%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP123-7.003 : TPTP v9.0.0. Released v1.2.0.
% 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 0.21s 0.42s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GRP123-7.003 : TPTP v9.0.0. Released v1.2.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 15:43:16 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.42 % SZS status Unsatisfiable
% 0.21/0.42 % SZS output start Proof
% 0.21/0.42 tff(product1_type, type, (
% 0.21/0.42 product1: ( $i * $i * $i ) > $o)).
% 0.21/0.42 tff(e_2_type, type, (
% 0.21/0.42 e_2: $i)).
% 0.21/0.42 tff(e_3_type, type, (
% 0.21/0.42 e_3: $i)).
% 0.21/0.42 tff(e_1_type, type, (
% 0.21/0.42 e_1: $i)).
% 0.21/0.42 tff(product2_type, type, (
% 0.21/0.42 product2: ( $i * $i * $i ) > $o)).
% 0.21/0.42 tff(equalish_type, type, (
% 0.21/0.42 equalish: ( $i * $i ) > $o)).
% 0.21/0.42 tff(group_element_type, type, (
% 0.21/0.42 group_element: $i > $o)).
% 0.21/0.42 tff(1,plain,
% 0.21/0.42 (^[X: $i] : refl(product1(X, X, X) <=> product1(X, X, X))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(2,plain,
% 0.21/0.42 (![X: $i] : product1(X, X, X) <=> ![X: $i] : product1(X, X, X)),
% 0.21/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.42 tff(3,plain,
% 0.21/0.42 (![X: $i] : product1(X, X, X) <=> ![X: $i] : product1(X, X, X)),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(4,axiom,(![X: $i] : product1(X, X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product1_idempotence')).
% 0.21/0.42 tff(5,plain,
% 0.21/0.42 (![X: $i] : product1(X, X, X)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.42 tff(6,plain,(
% 0.21/0.42 ![X: $i] : product1(X, X, X)),
% 0.21/0.42 inference(skolemize,[status(sab)],[5])).
% 0.21/0.42 tff(7,plain,
% 0.21/0.42 (![X: $i] : product1(X, X, X)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.42 tff(8,plain,
% 0.21/0.42 ((~![X: $i] : product1(X, X, X)) | product1(e_2, e_2, e_2)),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(9,plain,
% 0.21/0.42 (product1(e_2, e_2, e_2)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.42 tff(10,assumption,(~product2(e_1, e_1, e_1)), introduced(assumption)).
% 0.21/0.42 tff(11,assumption,(~product1(e_1, e_1, e_1)), introduced(assumption)).
% 0.21/0.42 tff(12,plain,
% 0.21/0.42 ((~![X: $i] : product1(X, X, X)) | product1(e_1, e_1, e_1)),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(13,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[12, 7, 11])).
% 0.21/0.42 tff(14,plain,(product1(e_1, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(15,plain,
% 0.21/0.42 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl((product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1))) <=> (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(16,plain,
% 0.21/0.42 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[15])).
% 0.21/0.42 tff(17,plain,
% 0.21/0.42 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(18,plain,
% 0.21/0.42 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : rewrite((((~product1(X, Y, Z1)) | (~product1(Z1, Y, Z2))) | product2(Z2, X, Y)) <=> (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(19,plain,
% 0.21/0.42 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product1(X, Y, Z1)) | (~product1(Z1, Y, Z2))) | product2(Z2, X, Y)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[18])).
% 0.21/0.42 tff(20,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product1(X, Y, Z1)) | (~product1(Z1, Y, Z2))) | product2(Z2, X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qg1a')).
% 0.21/0.42 tff(21,plain,
% 0.21/0.42 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.21/0.42 tff(22,plain,
% 0.21/0.42 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.21/0.42 tff(23,plain,(
% 0.21/0.42 ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[22])).
% 0.21/0.42 tff(24,plain,
% 0.21/0.42 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.21/0.42 tff(25,plain,
% 0.21/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | ((~product1(e_1, e_1, e_1)) | product2(e_1, e_1, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | (~product1(e_1, e_1, e_1)) | product2(e_1, e_1, e_1))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(26,plain,
% 0.21/0.42 ((product2(e_1, e_1, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_1, e_1))) <=> ((~product1(e_1, e_1, e_1)) | product2(e_1, e_1, e_1))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(27,plain,
% 0.21/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | (product2(e_1, e_1, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | ((~product1(e_1, e_1, e_1)) | product2(e_1, e_1, e_1)))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[26])).
% 0.21/0.42 tff(28,plain,
% 0.21/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | (product2(e_1, e_1, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | (~product1(e_1, e_1, e_1)) | product2(e_1, e_1, e_1))),
% 0.21/0.42 inference(transitivity,[status(thm)],[27, 25])).
% 0.21/0.42 tff(29,plain,
% 0.21/0.42 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | (product2(e_1, e_1, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_1, e_1)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(30,plain,
% 0.21/0.42 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | (~product1(e_1, e_1, e_1)) | product2(e_1, e_1, e_1)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.21/0.42 tff(31,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[30, 24, 14, 10])).
% 0.21/0.42 tff(32,plain,(product2(e_1, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(33,plain,
% 0.21/0.42 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W))) <=> (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(34,plain,
% 0.21/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[33])).
% 0.21/0.42 tff(35,plain,
% 0.21/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(36,plain,
% 0.21/0.42 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product2(X, Y, W)) | (~product2(X, Y, Z))) <=> ((~product2(X, Y, Z)) | (~product2(X, Y, W)))), ((((~product2(X, Y, W)) | (~product2(X, Y, Z))) | equalish(W, Z)) <=> (((~product2(X, Y, Z)) | (~product2(X, Y, W))) | equalish(W, Z)))), rewrite((((~product2(X, Y, Z)) | (~product2(X, Y, W))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))), ((((~product2(X, Y, W)) | (~product2(X, Y, Z))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(37,plain,
% 0.21/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product2(X, Y, W)) | (~product2(X, Y, Z))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[36])).
% 0.21/0.42 tff(38,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product2(X, Y, W)) | (~product2(X, Y, Z))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product2_total_function2')).
% 0.21/0.42 tff(39,plain,
% 0.21/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.21/0.42 tff(40,plain,
% 0.21/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.21/0.42 tff(41,plain,(
% 0.21/0.42 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[40])).
% 0.21/0.42 tff(42,plain,
% 0.21/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.21/0.42 tff(43,plain,
% 0.21/0.42 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(44,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.21/0.42 tff(45,plain,
% 0.21/0.42 (~equalish(e_2, e_1)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.21/0.42 tff(46,plain,
% 0.21/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | (equalish(e_2, e_1) | (~product2(e_1, e_1, e_1)) | (~product2(e_1, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | equalish(e_2, e_1) | (~product2(e_1, e_1, e_1)) | (~product2(e_1, e_1, e_2)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(47,plain,
% 0.21/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | (equalish(e_2, e_1) | (~product2(e_1, e_1, e_1)) | (~product2(e_1, e_1, e_2)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(48,plain,
% 0.21/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | equalish(e_2, e_1) | (~product2(e_1, e_1, e_1)) | (~product2(e_1, e_1, e_2))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.21/0.42 tff(49,plain,
% 0.21/0.42 ((~product2(e_1, e_1, e_1)) | (~product2(e_1, e_1, e_2))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[48, 45, 42])).
% 0.21/0.42 tff(50,plain,
% 0.21/0.42 (~product2(e_1, e_1, e_2)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[49, 32])).
% 0.21/0.42 tff(51,assumption,(product1(e_3, e_2, e_1)), introduced(assumption)).
% 0.21/0.42 tff(52,assumption,(product1(e_1, e_2, e_2)), introduced(assumption)).
% 0.21/0.42 tff(53,plain,
% 0.21/0.42 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X))) <=> (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(54,plain,
% 0.21/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[53])).
% 0.21/0.42 tff(55,plain,
% 0.21/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(56,plain,
% 0.21/0.42 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product1(W, Y, X)) | (~product1(Z, Y, X))) <=> ((~product1(Z, Y, X)) | (~product1(W, Y, X)))), ((((~product1(W, Y, X)) | (~product1(Z, Y, X))) | equalish(W, Z)) <=> (((~product1(Z, Y, X)) | (~product1(W, Y, X))) | equalish(W, Z)))), rewrite((((~product1(Z, Y, X)) | (~product1(W, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))), ((((~product1(W, Y, X)) | (~product1(Z, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(57,plain,
% 0.21/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product1(W, Y, X)) | (~product1(Z, Y, X))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[56])).
% 0.21/0.42 tff(58,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product1(W, Y, X)) | (~product1(Z, Y, X))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product1_left_cancellation')).
% 0.21/0.42 tff(59,plain,
% 0.21/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.21/0.43 tff(60,plain,
% 0.21/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.21/0.43 tff(61,plain,(
% 0.21/0.43 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[60])).
% 0.21/0.43 tff(62,plain,
% 0.21/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.21/0.43 tff(63,plain,
% 0.21/0.43 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(64,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.21/0.43 tff(65,plain,
% 0.21/0.43 (~equalish(e_1, e_2)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.21/0.43 tff(66,plain,
% 0.21/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_2) | (~product1(e_1, e_2, e_2)) | (~product1(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_1, e_2) | (~product1(e_1, e_2, e_2)) | (~product1(e_2, e_2, e_2)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(67,plain,
% 0.21/0.43 ((equalish(e_1, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_1, e_2, e_2))) <=> (equalish(e_1, e_2) | (~product1(e_1, e_2, e_2)) | (~product1(e_2, e_2, e_2)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(68,plain,
% 0.21/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_2) | (~product1(e_1, e_2, e_2)) | (~product1(e_2, e_2, e_2))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[67])).
% 0.21/0.43 tff(69,plain,
% 0.21/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_1, e_2) | (~product1(e_1, e_2, e_2)) | (~product1(e_2, e_2, e_2)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[68, 66])).
% 0.21/0.43 tff(70,plain,
% 0.21/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_1, e_2, e_2)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(71,plain,
% 0.21/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_1, e_2) | (~product1(e_1, e_2, e_2)) | (~product1(e_2, e_2, e_2))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.21/0.43 tff(72,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[71, 65, 62, 52, 9])).
% 0.21/0.43 tff(73,plain,(~product1(e_1, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(74,assumption,(product1(e_1, e_2, e_1)), introduced(assumption)).
% 0.21/0.43 tff(75,plain,
% 0.21/0.43 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y))) <=> (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(76,plain,
% 0.21/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[75])).
% 0.21/0.43 tff(77,plain,
% 0.21/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(78,plain,
% 0.21/0.43 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product1(X, W, Y)) | (~product1(X, Z, Y))) <=> ((~product1(X, Z, Y)) | (~product1(X, W, Y)))), ((((~product1(X, W, Y)) | (~product1(X, Z, Y))) | equalish(W, Z)) <=> (((~product1(X, Z, Y)) | (~product1(X, W, Y))) | equalish(W, Z)))), rewrite((((~product1(X, Z, Y)) | (~product1(X, W, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))), ((((~product1(X, W, Y)) | (~product1(X, Z, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(79,plain,
% 0.21/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product1(X, W, Y)) | (~product1(X, Z, Y))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[78])).
% 0.21/0.43 tff(80,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product1(X, W, Y)) | (~product1(X, Z, Y))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product1_right_cancellation')).
% 0.21/0.43 tff(81,plain,
% 0.21/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.21/0.43 tff(82,plain,
% 0.21/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.21/0.43 tff(83,plain,(
% 0.21/0.43 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[82])).
% 0.21/0.43 tff(84,plain,
% 0.21/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.21/0.43 tff(85,plain,
% 0.21/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_1) | (~product1(e_1, e_2, e_1)) | (~product1(e_1, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_2, e_1) | (~product1(e_1, e_2, e_1)) | (~product1(e_1, e_1, e_1)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(86,plain,
% 0.21/0.43 ((equalish(e_2, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_2, e_1))) <=> (equalish(e_2, e_1) | (~product1(e_1, e_2, e_1)) | (~product1(e_1, e_1, e_1)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(87,plain,
% 0.21/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_1) | (~product1(e_1, e_2, e_1)) | (~product1(e_1, e_1, e_1))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[86])).
% 0.21/0.43 tff(88,plain,
% 0.21/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_2, e_1) | (~product1(e_1, e_2, e_1)) | (~product1(e_1, e_1, e_1)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[87, 85])).
% 0.21/0.43 tff(89,plain,
% 0.21/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_2, e_1)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(90,plain,
% 0.21/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_2, e_1) | (~product1(e_1, e_2, e_1)) | (~product1(e_1, e_1, e_1))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.21/0.43 tff(91,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[90, 45, 84, 74, 14])).
% 0.21/0.43 tff(92,plain,(~product1(e_1, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(93,plain,
% 0.21/0.43 (^[Y: $i, X: $i] : refl((product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> (product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(94,plain,
% 0.21/0.43 (![Y: $i, X: $i] : (product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[93])).
% 0.21/0.43 tff(95,plain,
% 0.21/0.43 (![Y: $i, X: $i] : (product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(96,plain,
% 0.21/0.43 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) <=> (product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) <=> ((product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product1(X, Y, e_2)))), rewrite(((product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product1(X, Y, e_2)) <=> (product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) <=> (product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))), ((((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) | product1(X, Y, e_3)) <=> ((product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product1(X, Y, e_3)))), rewrite(((product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product1(X, Y, e_3)) <=> (product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), ((((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) | product1(X, Y, e_3)) <=> (product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(97,plain,
% 0.21/0.43 (![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) | product1(X, Y, e_3)) <=> ![Y: $i, X: $i] : (product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[96])).
% 0.21/0.43 tff(98,axiom,(![Y: $i, X: $i] : (((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) | product1(X, Y, e_3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product1_total_function1')).
% 0.21/0.43 tff(99,plain,
% 0.21/0.43 (![Y: $i, X: $i] : (product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.21/0.43 tff(100,plain,
% 0.21/0.43 (![Y: $i, X: $i] : (product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.21/0.43 tff(101,plain,(
% 0.21/0.43 ![Y: $i, X: $i] : (product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[100])).
% 0.21/0.43 tff(102,plain,
% 0.21/0.43 (![Y: $i, X: $i] : (product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[101, 94])).
% 0.21/0.43 tff(103,plain,
% 0.21/0.43 (group_element(e_2) <=> group_element(e_2)),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(104,axiom,(group_element(e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_2')).
% 0.21/0.43 tff(105,plain,
% 0.21/0.43 (group_element(e_2)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.21/0.43 tff(106,plain,
% 0.21/0.43 (group_element(e_1) <=> group_element(e_1)),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(107,axiom,(group_element(e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_1')).
% 0.21/0.43 tff(108,plain,
% 0.21/0.44 (group_element(e_1)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.21/0.44 tff(109,plain,
% 0.21/0.44 (((~![Y: $i, X: $i] : (product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product1(e_1, e_2, e_3) | (~group_element(e_2)) | product1(e_1, e_2, e_1) | product1(e_1, e_2, e_2) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product1(e_1, e_2, e_3) | (~group_element(e_2)) | product1(e_1, e_2, e_1) | product1(e_1, e_2, e_2) | (~group_element(e_1)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(110,plain,
% 0.21/0.44 ((product1(e_1, e_2, e_3) | product1(e_1, e_2, e_2) | product1(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1))) <=> (product1(e_1, e_2, e_3) | (~group_element(e_2)) | product1(e_1, e_2, e_1) | product1(e_1, e_2, e_2) | (~group_element(e_1)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(111,plain,
% 0.21/0.44 (((~![Y: $i, X: $i] : (product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product1(e_1, e_2, e_3) | product1(e_1, e_2, e_2) | product1(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product1(e_1, e_2, e_3) | (~group_element(e_2)) | product1(e_1, e_2, e_1) | product1(e_1, e_2, e_2) | (~group_element(e_1))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[110])).
% 0.21/0.44 tff(112,plain,
% 0.21/0.44 (((~![Y: $i, X: $i] : (product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product1(e_1, e_2, e_3) | product1(e_1, e_2, e_2) | product1(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : (product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product1(e_1, e_2, e_3) | (~group_element(e_2)) | product1(e_1, e_2, e_1) | product1(e_1, e_2, e_2) | (~group_element(e_1)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[111, 109])).
% 0.21/0.44 tff(113,plain,
% 0.21/0.44 ((~![Y: $i, X: $i] : (product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product1(e_1, e_2, e_3) | product1(e_1, e_2, e_2) | product1(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(114,plain,
% 0.21/0.44 ((~![Y: $i, X: $i] : (product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product1(e_1, e_2, e_3) | (~group_element(e_2)) | product1(e_1, e_2, e_1) | product1(e_1, e_2, e_2) | (~group_element(e_1))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.21/0.44 tff(115,plain,
% 0.21/0.44 (product1(e_1, e_2, e_3) | product1(e_1, e_2, e_2)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[114, 108, 105, 102, 92])).
% 0.21/0.44 tff(116,plain,
% 0.21/0.44 (product1(e_1, e_2, e_3)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[115, 73])).
% 0.21/0.44 tff(117,plain,
% 0.21/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | ((~product1(e_1, e_2, e_3)) | product2(e_1, e_1, e_2) | (~product1(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | (~product1(e_1, e_2, e_3)) | product2(e_1, e_1, e_2) | (~product1(e_3, e_2, e_1)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(118,plain,
% 0.21/0.44 ((product2(e_1, e_1, e_2) | (~product1(e_3, e_2, e_1)) | (~product1(e_1, e_2, e_3))) <=> ((~product1(e_1, e_2, e_3)) | product2(e_1, e_1, e_2) | (~product1(e_3, e_2, e_1)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(119,plain,
% 0.21/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | (product2(e_1, e_1, e_2) | (~product1(e_3, e_2, e_1)) | (~product1(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | ((~product1(e_1, e_2, e_3)) | product2(e_1, e_1, e_2) | (~product1(e_3, e_2, e_1))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[118])).
% 0.21/0.44 tff(120,plain,
% 0.21/0.44 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | (product2(e_1, e_1, e_2) | (~product1(e_3, e_2, e_1)) | (~product1(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | (~product1(e_1, e_2, e_3)) | product2(e_1, e_1, e_2) | (~product1(e_3, e_2, e_1)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[119, 117])).
% 0.21/0.44 tff(121,plain,
% 0.21/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | (product2(e_1, e_1, e_2) | (~product1(e_3, e_2, e_1)) | (~product1(e_1, e_2, e_3)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(122,plain,
% 0.21/0.44 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | (~product1(e_1, e_2, e_3)) | product2(e_1, e_1, e_2) | (~product1(e_3, e_2, e_1))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.21/0.44 tff(123,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[122, 24, 116, 51, 50])).
% 0.21/0.44 tff(124,plain,(~product1(e_3, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(125,assumption,(product1(e_3, e_2, e_3)), introduced(assumption)).
% 0.21/0.44 tff(126,plain,
% 0.21/0.44 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(127,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.21/0.44 tff(128,plain,
% 0.21/0.44 (~equalish(e_3, e_1)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.21/0.44 tff(129,plain,
% 0.21/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_1) | (~product1(e_1, e_2, e_3)) | (~product1(e_3, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_3, e_1) | (~product1(e_1, e_2, e_3)) | (~product1(e_3, e_2, e_3)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(130,plain,
% 0.21/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_1) | (~product1(e_1, e_2, e_3)) | (~product1(e_3, e_2, e_3)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(131,plain,
% 0.21/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_3, e_1) | (~product1(e_1, e_2, e_3)) | (~product1(e_3, e_2, e_3))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.21/0.44 tff(132,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[131, 128, 62, 116, 125])).
% 0.21/0.44 tff(133,plain,(~product1(e_3, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(134,plain,
% 0.21/0.44 (group_element(e_3) <=> group_element(e_3)),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(135,axiom,(group_element(e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_3')).
% 0.21/0.44 tff(136,plain,
% 0.21/0.44 (group_element(e_3)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.21/0.44 tff(137,plain,
% 0.21/0.44 (((~![Y: $i, X: $i] : (product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | (~group_element(e_3)) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_1) | product1(e_3, e_2, e_3))) <=> ((~![Y: $i, X: $i] : (product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | (~group_element(e_3)) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_1) | product1(e_3, e_2, e_3))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(138,plain,
% 0.21/0.44 ((product1(e_3, e_2, e_3) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3))) <=> ((~group_element(e_2)) | (~group_element(e_3)) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_1) | product1(e_3, e_2, e_3))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(139,plain,
% 0.21/0.44 (((~![Y: $i, X: $i] : (product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product1(e_3, e_2, e_3) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | (~group_element(e_3)) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_1) | product1(e_3, e_2, e_3)))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[138])).
% 0.21/0.44 tff(140,plain,
% 0.21/0.44 (((~![Y: $i, X: $i] : (product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product1(e_3, e_2, e_3) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | (~group_element(e_3)) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_1) | product1(e_3, e_2, e_3))),
% 0.21/0.44 inference(transitivity,[status(thm)],[139, 137])).
% 0.21/0.44 tff(141,plain,
% 0.21/0.44 ((~![Y: $i, X: $i] : (product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product1(e_3, e_2, e_3) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(142,plain,
% 0.21/0.44 ((~![Y: $i, X: $i] : (product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | (~group_element(e_3)) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_1) | product1(e_3, e_2, e_3)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.21/0.44 tff(143,plain,
% 0.21/0.44 (product1(e_3, e_2, e_2) | product1(e_3, e_2, e_1) | product1(e_3, e_2, e_3)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[142, 105, 136, 102])).
% 0.21/0.44 tff(144,plain,
% 0.21/0.44 (product1(e_3, e_2, e_2) | product1(e_3, e_2, e_1)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[143, 133])).
% 0.21/0.44 tff(145,plain,
% 0.21/0.44 (product1(e_3, e_2, e_2)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[144, 124])).
% 0.21/0.44 tff(146,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(147,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.21/0.44 tff(148,plain,
% 0.21/0.44 (~equalish(e_3, e_2)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.21/0.44 tff(149,plain,
% 0.21/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_2) | (~product1(e_3, e_2, e_2)) | (~product1(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_3, e_2) | (~product1(e_3, e_2, e_2)) | (~product1(e_2, e_2, e_2)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(150,plain,
% 0.21/0.44 ((equalish(e_3, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_3, e_2, e_2))) <=> (equalish(e_3, e_2) | (~product1(e_3, e_2, e_2)) | (~product1(e_2, e_2, e_2)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(151,plain,
% 0.21/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_3, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_2) | (~product1(e_3, e_2, e_2)) | (~product1(e_2, e_2, e_2))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[150])).
% 0.21/0.44 tff(152,plain,
% 0.21/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_3, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_3, e_2) | (~product1(e_3, e_2, e_2)) | (~product1(e_2, e_2, e_2)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[151, 149])).
% 0.21/0.44 tff(153,plain,
% 0.21/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_3, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_3, e_2, e_2)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(154,plain,
% 0.21/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_3, e_2) | (~product1(e_3, e_2, e_2)) | (~product1(e_2, e_2, e_2))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.21/0.45 tff(155,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[154, 148, 62, 145, 9])).
% 0.21/0.45 % SZS output end Proof
% 0.21/0.45 % E exiting
%------------------------------------------------------------------------------