%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP130-3.003 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:07:11 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP130-3.003 : TPTP v9.0.0. Released v1.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n006.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Thu Jun 19 15:43:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.43 % SZS status Unsatisfiable
% 0.19/0.43 % SZS output start Proof
% 0.19/0.43 tff(product_type, type, (
% 0.19/0.43 product: ( $i * $i * $i ) > $o)).
% 0.19/0.43 tff(e_3_type, type, (
% 0.19/0.43 e_3: $i)).
% 0.19/0.43 tff(e_1_type, type, (
% 0.19/0.43 e_1: $i)).
% 0.19/0.43 tff(e_2_type, type, (
% 0.19/0.43 e_2: $i)).
% 0.19/0.43 tff(group_element_type, type, (
% 0.19/0.43 group_element: $i > $o)).
% 0.19/0.43 tff(equalish_type, type, (
% 0.19/0.43 equalish: ( $i * $i ) > $o)).
% 0.19/0.43 tff(1,assumption,(product(e_2, e_1, e_3)), introduced(assumption)).
% 0.19/0.43 tff(2,assumption,(~product(e_3, e_1, e_3)), introduced(assumption)).
% 0.19/0.43 tff(3,assumption,(~product(e_1, e_1, e_3)), introduced(assumption)).
% 0.19/0.43 tff(4,assumption,(product(e_3, e_1, e_1)), introduced(assumption)).
% 0.19/0.43 tff(5,plain,
% 0.19/0.43 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl((product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1))) <=> (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(6,plain,
% 0.19/0.43 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[5])).
% 0.19/0.43 tff(7,plain,
% 0.19/0.43 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(8,plain,
% 0.19/0.43 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : trans(monotonicity(rewrite(((~product(X, Y, Z1)) | (~product(X, Z1, Z2))) <=> ((~product(X, Z1, Z2)) | (~product(X, Y, Z1)))), ((((~product(X, Y, Z1)) | (~product(X, Z1, Z2))) | product(Z2, Y, X)) <=> (((~product(X, Z1, Z2)) | (~product(X, Y, Z1))) | product(Z2, Y, X)))), rewrite((((~product(X, Z1, Z2)) | (~product(X, Y, Z1))) | product(Z2, Y, X)) <=> (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))), ((((~product(X, Y, Z1)) | (~product(X, Z1, Z2))) | product(Z2, Y, X)) <=> (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(9,plain,
% 0.19/0.43 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(X, Z1, Z2))) | product(Z2, Y, X)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[8])).
% 0.19/0.43 tff(10,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(X, Z1, Z2))) | product(Z2, Y, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qg3')).
% 0.19/0.43 tff(11,plain,
% 0.19/0.43 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.19/0.43 tff(12,plain,
% 0.19/0.43 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.19/0.43 tff(13,plain,(
% 0.19/0.43 ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[12])).
% 0.19/0.43 tff(14,plain,
% 0.19/0.43 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.19/0.43 tff(15,plain,
% 0.19/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_1)) | product(e_1, e_1, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_1)) | product(e_1, e_1, e_3))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(16,plain,
% 0.19/0.43 ((product(e_1, e_1, e_3) | (~product(e_3, e_1, e_1)) | (~product(e_3, e_1, e_1))) <=> ((~product(e_3, e_1, e_1)) | product(e_1, e_1, e_3))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(17,plain,
% 0.19/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_3, e_1, e_1)) | (~product(e_3, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_1)) | product(e_1, e_1, e_3)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[16])).
% 0.19/0.44 tff(18,plain,
% 0.19/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_3, e_1, e_1)) | (~product(e_3, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_1)) | product(e_1, e_1, e_3))),
% 0.19/0.44 inference(transitivity,[status(thm)],[17, 15])).
% 0.19/0.44 tff(19,plain,
% 0.19/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_3, e_1, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(20,plain,
% 0.19/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_1)) | product(e_1, e_1, e_3)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.19/0.44 tff(21,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[20, 14, 4, 3])).
% 0.19/0.44 tff(22,plain,((~product(e_3, e_1, e_1)) | product(e_1, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(23,plain,
% 0.19/0.44 (~product(e_3, e_1, e_1)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[22, 3])).
% 0.19/0.44 tff(24,plain,
% 0.19/0.44 (^[Y: $i, X: $i] : refl(((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) <=> ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(25,plain,
% 0.19/0.44 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) <=> ![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[24])).
% 0.19/0.44 tff(26,plain,
% 0.19/0.44 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) <=> ![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(27,plain,
% 0.19/0.44 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) <=> ((~group_element(X)) | product(X, Y, e_1) | (~group_element(Y)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> (((~group_element(X)) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_2)))), rewrite((((~group_element(X)) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_2)) <=> ((~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> ((~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> (((~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_3)))), rewrite((((~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_3)) <=> ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(28,plain,
% 0.19/0.44 (![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.44 tff(29,axiom,(![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_total_function1')).
% 0.19/0.44 tff(30,plain,
% 0.19/0.44 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.19/0.44 tff(31,plain,
% 0.19/0.44 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.19/0.44 tff(32,plain,(
% 0.19/0.44 ![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[31])).
% 0.19/0.44 tff(33,plain,
% 0.19/0.44 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.19/0.44 tff(34,plain,
% 0.19/0.44 (group_element(e_3) <=> group_element(e_3)),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(35,axiom,(group_element(e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_3')).
% 0.19/0.44 tff(36,plain,
% 0.19/0.44 (group_element(e_3)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.19/0.44 tff(37,plain,
% 0.19/0.44 (group_element(e_1) <=> group_element(e_1)),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(38,axiom,(group_element(e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_1')).
% 0.19/0.44 tff(39,plain,
% 0.19/0.44 (group_element(e_1)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.44 tff(40,plain,
% 0.19/0.44 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (product(e_3, e_1, e_1) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3) | (~group_element(e_1)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | product(e_3, e_1, e_1) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3) | (~group_element(e_1)) | (~group_element(e_3)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(41,plain,
% 0.19/0.44 (((~group_element(e_3)) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1))) <=> (product(e_3, e_1, e_1) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3) | (~group_element(e_1)) | (~group_element(e_3)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(42,plain,
% 0.19/0.44 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (product(e_3, e_1, e_1) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3) | (~group_element(e_1)) | (~group_element(e_3))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[41])).
% 0.19/0.44 tff(43,plain,
% 0.19/0.44 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | product(e_3, e_1, e_1) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3) | (~group_element(e_1)) | (~group_element(e_3)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[42, 40])).
% 0.19/0.44 tff(44,plain,
% 0.19/0.44 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(45,plain,
% 0.19/0.44 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | product(e_3, e_1, e_1) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3) | (~group_element(e_1)) | (~group_element(e_3))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.19/0.44 tff(46,plain,
% 0.19/0.44 (product(e_3, e_1, e_1) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[45, 39, 36, 33])).
% 0.19/0.44 tff(47,plain,
% 0.19/0.44 (product(e_3, e_1, e_2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[46, 23, 2])).
% 0.19/0.44 tff(48,assumption,(product(e_1, e_1, e_2)), introduced(assumption)).
% 0.19/0.44 tff(49,assumption,(product(e_3, e_1, e_2)), introduced(assumption)).
% 0.19/0.44 tff(50,plain,
% 0.19/0.44 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(51,plain,
% 0.19/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.44 tff(52,plain,
% 0.19/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(53,plain,
% 0.19/0.44 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(W, Y, X)) | (~product(Z, Y, X))) <=> ((~product(Z, Y, X)) | (~product(W, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> (((~product(Z, Y, X)) | (~product(W, Y, X))) | equalish(W, Z)))), rewrite((((~product(Z, Y, X)) | (~product(W, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(54,plain,
% 0.19/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.44 tff(55,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')).
% 0.19/0.44 tff(56,plain,
% 0.19/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.19/0.44 tff(57,plain,
% 0.19/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.19/0.44 tff(58,plain,(
% 0.19/0.44 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[57])).
% 0.19/0.44 tff(59,plain,
% 0.19/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.19/0.44 tff(60,plain,
% 0.19/0.44 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(61,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.19/0.44 tff(62,plain,
% 0.19/0.44 (~equalish(e_1, e_3)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.19/0.44 tff(63,plain,
% 0.19/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_1, e_2)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(64,plain,
% 0.19/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_1, e_2)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(65,plain,
% 0.19/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_1, e_2))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.19/0.44 tff(66,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[65, 62, 59, 49, 48])).
% 0.19/0.44 tff(67,plain,((~product(e_1, e_1, e_2)) | (~product(e_3, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(68,plain,
% 0.19/0.44 (~product(e_1, e_1, e_2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[67, 47])).
% 0.19/0.44 tff(69,plain,
% 0.19/0.44 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_1, e_2) | product(e_1, e_1, e_3) | product(e_1, e_1, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | product(e_1, e_1, e_2) | product(e_1, e_1, e_3) | product(e_1, e_1, e_1))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(70,plain,
% 0.19/0.44 (((~group_element(e_1)) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1))) <=> ((~group_element(e_1)) | product(e_1, e_1, e_2) | product(e_1, e_1, e_3) | product(e_1, e_1, e_1))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(71,plain,
% 0.19/0.44 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_1, e_2) | product(e_1, e_1, e_3) | product(e_1, e_1, e_1)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[70])).
% 0.19/0.44 tff(72,plain,
% 0.19/0.44 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | product(e_1, e_1, e_2) | product(e_1, e_1, e_3) | product(e_1, e_1, e_1))),
% 0.19/0.44 inference(transitivity,[status(thm)],[71, 69])).
% 0.19/0.44 tff(73,plain,
% 0.19/0.44 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(74,plain,
% 0.19/0.44 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | product(e_1, e_1, e_2) | product(e_1, e_1, e_3) | product(e_1, e_1, e_1)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.19/0.44 tff(75,plain,
% 0.19/0.44 (product(e_1, e_1, e_2) | product(e_1, e_1, e_1)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[74, 39, 33, 3])).
% 0.19/0.44 tff(76,plain,
% 0.19/0.44 (product(e_1, e_1, e_1)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[75, 68])).
% 0.19/0.44 tff(77,assumption,(product(e_1, e_1, e_1)), introduced(assumption)).
% 0.19/0.44 tff(78,assumption,(product(e_1, e_2, e_1)), introduced(assumption)).
% 0.19/0.44 tff(79,plain,
% 0.19/0.44 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(80,plain,
% 0.19/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[79])).
% 0.19/0.44 tff(81,plain,
% 0.19/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(82,plain,
% 0.19/0.45 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(X, W, Y)) | (~product(X, Z, Y))) <=> ((~product(X, Z, Y)) | (~product(X, W, Y)))), ((((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> (((~product(X, Z, Y)) | (~product(X, W, Y))) | equalish(W, Z)))), rewrite((((~product(X, Z, Y)) | (~product(X, W, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))), ((((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(83,plain,
% 0.19/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[82])).
% 0.19/0.45 tff(84,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_right_cancellation')).
% 0.19/0.45 tff(85,plain,
% 0.19/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.19/0.45 tff(86,plain,
% 0.19/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.19/0.45 tff(87,plain,(
% 0.19/0.45 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[86])).
% 0.19/0.45 tff(88,plain,
% 0.19/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[87, 80])).
% 0.19/0.45 tff(89,plain,
% 0.19/0.45 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(90,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.19/0.45 tff(91,plain,
% 0.19/0.45 (~equalish(e_2, e_1)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.19/0.45 tff(92,plain,
% 0.19/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(93,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(94,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.19/0.45 tff(95,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[94, 91, 88, 78, 77])).
% 0.19/0.45 tff(96,plain,((~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(97,plain,
% 0.19/0.45 (~product(e_1, e_2, e_1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[96, 76])).
% 0.19/0.45 tff(98,assumption,(product(e_1, e_3, e_1)), introduced(assumption)).
% 0.19/0.45 tff(99,plain,
% 0.19/0.45 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(100,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.19/0.45 tff(101,plain,
% 0.19/0.45 (~equalish(e_3, e_1)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.19/0.45 tff(102,plain,
% 0.19/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(103,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(104,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.19/0.45 tff(105,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[104, 101, 88, 98, 77])).
% 0.19/0.45 tff(106,plain,((~product(e_1, e_3, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(107,plain,
% 0.19/0.45 (~product(e_1, e_3, e_1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[106, 76])).
% 0.19/0.45 tff(108,assumption,(~product(e_1, e_3, e_1)), introduced(assumption)).
% 0.19/0.45 tff(109,assumption,(~product(e_3, e_3, e_1)), introduced(assumption)).
% 0.19/0.45 tff(110,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_1) | (~product(e_1, e_3, e_3)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(111,plain,
% 0.19/0.45 ((product(e_3, e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_3, e_3))) <=> (product(e_3, e_3, e_1) | (~product(e_1, e_3, e_3)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(112,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_1, e_3, e_3))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[111])).
% 0.19/0.45 tff(113,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_1) | (~product(e_1, e_3, e_3)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[112, 110])).
% 0.19/0.45 tff(114,plain,
% 0.19/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(115,plain,
% 0.19/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_1) | (~product(e_1, e_3, e_3))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.19/0.45 tff(116,plain,
% 0.19/0.45 (product(e_3, e_3, e_1) | (~product(e_1, e_3, e_3))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[115, 14])).
% 0.19/0.45 tff(117,plain,
% 0.19/0.45 (~product(e_1, e_3, e_3)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[116, 109])).
% 0.19/0.45 tff(118,assumption,(~product(e_1, e_2, e_1)), introduced(assumption)).
% 0.19/0.45 tff(119,assumption,(product(e_1, e_3, e_2)), introduced(assumption)).
% 0.19/0.45 tff(120,assumption,(product(e_1, e_2, e_2)), introduced(assumption)).
% 0.19/0.45 tff(121,plain,
% 0.19/0.45 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(122,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.19/0.45 tff(123,plain,
% 0.19/0.45 (~equalish(e_2, e_3)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.19/0.45 tff(124,plain,
% 0.19/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(125,plain,
% 0.19/0.45 ((equalish(e_2, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_2, e_2))) <=> (equalish(e_2, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(126,plain,
% 0.19/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_3, e_2))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[125])).
% 0.19/0.45 tff(127,plain,
% 0.19/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[126, 124])).
% 0.19/0.45 tff(128,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(129,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_3, e_2))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.19/0.45 tff(130,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[129, 123, 88, 119, 120])).
% 0.19/0.45 tff(131,plain,((~product(e_1, e_2, e_2)) | (~product(e_1, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(132,plain,
% 0.19/0.45 (~product(e_1, e_2, e_2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[131, 119])).
% 0.19/0.45 tff(133,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_2, e_3)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(134,plain,
% 0.19/0.45 ((product(e_3, e_3, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_2))) <=> (product(e_3, e_3, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_2, e_3)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(135,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_2, e_3))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[134])).
% 0.19/0.45 tff(136,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_2, e_3)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[135, 133])).
% 0.19/0.45 tff(137,plain,
% 0.19/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_2)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(138,plain,
% 0.19/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_2, e_3))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.19/0.45 tff(139,plain,
% 0.19/0.45 (product(e_3, e_3, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_2, e_3))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[138, 14])).
% 0.19/0.45 tff(140,plain,
% 0.19/0.45 (~product(e_1, e_2, e_3)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[139, 119, 109])).
% 0.19/0.45 tff(141,plain,
% 0.19/0.45 (group_element(e_2) <=> group_element(e_2)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(142,axiom,(group_element(e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_2')).
% 0.19/0.45 tff(143,plain,
% 0.19/0.45 (group_element(e_2)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.19/0.45 tff(144,plain,
% 0.19/0.45 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(145,plain,
% 0.19/0.45 (((~group_element(e_1)) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2))) <=> ((~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(146,plain,
% 0.19/0.45 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[145])).
% 0.19/0.45 tff(147,plain,
% 0.19/0.45 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1))),
% 0.19/0.45 inference(transitivity,[status(thm)],[146, 144])).
% 0.19/0.45 tff(148,plain,
% 0.19/0.45 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(149,plain,
% 0.19/0.45 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.19/0.45 tff(150,plain,
% 0.19/0.45 (product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[149, 39, 143, 33])).
% 0.19/0.45 tff(151,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[150, 140, 132, 118])).
% 0.19/0.45 tff(152,plain,((~product(e_1, e_3, e_2)) | product(e_1, e_2, e_1) | product(e_3, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(153,plain,
% 0.19/0.45 (~product(e_1, e_3, e_2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[152, 109, 118])).
% 0.19/0.45 tff(154,plain,
% 0.19/0.45 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(155,plain,
% 0.19/0.46 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(156,plain,
% 0.19/0.46 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.19/0.46 tff(157,plain,
% 0.19/0.46 (product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[156, 39, 36, 33])).
% 0.19/0.46 tff(158,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[157, 153, 117, 108])).
% 0.19/0.46 tff(159,plain,(product(e_3, e_3, e_1) | product(e_1, e_3, e_1) | product(e_1, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(160,plain,
% 0.19/0.46 (product(e_3, e_3, e_1)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[159, 107, 97])).
% 0.19/0.46 tff(161,assumption,(~product(e_2, e_3, e_3)), introduced(assumption)).
% 0.19/0.46 tff(162,assumption,(product(e_3, e_3, e_1)), introduced(assumption)).
% 0.19/0.46 tff(163,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_2)) | (~product(e_3, e_3, e_1)) | product(e_2, e_3, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_3, e_1)) | product(e_2, e_3, e_3))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(164,plain,
% 0.19/0.46 ((product(e_2, e_3, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_3, e_1))) <=> ((~product(e_3, e_1, e_2)) | (~product(e_3, e_3, e_1)) | product(e_2, e_3, e_3))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(165,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_2)) | (~product(e_3, e_3, e_1)) | product(e_2, e_3, e_3)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[164])).
% 0.19/0.46 tff(166,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_3, e_1)) | product(e_2, e_3, e_3))),
% 0.19/0.46 inference(transitivity,[status(thm)],[165, 163])).
% 0.19/0.46 tff(167,plain,
% 0.19/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_3, e_1)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(168,plain,
% 0.19/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_3, e_1)) | product(e_2, e_3, e_3)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.19/0.46 tff(169,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[168, 14, 49, 162, 161])).
% 0.19/0.46 tff(170,plain,(product(e_2, e_3, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(171,plain,
% 0.19/0.46 (product(e_2, e_3, e_3)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[170, 47, 160])).
% 0.19/0.46 tff(172,assumption,(product(e_2, e_1, e_2)), introduced(assumption)).
% 0.19/0.46 tff(173,plain,
% 0.19/0.46 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(174,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.19/0.46 tff(175,plain,
% 0.19/0.46 (~equalish(e_3, e_2)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.19/0.46 tff(176,plain,
% 0.19/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(177,plain,
% 0.19/0.46 ((equalish(e_3, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_1, e_2))) <=> (equalish(e_3, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(178,plain,
% 0.19/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_2))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[177])).
% 0.19/0.46 tff(179,plain,
% 0.19/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[178, 176])).
% 0.19/0.46 tff(180,plain,
% 0.19/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(181,plain,
% 0.19/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_2))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.19/0.46 tff(182,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[181, 175, 59, 49, 172])).
% 0.19/0.46 tff(183,plain,((~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(184,plain,
% 0.19/0.46 (~product(e_2, e_1, e_2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[183, 47])).
% 0.19/0.46 tff(185,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.19/0.46 tff(186,assumption,(~product(e_1, e_1, e_2)), introduced(assumption)).
% 0.19/0.46 tff(187,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_2) | (~product(e_2, e_1, e_1)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(188,plain,
% 0.19/0.46 ((product(e_1, e_1, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_1, e_1))) <=> (product(e_1, e_1, e_2) | (~product(e_2, e_1, e_1)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(189,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_2, e_1, e_1))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[188])).
% 0.19/0.46 tff(190,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_2) | (~product(e_2, e_1, e_1)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[189, 187])).
% 0.19/0.46 tff(191,plain,
% 0.19/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(192,plain,
% 0.19/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_2) | (~product(e_2, e_1, e_1))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.19/0.46 tff(193,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[192, 14, 186, 185])).
% 0.19/0.46 tff(194,plain,((~product(e_2, e_1, e_1)) | product(e_1, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(195,plain,
% 0.19/0.46 (~product(e_2, e_1, e_1)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[194, 68])).
% 0.19/0.46 tff(196,plain,
% 0.19/0.46 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(197,plain,
% 0.19/0.46 (((~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1))) <=> ((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(198,plain,
% 0.19/0.46 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[197])).
% 0.19/0.46 tff(199,plain,
% 0.19/0.46 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2))),
% 0.19/0.46 inference(transitivity,[status(thm)],[198, 196])).
% 0.19/0.46 tff(200,plain,
% 0.19/0.46 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(201,plain,
% 0.19/0.46 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.19/0.46 tff(202,plain,
% 0.19/0.46 (product(e_2, e_1, e_3)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[201, 39, 143, 33, 195, 184])).
% 0.19/0.46 tff(203,plain,
% 0.19/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_3, e_3)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(204,plain,
% 0.19/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_3, e_3)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(205,plain,
% 0.19/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_3, e_3))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.19/0.46 tff(206,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[205, 101, 88, 202, 171])).
% 0.19/0.46 tff(207,plain,(product(e_1, e_1, e_3) | product(e_3, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(208,plain,
% 0.19/0.46 (product(e_1, e_1, e_3)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[207, 2])).
% 0.19/0.46 tff(209,assumption,(product(e_1, e_1, e_3)), introduced(assumption)).
% 0.19/0.46 tff(210,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_3)) | product(e_3, e_3, e_1) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_3)) | product(e_3, e_3, e_1) | (~product(e_1, e_3, e_1)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(211,plain,
% 0.19/0.46 ((product(e_3, e_3, e_1) | (~product(e_1, e_1, e_3)) | (~product(e_1, e_3, e_1))) <=> ((~product(e_1, e_1, e_3)) | product(e_3, e_3, e_1) | (~product(e_1, e_3, e_1)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(212,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_1, e_1, e_3)) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_3)) | product(e_3, e_3, e_1) | (~product(e_1, e_3, e_1))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[211])).
% 0.19/0.46 tff(213,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_1, e_1, e_3)) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_3)) | product(e_3, e_3, e_1) | (~product(e_1, e_3, e_1)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[212, 210])).
% 0.19/0.46 tff(214,plain,
% 0.19/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_1, e_1, e_3)) | (~product(e_1, e_3, e_1)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(215,plain,
% 0.19/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_3)) | product(e_3, e_3, e_1) | (~product(e_1, e_3, e_1))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.19/0.46 tff(216,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[215, 14, 209, 98, 109])).
% 0.19/0.46 tff(217,plain,((~product(e_1, e_3, e_1)) | (~product(e_1, e_1, e_3)) | product(e_3, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(218,plain,
% 0.19/0.46 (~product(e_1, e_3, e_1)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[217, 109, 209])).
% 0.19/0.46 tff(219,plain,
% 0.19/0.46 (product(e_1, e_2, e_1)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[159, 218, 109])).
% 0.19/0.46 tff(220,plain,
% 0.19/0.46 (product(e_1, e_3, e_2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[157, 218, 117])).
% 0.19/0.46 tff(221,plain,
% 0.19/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_3, e_2)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(222,plain,
% 0.19/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_3, e_2)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(223,plain,
% 0.19/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_3, e_2))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.19/0.46 tff(224,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[223, 14, 220, 218, 219])).
% 0.19/0.46 tff(225,plain,(product(e_3, e_3, e_1) | (~product(e_1, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(226,plain,
% 0.19/0.46 (product(e_3, e_3, e_1)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[225, 208])).
% 0.19/0.46 tff(227,plain,
% 0.19/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_3, e_1, e_1)) | (~product(e_3, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_3, e_1, e_1)) | (~product(e_3, e_3, e_1)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(228,plain,
% 0.19/0.46 ((equalish(e_1, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_1, e_1))) <=> (equalish(e_1, e_3) | (~product(e_3, e_1, e_1)) | (~product(e_3, e_3, e_1)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(229,plain,
% 0.19/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_3, e_1, e_1)) | (~product(e_3, e_3, e_1))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[228])).
% 0.19/0.46 tff(230,plain,
% 0.19/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_3, e_1, e_1)) | (~product(e_3, e_3, e_1)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[229, 227])).
% 0.19/0.46 tff(231,plain,
% 0.19/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(232,plain,
% 0.19/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_3, e_1, e_1)) | (~product(e_3, e_3, e_1))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.19/0.46 tff(233,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[232, 62, 88, 4, 162])).
% 0.19/0.46 tff(234,plain,((~product(e_3, e_1, e_1)) | (~product(e_3, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(235,plain,
% 0.19/0.46 (~product(e_3, e_1, e_1)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[234, 226])).
% 0.19/0.46 tff(236,plain,
% 0.19/0.46 (product(e_3, e_1, e_2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[46, 235, 2])).
% 0.19/0.46 tff(237,plain,
% 0.19/0.46 (~product(e_2, e_1, e_2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[183, 236])).
% 0.19/0.46 tff(238,plain,
% 0.19/0.46 (~product(e_1, e_1, e_2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[67, 236])).
% 0.19/0.46 tff(239,plain,
% 0.19/0.46 (~product(e_2, e_1, e_1)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[194, 238])).
% 0.19/0.46 tff(240,plain,
% 0.19/0.46 (product(e_2, e_1, e_3)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[201, 39, 143, 33, 239, 237])).
% 0.19/0.46 tff(241,plain,
% 0.19/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_3)) | (~product(e_2, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(242,plain,
% 0.19/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(243,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_3)) | (~product(e_2, e_1, e_3))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.19/0.47 tff(244,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[243, 91, 59, 208, 240])).
% 0.19/0.47 tff(245,plain,(product(e_3, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(246,plain,
% 0.19/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(247,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(248,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.19/0.47 tff(249,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[248, 123, 59, 245, 1])).
% 0.19/0.47 tff(250,plain,(~product(e_2, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(251,assumption,(~product(e_2, e_1, e_3)), introduced(assumption)).
% 0.19/0.47 tff(252,assumption,(product(e_3, e_1, e_3)), introduced(assumption)).
% 0.19/0.47 tff(253,assumption,(product(e_3, e_3, e_2)), introduced(assumption)).
% 0.19/0.47 tff(254,plain,
% 0.19/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_3)) | product(e_2, e_1, e_3) | (~product(e_3, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_3)) | product(e_2, e_1, e_3) | (~product(e_3, e_3, e_2)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(255,plain,
% 0.19/0.47 ((product(e_2, e_1, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_1, e_3))) <=> ((~product(e_3, e_1, e_3)) | product(e_2, e_1, e_3) | (~product(e_3, e_3, e_2)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(256,plain,
% 0.19/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_3)) | product(e_2, e_1, e_3) | (~product(e_3, e_3, e_2))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[255])).
% 0.19/0.47 tff(257,plain,
% 0.19/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_3)) | product(e_2, e_1, e_3) | (~product(e_3, e_3, e_2)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[256, 254])).
% 0.19/0.47 tff(258,plain,
% 0.19/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_1, e_3)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(259,plain,
% 0.19/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_3)) | product(e_2, e_1, e_3) | (~product(e_3, e_3, e_2))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.19/0.47 tff(260,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[259, 14, 252, 251, 253])).
% 0.19/0.47 tff(261,plain,((~product(e_3, e_3, e_2)) | (~product(e_3, e_1, e_3)) | product(e_2, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(262,plain,
% 0.19/0.47 (~product(e_3, e_3, e_2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[261, 252, 251])).
% 0.19/0.47 tff(263,plain,
% 0.19/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_3)) | product(e_1, e_1, e_3) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_3)) | product(e_1, e_1, e_3) | (~product(e_3, e_3, e_1)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(264,plain,
% 0.19/0.47 ((product(e_1, e_1, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_1, e_3))) <=> ((~product(e_3, e_1, e_3)) | product(e_1, e_1, e_3) | (~product(e_3, e_3, e_1)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(265,plain,
% 0.19/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_3)) | product(e_1, e_1, e_3) | (~product(e_3, e_3, e_1))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[264])).
% 0.19/0.47 tff(266,plain,
% 0.19/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_3)) | product(e_1, e_1, e_3) | (~product(e_3, e_3, e_1)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[265, 263])).
% 0.19/0.47 tff(267,plain,
% 0.19/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_1, e_3)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(268,plain,
% 0.19/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_3)) | product(e_1, e_1, e_3) | (~product(e_3, e_3, e_1))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.19/0.47 tff(269,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[268, 14, 252, 3, 162])).
% 0.19/0.47 tff(270,plain,((~product(e_3, e_3, e_1)) | (~product(e_3, e_1, e_3)) | product(e_1, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(271,plain,
% 0.19/0.47 (~product(e_3, e_3, e_1)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[270, 252, 3])).
% 0.19/0.47 tff(272,plain,
% 0.19/0.47 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_3, e_1) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_3)) | product(e_3, e_3, e_1) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(273,plain,
% 0.19/0.47 (((~group_element(e_3)) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3))) <=> ((~group_element(e_3)) | product(e_3, e_3, e_1) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(274,plain,
% 0.19/0.47 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_3, e_1) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2)))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[273])).
% 0.19/0.47 tff(275,plain,
% 0.19/0.47 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_3)) | product(e_3, e_3, e_1) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2))),
% 0.19/0.47 inference(transitivity,[status(thm)],[274, 272])).
% 0.19/0.47 tff(276,plain,
% 0.19/0.47 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(277,plain,
% 0.19/0.47 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_3)) | product(e_3, e_3, e_1) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[276, 275])).
% 0.19/0.47 tff(278,plain,
% 0.19/0.47 (product(e_3, e_3, e_3) | product(e_3, e_3, e_2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[277, 36, 33, 271])).
% 0.19/0.47 tff(279,plain,
% 0.19/0.47 (product(e_3, e_3, e_3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[278, 262])).
% 0.19/0.47 tff(280,plain,
% 0.19/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(281,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(282,plain,
% 0.19/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_3))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.19/0.47 tff(283,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[282, 101, 88, 252, 279])).
% 0.19/0.47 tff(284,plain,((~product(e_3, e_1, e_3)) | product(e_2, e_1, e_3) | product(e_1, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(285,plain,
% 0.19/0.47 (product(e_2, e_1, e_3) | product(e_1, e_1, e_3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[284, 245])).
% 0.19/0.47 tff(286,plain,
% 0.19/0.47 (product(e_1, e_1, e_3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[285, 250])).
% 0.19/0.47 tff(287,plain,
% 0.19/0.47 (product(e_3, e_3, e_1)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[225, 286])).
% 0.19/0.47 tff(288,assumption,(product(e_1, e_3, e_3)), introduced(assumption)).
% 0.19/0.47 tff(289,plain,
% 0.19/0.47 (~product(e_3, e_1, e_1)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[234, 287])).
% 0.19/0.47 tff(290,plain,
% 0.19/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_1) | (~product(e_1, e_1, e_3)) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_1) | (~product(e_1, e_1, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(291,plain,
% 0.19/0.47 ((product(e_3, e_1, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_1, e_3))) <=> (product(e_3, e_1, e_1) | (~product(e_1, e_1, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(292,plain,
% 0.19/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_1) | (~product(e_1, e_1, e_3)) | (~product(e_1, e_3, e_3))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[291])).
% 0.19/0.47 tff(293,plain,
% 0.19/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_1) | (~product(e_1, e_1, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[292, 290])).
% 0.19/0.47 tff(294,plain,
% 0.19/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_1, e_3)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(295,plain,
% 0.19/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_1) | (~product(e_1, e_1, e_3)) | (~product(e_1, e_3, e_3))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[294, 293])).
% 0.19/0.47 tff(296,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[295, 14, 289, 286, 288])).
% 0.19/0.47 tff(297,plain,(~product(e_1, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(298,plain,
% 0.19/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_1)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(299,plain,
% 0.19/0.47 ((product(e_1, e_3, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_3, e_3))) <=> (product(e_1, e_3, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_1)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(300,plain,
% 0.19/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_1))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[299])).
% 0.19/0.47 tff(301,plain,
% 0.19/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_1)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[300, 298])).
% 0.19/0.47 tff(302,plain,
% 0.19/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_3, e_3)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(303,plain,
% 0.19/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_1))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[302, 301])).
% 0.19/0.47 tff(304,plain,
% 0.19/0.47 (~product(e_3, e_3, e_3)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[303, 14, 297, 287])).
% 0.19/0.47 tff(305,plain,
% 0.19/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_1)) | product(e_3, e_3, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_1)) | product(e_3, e_3, e_3))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(306,plain,
% 0.19/0.47 ((product(e_3, e_3, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_1))) <=> ((~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_1)) | product(e_3, e_3, e_3))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(307,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_1)) | product(e_3, e_3, e_3)))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[306])).
% 0.19/0.48 tff(308,plain,
% 0.19/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_1)) | product(e_3, e_3, e_3))),
% 0.19/0.48 inference(transitivity,[status(thm)],[307, 305])).
% 0.19/0.48 tff(309,plain,
% 0.19/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_1)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(310,plain,
% 0.19/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_1)) | product(e_3, e_3, e_3)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.19/0.48 tff(311,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[310, 14, 245, 287, 304])).
% 0.19/0.48 % SZS output end Proof
% 0.19/0.48 % E exiting
%------------------------------------------------------------------------------