%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP132-1.002 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:07:12 AM UTC 2025
% Result : Unsatisfiable 0.13s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP132-1.002 : TPTP v9.0.0. Released v1.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 15:44:11 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.38 % SZS status Unsatisfiable
% 0.13/0.38 % SZS output start Proof
% 0.13/0.38 tff(product_type, type, (
% 0.13/0.38 product: ( $i * $i * $i ) > $o)).
% 0.13/0.38 tff(e_1_type, type, (
% 0.13/0.38 e_1: $i)).
% 0.13/0.38 tff(e_2_type, type, (
% 0.13/0.38 e_2: $i)).
% 0.13/0.38 tff(equalish_type, type, (
% 0.13/0.38 equalish: ( $i * $i ) > $o)).
% 0.13/0.38 tff(group_element_type, type, (
% 0.13/0.38 group_element: $i > $o)).
% 0.13/0.38 tff(1,assumption,(product(e_2, e_1, e_2)), introduced(assumption)).
% 0.13/0.38 tff(2,assumption,(product(e_1, e_2, e_1)), introduced(assumption)).
% 0.13/0.38 tff(3,plain,
% 0.13/0.38 (^[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))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(4,plain,
% 0.13/0.38 (![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)))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.13/0.38 tff(5,plain,
% 0.13/0.38 (![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)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(6,plain,
% 0.13/0.38 (^[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)))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(7,plain,
% 0.13/0.38 (![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)))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[6])).
% 0.13/0.38 tff(8,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')).
% 0.13/0.38 tff(9,plain,
% 0.13/0.38 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.13/0.38 tff(10,plain,
% 0.13/0.38 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.13/0.38 tff(11,plain,(
% 0.13/0.38 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.13/0.38 inference(skolemize,[status(sab)],[10])).
% 0.13/0.38 tff(12,plain,
% 0.13/0.38 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.13/0.38 tff(13,plain,
% 0.13/0.38 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(14,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.13/0.38 tff(15,plain,
% 0.13/0.38 (~equalish(e_2, e_1)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.13/0.38 tff(16,plain,
% 0.13/0.38 (((~![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_2, e_1)) | (~product(e_1, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(17,plain,
% 0.13/0.38 ((equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1))) <=> (equalish(e_2, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(18,plain,
% 0.13/0.38 (((~![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_2, e_1)) | (~product(e_1, e_1, e_1))))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[17])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (((~![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_2, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.13/0.39 inference(transitivity,[status(thm)],[18, 16])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 ((~![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)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 ((~![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_2, e_1)) | (~product(e_1, e_1, e_1))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 ((~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_1))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[21, 15, 12])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 (~product(e_1, e_1, e_1)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[22, 2])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 (^[Y: $i, X: $i] : refl((product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 (![Y: $i, X: $i] : (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[24])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 (![Y: $i, X: $i] : (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (^[Y: $i, X: $i] : 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)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (![Y: $i, X: $i] : ((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> ![Y: $i, X: $i] : (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[27])).
% 0.13/0.39 tff(29,axiom,(![Y: $i, X: $i] : ((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_total_function1')).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 (![Y: $i, X: $i] : (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 (![Y: $i, X: $i] : (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.13/0.39 tff(32,plain,(
% 0.13/0.39 ![Y: $i, X: $i] : (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[31])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 (![Y: $i, X: $i] : (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 (group_element(e_1) <=> group_element(e_1)),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(35,axiom,(group_element(e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_1')).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 (group_element(e_1)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.13/0.39 tff(37,plain,
% 0.13/0.39 (((~![Y: $i, X: $i] : (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | product(e_1, e_1, e_1) | product(e_1, e_1, e_2))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | product(e_1, e_1, e_1) | product(e_1, e_1, e_2))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(38,plain,
% 0.13/0.39 ((product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_1))) <=> ((~group_element(e_1)) | product(e_1, e_1, e_1) | product(e_1, e_1, e_2))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(39,plain,
% 0.13/0.39 (((~![Y: $i, X: $i] : (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (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_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | product(e_1, e_1, e_1) | product(e_1, e_1, e_2)))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[38])).
% 0.13/0.39 tff(40,plain,
% 0.13/0.39 (((~![Y: $i, X: $i] : (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (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_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | product(e_1, e_1, e_1) | product(e_1, e_1, e_2))),
% 0.13/0.39 inference(transitivity,[status(thm)],[39, 37])).
% 0.13/0.39 tff(41,plain,
% 0.13/0.39 ((~![Y: $i, X: $i] : (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_1)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(42,plain,
% 0.13/0.39 ((~![Y: $i, X: $i] : (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | product(e_1, e_1, e_1) | product(e_1, e_1, e_2)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.13/0.39 tff(43,plain,
% 0.13/0.39 (product(e_1, e_1, e_2)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[42, 36, 33, 23])).
% 0.13/0.39 tff(44,plain,
% 0.13/0.39 (^[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))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(45,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[44])).
% 0.13/0.39 tff(46,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(47,plain,
% 0.13/0.39 (^[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)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(48,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[47])).
% 0.13/0.39 tff(49,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')).
% 0.13/0.39 tff(50,plain,
% 0.13/0.39 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.13/0.39 tff(51,plain,
% 0.13/0.39 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.13/0.39 tff(52,plain,(
% 0.13/0.39 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[51])).
% 0.13/0.39 tff(53,plain,
% 0.13/0.39 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.13/0.39 tff(54,plain,
% 0.13/0.39 (((~![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_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_1) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(55,plain,
% 0.13/0.39 ((~![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_2)) | (~product(e_2, e_1, e_2)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(56,plain,
% 0.13/0.39 ((~![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_2)) | (~product(e_2, e_1, e_2))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.13/0.39 tff(57,plain,
% 0.13/0.39 ((~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_2))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[56, 15, 53])).
% 0.13/0.39 tff(58,plain,
% 0.13/0.39 (~product(e_2, e_1, e_2)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[57, 43])).
% 0.13/0.39 tff(59,plain,
% 0.13/0.39 (^[Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : refl(((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2)) <=> ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(60,plain,
% 0.13/0.39 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2)) <=> ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[59])).
% 0.13/0.39 tff(61,plain,
% 0.13/0.39 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2)) <=> ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(62,plain,
% 0.13/0.39 (^[Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) <=> ((~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))), (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) <=> (((~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | (~product(Z2, X2, Y2))))), rewrite((((~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | (~product(Z2, X2, Y2))) <=> ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))), (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) <=> ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))))), ((((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) | equalish(Y1, Y2)) <=> (((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | equalish(Y1, Y2)))), rewrite((((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | equalish(Y1, Y2)) <=> ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))), ((((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) | equalish(Y1, Y2)) <=> ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(63,plain,
% 0.13/0.40 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) | equalish(Y1, Y2)) <=> ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[62])).
% 0.13/0.40 tff(64,axiom,(![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) | equalish(Y1, Y2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qg2_2')).
% 0.13/0.40 tff(65,plain,
% 0.13/0.40 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.13/0.40 tff(66,plain,
% 0.13/0.40 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.13/0.40 tff(67,plain,(
% 0.13/0.40 ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.13/0.40 inference(skolemize,[status(sab)],[66])).
% 0.13/0.40 tff(68,plain,
% 0.13/0.40 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.13/0.40 tff(69,plain,
% 0.13/0.40 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(70,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.13/0.40 tff(71,plain,
% 0.13/0.40 (~equalish(e_1, e_2)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.13/0.40 tff(72,plain,
% 0.13/0.40 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_1, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(73,plain,
% 0.13/0.40 (((~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_1)) | equalish(e_1, e_2)) <=> (equalish(e_1, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(74,plain,
% 0.13/0.40 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_1)) | equalish(e_1, e_2))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_1, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[73])).
% 0.13/0.40 tff(75,plain,
% 0.13/0.40 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_1)) | equalish(e_1, e_2))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2)))),
% 0.13/0.40 inference(transitivity,[status(thm)],[74, 72])).
% 0.13/0.40 tff(76,plain,
% 0.13/0.40 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_1)) | equalish(e_1, e_2))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(77,plain,
% 0.13/0.40 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.13/0.40 tff(78,plain,
% 0.13/0.40 (~product(e_2, e_1, e_1)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[77, 71, 68, 2, 43])).
% 0.13/0.40 tff(79,plain,
% 0.13/0.40 (group_element(e_2) <=> group_element(e_2)),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(80,axiom,(group_element(e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_2')).
% 0.13/0.40 tff(81,plain,
% 0.13/0.40 (group_element(e_2)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.13/0.40 tff(82,plain,
% 0.13/0.40 (((~![Y: $i, X: $i] : (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(83,plain,
% 0.13/0.40 ((product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2))) <=> ((~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(84,plain,
% 0.13/0.40 (((~![Y: $i, X: $i] : (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (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_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2)))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[83])).
% 0.13/0.40 tff(85,plain,
% 0.13/0.40 (((~![Y: $i, X: $i] : (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (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_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2))),
% 0.13/0.40 inference(transitivity,[status(thm)],[84, 82])).
% 0.13/0.40 tff(86,plain,
% 0.13/0.40 ((~![Y: $i, X: $i] : (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(87,plain,
% 0.13/0.40 ((~![Y: $i, X: $i] : (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.13/0.40 tff(88,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[87, 36, 81, 33, 78, 58])).
% 0.13/0.40 tff(89,plain,(~product(e_1, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(90,plain,
% 0.13/0.40 (((~![Y: $i, X: $i] : (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (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_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(91,plain,
% 0.13/0.40 ((~![Y: $i, X: $i] : (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(92,plain,
% 0.13/0.40 ((~![Y: $i, X: $i] : (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.13/0.40 tff(93,plain,
% 0.13/0.40 (product(e_1, e_2, e_2) | product(e_1, e_2, e_1)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[92, 36, 81, 33])).
% 0.13/0.40 tff(94,plain,
% 0.13/0.40 (product(e_1, e_2, e_2)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[93, 89])).
% 0.13/0.40 tff(95,plain,
% 0.13/0.40 (^[Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : refl((equalish(X1, X2) | (~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) <=> (equalish(X1, X2) | (~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(96,plain,
% 0.13/0.40 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (equalish(X1, X2) | (~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) <=> ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (equalish(X1, X2) | (~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[95])).
% 0.13/0.40 tff(97,plain,
% 0.13/0.40 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (equalish(X1, X2) | (~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) <=> ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (equalish(X1, X2) | (~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(98,plain,
% 0.13/0.40 (^[Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) <=> ((~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))), (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) <=> (((~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | (~product(Z2, X2, Y2))))), rewrite((((~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | (~product(Z2, X2, Y2))) <=> ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))), (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) <=> ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))))), ((((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) | equalish(X1, X2)) <=> (((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | equalish(X1, X2)))), rewrite((((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | equalish(X1, X2)) <=> (equalish(X1, X2) | (~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))), ((((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) | equalish(X1, X2)) <=> (equalish(X1, X2) | (~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(99,plain,
% 0.20/0.40 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) | equalish(X1, X2)) <=> ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (equalish(X1, X2) | (~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[98])).
% 0.20/0.40 tff(100,axiom,(![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) | equalish(X1, X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qg2_1')).
% 0.20/0.40 tff(101,plain,
% 0.20/0.40 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (equalish(X1, X2) | (~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.20/0.40 tff(102,plain,
% 0.20/0.40 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (equalish(X1, X2) | (~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.20/0.40 tff(103,plain,(
% 0.20/0.40 ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (equalish(X1, X2) | (~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[102])).
% 0.20/0.41 tff(104,plain,
% 0.20/0.41 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (equalish(X1, X2) | (~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.20/0.41 tff(105,plain,
% 0.20/0.41 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (equalish(X1, X2) | (~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))) | (equalish(e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (equalish(X1, X2) | (~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))) | equalish(e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(106,plain,
% 0.20/0.41 ((equalish(e_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_1, e_2))) <=> (equalish(e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(107,plain,
% 0.20/0.41 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (equalish(X1, X2) | (~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))) | (equalish(e_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (equalish(X1, X2) | (~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))) | (equalish(e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_2))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[106])).
% 0.20/0.41 tff(108,plain,
% 0.20/0.41 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (equalish(X1, X2) | (~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))) | (equalish(e_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (equalish(X1, X2) | (~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))) | equalish(e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[107, 105])).
% 0.20/0.41 tff(109,plain,
% 0.20/0.41 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (equalish(X1, X2) | (~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))) | (equalish(e_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(110,plain,
% 0.20/0.41 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (equalish(X1, X2) | (~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))) | equalish(e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_2))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.20/0.41 tff(111,plain,
% 0.20/0.41 ((~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_2))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[110, 15, 104])).
% 0.20/0.41 tff(112,plain,
% 0.20/0.41 ((~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_2))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[111, 94])).
% 0.20/0.41 tff(113,plain,
% 0.20/0.41 (~product(e_2, e_2, e_1)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[112, 1])).
% 0.20/0.41 tff(114,plain,
% 0.20/0.41 (((~![Y: $i, X: $i] : (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(115,plain,
% 0.20/0.41 ((product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_2))) <=> ((~group_element(e_2)) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(116,plain,
% 0.20/0.41 (((~![Y: $i, X: $i] : (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[115])).
% 0.20/0.41 tff(117,plain,
% 0.20/0.41 (((~![Y: $i, X: $i] : (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1))),
% 0.20/0.41 inference(transitivity,[status(thm)],[116, 114])).
% 0.20/0.41 tff(118,plain,
% 0.20/0.41 ((~![Y: $i, X: $i] : (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_2)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(119,plain,
% 0.20/0.41 ((~![Y: $i, X: $i] : (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.20/0.41 tff(120,plain,
% 0.20/0.41 (product(e_2, e_2, e_2)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[119, 81, 33, 113])).
% 0.20/0.41 tff(121,plain,
% 0.20/0.41 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (equalish(X1, X2) | (~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))) | (equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (equalish(X1, X2) | (~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))) | equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(122,plain,
% 0.20/0.41 ((equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2))) <=> (equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(123,plain,
% 0.20/0.41 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (equalish(X1, X2) | (~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (equalish(X1, X2) | (~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))) | (equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[122])).
% 0.20/0.41 tff(124,plain,
% 0.20/0.41 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (equalish(X1, X2) | (~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (equalish(X1, X2) | (~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))) | equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[123, 121])).
% 0.20/0.41 tff(125,plain,
% 0.20/0.41 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (equalish(X1, X2) | (~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(126,plain,
% 0.20/0.41 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (equalish(X1, X2) | (~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))) | equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.20/0.41 tff(127,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[126, 71, 104, 94, 120, 1])).
% 0.20/0.41 tff(128,plain,(~product(e_2, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(129,plain,
% 0.20/0.41 (product(e_2, e_1, e_1)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[87, 36, 81, 33, 128])).
% 0.20/0.41 tff(130,plain,
% 0.20/0.41 (((~![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_2, e_2, e_1)) | (~product(e_2, 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_2, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(131,plain,
% 0.20/0.41 ((equalish(e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_2, e_1))) <=> (equalish(e_2, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(132,plain,
% 0.20/0.41 (((~![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_2, e_1, e_1)) | (~product(e_2, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_1))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[131])).
% 0.20/0.42 tff(133,plain,
% 0.20/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[132, 130])).
% 0.20/0.42 tff(134,plain,
% 0.20/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_2, e_1)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(135,plain,
% 0.20/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_1))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.20/0.42 tff(136,plain,
% 0.20/0.42 ((~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_1))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[135, 15, 12])).
% 0.20/0.42 tff(137,plain,
% 0.20/0.42 (~product(e_2, e_2, e_1)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[136, 129])).
% 0.20/0.42 tff(138,plain,
% 0.20/0.42 (product(e_2, e_2, e_2)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[119, 81, 33, 137])).
% 0.20/0.42 tff(139,plain,
% 0.20/0.42 (((~![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)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(140,plain,
% 0.20/0.42 ((~![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)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(141,plain,
% 0.20/0.42 ((~![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))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.20/0.42 tff(142,plain,
% 0.20/0.42 ((~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[141, 15, 53])).
% 0.20/0.42 tff(143,plain,
% 0.20/0.42 (~product(e_1, e_1, e_1)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[142, 129])).
% 0.20/0.42 tff(144,plain,
% 0.20/0.42 (product(e_1, e_1, e_2)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[42, 36, 33, 143])).
% 0.20/0.42 tff(145,plain,
% 0.20/0.42 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(146,plain,
% 0.20/0.42 (((~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_1, e_2)) | equalish(e_1, e_2)) <=> (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(147,plain,
% 0.20/0.42 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_1, e_2)) | equalish(e_1, e_2))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[146])).
% 0.20/0.42 tff(148,plain,
% 0.20/0.42 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_1, e_2)) | equalish(e_1, e_2))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[147, 145])).
% 0.20/0.42 tff(149,plain,
% 0.20/0.42 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_1, e_2)) | equalish(e_1, e_2))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(150,plain,
% 0.20/0.42 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.20/0.42 tff(151,plain,
% 0.20/0.42 ((~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[150, 71, 68])).
% 0.20/0.42 tff(152,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[151, 144, 138, 129])).
% 0.20/0.42 % SZS output end Proof
% 0.20/0.42 % E exiting
%------------------------------------------------------------------------------