%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP125-1.003 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:07:06 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP125-1.003 : TPTP v9.0.0. Released v1.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 15:42:05 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.38 % SZS status Unsatisfiable
% 0.11/0.38 % SZS output start Proof
% 0.11/0.38 tff(product_type, type, (
% 0.11/0.38 product: ( $i * $i * $i ) > $o)).
% 0.11/0.38 tff(e_2_type, type, (
% 0.11/0.38 e_2: $i)).
% 0.11/0.38 tff(e_3_type, type, (
% 0.11/0.38 e_3: $i)).
% 0.11/0.38 tff(e_1_type, type, (
% 0.11/0.38 e_1: $i)).
% 0.11/0.38 tff(equalish_type, type, (
% 0.11/0.38 equalish: ( $i * $i ) > $o)).
% 0.11/0.38 tff(group_element_type, type, (
% 0.11/0.38 group_element: $i > $o)).
% 0.11/0.38 tff(1,assumption,(product(e_2, e_1, e_2)), introduced(assumption)).
% 0.11/0.38 tff(2,assumption,(~product(e_2, e_2, e_2)), introduced(assumption)).
% 0.11/0.38 tff(3,plain,
% 0.11/0.38 (^[X: $i] : refl(product(X, X, X) <=> product(X, X, X))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(4,plain,
% 0.11/0.38 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.11/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.11/0.38 tff(5,plain,
% 0.11/0.38 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(6,axiom,(![X: $i] : product(X, X, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_idempotence')).
% 0.11/0.38 tff(7,plain,
% 0.11/0.38 (![X: $i] : product(X, X, X)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.11/0.38 tff(8,plain,(
% 0.11/0.38 ![X: $i] : product(X, X, X)),
% 0.11/0.38 inference(skolemize,[status(sab)],[7])).
% 0.11/0.38 tff(9,plain,
% 0.11/0.38 (![X: $i] : product(X, X, X)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.11/0.38 tff(10,plain,
% 0.11/0.38 ((~![X: $i] : product(X, X, X)) | product(e_2, e_2, e_2)),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(11,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[10, 9, 2])).
% 0.11/0.38 tff(12,plain,(product(e_2, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.38 tff(13,plain,
% 0.11/0.38 (^[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))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(14,plain,
% 0.11/0.38 (![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)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.11/0.38 tff(15,plain,
% 0.11/0.38 (![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)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(16,plain,
% 0.11/0.38 (^[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)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(17,plain,
% 0.11/0.38 (![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)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[16])).
% 0.11/0.38 tff(18,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')).
% 0.11/0.38 tff(19,plain,
% 0.11/0.38 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.11/0.38 tff(20,plain,
% 0.11/0.38 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.11/0.38 tff(21,plain,(
% 0.11/0.38 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.11/0.38 inference(skolemize,[status(sab)],[20])).
% 0.11/0.38 tff(22,plain,
% 0.11/0.38 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.11/0.38 tff(23,plain,
% 0.11/0.38 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(24,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.11/0.39 tff(25,plain,
% 0.11/0.39 (~equalish(e_1, e_2)),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.11/0.39 tff(26,plain,
% 0.11/0.39 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(27,plain,
% 0.11/0.39 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(28,plain,
% 0.11/0.39 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.11/0.39 tff(29,plain,
% 0.11/0.39 ($false),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[28, 25, 22, 12, 1])).
% 0.11/0.39 tff(30,plain,(~product(e_2, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.39 tff(31,plain,
% 0.11/0.39 ((~![X: $i] : product(X, X, X)) | product(e_1, e_1, e_1)),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(32,plain,
% 0.11/0.39 (product(e_1, e_1, e_1)),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[31, 9])).
% 0.11/0.39 tff(33,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.11/0.39 tff(34,plain,
% 0.11/0.39 (^[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))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(35,plain,
% 0.11/0.39 (![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)))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[34])).
% 0.11/0.39 tff(36,plain,
% 0.11/0.39 (![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)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(37,plain,
% 0.11/0.39 (^[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)))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(38,plain,
% 0.11/0.39 (![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)))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[37])).
% 0.11/0.39 tff(39,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')).
% 0.11/0.39 tff(40,plain,
% 0.11/0.39 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.11/0.39 tff(41,plain,
% 0.11/0.39 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.11/0.39 tff(42,plain,(
% 0.11/0.39 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.11/0.39 inference(skolemize,[status(sab)],[41])).
% 0.11/0.39 tff(43,plain,
% 0.11/0.39 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.11/0.39 tff(44,plain,
% 0.11/0.39 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(45,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.11/0.39 tff(46,plain,
% 0.11/0.39 (~equalish(e_2, e_1)),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.11/0.39 tff(47,plain,
% 0.11/0.39 (((~![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_2, e_1, e_1)) | (~product(e_1, 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_2, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(48,plain,
% 0.11/0.39 ((equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1))) <=> (equalish(e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(49,plain,
% 0.11/0.39 (((~![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_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_2, e_1, e_1)) | (~product(e_1, e_1, e_1))))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[48])).
% 0.11/0.39 tff(50,plain,
% 0.11/0.39 (((~![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_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_2, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.11/0.39 inference(transitivity,[status(thm)],[49, 47])).
% 0.11/0.39 tff(51,plain,
% 0.11/0.39 ((~![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_1)) | (~product(e_2, e_1, e_1)))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(52,plain,
% 0.11/0.39 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.11/0.39 tff(53,plain,
% 0.11/0.39 ($false),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[52, 46, 43, 33, 32])).
% 0.11/0.39 tff(54,plain,(~product(e_2, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.39 tff(55,plain,
% 0.11/0.39 (^[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))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(56,plain,
% 0.11/0.39 (![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)))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[55])).
% 0.11/0.39 tff(57,plain,
% 0.11/0.39 (![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)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(58,plain,
% 0.11/0.39 (^[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)))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(59,plain,
% 0.11/0.39 (![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)))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[58])).
% 0.11/0.39 tff(60,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')).
% 0.11/0.39 tff(61,plain,
% 0.11/0.39 (![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)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.11/0.39 tff(62,plain,
% 0.11/0.39 (![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)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.11/0.39 tff(63,plain,(
% 0.11/0.39 ![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)))),
% 0.11/0.39 inference(skolemize,[status(sab)],[62])).
% 0.11/0.39 tff(64,plain,
% 0.11/0.39 (![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)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.11/0.39 tff(65,plain,
% 0.11/0.39 (group_element(e_2) <=> group_element(e_2)),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(66,axiom,(group_element(e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_2')).
% 0.11/0.39 tff(67,plain,
% 0.11/0.39 (group_element(e_2)),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.11/0.39 tff(68,plain,
% 0.11/0.39 (group_element(e_1) <=> group_element(e_1)),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(69,axiom,(group_element(e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_1')).
% 0.11/0.39 tff(70,plain,
% 0.11/0.39 (group_element(e_1)),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.11/0.39 tff(71,plain,
% 0.11/0.39 (((~![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)))) | ((~group_element(e_2)) | (~group_element(e_1)) | 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_2)) | (~group_element(e_1)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(72,plain,
% 0.11/0.39 ((product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2))) <=> ((~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(73,plain,
% 0.11/0.39 (((~![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_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[72])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3))),
% 0.19/0.40 inference(transitivity,[status(thm)],[73, 71])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 ((~![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)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 (product(e_2, e_1, e_2) | product(e_2, e_1, e_3)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[76, 70, 67, 64, 54])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 (product(e_2, e_1, e_3)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[77, 30])).
% 0.19/0.40 tff(79,assumption,(product(e_2, e_1, e_3)), introduced(assumption)).
% 0.19/0.40 tff(80,assumption,(~product(e_3, e_3, e_2)), introduced(assumption)).
% 0.19/0.40 tff(81,assumption,(product(e_1, e_2, e_1)), introduced(assumption)).
% 0.19/0.40 tff(82,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_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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 ((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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(84,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_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))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[83])).
% 0.19/0.40 tff(85,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_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)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[84, 82])).
% 0.19/0.40 tff(86,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_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_1))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.19/0.40 tff(88,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[87, 46, 22, 81, 32])).
% 0.19/0.40 tff(89,plain,(~product(e_1, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(90,assumption,(product(e_1, e_2, e_2)), introduced(assumption)).
% 0.19/0.40 tff(91,plain,
% 0.19/0.40 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(92,plain,
% 0.19/0.40 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(93,plain,
% 0.19/0.40 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.19/0.40 tff(94,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[93, 25, 43, 90, 12])).
% 0.19/0.40 tff(95,plain,(~product(e_1, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(96,plain,
% 0.19/0.40 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(97,plain,
% 0.19/0.40 ((~![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)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(98,plain,
% 0.19/0.40 ((~![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))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.19/0.40 tff(99,plain,
% 0.19/0.40 (product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[98, 70, 67, 64])).
% 0.19/0.40 tff(100,plain,
% 0.19/0.40 (product(e_1, e_2, e_3)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[99, 95, 89])).
% 0.19/0.40 tff(101,plain,
% 0.19/0.40 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl(((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1))) <=> ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(102,plain,
% 0.19/0.40 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[101])).
% 0.19/0.40 tff(103,plain,
% 0.19/0.40 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(104,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, X)) <=> ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(105,plain,
% 0.19/0.40 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, X)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[104])).
% 0.19/0.40 tff(106,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qg3')).
% 0.19/0.40 tff(107,plain,
% 0.19/0.40 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.19/0.40 tff(108,plain,
% 0.19/0.40 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.19/0.40 tff(109,plain,(
% 0.19/0.40 ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[108])).
% 0.19/0.40 tff(110,plain,
% 0.19/0.40 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.19/0.40 tff(111,plain,
% 0.19/0.40 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(112,plain,
% 0.19/0.40 (((~product(e_1, e_2, e_3)) | product(e_3, e_3, e_2) | (~product(e_2, e_1, e_3))) <=> (product(e_3, e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(113,plain,
% 0.19/0.40 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_3, e_3, e_2) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_3))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[112])).
% 0.19/0.40 tff(114,plain,
% 0.19/0.40 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_3, e_3, e_2) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[113, 111])).
% 0.19/0.40 tff(115,plain,
% 0.19/0.40 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_3, e_3, e_2) | (~product(e_2, e_1, e_3)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(116,plain,
% 0.19/0.40 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_3))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.19/0.40 tff(117,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[116, 110, 100, 80, 79])).
% 0.19/0.40 tff(118,plain,(product(e_3, e_3, e_2) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(119,plain,
% 0.19/0.40 (product(e_3, e_3, e_2)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[118, 78])).
% 0.19/0.40 tff(120,assumption,(product(e_3, e_3, e_2)), introduced(assumption)).
% 0.19/0.40 tff(121,assumption,(~product(e_2, e_2, e_3)), introduced(assumption)).
% 0.19/0.40 tff(122,plain,
% 0.19/0.40 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~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, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_2)) | product(e_2, e_2, e_3))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(123,plain,
% 0.19/0.40 (((~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))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(124,plain,
% 0.19/0.40 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~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, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_2)) | product(e_2, e_2, e_3)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[123])).
% 0.19/0.41 tff(125,plain,
% 0.19/0.41 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~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, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_2)) | product(e_2, e_2, e_3))),
% 0.19/0.41 inference(transitivity,[status(thm)],[124, 122])).
% 0.19/0.41 tff(126,plain,
% 0.19/0.41 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~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)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(127,plain,
% 0.19/0.41 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_2)) | product(e_2, e_2, e_3)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.19/0.41 tff(128,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[127, 110, 121, 120])).
% 0.19/0.41 tff(129,plain,((~product(e_3, e_3, e_2)) | product(e_2, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(130,plain,
% 0.19/0.41 (product(e_2, e_2, e_3)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[129, 119])).
% 0.19/0.41 tff(131,plain,
% 0.19/0.41 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(132,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.19/0.41 tff(133,plain,
% 0.19/0.41 (~equalish(e_2, e_3)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.19/0.41 tff(134,plain,
% 0.19/0.41 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_2, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_2, e_3, e_3)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(135,plain,
% 0.19/0.41 ((equalish(e_2, e_3) | (~product(e_2, e_3, e_3)) | (~product(e_2, e_2, e_3))) <=> (equalish(e_2, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_2, e_3, e_3)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(136,plain,
% 0.19/0.41 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_2, e_3, e_3)) | (~product(e_2, e_2, e_3)))) <=> ((~![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_2, e_2, e_3)) | (~product(e_2, e_3, e_3))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[135])).
% 0.19/0.41 tff(137,plain,
% 0.19/0.41 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_2, e_3, e_3)) | (~product(e_2, e_2, e_3)))) <=> ((~![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_2, e_2, e_3)) | (~product(e_2, e_3, e_3)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[136, 134])).
% 0.19/0.41 tff(138,plain,
% 0.19/0.41 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_2, e_3, e_3)) | (~product(e_2, e_2, e_3)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(139,plain,
% 0.19/0.41 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_2, e_3, e_3))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.19/0.41 tff(140,plain,
% 0.19/0.41 ((~product(e_2, e_2, e_3)) | (~product(e_2, e_3, e_3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[139, 133, 22])).
% 0.19/0.41 tff(141,plain,
% 0.19/0.41 (~product(e_2, e_3, e_3)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[140, 130])).
% 0.19/0.41 tff(142,plain,
% 0.19/0.41 ((~![X: $i] : product(X, X, X)) | product(e_3, e_3, e_3)),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(143,plain,
% 0.19/0.41 (product(e_3, e_3, e_3)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[142, 9])).
% 0.19/0.41 tff(144,plain,
% 0.19/0.41 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_2)) | product(e_2, e_3, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_2)) | product(e_2, e_3, e_3))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(145,plain,
% 0.19/0.41 (((~product(e_3, e_3, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_3, e_2))) <=> ((~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_2)) | product(e_2, e_3, e_3))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(146,plain,
% 0.19/0.41 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_2)) | product(e_2, e_3, e_3)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[145])).
% 0.19/0.41 tff(147,plain,
% 0.19/0.41 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_2)) | product(e_2, e_3, e_3))),
% 0.19/0.41 inference(transitivity,[status(thm)],[146, 144])).
% 0.19/0.41 tff(148,plain,
% 0.19/0.41 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | product(e_2, e_3, e_3) | (~product(e_3, e_3, e_2)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(149,plain,
% 0.19/0.41 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, X) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_2)) | product(e_2, e_3, e_3)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.19/0.41 tff(150,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[149, 110, 143, 141, 119])).
% 0.19/0.41 % SZS output end Proof
% 0.19/0.41 % E exiting
%------------------------------------------------------------------------------