%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP129-1.003 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:07:10 AM UTC 2025
% Result : Unsatisfiable 0.17s 0.38s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : GRP129-1.003 : TPTP v9.0.0. Released v1.2.0.
% 0.06/0.10 % Command : run_E %s %d THM
% 0.11/0.31 % Computer : n010.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Thu Jun 19 15:45:26 EDT 2025
% 0.11/0.31 % CPUTime :
% 0.17/0.38 % SZS status Unsatisfiable
% 0.17/0.38 % SZS output start Proof
% 0.17/0.38 tff(product_type, type, (
% 0.17/0.38 product: ( $i * $i * $i ) > $o)).
% 0.17/0.38 tff(e_2_type, type, (
% 0.17/0.38 e_2: $i)).
% 0.17/0.38 tff(e_3_type, type, (
% 0.17/0.38 e_3: $i)).
% 0.17/0.38 tff(e_1_type, type, (
% 0.17/0.38 e_1: $i)).
% 0.17/0.38 tff(equalish_type, type, (
% 0.17/0.38 equalish: ( $i * $i ) > $o)).
% 0.17/0.38 tff(group_element_type, type, (
% 0.17/0.38 group_element: $i > $o)).
% 0.17/0.38 tff(1,assumption,(product(e_3, e_1, e_2)), introduced(assumption)).
% 0.17/0.38 tff(2,assumption,(product(e_3, e_2, e_2)), introduced(assumption)).
% 0.17/0.38 tff(3,plain,
% 0.17/0.38 (^[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))))),
% 0.17/0.38 inference(bind,[status(th)],[])).
% 0.17/0.38 tff(4,plain,
% 0.17/0.38 (![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)))),
% 0.17/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.17/0.38 tff(5,plain,
% 0.17/0.38 (![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)))),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(6,plain,
% 0.17/0.38 (^[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)))))),
% 0.17/0.38 inference(bind,[status(th)],[])).
% 0.17/0.38 tff(7,plain,
% 0.17/0.38 (![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)))),
% 0.17/0.38 inference(quant_intro,[status(thm)],[6])).
% 0.17/0.38 tff(8,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_right_cancellation')).
% 0.17/0.38 tff(9,plain,
% 0.17/0.38 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.17/0.38 tff(10,plain,
% 0.17/0.38 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.17/0.38 tff(11,plain,(
% 0.17/0.38 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.17/0.38 inference(skolemize,[status(sab)],[10])).
% 0.17/0.38 tff(12,plain,
% 0.17/0.38 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.17/0.38 tff(13,plain,
% 0.17/0.38 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(14,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.17/0.38 tff(15,plain,
% 0.17/0.38 (~equalish(e_2, e_1)),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.17/0.38 tff(16,plain,
% 0.17/0.38 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(17,plain,
% 0.17/0.38 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.17/0.38 inference(quant_inst,[status(thm)],[])).
% 0.17/0.38 tff(18,plain,
% 0.17/0.38 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_2))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.17/0.38 tff(19,plain,
% 0.17/0.38 ($false),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[18, 15, 12, 1, 2])).
% 0.17/0.38 tff(20,plain,((~product(e_3, e_2, e_2)) | (~product(e_3, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.17/0.38 tff(21,plain,
% 0.17/0.38 (~product(e_3, e_2, e_2)),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[20, 1])).
% 0.17/0.38 tff(22,assumption,(~product(e_1, e_3, e_2)), introduced(assumption)).
% 0.17/0.38 tff(23,assumption,(product(e_1, e_3, e_3)), introduced(assumption)).
% 0.17/0.38 tff(24,assumption,(product(e_3, e_3, e_1)), introduced(assumption)).
% 0.17/0.38 tff(25,plain,
% 0.17/0.38 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(26,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.17/0.38 tff(27,plain,
% 0.17/0.38 (~equalish(e_1, e_3)),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.17/0.38 tff(28,plain,
% 0.17/0.38 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(29,plain,
% 0.17/0.38 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.17/0.38 inference(quant_inst,[status(thm)],[])).
% 0.17/0.38 tff(30,plain,
% 0.17/0.38 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_1, e_1))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.17/0.38 tff(31,plain,
% 0.17/0.38 ((~product(e_3, e_3, e_1)) | (~product(e_3, e_1, e_1))),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[30, 27, 12])).
% 0.17/0.38 tff(32,plain,
% 0.17/0.38 (~product(e_3, e_1, e_1)),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[31, 24])).
% 0.17/0.38 tff(33,plain,
% 0.17/0.38 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl((product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1))) <=> (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1))))),
% 0.17/0.38 inference(bind,[status(th)],[])).
% 0.17/0.38 tff(34,plain,
% 0.17/0.38 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.17/0.38 inference(quant_intro,[status(thm)],[33])).
% 0.17/0.38 tff(35,plain,
% 0.17/0.38 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(36,plain,
% 0.17/0.38 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : trans(monotonicity(rewrite(((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) <=> ((~product(X, Z1, Z2)) | (~product(Y, X, Z1)))), ((((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) | product(Z1, Y, Z2)) <=> (((~product(X, Z1, Z2)) | (~product(Y, X, Z1))) | product(Z1, Y, Z2)))), rewrite((((~product(X, Z1, Z2)) | (~product(Y, X, Z1))) | product(Z1, Y, Z2)) <=> (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))), ((((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) | product(Z1, Y, Z2)) <=> (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))))),
% 0.17/0.38 inference(bind,[status(th)],[])).
% 0.17/0.38 tff(37,plain,
% 0.17/0.38 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) | product(Z1, Y, Z2)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.17/0.38 inference(quant_intro,[status(thm)],[36])).
% 0.17/0.38 tff(38,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) | product(Z1, Y, Z2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qg3')).
% 0.17/0.38 tff(39,plain,
% 0.17/0.38 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.17/0.39 tff(40,plain,
% 0.17/0.39 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.17/0.39 tff(41,plain,(
% 0.17/0.39 ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.17/0.39 inference(skolemize,[status(sab)],[40])).
% 0.17/0.39 tff(42,plain,
% 0.17/0.39 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.17/0.39 tff(43,plain,
% 0.17/0.39 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_1)) | product(e_3, e_1, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_1)) | product(e_3, e_1, e_1))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(44,plain,
% 0.17/0.39 ((product(e_3, e_1, e_1) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_3))) <=> ((~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_1)) | product(e_3, e_1, e_1))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(45,plain,
% 0.17/0.39 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_1) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_1)) | product(e_3, e_1, e_1)))),
% 0.17/0.39 inference(monotonicity,[status(thm)],[44])).
% 0.17/0.39 tff(46,plain,
% 0.17/0.39 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_1) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_1)) | product(e_3, e_1, e_1))),
% 0.17/0.39 inference(transitivity,[status(thm)],[45, 43])).
% 0.17/0.39 tff(47,plain,
% 0.17/0.39 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_1) | (~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_3)))),
% 0.17/0.39 inference(quant_inst,[status(thm)],[])).
% 0.17/0.39 tff(48,plain,
% 0.17/0.39 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_1)) | product(e_3, e_1, e_1)),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.17/0.39 tff(49,plain,
% 0.17/0.39 ($false),
% 0.17/0.39 inference(unit_resolution,[status(thm)],[48, 42, 24, 32, 23])).
% 0.17/0.39 tff(50,plain,((~product(e_3, e_3, e_1)) | (~product(e_1, e_3, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.17/0.39 tff(51,plain,
% 0.17/0.39 (~product(e_3, e_3, e_1)),
% 0.17/0.39 inference(unit_resolution,[status(thm)],[50, 23])).
% 0.17/0.39 tff(52,assumption,(product(e_3, e_3, e_3)), introduced(assumption)).
% 0.17/0.39 tff(53,plain,
% 0.17/0.39 (^[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))))),
% 0.17/0.39 inference(bind,[status(th)],[])).
% 0.17/0.39 tff(54,plain,
% 0.17/0.39 (![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)))),
% 0.17/0.39 inference(quant_intro,[status(thm)],[53])).
% 0.17/0.39 tff(55,plain,
% 0.17/0.39 (![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)))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(56,plain,
% 0.17/0.39 (^[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)))))),
% 0.17/0.39 inference(bind,[status(th)],[])).
% 0.17/0.39 tff(57,plain,
% 0.17/0.39 (![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)))),
% 0.17/0.39 inference(quant_intro,[status(thm)],[56])).
% 0.17/0.39 tff(58,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')).
% 0.17/0.39 tff(59,plain,
% 0.17/0.39 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.17/0.39 tff(60,plain,
% 0.17/0.39 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.17/0.39 tff(61,plain,(
% 0.17/0.39 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.17/0.39 inference(skolemize,[status(sab)],[60])).
% 0.17/0.39 tff(62,plain,
% 0.17/0.39 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.17/0.39 tff(63,plain,
% 0.17/0.39 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(64,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.17/0.39 tff(65,plain,
% 0.17/0.39 (~equalish(e_3, e_1)),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.17/0.39 tff(66,plain,
% 0.17/0.39 (((~![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_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_3, e_1) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(67,plain,
% 0.17/0.39 ((equalish(e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3))) <=> (equalish(e_3, e_1) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(68,plain,
% 0.17/0.39 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3))))),
% 0.17/0.39 inference(monotonicity,[status(thm)],[67])).
% 0.17/0.39 tff(69,plain,
% 0.17/0.39 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.17/0.39 inference(transitivity,[status(thm)],[68, 66])).
% 0.17/0.39 tff(70,plain,
% 0.17/0.39 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.17/0.39 inference(quant_inst,[status(thm)],[])).
% 0.17/0.39 tff(71,plain,
% 0.17/0.39 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.17/0.39 tff(72,plain,
% 0.17/0.39 ($false),
% 0.17/0.39 inference(unit_resolution,[status(thm)],[71, 65, 62, 23, 52])).
% 0.17/0.39 tff(73,plain,((~product(e_3, e_3, e_3)) | (~product(e_1, e_3, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.17/0.39 tff(74,plain,
% 0.17/0.39 (~product(e_3, e_3, e_3)),
% 0.17/0.39 inference(unit_resolution,[status(thm)],[73, 23])).
% 0.17/0.39 tff(75,plain,
% 0.17/0.39 (^[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))))),
% 0.17/0.39 inference(bind,[status(th)],[])).
% 0.17/0.39 tff(76,plain,
% 0.17/0.39 (![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)))),
% 0.17/0.39 inference(quant_intro,[status(thm)],[75])).
% 0.17/0.39 tff(77,plain,
% 0.17/0.39 (![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)))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(78,plain,
% 0.17/0.39 (^[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)))))),
% 0.17/0.39 inference(bind,[status(th)],[])).
% 0.17/0.39 tff(79,plain,
% 0.17/0.39 (![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)))),
% 0.17/0.39 inference(quant_intro,[status(thm)],[78])).
% 0.17/0.39 tff(80,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')).
% 0.17/0.39 tff(81,plain,
% 0.17/0.39 (![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)))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.17/0.39 tff(82,plain,
% 0.17/0.39 (![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)))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.17/0.39 tff(83,plain,(
% 0.17/0.39 ![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)))),
% 0.17/0.39 inference(skolemize,[status(sab)],[82])).
% 0.17/0.39 tff(84,plain,
% 0.17/0.39 (![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)))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.17/0.39 tff(85,plain,
% 0.17/0.39 (group_element(e_3) <=> group_element(e_3)),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(86,axiom,(group_element(e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_3')).
% 0.17/0.39 tff(87,plain,
% 0.17/0.39 (group_element(e_3)),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.17/0.39 tff(88,plain,
% 0.17/0.39 (((~![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_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(89,plain,
% 0.17/0.40 ((product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_3))) <=> (product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(90,plain,
% 0.17/0.40 (((~![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_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3))))),
% 0.17/0.40 inference(monotonicity,[status(thm)],[89])).
% 0.17/0.40 tff(91,plain,
% 0.17/0.40 (((~![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_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3)))),
% 0.17/0.40 inference(transitivity,[status(thm)],[90, 88])).
% 0.17/0.40 tff(92,plain,
% 0.17/0.40 ((~![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_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)))),
% 0.17/0.40 inference(quant_inst,[status(thm)],[])).
% 0.17/0.40 tff(93,plain,
% 0.17/0.40 ((~![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_3, e_3, e_3) | product(e_3, e_3, e_2) | product(e_3, e_3, e_1) | (~group_element(e_3))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.17/0.40 tff(94,plain,
% 0.17/0.40 (product(e_3, e_3, e_2) | product(e_3, e_3, e_1)),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[93, 87, 84, 74])).
% 0.17/0.40 tff(95,plain,
% 0.17/0.40 (product(e_3, e_3, e_2)),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[94, 51])).
% 0.17/0.40 tff(96,plain,
% 0.17/0.40 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(97,plain,
% 0.17/0.40 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.17/0.40 inference(quant_inst,[status(thm)],[])).
% 0.17/0.40 tff(98,plain,
% 0.17/0.40 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_1, e_2))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.17/0.40 tff(99,plain,
% 0.17/0.40 ((~product(e_3, e_3, e_2)) | (~product(e_3, e_1, e_2))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[98, 27, 12])).
% 0.17/0.40 tff(100,plain,
% 0.17/0.40 (~product(e_3, e_1, e_2)),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[99, 95])).
% 0.17/0.40 tff(101,plain,
% 0.17/0.40 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_3, e_2)) | (~product(e_1, e_3, e_3)) | product(e_3, e_1, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_3, e_3)) | product(e_3, e_1, e_2))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(102,plain,
% 0.17/0.40 ((product(e_3, e_1, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_3, e_3))) <=> ((~product(e_3, e_3, e_2)) | (~product(e_1, e_3, e_3)) | product(e_3, e_1, e_2))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(103,plain,
% 0.17/0.40 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, 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(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_3, e_2)) | (~product(e_1, e_3, e_3)) | product(e_3, e_1, e_2)))),
% 0.17/0.40 inference(monotonicity,[status(thm)],[102])).
% 0.17/0.40 tff(104,plain,
% 0.17/0.40 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, 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(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_3, e_3)) | product(e_3, e_1, e_2))),
% 0.17/0.40 inference(transitivity,[status(thm)],[103, 101])).
% 0.17/0.40 tff(105,plain,
% 0.17/0.40 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_3, e_3)))),
% 0.17/0.40 inference(quant_inst,[status(thm)],[])).
% 0.17/0.40 tff(106,plain,
% 0.17/0.40 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_3, e_2)) | (~product(e_1, e_3, e_3)) | product(e_3, e_1, e_2)),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.17/0.40 tff(107,plain,
% 0.17/0.40 ($false),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[106, 42, 95, 100, 23])).
% 0.17/0.40 tff(108,plain,(~product(e_1, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.17/0.40 tff(109,plain,
% 0.17/0.40 (group_element(e_1) <=> group_element(e_1)),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(110,axiom,(group_element(e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_1')).
% 0.17/0.40 tff(111,plain,
% 0.17/0.40 (group_element(e_1)),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.17/0.40 tff(112,plain,
% 0.17/0.40 (((~![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_3, e_1) | (~group_element(e_1)) | product(e_1, e_3, e_2) | (~group_element(e_3)) | product(e_1, 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)))) | product(e_1, e_3, e_1) | (~group_element(e_1)) | product(e_1, e_3, e_2) | (~group_element(e_3)) | product(e_1, e_3, e_3))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(113,plain,
% 0.17/0.40 ((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_1) | (~group_element(e_1)) | product(e_1, e_3, e_2) | (~group_element(e_3)) | product(e_1, e_3, e_3))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(114,plain,
% 0.17/0.40 (((~![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_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_1) | (~group_element(e_1)) | product(e_1, e_3, e_2) | (~group_element(e_3)) | product(e_1, e_3, e_3)))),
% 0.17/0.40 inference(monotonicity,[status(thm)],[113])).
% 0.17/0.40 tff(115,plain,
% 0.17/0.40 (((~![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_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_1) | (~group_element(e_1)) | product(e_1, e_3, e_2) | (~group_element(e_3)) | product(e_1, e_3, e_3))),
% 0.17/0.40 inference(transitivity,[status(thm)],[114, 112])).
% 0.17/0.40 tff(116,plain,
% 0.17/0.40 ((~![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_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)))),
% 0.17/0.40 inference(quant_inst,[status(thm)],[])).
% 0.17/0.40 tff(117,plain,
% 0.17/0.40 ((~![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_3, e_1) | (~group_element(e_1)) | product(e_1, e_3, e_2) | (~group_element(e_3)) | product(e_1, e_3, e_3)),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.17/0.40 tff(118,plain,
% 0.17/0.40 (product(e_1, e_3, e_1) | product(e_1, e_3, e_2)),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[117, 111, 87, 84, 108])).
% 0.17/0.40 tff(119,plain,
% 0.17/0.40 (product(e_1, e_3, e_1)),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[118, 22])).
% 0.17/0.40 tff(120,assumption,(product(e_2, e_1, e_3)), introduced(assumption)).
% 0.17/0.40 tff(121,plain,
% 0.17/0.40 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_1, e_3, e_3) | (~product(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_1, e_3, e_3) | (~product(e_3, e_2, e_1)))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(122,plain,
% 0.17/0.40 ((product(e_1, e_3, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_2, e_1))) <=> ((~product(e_2, e_1, e_3)) | product(e_1, e_3, e_3) | (~product(e_3, e_2, e_1)))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(123,plain,
% 0.17/0.40 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_3, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_1, e_3, e_3) | (~product(e_3, e_2, e_1))))),
% 0.17/0.40 inference(monotonicity,[status(thm)],[122])).
% 0.17/0.40 tff(124,plain,
% 0.17/0.40 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_3, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_1, e_3, e_3) | (~product(e_3, e_2, e_1)))),
% 0.17/0.40 inference(transitivity,[status(thm)],[123, 121])).
% 0.17/0.40 tff(125,plain,
% 0.17/0.40 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_3, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_2, e_1)))),
% 0.17/0.40 inference(quant_inst,[status(thm)],[])).
% 0.17/0.40 tff(126,plain,
% 0.17/0.40 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_1, e_3, e_3) | (~product(e_3, e_2, e_1))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.17/0.40 tff(127,plain,
% 0.17/0.40 (~product(e_3, e_2, e_1)),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[126, 42, 120, 108])).
% 0.17/0.40 tff(128,assumption,(product(e_1, e_3, e_1)), introduced(assumption)).
% 0.17/0.40 tff(129,plain,
% 0.17/0.40 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_3, e_1)) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_1)) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_1))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(130,plain,
% 0.17/0.40 ((product(e_3, e_2, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_2, e_1, e_3))) <=> ((~product(e_1, e_3, e_1)) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_1))),
% 0.17/0.41 inference(rewrite,[status(thm)],[])).
% 0.17/0.41 tff(131,plain,
% 0.17/0.41 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_3, e_1)) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_1)))),
% 0.17/0.41 inference(monotonicity,[status(thm)],[130])).
% 0.17/0.41 tff(132,plain,
% 0.17/0.41 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_1)) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_1))),
% 0.17/0.41 inference(transitivity,[status(thm)],[131, 129])).
% 0.17/0.41 tff(133,plain,
% 0.17/0.41 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_2, e_1, e_3)))),
% 0.17/0.41 inference(quant_inst,[status(thm)],[])).
% 0.17/0.41 tff(134,plain,
% 0.17/0.41 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_1)) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_1)),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.17/0.41 tff(135,plain,
% 0.17/0.41 ($false),
% 0.17/0.41 inference(unit_resolution,[status(thm)],[134, 42, 128, 120, 127])).
% 0.17/0.41 tff(136,plain,((~product(e_2, e_1, e_3)) | (~product(e_1, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.17/0.41 tff(137,plain,
% 0.17/0.41 (~product(e_2, e_1, e_3)),
% 0.17/0.41 inference(unit_resolution,[status(thm)],[136, 119])).
% 0.17/0.41 tff(138,assumption,(product(e_1, e_2, e_1)), introduced(assumption)).
% 0.17/0.41 tff(139,plain,
% 0.17/0.41 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.17/0.41 inference(rewrite,[status(thm)],[])).
% 0.17/0.41 tff(140,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.17/0.41 tff(141,plain,
% 0.17/0.41 (~equalish(e_3, e_2)),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.17/0.41 tff(142,plain,
% 0.17/0.41 (((~![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_1, e_2, e_1)) | (~product(e_1, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.17/0.41 inference(rewrite,[status(thm)],[])).
% 0.17/0.41 tff(143,plain,
% 0.17/0.41 ((~![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_1, e_2, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.17/0.41 inference(quant_inst,[status(thm)],[])).
% 0.17/0.41 tff(144,plain,
% 0.17/0.41 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_3, e_1))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.17/0.41 tff(145,plain,
% 0.17/0.41 ($false),
% 0.17/0.41 inference(unit_resolution,[status(thm)],[144, 141, 12, 138, 128])).
% 0.17/0.41 tff(146,plain,((~product(e_1, e_3, e_1)) | (~product(e_1, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.17/0.41 tff(147,plain,
% 0.17/0.41 (~product(e_1, e_2, e_1)),
% 0.17/0.41 inference(unit_resolution,[status(thm)],[146, 119])).
% 0.17/0.41 tff(148,plain,
% 0.17/0.41 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_2)) | product(e_1, e_1, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_2)) | product(e_1, e_1, e_2))),
% 0.17/0.41 inference(rewrite,[status(thm)],[])).
% 0.17/0.41 tff(149,plain,
% 0.17/0.41 ((product(e_1, e_1, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_3, e_1))) <=> ((~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_2)) | product(e_1, e_1, e_2))),
% 0.17/0.41 inference(rewrite,[status(thm)],[])).
% 0.17/0.41 tff(150,plain,
% 0.17/0.41 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_2)) | product(e_1, e_1, e_2)))),
% 0.17/0.41 inference(monotonicity,[status(thm)],[149])).
% 0.17/0.41 tff(151,plain,
% 0.17/0.41 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_2)) | product(e_1, e_1, e_2))),
% 0.17/0.41 inference(transitivity,[status(thm)],[150, 148])).
% 0.17/0.41 tff(152,plain,
% 0.17/0.41 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_3, e_1)))),
% 0.17/0.41 inference(quant_inst,[status(thm)],[])).
% 0.17/0.41 tff(153,plain,
% 0.17/0.41 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_2)) | product(e_1, e_1, e_2)),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.17/0.41 tff(154,plain,
% 0.17/0.41 ((~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_2)) | product(e_1, e_1, e_2)),
% 0.17/0.41 inference(unit_resolution,[status(thm)],[153, 42])).
% 0.17/0.41 tff(155,plain,
% 0.17/0.41 (product(e_1, e_1, e_2)),
% 0.17/0.41 inference(unit_resolution,[status(thm)],[154, 1, 128])).
% 0.17/0.41 tff(156,plain,
% 0.17/0.41 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_1, e_2)))),
% 0.17/0.41 inference(rewrite,[status(thm)],[])).
% 0.17/0.41 tff(157,plain,
% 0.17/0.41 ((equalish(e_3, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_3, e_1, e_2))) <=> (equalish(e_3, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_1, e_2)))),
% 0.17/0.41 inference(rewrite,[status(thm)],[])).
% 0.17/0.41 tff(158,plain,
% 0.17/0.41 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_3, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_1, e_2))))),
% 0.17/0.41 inference(monotonicity,[status(thm)],[157])).
% 0.17/0.41 tff(159,plain,
% 0.17/0.41 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_3, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_1, e_2)))),
% 0.17/0.41 inference(transitivity,[status(thm)],[158, 156])).
% 0.17/0.41 tff(160,plain,
% 0.17/0.41 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.17/0.41 inference(quant_inst,[status(thm)],[])).
% 0.17/0.41 tff(161,plain,
% 0.17/0.41 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_1, e_1, e_2))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.17/0.41 tff(162,plain,
% 0.17/0.41 ($false),
% 0.17/0.41 inference(unit_resolution,[status(thm)],[161, 65, 62, 1, 155])).
% 0.17/0.41 tff(163,plain,((~product(e_3, e_1, e_2)) | (~product(e_1, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.17/0.41 tff(164,plain,
% 0.17/0.41 (~product(e_3, e_1, e_2)),
% 0.17/0.41 inference(unit_resolution,[status(thm)],[163, 119])).
% 0.17/0.42 tff(165,assumption,(product(e_3, e_1, e_3)), introduced(assumption)).
% 0.17/0.42 tff(166,plain,
% 0.17/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_3, e_1)) | product(e_1, e_3, e_3) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_3, e_1)) | product(e_1, e_3, e_3) | (~product(e_3, e_1, e_3)))),
% 0.17/0.42 inference(rewrite,[status(thm)],[])).
% 0.17/0.42 tff(167,plain,
% 0.17/0.42 ((product(e_1, e_3, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_1))) <=> ((~product(e_3, e_3, e_1)) | product(e_1, e_3, e_3) | (~product(e_3, e_1, e_3)))),
% 0.17/0.42 inference(rewrite,[status(thm)],[])).
% 0.17/0.42 tff(168,plain,
% 0.17/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_3, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_3, e_1)) | product(e_1, e_3, e_3) | (~product(e_3, e_1, e_3))))),
% 0.17/0.42 inference(monotonicity,[status(thm)],[167])).
% 0.17/0.42 tff(169,plain,
% 0.17/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_3, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_3, e_1)) | product(e_1, e_3, e_3) | (~product(e_3, e_1, e_3)))),
% 0.17/0.42 inference(transitivity,[status(thm)],[168, 166])).
% 0.17/0.42 tff(170,plain,
% 0.17/0.42 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_3, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_1)))),
% 0.17/0.42 inference(quant_inst,[status(thm)],[])).
% 0.17/0.42 tff(171,plain,
% 0.17/0.42 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_3, e_1)) | product(e_1, e_3, e_3) | (~product(e_3, e_1, e_3))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.17/0.42 tff(172,plain,
% 0.17/0.42 (~product(e_3, e_3, e_1)),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[171, 42, 165, 108])).
% 0.17/0.42 tff(173,plain,
% 0.17/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.17/0.42 inference(rewrite,[status(thm)],[])).
% 0.17/0.42 tff(174,plain,
% 0.17/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.17/0.42 inference(quant_inst,[status(thm)],[])).
% 0.17/0.42 tff(175,plain,
% 0.17/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.17/0.42 tff(176,plain,
% 0.17/0.42 ($false),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[175, 27, 12, 165, 52])).
% 0.17/0.42 tff(177,plain,((~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.17/0.42 tff(178,plain,
% 0.17/0.42 (~product(e_3, e_3, e_3)),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[177, 165])).
% 0.17/0.42 tff(179,plain,
% 0.17/0.42 (product(e_3, e_3, e_2)),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[93, 87, 84, 172, 178])).
% 0.17/0.42 tff(180,assumption,(product(e_3, e_3, e_2)), introduced(assumption)).
% 0.17/0.42 tff(181,assumption,(product(e_1, e_3, e_2)), introduced(assumption)).
% 0.17/0.42 tff(182,plain,
% 0.17/0.42 (((~![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)))),
% 0.17/0.42 inference(rewrite,[status(thm)],[])).
% 0.17/0.42 tff(183,plain,
% 0.17/0.42 ((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)))),
% 0.17/0.42 inference(rewrite,[status(thm)],[])).
% 0.17/0.42 tff(184,plain,
% 0.17/0.42 (((~![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))))),
% 0.17/0.42 inference(monotonicity,[status(thm)],[183])).
% 0.17/0.42 tff(185,plain,
% 0.17/0.42 (((~![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)))),
% 0.17/0.42 inference(transitivity,[status(thm)],[184, 182])).
% 0.17/0.42 tff(186,plain,
% 0.17/0.42 ((~![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)))),
% 0.17/0.42 inference(quant_inst,[status(thm)],[])).
% 0.17/0.42 tff(187,plain,
% 0.17/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_3, e_2))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.17/0.42 tff(188,plain,
% 0.17/0.42 ($false),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[187, 27, 62, 181, 180])).
% 0.17/0.42 tff(189,plain,((~product(e_1, e_3, e_2)) | (~product(e_3, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.17/0.42 tff(190,plain,
% 0.17/0.42 (~product(e_1, e_3, e_2)),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[189, 179])).
% 0.17/0.42 tff(191,plain,
% 0.17/0.42 (product(e_1, e_3, e_1)),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[118, 190])).
% 0.17/0.42 tff(192,plain,
% 0.17/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_3, e_1)) | product(e_3, e_3, e_1) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_1)) | product(e_3, e_3, e_1) | (~product(e_3, e_1, e_3)))),
% 0.17/0.42 inference(rewrite,[status(thm)],[])).
% 0.17/0.42 tff(193,plain,
% 0.17/0.42 ((product(e_3, e_3, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_3))) <=> ((~product(e_1, e_3, e_1)) | product(e_3, e_3, e_1) | (~product(e_3, e_1, e_3)))),
% 0.17/0.42 inference(rewrite,[status(thm)],[])).
% 0.17/0.42 tff(194,plain,
% 0.17/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_3, e_1)) | product(e_3, e_3, e_1) | (~product(e_3, e_1, e_3))))),
% 0.17/0.42 inference(monotonicity,[status(thm)],[193])).
% 0.17/0.42 tff(195,plain,
% 0.17/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_1)) | product(e_3, e_3, e_1) | (~product(e_3, e_1, e_3)))),
% 0.17/0.42 inference(transitivity,[status(thm)],[194, 192])).
% 0.17/0.42 tff(196,plain,
% 0.17/0.42 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_3, e_1, e_3)))),
% 0.17/0.42 inference(quant_inst,[status(thm)],[])).
% 0.17/0.42 tff(197,plain,
% 0.17/0.42 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_1)) | product(e_3, e_3, e_1) | (~product(e_3, e_1, e_3))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.17/0.42 tff(198,plain,
% 0.17/0.42 ($false),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[197, 42, 191, 172, 165])).
% 0.17/0.42 tff(199,plain,(~product(e_3, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.17/0.42 tff(200,assumption,(~product(e_3, e_1, e_3)), introduced(assumption)).
% 0.17/0.42 tff(201,assumption,(~product(e_3, e_1, e_1)), introduced(assumption)).
% 0.17/0.42 tff(202,assumption,(~product(e_3, e_1, e_2)), introduced(assumption)).
% 0.17/0.42 tff(203,plain,
% 0.17/0.42 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3) | (~group_element(e_3)) | product(e_3, e_1, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3) | (~group_element(e_3)) | product(e_3, e_1, e_1))),
% 0.17/0.42 inference(rewrite,[status(thm)],[])).
% 0.17/0.42 tff(204,plain,
% 0.17/0.42 ((product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3))) <=> ((~group_element(e_1)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3) | (~group_element(e_3)) | product(e_3, e_1, e_1))),
% 0.17/0.42 inference(rewrite,[status(thm)],[])).
% 0.17/0.42 tff(205,plain,
% 0.17/0.42 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3) | (~group_element(e_3)) | product(e_3, e_1, e_1)))),
% 0.17/0.42 inference(monotonicity,[status(thm)],[204])).
% 0.17/0.42 tff(206,plain,
% 0.17/0.42 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3) | (~group_element(e_3)) | product(e_3, e_1, e_1))),
% 0.17/0.42 inference(transitivity,[status(thm)],[205, 203])).
% 0.17/0.42 tff(207,plain,
% 0.17/0.42 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))),
% 0.17/0.42 inference(quant_inst,[status(thm)],[])).
% 0.17/0.42 tff(208,plain,
% 0.17/0.42 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3) | (~group_element(e_3)) | product(e_3, e_1, e_1)),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.17/0.42 tff(209,plain,
% 0.17/0.42 ($false),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[208, 111, 87, 84, 202, 201, 200])).
% 0.17/0.42 tff(210,plain,(product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.17/0.42 tff(211,plain,
% 0.17/0.42 (product(e_3, e_1, e_2) | product(e_3, e_1, e_1)),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[210, 199])).
% 0.17/0.42 tff(212,plain,
% 0.17/0.42 (product(e_3, e_1, e_1)),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[211, 164])).
% 0.17/0.42 tff(213,assumption,(product(e_3, e_1, e_1)), introduced(assumption)).
% 0.17/0.42 tff(214,assumption,(~product(e_1, e_2, e_1)), introduced(assumption)).
% 0.17/0.42 tff(215,plain,
% 0.17/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.17/0.43 inference(rewrite,[status(thm)],[])).
% 0.17/0.43 tff(216,plain,
% 0.17/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_2, e_3, e_1)))),
% 0.17/0.43 inference(quant_inst,[status(thm)],[])).
% 0.17/0.43 tff(217,plain,
% 0.17/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_2, e_3, e_1))),
% 0.17/0.43 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.17/0.43 tff(218,plain,
% 0.17/0.43 (~product(e_2, e_3, e_1)),
% 0.17/0.43 inference(unit_resolution,[status(thm)],[217, 42, 214, 213])).
% 0.17/0.43 tff(219,assumption,(~product(e_2, e_3, e_3)), introduced(assumption)).
% 0.17/0.43 tff(220,plain,
% 0.17/0.43 (group_element(e_2) <=> group_element(e_2)),
% 0.17/0.43 inference(rewrite,[status(thm)],[])).
% 0.17/0.43 tff(221,axiom,(group_element(e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_2')).
% 0.17/0.43 tff(222,plain,
% 0.17/0.43 (group_element(e_2)),
% 0.17/0.43 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.17/0.43 tff(223,plain,
% 0.17/0.43 (((~![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_2)) | (~group_element(e_3)) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, 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_2)) | (~group_element(e_3)) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1))),
% 0.17/0.43 inference(rewrite,[status(thm)],[])).
% 0.17/0.43 tff(224,plain,
% 0.17/0.43 ((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)) | (~group_element(e_3)) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1))),
% 0.17/0.43 inference(rewrite,[status(thm)],[])).
% 0.17/0.43 tff(225,plain,
% 0.17/0.43 (((~![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_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)) | (~group_element(e_3)) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1)))),
% 0.17/0.43 inference(monotonicity,[status(thm)],[224])).
% 0.17/0.43 tff(226,plain,
% 0.17/0.43 (((~![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_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)) | (~group_element(e_3)) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1))),
% 0.17/0.43 inference(transitivity,[status(thm)],[225, 223])).
% 0.17/0.43 tff(227,plain,
% 0.17/0.43 ((~![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_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)))),
% 0.17/0.43 inference(quant_inst,[status(thm)],[])).
% 0.17/0.43 tff(228,plain,
% 0.17/0.43 ((~![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_2)) | (~group_element(e_3)) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1)),
% 0.17/0.43 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.17/0.43 tff(229,plain,
% 0.17/0.43 (product(e_2, e_3, e_2) | product(e_2, e_3, e_1)),
% 0.17/0.43 inference(unit_resolution,[status(thm)],[228, 222, 87, 84, 219])).
% 0.17/0.43 tff(230,plain,
% 0.17/0.43 (product(e_2, e_3, e_2)),
% 0.17/0.43 inference(unit_resolution,[status(thm)],[229, 218])).
% 0.17/0.43 tff(231,assumption,(~product(e_2, e_1, e_3)), introduced(assumption)).
% 0.17/0.43 tff(232,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.17/0.43 tff(233,plain,
% 0.17/0.43 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.17/0.43 inference(rewrite,[status(thm)],[])).
% 0.17/0.43 tff(234,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.17/0.43 tff(235,plain,
% 0.17/0.43 (~equalish(e_2, e_3)),
% 0.17/0.43 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.17/0.43 tff(236,plain,
% 0.17/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, 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_3) | (~product(e_3, e_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.17/0.43 inference(rewrite,[status(thm)],[])).
% 0.17/0.43 tff(237,plain,
% 0.17/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.17/0.43 inference(quant_inst,[status(thm)],[])).
% 0.17/0.43 tff(238,plain,
% 0.17/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_1, e_1)) | (~product(e_2, e_1, e_1))),
% 0.17/0.43 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.17/0.43 tff(239,plain,
% 0.17/0.43 ($false),
% 0.17/0.43 inference(unit_resolution,[status(thm)],[238, 235, 62, 213, 232])).
% 0.17/0.43 tff(240,plain,((~product(e_2, e_1, e_1)) | (~product(e_3, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.17/0.43 tff(241,plain,
% 0.17/0.43 (~product(e_2, e_1, e_1)),
% 0.17/0.43 inference(unit_resolution,[status(thm)],[240, 213])).
% 0.17/0.43 tff(242,plain,
% 0.17/0.43 (((~![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_2)) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1))),
% 0.17/0.43 inference(rewrite,[status(thm)],[])).
% 0.17/0.43 tff(243,plain,
% 0.17/0.43 ((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_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1))),
% 0.17/0.43 inference(rewrite,[status(thm)],[])).
% 0.17/0.43 tff(244,plain,
% 0.17/0.43 (((~![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_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_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1)))),
% 0.17/0.43 inference(monotonicity,[status(thm)],[243])).
% 0.17/0.43 tff(245,plain,
% 0.17/0.43 (((~![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_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_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1))),
% 0.17/0.43 inference(transitivity,[status(thm)],[244, 242])).
% 0.17/0.43 tff(246,plain,
% 0.17/0.43 ((~![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_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)))),
% 0.17/0.44 inference(quant_inst,[status(thm)],[])).
% 0.17/0.44 tff(247,plain,
% 0.17/0.44 ((~![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)) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1)),
% 0.17/0.44 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.17/0.44 tff(248,plain,
% 0.17/0.44 (product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1)),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[247, 111, 222, 84])).
% 0.17/0.44 tff(249,plain,
% 0.17/0.44 (product(e_2, e_1, e_2)),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[248, 241, 231])).
% 0.17/0.44 tff(250,plain,
% 0.17/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_2, e_1, e_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_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_3, e_2)))),
% 0.17/0.44 inference(rewrite,[status(thm)],[])).
% 0.17/0.44 tff(251,plain,
% 0.17/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_3, e_2)))),
% 0.17/0.44 inference(quant_inst,[status(thm)],[])).
% 0.17/0.44 tff(252,plain,
% 0.17/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_3, e_2))),
% 0.17/0.44 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.17/0.44 tff(253,plain,
% 0.17/0.44 ($false),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[252, 65, 12, 249, 230])).
% 0.17/0.44 tff(254,plain,((~product(e_3, e_1, e_1)) | product(e_2, e_3, e_3) | product(e_1, e_2, e_1) | product(e_2, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.17/0.44 tff(255,plain,
% 0.17/0.44 (product(e_2, e_3, e_3)),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[254, 212, 147, 137])).
% 0.17/0.44 tff(256,assumption,(product(e_2, e_3, e_3)), introduced(assumption)).
% 0.17/0.44 tff(257,assumption,(product(e_3, e_2, e_3)), introduced(assumption)).
% 0.17/0.44 tff(258,plain,
% 0.17/0.44 (((~![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)))),
% 0.17/0.44 inference(rewrite,[status(thm)],[])).
% 0.17/0.44 tff(259,plain,
% 0.17/0.44 ((~![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)))),
% 0.17/0.44 inference(quant_inst,[status(thm)],[])).
% 0.17/0.44 tff(260,plain,
% 0.17/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3))),
% 0.17/0.44 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.17/0.44 tff(261,plain,
% 0.17/0.44 ($false),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[260, 235, 12, 257, 52])).
% 0.17/0.44 tff(262,plain,((~product(e_3, e_2, e_3)) | (~product(e_3, e_3, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.17/0.44 tff(263,plain,
% 0.17/0.44 (~product(e_3, e_2, e_3)),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[262, 52])).
% 0.17/0.44 tff(264,plain,
% 0.17/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_3, e_3)) | product(e_3, e_2, e_3) | (~product(e_2, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_3, e_3)) | product(e_3, e_2, e_3) | (~product(e_2, e_3, e_3)))),
% 0.17/0.44 inference(rewrite,[status(thm)],[])).
% 0.17/0.44 tff(265,plain,
% 0.17/0.44 ((product(e_3, e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_3, e_3))) <=> ((~product(e_3, e_3, e_3)) | product(e_3, e_2, e_3) | (~product(e_2, e_3, e_3)))),
% 0.17/0.44 inference(rewrite,[status(thm)],[])).
% 0.17/0.44 tff(266,plain,
% 0.17/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_3, e_3)) | product(e_3, e_2, e_3) | (~product(e_2, e_3, e_3))))),
% 0.17/0.44 inference(monotonicity,[status(thm)],[265])).
% 0.17/0.44 tff(267,plain,
% 0.17/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_3, e_3)) | product(e_3, e_2, e_3) | (~product(e_2, e_3, e_3)))),
% 0.17/0.44 inference(transitivity,[status(thm)],[266, 264])).
% 0.17/0.44 tff(268,plain,
% 0.17/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_3, e_3)))),
% 0.17/0.44 inference(quant_inst,[status(thm)],[])).
% 0.17/0.44 tff(269,plain,
% 0.17/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_3, e_3)) | product(e_3, e_2, e_3) | (~product(e_2, e_3, e_3))),
% 0.17/0.44 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.17/0.44 tff(270,plain,
% 0.17/0.44 ($false),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[269, 42, 263, 52, 256])).
% 0.17/0.44 tff(271,plain,((~product(e_3, e_3, e_3)) | (~product(e_2, e_3, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.17/0.44 tff(272,plain,
% 0.17/0.44 (~product(e_3, e_3, e_3)),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[271, 255])).
% 0.17/0.44 tff(273,plain,
% 0.17/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_3)))),
% 0.17/0.44 inference(rewrite,[status(thm)],[])).
% 0.17/0.44 tff(274,plain,
% 0.17/0.44 ((product(e_3, e_3, e_3) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_2, e_3))) <=> (product(e_3, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_3)))),
% 0.17/0.44 inference(rewrite,[status(thm)],[])).
% 0.17/0.44 tff(275,plain,
% 0.17/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_3, e_3) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_3))))),
% 0.17/0.44 inference(monotonicity,[status(thm)],[274])).
% 0.17/0.44 tff(276,plain,
% 0.17/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_3, e_3) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_3)))),
% 0.17/0.44 inference(transitivity,[status(thm)],[275, 273])).
% 0.17/0.44 tff(277,plain,
% 0.17/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_3, e_3) | (~product(e_2, e_3, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.17/0.44 inference(quant_inst,[status(thm)],[])).
% 0.17/0.44 tff(278,plain,
% 0.17/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_3, e_3))),
% 0.17/0.44 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.17/0.44 tff(279,plain,
% 0.17/0.44 (~product(e_3, e_2, e_3)),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[278, 42, 272, 255])).
% 0.17/0.44 tff(280,plain,
% 0.17/0.44 (~product(e_2, e_1, e_1)),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[240, 212])).
% 0.17/0.44 tff(281,plain,
% 0.17/0.44 (product(e_2, e_1, e_2)),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[248, 280, 137])).
% 0.17/0.44 tff(282,plain,
% 0.17/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_3, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_3, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_2, e_1)))),
% 0.17/0.44 inference(rewrite,[status(thm)],[])).
% 0.17/0.44 tff(283,plain,
% 0.17/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_3, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_2, e_1)))),
% 0.17/0.44 inference(quant_inst,[status(thm)],[])).
% 0.17/0.44 tff(284,plain,
% 0.17/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_3, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_2, e_1))),
% 0.17/0.44 inference(modus_ponens,[status(thm)],[283, 282])).
% 0.17/0.44 tff(285,plain,
% 0.17/0.44 (~product(e_3, e_2, e_1)),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[284, 42, 22, 281])).
% 0.17/0.44 tff(286,plain,
% 0.17/0.44 (((~![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)) | (~group_element(e_3)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1) | product(e_3, e_2, 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_3)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1) | product(e_3, e_2, e_2))),
% 0.17/0.44 inference(rewrite,[status(thm)],[])).
% 0.17/0.44 tff(287,plain,
% 0.17/0.44 ((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)) | (~group_element(e_3)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1) | product(e_3, e_2, e_2))),
% 0.17/0.44 inference(rewrite,[status(thm)],[])).
% 0.17/0.44 tff(288,plain,
% 0.17/0.44 (((~![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)) | (~group_element(e_3)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1) | product(e_3, e_2, e_2)))),
% 0.17/0.44 inference(monotonicity,[status(thm)],[287])).
% 0.17/0.44 tff(289,plain,
% 0.17/0.44 (((~![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)) | (~group_element(e_3)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1) | product(e_3, e_2, e_2))),
% 0.17/0.44 inference(transitivity,[status(thm)],[288, 286])).
% 0.17/0.44 tff(290,plain,
% 0.17/0.44 ((~![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)))),
% 0.17/0.44 inference(quant_inst,[status(thm)],[])).
% 0.17/0.44 tff(291,plain,
% 0.17/0.44 ((~![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)) | (~group_element(e_3)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1) | product(e_3, e_2, e_2)),
% 0.17/0.44 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.17/0.44 tff(292,plain,
% 0.17/0.44 (product(e_3, e_2, e_3) | product(e_3, e_2, e_2)),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[291, 222, 87, 84, 285])).
% 0.17/0.44 tff(293,plain,
% 0.17/0.44 (product(e_3, e_2, e_2)),
% 0.17/0.44 inference(unit_resolution,[status(thm)],[292, 279])).
% 0.17/0.44 tff(294,assumption,(product(e_2, e_1, e_2)), introduced(assumption)).
% 0.17/0.44 tff(295,assumption,(product(e_1, e_2, e_3)), introduced(assumption)).
% 0.17/0.45 tff(296,assumption,(~product(e_2, e_2, e_3)), introduced(assumption)).
% 0.17/0.45 tff(297,plain,
% 0.17/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3)))),
% 0.17/0.45 inference(rewrite,[status(thm)],[])).
% 0.17/0.45 tff(298,plain,
% 0.17/0.45 ((product(e_2, e_2, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2))) <=> (product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3)))),
% 0.17/0.45 inference(rewrite,[status(thm)],[])).
% 0.17/0.45 tff(299,plain,
% 0.17/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3))))),
% 0.17/0.45 inference(monotonicity,[status(thm)],[298])).
% 0.17/0.45 tff(300,plain,
% 0.17/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3)))),
% 0.17/0.45 inference(transitivity,[status(thm)],[299, 297])).
% 0.17/0.45 tff(301,plain,
% 0.17/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2)))),
% 0.17/0.45 inference(quant_inst,[status(thm)],[])).
% 0.17/0.45 tff(302,plain,
% 0.17/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3))),
% 0.17/0.45 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.17/0.45 tff(303,plain,
% 0.17/0.45 ($false),
% 0.17/0.45 inference(unit_resolution,[status(thm)],[302, 42, 295, 296, 294])).
% 0.17/0.45 tff(304,plain,(product(e_2, e_2, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.17/0.45 tff(305,plain,
% 0.17/0.45 (product(e_2, e_2, e_3)),
% 0.17/0.45 inference(unit_resolution,[status(thm)],[304, 295, 294])).
% 0.17/0.45 tff(306,plain,
% 0.17/0.45 (((~![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_2, e_3)) | (~product(e_1, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.17/0.45 inference(rewrite,[status(thm)],[])).
% 0.17/0.45 tff(307,plain,
% 0.17/0.45 ((equalish(e_2, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_2, e_3))) <=> (equalish(e_2, e_1) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.17/0.45 inference(rewrite,[status(thm)],[])).
% 0.17/0.45 tff(308,plain,
% 0.17/0.45 (((~![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_2, e_3)) | (~product(e_2, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_3))))),
% 0.17/0.45 inference(monotonicity,[status(thm)],[307])).
% 0.17/0.45 tff(309,plain,
% 0.17/0.45 (((~![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_2, e_3)) | (~product(e_2, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.17/0.45 inference(transitivity,[status(thm)],[308, 306])).
% 0.17/0.45 tff(310,plain,
% 0.17/0.45 ((~![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_2, e_3)) | (~product(e_2, e_2, e_3)))),
% 0.17/0.45 inference(quant_inst,[status(thm)],[])).
% 0.17/0.45 tff(311,plain,
% 0.17/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_3))),
% 0.17/0.45 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.17/0.45 tff(312,plain,
% 0.17/0.45 ($false),
% 0.17/0.45 inference(unit_resolution,[status(thm)],[311, 15, 62, 295, 305])).
% 0.17/0.45 tff(313,plain,((~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.17/0.45 tff(314,plain,
% 0.17/0.45 (~product(e_1, e_2, e_3)),
% 0.17/0.45 inference(unit_resolution,[status(thm)],[313, 281])).
% 0.17/0.45 tff(315,plain,
% 0.17/0.45 (((~![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_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)))),
% 0.17/0.45 inference(rewrite,[status(thm)],[])).
% 0.17/0.45 tff(316,plain,
% 0.17/0.45 ((~![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_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)))),
% 0.17/0.45 inference(quant_inst,[status(thm)],[])).
% 0.17/0.45 tff(317,plain,
% 0.17/0.45 ((~![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_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))),
% 0.17/0.45 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.17/0.45 tff(318,plain,
% 0.17/0.45 (product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1)),
% 0.17/0.45 inference(unit_resolution,[status(thm)],[317, 111, 222, 84])).
% 0.17/0.45 tff(319,plain,
% 0.17/0.45 (product(e_1, e_2, e_2)),
% 0.17/0.45 inference(unit_resolution,[status(thm)],[318, 314, 147])).
% 0.17/0.45 tff(320,plain,
% 0.17/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, 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_1) | (~product(e_1, e_2, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.17/0.45 inference(rewrite,[status(thm)],[])).
% 0.17/0.45 tff(321,plain,
% 0.17/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.17/0.45 inference(quant_inst,[status(thm)],[])).
% 0.17/0.45 tff(322,plain,
% 0.17/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_3, e_2, e_2))),
% 0.17/0.45 inference(modus_ponens,[status(thm)],[321, 320])).
% 0.17/0.45 tff(323,plain,
% 0.17/0.45 ($false),
% 0.17/0.45 inference(unit_resolution,[status(thm)],[322, 65, 62, 319, 293])).
% 0.17/0.45 tff(324,plain,(product(e_1, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.17/0.45 tff(325,plain,
% 0.17/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_2))),
% 0.17/0.45 inference(rewrite,[status(thm)],[])).
% 0.17/0.45 tff(326,plain,
% 0.17/0.45 ((product(e_3, e_2, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_3))) <=> ((~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_2))),
% 0.17/0.45 inference(rewrite,[status(thm)],[])).
% 0.17/0.45 tff(327,plain,
% 0.17/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_2)))),
% 0.17/0.46 inference(monotonicity,[status(thm)],[326])).
% 0.17/0.46 tff(328,plain,
% 0.17/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_2))),
% 0.17/0.46 inference(transitivity,[status(thm)],[327, 325])).
% 0.17/0.46 tff(329,plain,
% 0.17/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.17/0.46 inference(quant_inst,[status(thm)],[])).
% 0.17/0.46 tff(330,plain,
% 0.17/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_2)),
% 0.17/0.46 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.17/0.46 tff(331,plain,
% 0.17/0.46 (~product(e_2, e_1, e_3)),
% 0.17/0.46 inference(unit_resolution,[status(thm)],[330, 42, 324, 21])).
% 0.17/0.46 tff(332,assumption,(product(e_1, e_2, e_2)), introduced(assumption)).
% 0.17/0.46 tff(333,plain,
% 0.17/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.17/0.46 inference(rewrite,[status(thm)],[])).
% 0.17/0.46 tff(334,plain,
% 0.17/0.46 ((equalish(e_2, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_2, e_2))) <=> (equalish(e_2, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.17/0.46 inference(rewrite,[status(thm)],[])).
% 0.17/0.46 tff(335,plain,
% 0.17/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_3, e_2))))),
% 0.17/0.46 inference(monotonicity,[status(thm)],[334])).
% 0.17/0.46 tff(336,plain,
% 0.17/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.17/0.46 inference(transitivity,[status(thm)],[335, 333])).
% 0.17/0.46 tff(337,plain,
% 0.17/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.17/0.46 inference(quant_inst,[status(thm)],[])).
% 0.17/0.46 tff(338,plain,
% 0.17/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_3, e_2))),
% 0.17/0.46 inference(modus_ponens,[status(thm)],[337, 336])).
% 0.17/0.46 tff(339,plain,
% 0.17/0.46 ($false),
% 0.17/0.46 inference(unit_resolution,[status(thm)],[338, 235, 12, 332, 181])).
% 0.17/0.46 tff(340,plain,((~product(e_1, e_2, e_2)) | (~product(e_1, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.17/0.46 tff(341,plain,
% 0.17/0.46 (~product(e_1, e_2, e_2)),
% 0.17/0.46 inference(unit_resolution,[status(thm)],[340, 324])).
% 0.17/0.46 tff(342,assumption,(~product(e_1, e_2, e_2)), introduced(assumption)).
% 0.17/0.46 tff(343,plain,
% 0.17/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_3, e_1)))),
% 0.17/0.46 inference(rewrite,[status(thm)],[])).
% 0.17/0.46 tff(344,plain,
% 0.17/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_3, e_1)))),
% 0.17/0.46 inference(quant_inst,[status(thm)],[])).
% 0.17/0.46 tff(345,plain,
% 0.17/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_3, e_1))),
% 0.17/0.46 inference(modus_ponens,[status(thm)],[344, 343])).
% 0.17/0.46 tff(346,plain,
% 0.17/0.46 (~product(e_2, e_3, e_1)),
% 0.17/0.46 inference(unit_resolution,[status(thm)],[345, 42, 342, 1])).
% 0.17/0.46 tff(347,assumption,(~product(e_1, e_2, e_3)), introduced(assumption)).
% 0.17/0.46 tff(348,plain,
% 0.17/0.46 (product(e_1, e_2, e_1)),
% 0.17/0.46 inference(unit_resolution,[status(thm)],[318, 342, 347])).
% 0.17/0.46 tff(349,plain,
% 0.17/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_2, e_1)) | (~product(e_3, e_1, e_2)) | product(e_2, e_3, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_1)) | (~product(e_3, e_1, e_2)) | product(e_2, e_3, e_1))),
% 0.17/0.46 inference(rewrite,[status(thm)],[])).
% 0.17/0.46 tff(350,plain,
% 0.17/0.46 ((product(e_2, e_3, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_3, e_1, e_2))) <=> ((~product(e_1, e_2, e_1)) | (~product(e_3, e_1, e_2)) | product(e_2, e_3, e_1))),
% 0.17/0.46 inference(rewrite,[status(thm)],[])).
% 0.17/0.46 tff(351,plain,
% 0.17/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_2, e_1)) | (~product(e_3, e_1, e_2)) | product(e_2, e_3, e_1)))),
% 0.17/0.46 inference(monotonicity,[status(thm)],[350])).
% 0.17/0.46 tff(352,plain,
% 0.17/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_1)) | (~product(e_3, e_1, e_2)) | product(e_2, e_3, e_1))),
% 0.17/0.46 inference(transitivity,[status(thm)],[351, 349])).
% 0.17/0.46 tff(353,plain,
% 0.17/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_3, e_1, e_2)))),
% 0.17/0.46 inference(quant_inst,[status(thm)],[])).
% 0.17/0.46 tff(354,plain,
% 0.17/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_1)) | (~product(e_3, e_1, e_2)) | product(e_2, e_3, e_1)),
% 0.17/0.46 inference(modus_ponens,[status(thm)],[353, 352])).
% 0.17/0.46 tff(355,plain,
% 0.17/0.46 ($false),
% 0.17/0.46 inference(unit_resolution,[status(thm)],[354, 42, 348, 1, 346])).
% 0.17/0.46 tff(356,plain,(product(e_1, e_2, e_2) | (~product(e_3, e_1, e_2)) | product(e_1, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.17/0.46 tff(357,plain,
% 0.17/0.46 ((~product(e_3, e_1, e_2)) | product(e_1, e_2, e_3)),
% 0.17/0.46 inference(unit_resolution,[status(thm)],[356, 341])).
% 0.17/0.46 tff(358,plain,
% 0.17/0.46 (product(e_1, e_2, e_3)),
% 0.17/0.46 inference(unit_resolution,[status(thm)],[357, 1])).
% 0.17/0.46 tff(359,plain,
% 0.17/0.46 (~product(e_2, e_1, e_2)),
% 0.17/0.46 inference(unit_resolution,[status(thm)],[313, 358])).
% 0.17/0.46 tff(360,plain,
% 0.17/0.46 (product(e_2, e_1, e_1)),
% 0.17/0.46 inference(unit_resolution,[status(thm)],[248, 331, 359])).
% 0.17/0.46 tff(361,plain,
% 0.17/0.46 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W))) <=> (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W))))),
% 0.17/0.46 inference(bind,[status(th)],[])).
% 0.17/0.46 tff(362,plain,
% 0.17/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.17/0.46 inference(quant_intro,[status(thm)],[361])).
% 0.17/0.46 tff(363,plain,
% 0.17/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.17/0.46 inference(rewrite,[status(thm)],[])).
% 0.17/0.46 tff(364,plain,
% 0.17/0.46 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(X, Y, W)) | (~product(X, Y, Z))) <=> ((~product(X, Y, Z)) | (~product(X, Y, W)))), ((((~product(X, Y, W)) | (~product(X, Y, Z))) | equalish(W, Z)) <=> (((~product(X, Y, Z)) | (~product(X, Y, W))) | equalish(W, Z)))), rewrite((((~product(X, Y, Z)) | (~product(X, Y, W))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))), ((((~product(X, Y, W)) | (~product(X, Y, Z))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))))),
% 0.17/0.46 inference(bind,[status(th)],[])).
% 0.17/0.46 tff(365,plain,
% 0.17/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, Y, W)) | (~product(X, Y, Z))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.17/0.46 inference(quant_intro,[status(thm)],[364])).
% 0.17/0.46 tff(366,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, Y, W)) | (~product(X, Y, Z))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_total_function2')).
% 0.17/0.46 tff(367,plain,
% 0.17/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.17/0.46 inference(modus_ponens,[status(thm)],[366, 365])).
% 0.17/0.46 tff(368,plain,
% 0.17/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.17/0.46 inference(modus_ponens,[status(thm)],[367, 363])).
% 0.17/0.46 tff(369,plain,(
% 0.17/0.46 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.17/0.46 inference(skolemize,[status(sab)],[368])).
% 0.17/0.46 tff(370,plain,
% 0.17/0.46 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.17/0.46 inference(modus_ponens,[status(thm)],[369, 362])).
% 0.17/0.46 tff(371,plain,
% 0.17/0.46 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.17/0.46 inference(rewrite,[status(thm)],[])).
% 0.17/0.46 tff(372,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.17/0.46 tff(373,plain,
% 0.17/0.46 (~equalish(e_1, e_2)),
% 0.17/0.46 inference(modus_ponens,[status(thm)],[372, 371])).
% 0.17/0.46 tff(374,plain,
% 0.17/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_1, e_2) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_1, e_2) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_3, e_2)))),
% 0.17/0.46 inference(rewrite,[status(thm)],[])).
% 0.17/0.46 tff(375,plain,
% 0.17/0.46 ((equalish(e_1, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_3, e_1))) <=> (equalish(e_1, e_2) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_3, e_2)))),
% 0.17/0.46 inference(rewrite,[status(thm)],[])).
% 0.17/0.46 tff(376,plain,
% 0.17/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_1, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_1, e_2) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_3, e_2))))),
% 0.17/0.46 inference(monotonicity,[status(thm)],[375])).
% 0.17/0.46 tff(377,plain,
% 0.17/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_1, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_1, e_2) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_3, e_2)))),
% 0.17/0.46 inference(transitivity,[status(thm)],[376, 374])).
% 0.17/0.46 tff(378,plain,
% 0.17/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_1, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_3, e_1)))),
% 0.17/0.46 inference(quant_inst,[status(thm)],[])).
% 0.17/0.46 tff(379,plain,
% 0.17/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_1, e_2) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_3, e_2))),
% 0.17/0.46 inference(modus_ponens,[status(thm)],[378, 377])).
% 0.17/0.46 tff(380,plain,
% 0.17/0.46 ((~product(e_1, e_3, e_1)) | (~product(e_1, e_3, e_2))),
% 0.17/0.46 inference(unit_resolution,[status(thm)],[379, 373, 370])).
% 0.17/0.46 tff(381,plain,
% 0.17/0.46 (~product(e_1, e_3, e_1)),
% 0.17/0.46 inference(unit_resolution,[status(thm)],[380, 324])).
% 0.17/0.46 tff(382,plain,
% 0.17/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_3, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_3, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_3, e_2, e_1)))),
% 0.17/0.46 inference(rewrite,[status(thm)],[])).
% 0.17/0.46 tff(383,plain,
% 0.17/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_3, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_3, e_2, e_1)))),
% 0.17/0.46 inference(quant_inst,[status(thm)],[])).
% 0.17/0.46 tff(384,plain,
% 0.17/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_3, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_3, e_2, e_1))),
% 0.17/0.46 inference(modus_ponens,[status(thm)],[383, 382])).
% 0.17/0.46 tff(385,plain,
% 0.17/0.46 (~product(e_3, e_2, e_1)),
% 0.17/0.46 inference(unit_resolution,[status(thm)],[384, 42, 381, 360])).
% 0.17/0.46 tff(386,plain,
% 0.17/0.46 (product(e_3, e_2, e_3) | product(e_3, e_2, e_1)),
% 0.17/0.46 inference(unit_resolution,[status(thm)],[291, 222, 87, 84, 21])).
% 0.17/0.46 tff(387,plain,
% 0.17/0.46 (product(e_3, e_2, e_3)),
% 0.17/0.46 inference(unit_resolution,[status(thm)],[386, 385])).
% 0.17/0.46 tff(388,plain,
% 0.17/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_3, e_2)) | product(e_2, e_1, e_3) | (~product(e_3, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_2)) | product(e_2, e_1, e_3) | (~product(e_3, e_2, e_3)))),
% 0.17/0.46 inference(rewrite,[status(thm)],[])).
% 0.17/0.46 tff(389,plain,
% 0.17/0.46 ((product(e_2, e_1, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_1, e_3, e_2))) <=> ((~product(e_1, e_3, e_2)) | product(e_2, e_1, e_3) | (~product(e_3, e_2, e_3)))),
% 0.17/0.46 inference(rewrite,[status(thm)],[])).
% 0.17/0.46 tff(390,plain,
% 0.17/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_3, e_2)) | product(e_2, e_1, e_3) | (~product(e_3, e_2, e_3))))),
% 0.17/0.46 inference(monotonicity,[status(thm)],[389])).
% 0.17/0.46 tff(391,plain,
% 0.17/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_2)) | product(e_2, e_1, e_3) | (~product(e_3, e_2, e_3)))),
% 0.17/0.46 inference(transitivity,[status(thm)],[390, 388])).
% 0.17/0.46 tff(392,plain,
% 0.17/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_1, e_3, e_2)))),
% 0.17/0.46 inference(quant_inst,[status(thm)],[])).
% 0.17/0.46 tff(393,plain,
% 0.17/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_2)) | product(e_2, e_1, e_3) | (~product(e_3, e_2, e_3))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[392, 391])).
% 0.17/0.47 tff(394,plain,
% 0.17/0.47 ($false),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[393, 42, 324, 387, 331])).
% 0.17/0.47 tff(395,plain,(~product(e_3, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.17/0.47 tff(396,plain,
% 0.17/0.47 (product(e_3, e_1, e_1)),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[211, 395])).
% 0.17/0.47 tff(397,plain,
% 0.17/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_3, e_2)) | product(e_3, e_1, e_2) | (~product(e_1, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_2)) | product(e_3, e_1, e_2) | (~product(e_1, e_1, e_3)))),
% 0.17/0.47 inference(rewrite,[status(thm)],[])).
% 0.17/0.47 tff(398,plain,
% 0.17/0.47 ((product(e_3, e_1, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_1, e_3))) <=> ((~product(e_1, e_3, e_2)) | product(e_3, e_1, e_2) | (~product(e_1, e_1, e_3)))),
% 0.17/0.47 inference(rewrite,[status(thm)],[])).
% 0.17/0.47 tff(399,plain,
% 0.17/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_3, e_2)) | product(e_3, e_1, e_2) | (~product(e_1, e_1, e_3))))),
% 0.17/0.47 inference(monotonicity,[status(thm)],[398])).
% 0.17/0.47 tff(400,plain,
% 0.17/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_2)) | product(e_3, e_1, e_2) | (~product(e_1, e_1, e_3)))),
% 0.17/0.47 inference(transitivity,[status(thm)],[399, 397])).
% 0.17/0.47 tff(401,plain,
% 0.17/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_1, e_3)))),
% 0.17/0.47 inference(quant_inst,[status(thm)],[])).
% 0.17/0.47 tff(402,plain,
% 0.17/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_3, e_2)) | product(e_3, e_1, e_2) | (~product(e_1, e_1, e_3))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[401, 400])).
% 0.17/0.47 tff(403,plain,
% 0.17/0.47 (~product(e_1, e_1, e_3)),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[402, 42, 324, 395])).
% 0.17/0.47 tff(404,plain,
% 0.17/0.47 (~product(e_2, e_1, e_1)),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[240, 396])).
% 0.17/0.47 tff(405,plain,
% 0.17/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_1)))),
% 0.17/0.47 inference(rewrite,[status(thm)],[])).
% 0.17/0.47 tff(406,plain,
% 0.17/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_1)))),
% 0.17/0.47 inference(quant_inst,[status(thm)],[])).
% 0.17/0.47 tff(407,plain,
% 0.17/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_1))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[406, 405])).
% 0.17/0.47 tff(408,plain,
% 0.17/0.47 (~product(e_2, e_2, e_1)),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[407, 42, 341, 294])).
% 0.17/0.47 tff(409,plain,
% 0.17/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_2, e_1)) | product(e_2, e_2, e_1) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_1)) | product(e_2, e_2, e_1) | (~product(e_2, e_1, e_2)))),
% 0.17/0.47 inference(rewrite,[status(thm)],[])).
% 0.17/0.47 tff(410,plain,
% 0.17/0.47 ((product(e_2, e_2, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_2))) <=> ((~product(e_1, e_2, e_1)) | product(e_2, e_2, e_1) | (~product(e_2, e_1, e_2)))),
% 0.17/0.47 inference(rewrite,[status(thm)],[])).
% 0.17/0.47 tff(411,plain,
% 0.17/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_2, e_1)) | product(e_2, e_2, e_1) | (~product(e_2, e_1, e_2))))),
% 0.17/0.47 inference(monotonicity,[status(thm)],[410])).
% 0.17/0.47 tff(412,plain,
% 0.17/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_1)) | product(e_2, e_2, e_1) | (~product(e_2, e_1, e_2)))),
% 0.17/0.47 inference(transitivity,[status(thm)],[411, 409])).
% 0.17/0.47 tff(413,plain,
% 0.17/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_2)))),
% 0.17/0.47 inference(quant_inst,[status(thm)],[])).
% 0.17/0.47 tff(414,plain,
% 0.17/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_1)) | product(e_2, e_2, e_1) | (~product(e_2, e_1, e_2))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[413, 412])).
% 0.17/0.47 tff(415,plain,
% 0.17/0.47 ($false),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[414, 42, 138, 294, 408])).
% 0.17/0.47 tff(416,plain,((~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.17/0.47 tff(417,plain,
% 0.17/0.47 (~product(e_2, e_1, e_2)),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[416, 138])).
% 0.17/0.47 tff(418,plain,
% 0.17/0.47 (product(e_2, e_1, e_3)),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[248, 417, 404])).
% 0.17/0.47 tff(419,plain,
% 0.17/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_2, e_1)) | product(e_1, e_1, e_3) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_1)) | product(e_1, e_1, e_3) | (~product(e_2, e_1, e_3)))),
% 0.17/0.47 inference(rewrite,[status(thm)],[])).
% 0.17/0.47 tff(420,plain,
% 0.17/0.47 ((product(e_1, e_1, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_1))) <=> ((~product(e_1, e_2, e_1)) | product(e_1, e_1, e_3) | (~product(e_2, e_1, e_3)))),
% 0.17/0.47 inference(rewrite,[status(thm)],[])).
% 0.17/0.47 tff(421,plain,
% 0.17/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_2, e_1)) | product(e_1, e_1, e_3) | (~product(e_2, e_1, e_3))))),
% 0.17/0.47 inference(monotonicity,[status(thm)],[420])).
% 0.17/0.47 tff(422,plain,
% 0.17/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_1)) | product(e_1, e_1, e_3) | (~product(e_2, e_1, e_3)))),
% 0.17/0.47 inference(transitivity,[status(thm)],[421, 419])).
% 0.17/0.47 tff(423,plain,
% 0.17/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_1)))),
% 0.17/0.47 inference(quant_inst,[status(thm)],[])).
% 0.17/0.47 tff(424,plain,
% 0.17/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_1)) | product(e_1, e_1, e_3) | (~product(e_2, e_1, e_3))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[423, 422])).
% 0.17/0.47 tff(425,plain,
% 0.17/0.47 ($false),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[424, 42, 138, 418, 403])).
% 0.17/0.47 tff(426,plain,(~product(e_1, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.17/0.47 tff(427,plain,
% 0.17/0.47 (~product(e_2, e_3, e_1)),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[217, 42, 426, 396])).
% 0.17/0.47 tff(428,plain,
% 0.17/0.47 (~product(e_3, e_3, e_1)),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[31, 396])).
% 0.17/0.47 tff(429,plain,
% 0.17/0.47 (~product(e_3, e_3, e_2)),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[189, 324])).
% 0.17/0.47 tff(430,plain,
% 0.17/0.47 (product(e_3, e_3, e_3) | product(e_3, e_3, e_1)),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[93, 87, 84, 429])).
% 0.17/0.47 tff(431,plain,
% 0.17/0.47 (product(e_3, e_3, e_3)),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[430, 428])).
% 0.17/0.47 tff(432,plain,
% 0.17/0.47 (~product(e_2, e_3, e_3)),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[271, 431])).
% 0.17/0.47 tff(433,plain,
% 0.17/0.47 (product(e_2, e_3, e_2) | product(e_2, e_3, e_1)),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[228, 222, 87, 84, 432])).
% 0.17/0.47 tff(434,plain,
% 0.17/0.47 (product(e_2, e_3, e_2)),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[433, 427])).
% 0.17/0.47 tff(435,plain,
% 0.17/0.47 (product(e_1, e_2, e_3) | product(e_1, e_2, e_1)),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[318, 341])).
% 0.17/0.47 tff(436,plain,
% 0.17/0.47 (product(e_1, e_2, e_3)),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[435, 426])).
% 0.17/0.47 tff(437,plain,
% 0.17/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_3, e_2)))),
% 0.17/0.47 inference(rewrite,[status(thm)],[])).
% 0.17/0.47 tff(438,plain,
% 0.17/0.47 ((product(e_3, e_1, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_1, e_2, e_3))) <=> (product(e_3, e_1, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_3, e_2)))),
% 0.17/0.47 inference(rewrite,[status(thm)],[])).
% 0.17/0.47 tff(439,plain,
% 0.17/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_3, e_2))))),
% 0.17/0.47 inference(monotonicity,[status(thm)],[438])).
% 0.17/0.47 tff(440,plain,
% 0.17/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_3, e_2)))),
% 0.17/0.47 inference(transitivity,[status(thm)],[439, 437])).
% 0.17/0.47 tff(441,plain,
% 0.17/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_1, e_2, e_3)))),
% 0.17/0.47 inference(quant_inst,[status(thm)],[])).
% 0.17/0.47 tff(442,plain,
% 0.17/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_1, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_3, e_2))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[441, 440])).
% 0.17/0.47 tff(443,plain,
% 0.17/0.47 ($false),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[442, 42, 436, 395, 434])).
% 0.17/0.47 % SZS output end Proof
% 0.17/0.47 % E exiting
%------------------------------------------------------------------------------