%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP126-2.004 : 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 05:07:07 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : GRP126-2.004 : TPTP v9.0.0. Released v1.2.0.
% 0.01/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 15:44:26 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.43 % SZS status Unsatisfiable
% 0.19/0.43 % SZS output start Proof
% 0.19/0.43 tff(product_type, type, (
% 0.19/0.43 product: ( $i * $i * $i ) > $o)).
% 0.19/0.43 tff(e_4_type, type, (
% 0.19/0.43 e_4: $i)).
% 0.19/0.43 tff(e_1_type, type, (
% 0.19/0.43 e_1: $i)).
% 0.19/0.43 tff(e_3_type, type, (
% 0.19/0.43 e_3: $i)).
% 0.19/0.43 tff(e_2_type, type, (
% 0.19/0.43 e_2: $i)).
% 0.19/0.43 tff(equalish_type, type, (
% 0.19/0.43 equalish: ( $i * $i ) > $o)).
% 0.19/0.43 tff(next_type, type, (
% 0.19/0.43 next: ( $i * $i ) > $o)).
% 0.19/0.43 tff(greater_type, type, (
% 0.19/0.43 greater: ( $i * $i ) > $o)).
% 0.19/0.43 tff(group_element_type, type, (
% 0.19/0.43 group_element: $i > $o)).
% 0.19/0.43 tff(1,plain,
% 0.19/0.43 (^[X: $i] : refl(product(X, X, X) <=> product(X, X, X))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(2,plain,
% 0.19/0.43 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.19/0.43 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.43 tff(3,plain,
% 0.19/0.43 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(4,axiom,(![X: $i] : product(X, X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_idempotence')).
% 0.19/0.43 tff(5,plain,
% 0.19/0.43 (![X: $i] : product(X, X, X)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.43 tff(6,plain,(
% 0.19/0.43 ![X: $i] : product(X, X, X)),
% 0.19/0.43 inference(skolemize,[status(sab)],[5])).
% 0.19/0.43 tff(7,plain,
% 0.19/0.43 (![X: $i] : product(X, X, X)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.43 tff(8,plain,
% 0.19/0.43 ((~![X: $i] : product(X, X, X)) | product(e_4, e_4, e_4)),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(9,plain,
% 0.19/0.43 (product(e_4, e_4, e_4)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.43 tff(10,plain,
% 0.19/0.43 ((~![X: $i] : product(X, X, X)) | product(e_2, e_2, e_2)),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(11,plain,
% 0.19/0.43 (product(e_2, e_2, e_2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[10, 7])).
% 0.19/0.43 tff(12,assumption,(product(e_2, e_1, e_2)), introduced(assumption)).
% 0.19/0.43 tff(13,plain,
% 0.19/0.43 (^[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))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(14,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.43 tff(15,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(16,plain,
% 0.19/0.43 (^[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)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(17,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.43 tff(18,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_right_cancellation')).
% 0.19/0.43 tff(19,plain,
% 0.19/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.43 tff(20,plain,
% 0.19/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.19/0.43 tff(21,plain,(
% 0.19/0.43 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[20])).
% 0.19/0.43 tff(22,plain,
% 0.19/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.19/0.44 tff(23,plain,
% 0.19/0.44 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(24,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.19/0.44 tff(25,plain,
% 0.19/0.44 (~equalish(e_1, e_2)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.44 tff(26,plain,
% 0.19/0.44 (((~![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)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(27,plain,
% 0.19/0.44 ((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)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(28,plain,
% 0.19/0.44 (((~![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))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[27])).
% 0.19/0.44 tff(29,plain,
% 0.19/0.44 (((~![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)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[28, 26])).
% 0.19/0.44 tff(30,plain,
% 0.19/0.44 ((~![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)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(31,plain,
% 0.19/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.19/0.44 tff(32,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[31, 25, 22, 12, 11])).
% 0.19/0.44 tff(33,plain,(~product(e_2, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(34,assumption,(~product(e_1, e_1, e_1)), introduced(assumption)).
% 0.19/0.44 tff(35,plain,
% 0.19/0.44 ((~![X: $i] : product(X, X, X)) | product(e_1, e_1, e_1)),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(36,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[35, 7, 34])).
% 0.19/0.44 tff(37,plain,(product(e_1, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(38,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.19/0.44 tff(39,assumption,(product(e_1, e_1, e_1)), introduced(assumption)).
% 0.19/0.44 tff(40,plain,
% 0.19/0.44 (^[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))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(41,plain,
% 0.19/0.44 (![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)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[40])).
% 0.19/0.44 tff(42,plain,
% 0.19/0.44 (![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)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(43,plain,
% 0.19/0.44 (^[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)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(44,plain,
% 0.19/0.44 (![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)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[43])).
% 0.19/0.44 tff(45,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')).
% 0.19/0.44 tff(46,plain,
% 0.19/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.44 tff(47,plain,
% 0.19/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.19/0.44 tff(48,plain,(
% 0.19/0.44 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[47])).
% 0.19/0.44 tff(49,plain,
% 0.19/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.19/0.44 tff(50,plain,
% 0.19/0.44 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(51,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.19/0.44 tff(52,plain,
% 0.19/0.44 (~equalish(e_2, e_1)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.19/0.44 tff(53,plain,
% 0.19/0.44 (((~![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)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(54,plain,
% 0.19/0.44 ((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)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(55,plain,
% 0.19/0.44 (((~![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))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[54])).
% 0.19/0.44 tff(56,plain,
% 0.19/0.44 (((~![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)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[55, 53])).
% 0.19/0.44 tff(57,plain,
% 0.19/0.44 ((~![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)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(58,plain,
% 0.19/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.19/0.44 tff(59,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[58, 52, 49, 39, 38])).
% 0.19/0.44 tff(60,plain,((~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(61,plain,
% 0.19/0.44 (~product(e_2, e_1, e_1)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[60, 37])).
% 0.19/0.44 tff(62,plain,
% 0.19/0.44 (^[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))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(63,plain,
% 0.19/0.44 (![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)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[62])).
% 0.19/0.44 tff(64,plain,
% 0.19/0.44 (![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)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(65,plain,
% 0.19/0.44 (^[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)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(66,plain,
% 0.19/0.44 (![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)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.44 tff(67,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')).
% 0.19/0.44 tff(68,plain,
% 0.19/0.44 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.19/0.44 tff(69,plain,
% 0.19/0.44 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.19/0.44 tff(70,plain,(
% 0.19/0.44 ![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[69])).
% 0.19/0.44 tff(71,plain,
% 0.19/0.44 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.19/0.44 tff(72,plain,
% 0.19/0.44 (greater(e_4, e_3) <=> greater(e_4, e_3)),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(73,axiom,(greater(e_4, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_greater_e_3')).
% 0.19/0.44 tff(74,plain,
% 0.19/0.44 (greater(e_4, e_3)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.19/0.44 tff(75,plain,
% 0.19/0.44 (next(e_2, e_3) <=> next(e_2, e_3)),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(76,axiom,(next(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_then_e_3')).
% 0.19/0.44 tff(77,plain,
% 0.19/0.44 (next(e_2, e_3)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.19/0.44 tff(78,plain,
% 0.19/0.44 (((~![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)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(79,plain,
% 0.19/0.44 ((~![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)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(80,plain,
% 0.19/0.44 ((~![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))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.19/0.44 tff(81,plain,
% 0.19/0.44 (~product(e_2, e_1, e_4)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[80, 77, 74, 71])).
% 0.19/0.44 tff(82,plain,
% 0.19/0.44 (^[Y: $i, X: $i] : refl((product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(83,plain,
% 0.19/0.44 (![Y: $i, X: $i] : (product(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_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[82])).
% 0.19/0.44 tff(84,plain,
% 0.19/0.44 (![Y: $i, X: $i] : (product(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_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(85,plain,
% 0.19/0.44 (^[Y: $i, X: $i] : 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)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(86,plain,
% 0.19/0.44 (![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> ![Y: $i, X: $i] : (product(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)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[85])).
% 0.19/0.44 tff(87,axiom,(![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_total_function1')).
% 0.19/0.44 tff(88,plain,
% 0.19/0.44 (![Y: $i, X: $i] : (product(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)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.19/0.45 tff(89,plain,
% 0.19/0.45 (![Y: $i, X: $i] : (product(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)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.19/0.45 tff(90,plain,(
% 0.19/0.45 ![Y: $i, X: $i] : (product(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)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[89])).
% 0.19/0.45 tff(91,plain,
% 0.19/0.45 (![Y: $i, X: $i] : (product(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)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[90, 83])).
% 0.19/0.45 tff(92,plain,
% 0.19/0.45 (group_element(e_2) <=> group_element(e_2)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(93,axiom,(group_element(e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_2')).
% 0.19/0.45 tff(94,plain,
% 0.19/0.45 (group_element(e_2)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.19/0.45 tff(95,plain,
% 0.19/0.45 (group_element(e_1) <=> group_element(e_1)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(96,axiom,(group_element(e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_1')).
% 0.19/0.45 tff(97,plain,
% 0.19/0.45 (group_element(e_1)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.19/0.45 tff(98,plain,
% 0.19/0.45 (((~![Y: $i, X: $i] : (product(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) | (~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_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) | (~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)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(99,plain,
% 0.19/0.45 ((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) | (~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)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(100,plain,
% 0.19/0.45 (((~![Y: $i, X: $i] : (product(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_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_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) | (~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))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[99])).
% 0.19/0.45 tff(101,plain,
% 0.19/0.45 (((~![Y: $i, X: $i] : (product(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_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_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) | (~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)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[100, 98])).
% 0.19/0.45 tff(102,plain,
% 0.19/0.45 ((~![Y: $i, X: $i] : (product(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_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(103,plain,
% 0.19/0.45 ((~![Y: $i, X: $i] : (product(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) | (~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))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.19/0.45 tff(104,plain,
% 0.19/0.45 (product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[103, 97, 94, 91, 81])).
% 0.19/0.45 tff(105,plain,
% 0.19/0.45 (product(e_2, e_1, e_3) | product(e_2, e_1, e_2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[104, 61])).
% 0.19/0.45 tff(106,plain,
% 0.19/0.45 (product(e_2, e_1, e_3)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[105, 33])).
% 0.19/0.45 tff(107,assumption,(product(e_4, e_1, e_3)), introduced(assumption)).
% 0.19/0.45 tff(108,assumption,(product(e_2, e_1, e_3)), introduced(assumption)).
% 0.19/0.45 tff(109,plain,
% 0.19/0.45 ((~equalish(e_4, e_2)) <=> (~equalish(e_4, e_2))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(110,axiom,(~equalish(e_4, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_2')).
% 0.19/0.45 tff(111,plain,
% 0.19/0.45 (~equalish(e_4, e_2)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.19/0.45 tff(112,plain,
% 0.19/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_4, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_4, e_1, e_3)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(113,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_4, e_1, e_3)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(114,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_4, e_1, e_3))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.19/0.45 tff(115,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[114, 111, 49, 108, 107])).
% 0.19/0.45 tff(116,plain,((~product(e_4, e_1, e_3)) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(117,plain,
% 0.19/0.45 (~product(e_4, e_1, e_3)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[116, 106])).
% 0.19/0.45 tff(118,assumption,(product(e_3, e_1, e_4)), introduced(assumption)).
% 0.19/0.45 tff(119,assumption,(product(e_3, e_4, e_4)), introduced(assumption)).
% 0.19/0.45 tff(120,plain,
% 0.19/0.45 ((~equalish(e_4, e_1)) <=> (~equalish(e_4, e_1))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(121,axiom,(~equalish(e_4, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_1')).
% 0.19/0.45 tff(122,plain,
% 0.19/0.45 (~equalish(e_4, e_1)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.19/0.45 tff(123,plain,
% 0.19/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_3, 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_1) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_4, e_4)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(124,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_4, e_4)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(125,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_4, e_4))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.19/0.45 tff(126,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[125, 122, 22, 118, 119])).
% 0.19/0.45 tff(127,plain,((~product(e_3, e_4, e_4)) | (~product(e_3, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(128,plain,
% 0.19/0.45 (~product(e_3, e_4, e_4)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[127, 118])).
% 0.19/0.45 tff(129,assumption,(~product(e_3, e_4, e_4)), introduced(assumption)).
% 0.19/0.45 tff(130,assumption,(product(e_4, e_3, e_1)), introduced(assumption)).
% 0.19/0.45 tff(131,plain,
% 0.19/0.45 (greater(e_4, e_2) <=> greater(e_4, e_2)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(132,axiom,(greater(e_4, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_greater_e_2')).
% 0.19/0.45 tff(133,plain,
% 0.19/0.45 (greater(e_4, e_2)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.19/0.45 tff(134,plain,
% 0.19/0.45 (next(e_1, e_2) <=> next(e_1, e_2)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(135,axiom,(next(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_then_e_2')).
% 0.19/0.45 tff(136,plain,
% 0.19/0.45 (next(e_1, e_2)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.19/0.45 tff(137,plain,
% 0.19/0.45 (((~![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)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(138,plain,
% 0.19/0.45 ((~![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)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(139,plain,
% 0.19/0.45 ((~![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))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.19/0.45 tff(140,plain,
% 0.19/0.45 (~product(e_1, e_1, e_4)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[139, 136, 133, 71])).
% 0.19/0.45 tff(141,plain,
% 0.19/0.45 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl(((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))) <=> ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(142,plain,
% 0.19/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[141])).
% 0.19/0.45 tff(143,plain,
% 0.19/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(144,plain,
% 0.19/0.45 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : rewrite((((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, Y)) <=> ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(145,plain,
% 0.19/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, Y)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[144])).
% 0.19/0.45 tff(146,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qg4')).
% 0.19/0.45 tff(147,plain,
% 0.19/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.19/0.45 tff(148,plain,
% 0.19/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[147, 143])).
% 0.19/0.45 tff(149,plain,(
% 0.19/0.45 ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[148])).
% 0.19/0.45 tff(150,plain,
% 0.19/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[149, 142])).
% 0.19/0.45 tff(151,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_3, e_1)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(152,plain,
% 0.19/0.46 (((~product(e_4, e_3, e_1)) | product(e_1, e_1, e_4) | (~product(e_3, e_4, e_1))) <=> (product(e_1, e_1, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_3, e_1)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(153,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_3, e_1)) | product(e_1, e_1, e_4) | (~product(e_3, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_3, e_1))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[152])).
% 0.19/0.46 tff(154,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_3, e_1)) | product(e_1, e_1, e_4) | (~product(e_3, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_3, e_1)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[153, 151])).
% 0.19/0.46 tff(155,plain,
% 0.19/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_3, e_1)) | product(e_1, e_1, e_4) | (~product(e_3, e_4, e_1)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(156,plain,
% 0.19/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_4) | (~product(e_3, e_4, e_1)) | (~product(e_4, e_3, e_1))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.19/0.46 tff(157,plain,
% 0.19/0.46 ((~product(e_3, e_4, e_1)) | (~product(e_4, e_3, e_1))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[156, 150, 140])).
% 0.19/0.46 tff(158,plain,
% 0.19/0.46 (~product(e_3, e_4, e_1)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[157, 130])).
% 0.19/0.46 tff(159,assumption,(product(e_3, e_4, e_3)), introduced(assumption)).
% 0.19/0.46 tff(160,plain,
% 0.19/0.46 ((~![X: $i] : product(X, X, X)) | product(e_3, e_3, e_3)),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(161,plain,
% 0.19/0.46 (product(e_3, e_3, e_3)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[160, 7])).
% 0.19/0.46 tff(162,plain,
% 0.19/0.46 ((~equalish(e_4, e_3)) <=> (~equalish(e_4, e_3))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(163,axiom,(~equalish(e_4, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_3')).
% 0.19/0.46 tff(164,plain,
% 0.19/0.46 (~equalish(e_4, e_3)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.19/0.46 tff(165,plain,
% 0.19/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(166,plain,
% 0.19/0.46 ((~![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)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(167,plain,
% 0.19/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.19/0.46 tff(168,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[167, 164, 22, 161, 159])).
% 0.19/0.46 tff(169,plain,(~product(e_3, e_4, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(170,plain,
% 0.19/0.46 (group_element(e_4) <=> group_element(e_4)),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(171,axiom,(group_element(e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_4')).
% 0.19/0.46 tff(172,plain,
% 0.19/0.46 (group_element(e_4)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.19/0.46 tff(173,plain,
% 0.19/0.46 (group_element(e_3) <=> group_element(e_3)),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(174,axiom,(group_element(e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_3')).
% 0.19/0.46 tff(175,plain,
% 0.19/0.46 (group_element(e_3)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.19/0.46 tff(176,plain,
% 0.19/0.46 (((~![Y: $i, X: $i] : (product(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)) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | (~group_element(e_3)) | product(e_3, e_4, e_4) | product(e_3, e_4, e_1))) <=> ((~![Y: $i, X: $i] : (product(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)) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | (~group_element(e_3)) | product(e_3, e_4, e_4) | product(e_3, e_4, e_1))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(177,plain,
% 0.19/0.46 ((product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_3))) <=> ((~group_element(e_4)) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | (~group_element(e_3)) | product(e_3, e_4, e_4) | product(e_3, e_4, e_1))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(178,plain,
% 0.19/0.46 (((~![Y: $i, X: $i] : (product(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_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_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)) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | (~group_element(e_3)) | product(e_3, e_4, e_4) | product(e_3, e_4, e_1)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[177])).
% 0.19/0.46 tff(179,plain,
% 0.19/0.46 (((~![Y: $i, X: $i] : (product(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_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_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)) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | (~group_element(e_3)) | product(e_3, e_4, e_4) | product(e_3, e_4, e_1))),
% 0.19/0.46 inference(transitivity,[status(thm)],[178, 176])).
% 0.19/0.46 tff(180,plain,
% 0.19/0.46 ((~![Y: $i, X: $i] : (product(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_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)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(181,plain,
% 0.19/0.46 ((~![Y: $i, X: $i] : (product(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)) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | (~group_element(e_3)) | product(e_3, e_4, e_4) | product(e_3, e_4, e_1)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.19/0.46 tff(182,plain,
% 0.19/0.46 (product(e_3, e_4, e_2) | product(e_3, e_4, e_4) | product(e_3, e_4, e_1)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[181, 175, 172, 91, 169])).
% 0.19/0.46 tff(183,plain,
% 0.19/0.46 (product(e_3, e_4, e_2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[182, 158, 129])).
% 0.19/0.46 tff(184,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_4) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_3, e_1)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(185,plain,
% 0.19/0.47 (((~product(e_4, e_3, e_1)) | product(e_2, e_1, e_4) | (~product(e_3, e_4, e_2))) <=> (product(e_2, e_1, e_4) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_3, e_1)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(186,plain,
% 0.19/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_3, e_1)) | product(e_2, e_1, e_4) | (~product(e_3, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_3, e_1))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[185])).
% 0.19/0.47 tff(187,plain,
% 0.19/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_3, e_1)) | product(e_2, e_1, e_4) | (~product(e_3, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_4) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_3, e_1)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[186, 184])).
% 0.19/0.47 tff(188,plain,
% 0.19/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_3, e_1)) | product(e_2, e_1, e_4) | (~product(e_3, e_4, e_2)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(189,plain,
% 0.19/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_4) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_3, e_1))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.19/0.47 tff(190,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[189, 150, 81, 130, 183])).
% 0.19/0.47 tff(191,plain,((~product(e_4, e_3, e_1)) | product(e_3, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(192,plain,
% 0.19/0.47 (~product(e_4, e_3, e_1)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[191, 128])).
% 0.19/0.47 tff(193,assumption,(product(e_4, e_1, e_4)), introduced(assumption)).
% 0.19/0.47 tff(194,plain,
% 0.19/0.47 ((~equalish(e_3, e_4)) <=> (~equalish(e_3, e_4))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(195,axiom,(~equalish(e_3, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_4')).
% 0.19/0.47 tff(196,plain,
% 0.19/0.47 (~equalish(e_3, e_4)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.19/0.47 tff(197,plain,
% 0.19/0.47 (((~![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_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_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_4)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(198,plain,
% 0.19/0.47 ((equalish(e_3, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_3, e_1, e_4))) <=> (equalish(e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_4)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(199,plain,
% 0.19/0.47 (((~![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_1, e_4)) | (~product(e_3, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_4))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[198])).
% 0.19/0.47 tff(200,plain,
% 0.19/0.47 (((~![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_1, e_4)) | (~product(e_3, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_4)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[199, 197])).
% 0.19/0.47 tff(201,plain,
% 0.19/0.47 ((~![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_1, e_4)) | (~product(e_3, e_1, e_4)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(202,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_4))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.19/0.47 tff(203,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[202, 196, 49, 193, 118])).
% 0.19/0.47 tff(204,plain,((~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(205,plain,
% 0.19/0.47 (~product(e_4, e_1, e_4)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[204, 118])).
% 0.19/0.47 tff(206,assumption,(product(e_4, e_1, e_1)), introduced(assumption)).
% 0.19/0.47 tff(207,plain,
% 0.19/0.47 (((~![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_4, 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_4, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(208,plain,
% 0.19/0.47 ((equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1))) <=> (equalish(e_4, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(209,plain,
% 0.19/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[208])).
% 0.19/0.47 tff(210,plain,
% 0.19/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[209, 207])).
% 0.19/0.47 tff(211,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(212,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.19/0.47 tff(213,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[212, 122, 49, 37, 206])).
% 0.19/0.47 tff(214,plain,(~product(e_4, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(215,plain,
% 0.19/0.47 (((~![Y: $i, X: $i] : (product(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_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(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_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_4)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(216,plain,
% 0.19/0.47 ((product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_4))) <=> ((~group_element(e_1)) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_4)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(217,plain,
% 0.19/0.47 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_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_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_4))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[216])).
% 0.19/0.47 tff(218,plain,
% 0.19/0.47 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_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_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_4)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[217, 215])).
% 0.19/0.47 tff(219,plain,
% 0.19/0.47 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_4)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(220,plain,
% 0.19/0.47 ((~![Y: $i, X: $i] : (product(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_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_4))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.19/0.47 tff(221,plain,
% 0.19/0.47 (product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[220, 97, 172, 91])).
% 0.19/0.47 tff(222,plain,
% 0.19/0.47 (product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[221, 214])).
% 0.19/0.47 tff(223,plain,
% 0.19/0.47 (product(e_4, e_1, e_2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[222, 205, 117])).
% 0.19/0.47 tff(224,plain,
% 0.19/0.47 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(225,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.19/0.47 tff(226,plain,
% 0.19/0.47 (~equalish(e_1, e_3)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.19/0.47 tff(227,plain,
% 0.19/0.47 (((~![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_4, e_1, e_2)) | (~product(e_4, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_3, e_2)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(228,plain,
% 0.19/0.47 ((equalish(e_1, e_3) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_1, e_2))) <=> (equalish(e_1, e_3) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_3, e_2)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(229,plain,
% 0.19/0.47 (((~![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_4, e_3, e_2)) | (~product(e_4, 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_3) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_3, e_2))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[228])).
% 0.19/0.47 tff(230,plain,
% 0.19/0.47 (((~![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_4, e_3, e_2)) | (~product(e_4, 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_3) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_3, e_2)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[229, 227])).
% 0.19/0.48 tff(231,plain,
% 0.19/0.48 ((~![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_4, e_3, e_2)) | (~product(e_4, e_1, e_2)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(232,plain,
% 0.19/0.48 ((~![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_4, e_1, e_2)) | (~product(e_4, e_3, e_2))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.19/0.48 tff(233,plain,
% 0.19/0.48 ((~product(e_4, e_1, e_2)) | (~product(e_4, e_3, e_2))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[232, 226, 22])).
% 0.19/0.48 tff(234,plain,
% 0.19/0.48 (~product(e_4, e_3, e_2)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[233, 223])).
% 0.19/0.48 tff(235,assumption,(product(e_4, e_3, e_4)), introduced(assumption)).
% 0.19/0.48 tff(236,plain,
% 0.19/0.48 (((~![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_4, e_3, 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_3, e_4) | (~product(e_4, e_3, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(237,plain,
% 0.19/0.48 ((equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_3, e_4))) <=> (equalish(e_3, e_4) | (~product(e_4, e_3, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(238,plain,
% 0.19/0.48 (((~![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_4, e_4, e_4)) | (~product(e_4, 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_4) | (~product(e_4, e_3, e_4)) | (~product(e_4, e_4, e_4))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[237])).
% 0.19/0.48 tff(239,plain,
% 0.19/0.48 (((~![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_4, e_4, e_4)) | (~product(e_4, 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_4) | (~product(e_4, e_3, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[238, 236])).
% 0.19/0.48 tff(240,plain,
% 0.19/0.48 ((~![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_4, e_4, e_4)) | (~product(e_4, e_3, e_4)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(241,plain,
% 0.19/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_4, e_3, e_4)) | (~product(e_4, e_4, e_4))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.19/0.48 tff(242,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[241, 196, 22, 235, 9])).
% 0.19/0.48 tff(243,plain,(~product(e_4, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(244,assumption,(product(e_4, e_3, e_3)), introduced(assumption)).
% 0.19/0.48 tff(245,plain,
% 0.19/0.48 (((~![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)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(246,plain,
% 0.19/0.48 ((~![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)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(247,plain,
% 0.19/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_4, e_3, e_3))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.19/0.48 tff(248,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[247, 164, 49, 161, 244])).
% 0.19/0.48 tff(249,plain,(~product(e_4, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(250,plain,
% 0.19/0.48 (((~![Y: $i, X: $i] : (product(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)) | product(e_4, e_3, e_4) | (~group_element(e_3)) | product(e_4, e_3, e_3) | product(e_4, e_3, e_1) | product(e_4, e_3, e_2))) <=> ((~![Y: $i, X: $i] : (product(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)) | product(e_4, e_3, e_4) | (~group_element(e_3)) | product(e_4, e_3, e_3) | product(e_4, e_3, e_1) | product(e_4, e_3, e_2))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(251,plain,
% 0.19/0.48 ((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_4)) | product(e_4, e_3, e_4) | (~group_element(e_3)) | product(e_4, e_3, e_3) | product(e_4, e_3, e_1) | product(e_4, e_3, e_2))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(252,plain,
% 0.19/0.48 (((~![Y: $i, X: $i] : (product(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_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_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)) | product(e_4, e_3, e_4) | (~group_element(e_3)) | product(e_4, e_3, e_3) | product(e_4, e_3, e_1) | product(e_4, e_3, e_2)))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[251])).
% 0.19/0.48 tff(253,plain,
% 0.19/0.48 (((~![Y: $i, X: $i] : (product(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_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_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)) | product(e_4, e_3, e_4) | (~group_element(e_3)) | product(e_4, e_3, e_3) | product(e_4, e_3, e_1) | product(e_4, e_3, e_2))),
% 0.19/0.48 inference(transitivity,[status(thm)],[252, 250])).
% 0.19/0.48 tff(254,plain,
% 0.19/0.48 ((~![Y: $i, X: $i] : (product(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_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)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(255,plain,
% 0.19/0.48 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | product(e_4, e_3, e_4) | (~group_element(e_3)) | product(e_4, e_3, e_3) | product(e_4, e_3, e_1) | product(e_4, e_3, e_2)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.19/0.48 tff(256,plain,
% 0.19/0.48 (product(e_4, e_3, e_4) | product(e_4, e_3, e_1) | product(e_4, e_3, e_2)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[255, 175, 172, 91, 249])).
% 0.19/0.48 tff(257,plain,
% 0.19/0.48 (product(e_4, e_3, e_1) | product(e_4, e_3, e_2)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[256, 243])).
% 0.19/0.48 tff(258,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[257, 234, 192])).
% 0.19/0.48 tff(259,plain,(~product(e_3, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(260,assumption,(product(e_3, e_1, e_1)), introduced(assumption)).
% 0.19/0.48 tff(261,plain,
% 0.19/0.48 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(262,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.19/0.48 tff(263,plain,
% 0.19/0.48 (~equalish(e_3, e_1)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.19/0.48 tff(264,plain,
% 0.19/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(265,plain,
% 0.19/0.48 ((equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1))) <=> (equalish(e_3, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(266,plain,
% 0.19/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[265])).
% 0.19/0.48 tff(267,plain,
% 0.19/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[266, 264])).
% 0.19/0.48 tff(268,plain,
% 0.19/0.48 ((~![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)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(269,plain,
% 0.19/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.19/0.48 tff(270,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[269, 263, 49, 39, 260])).
% 0.19/0.48 tff(271,plain,((~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(272,plain,
% 0.19/0.48 (~product(e_3, e_1, e_1)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[271, 37])).
% 0.19/0.48 tff(273,assumption,(product(e_3, e_1, e_3)), introduced(assumption)).
% 0.19/0.48 tff(274,plain,
% 0.19/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(275,plain,
% 0.19/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(276,plain,
% 0.19/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.19/0.48 tff(277,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[276, 226, 22, 161, 273])).
% 0.19/0.48 tff(278,plain,(~product(e_3, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(279,plain,
% 0.19/0.48 (((~![Y: $i, X: $i] : (product(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_3, e_1, e_2) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | (~group_element(e_3)) | product(e_3, e_1, e_1))) <=> ((~![Y: $i, X: $i] : (product(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_3, e_1, e_2) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | (~group_element(e_3)) | product(e_3, e_1, e_1))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(280,plain,
% 0.19/0.48 ((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))) <=> ((~group_element(e_1)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | (~group_element(e_3)) | product(e_3, e_1, e_1))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(281,plain,
% 0.19/0.48 (((~![Y: $i, X: $i] : (product(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_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_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_3, e_1, e_2) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | (~group_element(e_3)) | product(e_3, e_1, e_1)))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[280])).
% 0.19/0.48 tff(282,plain,
% 0.19/0.48 (((~![Y: $i, X: $i] : (product(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_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_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_3, e_1, e_2) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | (~group_element(e_3)) | product(e_3, e_1, e_1))),
% 0.19/0.48 inference(transitivity,[status(thm)],[281, 279])).
% 0.19/0.48 tff(283,plain,
% 0.19/0.48 ((~![Y: $i, X: $i] : (product(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_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)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(284,plain,
% 0.19/0.48 ((~![Y: $i, X: $i] : (product(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_3, e_1, e_2) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | (~group_element(e_3)) | product(e_3, e_1, e_1)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[283, 282])).
% 0.19/0.48 tff(285,plain,
% 0.19/0.48 (product(e_3, e_1, e_2) | product(e_3, e_1, e_4) | product(e_3, e_1, e_1)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[284, 97, 175, 91, 278])).
% 0.19/0.48 tff(286,plain,
% 0.19/0.48 (product(e_3, e_1, e_2) | product(e_3, e_1, e_4)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[285, 272])).
% 0.19/0.48 tff(287,plain,
% 0.19/0.48 (product(e_3, e_1, e_2)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[286, 259])).
% 0.19/0.48 tff(288,assumption,(product(e_3, e_1, e_2)), introduced(assumption)).
% 0.19/0.48 tff(289,assumption,(product(e_4, e_1, e_2)), introduced(assumption)).
% 0.19/0.48 tff(290,plain,
% 0.19/0.48 (((~![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_2)) | (~product(e_4, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_4, e_1, e_2)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(291,plain,
% 0.19/0.48 ((~![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_2)) | (~product(e_4, e_1, e_2)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(292,plain,
% 0.19/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_4, e_1, e_2))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.19/0.49 tff(293,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[292, 164, 49, 289, 288])).
% 0.19/0.49 tff(294,plain,((~product(e_4, e_1, e_2)) | (~product(e_3, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(295,plain,
% 0.19/0.49 (~product(e_4, e_1, e_2)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[294, 287])).
% 0.19/0.49 tff(296,plain,
% 0.19/0.49 (product(e_4, e_1, e_4)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[222, 295, 117])).
% 0.19/0.49 tff(297,plain,
% 0.19/0.49 ((~equalish(e_1, e_4)) <=> (~equalish(e_1, e_4))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(298,axiom,(~equalish(e_1, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_4')).
% 0.19/0.49 tff(299,plain,
% 0.19/0.49 (~equalish(e_1, e_4)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.19/0.49 tff(300,plain,
% 0.19/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(301,plain,
% 0.19/0.49 ((equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4))) <=> (equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(302,plain,
% 0.19/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[301])).
% 0.19/0.49 tff(303,plain,
% 0.19/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[302, 300])).
% 0.19/0.49 tff(304,plain,
% 0.19/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(305,plain,
% 0.19/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.19/0.49 tff(306,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[305, 299, 22, 296, 9])).
% 0.19/0.49 % SZS output end Proof
% 0.19/0.49 % E exiting
%------------------------------------------------------------------------------