%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP134-1.003 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:07:13 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP134-1.003 : TPTP v9.0.0. Released v1.2.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 15:44:24 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.42 % SZS status Unsatisfiable
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 tff(product_type, type, (
% 0.20/0.42 product: ( $i * $i * $i ) > $o)).
% 0.20/0.42 tff(e_1_type, type, (
% 0.20/0.42 e_1: $i)).
% 0.20/0.42 tff(e_2_type, type, (
% 0.20/0.42 e_2: $i)).
% 0.20/0.42 tff(e_3_type, type, (
% 0.20/0.42 e_3: $i)).
% 0.20/0.42 tff(equalish_type, type, (
% 0.20/0.42 equalish: ( $i * $i ) > $o)).
% 0.20/0.42 tff(group_element_type, type, (
% 0.20/0.42 group_element: $i > $o)).
% 0.20/0.42 tff(1,assumption,(~product(e_2, e_1, e_1)), introduced(assumption)).
% 0.20/0.42 tff(2,assumption,(~product(e_1, e_2, e_1)), introduced(assumption)).
% 0.20/0.42 tff(3,assumption,(product(e_1, e_3, e_1)), introduced(assumption)).
% 0.20/0.42 tff(4,assumption,(product(e_1, e_1, e_1)), introduced(assumption)).
% 0.20/0.42 tff(5,plain,
% 0.20/0.42 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(6,plain,
% 0.20/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[5])).
% 0.20/0.42 tff(7,plain,
% 0.20/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(8,plain,
% 0.20/0.42 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(X, W, Y)) | (~product(X, Z, Y))) <=> ((~product(X, Z, Y)) | (~product(X, W, Y)))), ((((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> (((~product(X, Z, Y)) | (~product(X, W, Y))) | equalish(W, Z)))), rewrite((((~product(X, Z, Y)) | (~product(X, W, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))), ((((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(9,plain,
% 0.20/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[8])).
% 0.20/0.42 tff(10,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_right_cancellation')).
% 0.20/0.42 tff(11,plain,
% 0.20/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.20/0.42 tff(12,plain,
% 0.20/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.20/0.42 tff(13,plain,(
% 0.20/0.42 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[12])).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(16,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 (~equalish(e_1, e_3)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_1, e_1))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.20/0.42 tff(21,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[20, 17, 14, 3, 4])).
% 0.20/0.42 tff(22,plain,((~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 (~product(e_1, e_1, e_1)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[22, 3])).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl(((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))) <=> ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(27,plain,
% 0.20/0.42 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : rewrite((((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, Y)) <=> ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, Y)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.42 tff(29,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qg4')).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.20/0.42 tff(32,plain,(
% 0.20/0.42 ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[31])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 (((~product(e_1, e_3, e_1)) | product(e_1, e_1, e_1) | (~product(e_3, e_1, e_1))) <=> (product(e_1, e_1, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_1)) | product(e_1, e_1, e_1) | (~product(e_3, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_3, e_1))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[35])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_1)) | product(e_1, e_1, e_1) | (~product(e_3, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[36, 34])).
% 0.20/0.43 tff(38,plain,
% 0.20/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_1)) | product(e_1, e_1, e_1) | (~product(e_3, e_1, e_1)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(39,plain,
% 0.20/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_3, e_1))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.20/0.43 tff(40,plain,
% 0.20/0.43 (~product(e_3, e_1, e_1)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[39, 33, 3, 23])).
% 0.20/0.43 tff(41,plain,
% 0.20/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_3)) | product(e_3, e_1, e_1) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_3)) | product(e_3, e_1, e_1) | (~product(e_1, e_3, e_1)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(42,plain,
% 0.20/0.43 (((~product(e_1, e_3, e_1)) | product(e_3, e_1, e_1) | (~product(e_3, e_1, e_3))) <=> ((~product(e_3, e_1, e_3)) | product(e_3, e_1, e_1) | (~product(e_1, e_3, e_1)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(43,plain,
% 0.20/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_1)) | product(e_3, e_1, e_1) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_3)) | product(e_3, e_1, e_1) | (~product(e_1, e_3, e_1))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[42])).
% 0.20/0.43 tff(44,plain,
% 0.20/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_1)) | product(e_3, e_1, e_1) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_3)) | product(e_3, e_1, e_1) | (~product(e_1, e_3, e_1)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[43, 41])).
% 0.20/0.43 tff(45,plain,
% 0.20/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_1)) | product(e_3, e_1, e_1) | (~product(e_3, e_1, e_3)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(46,plain,
% 0.20/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_3)) | product(e_3, e_1, e_1) | (~product(e_1, e_3, e_1))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.43 tff(47,plain,
% 0.20/0.43 (~product(e_3, e_1, e_3)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[46, 33, 3, 40])).
% 0.20/0.43 tff(48,plain,
% 0.20/0.43 (^[Y: $i, X: $i] : refl((product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(49,plain,
% 0.20/0.43 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.43 tff(50,plain,
% 0.20/0.43 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(51,plain,
% 0.20/0.43 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) <=> (product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> ((product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_2)))), rewrite(((product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_2)) <=> (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ((product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_3)))), rewrite(((product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_3)) <=> (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(52,plain,
% 0.20/0.43 (![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[51])).
% 0.20/0.43 tff(53,axiom,(![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_total_function1')).
% 0.20/0.43 tff(54,plain,
% 0.20/0.43 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.43 tff(55,plain,
% 0.20/0.43 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.20/0.43 tff(56,plain,(
% 0.20/0.43 ![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[55])).
% 0.20/0.43 tff(57,plain,
% 0.20/0.43 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.20/0.43 tff(58,plain,
% 0.20/0.43 (group_element(e_3) <=> group_element(e_3)),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(59,axiom,(group_element(e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_3')).
% 0.20/0.43 tff(60,plain,
% 0.20/0.43 (group_element(e_3)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.43 tff(61,plain,
% 0.20/0.43 (group_element(e_1) <=> group_element(e_1)),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(62,axiom,(group_element(e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_1')).
% 0.20/0.43 tff(63,plain,
% 0.20/0.43 (group_element(e_1)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.43 tff(64,plain,
% 0.20/0.43 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3) | product(e_3, e_1, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3) | product(e_3, e_1, e_1))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 ((product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3))) <=> ((~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3) | product(e_3, e_1, e_1))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(66,plain,
% 0.20/0.43 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3) | product(e_3, e_1, e_1)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[65])).
% 0.20/0.43 tff(67,plain,
% 0.20/0.43 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3) | product(e_3, e_1, e_1))),
% 0.20/0.43 inference(transitivity,[status(thm)],[66, 64])).
% 0.20/0.43 tff(68,plain,
% 0.20/0.43 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(69,plain,
% 0.20/0.43 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3) | product(e_3, e_1, e_1)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.43 tff(70,plain,
% 0.20/0.43 (product(e_3, e_1, e_2) | product(e_3, e_1, e_3) | product(e_3, e_1, e_1)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[69, 63, 60, 57])).
% 0.20/0.43 tff(71,plain,
% 0.20/0.43 (product(e_3, e_1, e_2)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[70, 47, 40])).
% 0.20/0.43 tff(72,plain,
% 0.20/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_3, e_1)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(73,plain,
% 0.20/0.43 (((~product(e_1, e_3, e_1)) | product(e_2, e_1, e_1) | (~product(e_3, e_1, e_2))) <=> (product(e_2, e_1, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_3, e_1)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(74,plain,
% 0.20/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_1)) | product(e_2, e_1, e_1) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_3, e_1))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[73])).
% 0.20/0.43 tff(75,plain,
% 0.20/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_1)) | product(e_2, e_1, e_1) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_3, e_1)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[74, 72])).
% 0.20/0.43 tff(76,plain,
% 0.20/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_1)) | product(e_2, e_1, e_1) | (~product(e_3, e_1, e_2)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(77,plain,
% 0.20/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_3, e_1))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.44 tff(78,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[77, 33, 3, 71, 1])).
% 0.20/0.44 tff(79,plain,(product(e_2, e_1, e_1) | (~product(e_1, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(80,plain,
% 0.20/0.44 (product(e_2, e_1, e_1)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[79, 3])).
% 0.20/0.44 tff(81,plain,
% 0.20/0.44 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(82,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.20/0.44 tff(83,plain,
% 0.20/0.44 (~equalish(e_3, e_2)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.44 tff(84,plain,
% 0.20/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(85,plain,
% 0.20/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(86,plain,
% 0.20/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_3, e_1))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.44 tff(87,plain,
% 0.20/0.44 ((~product(e_1, e_2, e_1)) | (~product(e_1, e_3, e_1))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[86, 83, 14])).
% 0.20/0.44 tff(88,plain,
% 0.20/0.44 (~product(e_1, e_2, e_1)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[87, 3])).
% 0.20/0.44 tff(89,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.20/0.44 tff(90,assumption,(product(e_1, e_2, e_2)), introduced(assumption)).
% 0.20/0.44 tff(91,plain,
% 0.20/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(92,plain,
% 0.20/0.44 (((~product(e_1, e_2, e_2)) | product(e_1, e_2, e_1) | (~product(e_2, e_1, e_1))) <=> (product(e_1, e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(93,plain,
% 0.20/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_2)) | product(e_1, e_2, e_1) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_1, e_1))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[92])).
% 0.20/0.44 tff(94,plain,
% 0.20/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_2)) | product(e_1, e_2, e_1) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[93, 91])).
% 0.20/0.44 tff(95,plain,
% 0.20/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_2)) | product(e_1, e_2, e_1) | (~product(e_2, e_1, e_1)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(96,plain,
% 0.20/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_1, e_1))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.20/0.44 tff(97,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[96, 33, 2, 90, 89])).
% 0.20/0.44 tff(98,plain,((~product(e_1, e_2, e_2)) | product(e_1, e_2, e_1) | (~product(e_2, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(99,plain,
% 0.20/0.44 (~product(e_1, e_2, e_2)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[98, 88, 80])).
% 0.20/0.44 tff(100,assumption,(~product(e_1, e_2, e_2)), introduced(assumption)).
% 0.20/0.44 tff(101,assumption,(~product(e_1, e_2, e_3)), introduced(assumption)).
% 0.20/0.44 tff(102,plain,
% 0.20/0.44 (group_element(e_2) <=> group_element(e_2)),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(103,axiom,(group_element(e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_2')).
% 0.20/0.44 tff(104,plain,
% 0.20/0.44 (group_element(e_2)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.20/0.44 tff(105,plain,
% 0.20/0.44 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_2, e_2) | (~group_element(e_2)) | (~group_element(e_1)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_3))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_1, e_2, e_2) | (~group_element(e_2)) | (~group_element(e_1)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_3))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(106,plain,
% 0.20/0.44 ((product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1))) <=> (product(e_1, e_2, e_2) | (~group_element(e_2)) | (~group_element(e_1)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_3))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(107,plain,
% 0.20/0.44 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_2, e_2) | (~group_element(e_2)) | (~group_element(e_1)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_3)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[106])).
% 0.20/0.44 tff(108,plain,
% 0.20/0.44 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_1, e_2, e_2) | (~group_element(e_2)) | (~group_element(e_1)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_3))),
% 0.20/0.44 inference(transitivity,[status(thm)],[107, 105])).
% 0.20/0.44 tff(109,plain,
% 0.20/0.44 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(110,plain,
% 0.20/0.44 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_1, e_2, e_2) | (~group_element(e_2)) | (~group_element(e_1)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_3)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.20/0.44 tff(111,plain,
% 0.20/0.44 (product(e_1, e_2, e_2) | product(e_1, e_2, e_1)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[110, 63, 104, 57, 101])).
% 0.20/0.44 tff(112,plain,
% 0.20/0.44 (product(e_1, e_2, e_1)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[111, 100])).
% 0.20/0.44 tff(113,plain,
% 0.20/0.44 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(114,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.20/0.44 tff(115,plain,
% 0.20/0.44 (~equalish(e_1, e_2)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.20/0.45 tff(116,plain,
% 0.20/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(117,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(118,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_1))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.20/0.45 tff(119,plain,
% 0.20/0.45 ((~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_1))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[118, 115, 14])).
% 0.20/0.45 tff(120,plain,
% 0.20/0.45 (~product(e_1, e_1, e_1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[119, 112])).
% 0.20/0.45 tff(121,plain,
% 0.20/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_1)) | product(e_1, e_1, e_1) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_2, e_1)) | product(e_1, e_1, e_1) | (~product(e_2, e_1, e_1)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(122,plain,
% 0.20/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_1)) | product(e_1, e_1, e_1) | (~product(e_2, e_1, e_1)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(123,plain,
% 0.20/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_2, e_1)) | product(e_1, e_1, e_1) | (~product(e_2, e_1, e_1))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.20/0.45 tff(124,plain,
% 0.20/0.45 (~product(e_2, e_1, e_1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[123, 33, 112, 120])).
% 0.20/0.45 tff(125,assumption,(~product(e_3, e_1, e_1)), introduced(assumption)).
% 0.20/0.45 tff(126,plain,
% 0.20/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_3)) | product(e_3, e_1, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_3)) | product(e_3, e_1, e_1))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(127,plain,
% 0.20/0.45 (((~product(e_1, e_2, e_1)) | product(e_3, e_1, e_1) | (~product(e_2, e_1, e_3))) <=> ((~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_3)) | product(e_3, e_1, e_1))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(128,plain,
% 0.20/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_1)) | product(e_3, e_1, e_1) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_3)) | product(e_3, e_1, e_1)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[127])).
% 0.20/0.45 tff(129,plain,
% 0.20/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_1)) | product(e_3, e_1, e_1) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_3)) | product(e_3, e_1, e_1))),
% 0.20/0.45 inference(transitivity,[status(thm)],[128, 126])).
% 0.20/0.45 tff(130,plain,
% 0.20/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_1)) | product(e_3, e_1, e_1) | (~product(e_2, e_1, e_3)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(131,plain,
% 0.20/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_3)) | product(e_3, e_1, e_1)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.20/0.45 tff(132,plain,
% 0.20/0.45 (~product(e_2, e_1, e_3)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[131, 33, 112, 125])).
% 0.20/0.45 tff(133,plain,
% 0.20/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_2, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(134,plain,
% 0.20/0.45 (((~product(e_2, e_1, e_2)) | product(e_1, e_2, e_2) | (~product(e_1, e_2, e_1))) <=> (product(e_1, e_2, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(135,plain,
% 0.20/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_2)) | product(e_1, e_2, e_2) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_2))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[134])).
% 0.20/0.45 tff(136,plain,
% 0.20/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_2)) | product(e_1, e_2, e_2) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_2, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[135, 133])).
% 0.20/0.45 tff(137,plain,
% 0.20/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_2)) | product(e_1, e_2, e_2) | (~product(e_1, e_2, e_1)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(138,plain,
% 0.20/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_2, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_2))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.20/0.45 tff(139,plain,
% 0.20/0.45 (product(e_1, e_2, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_2))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[138, 33])).
% 0.20/0.45 tff(140,plain,
% 0.20/0.45 (~product(e_2, e_1, e_2)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[139, 112, 100])).
% 0.20/0.45 tff(141,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(142,plain,
% 0.20/0.45 ((product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2))) <=> ((~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(143,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[142])).
% 0.20/0.45 tff(144,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2))),
% 0.20/0.45 inference(transitivity,[status(thm)],[143, 141])).
% 0.20/0.45 tff(145,plain,
% 0.20/0.45 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(146,plain,
% 0.20/0.45 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.20/0.45 tff(147,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[146, 63, 104, 57, 140, 132, 124])).
% 0.20/0.45 tff(148,plain,(product(e_1, e_2, e_2) | product(e_3, e_1, e_1) | product(e_1, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(149,plain,
% 0.20/0.45 (product(e_1, e_2, e_3)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[148, 99, 40])).
% 0.20/0.45 tff(150,assumption,(product(e_1, e_2, e_3)), introduced(assumption)).
% 0.20/0.45 tff(151,assumption,(product(e_1, e_1, e_3)), introduced(assumption)).
% 0.20/0.45 tff(152,plain,
% 0.20/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_1, e_3)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(153,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_1, e_3)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(154,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_1, e_3))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.20/0.45 tff(155,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[154, 115, 14, 151, 150])).
% 0.20/0.45 tff(156,plain,((~product(e_1, e_1, e_3)) | (~product(e_1, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(157,plain,
% 0.20/0.45 (~product(e_1, e_1, e_3)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[156, 149])).
% 0.20/0.45 tff(158,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(159,plain,
% 0.20/0.45 ((product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_1))) <=> (product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(160,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[159])).
% 0.20/0.46 tff(161,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[160, 158])).
% 0.20/0.46 tff(162,plain,
% 0.20/0.46 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_1)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(163,plain,
% 0.20/0.46 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.20/0.46 tff(164,plain,
% 0.20/0.46 (product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[163, 63, 57])).
% 0.20/0.46 tff(165,plain,
% 0.20/0.46 (product(e_1, e_1, e_2)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[164, 157, 23])).
% 0.20/0.46 tff(166,plain,
% 0.20/0.46 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(167,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[166])).
% 0.20/0.46 tff(168,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(169,plain,
% 0.20/0.46 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(W, Y, X)) | (~product(Z, Y, X))) <=> ((~product(Z, Y, X)) | (~product(W, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> (((~product(Z, Y, X)) | (~product(W, Y, X))) | equalish(W, Z)))), rewrite((((~product(Z, Y, X)) | (~product(W, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(170,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[169])).
% 0.20/0.46 tff(171,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_left_cancellation')).
% 0.20/0.46 tff(172,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.20/0.46 tff(173,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[172, 168])).
% 0.20/0.46 tff(174,plain,(
% 0.20/0.46 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[173])).
% 0.20/0.46 tff(175,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[174, 167])).
% 0.20/0.46 tff(176,plain,
% 0.20/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_1, e_1, e_2)) | (~product(e_3, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_1, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(177,plain,
% 0.20/0.46 ((equalish(e_1, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_1, e_2))) <=> (equalish(e_1, e_3) | (~product(e_1, e_1, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(178,plain,
% 0.20/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_1, e_1, e_2)) | (~product(e_3, e_1, e_2))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[177])).
% 0.20/0.46 tff(179,plain,
% 0.20/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_1, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[178, 176])).
% 0.20/0.46 tff(180,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_1, e_2)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(181,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_1, e_2)) | (~product(e_3, e_1, e_2))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.20/0.46 tff(182,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[181, 17, 175, 165, 71])).
% 0.20/0.46 tff(183,plain,(~product(e_1, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(184,assumption,(~product(e_1, e_3, e_2)), introduced(assumption)).
% 0.20/0.46 tff(185,assumption,(~product(e_1, e_3, e_1)), introduced(assumption)).
% 0.20/0.46 tff(186,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_3, e_3) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_1, e_3, e_3) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(187,plain,
% 0.20/0.46 ((product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_1))) <=> (product(e_1, e_3, e_3) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(188,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_3, e_3) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[187])).
% 0.20/0.46 tff(189,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_1, e_3, e_3) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1))),
% 0.20/0.46 inference(transitivity,[status(thm)],[188, 186])).
% 0.20/0.46 tff(190,plain,
% 0.20/0.46 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_1)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(191,plain,
% 0.20/0.46 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_1, e_3, e_3) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.20/0.46 tff(192,plain,
% 0.20/0.46 (product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[191, 63, 60, 57])).
% 0.20/0.46 tff(193,plain,
% 0.20/0.46 (product(e_1, e_3, e_3)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[192, 185, 184])).
% 0.20/0.46 tff(194,assumption,(product(e_1, e_3, e_3)), introduced(assumption)).
% 0.20/0.46 tff(195,plain,
% 0.20/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(196,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(197,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_3))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.20/0.46 tff(198,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[197, 83, 14, 194, 150])).
% 0.20/0.46 tff(199,plain,((~product(e_1, e_3, e_3)) | (~product(e_1, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(200,plain,
% 0.20/0.46 (~product(e_1, e_2, e_3)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[199, 193])).
% 0.20/0.46 tff(201,plain,
% 0.20/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_1)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(202,plain,
% 0.20/0.46 (((~product(e_1, e_3, e_3)) | product(e_1, e_3, e_1) | (~product(e_3, e_1, e_1))) <=> (product(e_1, e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_1)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(203,plain,
% 0.20/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_3)) | product(e_1, e_3, e_1) | (~product(e_3, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_1))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[202])).
% 0.20/0.46 tff(204,plain,
% 0.20/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_3)) | product(e_1, e_3, e_1) | (~product(e_3, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_1)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[203, 201])).
% 0.20/0.46 tff(205,plain,
% 0.20/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_3)) | product(e_1, e_3, e_1) | (~product(e_3, e_1, e_1)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(206,plain,
% 0.20/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_1))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.20/0.46 tff(207,plain,
% 0.20/0.46 (~product(e_3, e_1, e_1)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[206, 33, 193, 185])).
% 0.20/0.46 tff(208,plain,
% 0.20/0.46 (product(e_1, e_2, e_2)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[148, 207, 200])).
% 0.20/0.46 tff(209,plain,
% 0.20/0.46 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W))) <=> (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(210,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[209])).
% 0.20/0.46 tff(211,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(212,plain,
% 0.20/0.46 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(X, Y, W)) | (~product(X, Y, Z))) <=> ((~product(X, Y, Z)) | (~product(X, Y, W)))), ((((~product(X, Y, W)) | (~product(X, Y, Z))) | equalish(W, Z)) <=> (((~product(X, Y, Z)) | (~product(X, Y, W))) | equalish(W, Z)))), rewrite((((~product(X, Y, Z)) | (~product(X, Y, W))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))), ((((~product(X, Y, W)) | (~product(X, Y, Z))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(213,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, Y, W)) | (~product(X, Y, Z))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[212])).
% 0.20/0.46 tff(214,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, Y, W)) | (~product(X, Y, Z))) | equalish(W, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_total_function2')).
% 0.20/0.46 tff(215,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.20/0.46 tff(216,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[215, 211])).
% 0.20/0.46 tff(217,plain,(
% 0.20/0.46 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[216])).
% 0.20/0.46 tff(218,plain,
% 0.20/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[217, 210])).
% 0.20/0.46 tff(219,plain,
% 0.20/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_1, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_1, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(220,plain,
% 0.20/0.46 ((equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_2, e_1))) <=> (equalish(e_1, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(221,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_1, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_2, e_2))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[220])).
% 0.20/0.47 tff(222,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_1, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[221, 219])).
% 0.20/0.47 tff(223,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_2, e_1)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(224,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_1, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_2, e_2))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.20/0.47 tff(225,plain,
% 0.20/0.47 ((~product(e_1, e_2, e_1)) | (~product(e_1, e_2, e_2))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[224, 115, 218])).
% 0.20/0.47 tff(226,plain,
% 0.20/0.47 (~product(e_1, e_2, e_1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[225, 208])).
% 0.20/0.47 tff(227,plain,
% 0.20/0.47 (~product(e_2, e_1, e_1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[96, 33, 226, 208])).
% 0.20/0.47 tff(228,assumption,(product(e_2, e_3, e_3)), introduced(assumption)).
% 0.20/0.47 tff(229,plain,
% 0.20/0.47 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(230,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.20/0.47 tff(231,plain,
% 0.20/0.47 (~equalish(e_2, e_1)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.20/0.47 tff(232,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_2, e_3, e_3)) | (~product(e_1, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_3, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(233,plain,
% 0.20/0.47 ((equalish(e_2, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_2, e_3, e_3))) <=> (equalish(e_2, e_1) | (~product(e_2, e_3, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(234,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_2, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_2, e_3, e_3)) | (~product(e_1, e_3, e_3))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[233])).
% 0.20/0.47 tff(235,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_2, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_3, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[234, 232])).
% 0.20/0.47 tff(236,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_2, e_3, e_3)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(237,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_3, e_3)) | (~product(e_1, e_3, e_3))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.20/0.47 tff(238,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[237, 231, 175, 228, 194])).
% 0.20/0.47 tff(239,plain,((~product(e_2, e_3, e_3)) | (~product(e_1, e_3, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(240,plain,
% 0.20/0.47 (~product(e_2, e_3, e_3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[239, 193])).
% 0.20/0.47 tff(241,assumption,(~product(e_2, e_3, e_1)), introduced(assumption)).
% 0.20/0.47 tff(242,assumption,(~product(e_2, e_3, e_3)), introduced(assumption)).
% 0.20/0.47 tff(243,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | product(e_2, e_3, e_3))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | product(e_2, e_3, e_3))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(244,plain,
% 0.20/0.47 ((product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_2))) <=> ((~group_element(e_2)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | product(e_2, e_3, e_3))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(245,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | product(e_2, e_3, e_3)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[244])).
% 0.20/0.47 tff(246,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | product(e_2, e_3, e_3))),
% 0.20/0.47 inference(transitivity,[status(thm)],[245, 243])).
% 0.20/0.47 tff(247,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_2)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(248,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | product(e_2, e_3, e_3)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.20/0.47 tff(249,plain,
% 0.20/0.47 (product(e_2, e_3, e_2)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[248, 104, 60, 57, 242, 241])).
% 0.20/0.47 tff(250,assumption,(product(e_2, e_1, e_2)), introduced(assumption)).
% 0.20/0.47 tff(251,assumption,(product(e_2, e_3, e_2)), introduced(assumption)).
% 0.20/0.47 tff(252,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(253,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(254,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_1, e_2))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[253, 252])).
% 0.20/0.47 tff(255,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[254, 17, 14, 251, 250])).
% 0.20/0.47 tff(256,plain,((~product(e_2, e_1, e_2)) | (~product(e_2, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(257,plain,
% 0.20/0.47 (~product(e_2, e_1, e_2)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[256, 249])).
% 0.20/0.47 tff(258,plain,
% 0.20/0.47 (product(e_2, e_1, e_3) | product(e_2, e_1, e_2)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[146, 63, 104, 57, 1])).
% 0.20/0.47 tff(259,plain,
% 0.20/0.47 (product(e_2, e_1, e_3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[258, 257])).
% 0.20/0.47 tff(260,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(261,plain,
% 0.20/0.47 (((~product(e_1, e_3, e_3)) | product(e_2, e_3, e_1) | (~product(e_3, e_1, e_2))) <=> (product(e_2, e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(262,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_3)) | product(e_2, e_3, e_1) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_2))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[261])).
% 0.20/0.47 tff(263,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_3)) | product(e_2, e_3, e_1) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[262, 260])).
% 0.20/0.47 tff(264,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_3)) | product(e_2, e_3, e_1) | (~product(e_3, e_1, e_2)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(265,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_2))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.20/0.47 tff(266,plain,
% 0.20/0.47 (~product(e_3, e_1, e_2)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[265, 33, 194, 241])).
% 0.20/0.47 tff(267,plain,
% 0.20/0.47 (product(e_3, e_1, e_3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[70, 266, 125])).
% 0.20/0.47 tff(268,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(269,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(270,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.20/0.47 tff(271,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[270, 83, 175, 267, 259])).
% 0.20/0.47 tff(272,plain,(product(e_2, e_3, e_1) | product(e_2, e_1, e_1) | product(e_3, e_1, e_1) | product(e_2, e_3, e_3) | (~product(e_1, e_3, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(273,plain,
% 0.20/0.47 (product(e_2, e_3, e_1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[272, 227, 207, 240, 193])).
% 0.20/0.47 tff(274,assumption,(~product(e_1, e_1, e_2)), introduced(assumption)).
% 0.20/0.47 tff(275,assumption,(product(e_2, e_3, e_1)), introduced(assumption)).
% 0.20/0.47 tff(276,assumption,(product(e_3, e_2, e_1)), introduced(assumption)).
% 0.20/0.47 tff(277,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(278,plain,
% 0.20/0.47 (((~product(e_2, e_3, e_1)) | product(e_1, e_1, e_2) | (~product(e_3, e_2, e_1))) <=> (product(e_1, e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(279,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_1)) | product(e_1, e_1, e_2) | (~product(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[278])).
% 0.20/0.47 tff(280,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_1)) | product(e_1, e_1, e_2) | (~product(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[279, 277])).
% 0.20/0.47 tff(281,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_1)) | product(e_1, e_1, e_2) | (~product(e_3, e_2, e_1)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(282,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_3, e_1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.20/0.47 tff(283,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[282, 33, 274, 275, 276])).
% 0.20/0.47 tff(284,plain,((~product(e_3, e_2, e_1)) | product(e_1, e_1, e_2) | (~product(e_2, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(285,plain,
% 0.20/0.47 (~product(e_3, e_2, e_1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[284, 275, 274])).
% 0.20/0.47 tff(286,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_2)) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_1))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(287,plain,
% 0.20/0.47 (((~product(e_1, e_2, e_2)) | product(e_3, e_2, e_1) | (~product(e_2, e_1, e_3))) <=> ((~product(e_1, e_2, e_2)) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_1))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(288,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_2)) | product(e_3, e_2, e_1) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_2)) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_1)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[287])).
% 0.20/0.48 tff(289,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_2)) | product(e_3, e_2, e_1) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_1))),
% 0.20/0.48 inference(transitivity,[status(thm)],[288, 286])).
% 0.20/0.48 tff(290,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_2)) | product(e_3, e_2, e_1) | (~product(e_2, e_1, e_3)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(291,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_1)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.20/0.48 tff(292,plain,
% 0.20/0.48 ((~product(e_1, e_2, e_2)) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_1)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[291, 33])).
% 0.20/0.48 tff(293,plain,
% 0.20/0.48 (~product(e_2, e_1, e_3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[292, 285, 90])).
% 0.20/0.48 tff(294,plain,
% 0.20/0.48 (product(e_2, e_1, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[258, 293])).
% 0.20/0.48 tff(295,assumption,(product(e_3, e_2, e_2)), introduced(assumption)).
% 0.20/0.48 tff(296,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_2)) | product(e_1, e_2, e_3) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_2, e_2)) | product(e_1, e_2, e_3) | (~product(e_2, e_3, e_1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(297,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_2)) | product(e_1, e_2, e_3) | (~product(e_2, e_3, e_1)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(298,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_2, e_2)) | product(e_1, e_2, e_3) | (~product(e_2, e_3, e_1))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.20/0.48 tff(299,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[298, 33, 295, 101, 275])).
% 0.20/0.48 tff(300,plain,((~product(e_3, e_2, e_2)) | product(e_1, e_2, e_3) | (~product(e_2, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(301,plain,
% 0.20/0.48 (~product(e_3, e_2, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[300, 275, 101])).
% 0.20/0.48 tff(302,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | product(e_3, e_2, e_2) | (~group_element(e_3)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_3, e_2, e_2) | (~group_element(e_3)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(303,plain,
% 0.20/0.48 ((product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3))) <=> ((~group_element(e_2)) | product(e_3, e_2, e_2) | (~group_element(e_3)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(304,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | product(e_3, e_2, e_2) | (~group_element(e_3)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[303])).
% 0.20/0.48 tff(305,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_3, e_2, e_2) | (~group_element(e_3)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1))),
% 0.20/0.48 inference(transitivity,[status(thm)],[304, 302])).
% 0.20/0.48 tff(306,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(307,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_3, e_2, e_2) | (~group_element(e_3)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[306, 305])).
% 0.20/0.48 tff(308,plain,
% 0.20/0.48 (product(e_3, e_2, e_2) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[307, 104, 60, 57])).
% 0.20/0.48 tff(309,plain,
% 0.20/0.48 (product(e_3, e_2, e_3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[308, 301, 285])).
% 0.20/0.48 tff(310,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_3)) | product(e_3, e_1, e_2) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_2, e_3)) | product(e_3, e_1, e_2) | (~product(e_2, e_3, e_1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(311,plain,
% 0.20/0.48 (((~product(e_2, e_3, e_1)) | product(e_3, e_1, e_2) | (~product(e_3, e_2, e_3))) <=> ((~product(e_3, e_2, e_3)) | product(e_3, e_1, e_2) | (~product(e_2, e_3, e_1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(312,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_1)) | product(e_3, e_1, e_2) | (~product(e_3, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_3)) | product(e_3, e_1, e_2) | (~product(e_2, e_3, e_1))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[311])).
% 0.20/0.48 tff(313,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_1)) | product(e_3, e_1, e_2) | (~product(e_3, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_2, e_3)) | product(e_3, e_1, e_2) | (~product(e_2, e_3, e_1)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[312, 310])).
% 0.20/0.48 tff(314,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_1)) | product(e_3, e_1, e_2) | (~product(e_3, e_2, e_3)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(315,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_2, e_3)) | product(e_3, e_1, e_2) | (~product(e_2, e_3, e_1))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[314, 313])).
% 0.20/0.48 tff(316,plain,
% 0.20/0.48 ((~product(e_3, e_2, e_3)) | product(e_3, e_1, e_2) | (~product(e_2, e_3, e_1))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[315, 33])).
% 0.20/0.48 tff(317,plain,
% 0.20/0.48 (product(e_3, e_1, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[316, 309, 275])).
% 0.20/0.48 tff(318,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(319,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(320,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_1, e_2))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[319, 318])).
% 0.20/0.48 tff(321,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[320, 83, 175, 317, 294])).
% 0.20/0.48 tff(322,plain,((~product(e_2, e_3, e_1)) | product(e_1, e_2, e_3) | product(e_2, e_1, e_1) | (~product(e_1, e_2, e_2)) | product(e_1, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(323,plain,
% 0.20/0.48 (product(e_1, e_1, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[322, 273, 200, 208, 227])).
% 0.20/0.48 tff(324,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_1) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_1) | (~product(e_1, e_1, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(325,plain,
% 0.20/0.48 (((~product(e_1, e_1, e_2)) | product(e_2, e_2, e_1) | (~product(e_1, e_1, e_2))) <=> (product(e_2, e_2, e_1) | (~product(e_1, e_1, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(326,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_2)) | product(e_2, e_2, e_1) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_1) | (~product(e_1, e_1, e_2))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[325])).
% 0.20/0.48 tff(327,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_2)) | product(e_2, e_2, e_1) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_1) | (~product(e_1, e_1, e_2)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[326, 324])).
% 0.20/0.48 tff(328,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_2)) | product(e_2, e_2, e_1) | (~product(e_1, e_1, e_2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(329,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_1) | (~product(e_1, e_1, e_2))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[328, 327])).
% 0.20/0.48 tff(330,plain,
% 0.20/0.48 (product(e_2, e_2, e_1) | (~product(e_1, e_1, e_2))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[329, 33])).
% 0.20/0.48 tff(331,plain,
% 0.20/0.48 (product(e_2, e_2, e_1)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[330, 323])).
% 0.20/0.48 tff(332,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_3, e_1)) | (~product(e_2, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_2, e_3, e_1)) | (~product(e_2, e_2, e_1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(333,plain,
% 0.20/0.48 ((equalish(e_3, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_3, e_1))) <=> (equalish(e_3, e_2) | (~product(e_2, e_3, e_1)) | (~product(e_2, e_2, e_1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(334,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_3, e_1)) | (~product(e_2, e_2, e_1))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[333])).
% 0.20/0.48 tff(335,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_2, e_3, e_1)) | (~product(e_2, e_2, e_1)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[334, 332])).
% 0.20/0.48 tff(336,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(337,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_2, e_3, e_1)) | (~product(e_2, e_2, e_1))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[336, 335])).
% 0.20/0.48 tff(338,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[337, 83, 14, 273, 331])).
% 0.20/0.48 tff(339,plain,(product(e_1, e_3, e_1) | product(e_1, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(340,plain,
% 0.20/0.48 (product(e_1, e_3, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[339, 183])).
% 0.20/0.48 tff(341,assumption,(product(e_1, e_3, e_2)), introduced(assumption)).
% 0.20/0.48 tff(342,plain,
% 0.20/0.48 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(343,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.20/0.48 tff(344,plain,
% 0.20/0.48 (~equalish(e_2, e_3)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[343, 342])).
% 0.20/0.48 tff(345,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(346,plain,
% 0.20/0.48 ((equalish(e_2, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_2, e_2))) <=> (equalish(e_2, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(347,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_3, e_2))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[346])).
% 0.20/0.48 tff(348,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[347, 345])).
% 0.20/0.48 tff(349,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(350,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_3, e_2))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[349, 348])).
% 0.20/0.48 tff(351,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[350, 344, 14, 90, 341])).
% 0.20/0.48 tff(352,plain,((~product(e_1, e_2, e_2)) | (~product(e_1, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(353,plain,
% 0.20/0.48 (~product(e_1, e_2, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[352, 340])).
% 0.20/0.48 tff(354,plain,
% 0.20/0.48 (product(e_1, e_2, e_1) | product(e_1, e_2, e_3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[110, 63, 104, 57, 353])).
% 0.20/0.48 tff(355,plain,
% 0.20/0.48 (product(e_1, e_2, e_3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[354, 2])).
% 0.20/0.48 tff(356,plain,
% 0.20/0.48 (~product(e_1, e_3, e_3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[199, 150])).
% 0.20/0.48 tff(357,assumption,(~product(e_1, e_3, e_3)), introduced(assumption)).
% 0.20/0.48 tff(358,assumption,(product(e_3, e_2, e_3)), introduced(assumption)).
% 0.20/0.48 tff(359,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(360,plain,
% 0.20/0.48 (((~product(e_3, e_2, e_3)) | product(e_1, e_3, e_3) | (~product(e_2, e_3, e_1))) <=> (product(e_1, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(361,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_3)) | product(e_1, e_3, e_3) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_1))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[360])).
% 0.20/0.48 tff(362,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_3)) | product(e_1, e_3, e_3) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_1)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[361, 359])).
% 0.20/0.48 tff(363,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_3)) | product(e_1, e_3, e_3) | (~product(e_2, e_3, e_1)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(364,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_1))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[363, 362])).
% 0.20/0.48 tff(365,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[364, 33, 357, 275, 358])).
% 0.20/0.48 tff(366,plain,((~product(e_3, e_2, e_3)) | product(e_1, e_3, e_3) | (~product(e_2, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(367,plain,
% 0.20/0.48 (~product(e_3, e_2, e_3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[366, 275, 357])).
% 0.20/0.48 tff(368,assumption,(product(e_3, e_1, e_2)), introduced(assumption)).
% 0.20/0.48 tff(369,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(370,plain,
% 0.20/0.48 ((equalish(e_2, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_2))) <=> (equalish(e_2, e_1) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(371,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_1, e_2))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[370])).
% 0.20/0.49 tff(372,plain,
% 0.20/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[371, 369])).
% 0.20/0.49 tff(373,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(374,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_1, e_2))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[373, 372])).
% 0.20/0.49 tff(375,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[374, 231, 14, 295, 368])).
% 0.20/0.49 tff(376,plain,((~product(e_3, e_2, e_2)) | (~product(e_3, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(377,plain,
% 0.20/0.49 (~product(e_3, e_2, e_2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[376, 368])).
% 0.20/0.49 tff(378,assumption,(~product(e_3, e_2, e_3)), introduced(assumption)).
% 0.20/0.49 tff(379,plain,
% 0.20/0.49 (product(e_3, e_2, e_2) | product(e_3, e_2, e_1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[307, 104, 60, 57, 378])).
% 0.20/0.49 tff(380,plain,
% 0.20/0.49 (product(e_3, e_2, e_1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[379, 377])).
% 0.20/0.49 tff(381,plain,
% 0.20/0.49 (product(e_1, e_1, e_2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[284, 380, 275])).
% 0.20/0.49 tff(382,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[181, 17, 175, 381, 368])).
% 0.20/0.49 tff(383,plain,((~product(e_3, e_1, e_2)) | (~product(e_2, e_3, e_1)) | product(e_3, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(384,plain,
% 0.20/0.49 (~product(e_3, e_1, e_2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[383, 275, 367])).
% 0.20/0.49 tff(385,plain,
% 0.20/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_3, e_1)) | (~product(e_1, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_3, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(386,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_3, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(387,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_3, e_1)) | (~product(e_1, e_3, e_1))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[386, 385])).
% 0.20/0.49 tff(388,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[387, 115, 175, 3, 275])).
% 0.20/0.49 tff(389,plain,((~product(e_1, e_3, e_1)) | (~product(e_2, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(390,plain,
% 0.20/0.49 (~product(e_1, e_3, e_1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[389, 275])).
% 0.20/0.49 tff(391,plain,
% 0.20/0.49 (product(e_1, e_3, e_2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[192, 390, 357])).
% 0.20/0.49 tff(392,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_2, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_1, e_1)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(393,plain,
% 0.20/0.49 (((~product(e_1, e_3, e_2)) | product(e_1, e_2, e_1) | (~product(e_3, e_1, e_1))) <=> (product(e_1, e_2, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_1, e_1)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(394,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_2)) | product(e_1, e_2, e_1) | (~product(e_3, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_1, e_1))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[393])).
% 0.20/0.49 tff(395,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_2)) | product(e_1, e_2, e_1) | (~product(e_3, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_2, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_1, e_1)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[394, 392])).
% 0.20/0.49 tff(396,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_2)) | product(e_1, e_2, e_1) | (~product(e_3, e_1, e_1)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(397,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_2, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_1, e_1))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[396, 395])).
% 0.20/0.49 tff(398,plain,
% 0.20/0.49 (~product(e_3, e_1, e_1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[397, 33, 2, 391])).
% 0.20/0.49 tff(399,plain,
% 0.20/0.49 (product(e_3, e_1, e_2) | product(e_3, e_1, e_3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[69, 63, 60, 57, 398])).
% 0.20/0.49 tff(400,plain,
% 0.20/0.49 (product(e_3, e_1, e_3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[399, 384])).
% 0.20/0.49 tff(401,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_2)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(402,plain,
% 0.20/0.49 (((~product(e_3, e_1, e_3)) | product(e_2, e_3, e_3) | (~product(e_1, e_3, e_2))) <=> (product(e_2, e_3, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_2)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(403,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_3)) | product(e_2, e_3, e_3) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_2))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[402])).
% 0.20/0.49 tff(404,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_3)) | product(e_2, e_3, e_3) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_2)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[403, 401])).
% 0.20/0.49 tff(405,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_3)) | product(e_2, e_3, e_3) | (~product(e_1, e_3, e_2)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(406,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_2))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[405, 404])).
% 0.20/0.49 tff(407,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[406, 33, 242, 391, 400])).
% 0.20/0.49 tff(408,plain,((~product(e_2, e_3, e_1)) | product(e_2, e_3, e_3) | product(e_1, e_3, e_3) | product(e_1, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(409,plain,
% 0.20/0.49 (~product(e_2, e_3, e_1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[408, 356, 242, 2])).
% 0.20/0.49 tff(410,plain,
% 0.20/0.49 (product(e_2, e_3, e_2) | product(e_2, e_3, e_1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[248, 104, 60, 57, 242])).
% 0.20/0.49 tff(411,plain,
% 0.20/0.49 (product(e_2, e_3, e_2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[410, 409])).
% 0.20/0.49 tff(412,plain,
% 0.20/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_1, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(413,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(414,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_1, e_3, e_2))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[413, 412])).
% 0.20/0.49 tff(415,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[414, 115, 175, 341, 251])).
% 0.20/0.49 tff(416,plain,((~product(e_1, e_3, e_2)) | (~product(e_2, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(417,plain,
% 0.20/0.49 (~product(e_1, e_3, e_2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[416, 411])).
% 0.20/0.49 tff(418,plain,
% 0.20/0.49 (product(e_1, e_3, e_1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[192, 417, 356])).
% 0.20/0.49 tff(419,plain,
% 0.20/0.49 (~product(e_1, e_1, e_1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[22, 418])).
% 0.20/0.49 tff(420,plain,
% 0.20/0.49 (~product(e_3, e_1, e_1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[39, 33, 418, 419])).
% 0.20/0.49 tff(421,plain,
% 0.20/0.49 (~product(e_3, e_1, e_3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[46, 33, 418, 420])).
% 0.20/0.49 tff(422,plain,
% 0.20/0.49 (product(e_3, e_1, e_2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[69, 63, 60, 57, 420, 421])).
% 0.20/0.49 tff(423,plain,
% 0.20/0.49 (~product(e_1, e_1, e_3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[156, 150])).
% 0.20/0.49 tff(424,plain,
% 0.20/0.49 (product(e_1, e_1, e_2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[164, 423, 419])).
% 0.20/0.49 tff(425,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[181, 17, 175, 424, 422])).
% 0.20/0.49 tff(426,plain,((~product(e_1, e_2, e_3)) | product(e_2, e_3, e_3) | product(e_1, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(427,plain,
% 0.20/0.49 (product(e_2, e_3, e_3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[426, 355, 2])).
% 0.20/0.49 tff(428,assumption,(product(e_2, e_1, e_3)), introduced(assumption)).
% 0.20/0.49 tff(429,plain,
% 0.20/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_2, e_3, e_3)) | (~product(e_2, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_2, e_3, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(430,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_2, e_3, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(431,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_2, e_3, e_3)) | (~product(e_2, e_1, e_3))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[430, 429])).
% 0.20/0.49 tff(432,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[431, 17, 14, 228, 428])).
% 0.20/0.49 tff(433,plain,((~product(e_2, e_1, e_3)) | (~product(e_2, e_3, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(434,plain,
% 0.20/0.49 (~product(e_2, e_1, e_3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[433, 427])).
% 0.20/0.49 tff(435,plain,
% 0.20/0.49 (product(e_2, e_1, e_2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[258, 434])).
% 0.20/0.49 tff(436,plain,
% 0.20/0.49 (~product(e_2, e_3, e_2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[416, 340])).
% 0.20/0.49 tff(437,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_2)) | product(e_2, e_3, e_2) | (~product(e_2, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_2, e_2)) | product(e_2, e_3, e_2) | (~product(e_2, e_3, e_3)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(438,plain,
% 0.20/0.49 (((~product(e_2, e_3, e_3)) | product(e_2, e_3, e_2) | (~product(e_3, e_2, e_2))) <=> ((~product(e_3, e_2, e_2)) | product(e_2, e_3, e_2) | (~product(e_2, e_3, e_3)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(439,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_3)) | product(e_2, e_3, e_2) | (~product(e_3, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_2)) | product(e_2, e_3, e_2) | (~product(e_2, e_3, e_3))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[438])).
% 0.20/0.49 tff(440,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_3)) | product(e_2, e_3, e_2) | (~product(e_3, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_2, e_2)) | product(e_2, e_3, e_2) | (~product(e_2, e_3, e_3)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[439, 437])).
% 0.20/0.49 tff(441,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_3)) | product(e_2, e_3, e_2) | (~product(e_3, e_2, e_2)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(442,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_2, e_2)) | product(e_2, e_3, e_2) | (~product(e_2, e_3, e_3))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[441, 440])).
% 0.20/0.49 tff(443,plain,
% 0.20/0.49 (~product(e_3, e_2, e_2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[442, 33, 427, 436])).
% 0.20/0.49 tff(444,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_2, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_2, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(445,plain,
% 0.20/0.49 (((~product(e_2, e_1, e_2)) | product(e_3, e_2, e_2) | (~product(e_1, e_2, e_3))) <=> (product(e_3, e_2, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(446,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_2)) | product(e_3, e_2, e_2) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_2, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[445])).
% 0.20/0.49 tff(447,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_2)) | product(e_3, e_2, e_2) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_2, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[446, 444])).
% 0.20/0.49 tff(448,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_2)) | product(e_3, e_2, e_2) | (~product(e_1, e_2, e_3)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(449,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_2, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[448, 447])).
% 0.20/0.50 tff(450,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[449, 33, 443, 355, 435])).
% 0.20/0.50 tff(451,plain,(product(e_1, e_2, e_1) | product(e_2, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(452,plain,
% 0.20/0.50 (product(e_1, e_2, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[451, 1])).
% 0.20/0.50 tff(453,plain,
% 0.20/0.50 ((~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_2))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[139, 353])).
% 0.20/0.50 tff(454,plain,
% 0.20/0.50 (~product(e_2, e_1, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[453, 452])).
% 0.20/0.50 tff(455,plain,
% 0.20/0.50 (product(e_2, e_1, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[258, 454])).
% 0.20/0.50 tff(456,plain,
% 0.20/0.50 (~product(e_2, e_3, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[433, 455])).
% 0.20/0.50 tff(457,plain,
% 0.20/0.50 (product(e_2, e_3, e_1) | product(e_2, e_3, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[248, 104, 60, 57, 436])).
% 0.20/0.50 tff(458,plain,
% 0.20/0.50 (product(e_2, e_3, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[457, 456])).
% 0.20/0.50 tff(459,plain,
% 0.20/0.50 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(460,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.20/0.50 tff(461,plain,
% 0.20/0.50 (~equalish(e_3, e_1)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[460, 459])).
% 0.20/0.50 tff(462,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_3, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_3, e_2, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(463,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_3, e_2, e_1)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(464,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_3, e_2, e_1))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[463, 462])).
% 0.20/0.50 tff(465,plain,
% 0.20/0.50 ((~product(e_1, e_2, e_1)) | (~product(e_3, e_2, e_1))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[464, 461, 175])).
% 0.20/0.50 tff(466,plain,
% 0.20/0.50 (~product(e_3, e_2, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[465, 452])).
% 0.20/0.50 tff(467,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_1, e_3) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_1, e_3) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_2, e_3)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(468,plain,
% 0.20/0.50 ((equalish(e_1, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_2, e_1))) <=> (equalish(e_1, e_3) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_2, e_3)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(469,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_1, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_1, e_3) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_2, e_3))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[468])).
% 0.20/0.50 tff(470,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_1, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_1, e_3) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_2, e_3)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[469, 467])).
% 0.20/0.50 tff(471,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_1, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_2, e_1)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(472,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_1, e_3) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_2, e_3))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[471, 470])).
% 0.20/0.50 tff(473,plain,
% 0.20/0.50 ((~product(e_1, e_2, e_1)) | (~product(e_1, e_2, e_3))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[472, 17, 218])).
% 0.20/0.50 tff(474,plain,
% 0.20/0.50 (~product(e_1, e_2, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[473, 452])).
% 0.20/0.50 tff(475,plain,
% 0.20/0.50 (~product(e_3, e_2, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[300, 458, 474])).
% 0.20/0.50 tff(476,plain,
% 0.20/0.50 (product(e_3, e_2, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[308, 475, 466])).
% 0.20/0.50 tff(477,plain,
% 0.20/0.50 (product(e_3, e_1, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[316, 476, 458])).
% 0.20/0.50 tff(478,plain,
% 0.20/0.50 (~product(e_1, e_1, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[119, 452])).
% 0.20/0.50 tff(479,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_1, e_3)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(480,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_1, e_3)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(481,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_1, e_3))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[480, 479])).
% 0.20/0.50 tff(482,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[481, 115, 175, 151, 428])).
% 0.20/0.50 tff(483,plain,((~product(e_1, e_1, e_3)) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(484,plain,
% 0.20/0.50 (~product(e_1, e_1, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[483, 455])).
% 0.20/0.50 tff(485,plain,
% 0.20/0.50 (product(e_1, e_1, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[164, 484, 478])).
% 0.20/0.50 tff(486,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[181, 17, 175, 485, 477])).
% 0.20/0.50 tff(487,plain,(product(e_2, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(488,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_3, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(489,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(490,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_3, e_1, e_1))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[489, 488])).
% 0.20/0.50 tff(491,plain,
% 0.20/0.50 ((~product(e_2, e_1, e_1)) | (~product(e_3, e_1, e_1))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[490, 83, 175])).
% 0.20/0.50 tff(492,plain,
% 0.20/0.50 (~product(e_3, e_1, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[491, 487])).
% 0.20/0.50 tff(493,plain,
% 0.20/0.50 (product(e_3, e_1, e_1) | product(e_1, e_2, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[148, 353])).
% 0.20/0.50 tff(494,plain,
% 0.20/0.50 (product(e_1, e_2, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[493, 492])).
% 0.20/0.50 tff(495,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(496,plain,
% 0.20/0.50 (((~product(e_1, e_2, e_3)) | product(e_1, e_3, e_1) | (~product(e_2, e_1, e_1))) <=> (product(e_1, e_3, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(497,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_1, e_3, e_1) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_1))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[496])).
% 0.20/0.50 tff(498,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_1, e_3, e_1) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[497, 495])).
% 0.20/0.50 tff(499,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_1, e_3, e_1) | (~product(e_2, e_1, e_1)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(500,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_1))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[499, 498])).
% 0.20/0.50 tff(501,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[500, 33, 183, 494, 487])).
% 0.20/0.50 % SZS output end Proof
% 0.20/0.50 % E exiting
%------------------------------------------------------------------------------