%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP130-1.003 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 0.22s 0.42s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GRP130-1.003 : TPTP v9.0.0. Released v1.2.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n012.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Jun 19 15:42:56 EDT 2025
% 0.15/0.36 % CPUTime :
% 0.22/0.42 % SZS status Unsatisfiable
% 0.22/0.42 % SZS output start Proof
% 0.22/0.42 tff(product_type, type, (
% 0.22/0.42 product: ( $i * $i * $i ) > $o)).
% 0.22/0.42 tff(e_3_type, type, (
% 0.22/0.42 e_3: $i)).
% 0.22/0.42 tff(e_2_type, type, (
% 0.22/0.42 e_2: $i)).
% 0.22/0.42 tff(e_1_type, type, (
% 0.22/0.42 e_1: $i)).
% 0.22/0.42 tff(equalish_type, type, (
% 0.22/0.42 equalish: ( $i * $i ) > $o)).
% 0.22/0.42 tff(group_element_type, type, (
% 0.22/0.42 group_element: $i > $o)).
% 0.22/0.42 tff(1,assumption,(~product(e_1, e_2, e_3)), introduced(assumption)).
% 0.22/0.42 tff(2,assumption,(product(e_1, e_3, e_3)), introduced(assumption)).
% 0.22/0.42 tff(3,assumption,(~product(e_3, e_3, e_1)), introduced(assumption)).
% 0.22/0.42 tff(4,plain,
% 0.22/0.42 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl((product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1))) <=> (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(5,plain,
% 0.22/0.42 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[4])).
% 0.22/0.43 tff(6,plain,
% 0.22/0.43 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(7,plain,
% 0.22/0.43 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : trans(monotonicity(rewrite(((~product(X, Y, Z1)) | (~product(X, Z1, Z2))) <=> ((~product(X, Z1, Z2)) | (~product(X, Y, Z1)))), ((((~product(X, Y, Z1)) | (~product(X, Z1, Z2))) | product(Z2, Y, X)) <=> (((~product(X, Z1, Z2)) | (~product(X, Y, Z1))) | product(Z2, Y, X)))), rewrite((((~product(X, Z1, Z2)) | (~product(X, Y, Z1))) | product(Z2, Y, X)) <=> (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))), ((((~product(X, Y, Z1)) | (~product(X, Z1, Z2))) | product(Z2, Y, X)) <=> (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(8,plain,
% 0.22/0.43 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(X, Z1, Z2))) | product(Z2, Y, X)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[7])).
% 0.22/0.43 tff(9,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(X, Z1, Z2))) | product(Z2, Y, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qg3')).
% 0.22/0.43 tff(10,plain,
% 0.22/0.43 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.22/0.43 tff(11,plain,
% 0.22/0.43 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.22/0.43 tff(12,plain,(
% 0.22/0.43 ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.22/0.43 inference(skolemize,[status(sab)],[11])).
% 0.22/0.43 tff(13,plain,
% 0.22/0.43 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.22/0.43 tff(14,plain,
% 0.22/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_1) | (~product(e_1, e_3, e_3)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(15,plain,
% 0.22/0.43 ((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_1, e_3, e_3)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(16,plain,
% 0.22/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_1, e_3, e_3))))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[15])).
% 0.22/0.43 tff(17,plain,
% 0.22/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_1) | (~product(e_1, e_3, e_3)))),
% 0.22/0.43 inference(transitivity,[status(thm)],[16, 14])).
% 0.22/0.43 tff(18,plain,
% 0.22/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(19,plain,
% 0.22/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_1) | (~product(e_1, e_3, e_3))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.22/0.43 tff(20,plain,
% 0.22/0.43 ($false),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[19, 13, 3, 2])).
% 0.22/0.43 tff(21,plain,((~product(e_1, e_3, e_3)) | product(e_3, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.43 tff(22,plain,
% 0.22/0.43 (product(e_3, e_3, e_1)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[21, 2])).
% 0.22/0.43 tff(23,plain,
% 0.22/0.43 (^[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))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(24,plain,
% 0.22/0.43 (![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)))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[23])).
% 0.22/0.43 tff(25,plain,
% 0.22/0.43 (![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)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(26,plain,
% 0.22/0.43 (^[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)))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(27,plain,
% 0.22/0.43 (![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)))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[26])).
% 0.22/0.43 tff(28,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_right_cancellation')).
% 0.22/0.43 tff(29,plain,
% 0.22/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.22/0.43 tff(30,plain,
% 0.22/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.22/0.43 tff(31,plain,(
% 0.22/0.43 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.22/0.43 inference(skolemize,[status(sab)],[30])).
% 0.22/0.43 tff(32,plain,
% 0.22/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.22/0.43 tff(33,plain,
% 0.22/0.43 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(34,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.22/0.43 tff(35,plain,
% 0.22/0.43 (~equalish(e_1, e_3)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.22/0.43 tff(36,plain,
% 0.22/0.43 (((~![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)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(37,plain,
% 0.22/0.43 ((~![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)))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(38,plain,
% 0.22/0.43 ((~![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))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.22/0.43 tff(39,plain,
% 0.22/0.43 ((~product(e_3, e_3, e_1)) | (~product(e_3, e_1, e_1))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[38, 35, 32])).
% 0.22/0.43 tff(40,plain,
% 0.22/0.43 (~product(e_3, e_1, e_1)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[39, 22])).
% 0.22/0.43 tff(41,plain,
% 0.22/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_3)) | product(e_3, e_1, e_1) | (~product(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_3)) | product(e_3, e_1, e_1) | (~product(e_1, e_3, e_3)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(42,plain,
% 0.22/0.43 ((product(e_3, e_1, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_1, e_3))) <=> ((~product(e_1, e_1, e_3)) | product(e_3, e_1, e_1) | (~product(e_1, e_3, e_3)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(43,plain,
% 0.22/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_3)) | product(e_3, e_1, e_1) | (~product(e_1, e_3, e_3))))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[42])).
% 0.22/0.43 tff(44,plain,
% 0.22/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_3)) | product(e_3, e_1, e_1) | (~product(e_1, e_3, e_3)))),
% 0.22/0.43 inference(transitivity,[status(thm)],[43, 41])).
% 0.22/0.43 tff(45,plain,
% 0.22/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_1) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_1, e_3)))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(46,plain,
% 0.22/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_3)) | product(e_3, e_1, e_1) | (~product(e_1, e_3, e_3))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.22/0.43 tff(47,plain,
% 0.22/0.43 (~product(e_1, e_1, e_3)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[46, 13, 40, 2])).
% 0.22/0.43 tff(48,assumption,(product(e_3, e_1, e_2)), introduced(assumption)).
% 0.22/0.43 tff(49,assumption,(product(e_3, e_2, e_2)), introduced(assumption)).
% 0.22/0.43 tff(50,plain,
% 0.22/0.43 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(51,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.22/0.43 tff(52,plain,
% 0.22/0.43 (~equalish(e_2, e_1)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.22/0.43 tff(53,plain,
% 0.22/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_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)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(54,plain,
% 0.22/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(55,plain,
% 0.22/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_2))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.22/0.44 tff(56,plain,
% 0.22/0.44 ($false),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[55, 52, 32, 48, 49])).
% 0.22/0.44 tff(57,plain,((~product(e_3, e_2, e_2)) | (~product(e_3, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.44 tff(58,plain,
% 0.22/0.44 (~product(e_3, e_2, e_2)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[57, 48])).
% 0.22/0.44 tff(59,assumption,(product(e_3, e_3, e_1)), introduced(assumption)).
% 0.22/0.44 tff(60,plain,
% 0.22/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_2, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_2, e_3)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(61,plain,
% 0.22/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_2, e_3)))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(62,plain,
% 0.22/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_2, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_2, e_3))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.22/0.44 tff(63,plain,
% 0.22/0.44 (~product(e_3, e_2, e_3)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[62, 13, 1, 59])).
% 0.22/0.44 tff(64,assumption,(~product(e_2, e_2, e_3)), introduced(assumption)).
% 0.22/0.44 tff(65,plain,
% 0.22/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_2)) | product(e_2, e_2, e_3) | (~product(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_2, e_2, e_3) | (~product(e_3, e_2, e_1)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(66,plain,
% 0.22/0.44 ((product(e_2, e_2, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_1))) <=> ((~product(e_3, e_1, e_2)) | product(e_2, e_2, e_3) | (~product(e_3, e_2, e_1)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(67,plain,
% 0.22/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_2)) | product(e_2, e_2, e_3) | (~product(e_3, e_2, e_1))))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[66])).
% 0.22/0.44 tff(68,plain,
% 0.22/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_2, e_2, e_3) | (~product(e_3, e_2, e_1)))),
% 0.22/0.44 inference(transitivity,[status(thm)],[67, 65])).
% 0.22/0.44 tff(69,plain,
% 0.22/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_2, e_1)))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(70,plain,
% 0.22/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_2, e_2, e_3) | (~product(e_3, e_2, e_1))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.22/0.44 tff(71,plain,
% 0.22/0.44 (~product(e_3, e_2, e_1)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[70, 13, 48, 64])).
% 0.22/0.44 tff(72,plain,
% 0.22/0.44 (^[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))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(73,plain,
% 0.22/0.44 (![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))) <=> ![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)))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[72])).
% 0.22/0.44 tff(74,plain,
% 0.22/0.44 (![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))) <=> ![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)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(75,plain,
% 0.22/0.44 (^[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)))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(76,plain,
% 0.22/0.44 (![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)))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[75])).
% 0.22/0.44 tff(77,axiom,(![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_total_function1')).
% 0.22/0.44 tff(78,plain,
% 0.22/0.44 (![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)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.22/0.44 tff(79,plain,
% 0.22/0.44 (![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)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.22/0.44 tff(80,plain,(
% 0.22/0.44 ![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)))),
% 0.22/0.44 inference(skolemize,[status(sab)],[79])).
% 0.22/0.44 tff(81,plain,
% 0.22/0.44 (![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)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.22/0.44 tff(82,plain,
% 0.22/0.44 (group_element(e_3) <=> group_element(e_3)),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(83,axiom,(group_element(e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_3')).
% 0.22/0.44 tff(84,plain,
% 0.22/0.44 (group_element(e_3)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.22/0.44 tff(85,plain,
% 0.22/0.44 (group_element(e_2) <=> group_element(e_2)),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(86,axiom,(group_element(e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_2')).
% 0.22/0.44 tff(87,plain,
% 0.22/0.44 (group_element(e_2)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.22/0.44 tff(88,plain,
% 0.22/0.44 (((~![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))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(89,plain,
% 0.22/0.44 ((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))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(90,plain,
% 0.22/0.44 (((~![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)))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[89])).
% 0.22/0.44 tff(91,plain,
% 0.22/0.44 (((~![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))),
% 0.22/0.44 inference(transitivity,[status(thm)],[90, 88])).
% 0.22/0.44 tff(92,plain,
% 0.22/0.44 ((~![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)))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(93,plain,
% 0.22/0.44 ((~![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)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.22/0.44 tff(94,plain,
% 0.22/0.44 (product(e_3, e_2, e_3) | product(e_3, e_2, e_2)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[93, 87, 84, 81, 71])).
% 0.22/0.44 tff(95,plain,
% 0.22/0.44 (product(e_3, e_2, e_2)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[94, 63])).
% 0.22/0.44 tff(96,plain,
% 0.22/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(97,plain,
% 0.22/0.44 ((product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_2, e_2))) <=> (product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(98,plain,
% 0.22/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2))))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[97])).
% 0.22/0.44 tff(99,plain,
% 0.22/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2)))),
% 0.22/0.44 inference(transitivity,[status(thm)],[98, 96])).
% 0.22/0.44 tff(100,plain,
% 0.22/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(101,plain,
% 0.22/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_3) | (~product(e_3, e_2, e_2))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.22/0.44 tff(102,plain,
% 0.22/0.44 ($false),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[101, 13, 64, 95])).
% 0.22/0.44 tff(103,plain,(product(e_2, e_2, e_3) | product(e_1, e_2, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.44 tff(104,plain,
% 0.22/0.44 (product(e_2, e_2, e_3)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[103, 48, 59, 1])).
% 0.22/0.44 tff(105,plain,
% 0.22/0.44 (^[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))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(106,plain,
% 0.22/0.44 (![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)))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[105])).
% 0.22/0.44 tff(107,plain,
% 0.22/0.44 (![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)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(108,plain,
% 0.22/0.44 (^[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)))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(109,plain,
% 0.22/0.44 (![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)))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[108])).
% 0.22/0.44 tff(110,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_left_cancellation')).
% 0.22/0.44 tff(111,plain,
% 0.22/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.22/0.44 tff(112,plain,
% 0.22/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.22/0.44 tff(113,plain,(
% 0.22/0.44 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.22/0.44 inference(skolemize,[status(sab)],[112])).
% 0.22/0.44 tff(114,plain,
% 0.22/0.44 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[113, 106])).
% 0.22/0.45 tff(115,plain,
% 0.22/0.45 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(116,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.22/0.45 tff(117,plain,
% 0.22/0.45 (~equalish(e_2, e_3)),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.22/0.45 tff(118,plain,
% 0.22/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, 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_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_2, e_3)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(119,plain,
% 0.22/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_2, e_3)))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(120,plain,
% 0.22/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_2, e_2, e_3))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.22/0.45 tff(121,plain,
% 0.22/0.45 ((~product(e_3, e_2, e_3)) | (~product(e_2, e_2, e_3))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[120, 117, 114])).
% 0.22/0.45 tff(122,plain,
% 0.22/0.45 (~product(e_3, e_2, e_3)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[121, 104])).
% 0.22/0.45 tff(123,plain,
% 0.22/0.45 (product(e_3, e_2, e_1) | product(e_3, e_2, e_2)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[93, 87, 84, 81, 122])).
% 0.22/0.45 tff(124,plain,
% 0.22/0.45 (product(e_3, e_2, e_1)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[123, 58])).
% 0.22/0.45 tff(125,assumption,(~product(e_1, e_1, e_3)), introduced(assumption)).
% 0.22/0.45 tff(126,plain,
% 0.22/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_2)) | product(e_1, e_1, e_3) | (~product(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_1, e_1, e_3) | (~product(e_3, e_2, e_1)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(127,plain,
% 0.22/0.45 ((product(e_1, e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_1, e_2))) <=> ((~product(e_3, e_1, e_2)) | product(e_1, e_1, e_3) | (~product(e_3, e_2, e_1)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(128,plain,
% 0.22/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_2)) | product(e_1, e_1, e_3) | (~product(e_3, e_2, e_1))))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[127])).
% 0.22/0.45 tff(129,plain,
% 0.22/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_1, e_1, e_3) | (~product(e_3, e_2, e_1)))),
% 0.22/0.45 inference(transitivity,[status(thm)],[128, 126])).
% 0.22/0.45 tff(130,plain,
% 0.22/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_1, e_2)))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(131,plain,
% 0.22/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_2)) | product(e_1, e_1, e_3) | (~product(e_3, e_2, e_1))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.22/0.45 tff(132,plain,
% 0.22/0.45 ($false),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[131, 13, 48, 125, 124])).
% 0.22/0.45 tff(133,plain,((~product(e_3, e_1, e_2)) | product(e_1, e_1, e_3) | (~product(e_3, e_3, e_1)) | product(e_1, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.45 tff(134,plain,
% 0.22/0.45 (~product(e_3, e_1, e_2)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[133, 47, 22, 1])).
% 0.22/0.45 tff(135,plain,
% 0.22/0.45 (group_element(e_1) <=> group_element(e_1)),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(136,axiom,(group_element(e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_1')).
% 0.22/0.45 tff(137,plain,
% 0.22/0.45 (group_element(e_1)),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.22/0.45 tff(138,plain,
% 0.22/0.45 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_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))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(139,plain,
% 0.22/0.45 ((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))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(140,plain,
% 0.22/0.45 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_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)))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[139])).
% 0.22/0.45 tff(141,plain,
% 0.22/0.45 (((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_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))),
% 0.22/0.45 inference(transitivity,[status(thm)],[140, 138])).
% 0.22/0.45 tff(142,plain,
% 0.22/0.45 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_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)))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(143,plain,
% 0.22/0.45 ((~![Y: $i, X: $i] : (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_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)),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.22/0.45 tff(144,plain,
% 0.22/0.45 (product(e_3, e_1, e_2) | product(e_3, e_1, e_3)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[143, 137, 84, 81, 40])).
% 0.22/0.45 tff(145,plain,
% 0.22/0.45 (product(e_3, e_1, e_3)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[144, 134])).
% 0.22/0.45 tff(146,plain,
% 0.22/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_1, e_3)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(147,plain,
% 0.22/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_1, e_3)))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(148,plain,
% 0.22/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_1, e_3))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.22/0.46 tff(149,plain,
% 0.22/0.46 ($false),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[148, 13, 22, 145, 47])).
% 0.22/0.46 tff(150,plain,((~product(e_1, e_3, e_3)) | product(e_1, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.46 tff(151,plain,
% 0.22/0.46 (~product(e_1, e_3, e_3)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[150, 1])).
% 0.22/0.46 tff(152,assumption,(~product(e_1, e_2, e_2)), introduced(assumption)).
% 0.22/0.46 tff(153,plain,
% 0.22/0.46 (((~![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)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(154,plain,
% 0.22/0.46 ((~![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)))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(155,plain,
% 0.22/0.46 ((~![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))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.22/0.46 tff(156,plain,
% 0.22/0.46 (product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[155, 137, 87, 81])).
% 0.22/0.46 tff(157,plain,
% 0.22/0.46 (product(e_1, e_2, e_1)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[156, 1, 152])).
% 0.22/0.46 tff(158,assumption,(product(e_1, e_2, e_1)), introduced(assumption)).
% 0.22/0.46 tff(159,assumption,(product(e_1, e_3, e_1)), introduced(assumption)).
% 0.22/0.46 tff(160,plain,
% 0.22/0.46 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(161,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.22/0.46 tff(162,plain,
% 0.22/0.46 (~equalish(e_3, e_2)),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.22/0.46 tff(163,plain,
% 0.22/0.46 (((~![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)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(164,plain,
% 0.22/0.46 ((~![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)))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(165,plain,
% 0.22/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_3, e_1))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.22/0.46 tff(166,plain,
% 0.22/0.46 ($false),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[165, 162, 32, 158, 159])).
% 0.22/0.46 tff(167,plain,((~product(e_1, e_3, e_1)) | (~product(e_1, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.46 tff(168,plain,
% 0.22/0.46 (~product(e_1, e_3, e_1)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[167, 158])).
% 0.22/0.46 tff(169,assumption,(~product(e_1, e_3, e_3)), introduced(assumption)).
% 0.22/0.46 tff(170,plain,
% 0.22/0.46 (((~![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))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(171,plain,
% 0.22/0.46 ((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))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(172,plain,
% 0.22/0.46 (((~![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)))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[171])).
% 0.22/0.46 tff(173,plain,
% 0.22/0.46 (((~![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))),
% 0.22/0.46 inference(transitivity,[status(thm)],[172, 170])).
% 0.22/0.46 tff(174,plain,
% 0.22/0.46 ((~![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)))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(175,plain,
% 0.22/0.46 ((~![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)),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.22/0.46 tff(176,plain,
% 0.22/0.46 (product(e_1, e_3, e_1) | product(e_1, e_3, e_2)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[175, 137, 84, 81, 169])).
% 0.22/0.46 tff(177,plain,
% 0.22/0.46 (product(e_1, e_3, e_2)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[176, 168])).
% 0.22/0.46 tff(178,plain,
% 0.22/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_3, e_2)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(179,plain,
% 0.22/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_3, e_2)))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(180,plain,
% 0.22/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_3, e_2))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.22/0.46 tff(181,plain,
% 0.22/0.46 ($false),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[180, 13, 158, 168, 177])).
% 0.22/0.46 tff(182,plain,((~product(e_1, e_2, e_1)) | product(e_1, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.46 tff(183,plain,
% 0.22/0.46 ($false),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[182, 157, 151])).
% 0.22/0.46 tff(184,plain,(product(e_1, e_2, e_3) | product(e_1, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.46 tff(185,plain,
% 0.22/0.46 (product(e_1, e_2, e_2)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[184, 1])).
% 0.22/0.46 tff(186,assumption,(product(e_1, e_2, e_2)), introduced(assumption)).
% 0.22/0.46 tff(187,plain,
% 0.22/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_2)) | product(e_2, e_2, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_2, e_2)) | product(e_2, e_2, e_1))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(188,plain,
% 0.22/0.46 ((product(e_2, e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_2, e_2))) <=> ((~product(e_1, e_2, e_2)) | product(e_2, e_2, e_1))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(189,plain,
% 0.22/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_1, e_2, e_2)) | product(e_2, e_2, e_1)))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[188])).
% 0.22/0.46 tff(190,plain,
% 0.22/0.46 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_2, e_2)) | product(e_2, e_2, e_1))),
% 0.22/0.46 inference(transitivity,[status(thm)],[189, 187])).
% 0.22/0.46 tff(191,plain,
% 0.22/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(192,plain,
% 0.22/0.46 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_2, e_2)) | product(e_2, e_2, e_1)),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.22/0.46 tff(193,plain,
% 0.22/0.46 ((~product(e_1, e_2, e_2)) | product(e_2, e_2, e_1)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[192, 13])).
% 0.22/0.46 tff(194,plain,
% 0.22/0.46 (product(e_2, e_2, e_1)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[193, 186])).
% 0.22/0.46 tff(195,plain,
% 0.22/0.46 (((~![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_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_1, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(196,plain,
% 0.22/0.46 ((equalish(e_1, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_1, e_2, e_2))) <=> (equalish(e_1, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(197,plain,
% 0.22/0.46 (((~![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_2, e_2)) | (~product(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_3, e_2, e_2))))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[196])).
% 0.22/0.46 tff(198,plain,
% 0.22/0.46 (((~![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_2, e_2)) | (~product(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.22/0.46 inference(transitivity,[status(thm)],[197, 195])).
% 0.22/0.46 tff(199,plain,
% 0.22/0.46 ((~![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_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(200,plain,
% 0.22/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_3, e_2, e_2))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.22/0.47 tff(201,plain,
% 0.22/0.47 ($false),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[200, 35, 114, 186, 49])).
% 0.22/0.47 tff(202,plain,((~product(e_1, e_2, e_2)) | (~product(e_3, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.47 tff(203,plain,
% 0.22/0.47 (~product(e_3, e_2, e_2)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[202, 186])).
% 0.22/0.47 tff(204,assumption,(~product(e_3, e_2, e_3)), introduced(assumption)).
% 0.22/0.47 tff(205,plain,
% 0.22/0.47 (product(e_3, e_2, e_1) | product(e_3, e_2, e_2)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[93, 87, 84, 81, 204])).
% 0.22/0.47 tff(206,plain,
% 0.22/0.47 (product(e_3, e_2, e_1)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[205, 203])).
% 0.22/0.47 tff(207,plain,
% 0.22/0.47 (((~![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_2, e_1)) | (~product(e_2, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_2, e_1)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(208,plain,
% 0.22/0.47 ((~![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_2, e_1)) | (~product(e_2, e_2, e_1)))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(209,plain,
% 0.22/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_2, e_1))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.22/0.47 tff(210,plain,
% 0.22/0.47 ($false),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[209, 117, 114, 206, 194])).
% 0.22/0.47 tff(211,plain,((~product(e_1, e_2, e_2)) | product(e_3, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.47 tff(212,plain,
% 0.22/0.47 (product(e_3, e_2, e_3)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[211, 185])).
% 0.22/0.47 tff(213,assumption,(product(e_3, e_1, e_3)), introduced(assumption)).
% 0.22/0.47 tff(214,assumption,(product(e_3, e_2, e_3)), introduced(assumption)).
% 0.22/0.47 tff(215,plain,
% 0.22/0.47 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(216,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.22/0.47 tff(217,plain,
% 0.22/0.47 (~equalish(e_1, e_2)),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.22/0.47 tff(218,plain,
% 0.22/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_3, e_2, 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_2) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(219,plain,
% 0.22/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(220,plain,
% 0.22/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_1, e_3))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.22/0.47 tff(221,plain,
% 0.22/0.47 ($false),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[220, 217, 32, 214, 213])).
% 0.22/0.47 tff(222,plain,((~product(e_3, e_1, e_3)) | (~product(e_3, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.47 tff(223,plain,
% 0.22/0.47 (~product(e_3, e_1, e_3)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[222, 212])).
% 0.22/0.47 tff(224,plain,
% 0.22/0.47 (~product(e_2, e_2, e_3)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[121, 212])).
% 0.22/0.47 tff(225,plain,
% 0.22/0.47 (~product(e_1, e_3, e_3)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[21, 3])).
% 0.22/0.47 tff(226,plain,
% 0.22/0.47 (~product(e_1, e_2, e_1)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[182, 225])).
% 0.22/0.47 tff(227,assumption,(product(e_3, e_3, e_3)), introduced(assumption)).
% 0.22/0.47 tff(228,plain,
% 0.22/0.47 (((~![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_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_3, e_2) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(229,plain,
% 0.22/0.47 ((equalish(e_3, e_2) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_3, e_3))) <=> (equalish(e_3, e_2) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(230,plain,
% 0.22/0.47 (((~![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_3, e_2, e_3)) | (~product(e_3, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3))))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[229])).
% 0.22/0.47 tff(231,plain,
% 0.22/0.47 (((~![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_3, e_2, e_3)) | (~product(e_3, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.22/0.47 inference(transitivity,[status(thm)],[230, 228])).
% 0.22/0.47 tff(232,plain,
% 0.22/0.47 ((~![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_3, e_2, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(233,plain,
% 0.22/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.22/0.47 tff(234,plain,
% 0.22/0.47 ($false),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[233, 162, 32, 214, 227])).
% 0.22/0.47 tff(235,plain,((~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.47 tff(236,plain,
% 0.22/0.47 (~product(e_3, e_3, e_3)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[235, 214])).
% 0.22/0.47 tff(237,plain,
% 0.22/0.47 (((~![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)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(238,plain,
% 0.22/0.47 ((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)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(239,plain,
% 0.22/0.47 (((~![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))))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[238])).
% 0.22/0.47 tff(240,plain,
% 0.22/0.47 (((~![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)))),
% 0.22/0.48 inference(transitivity,[status(thm)],[239, 237])).
% 0.22/0.48 tff(241,plain,
% 0.22/0.48 ((~![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)))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(242,plain,
% 0.22/0.48 ((~![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))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.22/0.48 tff(243,plain,
% 0.22/0.48 (product(e_3, e_3, e_3) | product(e_3, e_3, e_2)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[242, 84, 81, 3])).
% 0.22/0.48 tff(244,plain,
% 0.22/0.48 (product(e_3, e_3, e_2)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[243, 236])).
% 0.22/0.48 tff(245,plain,
% 0.22/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_2, e_3)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(246,plain,
% 0.22/0.48 ((product(e_3, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_3, e_2))) <=> (product(e_3, e_3, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_2, e_3)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(247,plain,
% 0.22/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_2, e_3))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[246])).
% 0.22/0.48 tff(248,plain,
% 0.22/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_2, e_3)))),
% 0.22/0.48 inference(transitivity,[status(thm)],[247, 245])).
% 0.22/0.48 tff(249,plain,
% 0.22/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_3, e_2)))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(250,plain,
% 0.22/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_3) | (~product(e_3, e_3, e_2)) | (~product(e_3, e_2, e_3))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.22/0.48 tff(251,plain,
% 0.22/0.48 ($false),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[250, 13, 244, 214, 236])).
% 0.22/0.48 tff(252,plain,((~product(e_3, e_2, e_3)) | product(e_3, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.48 tff(253,plain,
% 0.22/0.48 (~product(e_3, e_2, e_3)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[252, 3])).
% 0.22/0.48 tff(254,plain,
% 0.22/0.48 (~product(e_1, e_2, e_2)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[211, 253])).
% 0.22/0.48 tff(255,plain,
% 0.22/0.48 (product(e_1, e_2, e_3)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[156, 254, 226])).
% 0.22/0.48 tff(256,plain,
% 0.22/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_2)) | product(e_3, e_3, e_1) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_2)) | product(e_3, e_3, e_1) | (~product(e_1, e_2, e_3)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(257,plain,
% 0.22/0.48 ((product(e_3, e_3, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_2))) <=> ((~product(e_1, e_3, e_2)) | product(e_3, e_3, e_1) | (~product(e_1, e_2, e_3)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(258,plain,
% 0.22/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_2)) | product(e_3, e_3, e_1) | (~product(e_1, e_2, e_3))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[257])).
% 0.22/0.48 tff(259,plain,
% 0.22/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_2)) | product(e_3, e_3, e_1) | (~product(e_1, e_2, e_3)))),
% 0.22/0.48 inference(transitivity,[status(thm)],[258, 256])).
% 0.22/0.48 tff(260,plain,
% 0.22/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_2)))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(261,plain,
% 0.22/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_2)) | product(e_3, e_3, e_1) | (~product(e_1, e_2, e_3))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.22/0.48 tff(262,plain,
% 0.22/0.48 (~product(e_1, e_3, e_2)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[261, 13, 255, 3])).
% 0.22/0.48 tff(263,plain,
% 0.22/0.48 (product(e_1, e_3, e_1)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[175, 137, 84, 81, 262, 225])).
% 0.22/0.48 tff(264,plain,
% 0.22/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_1)) | product(e_1, e_2, e_1) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_1)) | product(e_1, e_2, e_1) | (~product(e_1, e_2, e_3)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(265,plain,
% 0.22/0.48 ((product(e_1, e_2, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_2, e_3))) <=> ((~product(e_1, e_3, e_1)) | product(e_1, e_2, e_1) | (~product(e_1, e_2, e_3)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(266,plain,
% 0.22/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_1)) | product(e_1, e_2, e_1) | (~product(e_1, e_2, e_3))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[265])).
% 0.22/0.48 tff(267,plain,
% 0.22/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_1)) | product(e_1, e_2, e_1) | (~product(e_1, e_2, e_3)))),
% 0.22/0.48 inference(transitivity,[status(thm)],[266, 264])).
% 0.22/0.48 tff(268,plain,
% 0.22/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_2, e_3)))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(269,plain,
% 0.22/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z2, Y, X) | (~product(X, Z1, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_3, e_1)) | product(e_1, e_2, e_1) | (~product(e_1, e_2, e_3))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.22/0.48 tff(270,plain,
% 0.22/0.48 ($false),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[269, 13, 255, 226, 263])).
% 0.22/0.48 tff(271,plain,(product(e_3, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.48 tff(272,plain,
% 0.22/0.48 (product(e_2, e_2, e_3) | product(e_1, e_2, e_3) | (~product(e_3, e_1, e_2))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[103, 271])).
% 0.22/0.48 tff(273,plain,
% 0.22/0.48 (~product(e_3, e_1, e_2)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[272, 224, 1])).
% 0.22/0.48 tff(274,plain,
% 0.22/0.48 (~product(e_3, e_1, e_1)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[39, 271])).
% 0.22/0.48 tff(275,plain,
% 0.22/0.48 (product(e_3, e_1, e_2) | product(e_3, e_1, e_3)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[143, 137, 84, 81, 274])).
% 0.22/0.48 tff(276,plain,
% 0.22/0.48 ($false),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[275, 273, 223])).
% 0.22/0.48 tff(277,plain,(product(e_1, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.48 tff(278,assumption,(product(e_2, e_2, e_3)), introduced(assumption)).
% 0.22/0.48 tff(279,assumption,(product(e_1, e_2, e_3)), introduced(assumption)).
% 0.22/0.48 tff(280,plain,
% 0.22/0.48 (((~![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)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(281,plain,
% 0.22/0.48 ((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)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(282,plain,
% 0.22/0.48 (((~![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))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[281])).
% 0.22/0.48 tff(283,plain,
% 0.22/0.48 (((~![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)))),
% 0.22/0.48 inference(transitivity,[status(thm)],[282, 280])).
% 0.22/0.48 tff(284,plain,
% 0.22/0.48 ((~![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)))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(285,plain,
% 0.22/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_3))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[284, 283])).
% 0.22/0.48 tff(286,plain,
% 0.22/0.48 ($false),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[285, 52, 114, 279, 278])).
% 0.22/0.48 tff(287,plain,((~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.48 tff(288,plain,
% 0.22/0.48 (~product(e_2, e_2, e_3)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[287, 277])).
% 0.22/0.48 tff(289,plain,
% 0.22/0.48 ($false),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[101, 13, 64, 49])).
% 0.22/0.48 tff(290,plain,((~product(e_3, e_2, e_2)) | product(e_2, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.48 tff(291,plain,
% 0.22/0.48 (~product(e_3, e_2, e_2)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[290, 288])).
% 0.22/0.48 tff(292,assumption,(product(e_3, e_2, e_1)), introduced(assumption)).
% 0.22/0.48 tff(293,plain,
% 0.22/0.48 (((~![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_1)) | (~product(e_3, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_2, e_1)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(294,plain,
% 0.22/0.49 ((~![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_1)) | (~product(e_3, e_2, e_1)))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(295,plain,
% 0.22/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_3, e_3, e_1)) | (~product(e_3, e_2, e_1))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[294, 293])).
% 0.22/0.49 tff(296,plain,
% 0.22/0.49 ($false),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[295, 117, 32, 271, 292])).
% 0.22/0.49 tff(297,plain,(~product(e_3, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.49 tff(298,plain,
% 0.22/0.49 (product(e_3, e_2, e_3) | product(e_3, e_2, e_2)),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[93, 87, 84, 81, 297])).
% 0.22/0.49 tff(299,plain,
% 0.22/0.49 (product(e_3, e_2, e_3)),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[298, 291])).
% 0.22/0.49 tff(300,plain,
% 0.22/0.49 (((~![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_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_1, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(301,plain,
% 0.22/0.49 ((~![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_2, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(302,plain,
% 0.22/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_1, e_2, e_3))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.22/0.49 tff(303,plain,
% 0.22/0.49 ($false),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[302, 35, 114, 277, 299])).
% 0.22/0.49 % SZS output end Proof
% 0.22/0.49 % E exiting
%------------------------------------------------------------------------------