%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP123-4.003 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:07:03 AM UTC 2025
% Result : Unsatisfiable 0.14s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP123-4.003 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n002.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Jun 19 15:42:46 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.14/0.40 % SZS status Unsatisfiable
% 0.14/0.40 % SZS output start Proof
% 0.14/0.40 tff(product_type, type, (
% 0.14/0.40 product: ( $i * $i * $i ) > $o)).
% 0.14/0.40 tff(e_2_type, type, (
% 0.14/0.40 e_2: $i)).
% 0.14/0.40 tff(e_1_type, type, (
% 0.14/0.40 e_1: $i)).
% 0.14/0.40 tff(e_3_type, type, (
% 0.14/0.40 e_3: $i)).
% 0.14/0.40 tff(equalish_type, type, (
% 0.14/0.40 equalish: ( $i * $i ) > $o)).
% 0.14/0.40 tff(group_element_type, type, (
% 0.14/0.40 group_element: $i > $o)).
% 0.14/0.40 tff(1,assumption,(~product(e_1, e_1, e_1)), introduced(assumption)).
% 0.14/0.40 tff(2,plain,
% 0.14/0.40 (^[X: $i] : refl(product(X, X, X) <=> product(X, X, X))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(3,plain,
% 0.14/0.40 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.14/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.14/0.40 tff(4,plain,
% 0.14/0.40 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(5,axiom,(![X: $i] : product(X, X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_idempotence')).
% 0.14/0.40 tff(6,plain,
% 0.14/0.40 (![X: $i] : product(X, X, X)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.14/0.40 tff(7,plain,(
% 0.14/0.40 ![X: $i] : product(X, X, X)),
% 0.14/0.40 inference(skolemize,[status(sab)],[6])).
% 0.14/0.40 tff(8,plain,
% 0.14/0.40 (![X: $i] : product(X, X, X)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.14/0.40 tff(9,plain,
% 0.14/0.40 ((~![X: $i] : product(X, X, X)) | product(e_1, e_1, e_1)),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(10,plain,
% 0.14/0.40 ($false),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.14/0.40 tff(11,plain,(product(e_1, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.40 tff(12,assumption,(~product(e_3, e_1, e_2)), introduced(assumption)).
% 0.14/0.40 tff(13,assumption,(product(e_1, e_1, e_2)), introduced(assumption)).
% 0.14/0.40 tff(14,plain,
% 0.14/0.40 (^[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))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(15,plain,
% 0.14/0.40 (![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)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[14])).
% 0.14/0.40 tff(16,plain,
% 0.14/0.40 (![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)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(17,plain,
% 0.14/0.40 (^[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)))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(18,plain,
% 0.14/0.40 (![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)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[17])).
% 0.14/0.40 tff(19,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')).
% 0.14/0.40 tff(20,plain,
% 0.14/0.40 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.14/0.40 tff(21,plain,
% 0.14/0.40 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.14/0.40 tff(22,plain,(
% 0.14/0.40 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.14/0.40 inference(skolemize,[status(sab)],[21])).
% 0.14/0.40 tff(23,plain,
% 0.14/0.40 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.14/0.40 tff(24,plain,
% 0.14/0.40 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(25,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.14/0.40 tff(26,plain,
% 0.14/0.40 (~equalish(e_2, e_1)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.14/0.40 tff(27,plain,
% 0.14/0.40 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_1, e_1)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(28,plain,
% 0.14/0.40 ((equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_1, e_2))) <=> (equalish(e_2, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_1, e_1)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(29,plain,
% 0.14/0.40 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_1, e_1))))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[28])).
% 0.14/0.40 tff(30,plain,
% 0.14/0.40 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_1, e_1)))),
% 0.14/0.40 inference(transitivity,[status(thm)],[29, 27])).
% 0.14/0.40 tff(31,plain,
% 0.14/0.40 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_1, e_2)))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(32,plain,
% 0.14/0.40 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_1, e_1))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.14/0.40 tff(33,plain,
% 0.14/0.40 ($false),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[32, 26, 23, 13, 11])).
% 0.14/0.40 tff(34,plain,(~product(e_1, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.40 tff(35,plain,
% 0.14/0.40 (group_element(e_2) <=> group_element(e_2)),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(36,axiom,(group_element(e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_2')).
% 0.14/0.40 tff(37,plain,
% 0.14/0.40 (group_element(e_2)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.14/0.40 tff(38,plain,
% 0.14/0.40 (group_element(e_1) <=> group_element(e_1)),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(39,axiom,(group_element(e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_1')).
% 0.14/0.40 tff(40,plain,
% 0.14/0.40 (group_element(e_1)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.14/0.40 tff(41,plain,
% 0.14/0.40 (^[Y: $i, X: $i] : refl((product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) <=> (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(42,plain,
% 0.14/0.40 (![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[41])).
% 0.14/0.40 tff(43,plain,
% 0.14/0.40 (![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(44,plain,
% 0.14/0.40 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) <=> (product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) <=> ((product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) | product(e_2, X, Y)))), rewrite(((product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) | product(e_2, X, Y)) <=> (product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) <=> (product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))))), ((((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) | product(e_3, X, Y)) <=> ((product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) | product(e_3, X, Y)))), rewrite(((product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X))) | product(e_3, X, Y)) <=> (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))), ((((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) | product(e_3, X, Y)) <=> (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(45,plain,
% 0.21/0.40 (![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) | product(e_3, X, Y)) <=> ![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[44])).
% 0.21/0.40 tff(46,axiom,(![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(e_1, X, Y)) | product(e_2, X, Y)) | product(e_3, X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','row_surjectivity')).
% 0.21/0.40 tff(47,plain,
% 0.21/0.40 (![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.21/0.40 tff(48,plain,
% 0.21/0.40 (![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.21/0.40 tff(49,plain,(
% 0.21/0.40 ![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.21/0.40 inference(skolemize,[status(sab)],[48])).
% 0.21/0.40 tff(50,plain,
% 0.21/0.40 (![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.21/0.40 tff(51,plain,
% 0.21/0.40 (((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_2) | product(e_2, e_1, e_2) | product(e_1, e_1, e_2) | (~group_element(e_2)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_1, e_2) | product(e_2, e_1, e_2) | product(e_1, e_1, e_2) | (~group_element(e_2)) | (~group_element(e_1)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(52,plain,
% 0.21/0.40 ((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_2) | product(e_2, e_1, e_2) | product(e_1, e_1, e_2) | (~group_element(e_2)) | (~group_element(e_1)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(53,plain,
% 0.21/0.40 ((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_1, e_2) | product(e_2, e_1, e_2) | product(e_1, e_1, e_2) | (~group_element(e_2)) | (~group_element(e_1))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.21/0.40 tff(54,plain,
% 0.21/0.40 (product(e_3, e_1, e_2) | product(e_2, e_1, e_2) | product(e_1, e_1, e_2)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[53, 50, 40, 37])).
% 0.21/0.41 tff(55,plain,
% 0.21/0.41 (product(e_3, e_1, e_2) | product(e_2, e_1, e_2)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[54, 34])).
% 0.21/0.41 tff(56,plain,
% 0.21/0.41 (product(e_2, e_1, e_2)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[55, 12])).
% 0.21/0.41 tff(57,assumption,(product(e_2, e_3, e_2)), introduced(assumption)).
% 0.21/0.41 tff(58,assumption,(product(e_2, e_1, e_2)), introduced(assumption)).
% 0.21/0.41 tff(59,plain,
% 0.21/0.41 (^[Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : refl(((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2)) <=> ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(60,plain,
% 0.21/0.41 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2)) <=> ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[59])).
% 0.21/0.41 tff(61,plain,
% 0.21/0.41 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2)) <=> ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(62,plain,
% 0.21/0.41 (^[Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, Y1, X1))) <=> ((~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))), (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, Y1, X1))) | (~product(Z2, Y2, X2))) <=> (((~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | (~product(Z2, Y2, X2))))), rewrite((((~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | (~product(Z2, Y2, X2))) <=> ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))), (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, Y1, X1))) | (~product(Z2, Y2, X2))) <=> ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))))), ((((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, Y1, X1))) | (~product(Z2, Y2, X2))) | equalish(Y1, Y2)) <=> (((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | equalish(Y1, Y2)))), rewrite((((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | equalish(Y1, Y2)) <=> ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))), ((((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, Y1, X1))) | (~product(Z2, Y2, X2))) | equalish(Y1, Y2)) <=> ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(63,plain,
% 0.21/0.41 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, Y1, X1))) | (~product(Z2, Y2, X2))) | equalish(Y1, Y2)) <=> ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[62])).
% 0.21/0.41 tff(64,axiom,(![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, Y1, X1))) | (~product(Z2, Y2, X2))) | equalish(Y1, Y2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qg1_2')).
% 0.21/0.41 tff(65,plain,
% 0.21/0.41 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.21/0.41 tff(66,plain,
% 0.21/0.41 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.21/0.41 tff(67,plain,(
% 0.21/0.41 ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.21/0.41 inference(skolemize,[status(sab)],[66])).
% 0.21/0.41 tff(68,plain,
% 0.21/0.41 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.21/0.41 tff(69,plain,
% 0.21/0.41 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(70,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.21/0.41 tff(71,plain,
% 0.21/0.41 (~equalish(e_3, e_1)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.21/0.41 tff(72,plain,
% 0.21/0.41 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_3, e_1) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_3, e_1) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(73,plain,
% 0.21/0.41 (((~product(e_2, e_1, e_2)) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_3, e_2)) | equalish(e_3, e_1)) <=> (equalish(e_3, e_1) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(74,plain,
% 0.21/0.41 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_2, e_1, e_2)) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_3, e_2)) | equalish(e_3, e_1))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_3, e_1) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_1, e_2))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[73])).
% 0.21/0.41 tff(75,plain,
% 0.21/0.41 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_2, e_1, e_2)) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_3, e_2)) | equalish(e_3, e_1))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_3, e_1) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[74, 72])).
% 0.21/0.41 tff(76,plain,
% 0.21/0.41 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_2, e_1, e_2)) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_3, e_2)) | equalish(e_3, e_1))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(77,plain,
% 0.21/0.41 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_3, e_1) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_1, e_2))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.21/0.41 tff(78,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[77, 71, 68, 58, 57])).
% 0.21/0.41 tff(79,plain,((~product(e_2, e_1, e_2)) | (~product(e_2, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(80,plain,
% 0.21/0.41 (~product(e_2, e_3, e_2)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[79, 56])).
% 0.21/0.41 tff(81,plain,
% 0.21/0.41 ((~![X: $i] : product(X, X, X)) | product(e_3, e_3, e_3)),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(82,plain,
% 0.21/0.41 (product(e_3, e_3, e_3)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[81, 8])).
% 0.21/0.41 tff(83,assumption,(product(e_3, e_3, e_2)), introduced(assumption)).
% 0.21/0.41 tff(84,plain,
% 0.21/0.41 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(85,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.21/0.41 tff(86,plain,
% 0.21/0.41 (~equalish(e_2, e_3)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.21/0.41 tff(87,plain,
% 0.21/0.41 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, 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_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_2)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(88,plain,
% 0.21/0.41 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_2)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(89,plain,
% 0.21/0.41 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Y, Z)) | (~product(X, Y, W)))) | equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_2))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.21/0.41 tff(90,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[89, 86, 23, 83, 82])).
% 0.21/0.41 tff(91,plain,(~product(e_3, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(92,plain,
% 0.21/0.41 (group_element(e_3) <=> group_element(e_3)),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(93,axiom,(group_element(e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_3')).
% 0.21/0.41 tff(94,plain,
% 0.21/0.41 (group_element(e_3)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.21/0.41 tff(95,plain,
% 0.21/0.41 (((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | product(e_3, e_3, e_2) | (~group_element(e_2)) | product(e_2, e_3, e_2) | product(e_1, e_3, e_2))) <=> ((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | product(e_3, e_3, e_2) | (~group_element(e_2)) | product(e_2, e_3, e_2) | product(e_1, e_3, e_2))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(96,plain,
% 0.21/0.41 ((product(e_3, e_3, e_2) | product(e_2, e_3, e_2) | product(e_1, e_3, e_2) | (~group_element(e_2)) | (~group_element(e_3))) <=> ((~group_element(e_3)) | product(e_3, e_3, e_2) | (~group_element(e_2)) | product(e_2, e_3, e_2) | product(e_1, e_3, e_2))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(97,plain,
% 0.21/0.41 (((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_3, e_2) | product(e_2, e_3, e_2) | product(e_1, e_3, e_2) | (~group_element(e_2)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | product(e_3, e_3, e_2) | (~group_element(e_2)) | product(e_2, e_3, e_2) | product(e_1, e_3, e_2)))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[96])).
% 0.21/0.41 tff(98,plain,
% 0.21/0.41 (((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_3, e_2) | product(e_2, e_3, e_2) | product(e_1, e_3, e_2) | (~group_element(e_2)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | product(e_3, e_3, e_2) | (~group_element(e_2)) | product(e_2, e_3, e_2) | product(e_1, e_3, e_2))),
% 0.21/0.42 inference(transitivity,[status(thm)],[97, 95])).
% 0.21/0.42 tff(99,plain,
% 0.21/0.42 ((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_3, e_2) | product(e_2, e_3, e_2) | product(e_1, e_3, e_2) | (~group_element(e_2)) | (~group_element(e_3)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(100,plain,
% 0.21/0.42 ((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | product(e_3, e_3, e_2) | (~group_element(e_2)) | product(e_2, e_3, e_2) | product(e_1, e_3, e_2)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.21/0.42 tff(101,plain,
% 0.21/0.42 (product(e_2, e_3, e_2) | product(e_1, e_3, e_2)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[100, 50, 37, 94, 91])).
% 0.21/0.42 tff(102,plain,
% 0.21/0.42 (product(e_1, e_3, e_2)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[101, 80])).
% 0.21/0.42 tff(103,plain,
% 0.21/0.42 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_3, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_3, e_1)) | (~product(e_1, e_1, e_1)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_3, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_3, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(104,plain,
% 0.21/0.42 (((~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_3, e_1)) | equalish(e_3, e_1)) <=> (equalish(e_3, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_3, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(105,plain,
% 0.21/0.42 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_3, e_1)) | equalish(e_3, e_1))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_3, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_3, e_1)) | (~product(e_1, e_1, e_1))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[104])).
% 0.21/0.42 tff(106,plain,
% 0.21/0.42 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_3, e_1)) | equalish(e_3, e_1))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_3, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_3, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[105, 103])).
% 0.21/0.42 tff(107,plain,
% 0.21/0.42 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_2)) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_3, e_1)) | equalish(e_3, e_1))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(108,plain,
% 0.21/0.42 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_3, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_3, e_1)) | (~product(e_1, e_1, e_1))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.21/0.42 tff(109,plain,
% 0.21/0.42 (~product(e_2, e_3, e_1)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[108, 71, 68, 102, 11])).
% 0.21/0.42 tff(110,plain,
% 0.21/0.42 (^[Y: $i, X: $i] : refl(((~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)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(111,plain,
% 0.21/0.42 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[110])).
% 0.21/0.42 tff(112,plain,
% 0.21/0.42 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(113,plain,
% 0.21/0.42 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_1))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> (((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_1)) | product(X, Y, e_2)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1)))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> (((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1)) | product(X, Y, e_3)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1)) | product(X, Y, e_3)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(114,plain,
% 0.21/0.42 (![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[113])).
% 0.21/0.42 tff(115,axiom,(![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_total_function1')).
% 0.21/0.42 tff(116,plain,
% 0.21/0.42 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.21/0.42 tff(117,plain,
% 0.21/0.42 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.21/0.42 tff(118,plain,(
% 0.21/0.42 ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.21/0.42 inference(skolemize,[status(sab)],[117])).
% 0.21/0.42 tff(119,plain,
% 0.21/0.42 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[118, 111])).
% 0.21/0.42 tff(120,plain,
% 0.21/0.42 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_3) | product(e_2, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_3) | product(e_2, e_3, e_1))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(121,plain,
% 0.21/0.42 (((~group_element(e_3)) | (~group_element(e_2)) | 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)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_3) | product(e_2, e_3, e_1))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(122,plain,
% 0.21/0.42 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_2)) | 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] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_3) | product(e_2, e_3, e_1)))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[121])).
% 0.21/0.42 tff(123,plain,
% 0.21/0.42 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_2)) | 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] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_3) | product(e_2, e_3, e_1))),
% 0.21/0.42 inference(transitivity,[status(thm)],[122, 120])).
% 0.21/0.42 tff(124,plain,
% 0.21/0.42 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_3, e_3) | product(e_2, e_3, e_2) | product(e_2, e_3, e_1))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(125,plain,
% 0.21/0.42 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_3, e_2) | product(e_2, e_3, e_3) | product(e_2, e_3, e_1)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.21/0.42 tff(126,plain,
% 0.21/0.42 (product(e_2, e_3, e_3)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[125, 37, 94, 119, 80, 109])).
% 0.21/0.42 tff(127,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.21/0.42 tff(128,plain,
% 0.21/0.42 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(129,plain,
% 0.21/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[128])).
% 0.21/0.42 tff(130,plain,
% 0.21/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(131,plain,
% 0.21/0.42 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(W, Y, X)) | (~product(Z, Y, X))) <=> ((~product(Z, Y, X)) | (~product(W, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> (((~product(Z, Y, X)) | (~product(W, Y, X))) | equalish(W, Z)))), rewrite((((~product(Z, Y, X)) | (~product(W, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(132,plain,
% 0.21/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[131])).
% 0.21/0.43 tff(133,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_left_cancellation')).
% 0.21/0.43 tff(134,plain,
% 0.21/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.21/0.43 tff(135,plain,
% 0.21/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[134, 130])).
% 0.21/0.43 tff(136,plain,(
% 0.21/0.43 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[135])).
% 0.21/0.43 tff(137,plain,
% 0.21/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[136, 129])).
% 0.21/0.43 tff(138,plain,
% 0.21/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(139,plain,
% 0.21/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(140,plain,
% 0.21/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.21/0.43 tff(141,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[140, 26, 137, 11, 127])).
% 0.21/0.43 tff(142,plain,(~product(e_2, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(143,plain,
% 0.21/0.43 (^[Y: $i, X: $i] : refl(((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(144,plain,
% 0.21/0.43 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[143])).
% 0.21/0.43 tff(145,plain,
% 0.21/0.43 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(146,plain,
% 0.21/0.43 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_1, Y))), (((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) <=> (((~group_element(Y)) | (~group_element(X)) | product(X, e_1, Y)) | product(X, e_2, Y)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product(X, e_1, Y)) | product(X, e_2, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_2, Y) | product(X, e_1, Y))), (((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_2, Y) | product(X, e_1, Y)))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) | product(X, e_3, Y)) <=> (((~group_element(Y)) | (~group_element(X)) | product(X, e_2, Y) | product(X, e_1, Y)) | product(X, e_3, Y)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product(X, e_2, Y) | product(X, e_1, Y)) | product(X, e_3, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) | product(X, e_3, Y)) <=> ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(147,plain,
% 0.21/0.43 (![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) | product(X, e_3, Y)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[146])).
% 0.21/0.43 tff(148,axiom,(![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product(X, e_1, Y)) | product(X, e_2, Y)) | product(X, e_3, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','column_surjectivity')).
% 0.21/0.43 tff(149,plain,
% 0.21/0.43 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.21/0.43 tff(150,plain,
% 0.21/0.43 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[149, 145])).
% 0.21/0.43 tff(151,plain,(
% 0.21/0.43 ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.21/0.43 inference(skolemize,[status(sab)],[150])).
% 0.21/0.43 tff(152,plain,
% 0.21/0.43 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[151, 144])).
% 0.21/0.43 tff(153,plain,
% 0.21/0.43 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_2, e_1) | product(e_2, e_1, e_1) | product(e_2, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_2, e_1) | product(e_2, e_1, e_1) | product(e_2, e_3, e_1))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(154,plain,
% 0.21/0.43 (((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_3, e_1) | product(e_2, e_2, e_1) | product(e_2, e_1, e_1)) <=> ((~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_2, e_1) | product(e_2, e_1, e_1) | product(e_2, e_3, e_1))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(155,plain,
% 0.21/0.43 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_3, e_1) | product(e_2, e_2, e_1) | product(e_2, e_1, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_2, e_1) | product(e_2, e_1, e_1) | product(e_2, e_3, e_1)))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[154])).
% 0.21/0.43 tff(156,plain,
% 0.21/0.43 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_3, e_1) | product(e_2, e_2, e_1) | product(e_2, e_1, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_2, e_1) | product(e_2, e_1, e_1) | product(e_2, e_3, e_1))),
% 0.21/0.43 inference(transitivity,[status(thm)],[155, 153])).
% 0.21/0.43 tff(157,plain,
% 0.21/0.43 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_3, e_1) | product(e_2, e_2, e_1) | product(e_2, e_1, e_1))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(158,plain,
% 0.21/0.43 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_2, e_1) | product(e_2, e_1, e_1) | product(e_2, e_3, e_1)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.21/0.43 tff(159,plain,
% 0.21/0.43 (product(e_2, e_2, e_1) | product(e_2, e_3, e_1)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[158, 152, 40, 37, 142])).
% 0.21/0.43 tff(160,plain,
% 0.21/0.43 (product(e_2, e_2, e_1)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[159, 109])).
% 0.21/0.43 tff(161,plain,
% 0.21/0.43 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_3)) | product(e_3, e_3, e_2) | product(e_3, e_2, e_2) | product(e_3, e_1, e_2) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_3)) | product(e_3, e_3, e_2) | product(e_3, e_2, e_2) | product(e_3, e_1, e_2) | (~group_element(e_2)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(162,plain,
% 0.21/0.43 (((~group_element(e_2)) | (~group_element(e_3)) | product(e_3, e_3, e_2) | product(e_3, e_2, e_2) | product(e_3, e_1, e_2)) <=> ((~group_element(e_3)) | product(e_3, e_3, e_2) | product(e_3, e_2, e_2) | product(e_3, e_1, e_2) | (~group_element(e_2)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(163,plain,
% 0.21/0.43 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_2)) | (~group_element(e_3)) | product(e_3, e_3, e_2) | product(e_3, e_2, e_2) | product(e_3, e_1, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_3)) | product(e_3, e_3, e_2) | product(e_3, e_2, e_2) | product(e_3, e_1, e_2) | (~group_element(e_2))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[162])).
% 0.21/0.43 tff(164,plain,
% 0.21/0.43 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_2)) | (~group_element(e_3)) | product(e_3, e_3, e_2) | product(e_3, e_2, e_2) | product(e_3, e_1, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_3)) | product(e_3, e_3, e_2) | product(e_3, e_2, e_2) | product(e_3, e_1, e_2) | (~group_element(e_2)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[163, 161])).
% 0.21/0.43 tff(165,plain,
% 0.21/0.43 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | ((~group_element(e_2)) | (~group_element(e_3)) | product(e_3, e_3, e_2) | product(e_3, e_2, e_2) | product(e_3, e_1, e_2))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(166,plain,
% 0.21/0.43 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, e_3, Y) | product(X, e_2, Y) | product(X, e_1, Y))) | (~group_element(e_3)) | product(e_3, e_3, e_2) | product(e_3, e_2, e_2) | product(e_3, e_1, e_2) | (~group_element(e_2))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.21/0.43 tff(167,plain,
% 0.21/0.43 (product(e_3, e_3, e_2) | product(e_3, e_2, e_2) | product(e_3, e_1, e_2)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[166, 152, 37, 94])).
% 0.21/0.43 tff(168,plain,
% 0.21/0.43 (product(e_3, e_2, e_2) | product(e_3, e_1, e_2)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[167, 91])).
% 0.21/0.43 tff(169,plain,
% 0.21/0.43 (product(e_3, e_2, e_2)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[168, 12])).
% 0.21/0.43 tff(170,plain,
% 0.21/0.43 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_2, e_3)) | (~product(e_3, e_2, e_2)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_2, e_3)) | (~product(e_3, e_2, e_2)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(171,plain,
% 0.21/0.44 (((~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_2, e_3)) | equalish(e_2, e_3)) <=> (equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_2, e_3)) | (~product(e_3, e_2, e_2)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(172,plain,
% 0.21/0.44 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_2, e_3)) | equalish(e_2, e_3))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_2, e_3)) | (~product(e_3, e_2, e_2))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[171])).
% 0.21/0.44 tff(173,plain,
% 0.21/0.44 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_2, e_3)) | equalish(e_2, e_3))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_2, e_3)) | (~product(e_3, e_2, e_2)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[172, 170])).
% 0.21/0.44 tff(174,plain,
% 0.21/0.44 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_2)) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_2, e_3)) | equalish(e_2, e_3))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(175,plain,
% 0.21/0.44 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_2, e_3)) | (~product(e_3, e_2, e_2))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.21/0.44 tff(176,plain,
% 0.21/0.44 (~product(e_2, e_2, e_3)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[175, 86, 68, 169, 82])).
% 0.21/0.44 tff(177,assumption,(product(e_3, e_2, e_3)), introduced(assumption)).
% 0.21/0.44 tff(178,plain,
% 0.21/0.44 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(179,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.21/0.44 tff(180,plain,
% 0.21/0.44 (~equalish(e_3, e_2)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.21/0.44 tff(181,plain,
% 0.21/0.44 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_3, e_2) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_3, e_2) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(182,plain,
% 0.21/0.44 (((~product(e_3, e_2, e_3)) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_3, e_3)) | equalish(e_3, e_2)) <=> (equalish(e_3, e_2) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(183,plain,
% 0.21/0.44 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_2, e_3)) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_3, e_3)) | equalish(e_3, e_2))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_3, e_2) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[182])).
% 0.21/0.44 tff(184,plain,
% 0.21/0.44 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_2, e_3)) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_3, e_3)) | equalish(e_3, e_2))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_3, e_2) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[183, 181])).
% 0.21/0.44 tff(185,plain,
% 0.21/0.44 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_2, e_3)) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_3, e_3)) | equalish(e_3, e_2))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(186,plain,
% 0.21/0.44 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_3, e_2) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.21/0.44 tff(187,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[186, 180, 68, 82, 177])).
% 0.21/0.44 tff(188,plain,(~product(e_3, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(189,plain,
% 0.21/0.44 (((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_3, e_2, e_3) | product(e_1, e_2, e_3))) <=> ((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_3, e_2, e_3) | product(e_1, e_2, e_3))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(190,plain,
% 0.21/0.44 ((product(e_3, e_2, e_3) | product(e_2, e_2, e_3) | product(e_1, e_2, e_3) | (~group_element(e_3)) | (~group_element(e_2))) <=> ((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_3, e_2, e_3) | product(e_1, e_2, e_3))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(191,plain,
% 0.21/0.44 (((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_2, e_3) | product(e_2, e_2, e_3) | product(e_1, e_2, e_3) | (~group_element(e_3)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_3, e_2, e_3) | product(e_1, e_2, e_3)))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[190])).
% 0.21/0.44 tff(192,plain,
% 0.21/0.44 (((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_2, e_3) | product(e_2, e_2, e_3) | product(e_1, e_2, e_3) | (~group_element(e_3)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_3, e_2, e_3) | product(e_1, e_2, e_3))),
% 0.21/0.44 inference(transitivity,[status(thm)],[191, 189])).
% 0.21/0.44 tff(193,plain,
% 0.21/0.44 ((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_2, e_3) | product(e_2, e_2, e_3) | product(e_1, e_2, e_3) | (~group_element(e_3)) | (~group_element(e_2)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(194,plain,
% 0.21/0.44 ((~![Y: $i, X: $i] : (product(e_3, X, Y) | product(e_2, X, Y) | product(e_1, X, Y) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_3, e_2, e_3) | product(e_1, e_2, e_3)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.21/0.44 tff(195,plain,
% 0.21/0.44 (product(e_2, e_2, e_3) | product(e_1, e_2, e_3)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[194, 50, 37, 94, 188])).
% 0.21/0.44 tff(196,plain,
% 0.21/0.44 (product(e_1, e_2, e_3)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[195, 176])).
% 0.21/0.44 tff(197,plain,
% 0.21/0.44 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_3, e_2) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_3, e_3)) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_2, e_1)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_3, e_2) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_3, e_3)) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_2, e_1)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(198,plain,
% 0.21/0.44 (((~product(e_2, e_2, e_1)) | (~product(e_2, e_3, e_3)) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_3, e_3)) | equalish(e_3, e_2)) <=> (equalish(e_3, e_2) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_3, e_3)) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_2, e_1)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(199,plain,
% 0.21/0.44 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_2, e_2, e_1)) | (~product(e_2, e_3, e_3)) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_3, e_3)) | equalish(e_3, e_2))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_3, e_2) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_3, e_3)) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_2, e_1))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[198])).
% 0.21/0.44 tff(200,plain,
% 0.21/0.44 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_2, e_2, e_1)) | (~product(e_2, e_3, e_3)) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_3, e_3)) | equalish(e_3, e_2))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_3, e_2) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_3, e_3)) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_2, e_1)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[199, 197])).
% 0.21/0.44 tff(201,plain,
% 0.21/0.44 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_2, e_2, e_1)) | (~product(e_2, e_3, e_3)) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_3, e_3)) | equalish(e_3, e_2))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(202,plain,
% 0.21/0.44 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_3, e_2) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_3, e_3)) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_2, e_1))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.21/0.45 tff(203,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[202, 180, 68, 82, 196, 160, 126])).
% 0.21/0.45 tff(204,plain,(product(e_3, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(205,assumption,(product(e_2, e_1, e_3)), introduced(assumption)).
% 0.21/0.45 tff(206,assumption,(product(e_3, e_1, e_2)), introduced(assumption)).
% 0.21/0.45 tff(207,plain,
% 0.21/0.45 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(208,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.21/0.45 tff(209,plain,
% 0.21/0.45 (~equalish(e_1, e_3)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.21/0.45 tff(210,plain,
% 0.21/0.45 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_2)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(211,plain,
% 0.21/0.45 (((~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_1, e_3)) | equalish(e_1, e_3)) <=> (equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(212,plain,
% 0.21/0.45 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_1, e_3)) | equalish(e_1, e_3))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_2))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[211])).
% 0.21/0.45 tff(213,plain,
% 0.21/0.45 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_1, e_3)) | equalish(e_1, e_3))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[212, 210])).
% 0.21/0.45 tff(214,plain,
% 0.21/0.45 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_2)) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_1, e_3)) | equalish(e_1, e_3))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(215,plain,
% 0.21/0.45 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_2))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.21/0.45 tff(216,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[215, 209, 68, 206, 82, 205])).
% 0.21/0.45 tff(217,plain,((~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(218,plain,
% 0.21/0.45 (~product(e_2, e_1, e_3)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[217, 204])).
% 0.21/0.45 tff(219,plain,
% 0.21/0.45 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (product(e_2, e_1, e_2) | (~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_2, e_1, e_2) | (~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(220,plain,
% 0.21/0.45 (((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1)) <=> (product(e_2, e_1, e_2) | (~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(221,plain,
% 0.21/0.45 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_1)) | (~group_element(e_2)) | 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] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | (product(e_2, e_1, e_2) | (~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1)))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[220])).
% 0.21/0.45 tff(222,plain,
% 0.21/0.45 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_1)) | (~group_element(e_2)) | 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] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_2, e_1, e_2) | (~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1))),
% 0.21/0.45 inference(transitivity,[status(thm)],[221, 219])).
% 0.21/0.45 tff(223,plain,
% 0.21/0.45 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(224,plain,
% 0.21/0.45 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1))) | product(e_2, e_1, e_2) | (~group_element(e_2)) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.21/0.45 tff(225,plain,
% 0.21/0.45 (product(e_2, e_1, e_2) | product(e_2, e_1, e_3)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[224, 40, 37, 119, 142])).
% 0.21/0.45 tff(226,plain,
% 0.21/0.45 (product(e_2, e_1, e_2)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[225, 218])).
% 0.21/0.45 tff(227,plain,
% 0.21/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_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_2) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(228,plain,
% 0.21/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(229,plain,
% 0.21/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_1, e_2))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.21/0.45 tff(230,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[229, 180, 137, 204, 226])).
% 0.21/0.45 % SZS output end Proof
% 0.21/0.46 % E exiting
%------------------------------------------------------------------------------