%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP134-2.003 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:07:13 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP134-2.003 : TPTP v9.0.0. Released v1.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.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 15:45:19 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.39 % SZS status Unsatisfiable
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(product_type, type, (
% 0.19/0.39 product: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(e_1_type, type, (
% 0.19/0.39 e_1: $i)).
% 0.19/0.39 tff(e_3_type, type, (
% 0.19/0.39 e_3: $i)).
% 0.19/0.39 tff(e_2_type, type, (
% 0.19/0.39 e_2: $i)).
% 0.19/0.39 tff(next_type, type, (
% 0.19/0.39 next: ( $i * $i ) > $o)).
% 0.19/0.39 tff(greater_type, type, (
% 0.19/0.39 greater: ( $i * $i ) > $o)).
% 0.19/0.39 tff(group_element_type, type, (
% 0.19/0.39 group_element: $i > $o)).
% 0.19/0.39 tff(equalish_type, type, (
% 0.19/0.39 equalish: ( $i * $i ) > $o)).
% 0.19/0.39 tff(1,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.19/0.39 tff(2,assumption,(~product(e_1, e_1, e_1)), introduced(assumption)).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (^[Y: $i, X: $i, X1: $i] : refl(((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y))) <=> ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y))) <=> ![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y))) <=> ![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 (^[Y: $i, X: $i, X1: $i] : trans(monotonicity(rewrite(((~product(X, e_1, Y)) | (~next(X, X1))) <=> ((~next(X, X1)) | (~product(X, e_1, Y)))), ((((~product(X, e_1, Y)) | (~next(X, X1))) | (~greater(Y, X1))) <=> (((~next(X, X1)) | (~product(X, e_1, Y))) | (~greater(Y, X1))))), rewrite((((~next(X, X1)) | (~product(X, e_1, Y))) | (~greater(Y, X1))) <=> ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))), ((((~product(X, e_1, Y)) | (~next(X, X1))) | (~greater(Y, X1))) <=> ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (![Y: $i, X: $i, X1: $i] : (((~product(X, e_1, Y)) | (~next(X, X1))) | (~greater(Y, X1))) <=> ![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.39 tff(8,axiom,(![Y: $i, X: $i, X1: $i] : (((~product(X, e_1, Y)) | (~next(X, X1))) | (~greater(Y, X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','no_redundancy')).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.19/0.39 tff(11,plain,(
% 0.19/0.39 ![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[10])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (greater(e_3, e_2) <=> greater(e_3, e_2)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(14,axiom,(greater(e_3, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_greater_e_2')).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (greater(e_3, e_2)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (next(e_1, e_2) <=> next(e_1, e_2)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(17,axiom,(next(e_1, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_then_e_2')).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 (next(e_1, e_2)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_3, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_3, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_3, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_3, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (~product(e_1, e_1, e_3)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[21, 18, 15, 12])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (^[Y: $i, X: $i] : refl((product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) <=> (product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> ((product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_2)))), rewrite(((product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_2)) <=> (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ((product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_3)))), rewrite(((product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_3)) <=> (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.39 tff(28,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')).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.19/0.39 tff(31,plain,(
% 0.19/0.39 ![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[30])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (group_element(e_1) <=> group_element(e_1)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(34,axiom,(group_element(e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_1')).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 (group_element(e_1)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 ((product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_1))) <=> (product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[37])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))),
% 0.19/0.39 inference(transitivity,[status(thm)],[38, 36])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_1)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (product(e_1, e_1, e_2) | product(e_1, e_1, e_1)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[41, 35, 32, 22])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 (product(e_1, e_1, e_2)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[42, 2])).
% 0.19/0.39 tff(44,assumption,(product(e_1, e_3, e_2)), introduced(assumption)).
% 0.19/0.39 tff(45,assumption,(product(e_1, e_1, e_2)), introduced(assumption)).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 (^[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))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[46])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(49,plain,
% 0.19/0.40 (^[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)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[49])).
% 0.19/0.40 tff(51,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')).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.19/0.40 tff(54,plain,(
% 0.19/0.40 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[53])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(57,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 (~equalish(e_3, e_1)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 (((~![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_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_3, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 ((~![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_2)) | (~product(e_1, e_3, e_2)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_3, e_2))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[61, 58, 55, 45, 44])).
% 0.19/0.40 tff(63,plain,((~product(e_1, e_3, e_2)) | (~product(e_1, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (~product(e_1, e_3, e_2)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[63, 43])).
% 0.19/0.40 tff(65,assumption,(product(e_1, e_3, e_3)), introduced(assumption)).
% 0.19/0.40 tff(66,assumption,(product(e_3, e_1, e_1)), introduced(assumption)).
% 0.19/0.40 tff(67,assumption,(product(e_3, e_3, e_1)), introduced(assumption)).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl(((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))) <=> ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[68])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : rewrite((((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, Y)) <=> ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, Y)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[71])).
% 0.19/0.40 tff(73,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qg4')).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.19/0.40 tff(76,plain,(
% 0.19/0.40 ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[75])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_3) | (~product(e_3, e_3, e_1)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 (((~product(e_3, e_3, e_1)) | product(e_1, e_1, e_3) | (~product(e_3, e_3, e_1))) <=> (product(e_1, e_1, e_3) | (~product(e_3, e_3, e_1)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_1)) | product(e_1, e_1, e_3) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_3, e_3, e_1))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[79])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_1)) | product(e_1, e_1, e_3) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_3) | (~product(e_3, e_3, e_1)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[80, 78])).
% 0.19/0.40 tff(82,plain,
% 0.19/0.40 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_1)) | product(e_1, e_1, e_3) | (~product(e_3, e_3, e_1)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_3) | (~product(e_3, e_3, e_1))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.19/0.40 tff(84,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[83, 77, 22, 67])).
% 0.19/0.40 tff(85,plain,(~product(e_3, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(86,plain,
% 0.19/0.40 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 (((~product(e_1, e_3, 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_1, e_3, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(88,plain,
% 0.19/0.40 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_3)) | product(e_3, e_3, e_1) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_3))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[87])).
% 0.19/0.40 tff(89,plain,
% 0.19/0.40 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_3)) | product(e_3, e_3, e_1) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[88, 86])).
% 0.19/0.40 tff(90,plain,
% 0.19/0.40 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_3)) | product(e_3, e_3, e_1) | (~product(e_3, e_1, e_3)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(91,plain,
% 0.19/0.40 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_1, e_3))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.19/0.40 tff(92,plain,
% 0.19/0.40 (~product(e_3, e_1, e_3)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[91, 77, 85, 65])).
% 0.19/0.40 tff(93,plain,
% 0.19/0.40 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_3)) | product(e_3, e_1, e_3) | (~product(e_3, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_3)) | product(e_3, e_1, e_3) | (~product(e_3, e_1, e_1)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(94,plain,
% 0.19/0.40 (((~product(e_3, e_1, e_1)) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_3))) <=> ((~product(e_1, e_3, e_3)) | product(e_3, e_1, e_3) | (~product(e_3, e_1, e_1)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(95,plain,
% 0.19/0.40 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_1)) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_3)) | product(e_3, e_1, e_3) | (~product(e_3, e_1, e_1))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[94])).
% 0.19/0.40 tff(96,plain,
% 0.19/0.40 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_1)) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_3)) | product(e_3, e_1, e_3) | (~product(e_3, e_1, e_1)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[95, 93])).
% 0.19/0.40 tff(97,plain,
% 0.19/0.40 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_1)) | product(e_3, e_1, e_3) | (~product(e_1, e_3, e_3)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(98,plain,
% 0.19/0.40 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_3)) | product(e_3, e_1, e_3) | (~product(e_3, e_1, e_1))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.19/0.40 tff(99,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[98, 77, 65, 92, 66])).
% 0.19/0.40 tff(100,plain,((~product(e_3, e_1, e_1)) | (~product(e_1, e_3, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(101,plain,
% 0.19/0.40 (~product(e_3, e_1, e_1)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[100, 65])).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 (group_element(e_3) <=> group_element(e_3)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(103,axiom,(group_element(e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_3')).
% 0.19/0.41 tff(104,plain,
% 0.19/0.41 (group_element(e_3)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.19/0.41 tff(105,plain,
% 0.19/0.41 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(106,plain,
% 0.19/0.41 ((product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3))) <=> ((~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(107,plain,
% 0.19/0.41 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[106])).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1))),
% 0.19/0.41 inference(transitivity,[status(thm)],[107, 105])).
% 0.19/0.41 tff(109,plain,
% 0.19/0.41 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(110,plain,
% 0.19/0.41 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.19/0.41 tff(111,plain,
% 0.19/0.41 (product(e_3, e_1, e_2) | product(e_3, e_1, e_1)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[110, 35, 104, 32, 92])).
% 0.19/0.41 tff(112,plain,
% 0.19/0.41 (product(e_3, e_1, e_2)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[111, 101])).
% 0.19/0.41 tff(113,assumption,(product(e_3, e_3, e_3)), introduced(assumption)).
% 0.19/0.41 tff(114,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(115,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[114])).
% 0.19/0.41 tff(116,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(117,plain,
% 0.19/0.41 (^[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)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(118,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[117])).
% 0.19/0.41 tff(119,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')).
% 0.19/0.41 tff(120,plain,
% 0.19/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.19/0.41 tff(121,plain,
% 0.19/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[120, 116])).
% 0.19/0.41 tff(122,plain,(
% 0.19/0.41 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[121])).
% 0.19/0.41 tff(123,plain,
% 0.19/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[122, 115])).
% 0.19/0.41 tff(124,plain,
% 0.19/0.41 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(125,plain,
% 0.19/0.41 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(126,plain,
% 0.19/0.41 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.19/0.41 tff(127,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[126, 58, 123, 113, 65])).
% 0.19/0.41 tff(128,plain,((~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(129,plain,
% 0.19/0.41 (~product(e_3, e_3, e_3)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[128, 65])).
% 0.19/0.41 tff(130,plain,
% 0.19/0.41 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_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] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(131,plain,
% 0.19/0.41 ((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_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(132,plain,
% 0.19/0.41 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_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)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[131])).
% 0.19/0.42 tff(133,plain,
% 0.19/0.42 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_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)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[132, 130])).
% 0.19/0.42 tff(134,plain,
% 0.19/0.42 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_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)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(135,plain,
% 0.19/0.42 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.19/0.42 tff(136,plain,
% 0.19/0.42 (product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[135, 104, 32])).
% 0.19/0.42 tff(137,plain,
% 0.19/0.42 (product(e_3, e_3, e_3) | product(e_3, e_3, e_2)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[136, 85])).
% 0.19/0.42 tff(138,plain,
% 0.19/0.42 (product(e_3, e_3, e_2)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[137, 129])).
% 0.19/0.42 tff(139,plain,
% 0.19/0.42 (((~![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_3, e_2)) | (~product(e_3, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(140,plain,
% 0.19/0.42 ((equalish(e_3, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_3, e_2))) <=> (equalish(e_3, e_1) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(141,plain,
% 0.19/0.42 (((~![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_2)) | (~product(e_3, 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_3, e_1) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_1, e_2))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[140])).
% 0.19/0.42 tff(142,plain,
% 0.19/0.42 (((~![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_2)) | (~product(e_3, 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_3, e_1) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[141, 139])).
% 0.19/0.42 tff(143,plain,
% 0.19/0.42 ((~![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_2)) | (~product(e_3, e_3, e_2)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(144,plain,
% 0.19/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_1, e_2))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.19/0.42 tff(145,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[144, 58, 55, 138, 112])).
% 0.19/0.42 tff(146,plain,(~product(e_1, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(147,plain,
% 0.19/0.42 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(148,plain,
% 0.19/0.42 ((product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_1))) <=> ((~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(149,plain,
% 0.19/0.42 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[148])).
% 0.19/0.42 tff(150,plain,
% 0.19/0.42 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1))),
% 0.19/0.42 inference(transitivity,[status(thm)],[149, 147])).
% 0.19/0.42 tff(151,plain,
% 0.19/0.42 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_1)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(152,plain,
% 0.19/0.42 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.19/0.42 tff(153,plain,
% 0.19/0.42 (product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[152, 35, 104, 32])).
% 0.19/0.42 tff(154,plain,
% 0.19/0.42 (product(e_1, e_3, e_2) | product(e_1, e_3, e_1)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[153, 146])).
% 0.19/0.42 tff(155,plain,
% 0.19/0.42 (product(e_1, e_3, e_1)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[154, 64])).
% 0.19/0.42 tff(156,plain,
% 0.19/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(157,plain,
% 0.19/0.42 (((~product(e_1, e_3, e_1)) | product(e_1, e_1, e_1) | (~product(e_3, e_1, e_1))) <=> (product(e_1, e_1, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(158,plain,
% 0.19/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_1)) | product(e_1, e_1, e_1) | (~product(e_3, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_1))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[157])).
% 0.19/0.42 tff(159,plain,
% 0.19/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_1)) | product(e_1, e_1, e_1) | (~product(e_3, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[158, 156])).
% 0.19/0.42 tff(160,plain,
% 0.19/0.42 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_1)) | product(e_1, e_1, e_1) | (~product(e_3, e_1, e_1)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(161,plain,
% 0.19/0.42 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_1))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.19/0.42 tff(162,plain,
% 0.19/0.42 (~product(e_3, e_1, e_1)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[161, 77, 2, 155])).
% 0.19/0.42 tff(163,plain,
% 0.19/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_3)) | product(e_3, e_1, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_3)) | product(e_3, e_1, e_1))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(164,plain,
% 0.19/0.42 (((~product(e_1, e_3, e_1)) | product(e_3, e_1, e_1) | (~product(e_3, e_1, e_3))) <=> ((~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_3)) | product(e_3, e_1, e_1))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(165,plain,
% 0.19/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_1)) | product(e_3, e_1, e_1) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_3)) | product(e_3, e_1, e_1)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[164])).
% 0.19/0.42 tff(166,plain,
% 0.19/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_1)) | product(e_3, e_1, e_1) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_3)) | product(e_3, e_1, e_1))),
% 0.19/0.42 inference(transitivity,[status(thm)],[165, 163])).
% 0.19/0.42 tff(167,plain,
% 0.19/0.42 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_1)) | product(e_3, e_1, e_1) | (~product(e_3, e_1, e_3)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(168,plain,
% 0.19/0.42 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_3)) | product(e_3, e_1, e_1)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.19/0.42 tff(169,plain,
% 0.19/0.42 (~product(e_3, e_1, e_3)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[168, 77, 155, 162])).
% 0.19/0.42 tff(170,plain,
% 0.19/0.42 (product(e_3, e_1, e_2)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[110, 35, 104, 32, 162, 169])).
% 0.19/0.42 tff(171,plain,
% 0.19/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_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_1) | (~product(e_1, e_1, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(172,plain,
% 0.19/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(173,plain,
% 0.19/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_3, e_1, e_2))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.19/0.43 tff(174,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[173, 58, 123, 43, 170])).
% 0.19/0.43 tff(175,plain,(product(e_1, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(176,plain,
% 0.19/0.43 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(177,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.19/0.43 tff(178,plain,
% 0.19/0.43 (~equalish(e_2, e_1)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.19/0.43 tff(179,plain,
% 0.19/0.43 (((~![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_1)) | (~product(e_2, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(180,plain,
% 0.19/0.43 ((~![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_1)) | (~product(e_2, e_1, e_1)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(181,plain,
% 0.19/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.19/0.43 tff(182,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[181, 178, 123, 175, 1])).
% 0.19/0.43 tff(183,plain,(~product(e_2, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(184,assumption,(product(e_1, e_2, e_2)), introduced(assumption)).
% 0.19/0.43 tff(185,assumption,(product(e_1, e_3, e_1)), introduced(assumption)).
% 0.19/0.43 tff(186,assumption,(product(e_1, e_1, e_1)), introduced(assumption)).
% 0.19/0.43 tff(187,plain,
% 0.19/0.43 (((~![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_3, e_1)) | (~product(e_1, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(188,plain,
% 0.19/0.43 ((equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1))) <=> (equalish(e_3, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(189,plain,
% 0.19/0.43 (((~![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_3, e_1)) | (~product(e_1, e_1, e_1))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[188])).
% 0.19/0.43 tff(190,plain,
% 0.19/0.43 (((~![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_3, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[189, 187])).
% 0.19/0.43 tff(191,plain,
% 0.19/0.43 ((~![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)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(192,plain,
% 0.19/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_1, e_1))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.19/0.43 tff(193,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[192, 58, 55, 186, 185])).
% 0.19/0.43 tff(194,plain,((~product(e_1, e_3, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(195,plain,
% 0.19/0.43 (~product(e_1, e_3, e_1)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[194, 175])).
% 0.19/0.43 tff(196,plain,
% 0.19/0.43 (product(e_1, e_3, e_2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[154, 195])).
% 0.19/0.43 tff(197,plain,
% 0.19/0.43 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(198,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.19/0.43 tff(199,plain,
% 0.19/0.43 (~equalish(e_2, e_3)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.19/0.43 tff(200,plain,
% 0.19/0.43 (((~![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_3, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(201,plain,
% 0.19/0.43 ((~![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)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(202,plain,
% 0.19/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_2, e_2))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.19/0.43 tff(203,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[202, 199, 55, 196, 184])).
% 0.19/0.43 tff(204,plain,(~product(e_1, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(205,assumption,(product(e_1, e_2, e_1)), introduced(assumption)).
% 0.19/0.43 tff(206,plain,
% 0.19/0.43 (((~![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)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(207,plain,
% 0.19/0.43 ((~![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)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(208,plain,
% 0.19/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.19/0.43 tff(209,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[208, 178, 55, 186, 205])).
% 0.19/0.43 tff(210,plain,((~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(211,plain,
% 0.19/0.43 (~product(e_1, e_2, e_1)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[210, 175])).
% 0.19/0.43 tff(212,plain,
% 0.19/0.43 (group_element(e_2) <=> group_element(e_2)),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(213,axiom,(group_element(e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_2')).
% 0.19/0.43 tff(214,plain,
% 0.19/0.43 (group_element(e_2)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.19/0.43 tff(215,plain,
% 0.19/0.43 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | product(e_1, e_2, e_3))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | product(e_1, e_2, e_3))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(216,plain,
% 0.19/0.43 ((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_1)) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | product(e_1, e_2, e_3))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(217,plain,
% 0.19/0.44 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | product(e_1, e_2, e_3)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[216])).
% 0.19/0.44 tff(218,plain,
% 0.19/0.44 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | product(e_1, e_2, e_3))),
% 0.19/0.44 inference(transitivity,[status(thm)],[217, 215])).
% 0.19/0.44 tff(219,plain,
% 0.19/0.44 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(220,plain,
% 0.19/0.44 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | product(e_1, e_2, e_3)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.19/0.44 tff(221,plain,
% 0.19/0.44 (product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | product(e_1, e_2, e_3)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[220, 35, 214, 32])).
% 0.19/0.44 tff(222,plain,
% 0.19/0.44 (product(e_1, e_2, e_2) | product(e_1, e_2, e_3)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[221, 211])).
% 0.19/0.44 tff(223,plain,
% 0.19/0.44 (product(e_1, e_2, e_3)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[222, 204])).
% 0.19/0.44 tff(224,plain,
% 0.19/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(225,plain,
% 0.19/0.44 (((~product(e_1, e_2, e_3)) | product(e_3, e_3, e_1) | (~product(e_2, e_1, e_3))) <=> (product(e_3, e_3, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(226,plain,
% 0.19/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_3, e_3, e_1) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_3))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[225])).
% 0.19/0.44 tff(227,plain,
% 0.19/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_3, e_3, e_1) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[226, 224])).
% 0.19/0.44 tff(228,plain,
% 0.19/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_3, e_3, e_1) | (~product(e_2, e_1, e_3)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(229,plain,
% 0.19/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_3))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.19/0.44 tff(230,plain,
% 0.19/0.44 (~product(e_2, e_1, e_3)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[229, 77, 85, 223])).
% 0.19/0.44 tff(231,plain,
% 0.19/0.44 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(232,plain,
% 0.19/0.44 ((product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2))) <=> ((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(233,plain,
% 0.19/0.44 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[232])).
% 0.19/0.44 tff(234,plain,
% 0.19/0.44 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3))),
% 0.19/0.44 inference(transitivity,[status(thm)],[233, 231])).
% 0.19/0.44 tff(235,plain,
% 0.19/0.44 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(236,plain,
% 0.19/0.44 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.19/0.44 tff(237,plain,
% 0.19/0.44 (product(e_2, e_1, e_1) | product(e_2, e_1, e_2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[236, 35, 214, 32, 230])).
% 0.19/0.44 tff(238,plain,
% 0.19/0.44 (product(e_2, e_1, e_2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[237, 183])).
% 0.19/0.44 tff(239,assumption,(product(e_3, e_1, e_2)), introduced(assumption)).
% 0.19/0.44 tff(240,assumption,(product(e_2, e_1, e_2)), introduced(assumption)).
% 0.19/0.44 tff(241,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_2, e_3) | (~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_2, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(242,plain,
% 0.19/0.44 ((equalish(e_2, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_2))) <=> (equalish(e_2, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(243,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_2, e_3) | (~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_2, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_1, e_2))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[242])).
% 0.19/0.44 tff(244,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_2, e_3) | (~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_2, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[243, 241])).
% 0.19/0.44 tff(245,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_2, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(246,plain,
% 0.19/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_1, e_2))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.19/0.44 tff(247,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[246, 199, 123, 240, 239])).
% 0.19/0.44 tff(248,plain,((~product(e_2, e_1, e_2)) | (~product(e_3, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(249,plain,
% 0.19/0.44 (~product(e_3, e_1, e_2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[248, 238])).
% 0.19/0.44 tff(250,assumption,(product(e_3, e_1, e_3)), introduced(assumption)).
% 0.19/0.44 tff(251,assumption,(product(e_3, e_3, e_2)), introduced(assumption)).
% 0.19/0.44 tff(252,plain,
% 0.19/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_2)) | product(e_2, e_2, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_2)) | product(e_2, e_2, e_3))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(253,plain,
% 0.19/0.44 (((~product(e_3, e_3, e_2)) | product(e_2, e_2, e_3) | (~product(e_3, e_3, e_2))) <=> ((~product(e_3, e_3, e_2)) | product(e_2, e_2, e_3))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(254,plain,
% 0.19/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_2)) | product(e_2, e_2, e_3) | (~product(e_3, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_2)) | product(e_2, e_2, e_3)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[253])).
% 0.19/0.44 tff(255,plain,
% 0.19/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_2)) | product(e_2, e_2, e_3) | (~product(e_3, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_2)) | product(e_2, e_2, e_3))),
% 0.19/0.44 inference(transitivity,[status(thm)],[254, 252])).
% 0.19/0.44 tff(256,plain,
% 0.19/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_2)) | product(e_2, e_2, e_3) | (~product(e_3, e_3, e_2)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(257,plain,
% 0.19/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_2)) | product(e_2, e_2, e_3)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.19/0.44 tff(258,plain,
% 0.19/0.44 ((~product(e_3, e_3, e_2)) | product(e_2, e_2, e_3)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[257, 77])).
% 0.19/0.45 tff(259,plain,
% 0.19/0.45 (product(e_2, e_2, e_3)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[258, 251])).
% 0.19/0.45 tff(260,assumption,(product(e_2, e_2, e_3)), introduced(assumption)).
% 0.19/0.45 tff(261,assumption,(product(e_2, e_2, e_1)), introduced(assumption)).
% 0.19/0.45 tff(262,plain,
% 0.19/0.45 (^[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))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(263,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[262])).
% 0.19/0.45 tff(264,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(265,plain,
% 0.19/0.45 (^[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)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(266,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[265])).
% 0.19/0.45 tff(267,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')).
% 0.19/0.45 tff(268,plain,
% 0.19/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.19/0.45 tff(269,plain,
% 0.19/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[268, 264])).
% 0.19/0.45 tff(270,plain,(
% 0.19/0.45 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[269])).
% 0.19/0.45 tff(271,plain,
% 0.19/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[270, 263])).
% 0.19/0.45 tff(272,plain,
% 0.19/0.45 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(273,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.19/0.45 tff(274,plain,
% 0.19/0.45 (~equalish(e_1, e_3)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.19/0.45 tff(275,plain,
% 0.19/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_1, e_3) | (~product(e_2, e_2, e_1)) | (~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_1, e_3) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_2, e_3)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(276,plain,
% 0.19/0.45 ((equalish(e_1, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_2, e_2, e_1))) <=> (equalish(e_1, e_3) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_2, e_3)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(277,plain,
% 0.19/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_1, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_2, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_1, e_3) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_2, e_3))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[276])).
% 0.19/0.45 tff(278,plain,
% 0.19/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_1, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_2, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_1, e_3) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_2, e_3)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[277, 275])).
% 0.19/0.45 tff(279,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_1, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_2, e_2, e_1)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(280,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_1, e_3) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_2, e_3))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.19/0.45 tff(281,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[280, 274, 271, 261, 260])).
% 0.19/0.45 tff(282,plain,((~product(e_2, e_2, e_1)) | (~product(e_2, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(283,plain,
% 0.19/0.45 (~product(e_2, e_2, e_1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[282, 259])).
% 0.19/0.45 tff(284,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_2)) | product(e_2, e_2, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_2, e_2, e_1))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(285,plain,
% 0.19/0.45 (((~product(e_1, e_1, e_2)) | product(e_2, e_2, e_1) | (~product(e_1, e_1, e_2))) <=> ((~product(e_1, e_1, e_2)) | product(e_2, e_2, e_1))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(286,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_2)) | product(e_2, e_2, e_1) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_2)) | product(e_2, e_2, e_1)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[285])).
% 0.19/0.45 tff(287,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_2)) | product(e_2, e_2, e_1) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_2, e_2, e_1))),
% 0.19/0.45 inference(transitivity,[status(thm)],[286, 284])).
% 0.19/0.45 tff(288,plain,
% 0.19/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_2)) | product(e_2, e_2, e_1) | (~product(e_1, e_1, e_2)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(289,plain,
% 0.19/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_2, e_2, e_1)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[288, 287])).
% 0.19/0.45 tff(290,plain,
% 0.19/0.45 ((~product(e_1, e_1, e_2)) | product(e_2, e_2, e_1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[289, 77])).
% 0.19/0.45 tff(291,plain,
% 0.19/0.45 (~product(e_1, e_1, e_2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[290, 283])).
% 0.19/0.45 tff(292,plain,
% 0.19/0.45 (product(e_1, e_1, e_1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[42, 291])).
% 0.19/0.45 tff(293,plain,
% 0.19/0.45 (~product(e_1, e_3, e_1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[194, 292])).
% 0.19/0.45 tff(294,plain,
% 0.19/0.45 (product(e_1, e_3, e_2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[154, 293])).
% 0.19/0.45 tff(295,plain,
% 0.19/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_3, e_2)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(296,plain,
% 0.19/0.45 ((equalish(e_1, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_3, e_2))) <=> (equalish(e_1, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_3, e_2)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(297,plain,
% 0.19/0.45 (((~![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_3, e_2)) | (~product(e_1, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_3, e_2))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[296])).
% 0.19/0.45 tff(298,plain,
% 0.19/0.45 (((~![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_3, e_2)) | (~product(e_1, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_3, e_2)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[297, 295])).
% 0.19/0.45 tff(299,plain,
% 0.19/0.45 ((~![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_3, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(300,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_3, e_2))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[299, 298])).
% 0.19/0.45 tff(301,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[300, 274, 123, 251, 294])).
% 0.19/0.45 tff(302,plain,(~product(e_3, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(303,plain,
% 0.19/0.45 (product(e_3, e_3, e_3)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[137, 302])).
% 0.19/0.45 tff(304,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_1, e_3) | (~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_1, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(305,plain,
% 0.19/0.45 ((equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3))) <=> (equalish(e_1, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(306,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_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_3))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[305])).
% 0.19/0.45 tff(307,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_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[306, 304])).
% 0.19/0.45 tff(308,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_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(309,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_3))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[308, 307])).
% 0.19/0.45 tff(310,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[309, 274, 55, 303, 250])).
% 0.19/0.45 tff(311,plain,(~product(e_3, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(312,plain,
% 0.19/0.45 (product(e_3, e_1, e_2) | product(e_3, e_1, e_1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[110, 35, 104, 32, 311])).
% 0.19/0.45 tff(313,plain,
% 0.19/0.45 (product(e_3, e_1, e_1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[312, 249])).
% 0.19/0.45 tff(314,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_2)) | product(e_2, e_1, e_3) | (~product(e_3, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_2)) | product(e_2, e_1, e_3) | (~product(e_3, e_1, e_1)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(315,plain,
% 0.19/0.45 (((~product(e_3, e_1, e_1)) | product(e_2, e_1, e_3) | (~product(e_1, e_3, e_2))) <=> ((~product(e_1, e_3, e_2)) | product(e_2, e_1, e_3) | (~product(e_3, e_1, e_1)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(316,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_1)) | product(e_2, e_1, e_3) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_2)) | product(e_2, e_1, e_3) | (~product(e_3, e_1, e_1))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[315])).
% 0.19/0.45 tff(317,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_1)) | product(e_2, e_1, e_3) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_2)) | product(e_2, e_1, e_3) | (~product(e_3, e_1, e_1)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[316, 314])).
% 0.19/0.45 tff(318,plain,
% 0.19/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_1)) | product(e_2, e_1, e_3) | (~product(e_1, e_3, e_2)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(319,plain,
% 0.19/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_2)) | product(e_2, e_1, e_3) | (~product(e_3, e_1, e_1))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[318, 317])).
% 0.19/0.45 tff(320,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[319, 77, 196, 230, 313])).
% 0.19/0.45 % SZS output end Proof
% 0.19/0.45 % E exiting
%------------------------------------------------------------------------------