%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP124-9.004 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:07:05 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GRP124-9.004 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 15:41:50 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.44 % SZS status Unsatisfiable
% 0.19/0.44 % SZS output start Proof
% 0.19/0.44 tff(product1_type, type, (
% 0.19/0.44 product1: ( $i * $i * $i ) > $o)).
% 0.19/0.44 tff(e_3_type, type, (
% 0.19/0.44 e_3: $i)).
% 0.19/0.44 tff(e_2_type, type, (
% 0.19/0.44 e_2: $i)).
% 0.19/0.44 tff(e_1_type, type, (
% 0.19/0.44 e_1: $i)).
% 0.19/0.44 tff(e_4_type, type, (
% 0.19/0.44 e_4: $i)).
% 0.19/0.44 tff(equalish_type, type, (
% 0.19/0.44 equalish: ( $i * $i ) > $o)).
% 0.19/0.44 tff(product2_type, type, (
% 0.19/0.44 product2: ( $i * $i * $i ) > $o)).
% 0.19/0.44 tff(group_element_type, type, (
% 0.19/0.44 group_element: $i > $o)).
% 0.19/0.44 tff(1,assumption,(product1(e_4, e_2, e_2)), introduced(assumption)).
% 0.19/0.44 tff(2,assumption,(~product1(e_2, e_2, e_2)), introduced(assumption)).
% 0.19/0.44 tff(3,plain,
% 0.19/0.44 (^[X: $i] : refl(product1(X, X, X) <=> product1(X, X, X))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(4,plain,
% 0.19/0.44 (![X: $i] : product1(X, X, X) <=> ![X: $i] : product1(X, X, X)),
% 0.19/0.44 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.44 tff(5,plain,
% 0.19/0.44 (![X: $i] : product1(X, X, X) <=> ![X: $i] : product1(X, X, X)),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(6,axiom,(![X: $i] : product1(X, X, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product1_idempotence')).
% 0.19/0.44 tff(7,plain,
% 0.19/0.44 (![X: $i] : product1(X, X, X)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.44 tff(8,plain,(
% 0.19/0.44 ![X: $i] : product1(X, X, X)),
% 0.19/0.44 inference(skolemize,[status(sab)],[7])).
% 0.19/0.44 tff(9,plain,
% 0.19/0.44 (![X: $i] : product1(X, X, X)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.19/0.44 tff(10,plain,
% 0.19/0.44 ((~![X: $i] : product1(X, X, X)) | product1(e_2, e_2, e_2)),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(11,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[10, 9, 2])).
% 0.19/0.44 tff(12,plain,(product1(e_2, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(13,plain,
% 0.19/0.44 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X))) <=> (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(14,plain,
% 0.19/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.44 tff(15,plain,
% 0.19/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(16,plain,
% 0.19/0.44 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product1(W, Y, X)) | (~product1(Z, Y, X))) <=> ((~product1(Z, Y, X)) | (~product1(W, Y, X)))), ((((~product1(W, Y, X)) | (~product1(Z, Y, X))) | equalish(W, Z)) <=> (((~product1(Z, Y, X)) | (~product1(W, Y, X))) | equalish(W, Z)))), rewrite((((~product1(Z, Y, X)) | (~product1(W, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))), ((((~product1(W, Y, X)) | (~product1(Z, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(17,plain,
% 0.19/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product1(W, Y, X)) | (~product1(Z, Y, X))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.44 tff(18,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product1(W, Y, X)) | (~product1(Z, Y, X))) | equalish(W, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product1_left_cancellation')).
% 0.19/0.44 tff(19,plain,
% 0.19/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.44 tff(20,plain,
% 0.19/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.19/0.44 tff(21,plain,(
% 0.19/0.44 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[20])).
% 0.19/0.44 tff(22,plain,
% 0.19/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.19/0.44 tff(23,plain,
% 0.19/0.44 ((~equalish(e_4, e_2)) <=> (~equalish(e_4, e_2))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(24,axiom,(~equalish(e_4, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_is_not_e_2')).
% 0.19/0.44 tff(25,plain,
% 0.19/0.44 (~equalish(e_4, 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) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_4, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_4, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_4, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_4, e_2, e_2)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(27,plain,
% 0.19/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_4, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_4, e_2, e_2)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(28,plain,
% 0.19/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_4, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_4, e_2, e_2))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.44 tff(29,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[28, 25, 22, 12, 1])).
% 0.19/0.44 tff(30,plain,(~product1(e_4, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(31,assumption,(~product1(e_3, e_2, e_1)), introduced(assumption)).
% 0.19/0.44 tff(32,plain,
% 0.19/0.44 (^[X: $i] : refl(product2(X, X, X) <=> product2(X, X, X))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(33,plain,
% 0.19/0.44 (![X: $i] : product2(X, X, X) <=> ![X: $i] : product2(X, X, X)),
% 0.19/0.44 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.44 tff(34,plain,
% 0.19/0.44 (![X: $i] : product2(X, X, X) <=> ![X: $i] : product2(X, X, X)),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(35,axiom,(![X: $i] : product2(X, X, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product2_idempotence')).
% 0.19/0.44 tff(36,plain,
% 0.19/0.44 (![X: $i] : product2(X, X, X)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.19/0.44 tff(37,plain,(
% 0.19/0.44 ![X: $i] : product2(X, X, X)),
% 0.19/0.44 inference(skolemize,[status(sab)],[36])).
% 0.19/0.44 tff(38,plain,
% 0.19/0.44 (![X: $i] : product2(X, X, X)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.19/0.44 tff(39,plain,
% 0.19/0.44 ((~![X: $i] : product2(X, X, X)) | product2(e_3, e_3, e_3)),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(40,plain,
% 0.19/0.44 (product2(e_3, e_3, e_3)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.19/0.44 tff(41,assumption,(product2(e_3, e_2, e_3)), introduced(assumption)).
% 0.19/0.44 tff(42,plain,
% 0.19/0.44 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y))) <=> (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(43,plain,
% 0.19/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[42])).
% 0.19/0.44 tff(44,plain,
% 0.19/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(45,plain,
% 0.19/0.44 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product2(X, W, Y)) | (~product2(X, Z, Y))) <=> ((~product2(X, Z, Y)) | (~product2(X, W, Y)))), ((((~product2(X, W, Y)) | (~product2(X, Z, Y))) | equalish(W, Z)) <=> (((~product2(X, Z, Y)) | (~product2(X, W, Y))) | equalish(W, Z)))), rewrite((((~product2(X, Z, Y)) | (~product2(X, W, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))), ((((~product2(X, W, Y)) | (~product2(X, Z, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(46,plain,
% 0.19/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product2(X, W, Y)) | (~product2(X, Z, Y))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[45])).
% 0.19/0.45 tff(47,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product2(X, W, Y)) | (~product2(X, Z, Y))) | equalish(W, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product2_right_cancellation')).
% 0.19/0.45 tff(48,plain,
% 0.19/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.19/0.45 tff(49,plain,
% 0.19/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.19/0.45 tff(50,plain,(
% 0.19/0.45 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[49])).
% 0.19/0.45 tff(51,plain,
% 0.19/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.19/0.45 tff(52,plain,
% 0.19/0.45 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(53,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.19/0.45 tff(54,plain,
% 0.19/0.45 (~equalish(e_2, e_3)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.19/0.45 tff(55,plain,
% 0.19/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_2, e_3) | (~product2(e_3, e_2, e_3)) | (~product2(e_3, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_2, e_3) | (~product2(e_3, e_2, e_3)) | (~product2(e_3, e_3, e_3)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(56,plain,
% 0.19/0.45 ((equalish(e_2, e_3) | (~product2(e_3, e_3, e_3)) | (~product2(e_3, e_2, e_3))) <=> (equalish(e_2, e_3) | (~product2(e_3, e_2, e_3)) | (~product2(e_3, e_3, e_3)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(57,plain,
% 0.19/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_2, e_3) | (~product2(e_3, e_3, e_3)) | (~product2(e_3, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_2, e_3) | (~product2(e_3, e_2, e_3)) | (~product2(e_3, e_3, e_3))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[56])).
% 0.19/0.45 tff(58,plain,
% 0.19/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_2, e_3) | (~product2(e_3, e_3, e_3)) | (~product2(e_3, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_2, e_3) | (~product2(e_3, e_2, e_3)) | (~product2(e_3, e_3, e_3)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[57, 55])).
% 0.19/0.45 tff(59,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_2, e_3) | (~product2(e_3, e_3, e_3)) | (~product2(e_3, e_2, e_3)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(60,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_2, e_3) | (~product2(e_3, e_2, e_3)) | (~product2(e_3, e_3, e_3))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.19/0.45 tff(61,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[60, 54, 51, 41, 40])).
% 0.19/0.45 tff(62,plain,(~product2(e_3, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(63,assumption,(~product1(e_4, e_3, e_1)), introduced(assumption)).
% 0.19/0.45 tff(64,assumption,(~product2(e_3, e_2, e_3)), introduced(assumption)).
% 0.19/0.45 tff(65,plain,
% 0.19/0.45 ((~![X: $i] : product1(X, X, X)) | product1(e_3, e_3, e_3)),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(66,plain,
% 0.19/0.45 (product1(e_3, e_3, e_3)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[65, 9])).
% 0.19/0.45 tff(67,plain,
% 0.19/0.45 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl(((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1))) <=> ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(68,plain,
% 0.19/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[67])).
% 0.19/0.45 tff(69,plain,
% 0.19/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(70,plain,
% 0.19/0.45 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : rewrite((((~product1(X, Y, Z1)) | (~product1(Z1, X, Z2))) | product2(Z2, Y, X)) <=> ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(71,plain,
% 0.19/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product1(X, Y, Z1)) | (~product1(Z1, X, Z2))) | product2(Z2, Y, X)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[70])).
% 0.19/0.45 tff(72,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product1(X, Y, Z1)) | (~product1(Z1, X, Z2))) | product2(Z2, Y, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qg2a')).
% 0.19/0.45 tff(73,plain,
% 0.19/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.19/0.45 tff(74,plain,
% 0.19/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.19/0.45 tff(75,plain,(
% 0.19/0.45 ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[74])).
% 0.19/0.45 tff(76,plain,
% 0.19/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.19/0.45 tff(77,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (product2(e_3, e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_3, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | product2(e_3, e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_3, e_2, e_3)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(78,plain,
% 0.19/0.45 (((~product1(e_3, e_3, e_3)) | product2(e_3, e_2, e_3) | (~product1(e_3, e_2, e_3))) <=> (product2(e_3, e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_3, e_2, e_3)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(79,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_3, e_3, e_3)) | product2(e_3, e_2, e_3) | (~product1(e_3, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (product2(e_3, e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_3, e_2, e_3))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[78])).
% 0.19/0.45 tff(80,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_3, e_3, e_3)) | product2(e_3, e_2, e_3) | (~product1(e_3, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | product2(e_3, e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_3, e_2, e_3)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[79, 77])).
% 0.19/0.45 tff(81,plain,
% 0.19/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_3, e_3, e_3)) | product2(e_3, e_2, e_3) | (~product1(e_3, e_2, e_3)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(82,plain,
% 0.19/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | product2(e_3, e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_3, e_2, e_3))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.19/0.45 tff(83,plain,
% 0.19/0.45 (~product1(e_3, e_2, e_3)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[82, 76, 66, 64])).
% 0.19/0.45 tff(84,assumption,(product1(e_3, e_2, e_2)), introduced(assumption)).
% 0.19/0.45 tff(85,plain,
% 0.19/0.45 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(86,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.19/0.45 tff(87,plain,
% 0.19/0.45 (~equalish(e_3, e_2)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.19/0.45 tff(88,plain,
% 0.19/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_2) | (~product1(e_3, e_2, e_2)) | (~product1(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_3, e_2) | (~product1(e_3, e_2, e_2)) | (~product1(e_2, e_2, e_2)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(89,plain,
% 0.19/0.45 ((equalish(e_3, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_3, e_2, e_2))) <=> (equalish(e_3, e_2) | (~product1(e_3, e_2, e_2)) | (~product1(e_2, e_2, e_2)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(90,plain,
% 0.19/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_3, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_2) | (~product1(e_3, e_2, e_2)) | (~product1(e_2, e_2, e_2))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[89])).
% 0.19/0.45 tff(91,plain,
% 0.19/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_3, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_3, e_2) | (~product1(e_3, e_2, e_2)) | (~product1(e_2, e_2, e_2)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[90, 88])).
% 0.19/0.45 tff(92,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_3, e_2, e_2)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(93,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_3, e_2) | (~product1(e_3, e_2, e_2)) | (~product1(e_2, e_2, e_2))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.19/0.45 tff(94,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[93, 87, 22, 84, 12])).
% 0.19/0.45 tff(95,plain,(~product1(e_3, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(96,plain,
% 0.19/0.45 (^[Y: $i, X: $i] : refl(((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1)) <=> ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1)))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(97,plain,
% 0.19/0.45 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[96])).
% 0.19/0.45 tff(98,plain,
% 0.19/0.45 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(99,plain,
% 0.19/0.45 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) <=> ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_1))), (((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) <=> (((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_1)) | product1(X, Y, e_2)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_1)) | product1(X, Y, e_2)) <=> ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_2) | product1(X, Y, e_1))), (((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) <=> ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_2) | product1(X, Y, e_1)))), ((((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) | product1(X, Y, e_3)) <=> (((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_2) | product1(X, Y, e_1)) | product1(X, Y, e_3)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_2) | product1(X, Y, e_1)) | product1(X, Y, e_3)) <=> ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))), ((((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) | product1(X, Y, e_3)) <=> ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1)))), (((((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) | product1(X, Y, e_3)) | product1(X, Y, e_4)) <=> (((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1)) | product1(X, Y, e_4)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1)) | product1(X, Y, e_4)) <=> ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))), (((((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) | product1(X, Y, e_3)) | product1(X, Y, e_4)) <=> ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(100,plain,
% 0.19/0.45 (![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) | product1(X, Y, e_3)) | product1(X, Y, e_4)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[99])).
% 0.19/0.45 tff(101,axiom,(![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) | product1(X, Y, e_3)) | product1(X, Y, e_4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product1_total_function1')).
% 0.19/0.45 tff(102,plain,
% 0.19/0.45 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.19/0.45 tff(103,plain,
% 0.19/0.45 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.19/0.45 tff(104,plain,(
% 0.19/0.45 ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))),
% 0.19/0.45 inference(skolemize,[status(sab)],[103])).
% 0.19/0.45 tff(105,plain,
% 0.19/0.45 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.19/0.45 tff(106,plain,
% 0.19/0.45 (group_element(e_3) <=> group_element(e_3)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(107,axiom,(group_element(e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_3')).
% 0.19/0.45 tff(108,plain,
% 0.19/0.45 (group_element(e_3)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.19/0.45 tff(109,plain,
% 0.19/0.46 (group_element(e_2) <=> group_element(e_2)),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(110,axiom,(group_element(e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_2')).
% 0.19/0.46 tff(111,plain,
% 0.19/0.46 (group_element(e_2)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.19/0.46 tff(112,plain,
% 0.19/0.46 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_2)) | product1(e_3, e_2, e_2) | (~group_element(e_3)) | product1(e_3, e_2, e_3) | product1(e_3, e_2, e_1) | product1(e_3, e_2, e_4))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_2)) | product1(e_3, e_2, e_2) | (~group_element(e_3)) | product1(e_3, e_2, e_3) | product1(e_3, e_2, e_1) | product1(e_3, e_2, e_4))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(113,plain,
% 0.19/0.46 (((~group_element(e_2)) | (~group_element(e_3)) | product1(e_3, e_2, e_4) | product1(e_3, e_2, e_3) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_1)) <=> ((~group_element(e_2)) | product1(e_3, e_2, e_2) | (~group_element(e_3)) | product1(e_3, e_2, e_3) | product1(e_3, e_2, e_1) | product1(e_3, e_2, e_4))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(114,plain,
% 0.19/0.46 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_3)) | product1(e_3, e_2, e_4) | product1(e_3, e_2, e_3) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_2)) | product1(e_3, e_2, e_2) | (~group_element(e_3)) | product1(e_3, e_2, e_3) | product1(e_3, e_2, e_1) | product1(e_3, e_2, e_4)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[113])).
% 0.19/0.46 tff(115,plain,
% 0.19/0.46 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_3)) | product1(e_3, e_2, e_4) | product1(e_3, e_2, e_3) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_2)) | product1(e_3, e_2, e_2) | (~group_element(e_3)) | product1(e_3, e_2, e_3) | product1(e_3, e_2, e_1) | product1(e_3, e_2, e_4))),
% 0.19/0.46 inference(transitivity,[status(thm)],[114, 112])).
% 0.19/0.46 tff(116,plain,
% 0.19/0.46 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_3)) | product1(e_3, e_2, e_4) | product1(e_3, e_2, e_3) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_1))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(117,plain,
% 0.19/0.46 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_2)) | product1(e_3, e_2, e_2) | (~group_element(e_3)) | product1(e_3, e_2, e_3) | product1(e_3, e_2, e_1) | product1(e_3, e_2, e_4)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.19/0.46 tff(118,plain,
% 0.19/0.46 (product1(e_3, e_2, e_3) | product1(e_3, e_2, e_1) | product1(e_3, e_2, e_4)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[117, 111, 108, 105, 95])).
% 0.19/0.46 tff(119,plain,
% 0.19/0.46 (product1(e_3, e_2, e_4)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[118, 83, 31])).
% 0.19/0.46 tff(120,assumption,(~product2(e_2, e_2, e_2)), introduced(assumption)).
% 0.19/0.46 tff(121,plain,
% 0.19/0.46 ((~![X: $i] : product2(X, X, X)) | product2(e_2, e_2, e_2)),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(122,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[121, 38, 120])).
% 0.19/0.46 tff(123,plain,(product2(e_2, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(124,plain,
% 0.19/0.46 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W))) <=> (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(125,plain,
% 0.19/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[124])).
% 0.19/0.46 tff(126,plain,
% 0.19/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(127,plain,
% 0.19/0.46 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product2(X, Y, W)) | (~product2(X, Y, Z))) <=> ((~product2(X, Y, Z)) | (~product2(X, Y, W)))), ((((~product2(X, Y, W)) | (~product2(X, Y, Z))) | equalish(W, Z)) <=> (((~product2(X, Y, Z)) | (~product2(X, Y, W))) | equalish(W, Z)))), rewrite((((~product2(X, Y, Z)) | (~product2(X, Y, W))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))), ((((~product2(X, Y, W)) | (~product2(X, Y, Z))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(128,plain,
% 0.19/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product2(X, Y, W)) | (~product2(X, Y, Z))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[127])).
% 0.19/0.46 tff(129,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product2(X, Y, W)) | (~product2(X, Y, Z))) | equalish(W, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product2_total_function2')).
% 0.19/0.46 tff(130,plain,
% 0.19/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.19/0.46 tff(131,plain,
% 0.19/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[130, 126])).
% 0.19/0.46 tff(132,plain,(
% 0.19/0.46 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[131])).
% 0.19/0.46 tff(133,plain,
% 0.19/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[132, 125])).
% 0.19/0.46 tff(134,plain,
% 0.19/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | (equalish(e_3, e_2) | (~product2(e_2, e_2, e_2)) | (~product2(e_2, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | equalish(e_3, e_2) | (~product2(e_2, e_2, e_2)) | (~product2(e_2, e_2, e_3)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(135,plain,
% 0.19/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | (equalish(e_3, e_2) | (~product2(e_2, e_2, e_2)) | (~product2(e_2, e_2, e_3)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(136,plain,
% 0.19/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | equalish(e_3, e_2) | (~product2(e_2, e_2, e_2)) | (~product2(e_2, e_2, e_3))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.19/0.46 tff(137,plain,
% 0.19/0.46 (~product2(e_2, e_2, e_3)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[136, 87, 133, 123])).
% 0.19/0.46 tff(138,assumption,(product1(e_4, e_3, e_2)), introduced(assumption)).
% 0.19/0.46 tff(139,assumption,(product1(e_3, e_2, e_4)), introduced(assumption)).
% 0.19/0.46 tff(140,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (product2(e_2, e_2, e_3) | (~product1(e_3, e_2, e_4)) | (~product1(e_4, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | product2(e_2, e_2, e_3) | (~product1(e_3, e_2, e_4)) | (~product1(e_4, e_3, e_2)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(141,plain,
% 0.19/0.46 (((~product1(e_4, e_3, e_2)) | product2(e_2, e_2, e_3) | (~product1(e_3, e_2, e_4))) <=> (product2(e_2, e_2, e_3) | (~product1(e_3, e_2, e_4)) | (~product1(e_4, e_3, e_2)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(142,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_4, e_3, e_2)) | product2(e_2, e_2, e_3) | (~product1(e_3, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (product2(e_2, e_2, e_3) | (~product1(e_3, e_2, e_4)) | (~product1(e_4, e_3, e_2))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[141])).
% 0.19/0.46 tff(143,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_4, e_3, e_2)) | product2(e_2, e_2, e_3) | (~product1(e_3, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | product2(e_2, e_2, e_3) | (~product1(e_3, e_2, e_4)) | (~product1(e_4, e_3, e_2)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[142, 140])).
% 0.19/0.46 tff(144,plain,
% 0.19/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_4, e_3, e_2)) | product2(e_2, e_2, e_3) | (~product1(e_3, e_2, e_4)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(145,plain,
% 0.19/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | product2(e_2, e_2, e_3) | (~product1(e_3, e_2, e_4)) | (~product1(e_4, e_3, e_2))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.19/0.46 tff(146,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[145, 76, 139, 138, 137])).
% 0.19/0.46 tff(147,plain,((~product1(e_4, e_3, e_2)) | (~product1(e_3, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(148,plain,
% 0.19/0.46 (~product1(e_4, e_3, e_2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[147, 119])).
% 0.19/0.46 tff(149,assumption,(product1(e_4, e_3, e_4)), introduced(assumption)).
% 0.19/0.46 tff(150,assumption,(~product1(e_4, e_4, e_4)), introduced(assumption)).
% 0.19/0.46 tff(151,plain,
% 0.19/0.46 ((~![X: $i] : product1(X, X, X)) | product1(e_4, e_4, e_4)),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(152,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[151, 9, 150])).
% 0.19/0.46 tff(153,plain,(product1(e_4, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(154,plain,
% 0.19/0.46 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y))) <=> (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(155,plain,
% 0.19/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[154])).
% 0.19/0.46 tff(156,plain,
% 0.19/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(157,plain,
% 0.19/0.46 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product1(X, W, Y)) | (~product1(X, Z, Y))) <=> ((~product1(X, Z, Y)) | (~product1(X, W, Y)))), ((((~product1(X, W, Y)) | (~product1(X, Z, Y))) | equalish(W, Z)) <=> (((~product1(X, Z, Y)) | (~product1(X, W, Y))) | equalish(W, Z)))), rewrite((((~product1(X, Z, Y)) | (~product1(X, W, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))), ((((~product1(X, W, Y)) | (~product1(X, Z, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(158,plain,
% 0.19/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product1(X, W, Y)) | (~product1(X, Z, Y))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[157])).
% 0.19/0.46 tff(159,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product1(X, W, Y)) | (~product1(X, Z, Y))) | equalish(W, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product1_right_cancellation')).
% 0.19/0.46 tff(160,plain,
% 0.19/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.19/0.46 tff(161,plain,
% 0.19/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[160, 156])).
% 0.19/0.46 tff(162,plain,(
% 0.19/0.46 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[161])).
% 0.19/0.46 tff(163,plain,
% 0.19/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[162, 155])).
% 0.19/0.46 tff(164,plain,
% 0.19/0.46 ((~equalish(e_3, e_4)) <=> (~equalish(e_3, e_4))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(165,axiom,(~equalish(e_3, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_4')).
% 0.19/0.46 tff(166,plain,
% 0.19/0.46 (~equalish(e_3, e_4)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.19/0.46 tff(167,plain,
% 0.19/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_3, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_4, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_3, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_4, e_3, e_4)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(168,plain,
% 0.19/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_3, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_4, e_3, e_4)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(169,plain,
% 0.19/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_3, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_4, e_3, e_4))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.19/0.46 tff(170,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[169, 166, 163, 153, 149])).
% 0.19/0.46 tff(171,plain,(~product1(e_4, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(172,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(173,axiom,(group_element(e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_4')).
% 0.19/0.46 tff(174,plain,
% 0.19/0.46 (group_element(e_4)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.19/0.46 tff(175,plain,
% 0.19/0.46 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_4)) | (~group_element(e_3)) | product1(e_4, e_3, e_4) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_1) | product1(e_4, e_3, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_4)) | (~group_element(e_3)) | product1(e_4, e_3, e_4) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_1) | product1(e_4, e_3, e_2))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(176,plain,
% 0.19/0.46 (((~group_element(e_3)) | (~group_element(e_4)) | product1(e_4, e_3, e_4) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_2) | product1(e_4, e_3, e_1)) <=> ((~group_element(e_4)) | (~group_element(e_3)) | product1(e_4, e_3, e_4) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_1) | product1(e_4, e_3, e_2))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(177,plain,
% 0.19/0.46 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_4)) | product1(e_4, e_3, e_4) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_2) | product1(e_4, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_4)) | (~group_element(e_3)) | product1(e_4, e_3, e_4) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_1) | product1(e_4, e_3, e_2)))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[176])).
% 0.19/0.47 tff(178,plain,
% 0.19/0.47 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_4)) | product1(e_4, e_3, e_4) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_2) | product1(e_4, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_4)) | (~group_element(e_3)) | product1(e_4, e_3, e_4) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_1) | product1(e_4, e_3, e_2))),
% 0.19/0.47 inference(transitivity,[status(thm)],[177, 175])).
% 0.19/0.47 tff(179,plain,
% 0.19/0.47 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_4)) | product1(e_4, e_3, e_4) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_2) | product1(e_4, e_3, e_1))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(180,plain,
% 0.19/0.47 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_4)) | (~group_element(e_3)) | product1(e_4, e_3, e_4) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_1) | product1(e_4, e_3, e_2)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.19/0.47 tff(181,plain,
% 0.19/0.47 (product1(e_4, e_3, e_4) | product1(e_4, e_3, e_3) | product1(e_4, e_3, e_1) | product1(e_4, e_3, e_2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[180, 108, 174, 105])).
% 0.19/0.47 tff(182,plain,
% 0.19/0.47 (product1(e_4, e_3, e_3) | product1(e_4, e_3, e_1) | product1(e_4, e_3, e_2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[181, 171])).
% 0.19/0.47 tff(183,plain,
% 0.19/0.47 (product1(e_4, e_3, e_3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[182, 148, 63])).
% 0.19/0.47 tff(184,plain,
% 0.19/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (product2(e_3, e_2, e_3) | (~product1(e_3, e_2, e_4)) | (~product1(e_4, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | product2(e_3, e_2, e_3) | (~product1(e_3, e_2, e_4)) | (~product1(e_4, e_3, e_3)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(185,plain,
% 0.19/0.47 (((~product1(e_4, e_3, e_3)) | product2(e_3, e_2, e_3) | (~product1(e_3, e_2, e_4))) <=> (product2(e_3, e_2, e_3) | (~product1(e_3, e_2, e_4)) | (~product1(e_4, e_3, e_3)))),
% 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] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_4, e_3, e_3)) | product2(e_3, e_2, e_3) | (~product1(e_3, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (product2(e_3, e_2, e_3) | (~product1(e_3, e_2, e_4)) | (~product1(e_4, e_3, e_3))))),
% 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] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_4, e_3, e_3)) | product2(e_3, e_2, e_3) | (~product1(e_3, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | product2(e_3, e_2, e_3) | (~product1(e_3, e_2, e_4)) | (~product1(e_4, e_3, e_3)))),
% 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] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_4, e_3, e_3)) | product2(e_3, e_2, e_3) | (~product1(e_3, e_2, e_4)))),
% 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: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | product2(e_3, e_2, e_3) | (~product1(e_3, e_2, e_4)) | (~product1(e_4, e_3, e_3))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.19/0.47 tff(190,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[189, 76, 64, 119, 183])).
% 0.19/0.47 tff(191,plain,(product2(e_3, e_2, e_3) | product1(e_4, e_3, e_1) | product1(e_3, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(192,plain,
% 0.19/0.47 (product1(e_4, e_3, e_1) | product1(e_3, e_2, e_1)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[191, 62])).
% 0.19/0.47 tff(193,plain,
% 0.19/0.47 (product1(e_4, e_3, e_1)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[192, 31])).
% 0.19/0.47 tff(194,assumption,(product1(e_4, e_3, e_1)), introduced(assumption)).
% 0.19/0.47 tff(195,assumption,(product1(e_4, e_2, e_1)), introduced(assumption)).
% 0.19/0.47 tff(196,plain,
% 0.19/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_3) | (~product1(e_4, e_2, e_1)) | (~product1(e_4, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_2, e_3) | (~product1(e_4, e_2, e_1)) | (~product1(e_4, e_3, e_1)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(197,plain,
% 0.19/0.47 ((equalish(e_2, e_3) | (~product1(e_4, e_3, e_1)) | (~product1(e_4, e_2, e_1))) <=> (equalish(e_2, e_3) | (~product1(e_4, e_2, e_1)) | (~product1(e_4, e_3, e_1)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(198,plain,
% 0.19/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_3) | (~product1(e_4, e_3, e_1)) | (~product1(e_4, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_3) | (~product1(e_4, e_2, e_1)) | (~product1(e_4, e_3, e_1))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[197])).
% 0.19/0.47 tff(199,plain,
% 0.19/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_3) | (~product1(e_4, e_3, e_1)) | (~product1(e_4, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_2, e_3) | (~product1(e_4, e_2, e_1)) | (~product1(e_4, e_3, e_1)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[198, 196])).
% 0.19/0.47 tff(200,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_3) | (~product1(e_4, e_3, e_1)) | (~product1(e_4, e_2, e_1)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(201,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_2, e_3) | (~product1(e_4, e_2, e_1)) | (~product1(e_4, e_3, e_1))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.19/0.47 tff(202,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[201, 54, 163, 195, 194])).
% 0.19/0.47 tff(203,plain,((~product1(e_4, e_2, e_1)) | (~product1(e_4, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(204,plain,
% 0.19/0.47 (~product1(e_4, e_2, e_1)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[203, 193])).
% 0.19/0.47 tff(205,plain,
% 0.19/0.47 ((~equalish(e_2, e_4)) <=> (~equalish(e_2, e_4))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(206,axiom,(~equalish(e_2, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_4')).
% 0.19/0.47 tff(207,plain,
% 0.19/0.47 (~equalish(e_2, e_4)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.19/0.47 tff(208,plain,
% 0.19/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_4, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_2, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_4, e_2, e_4)))),
% 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) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_4, e_2, e_4)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(210,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_2, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_4, e_2, e_4))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.19/0.47 tff(211,plain,
% 0.19/0.47 ((~product1(e_4, e_4, e_4)) | (~product1(e_4, e_2, e_4))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[210, 207, 163])).
% 0.19/0.47 tff(212,plain,
% 0.19/0.47 (~product1(e_4, e_2, e_4)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[211, 153])).
% 0.19/0.47 tff(213,plain,
% 0.19/0.47 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_4)) | product1(e_4, e_2, e_1) | product1(e_4, e_2, e_2) | product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_2)) | (~group_element(e_4)) | product1(e_4, e_2, e_1) | product1(e_4, e_2, e_2) | product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(214,plain,
% 0.19/0.47 (((~group_element(e_2)) | (~group_element(e_4)) | product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3) | product1(e_4, e_2, e_2) | product1(e_4, e_2, e_1)) <=> ((~group_element(e_2)) | (~group_element(e_4)) | product1(e_4, e_2, e_1) | product1(e_4, e_2, e_2) | product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(215,plain,
% 0.19/0.47 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_4)) | product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3) | product1(e_4, e_2, e_2) | product1(e_4, e_2, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_4)) | product1(e_4, e_2, e_1) | product1(e_4, e_2, e_2) | product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3)))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[214])).
% 0.19/0.47 tff(216,plain,
% 0.19/0.47 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_4)) | product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3) | product1(e_4, e_2, e_2) | product1(e_4, e_2, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_2)) | (~group_element(e_4)) | product1(e_4, e_2, e_1) | product1(e_4, e_2, e_2) | product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3))),
% 0.19/0.47 inference(transitivity,[status(thm)],[215, 213])).
% 0.19/0.47 tff(217,plain,
% 0.19/0.47 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_4)) | product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3) | product1(e_4, e_2, e_2) | product1(e_4, e_2, e_1))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(218,plain,
% 0.19/0.47 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_2)) | (~group_element(e_4)) | product1(e_4, e_2, e_1) | product1(e_4, e_2, e_2) | product1(e_4, e_2, e_4) | product1(e_4, e_2, e_3)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.19/0.47 tff(219,plain,
% 0.19/0.47 (product1(e_4, e_2, e_1) | product1(e_4, e_2, e_2) | product1(e_4, e_2, e_3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[218, 111, 174, 105, 212])).
% 0.19/0.47 tff(220,plain,
% 0.19/0.47 (product1(e_4, e_2, e_3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[219, 204, 30])).
% 0.19/0.47 tff(221,plain,
% 0.19/0.47 (~product1(e_3, e_2, e_3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[82, 76, 66, 62])).
% 0.19/0.47 tff(222,plain,
% 0.19/0.47 (product1(e_3, e_2, e_1) | product1(e_3, e_2, e_4)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[118, 221])).
% 0.19/0.47 tff(223,plain,
% 0.19/0.47 (product1(e_3, e_2, e_4)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[222, 31])).
% 0.19/0.47 tff(224,assumption,(product1(e_1, e_2, e_4)), introduced(assumption)).
% 0.19/0.47 tff(225,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(226,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.19/0.47 tff(227,plain,
% 0.19/0.47 (~equalish(e_1, e_3)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.19/0.47 tff(228,plain,
% 0.19/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_3) | (~product1(e_1, e_2, e_4)) | (~product1(e_3, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_1, e_3) | (~product1(e_1, e_2, e_4)) | (~product1(e_3, e_2, e_4)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(229,plain,
% 0.19/0.47 ((equalish(e_1, e_3) | (~product1(e_3, e_2, e_4)) | (~product1(e_1, e_2, e_4))) <=> (equalish(e_1, e_3) | (~product1(e_1, e_2, e_4)) | (~product1(e_3, e_2, e_4)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(230,plain,
% 0.19/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_3) | (~product1(e_3, e_2, e_4)) | (~product1(e_1, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_3) | (~product1(e_1, e_2, e_4)) | (~product1(e_3, e_2, e_4))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[229])).
% 0.19/0.47 tff(231,plain,
% 0.19/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_3) | (~product1(e_3, e_2, e_4)) | (~product1(e_1, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_1, e_3) | (~product1(e_1, e_2, e_4)) | (~product1(e_3, e_2, e_4)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[230, 228])).
% 0.19/0.47 tff(232,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_3) | (~product1(e_3, e_2, e_4)) | (~product1(e_1, e_2, e_4)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(233,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_1, e_3) | (~product1(e_1, e_2, e_4)) | (~product1(e_3, e_2, e_4))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.19/0.47 tff(234,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[233, 227, 22, 139, 224])).
% 0.19/0.47 tff(235,plain,((~product1(e_1, e_2, e_4)) | (~product1(e_3, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(236,plain,
% 0.19/0.47 (~product1(e_1, e_2, e_4)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[235, 223])).
% 0.19/0.47 tff(237,plain,
% 0.19/0.47 ((~![X: $i] : product1(X, X, X)) | product1(e_1, e_1, e_1)),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(238,plain,
% 0.19/0.47 (product1(e_1, e_1, e_1)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[237, 9])).
% 0.19/0.47 tff(239,assumption,(product1(e_1, e_2, e_1)), introduced(assumption)).
% 0.19/0.47 tff(240,plain,
% 0.19/0.47 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(241,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.19/0.47 tff(242,plain,
% 0.19/0.47 (~equalish(e_2, e_1)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.19/0.47 tff(243,plain,
% 0.19/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_1) | (~product1(e_1, e_2, e_1)) | (~product1(e_1, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_2, e_1) | (~product1(e_1, e_2, e_1)) | (~product1(e_1, e_1, e_1)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(244,plain,
% 0.19/0.47 ((equalish(e_2, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_2, e_1))) <=> (equalish(e_2, e_1) | (~product1(e_1, e_2, e_1)) | (~product1(e_1, e_1, e_1)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(245,plain,
% 0.19/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_1) | (~product1(e_1, e_2, e_1)) | (~product1(e_1, e_1, e_1))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[244])).
% 0.19/0.47 tff(246,plain,
% 0.19/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_2, e_1) | (~product1(e_1, e_2, e_1)) | (~product1(e_1, e_1, e_1)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[245, 243])).
% 0.19/0.47 tff(247,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_2, e_1)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(248,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_2, e_1) | (~product1(e_1, e_2, e_1)) | (~product1(e_1, e_1, e_1))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.19/0.47 tff(249,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[248, 242, 163, 239, 238])).
% 0.19/0.47 tff(250,plain,(~product1(e_1, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(251,assumption,(product1(e_1, e_2, e_2)), introduced(assumption)).
% 0.19/0.47 tff(252,plain,
% 0.19/0.47 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(253,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.19/0.47 tff(254,plain,
% 0.19/0.47 (~equalish(e_1, e_2)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[253, 252])).
% 0.19/0.47 tff(255,plain,
% 0.19/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_1, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_1, e_2, e_2)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(256,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_1, e_2, e_2)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(257,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_1, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_1, e_2, e_2))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.19/0.47 tff(258,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[257, 254, 22, 251, 12])).
% 0.19/0.47 tff(259,plain,(~product1(e_1, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(260,plain,
% 0.19/0.47 (group_element(e_1) <=> group_element(e_1)),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(261,axiom,(group_element(e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_1')).
% 0.19/0.47 tff(262,plain,
% 0.19/0.47 (group_element(e_1)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.19/0.47 tff(263,plain,
% 0.19/0.47 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_1)) | product1(e_1, e_2, e_3) | product1(e_1, e_2, e_2) | product1(e_1, e_2, e_1) | product1(e_1, e_2, e_4))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_2)) | (~group_element(e_1)) | product1(e_1, e_2, e_3) | product1(e_1, e_2, e_2) | product1(e_1, e_2, e_1) | product1(e_1, e_2, e_4))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(264,plain,
% 0.19/0.48 (((~group_element(e_2)) | (~group_element(e_1)) | product1(e_1, e_2, e_4) | product1(e_1, e_2, e_3) | product1(e_1, e_2, e_2) | product1(e_1, e_2, e_1)) <=> ((~group_element(e_2)) | (~group_element(e_1)) | product1(e_1, e_2, e_3) | product1(e_1, e_2, e_2) | product1(e_1, e_2, e_1) | product1(e_1, e_2, e_4))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(265,plain,
% 0.19/0.48 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_1)) | product1(e_1, e_2, e_4) | product1(e_1, e_2, e_3) | product1(e_1, e_2, e_2) | product1(e_1, e_2, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_1)) | product1(e_1, e_2, e_3) | product1(e_1, e_2, e_2) | product1(e_1, e_2, e_1) | product1(e_1, e_2, e_4)))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[264])).
% 0.19/0.48 tff(266,plain,
% 0.19/0.48 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_1)) | product1(e_1, e_2, e_4) | product1(e_1, e_2, e_3) | product1(e_1, e_2, e_2) | product1(e_1, e_2, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_2)) | (~group_element(e_1)) | product1(e_1, e_2, e_3) | product1(e_1, e_2, e_2) | product1(e_1, e_2, e_1) | product1(e_1, e_2, e_4))),
% 0.19/0.48 inference(transitivity,[status(thm)],[265, 263])).
% 0.19/0.48 tff(267,plain,
% 0.19/0.48 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_1)) | product1(e_1, e_2, e_4) | product1(e_1, e_2, e_3) | product1(e_1, e_2, e_2) | product1(e_1, e_2, e_1))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(268,plain,
% 0.19/0.48 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_2)) | (~group_element(e_1)) | product1(e_1, e_2, e_3) | product1(e_1, e_2, e_2) | product1(e_1, e_2, e_1) | product1(e_1, e_2, e_4)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.19/0.48 tff(269,plain,
% 0.19/0.48 (product1(e_1, e_2, e_3) | product1(e_1, e_2, e_1) | product1(e_1, e_2, e_4)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[268, 262, 111, 105, 259])).
% 0.19/0.48 tff(270,plain,
% 0.19/0.48 (product1(e_1, e_2, e_3) | product1(e_1, e_2, e_4)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[269, 250])).
% 0.19/0.48 tff(271,plain,
% 0.19/0.48 (product1(e_1, e_2, e_3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[270, 236])).
% 0.19/0.48 tff(272,assumption,(product1(e_4, e_2, e_3)), introduced(assumption)).
% 0.19/0.48 tff(273,assumption,(product1(e_1, e_2, e_3)), introduced(assumption)).
% 0.19/0.48 tff(274,plain,
% 0.19/0.48 ((~equalish(e_1, e_4)) <=> (~equalish(e_1, e_4))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(275,axiom,(~equalish(e_1, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_4')).
% 0.19/0.48 tff(276,plain,
% 0.19/0.48 (~equalish(e_1, e_4)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.19/0.48 tff(277,plain,
% 0.19/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_4) | (~product1(e_1, e_2, e_3)) | (~product1(e_4, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_1, e_4) | (~product1(e_1, e_2, e_3)) | (~product1(e_4, e_2, e_3)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(278,plain,
% 0.19/0.48 ((equalish(e_1, e_4) | (~product1(e_4, e_2, e_3)) | (~product1(e_1, e_2, e_3))) <=> (equalish(e_1, e_4) | (~product1(e_1, e_2, e_3)) | (~product1(e_4, e_2, e_3)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(279,plain,
% 0.19/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_4) | (~product1(e_4, e_2, e_3)) | (~product1(e_1, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_4) | (~product1(e_1, e_2, e_3)) | (~product1(e_4, e_2, e_3))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[278])).
% 0.19/0.48 tff(280,plain,
% 0.19/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_4) | (~product1(e_4, e_2, e_3)) | (~product1(e_1, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_1, e_4) | (~product1(e_1, e_2, e_3)) | (~product1(e_4, e_2, e_3)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[279, 277])).
% 0.19/0.48 tff(281,plain,
% 0.19/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_4) | (~product1(e_4, e_2, e_3)) | (~product1(e_1, e_2, e_3)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(282,plain,
% 0.19/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_1, e_4) | (~product1(e_1, e_2, e_3)) | (~product1(e_4, e_2, e_3))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.19/0.48 tff(283,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[282, 276, 22, 273, 272])).
% 0.19/0.48 tff(284,plain,((~product1(e_1, e_2, e_3)) | (~product1(e_4, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(285,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[284, 271, 220])).
% 0.19/0.48 tff(286,plain,(product1(e_3, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(287,assumption,(product1(e_3, e_2, e_1)), introduced(assumption)).
% 0.19/0.48 tff(288,plain,
% 0.19/0.48 ((~equalish(e_4, e_3)) <=> (~equalish(e_4, e_3))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(289,axiom,(~equalish(e_4, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_is_not_e_3')).
% 0.19/0.48 tff(290,plain,
% 0.19/0.48 (~equalish(e_4, e_3)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.19/0.48 tff(291,plain,
% 0.19/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_4, e_3) | (~product1(e_4, e_2, e_1)) | (~product1(e_3, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_4, e_3) | (~product1(e_4, e_2, e_1)) | (~product1(e_3, e_2, e_1)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(292,plain,
% 0.19/0.48 ((equalish(e_4, e_3) | (~product1(e_3, e_2, e_1)) | (~product1(e_4, e_2, e_1))) <=> (equalish(e_4, e_3) | (~product1(e_4, e_2, e_1)) | (~product1(e_3, e_2, e_1)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(293,plain,
% 0.19/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_4, e_3) | (~product1(e_3, e_2, e_1)) | (~product1(e_4, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_4, e_3) | (~product1(e_4, e_2, e_1)) | (~product1(e_3, e_2, e_1))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[292])).
% 0.19/0.48 tff(294,plain,
% 0.19/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_4, e_3) | (~product1(e_3, e_2, e_1)) | (~product1(e_4, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_4, e_3) | (~product1(e_4, e_2, e_1)) | (~product1(e_3, e_2, e_1)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[293, 291])).
% 0.19/0.48 tff(295,plain,
% 0.19/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_4, e_3) | (~product1(e_3, e_2, e_1)) | (~product1(e_4, e_2, e_1)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(296,plain,
% 0.19/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_4, e_3) | (~product1(e_4, e_2, e_1)) | (~product1(e_3, e_2, e_1))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.19/0.48 tff(297,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[296, 290, 22, 287, 195])).
% 0.19/0.48 tff(298,plain,((~product1(e_4, e_2, e_1)) | (~product1(e_3, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(299,plain,
% 0.19/0.48 (~product1(e_4, e_2, e_1)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[298, 286])).
% 0.19/0.48 tff(300,plain,
% 0.19/0.48 (product1(e_4, e_2, e_3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[219, 299, 30])).
% 0.19/0.48 tff(301,plain,
% 0.19/0.48 (~product1(e_1, e_2, e_3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[284, 300])).
% 0.19/0.48 tff(302,assumption,(product1(e_1, e_3, e_2)), introduced(assumption)).
% 0.19/0.48 tff(303,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (product2(e_2, e_2, e_3) | (~product1(e_1, e_3, e_2)) | (~product1(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | product2(e_2, e_2, e_3) | (~product1(e_1, e_3, e_2)) | (~product1(e_3, e_2, e_1)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(304,plain,
% 0.19/0.48 (((~product1(e_1, e_3, e_2)) | product2(e_2, e_2, e_3) | (~product1(e_3, e_2, e_1))) <=> (product2(e_2, e_2, e_3) | (~product1(e_1, e_3, e_2)) | (~product1(e_3, e_2, e_1)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(305,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_1, e_3, e_2)) | product2(e_2, e_2, e_3) | (~product1(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (product2(e_2, e_2, e_3) | (~product1(e_1, e_3, e_2)) | (~product1(e_3, e_2, e_1))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[304])).
% 0.19/0.48 tff(306,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_1, e_3, e_2)) | product2(e_2, e_2, e_3) | (~product1(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | product2(e_2, e_2, e_3) | (~product1(e_1, e_3, e_2)) | (~product1(e_3, e_2, e_1)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[305, 303])).
% 0.19/0.48 tff(307,plain,
% 0.19/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_1, e_3, e_2)) | product2(e_2, e_2, e_3) | (~product1(e_3, e_2, e_1)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(308,plain,
% 0.19/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | product2(e_2, e_2, e_3) | (~product1(e_1, e_3, e_2)) | (~product1(e_3, e_2, e_1))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.19/0.48 tff(309,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[308, 76, 302, 287, 137])).
% 0.19/0.48 tff(310,plain,((~product1(e_1, e_3, e_2)) | (~product1(e_3, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(311,plain,
% 0.19/0.48 (~product1(e_1, e_3, e_2)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[310, 286])).
% 0.19/0.48 tff(312,assumption,(product1(e_1, e_3, e_1)), introduced(assumption)).
% 0.19/0.48 tff(313,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(314,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.19/0.48 tff(315,plain,
% 0.19/0.48 (~equalish(e_3, e_1)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[314, 313])).
% 0.19/0.48 tff(316,plain,
% 0.19/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_3, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_3, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_3, e_1)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(317,plain,
% 0.19/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_3, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_3, e_1)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(318,plain,
% 0.19/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_3, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_3, e_1))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[317, 316])).
% 0.19/0.48 tff(319,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[318, 315, 163, 312, 238])).
% 0.19/0.48 tff(320,plain,(~product1(e_1, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(321,assumption,(product1(e_1, e_3, e_3)), introduced(assumption)).
% 0.19/0.48 tff(322,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (product2(e_3, e_2, e_3) | (~product1(e_3, e_2, e_1)) | (~product1(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | product2(e_3, e_2, e_3) | (~product1(e_3, e_2, e_1)) | (~product1(e_1, e_3, e_3)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(323,plain,
% 0.19/0.48 (((~product1(e_1, e_3, e_3)) | product2(e_3, e_2, e_3) | (~product1(e_3, e_2, e_1))) <=> (product2(e_3, e_2, e_3) | (~product1(e_3, e_2, e_1)) | (~product1(e_1, e_3, e_3)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(324,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_1, e_3, e_3)) | product2(e_3, e_2, e_3) | (~product1(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (product2(e_3, e_2, e_3) | (~product1(e_3, e_2, e_1)) | (~product1(e_1, e_3, e_3))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[323])).
% 0.19/0.48 tff(325,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_1, e_3, e_3)) | product2(e_3, e_2, e_3) | (~product1(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | product2(e_3, e_2, e_3) | (~product1(e_3, e_2, e_1)) | (~product1(e_1, e_3, e_3)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[324, 322])).
% 0.19/0.48 tff(326,plain,
% 0.19/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_1, e_3, e_3)) | product2(e_3, e_2, e_3) | (~product1(e_3, e_2, e_1)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(327,plain,
% 0.19/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | product2(e_3, e_2, e_3) | (~product1(e_3, e_2, e_1)) | (~product1(e_1, e_3, e_3))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[326, 325])).
% 0.19/0.48 tff(328,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[327, 76, 321, 62, 287])).
% 0.19/0.48 tff(329,plain,((~product1(e_1, e_3, e_3)) | (~product1(e_3, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(330,plain,
% 0.19/0.48 (~product1(e_1, e_3, e_3)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[329, 286])).
% 0.19/0.48 tff(331,plain,
% 0.19/0.48 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (product1(e_1, e_3, e_1) | product1(e_1, e_3, e_3) | product1(e_1, e_3, e_2) | (~group_element(e_1)) | product1(e_1, e_3, e_4) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | product1(e_1, e_3, e_1) | product1(e_1, e_3, e_3) | product1(e_1, e_3, e_2) | (~group_element(e_1)) | product1(e_1, e_3, e_4) | (~group_element(e_3)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(332,plain,
% 0.19/0.49 (((~group_element(e_3)) | (~group_element(e_1)) | product1(e_1, e_3, e_4) | product1(e_1, e_3, e_3) | product1(e_1, e_3, e_2) | product1(e_1, e_3, e_1)) <=> (product1(e_1, e_3, e_1) | product1(e_1, e_3, e_3) | product1(e_1, e_3, e_2) | (~group_element(e_1)) | product1(e_1, e_3, e_4) | (~group_element(e_3)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(333,plain,
% 0.19/0.49 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_1)) | product1(e_1, e_3, e_4) | product1(e_1, e_3, e_3) | product1(e_1, e_3, e_2) | product1(e_1, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (product1(e_1, e_3, e_1) | product1(e_1, e_3, e_3) | product1(e_1, e_3, e_2) | (~group_element(e_1)) | product1(e_1, e_3, e_4) | (~group_element(e_3))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[332])).
% 0.19/0.49 tff(334,plain,
% 0.19/0.49 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_1)) | product1(e_1, e_3, e_4) | product1(e_1, e_3, e_3) | product1(e_1, e_3, e_2) | product1(e_1, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | product1(e_1, e_3, e_1) | product1(e_1, e_3, e_3) | product1(e_1, e_3, e_2) | (~group_element(e_1)) | product1(e_1, e_3, e_4) | (~group_element(e_3)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[333, 331])).
% 0.19/0.49 tff(335,plain,
% 0.19/0.49 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_1)) | product1(e_1, e_3, e_4) | product1(e_1, e_3, e_3) | product1(e_1, e_3, e_2) | product1(e_1, e_3, e_1))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(336,plain,
% 0.19/0.49 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | product1(e_1, e_3, e_1) | product1(e_1, e_3, e_3) | product1(e_1, e_3, e_2) | (~group_element(e_1)) | product1(e_1, e_3, e_4) | (~group_element(e_3))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[335, 334])).
% 0.19/0.49 tff(337,plain,
% 0.19/0.49 (product1(e_1, e_3, e_1) | product1(e_1, e_3, e_3) | product1(e_1, e_3, e_2) | product1(e_1, e_3, e_4)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[336, 262, 108, 105])).
% 0.19/0.49 tff(338,plain,
% 0.19/0.49 (product1(e_1, e_3, e_4)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[337, 330, 320, 311])).
% 0.19/0.49 tff(339,assumption,(product1(e_1, e_3, e_4)), introduced(assumption)).
% 0.19/0.49 tff(340,plain,
% 0.19/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_3, e_2) | (~product1(e_1, e_2, e_4)) | (~product1(e_1, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_3, e_2) | (~product1(e_1, e_2, e_4)) | (~product1(e_1, e_3, e_4)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(341,plain,
% 0.19/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_3, e_2) | (~product1(e_1, e_2, e_4)) | (~product1(e_1, e_3, e_4)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(342,plain,
% 0.19/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_3, e_2) | (~product1(e_1, e_2, e_4)) | (~product1(e_1, e_3, e_4))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[341, 340])).
% 0.19/0.49 tff(343,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[342, 87, 163, 339, 224])).
% 0.19/0.49 tff(344,plain,((~product1(e_1, e_3, e_4)) | (~product1(e_1, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(345,plain,
% 0.19/0.49 (~product1(e_1, e_2, e_4)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[344, 338])).
% 0.19/0.49 tff(346,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[270, 345, 301])).
% 0.19/0.49 % SZS output end Proof
% 0.19/0.49 % E exiting
%------------------------------------------------------------------------------