%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP123-9.003 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP123-9.003 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 15:41:39 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.41 % SZS status Unsatisfiable
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(product2_type, type, (
% 0.19/0.41 product2: ( $i * $i * $i ) > $o)).
% 0.19/0.41 tff(e_3_type, type, (
% 0.19/0.41 e_3: $i)).
% 0.19/0.41 tff(e_2_type, type, (
% 0.19/0.41 e_2: $i)).
% 0.19/0.41 tff(product1_type, type, (
% 0.19/0.41 product1: ( $i * $i * $i ) > $o)).
% 0.19/0.41 tff(e_1_type, type, (
% 0.19/0.41 e_1: $i)).
% 0.19/0.41 tff(equalish_type, type, (
% 0.19/0.41 equalish: ( $i * $i ) > $o)).
% 0.19/0.41 tff(group_element_type, type, (
% 0.19/0.41 group_element: $i > $o)).
% 0.19/0.41 tff(1,plain,
% 0.19/0.41 (^[X: $i] : refl(product2(X, X, X) <=> product2(X, X, X))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(2,plain,
% 0.19/0.41 (![X: $i] : product2(X, X, X) <=> ![X: $i] : product2(X, X, X)),
% 0.19/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.41 tff(3,plain,
% 0.19/0.41 (![X: $i] : product2(X, X, X) <=> ![X: $i] : product2(X, X, X)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(4,axiom,(![X: $i] : product2(X, X, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product2_idempotence')).
% 0.19/0.41 tff(5,plain,
% 0.19/0.41 (![X: $i] : product2(X, X, X)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.41 tff(6,plain,(
% 0.19/0.41 ![X: $i] : product2(X, X, X)),
% 0.19/0.41 inference(skolemize,[status(sab)],[5])).
% 0.19/0.41 tff(7,plain,
% 0.19/0.41 (![X: $i] : product2(X, X, X)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 ((~![X: $i] : product2(X, X, X)) | product2(e_3, e_3, e_3)),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(9,plain,
% 0.19/0.41 (product2(e_3, e_3, e_3)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.41 tff(10,assumption,(~product1(e_2, e_2, e_2)), introduced(assumption)).
% 0.19/0.41 tff(11,plain,
% 0.19/0.41 (^[X: $i] : refl(product1(X, X, X) <=> product1(X, X, X))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 (![X: $i] : product1(X, X, X) <=> ![X: $i] : product1(X, X, X)),
% 0.19/0.41 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.41 tff(13,plain,
% 0.19/0.41 (![X: $i] : product1(X, X, X) <=> ![X: $i] : product1(X, X, X)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(14,axiom,(![X: $i] : product1(X, X, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product1_idempotence')).
% 0.19/0.41 tff(15,plain,
% 0.19/0.41 (![X: $i] : product1(X, X, X)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.19/0.41 tff(16,plain,(
% 0.19/0.41 ![X: $i] : product1(X, X, X)),
% 0.19/0.41 inference(skolemize,[status(sab)],[15])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 (![X: $i] : product1(X, X, X)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 ((~![X: $i] : product1(X, X, X)) | product1(e_2, e_2, e_2)),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[18, 17, 10])).
% 0.19/0.41 tff(20,plain,(product1(e_2, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(21,assumption,(product1(e_2, e_2, e_2)), introduced(assumption)).
% 0.19/0.41 tff(22,assumption,(product1(e_3, e_2, e_2)), introduced(assumption)).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 (^[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)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(27,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.42 tff(28,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product1(W, Y, X)) | (~product1(Z, Y, X))) | equalish(W, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product1_left_cancellation')).
% 0.19/0.42 tff(29,plain,
% 0.19/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.42 tff(30,plain,
% 0.19/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.19/0.42 tff(31,plain,(
% 0.19/0.42 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[30])).
% 0.19/0.42 tff(32,plain,
% 0.19/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.19/0.42 tff(33,plain,
% 0.19/0.42 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(34,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.19/0.42 tff(35,plain,
% 0.19/0.42 (~equalish(e_3, e_2)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.42 tff(36,plain,
% 0.19/0.42 (((~![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)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(37,plain,
% 0.19/0.42 ((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)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(38,plain,
% 0.19/0.42 (((~![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))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[37])).
% 0.19/0.42 tff(39,plain,
% 0.19/0.42 (((~![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)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[38, 36])).
% 0.19/0.42 tff(40,plain,
% 0.19/0.42 ((~![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)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(41,plain,
% 0.19/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_3, e_2) | (~product1(e_3, e_2, e_2)) | (~product1(e_2, e_2, e_2))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.42 tff(42,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[41, 35, 32, 22, 21])).
% 0.19/0.42 tff(43,plain,((~product1(e_3, e_2, e_2)) | (~product1(e_2, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(44,plain,
% 0.19/0.42 (~product1(e_3, e_2, e_2)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[43, 20])).
% 0.19/0.42 tff(45,assumption,(product1(e_3, e_2, e_3)), introduced(assumption)).
% 0.19/0.42 tff(46,plain,
% 0.19/0.42 ((~![X: $i] : product1(X, X, X)) | product1(e_3, e_3, e_3)),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(47,plain,
% 0.19/0.42 (product1(e_3, e_3, e_3)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[46, 17])).
% 0.19/0.42 tff(48,plain,
% 0.19/0.42 (^[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))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(49,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[48])).
% 0.19/0.42 tff(50,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(51,plain,
% 0.19/0.42 (^[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)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(52,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[51])).
% 0.19/0.42 tff(53,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product1(X, W, Y)) | (~product1(X, Z, Y))) | equalish(W, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product1_right_cancellation')).
% 0.19/0.42 tff(54,plain,
% 0.19/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.19/0.42 tff(55,plain,
% 0.19/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.19/0.42 tff(56,plain,(
% 0.19/0.42 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[55])).
% 0.19/0.42 tff(57,plain,
% 0.19/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.19/0.42 tff(58,plain,
% 0.19/0.42 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(59,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.19/0.42 tff(60,plain,
% 0.19/0.42 (~equalish(e_2, e_3)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.19/0.42 tff(61,plain,
% 0.19/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_3, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_3, e_2, e_3)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(62,plain,
% 0.19/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_3, e_2, e_3)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(63,plain,
% 0.19/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_3, e_2, e_3))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.42 tff(64,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[63, 60, 57, 47, 45])).
% 0.19/0.42 tff(65,plain,(~product1(e_3, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(66,plain,
% 0.19/0.42 (^[Y: $i, X: $i] : refl(((~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)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(67,plain,
% 0.19/0.42 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[66])).
% 0.19/0.42 tff(68,plain,
% 0.19/0.42 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1)) <=> ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(69,plain,
% 0.19/0.42 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) <=> ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_1))), (((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) <=> (((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_1)) | product1(X, Y, e_2)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_1)) | product1(X, Y, e_2)) <=> ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_2) | product1(X, Y, e_1))), (((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) <=> ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_2) | product1(X, Y, e_1)))), ((((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) | product1(X, Y, e_3)) <=> (((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_2) | product1(X, Y, e_1)) | product1(X, Y, e_3)))), rewrite((((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_2) | product1(X, Y, e_1)) | product1(X, Y, e_3)) <=> ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))), ((((((~group_element(X)) | (~group_element(Y))) | product1(X, Y, e_1)) | product1(X, Y, e_2)) | product1(X, Y, e_3)) <=> ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(70,plain,
% 0.19/0.42 (![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] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[69])).
% 0.19/0.42 tff(71,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/sandbox/benchmark/theBenchmark.p','product1_total_function1')).
% 0.19/0.42 tff(72,plain,
% 0.19/0.42 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.19/0.42 tff(73,plain,
% 0.19/0.42 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.19/0.42 tff(74,plain,(
% 0.19/0.42 ![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))),
% 0.19/0.42 inference(skolemize,[status(sab)],[73])).
% 0.19/0.42 tff(75,plain,
% 0.19/0.42 (![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.19/0.42 tff(76,plain,
% 0.19/0.42 (group_element(e_3) <=> group_element(e_3)),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(77,axiom,(group_element(e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_3')).
% 0.19/0.42 tff(78,plain,
% 0.19/0.42 (group_element(e_3)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.19/0.42 tff(79,plain,
% 0.19/0.42 (group_element(e_2) <=> group_element(e_2)),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(80,axiom,(group_element(e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_2')).
% 0.19/0.43 tff(81,plain,
% 0.19/0.43 (group_element(e_2)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.19/0.43 tff(82,plain,
% 0.19/0.43 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_2)) | product1(e_3, e_2, e_1) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_3)) | (~group_element(e_2)) | product1(e_3, e_2, e_1) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_3))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(83,plain,
% 0.19/0.43 (((~group_element(e_2)) | (~group_element(e_3)) | product1(e_3, e_2, e_3) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_1)) <=> ((~group_element(e_3)) | (~group_element(e_2)) | product1(e_3, e_2, e_1) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_3))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(84,plain,
% 0.19/0.43 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_3)) | product1(e_3, e_2, e_3) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_2)) | product1(e_3, e_2, e_1) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_3)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[83])).
% 0.19/0.43 tff(85,plain,
% 0.19/0.43 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_3)) | product1(e_3, e_2, e_3) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_3)) | (~group_element(e_2)) | product1(e_3, e_2, e_1) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_3))),
% 0.19/0.43 inference(transitivity,[status(thm)],[84, 82])).
% 0.19/0.43 tff(86,plain,
% 0.19/0.43 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_3)) | product1(e_3, e_2, e_3) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_1))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(87,plain,
% 0.19/0.43 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_3)) | (~group_element(e_2)) | product1(e_3, e_2, e_1) | product1(e_3, e_2, e_2) | product1(e_3, e_2, e_3)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.19/0.43 tff(88,plain,
% 0.19/0.43 (product1(e_3, e_2, e_1) | product1(e_3, e_2, e_2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[87, 81, 78, 75, 65])).
% 0.19/0.43 tff(89,plain,
% 0.19/0.43 (product1(e_3, e_2, e_1)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[88, 44])).
% 0.19/0.43 tff(90,assumption,(product1(e_2, e_3, e_2)), introduced(assumption)).
% 0.19/0.43 tff(91,plain,
% 0.19/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_3, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_2, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_3, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_2, e_3, e_2)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(92,plain,
% 0.19/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_3, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_2, e_3, e_2)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(93,plain,
% 0.19/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_3, e_2) | (~product1(e_2, e_2, e_2)) | (~product1(e_2, e_3, e_2))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.19/0.43 tff(94,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[93, 35, 57, 21, 90])).
% 0.19/0.43 tff(95,plain,((~product1(e_2, e_3, e_2)) | (~product1(e_2, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(96,plain,
% 0.19/0.43 (~product1(e_2, e_3, e_2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[95, 20])).
% 0.19/0.43 tff(97,assumption,(product1(e_2, e_3, e_3)), introduced(assumption)).
% 0.19/0.43 tff(98,plain,
% 0.19/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_2, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_2, e_3, e_3)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(99,plain,
% 0.19/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_2, e_3, e_3)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(100,plain,
% 0.19/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_2, e_3, e_3))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.19/0.43 tff(101,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[100, 60, 32, 47, 97])).
% 0.19/0.43 tff(102,plain,(~product1(e_2, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(103,plain,
% 0.19/0.43 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_2)) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_1) | product1(e_2, e_3, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_3)) | (~group_element(e_2)) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_1) | product1(e_2, e_3, e_2))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(104,plain,
% 0.19/0.43 (((~group_element(e_3)) | (~group_element(e_2)) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_1)) <=> ((~group_element(e_3)) | (~group_element(e_2)) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_1) | product1(e_2, e_3, e_2))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(105,plain,
% 0.19/0.43 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_2)) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_2)) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_1) | product1(e_2, e_3, e_2)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[104])).
% 0.19/0.43 tff(106,plain,
% 0.19/0.43 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_2)) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_3)) | (~group_element(e_2)) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_1) | product1(e_2, e_3, e_2))),
% 0.19/0.43 inference(transitivity,[status(thm)],[105, 103])).
% 0.19/0.43 tff(107,plain,
% 0.19/0.43 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_2)) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_1))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(108,plain,
% 0.19/0.43 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_3)) | (~group_element(e_2)) | product1(e_2, e_3, e_3) | product1(e_2, e_3, e_1) | product1(e_2, e_3, e_2)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.19/0.43 tff(109,plain,
% 0.19/0.43 (product1(e_2, e_3, e_1) | product1(e_2, e_3, e_2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[108, 81, 78, 75, 102])).
% 0.19/0.43 tff(110,plain,
% 0.19/0.43 (product1(e_2, e_3, e_1)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[109, 96])).
% 0.19/0.43 tff(111,assumption,(product1(e_2, e_3, e_1)), introduced(assumption)).
% 0.19/0.43 tff(112,assumption,(product1(e_1, e_3, e_1)), introduced(assumption)).
% 0.19/0.43 tff(113,plain,
% 0.19/0.43 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(114,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.19/0.43 tff(115,plain,
% 0.19/0.43 (~equalish(e_2, e_1)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.19/0.43 tff(116,plain,
% 0.19/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_1) | (~product1(e_1, e_3, e_1)) | (~product1(e_2, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_1) | (~product1(e_1, e_3, e_1)) | (~product1(e_2, e_3, e_1)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(117,plain,
% 0.19/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_2, e_1) | (~product1(e_1, e_3, e_1)) | (~product1(e_2, e_3, e_1)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(118,plain,
% 0.19/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_1) | (~product1(e_1, e_3, e_1)) | (~product1(e_2, e_3, e_1))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.19/0.43 tff(119,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[118, 115, 32, 112, 111])).
% 0.19/0.43 tff(120,plain,((~product1(e_2, e_3, e_1)) | (~product1(e_1, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(121,plain,
% 0.19/0.43 (~product1(e_1, e_3, e_1)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[120, 110])).
% 0.19/0.43 tff(122,assumption,(product1(e_1, e_3, e_3)), introduced(assumption)).
% 0.19/0.43 tff(123,plain,
% 0.19/0.43 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(124,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.19/0.43 tff(125,plain,
% 0.19/0.43 (~equalish(e_1, e_3)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.19/0.43 tff(126,plain,
% 0.19/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_1, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_1, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_1, e_3, e_3)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(127,plain,
% 0.19/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_1, e_3, e_3)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(128,plain,
% 0.19/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_1, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_1, e_3, e_3))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.19/0.43 tff(129,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[128, 125, 32, 47, 122])).
% 0.19/0.43 tff(130,plain,(~product1(e_1, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(131,plain,
% 0.19/0.43 (group_element(e_1) <=> group_element(e_1)),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(132,axiom,(group_element(e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_1')).
% 0.19/0.43 tff(133,plain,
% 0.19/0.43 (group_element(e_1)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.19/0.43 tff(134,plain,
% 0.19/0.43 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_1)) | product1(e_1, e_3, e_1) | product1(e_1, e_3, e_2) | product1(e_1, e_3, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_3)) | (~group_element(e_1)) | product1(e_1, e_3, e_1) | product1(e_1, e_3, e_2) | product1(e_1, e_3, e_3))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(135,plain,
% 0.19/0.44 (((~group_element(e_3)) | (~group_element(e_1)) | product1(e_1, e_3, e_3) | product1(e_1, e_3, e_2) | product1(e_1, e_3, e_1)) <=> ((~group_element(e_3)) | (~group_element(e_1)) | product1(e_1, e_3, e_1) | product1(e_1, e_3, e_2) | product1(e_1, e_3, e_3))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(136,plain,
% 0.19/0.44 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_1)) | product1(e_1, e_3, e_3) | product1(e_1, e_3, e_2) | product1(e_1, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_1)) | product1(e_1, e_3, e_1) | product1(e_1, e_3, e_2) | product1(e_1, e_3, e_3)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[135])).
% 0.19/0.44 tff(137,plain,
% 0.19/0.44 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_1)) | product1(e_1, e_3, e_3) | product1(e_1, e_3, e_2) | product1(e_1, e_3, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_3)) | (~group_element(e_1)) | product1(e_1, e_3, e_1) | product1(e_1, e_3, e_2) | product1(e_1, e_3, e_3))),
% 0.19/0.44 inference(transitivity,[status(thm)],[136, 134])).
% 0.19/0.44 tff(138,plain,
% 0.19/0.44 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_3)) | (~group_element(e_1)) | product1(e_1, e_3, e_3) | product1(e_1, e_3, e_2) | product1(e_1, e_3, e_1))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(139,plain,
% 0.19/0.44 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (~group_element(e_3)) | (~group_element(e_1)) | product1(e_1, e_3, e_1) | product1(e_1, e_3, e_2) | product1(e_1, e_3, e_3)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.19/0.44 tff(140,plain,
% 0.19/0.44 (product1(e_1, e_3, e_1) | product1(e_1, e_3, e_2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[139, 133, 78, 75, 130])).
% 0.19/0.44 tff(141,plain,
% 0.19/0.44 (product1(e_1, e_3, e_2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[140, 121])).
% 0.19/0.44 tff(142,assumption,(product1(e_1, e_3, e_2)), introduced(assumption)).
% 0.19/0.44 tff(143,assumption,(product1(e_1, e_2, e_2)), introduced(assumption)).
% 0.19/0.44 tff(144,plain,
% 0.19/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_3) | (~product1(e_1, e_3, e_2)) | (~product1(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_2, e_3) | (~product1(e_1, e_3, e_2)) | (~product1(e_1, e_2, e_2)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(145,plain,
% 0.19/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_2, e_3) | (~product1(e_1, e_3, e_2)) | (~product1(e_1, e_2, e_2)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(146,plain,
% 0.19/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_2, e_3) | (~product1(e_1, e_3, e_2)) | (~product1(e_1, e_2, e_2))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.19/0.44 tff(147,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[146, 60, 57, 143, 142])).
% 0.19/0.44 tff(148,plain,((~product1(e_1, e_2, e_2)) | (~product1(e_1, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(149,plain,
% 0.19/0.44 (~product1(e_1, e_2, e_2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[148, 141])).
% 0.19/0.44 tff(150,assumption,(product1(e_1, e_2, e_1)), introduced(assumption)).
% 0.19/0.44 tff(151,plain,
% 0.19/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_3) | (~product1(e_3, e_2, e_1)) | (~product1(e_1, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_1, e_3) | (~product1(e_3, e_2, e_1)) | (~product1(e_1, e_2, e_1)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(152,plain,
% 0.19/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | (equalish(e_1, e_3) | (~product1(e_3, e_2, e_1)) | (~product1(e_1, e_2, e_1)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(153,plain,
% 0.19/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_1, e_3) | (~product1(e_3, e_2, e_1)) | (~product1(e_1, e_2, e_1))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.19/0.44 tff(154,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[153, 125, 32, 150, 89])).
% 0.19/0.44 tff(155,plain,(~product1(e_1, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(156,plain,
% 0.19/0.44 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (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))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | 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))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(157,plain,
% 0.19/0.44 (((~group_element(e_2)) | (~group_element(e_1)) | product1(e_1, e_2, e_3) | product1(e_1, e_2, e_2) | product1(e_1, e_2, e_1)) <=> (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))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(158,plain,
% 0.19/0.44 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_1)) | product1(e_1, e_2, e_3) | product1(e_1, e_2, e_2) | product1(e_1, e_2, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | (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)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[157])).
% 0.19/0.44 tff(159,plain,
% 0.19/0.44 (((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_1)) | product1(e_1, e_2, e_3) | product1(e_1, e_2, e_2) | product1(e_1, e_2, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | 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))),
% 0.19/0.44 inference(transitivity,[status(thm)],[158, 156])).
% 0.19/0.44 tff(160,plain,
% 0.19/0.44 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | ((~group_element(e_2)) | (~group_element(e_1)) | product1(e_1, e_2, e_3) | product1(e_1, e_2, e_2) | product1(e_1, e_2, e_1))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(161,plain,
% 0.19/0.44 ((~![Y: $i, X: $i] : ((~group_element(Y)) | (~group_element(X)) | product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1))) | 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)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.19/0.45 tff(162,plain,
% 0.19/0.45 (product1(e_1, e_2, e_2) | product1(e_1, e_2, e_1) | product1(e_1, e_2, e_3)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[161, 133, 81, 75])).
% 0.19/0.45 tff(163,plain,
% 0.19/0.45 (product1(e_1, e_2, e_3)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[162, 155, 149])).
% 0.19/0.45 tff(164,plain,
% 0.19/0.45 (^[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))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(165,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[164])).
% 0.19/0.45 tff(166,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(167,plain,
% 0.19/0.45 (^[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))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(168,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[167])).
% 0.19/0.45 tff(169,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product1(X, Y, Z1)) | (~product1(Z1, Y, Z2))) | product2(Z2, X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qg1a')).
% 0.19/0.45 tff(170,plain,
% 0.19/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.19/0.45 tff(171,plain,
% 0.19/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[170, 166])).
% 0.19/0.45 tff(172,plain,(
% 0.19/0.45 ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[171])).
% 0.19/0.45 tff(173,plain,
% 0.19/0.45 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[172, 165])).
% 0.19/0.45 tff(174,plain,
% 0.19/0.45 (((~![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)) | (~product1(e_3, e_2, e_1)) | product2(e_3, e_3, e_2))) <=> ((~![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)) | (~product1(e_3, e_2, e_1)) | product2(e_3, e_3, e_2))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(175,plain,
% 0.19/0.45 ((product2(e_3, e_3, e_2) | (~product1(e_1, e_2, e_3)) | (~product1(e_3, e_2, e_1))) <=> ((~product1(e_1, e_2, e_3)) | (~product1(e_3, e_2, e_1)) | product2(e_3, e_3, e_2))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(176,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | (product2(e_3, e_3, e_2) | (~product1(e_1, e_2, e_3)) | (~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)) | (~product1(e_3, e_2, e_1)) | product2(e_3, e_3, e_2)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[175])).
% 0.19/0.45 tff(177,plain,
% 0.19/0.45 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | (product2(e_3, e_3, e_2) | (~product1(e_1, e_2, e_3)) | (~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)) | (~product1(e_3, e_2, e_1)) | product2(e_3, e_3, e_2))),
% 0.19/0.45 inference(transitivity,[status(thm)],[176, 174])).
% 0.19/0.45 tff(178,plain,
% 0.19/0.45 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | (product2(e_3, e_3, e_2) | (~product1(e_1, e_2, e_3)) | (~product1(e_3, e_2, e_1)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(179,plain,
% 0.19/0.45 ((~![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)) | (~product1(e_3, e_2, e_1)) | product2(e_3, e_3, e_2)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.19/0.45 tff(180,plain,
% 0.19/0.45 (product2(e_3, e_3, e_2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[179, 173, 163, 89])).
% 0.19/0.45 tff(181,plain,
% 0.19/0.45 (^[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))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(182,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[181])).
% 0.19/0.45 tff(183,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(184,plain,
% 0.19/0.45 (^[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)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(185,plain,
% 0.19/0.45 (![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)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[184])).
% 0.19/0.45 tff(186,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product2(X, Y, W)) | (~product2(X, Y, Z))) | equalish(W, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product2_total_function2')).
% 0.19/0.45 tff(187,plain,
% 0.19/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.19/0.45 tff(188,plain,
% 0.19/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[187, 183])).
% 0.19/0.45 tff(189,plain,(
% 0.19/0.45 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[188])).
% 0.19/0.45 tff(190,plain,
% 0.19/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[189, 182])).
% 0.19/0.45 tff(191,plain,
% 0.19/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | (equalish(e_3, e_2) | (~product2(e_3, e_3, e_2)) | (~product2(e_3, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | equalish(e_3, e_2) | (~product2(e_3, e_3, e_2)) | (~product2(e_3, e_3, e_3)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(192,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | (equalish(e_3, e_2) | (~product2(e_3, e_3, e_2)) | (~product2(e_3, e_3, e_3)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(193,plain,
% 0.19/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | equalish(e_3, e_2) | (~product2(e_3, e_3, e_2)) | (~product2(e_3, e_3, e_3))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.19/0.45 tff(194,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[193, 35, 190, 180, 9])).
% 0.19/0.45 % SZS output end Proof
% 0.19/0.45 % E exiting
%------------------------------------------------------------------------------