%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP129-4.004 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:07:10 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP129-4.004 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n011.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 15:43:56 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.41 % SZS status Unsatisfiable
% 0.12/0.41 % SZS output start Proof
% 0.12/0.41 tff(product_type, type, (
% 0.12/0.41 product: ( $i * $i * $i ) > $o)).
% 0.12/0.41 tff(e_2_type, type, (
% 0.12/0.41 e_2: $i)).
% 0.12/0.41 tff(e_3_type, type, (
% 0.12/0.41 e_3: $i)).
% 0.12/0.41 tff(e_4_type, type, (
% 0.12/0.41 e_4: $i)).
% 0.12/0.41 tff(e_1_type, type, (
% 0.12/0.41 e_1: $i)).
% 0.12/0.41 tff(group_element_type, type, (
% 0.12/0.41 group_element: $i > $o)).
% 0.12/0.41 tff(equalish_type, type, (
% 0.12/0.41 equalish: ( $i * $i ) > $o)).
% 0.12/0.41 tff(1,assumption,(~product(e_4, e_3, e_2)), introduced(assumption)).
% 0.12/0.41 tff(2,assumption,(~product(e_2, e_4, e_2)), introduced(assumption)).
% 0.12/0.41 tff(3,assumption,(~product(e_3, e_3, e_3)), introduced(assumption)).
% 0.12/0.41 tff(4,assumption,(product(e_3, e_3, e_2)), introduced(assumption)).
% 0.12/0.41 tff(5,plain,
% 0.12/0.41 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl(((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1)) <=> ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1)))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(6,plain,
% 0.12/0.41 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[5])).
% 0.12/0.41 tff(7,plain,
% 0.12/0.41 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(8,plain,
% 0.12/0.41 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : trans(monotonicity(rewrite((product(Y, X, Z1) | (~product(Z1, Y, Z2))) <=> ((~product(Z1, Y, Z2)) | product(Y, X, Z1))), (((product(Y, X, Z1) | (~product(Z1, Y, Z2))) | (~product(X, Z1, Z2))) <=> (((~product(Z1, Y, Z2)) | product(Y, X, Z1)) | (~product(X, Z1, Z2))))), rewrite((((~product(Z1, Y, Z2)) | product(Y, X, Z1)) | (~product(X, Z1, Z2))) <=> ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))), (((product(Y, X, Z1) | (~product(Z1, Y, Z2))) | (~product(X, Z1, Z2))) <=> ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(9,plain,
% 0.12/0.41 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((product(Y, X, Z1) | (~product(Z1, Y, Z2))) | (~product(X, Z1, Z2))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[8])).
% 0.12/0.41 tff(10,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : ((product(Y, X, Z1) | (~product(Z1, Y, Z2))) | (~product(X, Z1, Z2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qg3_1')).
% 0.12/0.41 tff(11,plain,
% 0.12/0.41 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.12/0.41 tff(12,plain,
% 0.12/0.41 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.12/0.41 tff(13,plain,(
% 0.12/0.41 ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))),
% 0.12/0.41 inference(skolemize,[status(sab)],[12])).
% 0.12/0.41 tff(14,plain,
% 0.12/0.41 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.12/0.41 tff(15,plain,
% 0.12/0.41 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (product(e_3, e_3, e_3) | (~product(e_3, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_3, e_3, e_3) | (~product(e_3, e_3, e_2)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(16,plain,
% 0.12/0.41 (((~product(e_3, e_3, e_2)) | (~product(e_3, e_3, e_2)) | product(e_3, e_3, e_3)) <=> (product(e_3, e_3, e_3) | (~product(e_3, e_3, e_2)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(17,plain,
% 0.12/0.41 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_3, e_2)) | (~product(e_3, e_3, e_2)) | product(e_3, e_3, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (product(e_3, e_3, e_3) | (~product(e_3, e_3, e_2))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[16])).
% 0.21/0.42 tff(18,plain,
% 0.21/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_3, e_2)) | (~product(e_3, e_3, e_2)) | product(e_3, e_3, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_3, e_3, e_3) | (~product(e_3, e_3, e_2)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[17, 15])).
% 0.21/0.42 tff(19,plain,
% 0.21/0.42 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_3, e_2)) | (~product(e_3, e_3, e_2)) | product(e_3, e_3, e_3))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(20,plain,
% 0.21/0.42 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_3, e_3, e_3) | (~product(e_3, e_3, e_2))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.21/0.42 tff(21,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[20, 14, 4, 3])).
% 0.21/0.42 tff(22,plain,((~product(e_3, e_3, e_2)) | product(e_3, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(23,plain,
% 0.21/0.42 (~product(e_3, e_3, e_2)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[22, 3])).
% 0.21/0.42 tff(24,assumption,(product(e_3, e_3, e_4)), introduced(assumption)).
% 0.21/0.42 tff(25,plain,
% 0.21/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (product(e_3, e_3, e_3) | (~product(e_3, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_3, e_3, e_3) | (~product(e_3, e_3, e_4)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(26,plain,
% 0.21/0.42 (((~product(e_3, e_3, e_4)) | (~product(e_3, e_3, e_4)) | product(e_3, e_3, e_3)) <=> (product(e_3, e_3, e_3) | (~product(e_3, e_3, e_4)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(27,plain,
% 0.21/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_3, e_4)) | (~product(e_3, e_3, e_4)) | product(e_3, e_3, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (product(e_3, e_3, e_3) | (~product(e_3, e_3, e_4))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[26])).
% 0.21/0.42 tff(28,plain,
% 0.21/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_3, e_4)) | (~product(e_3, e_3, e_4)) | product(e_3, e_3, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_3, e_3, e_3) | (~product(e_3, e_3, e_4)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[27, 25])).
% 0.21/0.42 tff(29,plain,
% 0.21/0.42 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_3, e_4)) | (~product(e_3, e_3, e_4)) | product(e_3, e_3, e_3))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(30,plain,
% 0.21/0.42 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_3, e_3, e_3) | (~product(e_3, e_3, e_4))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.21/0.42 tff(31,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[30, 14, 24, 3])).
% 0.21/0.42 tff(32,plain,((~product(e_3, e_3, e_4)) | product(e_3, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(33,plain,
% 0.21/0.42 (~product(e_3, e_3, e_4)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[32, 3])).
% 0.21/0.42 tff(34,plain,
% 0.21/0.42 (^[Y: $i, X: $i] : refl(((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(35,plain,
% 0.21/0.42 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[34])).
% 0.21/0.42 tff(36,plain,
% 0.21/0.42 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(37,plain,
% 0.21/0.42 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_1))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> (((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_1)) | product(X, Y, e_2)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1)))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> (((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1)) | product(X, Y, e_3)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1)) | product(X, Y, e_3)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)))), (((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> (((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)) | product(X, Y, e_4)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)) | product(X, Y, e_4)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))), (((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(38,plain,
% 0.21/0.42 (![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[37])).
% 0.21/0.42 tff(39,axiom,(![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_total_function1')).
% 0.21/0.42 tff(40,plain,
% 0.21/0.42 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.21/0.42 tff(41,plain,
% 0.21/0.42 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.21/0.42 tff(42,plain,(
% 0.21/0.42 ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.21/0.42 inference(skolemize,[status(sab)],[41])).
% 0.21/0.42 tff(43,plain,
% 0.21/0.42 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.21/0.42 tff(44,plain,
% 0.21/0.42 (group_element(e_3) <=> group_element(e_3)),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(45,axiom,(group_element(e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_3')).
% 0.21/0.42 tff(46,plain,
% 0.21/0.42 (group_element(e_3)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.21/0.42 tff(47,plain,
% 0.21/0.42 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (product(e_3, e_3, e_1) | product(e_3, e_3, e_4) | product(e_3, e_3, e_2) | product(e_3, e_3, e_3) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_3, e_3, e_1) | product(e_3, e_3, e_4) | product(e_3, e_3, e_2) | product(e_3, e_3, e_3) | (~group_element(e_3)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(48,plain,
% 0.21/0.42 (((~group_element(e_3)) | (~group_element(e_3)) | product(e_3, e_3, e_4) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1)) <=> (product(e_3, e_3, e_1) | product(e_3, e_3, e_4) | product(e_3, e_3, e_2) | product(e_3, e_3, e_3) | (~group_element(e_3)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(49,plain,
% 0.21/0.42 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_3)) | product(e_3, e_3, e_4) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (product(e_3, e_3, e_1) | product(e_3, e_3, e_4) | product(e_3, e_3, e_2) | product(e_3, e_3, e_3) | (~group_element(e_3))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[48])).
% 0.21/0.42 tff(50,plain,
% 0.21/0.42 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_3)) | product(e_3, e_3, e_4) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_3, e_3, e_1) | product(e_3, e_3, e_4) | product(e_3, e_3, e_2) | product(e_3, e_3, e_3) | (~group_element(e_3)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[49, 47])).
% 0.21/0.42 tff(51,plain,
% 0.21/0.42 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_3)) | product(e_3, e_3, e_4) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(52,plain,
% 0.21/0.42 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_3, e_3, e_1) | product(e_3, e_3, e_4) | product(e_3, e_3, e_2) | product(e_3, e_3, e_3) | (~group_element(e_3))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.21/0.42 tff(53,plain,
% 0.21/0.42 (product(e_3, e_3, e_1) | product(e_3, e_3, e_4) | product(e_3, e_3, e_2) | product(e_3, e_3, e_3)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[52, 46, 43])).
% 0.21/0.42 tff(54,plain,
% 0.21/0.42 (product(e_3, e_3, e_1)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[53, 33, 23, 3])).
% 0.21/0.42 tff(55,plain,
% 0.21/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (product(e_3, e_3, e_3) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_3, e_3, e_3) | (~product(e_3, e_3, e_1)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(56,plain,
% 0.21/0.43 (((~product(e_3, e_3, e_1)) | (~product(e_3, e_3, e_1)) | product(e_3, e_3, e_3)) <=> (product(e_3, e_3, e_3) | (~product(e_3, e_3, e_1)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(57,plain,
% 0.21/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_3, e_1)) | (~product(e_3, e_3, e_1)) | product(e_3, e_3, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (product(e_3, e_3, e_3) | (~product(e_3, e_3, e_1))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[56])).
% 0.21/0.43 tff(58,plain,
% 0.21/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_3, e_1)) | (~product(e_3, e_3, e_1)) | product(e_3, e_3, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_3, e_3, e_3) | (~product(e_3, e_3, e_1)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[57, 55])).
% 0.21/0.43 tff(59,plain,
% 0.21/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_3, e_1)) | (~product(e_3, e_3, e_1)) | product(e_3, e_3, e_3))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(60,plain,
% 0.21/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_3, e_3, e_3) | (~product(e_3, e_3, e_1))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.21/0.43 tff(61,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[60, 14, 54, 3])).
% 0.21/0.43 tff(62,plain,(product(e_3, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(63,plain,
% 0.21/0.43 (^[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))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(64,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[63])).
% 0.21/0.43 tff(65,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(66,plain,
% 0.21/0.43 (^[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)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(67,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[66])).
% 0.21/0.43 tff(68,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')).
% 0.21/0.43 tff(69,plain,
% 0.21/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.21/0.43 tff(70,plain,
% 0.21/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.21/0.43 tff(71,plain,(
% 0.21/0.43 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[70])).
% 0.21/0.43 tff(72,plain,
% 0.21/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.21/0.43 tff(73,plain,
% 0.21/0.43 ((~equalish(e_4, e_3)) <=> (~equalish(e_4, e_3))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(74,axiom,(~equalish(e_4, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_is_not_e_3')).
% 0.21/0.43 tff(75,plain,
% 0.21/0.43 (~equalish(e_4, e_3)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.21/0.43 tff(76,plain,
% 0.21/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_4)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(77,plain,
% 0.21/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_4)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(78,plain,
% 0.21/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_4))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.21/0.43 tff(79,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[78, 75, 72, 24, 62])).
% 0.21/0.43 tff(80,plain,(~product(e_3, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(81,plain,
% 0.21/0.43 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(82,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.21/0.43 tff(83,plain,
% 0.21/0.43 (~equalish(e_2, e_3)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.21/0.43 tff(84,plain,
% 0.21/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_2, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_3, e_3)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(85,plain,
% 0.21/0.43 ((equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_2))) <=> (equalish(e_2, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_3, e_3)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(86,plain,
% 0.21/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_3, e_3))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[85])).
% 0.21/0.43 tff(87,plain,
% 0.21/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_2, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_3, e_3)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[86, 84])).
% 0.21/0.43 tff(88,plain,
% 0.21/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_2)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(89,plain,
% 0.21/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_2, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_3, e_3))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.21/0.43 tff(90,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[89, 83, 72, 4, 62])).
% 0.21/0.43 tff(91,plain,(~product(e_3, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(92,assumption,(~product(e_3, e_3, e_2)), introduced(assumption)).
% 0.21/0.43 tff(93,assumption,(~product(e_3, e_3, e_4)), introduced(assumption)).
% 0.21/0.43 tff(94,assumption,(~product(e_3, e_4, e_2)), introduced(assumption)).
% 0.21/0.43 tff(95,assumption,(product(e_4, e_4, e_2)), introduced(assumption)).
% 0.21/0.43 tff(96,plain,
% 0.21/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (product(e_4, e_4, e_4) | (~product(e_4, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_4, e_4, e_4) | (~product(e_4, e_4, e_2)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(97,plain,
% 0.21/0.43 (((~product(e_4, e_4, e_2)) | (~product(e_4, e_4, e_2)) | product(e_4, e_4, e_4)) <=> (product(e_4, e_4, e_4) | (~product(e_4, e_4, e_2)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(98,plain,
% 0.21/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_4, e_4, e_2)) | (~product(e_4, e_4, e_2)) | product(e_4, e_4, e_4))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (product(e_4, e_4, e_4) | (~product(e_4, e_4, e_2))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[97])).
% 0.21/0.43 tff(99,plain,
% 0.21/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_4, e_4, e_2)) | (~product(e_4, e_4, e_2)) | product(e_4, e_4, e_4))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_4, e_4, e_4) | (~product(e_4, e_4, e_2)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[98, 96])).
% 0.21/0.43 tff(100,plain,
% 0.21/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_4, e_4, e_2)) | (~product(e_4, e_4, e_2)) | product(e_4, e_4, e_4))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(101,plain,
% 0.21/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_4, e_4, e_4) | (~product(e_4, e_4, e_2))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.21/0.43 tff(102,plain,
% 0.21/0.43 (product(e_4, e_4, e_4)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[101, 14, 95])).
% 0.21/0.43 tff(103,plain,
% 0.21/0.43 ((~equalish(e_4, e_2)) <=> (~equalish(e_4, e_2))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(104,axiom,(~equalish(e_4, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_is_not_e_2')).
% 0.21/0.43 tff(105,plain,
% 0.21/0.43 (~equalish(e_4, e_2)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.21/0.43 tff(106,plain,
% 0.21/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_4, e_2) | (~product(e_4, e_4, e_2)) | (~product(e_4, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_4, e_2) | (~product(e_4, e_4, e_2)) | (~product(e_4, e_4, e_4)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(107,plain,
% 0.21/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_4, e_2) | (~product(e_4, e_4, e_2)) | (~product(e_4, e_4, e_4)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(108,plain,
% 0.21/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_4, e_2) | (~product(e_4, e_4, e_2)) | (~product(e_4, e_4, e_4))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.21/0.43 tff(109,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[108, 105, 72, 95, 102])).
% 0.21/0.43 tff(110,plain,(~product(e_4, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(111,plain,
% 0.21/0.43 (group_element(e_4) <=> group_element(e_4)),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(112,axiom,(group_element(e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_4')).
% 0.21/0.43 tff(113,plain,
% 0.21/0.43 (group_element(e_4)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.21/0.44 tff(114,plain,
% 0.21/0.44 (group_element(e_2) <=> group_element(e_2)),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(115,axiom,(group_element(e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_2')).
% 0.21/0.44 tff(116,plain,
% 0.21/0.44 (group_element(e_2)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.21/0.44 tff(117,plain,
% 0.21/0.44 (^[Y: $i, X: $i] : refl((product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) <=> (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(118,plain,
% 0.21/0.44 (![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[117])).
% 0.21/0.44 tff(119,plain,
% 0.21/0.44 (![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(120,plain,
% 0.21/0.44 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) <=> (product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) <=> ((product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) | product(e_2, X, Y)))), rewrite(((product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) | product(e_2, X, Y)) <=> (product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) <=> (product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))))), ((((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) | product(e_3, X, Y)) <=> ((product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) | product(e_3, X, Y)))), rewrite(((product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) | product(e_3, X, Y)) <=> (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))), ((((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) | product(e_3, X, Y)) <=> (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))))), (((((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) | product(e_3, X, Y)) | product(e_4, X, Y)) <=> ((product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) | product(e_4, X, Y)))), rewrite(((product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) | product(e_4, X, Y)) <=> (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))), (((((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) | product(e_3, X, Y)) | product(e_4, X, Y)) <=> (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(121,plain,
% 0.21/0.44 (![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) | product(e_3, X, Y)) | product(e_4, X, Y)) <=> ![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[120])).
% 0.21/0.44 tff(122,axiom,(![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) | product(e_3, X, Y)) | product(e_4, X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','row_surjectivity')).
% 0.21/0.44 tff(123,plain,
% 0.21/0.44 (![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.21/0.44 tff(124,plain,
% 0.21/0.44 (![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.21/0.44 tff(125,plain,(
% 0.21/0.44 ![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[124])).
% 0.21/0.44 tff(126,plain,
% 0.21/0.44 (![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[125, 118])).
% 0.21/0.44 tff(127,plain,
% 0.21/0.44 (((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_4, e_2) | (~group_element(e_2)) | (~group_element(e_4)) | product(e_1, e_4, e_2) | product(e_2, e_4, e_2) | product(e_4, e_4, e_2))) <=> ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_4, e_2) | (~group_element(e_2)) | (~group_element(e_4)) | product(e_1, e_4, e_2) | product(e_2, e_4, e_2) | product(e_4, e_4, e_2))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(128,plain,
% 0.21/0.44 ((product(e_4, e_4, e_2) | product(e_3, e_4, e_2) | product(e_2, e_4, e_2) | product(e_1, e_4, e_2) | (~group_element(e_2)) | (~group_element(e_4))) <=> (product(e_3, e_4, e_2) | (~group_element(e_2)) | (~group_element(e_4)) | product(e_1, e_4, e_2) | product(e_2, e_4, e_2) | product(e_4, e_4, e_2))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(129,plain,
% 0.21/0.44 (((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_4, e_2) | product(e_3, e_4, e_2) | product(e_2, e_4, e_2) | product(e_1, e_4, e_2) | (~group_element(e_2)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_4, e_2) | (~group_element(e_2)) | (~group_element(e_4)) | product(e_1, e_4, e_2) | product(e_2, e_4, e_2) | product(e_4, e_4, e_2)))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[128])).
% 0.21/0.44 tff(130,plain,
% 0.21/0.44 (((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_4, e_2) | product(e_3, e_4, e_2) | product(e_2, e_4, e_2) | product(e_1, e_4, e_2) | (~group_element(e_2)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_4, e_2) | (~group_element(e_2)) | (~group_element(e_4)) | product(e_1, e_4, e_2) | product(e_2, e_4, e_2) | product(e_4, e_4, e_2))),
% 0.21/0.44 inference(transitivity,[status(thm)],[129, 127])).
% 0.21/0.44 tff(131,plain,
% 0.21/0.44 ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_4, e_2) | product(e_3, e_4, e_2) | product(e_2, e_4, e_2) | product(e_1, e_4, e_2) | (~group_element(e_2)) | (~group_element(e_4)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(132,plain,
% 0.21/0.44 ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_4, e_2) | (~group_element(e_2)) | (~group_element(e_4)) | product(e_1, e_4, e_2) | product(e_2, e_4, e_2) | product(e_4, e_4, e_2)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.21/0.44 tff(133,plain,
% 0.21/0.44 (product(e_3, e_4, e_2) | product(e_1, e_4, e_2) | product(e_2, e_4, e_2)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[132, 126, 116, 113, 110])).
% 0.21/0.44 tff(134,plain,
% 0.21/0.44 (product(e_1, e_4, e_2)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[133, 94, 2])).
% 0.21/0.44 tff(135,assumption,(product(e_4, e_3, e_2)), introduced(assumption)).
% 0.21/0.44 tff(136,plain,
% 0.21/0.44 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl((product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1))) <=> (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(137,plain,
% 0.21/0.44 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[136])).
% 0.21/0.44 tff(138,plain,
% 0.21/0.44 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(139,plain,
% 0.21/0.44 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : trans(monotonicity(rewrite((product(X, Z1, Z2) | (~product(Z1, Y, Z2))) <=> (product(X, Z1, Z2) | (~product(Z1, Y, Z2)))), (((product(X, Z1, Z2) | (~product(Z1, Y, Z2))) | (~product(Y, X, Z1))) <=> ((product(X, Z1, Z2) | (~product(Z1, Y, Z2))) | (~product(Y, X, Z1))))), rewrite(((product(X, Z1, Z2) | (~product(Z1, Y, Z2))) | (~product(Y, X, Z1))) <=> (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))), (((product(X, Z1, Z2) | (~product(Z1, Y, Z2))) | (~product(Y, X, Z1))) <=> (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(140,plain,
% 0.21/0.44 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((product(X, Z1, Z2) | (~product(Z1, Y, Z2))) | (~product(Y, X, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[139])).
% 0.21/0.44 tff(141,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : ((product(X, Z1, Z2) | (~product(Z1, Y, Z2))) | (~product(Y, X, Z1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qg3_2')).
% 0.21/0.44 tff(142,plain,
% 0.21/0.44 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.21/0.44 tff(143,plain,
% 0.21/0.44 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[142, 138])).
% 0.21/0.44 tff(144,plain,(
% 0.21/0.44 ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[143])).
% 0.21/0.44 tff(145,plain,
% 0.21/0.44 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[144, 137])).
% 0.21/0.44 tff(146,plain,
% 0.21/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_4, e_2) | (~product(e_3, e_4, e_4)) | (~product(e_4, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_4, e_2) | (~product(e_3, e_4, e_4)) | (~product(e_4, e_3, e_2)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(147,plain,
% 0.21/0.44 ((product(e_4, e_4, e_2) | (~product(e_4, e_3, e_2)) | (~product(e_3, e_4, e_4))) <=> (product(e_4, e_4, e_2) | (~product(e_3, e_4, e_4)) | (~product(e_4, e_3, e_2)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(148,plain,
% 0.21/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_4, e_2) | (~product(e_4, e_3, e_2)) | (~product(e_3, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_4, e_2) | (~product(e_3, e_4, e_4)) | (~product(e_4, e_3, e_2))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[147])).
% 0.21/0.45 tff(149,plain,
% 0.21/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_4, e_2) | (~product(e_4, e_3, e_2)) | (~product(e_3, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_4, e_2) | (~product(e_3, e_4, e_4)) | (~product(e_4, e_3, e_2)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[148, 146])).
% 0.21/0.45 tff(150,plain,
% 0.21/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_4, e_2) | (~product(e_4, e_3, e_2)) | (~product(e_3, e_4, e_4)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(151,plain,
% 0.21/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_4, e_2) | (~product(e_3, e_4, e_4)) | (~product(e_4, e_3, e_2))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.21/0.45 tff(152,plain,
% 0.21/0.45 (~product(e_3, e_4, e_4)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[151, 145, 110, 135])).
% 0.21/0.45 tff(153,plain,
% 0.21/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_2, e_4)) | product(e_2, e_4, e_2) | (~product(e_4, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_2, e_4)) | product(e_2, e_4, e_2) | (~product(e_4, e_3, e_2)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(154,plain,
% 0.21/0.45 ((product(e_2, e_4, e_2) | (~product(e_4, e_3, e_2)) | (~product(e_3, e_2, e_4))) <=> ((~product(e_3, e_2, e_4)) | product(e_2, e_4, e_2) | (~product(e_4, e_3, e_2)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(155,plain,
% 0.21/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_2) | (~product(e_4, e_3, e_2)) | (~product(e_3, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_2, e_4)) | product(e_2, e_4, e_2) | (~product(e_4, e_3, e_2))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[154])).
% 0.21/0.45 tff(156,plain,
% 0.21/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_2) | (~product(e_4, e_3, e_2)) | (~product(e_3, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_2, e_4)) | product(e_2, e_4, e_2) | (~product(e_4, e_3, e_2)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[155, 153])).
% 0.21/0.45 tff(157,plain,
% 0.21/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_2) | (~product(e_4, e_3, e_2)) | (~product(e_3, e_2, e_4)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(158,plain,
% 0.21/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_2, e_4)) | product(e_2, e_4, e_2) | (~product(e_4, e_3, e_2))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.21/0.45 tff(159,plain,
% 0.21/0.45 (~product(e_3, e_2, e_4)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[158, 145, 2, 135])).
% 0.21/0.45 tff(160,plain,
% 0.21/0.45 (^[Y: $i, X: $i] : refl(((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(161,plain,
% 0.21/0.45 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[160])).
% 0.21/0.45 tff(162,plain,
% 0.21/0.45 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(163,plain,
% 0.21/0.45 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_1, Y))), (((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) <=> (((~group_element(Y)) | (~group_element(X)) | product(X, e_1, Y)) | product(X, e_2, Y)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product(X, e_1, Y)) | product(X, e_2, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_2, Y) | product(X, e_1, Y))), (((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_2, Y) | product(X, e_1, Y)))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) | product(X, e_3, Y)) <=> (((~group_element(Y)) | (~group_element(X)) | product(X, e_2, Y) | product(X, e_1, Y)) | product(X, e_3, Y)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product(X, e_2, Y) | product(X, e_1, Y)) | product(X, e_3, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) | product(X, e_3, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)))), (((((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) | product(X, e_3, Y)) | product(X, e_4, Y)) <=> (((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)) | product(X, e_4, Y)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)) | product(X, e_4, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))), (((((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) | product(X, e_3, Y)) | product(X, e_4, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(164,plain,
% 0.21/0.45 (![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) | product(X, e_3, Y)) | product(X, e_4, Y)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[163])).
% 0.21/0.45 tff(165,axiom,(![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) | product(X, e_3, Y)) | product(X, e_4, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','column_surjectivity')).
% 0.21/0.45 tff(166,plain,
% 0.21/0.45 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.21/0.45 tff(167,plain,
% 0.21/0.45 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[166, 162])).
% 0.21/0.45 tff(168,plain,(
% 0.21/0.45 ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.21/0.45 inference(skolemize,[status(sab)],[167])).
% 0.21/0.45 tff(169,plain,
% 0.21/0.45 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[168, 161])).
% 0.21/0.45 tff(170,plain,
% 0.21/0.45 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (product(e_3, e_3, e_4) | (~group_element(e_3)) | product(e_3, e_1, e_4) | (~group_element(e_4)) | product(e_3, e_4, e_4) | product(e_3, e_2, e_4))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | product(e_3, e_3, e_4) | (~group_element(e_3)) | product(e_3, e_1, e_4) | (~group_element(e_4)) | product(e_3, e_4, e_4) | product(e_3, e_2, e_4))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(171,plain,
% 0.21/0.45 (((~group_element(e_4)) | (~group_element(e_3)) | product(e_3, e_4, e_4) | product(e_3, e_3, e_4) | product(e_3, e_2, e_4) | product(e_3, e_1, e_4)) <=> (product(e_3, e_3, e_4) | (~group_element(e_3)) | product(e_3, e_1, e_4) | (~group_element(e_4)) | product(e_3, e_4, e_4) | product(e_3, e_2, e_4))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(172,plain,
% 0.21/0.45 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_4)) | (~group_element(e_3)) | product(e_3, e_4, e_4) | product(e_3, e_3, e_4) | product(e_3, e_2, e_4) | product(e_3, e_1, e_4))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (product(e_3, e_3, e_4) | (~group_element(e_3)) | product(e_3, e_1, e_4) | (~group_element(e_4)) | product(e_3, e_4, e_4) | product(e_3, e_2, e_4)))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[171])).
% 0.21/0.45 tff(173,plain,
% 0.21/0.45 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_4)) | (~group_element(e_3)) | product(e_3, e_4, e_4) | product(e_3, e_3, e_4) | product(e_3, e_2, e_4) | product(e_3, e_1, e_4))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | product(e_3, e_3, e_4) | (~group_element(e_3)) | product(e_3, e_1, e_4) | (~group_element(e_4)) | product(e_3, e_4, e_4) | product(e_3, e_2, e_4))),
% 0.21/0.45 inference(transitivity,[status(thm)],[172, 170])).
% 0.21/0.45 tff(174,plain,
% 0.21/0.45 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_4)) | (~group_element(e_3)) | product(e_3, e_4, e_4) | product(e_3, e_3, e_4) | product(e_3, e_2, e_4) | product(e_3, e_1, e_4))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(175,plain,
% 0.21/0.45 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | product(e_3, e_3, e_4) | (~group_element(e_3)) | product(e_3, e_1, e_4) | (~group_element(e_4)) | product(e_3, e_4, e_4) | product(e_3, e_2, e_4)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.21/0.45 tff(176,plain,
% 0.21/0.45 (product(e_3, e_1, e_4)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[175, 169, 46, 113, 93, 159, 152])).
% 0.21/0.45 tff(177,assumption,(product(e_3, e_1, e_4)), introduced(assumption)).
% 0.21/0.45 tff(178,assumption,(product(e_3, e_1, e_2)), introduced(assumption)).
% 0.21/0.45 tff(179,plain,
% 0.21/0.45 ((~equalish(e_2, e_4)) <=> (~equalish(e_2, e_4))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(180,axiom,(~equalish(e_2, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_4')).
% 0.21/0.45 tff(181,plain,
% 0.21/0.45 (~equalish(e_2, e_4)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.21/0.45 tff(182,plain,
% 0.21/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_4) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_2, e_4) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_1, e_4)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(183,plain,
% 0.21/0.46 ((equalish(e_2, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_1, e_2))) <=> (equalish(e_2, e_4) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_1, e_4)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(184,plain,
% 0.21/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_4) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_1, e_4))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[183])).
% 0.21/0.46 tff(185,plain,
% 0.21/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_2, e_4) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_1, e_4)))),
% 0.21/0.46 inference(transitivity,[status(thm)],[184, 182])).
% 0.21/0.46 tff(186,plain,
% 0.21/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_1, e_2)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(187,plain,
% 0.21/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_2, e_4) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_1, e_4))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.21/0.46 tff(188,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[187, 181, 72, 178, 177])).
% 0.21/0.46 tff(189,plain,((~product(e_3, e_1, e_2)) | (~product(e_3, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(190,plain,
% 0.21/0.46 (~product(e_3, e_1, e_2)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[189, 176])).
% 0.21/0.46 tff(191,assumption,(product(e_3, e_4, e_2)), introduced(assumption)).
% 0.21/0.46 tff(192,plain,
% 0.21/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_4, e_2)) | (~product(e_4, e_3, e_2)) | product(e_3, e_3, e_4))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_3, e_2)) | product(e_3, e_3, e_4))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(193,plain,
% 0.21/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_4, e_2)) | (~product(e_4, e_3, e_2)) | product(e_3, e_3, e_4))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(194,plain,
% 0.21/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_3, e_2)) | product(e_3, e_3, e_4)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.21/0.46 tff(195,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[194, 14, 191, 93, 135])).
% 0.21/0.46 tff(196,plain,((~product(e_3, e_4, e_2)) | product(e_3, e_3, e_4) | (~product(e_4, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(197,plain,
% 0.21/0.46 (~product(e_3, e_4, e_2)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[196, 135, 93])).
% 0.21/0.46 tff(198,plain,
% 0.21/0.46 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (product(e_3, e_4, e_2) | (~group_element(e_2)) | product(e_3, e_2, e_2) | product(e_3, e_3, e_2) | product(e_3, e_1, e_2) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | product(e_3, e_4, e_2) | (~group_element(e_2)) | product(e_3, e_2, e_2) | product(e_3, e_3, e_2) | product(e_3, e_1, e_2) | (~group_element(e_3)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(199,plain,
% 0.21/0.46 (((~group_element(e_2)) | (~group_element(e_3)) | product(e_3, e_4, e_2) | product(e_3, e_3, e_2) | product(e_3, e_2, e_2) | product(e_3, e_1, e_2)) <=> (product(e_3, e_4, e_2) | (~group_element(e_2)) | product(e_3, e_2, e_2) | product(e_3, e_3, e_2) | product(e_3, e_1, e_2) | (~group_element(e_3)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(200,plain,
% 0.21/0.46 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_2)) | (~group_element(e_3)) | product(e_3, e_4, e_2) | product(e_3, e_3, e_2) | product(e_3, e_2, e_2) | product(e_3, e_1, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (product(e_3, e_4, e_2) | (~group_element(e_2)) | product(e_3, e_2, e_2) | product(e_3, e_3, e_2) | product(e_3, e_1, e_2) | (~group_element(e_3))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[199])).
% 0.21/0.46 tff(201,plain,
% 0.21/0.46 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_2)) | (~group_element(e_3)) | product(e_3, e_4, e_2) | product(e_3, e_3, e_2) | product(e_3, e_2, e_2) | product(e_3, e_1, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | product(e_3, e_4, e_2) | (~group_element(e_2)) | product(e_3, e_2, e_2) | product(e_3, e_3, e_2) | product(e_3, e_1, e_2) | (~group_element(e_3)))),
% 0.21/0.46 inference(transitivity,[status(thm)],[200, 198])).
% 0.21/0.46 tff(202,plain,
% 0.21/0.46 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_2)) | (~group_element(e_3)) | product(e_3, e_4, e_2) | product(e_3, e_3, e_2) | product(e_3, e_2, e_2) | product(e_3, e_1, e_2))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(203,plain,
% 0.21/0.46 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | product(e_3, e_4, e_2) | (~group_element(e_2)) | product(e_3, e_2, e_2) | product(e_3, e_3, e_2) | product(e_3, e_1, e_2) | (~group_element(e_3))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.21/0.46 tff(204,plain,
% 0.21/0.46 (product(e_3, e_4, e_2) | product(e_3, e_2, e_2) | product(e_3, e_3, e_2) | product(e_3, e_1, e_2)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[203, 169, 116, 46])).
% 0.21/0.46 tff(205,plain,
% 0.21/0.46 (product(e_3, e_2, e_2)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[204, 197, 92, 190])).
% 0.21/0.46 tff(206,plain,
% 0.21/0.46 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl(((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1))) <=> ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(207,plain,
% 0.21/0.46 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[206])).
% 0.21/0.46 tff(208,plain,
% 0.21/0.46 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(209,plain,
% 0.21/0.46 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : trans(monotonicity(rewrite(((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) <=> ((~product(X, Z1, Z2)) | (~product(Y, X, Z1)))), ((((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) | product(Z1, Y, Z2)) <=> (((~product(X, Z1, Z2)) | (~product(Y, X, Z1))) | product(Z1, Y, Z2)))), rewrite((((~product(X, Z1, Z2)) | (~product(Y, X, Z1))) | product(Z1, Y, Z2)) <=> ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))), ((((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) | product(Z1, Y, Z2)) <=> ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(210,plain,
% 0.21/0.46 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) | product(Z1, Y, Z2)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[209])).
% 0.21/0.46 tff(211,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) | product(Z1, Y, Z2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qg3')).
% 0.21/0.46 tff(212,plain,
% 0.21/0.46 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.21/0.46 tff(213,plain,
% 0.21/0.46 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[212, 208])).
% 0.21/0.46 tff(214,plain,(
% 0.21/0.46 ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[213])).
% 0.21/0.46 tff(215,plain,
% 0.21/0.46 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[214, 207])).
% 0.21/0.46 tff(216,plain,
% 0.21/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_3, e_2, e_2)) | product(e_2, e_4, e_2) | (~product(e_4, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (~product(e_3, e_2, e_2)) | product(e_2, e_4, e_2) | (~product(e_4, e_3, e_2)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(217,plain,
% 0.21/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_3, e_2, e_2)) | product(e_2, e_4, e_2) | (~product(e_4, e_3, e_2)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(218,plain,
% 0.21/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (~product(e_3, e_2, e_2)) | product(e_2, e_4, e_2) | (~product(e_4, e_3, e_2))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.21/0.46 tff(219,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[218, 215, 205, 2, 135])).
% 0.21/0.46 tff(220,plain,((~product(e_4, e_3, e_2)) | product(e_2, e_4, e_2) | product(e_3, e_3, e_2) | product(e_3, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(221,plain,
% 0.21/0.46 (~product(e_4, e_3, e_2)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[220, 2, 92, 93])).
% 0.21/0.46 tff(222,plain,
% 0.21/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (product(e_4, e_3, e_2) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_4, e_3, e_2) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_4, e_2)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(223,plain,
% 0.21/0.46 (((~product(e_1, e_4, e_2)) | product(e_4, e_3, e_2) | (~product(e_3, e_1, e_4))) <=> (product(e_4, e_3, e_2) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_4, e_2)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(224,plain,
% 0.21/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_1, e_4, e_2)) | product(e_4, e_3, e_2) | (~product(e_3, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (product(e_4, e_3, e_2) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_4, e_2))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[223])).
% 0.21/0.46 tff(225,plain,
% 0.21/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_1, e_4, e_2)) | product(e_4, e_3, e_2) | (~product(e_3, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_4, e_3, e_2) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_4, e_2)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[224, 222])).
% 0.21/0.47 tff(226,plain,
% 0.21/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_1, e_4, e_2)) | product(e_4, e_3, e_2) | (~product(e_3, e_1, e_4)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(227,plain,
% 0.21/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_4, e_3, e_2) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_4, e_2))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.21/0.47 tff(228,plain,
% 0.21/0.47 (~product(e_3, e_1, e_4)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[227, 215, 221, 134])).
% 0.21/0.47 tff(229,plain,
% 0.21/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (product(e_4, e_4, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_4, e_4, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_1, e_4)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(230,plain,
% 0.21/0.47 (((~product(e_1, e_4, e_2)) | product(e_4, e_4, e_2) | (~product(e_4, e_1, e_4))) <=> (product(e_4, e_4, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_1, e_4)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(231,plain,
% 0.21/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_1, e_4, e_2)) | product(e_4, e_4, e_2) | (~product(e_4, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (product(e_4, e_4, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_1, e_4))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[230])).
% 0.21/0.47 tff(232,plain,
% 0.21/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_1, e_4, e_2)) | product(e_4, e_4, e_2) | (~product(e_4, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_4, e_4, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_1, e_4)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[231, 229])).
% 0.21/0.47 tff(233,plain,
% 0.21/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_1, e_4, e_2)) | product(e_4, e_4, e_2) | (~product(e_4, e_1, e_4)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(234,plain,
% 0.21/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_4, e_4, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_1, e_4))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.21/0.47 tff(235,plain,
% 0.21/0.47 (~product(e_4, e_1, e_4)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[234, 215, 110, 134])).
% 0.21/0.47 tff(236,assumption,(~product(e_4, e_1, e_4)), introduced(assumption)).
% 0.21/0.47 tff(237,assumption,(~product(e_3, e_1, e_4)), introduced(assumption)).
% 0.21/0.47 tff(238,assumption,(product(e_3, e_2, e_2)), introduced(assumption)).
% 0.21/0.47 tff(239,plain,
% 0.21/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_4) | (~product(e_3, e_2, e_4)) | (~product(e_3, 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_2, e_4) | (~product(e_3, e_2, e_4)) | (~product(e_3, e_2, e_2)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(240,plain,
% 0.21/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_4) | (~product(e_3, e_2, e_4)) | (~product(e_3, e_2, e_2)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(241,plain,
% 0.21/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_2, e_4) | (~product(e_3, e_2, e_4)) | (~product(e_3, e_2, e_2))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.21/0.47 tff(242,plain,
% 0.21/0.47 ((~product(e_3, e_2, e_4)) | (~product(e_3, e_2, e_2))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[241, 181, 72])).
% 0.21/0.47 tff(243,plain,
% 0.21/0.47 (~product(e_3, e_2, e_4)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[242, 238])).
% 0.21/0.47 tff(244,plain,
% 0.21/0.47 (product(e_3, e_1, e_4) | product(e_3, e_4, e_4) | product(e_3, e_2, e_4)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[175, 169, 46, 113, 93])).
% 0.21/0.47 tff(245,plain,
% 0.21/0.47 (product(e_3, e_4, e_4)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[244, 243, 237])).
% 0.21/0.47 tff(246,plain,
% 0.21/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_3, e_4, e_4)) | (~product(e_1, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_4) | (~product(e_3, e_4, e_4)) | (~product(e_1, e_3, e_4)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(247,plain,
% 0.21/0.47 (((~product(e_3, e_4, e_4)) | product(e_4, e_1, e_4) | (~product(e_1, e_3, e_4))) <=> (product(e_4, e_1, e_4) | (~product(e_3, e_4, e_4)) | (~product(e_1, e_3, e_4)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(248,plain,
% 0.21/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_3, e_4, e_4)) | product(e_4, e_1, e_4) | (~product(e_1, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_3, e_4, e_4)) | (~product(e_1, e_3, e_4))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[247])).
% 0.21/0.47 tff(249,plain,
% 0.21/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_3, e_4, e_4)) | product(e_4, e_1, e_4) | (~product(e_1, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_4) | (~product(e_3, e_4, e_4)) | (~product(e_1, e_3, e_4)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[248, 246])).
% 0.21/0.47 tff(250,plain,
% 0.21/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_3, e_4, e_4)) | product(e_4, e_1, e_4) | (~product(e_1, e_3, e_4)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(251,plain,
% 0.21/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_4) | (~product(e_3, e_4, e_4)) | (~product(e_1, e_3, e_4))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.21/0.47 tff(252,plain,
% 0.21/0.47 (~product(e_1, e_3, e_4)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[251, 215, 245, 236])).
% 0.21/0.47 tff(253,plain,
% 0.21/0.47 (^[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))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(254,plain,
% 0.21/0.47 (![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)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[253])).
% 0.21/0.47 tff(255,plain,
% 0.21/0.47 (![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)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(256,plain,
% 0.21/0.47 (^[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)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(257,plain,
% 0.21/0.47 (![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)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[256])).
% 0.21/0.47 tff(258,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')).
% 0.21/0.47 tff(259,plain,
% 0.21/0.47 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.21/0.47 tff(260,plain,
% 0.21/0.47 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[259, 255])).
% 0.21/0.47 tff(261,plain,(
% 0.21/0.47 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[260])).
% 0.21/0.47 tff(262,plain,
% 0.21/0.47 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[261, 254])).
% 0.21/0.47 tff(263,plain,
% 0.21/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_2, e_4, e_4)) | (~product(e_3, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_2, e_4, e_4)) | (~product(e_3, e_4, e_4)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(264,plain,
% 0.21/0.47 ((equalish(e_2, e_3) | (~product(e_3, e_4, e_4)) | (~product(e_2, e_4, e_4))) <=> (equalish(e_2, e_3) | (~product(e_2, e_4, e_4)) | (~product(e_3, e_4, e_4)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(265,plain,
% 0.21/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_4, e_4)) | (~product(e_2, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_2, e_4, e_4)) | (~product(e_3, e_4, e_4))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[264])).
% 0.21/0.47 tff(266,plain,
% 0.21/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_4, e_4)) | (~product(e_2, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_2, e_4, e_4)) | (~product(e_3, e_4, e_4)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[265, 263])).
% 0.21/0.47 tff(267,plain,
% 0.21/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_4, e_4)) | (~product(e_2, e_4, e_4)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(268,plain,
% 0.21/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_2, e_4, e_4)) | (~product(e_3, e_4, e_4))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.21/0.47 tff(269,plain,
% 0.21/0.47 ((~product(e_2, e_4, e_4)) | (~product(e_3, e_4, e_4))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[268, 83, 262])).
% 0.21/0.47 tff(270,plain,
% 0.21/0.47 (~product(e_2, e_4, e_4)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[269, 245])).
% 0.21/0.47 tff(271,plain,
% 0.21/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_4, e_3)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(272,plain,
% 0.21/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_4, e_3)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(273,plain,
% 0.21/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_4, e_3))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.21/0.47 tff(274,plain,
% 0.21/0.47 (~product(e_2, e_4, e_3)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[273, 145, 238, 1])).
% 0.21/0.47 tff(275,plain,
% 0.21/0.47 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_4)) | product(e_2, e_4, e_2) | product(e_2, e_4, e_4) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (~group_element(e_2)) | (~group_element(e_4)) | product(e_2, e_4, e_2) | product(e_2, e_4, e_4) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(276,plain,
% 0.21/0.47 (((~group_element(e_4)) | (~group_element(e_2)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1)) <=> ((~group_element(e_2)) | (~group_element(e_4)) | product(e_2, e_4, e_2) | product(e_2, e_4, e_4) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(277,plain,
% 0.21/0.47 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_4)) | (~group_element(e_2)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_4)) | product(e_2, e_4, e_2) | product(e_2, e_4, e_4) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3)))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[276])).
% 0.21/0.47 tff(278,plain,
% 0.21/0.47 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_4)) | (~group_element(e_2)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (~group_element(e_2)) | (~group_element(e_4)) | product(e_2, e_4, e_2) | product(e_2, e_4, e_4) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3))),
% 0.21/0.47 inference(transitivity,[status(thm)],[277, 275])).
% 0.21/0.47 tff(279,plain,
% 0.21/0.47 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_4)) | (~group_element(e_2)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(280,plain,
% 0.21/0.47 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (~group_element(e_2)) | (~group_element(e_4)) | product(e_2, e_4, e_2) | product(e_2, e_4, e_4) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.21/0.47 tff(281,plain,
% 0.21/0.47 (product(e_2, e_4, e_4) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[280, 116, 113, 43, 2])).
% 0.21/0.47 tff(282,plain,
% 0.21/0.47 (product(e_2, e_4, e_1)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[281, 274, 270])).
% 0.21/0.47 tff(283,assumption,(product(e_2, e_4, e_1)), introduced(assumption)).
% 0.21/0.47 tff(284,assumption,(product(e_4, e_4, e_1)), introduced(assumption)).
% 0.21/0.47 tff(285,plain,
% 0.21/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_4, e_1)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(286,plain,
% 0.21/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_4, e_1)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(287,plain,
% 0.21/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_4, e_1))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.21/0.48 tff(288,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[287, 105, 262, 284, 283])).
% 0.21/0.48 tff(289,plain,((~product(e_4, e_4, e_1)) | (~product(e_2, e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(290,plain,
% 0.21/0.48 (~product(e_4, e_4, e_1)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[289, 282])).
% 0.21/0.48 tff(291,plain,
% 0.21/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_4, e_2, e_4)) | product(e_4, e_4, e_1) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (~product(e_4, e_2, e_4)) | product(e_4, e_4, e_1) | (~product(e_2, e_4, e_1)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(292,plain,
% 0.21/0.48 (((~product(e_2, e_4, e_1)) | product(e_4, e_4, e_1) | (~product(e_4, e_2, e_4))) <=> ((~product(e_4, e_2, e_4)) | product(e_4, e_4, e_1) | (~product(e_2, e_4, e_1)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(293,plain,
% 0.21/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_2, e_4, e_1)) | product(e_4, e_4, e_1) | (~product(e_4, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_4, e_2, e_4)) | product(e_4, e_4, e_1) | (~product(e_2, e_4, e_1))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[292])).
% 0.21/0.48 tff(294,plain,
% 0.21/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_2, e_4, e_1)) | product(e_4, e_4, e_1) | (~product(e_4, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (~product(e_4, e_2, e_4)) | product(e_4, e_4, e_1) | (~product(e_2, e_4, e_1)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[293, 291])).
% 0.21/0.48 tff(295,plain,
% 0.21/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_2, e_4, e_1)) | product(e_4, e_4, e_1) | (~product(e_4, e_2, e_4)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(296,plain,
% 0.21/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (~product(e_4, e_2, e_4)) | product(e_4, e_4, e_1) | (~product(e_2, e_4, e_1))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.21/0.48 tff(297,plain,
% 0.21/0.48 (~product(e_4, e_2, e_4)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[296, 215, 290, 282])).
% 0.21/0.48 tff(298,plain,
% 0.21/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (product(e_4, e_2, e_4) | (~product(e_3, e_4, e_4)) | (~product(e_2, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_4, e_2, e_4) | (~product(e_3, e_4, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(299,plain,
% 0.21/0.48 (((~product(e_3, e_4, e_4)) | product(e_4, e_2, e_4) | (~product(e_2, e_3, e_4))) <=> (product(e_4, e_2, e_4) | (~product(e_3, e_4, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(300,plain,
% 0.21/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_3, e_4, e_4)) | product(e_4, e_2, e_4) | (~product(e_2, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (product(e_4, e_2, e_4) | (~product(e_3, e_4, e_4)) | (~product(e_2, e_3, e_4))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[299])).
% 0.21/0.48 tff(301,plain,
% 0.21/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_3, e_4, e_4)) | product(e_4, e_2, e_4) | (~product(e_2, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_4, e_2, e_4) | (~product(e_3, e_4, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[300, 298])).
% 0.21/0.48 tff(302,plain,
% 0.21/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_3, e_4, e_4)) | product(e_4, e_2, e_4) | (~product(e_2, e_3, e_4)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(303,plain,
% 0.21/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_4, e_2, e_4) | (~product(e_3, e_4, e_4)) | (~product(e_2, e_3, e_4))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[302, 301])).
% 0.21/0.48 tff(304,plain,
% 0.21/0.48 (~product(e_2, e_3, e_4)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[303, 215, 297, 245])).
% 0.21/0.48 tff(305,plain,
% 0.21/0.48 (((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_3, e_4) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_4) | product(e_2, e_3, e_4) | product(e_1, e_3, e_4))) <=> ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_3, e_4) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_4) | product(e_2, e_3, e_4) | product(e_1, e_3, e_4))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(306,plain,
% 0.21/0.48 ((product(e_4, e_3, e_4) | product(e_3, e_3, e_4) | product(e_2, e_3, e_4) | product(e_1, e_3, e_4) | (~group_element(e_4)) | (~group_element(e_3))) <=> (product(e_3, e_3, e_4) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_4) | product(e_2, e_3, e_4) | product(e_1, e_3, e_4))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(307,plain,
% 0.21/0.48 (((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_3, e_4) | product(e_3, e_3, e_4) | product(e_2, e_3, e_4) | product(e_1, e_3, e_4) | (~group_element(e_4)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_3, e_4) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_4) | product(e_2, e_3, e_4) | product(e_1, e_3, e_4)))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[306])).
% 0.21/0.48 tff(308,plain,
% 0.21/0.48 (((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_3, e_4) | product(e_3, e_3, e_4) | product(e_2, e_3, e_4) | product(e_1, e_3, e_4) | (~group_element(e_4)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_3, e_4) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_4) | product(e_2, e_3, e_4) | product(e_1, e_3, e_4))),
% 0.21/0.48 inference(transitivity,[status(thm)],[307, 305])).
% 0.21/0.48 tff(309,plain,
% 0.21/0.48 ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_3, e_4) | product(e_3, e_3, e_4) | product(e_2, e_3, e_4) | product(e_1, e_3, e_4) | (~group_element(e_4)) | (~group_element(e_3)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(310,plain,
% 0.21/0.48 ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_3, e_4) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_4) | product(e_2, e_3, e_4) | product(e_1, e_3, e_4)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.21/0.48 tff(311,plain,
% 0.21/0.48 (product(e_4, e_3, e_4) | product(e_2, e_3, e_4) | product(e_1, e_3, e_4)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[310, 126, 46, 113, 93])).
% 0.21/0.48 tff(312,plain,
% 0.21/0.48 (product(e_4, e_3, e_4)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[311, 304, 252])).
% 0.21/0.48 tff(313,plain,
% 0.21/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_4, e_4)) | (~product(e_4, e_3, e_4)) | product(e_3, e_3, e_4))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (~product(e_3, e_4, e_4)) | (~product(e_4, e_3, e_4)) | product(e_3, e_3, e_4))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(314,plain,
% 0.21/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_4, e_4)) | (~product(e_4, e_3, e_4)) | product(e_3, e_3, e_4))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(315,plain,
% 0.21/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (~product(e_3, e_4, e_4)) | (~product(e_4, e_3, e_4)) | product(e_3, e_3, e_4)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[314, 313])).
% 0.21/0.48 tff(316,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[315, 14, 93, 245, 312])).
% 0.21/0.48 tff(317,plain,((~product(e_3, e_2, e_2)) | product(e_3, e_3, e_4) | product(e_2, e_4, e_2) | product(e_4, e_1, e_4) | product(e_4, e_3, e_2) | product(e_3, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(318,plain,
% 0.21/0.48 (~product(e_3, e_2, e_2)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[317, 235, 2, 93, 221, 228])).
% 0.21/0.48 tff(319,plain,
% 0.21/0.48 (product(e_3, e_1, e_2)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[204, 318, 92, 94])).
% 0.21/0.48 tff(320,plain,
% 0.21/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_1, e_2)) | product(e_4, e_3, e_1) | (~product(e_1, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (~product(e_3, e_1, e_2)) | product(e_4, e_3, e_1) | (~product(e_1, e_4, e_2)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(321,plain,
% 0.21/0.48 (((~product(e_3, e_1, e_2)) | (~product(e_1, e_4, e_2)) | product(e_4, e_3, e_1)) <=> ((~product(e_3, e_1, e_2)) | product(e_4, e_3, e_1) | (~product(e_1, e_4, e_2)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(322,plain,
% 0.21/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_1, e_2)) | (~product(e_1, e_4, e_2)) | product(e_4, e_3, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_1, e_2)) | product(e_4, e_3, e_1) | (~product(e_1, e_4, e_2))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[321])).
% 0.21/0.48 tff(323,plain,
% 0.21/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_1, e_2)) | (~product(e_1, e_4, e_2)) | product(e_4, e_3, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (~product(e_3, e_1, e_2)) | product(e_4, e_3, e_1) | (~product(e_1, e_4, e_2)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[322, 320])).
% 0.21/0.48 tff(324,plain,
% 0.21/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_1, e_2)) | (~product(e_1, e_4, e_2)) | product(e_4, e_3, e_1))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(325,plain,
% 0.21/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (~product(e_3, e_1, e_2)) | product(e_4, e_3, e_1) | (~product(e_1, e_4, e_2))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[324, 323])).
% 0.21/0.48 tff(326,plain,
% 0.21/0.48 (product(e_4, e_3, e_1)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[325, 14, 319, 134])).
% 0.21/0.48 tff(327,assumption,(product(e_4, e_3, e_1)), introduced(assumption)).
% 0.21/0.48 tff(328,assumption,(product(e_4, e_3, e_4)), introduced(assumption)).
% 0.21/0.48 tff(329,plain,
% 0.21/0.48 ((~equalish(e_4, e_1)) <=> (~equalish(e_4, e_1))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(330,axiom,(~equalish(e_4, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_is_not_e_1')).
% 0.21/0.48 tff(331,plain,
% 0.21/0.48 (~equalish(e_4, e_1)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[330, 329])).
% 0.21/0.48 tff(332,plain,
% 0.21/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_4, e_1) | (~product(e_4, e_3, e_4)) | (~product(e_4, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_4, e_1) | (~product(e_4, e_3, e_4)) | (~product(e_4, e_3, e_1)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(333,plain,
% 0.21/0.48 ((equalish(e_4, e_1) | (~product(e_4, e_3, e_1)) | (~product(e_4, e_3, e_4))) <=> (equalish(e_4, e_1) | (~product(e_4, e_3, e_4)) | (~product(e_4, e_3, e_1)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(334,plain,
% 0.21/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_4, e_1) | (~product(e_4, e_3, e_1)) | (~product(e_4, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_4, e_1) | (~product(e_4, e_3, e_4)) | (~product(e_4, e_3, e_1))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[333])).
% 0.21/0.48 tff(335,plain,
% 0.21/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_4, e_1) | (~product(e_4, e_3, e_1)) | (~product(e_4, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_4, e_1) | (~product(e_4, e_3, e_4)) | (~product(e_4, e_3, e_1)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[334, 332])).
% 0.21/0.48 tff(336,plain,
% 0.21/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_4, e_1) | (~product(e_4, e_3, e_1)) | (~product(e_4, e_3, e_4)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(337,plain,
% 0.21/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_4, e_1) | (~product(e_4, e_3, e_4)) | (~product(e_4, e_3, e_1))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[336, 335])).
% 0.21/0.48 tff(338,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[337, 331, 72, 328, 327])).
% 0.21/0.48 tff(339,plain,((~product(e_4, e_3, e_4)) | (~product(e_4, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(340,plain,
% 0.21/0.48 (~product(e_4, e_3, e_4)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[339, 326])).
% 0.21/0.48 tff(341,plain,
% 0.21/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_3, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_3, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_4, e_3)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(342,plain,
% 0.21/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_3, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_4, e_3)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(343,plain,
% 0.21/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_3, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_4, e_3))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[342, 341])).
% 0.21/0.49 tff(344,plain,
% 0.21/0.49 (~product(e_1, e_4, e_3)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[343, 145, 319, 221])).
% 0.21/0.49 tff(345,assumption,(~product(e_3, e_2, e_4)), introduced(assumption)).
% 0.21/0.49 tff(346,plain,
% 0.21/0.49 (product(e_3, e_4, e_4)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[244, 345, 237])).
% 0.21/0.49 tff(347,plain,
% 0.21/0.49 (~product(e_2, e_4, e_4)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[269, 346])).
% 0.21/0.49 tff(348,plain,
% 0.21/0.49 (~product(e_1, e_3, e_4)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[251, 215, 346, 236])).
% 0.21/0.49 tff(349,plain,
% 0.21/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_3, e_4) | (~product(e_3, e_4, e_4)) | (~product(e_4, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_3, e_4) | (~product(e_3, e_4, e_4)) | (~product(e_4, e_1, e_3)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(350,plain,
% 0.21/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_3, e_4) | (~product(e_3, e_4, e_4)) | (~product(e_4, e_1, e_3)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(351,plain,
% 0.21/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_3, e_4) | (~product(e_3, e_4, e_4)) | (~product(e_4, e_1, e_3))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[350, 349])).
% 0.21/0.49 tff(352,plain,
% 0.21/0.49 (~product(e_4, e_1, e_3)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[351, 145, 346, 348])).
% 0.21/0.49 tff(353,assumption,(~product(e_1, e_3, e_4)), introduced(assumption)).
% 0.21/0.49 tff(354,assumption,(~product(e_4, e_1, e_3)), introduced(assumption)).
% 0.21/0.49 tff(355,assumption,(product(e_2, e_4, e_3)), introduced(assumption)).
% 0.21/0.49 tff(356,plain,
% 0.21/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_3) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_3) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_4, e_3)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(357,plain,
% 0.21/0.49 (((~product(e_2, e_4, e_3)) | product(e_4, e_1, e_3) | (~product(e_1, e_2, e_4))) <=> (product(e_4, e_1, e_3) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_4, e_3)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(358,plain,
% 0.21/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_2, e_4, e_3)) | product(e_4, e_1, e_3) | (~product(e_1, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_3) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_4, e_3))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[357])).
% 0.21/0.49 tff(359,plain,
% 0.21/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_2, e_4, e_3)) | product(e_4, e_1, e_3) | (~product(e_1, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_3) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_4, e_3)))),
% 0.21/0.49 inference(transitivity,[status(thm)],[358, 356])).
% 0.21/0.49 tff(360,plain,
% 0.21/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_2, e_4, e_3)) | product(e_4, e_1, e_3) | (~product(e_1, e_2, e_4)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(361,plain,
% 0.21/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_3) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_4, e_3))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[360, 359])).
% 0.21/0.49 tff(362,plain,
% 0.21/0.49 (~product(e_1, e_2, e_4)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[361, 215, 355, 354])).
% 0.21/0.49 tff(363,assumption,(~product(e_1, e_2, e_4)), introduced(assumption)).
% 0.21/0.49 tff(364,assumption,(product(e_2, e_3, e_4)), introduced(assumption)).
% 0.21/0.49 tff(365,plain,
% 0.21/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_1, e_2)) | product(e_1, e_2, e_4) | (~product(e_2, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_1, e_2, e_4) | (~product(e_2, e_3, e_4)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(366,plain,
% 0.21/0.49 ((product(e_1, e_2, e_4) | (~product(e_2, e_3, e_4)) | (~product(e_3, e_1, e_2))) <=> ((~product(e_3, e_1, e_2)) | product(e_1, e_2, e_4) | (~product(e_2, e_3, e_4)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(367,plain,
% 0.21/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_4) | (~product(e_2, e_3, e_4)) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_1, e_2)) | product(e_1, e_2, e_4) | (~product(e_2, e_3, e_4))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[366])).
% 0.21/0.49 tff(368,plain,
% 0.21/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_4) | (~product(e_2, e_3, e_4)) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_1, e_2, e_4) | (~product(e_2, e_3, e_4)))),
% 0.21/0.49 inference(transitivity,[status(thm)],[367, 365])).
% 0.21/0.49 tff(369,plain,
% 0.21/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_4) | (~product(e_2, e_3, e_4)) | (~product(e_3, e_1, e_2)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(370,plain,
% 0.21/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_1, e_2, e_4) | (~product(e_2, e_3, e_4))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[369, 368])).
% 0.21/0.49 tff(371,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[370, 145, 178, 364, 363])).
% 0.21/0.49 tff(372,plain,((~product(e_2, e_3, e_4)) | (~product(e_3, e_1, e_2)) | product(e_1, e_2, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(373,plain,
% 0.21/0.49 (~product(e_2, e_3, e_4)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[372, 362, 178])).
% 0.21/0.49 tff(374,plain,
% 0.21/0.49 (product(e_4, e_3, e_4)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[311, 373, 353])).
% 0.21/0.49 tff(375,plain,
% 0.21/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_4) | (~product(e_4, e_3, e_4)) | (~product(e_2, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_3, e_2, e_4) | (~product(e_4, e_3, e_4)) | (~product(e_2, e_4, e_3)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(376,plain,
% 0.21/0.49 (((~product(e_4, e_3, e_4)) | product(e_3, e_2, e_4) | (~product(e_2, e_4, e_3))) <=> (product(e_3, e_2, e_4) | (~product(e_4, e_3, e_4)) | (~product(e_2, e_4, e_3)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(377,plain,
% 0.21/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_4, e_3, e_4)) | product(e_3, e_2, e_4) | (~product(e_2, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_4) | (~product(e_4, e_3, e_4)) | (~product(e_2, e_4, e_3))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[376])).
% 0.21/0.49 tff(378,plain,
% 0.21/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_4, e_3, e_4)) | product(e_3, e_2, e_4) | (~product(e_2, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_3, e_2, e_4) | (~product(e_4, e_3, e_4)) | (~product(e_2, e_4, e_3)))),
% 0.21/0.49 inference(transitivity,[status(thm)],[377, 375])).
% 0.21/0.49 tff(379,plain,
% 0.21/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_4, e_3, e_4)) | product(e_3, e_2, e_4) | (~product(e_2, e_4, e_3)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(380,plain,
% 0.21/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_3, e_2, e_4) | (~product(e_4, e_3, e_4)) | (~product(e_2, e_4, e_3))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.21/0.49 tff(381,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[380, 215, 345, 355, 374])).
% 0.21/0.49 tff(382,plain,((~product(e_2, e_4, e_3)) | product(e_3, e_2, e_4) | product(e_1, e_3, e_4) | product(e_3, e_3, e_4) | (~product(e_3, e_1, e_2)) | product(e_4, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(383,plain,
% 0.21/0.49 (~product(e_2, e_4, e_3)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[382, 345, 348, 93, 178, 352])).
% 0.21/0.49 tff(384,plain,
% 0.21/0.49 (product(e_2, e_4, e_1)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[281, 383, 347])).
% 0.21/0.49 tff(385,plain,
% 0.21/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_2, e_4, e_1)) | (~product(e_4, e_3, e_1)) | product(e_3, e_2, e_4))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_3, e_1)) | product(e_3, e_2, e_4))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(386,plain,
% 0.21/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_2, e_4, e_1)) | (~product(e_4, e_3, e_1)) | product(e_3, e_2, e_4))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(387,plain,
% 0.21/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_3, e_1)) | product(e_3, e_2, e_4)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[386, 385])).
% 0.21/0.49 tff(388,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[387, 14, 345, 384, 327])).
% 0.21/0.49 tff(389,plain,(product(e_3, e_2, e_4) | (~product(e_4, e_3, e_1)) | product(e_2, e_4, e_2) | product(e_3, e_3, e_4) | (~product(e_3, e_1, e_2)) | product(e_4, e_1, e_4) | product(e_3, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(390,plain,
% 0.21/0.49 (product(e_3, e_2, e_4)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[389, 326, 2, 93, 319, 235, 228])).
% 0.21/0.49 tff(391,plain,
% 0.21/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_2, e_4)) | product(e_4, e_3, e_4) | (~product(e_2, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_2, e_4)) | product(e_4, e_3, e_4) | (~product(e_2, e_4, e_3)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(392,plain,
% 0.21/0.49 ((product(e_4, e_3, e_4) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_4, e_3))) <=> ((~product(e_3, e_2, e_4)) | product(e_4, e_3, e_4) | (~product(e_2, e_4, e_3)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(393,plain,
% 0.21/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_3, e_4) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_2, e_4)) | product(e_4, e_3, e_4) | (~product(e_2, e_4, e_3))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[392])).
% 0.21/0.49 tff(394,plain,
% 0.21/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_3, e_4) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_2, e_4)) | product(e_4, e_3, e_4) | (~product(e_2, e_4, e_3)))),
% 0.21/0.49 inference(transitivity,[status(thm)],[393, 391])).
% 0.21/0.49 tff(395,plain,
% 0.21/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_3, e_4) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_4, e_3)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(396,plain,
% 0.21/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_2, e_4)) | product(e_4, e_3, e_4) | (~product(e_2, e_4, e_3))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[395, 394])).
% 0.21/0.49 tff(397,plain,
% 0.21/0.49 (~product(e_2, e_4, e_3)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[396, 145, 390, 340])).
% 0.21/0.49 tff(398,assumption,(~product(e_2, e_4, e_3)), introduced(assumption)).
% 0.21/0.49 tff(399,assumption,(product(e_1, e_3, e_4)), introduced(assumption)).
% 0.21/0.49 tff(400,plain,
% 0.21/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_4) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_4) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_4)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(401,plain,
% 0.21/0.49 ((product(e_3, e_1, e_4) | (~product(e_1, e_3, e_4)) | (~product(e_3, e_3, e_1))) <=> (product(e_3, e_1, e_4) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_4)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(402,plain,
% 0.21/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_4) | (~product(e_1, e_3, e_4)) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_4) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_4))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[401])).
% 0.21/0.49 tff(403,plain,
% 0.21/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_4) | (~product(e_1, e_3, e_4)) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_4) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_4)))),
% 0.21/0.49 inference(transitivity,[status(thm)],[402, 400])).
% 0.21/0.49 tff(404,plain,
% 0.21/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_4) | (~product(e_1, e_3, e_4)) | (~product(e_3, e_3, e_1)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(405,plain,
% 0.21/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_4) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_4))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[404, 403])).
% 0.21/0.49 tff(406,plain,
% 0.21/0.49 (~product(e_3, e_3, e_1)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[405, 145, 237, 399])).
% 0.21/0.49 tff(407,plain,
% 0.21/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_3, e_4, e_3)) | (~product(e_4, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_3, e_3, e_1) | (~product(e_3, e_4, e_3)) | (~product(e_4, e_3, e_1)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(408,plain,
% 0.21/0.49 (((~product(e_4, e_3, e_1)) | product(e_3, e_3, e_1) | (~product(e_3, e_4, e_3))) <=> (product(e_3, e_3, e_1) | (~product(e_3, e_4, e_3)) | (~product(e_4, e_3, e_1)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(409,plain,
% 0.21/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_4, e_3, e_1)) | product(e_3, e_3, e_1) | (~product(e_3, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_3, e_4, e_3)) | (~product(e_4, e_3, e_1))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[408])).
% 0.21/0.50 tff(410,plain,
% 0.21/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_4, e_3, e_1)) | product(e_3, e_3, e_1) | (~product(e_3, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_3, e_3, e_1) | (~product(e_3, e_4, e_3)) | (~product(e_4, e_3, e_1)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[409, 407])).
% 0.21/0.50 tff(411,plain,
% 0.21/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_4, e_3, e_1)) | product(e_3, e_3, e_1) | (~product(e_3, e_4, e_3)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(412,plain,
% 0.21/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_3, e_3, e_1) | (~product(e_3, e_4, e_3)) | (~product(e_4, e_3, e_1))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[411, 410])).
% 0.21/0.50 tff(413,plain,
% 0.21/0.50 (~product(e_3, e_4, e_3)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[412, 215, 406, 327])).
% 0.21/0.50 tff(414,plain,
% 0.21/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_1, e_3, e_4)) | (~product(e_3, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_4) | (~product(e_1, e_3, e_4)) | (~product(e_3, e_4, e_1)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(415,plain,
% 0.21/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_1, e_3, e_4)) | (~product(e_3, e_4, e_1)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(416,plain,
% 0.21/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_4) | (~product(e_1, e_3, e_4)) | (~product(e_3, e_4, e_1))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[415, 414])).
% 0.21/0.50 tff(417,plain,
% 0.21/0.50 (~product(e_3, e_4, e_1)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[416, 145, 399, 236])).
% 0.21/0.50 tff(418,plain,
% 0.21/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (product(e_3, e_4, e_1) | (~product(e_4, e_4, e_3)) | (~product(e_4, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_3, e_4, e_1) | (~product(e_4, e_4, e_3)) | (~product(e_4, e_3, e_1)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(419,plain,
% 0.21/0.50 (((~product(e_4, e_3, e_1)) | product(e_3, e_4, e_1) | (~product(e_4, e_4, e_3))) <=> (product(e_3, e_4, e_1) | (~product(e_4, e_4, e_3)) | (~product(e_4, e_3, e_1)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(420,plain,
% 0.21/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_4, e_3, e_1)) | product(e_3, e_4, e_1) | (~product(e_4, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (product(e_3, e_4, e_1) | (~product(e_4, e_4, e_3)) | (~product(e_4, e_3, e_1))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[419])).
% 0.21/0.50 tff(421,plain,
% 0.21/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_4, e_3, e_1)) | product(e_3, e_4, e_1) | (~product(e_4, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_3, e_4, e_1) | (~product(e_4, e_4, e_3)) | (~product(e_4, e_3, e_1)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[420, 418])).
% 0.21/0.50 tff(422,plain,
% 0.21/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_4, e_3, e_1)) | product(e_3, e_4, e_1) | (~product(e_4, e_4, e_3)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(423,plain,
% 0.21/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_3, e_4, e_1) | (~product(e_4, e_4, e_3)) | (~product(e_4, e_3, e_1))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[422, 421])).
% 0.21/0.50 tff(424,plain,
% 0.21/0.50 (~product(e_4, e_4, e_3)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[423, 215, 327, 417])).
% 0.21/0.50 tff(425,assumption,(~product(e_1, e_4, e_3)), introduced(assumption)).
% 0.21/0.50 tff(426,plain,
% 0.21/0.50 (((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | (~group_element(e_4)) | product(e_1, e_4, e_3) | product(e_3, e_4, e_3) | product(e_2, e_4, e_3) | product(e_4, e_4, e_3))) <=> ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_1, e_4, e_3) | product(e_3, e_4, e_3) | product(e_2, e_4, e_3) | product(e_4, e_4, e_3))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(427,plain,
% 0.21/0.50 ((product(e_4, e_4, e_3) | product(e_3, e_4, e_3) | product(e_2, e_4, e_3) | product(e_1, e_4, e_3) | (~group_element(e_3)) | (~group_element(e_4))) <=> ((~group_element(e_3)) | (~group_element(e_4)) | product(e_1, e_4, e_3) | product(e_3, e_4, e_3) | product(e_2, e_4, e_3) | product(e_4, e_4, e_3))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(428,plain,
% 0.21/0.50 (((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_4, e_3) | product(e_3, e_4, e_3) | product(e_2, e_4, e_3) | product(e_1, e_4, e_3) | (~group_element(e_3)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | (~group_element(e_4)) | product(e_1, e_4, e_3) | product(e_3, e_4, e_3) | product(e_2, e_4, e_3) | product(e_4, e_4, e_3)))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[427])).
% 0.21/0.50 tff(429,plain,
% 0.21/0.50 (((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_4, e_3) | product(e_3, e_4, e_3) | product(e_2, e_4, e_3) | product(e_1, e_4, e_3) | (~group_element(e_3)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_1, e_4, e_3) | product(e_3, e_4, e_3) | product(e_2, e_4, e_3) | product(e_4, e_4, e_3))),
% 0.21/0.50 inference(transitivity,[status(thm)],[428, 426])).
% 0.21/0.50 tff(430,plain,
% 0.21/0.50 ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_4, e_3) | product(e_3, e_4, e_3) | product(e_2, e_4, e_3) | product(e_1, e_4, e_3) | (~group_element(e_3)) | (~group_element(e_4)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(431,plain,
% 0.21/0.50 ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_1, e_4, e_3) | product(e_3, e_4, e_3) | product(e_2, e_4, e_3) | product(e_4, e_4, e_3)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[430, 429])).
% 0.21/0.50 tff(432,plain,
% 0.21/0.50 (product(e_3, e_4, e_3) | product(e_2, e_4, e_3) | product(e_4, e_4, e_3)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[431, 126, 46, 113, 425])).
% 0.21/0.50 tff(433,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[432, 424, 413, 398])).
% 0.21/0.50 tff(434,plain,((~product(e_1, e_3, e_4)) | product(e_2, e_4, e_3) | product(e_1, e_4, e_3) | (~product(e_4, e_3, e_1)) | product(e_4, e_1, e_4) | product(e_3, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(435,plain,
% 0.21/0.50 (~product(e_1, e_3, e_4)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[434, 397, 344, 326, 235, 228])).
% 0.21/0.50 tff(436,plain,
% 0.21/0.50 (product(e_2, e_3, e_4)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[311, 435, 340])).
% 0.21/0.50 tff(437,plain,
% 0.21/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (product(e_3, e_3, e_2) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_3, e_3, e_2) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(438,plain,
% 0.21/0.50 (((~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_4)) | product(e_3, e_3, e_2)) <=> (product(e_3, e_3, e_2) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(439,plain,
% 0.21/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_4)) | product(e_3, e_3, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (product(e_3, e_3, e_2) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_4))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[438])).
% 0.21/0.50 tff(440,plain,
% 0.21/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_4)) | product(e_3, e_3, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_3, e_3, e_2) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[439, 437])).
% 0.21/0.50 tff(441,plain,
% 0.21/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_4)) | product(e_3, e_3, e_2))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(442,plain,
% 0.21/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_3, e_3, e_2) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_4))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[441, 440])).
% 0.21/0.50 tff(443,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[442, 14, 92, 390, 436])).
% 0.21/0.50 tff(444,plain,(product(e_3, e_4, e_2) | product(e_3, e_3, e_2) | product(e_3, e_3, e_4) | product(e_2, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(445,plain,
% 0.21/0.50 (product(e_3, e_4, e_2)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[444, 92, 93, 2])).
% 0.21/0.50 tff(446,assumption,(product(e_3, e_4, e_4)), introduced(assumption)).
% 0.21/0.50 tff(447,plain,
% 0.21/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_4, e_2) | (~product(e_3, e_4, e_2)) | (~product(e_3, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_4, e_2) | (~product(e_3, e_4, e_2)) | (~product(e_3, e_4, e_4)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(448,plain,
% 0.21/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_4, e_2) | (~product(e_3, e_4, e_2)) | (~product(e_3, e_4, e_4)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(449,plain,
% 0.21/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_4, e_2) | (~product(e_3, e_4, e_2)) | (~product(e_3, e_4, e_4))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[448, 447])).
% 0.21/0.50 tff(450,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[449, 105, 72, 191, 446])).
% 0.21/0.50 tff(451,plain,((~product(e_3, e_4, e_4)) | (~product(e_3, e_4, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(452,plain,
% 0.21/0.50 (~product(e_3, e_4, e_4)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[451, 445])).
% 0.21/0.50 tff(453,plain,
% 0.21/0.50 (product(e_3, e_1, e_4) | product(e_3, e_4, e_4)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[175, 169, 46, 113, 93, 345])).
% 0.21/0.50 tff(454,plain,
% 0.21/0.50 (product(e_3, e_1, e_4)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[453, 452])).
% 0.21/0.50 tff(455,assumption,(product(e_2, e_3, e_2)), introduced(assumption)).
% 0.21/0.50 tff(456,plain,
% 0.21/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_4) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_2, e_4) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_3, e_4)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(457,plain,
% 0.21/0.50 ((equalish(e_2, e_4) | (~product(e_2, e_3, e_4)) | (~product(e_2, e_3, e_2))) <=> (equalish(e_2, e_4) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_3, e_4)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(458,plain,
% 0.21/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_4) | (~product(e_2, e_3, e_4)) | (~product(e_2, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_4) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_3, e_4))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[457])).
% 0.21/0.50 tff(459,plain,
% 0.21/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_4) | (~product(e_2, e_3, e_4)) | (~product(e_2, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_2, e_4) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_3, e_4)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[458, 456])).
% 0.21/0.50 tff(460,plain,
% 0.21/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_4) | (~product(e_2, e_3, e_4)) | (~product(e_2, e_3, e_2)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(461,plain,
% 0.21/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_2, e_4) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_3, e_4))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[460, 459])).
% 0.21/0.50 tff(462,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[461, 181, 72, 455, 364])).
% 0.21/0.50 tff(463,plain,((~product(e_2, e_3, e_2)) | (~product(e_2, e_3, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(464,plain,
% 0.21/0.50 (~product(e_2, e_3, e_2)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[463, 364])).
% 0.21/0.50 tff(465,plain,
% 0.21/0.50 (((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | product(e_3, e_3, e_2) | (~group_element(e_3)) | product(e_4, e_3, e_2) | product(e_2, e_3, e_2) | product(e_1, e_3, e_2))) <=> ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_3, e_3, e_2) | (~group_element(e_3)) | product(e_4, e_3, e_2) | product(e_2, e_3, e_2) | product(e_1, e_3, e_2))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(466,plain,
% 0.21/0.50 ((product(e_4, e_3, e_2) | product(e_3, e_3, e_2) | product(e_2, e_3, e_2) | product(e_1, e_3, e_2) | (~group_element(e_2)) | (~group_element(e_3))) <=> ((~group_element(e_2)) | product(e_3, e_3, e_2) | (~group_element(e_3)) | product(e_4, e_3, e_2) | product(e_2, e_3, e_2) | product(e_1, e_3, e_2))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(467,plain,
% 0.21/0.50 (((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_3, e_2) | product(e_3, e_3, e_2) | product(e_2, e_3, e_2) | product(e_1, e_3, e_2) | (~group_element(e_2)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | product(e_3, e_3, e_2) | (~group_element(e_3)) | product(e_4, e_3, e_2) | product(e_2, e_3, e_2) | product(e_1, e_3, e_2)))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[466])).
% 0.21/0.50 tff(468,plain,
% 0.21/0.50 (((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_3, e_2) | product(e_3, e_3, e_2) | product(e_2, e_3, e_2) | product(e_1, e_3, e_2) | (~group_element(e_2)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_3, e_3, e_2) | (~group_element(e_3)) | product(e_4, e_3, e_2) | product(e_2, e_3, e_2) | product(e_1, e_3, e_2))),
% 0.21/0.50 inference(transitivity,[status(thm)],[467, 465])).
% 0.21/0.50 tff(469,plain,
% 0.21/0.50 ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_3, e_2) | product(e_3, e_3, e_2) | product(e_2, e_3, e_2) | product(e_1, e_3, e_2) | (~group_element(e_2)) | (~group_element(e_3)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(470,plain,
% 0.21/0.50 ((~![Y: $i, X: $i] : (product(e_4, X, Y) | product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_3, e_3, e_2) | (~group_element(e_3)) | product(e_4, e_3, e_2) | product(e_2, e_3, e_2) | product(e_1, e_3, e_2)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[469, 468])).
% 0.21/0.50 tff(471,plain,
% 0.21/0.50 (product(e_1, e_3, e_2)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[470, 126, 116, 46, 92, 1, 464])).
% 0.21/0.50 tff(472,plain,
% 0.21/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_1, e_3, e_2)) | (~product(e_3, e_4, e_2)) | product(e_4, e_1, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_4, e_2)) | product(e_4, e_1, e_3))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(473,plain,
% 0.21/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_1, e_3, e_2)) | (~product(e_3, e_4, e_2)) | product(e_4, e_1, e_3))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(474,plain,
% 0.21/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_4, e_2)) | product(e_4, e_1, e_3)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[473, 472])).
% 0.21/0.50 tff(475,plain,
% 0.21/0.50 (product(e_4, e_1, e_3)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[474, 14, 191, 471])).
% 0.21/0.50 tff(476,plain,
% 0.21/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_2, e_3, e_4)) | (~product(e_3, e_1, e_4)) | product(e_1, e_2, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (~product(e_2, e_3, e_4)) | (~product(e_3, e_1, e_4)) | product(e_1, e_2, e_3))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(477,plain,
% 0.21/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_2, e_3, e_4)) | (~product(e_3, e_1, e_4)) | product(e_1, e_2, e_3))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(478,plain,
% 0.21/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (~product(e_2, e_3, e_4)) | (~product(e_3, e_1, e_4)) | product(e_1, e_2, e_3)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[477, 476])).
% 0.21/0.50 tff(479,plain,
% 0.21/0.50 (product(e_1, e_2, e_3)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[478, 14, 177, 364])).
% 0.21/0.50 tff(480,assumption,(product(e_2, e_2, e_3)), introduced(assumption)).
% 0.21/0.50 tff(481,plain,
% 0.21/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (product(e_2, e_2, e_2) | (~product(e_2, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_2, e_2, e_2) | (~product(e_2, e_2, e_3)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(482,plain,
% 0.21/0.51 (((~product(e_2, e_2, e_3)) | (~product(e_2, e_2, e_3)) | product(e_2, e_2, e_2)) <=> (product(e_2, e_2, e_2) | (~product(e_2, e_2, e_3)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(483,plain,
% 0.21/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_2, e_2, e_3)) | (~product(e_2, e_2, e_3)) | product(e_2, e_2, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (product(e_2, e_2, e_2) | (~product(e_2, e_2, e_3))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[482])).
% 0.21/0.51 tff(484,plain,
% 0.21/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_2, e_2, e_3)) | (~product(e_2, e_2, e_3)) | product(e_2, e_2, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_2, e_2, e_2) | (~product(e_2, e_2, e_3)))),
% 0.21/0.51 inference(transitivity,[status(thm)],[483, 481])).
% 0.21/0.51 tff(485,plain,
% 0.21/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_2, e_2, e_3)) | (~product(e_2, e_2, e_3)) | product(e_2, e_2, e_2))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(486,plain,
% 0.21/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_2, e_2, e_2) | (~product(e_2, e_2, e_3))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[485, 484])).
% 0.21/0.51 tff(487,plain,
% 0.21/0.51 (product(e_2, e_2, e_2)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[486, 14, 480])).
% 0.21/0.51 tff(488,plain,
% 0.21/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_3) | (~product(e_2, e_2, e_2)) | (~product(e_2, 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_2, e_3) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_2, e_3)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(489,plain,
% 0.21/0.51 ((equalish(e_2, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_2, e_2, e_2))) <=> (equalish(e_2, e_3) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_2, e_3)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(490,plain,
% 0.21/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_2, 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_2, e_3) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_2, e_3))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[489])).
% 0.21/0.51 tff(491,plain,
% 0.21/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_2, 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_2, e_3) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_2, e_3)))),
% 0.21/0.51 inference(transitivity,[status(thm)],[490, 488])).
% 0.21/0.51 tff(492,plain,
% 0.21/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_2, e_2, e_2)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(493,plain,
% 0.21/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_2, e_3) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_2, e_3))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[492, 491])).
% 0.21/0.51 tff(494,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[493, 83, 72, 487, 480])).
% 0.21/0.51 tff(495,plain,(~product(e_2, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.51 tff(496,plain,
% 0.21/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_3)) | product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(497,plain,
% 0.21/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(498,plain,
% 0.21/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_3)) | product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[497, 496])).
% 0.21/0.51 tff(499,plain,
% 0.21/0.51 (~product(e_2, e_1, e_2)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[498, 215, 495, 479])).
% 0.21/0.51 tff(500,plain,
% 0.21/0.51 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_2)) | product(e_2, e_1, e_2) | product(e_2, e_3, e_2) | product(e_2, e_2, e_2) | product(e_2, e_4, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_2)) | product(e_2, e_1, e_2) | product(e_2, e_3, e_2) | product(e_2, e_2, e_2) | product(e_2, e_4, e_2))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(501,plain,
% 0.21/0.51 (((~group_element(e_2)) | (~group_element(e_2)) | product(e_2, e_4, e_2) | product(e_2, e_3, e_2) | product(e_2, e_2, e_2) | product(e_2, e_1, e_2)) <=> ((~group_element(e_2)) | product(e_2, e_1, e_2) | product(e_2, e_3, e_2) | product(e_2, e_2, e_2) | product(e_2, e_4, e_2))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(502,plain,
% 0.21/0.51 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_2)) | (~group_element(e_2)) | product(e_2, e_4, e_2) | product(e_2, e_3, e_2) | product(e_2, e_2, e_2) | product(e_2, e_1, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_2)) | product(e_2, e_1, e_2) | product(e_2, e_3, e_2) | product(e_2, e_2, e_2) | product(e_2, e_4, e_2)))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[501])).
% 0.21/0.51 tff(503,plain,
% 0.21/0.51 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_2)) | (~group_element(e_2)) | product(e_2, e_4, e_2) | product(e_2, e_3, e_2) | product(e_2, e_2, e_2) | product(e_2, e_1, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_2)) | product(e_2, e_1, e_2) | product(e_2, e_3, e_2) | product(e_2, e_2, e_2) | product(e_2, e_4, e_2))),
% 0.21/0.51 inference(transitivity,[status(thm)],[502, 500])).
% 0.21/0.51 tff(504,plain,
% 0.21/0.51 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_2)) | (~group_element(e_2)) | product(e_2, e_4, e_2) | product(e_2, e_3, e_2) | product(e_2, e_2, e_2) | product(e_2, e_1, e_2))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(505,plain,
% 0.21/0.51 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_2)) | product(e_2, e_1, e_2) | product(e_2, e_3, e_2) | product(e_2, e_2, e_2) | product(e_2, e_4, e_2)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[504, 503])).
% 0.21/0.51 tff(506,plain,
% 0.21/0.51 (product(e_2, e_1, e_2) | product(e_2, e_3, e_2) | product(e_2, e_2, e_2)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[505, 169, 116, 2])).
% 0.21/0.51 tff(507,plain,
% 0.21/0.51 (product(e_2, e_2, e_2)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[506, 499, 464])).
% 0.21/0.51 tff(508,plain,
% 0.21/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_4, e_2, e_2)) | product(e_2, e_4, e_2) | (~product(e_2, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (~product(e_4, e_2, e_2)) | product(e_2, e_4, e_2) | (~product(e_2, e_2, e_2)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(509,plain,
% 0.21/0.51 (((~product(e_2, e_2, e_2)) | product(e_2, e_4, e_2) | (~product(e_4, e_2, e_2))) <=> ((~product(e_4, e_2, e_2)) | product(e_2, e_4, e_2) | (~product(e_2, e_2, e_2)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(510,plain,
% 0.21/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_2, e_2, e_2)) | product(e_2, e_4, e_2) | (~product(e_4, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_4, e_2, e_2)) | product(e_2, e_4, e_2) | (~product(e_2, e_2, e_2))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[509])).
% 0.21/0.51 tff(511,plain,
% 0.21/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_2, e_2, e_2)) | product(e_2, e_4, e_2) | (~product(e_4, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (~product(e_4, e_2, e_2)) | product(e_2, e_4, e_2) | (~product(e_2, e_2, e_2)))),
% 0.21/0.51 inference(transitivity,[status(thm)],[510, 508])).
% 0.21/0.51 tff(512,plain,
% 0.21/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_2, e_2, e_2)) | product(e_2, e_4, e_2) | (~product(e_4, e_2, e_2)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(513,plain,
% 0.21/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (~product(e_4, e_2, e_2)) | product(e_2, e_4, e_2) | (~product(e_2, e_2, e_2))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[512, 511])).
% 0.21/0.51 tff(514,plain,
% 0.21/0.51 (~product(e_4, e_2, e_2)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[513, 215, 2, 507])).
% 0.21/0.51 tff(515,plain,
% 0.21/0.51 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (product(e_4, e_1, e_2) | (~group_element(e_2)) | product(e_4, e_3, e_2) | (~group_element(e_4)) | product(e_4, e_2, e_2) | product(e_4, e_4, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | product(e_4, e_1, e_2) | (~group_element(e_2)) | product(e_4, e_3, e_2) | (~group_element(e_4)) | product(e_4, e_2, e_2) | product(e_4, e_4, e_2))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(516,plain,
% 0.21/0.51 (((~group_element(e_2)) | (~group_element(e_4)) | product(e_4, e_4, e_2) | product(e_4, e_3, e_2) | product(e_4, e_2, e_2) | product(e_4, e_1, e_2)) <=> (product(e_4, e_1, e_2) | (~group_element(e_2)) | product(e_4, e_3, e_2) | (~group_element(e_4)) | product(e_4, e_2, e_2) | product(e_4, e_4, e_2))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(517,plain,
% 0.21/0.51 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_2)) | (~group_element(e_4)) | product(e_4, e_4, e_2) | product(e_4, e_3, e_2) | product(e_4, e_2, e_2) | product(e_4, e_1, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (product(e_4, e_1, e_2) | (~group_element(e_2)) | product(e_4, e_3, e_2) | (~group_element(e_4)) | product(e_4, e_2, e_2) | product(e_4, e_4, e_2)))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[516])).
% 0.21/0.51 tff(518,plain,
% 0.21/0.51 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_2)) | (~group_element(e_4)) | product(e_4, e_4, e_2) | product(e_4, e_3, e_2) | product(e_4, e_2, e_2) | product(e_4, e_1, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | product(e_4, e_1, e_2) | (~group_element(e_2)) | product(e_4, e_3, e_2) | (~group_element(e_4)) | product(e_4, e_2, e_2) | product(e_4, e_4, e_2))),
% 0.21/0.51 inference(transitivity,[status(thm)],[517, 515])).
% 0.21/0.51 tff(519,plain,
% 0.21/0.51 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_2)) | (~group_element(e_4)) | product(e_4, e_4, e_2) | product(e_4, e_3, e_2) | product(e_4, e_2, e_2) | product(e_4, e_1, e_2))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(520,plain,
% 0.21/0.51 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | product(e_4, e_1, e_2) | (~group_element(e_2)) | product(e_4, e_3, e_2) | (~group_element(e_4)) | product(e_4, e_2, e_2) | product(e_4, e_4, e_2)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[519, 518])).
% 0.21/0.51 tff(521,plain,
% 0.21/0.51 (product(e_4, e_1, e_2) | product(e_4, e_3, e_2) | product(e_4, e_2, e_2)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[520, 169, 116, 113, 110])).
% 0.21/0.51 tff(522,plain,
% 0.21/0.51 (product(e_4, e_1, e_2)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[521, 514, 1])).
% 0.21/0.51 tff(523,plain,
% 0.21/0.51 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(524,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.21/0.51 tff(525,plain,
% 0.21/0.51 (~equalish(e_3, e_2)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[524, 523])).
% 0.21/0.51 tff(526,plain,
% 0.21/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_3, e_2) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_3, e_2) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_1, e_3)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(527,plain,
% 0.21/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_3, e_2) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_1, e_3)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(528,plain,
% 0.21/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_3, e_2) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_1, e_3))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[527, 526])).
% 0.21/0.51 tff(529,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[528, 525, 72, 522, 475])).
% 0.21/0.51 tff(530,plain,((~product(e_2, e_3, e_4)) | product(e_4, e_3, e_2) | product(e_2, e_4, e_2) | (~product(e_3, e_4, e_2)) | product(e_3, e_3, e_2) | (~product(e_3, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.51 tff(531,plain,
% 0.21/0.51 (~product(e_2, e_3, e_4)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[530, 454, 2, 445, 92, 1])).
% 0.21/0.51 tff(532,plain,
% 0.21/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_3, e_2) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_3, e_2) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_3, e_3)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(533,plain,
% 0.21/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_3, e_2) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_3, e_3)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(534,plain,
% 0.21/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_3, e_2) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_3, e_3))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[533, 532])).
% 0.21/0.52 tff(535,plain,
% 0.21/0.52 (~product(e_4, e_3, e_3)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[534, 145, 191, 92])).
% 0.21/0.52 tff(536,plain,
% 0.21/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_3, e_4, e_2)) | product(e_4, e_4, e_2) | (~product(e_4, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (~product(e_3, e_4, e_2)) | product(e_4, e_4, e_2) | (~product(e_4, e_3, e_4)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(537,plain,
% 0.21/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_3, e_4, e_2)) | product(e_4, e_4, e_2) | (~product(e_4, e_3, e_4)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(538,plain,
% 0.21/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (~product(e_3, e_4, e_2)) | product(e_4, e_4, e_2) | (~product(e_4, e_3, e_4))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[537, 536])).
% 0.21/0.52 tff(539,plain,
% 0.21/0.52 (~product(e_4, e_3, e_4)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[538, 215, 191, 110])).
% 0.21/0.52 tff(540,plain,
% 0.21/0.52 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | product(e_4, e_3, e_2) | (~group_element(e_4)) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (~group_element(e_3)) | product(e_4, e_3, e_2) | (~group_element(e_4)) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_1))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(541,plain,
% 0.21/0.52 (((~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1)) <=> ((~group_element(e_3)) | product(e_4, e_3, e_2) | (~group_element(e_4)) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_1))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(542,plain,
% 0.21/0.52 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | product(e_4, e_3, e_2) | (~group_element(e_4)) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_1)))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[541])).
% 0.21/0.52 tff(543,plain,
% 0.21/0.52 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (~group_element(e_3)) | product(e_4, e_3, e_2) | (~group_element(e_4)) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_1))),
% 0.21/0.52 inference(transitivity,[status(thm)],[542, 540])).
% 0.21/0.52 tff(544,plain,
% 0.21/0.52 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_4)) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(545,plain,
% 0.21/0.52 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (~group_element(e_3)) | product(e_4, e_3, e_2) | (~group_element(e_4)) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_1)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[544, 543])).
% 0.21/0.52 tff(546,plain,
% 0.21/0.52 (product(e_4, e_3, e_3) | product(e_4, e_3, e_1)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[545, 46, 113, 43, 1, 539])).
% 0.21/0.52 tff(547,plain,
% 0.21/0.52 (product(e_4, e_3, e_1)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[546, 535])).
% 0.21/0.52 tff(548,assumption,(product(e_3, e_3, e_1)), introduced(assumption)).
% 0.21/0.52 tff(549,plain,
% 0.21/0.52 ((~equalish(e_3, e_4)) <=> (~equalish(e_3, e_4))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(550,axiom,(~equalish(e_3, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_4')).
% 0.21/0.52 tff(551,plain,
% 0.21/0.52 (~equalish(e_3, e_4)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[550, 549])).
% 0.21/0.52 tff(552,plain,
% 0.21/0.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_3, e_3, e_1)) | (~product(e_4, 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_3, e_4) | (~product(e_3, e_3, e_1)) | (~product(e_4, e_3, e_1)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(553,plain,
% 0.21/0.52 ((equalish(e_3, e_4) | (~product(e_4, e_3, e_1)) | (~product(e_3, e_3, e_1))) <=> (equalish(e_3, e_4) | (~product(e_3, e_3, e_1)) | (~product(e_4, e_3, e_1)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(554,plain,
% 0.21/0.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_4, e_3, e_1)) | (~product(e_3, 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_3, e_4) | (~product(e_3, e_3, e_1)) | (~product(e_4, e_3, e_1))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[553])).
% 0.21/0.52 tff(555,plain,
% 0.21/0.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_4, e_3, e_1)) | (~product(e_3, 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_3, e_4) | (~product(e_3, e_3, e_1)) | (~product(e_4, e_3, e_1)))),
% 0.21/0.52 inference(transitivity,[status(thm)],[554, 552])).
% 0.21/0.52 tff(556,plain,
% 0.21/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_4, e_3, e_1)) | (~product(e_3, e_3, e_1)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(557,plain,
% 0.21/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_4) | (~product(e_3, e_3, e_1)) | (~product(e_4, e_3, e_1))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[556, 555])).
% 0.21/0.52 tff(558,plain,
% 0.21/0.52 ($false),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[557, 551, 262, 548, 547])).
% 0.21/0.52 tff(559,plain,((~product(e_3, e_3, e_1)) | product(e_4, e_3, e_2) | (~product(e_3, e_4, e_2)) | product(e_3, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.52 tff(560,plain,
% 0.21/0.52 (~product(e_3, e_3, e_1)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[559, 445, 1, 92])).
% 0.21/0.52 tff(561,assumption,(~product(e_3, e_3, e_1)), introduced(assumption)).
% 0.21/0.52 tff(562,plain,
% 0.21/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (product(e_3, e_3, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_3, e_3, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_4)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(563,plain,
% 0.21/0.52 (((~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_4)) | product(e_3, e_3, e_1)) <=> (product(e_3, e_3, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_4)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(564,plain,
% 0.21/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_4)) | product(e_3, e_3, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (product(e_3, e_3, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_4))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[563])).
% 0.21/0.52 tff(565,plain,
% 0.21/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_4)) | product(e_3, e_3, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_3, e_3, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_4)))),
% 0.21/0.52 inference(transitivity,[status(thm)],[564, 562])).
% 0.21/0.52 tff(566,plain,
% 0.21/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_4)) | product(e_3, e_3, e_1))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(567,plain,
% 0.21/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_3, e_3, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_4))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[566, 565])).
% 0.21/0.52 tff(568,plain,
% 0.21/0.52 ($false),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[567, 14, 561, 177, 399])).
% 0.21/0.52 tff(569,plain,((~product(e_1, e_3, e_4)) | product(e_3, e_3, e_1) | (~product(e_3, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.52 tff(570,plain,
% 0.21/0.52 (~product(e_1, e_3, e_4)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[569, 454, 560])).
% 0.21/0.52 tff(571,plain,
% 0.21/0.52 (~product(e_4, e_3, e_4)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[538, 215, 445, 110])).
% 0.21/0.52 tff(572,plain,
% 0.21/0.52 (product(e_2, e_3, e_4) | product(e_1, e_3, e_4)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[310, 126, 46, 113, 93, 571])).
% 0.21/0.52 tff(573,plain,
% 0.21/0.52 ($false),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[572, 570, 531])).
% 0.21/0.52 tff(574,plain,(product(e_3, e_3, e_2) | product(e_3, e_3, e_4) | product(e_2, e_4, e_2) | product(e_4, e_3, e_2) | product(e_3, e_2, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.52 tff(575,plain,
% 0.21/0.52 (product(e_2, e_4, e_2) | product(e_4, e_3, e_2) | product(e_3, e_2, e_4)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[574, 91, 80])).
% 0.21/0.52 tff(576,plain,
% 0.21/0.52 (product(e_3, e_2, e_4)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[575, 2, 1])).
% 0.21/0.52 tff(577,plain,
% 0.21/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_3, e_4) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_3, e_4) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_3)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(578,plain,
% 0.21/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_3, e_4) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_3)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(579,plain,
% 0.21/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_3, e_4) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_3, e_3))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[578, 577])).
% 0.21/0.52 tff(580,plain,
% 0.21/0.52 (~product(e_2, e_3, e_3)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[579, 145, 80, 576])).
% 0.21/0.52 tff(581,plain,
% 0.21/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_3, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_3, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_2, e_3)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(582,plain,
% 0.21/0.52 ((product(e_2, e_3, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3))) <=> ((~product(e_3, e_3, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_2, e_3)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(583,plain,
% 0.21/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_3, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_2, e_3))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[582])).
% 0.21/0.52 tff(584,plain,
% 0.21/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_3, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_2, e_3)))),
% 0.21/0.52 inference(transitivity,[status(thm)],[583, 581])).
% 0.21/0.52 tff(585,plain,
% 0.21/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(586,plain,
% 0.21/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_3, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_2, e_3))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[585, 584])).
% 0.21/0.52 tff(587,plain,
% 0.21/0.52 (~product(e_3, e_2, e_3)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[586, 145, 62, 580])).
% 0.21/0.52 tff(588,plain,
% 0.21/0.52 (product(e_3, e_4, e_2) | product(e_2, e_4, e_2)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[444, 91, 80])).
% 0.21/0.52 tff(589,plain,
% 0.21/0.52 (product(e_3, e_4, e_2)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[588, 2])).
% 0.21/0.52 tff(590,plain,
% 0.21/0.52 (~product(e_4, e_3, e_4)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[538, 215, 589, 110])).
% 0.21/0.52 tff(591,plain,
% 0.21/0.52 (~product(e_2, e_4, e_3)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[396, 145, 576, 590])).
% 0.21/0.52 tff(592,plain,
% 0.21/0.52 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_2)) | (~group_element(e_3)) | product(e_2, e_3, e_3) | product(e_2, e_2, e_3) | product(e_2, e_4, e_3) | product(e_2, e_1, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_2)) | (~group_element(e_3)) | product(e_2, e_3, e_3) | product(e_2, e_2, e_3) | product(e_2, e_4, e_3) | product(e_2, e_1, e_3))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(593,plain,
% 0.21/0.52 (((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_4, e_3) | product(e_2, e_3, e_3) | product(e_2, e_2, e_3) | product(e_2, e_1, e_3)) <=> ((~group_element(e_2)) | (~group_element(e_3)) | product(e_2, e_3, e_3) | product(e_2, e_2, e_3) | product(e_2, e_4, e_3) | product(e_2, e_1, e_3))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(594,plain,
% 0.21/0.52 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_4, e_3) | product(e_2, e_3, e_3) | product(e_2, e_2, e_3) | product(e_2, e_1, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_2)) | (~group_element(e_3)) | product(e_2, e_3, e_3) | product(e_2, e_2, e_3) | product(e_2, e_4, e_3) | product(e_2, e_1, e_3)))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[593])).
% 0.21/0.53 tff(595,plain,
% 0.21/0.53 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_4, e_3) | product(e_2, e_3, e_3) | product(e_2, e_2, e_3) | product(e_2, e_1, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_2)) | (~group_element(e_3)) | product(e_2, e_3, e_3) | product(e_2, e_2, e_3) | product(e_2, e_4, e_3) | product(e_2, e_1, e_3))),
% 0.21/0.53 inference(transitivity,[status(thm)],[594, 592])).
% 0.21/0.53 tff(596,plain,
% 0.21/0.53 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_4, e_3) | product(e_2, e_3, e_3) | product(e_2, e_2, e_3) | product(e_2, e_1, e_3))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(597,plain,
% 0.21/0.53 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_4, Y) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_2)) | (~group_element(e_3)) | product(e_2, e_3, e_3) | product(e_2, e_2, e_3) | product(e_2, e_4, e_3) | product(e_2, e_1, e_3)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[596, 595])).
% 0.21/0.53 tff(598,plain,
% 0.21/0.53 (product(e_2, e_3, e_3) | product(e_2, e_4, e_3) | product(e_2, e_1, e_3)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[597, 169, 116, 46, 495])).
% 0.21/0.53 tff(599,plain,
% 0.21/0.53 (product(e_2, e_1, e_3)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[598, 591, 580])).
% 0.21/0.53 tff(600,plain,
% 0.21/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_3, e_2)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(601,plain,
% 0.21/0.53 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_3, e_2)))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(602,plain,
% 0.21/0.53 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_3, e_2))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[601, 600])).
% 0.21/0.53 tff(603,plain,
% 0.21/0.53 (~product(e_1, e_3, e_2)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[602, 145, 599, 587])).
% 0.21/0.53 tff(604,plain,
% 0.21/0.53 (product(e_4, e_3, e_2) | product(e_2, e_3, e_2) | product(e_1, e_3, e_2)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[470, 126, 116, 46, 91])).
% 0.21/0.53 tff(605,plain,
% 0.21/0.53 (product(e_2, e_3, e_2)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[604, 603, 1])).
% 0.21/0.53 tff(606,plain,
% 0.21/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_2, e_3, e_2)) | (~product(e_3, e_4, e_2)) | product(e_4, e_2, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (~product(e_2, e_3, e_2)) | (~product(e_3, e_4, e_2)) | product(e_4, e_2, e_3))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(607,plain,
% 0.21/0.53 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_2, e_3, e_2)) | (~product(e_3, e_4, e_2)) | product(e_4, e_2, e_3))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(608,plain,
% 0.21/0.53 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (~product(e_2, e_3, e_2)) | (~product(e_3, e_4, e_2)) | product(e_4, e_2, e_3)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[607, 606])).
% 0.21/0.53 tff(609,plain,
% 0.21/0.53 (product(e_4, e_2, e_3)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[608, 14, 589, 605])).
% 0.21/0.53 tff(610,plain,
% 0.21/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_3) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_2, e_3, e_3) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_2, e_3)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(611,plain,
% 0.21/0.53 (((~product(e_4, e_2, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_4, e_2))) <=> (product(e_2, e_3, e_3) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_2, e_3)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(612,plain,
% 0.21/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_4, e_2, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_3) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_2, e_3))))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[611])).
% 0.21/0.53 tff(613,plain,
% 0.21/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_4, e_2, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_2, e_3, e_3) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_2, e_3)))),
% 0.21/0.53 inference(transitivity,[status(thm)],[612, 610])).
% 0.21/0.53 tff(614,plain,
% 0.21/0.53 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | ((~product(e_4, e_2, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_4, e_2)))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(615,plain,
% 0.21/0.53 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | product(Z1, Y, Z2) | (~product(Y, X, Z1)))) | product(e_2, e_3, e_3) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_2, e_3))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[614, 613])).
% 0.21/0.53 tff(616,plain,
% 0.21/0.53 ($false),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[615, 215, 589, 580, 609])).
% 0.21/0.53 tff(617,plain,(product(e_2, e_4, e_2) | product(e_4, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.53 tff(618,plain,
% 0.21/0.53 (product(e_2, e_4, e_2)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[617, 1])).
% 0.21/0.53 tff(619,plain,
% 0.21/0.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_2, e_4, e_2)) | (~product(e_3, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_2, e_4, e_2)) | (~product(e_3, e_4, e_2)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(620,plain,
% 0.21/0.53 ((equalish(e_2, e_3) | (~product(e_3, e_4, e_2)) | (~product(e_2, e_4, e_2))) <=> (equalish(e_2, e_3) | (~product(e_2, e_4, e_2)) | (~product(e_3, e_4, e_2)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(621,plain,
% 0.21/0.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_4, e_2)) | (~product(e_2, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_2, e_4, e_2)) | (~product(e_3, e_4, e_2))))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[620])).
% 0.21/0.53 tff(622,plain,
% 0.21/0.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_4, e_2)) | (~product(e_2, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_2, e_4, e_2)) | (~product(e_3, e_4, e_2)))),
% 0.21/0.53 inference(transitivity,[status(thm)],[621, 619])).
% 0.21/0.53 tff(623,plain,
% 0.21/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_4, e_2)) | (~product(e_2, e_4, e_2)))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(624,plain,
% 0.21/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_2, e_4, e_2)) | (~product(e_3, e_4, e_2))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[623, 622])).
% 0.21/0.53 tff(625,plain,
% 0.21/0.53 ((~product(e_2, e_4, e_2)) | (~product(e_3, e_4, e_2))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[624, 83, 262])).
% 0.21/0.53 tff(626,plain,
% 0.21/0.53 (~product(e_3, e_4, e_2)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[625, 618])).
% 0.21/0.53 tff(627,assumption,(product(e_2, e_4, e_2)), introduced(assumption)).
% 0.21/0.53 tff(628,plain,
% 0.21/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (product(e_4, e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_4, e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_4, e_2)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(629,plain,
% 0.21/0.53 (((~product(e_3, e_2, e_2)) | (~product(e_2, e_4, e_2)) | product(e_4, e_3, e_2)) <=> (product(e_4, e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_4, e_2)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(630,plain,
% 0.21/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_2, e_2)) | (~product(e_2, e_4, e_2)) | product(e_4, e_3, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (product(e_4, e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_4, e_2))))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[629])).
% 0.21/0.53 tff(631,plain,
% 0.21/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_2, e_2)) | (~product(e_2, e_4, e_2)) | product(e_4, e_3, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_4, e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_4, e_2)))),
% 0.21/0.53 inference(transitivity,[status(thm)],[630, 628])).
% 0.21/0.53 tff(632,plain,
% 0.21/0.53 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_3, e_2, e_2)) | (~product(e_2, e_4, e_2)) | product(e_4, e_3, e_2))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(633,plain,
% 0.21/0.53 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | product(e_4, e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_4, e_2))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[632, 631])).
% 0.21/0.53 tff(634,plain,
% 0.21/0.53 ($false),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[633, 14, 238, 627, 1])).
% 0.21/0.53 tff(635,plain,((~product(e_3, e_2, e_2)) | (~product(e_2, e_4, e_2)) | product(e_4, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.53 tff(636,plain,
% 0.21/0.53 (~product(e_3, e_2, e_2)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[635, 627, 1])).
% 0.21/0.53 tff(637,plain,
% 0.21/0.53 (product(e_3, e_1, e_2)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[204, 636, 91, 94])).
% 0.21/0.53 tff(638,assumption,(product(e_4, e_1, e_2)), introduced(assumption)).
% 0.21/0.53 tff(639,plain,
% 0.21/0.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_4, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_4, e_1, e_2)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(640,plain,
% 0.21/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_4, e_1, e_2)))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(641,plain,
% 0.21/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_4, e_1, e_2))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[640, 639])).
% 0.21/0.53 tff(642,plain,
% 0.21/0.53 ($false),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[641, 75, 262, 638, 178])).
% 0.21/0.53 tff(643,plain,((~product(e_4, e_1, e_2)) | (~product(e_3, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.53 tff(644,plain,
% 0.21/0.53 (~product(e_4, e_1, e_2)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[643, 637])).
% 0.21/0.53 tff(645,plain,
% 0.21/0.53 (product(e_4, e_2, e_2)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[521, 644, 1])).
% 0.21/0.53 tff(646,plain,
% 0.21/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_4, e_2, e_2)) | (~product(e_2, e_4, e_2)) | product(e_4, e_4, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (~product(e_4, e_2, e_2)) | (~product(e_2, e_4, e_2)) | product(e_4, e_4, e_2))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(647,plain,
% 0.21/0.53 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_4, e_2, e_2)) | (~product(e_2, e_4, e_2)) | product(e_4, e_4, e_2))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(648,plain,
% 0.21/0.53 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (~product(e_4, e_2, e_2)) | (~product(e_2, e_4, e_2)) | product(e_4, e_4, e_2)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[647, 646])).
% 0.21/0.53 tff(649,plain,
% 0.21/0.53 ($false),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[648, 14, 645, 627, 110])).
% 0.21/0.53 tff(650,plain,((~product(e_2, e_4, e_2)) | product(e_4, e_3, e_2) | product(e_3, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.53 tff(651,plain,
% 0.21/0.53 ($false),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[650, 626, 618, 1])).
% 0.21/0.53 tff(652,plain,(product(e_4, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.53 tff(653,plain,
% 0.21/0.53 ((~product(e_4, e_3, e_2)) | product(e_2, e_4, e_2)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[220, 91, 80])).
% 0.21/0.53 tff(654,plain,
% 0.21/0.53 (product(e_2, e_4, e_2)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[653, 652])).
% 0.21/0.53 tff(655,plain,
% 0.21/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_2, e_4, e_2)) | (~product(e_4, e_3, e_2)) | product(e_3, e_2, e_4))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (~product(e_2, e_4, e_2)) | (~product(e_4, e_3, e_2)) | product(e_3, e_2, e_4))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(656,plain,
% 0.21/0.53 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | ((~product(e_2, e_4, e_2)) | (~product(e_4, e_3, e_2)) | product(e_3, e_2, e_4))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(657,plain,
% 0.21/0.53 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(X, Z1, Z2)) | (~product(Z1, Y, Z2)) | product(Y, X, Z1))) | (~product(e_2, e_4, e_2)) | (~product(e_4, e_3, e_2)) | product(e_3, e_2, e_4)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[656, 655])).
% 0.21/0.53 tff(658,plain,
% 0.21/0.53 (product(e_3, e_2, e_4)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[657, 14, 654, 652])).
% 0.21/0.53 tff(659,plain,
% 0.21/0.53 (~product(e_3, e_2, e_2)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[242, 658])).
% 0.21/0.53 tff(660,plain,
% 0.21/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_4, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_2, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_4, e_3, e_2)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(661,plain,
% 0.21/0.53 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_4, e_3, e_2)))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(662,plain,
% 0.21/0.53 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_2, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_4, e_3, e_2))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[661, 660])).
% 0.21/0.53 tff(663,plain,
% 0.21/0.53 ($false),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[662, 145, 659, 654, 652])).
% 0.21/0.53 % SZS output end Proof
% 0.21/0.54 % E exiting
%------------------------------------------------------------------------------