product(e_1, e_6, e_5)),
% 0.42/0.57 inference(unit_resolution,[status(thm)],[331, 272, 271])).
% 0.42/0.57 tff(333,assumption,(product(e_1, e_6, e_5)), introduced(assumption)).
% 0.42/0.57 tff(334,assumption,(product(e_1, e_4, e_5)), introduced(assumption)).
% 0.42/0.57 tff(335,plain,
% 0.42/0.57 ((~equalish(e_4, e_6)) <=> (~equalish(e_4, e_6))),
% 0.42/0.57 inference(rewrite,[status(thm)],[])).
% 0.42/0.57 tff(336,axiom,(~equalish(e_4, e_6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_6')).
% 0.42/0.57 tff(337,plain,
% 0.42/0.57 (~equalish(e_4, e_6)),
% 0.42/0.57 inference(modus_ponens,[status(thm)],[336, 335])).
% 0.42/0.57 tff(338,plain,
% 0.42/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_4, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_4, e_5)))),
% 0.42/0.57 inference(rewrite,[status(thm)],[])).
% 0.42/0.57 tff(339,plain,
% 0.42/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_4, e_5)))),
% 0.42/0.57 inference(quant_inst,[status(thm)],[])).
% 0.42/0.57 tff(340,plain,
% 0.42/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_4, e_5))),
% 0.42/0.57 inference(modus_ponens,[status(thm)],[339, 338])).
% 0.42/0.57 tff(341,plain,
% 0.42/0.57 ($false),
% 0.42/0.57 inference(unit_resolution,[status(thm)],[340, 337, 65, 334, 333])).
% 0.42/0.57 tff(342,plain,((~product(e_1, e_4, e_5)) | (~product(e_1, e_6, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.42/0.57 tff(343,plain,
% 0.42/0.57 (~product(e_1, e_4, e_5)),
% 0.42/0.57 inference(unit_resolution,[status(thm)],[342, 332])).
% 0.42/0.57 tff(344,assumption,(~product(e_1, e_4, e_3)), introduced(assumption)).
% 0.42/0.57 tff(345,plain,
% 0.42/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.42/0.57 inference(rewrite,[status(thm)],[])).
% 0.42/0.57 tff(346,plain,
% 0.42/0.57 ((product(e_3, e_1, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_3, e_2))) <=> (product(e_3, e_1, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.42/0.57 inference(rewrite,[status(thm)],[])).
% 0.42/0.57 tff(347,plain,
% 0.42/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_3))))),
% 0.42/0.57 inference(monotonicity,[status(thm)],[346])).
% 0.42/0.57 tff(348,plain,
% 0.42/0.57 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.42/0.57 inference(transitivity,[status(thm)],[347, 345])).
% 0.42/0.57 tff(349,plain,
% 0.42/0.57 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_3, e_2)))),
% 0.42/0.57 inference(quant_inst,[status(thm)],[])).
% 0.42/0.57 tff(350,plain,
% 0.42/0.57 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_3))),
% 0.42/0.57 inference(modus_ponens,[status(thm)],[349, 348])).
% 0.42/0.57 tff(351,plain,
% 0.42/0.57 (~product(e_1, e_3, e_2)),
% 0.42/0.57 inference(unit_resolution,[status(thm)],[350, 35, 151, 173])).
% 0.42/0.57 tff(352,assumption,(product(e_1, e_3, e_5)), introduced(assumption)).
% 0.42/0.57 tff(353,plain,
% 0.42/0.57 ((~equalish(e_6, e_3)) <=> (~equalish(e_6, e_3))),
% 0.42/0.57 inference(rewrite,[status(thm)],[])).
% 0.42/0.57 tff(354,axiom,(~equalish(e_6, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_6_is_not_e_3')).
% 0.42/0.57 tff(355,plain,
% 0.42/0.57 (~equalish(e_6, e_3)),
% 0.42/0.57 inference(modus_ponens,[status(thm)],[354, 353])).
% 0.42/0.57 tff(356,plain,
% 0.42/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_3) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_3, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_3) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_3, e_5)))),
% 0.42/0.58 inference(rewrite,[status(thm)],[])).
% 0.42/0.58 tff(357,plain,
% 0.42/0.58 ((equalish(e_6, e_3) | (~product(e_1, e_3, e_5)) | (~product(e_1, e_6, e_5))) <=> (equalish(e_6, e_3) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_3, e_5)))),
% 0.42/0.58 inference(rewrite,[status(thm)],[])).
% 0.42/0.58 tff(358,plain,
% 0.42/0.58 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_3) | (~product(e_1, e_3, e_5)) | (~product(e_1, e_6, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_3) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_3, e_5))))),
% 0.42/0.58 inference(monotonicity,[status(thm)],[357])).
% 0.42/0.58 tff(359,plain,
% 0.42/0.58 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_3) | (~product(e_1, e_3, e_5)) | (~product(e_1, e_6, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_3) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_3, e_5)))),
% 0.42/0.58 inference(transitivity,[status(thm)],[358, 356])).
% 0.42/0.58 tff(360,plain,
% 0.42/0.58 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_3) | (~product(e_1, e_3, e_5)) | (~product(e_1, e_6, e_5)))),
% 0.42/0.58 inference(quant_inst,[status(thm)],[])).
% 0.42/0.58 tff(361,plain,
% 0.42/0.58 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_3) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_3, e_5))),
% 0.42/0.58 inference(modus_ponens,[status(thm)],[360, 359])).
% 0.42/0.58 tff(362,plain,
% 0.42/0.58 ($false),
% 0.42/0.58 inference(unit_resolution,[status(thm)],[361, 355, 65, 333, 352])).
% 0.42/0.58 tff(363,plain,((~product(e_1, e_6, e_5)) | (~product(e_1, e_3, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.42/0.58 tff(364,plain,
% 0.42/0.58 (~product(e_1, e_3, e_5)),
% 0.42/0.58 inference(unit_resolution,[status(thm)],[363, 332])).
% 0.42/0.58 tff(365,assumption,(~product(e_1, e_5, e_3)), introduced(assumption)).
% 0.42/0.58 tff(366,plain,
% 0.42/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_1, e_5, e_2)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_5) | (~product(e_1, e_5, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.42/0.58 inference(rewrite,[status(thm)],[])).
% 0.42/0.58 tff(367,plain,
% 0.42/0.58 ((product(e_3, e_1, e_5) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_5, e_2))) <=> (product(e_3, e_1, e_5) | (~product(e_1, e_5, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.42/0.58 inference(rewrite,[status(thm)],[])).
% 0.42/0.58 tff(368,plain,
% 0.42/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_5, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_1, e_5, e_2)) | (~product(e_2, e_1, e_3))))),
% 0.42/0.58 inference(monotonicity,[status(thm)],[367])).
% 0.42/0.58 tff(369,plain,
% 0.42/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_5, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_5) | (~product(e_1, e_5, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.42/0.58 inference(transitivity,[status(thm)],[368, 366])).
% 0.42/0.58 tff(370,plain,
% 0.42/0.58 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_5, e_2)))),
% 0.42/0.58 inference(quant_inst,[status(thm)],[])).
% 0.42/0.58 tff(371,plain,
% 0.42/0.58 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_5) | (~product(e_1, e_5, e_2)) | (~product(e_2, e_1, e_3))),
% 0.42/0.58 inference(modus_ponens,[status(thm)],[370, 369])).
% 0.42/0.58 tff(372,plain,
% 0.42/0.58 (~product(e_1, e_5, e_2)),
% 0.42/0.58 inference(unit_resolution,[status(thm)],[371, 35, 199, 151])).
% 0.42/0.58 tff(373,assumption,(~product(e_3, e_3, e_3)), introduced(assumption)).
% 0.42/0.58 tff(374,plain,
% 0.42/0.58 ((~![X: $i] : product(X, X, X)) | product(e_3, e_3, e_3)),
% 0.42/0.58 inference(quant_inst,[status(thm)],[])).
% 0.42/0.58 tff(375,plain,
% 0.42/0.58 ($false),
% 0.42/0.58 inference(unit_resolution,[status(thm)],[374, 52, 373])).
% 0.42/0.58 tff(376,plain,(product(e_3, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.42/0.58 tff(377,assumption,(product(e_3, e_3, e_3)), introduced(assumption)).
% 0.42/0.58 tff(378,assumption,(product(e_1, e_3, e_3)), introduced(assumption)).
% 0.42/0.58 tff(379,plain,
% 0.42/0.58 (((~![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_3, e_3)) | (~product(e_3, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.42/0.58 inference(rewrite,[status(thm)],[])).
% 0.42/0.58 tff(380,plain,
% 0.42/0.58 ((~![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_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.42/0.58 inference(quant_inst,[status(thm)],[])).
% 0.42/0.58 tff(381,plain,
% 0.42/0.58 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3))),
% 0.42/0.58 inference(modus_ponens,[status(thm)],[380, 379])).
% 0.42/0.58 tff(382,plain,
% 0.42/0.58 ($false),
% 0.42/0.58 inference(unit_resolution,[status(thm)],[381, 177, 91, 378, 377])).
% 0.42/0.58 tff(383,plain,((~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.42/0.58 tff(384,plain,
% 0.42/0.58 (~product(e_1, e_3, e_3)),
% 0.42/0.58 inference(unit_resolution,[status(thm)],[383, 376])).
% 0.42/0.58 tff(385,plain,
% 0.42/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_5) | (~product(e_1, e_5, e_1)) | (~product(e_1, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_5) | (~product(e_1, e_5, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.42/0.58 inference(rewrite,[status(thm)],[])).
% 0.42/0.58 tff(386,plain,
% 0.42/0.58 ((product(e_1, e_1, e_5) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_5, e_1))) <=> (product(e_1, e_1, e_5) | (~product(e_1, e_5, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.42/0.58 inference(rewrite,[status(thm)],[])).
% 0.42/0.58 tff(387,plain,
% 0.42/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_5) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_5, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_5) | (~product(e_1, e_5, e_1)) | (~product(e_1, e_1, e_1))))),
% 0.42/0.58 inference(monotonicity,[status(thm)],[386])).
% 0.42/0.58 tff(388,plain,
% 0.42/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_5) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_5, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_5) | (~product(e_1, e_5, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.42/0.58 inference(transitivity,[status(thm)],[387, 385])).
% 0.42/0.58 tff(389,plain,
% 0.42/0.58 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_5) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_5, e_1)))),
% 0.42/0.58 inference(quant_inst,[status(thm)],[])).
% 0.42/0.58 tff(390,plain,
% 0.42/0.58 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_5) | (~product(e_1, e_5, e_1)) | (~product(e_1, e_1, e_1))),
% 0.42/0.58 inference(modus_ponens,[status(thm)],[389, 388])).
% 0.42/0.58 tff(391,plain,
% 0.42/0.58 (~product(e_1, e_5, e_1)),
% 0.42/0.58 inference(unit_resolution,[status(thm)],[390, 35, 25, 81])).
% 0.42/0.58 tff(392,plain,
% 0.42/0.58 (greater(e_3, e_2) <=> greater(e_3, e_2)),
% 0.42/0.58 inference(rewrite,[status(thm)],[])).
% 0.42/0.58 tff(393,axiom,(greater(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_greater_e_2')).
% 0.42/0.58 tff(394,plain,
% 0.42/0.58 (greater(e_3, e_2)),
% 0.42/0.58 inference(modus_ponens,[status(thm)],[393, 392])).
% 0.42/0.58 tff(395,plain,
% 0.42/0.58 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_3, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_3, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))),
% 0.42/0.58 inference(rewrite,[status(thm)],[])).
% 0.42/0.58 tff(396,plain,
% 0.42/0.58 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_3, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))),
% 0.42/0.58 inference(quant_inst,[status(thm)],[])).
% 0.42/0.58 tff(397,plain,
% 0.42/0.58 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_3, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3))),
% 0.42/0.58 inference(modus_ponens,[status(thm)],[396, 395])).
% 0.42/0.58 tff(398,plain,
% 0.42/0.58 (~product(e_1, e_1, e_3)),
% 0.42/0.58 inference(unit_resolution,[status(thm)],[397, 21, 394, 15])).
% 0.42/0.58 tff(399,plain,
% 0.42/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_3) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.42/0.58 inference(rewrite,[status(thm)],[])).
% 0.42/0.58 tff(400,plain,
% 0.42/0.58 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.42/0.58 inference(quant_inst,[status(thm)],[])).
% 0.42/0.58 tff(401,plain,
% 0.42/0.58 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_3) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1))),
% 0.42/0.58 inference(modus_ponens,[status(thm)],[400, 399])).
% 0.42/0.58 tff(402,plain,
% 0.42/0.58 (~product(e_1, e_3, e_1)),
% 0.42/0.58 inference(unit_resolution,[status(thm)],[401, 35, 398, 81])).
% 0.42/0.58 tff(403,plain,
% 0.42/0.58 (greater(e_4, e_2) <=> greater(e_4, e_2)),
% 0.42/0.58 inference(rewrite,[status(thm)],[])).
% 0.42/0.58 tff(404,axiom,(greater(e_4, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_greater_e_2')).
% 0.42/0.58 tff(405,plain,
% 0.42/0.58 (greater(e_4, e_2)),
% 0.42/0.58 inference(modus_ponens,[status(thm)],[404, 403])).
% 0.42/0.58 tff(406,plain,
% 0.42/0.58 (((~![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)))),
% 0.42/0.58 inference(rewrite,[status(thm)],[])).
% 0.42/0.58 tff(407,plain,
% 0.42/0.58 ((~![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)))),
% 0.42/0.58 inference(quant_inst,[status(thm)],[])).
% 0.42/0.58 tff(408,plain,
% 0.42/0.58 ((~![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))),
% 0.42/0.58 inference(modus_ponens,[status(thm)],[407, 406])).
% 0.42/0.58 tff(409,plain,
% 0.42/0.58 (~product(e_1, e_1, e_4)),
% 0.42/0.58 inference(unit_resolution,[status(thm)],[408, 21, 405, 15])).
% 0.42/0.58 tff(410,plain,
% 0.42/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_4) | (~product(e_1, e_4, e_1)) | (~product(e_1, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_4) | (~product(e_1, e_4, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.42/0.58 inference(rewrite,[status(thm)],[])).
% 0.42/0.58 tff(411,plain,
% 0.42/0.58 ((product(e_1, e_1, e_4) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1))) <=> (product(e_1, e_1, e_4) | (~product(e_1, e_4, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.42/0.58 inference(rewrite,[status(thm)],[])).
% 0.42/0.58 tff(412,plain,
% 0.42/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_4) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_4) | (~product(e_1, e_4, e_1)) | (~product(e_1, e_1, e_1))))),
% 0.42/0.58 inference(monotonicity,[status(thm)],[411])).
% 0.42/0.58 tff(413,plain,
% 0.42/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_4) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_4) | (~product(e_1, e_4, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.42/0.58 inference(transitivity,[status(thm)],[412, 410])).
% 0.42/0.58 tff(414,plain,
% 0.42/0.58 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_4) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1)))),
% 0.42/0.58 inference(quant_inst,[status(thm)],[])).
% 0.42/0.58 tff(415,plain,
% 0.42/0.58 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_4) | (~product(e_1, e_4, e_1)) | (~product(e_1, e_1, e_1))),
% 0.42/0.58 inference(modus_ponens,[status(thm)],[414, 413])).
% 0.42/0.58 tff(416,plain,
% 0.42/0.58 (~product(e_1, e_4, e_1)),
% 0.42/0.58 inference(unit_resolution,[status(thm)],[415, 35, 409, 81])).
% 0.42/0.58 tff(417,assumption,(~product(e_1, e_6, e_2)), introduced(assumption)).
% 0.42/0.58 tff(418,assumption,(~product(e_1, e_6, e_3)), introduced(assumption)).
% 0.42/0.58 tff(419,assumption,(~product(e_1, e_6, e_1)), introduced(assumption)).
% 0.42/0.58 tff(420,assumption,(~product(e_1, e_3, e_2)), introduced(assumption)).
% 0.42/0.58 tff(421,assumption,(~product(e_1, e_5, e_6)), introduced(assumption)).
% 0.42/0.58 tff(422,assumption,(~product(e_1, e_3, e_3)), introduced(assumption)).
% 0.42/0.58 tff(423,assumption,(~product(e_1, e_3, e_5)), introduced(assumption)).
% 0.42/0.58 tff(424,assumption,(~product(e_1, e_4, e_1)), introduced(assumption)).
% 0.42/0.58 tff(425,assumption,(~product(e_1, e_5, e_1)), introduced(assumption)).
% 0.42/0.58 tff(426,assumption,(~product(e_1, e_5, e_2)), introduced(assumption)).
% 0.42/0.58 tff(427,assumption,(~product(e_1, e_3, e_1)), introduced(assumption)).
% 0.42/0.58 tff(428,assumption,(~product(e_1, e_4, e_6)), introduced(assumption)).
% 0.42/0.58 tff(429,plain,
% 0.42/0.58 (~product(e_1, e_4, e_5)),
% 0.42/0.58 inference(unit_resolution,[status(thm)],[342, 333])).
% 0.42/0.58 tff(430,plain,
% 0.42/0.58 (group_element(e_4) <=> group_element(e_4)),
% 0.42/0.58 inference(rewrite,[status(thm)],[])).
% 0.42/0.58 tff(431,axiom,(group_element(e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_4')).
% 0.42/0.58 tff(432,plain,
% 0.42/0.58 (group_element(e_4)),
% 0.42/0.58 inference(modus_ponens,[status(thm)],[431, 430])).
% 0.42/0.58 tff(433,plain,
% 0.42/0.58 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_1) | product(e_1, e_4, e_6) | 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))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_1) | product(e_1, e_4, e_6) | 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))),
% 0.42/0.58 inference(rewrite,[status(thm)],[])).
% 0.42/0.58 tff(434,plain,
% 0.42/0.58 ((product(e_1, e_4, e_6) | 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_1) | product(e_1, e_4, e_6) | 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))),
% 0.42/0.58 inference(rewrite,[status(thm)],[])).
% 0.42/0.58 tff(435,plain,
% 0.42/0.58 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6) | 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_6) | product(X, Y, e_5) | product(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_1) | product(e_1, e_4, e_6) | 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)))),
% 0.42/0.58 inference(monotonicity,[status(thm)],[434])).
% 0.42/0.58 tff(436,plain,
% 0.42/0.58 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6) | 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_6) | product(X, Y, e_5) | product(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_1) | product(e_1, e_4, e_6) | 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))),
% 0.42/0.58 inference(transitivity,[status(thm)],[435, 433])).
% 0.42/0.58 tff(437,plain,
% 0.42/0.58 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6) | 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)))),
% 0.42/0.58 inference(quant_inst,[status(thm)],[])).
% 0.42/0.58 tff(438,plain,
% 0.42/0.58 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_1) | product(e_1, e_4, e_6) | 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)),
% 0.42/0.58 inference(modus_ponens,[status(thm)],[437, 436])).
% 0.42/0.58 tff(439,plain,
% 0.42/0.58 (product(e_1, e_4, e_6) | 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)),
% 0.42/0.58 inference(unit_resolution,[status(thm)],[438, 142, 432, 136, 424])).
% 0.42/0.58 tff(440,plain,
% 0.42/0.58 (product(e_1, e_4, e_4)),
% 0.42/0.58 inference(unit_resolution,[status(thm)],[439, 429, 428, 344, 234])).
% 0.42/0.58 tff(441,assumption,(product(e_1, e_5, e_4)), introduced(assumption)).
% 0.42/0.58 tff(442,assumption,(product(e_1, e_4, e_4)), introduced(assumption)).
% 0.42/0.58 tff(443,plain,
% 0.42/0.58 ((~equalish(e_5, e_4)) <=> (~equalish(e_5, e_4))),
% 0.42/0.58 inference(rewrite,[status(thm)],[])).
% 0.42/0.58 tff(444,axiom,(~equalish(e_5, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_is_not_e_4')).
% 0.42/0.58 tff(445,plain,
% 0.42/0.58 (~equalish(e_5, e_4)),
% 0.42/0.58 inference(modus_ponens,[status(thm)],[444, 443])).
% 0.42/0.58 tff(446,plain,
% 0.42/0.58 (((~![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_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_4) | (~product(e_1, e_4, e_4)) | (~product(e_1, e_5, e_4)))),
% 0.42/0.58 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(447,plain,
% 0.42/0.59 ((~![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_4)) | (~product(e_1, e_5, e_4)))),
% 0.42/0.59 inference(quant_inst,[status(thm)],[])).
% 0.42/0.59 tff(448,plain,
% 0.42/0.59 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_4) | (~product(e_1, e_4, e_4)) | (~product(e_1, e_5, e_4))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[447, 446])).
% 0.42/0.59 tff(449,plain,
% 0.42/0.59 ($false),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[448, 445, 65, 442, 441])).
% 0.42/0.59 tff(450,plain,((~product(e_1, e_5, e_4)) | (~product(e_1, e_4, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.42/0.59 tff(451,plain,
% 0.42/0.59 (~product(e_1, e_5, e_4)),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[450, 440])).
% 0.42/0.59 tff(452,plain,
% 0.42/0.59 (group_element(e_5) <=> group_element(e_5)),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(453,axiom,(group_element(e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_5')).
% 0.42/0.59 tff(454,plain,
% 0.42/0.59 (group_element(e_5)),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[453, 452])).
% 0.42/0.59 tff(455,plain,
% 0.42/0.59 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_1, e_5, e_1) | product(e_1, e_5, e_6) | 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) | (~group_element(e_5)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_1, e_5, e_1) | product(e_1, e_5, e_6) | 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) | (~group_element(e_5)))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(456,plain,
% 0.42/0.59 ((product(e_1, e_5, e_6) | 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)) | product(e_1, e_5, e_1) | product(e_1, e_5, e_6) | 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) | (~group_element(e_5)))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(457,plain,
% 0.42/0.59 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6) | 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_6) | product(X, Y, e_5) | product(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_1, e_5, e_1) | product(e_1, e_5, e_6) | 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) | (~group_element(e_5))))),
% 0.42/0.59 inference(monotonicity,[status(thm)],[456])).
% 0.42/0.59 tff(458,plain,
% 0.42/0.59 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6) | 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_6) | product(X, Y, e_5) | product(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_1, e_5, e_1) | product(e_1, e_5, e_6) | 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) | (~group_element(e_5)))),
% 0.42/0.59 inference(transitivity,[status(thm)],[457, 455])).
% 0.42/0.59 tff(459,plain,
% 0.42/0.59 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6) | 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)))),
% 0.42/0.59 inference(quant_inst,[status(thm)],[])).
% 0.42/0.59 tff(460,plain,
% 0.42/0.59 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_1, e_5, e_1) | product(e_1, e_5, e_6) | 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) | (~group_element(e_5))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[459, 458])).
% 0.42/0.59 tff(461,plain,
% 0.42/0.59 (product(e_1, e_5, e_6) | 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)),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[460, 142, 454, 136, 425])).
% 0.42/0.59 tff(462,plain,
% 0.42/0.59 (product(e_1, e_5, e_5)),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[461, 451, 421, 365, 426])).
% 0.42/0.59 tff(463,plain,
% 0.42/0.59 ((~equalish(e_5, e_6)) <=> (~equalish(e_5, e_6))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(464,axiom,(~equalish(e_5, e_6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_is_not_e_6')).
% 0.42/0.59 tff(465,plain,
% 0.42/0.59 (~equalish(e_5, e_6)),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[464, 463])).
% 0.42/0.59 tff(466,plain,
% 0.42/0.59 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_5, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_5, e_5)))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(467,plain,
% 0.42/0.59 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_5, e_5)))),
% 0.42/0.59 inference(quant_inst,[status(thm)],[])).
% 0.42/0.59 tff(468,plain,
% 0.42/0.59 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_5, e_5))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[467, 466])).
% 0.42/0.59 tff(469,plain,
% 0.42/0.59 ($false),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[468, 465, 65, 462, 333])).
% 0.42/0.59 tff(470,plain,((~product(e_1, e_6, e_5)) | product(e_1, e_5, e_6) | product(e_1, e_5, e_3) | product(e_1, e_5, e_2) | product(e_1, e_5, e_1) | product(e_1, e_4, e_6) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.42/0.59 tff(471,plain,
% 0.42/0.59 (~product(e_1, e_6, e_5)),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[470, 428, 365, 426, 425, 421, 344, 234, 424])).
% 0.42/0.59 tff(472,plain,
% 0.42/0.59 (product(e_1, e_6, e_6) | product(e_1, e_6, e_5) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3) | product(e_1, e_6, e_2)),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[328, 142, 322, 136, 419])).
% 0.42/0.59 tff(473,plain,
% 0.42/0.59 (product(e_1, e_6, e_6)),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[472, 471, 272, 418, 417])).
% 0.42/0.59 tff(474,assumption,(product(e_1, e_3, e_6)), introduced(assumption)).
% 0.42/0.59 tff(475,plain,
% 0.42/0.59 ((~equalish(e_3, e_6)) <=> (~equalish(e_3, e_6))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(476,axiom,(~equalish(e_3, e_6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_6')).
% 0.42/0.59 tff(477,plain,
% 0.42/0.59 (~equalish(e_3, e_6)),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[476, 475])).
% 0.42/0.59 tff(478,plain,
% 0.42/0.59 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_6) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_3, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_6) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_3, e_6)))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(479,plain,
% 0.42/0.59 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_6) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_3, e_6)))),
% 0.42/0.59 inference(quant_inst,[status(thm)],[])).
% 0.42/0.59 tff(480,plain,
% 0.42/0.59 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_6) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_3, e_6))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[479, 478])).
% 0.42/0.59 tff(481,plain,
% 0.42/0.59 ($false),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[480, 477, 65, 301, 474])).
% 0.42/0.59 tff(482,plain,((~product(e_1, e_3, e_6)) | (~product(e_1, e_6, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.42/0.59 tff(483,plain,
% 0.42/0.59 (~product(e_1, e_3, e_6)),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[482, 473])).
% 0.42/0.59 tff(484,plain,
% 0.42/0.59 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6) | 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_6) | product(X, Y, e_5) | product(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_6) | 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))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(485,plain,
% 0.42/0.59 ((product(e_1, e_3, e_6) | 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_6) | 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))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(486,plain,
% 0.42/0.59 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6) | 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_6) | product(X, Y, e_5) | product(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_6) | 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)))),
% 0.42/0.59 inference(monotonicity,[status(thm)],[485])).
% 0.42/0.59 tff(487,plain,
% 0.42/0.59 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6) | 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_6) | product(X, Y, e_5) | product(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_6) | 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))),
% 0.42/0.59 inference(transitivity,[status(thm)],[486, 484])).
% 0.42/0.59 tff(488,plain,
% 0.42/0.59 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6) | 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)))),
% 0.42/0.59 inference(quant_inst,[status(thm)],[])).
% 0.42/0.59 tff(489,plain,
% 0.42/0.59 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6) | 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)),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[488, 487])).
% 0.42/0.59 tff(490,plain,
% 0.42/0.59 (product(e_1, e_3, e_6) | 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)),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[489, 142, 202, 136, 420])).
% 0.42/0.59 tff(491,plain,
% 0.42/0.59 (product(e_1, e_3, e_4)),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[490, 483, 423, 422, 427])).
% 0.42/0.59 tff(492,assumption,(product(e_1, e_3, e_4)), introduced(assumption)).
% 0.42/0.59 tff(493,plain,
% 0.42/0.59 ((~equalish(e_4, e_3)) <=> (~equalish(e_4, e_3))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(494,axiom,(~equalish(e_4, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_3')).
% 0.42/0.59 tff(495,plain,
% 0.42/0.59 (~equalish(e_4, e_3)),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[494, 493])).
% 0.42/0.59 tff(496,plain,
% 0.42/0.59 (((~![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_4)) | (~product(e_1, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_4, e_4)))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(497,plain,
% 0.42/0.59 ((~![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_4)) | (~product(e_1, e_4, e_4)))),
% 0.42/0.59 inference(quant_inst,[status(thm)],[])).
% 0.42/0.59 tff(498,plain,
% 0.42/0.59 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_4, e_4))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[497, 496])).
% 0.42/0.59 tff(499,plain,
% 0.42/0.59 ($false),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[498, 495, 65, 442, 492])).
% 0.42/0.59 tff(500,plain,((~product(e_1, e_4, e_4)) | (~product(e_1, e_3, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.42/0.59 tff(501,plain,
% 0.42/0.59 (~product(e_1, e_4, e_4)),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[500, 491])).
% 0.42/0.59 tff(502,plain,
% 0.42/0.59 (product(e_1, e_4, e_5)),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[439, 501, 428, 344, 234])).
% 0.42/0.59 tff(503,assumption,(product(e_1, e_5, e_5)), introduced(assumption)).
% 0.42/0.59 tff(504,plain,
% 0.42/0.59 (((~![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_5)) | (~product(e_1, e_5, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_4) | (~product(e_1, e_4, e_5)) | (~product(e_1, e_5, e_5)))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(505,plain,
% 0.42/0.59 ((~![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_5)) | (~product(e_1, e_5, e_5)))),
% 0.42/0.59 inference(quant_inst,[status(thm)],[])).
% 0.42/0.59 tff(506,plain,
% 0.42/0.59 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_4) | (~product(e_1, e_4, e_5)) | (~product(e_1, e_5, e_5))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[505, 504])).
% 0.42/0.59 tff(507,plain,
% 0.42/0.59 ($false),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[506, 445, 65, 334, 503])).
% 0.42/0.59 tff(508,plain,((~product(e_1, e_5, e_5)) | (~product(e_1, e_4, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.42/0.60 tff(509,plain,
% 0.42/0.60 (~product(e_1, e_5, e_5)),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[508, 502])).
% 0.42/0.60 tff(510,plain,
% 0.42/0.60 (product(e_1, e_5, e_4)),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[461, 509, 421, 365, 426])).
% 0.42/0.60 tff(511,plain,
% 0.42/0.60 ((~equalish(e_3, e_5)) <=> (~equalish(e_3, e_5))),
% 0.42/0.60 inference(rewrite,[status(thm)],[])).
% 0.42/0.60 tff(512,axiom,(~equalish(e_3, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_5')).
% 0.42/0.60 tff(513,plain,
% 0.42/0.60 (~equalish(e_3, e_5)),
% 0.42/0.60 inference(modus_ponens,[status(thm)],[512, 511])).
% 0.42/0.60 tff(514,plain,
% 0.42/0.60 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_1, e_3, 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_3, e_5) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_5, e_4)))),
% 0.42/0.60 inference(rewrite,[status(thm)],[])).
% 0.42/0.60 tff(515,plain,
% 0.42/0.60 ((equalish(e_3, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_1, e_3, e_4))) <=> (equalish(e_3, e_5) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_5, e_4)))),
% 0.42/0.60 inference(rewrite,[status(thm)],[])).
% 0.42/0.60 tff(516,plain,
% 0.42/0.60 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_1, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_5, e_4))))),
% 0.42/0.60 inference(monotonicity,[status(thm)],[515])).
% 0.42/0.60 tff(517,plain,
% 0.42/0.60 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_1, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_5) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_5, e_4)))),
% 0.42/0.60 inference(transitivity,[status(thm)],[516, 514])).
% 0.42/0.60 tff(518,plain,
% 0.42/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_1, e_3, e_4)))),
% 0.42/0.60 inference(quant_inst,[status(thm)],[])).
% 0.42/0.60 tff(519,plain,
% 0.42/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_5) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_5, e_4))),
% 0.42/0.60 inference(modus_ponens,[status(thm)],[518, 517])).
% 0.42/0.60 tff(520,plain,
% 0.42/0.60 ($false),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[519, 513, 65, 510, 491])).
% 0.42/0.60 tff(521,plain,(product(e_1, e_4, e_6) | product(e_1, e_5, e_6) | product(e_1, e_5, e_3) | product(e_1, e_5, e_2) | product(e_1, e_5, e_1) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | product(e_1, e_3, e_5) | product(e_1, e_3, e_3) | product(e_1, e_3, e_1) | product(e_1, e_3, e_2) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3) | product(e_1, e_6, e_2) | product(e_1, e_6, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.42/0.60 tff(522,plain,
% 0.42/0.60 (product(e_1, e_4, e_6)),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[521, 427, 365, 426, 425, 344, 234, 424, 423, 422, 421, 420, 272, 418, 417, 419])).
% 0.42/0.60 tff(523,assumption,(product(e_1, e_4, e_6)), introduced(assumption)).
% 0.42/0.60 tff(524,plain,
% 0.42/0.60 ((~equalish(e_6, e_4)) <=> (~equalish(e_6, e_4))),
% 0.42/0.60 inference(rewrite,[status(thm)],[])).
% 0.42/0.60 tff(525,axiom,(~equalish(e_6, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_6_is_not_e_4')).
% 0.42/0.60 tff(526,plain,
% 0.42/0.60 (~equalish(e_6, e_4)),
% 0.42/0.60 inference(modus_ponens,[status(thm)],[525, 524])).
% 0.42/0.60 tff(527,plain,
% 0.42/0.60 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_4) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_4, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_4) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_4, e_6)))),
% 0.42/0.60 inference(rewrite,[status(thm)],[])).
% 0.42/0.60 tff(528,plain,
% 0.42/0.60 ((equalish(e_6, e_4) | (~product(e_1, e_4, e_6)) | (~product(e_1, e_6, e_6))) <=> (equalish(e_6, e_4) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_4, e_6)))),
% 0.42/0.60 inference(rewrite,[status(thm)],[])).
% 0.42/0.60 tff(529,plain,
% 0.42/0.60 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_4) | (~product(e_1, e_4, e_6)) | (~product(e_1, e_6, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_4) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_4, e_6))))),
% 0.42/0.60 inference(monotonicity,[status(thm)],[528])).
% 0.42/0.60 tff(530,plain,
% 0.42/0.60 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_4) | (~product(e_1, e_4, e_6)) | (~product(e_1, e_6, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_4) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_4, e_6)))),
% 0.42/0.60 inference(transitivity,[status(thm)],[529, 527])).
% 0.42/0.60 tff(531,plain,
% 0.42/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_4) | (~product(e_1, e_4, e_6)) | (~product(e_1, e_6, e_6)))),
% 0.42/0.60 inference(quant_inst,[status(thm)],[])).
% 0.42/0.60 tff(532,plain,
% 0.42/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_4) | (~product(e_1, e_6, e_6)) | (~product(e_1, e_4, e_6))),
% 0.42/0.60 inference(modus_ponens,[status(thm)],[531, 530])).
% 0.42/0.60 tff(533,plain,
% 0.42/0.60 ($false),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[532, 526, 65, 523, 301])).
% 0.42/0.60 tff(534,plain,((~product(e_1, e_6, e_6)) | (~product(e_1, e_4, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.42/0.60 tff(535,plain,
% 0.42/0.60 (~product(e_1, e_6, e_6)),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[534, 522])).
% 0.42/0.60 tff(536,plain,
% 0.42/0.60 (product(e_1, e_6, e_5)),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[472, 535, 272, 418, 417])).
% 0.42/0.60 tff(537,plain,
% 0.42/0.60 ((~equalish(e_3, e_4)) <=> (~equalish(e_3, e_4))),
% 0.42/0.60 inference(rewrite,[status(thm)],[])).
% 0.42/0.60 tff(538,axiom,(~equalish(e_3, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_4')).
% 0.42/0.60 tff(539,plain,
% 0.42/0.60 (~equalish(e_3, e_4)),
% 0.42/0.60 inference(modus_ponens,[status(thm)],[538, 537])).
% 0.42/0.60 tff(540,plain,
% 0.42/0.60 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_4) | (~product(e_1, e_4, e_6)) | (~product(e_1, e_3, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_1, e_4, e_6)) | (~product(e_1, e_3, e_6)))),
% 0.42/0.60 inference(rewrite,[status(thm)],[])).
% 0.42/0.60 tff(541,plain,
% 0.42/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_4) | (~product(e_1, e_4, e_6)) | (~product(e_1, e_3, e_6)))),
% 0.42/0.60 inference(quant_inst,[status(thm)],[])).
% 0.42/0.60 tff(542,plain,
% 0.42/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_1, e_4, e_6)) | (~product(e_1, e_3, e_6))),
% 0.42/0.60 inference(modus_ponens,[status(thm)],[541, 540])).
% 0.42/0.60 tff(543,plain,
% 0.42/0.60 ($false),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[542, 539, 65, 523, 474])).
% 0.42/0.60 tff(544,plain,((~product(e_1, e_3, e_6)) | (~product(e_1, e_4, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.42/0.60 tff(545,plain,
% 0.42/0.60 (~product(e_1, e_3, e_6)),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[544, 522])).
% 0.42/0.60 tff(546,plain,
% 0.42/0.60 (product(e_1, e_3, e_4)),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[490, 545, 423, 422, 427])).
% 0.42/0.60 tff(547,plain,
% 0.42/0.60 ($false),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[519, 513, 65, 441, 492])).
% 0.42/0.60 tff(548,plain,((~product(e_1, e_3, e_4)) | (~product(e_1, e_5, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.42/0.60 tff(549,plain,
% 0.42/0.60 (~product(e_1, e_5, e_4)),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[548, 546])).
% 0.42/0.60 tff(550,plain,
% 0.42/0.60 (product(e_1, e_5, e_5)),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[461, 549, 421, 365, 426])).
% 0.42/0.60 tff(551,plain,
% 0.42/0.60 ($false),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[468, 465, 65, 550, 536])).
% 0.42/0.60 tff(552,plain,(product(e_1, e_3, e_1) | product(e_1, e_5, e_6) | product(e_1, e_5, e_3) | product(e_1, e_5, e_2) | product(e_1, e_5, e_1) | product(e_1, e_3, e_5) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3) | product(e_1, e_6, e_2) | product(e_1, e_6, e_1) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.42/0.60 tff(553,plain,
% 0.42/0.60 (product(e_1, e_5, e_6) | product(e_1, e_5, e_3) | product(e_1, e_5, e_2) | product(e_1, e_3, e_5) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3) | product(e_1, e_6, e_2) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2)),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[552, 416, 402, 391, 319])).
% 0.42/0.60 tff(554,plain,
% 0.42/0.60 (product(e_1, e_5, e_6) | product(e_1, e_5, e_3) | product(e_1, e_5, e_2) | product(e_1, e_3, e_5) | product(e_1, e_3, e_2) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3) | product(e_1, e_6, e_2) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2)),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[553, 384])).
% 0.42/0.60 tff(555,plain,
% 0.42/0.60 (product(e_1, e_5, e_6) | product(e_1, e_5, e_3) | product(e_1, e_3, e_5) | product(e_1, e_3, e_2) | product(e_1, e_6, e_4) | product(e_1, e_6, e_3) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2)),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[554, 372, 298])).
% 0.42/0.60 tff(556,plain,
% 0.42/0.60 (product(e_1, e_5, e_6)),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[555, 234, 271, 344, 351, 365, 272, 364])).
% 0.42/0.60 tff(557,plain,
% 0.42/0.60 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_1, e_3, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_1, e_3, e_6)))),
% 0.42/0.60 inference(rewrite,[status(thm)],[])).
% 0.42/0.60 tff(558,plain,
% 0.42/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_1, e_3, e_6)))),
% 0.42/0.60 inference(quant_inst,[status(thm)],[])).
% 0.42/0.60 tff(559,plain,
% 0.42/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_1, e_3, e_6))),
% 0.42/0.60 inference(modus_ponens,[status(thm)],[558, 557])).
% 0.42/0.60 tff(560,plain,
% 0.42/0.60 ($false),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[559, 513, 65, 4, 474])).
% 0.42/0.60 tff(561,plain,((~product(e_1, e_3, e_6)) | (~product(e_1, e_5, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.42/0.60 tff(562,plain,
% 0.42/0.60 (~product(e_1, e_3, e_6)),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[561, 556])).
% 0.42/0.60 tff(563,plain,
% 0.42/0.60 (product(e_1, e_3, e_2) | product(e_1, e_3, e_6) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3)),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[489, 142, 202, 136, 402])).
% 0.42/0.60 tff(564,plain,
% 0.42/0.60 (product(e_1, e_3, e_2) | product(e_1, e_3, e_6) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4)),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[563, 384])).
% 0.42/0.60 tff(565,plain,
% 0.42/0.60 (product(e_1, e_3, e_4)),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[564, 562, 364, 351])).
% 0.42/0.60 tff(566,plain,
% 0.42/0.60 (~product(e_1, e_4, e_4)),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[500, 565])).
% 0.42/0.60 tff(567,plain,
% 0.42/0.60 (product(e_1, e_4, e_6) | 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)),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[438, 142, 432, 136, 416])).
% 0.42/0.60 tff(568,plain,
% 0.42/0.60 (product(e_1, e_4, e_6)),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[567, 566, 344, 343, 234])).
% 0.42/0.60 tff(569,plain,
% 0.42/0.60 (((~![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_5, e_6)) | (~product(e_1, e_4, e_6)))) <=> ((~![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_5, e_6)) | (~product(e_1, e_4, e_6)))),
% 0.42/0.60 inference(rewrite,[status(thm)],[])).
% 0.42/0.60 tff(570,plain,
% 0.42/0.60 ((equalish(e_5, e_4) | (~product(e_1, e_4, e_6)) | (~product(e_1, e_5, e_6))) <=> (equalish(e_5, e_4) | (~product(e_1, e_5, e_6)) | (~product(e_1, e_4, e_6)))),
% 0.42/0.60 inference(rewrite,[status(thm)],[])).
% 0.42/0.60 tff(571,plain,
% 0.42/0.60 (((~![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_6)) | (~product(e_1, e_5, e_6)))) <=> ((~![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_5, e_6)) | (~product(e_1, e_4, e_6))))),
% 0.42/0.60 inference(monotonicity,[status(thm)],[570])).
% 0.42/0.60 tff(572,plain,
% 0.42/0.60 (((~![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_6)) | (~product(e_1, e_5, e_6)))) <=> ((~![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_5, e_6)) | (~product(e_1, e_4, e_6)))),
% 0.42/0.60 inference(transitivity,[status(thm)],[571, 569])).
% 0.42/0.60 tff(573,plain,
% 0.42/0.60 ((~![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_6)) | (~product(e_1, e_5, e_6)))),
% 0.42/0.60 inference(quant_inst,[status(thm)],[])).
% 0.42/0.60 tff(574,plain,
% 0.42/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_4) | (~product(e_1, e_5, e_6)) | (~product(e_1, e_4, e_6))),
% 0.42/0.60 inference(modus_ponens,[status(thm)],[573, 572])).
% 0.42/0.60 tff(575,plain,
% 0.42/0.60 ($false),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[574, 445, 65, 556, 568])).
% 0.42/0.60 tff(576,plain,(product(e_1, e_4, e_2) | product(e_1, e_4, e_3) | product(e_1, e_5, e_3) | product(e_1, e_6, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.42/0.60 tff(577,plain,
% 0.42/0.60 (product(e_1, e_6, e_4)),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[576, 233, 226, 219])).
% 0.42/0.60 tff(578,assumption,(product(e_1, e_2, e_4)), introduced(assumption)).
% 0.42/0.60 tff(579,assumption,(product(e_1, e_6, e_4)), introduced(assumption)).
% 0.42/0.60 tff(580,plain,
% 0.42/0.60 ((~equalish(e_2, e_6)) <=> (~equalish(e_2, e_6))),
% 0.42/0.60 inference(rewrite,[status(thm)],[])).
% 0.42/0.60 tff(581,axiom,(~equalish(e_2, e_6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_6')).
% 0.42/0.60 tff(582,plain,
% 0.42/0.60 (~equalish(e_2, e_6)),
% 0.42/0.60 inference(modus_ponens,[status(thm)],[581, 580])).
% 0.42/0.60 tff(583,plain,
% 0.42/0.60 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_6) | (~product(e_1, e_6, 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_2, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_1, e_2, e_4)))),
% 0.42/0.60 inference(rewrite,[status(thm)],[])).
% 0.42/0.60 tff(584,plain,
% 0.42/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_1, e_2, e_4)))),
% 0.42/0.60 inference(quant_inst,[status(thm)],[])).
% 0.42/0.60 tff(585,plain,
% 0.42/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_1, e_2, e_4))),
% 0.42/0.60 inference(modus_ponens,[status(thm)],[584, 583])).
% 0.42/0.60 tff(586,plain,
% 0.42/0.60 ($false),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[585, 582, 65, 579, 578])).
% 0.42/0.60 tff(587,plain,((~product(e_1, e_2, e_4)) | (~product(e_1, e_6, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.42/0.60 tff(588,plain,
% 0.42/0.60 (~product(e_1, e_2, e_4)),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[587, 577])).
% 0.42/0.60 tff(589,plain,
% 0.42/0.60 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_2, e_3)))),
% 0.42/0.60 inference(rewrite,[status(thm)],[])).
% 0.42/0.60 tff(590,plain,
% 0.42/0.60 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_2, e_3)))),
% 0.42/0.60 inference(quant_inst,[status(thm)],[])).
% 0.42/0.60 tff(591,plain,
% 0.42/0.60 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_2, e_3))),
% 0.42/0.60 inference(modus_ponens,[status(thm)],[590, 589])).
% 0.42/0.60 tff(592,plain,
% 0.42/0.60 (~product(e_1, e_2, e_3)),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[591, 35, 76, 212])).
% 0.42/0.60 tff(593,plain,
% 0.42/0.60 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_1, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_1, e_3, e_4)))),
% 0.42/0.60 inference(rewrite,[status(thm)],[])).
% 0.42/0.60 tff(594,plain,
% 0.42/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_1, e_3, e_4)))),
% 0.42/0.60 inference(quant_inst,[status(thm)],[])).
% 0.42/0.60 tff(595,plain,
% 0.42/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_1, e_3, e_4))),
% 0.42/0.60 inference(modus_ponens,[status(thm)],[594, 593])).
% 0.42/0.60 tff(596,plain,
% 0.42/0.60 ($false),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[595, 477, 65, 492, 579])).
% 0.42/0.60 tff(597,plain,((~product(e_1, e_3, e_4)) | (~product(e_1, e_6, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.42/0.60 tff(598,plain,
% 0.42/0.60 (~product(e_1, e_3, e_4)),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[597, 577])).
% 0.42/0.60 tff(599,plain,
% 0.42/0.60 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_6) | (~product(e_1, e_6, 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_6) | (~product(e_1, e_6, e_4)) | (~product(e_1, e_5, e_4)))),
% 0.42/0.60 inference(rewrite,[status(thm)],[])).
% 0.42/0.60 tff(600,plain,
% 0.42/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_1, e_5, e_4)))),
% 0.42/0.60 inference(quant_inst,[status(thm)],[])).
% 0.42/0.60 tff(601,plain,
% 0.42/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_1, e_5, e_4))),
% 0.42/0.60 inference(modus_ponens,[status(thm)],[600, 599])).
% 0.42/0.60 tff(602,plain,
% 0.42/0.60 ($false),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[601, 465, 65, 441, 579])).
% 0.42/0.60 tff(603,plain,((~product(e_1, e_5, e_4)) | (~product(e_1, e_6, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.42/0.60 tff(604,plain,
% 0.42/0.60 (~product(e_1, e_5, e_4)),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[603, 577])).
% 0.42/0.60 tff(605,plain,
% 0.42/0.60 ((~![X: $i] : product(X, X, X)) | product(e_5, e_5, e_5)),
% 0.42/0.60 inference(quant_inst,[status(thm)],[])).
% 0.42/0.60 tff(606,plain,
% 0.42/0.60 (product(e_5, e_5, e_5)),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[605, 52])).
% 0.42/0.60 tff(607,plain,
% 0.42/0.60 ((~equalish(e_1, e_5)) <=> (~equalish(e_1, e_5))),
% 0.42/0.60 inference(rewrite,[status(thm)],[])).
% 0.42/0.60 tff(608,axiom,(~equalish(e_1, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_5')).
% 0.42/0.60 tff(609,plain,
% 0.42/0.60 (~equalish(e_1, e_5)),
% 0.42/0.60 inference(modus_ponens,[status(thm)],[608, 607])).
% 0.42/0.60 tff(610,plain,
% 0.42/0.60 (((~![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)))),
% 0.42/0.61 inference(rewrite,[status(thm)],[])).
% 0.42/0.61 tff(611,plain,
% 0.42/0.61 ((~![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)))),
% 0.42/0.61 inference(quant_inst,[status(thm)],[])).
% 0.42/0.61 tff(612,plain,
% 0.42/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_1, e_5, e_5))),
% 0.42/0.61 inference(modus_ponens,[status(thm)],[611, 610])).
% 0.42/0.61 tff(613,plain,
% 0.42/0.61 ($false),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[612, 609, 91, 503, 606])).
% 0.42/0.61 tff(614,plain,(~product(e_1, e_5, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.42/0.61 tff(615,plain,
% 0.42/0.61 (product(e_1, e_5, e_6) | 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)),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[460, 142, 454, 136, 391])).
% 0.42/0.61 tff(616,plain,
% 0.42/0.61 (product(e_1, e_5, e_6) | product(e_1, e_5, e_4) | product(e_1, e_5, e_3) | product(e_1, e_5, e_2)),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[615, 614])).
% 0.42/0.61 tff(617,plain,
% 0.42/0.61 (product(e_1, e_5, e_6) | product(e_1, e_5, e_4) | product(e_1, e_5, e_3)),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[616, 372])).
% 0.42/0.61 tff(618,plain,
% 0.42/0.61 (product(e_1, e_5, e_6)),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[617, 604, 226])).
% 0.42/0.61 tff(619,plain,
% 0.42/0.61 (~product(e_1, e_3, e_6)),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[561, 618])).
% 0.42/0.61 tff(620,plain,
% 0.42/0.61 (product(e_1, e_3, e_6) | product(e_1, e_3, e_5) | product(e_1, e_3, e_4)),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[564, 351])).
% 0.42/0.61 tff(621,plain,
% 0.42/0.61 (product(e_1, e_3, e_5)),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[620, 619, 598])).
% 0.42/0.61 tff(622,assumption,(product(e_1, e_2, e_5)), introduced(assumption)).
% 0.42/0.61 tff(623,plain,
% 0.42/0.61 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.42/0.61 inference(rewrite,[status(thm)],[])).
% 0.42/0.61 tff(624,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.42/0.61 tff(625,plain,
% 0.42/0.61 (~equalish(e_2, e_3)),
% 0.42/0.61 inference(modus_ponens,[status(thm)],[624, 623])).
% 0.42/0.61 tff(626,plain,
% 0.42/0.61 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_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)))),
% 0.42/0.61 inference(rewrite,[status(thm)],[])).
% 0.42/0.61 tff(627,plain,
% 0.42/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_1, e_3, e_5)) | (~product(e_1, e_2, e_5)))),
% 0.42/0.61 inference(quant_inst,[status(thm)],[])).
% 0.42/0.61 tff(628,plain,
% 0.42/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_1, e_3, e_5)) | (~product(e_1, e_2, e_5))),
% 0.42/0.61 inference(modus_ponens,[status(thm)],[627, 626])).
% 0.42/0.61 tff(629,plain,
% 0.42/0.61 ($false),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[628, 625, 65, 352, 622])).
% 0.42/0.61 tff(630,plain,((~product(e_1, e_2, e_5)) | (~product(e_1, e_3, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.42/0.61 tff(631,plain,
% 0.42/0.61 (~product(e_1, e_2, e_5)),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[630, 621])).
% 0.42/0.61 tff(632,assumption,(product(e_1, e_2, e_2)), introduced(assumption)).
% 0.42/0.61 tff(633,plain,
% 0.42/0.61 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.42/0.61 inference(rewrite,[status(thm)],[])).
% 0.42/0.61 tff(634,plain,
% 0.42/0.61 ((equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2))) <=> (equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.42/0.61 inference(rewrite,[status(thm)],[])).
% 0.42/0.61 tff(635,plain,
% 0.42/0.61 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2))))),
% 0.42/0.61 inference(monotonicity,[status(thm)],[634])).
% 0.42/0.61 tff(636,plain,
% 0.42/0.61 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.42/0.61 inference(transitivity,[status(thm)],[635, 633])).
% 0.42/0.61 tff(637,plain,
% 0.42/0.61 ((~![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)))),
% 0.42/0.61 inference(quant_inst,[status(thm)],[])).
% 0.42/0.61 tff(638,plain,
% 0.42/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2))),
% 0.42/0.61 inference(modus_ponens,[status(thm)],[637, 636])).
% 0.42/0.61 tff(639,plain,
% 0.42/0.61 ($false),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[638, 68, 91, 632, 54])).
% 0.42/0.61 tff(640,plain,(~product(e_1, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.42/0.61 tff(641,plain,
% 0.42/0.61 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.42/0.61 inference(rewrite,[status(thm)],[])).
% 0.42/0.61 tff(642,plain,
% 0.42/0.61 ((product(e_3, e_1, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_1, e_2))) <=> (product(e_3, e_1, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.42/0.61 inference(rewrite,[status(thm)],[])).
% 0.42/0.61 tff(643,plain,
% 0.42/0.61 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_3))))),
% 0.42/0.61 inference(monotonicity,[status(thm)],[642])).
% 0.42/0.61 tff(644,plain,
% 0.42/0.61 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.42/0.61 inference(transitivity,[status(thm)],[643, 641])).
% 0.42/0.61 tff(645,plain,
% 0.42/0.61 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_1, e_2)))),
% 0.42/0.61 inference(quant_inst,[status(thm)],[])).
% 0.42/0.61 tff(646,plain,
% 0.42/0.61 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_3))),
% 0.42/0.61 inference(modus_ponens,[status(thm)],[645, 644])).
% 0.42/0.61 tff(647,plain,
% 0.42/0.61 (~product(e_1, e_1, e_2)),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[646, 35, 151, 182])).
% 0.42/0.61 tff(648,plain,
% 0.42/0.61 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_2) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.42/0.61 inference(rewrite,[status(thm)],[])).
% 0.42/0.61 tff(649,plain,
% 0.42/0.61 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.42/0.61 inference(quant_inst,[status(thm)],[])).
% 0.42/0.61 tff(650,plain,
% 0.42/0.61 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_2) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1))),
% 0.42/0.61 inference(modus_ponens,[status(thm)],[649, 648])).
% 0.42/0.61 tff(651,plain,
% 0.42/0.61 (~product(e_1, e_2, e_1)),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[650, 35, 647, 81])).
% 0.42/0.61 tff(652,plain,
% 0.42/0.61 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_3) | product(e_1, e_2, e_4) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | product(e_1, e_2, e_6) | product(e_1, e_2, e_5))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_3) | product(e_1, e_2, e_4) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | product(e_1, e_2, e_6) | product(e_1, e_2, e_5))),
% 0.42/0.61 inference(rewrite,[status(thm)],[])).
% 0.42/0.61 tff(653,plain,
% 0.42/0.61 ((product(e_1, e_2, e_6) | 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_3) | product(e_1, e_2, e_4) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | product(e_1, e_2, e_6) | product(e_1, e_2, e_5))),
% 0.42/0.61 inference(rewrite,[status(thm)],[])).
% 0.42/0.61 tff(654,plain,
% 0.42/0.61 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6) | 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_6) | product(X, Y, e_5) | product(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_3) | product(e_1, e_2, e_4) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | product(e_1, e_2, e_6) | product(e_1, e_2, e_5)))),
% 0.42/0.61 inference(monotonicity,[status(thm)],[653])).
% 0.42/0.61 tff(655,plain,
% 0.42/0.61 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6) | 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_6) | product(X, Y, e_5) | product(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_3) | product(e_1, e_2, e_4) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | product(e_1, e_2, e_6) | product(e_1, e_2, e_5))),
% 0.42/0.61 inference(transitivity,[status(thm)],[654, 652])).
% 0.42/0.61 tff(656,plain,
% 0.42/0.61 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6) | 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)))),
% 0.42/0.61 inference(quant_inst,[status(thm)],[])).
% 0.42/0.61 tff(657,plain,
% 0.42/0.61 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_3) | product(e_1, e_2, e_4) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | product(e_1, e_2, e_6) | product(e_1, e_2, e_5)),
% 0.42/0.61 inference(modus_ponens,[status(thm)],[656, 655])).
% 0.42/0.61 tff(658,plain,
% 0.42/0.61 (product(e_1, e_2, e_3) | product(e_1, e_2, e_4) | product(e_1, e_2, e_2) | product(e_1, e_2, e_6) | product(e_1, e_2, e_5)),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[657, 142, 139, 136, 651])).
% 0.42/0.61 tff(659,plain,
% 0.42/0.61 (product(e_1, e_2, e_3) | product(e_1, e_2, e_4) | product(e_1, e_2, e_6) | product(e_1, e_2, e_5)),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[658, 640])).
% 0.42/0.61 tff(660,plain,
% 0.42/0.61 (product(e_1, e_2, e_6)),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[659, 631, 592, 588])).
% 0.42/0.61 tff(661,plain,
% 0.42/0.61 ((~equalish(e_5, e_2)) <=> (~equalish(e_5, e_2))),
% 0.42/0.61 inference(rewrite,[status(thm)],[])).
% 0.42/0.61 tff(662,axiom,(~equalish(e_5, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_is_not_e_2')).
% 0.42/0.61 tff(663,plain,
% 0.42/0.61 (~equalish(e_5, e_2)),
% 0.42/0.61 inference(modus_ponens,[status(thm)],[662, 661])).
% 0.42/0.61 tff(664,plain,
% 0.42/0.61 (((~![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_6)) | (~product(e_1, e_2, e_6)))) <=> ((~![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_6)) | (~product(e_1, e_2, e_6)))),
% 0.42/0.61 inference(rewrite,[status(thm)],[])).
% 0.42/0.61 tff(665,plain,
% 0.42/0.61 ((equalish(e_5, e_2) | (~product(e_1, e_2, e_6)) | (~product(e_1, e_5, e_6))) <=> (equalish(e_5, e_2) | (~product(e_1, e_5, e_6)) | (~product(e_1, e_2, e_6)))),
% 0.42/0.61 inference(rewrite,[status(thm)],[])).
% 0.42/0.61 tff(666,plain,
% 0.42/0.61 (((~![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_6)) | (~product(e_1, e_5, e_6)))) <=> ((~![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_6)) | (~product(e_1, e_2, e_6))))),
% 0.42/0.61 inference(monotonicity,[status(thm)],[665])).
% 0.42/0.61 tff(667,plain,
% 0.42/0.61 (((~![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_6)) | (~product(e_1, e_5, e_6)))) <=> ((~![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_6)) | (~product(e_1, e_2, e_6)))),
% 0.42/0.61 inference(transitivity,[status(thm)],[666, 664])).
% 0.42/0.61 tff(668,plain,
% 0.42/0.61 ((~![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_6)) | (~product(e_1, e_5, e_6)))),
% 0.42/0.61 inference(quant_inst,[status(thm)],[])).
% 0.42/0.61 tff(669,plain,
% 0.42/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_2) | (~product(e_1, e_5, e_6)) | (~product(e_1, e_2, e_6))),
% 0.42/0.61 inference(modus_ponens,[status(thm)],[668, 667])).
% 0.42/0.61 tff(670,plain,
% 0.42/0.61 ($false),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[669, 663, 65, 618, 660])).
% 0.42/0.61 tff(671,plain,(product(e_3, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.42/0.61 tff(672,plain,
% 0.42/0.61 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_6, 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_6, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_6, e_1, e_4)))),
% 0.42/0.61 inference(rewrite,[status(thm)],[])).
% 0.42/0.61 tff(673,plain,
% 0.42/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_6, e_1, e_4)))),
% 0.42/0.62 inference(quant_inst,[status(thm)],[])).
% 0.42/0.62 tff(674,plain,
% 0.42/0.62 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_6, e_1, e_4))),
% 0.42/0.62 inference(modus_ponens,[status(thm)],[673, 672])).
% 0.42/0.62 tff(675,plain,
% 0.42/0.62 ($false),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[674, 355, 91, 671, 160])).
% 0.42/0.62 tff(676,plain,(~product(e_6, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.42/0.62 tff(677,assumption,(product(e_6, e_1, e_2)), introduced(assumption)).
% 0.42/0.62 tff(678,plain,
% 0.42/0.62 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_6, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_6, e_1, e_2)))),
% 0.42/0.62 inference(rewrite,[status(thm)],[])).
% 0.42/0.62 tff(679,plain,
% 0.42/0.62 ((product(e_2, e_1, e_5) | (~product(e_6, e_1, e_2)) | (~product(e_1, e_5, e_6))) <=> (product(e_2, e_1, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_6, e_1, e_2)))),
% 0.42/0.62 inference(rewrite,[status(thm)],[])).
% 0.42/0.62 tff(680,plain,
% 0.42/0.62 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_6, e_1, e_2)) | (~product(e_1, e_5, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_6, e_1, e_2))))),
% 0.42/0.62 inference(monotonicity,[status(thm)],[679])).
% 0.42/0.62 tff(681,plain,
% 0.42/0.62 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_6, e_1, e_2)) | (~product(e_1, e_5, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_6, e_1, e_2)))),
% 0.42/0.62 inference(transitivity,[status(thm)],[680, 678])).
% 0.42/0.62 tff(682,plain,
% 0.42/0.62 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_6, e_1, e_2)) | (~product(e_1, e_5, e_6)))),
% 0.42/0.62 inference(quant_inst,[status(thm)],[])).
% 0.42/0.62 tff(683,plain,
% 0.42/0.62 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_6, e_1, e_2))),
% 0.42/0.62 inference(modus_ponens,[status(thm)],[682, 681])).
% 0.42/0.62 tff(684,plain,
% 0.42/0.62 ($false),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[683, 35, 119, 4, 677])).
% 0.42/0.62 tff(685,plain,((~product(e_6, e_1, e_2)) | (~product(e_1, e_5, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.42/0.62 tff(686,plain,
% 0.42/0.62 (~product(e_6, e_1, e_2)),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[685, 4])).
% 0.42/0.62 tff(687,assumption,(product(e_4, e_6, e_6)), introduced(assumption)).
% 0.42/0.62 tff(688,plain,
% 0.42/0.62 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_4, e_6, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_4, e_6, e_6)))),
% 0.42/0.62 inference(rewrite,[status(thm)],[])).
% 0.42/0.62 tff(689,plain,
% 0.42/0.62 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_4, e_6, e_6)))),
% 0.42/0.62 inference(quant_inst,[status(thm)],[])).
% 0.42/0.62 tff(690,plain,
% 0.42/0.62 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_4, e_6, e_6))),
% 0.42/0.62 inference(modus_ponens,[status(thm)],[689, 688])).
% 0.42/0.62 tff(691,plain,
% 0.42/0.62 ($false),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[690, 337, 91, 300, 687])).
% 0.42/0.62 tff(692,plain,(~product(e_4, e_6, e_6)), inference(lemma,lemma(discharge,[]))).
% 0.42/0.62 tff(693,assumption,(product(e_5, e_6, e_6)), introduced(assumption)).
% 0.42/0.62 tff(694,plain,
% 0.42/0.62 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_5, e_6, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_5, e_6, e_6)))),
% 0.42/0.62 inference(rewrite,[status(thm)],[])).
% 0.42/0.62 tff(695,plain,
% 0.42/0.62 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_5, e_6, e_6)))),
% 0.42/0.62 inference(quant_inst,[status(thm)],[])).
% 0.42/0.62 tff(696,plain,
% 0.42/0.62 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_5, e_6, e_6))),
% 0.42/0.62 inference(modus_ponens,[status(thm)],[695, 694])).
% 0.42/0.62 tff(697,plain,
% 0.42/0.62 ($false),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[696, 465, 91, 300, 693])).
% 0.42/0.62 tff(698,plain,(~product(e_5, e_6, e_6)), inference(lemma,lemma(discharge,[]))).
% 0.42/0.62 tff(699,plain,
% 0.42/0.62 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_6, e_5)) | product(e_5, e_6, e_6) | (~product(e_6, e_6, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_6, e_5)) | product(e_5, e_6, e_6) | (~product(e_6, e_6, e_1)))),
% 0.42/0.62 inference(rewrite,[status(thm)],[])).
% 0.42/0.62 tff(700,plain,
% 0.42/0.62 ((product(e_5, e_6, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_6, e_6, e_1))) <=> ((~product(e_1, e_6, e_5)) | product(e_5, e_6, e_6) | (~product(e_6, e_6, e_1)))),
% 0.42/0.62 inference(rewrite,[status(thm)],[])).
% 0.42/0.62 tff(701,plain,
% 0.42/0.62 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_6, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_6, e_6, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_6, e_5)) | product(e_5, e_6, e_6) | (~product(e_6, e_6, e_1))))),
% 0.42/0.62 inference(monotonicity,[status(thm)],[700])).
% 0.42/0.62 tff(702,plain,
% 0.42/0.62 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_6, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_6, e_6, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_6, e_5)) | product(e_5, e_6, e_6) | (~product(e_6, e_6, e_1)))),
% 0.42/0.62 inference(transitivity,[status(thm)],[701, 699])).
% 0.42/0.62 tff(703,plain,
% 0.42/0.62 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_6, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_6, e_6, e_1)))),
% 0.42/0.62 inference(quant_inst,[status(thm)],[])).
% 0.42/0.62 tff(704,plain,
% 0.42/0.62 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_6, e_5)) | product(e_5, e_6, e_6) | (~product(e_6, e_6, e_1))),
% 0.42/0.62 inference(modus_ponens,[status(thm)],[703, 702])).
% 0.42/0.62 tff(705,plain,
% 0.42/0.62 (~product(e_6, e_6, e_1)),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[704, 35, 333, 698])).
% 0.42/0.62 tff(706,plain,
% 0.42/0.62 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_6, e_6, e_6)) | (~product(e_6, e_1, e_6)) | product(e_6, e_6, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_6, e_6, e_6)) | (~product(e_6, e_1, e_6)) | product(e_6, e_6, e_1))),
% 0.42/0.62 inference(rewrite,[status(thm)],[])).
% 0.42/0.62 tff(707,plain,
% 0.42/0.62 ((product(e_6, e_6, e_1) | (~product(e_6, e_6, e_6)) | (~product(e_6, e_1, e_6))) <=> ((~product(e_6, e_6, e_6)) | (~product(e_6, e_1, e_6)) | product(e_6, e_6, e_1))),
% 0.42/0.62 inference(rewrite,[status(thm)],[])).
% 0.42/0.62 tff(708,plain,
% 0.42/0.62 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_6, e_6, e_1) | (~product(e_6, e_6, e_6)) | (~product(e_6, e_1, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_6, e_6, e_6)) | (~product(e_6, e_1, e_6)) | product(e_6, e_6, e_1)))),
% 0.42/0.62 inference(monotonicity,[status(thm)],[707])).
% 0.42/0.62 tff(709,plain,
% 0.42/0.62 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_6, e_6, e_1) | (~product(e_6, e_6, e_6)) | (~product(e_6, e_1, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_6, e_6, e_6)) | (~product(e_6, e_1, e_6)) | product(e_6, e_6, e_1))),
% 0.42/0.62 inference(transitivity,[status(thm)],[708, 706])).
% 0.42/0.62 tff(710,plain,
% 0.42/0.62 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_6, e_6, e_1) | (~product(e_6, e_6, e_6)) | (~product(e_6, e_1, e_6)))),
% 0.42/0.62 inference(quant_inst,[status(thm)],[])).
% 0.42/0.62 tff(711,plain,
% 0.42/0.62 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_6, e_6, e_6)) | (~product(e_6, e_1, e_6)) | product(e_6, e_6, e_1)),
% 0.42/0.62 inference(modus_ponens,[status(thm)],[710, 709])).
% 0.42/0.62 tff(712,plain,
% 0.42/0.62 (~product(e_6, e_1, e_6)),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[711, 35, 300, 705])).
% 0.42/0.62 tff(713,assumption,(product(e_5, e_1, e_3)), introduced(assumption)).
% 0.42/0.62 tff(714,plain,
% 0.42/0.62 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_5, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_5, e_1, e_3)))),
% 0.42/0.62 inference(rewrite,[status(thm)],[])).
% 0.42/0.62 tff(715,plain,
% 0.42/0.62 ((product(e_3, e_1, e_6) | (~product(e_5, e_1, e_3)) | (~product(e_1, e_6, e_5))) <=> (product(e_3, e_1, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_5, e_1, e_3)))),
% 0.42/0.62 inference(rewrite,[status(thm)],[])).
% 0.42/0.62 tff(716,plain,
% 0.42/0.62 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_6) | (~product(e_5, e_1, e_3)) | (~product(e_1, e_6, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_5, e_1, e_3))))),
% 0.42/0.62 inference(monotonicity,[status(thm)],[715])).
% 0.42/0.62 tff(717,plain,
% 0.42/0.62 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_6) | (~product(e_5, e_1, e_3)) | (~product(e_1, e_6, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_5, e_1, e_3)))),
% 0.42/0.62 inference(transitivity,[status(thm)],[716, 714])).
% 0.42/0.62 tff(718,plain,
% 0.42/0.62 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_6) | (~product(e_5, e_1, e_3)) | (~product(e_1, e_6, e_5)))),
% 0.42/0.62 inference(quant_inst,[status(thm)],[])).
% 0.42/0.62 tff(719,plain,
% 0.42/0.62 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_5, e_1, e_3))),
% 0.42/0.62 inference(modus_ponens,[status(thm)],[718, 717])).
% 0.42/0.62 tff(720,plain,
% 0.42/0.62 ($false),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[719, 35, 192, 333, 713])).
% 0.42/0.62 tff(721,plain,((~product(e_5, e_1, e_3)) | (~product(e_1, e_6, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.42/0.62 tff(722,plain,
% 0.42/0.62 (~product(e_5, e_1, e_3)),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[721, 333])).
% 0.42/0.62 tff(723,plain,
% 0.42/0.62 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_6) | (~product(e_1, e_6, 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_6) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_2, e_5)))),
% 0.42/0.62 inference(rewrite,[status(thm)],[])).
% 0.42/0.62 tff(724,plain,
% 0.42/0.62 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_2, e_5)))),
% 0.42/0.62 inference(quant_inst,[status(thm)],[])).
% 0.42/0.62 tff(725,plain,
% 0.42/0.62 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_1, e_2, e_5))),
% 0.42/0.62 inference(modus_ponens,[status(thm)],[724, 723])).
% 0.42/0.62 tff(726,plain,
% 0.42/0.62 ($false),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[725, 582, 65, 333, 622])).
% 0.42/0.62 tff(727,plain,((~product(e_1, e_2, e_5)) | (~product(e_1, e_6, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.42/0.62 tff(728,plain,
% 0.42/0.62 (~product(e_1, e_2, e_5)),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[727, 333])).
% 0.42/0.62 tff(729,assumption,(product(e_5, e_1, e_2)), introduced(assumption)).
% 0.42/0.62 tff(730,plain,
% 0.42/0.62 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_5, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_5, e_1, e_2)))),
% 0.42/0.62 inference(rewrite,[status(thm)],[])).
% 0.42/0.62 tff(731,plain,
% 0.42/0.62 ((product(e_2, e_1, e_6) | (~product(e_5, e_1, e_2)) | (~product(e_1, e_6, e_5))) <=> (product(e_2, e_1, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_5, e_1, e_2)))),
% 0.42/0.62 inference(rewrite,[status(thm)],[])).
% 0.42/0.62 tff(732,plain,
% 0.42/0.62 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_6) | (~product(e_5, e_1, e_2)) | (~product(e_1, e_6, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_5, e_1, e_2))))),
% 0.42/0.62 inference(monotonicity,[status(thm)],[731])).
% 0.42/0.62 tff(733,plain,
% 0.42/0.62 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_6) | (~product(e_5, e_1, e_2)) | (~product(e_1, e_6, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_5, e_1, e_2)))),
% 0.42/0.62 inference(transitivity,[status(thm)],[732, 730])).
% 0.42/0.62 tff(734,plain,
% 0.42/0.62 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_6) | (~product(e_5, e_1, e_2)) | (~product(e_1, e_6, e_5)))),
% 0.42/0.62 inference(quant_inst,[status(thm)],[])).
% 0.42/0.62 tff(735,plain,
% 0.42/0.62 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_6) | (~product(e_1, e_6, e_5)) | (~product(e_5, e_1, e_2))),
% 0.42/0.62 inference(modus_ponens,[status(thm)],[734, 733])).
% 0.42/0.62 tff(736,plain,
% 0.42/0.62 ($false),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[735, 35, 112, 333, 729])).
% 0.42/0.62 tff(737,plain,((~product(e_5, e_1, e_2)) | (~product(e_1, e_6, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.42/0.62 tff(738,plain,
% 0.42/0.62 (~product(e_5, e_1, e_2)),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[737, 333])).
% 0.42/0.62 tff(739,assumption,(~product(e_1, e_3, e_4)), introduced(assumption)).
% 0.42/0.62 tff(740,plain,
% 0.42/0.62 (~product(e_1, e_3, e_5)),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[363, 333])).
% 0.42/0.62 tff(741,plain,
% 0.42/0.62 (product(e_1, e_3, e_6)),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[620, 740, 739])).
% 0.42/0.62 tff(742,plain,
% 0.42/0.62 (~product(e_1, e_6, e_4)),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[603, 441])).
% 0.42/0.62 tff(743,plain,
% 0.42/0.62 (product(e_1, e_6, e_5) | product(e_1, e_6, e_4)),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[331, 271])).
% 0.42/0.62 tff(744,plain,
% 0.42/0.62 (product(e_1, e_6, e_5)),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[743, 742])).
% 0.42/0.62 tff(745,plain,
% 0.42/0.62 (~product(e_1, e_3, e_5)),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[363, 744])).
% 0.42/0.62 tff(746,plain,
% 0.42/0.62 (~product(e_1, e_2, e_5)),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[727, 744])).
% 0.42/0.62 tff(747,assumption,(~product(e_1, e_2, e_5)), introduced(assumption)).
% 0.42/0.62 tff(748,plain,
% 0.42/0.62 ((~equalish(e_2, e_5)) <=> (~equalish(e_2, e_5))),
% 0.42/0.62 inference(rewrite,[status(thm)],[])).
% 0.42/0.62 tff(749,axiom,(~equalish(e_2, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_5')).
% 0.42/0.62 tff(750,plain,
% 0.42/0.62 (~equalish(e_2, e_5)),
% 0.42/0.62 inference(modus_ponens,[status(thm)],[749, 748])).
% 0.42/0.62 tff(751,plain,
% 0.42/0.62 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_5) | (~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_2, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_1, e_2, e_4)))),
% 0.42/0.62 inference(rewrite,[status(thm)],[])).
% 0.42/0.62 tff(752,plain,
% 0.42/0.62 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_1, e_2, e_4)))),
% 0.42/0.62 inference(quant_inst,[status(thm)],[])).
% 0.42/0.62 tff(753,plain,
% 0.42/0.62 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_1, e_2, e_4))),
% 0.42/0.62 inference(modus_ponens,[status(thm)],[752, 751])).
% 0.42/0.62 tff(754,plain,
% 0.42/0.62 ($false),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[753, 750, 65, 441, 578])).
% 0.42/0.62 tff(755,plain,((~product(e_1, e_2, e_4)) | (~product(e_1, e_5, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.42/0.62 tff(756,plain,
% 0.42/0.62 (~product(e_1, e_2, e_4)),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[755, 441])).
% 0.42/0.62 tff(757,assumption,(product(e_4, e_1, e_2)), introduced(assumption)).
% 0.42/0.62 tff(758,plain,
% 0.42/0.62 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_4, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_4, e_1, e_2)))),
% 0.42/0.62 inference(rewrite,[status(thm)],[])).
% 0.42/0.62 tff(759,plain,
% 0.42/0.62 ((product(e_2, e_1, e_5) | (~product(e_4, e_1, e_2)) | (~product(e_1, e_5, e_4))) <=> (product(e_2, e_1, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_4, e_1, e_2)))),
% 0.42/0.62 inference(rewrite,[status(thm)],[])).
% 0.42/0.62 tff(760,plain,
% 0.42/0.62 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_4, e_1, e_2)) | (~product(e_1, e_5, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_4, e_1, e_2))))),
% 0.42/0.62 inference(monotonicity,[status(thm)],[759])).
% 0.42/0.62 tff(761,plain,
% 0.42/0.62 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_4, e_1, e_2)) | (~product(e_1, e_5, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_4, e_1, e_2)))),
% 0.42/0.62 inference(transitivity,[status(thm)],[760, 758])).
% 0.42/0.62 tff(762,plain,
% 0.42/0.62 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_4, e_1, e_2)) | (~product(e_1, e_5, e_4)))),
% 0.42/0.62 inference(quant_inst,[status(thm)],[])).
% 0.42/0.62 tff(763,plain,
% 0.42/0.62 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_5) | (~product(e_1, e_5, e_4)) | (~product(e_4, e_1, e_2))),
% 0.42/0.63 inference(modus_ponens,[status(thm)],[762, 761])).
% 0.42/0.63 tff(764,plain,
% 0.42/0.63 ($false),
% 0.42/0.63 inference(unit_resolution,[status(thm)],[763, 35, 119, 757, 441])).
% 0.42/0.63 tff(765,plain,((~product(e_4, e_1, e_2)) | (~product(e_1, e_5, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.42/0.63 tff(766,plain,
% 0.42/0.63 (~product(e_4, e_1, e_2)),
% 0.42/0.63 inference(unit_resolution,[status(thm)],[765, 441])).
% 0.42/0.63 tff(767,plain,
% 0.42/0.63 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_2) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_2) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_2, e_3)))),
% 0.42/0.63 inference(rewrite,[status(thm)],[])).
% 0.42/0.63 tff(768,plain,
% 0.42/0.63 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_2) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_2, e_3)))),
% 0.42/0.63 inference(quant_inst,[status(thm)],[])).
% 0.42/0.63 tff(769,plain,
% 0.42/0.63 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_2) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_2, e_3))),
% 0.42/0.63 inference(modus_ponens,[status(thm)],[768, 767])).
% 0.42/0.63 tff(770,plain,
% 0.42/0.63 (~product(e_1, e_2, e_3)),
% 0.42/0.63 inference(unit_resolution,[status(thm)],[769, 35, 236, 766])).
% 0.42/0.63 tff(771,plain,
% 0.42/0.63 (product(e_1, e_2, e_6)),
% 0.42/0.63 inference(unit_resolution,[status(thm)],[658, 770, 640, 756, 747])).
% 0.42/0.63 tff(772,plain,
% 0.42/0.63 (~product(e_1, e_3, e_4)),
% 0.42/0.63 inference(unit_resolution,[status(thm)],[548, 441])).
% 0.42/0.63 tff(773,plain,
% 0.42/0.63 (product(e_1, e_3, e_6)),
% 0.42/0.63 inference(unit_resolution,[status(thm)],[564, 772, 423, 351])).
% 0.42/0.63 tff(774,plain,
% 0.42/0.63 (((~![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_6)) | (~product(e_1, e_2, e_6)))) <=> ((~![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_6)) | (~product(e_1, e_2, e_6)))),
% 0.42/0.63 inference(rewrite,[status(thm)],[])).
% 0.42/0.63 tff(775,plain,
% 0.42/0.63 ((~![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_6)) | (~product(e_1, e_2, e_6)))),
% 0.42/0.63 inference(quant_inst,[status(thm)],[])).
% 0.42/0.63 tff(776,plain,
% 0.42/0.63 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_1, e_3, e_6)) | (~product(e_1, e_2, e_6))),
% 0.42/0.63 inference(modus_ponens,[status(thm)],[775, 774])).
% 0.42/0.63 tff(777,plain,
% 0.42/0.63 ($false),
% 0.42/0.63 inference(unit_resolution,[status(thm)],[776, 625, 65, 773, 771])).
% 0.42/0.63 tff(778,plain,((~product(e_1, e_5, e_4)) | product(e_1, e_2, e_5) | (~product(e_3, e_1, e_4)) | product(e_1, e_3, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.42/0.63 tff(779,plain,
% 0.42/0.63 ((~product(e_1, e_5, e_4)) | product(e_1, e_2, e_5) | product(e_1, e_3, e_5)),
% 0.42/0.63 inference(unit_resolution,[status(thm)],[778, 671])).
% 0.42/0.63 tff(780,plain,
% 0.42/0.63 ($false),
% 0.42/0.63 inference(unit_resolution,[status(thm)],[779, 746, 745, 441])).
% 0.42/0.63 tff(781,plain,(~product(e_1, e_5, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.42/0.63 tff(782,assumption,(~product(e_1, e_5, e_4)), introduced(assumption)).
% 0.42/0.63 tff(783,plain,
% 0.42/0.63 (~product(e_1, e_5, e_6)),
% 0.42/0.63 inference(unit_resolution,[status(thm)],[561, 474])).
% 0.42/0.63 tff(784,plain,
% 0.42/0.63 (product(e_1, e_5, e_3)),
% 0.42/0.63 inference(unit_resolution,[status(thm)],[617, 783, 782])).
% 0.42/0.63 tff(785,assumption,(product(e_1, e_2, e_3)), introduced(assumption)).
% 0.42/0.63 tff(786,assumption,(product(e_1, e_5, e_3)), introduced(assumption)).
% 0.42/0.63 tff(787,plain,
% 0.42/0.63 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_5) | (~product(e_1, e_5, e_3)) | (~product(e_1, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_5) | (~product(e_1, e_5, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(788,plain,
% 0.48/0.63 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_5) | (~product(e_1, e_5, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(789,plain,
% 0.48/0.63 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_5) | (~product(e_1, e_5, e_3)) | (~product(e_1, e_2, e_3))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[788, 787])).
% 0.48/0.63 tff(790,plain,
% 0.48/0.63 ($false),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[789, 750, 65, 786, 785])).
% 0.48/0.63 tff(791,plain,((~product(e_1, e_2, e_3)) | (~product(e_1, e_5, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.63 tff(792,plain,
% 0.48/0.63 (~product(e_1, e_2, e_3)),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[791, 784])).
% 0.48/0.63 tff(793,assumption,(~product(e_5, e_1, e_2)), introduced(assumption)).
% 0.48/0.63 tff(794,assumption,(~product(e_4, e_1, e_5)), introduced(assumption)).
% 0.48/0.63 tff(795,plain,
% 0.48/0.63 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_5) | (~product(e_1, e_5, e_3)) | (~product(e_3, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_5) | (~product(e_1, e_5, e_3)) | (~product(e_3, e_1, e_4)))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(796,plain,
% 0.48/0.63 ((product(e_4, e_1, e_5) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_5, e_3))) <=> (product(e_4, e_1, e_5) | (~product(e_1, e_5, e_3)) | (~product(e_3, e_1, e_4)))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(797,plain,
% 0.48/0.63 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_5) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_5, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_5) | (~product(e_1, e_5, e_3)) | (~product(e_3, e_1, e_4))))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[796])).
% 0.48/0.63 tff(798,plain,
% 0.48/0.63 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_5) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_5, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_5) | (~product(e_1, e_5, e_3)) | (~product(e_3, e_1, e_4)))),
% 0.48/0.63 inference(transitivity,[status(thm)],[797, 795])).
% 0.48/0.63 tff(799,plain,
% 0.48/0.63 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_5) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_5, e_3)))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(800,plain,
% 0.48/0.63 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_5) | (~product(e_1, e_5, e_3)) | (~product(e_3, e_1, e_4))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[799, 798])).
% 0.48/0.63 tff(801,plain,
% 0.48/0.63 ($false),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[800, 35, 671, 794, 786])).
% 0.48/0.63 tff(802,plain,(product(e_4, e_1, e_5) | (~product(e_1, e_5, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.63 tff(803,plain,
% 0.48/0.63 (product(e_4, e_1, e_5)),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[802, 784])).
% 0.48/0.63 tff(804,plain,
% 0.48/0.63 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_2, e_4)) | (~product(e_4, e_1, e_5)) | product(e_5, e_1, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_4)) | (~product(e_4, e_1, e_5)) | product(e_5, e_1, e_2))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(805,plain,
% 0.48/0.63 ((product(e_5, e_1, e_2) | (~product(e_4, e_1, e_5)) | (~product(e_1, e_2, e_4))) <=> ((~product(e_1, e_2, e_4)) | (~product(e_4, e_1, e_5)) | product(e_5, e_1, e_2))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(806,plain,
% 0.48/0.63 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_1, e_2) | (~product(e_4, e_1, e_5)) | (~product(e_1, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_2, e_4)) | (~product(e_4, e_1, e_5)) | product(e_5, e_1, e_2)))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[805])).
% 0.48/0.63 tff(807,plain,
% 0.48/0.63 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_1, e_2) | (~product(e_4, e_1, e_5)) | (~product(e_1, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_4)) | (~product(e_4, e_1, e_5)) | product(e_5, e_1, e_2))),
% 0.48/0.63 inference(transitivity,[status(thm)],[806, 804])).
% 0.48/0.63 tff(808,plain,
% 0.48/0.63 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_1, e_2) | (~product(e_4, e_1, e_5)) | (~product(e_1, e_2, e_4)))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(809,plain,
% 0.48/0.63 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_4)) | (~product(e_4, e_1, e_5)) | product(e_5, e_1, e_2)),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[808, 807])).
% 0.48/0.63 tff(810,plain,
% 0.48/0.63 ((~product(e_1, e_2, e_4)) | (~product(e_4, e_1, e_5)) | product(e_5, e_1, e_2)),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[809, 35])).
% 0.48/0.63 tff(811,plain,
% 0.48/0.63 (~product(e_1, e_2, e_4)),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[810, 803, 793])).
% 0.48/0.63 tff(812,plain,
% 0.48/0.63 (product(e_1, e_2, e_6)),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[659, 811, 747, 792])).
% 0.48/0.63 tff(813,plain,
% 0.48/0.63 ($false),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[776, 625, 65, 474, 812])).
% 0.48/0.63 tff(814,plain,((~product(e_1, e_3, e_6)) | product(e_1, e_2, e_5) | product(e_5, e_1, e_2) | product(e_1, e_5, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.48/0.63 tff(815,plain,
% 0.48/0.63 ((~product(e_1, e_3, e_6)) | product(e_1, e_2, e_5) | product(e_5, e_1, e_2)),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[814, 781])).
% 0.48/0.63 tff(816,plain,
% 0.48/0.63 ($false),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[815, 741, 738, 728])).
% 0.48/0.63 tff(817,plain,((~product(e_1, e_6, e_5)) | product(e_1, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.48/0.63 tff(818,plain,
% 0.48/0.63 (product(e_1, e_3, e_4)),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[817, 333])).
% 0.48/0.63 tff(819,plain,
% 0.48/0.63 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_3, e_4)) | (~product(e_4, e_1, e_5)) | product(e_5, e_1, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_4)) | (~product(e_4, e_1, e_5)) | product(e_5, e_1, e_3))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(820,plain,
% 0.48/0.63 ((product(e_5, e_1, e_3) | (~product(e_4, e_1, e_5)) | (~product(e_1, e_3, e_4))) <=> ((~product(e_1, e_3, e_4)) | (~product(e_4, e_1, e_5)) | product(e_5, e_1, e_3))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(821,plain,
% 0.48/0.63 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_1, e_3) | (~product(e_4, e_1, e_5)) | (~product(e_1, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_3, e_4)) | (~product(e_4, e_1, e_5)) | product(e_5, e_1, e_3)))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[820])).
% 0.48/0.63 tff(822,plain,
% 0.48/0.63 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_1, e_3) | (~product(e_4, e_1, e_5)) | (~product(e_1, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_4)) | (~product(e_4, e_1, e_5)) | product(e_5, e_1, e_3))),
% 0.48/0.63 inference(transitivity,[status(thm)],[821, 819])).
% 0.48/0.63 tff(823,plain,
% 0.48/0.63 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_1, e_3) | (~product(e_4, e_1, e_5)) | (~product(e_1, e_3, e_4)))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(824,plain,
% 0.48/0.63 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_4)) | (~product(e_4, e_1, e_5)) | product(e_5, e_1, e_3)),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[823, 822])).
% 0.48/0.63 tff(825,plain,
% 0.48/0.63 ((~product(e_1, e_3, e_4)) | (~product(e_4, e_1, e_5)) | product(e_5, e_1, e_3)),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[824, 35])).
% 0.48/0.63 tff(826,plain,
% 0.48/0.63 (~product(e_4, e_1, e_5)),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[825, 818, 722])).
% 0.48/0.63 tff(827,plain,
% 0.48/0.63 (~product(e_1, e_5, e_3)),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[802, 826])).
% 0.48/0.63 tff(828,plain,
% 0.48/0.63 (product(e_1, e_5, e_6) | product(e_1, e_5, e_3)),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[617, 781])).
% 0.48/0.63 tff(829,plain,
% 0.48/0.63 (product(e_1, e_5, e_6)),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[828, 827])).
% 0.48/0.63 tff(830,assumption,(product(e_6, e_5, e_5)), introduced(assumption)).
% 0.48/0.63 tff(831,plain,
% 0.48/0.63 ((~equalish(e_6, e_5)) <=> (~equalish(e_6, e_5))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(832,axiom,(~equalish(e_6, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_6_is_not_e_5')).
% 0.48/0.63 tff(833,plain,
% 0.48/0.63 (~equalish(e_6, e_5)),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[832, 831])).
% 0.48/0.63 tff(834,plain,
% 0.48/0.63 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_6, 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_6, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_6, e_5, e_5)))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(835,plain,
% 0.48/0.63 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_6, e_5, e_5)))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(836,plain,
% 0.48/0.63 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_6, e_5, e_5))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[835, 834])).
% 0.48/0.63 tff(837,plain,
% 0.48/0.63 ($false),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[836, 833, 91, 606, 830])).
% 0.48/0.63 tff(838,plain,(~product(e_6, e_5, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.48/0.63 tff(839,plain,
% 0.48/0.63 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_5, e_6)) | product(e_6, e_5, e_5) | (~product(e_5, e_5, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_5, e_6)) | product(e_6, e_5, e_5) | (~product(e_5, e_5, e_1)))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(840,plain,
% 0.48/0.63 ((product(e_6, e_5, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_5, e_5, e_1))) <=> ((~product(e_1, e_5, e_6)) | product(e_6, e_5, e_5) | (~product(e_5, e_5, e_1)))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(841,plain,
% 0.48/0.63 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_6, e_5, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_5, e_5, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_5, e_6)) | product(e_6, e_5, e_5) | (~product(e_5, e_5, e_1))))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[840])).
% 0.48/0.63 tff(842,plain,
% 0.48/0.63 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_6, e_5, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_5, e_5, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_5, e_6)) | product(e_6, e_5, e_5) | (~product(e_5, e_5, e_1)))),
% 0.48/0.64 inference(transitivity,[status(thm)],[841, 839])).
% 0.48/0.64 tff(843,plain,
% 0.48/0.64 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_6, e_5, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_5, e_5, e_1)))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(844,plain,
% 0.48/0.64 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_5, e_6)) | product(e_6, e_5, e_5) | (~product(e_5, e_5, e_1))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[843, 842])).
% 0.48/0.64 tff(845,plain,
% 0.48/0.64 (~product(e_5, e_5, e_1)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[844, 35, 829, 838])).
% 0.48/0.64 tff(846,plain,
% 0.48/0.64 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_5, e_5, e_5)) | product(e_5, e_5, e_1) | (~product(e_5, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_5, e_5, e_5)) | product(e_5, e_5, e_1) | (~product(e_5, e_1, e_5)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(847,plain,
% 0.48/0.64 ((product(e_5, e_5, e_1) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_1, e_5))) <=> ((~product(e_5, e_5, e_5)) | product(e_5, e_5, e_1) | (~product(e_5, e_1, e_5)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(848,plain,
% 0.48/0.64 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_5, e_1) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_5, e_5, e_5)) | product(e_5, e_5, e_1) | (~product(e_5, e_1, e_5))))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[847])).
% 0.48/0.64 tff(849,plain,
% 0.48/0.64 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_5, e_1) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_5, e_5, e_5)) | product(e_5, e_5, e_1) | (~product(e_5, e_1, e_5)))),
% 0.48/0.64 inference(transitivity,[status(thm)],[848, 846])).
% 0.48/0.64 tff(850,plain,
% 0.48/0.64 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_5, e_1) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_1, e_5)))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(851,plain,
% 0.48/0.64 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_5, e_5, e_5)) | product(e_5, e_5, e_1) | (~product(e_5, e_1, e_5))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[850, 849])).
% 0.48/0.64 tff(852,plain,
% 0.48/0.64 (~product(e_5, e_1, e_5)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[851, 35, 606, 845])).
% 0.48/0.64 tff(853,plain,
% 0.48/0.64 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_5, e_6)) | product(e_5, e_1, e_5) | (~product(e_6, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_5, e_6)) | product(e_5, e_1, e_5) | (~product(e_6, e_1, e_5)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(854,plain,
% 0.48/0.64 ((product(e_5, e_1, e_5) | (~product(e_6, e_1, e_5)) | (~product(e_1, e_5, e_6))) <=> ((~product(e_1, e_5, e_6)) | product(e_5, e_1, e_5) | (~product(e_6, e_1, e_5)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(855,plain,
% 0.48/0.64 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_1, e_5) | (~product(e_6, e_1, e_5)) | (~product(e_1, e_5, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_5, e_6)) | product(e_5, e_1, e_5) | (~product(e_6, e_1, e_5))))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[854])).
% 0.48/0.64 tff(856,plain,
% 0.48/0.64 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_1, e_5) | (~product(e_6, e_1, e_5)) | (~product(e_1, e_5, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_5, e_6)) | product(e_5, e_1, e_5) | (~product(e_6, e_1, e_5)))),
% 0.48/0.64 inference(transitivity,[status(thm)],[855, 853])).
% 0.48/0.64 tff(857,plain,
% 0.48/0.64 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_1, e_5) | (~product(e_6, e_1, e_5)) | (~product(e_1, e_5, e_6)))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(858,plain,
% 0.48/0.64 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_5, e_6)) | product(e_5, e_1, e_5) | (~product(e_6, e_1, e_5))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[857, 856])).
% 0.48/0.64 tff(859,plain,
% 0.48/0.64 ((~product(e_1, e_5, e_6)) | product(e_5, e_1, e_5) | (~product(e_6, e_1, e_5))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[858, 35])).
% 0.48/0.64 tff(860,plain,
% 0.48/0.64 (~product(e_6, e_1, e_5)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[859, 852, 829])).
% 0.48/0.64 tff(861,plain,
% 0.48/0.64 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_6, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_6, e_1, e_3)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(862,plain,
% 0.48/0.64 ((product(e_3, e_1, e_5) | (~product(e_6, e_1, e_3)) | (~product(e_1, e_5, e_6))) <=> (product(e_3, e_1, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_6, e_1, e_3)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(863,plain,
% 0.48/0.64 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_6, e_1, e_3)) | (~product(e_1, e_5, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_6, e_1, e_3))))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[862])).
% 0.48/0.64 tff(864,plain,
% 0.48/0.64 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_6, e_1, e_3)) | (~product(e_1, e_5, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_6, e_1, e_3)))),
% 0.48/0.64 inference(transitivity,[status(thm)],[863, 861])).
% 0.48/0.64 tff(865,plain,
% 0.48/0.64 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_5) | (~product(e_6, e_1, e_3)) | (~product(e_1, e_5, e_6)))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(866,plain,
% 0.48/0.64 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_6, e_1, e_3))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[865, 864])).
% 0.48/0.64 tff(867,plain,
% 0.48/0.64 ($false),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[866, 35, 199, 4, 45])).
% 0.48/0.64 tff(868,plain,((~product(e_6, e_1, e_3)) | (~product(e_1, e_5, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.64 tff(869,plain,
% 0.48/0.64 (~product(e_6, e_1, e_3)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[868, 829])).
% 0.48/0.64 tff(870,plain,
% 0.48/0.64 (~product(e_6, e_1, e_1)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[43, 829])).
% 0.48/0.64 tff(871,plain,
% 0.48/0.64 (~product(e_6, e_1, e_2)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[685, 829])).
% 0.48/0.64 tff(872,plain,
% 0.48/0.64 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6)) | product(e_6, e_1, e_6) | product(e_6, e_1, e_1) | product(e_6, e_1, e_5) | product(e_6, e_1, e_3) | product(e_6, e_1, e_2) | product(e_6, e_1, e_4))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6)) | product(e_6, e_1, e_6) | product(e_6, e_1, e_1) | product(e_6, e_1, e_5) | product(e_6, e_1, e_3) | product(e_6, e_1, e_2) | product(e_6, e_1, e_4))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(873,plain,
% 0.48/0.64 ((product(e_6, e_1, e_6) | product(e_6, e_1, e_5) | product(e_6, e_1, e_4) | product(e_6, e_1, e_3) | product(e_6, e_1, e_2) | product(e_6, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_6))) <=> ((~group_element(e_1)) | (~group_element(e_6)) | product(e_6, e_1, e_6) | product(e_6, e_1, e_1) | product(e_6, e_1, e_5) | product(e_6, e_1, e_3) | product(e_6, e_1, e_2) | product(e_6, e_1, e_4))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(874,plain,
% 0.48/0.64 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6, e_1, e_6) | product(e_6, e_1, e_5) | product(e_6, e_1, e_4) | product(e_6, e_1, e_3) | product(e_6, e_1, e_2) | product(e_6, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_6)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6)) | product(e_6, e_1, e_6) | product(e_6, e_1, e_1) | product(e_6, e_1, e_5) | product(e_6, e_1, e_3) | product(e_6, e_1, e_2) | product(e_6, e_1, e_4)))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[873])).
% 0.48/0.64 tff(875,plain,
% 0.48/0.64 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6, e_1, e_6) | product(e_6, e_1, e_5) | product(e_6, e_1, e_4) | product(e_6, e_1, e_3) | product(e_6, e_1, e_2) | product(e_6, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_6)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6)) | product(e_6, e_1, e_6) | product(e_6, e_1, e_1) | product(e_6, e_1, e_5) | product(e_6, e_1, e_3) | product(e_6, e_1, e_2) | product(e_6, e_1, e_4))),
% 0.48/0.64 inference(transitivity,[status(thm)],[874, 872])).
% 0.48/0.64 tff(876,plain,
% 0.48/0.64 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6, e_1, e_6) | product(e_6, e_1, e_5) | product(e_6, e_1, e_4) | product(e_6, e_1, e_3) | product(e_6, e_1, e_2) | product(e_6, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_6)))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(877,plain,
% 0.48/0.64 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6)) | product(e_6, e_1, e_6) | product(e_6, e_1, e_1) | product(e_6, e_1, e_5) | product(e_6, e_1, e_3) | product(e_6, e_1, e_2) | product(e_6, e_1, e_4)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[876, 875])).
% 0.48/0.64 tff(878,plain,
% 0.48/0.64 (product(e_6, e_1, e_4)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[877, 142, 322, 136, 871, 870, 869, 860, 712])).
% 0.48/0.64 tff(879,plain,
% 0.48/0.64 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_6, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_6, e_1, e_4)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(880,plain,
% 0.48/0.64 ((product(e_4, e_1, e_5) | (~product(e_6, e_1, e_4)) | (~product(e_1, e_5, e_6))) <=> (product(e_4, e_1, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_6, e_1, e_4)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(881,plain,
% 0.48/0.64 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_5) | (~product(e_6, e_1, e_4)) | (~product(e_1, e_5, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_6, e_1, e_4))))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[880])).
% 0.48/0.64 tff(882,plain,
% 0.48/0.64 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_5) | (~product(e_6, e_1, e_4)) | (~product(e_1, e_5, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_6, e_1, e_4)))),
% 0.48/0.64 inference(transitivity,[status(thm)],[881, 879])).
% 0.48/0.64 tff(883,plain,
% 0.48/0.64 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_5) | (~product(e_6, e_1, e_4)) | (~product(e_1, e_5, e_6)))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(884,plain,
% 0.48/0.64 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_5) | (~product(e_1, e_5, e_6)) | (~product(e_6, e_1, e_4))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[883, 882])).
% 0.48/0.64 tff(885,plain,
% 0.48/0.64 ($false),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[884, 35, 826, 829, 878])).
% 0.48/0.64 tff(886,plain,(~product(e_1, e_6, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.48/0.64 tff(887,plain,
% 0.48/0.64 (product(e_1, e_6, e_4)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[743, 886])).
% 0.48/0.64 tff(888,plain,
% 0.48/0.64 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_6, e_4)) | product(e_4, e_6, e_6) | (~product(e_6, e_6, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_6, e_4)) | product(e_4, e_6, e_6) | (~product(e_6, e_6, e_1)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(889,plain,
% 0.48/0.64 ((product(e_4, e_6, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_6, e_6, e_1))) <=> ((~product(e_1, e_6, e_4)) | product(e_4, e_6, e_6) | (~product(e_6, e_6, e_1)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(890,plain,
% 0.48/0.64 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_6, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_6, e_6, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_6, e_4)) | product(e_4, e_6, e_6) | (~product(e_6, e_6, e_1))))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[889])).
% 0.48/0.64 tff(891,plain,
% 0.48/0.64 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_6, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_6, e_6, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_6, e_4)) | product(e_4, e_6, e_6) | (~product(e_6, e_6, e_1)))),
% 0.48/0.64 inference(transitivity,[status(thm)],[890, 888])).
% 0.48/0.64 tff(892,plain,
% 0.48/0.64 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_6, e_6) | (~product(e_1, e_6, e_4)) | (~product(e_6, e_6, e_1)))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(893,plain,
% 0.48/0.64 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_6, e_4)) | product(e_4, e_6, e_6) | (~product(e_6, e_6, e_1))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[892, 891])).
% 0.48/0.64 tff(894,plain,
% 0.48/0.64 (~product(e_6, e_6, e_1)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[893, 35, 887, 692])).
% 0.48/0.64 tff(895,plain,
% 0.48/0.64 (~product(e_6, e_1, e_6)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[711, 35, 300, 894])).
% 0.48/0.64 tff(896,plain,
% 0.48/0.64 (product(e_6, e_1, e_1) | product(e_6, e_1, e_5) | product(e_6, e_1, e_3) | product(e_6, e_1, e_2) | product(e_6, e_1, e_4)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[877, 142, 322, 136, 895])).
% 0.48/0.64 tff(897,plain,
% 0.48/0.64 (product(e_6, e_1, e_5)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[896, 686, 676, 159, 44])).
% 0.48/0.64 tff(898,plain,
% 0.48/0.64 (product(e_5, e_1, e_5)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[859, 897, 4])).
% 0.48/0.64 tff(899,plain,
% 0.48/0.64 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_5) | (~product(e_6, e_1, e_5)) | (~product(e_5, e_1, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_5) | (~product(e_6, e_1, e_5)) | (~product(e_5, e_1, e_5)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(900,plain,
% 0.48/0.65 ((equalish(e_6, e_5) | (~product(e_5, e_1, e_5)) | (~product(e_6, e_1, e_5))) <=> (equalish(e_6, e_5) | (~product(e_6, e_1, e_5)) | (~product(e_5, e_1, e_5)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(901,plain,
% 0.48/0.65 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_5) | (~product(e_5, e_1, e_5)) | (~product(e_6, e_1, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_5) | (~product(e_6, e_1, e_5)) | (~product(e_5, e_1, e_5))))),
% 0.48/0.65 inference(monotonicity,[status(thm)],[900])).
% 0.48/0.65 tff(902,plain,
% 0.48/0.65 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_5) | (~product(e_5, e_1, e_5)) | (~product(e_6, e_1, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_5) | (~product(e_6, e_1, e_5)) | (~product(e_5, e_1, e_5)))),
% 0.48/0.65 inference(transitivity,[status(thm)],[901, 899])).
% 0.48/0.65 tff(903,plain,
% 0.48/0.65 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_5) | (~product(e_5, e_1, e_5)) | (~product(e_6, e_1, e_5)))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(904,plain,
% 0.48/0.65 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_5) | (~product(e_6, e_1, e_5)) | (~product(e_5, e_1, e_5))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[903, 902])).
% 0.48/0.65 tff(905,plain,
% 0.48/0.65 ($false),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[904, 833, 91, 897, 898])).
% 0.48/0.65 tff(906,plain,(~product(e_1, e_5, e_6)), inference(lemma,lemma(discharge,[]))).
% 0.48/0.65 tff(907,plain,
% 0.48/0.65 (product(e_1, e_5, e_3)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[828, 906])).
% 0.48/0.65 tff(908,plain,
% 0.48/0.65 (product(e_4, e_1, e_5)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[802, 907])).
% 0.48/0.65 tff(909,plain,
% 0.48/0.65 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_4, e_3, e_5)) | (~product(e_4, 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_3, e_1) | (~product(e_4, e_3, e_5)) | (~product(e_4, e_1, e_5)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(910,plain,
% 0.48/0.65 ((equalish(e_3, e_1) | (~product(e_4, e_1, e_5)) | (~product(e_4, e_3, e_5))) <=> (equalish(e_3, e_1) | (~product(e_4, e_3, e_5)) | (~product(e_4, e_1, e_5)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(911,plain,
% 0.48/0.65 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_4, e_1, e_5)) | (~product(e_4, e_3, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_4, e_3, e_5)) | (~product(e_4, e_1, e_5))))),
% 0.48/0.65 inference(monotonicity,[status(thm)],[910])).
% 0.48/0.65 tff(912,plain,
% 0.48/0.65 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_4, e_1, e_5)) | (~product(e_4, e_3, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_4, e_3, e_5)) | (~product(e_4, e_1, e_5)))),
% 0.48/0.65 inference(transitivity,[status(thm)],[911, 909])).
% 0.48/0.65 tff(913,plain,
% 0.48/0.65 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_4, e_1, e_5)) | (~product(e_4, e_3, e_5)))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(914,plain,
% 0.48/0.65 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_4, e_3, e_5)) | (~product(e_4, e_1, e_5))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[913, 912])).
% 0.48/0.65 tff(915,plain,
% 0.48/0.65 ($false),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[914, 177, 65, 908, 3])).
% 0.48/0.65 tff(916,plain,(~product(e_4, e_3, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.48/0.65 tff(917,assumption,(product(e_4, e_3, e_3)), introduced(assumption)).
% 0.48/0.65 tff(918,plain,
% 0.48/0.65 (((~![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_3, e_3)) | (~product(e_4, 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_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_4, e_3, e_3)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(919,plain,
% 0.48/0.65 ((~![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_3, e_3)) | (~product(e_4, e_3, e_3)))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(920,plain,
% 0.48/0.65 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_4, e_3, e_3))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[919, 918])).
% 0.48/0.65 tff(921,plain,
% 0.48/0.65 ($false),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[920, 495, 91, 376, 917])).
% 0.48/0.65 tff(922,plain,(~product(e_4, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.48/0.65 tff(923,assumption,(product(e_4, e_3, e_6)), introduced(assumption)).
% 0.48/0.65 tff(924,plain,
% 0.48/0.65 (~product(e_1, e_3, e_4)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[597, 887])).
% 0.48/0.65 tff(925,assumption,(~product(e_5, e_1, e_6)), introduced(assumption)).
% 0.48/0.65 tff(926,assumption,(product(e_4, e_1, e_5)), introduced(assumption)).
% 0.48/0.65 tff(927,plain,
% 0.48/0.65 (product(e_5, e_1, e_3)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[825, 492, 926])).
% 0.48/0.65 tff(928,plain,
% 0.48/0.65 (~product(e_1, e_6, e_4)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[597, 492])).
% 0.48/0.65 tff(929,plain,
% 0.48/0.65 (product(e_1, e_6, e_5)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[743, 928])).
% 0.48/0.65 tff(930,plain,
% 0.48/0.65 ($false),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[721, 929, 927])).
% 0.48/0.65 tff(931,plain,((~product(e_1, e_3, e_4)) | (~product(e_4, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.65 tff(932,plain,
% 0.48/0.65 (~product(e_1, e_3, e_4)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[931, 926])).
% 0.48/0.65 tff(933,plain,
% 0.48/0.65 (~product(e_1, e_6, e_5)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[817, 932])).
% 0.48/0.65 tff(934,plain,
% 0.48/0.65 (product(e_1, e_6, e_4)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[743, 933])).
% 0.48/0.65 tff(935,plain,
% 0.48/0.65 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_6, e_4)) | (~product(e_4, e_1, e_5)) | product(e_5, e_1, e_6))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_6, e_4)) | (~product(e_4, e_1, e_5)) | product(e_5, e_1, e_6))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(936,plain,
% 0.48/0.65 ((product(e_5, e_1, e_6) | (~product(e_4, e_1, e_5)) | (~product(e_1, e_6, e_4))) <=> ((~product(e_1, e_6, e_4)) | (~product(e_4, e_1, e_5)) | product(e_5, e_1, e_6))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(937,plain,
% 0.48/0.65 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_1, e_6) | (~product(e_4, e_1, e_5)) | (~product(e_1, e_6, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_6, e_4)) | (~product(e_4, e_1, e_5)) | product(e_5, e_1, e_6)))),
% 0.48/0.65 inference(monotonicity,[status(thm)],[936])).
% 0.48/0.65 tff(938,plain,
% 0.48/0.65 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_1, e_6) | (~product(e_4, e_1, e_5)) | (~product(e_1, e_6, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_6, e_4)) | (~product(e_4, e_1, e_5)) | product(e_5, e_1, e_6))),
% 0.48/0.65 inference(transitivity,[status(thm)],[937, 935])).
% 0.48/0.65 tff(939,plain,
% 0.48/0.65 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_1, e_6) | (~product(e_4, e_1, e_5)) | (~product(e_1, e_6, e_4)))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(940,plain,
% 0.48/0.65 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_6, e_4)) | (~product(e_4, e_1, e_5)) | product(e_5, e_1, e_6)),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[939, 938])).
% 0.48/0.65 tff(941,plain,
% 0.48/0.65 ($false),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[940, 35, 926, 934, 925])).
% 0.48/0.65 tff(942,plain,(product(e_5, e_1, e_6) | (~product(e_4, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.65 tff(943,plain,
% 0.48/0.65 (product(e_5, e_1, e_6)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[942, 908])).
% 0.48/0.65 tff(944,assumption,(product(e_5, e_1, e_6)), introduced(assumption)).
% 0.48/0.65 tff(945,plain,
% 0.48/0.65 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_3, e_5)) | product(e_6, e_1, e_3) | (~product(e_5, e_1, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_5)) | product(e_6, e_1, e_3) | (~product(e_5, e_1, e_6)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(946,plain,
% 0.48/0.65 ((product(e_6, e_1, e_3) | (~product(e_5, e_1, e_6)) | (~product(e_1, e_3, e_5))) <=> ((~product(e_1, e_3, e_5)) | product(e_6, e_1, e_3) | (~product(e_5, e_1, e_6)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(947,plain,
% 0.48/0.65 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_6, e_1, e_3) | (~product(e_5, e_1, e_6)) | (~product(e_1, e_3, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_3, e_5)) | product(e_6, e_1, e_3) | (~product(e_5, e_1, e_6))))),
% 0.48/0.65 inference(monotonicity,[status(thm)],[946])).
% 0.48/0.65 tff(948,plain,
% 0.48/0.65 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_6, e_1, e_3) | (~product(e_5, e_1, e_6)) | (~product(e_1, e_3, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_5)) | product(e_6, e_1, e_3) | (~product(e_5, e_1, e_6)))),
% 0.48/0.65 inference(transitivity,[status(thm)],[947, 945])).
% 0.48/0.65 tff(949,plain,
% 0.48/0.65 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_6, e_1, e_3) | (~product(e_5, e_1, e_6)) | (~product(e_1, e_3, e_5)))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(950,plain,
% 0.48/0.65 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_5)) | product(e_6, e_1, e_3) | (~product(e_5, e_1, e_6))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[949, 948])).
% 0.48/0.65 tff(951,plain,
% 0.48/0.65 ($false),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[950, 35, 352, 159, 944])).
% 0.48/0.65 tff(952,plain,((~product(e_1, e_3, e_5)) | (~product(e_5, e_1, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.65 tff(953,plain,
% 0.48/0.65 (~product(e_1, e_3, e_5)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[952, 943])).
% 0.48/0.65 tff(954,plain,
% 0.48/0.65 (product(e_1, e_3, e_6)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[620, 953, 924])).
% 0.48/0.65 tff(955,plain,
% 0.48/0.65 ((~equalish(e_4, e_1)) <=> (~equalish(e_4, e_1))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(956,axiom,(~equalish(e_4, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_1')).
% 0.48/0.65 tff(957,plain,
% 0.48/0.65 (~equalish(e_4, e_1)),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[956, 955])).
% 0.48/0.65 tff(958,plain,
% 0.48/0.65 (((~![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_3, e_6)) | (~product(e_4, e_3, e_6)))) <=> ((~![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_3, e_6)) | (~product(e_4, e_3, e_6)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(959,plain,
% 0.48/0.65 ((~![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_3, e_6)) | (~product(e_4, e_3, e_6)))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(960,plain,
% 0.48/0.65 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_3, e_6)) | (~product(e_4, e_3, e_6))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[959, 958])).
% 0.48/0.65 tff(961,plain,
% 0.48/0.65 ($false),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[960, 957, 91, 954, 923])).
% 0.48/0.65 tff(962,plain,(~product(e_4, e_3, e_6)), inference(lemma,lemma(discharge,[]))).
% 0.48/0.65 tff(963,assumption,(product(e_4, e_3, e_4)), introduced(assumption)).
% 0.48/0.65 tff(964,assumption,(product(e_4, e_3, e_1)), introduced(assumption)).
% 0.48/0.65 tff(965,plain,
% 0.48/0.65 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_3, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_3, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_3, e_1)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(966,plain,
% 0.48/0.65 ((product(e_1, e_3, e_1) | (~product(e_4, e_3, e_1)) | (~product(e_3, e_1, e_4))) <=> (product(e_1, e_3, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_3, e_1)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(967,plain,
% 0.48/0.65 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_3, e_1) | (~product(e_4, e_3, e_1)) | (~product(e_3, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_3, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_3, e_1))))),
% 0.48/0.65 inference(monotonicity,[status(thm)],[966])).
% 0.48/0.65 tff(968,plain,
% 0.48/0.65 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_3, e_1) | (~product(e_4, e_3, e_1)) | (~product(e_3, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_3, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_3, e_1)))),
% 0.48/0.65 inference(transitivity,[status(thm)],[967, 965])).
% 0.48/0.65 tff(969,plain,
% 0.48/0.65 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_3, e_1) | (~product(e_4, e_3, e_1)) | (~product(e_3, e_1, e_4)))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(970,plain,
% 0.48/0.65 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_3, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_3, e_1))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[969, 968])).
% 0.48/0.65 tff(971,plain,
% 0.48/0.65 ($false),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[970, 35, 671, 402, 964])).
% 0.48/0.65 tff(972,plain,(~product(e_4, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.48/0.65 tff(973,plain,
% 0.48/0.65 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_4, e_3, e_1) | (~product(e_4, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_1, e_4)) | product(e_4, e_3, e_1) | (~product(e_4, e_3, e_4)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(974,plain,
% 0.48/0.65 ((product(e_4, e_3, e_1) | (~product(e_4, e_3, e_4)) | (~product(e_3, e_1, e_4))) <=> ((~product(e_3, e_1, e_4)) | product(e_4, e_3, e_1) | (~product(e_4, e_3, e_4)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(975,plain,
% 0.48/0.65 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_3, e_1) | (~product(e_4, e_3, e_4)) | (~product(e_3, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_4, e_3, e_1) | (~product(e_4, e_3, e_4))))),
% 0.48/0.65 inference(monotonicity,[status(thm)],[974])).
% 0.48/0.65 tff(976,plain,
% 0.48/0.65 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_3, e_1) | (~product(e_4, e_3, e_4)) | (~product(e_3, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_1, e_4)) | product(e_4, e_3, e_1) | (~product(e_4, e_3, e_4)))),
% 0.48/0.65 inference(transitivity,[status(thm)],[975, 973])).
% 0.48/0.65 tff(977,plain,
% 0.48/0.65 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_3, e_1) | (~product(e_4, e_3, e_4)) | (~product(e_3, e_1, e_4)))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(978,plain,
% 0.48/0.65 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_1, e_4)) | product(e_4, e_3, e_1) | (~product(e_4, e_3, e_4))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[977, 976])).
% 0.48/0.65 tff(979,plain,
% 0.48/0.65 ($false),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[978, 35, 671, 972, 963])).
% 0.48/0.65 tff(980,plain,(~product(e_4, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.48/0.65 tff(981,plain,
% 0.48/0.65 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_3)) | (~group_element(e_4)) | product(e_4, e_3, e_2) | product(e_4, e_3, e_3) | product(e_4, e_3, e_1) | product(e_4, e_3, e_5) | product(e_4, e_3, e_4) | product(e_4, e_3, e_6))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_3)) | (~group_element(e_4)) | product(e_4, e_3, e_2) | product(e_4, e_3, e_3) | product(e_4, e_3, e_1) | product(e_4, e_3, e_5) | product(e_4, e_3, e_4) | product(e_4, e_3, e_6))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(982,plain,
% 0.48/0.65 ((product(e_4, e_3, e_6) | product(e_4, e_3, e_5) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_4))) <=> ((~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_2) | product(e_4, e_3, e_3) | product(e_4, e_3, e_1) | product(e_4, e_3, e_5) | product(e_4, e_3, e_4) | product(e_4, e_3, e_6))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(983,plain,
% 0.48/0.65 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_3, e_6) | product(e_4, e_3, e_5) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_3)) | (~group_element(e_4)) | product(e_4, e_3, e_2) | product(e_4, e_3, e_3) | product(e_4, e_3, e_1) | product(e_4, e_3, e_5) | product(e_4, e_3, e_4) | product(e_4, e_3, e_6)))),
% 0.48/0.66 inference(monotonicity,[status(thm)],[982])).
% 0.48/0.66 tff(984,plain,
% 0.48/0.66 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_3, e_6) | product(e_4, e_3, e_5) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_3)) | (~group_element(e_4)) | product(e_4, e_3, e_2) | product(e_4, e_3, e_3) | product(e_4, e_3, e_1) | product(e_4, e_3, e_5) | product(e_4, e_3, e_4) | product(e_4, e_3, e_6))),
% 0.48/0.66 inference(transitivity,[status(thm)],[983, 981])).
% 0.48/0.66 tff(985,plain,
% 0.48/0.66 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_3, e_6) | product(e_4, e_3, e_5) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_4)))),
% 0.48/0.66 inference(quant_inst,[status(thm)],[])).
% 0.48/0.66 tff(986,plain,
% 0.48/0.66 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_3)) | (~group_element(e_4)) | product(e_4, e_3, e_2) | product(e_4, e_3, e_3) | product(e_4, e_3, e_1) | product(e_4, e_3, e_5) | product(e_4, e_3, e_4) | product(e_4, e_3, e_6)),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[985, 984])).
% 0.48/0.66 tff(987,plain,
% 0.48/0.66 (product(e_4, e_3, e_2) | product(e_4, e_3, e_3) | product(e_4, e_3, e_1) | product(e_4, e_3, e_5) | product(e_4, e_3, e_4) | product(e_4, e_3, e_6)),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[986, 202, 432, 136])).
% 0.48/0.66 tff(988,plain,
% 0.48/0.66 (product(e_4, e_3, e_2) | product(e_4, e_3, e_3) | product(e_4, e_3, e_5) | product(e_4, e_3, e_4) | product(e_4, e_3, e_6)),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[987, 972])).
% 0.48/0.66 tff(989,plain,
% 0.48/0.66 (product(e_4, e_3, e_2) | product(e_4, e_3, e_3) | product(e_4, e_3, e_5)),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[988, 980, 962])).
% 0.48/0.66 tff(990,plain,
% 0.48/0.66 (product(e_4, e_3, e_2) | product(e_4, e_3, e_5)),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[989, 922])).
% 0.48/0.66 tff(991,plain,
% 0.48/0.66 (product(e_4, e_3, e_2)),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[990, 916])).
% 0.48/0.66 tff(992,assumption,(product(e_4, e_3, e_2)), introduced(assumption)).
% 0.48/0.66 tff(993,assumption,(product(e_5, e_3, e_2)), introduced(assumption)).
% 0.48/0.66 tff(994,plain,
% 0.48/0.66 ((~equalish(e_4, e_5)) <=> (~equalish(e_4, e_5))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(995,axiom,(~equalish(e_4, e_5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_5')).
% 0.48/0.66 tff(996,plain,
% 0.48/0.66 (~equalish(e_4, e_5)),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[995, 994])).
% 0.48/0.66 tff(997,plain,
% 0.48/0.66 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_5) | (~product(e_5, e_3, e_2)) | (~product(e_4, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_5) | (~product(e_5, e_3, e_2)) | (~product(e_4, e_3, e_2)))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(998,plain,
% 0.48/0.66 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_5) | (~product(e_5, e_3, e_2)) | (~product(e_4, e_3, e_2)))),
% 0.48/0.66 inference(quant_inst,[status(thm)],[])).
% 0.48/0.66 tff(999,plain,
% 0.48/0.66 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_5) | (~product(e_5, e_3, e_2)) | (~product(e_4, e_3, e_2))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[998, 997])).
% 0.48/0.66 tff(1000,plain,
% 0.48/0.66 ($false),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[999, 996, 91, 993, 992])).
% 0.48/0.66 tff(1001,plain,((~product(e_4, e_3, e_2)) | (~product(e_5, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.66 tff(1002,plain,
% 0.48/0.66 (~product(e_5, e_3, e_2)),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[1001, 991])).
% 0.48/0.66 tff(1003,assumption,(product(e_5, e_3, e_1)), introduced(assumption)).
% 0.48/0.66 tff(1004,plain,
% 0.48/0.66 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_3, e_3) | (~product(e_3, e_3, e_5)) | (~product(e_5, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_3, e_3) | (~product(e_3, e_3, e_5)) | (~product(e_5, e_3, e_1)))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(1005,plain,
% 0.48/0.66 ((product(e_1, e_3, e_3) | (~product(e_5, e_3, e_1)) | (~product(e_3, e_3, e_5))) <=> (product(e_1, e_3, e_3) | (~product(e_3, e_3, e_5)) | (~product(e_5, e_3, e_1)))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(1006,plain,
% 0.48/0.66 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_3, e_3) | (~product(e_5, e_3, e_1)) | (~product(e_3, e_3, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_3, e_3) | (~product(e_3, e_3, e_5)) | (~product(e_5, e_3, e_1))))),
% 0.48/0.66 inference(monotonicity,[status(thm)],[1005])).
% 0.48/0.66 tff(1007,plain,
% 0.48/0.66 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_3, e_3) | (~product(e_5, e_3, e_1)) | (~product(e_3, e_3, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_3, e_3) | (~product(e_3, e_3, e_5)) | (~product(e_5, e_3, e_1)))),
% 0.48/0.66 inference(transitivity,[status(thm)],[1006, 1004])).
% 0.48/0.66 tff(1008,plain,
% 0.48/0.66 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_3, e_3) | (~product(e_5, e_3, e_1)) | (~product(e_3, e_3, e_5)))),
% 0.48/0.66 inference(quant_inst,[status(thm)],[])).
% 0.48/0.66 tff(1009,plain,
% 0.48/0.66 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_3, e_3) | (~product(e_3, e_3, e_5)) | (~product(e_5, e_3, e_1))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[1008, 1007])).
% 0.48/0.66 tff(1010,plain,
% 0.48/0.66 (~product(e_3, e_3, e_5)),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[1009, 35, 384, 1003])).
% 0.48/0.66 tff(1011,plain,
% 0.48/0.66 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_3, e_5) | (~product(e_3, e_5, e_3)) | (~product(e_3, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_3, e_5) | (~product(e_3, e_5, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(1012,plain,
% 0.48/0.66 ((product(e_3, e_3, e_5) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_5, e_3))) <=> (product(e_3, e_3, e_5) | (~product(e_3, e_5, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(1013,plain,
% 0.48/0.66 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_3, e_5) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_5, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_3, e_5) | (~product(e_3, e_5, e_3)) | (~product(e_3, e_3, e_3))))),
% 0.51/0.66 inference(monotonicity,[status(thm)],[1012])).
% 0.51/0.66 tff(1014,plain,
% 0.51/0.66 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_3, e_5) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_5, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_3, e_5) | (~product(e_3, e_5, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.51/0.66 inference(transitivity,[status(thm)],[1013, 1011])).
% 0.51/0.66 tff(1015,plain,
% 0.51/0.66 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_3, e_5) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_5, e_3)))),
% 0.51/0.66 inference(quant_inst,[status(thm)],[])).
% 0.51/0.66 tff(1016,plain,
% 0.51/0.66 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_3, e_5) | (~product(e_3, e_5, e_3)) | (~product(e_3, e_3, e_3))),
% 0.51/0.66 inference(modus_ponens,[status(thm)],[1015, 1014])).
% 0.51/0.66 tff(1017,plain,
% 0.51/0.66 (~product(e_3, e_5, e_3)),
% 0.51/0.66 inference(unit_resolution,[status(thm)],[1016, 35, 376, 1010])).
% 0.51/0.66 tff(1018,plain,
% 0.51/0.66 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_5, e_3)) | product(e_3, e_5, e_3) | (~product(e_5, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_5, e_3)) | product(e_3, e_5, e_3) | (~product(e_5, e_3, e_1)))),
% 0.51/0.66 inference(rewrite,[status(thm)],[])).
% 0.51/0.66 tff(1019,plain,
% 0.51/0.66 ((product(e_3, e_5, e_3) | (~product(e_1, e_5, e_3)) | (~product(e_5, e_3, e_1))) <=> ((~product(e_1, e_5, e_3)) | product(e_3, e_5, e_3) | (~product(e_5, e_3, e_1)))),
% 0.51/0.66 inference(rewrite,[status(thm)],[])).
% 0.51/0.66 tff(1020,plain,
% 0.51/0.66 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_5, e_3) | (~product(e_1, e_5, e_3)) | (~product(e_5, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_5, e_3)) | product(e_3, e_5, e_3) | (~product(e_5, e_3, e_1))))),
% 0.51/0.66 inference(monotonicity,[status(thm)],[1019])).
% 0.51/0.66 tff(1021,plain,
% 0.51/0.66 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_5, e_3) | (~product(e_1, e_5, e_3)) | (~product(e_5, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_5, e_3)) | product(e_3, e_5, e_3) | (~product(e_5, e_3, e_1)))),
% 0.51/0.66 inference(transitivity,[status(thm)],[1020, 1018])).
% 0.51/0.66 tff(1022,plain,
% 0.51/0.66 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_5, e_3) | (~product(e_1, e_5, e_3)) | (~product(e_5, e_3, e_1)))),
% 0.51/0.66 inference(quant_inst,[status(thm)],[])).
% 0.51/0.66 tff(1023,plain,
% 0.51/0.66 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_5, e_3)) | product(e_3, e_5, e_3) | (~product(e_5, e_3, e_1))),
% 0.51/0.66 inference(modus_ponens,[status(thm)],[1022, 1021])).
% 0.51/0.66 tff(1024,plain,
% 0.51/0.66 ($false),
% 0.51/0.66 inference(unit_resolution,[status(thm)],[1023, 35, 786, 1003, 1017])).
% 0.51/0.66 tff(1025,plain,((~product(e_5, e_3, e_1)) | (~product(e_1, e_5, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.66 tff(1026,plain,
% 0.51/0.66 (~product(e_5, e_3, e_1)),
% 0.51/0.66 inference(unit_resolution,[status(thm)],[1025, 907])).
% 0.51/0.66 tff(1027,assumption,(product(e_5, e_3, e_6)), introduced(assumption)).
% 0.51/0.66 tff(1028,plain,
% 0.51/0.66 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.51/0.66 inference(rewrite,[status(thm)],[])).
% 0.51/0.66 tff(1029,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.51/0.66 tff(1030,plain,
% 0.51/0.66 (~equalish(e_1, e_3)),
% 0.51/0.66 inference(modus_ponens,[status(thm)],[1029, 1028])).
% 0.51/0.66 tff(1031,plain,
% 0.51/0.66 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_5, e_1, e_6)) | (~product(e_5, e_3, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_5, e_1, e_6)) | (~product(e_5, e_3, e_6)))),
% 0.51/0.66 inference(rewrite,[status(thm)],[])).
% 0.51/0.66 tff(1032,plain,
% 0.51/0.66 ((equalish(e_1, e_3) | (~product(e_5, e_3, e_6)) | (~product(e_5, e_1, e_6))) <=> (equalish(e_1, e_3) | (~product(e_5, e_1, e_6)) | (~product(e_5, e_3, e_6)))),
% 0.51/0.66 inference(rewrite,[status(thm)],[])).
% 0.51/0.66 tff(1033,plain,
% 0.51/0.66 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_5, e_3, e_6)) | (~product(e_5, e_1, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_5, e_1, e_6)) | (~product(e_5, e_3, e_6))))),
% 0.51/0.66 inference(monotonicity,[status(thm)],[1032])).
% 0.51/0.66 tff(1034,plain,
% 0.51/0.66 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_5, e_3, e_6)) | (~product(e_5, e_1, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_5, e_1, e_6)) | (~product(e_5, e_3, e_6)))),
% 0.51/0.66 inference(transitivity,[status(thm)],[1033, 1031])).
% 0.51/0.66 tff(1035,plain,
% 0.51/0.66 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_5, e_3, e_6)) | (~product(e_5, e_1, e_6)))),
% 0.51/0.66 inference(quant_inst,[status(thm)],[])).
% 0.51/0.66 tff(1036,plain,
% 0.51/0.66 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_5, e_1, e_6)) | (~product(e_5, e_3, e_6))),
% 0.51/0.66 inference(modus_ponens,[status(thm)],[1035, 1034])).
% 0.51/0.66 tff(1037,plain,
% 0.51/0.66 ($false),
% 0.51/0.66 inference(unit_resolution,[status(thm)],[1036, 1030, 65, 1027, 944])).
% 0.51/0.66 tff(1038,plain,((~product(e_5, e_1, e_6)) | (~product(e_5, e_3, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.66 tff(1039,plain,
% 0.51/0.66 (~product(e_5, e_3, e_6)),
% 0.51/0.66 inference(unit_resolution,[status(thm)],[1038, 943])).
% 0.51/0.66 tff(1040,assumption,(product(e_5, e_3, e_5)), introduced(assumption)).
% 0.51/0.66 tff(1041,plain,
% 0.51/0.66 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_3, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_3, e_5)))),
% 0.51/0.66 inference(rewrite,[status(thm)],[])).
% 0.51/0.66 tff(1042,plain,
% 0.51/0.66 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_3, e_5)))),
% 0.51/0.66 inference(quant_inst,[status(thm)],[])).
% 0.51/0.66 tff(1043,plain,
% 0.51/0.66 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_3, e_5))),
% 0.51/0.66 inference(modus_ponens,[status(thm)],[1042, 1041])).
% 0.51/0.66 tff(1044,plain,
% 0.51/0.66 ($false),
% 0.51/0.66 inference(unit_resolution,[status(thm)],[1043, 513, 65, 606, 1040])).
% 0.51/0.66 tff(1045,plain,(~product(e_5, e_3, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.66 tff(1046,assumption,(product(e_5, e_3, e_3)), introduced(assumption)).
% 0.51/0.66 tff(1047,plain,
% 0.51/0.66 ((~equalish(e_5, e_3)) <=> (~equalish(e_5, e_3))),
% 0.51/0.66 inference(rewrite,[status(thm)],[])).
% 0.51/0.66 tff(1048,axiom,(~equalish(e_5, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_5_is_not_e_3')).
% 0.51/0.66 tff(1049,plain,
% 0.51/0.66 (~equalish(e_5, e_3)),
% 0.51/0.66 inference(modus_ponens,[status(thm)],[1048, 1047])).
% 0.51/0.66 tff(1050,plain,
% 0.51/0.66 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_5, e_3, e_3)) | (~product(e_3, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_3) | (~product(e_5, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(1051,plain,
% 0.51/0.67 ((equalish(e_5, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_5, e_3, e_3))) <=> (equalish(e_5, e_3) | (~product(e_5, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(1052,plain,
% 0.51/0.67 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_5, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_5, e_3, e_3)) | (~product(e_3, e_3, e_3))))),
% 0.51/0.67 inference(monotonicity,[status(thm)],[1051])).
% 0.51/0.67 tff(1053,plain,
% 0.51/0.67 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_5, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_3) | (~product(e_5, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.51/0.67 inference(transitivity,[status(thm)],[1052, 1050])).
% 0.51/0.67 tff(1054,plain,
% 0.51/0.67 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_5, e_3, e_3)))),
% 0.51/0.67 inference(quant_inst,[status(thm)],[])).
% 0.51/0.67 tff(1055,plain,
% 0.51/0.67 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_3) | (~product(e_5, e_3, e_3)) | (~product(e_3, e_3, e_3))),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[1054, 1053])).
% 0.51/0.67 tff(1056,plain,
% 0.51/0.67 ($false),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[1055, 1049, 91, 376, 1046])).
% 0.51/0.67 tff(1057,plain,(~product(e_5, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.67 tff(1058,plain,
% 0.51/0.67 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_3)) | (~group_element(e_5)) | product(e_5, e_3, e_1) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_4) | product(e_5, e_3, e_6) | product(e_5, e_3, e_5))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_3)) | (~group_element(e_5)) | product(e_5, e_3, e_1) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_4) | product(e_5, e_3, e_6) | product(e_5, e_3, e_5))),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(1059,plain,
% 0.51/0.67 ((product(e_5, e_3, e_6) | product(e_5, e_3, e_5) | product(e_5, e_3, e_4) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_5))) <=> ((~group_element(e_3)) | (~group_element(e_5)) | product(e_5, e_3, e_1) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_4) | product(e_5, e_3, e_6) | product(e_5, e_3, e_5))),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(1060,plain,
% 0.51/0.67 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_3, e_6) | product(e_5, e_3, e_5) | product(e_5, e_3, e_4) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_5)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_3)) | (~group_element(e_5)) | product(e_5, e_3, e_1) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_4) | product(e_5, e_3, e_6) | product(e_5, e_3, e_5)))),
% 0.51/0.67 inference(monotonicity,[status(thm)],[1059])).
% 0.51/0.67 tff(1061,plain,
% 0.51/0.67 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_3, e_6) | product(e_5, e_3, e_5) | product(e_5, e_3, e_4) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_5)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_3)) | (~group_element(e_5)) | product(e_5, e_3, e_1) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_4) | product(e_5, e_3, e_6) | product(e_5, e_3, e_5))),
% 0.51/0.67 inference(transitivity,[status(thm)],[1060, 1058])).
% 0.51/0.67 tff(1062,plain,
% 0.51/0.67 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_3, e_6) | product(e_5, e_3, e_5) | product(e_5, e_3, e_4) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_5)))),
% 0.51/0.67 inference(quant_inst,[status(thm)],[])).
% 0.51/0.67 tff(1063,plain,
% 0.51/0.67 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_3)) | (~group_element(e_5)) | product(e_5, e_3, e_1) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_4) | product(e_5, e_3, e_6) | product(e_5, e_3, e_5)),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[1062, 1061])).
% 0.51/0.67 tff(1064,plain,
% 0.51/0.67 (product(e_5, e_3, e_1) | product(e_5, e_3, e_3) | product(e_5, e_3, e_2) | product(e_5, e_3, e_4) | product(e_5, e_3, e_6) | product(e_5, e_3, e_5)),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[1063, 202, 454, 136])).
% 0.51/0.67 tff(1065,plain,
% 0.51/0.67 (product(e_5, e_3, e_1) | product(e_5, e_3, e_2) | product(e_5, e_3, e_4) | product(e_5, e_3, e_6) | product(e_5, e_3, e_5)),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[1064, 1057])).
% 0.51/0.67 tff(1066,plain,
% 0.51/0.67 (product(e_5, e_3, e_1) | product(e_5, e_3, e_2) | product(e_5, e_3, e_4) | product(e_5, e_3, e_6)),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[1065, 1045])).
% 0.51/0.67 tff(1067,plain,
% 0.51/0.67 (product(e_5, e_3, e_2) | product(e_5, e_3, e_4)),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[1066, 1039, 1026])).
% 0.51/0.67 tff(1068,plain,
% 0.51/0.67 (product(e_5, e_3, e_4)),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[1067, 1002])).
% 0.51/0.67 tff(1069,assumption,(product(e_6, e_3, e_4)), introduced(assumption)).
% 0.51/0.67 tff(1070,assumption,(product(e_5, e_3, e_4)), introduced(assumption)).
% 0.51/0.67 tff(1071,plain,
% 0.51/0.67 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_6) | (~product(e_5, e_3, e_4)) | (~product(e_6, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_6) | (~product(e_5, e_3, e_4)) | (~product(e_6, e_3, e_4)))),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(1072,plain,
% 0.51/0.67 ((equalish(e_5, e_6) | (~product(e_6, e_3, e_4)) | (~product(e_5, e_3, e_4))) <=> (equalish(e_5, e_6) | (~product(e_5, e_3, e_4)) | (~product(e_6, e_3, e_4)))),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(1073,plain,
% 0.51/0.67 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_6) | (~product(e_6, e_3, e_4)) | (~product(e_5, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_6) | (~product(e_5, e_3, e_4)) | (~product(e_6, e_3, e_4))))),
% 0.51/0.67 inference(monotonicity,[status(thm)],[1072])).
% 0.51/0.67 tff(1074,plain,
% 0.51/0.67 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_6) | (~product(e_6, e_3, e_4)) | (~product(e_5, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_6) | (~product(e_5, e_3, e_4)) | (~product(e_6, e_3, e_4)))),
% 0.51/0.67 inference(transitivity,[status(thm)],[1073, 1071])).
% 0.51/0.67 tff(1075,plain,
% 0.51/0.67 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_6) | (~product(e_6, e_3, e_4)) | (~product(e_5, e_3, e_4)))),
% 0.51/0.67 inference(quant_inst,[status(thm)],[])).
% 0.51/0.67 tff(1076,plain,
% 0.51/0.67 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_6) | (~product(e_5, e_3, e_4)) | (~product(e_6, e_3, e_4))),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[1075, 1074])).
% 0.51/0.67 tff(1077,plain,
% 0.51/0.67 ($false),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[1076, 465, 91, 1070, 1069])).
% 0.51/0.67 tff(1078,plain,((~product(e_5, e_3, e_4)) | (~product(e_6, e_3, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.67 tff(1079,plain,
% 0.51/0.67 (~product(e_6, e_3, e_4)),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[1078, 1068])).
% 0.51/0.67 tff(1080,plain,
% 0.51/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_3, e_6)) | product(e_6, e_3, e_4) | (~product(e_3, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_6)) | product(e_6, e_3, e_4) | (~product(e_3, e_4, e_1)))),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(1081,plain,
% 0.51/0.67 ((product(e_6, e_3, e_4) | (~product(e_1, e_3, e_6)) | (~product(e_3, e_4, e_1))) <=> ((~product(e_1, e_3, e_6)) | product(e_6, e_3, e_4) | (~product(e_3, e_4, e_1)))),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(1082,plain,
% 0.51/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_6, e_3, e_4) | (~product(e_1, e_3, e_6)) | (~product(e_3, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_3, e_6)) | product(e_6, e_3, e_4) | (~product(e_3, e_4, e_1))))),
% 0.51/0.67 inference(monotonicity,[status(thm)],[1081])).
% 0.51/0.67 tff(1083,plain,
% 0.51/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_6, e_3, e_4) | (~product(e_1, e_3, e_6)) | (~product(e_3, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_6)) | product(e_6, e_3, e_4) | (~product(e_3, e_4, e_1)))),
% 0.51/0.67 inference(transitivity,[status(thm)],[1082, 1080])).
% 0.51/0.67 tff(1084,plain,
% 0.51/0.67 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_6, e_3, e_4) | (~product(e_1, e_3, e_6)) | (~product(e_3, e_4, e_1)))),
% 0.51/0.67 inference(quant_inst,[status(thm)],[])).
% 0.51/0.67 tff(1085,plain,
% 0.51/0.67 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_6)) | product(e_6, e_3, e_4) | (~product(e_3, e_4, e_1))),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[1084, 1083])).
% 0.51/0.67 tff(1086,plain,
% 0.51/0.67 ($false),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[1085, 35, 954, 1079, 2])).
% 0.51/0.67 tff(1087,plain,(~product(e_3, e_4, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.67 tff(1088,plain,
% 0.51/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_4, e_5)) | (~product(e_5, e_3, e_4)) | product(e_4, e_3, e_4))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_4, e_5)) | (~product(e_5, e_3, e_4)) | product(e_4, e_3, e_4))),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(1089,plain,
% 0.51/0.67 ((product(e_4, e_3, e_4) | (~product(e_5, e_3, e_4)) | (~product(e_3, e_4, e_5))) <=> ((~product(e_3, e_4, e_5)) | (~product(e_5, e_3, e_4)) | product(e_4, e_3, e_4))),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(1090,plain,
% 0.51/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_3, e_4) | (~product(e_5, e_3, e_4)) | (~product(e_3, e_4, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_4, e_5)) | (~product(e_5, e_3, e_4)) | product(e_4, e_3, e_4)))),
% 0.51/0.67 inference(monotonicity,[status(thm)],[1089])).
% 0.51/0.67 tff(1091,plain,
% 0.51/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_3, e_4) | (~product(e_5, e_3, e_4)) | (~product(e_3, e_4, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_4, e_5)) | (~product(e_5, e_3, e_4)) | product(e_4, e_3, e_4))),
% 0.51/0.67 inference(transitivity,[status(thm)],[1090, 1088])).
% 0.51/0.67 tff(1092,plain,
% 0.51/0.67 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_3, e_4) | (~product(e_5, e_3, e_4)) | (~product(e_3, e_4, e_5)))),
% 0.51/0.67 inference(quant_inst,[status(thm)],[])).
% 0.51/0.67 tff(1093,plain,
% 0.51/0.67 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_4, e_5)) | (~product(e_5, e_3, e_4)) | product(e_4, e_3, e_4)),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[1092, 1091])).
% 0.51/0.67 tff(1094,plain,
% 0.51/0.67 (~product(e_3, e_4, e_5)),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[1093, 35, 1068, 980])).
% 0.51/0.67 tff(1095,assumption,(product(e_3, e_4, e_4)), introduced(assumption)).
% 0.51/0.67 tff(1096,plain,
% 0.51/0.67 ((~![X: $i] : product(X, X, X)) | product(e_4, e_4, e_4)),
% 0.51/0.67 inference(quant_inst,[status(thm)],[])).
% 0.51/0.67 tff(1097,plain,
% 0.51/0.67 (product(e_4, e_4, e_4)),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[1096, 52])).
% 0.51/0.67 tff(1098,plain,
% 0.51/0.67 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_4, e_4)))),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(1099,plain,
% 0.51/0.67 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_4, e_4)))),
% 0.51/0.67 inference(quant_inst,[status(thm)],[])).
% 0.51/0.67 tff(1100,plain,
% 0.51/0.67 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_4, e_4))),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[1099, 1098])).
% 0.51/0.67 tff(1101,plain,
% 0.51/0.67 ($false),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[1100, 539, 91, 1097, 1095])).
% 0.51/0.67 tff(1102,plain,(~product(e_3, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.67 tff(1103,assumption,(product(e_3, e_4, e_3)), introduced(assumption)).
% 0.51/0.67 tff(1104,plain,
% 0.51/0.67 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_3, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(1105,plain,
% 0.51/0.67 ((equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3))) <=> (equalish(e_4, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(1106,plain,
% 0.51/0.67 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_3, e_3, e_3))))),
% 0.51/0.67 inference(monotonicity,[status(thm)],[1105])).
% 0.51/0.67 tff(1107,plain,
% 0.51/0.67 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.51/0.67 inference(transitivity,[status(thm)],[1106, 1104])).
% 0.51/0.67 tff(1108,plain,
% 0.51/0.67 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3)))),
% 0.51/0.67 inference(quant_inst,[status(thm)],[])).
% 0.51/0.67 tff(1109,plain,
% 0.51/0.67 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_3, e_4, e_3)) | (~product(e_3, e_3, e_3))),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[1108, 1107])).
% 0.51/0.67 tff(1110,plain,
% 0.51/0.67 ($false),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[1109, 495, 65, 376, 1103])).
% 0.51/0.67 tff(1111,plain,(~product(e_3, e_4, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.67 tff(1112,assumption,(product(e_3, e_4, e_2)), introduced(assumption)).
% 0.51/0.67 tff(1113,plain,
% 0.51/0.67 (~product(e_1, e_4, e_6)),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[544, 954])).
% 0.51/0.67 tff(1114,plain,
% 0.51/0.67 (~product(e_1, e_2, e_4)),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[587, 887])).
% 0.51/0.67 tff(1115,plain,
% 0.51/0.67 (~product(e_1, e_2, e_3)),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[791, 907])).
% 0.51/0.67 tff(1116,assumption,(product(e_1, e_2, e_6)), introduced(assumption)).
% 0.51/0.67 tff(1117,plain,
% 0.51/0.67 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_1, e_3, e_6)) | (~product(e_1, e_2, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_1, e_3, e_6)) | (~product(e_1, e_2, e_6)))),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(1118,plain,
% 0.51/0.67 ((equalish(e_3, e_2) | (~product(e_1, e_2, e_6)) | (~product(e_1, e_3, e_6))) <=> (equalish(e_3, e_2) | (~product(e_1, e_3, e_6)) | (~product(e_1, e_2, e_6)))),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(1119,plain,
% 0.51/0.67 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_1, e_2, e_6)) | (~product(e_1, e_3, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_1, e_3, e_6)) | (~product(e_1, e_2, e_6))))),
% 0.51/0.67 inference(monotonicity,[status(thm)],[1118])).
% 0.51/0.67 tff(1120,plain,
% 0.51/0.67 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_1, e_2, e_6)) | (~product(e_1, e_3, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_1, e_3, e_6)) | (~product(e_1, e_2, e_6)))),
% 0.51/0.67 inference(transitivity,[status(thm)],[1119, 1117])).
% 0.51/0.67 tff(1121,plain,
% 0.51/0.67 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_1, e_2, e_6)) | (~product(e_1, e_3, e_6)))),
% 0.51/0.67 inference(quant_inst,[status(thm)],[])).
% 0.51/0.67 tff(1122,plain,
% 0.51/0.67 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_1, e_3, e_6)) | (~product(e_1, e_2, e_6))),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[1121, 1120])).
% 0.51/0.67 tff(1123,plain,
% 0.51/0.67 ($false),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[1122, 165, 65, 474, 1116])).
% 0.51/0.67 tff(1124,plain,((~product(e_1, e_3, e_6)) | (~product(e_1, e_2, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.67 tff(1125,plain,
% 0.51/0.67 (~product(e_1, e_2, e_6)),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[1124, 954])).
% 0.51/0.67 tff(1126,plain,
% 0.51/0.67 (product(e_1, e_2, e_5)),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[659, 1125, 1115, 1114])).
% 0.51/0.67 tff(1127,plain,
% 0.51/0.67 ((~equalish(e_4, e_2)) <=> (~equalish(e_4, e_2))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(1128,axiom,(~equalish(e_4, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_2')).
% 0.51/0.68 tff(1129,plain,
% 0.51/0.68 (~equalish(e_4, e_2)),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[1128, 1127])).
% 0.51/0.68 tff(1130,plain,
% 0.51/0.68 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_1, e_4, e_5)) | (~product(e_1, e_2, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_2) | (~product(e_1, e_4, e_5)) | (~product(e_1, e_2, e_5)))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(1131,plain,
% 0.51/0.68 ((equalish(e_4, e_2) | (~product(e_1, e_2, e_5)) | (~product(e_1, e_4, e_5))) <=> (equalish(e_4, e_2) | (~product(e_1, e_4, e_5)) | (~product(e_1, e_2, e_5)))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(1132,plain,
% 0.51/0.68 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_1, e_2, e_5)) | (~product(e_1, e_4, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_1, e_4, e_5)) | (~product(e_1, e_2, e_5))))),
% 0.51/0.68 inference(monotonicity,[status(thm)],[1131])).
% 0.51/0.68 tff(1133,plain,
% 0.51/0.68 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_1, e_2, e_5)) | (~product(e_1, e_4, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_2) | (~product(e_1, e_4, e_5)) | (~product(e_1, e_2, e_5)))),
% 0.51/0.68 inference(transitivity,[status(thm)],[1132, 1130])).
% 0.51/0.68 tff(1134,plain,
% 0.51/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_1, e_2, e_5)) | (~product(e_1, e_4, e_5)))),
% 0.51/0.68 inference(quant_inst,[status(thm)],[])).
% 0.51/0.68 tff(1135,plain,
% 0.51/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_2) | (~product(e_1, e_4, e_5)) | (~product(e_1, e_2, e_5))),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[1134, 1133])).
% 0.51/0.68 tff(1136,plain,
% 0.51/0.68 ($false),
% 0.51/0.68 inference(unit_resolution,[status(thm)],[1135, 1129, 65, 334, 622])).
% 0.51/0.68 tff(1137,plain,((~product(e_1, e_4, e_5)) | (~product(e_1, e_2, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.68 tff(1138,plain,
% 0.51/0.68 (~product(e_1, e_4, e_5)),
% 0.51/0.68 inference(unit_resolution,[status(thm)],[1137, 1126])).
% 0.51/0.68 tff(1139,plain,
% 0.51/0.68 ((~equalish(e_1, e_4)) <=> (~equalish(e_1, e_4))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(1140,axiom,(~equalish(e_1, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_4')).
% 0.51/0.68 tff(1141,plain,
% 0.51/0.68 (~equalish(e_1, e_4)),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[1140, 1139])).
% 0.51/0.68 tff(1142,plain,
% 0.51/0.68 (((~![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_1, e_4, e_4)) | (~product(e_4, 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_1, e_4, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(1143,plain,
% 0.51/0.68 ((equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_1, e_4, e_4))) <=> (equalish(e_1, e_4) | (~product(e_1, e_4, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(1144,plain,
% 0.51/0.68 (((~![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_1, e_4, e_4)) | (~product(e_4, e_4, e_4))))),
% 0.51/0.68 inference(monotonicity,[status(thm)],[1143])).
% 0.51/0.68 tff(1145,plain,
% 0.51/0.68 (((~![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_1, e_4, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.51/0.68 inference(transitivity,[status(thm)],[1144, 1142])).
% 0.51/0.68 tff(1146,plain,
% 0.51/0.68 ((~![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)))),
% 0.51/0.68 inference(quant_inst,[status(thm)],[])).
% 0.51/0.68 tff(1147,plain,
% 0.51/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_4) | (~product(e_1, e_4, e_4)) | (~product(e_4, e_4, e_4))),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[1146, 1145])).
% 0.51/0.68 tff(1148,plain,
% 0.51/0.68 ($false),
% 0.51/0.68 inference(unit_resolution,[status(thm)],[1147, 1141, 91, 442, 1097])).
% 0.51/0.68 tff(1149,plain,(~product(e_1, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.68 tff(1150,assumption,(product(e_4, e_1, e_4)), introduced(assumption)).
% 0.51/0.68 tff(1151,plain,
% 0.51/0.68 (((~![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)))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(1152,plain,
% 0.51/0.68 ((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)))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(1153,plain,
% 0.51/0.68 (((~![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))))),
% 0.51/0.68 inference(monotonicity,[status(thm)],[1152])).
% 0.51/0.68 tff(1154,plain,
% 0.51/0.68 (((~![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)))),
% 0.51/0.68 inference(transitivity,[status(thm)],[1153, 1151])).
% 0.51/0.68 tff(1155,plain,
% 0.51/0.68 ((~![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)))),
% 0.51/0.68 inference(quant_inst,[status(thm)],[])).
% 0.51/0.68 tff(1156,plain,
% 0.51/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_4, e_1, e_4)) | (~product(e_3, e_1, e_4))),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[1155, 1154])).
% 0.51/0.68 tff(1157,plain,
% 0.51/0.68 ($false),
% 0.51/0.68 inference(unit_resolution,[status(thm)],[1156, 495, 91, 236, 1150])).
% 0.51/0.68 tff(1158,plain,((~product(e_4, e_1, e_4)) | (~product(e_3, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.68 tff(1159,plain,
% 0.51/0.68 (~product(e_4, e_1, e_4)),
% 0.51/0.68 inference(unit_resolution,[status(thm)],[1158, 671])).
% 0.51/0.68 tff(1160,plain,
% 0.51/0.68 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_4)))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(1161,plain,
% 0.51/0.68 ((product(e_4, e_1, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_4, e_3))) <=> (product(e_4, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_4)))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(1162,plain,
% 0.51/0.68 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_4))))),
% 0.51/0.68 inference(monotonicity,[status(thm)],[1161])).
% 0.51/0.68 tff(1163,plain,
% 0.51/0.68 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_4)))),
% 0.51/0.68 inference(transitivity,[status(thm)],[1162, 1160])).
% 0.51/0.68 tff(1164,plain,
% 0.51/0.68 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_4, e_3)))),
% 0.51/0.68 inference(quant_inst,[status(thm)],[])).
% 0.51/0.68 tff(1165,plain,
% 0.51/0.68 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_4))),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[1164, 1163])).
% 0.51/0.68 tff(1166,plain,
% 0.51/0.68 (product(e_4, e_1, e_4) | (~product(e_1, e_4, e_3)) | (~product(e_3, e_1, e_4))),
% 0.51/0.68 inference(unit_resolution,[status(thm)],[1165, 35])).
% 0.51/0.68 tff(1167,plain,
% 0.51/0.68 (~product(e_1, e_4, e_3)),
% 0.51/0.68 inference(unit_resolution,[status(thm)],[1166, 1159, 671])).
% 0.51/0.68 tff(1168,plain,
% 0.51/0.68 (product(e_1, e_4, e_6) | product(e_1, e_4, e_5) | product(e_1, e_4, e_2)),
% 0.51/0.68 inference(unit_resolution,[status(thm)],[567, 1167, 1149])).
% 0.51/0.68 tff(1169,plain,
% 0.51/0.68 (product(e_1, e_4, e_2)),
% 0.51/0.68 inference(unit_resolution,[status(thm)],[1168, 1138, 1113])).
% 0.51/0.68 tff(1170,plain,
% 0.51/0.68 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_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)))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(1171,plain,
% 0.51/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_4, e_2)) | (~product(e_3, e_4, e_2)))),
% 0.51/0.68 inference(quant_inst,[status(thm)],[])).
% 0.51/0.68 tff(1172,plain,
% 0.51/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_4, e_2)) | (~product(e_3, e_4, e_2))),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[1171, 1170])).
% 0.51/0.68 tff(1173,plain,
% 0.51/0.68 ($false),
% 0.51/0.68 inference(unit_resolution,[status(thm)],[1172, 177, 91, 1169, 1112])).
% 0.51/0.68 tff(1174,plain,(~product(e_3, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.68 tff(1175,plain,
% 0.51/0.68 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_3)) | (~group_element(e_4)) | product(e_3, e_4, e_1) | product(e_3, e_4, e_5) | product(e_3, e_4, e_2) | product(e_3, e_4, e_6) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_3)) | (~group_element(e_4)) | product(e_3, e_4, e_1) | product(e_3, e_4, e_5) | product(e_3, e_4, e_2) | product(e_3, e_4, e_6) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(1176,plain,
% 0.51/0.68 ((product(e_3, e_4, e_6) | product(e_3, e_4, e_5) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_3))) <=> ((~group_element(e_3)) | (~group_element(e_4)) | product(e_3, e_4, e_1) | product(e_3, e_4, e_5) | product(e_3, e_4, e_2) | product(e_3, e_4, e_6) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(1177,plain,
% 0.51/0.68 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_4, e_6) | product(e_3, e_4, e_5) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_3)) | (~group_element(e_4)) | product(e_3, e_4, e_1) | product(e_3, e_4, e_5) | product(e_3, e_4, e_2) | product(e_3, e_4, e_6) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3)))),
% 0.51/0.68 inference(monotonicity,[status(thm)],[1176])).
% 0.51/0.68 tff(1178,plain,
% 0.51/0.68 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_4, e_6) | product(e_3, e_4, e_5) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_3)) | (~group_element(e_4)) | product(e_3, e_4, e_1) | product(e_3, e_4, e_5) | product(e_3, e_4, e_2) | product(e_3, e_4, e_6) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3))),
% 0.51/0.68 inference(transitivity,[status(thm)],[1177, 1175])).
% 0.51/0.68 tff(1179,plain,
% 0.51/0.68 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_4, e_6) | product(e_3, e_4, e_5) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_3)))),
% 0.51/0.68 inference(quant_inst,[status(thm)],[])).
% 0.51/0.68 tff(1180,plain,
% 0.51/0.68 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_3)) | (~group_element(e_4)) | product(e_3, e_4, e_1) | product(e_3, e_4, e_5) | product(e_3, e_4, e_2) | product(e_3, e_4, e_6) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3)),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[1179, 1178])).
% 0.51/0.68 tff(1181,plain,
% 0.51/0.68 (product(e_3, e_4, e_1) | product(e_3, e_4, e_5) | product(e_3, e_4, e_6) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3)),
% 0.51/0.68 inference(unit_resolution,[status(thm)],[1180, 202, 432, 136, 1174])).
% 0.51/0.68 tff(1182,plain,
% 0.51/0.68 (product(e_3, e_4, e_1) | product(e_3, e_4, e_5) | product(e_3, e_4, e_6) | product(e_3, e_4, e_4)),
% 0.51/0.68 inference(unit_resolution,[status(thm)],[1181, 1111])).
% 0.51/0.68 tff(1183,plain,
% 0.51/0.68 (product(e_3, e_4, e_1) | product(e_3, e_4, e_5) | product(e_3, e_4, e_6)),
% 0.51/0.68 inference(unit_resolution,[status(thm)],[1182, 1102])).
% 0.51/0.68 tff(1184,plain,
% 0.51/0.68 (product(e_3, e_4, e_1) | product(e_3, e_4, e_6)),
% 0.51/0.68 inference(unit_resolution,[status(thm)],[1183, 1094])).
% 0.51/0.68 tff(1185,plain,
% 0.51/0.68 (product(e_3, e_4, e_6)),
% 0.51/0.68 inference(unit_resolution,[status(thm)],[1184, 1087])).
% 0.51/0.68 tff(1186,assumption,(product(e_6, e_4, e_6)), introduced(assumption)).
% 0.51/0.68 tff(1187,plain,
% 0.51/0.68 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_6, e_4, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_6, e_4, e_6)))),
% 0.51/0.69 inference(rewrite,[status(thm)],[])).
% 0.51/0.69 tff(1188,plain,
% 0.51/0.69 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_6, e_4, e_6)))),
% 0.51/0.69 inference(quant_inst,[status(thm)],[])).
% 0.51/0.69 tff(1189,plain,
% 0.51/0.69 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_6, e_4, e_6))),
% 0.51/0.69 inference(modus_ponens,[status(thm)],[1188, 1187])).
% 0.51/0.69 tff(1190,plain,
% 0.51/0.69 ($false),
% 0.51/0.69 inference(unit_resolution,[status(thm)],[1189, 337, 65, 300, 1186])).
% 0.51/0.69 tff(1191,plain,(~product(e_6, e_4, e_6)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.69 tff(1192,plain,
% 0.51/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_6, e_4, e_6) | (~product(e_3, e_4, e_6)) | (~product(e_4, e_6, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_6, e_4, e_6) | (~product(e_3, e_4, e_6)) | (~product(e_4, e_6, e_3)))),
% 0.51/0.69 inference(rewrite,[status(thm)],[])).
% 0.51/0.69 tff(1193,plain,
% 0.51/0.69 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_6, e_4, e_6) | (~product(e_3, e_4, e_6)) | (~product(e_4, e_6, e_3)))),
% 0.51/0.69 inference(quant_inst,[status(thm)],[])).
% 0.51/0.69 tff(1194,plain,
% 0.51/0.69 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_6, e_4, e_6) | (~product(e_3, e_4, e_6)) | (~product(e_4, e_6, e_3))),
% 0.51/0.69 inference(modus_ponens,[status(thm)],[1193, 1192])).
% 0.51/0.69 tff(1195,plain,
% 0.51/0.69 (~product(e_4, e_6, e_3)),
% 0.51/0.69 inference(unit_resolution,[status(thm)],[1194, 35, 1191, 1185])).
% 0.51/0.69 tff(1196,assumption,(product(e_6, e_3, e_1)), introduced(assumption)).
% 0.51/0.69 tff(1197,assumption,(~product(e_4, e_6, e_3)), introduced(assumption)).
% 0.51/0.69 tff(1198,plain,
% 0.51/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_6, e_4)) | product(e_4, e_6, e_3) | (~product(e_6, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_6, e_4)) | product(e_4, e_6, e_3) | (~product(e_6, e_3, e_1)))),
% 0.51/0.69 inference(rewrite,[status(thm)],[])).
% 0.51/0.69 tff(1199,plain,
% 0.51/0.69 ((product(e_4, e_6, e_3) | (~product(e_1, e_6, e_4)) | (~product(e_6, e_3, e_1))) <=> ((~product(e_1, e_6, e_4)) | product(e_4, e_6, e_3) | (~product(e_6, e_3, e_1)))),
% 0.51/0.69 inference(rewrite,[status(thm)],[])).
% 0.51/0.69 tff(1200,plain,
% 0.51/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_6, e_3) | (~product(e_1, e_6, e_4)) | (~product(e_6, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_6, e_4)) | product(e_4, e_6, e_3) | (~product(e_6, e_3, e_1))))),
% 0.51/0.69 inference(monotonicity,[status(thm)],[1199])).
% 0.51/0.69 tff(1201,plain,
% 0.51/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_6, e_3) | (~product(e_1, e_6, e_4)) | (~product(e_6, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_6, e_4)) | product(e_4, e_6, e_3) | (~product(e_6, e_3, e_1)))),
% 0.51/0.69 inference(transitivity,[status(thm)],[1200, 1198])).
% 0.51/0.69 tff(1202,plain,
% 0.51/0.69 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_6, e_3) | (~product(e_1, e_6, e_4)) | (~product(e_6, e_3, e_1)))),
% 0.51/0.69 inference(quant_inst,[status(thm)],[])).
% 0.51/0.69 tff(1203,plain,
% 0.51/0.69 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_6, e_4)) | product(e_4, e_6, e_3) | (~product(e_6, e_3, e_1))),
% 0.51/0.69 inference(modus_ponens,[status(thm)],[1202, 1201])).
% 0.51/0.69 tff(1204,plain,
% 0.51/0.69 ($false),
% 0.51/0.69 inference(unit_resolution,[status(thm)],[1203, 35, 887, 1197, 1196])).
% 0.51/0.69 tff(1205,plain,(product(e_4, e_6, e_3) | (~product(e_6, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.69 tff(1206,plain,
% 0.51/0.69 (~product(e_6, e_3, e_1)),
% 0.51/0.69 inference(unit_resolution,[status(thm)],[1205, 1195])).
% 0.51/0.69 tff(1207,assumption,(product(e_6, e_3, e_6)), introduced(assumption)).
% 0.51/0.69 tff(1208,plain,
% 0.51/0.69 ((~equalish(e_6, e_1)) <=> (~equalish(e_6, e_1))),
% 0.51/0.69 inference(rewrite,[status(thm)],[])).
% 0.51/0.69 tff(1209,axiom,(~equalish(e_6, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_6_is_not_e_1')).
% 0.51/0.69 tff(1210,plain,
% 0.51/0.69 (~equalish(e_6, e_1)),
% 0.51/0.69 inference(modus_ponens,[status(thm)],[1209, 1208])).
% 0.51/0.69 tff(1211,plain,
% 0.51/0.69 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_1) | (~product(e_1, e_3, e_6)) | (~product(e_6, e_3, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_1) | (~product(e_1, e_3, e_6)) | (~product(e_6, e_3, e_6)))),
% 0.51/0.69 inference(rewrite,[status(thm)],[])).
% 0.51/0.69 tff(1212,plain,
% 0.51/0.69 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_1) | (~product(e_1, e_3, e_6)) | (~product(e_6, e_3, e_6)))),
% 0.51/0.69 inference(quant_inst,[status(thm)],[])).
% 0.51/0.69 tff(1213,plain,
% 0.51/0.69 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_1) | (~product(e_1, e_3, e_6)) | (~product(e_6, e_3, e_6))),
% 0.51/0.69 inference(modus_ponens,[status(thm)],[1212, 1211])).
% 0.51/0.69 tff(1214,plain,
% 0.51/0.69 ($false),
% 0.51/0.69 inference(unit_resolution,[status(thm)],[1213, 1210, 91, 954, 1207])).
% 0.51/0.69 tff(1215,plain,(~product(e_6, e_3, e_6)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.69 tff(1216,assumption,(product(e_6, e_3, e_2)), introduced(assumption)).
% 0.51/0.69 tff(1217,assumption,(product(e_6, e_1, e_5)), introduced(assumption)).
% 0.51/0.69 tff(1218,plain,
% 0.51/0.69 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_4) | (~product(e_4, e_1, e_5)) | (~product(e_6, e_1, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_4) | (~product(e_4, e_1, e_5)) | (~product(e_6, e_1, e_5)))),
% 0.51/0.69 inference(rewrite,[status(thm)],[])).
% 0.51/0.69 tff(1219,plain,
% 0.51/0.69 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_4) | (~product(e_4, e_1, e_5)) | (~product(e_6, e_1, e_5)))),
% 0.51/0.69 inference(quant_inst,[status(thm)],[])).
% 0.51/0.69 tff(1220,plain,
% 0.51/0.69 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_4) | (~product(e_4, e_1, e_5)) | (~product(e_6, e_1, e_5))),
% 0.51/0.69 inference(modus_ponens,[status(thm)],[1219, 1218])).
% 0.51/0.69 tff(1221,plain,
% 0.51/0.69 ($false),
% 0.51/0.69 inference(unit_resolution,[status(thm)],[1220, 526, 91, 926, 1217])).
% 0.51/0.69 tff(1222,plain,((~product(e_6, e_1, e_5)) | (~product(e_4, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.69 tff(1223,plain,
% 0.51/0.69 (~product(e_6, e_1, e_5)),
% 0.51/0.69 inference(unit_resolution,[status(thm)],[1222, 908])).
% 0.51/0.69 tff(1224,plain,
% 0.51/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_1, e_3, e_6)) | (~product(e_6, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_3) | (~product(e_1, e_3, e_6)) | (~product(e_6, e_1, e_1)))),
% 0.51/0.69 inference(rewrite,[status(thm)],[])).
% 0.51/0.69 tff(1225,plain,
% 0.51/0.69 ((product(e_1, e_1, e_3) | (~product(e_6, e_1, e_1)) | (~product(e_1, e_3, e_6))) <=> (product(e_1, e_1, e_3) | (~product(e_1, e_3, e_6)) | (~product(e_6, e_1, e_1)))),
% 0.51/0.69 inference(rewrite,[status(thm)],[])).
% 0.51/0.69 tff(1226,plain,
% 0.51/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_6, e_1, e_1)) | (~product(e_1, e_3, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_1, e_3, e_6)) | (~product(e_6, e_1, e_1))))),
% 0.51/0.69 inference(monotonicity,[status(thm)],[1225])).
% 0.51/0.69 tff(1227,plain,
% 0.51/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_6, e_1, e_1)) | (~product(e_1, e_3, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_3) | (~product(e_1, e_3, e_6)) | (~product(e_6, e_1, e_1)))),
% 0.51/0.69 inference(transitivity,[status(thm)],[1226, 1224])).
% 0.51/0.69 tff(1228,plain,
% 0.51/0.69 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_6, e_1, e_1)) | (~product(e_1, e_3, e_6)))),
% 0.51/0.69 inference(quant_inst,[status(thm)],[])).
% 0.51/0.69 tff(1229,plain,
% 0.51/0.69 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_3) | (~product(e_1, e_3, e_6)) | (~product(e_6, e_1, e_1))),
% 0.51/0.69 inference(modus_ponens,[status(thm)],[1228, 1227])).
% 0.51/0.69 tff(1230,plain,
% 0.51/0.69 ($false),
% 0.51/0.69 inference(unit_resolution,[status(thm)],[1229, 35, 398, 474, 5])).
% 0.51/0.69 tff(1231,plain,((~product(e_6, e_1, e_1)) | (~product(e_1, e_3, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.69 tff(1232,plain,
% 0.51/0.69 (~product(e_6, e_1, e_1)),
% 0.51/0.69 inference(unit_resolution,[status(thm)],[1231, 954])).
% 0.51/0.69 tff(1233,plain,
% 0.51/0.69 (product(e_6, e_1, e_2)),
% 0.51/0.69 inference(unit_resolution,[status(thm)],[896, 1232, 676, 159, 1223])).
% 0.51/0.69 tff(1234,plain,
% 0.51/0.69 (((~![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_6, e_3, e_2)) | (~product(e_6, 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_3, e_1) | (~product(e_6, e_3, e_2)) | (~product(e_6, e_1, e_2)))),
% 0.51/0.69 inference(rewrite,[status(thm)],[])).
% 0.51/0.69 tff(1235,plain,
% 0.51/0.69 ((equalish(e_3, e_1) | (~product(e_6, e_1, e_2)) | (~product(e_6, e_3, e_2))) <=> (equalish(e_3, e_1) | (~product(e_6, e_3, e_2)) | (~product(e_6, e_1, e_2)))),
% 0.51/0.69 inference(rewrite,[status(thm)],[])).
% 0.51/0.69 tff(1236,plain,
% 0.51/0.69 (((~![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_6, e_1, e_2)) | (~product(e_6, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_6, e_3, e_2)) | (~product(e_6, e_1, e_2))))),
% 0.51/0.69 inference(monotonicity,[status(thm)],[1235])).
% 0.51/0.69 tff(1237,plain,
% 0.51/0.69 (((~![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_6, e_1, e_2)) | (~product(e_6, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_6, e_3, e_2)) | (~product(e_6, e_1, e_2)))),
% 0.51/0.69 inference(transitivity,[status(thm)],[1236, 1234])).
% 0.51/0.69 tff(1238,plain,
% 0.51/0.69 ((~![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_6, e_1, e_2)) | (~product(e_6, e_3, e_2)))),
% 0.51/0.69 inference(quant_inst,[status(thm)],[])).
% 0.51/0.69 tff(1239,plain,
% 0.51/0.69 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_6, e_3, e_2)) | (~product(e_6, e_1, e_2))),
% 0.51/0.69 inference(modus_ponens,[status(thm)],[1238, 1237])).
% 0.51/0.69 tff(1240,plain,
% 0.51/0.69 ($false),
% 0.51/0.69 inference(unit_resolution,[status(thm)],[1239, 177, 65, 1233, 1216])).
% 0.51/0.69 tff(1241,plain,(~product(e_6, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.69 tff(1242,assumption,(product(e_6, e_3, e_3)), introduced(assumption)).
% 0.51/0.69 tff(1243,plain,
% 0.51/0.69 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_3) | (~product(e_6, e_3, e_3)) | (~product(e_3, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_3) | (~product(e_6, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.51/0.69 inference(rewrite,[status(thm)],[])).
% 0.51/0.69 tff(1244,plain,
% 0.51/0.69 ((equalish(e_6, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_6, e_3, e_3))) <=> (equalish(e_6, e_3) | (~product(e_6, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.51/0.69 inference(rewrite,[status(thm)],[])).
% 0.51/0.69 tff(1245,plain,
% 0.51/0.69 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_6, 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_6, e_3) | (~product(e_6, e_3, e_3)) | (~product(e_3, e_3, e_3))))),
% 0.51/0.69 inference(monotonicity,[status(thm)],[1244])).
% 0.51/0.69 tff(1246,plain,
% 0.51/0.69 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_6, 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_6, e_3) | (~product(e_6, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.51/0.69 inference(transitivity,[status(thm)],[1245, 1243])).
% 0.51/0.69 tff(1247,plain,
% 0.51/0.69 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_6, e_3, e_3)))),
% 0.51/0.69 inference(quant_inst,[status(thm)],[])).
% 0.51/0.69 tff(1248,plain,
% 0.51/0.69 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_3) | (~product(e_6, e_3, e_3)) | (~product(e_3, e_3, e_3))),
% 0.51/0.69 inference(modus_ponens,[status(thm)],[1247, 1246])).
% 0.51/0.69 tff(1249,plain,
% 0.51/0.69 ($false),
% 0.51/0.69 inference(unit_resolution,[status(thm)],[1248, 355, 91, 376, 1242])).
% 0.51/0.69 tff(1250,plain,(~product(e_6, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.69 tff(1251,plain,
% 0.51/0.69 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_3)) | (~group_element(e_6)) | product(e_6, e_3, e_2) | product(e_6, e_3, e_4) | product(e_6, e_3, e_5) | product(e_6, e_3, e_6) | product(e_6, e_3, e_1) | product(e_6, e_3, e_3))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_3)) | (~group_element(e_6)) | product(e_6, e_3, e_2) | product(e_6, e_3, e_4) | product(e_6, e_3, e_5) | product(e_6, e_3, e_6) | product(e_6, e_3, e_1) | product(e_6, e_3, e_3))),
% 0.51/0.69 inference(rewrite,[status(thm)],[])).
% 0.51/0.69 tff(1252,plain,
% 0.51/0.69 ((product(e_6, e_3, e_6) | product(e_6, e_3, e_5) | product(e_6, e_3, e_4) | product(e_6, e_3, e_3) | product(e_6, e_3, e_2) | product(e_6, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_6))) <=> ((~group_element(e_3)) | (~group_element(e_6)) | product(e_6, e_3, e_2) | product(e_6, e_3, e_4) | product(e_6, e_3, e_5) | product(e_6, e_3, e_6) | product(e_6, e_3, e_1) | product(e_6, e_3, e_3))),
% 0.51/0.69 inference(rewrite,[status(thm)],[])).
% 0.51/0.69 tff(1253,plain,
% 0.51/0.69 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6, e_3, e_6) | product(e_6, e_3, e_5) | product(e_6, e_3, e_4) | product(e_6, e_3, e_3) | product(e_6, e_3, e_2) | product(e_6, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_6)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_3)) | (~group_element(e_6)) | product(e_6, e_3, e_2) | product(e_6, e_3, e_4) | product(e_6, e_3, e_5) | product(e_6, e_3, e_6) | product(e_6, e_3, e_1) | product(e_6, e_3, e_3)))),
% 0.51/0.70 inference(monotonicity,[status(thm)],[1252])).
% 0.51/0.70 tff(1254,plain,
% 0.51/0.70 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6, e_3, e_6) | product(e_6, e_3, e_5) | product(e_6, e_3, e_4) | product(e_6, e_3, e_3) | product(e_6, e_3, e_2) | product(e_6, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_6)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_3)) | (~group_element(e_6)) | product(e_6, e_3, e_2) | product(e_6, e_3, e_4) | product(e_6, e_3, e_5) | product(e_6, e_3, e_6) | product(e_6, e_3, e_1) | product(e_6, e_3, e_3))),
% 0.51/0.70 inference(transitivity,[status(thm)],[1253, 1251])).
% 0.51/0.70 tff(1255,plain,
% 0.51/0.70 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6, e_3, e_6) | product(e_6, e_3, e_5) | product(e_6, e_3, e_4) | product(e_6, e_3, e_3) | product(e_6, e_3, e_2) | product(e_6, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_6)))),
% 0.51/0.70 inference(quant_inst,[status(thm)],[])).
% 0.51/0.70 tff(1256,plain,
% 0.51/0.70 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_3)) | (~group_element(e_6)) | product(e_6, e_3, e_2) | product(e_6, e_3, e_4) | product(e_6, e_3, e_5) | product(e_6, e_3, e_6) | product(e_6, e_3, e_1) | product(e_6, e_3, e_3)),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[1255, 1254])).
% 0.51/0.70 tff(1257,plain,
% 0.51/0.70 (product(e_6, e_3, e_2) | product(e_6, e_3, e_4) | product(e_6, e_3, e_5) | product(e_6, e_3, e_6) | product(e_6, e_3, e_1) | product(e_6, e_3, e_3)),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[1256, 202, 322, 136])).
% 0.51/0.70 tff(1258,plain,
% 0.51/0.70 (product(e_6, e_3, e_2) | product(e_6, e_3, e_4) | product(e_6, e_3, e_5) | product(e_6, e_3, e_6) | product(e_6, e_3, e_1)),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[1257, 1250])).
% 0.51/0.70 tff(1259,plain,
% 0.51/0.70 (product(e_6, e_3, e_5) | product(e_6, e_3, e_1)),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[1258, 1241, 1079, 1215])).
% 0.51/0.70 tff(1260,plain,
% 0.51/0.70 (product(e_6, e_3, e_5)),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[1259, 1206])).
% 0.51/0.70 tff(1261,assumption,(product(e_6, e_3, e_5)), introduced(assumption)).
% 0.51/0.70 tff(1262,assumption,(product(e_6, e_4, e_5)), introduced(assumption)).
% 0.51/0.70 tff(1263,plain,
% 0.51/0.70 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_4) | (~product(e_6, e_4, e_5)) | (~product(e_6, e_3, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_6, e_4, e_5)) | (~product(e_6, e_3, e_5)))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(1264,plain,
% 0.51/0.70 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_4) | (~product(e_6, e_4, e_5)) | (~product(e_6, e_3, e_5)))),
% 0.51/0.70 inference(quant_inst,[status(thm)],[])).
% 0.51/0.70 tff(1265,plain,
% 0.51/0.70 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_6, e_4, e_5)) | (~product(e_6, e_3, e_5))),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[1264, 1263])).
% 0.51/0.70 tff(1266,plain,
% 0.51/0.70 ($false),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[1265, 539, 65, 1262, 1261])).
% 0.51/0.70 tff(1267,plain,((~product(e_6, e_3, e_5)) | (~product(e_6, e_4, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.70 tff(1268,plain,
% 0.51/0.70 (~product(e_6, e_4, e_5)),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[1267, 1260])).
% 0.51/0.70 tff(1269,assumption,(product(e_6, e_4, e_2)), introduced(assumption)).
% 0.51/0.70 tff(1270,assumption,(product(e_1, e_4, e_2)), introduced(assumption)).
% 0.51/0.70 tff(1271,plain,
% 0.51/0.70 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_1) | (~product(e_1, e_4, e_2)) | (~product(e_6, 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_6, e_1) | (~product(e_1, e_4, e_2)) | (~product(e_6, e_4, e_2)))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(1272,plain,
% 0.51/0.70 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_1) | (~product(e_1, e_4, e_2)) | (~product(e_6, e_4, e_2)))),
% 0.51/0.70 inference(quant_inst,[status(thm)],[])).
% 0.51/0.70 tff(1273,plain,
% 0.51/0.70 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_1) | (~product(e_1, e_4, e_2)) | (~product(e_6, e_4, e_2))),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[1272, 1271])).
% 0.51/0.70 tff(1274,plain,
% 0.51/0.70 ($false),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[1273, 1210, 91, 1270, 1269])).
% 0.51/0.70 tff(1275,plain,((~product(e_6, e_4, e_2)) | (~product(e_1, e_4, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.70 tff(1276,plain,
% 0.51/0.70 (~product(e_6, e_4, e_2)),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[1275, 1169])).
% 0.51/0.70 tff(1277,assumption,(product(e_4, e_6, e_4)), introduced(assumption)).
% 0.51/0.70 tff(1278,plain,
% 0.51/0.70 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_6, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_6, e_4)))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(1279,plain,
% 0.51/0.70 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_6, e_4)))),
% 0.51/0.70 inference(quant_inst,[status(thm)],[])).
% 0.51/0.70 tff(1280,plain,
% 0.51/0.70 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_6, e_4))),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[1279, 1278])).
% 0.51/0.70 tff(1281,plain,
% 0.51/0.70 ($false),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[1280, 526, 65, 1097, 1277])).
% 0.51/0.70 tff(1282,plain,(~product(e_4, e_6, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.70 tff(1283,plain,
% 0.51/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_6, e_4)) | (~product(e_6, e_4, e_1)) | product(e_4, e_6, e_4))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_6, e_4)) | (~product(e_6, e_4, e_1)) | product(e_4, e_6, e_4))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(1284,plain,
% 0.51/0.70 ((product(e_4, e_6, e_4) | (~product(e_1, e_6, e_4)) | (~product(e_6, e_4, e_1))) <=> ((~product(e_1, e_6, e_4)) | (~product(e_6, e_4, e_1)) | product(e_4, e_6, e_4))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(1285,plain,
% 0.51/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_6, e_4) | (~product(e_1, e_6, e_4)) | (~product(e_6, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_6, e_4)) | (~product(e_6, e_4, e_1)) | product(e_4, e_6, e_4)))),
% 0.51/0.70 inference(monotonicity,[status(thm)],[1284])).
% 0.51/0.70 tff(1286,plain,
% 0.51/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_6, e_4) | (~product(e_1, e_6, e_4)) | (~product(e_6, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_6, e_4)) | (~product(e_6, e_4, e_1)) | product(e_4, e_6, e_4))),
% 0.51/0.70 inference(transitivity,[status(thm)],[1285, 1283])).
% 0.51/0.70 tff(1287,plain,
% 0.51/0.70 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_6, e_4) | (~product(e_1, e_6, e_4)) | (~product(e_6, e_4, e_1)))),
% 0.51/0.70 inference(quant_inst,[status(thm)],[])).
% 0.51/0.70 tff(1288,plain,
% 0.51/0.70 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_6, e_4)) | (~product(e_6, e_4, e_1)) | product(e_4, e_6, e_4)),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[1287, 1286])).
% 0.51/0.70 tff(1289,plain,
% 0.51/0.70 (~product(e_6, e_4, e_1)),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[1288, 35, 887, 1282])).
% 0.51/0.70 tff(1290,assumption,(product(e_6, e_4, e_4)), introduced(assumption)).
% 0.51/0.70 tff(1291,plain,
% 0.51/0.70 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_6, 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_6, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_6, e_4, e_4)))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(1292,plain,
% 0.51/0.70 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_6, e_4, e_4)))),
% 0.51/0.70 inference(quant_inst,[status(thm)],[])).
% 0.51/0.70 tff(1293,plain,
% 0.51/0.70 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_6, e_4, e_4))),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[1292, 1291])).
% 0.51/0.70 tff(1294,plain,
% 0.51/0.70 ($false),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[1293, 526, 91, 1097, 1290])).
% 0.51/0.70 tff(1295,plain,(~product(e_6, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.70 tff(1296,plain,
% 0.51/0.70 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_4)) | (~group_element(e_6)) | product(e_6, e_4, e_1) | product(e_6, e_4, e_3) | product(e_6, e_4, e_6) | product(e_6, e_4, e_5) | product(e_6, e_4, e_4) | product(e_6, e_4, e_2))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_4)) | (~group_element(e_6)) | product(e_6, e_4, e_1) | product(e_6, e_4, e_3) | product(e_6, e_4, e_6) | product(e_6, e_4, e_5) | product(e_6, e_4, e_4) | product(e_6, e_4, e_2))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(1297,plain,
% 0.51/0.70 ((product(e_6, e_4, e_6) | product(e_6, e_4, e_5) | product(e_6, e_4, e_4) | product(e_6, e_4, e_3) | product(e_6, e_4, e_2) | product(e_6, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_6))) <=> ((~group_element(e_4)) | (~group_element(e_6)) | product(e_6, e_4, e_1) | product(e_6, e_4, e_3) | product(e_6, e_4, e_6) | product(e_6, e_4, e_5) | product(e_6, e_4, e_4) | product(e_6, e_4, e_2))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(1298,plain,
% 0.51/0.70 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6, e_4, e_6) | product(e_6, e_4, e_5) | product(e_6, e_4, e_4) | product(e_6, e_4, e_3) | product(e_6, e_4, e_2) | product(e_6, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_6)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_4)) | (~group_element(e_6)) | product(e_6, e_4, e_1) | product(e_6, e_4, e_3) | product(e_6, e_4, e_6) | product(e_6, e_4, e_5) | product(e_6, e_4, e_4) | product(e_6, e_4, e_2)))),
% 0.51/0.70 inference(monotonicity,[status(thm)],[1297])).
% 0.51/0.70 tff(1299,plain,
% 0.51/0.70 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6, e_4, e_6) | product(e_6, e_4, e_5) | product(e_6, e_4, e_4) | product(e_6, e_4, e_3) | product(e_6, e_4, e_2) | product(e_6, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_6)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_4)) | (~group_element(e_6)) | product(e_6, e_4, e_1) | product(e_6, e_4, e_3) | product(e_6, e_4, e_6) | product(e_6, e_4, e_5) | product(e_6, e_4, e_4) | product(e_6, e_4, e_2))),
% 0.51/0.70 inference(transitivity,[status(thm)],[1298, 1296])).
% 0.51/0.70 tff(1300,plain,
% 0.51/0.70 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_6, e_4, e_6) | product(e_6, e_4, e_5) | product(e_6, e_4, e_4) | product(e_6, e_4, e_3) | product(e_6, e_4, e_2) | product(e_6, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_6)))),
% 0.51/0.70 inference(quant_inst,[status(thm)],[])).
% 0.51/0.70 tff(1301,plain,
% 0.51/0.70 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_4)) | (~group_element(e_6)) | product(e_6, e_4, e_1) | product(e_6, e_4, e_3) | product(e_6, e_4, e_6) | product(e_6, e_4, e_5) | product(e_6, e_4, e_4) | product(e_6, e_4, e_2)),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[1300, 1299])).
% 0.51/0.70 tff(1302,plain,
% 0.51/0.70 (product(e_6, e_4, e_1) | product(e_6, e_4, e_3) | product(e_6, e_4, e_6) | product(e_6, e_4, e_5) | product(e_6, e_4, e_4) | product(e_6, e_4, e_2)),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[1301, 432, 322, 136])).
% 0.51/0.70 tff(1303,plain,
% 0.51/0.70 (product(e_6, e_4, e_3) | product(e_6, e_4, e_6) | product(e_6, e_4, e_5)),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[1302, 1295, 1289, 1276])).
% 0.51/0.70 tff(1304,plain,
% 0.51/0.70 (product(e_6, e_4, e_3) | product(e_6, e_4, e_5)),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[1303, 1191])).
% 0.51/0.70 tff(1305,plain,
% 0.51/0.70 (product(e_6, e_4, e_3)),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[1304, 1268])).
% 0.51/0.70 tff(1306,plain,
% 0.51/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_2, e_6)) | product(e_3, e_4, e_2) | (~product(e_6, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_2, e_6)) | product(e_3, e_4, e_2) | (~product(e_6, e_4, e_3)))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(1307,plain,
% 0.51/0.70 ((product(e_3, e_4, e_2) | (~product(e_6, e_4, e_3)) | (~product(e_4, e_2, e_6))) <=> ((~product(e_4, e_2, e_6)) | product(e_3, e_4, e_2) | (~product(e_6, e_4, e_3)))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(1308,plain,
% 0.51/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_4, e_2) | (~product(e_6, e_4, e_3)) | (~product(e_4, e_2, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_2, e_6)) | product(e_3, e_4, e_2) | (~product(e_6, e_4, e_3))))),
% 0.51/0.70 inference(monotonicity,[status(thm)],[1307])).
% 0.51/0.70 tff(1309,plain,
% 0.51/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_4, e_2) | (~product(e_6, e_4, e_3)) | (~product(e_4, e_2, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_2, e_6)) | product(e_3, e_4, e_2) | (~product(e_6, e_4, e_3)))),
% 0.51/0.70 inference(transitivity,[status(thm)],[1308, 1306])).
% 0.51/0.70 tff(1310,plain,
% 0.51/0.70 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_4, e_2) | (~product(e_6, e_4, e_3)) | (~product(e_4, e_2, e_6)))),
% 0.51/0.70 inference(quant_inst,[status(thm)],[])).
% 0.51/0.70 tff(1311,plain,
% 0.51/0.70 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_2, e_6)) | product(e_3, e_4, e_2) | (~product(e_6, e_4, e_3))),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[1310, 1309])).
% 0.51/0.70 tff(1312,plain,
% 0.51/0.70 ((~product(e_4, e_2, e_6)) | product(e_3, e_4, e_2) | (~product(e_6, e_4, e_3))),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[1311, 35])).
% 0.51/0.70 tff(1313,plain,
% 0.51/0.70 ((~product(e_4, e_2, e_6)) | (~product(e_6, e_4, e_3))),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[1312, 1174])).
% 0.51/0.70 tff(1314,plain,
% 0.51/0.70 (~product(e_4, e_2, e_6)),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[1313, 1305])).
% 0.51/0.70 tff(1315,assumption,(product(e_4, e_2, e_1)), introduced(assumption)).
% 0.51/0.70 tff(1316,plain,
% 0.51/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_2, e_2, e_4)) | (~product(e_4, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_2) | (~product(e_2, e_2, e_4)) | (~product(e_4, e_2, e_1)))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(1317,plain,
% 0.51/0.70 ((product(e_1, e_2, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_2, e_4))) <=> (product(e_1, e_2, e_2) | (~product(e_2, e_2, e_4)) | (~product(e_4, e_2, e_1)))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(1318,plain,
% 0.51/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_2, e_2, e_4)) | (~product(e_4, e_2, e_1))))),
% 0.51/0.70 inference(monotonicity,[status(thm)],[1317])).
% 0.51/0.70 tff(1319,plain,
% 0.51/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_2) | (~product(e_2, e_2, e_4)) | (~product(e_4, e_2, e_1)))),
% 0.51/0.70 inference(transitivity,[status(thm)],[1318, 1316])).
% 0.51/0.70 tff(1320,plain,
% 0.51/0.70 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_2, e_4)))),
% 0.51/0.70 inference(quant_inst,[status(thm)],[])).
% 0.51/0.70 tff(1321,plain,
% 0.51/0.70 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_2) | (~product(e_2, e_2, e_4)) | (~product(e_4, e_2, e_1))),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[1320, 1319])).
% 0.51/0.70 tff(1322,plain,
% 0.51/0.70 (~product(e_2, e_2, e_4)),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[1321, 35, 1315, 640])).
% 0.51/0.70 tff(1323,plain,
% 0.51/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_4) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_2, e_4) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2)))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(1324,plain,
% 0.51/0.70 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_4) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2)))),
% 0.51/0.70 inference(quant_inst,[status(thm)],[])).
% 0.51/0.70 tff(1325,plain,
% 0.51/0.70 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_2, e_4) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2))),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[1324, 1323])).
% 0.51/0.70 tff(1326,plain,
% 0.51/0.70 (~product(e_2, e_4, e_2)),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[1325, 35, 54, 1322])).
% 0.51/0.71 tff(1327,plain,
% 0.51/0.71 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_4, e_2)) | product(e_2, e_4, e_2) | (~product(e_4, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_4, e_2)) | product(e_2, e_4, e_2) | (~product(e_4, e_2, e_1)))),
% 0.51/0.71 inference(rewrite,[status(thm)],[])).
% 0.51/0.71 tff(1328,plain,
% 0.51/0.71 ((product(e_2, e_4, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_1))) <=> ((~product(e_1, e_4, e_2)) | product(e_2, e_4, e_2) | (~product(e_4, e_2, e_1)))),
% 0.51/0.71 inference(rewrite,[status(thm)],[])).
% 0.51/0.71 tff(1329,plain,
% 0.51/0.71 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_4, e_2)) | product(e_2, e_4, e_2) | (~product(e_4, e_2, e_1))))),
% 0.51/0.71 inference(monotonicity,[status(thm)],[1328])).
% 0.51/0.71 tff(1330,plain,
% 0.51/0.71 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_4, e_2)) | product(e_2, e_4, e_2) | (~product(e_4, e_2, e_1)))),
% 0.51/0.71 inference(transitivity,[status(thm)],[1329, 1327])).
% 0.51/0.71 tff(1331,plain,
% 0.51/0.71 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_1)))),
% 0.51/0.71 inference(quant_inst,[status(thm)],[])).
% 0.51/0.71 tff(1332,plain,
% 0.51/0.71 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_4, e_2)) | product(e_2, e_4, e_2) | (~product(e_4, e_2, e_1))),
% 0.51/0.71 inference(modus_ponens,[status(thm)],[1331, 1330])).
% 0.51/0.71 tff(1333,plain,
% 0.51/0.71 ($false),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[1332, 35, 1270, 1315, 1326])).
% 0.51/0.71 tff(1334,plain,((~product(e_4, e_2, e_1)) | (~product(e_1, e_4, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.71 tff(1335,plain,
% 0.51/0.71 (~product(e_4, e_2, e_1)),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[1334, 1169])).
% 0.51/0.71 tff(1336,assumption,(product(e_4, e_2, e_5)), introduced(assumption)).
% 0.51/0.71 tff(1337,plain,
% 0.51/0.71 (((~![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_4, e_2, e_5)) | (~product(e_4, 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_2) | (~product(e_4, e_2, e_5)) | (~product(e_4, e_1, e_5)))),
% 0.51/0.71 inference(rewrite,[status(thm)],[])).
% 0.51/0.71 tff(1338,plain,
% 0.51/0.71 ((~![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_4, e_2, e_5)) | (~product(e_4, e_1, e_5)))),
% 0.51/0.71 inference(quant_inst,[status(thm)],[])).
% 0.51/0.71 tff(1339,plain,
% 0.51/0.71 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_4, e_2, e_5)) | (~product(e_4, e_1, e_5))),
% 0.51/0.71 inference(modus_ponens,[status(thm)],[1338, 1337])).
% 0.51/0.71 tff(1340,plain,
% 0.51/0.71 ($false),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[1339, 68, 65, 926, 1336])).
% 0.51/0.71 tff(1341,plain,((~product(e_4, e_1, e_5)) | (~product(e_4, e_2, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.71 tff(1342,plain,
% 0.51/0.71 (~product(e_4, e_2, e_5)),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[1341, 908])).
% 0.51/0.71 tff(1343,assumption,(product(e_4, e_2, e_4)), introduced(assumption)).
% 0.51/0.71 tff(1344,plain,
% 0.51/0.71 ((~equalish(e_2, e_4)) <=> (~equalish(e_2, e_4))),
% 0.51/0.71 inference(rewrite,[status(thm)],[])).
% 0.51/0.71 tff(1345,axiom,(~equalish(e_2, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_4')).
% 0.51/0.71 tff(1346,plain,
% 0.51/0.71 (~equalish(e_2, e_4)),
% 0.51/0.71 inference(modus_ponens,[status(thm)],[1345, 1344])).
% 0.51/0.71 tff(1347,plain,
% 0.51/0.71 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_4, e_2, e_4)) | (~product(e_4, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_4, e_2, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.51/0.71 inference(rewrite,[status(thm)],[])).
% 0.51/0.71 tff(1348,plain,
% 0.51/0.71 ((equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4))) <=> (equalish(e_2, e_4) | (~product(e_4, e_2, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.51/0.71 inference(rewrite,[status(thm)],[])).
% 0.51/0.71 tff(1349,plain,
% 0.51/0.71 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_4, e_2, e_4)) | (~product(e_4, e_4, e_4))))),
% 0.51/0.71 inference(monotonicity,[status(thm)],[1348])).
% 0.51/0.71 tff(1350,plain,
% 0.51/0.71 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_4, e_2, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.51/0.71 inference(transitivity,[status(thm)],[1349, 1347])).
% 0.51/0.71 tff(1351,plain,
% 0.51/0.71 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4)))),
% 0.51/0.71 inference(quant_inst,[status(thm)],[])).
% 0.51/0.71 tff(1352,plain,
% 0.51/0.71 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_4, e_2, e_4)) | (~product(e_4, e_4, e_4))),
% 0.51/0.71 inference(modus_ponens,[status(thm)],[1351, 1350])).
% 0.51/0.71 tff(1353,plain,
% 0.51/0.71 ($false),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[1352, 1346, 65, 1343, 1097])).
% 0.51/0.71 tff(1354,plain,(~product(e_4, e_2, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.71 tff(1355,assumption,(product(e_4, e_2, e_2)), introduced(assumption)).
% 0.51/0.71 tff(1356,plain,
% 0.51/0.71 (((~![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_2, e_2)) | (~product(e_4, 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_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_2, e_2)))),
% 0.51/0.71 inference(rewrite,[status(thm)],[])).
% 0.51/0.71 tff(1357,plain,
% 0.51/0.71 ((~![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_2, e_2)) | (~product(e_4, e_2, e_2)))),
% 0.51/0.71 inference(quant_inst,[status(thm)],[])).
% 0.51/0.71 tff(1358,plain,
% 0.51/0.71 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_2, e_2))),
% 0.51/0.71 inference(modus_ponens,[status(thm)],[1357, 1356])).
% 0.51/0.71 tff(1359,plain,
% 0.51/0.71 ($false),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[1358, 1129, 91, 1355, 54])).
% 0.51/0.71 tff(1360,plain,(~product(e_4, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.71 tff(1361,plain,
% 0.51/0.71 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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)) | (~group_element(e_4)) | product(e_4, e_2, e_6) | product(e_4, e_2, e_5) | product(e_4, e_2, e_2) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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)) | (~group_element(e_4)) | product(e_4, e_2, e_6) | product(e_4, e_2, e_5) | product(e_4, e_2, e_2) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_1))),
% 0.51/0.71 inference(rewrite,[status(thm)],[])).
% 0.51/0.71 tff(1362,plain,
% 0.51/0.71 ((product(e_4, e_2, e_6) | product(e_4, e_2, e_5) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_4))) <=> ((~group_element(e_2)) | (~group_element(e_4)) | product(e_4, e_2, e_6) | product(e_4, e_2, e_5) | product(e_4, e_2, e_2) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_1))),
% 0.51/0.71 inference(rewrite,[status(thm)],[])).
% 0.51/0.71 tff(1363,plain,
% 0.51/0.71 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_2, e_6) | product(e_4, e_2, e_5) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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)) | (~group_element(e_4)) | product(e_4, e_2, e_6) | product(e_4, e_2, e_5) | product(e_4, e_2, e_2) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_1)))),
% 0.51/0.71 inference(monotonicity,[status(thm)],[1362])).
% 0.51/0.71 tff(1364,plain,
% 0.51/0.71 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_2, e_6) | product(e_4, e_2, e_5) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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)) | (~group_element(e_4)) | product(e_4, e_2, e_6) | product(e_4, e_2, e_5) | product(e_4, e_2, e_2) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_1))),
% 0.51/0.71 inference(transitivity,[status(thm)],[1363, 1361])).
% 0.51/0.71 tff(1365,plain,
% 0.51/0.71 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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_2, e_6) | product(e_4, e_2, e_5) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_4)))),
% 0.51/0.71 inference(quant_inst,[status(thm)],[])).
% 0.51/0.71 tff(1366,plain,
% 0.51/0.71 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(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)) | (~group_element(e_4)) | product(e_4, e_2, e_6) | product(e_4, e_2, e_5) | product(e_4, e_2, e_2) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_1)),
% 0.51/0.71 inference(modus_ponens,[status(thm)],[1365, 1364])).
% 0.51/0.71 tff(1367,plain,
% 0.51/0.71 (product(e_4, e_2, e_6) | product(e_4, e_2, e_5) | product(e_4, e_2, e_2) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_1)),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[1366, 139, 432, 136])).
% 0.51/0.71 tff(1368,plain,
% 0.51/0.71 (product(e_4, e_2, e_6) | product(e_4, e_2, e_5) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_1)),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[1367, 1360])).
% 0.51/0.71 tff(1369,plain,
% 0.51/0.71 (product(e_4, e_2, e_6) | product(e_4, e_2, e_5) | product(e_4, e_2, e_3) | product(e_4, e_2, e_1)),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[1368, 1354])).
% 0.51/0.71 tff(1370,plain,
% 0.51/0.71 (product(e_4, e_2, e_6) | product(e_4, e_2, e_3)),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[1369, 1342, 1335])).
% 0.51/0.71 tff(1371,plain,
% 0.51/0.71 (product(e_4, e_2, e_3)),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[1370, 1314])).
% 0.51/0.71 tff(1372,plain,
% 0.51/0.71 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_4) | (~product(e_4, e_2, e_3)) | (~product(e_5, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_4) | (~product(e_4, e_2, e_3)) | (~product(e_5, e_2, e_3)))),
% 0.51/0.71 inference(rewrite,[status(thm)],[])).
% 0.51/0.71 tff(1373,plain,
% 0.51/0.71 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_4) | (~product(e_4, e_2, e_3)) | (~product(e_5, e_2, e_3)))),
% 0.51/0.71 inference(quant_inst,[status(thm)],[])).
% 0.51/0.71 tff(1374,plain,
% 0.51/0.71 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_4) | (~product(e_4, e_2, e_3)) | (~product(e_5, e_2, e_3))),
% 0.51/0.71 inference(modus_ponens,[status(thm)],[1373, 1372])).
% 0.51/0.71 tff(1375,plain,
% 0.51/0.71 ($false),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[1374, 445, 91, 1371, 1])).
% 0.51/0.71 tff(1376,plain,(~product(e_5, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.71 tff(1377,plain,
% 0.51/0.71 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_2, e_5)) | product(e_5, e_2, e_3) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_5)) | product(e_5, e_2, e_3) | (~product(e_2, e_3, e_1)))),
% 0.51/0.71 inference(rewrite,[status(thm)],[])).
% 0.51/0.71 tff(1378,plain,
% 0.51/0.71 ((product(e_5, e_2, e_3) | (~product(e_1, e_2, e_5)) | (~product(e_2, e_3, e_1))) <=> ((~product(e_1, e_2, e_5)) | product(e_5, e_2, e_3) | (~product(e_2, e_3, e_1)))),
% 0.51/0.71 inference(rewrite,[status(thm)],[])).
% 0.51/0.71 tff(1379,plain,
% 0.51/0.71 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_2, e_3) | (~product(e_1, e_2, e_5)) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_2, e_5)) | product(e_5, e_2, e_3) | (~product(e_2, e_3, e_1))))),
% 0.51/0.71 inference(monotonicity,[status(thm)],[1378])).
% 0.51/0.71 tff(1380,plain,
% 0.51/0.71 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_2, e_3) | (~product(e_1, e_2, e_5)) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_5)) | product(e_5, e_2, e_3) | (~product(e_2, e_3, e_1)))),
% 0.51/0.71 inference(transitivity,[status(thm)],[1379, 1377])).
% 0.51/0.71 tff(1381,plain,
% 0.51/0.71 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_5, e_2, e_3) | (~product(e_1, e_2, e_5)) | (~product(e_2, e_3, e_1)))),
% 0.51/0.71 inference(quant_inst,[status(thm)],[])).
% 0.51/0.71 tff(1382,plain,
% 0.51/0.71 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_5)) | product(e_5, e_2, e_3) | (~product(e_2, e_3, e_1))),
% 0.51/0.71 inference(modus_ponens,[status(thm)],[1381, 1380])).
% 0.51/0.71 tff(1383,plain,
% 0.51/0.71 (~product(e_2, e_3, e_1)),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[1382, 35, 1126, 1376])).
% 0.51/0.71 tff(1384,plain,
% 0.51/0.71 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_2, e_3, e_1) | (~product(e_4, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_1, e_4)) | product(e_2, e_3, e_1) | (~product(e_4, e_3, e_2)))),
% 0.51/0.71 inference(rewrite,[status(thm)],[])).
% 0.51/0.71 tff(1385,plain,
% 0.51/0.71 ((product(e_2, e_3, e_1) | (~product(e_4, e_3, e_2)) | (~product(e_3, e_1, e_4))) <=> ((~product(e_3, e_1, e_4)) | product(e_2, e_3, e_1) | (~product(e_4, e_3, e_2)))),
% 0.51/0.72 inference(rewrite,[status(thm)],[])).
% 0.51/0.72 tff(1386,plain,
% 0.51/0.72 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_1) | (~product(e_4, e_3, e_2)) | (~product(e_3, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_2, e_3, e_1) | (~product(e_4, e_3, e_2))))),
% 0.51/0.72 inference(monotonicity,[status(thm)],[1385])).
% 0.51/0.72 tff(1387,plain,
% 0.51/0.72 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_1) | (~product(e_4, e_3, e_2)) | (~product(e_3, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_1, e_4)) | product(e_2, e_3, e_1) | (~product(e_4, e_3, e_2)))),
% 0.51/0.72 inference(transitivity,[status(thm)],[1386, 1384])).
% 0.51/0.72 tff(1388,plain,
% 0.51/0.72 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_1) | (~product(e_4, e_3, e_2)) | (~product(e_3, e_1, e_4)))),
% 0.51/0.72 inference(quant_inst,[status(thm)],[])).
% 0.51/0.72 tff(1389,plain,
% 0.51/0.72 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_1, e_4)) | product(e_2, e_3, e_1) | (~product(e_4, e_3, e_2))),
% 0.51/0.72 inference(modus_ponens,[status(thm)],[1388, 1387])).
% 0.51/0.72 tff(1390,plain,
% 0.51/0.72 ($false),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[1389, 35, 671, 991, 1383])).
% 0.51/0.72 % SZS output end Proof
% 0.51/0.72 % E exiting
%------------------------------------------------------------------------------