%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP128-1.003 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:07:09 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP128-1.003 : TPTP v9.0.0. Released v1.2.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n003.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 15:43:39 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.41 % SZS status Unsatisfiable
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 tff(product_type, type, (
% 0.21/0.41 product: ( $i * $i * $i ) > $o)).
% 0.21/0.41 tff(e_3_type, type, (
% 0.21/0.41 e_3: $i)).
% 0.21/0.41 tff(e_2_type, type, (
% 0.21/0.41 e_2: $i)).
% 0.21/0.41 tff(e_1_type, type, (
% 0.21/0.41 e_1: $i)).
% 0.21/0.41 tff(equalish_type, type, (
% 0.21/0.41 equalish: ( $i * $i ) > $o)).
% 0.21/0.41 tff(group_element_type, type, (
% 0.21/0.41 group_element: $i > $o)).
% 0.21/0.41 tff(1,assumption,(product(e_3, e_3, e_2)), introduced(assumption)).
% 0.21/0.41 tff(2,assumption,(product(e_1, e_3, e_2)), introduced(assumption)).
% 0.21/0.41 tff(3,plain,
% 0.21/0.41 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(4,plain,
% 0.21/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.41 tff(5,plain,
% 0.21/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(6,plain,
% 0.21/0.41 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(W, Y, X)) | (~product(Z, Y, X))) <=> ((~product(Z, Y, X)) | (~product(W, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> (((~product(Z, Y, X)) | (~product(W, Y, X))) | equalish(W, Z)))), rewrite((((~product(Z, Y, X)) | (~product(W, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(7,plain,
% 0.21/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[6])).
% 0.21/0.41 tff(8,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_left_cancellation')).
% 0.21/0.41 tff(9,plain,
% 0.21/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.21/0.41 tff(10,plain,
% 0.21/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.21/0.41 tff(11,plain,(
% 0.21/0.41 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[10])).
% 0.21/0.41 tff(12,plain,
% 0.21/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.21/0.41 tff(13,plain,
% 0.21/0.41 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(14,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.21/0.41 tff(15,plain,
% 0.21/0.41 (~equalish(e_1, e_3)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.21/0.41 tff(16,plain,
% 0.21/0.41 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_3, e_2)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(17,plain,
% 0.21/0.41 ((equalish(e_1, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_3, e_2))) <=> (equalish(e_1, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_3, e_2)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(18,plain,
% 0.21/0.41 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_3, e_2))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[17])).
% 0.21/0.41 tff(19,plain,
% 0.21/0.41 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_3, e_2)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[18, 16])).
% 0.21/0.41 tff(20,plain,
% 0.21/0.41 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(21,plain,
% 0.21/0.41 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_3, e_2))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.21/0.41 tff(22,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[21, 15, 12, 2, 1])).
% 0.21/0.41 tff(23,plain,((~product(e_1, e_3, e_2)) | (~product(e_3, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(24,plain,
% 0.21/0.41 (~product(e_1, e_3, e_2)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[23, 1])).
% 0.21/0.41 tff(25,assumption,(~product(e_2, e_3, e_1)), introduced(assumption)).
% 0.21/0.41 tff(26,assumption,(product(e_3, e_3, e_1)), introduced(assumption)).
% 0.21/0.41 tff(27,assumption,(product(e_2, e_3, e_2)), introduced(assumption)).
% 0.21/0.41 tff(28,plain,
% 0.21/0.41 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl((product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1))) <=> (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(29,plain,
% 0.21/0.41 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[28])).
% 0.21/0.41 tff(30,plain,
% 0.21/0.41 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(31,plain,
% 0.21/0.41 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : rewrite((((~product(X, Y, Z1)) | (~product(Z1, Y, Z2))) | product(X, Z1, Z2)) <=> (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(32,plain,
% 0.21/0.41 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Z1, Y, Z2))) | product(X, Z1, Z2)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[31])).
% 0.21/0.41 tff(33,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Z1, Y, Z2))) | product(X, Z1, Z2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qg3')).
% 0.21/0.41 tff(34,plain,
% 0.21/0.41 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.21/0.41 tff(35,plain,
% 0.21/0.41 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.21/0.41 tff(36,plain,(
% 0.21/0.41 ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[35])).
% 0.21/0.41 tff(37,plain,
% 0.21/0.41 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.21/0.41 tff(38,plain,
% 0.21/0.41 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_2)) | product(e_2, e_2, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_3, e_2)) | product(e_2, e_2, e_2))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(39,plain,
% 0.21/0.41 ((product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_3, e_2))) <=> ((~product(e_2, e_3, e_2)) | product(e_2, e_2, e_2))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(40,plain,
% 0.21/0.41 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_3, e_2)) | product(e_2, e_2, e_2)))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[39])).
% 0.21/0.41 tff(41,plain,
% 0.21/0.41 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_3, e_2)) | product(e_2, e_2, e_2))),
% 0.21/0.41 inference(transitivity,[status(thm)],[40, 38])).
% 0.21/0.41 tff(42,plain,
% 0.21/0.41 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_3, e_2)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(43,plain,
% 0.21/0.41 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_3, e_2)) | product(e_2, e_2, e_2)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.21/0.41 tff(44,plain,
% 0.21/0.41 ((~product(e_2, e_3, e_2)) | product(e_2, e_2, e_2)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[43, 37])).
% 0.21/0.41 tff(45,plain,
% 0.21/0.41 (product(e_2, e_2, e_2)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[44, 27])).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 (^[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))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(47,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[46])).
% 0.21/0.41 tff(48,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(49,plain,
% 0.21/0.41 (^[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)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(50,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[49])).
% 0.21/0.41 tff(51,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_right_cancellation')).
% 0.21/0.41 tff(52,plain,
% 0.21/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.21/0.41 tff(53,plain,
% 0.21/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.21/0.41 tff(54,plain,(
% 0.21/0.41 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[53])).
% 0.21/0.41 tff(55,plain,
% 0.21/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.21/0.41 tff(56,plain,
% 0.21/0.41 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(57,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.21/0.41 tff(58,plain,
% 0.21/0.41 (~equalish(e_3, e_2)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.21/0.41 tff(59,plain,
% 0.21/0.41 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(60,plain,
% 0.21/0.41 ((equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_3, e_2))) <=> (equalish(e_3, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(61,plain,
% 0.21/0.41 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_2, e_2))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[60])).
% 0.21/0.41 tff(62,plain,
% 0.21/0.41 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[61, 59])).
% 0.21/0.41 tff(63,plain,
% 0.21/0.41 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_3, e_2)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(64,plain,
% 0.21/0.41 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_2, e_2))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.21/0.41 tff(65,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[64, 58, 55, 27, 45])).
% 0.21/0.41 tff(66,plain,(~product(e_2, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(67,plain,
% 0.21/0.41 (^[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))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(68,plain,
% 0.21/0.41 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> ![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)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[67])).
% 0.21/0.41 tff(69,plain,
% 0.21/0.41 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> ![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)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(70,plain,
% 0.21/0.41 (^[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)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(71,plain,
% 0.21/0.42 (![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ![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)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[70])).
% 0.21/0.42 tff(72,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/sandbox2/benchmark/theBenchmark.p','product_total_function1')).
% 0.21/0.42 tff(73,plain,
% 0.21/0.42 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.21/0.42 tff(74,plain,
% 0.21/0.42 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.21/0.42 tff(75,plain,(
% 0.21/0.42 ![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[74])).
% 0.21/0.42 tff(76,plain,
% 0.21/0.42 (![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.21/0.42 tff(77,plain,
% 0.21/0.42 (group_element(e_3) <=> group_element(e_3)),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(78,axiom,(group_element(e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_3')).
% 0.21/0.42 tff(79,plain,
% 0.21/0.42 (group_element(e_3)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.21/0.42 tff(80,plain,
% 0.21/0.42 (group_element(e_2) <=> group_element(e_2)),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(81,axiom,(group_element(e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_2')).
% 0.21/0.42 tff(82,plain,
% 0.21/0.42 (group_element(e_2)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.21/0.42 tff(83,plain,
% 0.21/0.42 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | product(e_2, e_3, 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)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | product(e_2, e_3, e_3))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(84,plain,
% 0.21/0.42 ((product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_2))) <=> ((~group_element(e_2)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | product(e_2, e_3, e_3))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(85,plain,
% 0.21/0.42 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | (~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)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | product(e_2, e_3, e_3)))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[84])).
% 0.21/0.42 tff(86,plain,
% 0.21/0.42 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | (~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)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | product(e_2, e_3, e_3))),
% 0.21/0.42 inference(transitivity,[status(thm)],[85, 83])).
% 0.21/0.42 tff(87,plain,
% 0.21/0.42 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_2)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(88,plain,
% 0.21/0.42 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1) | (~group_element(e_3)) | product(e_2, e_3, e_3)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.21/0.42 tff(89,plain,
% 0.21/0.42 (product(e_2, e_3, e_1) | product(e_2, e_3, e_3)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[88, 82, 79, 76, 66])).
% 0.21/0.42 tff(90,plain,
% 0.21/0.42 (product(e_2, e_3, e_3)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[89, 25])).
% 0.21/0.42 tff(91,plain,
% 0.21/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_1) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_1) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_3, e_1)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(92,plain,
% 0.21/0.42 ((product(e_2, e_3, e_1) | (~product(e_3, e_3, e_1)) | (~product(e_2, e_3, e_3))) <=> (product(e_2, e_3, e_1) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_3, e_1)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(93,plain,
% 0.21/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_1) | (~product(e_3, e_3, e_1)) | (~product(e_2, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_1) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_3, e_1))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[92])).
% 0.21/0.42 tff(94,plain,
% 0.21/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_1) | (~product(e_3, e_3, e_1)) | (~product(e_2, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_1) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_3, e_1)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[93, 91])).
% 0.21/0.42 tff(95,plain,
% 0.21/0.42 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_1) | (~product(e_3, e_3, e_1)) | (~product(e_2, e_3, e_3)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(96,plain,
% 0.21/0.42 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_1) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_3, e_1))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.21/0.42 tff(97,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[96, 37, 90, 25, 26])).
% 0.21/0.43 tff(98,plain,((~product(e_3, e_3, e_1)) | product(e_2, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(99,plain,
% 0.21/0.43 (~product(e_3, e_3, e_1)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[98, 25])).
% 0.21/0.43 tff(100,assumption,(product(e_3, e_3, e_3)), introduced(assumption)).
% 0.21/0.43 tff(101,assumption,(product(e_2, e_3, e_3)), introduced(assumption)).
% 0.21/0.43 tff(102,plain,
% 0.21/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(103,plain,
% 0.21/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(104,plain,
% 0.21/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_3, e_3))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.21/0.43 tff(105,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[104, 58, 12, 101, 100])).
% 0.21/0.43 tff(106,plain,((~product(e_3, e_3, e_3)) | (~product(e_2, e_3, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(107,plain,
% 0.21/0.43 (~product(e_3, e_3, e_3)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[106, 90])).
% 0.21/0.43 tff(108,plain,
% 0.21/0.43 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(109,plain,
% 0.21/0.43 ((product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_3))) <=> ((~group_element(e_3)) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(110,plain,
% 0.21/0.43 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1)))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[109])).
% 0.21/0.43 tff(111,plain,
% 0.21/0.43 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1))),
% 0.21/0.43 inference(transitivity,[status(thm)],[110, 108])).
% 0.21/0.43 tff(112,plain,
% 0.21/0.43 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_3)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(113,plain,
% 0.21/0.43 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.21/0.43 tff(114,plain,
% 0.21/0.43 (product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[113, 79, 76])).
% 0.21/0.43 tff(115,plain,
% 0.21/0.43 (product(e_3, e_3, e_2)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[114, 107, 99])).
% 0.21/0.43 tff(116,plain,
% 0.21/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_2) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_2) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_3, e_2)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(117,plain,
% 0.21/0.43 ((product(e_2, e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_2, e_3, e_3))) <=> (product(e_2, e_3, e_2) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_3, e_2)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(118,plain,
% 0.21/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_2, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_2) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_3, e_2))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[117])).
% 0.21/0.43 tff(119,plain,
% 0.21/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_2, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_2) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_3, e_2)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[118, 116])).
% 0.21/0.43 tff(120,plain,
% 0.21/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_2, e_3, e_3)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(121,plain,
% 0.21/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_3, e_2) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_3, e_2))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.21/0.43 tff(122,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[121, 37, 90, 66, 115])).
% 0.21/0.43 tff(123,plain,(product(e_2, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(124,assumption,(product(e_2, e_3, e_1)), introduced(assumption)).
% 0.21/0.43 tff(125,assumption,(product(e_1, e_3, e_1)), introduced(assumption)).
% 0.21/0.43 tff(126,plain,
% 0.21/0.43 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(127,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.21/0.43 tff(128,plain,
% 0.21/0.43 (~equalish(e_1, e_2)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.21/0.43 tff(129,plain,
% 0.21/0.43 (((~![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_1, e_3, e_1)) | (~product(e_2, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_1, e_3, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(130,plain,
% 0.21/0.43 ((equalish(e_1, e_2) | (~product(e_2, e_3, e_1)) | (~product(e_1, e_3, e_1))) <=> (equalish(e_1, e_2) | (~product(e_1, e_3, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(131,plain,
% 0.21/0.43 (((~![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_3, e_1)) | (~product(e_1, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_1, e_3, e_1)) | (~product(e_2, e_3, e_1))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[130])).
% 0.21/0.43 tff(132,plain,
% 0.21/0.43 (((~![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_3, e_1)) | (~product(e_1, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_1, e_3, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[131, 129])).
% 0.21/0.43 tff(133,plain,
% 0.21/0.43 ((~![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_3, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(134,plain,
% 0.21/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_1, e_3, e_1)) | (~product(e_2, e_3, e_1))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.21/0.43 tff(135,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[134, 128, 12, 125, 124])).
% 0.21/0.43 tff(136,plain,((~product(e_1, e_3, e_1)) | (~product(e_2, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(137,plain,
% 0.21/0.43 (~product(e_1, e_3, e_1)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[136, 123])).
% 0.21/0.43 tff(138,plain,
% 0.21/0.43 (group_element(e_1) <=> group_element(e_1)),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(139,axiom,(group_element(e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_1')).
% 0.21/0.43 tff(140,plain,
% 0.21/0.43 (group_element(e_1)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.21/0.43 tff(141,plain,
% 0.21/0.43 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_3, e_3) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_1, e_3, e_3) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(142,plain,
% 0.21/0.43 ((product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_1))) <=> (product(e_1, e_3, e_3) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(143,plain,
% 0.21/0.43 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_3, e_3) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1)))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[142])).
% 0.21/0.43 tff(144,plain,
% 0.21/0.43 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_1, e_3, e_3) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1))),
% 0.21/0.43 inference(transitivity,[status(thm)],[143, 141])).
% 0.21/0.43 tff(145,plain,
% 0.21/0.43 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_1)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(146,plain,
% 0.21/0.43 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_1, e_3, e_3) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.21/0.44 tff(147,plain,
% 0.21/0.44 (product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[146, 140, 79, 76])).
% 0.21/0.44 tff(148,plain,
% 0.21/0.44 (product(e_1, e_3, e_3) | product(e_1, e_3, e_2)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[147, 137])).
% 0.21/0.44 tff(149,plain,
% 0.21/0.44 (product(e_1, e_3, e_3)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[148, 24])).
% 0.21/0.44 tff(150,plain,
% 0.21/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_2) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_2) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_2)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(151,plain,
% 0.21/0.44 ((product(e_1, e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_3, e_3))) <=> (product(e_1, e_3, e_2) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_2)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(152,plain,
% 0.21/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_2) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_2))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[151])).
% 0.21/0.44 tff(153,plain,
% 0.21/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_2) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_2)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[152, 150])).
% 0.21/0.44 tff(154,plain,
% 0.21/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_3, e_3)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(155,plain,
% 0.21/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_2) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_2))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.21/0.44 tff(156,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[155, 37, 149, 24, 1])).
% 0.21/0.44 tff(157,plain,(~product(e_3, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(158,plain,
% 0.21/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_3, e_3, e_1)) | (~product(e_2, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_3, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(159,plain,
% 0.21/0.44 ((equalish(e_3, e_2) | (~product(e_2, e_3, e_1)) | (~product(e_3, e_3, e_1))) <=> (equalish(e_3, e_2) | (~product(e_3, e_3, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(160,plain,
% 0.21/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_3, e_1)) | (~product(e_3, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_3, e_3, e_1)) | (~product(e_2, e_3, e_1))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[159])).
% 0.21/0.44 tff(161,plain,
% 0.21/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_3, e_1)) | (~product(e_3, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_3, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[160, 158])).
% 0.21/0.44 tff(162,plain,
% 0.21/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_3, e_1)) | (~product(e_3, e_3, e_1)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(163,plain,
% 0.21/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_3, e_1)) | (~product(e_2, e_3, e_1))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.21/0.44 tff(164,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[163, 58, 12, 123, 26])).
% 0.21/0.44 tff(165,plain,(~product(e_3, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(166,plain,
% 0.21/0.44 (product(e_3, e_3, e_3)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[114, 165, 157])).
% 0.21/0.44 tff(167,assumption,(product(e_3, e_2, e_3)), introduced(assumption)).
% 0.21/0.44 tff(168,plain,
% 0.21/0.44 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(169,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.21/0.44 tff(170,plain,
% 0.21/0.44 (~equalish(e_2, e_3)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.21/0.44 tff(171,plain,
% 0.21/0.44 (((~![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_3, e_3, e_3)) | (~product(e_3, 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_3, e_3, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(172,plain,
% 0.21/0.44 ((~![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_3, e_3, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(173,plain,
% 0.21/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.21/0.44 tff(174,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[173, 170, 55, 167, 166])).
% 0.21/0.44 tff(175,plain,(~product(e_3, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(176,assumption,(product(e_1, e_3, e_3)), introduced(assumption)).
% 0.21/0.44 tff(177,plain,
% 0.21/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(178,plain,
% 0.21/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(179,plain,
% 0.21/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.21/0.44 tff(180,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[179, 15, 12, 176, 166])).
% 0.21/0.44 tff(181,plain,(~product(e_1, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(182,plain,
% 0.21/0.44 (product(e_1, e_3, e_2)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[148, 181])).
% 0.21/0.44 tff(183,assumption,(~product(e_1, e_2, e_1)), introduced(assumption)).
% 0.21/0.44 tff(184,plain,
% 0.21/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_2, e_3, e_1)) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_2, e_1) | (~product(e_2, e_3, e_1)) | (~product(e_1, e_3, e_2)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(185,plain,
% 0.21/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_2, e_3, e_1)) | (~product(e_1, e_3, e_2)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(186,plain,
% 0.21/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_2, e_1) | (~product(e_2, e_3, e_1)) | (~product(e_1, e_3, e_2))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.21/0.44 tff(187,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[186, 37, 183, 182, 123])).
% 0.21/0.44 tff(188,plain,(product(e_1, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(189,assumption,(product(e_3, e_2, e_1)), introduced(assumption)).
% 0.21/0.44 tff(190,assumption,(product(e_1, e_2, e_1)), introduced(assumption)).
% 0.21/0.44 tff(191,plain,
% 0.21/0.44 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(192,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.21/0.44 tff(193,plain,
% 0.21/0.44 (~equalish(e_3, e_1)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.21/0.44 tff(194,plain,
% 0.21/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_3, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_3, e_2, e_1)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(195,plain,
% 0.21/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_3, e_2, e_1)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(196,plain,
% 0.21/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_3, e_2, e_1))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.21/0.44 tff(197,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[196, 193, 12, 190, 189])).
% 0.21/0.44 tff(198,plain,((~product(e_3, e_2, e_1)) | (~product(e_1, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(199,plain,
% 0.21/0.44 (~product(e_3, e_2, e_1)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[198, 188])).
% 0.21/0.44 tff(200,plain,
% 0.21/0.44 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | product(e_3, e_2, e_2) | (~group_element(e_3)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_3, e_2, e_2) | (~group_element(e_3)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(201,plain,
% 0.21/0.44 ((product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3))) <=> ((~group_element(e_2)) | product(e_3, e_2, e_2) | (~group_element(e_3)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(202,plain,
% 0.21/0.44 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | product(e_3, e_2, e_2) | (~group_element(e_3)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1)))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[201])).
% 0.21/0.45 tff(203,plain,
% 0.21/0.45 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_3, e_2, e_2) | (~group_element(e_3)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1))),
% 0.21/0.45 inference(transitivity,[status(thm)],[202, 200])).
% 0.21/0.45 tff(204,plain,
% 0.21/0.45 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(205,plain,
% 0.21/0.45 ((~![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)) | product(e_3, e_2, e_2) | (~group_element(e_3)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.21/0.45 tff(206,plain,
% 0.21/0.45 (product(e_3, e_2, e_2) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[205, 82, 79, 76])).
% 0.21/0.45 tff(207,plain,
% 0.21/0.45 (product(e_3, e_2, e_2)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[206, 199, 175])).
% 0.21/0.45 tff(208,assumption,(product(e_2, e_2, e_2)), introduced(assumption)).
% 0.21/0.45 tff(209,assumption,(product(e_3, e_2, e_2)), introduced(assumption)).
% 0.21/0.45 tff(210,plain,
% 0.21/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, 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_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(211,plain,
% 0.21/0.45 ((equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2))) <=> (equalish(e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(212,plain,
% 0.21/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, 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_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[211])).
% 0.21/0.45 tff(213,plain,
% 0.21/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, 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_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[212, 210])).
% 0.21/0.45 tff(214,plain,
% 0.21/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(215,plain,
% 0.21/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.21/0.45 tff(216,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[215, 58, 12, 209, 208])).
% 0.21/0.45 tff(217,plain,((~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(218,plain,
% 0.21/0.45 (~product(e_2, e_2, e_2)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[217, 207])).
% 0.21/0.45 tff(219,assumption,(product(e_2, e_2, e_1)), introduced(assumption)).
% 0.21/0.45 tff(220,plain,
% 0.21/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_2, e_3, 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_3) | (~product(e_2, e_3, e_1)) | (~product(e_2, e_2, e_1)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(221,plain,
% 0.21/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_2, e_2, e_1)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(222,plain,
% 0.21/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_2, e_3, e_1)) | (~product(e_2, e_2, e_1))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.21/0.45 tff(223,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[222, 170, 55, 123, 219])).
% 0.21/0.45 tff(224,plain,(~product(e_2, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(225,plain,
% 0.21/0.45 (((~![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)) | product(e_2, e_2, e_2) | product(e_2, e_2, e_3) | product(e_2, e_2, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_2, e_2, e_2) | product(e_2, e_2, e_3) | product(e_2, e_2, e_1))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(226,plain,
% 0.21/0.45 ((product(e_2, e_2, e_3) | 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_3) | product(e_2, e_2, e_1))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(227,plain,
% 0.21/0.45 (((~![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_2, e_3) | 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_3) | 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_3) | product(e_2, e_2, e_1)))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[226])).
% 0.21/0.45 tff(228,plain,
% 0.21/0.45 (((~![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_2, e_3) | 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_3) | 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_3) | product(e_2, e_2, e_1))),
% 0.21/0.45 inference(transitivity,[status(thm)],[227, 225])).
% 0.21/0.45 tff(229,plain,
% 0.21/0.45 ((~![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_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_2)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(230,plain,
% 0.21/0.45 ((~![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)) | product(e_2, e_2, e_2) | product(e_2, e_2, e_3) | product(e_2, e_2, e_1)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.21/0.45 tff(231,plain,
% 0.21/0.45 (product(e_2, e_2, e_2) | product(e_2, e_2, e_3) | product(e_2, e_2, e_1)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[230, 82, 76])).
% 0.21/0.45 tff(232,plain,
% 0.21/0.45 (product(e_2, e_2, e_2) | product(e_2, e_2, e_3)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[231, 224])).
% 0.21/0.45 tff(233,plain,
% 0.21/0.45 (product(e_2, e_2, e_3)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[232, 218])).
% 0.21/0.45 tff(234,plain,
% 0.21/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_2)) | product(e_2, e_3, e_2) | (~product(e_2, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_2, e_2)) | product(e_2, e_3, e_2) | (~product(e_2, e_2, e_3)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(235,plain,
% 0.21/0.46 ((product(e_2, e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_3))) <=> ((~product(e_3, e_2, e_2)) | product(e_2, e_3, e_2) | (~product(e_2, e_2, e_3)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(236,plain,
% 0.21/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_2, e_2)) | product(e_2, e_3, e_2) | (~product(e_2, e_2, e_3))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[235])).
% 0.21/0.46 tff(237,plain,
% 0.21/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_2, e_2)) | product(e_2, e_3, e_2) | (~product(e_2, e_2, e_3)))),
% 0.21/0.46 inference(transitivity,[status(thm)],[236, 234])).
% 0.21/0.46 tff(238,plain,
% 0.21/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_3)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(239,plain,
% 0.21/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_2, e_2)) | product(e_2, e_3, e_2) | (~product(e_2, e_2, e_3))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.21/0.46 tff(240,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[239, 37, 207, 66, 233])).
% 0.21/0.46 % SZS output end Proof
% 0.21/0.46 % E exiting
%------------------------------------------------------------------------------