%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP124-8.004 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:07:05 AM UTC 2025
% Result : Unsatisfiable 0.38s 0.53s
% Output : Proof 0.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GRP124-8.004 : TPTP v9.0.0. Released v1.2.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n010.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Thu Jun 19 15:43:56 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.38/0.53 % SZS status Unsatisfiable
% 0.38/0.53 % SZS output start Proof
% 0.38/0.53 tff(product1_type, type, (
% 0.38/0.53 product1: ( $i * $i * $i ) > $o)).
% 0.38/0.53 tff(e_2_type, type, (
% 0.38/0.53 e_2: $i)).
% 0.38/0.53 tff(e_4_type, type, (
% 0.38/0.53 e_4: $i)).
% 0.38/0.53 tff(e_3_type, type, (
% 0.38/0.53 e_3: $i)).
% 0.38/0.53 tff(e_1_type, type, (
% 0.38/0.53 e_1: $i)).
% 0.38/0.53 tff(equalish_type, type, (
% 0.38/0.53 equalish: ( $i * $i ) > $o)).
% 0.38/0.53 tff(group_element_type, type, (
% 0.38/0.53 group_element: $i > $o)).
% 0.38/0.53 tff(product2_type, type, (
% 0.38/0.53 product2: ( $i * $i * $i ) > $o)).
% 0.38/0.53 tff(1,assumption,(product1(e_3, e_4, e_2)), introduced(assumption)).
% 0.38/0.53 tff(2,assumption,(product1(e_2, e_4, e_1)), introduced(assumption)).
% 0.38/0.53 tff(3,assumption,(product1(e_2, e_3, e_1)), introduced(assumption)).
% 0.38/0.53 tff(4,plain,
% 0.38/0.53 (^[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))))),
% 0.38/0.53 inference(bind,[status(th)],[])).
% 0.38/0.53 tff(5,plain,
% 0.38/0.53 (![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)))),
% 0.38/0.53 inference(quant_intro,[status(thm)],[4])).
% 0.38/0.53 tff(6,plain,
% 0.38/0.53 (![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)))),
% 0.38/0.53 inference(rewrite,[status(thm)],[])).
% 0.38/0.53 tff(7,plain,
% 0.38/0.53 (^[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)))))),
% 0.38/0.53 inference(bind,[status(th)],[])).
% 0.38/0.53 tff(8,plain,
% 0.38/0.53 (![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)))),
% 0.38/0.53 inference(quant_intro,[status(thm)],[7])).
% 0.38/0.53 tff(9,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product1(X, W, Y)) | (~product1(X, Z, Y))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product1_right_cancellation')).
% 0.38/0.53 tff(10,plain,
% 0.38/0.53 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.38/0.53 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.38/0.53 tff(11,plain,
% 0.38/0.53 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.38/0.53 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.38/0.53 tff(12,plain,(
% 0.38/0.53 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.38/0.53 inference(skolemize,[status(sab)],[11])).
% 0.38/0.53 tff(13,plain,
% 0.38/0.53 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.38/0.53 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.38/0.53 tff(14,plain,
% 0.38/0.53 ((~equalish(e_4, e_3)) <=> (~equalish(e_4, e_3))),
% 0.38/0.53 inference(rewrite,[status(thm)],[])).
% 0.38/0.53 tff(15,axiom,(~equalish(e_4, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_3')).
% 0.38/0.53 tff(16,plain,
% 0.38/0.53 (~equalish(e_4, e_3)),
% 0.38/0.53 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.38/0.53 tff(17,plain,
% 0.38/0.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_4, e_3) | (~product1(e_2, e_4, e_1)) | (~product1(e_2, 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_4, e_3) | (~product1(e_2, e_4, e_1)) | (~product1(e_2, e_3, e_1)))),
% 0.38/0.53 inference(rewrite,[status(thm)],[])).
% 0.38/0.53 tff(18,plain,
% 0.38/0.53 ((equalish(e_4, e_3) | (~product1(e_2, e_3, e_1)) | (~product1(e_2, e_4, e_1))) <=> (equalish(e_4, e_3) | (~product1(e_2, e_4, e_1)) | (~product1(e_2, e_3, e_1)))),
% 0.38/0.53 inference(rewrite,[status(thm)],[])).
% 0.38/0.53 tff(19,plain,
% 0.38/0.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_4, e_3) | (~product1(e_2, e_3, e_1)) | (~product1(e_2, e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_4, e_3) | (~product1(e_2, e_4, e_1)) | (~product1(e_2, e_3, e_1))))),
% 0.38/0.53 inference(monotonicity,[status(thm)],[18])).
% 0.38/0.53 tff(20,plain,
% 0.38/0.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_4, e_3) | (~product1(e_2, e_3, e_1)) | (~product1(e_2, e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_4, e_3) | (~product1(e_2, e_4, e_1)) | (~product1(e_2, e_3, e_1)))),
% 0.38/0.53 inference(transitivity,[status(thm)],[19, 17])).
% 0.38/0.53 tff(21,plain,
% 0.38/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_4, e_3) | (~product1(e_2, e_3, e_1)) | (~product1(e_2, e_4, e_1)))),
% 0.38/0.53 inference(quant_inst,[status(thm)],[])).
% 0.38/0.53 tff(22,plain,
% 0.38/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_4, e_3) | (~product1(e_2, e_4, e_1)) | (~product1(e_2, e_3, e_1))),
% 0.38/0.53 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.38/0.53 tff(23,plain,
% 0.38/0.53 ($false),
% 0.38/0.53 inference(unit_resolution,[status(thm)],[22, 16, 13, 3, 2])).
% 0.38/0.53 tff(24,plain,((~product1(e_2, e_4, e_1)) | (~product1(e_2, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.53 tff(25,plain,
% 0.38/0.53 (~product1(e_2, e_3, e_1)),
% 0.38/0.53 inference(unit_resolution,[status(thm)],[24, 2])).
% 0.38/0.53 tff(26,plain,
% 0.38/0.53 (^[X: $i] : refl(product1(X, X, X) <=> product1(X, X, X))),
% 0.38/0.53 inference(bind,[status(th)],[])).
% 0.38/0.53 tff(27,plain,
% 0.38/0.53 (![X: $i] : product1(X, X, X) <=> ![X: $i] : product1(X, X, X)),
% 0.38/0.53 inference(quant_intro,[status(thm)],[26])).
% 0.38/0.53 tff(28,plain,
% 0.38/0.53 (![X: $i] : product1(X, X, X) <=> ![X: $i] : product1(X, X, X)),
% 0.38/0.53 inference(rewrite,[status(thm)],[])).
% 0.38/0.53 tff(29,axiom,(![X: $i] : product1(X, X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product1_idempotence')).
% 0.38/0.53 tff(30,plain,
% 0.38/0.53 (![X: $i] : product1(X, X, X)),
% 0.38/0.53 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.38/0.53 tff(31,plain,(
% 0.38/0.53 ![X: $i] : product1(X, X, X)),
% 0.38/0.53 inference(skolemize,[status(sab)],[30])).
% 0.38/0.53 tff(32,plain,
% 0.38/0.53 (![X: $i] : product1(X, X, X)),
% 0.38/0.53 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.38/0.53 tff(33,plain,
% 0.38/0.53 ((~![X: $i] : product1(X, X, X)) | product1(e_3, e_3, e_3)),
% 0.38/0.53 inference(quant_inst,[status(thm)],[])).
% 0.38/0.53 tff(34,plain,
% 0.38/0.53 (product1(e_3, e_3, e_3)),
% 0.38/0.53 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.38/0.53 tff(35,assumption,(product1(e_2, e_3, e_3)), introduced(assumption)).
% 0.38/0.53 tff(36,plain,
% 0.38/0.53 (^[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))))),
% 0.38/0.53 inference(bind,[status(th)],[])).
% 0.38/0.53 tff(37,plain,
% 0.38/0.53 (![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)))),
% 0.38/0.53 inference(quant_intro,[status(thm)],[36])).
% 0.38/0.53 tff(38,plain,
% 0.38/0.53 (![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)))),
% 0.38/0.53 inference(rewrite,[status(thm)],[])).
% 0.38/0.53 tff(39,plain,
% 0.38/0.53 (^[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)))))),
% 0.38/0.53 inference(bind,[status(th)],[])).
% 0.38/0.53 tff(40,plain,
% 0.38/0.53 (![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)))),
% 0.38/0.53 inference(quant_intro,[status(thm)],[39])).
% 0.38/0.53 tff(41,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product1(W, Y, X)) | (~product1(Z, Y, X))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product1_left_cancellation')).
% 0.38/0.53 tff(42,plain,
% 0.38/0.53 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.38/0.53 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.38/0.53 tff(43,plain,
% 0.38/0.53 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.38/0.53 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.38/0.53 tff(44,plain,(
% 0.38/0.53 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.38/0.53 inference(skolemize,[status(sab)],[43])).
% 0.38/0.54 tff(45,plain,
% 0.38/0.54 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.38/0.54 tff(46,plain,
% 0.38/0.54 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(47,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.38/0.54 tff(48,plain,
% 0.38/0.54 (~equalish(e_2, e_3)),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.38/0.54 tff(49,plain,
% 0.38/0.54 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_3) | (~product1(e_2, e_3, e_3)) | (~product1(e_3, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_3) | (~product1(e_2, e_3, e_3)) | (~product1(e_3, e_3, e_3)))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(50,plain,
% 0.38/0.54 ((equalish(e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_2, e_3, e_3))) <=> (equalish(e_2, e_3) | (~product1(e_2, e_3, e_3)) | (~product1(e_3, e_3, e_3)))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(51,plain,
% 0.38/0.54 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_2, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_3) | (~product1(e_2, e_3, e_3)) | (~product1(e_3, e_3, e_3))))),
% 0.38/0.54 inference(monotonicity,[status(thm)],[50])).
% 0.38/0.54 tff(52,plain,
% 0.38/0.54 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_2, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_3) | (~product1(e_2, e_3, e_3)) | (~product1(e_3, e_3, e_3)))),
% 0.38/0.54 inference(transitivity,[status(thm)],[51, 49])).
% 0.38/0.54 tff(53,plain,
% 0.38/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_2, e_3, e_3)))),
% 0.38/0.54 inference(quant_inst,[status(thm)],[])).
% 0.38/0.54 tff(54,plain,
% 0.38/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_3) | (~product1(e_2, e_3, e_3)) | (~product1(e_3, e_3, e_3))),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.38/0.54 tff(55,plain,
% 0.38/0.54 ($false),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[54, 48, 45, 35, 34])).
% 0.38/0.54 tff(56,plain,(~product1(e_2, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.38/0.54 tff(57,plain,
% 0.38/0.54 ((~![X: $i] : product1(X, X, X)) | product1(e_2, e_2, e_2)),
% 0.38/0.54 inference(quant_inst,[status(thm)],[])).
% 0.38/0.54 tff(58,plain,
% 0.38/0.54 (product1(e_2, e_2, e_2)),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[57, 32])).
% 0.38/0.54 tff(59,assumption,(product1(e_2, e_3, e_2)), introduced(assumption)).
% 0.38/0.54 tff(60,plain,
% 0.38/0.54 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(61,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.38/0.54 tff(62,plain,
% 0.38/0.54 (~equalish(e_3, e_2)),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.38/0.54 tff(63,plain,
% 0.38/0.54 (((~![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_2, e_2, e_2)) | (~product1(e_2, e_3, e_2)))) <=> ((~![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_2, e_2, e_2)) | (~product1(e_2, e_3, e_2)))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(64,plain,
% 0.38/0.54 ((~![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_2, e_2, e_2)) | (~product1(e_2, e_3, e_2)))),
% 0.38/0.54 inference(quant_inst,[status(thm)],[])).
% 0.38/0.54 tff(65,plain,
% 0.38/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_3, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_2, e_3, e_2))),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.38/0.54 tff(66,plain,
% 0.38/0.54 ($false),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[65, 62, 13, 59, 58])).
% 0.38/0.54 tff(67,plain,(~product1(e_2, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.38/0.54 tff(68,plain,
% 0.38/0.54 (^[Y: $i, X: $i] : refl(((~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) | (~group_element(Y))))),
% 0.38/0.54 inference(bind,[status(th)],[])).
% 0.38/0.54 tff(69,plain,
% 0.38/0.54 (![Y: $i, X: $i] : ((~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))) <=> ![Y: $i, X: $i] : ((~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)))),
% 0.38/0.54 inference(quant_intro,[status(thm)],[68])).
% 0.38/0.54 tff(70,plain,
% 0.38/0.54 (![Y: $i, X: $i] : ((~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))) <=> ![Y: $i, X: $i] : ((~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)))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(71,plain,
% 0.38/0.54 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) <=> ((~group_element(X)) | product1(X, Y, e_1) | (~group_element(Y)))), (((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) <=> (((~group_element(X)) | product1(X, Y, e_1) | (~group_element(Y))) | product1(X, Y, e_2)))), rewrite((((~group_element(X)) | product1(X, Y, e_1) | (~group_element(Y))) | product1(X, Y, e_2)) <=> ((~group_element(X)) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)))), (((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) <=> ((~group_element(X)) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y))))), ((((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) | product1(X, Y, e_3)) <=> (((~group_element(X)) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y))) | product1(X, Y, e_3)))), rewrite((((~group_element(X)) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y))) | product1(X, Y, e_3)) <=> ((~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)))), ((((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) | product1(X, Y, e_3)) <=> ((~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y))))), (((((((~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(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y))) | product1(X, Y, e_4)))), rewrite((((~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y))) | product1(X, Y, e_4)) <=> ((~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)) | (~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(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)))))),
% 0.38/0.54 inference(bind,[status(th)],[])).
% 0.38/0.54 tff(72,plain,
% 0.38/0.54 (![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(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)))),
% 0.38/0.54 inference(quant_intro,[status(thm)],[71])).
% 0.38/0.54 tff(73,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/sandbox2/benchmark/theBenchmark.p','product1_total_function1')).
% 0.38/0.54 tff(74,plain,
% 0.38/0.54 (![Y: $i, X: $i] : ((~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)))),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.38/0.54 tff(75,plain,
% 0.38/0.54 (![Y: $i, X: $i] : ((~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)))),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.38/0.54 tff(76,plain,(
% 0.38/0.54 ![Y: $i, X: $i] : ((~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)))),
% 0.38/0.54 inference(skolemize,[status(sab)],[75])).
% 0.38/0.54 tff(77,plain,
% 0.38/0.54 (![Y: $i, X: $i] : ((~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)))),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.38/0.54 tff(78,plain,
% 0.38/0.54 (group_element(e_3) <=> group_element(e_3)),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(79,axiom,(group_element(e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_3')).
% 0.38/0.54 tff(80,plain,
% 0.38/0.54 (group_element(e_3)),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.38/0.54 tff(81,plain,
% 0.38/0.54 (group_element(e_2) <=> group_element(e_2)),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(82,axiom,(group_element(e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_2')).
% 0.38/0.54 tff(83,plain,
% 0.38/0.54 (group_element(e_2)),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.38/0.54 tff(84,plain,
% 0.38/0.54 (((~![Y: $i, X: $i] : ((~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(e_2)) | (~group_element(e_3)) | product1(e_2, e_3, e_4) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~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(e_2)) | (~group_element(e_3)) | product1(e_2, e_3, e_4) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_1))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(85,plain,
% 0.38/0.54 (((~group_element(e_2)) | product1(e_2, e_3, e_4) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_1) | (~group_element(e_3))) <=> ((~group_element(e_2)) | (~group_element(e_3)) | product1(e_2, e_3, e_4) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_1))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(86,plain,
% 0.38/0.54 (((~![Y: $i, X: $i] : ((~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(e_2)) | product1(e_2, e_3, e_4) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_1) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : ((~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(e_2)) | (~group_element(e_3)) | product1(e_2, e_3, e_4) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_1)))),
% 0.38/0.54 inference(monotonicity,[status(thm)],[85])).
% 0.38/0.54 tff(87,plain,
% 0.38/0.54 (((~![Y: $i, X: $i] : ((~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(e_2)) | product1(e_2, e_3, e_4) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_1) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : ((~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(e_2)) | (~group_element(e_3)) | product1(e_2, e_3, e_4) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_1))),
% 0.38/0.54 inference(transitivity,[status(thm)],[86, 84])).
% 0.38/0.54 tff(88,plain,
% 0.38/0.54 ((~![Y: $i, X: $i] : ((~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(e_2)) | product1(e_2, e_3, e_4) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_1) | (~group_element(e_3)))),
% 0.38/0.54 inference(quant_inst,[status(thm)],[])).
% 0.38/0.54 tff(89,plain,
% 0.38/0.54 ((~![Y: $i, X: $i] : ((~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(e_2)) | (~group_element(e_3)) | product1(e_2, e_3, e_4) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_1)),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.38/0.54 tff(90,plain,
% 0.38/0.54 (product1(e_2, e_3, e_4) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_1)),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[89, 83, 80, 77])).
% 0.38/0.54 tff(91,plain,
% 0.38/0.54 (product1(e_2, e_3, e_4) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_1)),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[90, 67])).
% 0.38/0.54 tff(92,plain,
% 0.38/0.54 (product1(e_2, e_3, e_4) | product1(e_2, e_3, e_1)),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[91, 56])).
% 0.38/0.54 tff(93,plain,
% 0.38/0.54 (product1(e_2, e_3, e_4)),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[92, 25])).
% 0.38/0.54 tff(94,assumption,(product1(e_2, e_1, e_4)), introduced(assumption)).
% 0.38/0.54 tff(95,assumption,(product1(e_2, e_3, e_4)), introduced(assumption)).
% 0.38/0.54 tff(96,plain,
% 0.38/0.54 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(97,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.38/0.54 tff(98,plain,
% 0.38/0.54 (~equalish(e_1, e_3)),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.38/0.54 tff(99,plain,
% 0.38/0.54 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_1, e_3) | (~product1(e_2, e_1, e_4)) | (~product1(e_2, 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_1, e_3) | (~product1(e_2, e_1, e_4)) | (~product1(e_2, e_3, e_4)))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(100,plain,
% 0.38/0.54 ((equalish(e_1, e_3) | (~product1(e_2, e_3, e_4)) | (~product1(e_2, e_1, e_4))) <=> (equalish(e_1, e_3) | (~product1(e_2, e_1, e_4)) | (~product1(e_2, e_3, e_4)))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(101,plain,
% 0.38/0.54 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_1, e_3) | (~product1(e_2, e_3, e_4)) | (~product1(e_2, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_1, e_3) | (~product1(e_2, e_1, e_4)) | (~product1(e_2, e_3, e_4))))),
% 0.38/0.54 inference(monotonicity,[status(thm)],[100])).
% 0.38/0.54 tff(102,plain,
% 0.38/0.54 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_1, e_3) | (~product1(e_2, e_3, e_4)) | (~product1(e_2, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_1, e_3) | (~product1(e_2, e_1, e_4)) | (~product1(e_2, e_3, e_4)))),
% 0.38/0.54 inference(transitivity,[status(thm)],[101, 99])).
% 0.38/0.54 tff(103,plain,
% 0.38/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_1, e_3) | (~product1(e_2, e_3, e_4)) | (~product1(e_2, e_1, e_4)))),
% 0.38/0.54 inference(quant_inst,[status(thm)],[])).
% 0.38/0.54 tff(104,plain,
% 0.38/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_1, e_3) | (~product1(e_2, e_1, e_4)) | (~product1(e_2, e_3, e_4))),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.38/0.54 tff(105,plain,
% 0.38/0.54 ($false),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[104, 98, 13, 95, 94])).
% 0.38/0.54 tff(106,plain,((~product1(e_2, e_1, e_4)) | (~product1(e_2, e_3, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.54 tff(107,plain,
% 0.38/0.54 (~product1(e_2, e_1, e_4)),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[106, 93])).
% 0.38/0.54 tff(108,assumption,(~product2(e_1, e_1, e_1)), introduced(assumption)).
% 0.38/0.54 tff(109,plain,
% 0.38/0.54 (^[X: $i] : refl(product2(X, X, X) <=> product2(X, X, X))),
% 0.38/0.54 inference(bind,[status(th)],[])).
% 0.38/0.54 tff(110,plain,
% 0.38/0.54 (![X: $i] : product2(X, X, X) <=> ![X: $i] : product2(X, X, X)),
% 0.38/0.54 inference(quant_intro,[status(thm)],[109])).
% 0.38/0.54 tff(111,plain,
% 0.38/0.54 (![X: $i] : product2(X, X, X) <=> ![X: $i] : product2(X, X, X)),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(112,axiom,(![X: $i] : product2(X, X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product2_idempotence')).
% 0.38/0.54 tff(113,plain,
% 0.38/0.54 (![X: $i] : product2(X, X, X)),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.38/0.54 tff(114,plain,(
% 0.38/0.54 ![X: $i] : product2(X, X, X)),
% 0.38/0.54 inference(skolemize,[status(sab)],[113])).
% 0.38/0.54 tff(115,plain,
% 0.38/0.54 (![X: $i] : product2(X, X, X)),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.38/0.54 tff(116,plain,
% 0.38/0.54 ((~![X: $i] : product2(X, X, X)) | product2(e_1, e_1, e_1)),
% 0.38/0.54 inference(quant_inst,[status(thm)],[])).
% 0.38/0.54 tff(117,plain,
% 0.38/0.54 ($false),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[116, 115, 108])).
% 0.38/0.54 tff(118,plain,(product2(e_1, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.38/0.54 tff(119,assumption,(product2(e_1, e_1, e_4)), introduced(assumption)).
% 0.38/0.54 tff(120,plain,
% 0.38/0.54 (^[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))))),
% 0.38/0.54 inference(bind,[status(th)],[])).
% 0.38/0.54 tff(121,plain,
% 0.38/0.54 (![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)))),
% 0.38/0.54 inference(quant_intro,[status(thm)],[120])).
% 0.38/0.54 tff(122,plain,
% 0.38/0.54 (![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)))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(123,plain,
% 0.38/0.54 (^[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)))))),
% 0.38/0.54 inference(bind,[status(th)],[])).
% 0.38/0.54 tff(124,plain,
% 0.38/0.54 (![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)))),
% 0.38/0.54 inference(quant_intro,[status(thm)],[123])).
% 0.38/0.54 tff(125,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product2(X, Y, W)) | (~product2(X, Y, Z))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product2_total_function2')).
% 0.38/0.54 tff(126,plain,
% 0.38/0.54 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.38/0.54 tff(127,plain,
% 0.38/0.54 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.38/0.54 tff(128,plain,(
% 0.38/0.54 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.38/0.54 inference(skolemize,[status(sab)],[127])).
% 0.38/0.54 tff(129,plain,
% 0.38/0.54 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[128, 121])).
% 0.38/0.54 tff(130,plain,
% 0.38/0.54 ((~equalish(e_4, e_1)) <=> (~equalish(e_4, e_1))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(131,axiom,(~equalish(e_4, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_1')).
% 0.38/0.54 tff(132,plain,
% 0.38/0.54 (~equalish(e_4, e_1)),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.38/0.54 tff(133,plain,
% 0.38/0.54 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | (equalish(e_4, e_1) | (~product2(e_1, e_1, e_4)) | (~product2(e_1, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | equalish(e_4, e_1) | (~product2(e_1, e_1, e_4)) | (~product2(e_1, e_1, e_1)))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(134,plain,
% 0.38/0.54 ((equalish(e_4, e_1) | (~product2(e_1, e_1, e_1)) | (~product2(e_1, e_1, e_4))) <=> (equalish(e_4, e_1) | (~product2(e_1, e_1, e_4)) | (~product2(e_1, e_1, e_1)))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(135,plain,
% 0.38/0.54 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | (equalish(e_4, e_1) | (~product2(e_1, e_1, e_1)) | (~product2(e_1, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | (equalish(e_4, e_1) | (~product2(e_1, e_1, e_4)) | (~product2(e_1, e_1, e_1))))),
% 0.38/0.54 inference(monotonicity,[status(thm)],[134])).
% 0.38/0.54 tff(136,plain,
% 0.38/0.54 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | (equalish(e_4, e_1) | (~product2(e_1, e_1, e_1)) | (~product2(e_1, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | equalish(e_4, e_1) | (~product2(e_1, e_1, e_4)) | (~product2(e_1, e_1, e_1)))),
% 0.38/0.54 inference(transitivity,[status(thm)],[135, 133])).
% 0.38/0.54 tff(137,plain,
% 0.38/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | (equalish(e_4, e_1) | (~product2(e_1, e_1, e_1)) | (~product2(e_1, e_1, e_4)))),
% 0.38/0.54 inference(quant_inst,[status(thm)],[])).
% 0.38/0.54 tff(138,plain,
% 0.38/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | equalish(e_4, e_1) | (~product2(e_1, e_1, e_4)) | (~product2(e_1, e_1, e_1))),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.38/0.54 tff(139,plain,
% 0.38/0.54 ($false),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[138, 132, 129, 119, 118])).
% 0.38/0.54 tff(140,plain,(~product2(e_1, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.38/0.54 tff(141,assumption,(~product2(e_1, e_1, e_4)), introduced(assumption)).
% 0.38/0.54 tff(142,assumption,(product1(e_4, e_1, e_2)), introduced(assumption)).
% 0.38/0.54 tff(143,plain,
% 0.38/0.54 (^[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))))),
% 0.38/0.54 inference(bind,[status(th)],[])).
% 0.38/0.54 tff(144,plain,
% 0.38/0.54 (![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)))),
% 0.38/0.55 inference(quant_intro,[status(thm)],[143])).
% 0.38/0.55 tff(145,plain,
% 0.38/0.55 (![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)))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(146,plain,
% 0.38/0.55 (^[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))))),
% 0.38/0.55 inference(bind,[status(th)],[])).
% 0.38/0.55 tff(147,plain,
% 0.38/0.55 (![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)))),
% 0.38/0.55 inference(quant_intro,[status(thm)],[146])).
% 0.38/0.55 tff(148,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product1(X, Y, Z1)) | (~product1(Z1, X, Z2))) | product2(Z2, Y, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qg2a')).
% 0.38/0.55 tff(149,plain,
% 0.38/0.55 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.38/0.55 tff(150,plain,
% 0.38/0.55 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[149, 145])).
% 0.38/0.55 tff(151,plain,(
% 0.38/0.55 ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.38/0.55 inference(skolemize,[status(sab)],[150])).
% 0.38/0.55 tff(152,plain,
% 0.38/0.55 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[151, 144])).
% 0.38/0.55 tff(153,plain,
% 0.38/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_4, e_1, e_2)) | product2(e_1, e_1, e_4) | (~product1(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_4, e_1, e_2)) | product2(e_1, e_1, e_4) | (~product1(e_2, e_4, e_1)))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(154,plain,
% 0.38/0.55 (((~product1(e_2, e_4, e_1)) | product2(e_1, e_1, e_4) | (~product1(e_4, e_1, e_2))) <=> ((~product1(e_4, e_1, e_2)) | product2(e_1, e_1, e_4) | (~product1(e_2, e_4, e_1)))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(155,plain,
% 0.38/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_2, e_4, e_1)) | product2(e_1, e_1, e_4) | (~product1(e_4, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_4, e_1, e_2)) | product2(e_1, e_1, e_4) | (~product1(e_2, e_4, e_1))))),
% 0.38/0.55 inference(monotonicity,[status(thm)],[154])).
% 0.38/0.55 tff(156,plain,
% 0.38/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_2, e_4, e_1)) | product2(e_1, e_1, e_4) | (~product1(e_4, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_4, e_1, e_2)) | product2(e_1, e_1, e_4) | (~product1(e_2, e_4, e_1)))),
% 0.38/0.55 inference(transitivity,[status(thm)],[155, 153])).
% 0.38/0.55 tff(157,plain,
% 0.38/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_2, e_4, e_1)) | product2(e_1, e_1, e_4) | (~product1(e_4, e_1, e_2)))),
% 0.38/0.55 inference(quant_inst,[status(thm)],[])).
% 0.38/0.55 tff(158,plain,
% 0.38/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_4, e_1, e_2)) | product2(e_1, e_1, e_4) | (~product1(e_2, e_4, e_1))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.38/0.55 tff(159,plain,
% 0.38/0.55 ($false),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[158, 152, 142, 141, 2])).
% 0.38/0.55 tff(160,plain,(product2(e_1, e_1, e_4) | (~product1(e_4, e_1, e_2)) | (~product1(e_2, e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.55 tff(161,plain,
% 0.38/0.55 ((~product1(e_4, e_1, e_2)) | (~product1(e_2, e_4, e_1))),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[160, 140])).
% 0.38/0.55 tff(162,plain,
% 0.38/0.55 (~product1(e_4, e_1, e_2)),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[161, 2])).
% 0.38/0.55 tff(163,plain,
% 0.38/0.55 ((~![X: $i] : product1(X, X, X)) | product1(e_4, e_4, e_4)),
% 0.38/0.55 inference(quant_inst,[status(thm)],[])).
% 0.38/0.55 tff(164,plain,
% 0.38/0.55 (product1(e_4, e_4, e_4)),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[163, 32])).
% 0.38/0.55 tff(165,plain,
% 0.38/0.55 ((~![X: $i] : product2(X, X, X)) | product2(e_4, e_4, e_4)),
% 0.38/0.55 inference(quant_inst,[status(thm)],[])).
% 0.38/0.55 tff(166,plain,
% 0.38/0.55 (product2(e_4, e_4, e_4)),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[165, 115])).
% 0.38/0.55 tff(167,assumption,(product2(e_4, e_1, e_4)), introduced(assumption)).
% 0.38/0.55 tff(168,plain,
% 0.38/0.55 (^[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))))),
% 0.38/0.55 inference(bind,[status(th)],[])).
% 0.38/0.55 tff(169,plain,
% 0.38/0.55 (![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)))),
% 0.38/0.55 inference(quant_intro,[status(thm)],[168])).
% 0.38/0.55 tff(170,plain,
% 0.38/0.55 (![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)))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(171,plain,
% 0.38/0.55 (^[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)))))),
% 0.38/0.55 inference(bind,[status(th)],[])).
% 0.38/0.55 tff(172,plain,
% 0.38/0.55 (![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)))),
% 0.38/0.55 inference(quant_intro,[status(thm)],[171])).
% 0.38/0.55 tff(173,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product2(X, W, Y)) | (~product2(X, Z, Y))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product2_right_cancellation')).
% 0.38/0.55 tff(174,plain,
% 0.38/0.55 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.38/0.55 tff(175,plain,
% 0.38/0.55 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[174, 170])).
% 0.38/0.55 tff(176,plain,(
% 0.38/0.55 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.38/0.55 inference(skolemize,[status(sab)],[175])).
% 0.38/0.55 tff(177,plain,
% 0.38/0.55 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[176, 169])).
% 0.38/0.55 tff(178,plain,
% 0.38/0.55 ((~equalish(e_1, e_4)) <=> (~equalish(e_1, e_4))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(179,axiom,(~equalish(e_1, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_4')).
% 0.38/0.55 tff(180,plain,
% 0.38/0.55 (~equalish(e_1, e_4)),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.38/0.55 tff(181,plain,
% 0.38/0.55 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_1, e_4) | (~product2(e_4, e_1, e_4)) | (~product2(e_4, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_1, e_4) | (~product2(e_4, e_1, e_4)) | (~product2(e_4, e_4, e_4)))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(182,plain,
% 0.38/0.55 ((equalish(e_1, e_4) | (~product2(e_4, e_4, e_4)) | (~product2(e_4, e_1, e_4))) <=> (equalish(e_1, e_4) | (~product2(e_4, e_1, e_4)) | (~product2(e_4, e_4, e_4)))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(183,plain,
% 0.38/0.55 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_1, e_4) | (~product2(e_4, e_4, e_4)) | (~product2(e_4, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_1, e_4) | (~product2(e_4, e_1, e_4)) | (~product2(e_4, e_4, e_4))))),
% 0.38/0.55 inference(monotonicity,[status(thm)],[182])).
% 0.38/0.55 tff(184,plain,
% 0.38/0.55 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_1, e_4) | (~product2(e_4, e_4, e_4)) | (~product2(e_4, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_1, e_4) | (~product2(e_4, e_1, e_4)) | (~product2(e_4, e_4, e_4)))),
% 0.38/0.55 inference(transitivity,[status(thm)],[183, 181])).
% 0.38/0.55 tff(185,plain,
% 0.38/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_1, e_4) | (~product2(e_4, e_4, e_4)) | (~product2(e_4, e_1, e_4)))),
% 0.38/0.55 inference(quant_inst,[status(thm)],[])).
% 0.38/0.55 tff(186,plain,
% 0.38/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_1, e_4) | (~product2(e_4, e_1, e_4)) | (~product2(e_4, e_4, e_4))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.38/0.55 tff(187,plain,
% 0.38/0.55 ($false),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[186, 180, 177, 167, 166])).
% 0.38/0.55 tff(188,plain,(~product2(e_4, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.38/0.55 tff(189,plain,
% 0.38/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_4, e_1, e_4)) | product2(e_4, e_1, e_4) | (~product1(e_4, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_4, e_1, e_4)) | product2(e_4, e_1, e_4) | (~product1(e_4, e_4, e_4)))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(190,plain,
% 0.38/0.55 (((~product1(e_4, e_4, e_4)) | product2(e_4, e_1, e_4) | (~product1(e_4, e_1, e_4))) <=> ((~product1(e_4, e_1, e_4)) | product2(e_4, e_1, e_4) | (~product1(e_4, e_4, e_4)))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(191,plain,
% 0.38/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_4, e_4, e_4)) | product2(e_4, e_1, e_4) | (~product1(e_4, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_4, e_1, e_4)) | product2(e_4, e_1, e_4) | (~product1(e_4, e_4, e_4))))),
% 0.38/0.55 inference(monotonicity,[status(thm)],[190])).
% 0.38/0.55 tff(192,plain,
% 0.38/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_4, e_4, e_4)) | product2(e_4, e_1, e_4) | (~product1(e_4, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_4, e_1, e_4)) | product2(e_4, e_1, e_4) | (~product1(e_4, e_4, e_4)))),
% 0.38/0.55 inference(transitivity,[status(thm)],[191, 189])).
% 0.38/0.55 tff(193,plain,
% 0.38/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_4, e_4, e_4)) | product2(e_4, e_1, e_4) | (~product1(e_4, e_1, e_4)))),
% 0.38/0.55 inference(quant_inst,[status(thm)],[])).
% 0.38/0.55 tff(194,plain,
% 0.38/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_4, e_1, e_4)) | product2(e_4, e_1, e_4) | (~product1(e_4, e_4, e_4))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.38/0.55 tff(195,plain,
% 0.38/0.55 (~product1(e_4, e_1, e_4)),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[194, 152, 188, 164])).
% 0.38/0.55 tff(196,assumption,(~product1(e_1, e_1, e_1)), introduced(assumption)).
% 0.38/0.55 tff(197,plain,
% 0.38/0.55 ((~![X: $i] : product1(X, X, X)) | product1(e_1, e_1, e_1)),
% 0.38/0.55 inference(quant_inst,[status(thm)],[])).
% 0.38/0.55 tff(198,plain,
% 0.38/0.55 ($false),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[197, 32, 196])).
% 0.38/0.55 tff(199,plain,(product1(e_1, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.38/0.55 tff(200,assumption,(product1(e_1, e_1, e_1)), introduced(assumption)).
% 0.38/0.55 tff(201,assumption,(product1(e_4, e_1, e_1)), introduced(assumption)).
% 0.38/0.55 tff(202,plain,
% 0.38/0.55 (((~![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_1, e_1)) | (~product1(e_1, e_1, e_1)))) <=> ((~![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_1, e_1)) | (~product1(e_1, e_1, e_1)))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(203,plain,
% 0.38/0.55 ((~![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_1, e_1)) | (~product1(e_1, e_1, e_1)))),
% 0.38/0.55 inference(quant_inst,[status(thm)],[])).
% 0.38/0.55 tff(204,plain,
% 0.38/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_1, e_4) | (~product1(e_4, e_1, e_1)) | (~product1(e_1, e_1, e_1))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.38/0.55 tff(205,plain,
% 0.38/0.55 ($false),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[204, 180, 45, 201, 200])).
% 0.38/0.55 tff(206,plain,((~product1(e_1, e_1, e_1)) | (~product1(e_4, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.55 tff(207,plain,
% 0.38/0.55 (~product1(e_4, e_1, e_1)),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[206, 199])).
% 0.38/0.55 tff(208,assumption,(~product1(e_4, e_1, e_4)), introduced(assumption)).
% 0.38/0.55 tff(209,assumption,(~product1(e_4, e_1, e_3)), introduced(assumption)).
% 0.38/0.55 tff(210,assumption,(~product1(e_4, e_1, e_1)), introduced(assumption)).
% 0.38/0.55 tff(211,assumption,(~product1(e_4, e_1, e_2)), introduced(assumption)).
% 0.38/0.55 tff(212,plain,
% 0.38/0.55 (group_element(e_4) <=> group_element(e_4)),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(213,axiom,(group_element(e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_4')).
% 0.38/0.55 tff(214,plain,
% 0.38/0.55 (group_element(e_4)),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.38/0.55 tff(215,plain,
% 0.38/0.55 (group_element(e_1) <=> group_element(e_1)),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(216,axiom,(group_element(e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_1')).
% 0.38/0.55 tff(217,plain,
% 0.38/0.55 (group_element(e_1)),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.38/0.55 tff(218,plain,
% 0.38/0.55 (((~![Y: $i, X: $i] : ((~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(e_1)) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_4) | product1(e_4, e_1, e_3) | product1(e_4, e_1, e_1) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_4) | product1(e_4, e_1, e_3) | product1(e_4, e_1, e_1) | (~group_element(e_4)))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(219,plain,
% 0.38/0.55 (((~group_element(e_4)) | product1(e_4, e_1, e_4) | product1(e_4, e_1, e_3) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_1) | (~group_element(e_1))) <=> ((~group_element(e_1)) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_4) | product1(e_4, e_1, e_3) | product1(e_4, e_1, e_1) | (~group_element(e_4)))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(220,plain,
% 0.38/0.55 (((~![Y: $i, X: $i] : ((~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(e_4)) | product1(e_4, e_1, e_4) | product1(e_4, e_1, e_3) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_4) | product1(e_4, e_1, e_3) | product1(e_4, e_1, e_1) | (~group_element(e_4))))),
% 0.38/0.55 inference(monotonicity,[status(thm)],[219])).
% 0.38/0.55 tff(221,plain,
% 0.38/0.55 (((~![Y: $i, X: $i] : ((~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(e_4)) | product1(e_4, e_1, e_4) | product1(e_4, e_1, e_3) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_4) | product1(e_4, e_1, e_3) | product1(e_4, e_1, e_1) | (~group_element(e_4)))),
% 0.38/0.55 inference(transitivity,[status(thm)],[220, 218])).
% 0.38/0.55 tff(222,plain,
% 0.38/0.55 ((~![Y: $i, X: $i] : ((~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(e_4)) | product1(e_4, e_1, e_4) | product1(e_4, e_1, e_3) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_1) | (~group_element(e_1)))),
% 0.38/0.55 inference(quant_inst,[status(thm)],[])).
% 0.38/0.55 tff(223,plain,
% 0.38/0.55 ((~![Y: $i, X: $i] : ((~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | product1(e_4, e_1, e_2) | product1(e_4, e_1, e_4) | product1(e_4, e_1, e_3) | product1(e_4, e_1, e_1) | (~group_element(e_4))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.38/0.55 tff(224,plain,
% 0.38/0.55 ($false),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[223, 217, 214, 77, 211, 210, 209, 208])).
% 0.38/0.55 tff(225,plain,(product1(e_4, e_1, e_2) | product1(e_4, e_1, e_1) | product1(e_4, e_1, e_3) | product1(e_4, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.38/0.55 tff(226,plain,
% 0.38/0.55 (product1(e_4, e_1, e_2) | product1(e_4, e_1, e_3) | product1(e_4, e_1, e_4)),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[225, 207])).
% 0.38/0.55 tff(227,plain,
% 0.38/0.55 (product1(e_4, e_1, e_2) | product1(e_4, e_1, e_3)),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[226, 195])).
% 0.38/0.55 tff(228,plain,
% 0.38/0.55 (product1(e_4, e_1, e_3)),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[227, 162])).
% 0.38/0.55 tff(229,assumption,(product1(e_2, e_1, e_3)), introduced(assumption)).
% 0.38/0.55 tff(230,assumption,(product1(e_4, e_1, e_3)), introduced(assumption)).
% 0.38/0.55 tff(231,plain,
% 0.38/0.55 ((~equalish(e_4, e_2)) <=> (~equalish(e_4, e_2))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(232,axiom,(~equalish(e_4, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_2')).
% 0.38/0.55 tff(233,plain,
% 0.38/0.55 (~equalish(e_4, e_2)),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.38/0.55 tff(234,plain,
% 0.38/0.55 (((~![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_4, e_1, e_3)) | (~product1(e_2, e_1, e_3)))) <=> ((~![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_4, e_1, e_3)) | (~product1(e_2, e_1, e_3)))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(235,plain,
% 0.38/0.55 ((equalish(e_4, e_2) | (~product1(e_2, e_1, e_3)) | (~product1(e_4, e_1, e_3))) <=> (equalish(e_4, e_2) | (~product1(e_4, e_1, e_3)) | (~product1(e_2, e_1, e_3)))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(236,plain,
% 0.38/0.55 (((~![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_1, e_3)) | (~product1(e_4, e_1, e_3)))) <=> ((~![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_4, e_1, e_3)) | (~product1(e_2, e_1, e_3))))),
% 0.38/0.55 inference(monotonicity,[status(thm)],[235])).
% 0.38/0.55 tff(237,plain,
% 0.38/0.55 (((~![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_1, e_3)) | (~product1(e_4, e_1, e_3)))) <=> ((~![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_4, e_1, e_3)) | (~product1(e_2, e_1, e_3)))),
% 0.38/0.56 inference(transitivity,[status(thm)],[236, 234])).
% 0.38/0.56 tff(238,plain,
% 0.38/0.56 ((~![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_1, e_3)) | (~product1(e_4, e_1, e_3)))),
% 0.38/0.56 inference(quant_inst,[status(thm)],[])).
% 0.38/0.56 tff(239,plain,
% 0.38/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_4, e_2) | (~product1(e_4, e_1, e_3)) | (~product1(e_2, e_1, e_3))),
% 0.38/0.56 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.38/0.56 tff(240,plain,
% 0.38/0.56 ($false),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[239, 233, 45, 230, 229])).
% 0.38/0.56 tff(241,plain,((~product1(e_4, e_1, e_3)) | (~product1(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.56 tff(242,plain,
% 0.38/0.56 (~product1(e_2, e_1, e_3)),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[241, 228])).
% 0.38/0.56 tff(243,assumption,(product1(e_2, e_1, e_1)), introduced(assumption)).
% 0.38/0.56 tff(244,plain,
% 0.38/0.56 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(245,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.38/0.56 tff(246,plain,
% 0.38/0.56 (~equalish(e_2, e_1)),
% 0.38/0.56 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.38/0.56 tff(247,plain,
% 0.38/0.56 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_1) | (~product1(e_2, e_1, e_1)) | (~product1(e_1, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_1) | (~product1(e_2, e_1, e_1)) | (~product1(e_1, e_1, e_1)))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(248,plain,
% 0.38/0.56 ((equalish(e_2, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_2, e_1, e_1))) <=> (equalish(e_2, e_1) | (~product1(e_2, e_1, e_1)) | (~product1(e_1, e_1, e_1)))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(249,plain,
% 0.38/0.56 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_2, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_1) | (~product1(e_2, e_1, e_1)) | (~product1(e_1, e_1, e_1))))),
% 0.38/0.56 inference(monotonicity,[status(thm)],[248])).
% 0.38/0.56 tff(250,plain,
% 0.38/0.56 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_2, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_1) | (~product1(e_2, e_1, e_1)) | (~product1(e_1, e_1, e_1)))),
% 0.38/0.56 inference(transitivity,[status(thm)],[249, 247])).
% 0.38/0.56 tff(251,plain,
% 0.38/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_2, e_1, e_1)))),
% 0.38/0.56 inference(quant_inst,[status(thm)],[])).
% 0.38/0.56 tff(252,plain,
% 0.38/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_1) | (~product1(e_2, e_1, e_1)) | (~product1(e_1, e_1, e_1))),
% 0.38/0.56 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.38/0.56 tff(253,plain,
% 0.38/0.56 ($false),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[252, 246, 45, 243, 199])).
% 0.38/0.56 tff(254,plain,(~product1(e_2, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.38/0.56 tff(255,assumption,(product2(e_2, e_1, e_2)), introduced(assumption)).
% 0.38/0.56 tff(256,plain,
% 0.38/0.56 ((~![X: $i] : product2(X, X, X)) | product2(e_2, e_2, e_2)),
% 0.38/0.56 inference(quant_inst,[status(thm)],[])).
% 0.38/0.56 tff(257,plain,
% 0.38/0.56 (product2(e_2, e_2, e_2)),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[256, 115])).
% 0.38/0.56 tff(258,plain,
% 0.38/0.56 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(259,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.38/0.56 tff(260,plain,
% 0.38/0.56 (~equalish(e_1, e_2)),
% 0.38/0.56 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.38/0.56 tff(261,plain,
% 0.38/0.56 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_1, e_2) | (~product2(e_2, e_2, e_2)) | (~product2(e_2, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_1, e_2) | (~product2(e_2, e_2, e_2)) | (~product2(e_2, e_1, e_2)))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(262,plain,
% 0.38/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_1, e_2) | (~product2(e_2, e_2, e_2)) | (~product2(e_2, e_1, e_2)))),
% 0.38/0.56 inference(quant_inst,[status(thm)],[])).
% 0.38/0.56 tff(263,plain,
% 0.38/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_1, e_2) | (~product2(e_2, e_2, e_2)) | (~product2(e_2, e_1, e_2))),
% 0.38/0.56 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.38/0.56 tff(264,plain,
% 0.38/0.56 ($false),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[263, 260, 177, 257, 255])).
% 0.38/0.56 tff(265,plain,(~product2(e_2, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.38/0.56 tff(266,plain,
% 0.38/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_2, e_2, e_2)) | (~product1(e_2, e_1, e_2)) | product2(e_2, e_1, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_2, e_2, e_2)) | (~product1(e_2, e_1, e_2)) | product2(e_2, e_1, e_2))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(267,plain,
% 0.38/0.56 (((~product1(e_2, e_2, e_2)) | product2(e_2, e_1, e_2) | (~product1(e_2, e_1, e_2))) <=> ((~product1(e_2, e_2, e_2)) | (~product1(e_2, e_1, e_2)) | product2(e_2, e_1, e_2))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(268,plain,
% 0.38/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_2, e_2, e_2)) | product2(e_2, e_1, e_2) | (~product1(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_2, e_2, e_2)) | (~product1(e_2, e_1, e_2)) | product2(e_2, e_1, e_2)))),
% 0.38/0.56 inference(monotonicity,[status(thm)],[267])).
% 0.38/0.56 tff(269,plain,
% 0.38/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_2, e_2, e_2)) | product2(e_2, e_1, e_2) | (~product1(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_2, e_2, e_2)) | (~product1(e_2, e_1, e_2)) | product2(e_2, e_1, e_2))),
% 0.38/0.56 inference(transitivity,[status(thm)],[268, 266])).
% 0.38/0.56 tff(270,plain,
% 0.38/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_2, e_2, e_2)) | product2(e_2, e_1, e_2) | (~product1(e_2, e_1, e_2)))),
% 0.38/0.56 inference(quant_inst,[status(thm)],[])).
% 0.38/0.56 tff(271,plain,
% 0.38/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_2, e_2, e_2)) | (~product1(e_2, e_1, e_2)) | product2(e_2, e_1, e_2)),
% 0.38/0.56 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.38/0.56 tff(272,plain,
% 0.38/0.56 (~product1(e_2, e_1, e_2)),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[271, 152, 58, 265])).
% 0.38/0.56 tff(273,plain,
% 0.38/0.56 (((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_2)) | product1(e_2, e_1, e_2) | product1(e_2, e_1, e_1) | product1(e_2, e_1, e_4) | product1(e_2, e_1, e_3))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_2)) | product1(e_2, e_1, e_2) | product1(e_2, e_1, e_1) | product1(e_2, e_1, e_4) | product1(e_2, e_1, e_3))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(274,plain,
% 0.38/0.56 (((~group_element(e_2)) | product1(e_2, e_1, e_4) | product1(e_2, e_1, e_3) | product1(e_2, e_1, e_2) | product1(e_2, e_1, e_1) | (~group_element(e_1))) <=> ((~group_element(e_1)) | (~group_element(e_2)) | product1(e_2, e_1, e_2) | product1(e_2, e_1, e_1) | product1(e_2, e_1, e_4) | product1(e_2, e_1, e_3))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(275,plain,
% 0.38/0.56 (((~![Y: $i, X: $i] : ((~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(e_2)) | product1(e_2, e_1, e_4) | product1(e_2, e_1, e_3) | product1(e_2, e_1, e_2) | product1(e_2, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_2)) | product1(e_2, e_1, e_2) | product1(e_2, e_1, e_1) | product1(e_2, e_1, e_4) | product1(e_2, e_1, e_3)))),
% 0.38/0.56 inference(monotonicity,[status(thm)],[274])).
% 0.38/0.56 tff(276,plain,
% 0.38/0.56 (((~![Y: $i, X: $i] : ((~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(e_2)) | product1(e_2, e_1, e_4) | product1(e_2, e_1, e_3) | product1(e_2, e_1, e_2) | product1(e_2, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_2)) | product1(e_2, e_1, e_2) | product1(e_2, e_1, e_1) | product1(e_2, e_1, e_4) | product1(e_2, e_1, e_3))),
% 0.38/0.56 inference(transitivity,[status(thm)],[275, 273])).
% 0.38/0.56 tff(277,plain,
% 0.38/0.56 ((~![Y: $i, X: $i] : ((~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(e_2)) | product1(e_2, e_1, e_4) | product1(e_2, e_1, e_3) | product1(e_2, e_1, e_2) | product1(e_2, e_1, e_1) | (~group_element(e_1)))),
% 0.38/0.56 inference(quant_inst,[status(thm)],[])).
% 0.38/0.56 tff(278,plain,
% 0.38/0.56 ((~![Y: $i, X: $i] : ((~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_2)) | product1(e_2, e_1, e_2) | product1(e_2, e_1, e_1) | product1(e_2, e_1, e_4) | product1(e_2, e_1, e_3)),
% 0.38/0.56 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.38/0.56 tff(279,plain,
% 0.38/0.56 (product1(e_2, e_1, e_1) | product1(e_2, e_1, e_4) | product1(e_2, e_1, e_3)),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[278, 217, 83, 77, 272])).
% 0.38/0.56 tff(280,plain,
% 0.38/0.56 (product1(e_2, e_1, e_4) | product1(e_2, e_1, e_3)),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[279, 254])).
% 0.38/0.56 tff(281,plain,
% 0.38/0.56 ($false),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[280, 242, 107])).
% 0.38/0.56 tff(282,plain,(~product1(e_2, e_4, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.38/0.56 tff(283,assumption,(product1(e_2, e_4, e_4)), introduced(assumption)).
% 0.38/0.56 tff(284,plain,
% 0.38/0.56 ((~equalish(e_2, e_4)) <=> (~equalish(e_2, e_4))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(285,axiom,(~equalish(e_2, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_4')).
% 0.38/0.56 tff(286,plain,
% 0.38/0.56 (~equalish(e_2, e_4)),
% 0.38/0.56 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.38/0.56 tff(287,plain,
% 0.38/0.56 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_2, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_2, e_4, e_4)))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(288,plain,
% 0.38/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_2, e_4, e_4)))),
% 0.38/0.56 inference(quant_inst,[status(thm)],[])).
% 0.38/0.56 tff(289,plain,
% 0.38/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_2, e_4, e_4))),
% 0.38/0.56 inference(modus_ponens,[status(thm)],[288, 287])).
% 0.38/0.56 tff(290,plain,
% 0.38/0.56 ($false),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[289, 286, 45, 283, 164])).
% 0.38/0.56 tff(291,plain,(~product1(e_2, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.38/0.56 tff(292,assumption,(product1(e_2, e_4, e_2)), introduced(assumption)).
% 0.38/0.56 tff(293,plain,
% 0.38/0.56 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_4, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_2, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_4, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_2, e_4, e_2)))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(294,plain,
% 0.38/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_4, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_2, e_4, e_2)))),
% 0.38/0.56 inference(quant_inst,[status(thm)],[])).
% 0.38/0.56 tff(295,plain,
% 0.38/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_4, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_2, e_4, e_2))),
% 0.38/0.56 inference(modus_ponens,[status(thm)],[294, 293])).
% 0.38/0.56 tff(296,plain,
% 0.38/0.56 ($false),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[295, 233, 13, 58, 292])).
% 0.38/0.56 tff(297,plain,(~product1(e_2, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.38/0.56 tff(298,plain,
% 0.38/0.56 (((~![Y: $i, X: $i] : ((~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(e_2)) | product1(e_2, e_4, e_3) | product1(e_2, e_4, e_2) | (~group_element(e_4)) | product1(e_2, e_4, e_1) | product1(e_2, e_4, e_4))) <=> ((~![Y: $i, X: $i] : ((~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(e_2)) | product1(e_2, e_4, e_3) | product1(e_2, e_4, e_2) | (~group_element(e_4)) | product1(e_2, e_4, e_1) | product1(e_2, e_4, e_4))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(299,plain,
% 0.38/0.56 (((~group_element(e_2)) | product1(e_2, e_4, e_4) | product1(e_2, e_4, e_3) | product1(e_2, e_4, e_2) | product1(e_2, e_4, e_1) | (~group_element(e_4))) <=> ((~group_element(e_2)) | product1(e_2, e_4, e_3) | product1(e_2, e_4, e_2) | (~group_element(e_4)) | product1(e_2, e_4, e_1) | product1(e_2, e_4, e_4))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(300,plain,
% 0.38/0.56 (((~![Y: $i, X: $i] : ((~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(e_2)) | product1(e_2, e_4, e_4) | product1(e_2, e_4, e_3) | product1(e_2, e_4, e_2) | product1(e_2, e_4, e_1) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : ((~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(e_2)) | product1(e_2, e_4, e_3) | product1(e_2, e_4, e_2) | (~group_element(e_4)) | product1(e_2, e_4, e_1) | product1(e_2, e_4, e_4)))),
% 0.38/0.56 inference(monotonicity,[status(thm)],[299])).
% 0.38/0.56 tff(301,plain,
% 0.38/0.56 (((~![Y: $i, X: $i] : ((~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(e_2)) | product1(e_2, e_4, e_4) | product1(e_2, e_4, e_3) | product1(e_2, e_4, e_2) | product1(e_2, e_4, e_1) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : ((~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(e_2)) | product1(e_2, e_4, e_3) | product1(e_2, e_4, e_2) | (~group_element(e_4)) | product1(e_2, e_4, e_1) | product1(e_2, e_4, e_4))),
% 0.38/0.56 inference(transitivity,[status(thm)],[300, 298])).
% 0.38/0.56 tff(302,plain,
% 0.38/0.56 ((~![Y: $i, X: $i] : ((~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(e_2)) | product1(e_2, e_4, e_4) | product1(e_2, e_4, e_3) | product1(e_2, e_4, e_2) | product1(e_2, e_4, e_1) | (~group_element(e_4)))),
% 0.38/0.56 inference(quant_inst,[status(thm)],[])).
% 0.38/0.56 tff(303,plain,
% 0.38/0.56 ((~![Y: $i, X: $i] : ((~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(e_2)) | product1(e_2, e_4, e_3) | product1(e_2, e_4, e_2) | (~group_element(e_4)) | product1(e_2, e_4, e_1) | product1(e_2, e_4, e_4)),
% 0.38/0.56 inference(modus_ponens,[status(thm)],[302, 301])).
% 0.38/0.56 tff(304,plain,
% 0.38/0.56 (product1(e_2, e_4, e_3) | product1(e_2, e_4, e_1) | product1(e_2, e_4, e_4)),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[303, 83, 214, 77, 297])).
% 0.38/0.56 tff(305,plain,
% 0.38/0.56 (product1(e_2, e_4, e_3) | product1(e_2, e_4, e_1)),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[304, 291])).
% 0.38/0.56 tff(306,plain,
% 0.38/0.56 (product1(e_2, e_4, e_3)),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[305, 282])).
% 0.38/0.56 tff(307,assumption,(product1(e_1, e_4, e_3)), introduced(assumption)).
% 0.38/0.56 tff(308,assumption,(product1(e_2, e_4, e_3)), introduced(assumption)).
% 0.38/0.56 tff(309,plain,
% 0.38/0.56 (((~![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_4, e_3)) | (~product1(e_1, e_4, 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_2) | (~product1(e_2, e_4, e_3)) | (~product1(e_1, e_4, e_3)))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(310,plain,
% 0.38/0.56 ((~![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_4, e_3)) | (~product1(e_1, e_4, e_3)))),
% 0.38/0.56 inference(quant_inst,[status(thm)],[])).
% 0.38/0.56 tff(311,plain,
% 0.38/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_1, e_2) | (~product1(e_2, e_4, e_3)) | (~product1(e_1, e_4, e_3))),
% 0.38/0.56 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.38/0.56 tff(312,plain,
% 0.38/0.56 ($false),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[311, 260, 45, 308, 307])).
% 0.38/0.56 tff(313,plain,((~product1(e_1, e_4, e_3)) | (~product1(e_2, e_4, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.56 tff(314,plain,
% 0.38/0.56 (~product1(e_1, e_4, e_3)),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[313, 306])).
% 0.38/0.56 tff(315,assumption,(product1(e_1, e_4, e_1)), introduced(assumption)).
% 0.38/0.56 tff(316,plain,
% 0.38/0.56 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_4, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_4, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_4, e_1)))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(317,plain,
% 0.38/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_4, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_4, e_1)))),
% 0.38/0.56 inference(quant_inst,[status(thm)],[])).
% 0.38/0.56 tff(318,plain,
% 0.38/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_4, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_4, e_1))),
% 0.38/0.56 inference(modus_ponens,[status(thm)],[317, 316])).
% 0.38/0.56 tff(319,plain,
% 0.38/0.56 ($false),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[318, 132, 13, 199, 315])).
% 0.38/0.56 tff(320,plain,(~product1(e_1, e_4, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.38/0.56 tff(321,assumption,(product1(e_1, e_4, e_4)), introduced(assumption)).
% 0.38/0.56 tff(322,plain,
% 0.38/0.56 (((~![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_4, e_4)) | (~product1(e_1, e_4, 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_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_1, e_4, e_4)))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(323,plain,
% 0.38/0.57 ((~![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_4, e_4)) | (~product1(e_1, e_4, e_4)))),
% 0.38/0.57 inference(quant_inst,[status(thm)],[])).
% 0.38/0.57 tff(324,plain,
% 0.38/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_1, e_4) | (~product1(e_4, e_4, e_4)) | (~product1(e_1, e_4, e_4))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[323, 322])).
% 0.38/0.57 tff(325,plain,
% 0.38/0.57 ($false),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[324, 180, 45, 321, 164])).
% 0.38/0.57 tff(326,plain,(~product1(e_1, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.38/0.57 tff(327,plain,
% 0.38/0.57 (((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_4)) | product1(e_1, e_4, e_4) | product1(e_1, e_4, e_2) | product1(e_1, e_4, e_3) | product1(e_1, e_4, e_1))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_4)) | product1(e_1, e_4, e_4) | product1(e_1, e_4, e_2) | product1(e_1, e_4, e_3) | product1(e_1, e_4, e_1))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(328,plain,
% 0.38/0.57 (((~group_element(e_1)) | product1(e_1, e_4, e_4) | product1(e_1, e_4, e_3) | product1(e_1, e_4, e_2) | product1(e_1, e_4, e_1) | (~group_element(e_4))) <=> ((~group_element(e_1)) | (~group_element(e_4)) | product1(e_1, e_4, e_4) | product1(e_1, e_4, e_2) | product1(e_1, e_4, e_3) | product1(e_1, e_4, e_1))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(329,plain,
% 0.38/0.57 (((~![Y: $i, X: $i] : ((~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(e_1)) | product1(e_1, e_4, e_4) | product1(e_1, e_4, e_3) | product1(e_1, e_4, e_2) | product1(e_1, e_4, e_1) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_4)) | product1(e_1, e_4, e_4) | product1(e_1, e_4, e_2) | product1(e_1, e_4, e_3) | product1(e_1, e_4, e_1)))),
% 0.38/0.57 inference(monotonicity,[status(thm)],[328])).
% 0.38/0.57 tff(330,plain,
% 0.38/0.57 (((~![Y: $i, X: $i] : ((~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(e_1)) | product1(e_1, e_4, e_4) | product1(e_1, e_4, e_3) | product1(e_1, e_4, e_2) | product1(e_1, e_4, e_1) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_4)) | product1(e_1, e_4, e_4) | product1(e_1, e_4, e_2) | product1(e_1, e_4, e_3) | product1(e_1, e_4, e_1))),
% 0.38/0.57 inference(transitivity,[status(thm)],[329, 327])).
% 0.38/0.57 tff(331,plain,
% 0.38/0.57 ((~![Y: $i, X: $i] : ((~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(e_1)) | product1(e_1, e_4, e_4) | product1(e_1, e_4, e_3) | product1(e_1, e_4, e_2) | product1(e_1, e_4, e_1) | (~group_element(e_4)))),
% 0.38/0.57 inference(quant_inst,[status(thm)],[])).
% 0.38/0.57 tff(332,plain,
% 0.38/0.57 ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_4)) | product1(e_1, e_4, e_4) | product1(e_1, e_4, e_2) | product1(e_1, e_4, e_3) | product1(e_1, e_4, e_1)),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.38/0.57 tff(333,plain,
% 0.38/0.57 (product1(e_1, e_4, e_4) | product1(e_1, e_4, e_2) | product1(e_1, e_4, e_3) | product1(e_1, e_4, e_1)),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[332, 217, 214, 77])).
% 0.38/0.57 tff(334,plain,
% 0.38/0.57 (product1(e_1, e_4, e_2) | product1(e_1, e_4, e_3)),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[333, 326, 320])).
% 0.38/0.57 tff(335,plain,
% 0.38/0.57 (product1(e_1, e_4, e_2)),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[334, 314])).
% 0.38/0.57 tff(336,plain,
% 0.38/0.57 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(337,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.38/0.57 tff(338,plain,
% 0.38/0.57 (~equalish(e_3, e_1)),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[337, 336])).
% 0.38/0.57 tff(339,plain,
% 0.38/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_1) | (~product1(e_1, e_4, e_2)) | (~product1(e_3, e_4, 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_1) | (~product1(e_1, e_4, e_2)) | (~product1(e_3, e_4, e_2)))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(340,plain,
% 0.38/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_1) | (~product1(e_1, e_4, e_2)) | (~product1(e_3, e_4, e_2)))),
% 0.38/0.57 inference(quant_inst,[status(thm)],[])).
% 0.38/0.57 tff(341,plain,
% 0.38/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_3, e_1) | (~product1(e_1, e_4, e_2)) | (~product1(e_3, e_4, e_2))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[340, 339])).
% 0.38/0.57 tff(342,plain,
% 0.38/0.57 ($false),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[341, 338, 45, 335, 1])).
% 0.38/0.57 tff(343,plain,(~product1(e_3, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.38/0.57 tff(344,assumption,(product1(e_3, e_1, e_3)), introduced(assumption)).
% 0.38/0.57 tff(345,plain,
% 0.38/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_1, e_3) | (~product1(e_3, e_1, e_3)) | (~product1(e_3, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_1, e_3) | (~product1(e_3, e_1, e_3)) | (~product1(e_3, e_3, e_3)))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(346,plain,
% 0.38/0.57 ((equalish(e_1, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_3, e_1, e_3))) <=> (equalish(e_1, e_3) | (~product1(e_3, e_1, e_3)) | (~product1(e_3, e_3, e_3)))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(347,plain,
% 0.38/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_1, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_3, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_1, e_3) | (~product1(e_3, e_1, e_3)) | (~product1(e_3, e_3, e_3))))),
% 0.38/0.57 inference(monotonicity,[status(thm)],[346])).
% 0.38/0.57 tff(348,plain,
% 0.38/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_1, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_3, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_1, e_3) | (~product1(e_3, e_1, e_3)) | (~product1(e_3, e_3, e_3)))),
% 0.38/0.57 inference(transitivity,[status(thm)],[347, 345])).
% 0.38/0.57 tff(349,plain,
% 0.38/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_1, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_3, e_1, e_3)))),
% 0.38/0.57 inference(quant_inst,[status(thm)],[])).
% 0.38/0.57 tff(350,plain,
% 0.38/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_1, e_3) | (~product1(e_3, e_1, e_3)) | (~product1(e_3, e_3, e_3))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[349, 348])).
% 0.38/0.57 tff(351,plain,
% 0.38/0.57 ($false),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[350, 98, 13, 344, 34])).
% 0.38/0.57 tff(352,plain,(~product1(e_3, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.38/0.57 tff(353,plain,
% 0.38/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_4, e_1) | (~product1(e_2, e_4, e_3)) | (~product1(e_2, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_4, e_1) | (~product1(e_2, e_4, e_3)) | (~product1(e_2, e_1, e_3)))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(354,plain,
% 0.38/0.57 ((equalish(e_4, e_1) | (~product1(e_2, e_1, e_3)) | (~product1(e_2, e_4, e_3))) <=> (equalish(e_4, e_1) | (~product1(e_2, e_4, e_3)) | (~product1(e_2, e_1, e_3)))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(355,plain,
% 0.38/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_4, e_1) | (~product1(e_2, e_1, e_3)) | (~product1(e_2, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_4, e_1) | (~product1(e_2, e_4, e_3)) | (~product1(e_2, e_1, e_3))))),
% 0.38/0.57 inference(monotonicity,[status(thm)],[354])).
% 0.38/0.57 tff(356,plain,
% 0.38/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_4, e_1) | (~product1(e_2, e_1, e_3)) | (~product1(e_2, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_4, e_1) | (~product1(e_2, e_4, e_3)) | (~product1(e_2, e_1, e_3)))),
% 0.38/0.57 inference(transitivity,[status(thm)],[355, 353])).
% 0.38/0.57 tff(357,plain,
% 0.38/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_4, e_1) | (~product1(e_2, e_1, e_3)) | (~product1(e_2, e_4, e_3)))),
% 0.38/0.57 inference(quant_inst,[status(thm)],[])).
% 0.38/0.57 tff(358,plain,
% 0.38/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_4, e_1) | (~product1(e_2, e_4, e_3)) | (~product1(e_2, e_1, e_3))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[357, 356])).
% 0.38/0.57 tff(359,plain,
% 0.38/0.57 ($false),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[358, 132, 13, 308, 229])).
% 0.38/0.57 tff(360,plain,((~product1(e_2, e_4, e_3)) | (~product1(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.57 tff(361,plain,
% 0.38/0.57 (~product1(e_2, e_1, e_3)),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[360, 306])).
% 0.38/0.57 tff(362,plain,
% 0.38/0.57 (product1(e_2, e_1, e_4)),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[280, 361])).
% 0.38/0.57 tff(363,assumption,(product1(e_3, e_1, e_4)), introduced(assumption)).
% 0.38/0.57 tff(364,plain,
% 0.38/0.57 (((~![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_1, e_4)) | (~product1(e_3, e_1, e_4)))) <=> ((~![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_1, e_4)) | (~product1(e_3, e_1, e_4)))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(365,plain,
% 0.38/0.57 ((~![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_1, e_4)) | (~product1(e_3, e_1, e_4)))),
% 0.38/0.57 inference(quant_inst,[status(thm)],[])).
% 0.38/0.57 tff(366,plain,
% 0.38/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_3, e_2) | (~product1(e_2, e_1, e_4)) | (~product1(e_3, e_1, e_4))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[365, 364])).
% 0.38/0.57 tff(367,plain,
% 0.38/0.57 ($false),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[366, 62, 45, 363, 362])).
% 0.38/0.57 tff(368,plain,(~product1(e_3, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.38/0.57 tff(369,assumption,(product1(e_3, e_1, e_1)), introduced(assumption)).
% 0.38/0.57 tff(370,plain,
% 0.38/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_1) | (~product1(e_3, e_1, e_1)) | (~product1(e_1, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_3, e_1) | (~product1(e_3, e_1, e_1)) | (~product1(e_1, e_1, e_1)))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(371,plain,
% 0.38/0.57 ((equalish(e_3, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_3, e_1, e_1))) <=> (equalish(e_3, e_1) | (~product1(e_3, e_1, e_1)) | (~product1(e_1, e_1, e_1)))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(372,plain,
% 0.38/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_3, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_1) | (~product1(e_3, e_1, e_1)) | (~product1(e_1, e_1, e_1))))),
% 0.38/0.57 inference(monotonicity,[status(thm)],[371])).
% 0.38/0.57 tff(373,plain,
% 0.38/0.57 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_3, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_3, e_1) | (~product1(e_3, e_1, e_1)) | (~product1(e_1, e_1, e_1)))),
% 0.38/0.57 inference(transitivity,[status(thm)],[372, 370])).
% 0.38/0.57 tff(374,plain,
% 0.38/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_3, e_1, e_1)))),
% 0.38/0.57 inference(quant_inst,[status(thm)],[])).
% 0.38/0.57 tff(375,plain,
% 0.38/0.57 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_3, e_1) | (~product1(e_3, e_1, e_1)) | (~product1(e_1, e_1, e_1))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[374, 373])).
% 0.38/0.57 tff(376,plain,
% 0.38/0.57 ($false),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[375, 338, 45, 369, 199])).
% 0.38/0.57 tff(377,plain,(~product1(e_3, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.38/0.57 tff(378,plain,
% 0.38/0.57 (((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_3)) | product1(e_3, e_1, e_4) | product1(e_3, e_1, e_2) | product1(e_3, e_1, e_3) | product1(e_3, e_1, e_1))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_3)) | product1(e_3, e_1, e_4) | product1(e_3, e_1, e_2) | product1(e_3, e_1, e_3) | product1(e_3, e_1, e_1))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(379,plain,
% 0.38/0.57 (((~group_element(e_3)) | product1(e_3, e_1, e_4) | product1(e_3, e_1, e_3) | product1(e_3, e_1, e_2) | product1(e_3, e_1, e_1) | (~group_element(e_1))) <=> ((~group_element(e_1)) | (~group_element(e_3)) | product1(e_3, e_1, e_4) | product1(e_3, e_1, e_2) | product1(e_3, e_1, e_3) | product1(e_3, e_1, e_1))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(380,plain,
% 0.38/0.57 (((~![Y: $i, X: $i] : ((~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(e_3)) | product1(e_3, e_1, e_4) | product1(e_3, e_1, e_3) | product1(e_3, e_1, e_2) | product1(e_3, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_3)) | product1(e_3, e_1, e_4) | product1(e_3, e_1, e_2) | product1(e_3, e_1, e_3) | product1(e_3, e_1, e_1)))),
% 0.38/0.57 inference(monotonicity,[status(thm)],[379])).
% 0.38/0.57 tff(381,plain,
% 0.38/0.57 (((~![Y: $i, X: $i] : ((~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(e_3)) | product1(e_3, e_1, e_4) | product1(e_3, e_1, e_3) | product1(e_3, e_1, e_2) | product1(e_3, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_3)) | product1(e_3, e_1, e_4) | product1(e_3, e_1, e_2) | product1(e_3, e_1, e_3) | product1(e_3, e_1, e_1))),
% 0.38/0.58 inference(transitivity,[status(thm)],[380, 378])).
% 0.38/0.58 tff(382,plain,
% 0.38/0.58 ((~![Y: $i, X: $i] : ((~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(e_3)) | product1(e_3, e_1, e_4) | product1(e_3, e_1, e_3) | product1(e_3, e_1, e_2) | product1(e_3, e_1, e_1) | (~group_element(e_1)))),
% 0.38/0.58 inference(quant_inst,[status(thm)],[])).
% 0.38/0.58 tff(383,plain,
% 0.38/0.58 ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_3)) | product1(e_3, e_1, e_4) | product1(e_3, e_1, e_2) | product1(e_3, e_1, e_3) | product1(e_3, e_1, e_1)),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[382, 381])).
% 0.38/0.58 tff(384,plain,
% 0.38/0.58 (product1(e_3, e_1, e_4) | product1(e_3, e_1, e_2) | product1(e_3, e_1, e_3) | product1(e_3, e_1, e_1)),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[383, 217, 80, 77])).
% 0.38/0.58 tff(385,plain,
% 0.38/0.58 (product1(e_3, e_1, e_2)),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[384, 377, 368, 352])).
% 0.38/0.58 tff(386,assumption,(product1(e_3, e_1, e_2)), introduced(assumption)).
% 0.38/0.58 tff(387,plain,
% 0.38/0.58 (((~![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_1, e_2)) | (~product1(e_3, e_1, 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_3) | (~product1(e_4, e_1, e_2)) | (~product1(e_3, e_1, e_2)))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(388,plain,
% 0.38/0.58 ((equalish(e_4, e_3) | (~product1(e_3, e_1, e_2)) | (~product1(e_4, e_1, e_2))) <=> (equalish(e_4, e_3) | (~product1(e_4, e_1, e_2)) | (~product1(e_3, e_1, e_2)))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(389,plain,
% 0.38/0.58 (((~![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_1, e_2)) | (~product1(e_4, e_1, 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_3) | (~product1(e_4, e_1, e_2)) | (~product1(e_3, e_1, e_2))))),
% 0.38/0.58 inference(monotonicity,[status(thm)],[388])).
% 0.38/0.58 tff(390,plain,
% 0.38/0.58 (((~![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_1, e_2)) | (~product1(e_4, e_1, 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_3) | (~product1(e_4, e_1, e_2)) | (~product1(e_3, e_1, e_2)))),
% 0.38/0.58 inference(transitivity,[status(thm)],[389, 387])).
% 0.38/0.58 tff(391,plain,
% 0.38/0.58 ((~![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_1, e_2)) | (~product1(e_4, e_1, e_2)))),
% 0.38/0.58 inference(quant_inst,[status(thm)],[])).
% 0.38/0.58 tff(392,plain,
% 0.38/0.58 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_4, e_3) | (~product1(e_4, e_1, e_2)) | (~product1(e_3, e_1, e_2))),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[391, 390])).
% 0.38/0.58 tff(393,plain,
% 0.38/0.58 ($false),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[392, 16, 45, 142, 386])).
% 0.38/0.58 tff(394,plain,((~product1(e_4, e_1, e_2)) | (~product1(e_3, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.58 tff(395,plain,
% 0.38/0.58 (~product1(e_4, e_1, e_2)),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[394, 385])).
% 0.38/0.58 tff(396,plain,
% 0.38/0.58 (product1(e_4, e_1, e_3)),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[227, 395])).
% 0.38/0.58 tff(397,assumption,(product1(e_3, e_4, e_1)), introduced(assumption)).
% 0.38/0.58 tff(398,plain,
% 0.38/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (product2(e_1, e_1, e_4) | (~product1(e_4, e_1, e_3)) | (~product1(e_3, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | product2(e_1, e_1, e_4) | (~product1(e_4, e_1, e_3)) | (~product1(e_3, e_4, e_1)))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(399,plain,
% 0.38/0.58 (((~product1(e_3, e_4, e_1)) | product2(e_1, e_1, e_4) | (~product1(e_4, e_1, e_3))) <=> (product2(e_1, e_1, e_4) | (~product1(e_4, e_1, e_3)) | (~product1(e_3, e_4, e_1)))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(400,plain,
% 0.38/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_3, e_4, e_1)) | product2(e_1, e_1, e_4) | (~product1(e_4, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (product2(e_1, e_1, e_4) | (~product1(e_4, e_1, e_3)) | (~product1(e_3, e_4, e_1))))),
% 0.38/0.58 inference(monotonicity,[status(thm)],[399])).
% 0.38/0.58 tff(401,plain,
% 0.38/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_3, e_4, e_1)) | product2(e_1, e_1, e_4) | (~product1(e_4, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | product2(e_1, e_1, e_4) | (~product1(e_4, e_1, e_3)) | (~product1(e_3, e_4, e_1)))),
% 0.38/0.58 inference(transitivity,[status(thm)],[400, 398])).
% 0.38/0.58 tff(402,plain,
% 0.38/0.58 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_3, e_4, e_1)) | product2(e_1, e_1, e_4) | (~product1(e_4, e_1, e_3)))),
% 0.38/0.58 inference(quant_inst,[status(thm)],[])).
% 0.38/0.58 tff(403,plain,
% 0.38/0.58 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | product2(e_1, e_1, e_4) | (~product1(e_4, e_1, e_3)) | (~product1(e_3, e_4, e_1))),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[402, 401])).
% 0.38/0.58 tff(404,plain,
% 0.38/0.58 ($false),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[403, 152, 140, 230, 397])).
% 0.38/0.58 tff(405,plain,((~product1(e_3, e_4, e_1)) | (~product1(e_4, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.58 tff(406,plain,
% 0.38/0.58 (~product1(e_3, e_4, e_1)),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[405, 396])).
% 0.38/0.58 tff(407,assumption,(product1(e_3, e_4, e_4)), introduced(assumption)).
% 0.38/0.58 tff(408,plain,
% 0.38/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_3, e_4, e_4)) | (~product1(e_4, e_1, e_3)) | product2(e_4, e_1, e_4))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_3, e_4, e_4)) | (~product1(e_4, e_1, e_3)) | product2(e_4, e_1, e_4))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(409,plain,
% 0.38/0.58 (((~product1(e_3, e_4, e_4)) | product2(e_4, e_1, e_4) | (~product1(e_4, e_1, e_3))) <=> ((~product1(e_3, e_4, e_4)) | (~product1(e_4, e_1, e_3)) | product2(e_4, e_1, e_4))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(410,plain,
% 0.38/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_3, e_4, e_4)) | product2(e_4, e_1, e_4) | (~product1(e_4, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_3, e_4, e_4)) | (~product1(e_4, e_1, e_3)) | product2(e_4, e_1, e_4)))),
% 0.38/0.58 inference(monotonicity,[status(thm)],[409])).
% 0.38/0.58 tff(411,plain,
% 0.38/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_3, e_4, e_4)) | product2(e_4, e_1, e_4) | (~product1(e_4, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_3, e_4, e_4)) | (~product1(e_4, e_1, e_3)) | product2(e_4, e_1, e_4))),
% 0.38/0.58 inference(transitivity,[status(thm)],[410, 408])).
% 0.38/0.58 tff(412,plain,
% 0.38/0.58 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_3, e_4, e_4)) | product2(e_4, e_1, e_4) | (~product1(e_4, e_1, e_3)))),
% 0.38/0.58 inference(quant_inst,[status(thm)],[])).
% 0.38/0.58 tff(413,plain,
% 0.38/0.58 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_3, e_4, e_4)) | (~product1(e_4, e_1, e_3)) | product2(e_4, e_1, e_4)),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[412, 411])).
% 0.38/0.58 tff(414,plain,
% 0.38/0.58 ($false),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[413, 152, 407, 188, 230])).
% 0.38/0.58 tff(415,plain,((~product1(e_3, e_4, e_4)) | (~product1(e_4, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.58 tff(416,plain,
% 0.38/0.58 (~product1(e_3, e_4, e_4)),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[415, 396])).
% 0.38/0.58 tff(417,plain,
% 0.38/0.58 ((~![X: $i] : product2(X, X, X)) | product2(e_3, e_3, e_3)),
% 0.38/0.58 inference(quant_inst,[status(thm)],[])).
% 0.38/0.58 tff(418,plain,
% 0.38/0.58 (product2(e_3, e_3, e_3)),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[417, 115])).
% 0.38/0.58 tff(419,assumption,(product2(e_3, e_4, e_3)), introduced(assumption)).
% 0.38/0.58 tff(420,plain,
% 0.38/0.58 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_4, e_3) | (~product2(e_3, e_4, 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_4, e_3) | (~product2(e_3, e_4, e_3)) | (~product2(e_3, e_3, e_3)))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(421,plain,
% 0.38/0.58 ((equalish(e_4, e_3) | (~product2(e_3, e_3, e_3)) | (~product2(e_3, e_4, e_3))) <=> (equalish(e_4, e_3) | (~product2(e_3, e_4, e_3)) | (~product2(e_3, e_3, e_3)))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(422,plain,
% 0.38/0.58 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_4, e_3) | (~product2(e_3, e_3, e_3)) | (~product2(e_3, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_4, e_3) | (~product2(e_3, e_4, e_3)) | (~product2(e_3, e_3, e_3))))),
% 0.38/0.58 inference(monotonicity,[status(thm)],[421])).
% 0.38/0.58 tff(423,plain,
% 0.38/0.58 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_4, e_3) | (~product2(e_3, e_3, e_3)) | (~product2(e_3, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_4, e_3) | (~product2(e_3, e_4, e_3)) | (~product2(e_3, e_3, e_3)))),
% 0.38/0.58 inference(transitivity,[status(thm)],[422, 420])).
% 0.38/0.58 tff(424,plain,
% 0.38/0.58 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_4, e_3) | (~product2(e_3, e_3, e_3)) | (~product2(e_3, e_4, e_3)))),
% 0.38/0.58 inference(quant_inst,[status(thm)],[])).
% 0.38/0.58 tff(425,plain,
% 0.38/0.58 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_4, e_3) | (~product2(e_3, e_4, e_3)) | (~product2(e_3, e_3, e_3))),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[424, 423])).
% 0.38/0.58 tff(426,plain,
% 0.38/0.58 ($false),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[425, 16, 177, 419, 418])).
% 0.38/0.58 tff(427,plain,(~product2(e_3, e_4, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.38/0.58 tff(428,plain,
% 0.38/0.58 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_3, e_4, e_3)) | product2(e_3, e_4, e_3) | (~product1(e_3, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_3, e_4, e_3)) | product2(e_3, e_4, e_3) | (~product1(e_3, e_3, e_3)))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(429,plain,
% 0.38/0.58 (((~product1(e_3, e_3, e_3)) | product2(e_3, e_4, e_3) | (~product1(e_3, e_4, e_3))) <=> ((~product1(e_3, e_4, e_3)) | product2(e_3, e_4, e_3) | (~product1(e_3, e_3, e_3)))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(430,plain,
% 0.38/0.58 (((~![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_4, e_3) | (~product1(e_3, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | ((~product1(e_3, e_4, e_3)) | product2(e_3, e_4, e_3) | (~product1(e_3, e_3, e_3))))),
% 0.38/0.58 inference(monotonicity,[status(thm)],[429])).
% 0.38/0.58 tff(431,plain,
% 0.38/0.58 (((~![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_4, e_3) | (~product1(e_3, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_3, e_4, e_3)) | product2(e_3, e_4, e_3) | (~product1(e_3, e_3, e_3)))),
% 0.38/0.58 inference(transitivity,[status(thm)],[430, 428])).
% 0.38/0.58 tff(432,plain,
% 0.38/0.58 ((~![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_4, e_3) | (~product1(e_3, e_4, e_3)))),
% 0.38/0.58 inference(quant_inst,[status(thm)],[])).
% 0.38/0.58 tff(433,plain,
% 0.38/0.58 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product1(Z1, X, Z2)) | product2(Z2, Y, X) | (~product1(X, Y, Z1)))) | (~product1(e_3, e_4, e_3)) | product2(e_3, e_4, e_3) | (~product1(e_3, e_3, e_3))),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[432, 431])).
% 0.38/0.58 tff(434,plain,
% 0.38/0.58 (~product1(e_3, e_4, e_3)),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[433, 152, 34, 427])).
% 0.38/0.58 tff(435,plain,
% 0.38/0.58 (((~![Y: $i, X: $i] : ((~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(e_3)) | product1(e_3, e_4, e_4) | (~group_element(e_4)) | product1(e_3, e_4, e_2) | product1(e_3, e_4, e_1) | product1(e_3, e_4, e_3))) <=> ((~![Y: $i, X: $i] : ((~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(e_3)) | product1(e_3, e_4, e_4) | (~group_element(e_4)) | product1(e_3, e_4, e_2) | product1(e_3, e_4, e_1) | product1(e_3, e_4, e_3))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(436,plain,
% 0.38/0.58 (((~group_element(e_3)) | product1(e_3, e_4, e_4) | product1(e_3, e_4, e_3) | product1(e_3, e_4, e_2) | product1(e_3, e_4, e_1) | (~group_element(e_4))) <=> ((~group_element(e_3)) | product1(e_3, e_4, e_4) | (~group_element(e_4)) | product1(e_3, e_4, e_2) | product1(e_3, e_4, e_1) | product1(e_3, e_4, e_3))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(437,plain,
% 0.38/0.58 (((~![Y: $i, X: $i] : ((~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(e_3)) | product1(e_3, e_4, e_4) | product1(e_3, e_4, e_3) | product1(e_3, e_4, e_2) | product1(e_3, e_4, e_1) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : ((~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(e_3)) | product1(e_3, e_4, e_4) | (~group_element(e_4)) | product1(e_3, e_4, e_2) | product1(e_3, e_4, e_1) | product1(e_3, e_4, e_3)))),
% 0.38/0.58 inference(monotonicity,[status(thm)],[436])).
% 0.38/0.58 tff(438,plain,
% 0.38/0.58 (((~![Y: $i, X: $i] : ((~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(e_3)) | product1(e_3, e_4, e_4) | product1(e_3, e_4, e_3) | product1(e_3, e_4, e_2) | product1(e_3, e_4, e_1) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : ((~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(e_3)) | product1(e_3, e_4, e_4) | (~group_element(e_4)) | product1(e_3, e_4, e_2) | product1(e_3, e_4, e_1) | product1(e_3, e_4, e_3))),
% 0.38/0.58 inference(transitivity,[status(thm)],[437, 435])).
% 0.38/0.58 tff(439,plain,
% 0.38/0.58 ((~![Y: $i, X: $i] : ((~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(e_3)) | product1(e_3, e_4, e_4) | product1(e_3, e_4, e_3) | product1(e_3, e_4, e_2) | product1(e_3, e_4, e_1) | (~group_element(e_4)))),
% 0.38/0.59 inference(quant_inst,[status(thm)],[])).
% 0.38/0.59 tff(440,plain,
% 0.38/0.59 ((~![Y: $i, X: $i] : ((~group_element(X)) | product1(X, Y, e_4) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_3)) | product1(e_3, e_4, e_4) | (~group_element(e_4)) | product1(e_3, e_4, e_2) | product1(e_3, e_4, e_1) | product1(e_3, e_4, e_3)),
% 0.38/0.59 inference(modus_ponens,[status(thm)],[439, 438])).
% 0.38/0.59 tff(441,plain,
% 0.38/0.59 (product1(e_3, e_4, e_4) | product1(e_3, e_4, e_2) | product1(e_3, e_4, e_1)),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[440, 80, 214, 77, 434])).
% 0.38/0.59 tff(442,plain,
% 0.38/0.59 ($false),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[441, 416, 406, 343])).
% 0.38/0.59 % SZS output end Proof
% 0.38/0.59 % E exiting
%------------------------------------------------------------------------------