%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP123-6.003 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : GRP123-6.003 : TPTP v9.0.0. Released v1.2.0.
% 0.02/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 15:41:20 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.40 % SZS status Unsatisfiable
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(product2_type, type, (
% 0.20/0.40 product2: ( $i * $i * $i ) > $o)).
% 0.20/0.40 tff(e_2_type, type, (
% 0.20/0.40 e_2: $i)).
% 0.20/0.40 tff(e_3_type, type, (
% 0.20/0.40 e_3: $i)).
% 0.20/0.40 tff(product1_type, type, (
% 0.20/0.40 product1: ( $i * $i * $i ) > $o)).
% 0.20/0.40 tff(e_1_type, type, (
% 0.20/0.40 e_1: $i)).
% 0.20/0.40 tff(equalish_type, type, (
% 0.20/0.40 equalish: ( $i * $i ) > $o)).
% 0.20/0.40 tff(group_element_type, type, (
% 0.20/0.40 group_element: $i > $o)).
% 0.20/0.40 tff(1,plain,
% 0.20/0.40 (^[X: $i] : refl(product2(X, X, X) <=> product2(X, X, X))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (![X: $i] : product2(X, X, X) <=> ![X: $i] : product2(X, X, X)),
% 0.20/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (![X: $i] : product2(X, X, X) <=> ![X: $i] : product2(X, X, X)),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(4,axiom,(![X: $i] : product2(X, X, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product2_idempotence')).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (![X: $i] : product2(X, X, X)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.40 tff(6,plain,(
% 0.20/0.40 ![X: $i] : product2(X, X, X)),
% 0.20/0.40 inference(skolemize,[status(sab)],[5])).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 (![X: $i] : product2(X, X, X)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 ((~![X: $i] : product2(X, X, X)) | product2(e_2, e_2, e_2)),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (product2(e_2, e_2, e_2)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (^[X: $i] : refl(product1(X, X, X) <=> product1(X, X, X))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (![X: $i] : product1(X, X, X) <=> ![X: $i] : product1(X, X, X)),
% 0.20/0.40 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (![X: $i] : product1(X, X, X) <=> ![X: $i] : product1(X, X, X)),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(13,axiom,(![X: $i] : product1(X, X, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product1_idempotence')).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (![X: $i] : product1(X, X, X)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.40 tff(15,plain,(
% 0.20/0.40 ![X: $i] : product1(X, X, X)),
% 0.20/0.40 inference(skolemize,[status(sab)],[14])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 (![X: $i] : product1(X, X, X)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 ((~![X: $i] : product1(X, X, X)) | product1(e_1, e_1, e_1)),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (product1(e_1, e_1, e_1)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.20/0.40 tff(19,assumption,(product1(e_1, e_3, e_1)), introduced(assumption)).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 (^[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))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 (![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)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[20])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (![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)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 (^[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)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 (![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)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[23])).
% 0.20/0.41 tff(25,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')).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.20/0.41 tff(28,plain,(
% 0.20/0.41 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[27])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(31,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 (~equalish(e_3, e_1)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_3, e_1) | (~product1(e_1, e_3, 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_3, e_1) | (~product1(e_1, e_3, e_1)) | (~product1(e_1, e_1, e_1)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 ((equalish(e_3, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_3, e_1))) <=> (equalish(e_3, e_1) | (~product1(e_1, e_3, e_1)) | (~product1(e_1, e_1, e_1)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_3, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_3, e_1) | (~product1(e_1, e_3, e_1)) | (~product1(e_1, e_1, e_1))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[34])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_3, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_3, e_1) | (~product1(e_1, e_3, e_1)) | (~product1(e_1, e_1, e_1)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[35, 33])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | (equalish(e_3, e_1) | (~product1(e_1, e_1, e_1)) | (~product1(e_1, e_3, e_1)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(X, Z, Y)) | (~product1(X, W, Y)))) | equalish(e_3, e_1) | (~product1(e_1, e_3, e_1)) | (~product1(e_1, e_1, e_1))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[38, 32, 29, 19, 18])).
% 0.20/0.41 tff(40,plain,(~product1(e_1, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(41,assumption,(product2(e_3, e_1, e_3)), introduced(assumption)).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 ((~![X: $i] : product2(X, X, X)) | product2(e_3, e_3, e_3)),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 (product2(e_3, e_3, e_3)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[42, 7])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y))) <=> (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[44])).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product2(X, W, Y)) | (~product2(X, Z, Y))) <=> ((~product2(X, Z, Y)) | (~product2(X, W, Y)))), ((((~product2(X, W, Y)) | (~product2(X, Z, Y))) | equalish(W, Z)) <=> (((~product2(X, Z, Y)) | (~product2(X, W, Y))) | equalish(W, Z)))), rewrite((((~product2(X, Z, Y)) | (~product2(X, W, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))), ((((~product2(X, W, Y)) | (~product2(X, Z, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product2(X, W, Y)) | (~product2(X, Z, Y))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[47])).
% 0.20/0.41 tff(49,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product2(X, W, Y)) | (~product2(X, Z, Y))) | equalish(W, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product2_right_cancellation')).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.20/0.41 tff(52,plain,(
% 0.20/0.41 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[51])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(55,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.20/0.41 tff(56,plain,
% 0.20/0.41 (~equalish(e_1, e_3)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_1, e_3) | (~product2(e_3, e_3, e_3)) | (~product2(e_3, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_1, e_3) | (~product2(e_3, e_3, e_3)) | (~product2(e_3, e_1, e_3)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_1, e_3) | (~product2(e_3, e_3, e_3)) | (~product2(e_3, e_1, e_3)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_1, e_3) | (~product2(e_3, e_3, e_3)) | (~product2(e_3, e_1, e_3))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[59, 56, 53, 43, 41])).
% 0.20/0.41 tff(61,plain,(~product2(e_3, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 ((~![X: $i] : product1(X, X, X)) | product1(e_3, e_3, e_3)),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 (product1(e_3, e_3, e_3)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[62, 16])).
% 0.20/0.41 tff(64,plain,
% 0.20/0.41 (^[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))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[64])).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 (^[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))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(68,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[67])).
% 0.20/0.41 tff(69,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')).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.41 tff(71,plain,
% 0.20/0.41 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.20/0.41 tff(72,plain,(
% 0.20/0.41 ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[71])).
% 0.20/0.41 tff(73,plain,
% 0.20/0.41 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.20/0.41 tff(74,plain,
% 0.20/0.41 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | ((~product1(e_3, e_3, e_3)) | (~product1(e_1, e_3, e_3)) | product2(e_3, e_1, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | (~product1(e_3, e_3, e_3)) | (~product1(e_1, e_3, e_3)) | product2(e_3, e_1, e_3))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(75,plain,
% 0.20/0.41 ((product2(e_3, e_1, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_1, e_3, e_3))) <=> ((~product1(e_3, e_3, e_3)) | (~product1(e_1, e_3, e_3)) | product2(e_3, e_1, e_3))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(76,plain,
% 0.20/0.41 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | (product2(e_3, e_1, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | ((~product1(e_3, e_3, e_3)) | (~product1(e_1, e_3, e_3)) | product2(e_3, e_1, e_3)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[75])).
% 0.20/0.41 tff(77,plain,
% 0.20/0.41 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | (product2(e_3, e_1, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_1, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | (~product1(e_3, e_3, e_3)) | (~product1(e_1, e_3, e_3)) | product2(e_3, e_1, e_3))),
% 0.20/0.41 inference(transitivity,[status(thm)],[76, 74])).
% 0.20/0.41 tff(78,plain,
% 0.20/0.41 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | (product2(e_3, e_1, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_1, e_3, e_3)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(79,plain,
% 0.20/0.41 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | (~product1(e_3, e_3, e_3)) | (~product1(e_1, e_3, e_3)) | product2(e_3, e_1, e_3)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.41 tff(80,plain,
% 0.20/0.41 (~product1(e_1, e_3, e_3)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[79, 73, 63, 61])).
% 0.20/0.41 tff(81,plain,
% 0.20/0.41 (^[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))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(82,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[81])).
% 0.20/0.41 tff(83,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(84,plain,
% 0.20/0.41 (^[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)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(85,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[84])).
% 0.20/0.41 tff(86,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')).
% 0.20/0.41 tff(87,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.41 tff(88,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.20/0.41 tff(89,plain,(
% 0.20/0.41 ![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)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[88])).
% 0.20/0.41 tff(90,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.20/0.41 tff(91,plain,
% 0.20/0.41 (group_element(e_3) <=> group_element(e_3)),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(92,axiom,(group_element(e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_3')).
% 0.20/0.42 tff(93,plain,
% 0.20/0.42 (group_element(e_3)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.42 tff(94,plain,
% 0.20/0.42 (group_element(e_1) <=> group_element(e_1)),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(95,axiom,(group_element(e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_1')).
% 0.20/0.42 tff(96,plain,
% 0.20/0.42 (group_element(e_1)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.20/0.42 tff(97,plain,
% 0.20/0.42 (((~![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_1)) | (~group_element(e_3)) | 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] : (product1(X, Y, e_3) | product1(X, Y, e_2) | product1(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_3)) | product1(e_1, e_3, e_3) | product1(e_1, e_3, e_2) | product1(e_1, e_3, e_1))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(98,plain,
% 0.20/0.42 ((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))) <=> ((~group_element(e_1)) | (~group_element(e_3)) | product1(e_1, e_3, e_3) | product1(e_1, e_3, e_2) | product1(e_1, e_3, e_1))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(99,plain,
% 0.20/0.42 (((~![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_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)))) <=> ((~![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_1)) | (~group_element(e_3)) | product1(e_1, e_3, e_3) | product1(e_1, e_3, e_2) | product1(e_1, e_3, e_1)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[98])).
% 0.20/0.42 tff(100,plain,
% 0.20/0.42 (((~![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_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)))) <=> ((~![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_1)) | (~group_element(e_3)) | product1(e_1, e_3, e_3) | product1(e_1, e_3, e_2) | product1(e_1, e_3, e_1))),
% 0.20/0.42 inference(transitivity,[status(thm)],[99, 97])).
% 0.20/0.42 tff(101,plain,
% 0.20/0.42 ((~![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_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)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(102,plain,
% 0.20/0.42 ((~![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_1)) | (~group_element(e_3)) | product1(e_1, e_3, e_3) | product1(e_1, e_3, e_2) | product1(e_1, e_3, e_1)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.20/0.42 tff(103,plain,
% 0.20/0.42 (product1(e_1, e_3, e_2) | product1(e_1, e_3, e_1)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[102, 96, 93, 90, 80])).
% 0.20/0.42 tff(104,plain,
% 0.20/0.42 (product1(e_1, e_3, e_2)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[103, 40])).
% 0.20/0.42 tff(105,assumption,(product1(e_2, e_3, e_2)), introduced(assumption)).
% 0.20/0.42 tff(106,plain,
% 0.20/0.42 (^[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))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(107,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[106])).
% 0.20/0.42 tff(108,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(109,plain,
% 0.20/0.42 (^[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)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(110,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[109])).
% 0.20/0.42 tff(111,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')).
% 0.20/0.42 tff(112,plain,
% 0.20/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.20/0.42 tff(113,plain,
% 0.20/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.20/0.42 tff(114,plain,(
% 0.20/0.42 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[113])).
% 0.20/0.42 tff(115,plain,
% 0.20/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.20/0.42 tff(116,plain,
% 0.20/0.42 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(117,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.20/0.42 tff(118,plain,
% 0.20/0.42 (~equalish(e_2, e_1)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.20/0.42 tff(119,plain,
% 0.20/0.42 (((~![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_2, e_3, e_2)) | (~product1(e_1, e_3, e_2)))) <=> ((~![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_2, e_3, e_2)) | (~product1(e_1, e_3, e_2)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(120,plain,
% 0.20/0.42 ((equalish(e_2, e_1) | (~product1(e_1, e_3, e_2)) | (~product1(e_2, e_3, e_2))) <=> (equalish(e_2, e_1) | (~product1(e_2, e_3, e_2)) | (~product1(e_1, e_3, e_2)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(121,plain,
% 0.20/0.42 (((~![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_2)) | (~product1(e_2, e_3, e_2)))) <=> ((~![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_2, e_3, e_2)) | (~product1(e_1, e_3, e_2))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[120])).
% 0.20/0.42 tff(122,plain,
% 0.20/0.42 (((~![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_2)) | (~product1(e_2, e_3, e_2)))) <=> ((~![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_2, e_3, e_2)) | (~product1(e_1, e_3, e_2)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[121, 119])).
% 0.20/0.42 tff(123,plain,
% 0.20/0.42 ((~![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_2)) | (~product1(e_2, e_3, e_2)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(124,plain,
% 0.20/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product1(Z, Y, X)) | (~product1(W, Y, X)))) | equalish(e_2, e_1) | (~product1(e_2, e_3, e_2)) | (~product1(e_1, e_3, e_2))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.20/0.42 tff(125,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[124, 118, 115, 105, 104])).
% 0.20/0.42 tff(126,plain,(~product1(e_2, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(127,assumption,(product2(e_3, e_2, e_3)), introduced(assumption)).
% 0.20/0.42 tff(128,plain,
% 0.20/0.42 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(129,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.20/0.42 tff(130,plain,
% 0.20/0.42 (~equalish(e_2, e_3)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.20/0.42 tff(131,plain,
% 0.20/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_2, e_3) | (~product2(e_3, e_2, e_3)) | (~product2(e_3, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_2, e_3) | (~product2(e_3, e_2, e_3)) | (~product2(e_3, e_3, e_3)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(132,plain,
% 0.20/0.42 ((equalish(e_2, e_3) | (~product2(e_3, e_3, e_3)) | (~product2(e_3, e_2, e_3))) <=> (equalish(e_2, e_3) | (~product2(e_3, e_2, e_3)) | (~product2(e_3, e_3, e_3)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(133,plain,
% 0.20/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_2, e_3) | (~product2(e_3, e_3, e_3)) | (~product2(e_3, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_2, e_3) | (~product2(e_3, e_2, e_3)) | (~product2(e_3, e_3, e_3))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[132])).
% 0.20/0.42 tff(134,plain,
% 0.20/0.42 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_2, e_3) | (~product2(e_3, e_3, e_3)) | (~product2(e_3, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_2, e_3) | (~product2(e_3, e_2, e_3)) | (~product2(e_3, e_3, e_3)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[133, 131])).
% 0.20/0.42 tff(135,plain,
% 0.20/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | (equalish(e_2, e_3) | (~product2(e_3, e_3, e_3)) | (~product2(e_3, e_2, e_3)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(136,plain,
% 0.20/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Z, Y)) | (~product2(X, W, Y)))) | equalish(e_2, e_3) | (~product2(e_3, e_2, e_3)) | (~product2(e_3, e_3, e_3))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.20/0.42 tff(137,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[136, 130, 53, 127, 43])).
% 0.20/0.42 tff(138,plain,(~product2(e_3, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(139,plain,
% 0.20/0.42 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | (product2(e_3, e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_2, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | product2(e_3, e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_2, e_3, e_3)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(140,plain,
% 0.20/0.42 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | (product2(e_3, e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_2, e_3, e_3)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(141,plain,
% 0.20/0.42 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | product2(e_3, e_2, e_3) | (~product1(e_3, e_3, e_3)) | (~product1(e_2, e_3, e_3))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.20/0.42 tff(142,plain,
% 0.20/0.42 (~product1(e_2, e_3, e_3)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[141, 73, 63, 138])).
% 0.20/0.43 tff(143,plain,
% 0.20/0.43 (group_element(e_2) <=> group_element(e_2)),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(144,axiom,(group_element(e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_2')).
% 0.20/0.43 tff(145,plain,
% 0.20/0.43 (group_element(e_2)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.20/0.43 tff(146,plain,
% 0.20/0.43 (((~![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)))) | ((~group_element(e_2)) | (~group_element(e_3)) | product1(e_2, e_3, e_1) | product1(e_2, e_3, e_2) | product1(e_2, e_3, 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_2, e_3, e_1) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_3))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(147,plain,
% 0.20/0.43 ((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))) <=> ((~group_element(e_2)) | (~group_element(e_3)) | product1(e_2, e_3, e_1) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_3))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(148,plain,
% 0.20/0.43 (((~![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)))) | (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)))) <=> ((~![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_2, e_3, e_1) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_3)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[147])).
% 0.20/0.43 tff(149,plain,
% 0.20/0.43 (((~![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)))) | (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)))) <=> ((~![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_2, e_3, e_1) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_3))),
% 0.20/0.43 inference(transitivity,[status(thm)],[148, 146])).
% 0.20/0.43 tff(150,plain,
% 0.20/0.43 ((~![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)))) | (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)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(151,plain,
% 0.20/0.43 ((~![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)))) | (~group_element(e_2)) | (~group_element(e_3)) | product1(e_2, e_3, e_1) | product1(e_2, e_3, e_2) | product1(e_2, e_3, e_3)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.20/0.43 tff(152,plain,
% 0.20/0.43 (product1(e_2, e_3, e_1) | product1(e_2, e_3, e_2)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[151, 145, 93, 90, 142])).
% 0.20/0.43 tff(153,plain,
% 0.20/0.43 (product1(e_2, e_3, e_1)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[152, 126])).
% 0.20/0.43 tff(154,plain,
% 0.20/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | ((~product1(e_2, e_3, e_1)) | product2(e_2, e_2, e_3) | (~product1(e_1, 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_2, e_3, e_1)) | product2(e_2, e_2, e_3) | (~product1(e_1, e_3, e_2)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(155,plain,
% 0.20/0.43 ((product2(e_2, e_2, e_3) | (~product1(e_1, e_3, e_2)) | (~product1(e_2, e_3, e_1))) <=> ((~product1(e_2, e_3, e_1)) | product2(e_2, e_2, e_3) | (~product1(e_1, e_3, e_2)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(156,plain,
% 0.20/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | (product2(e_2, e_2, e_3) | (~product1(e_1, e_3, e_2)) | (~product1(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | ((~product1(e_2, e_3, e_1)) | product2(e_2, e_2, e_3) | (~product1(e_1, e_3, e_2))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[155])).
% 0.20/0.43 tff(157,plain,
% 0.20/0.43 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | (product2(e_2, e_2, e_3) | (~product1(e_1, e_3, e_2)) | (~product1(e_2, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | (~product1(e_2, e_3, e_1)) | product2(e_2, e_2, e_3) | (~product1(e_1, e_3, e_2)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[156, 154])).
% 0.20/0.43 tff(158,plain,
% 0.20/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | (product2(e_2, e_2, e_3) | (~product1(e_1, e_3, e_2)) | (~product1(e_2, e_3, e_1)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(159,plain,
% 0.20/0.43 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product2(Z2, X, Y) | (~product1(Z1, Y, Z2)) | (~product1(X, Y, Z1)))) | (~product1(e_2, e_3, e_1)) | product2(e_2, e_2, e_3) | (~product1(e_1, e_3, e_2))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.20/0.43 tff(160,plain,
% 0.20/0.43 ((~product1(e_2, e_3, e_1)) | product2(e_2, e_2, e_3) | (~product1(e_1, e_3, e_2))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[159, 73])).
% 0.20/0.43 tff(161,plain,
% 0.20/0.43 (product2(e_2, e_2, e_3)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[160, 153, 104])).
% 0.20/0.43 tff(162,plain,
% 0.20/0.43 (^[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))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(163,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[162])).
% 0.20/0.43 tff(164,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(165,plain,
% 0.20/0.43 (^[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)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(166,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[165])).
% 0.20/0.43 tff(167,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')).
% 0.20/0.43 tff(168,plain,
% 0.20/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.20/0.43 tff(169,plain,
% 0.20/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[168, 164])).
% 0.20/0.43 tff(170,plain,(
% 0.20/0.43 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[169])).
% 0.20/0.43 tff(171,plain,
% 0.20/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[170, 163])).
% 0.20/0.43 tff(172,plain,
% 0.20/0.43 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(173,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.20/0.43 tff(174,plain,
% 0.20/0.43 (~equalish(e_3, e_2)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.20/0.43 tff(175,plain,
% 0.20/0.43 (((~![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_2, e_2, e_2)) | (~product2(e_2, e_2, 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_2, e_2, e_2)) | (~product2(e_2, e_2, e_3)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(176,plain,
% 0.20/0.43 ((~![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_2, e_2, e_2)) | (~product2(e_2, e_2, e_3)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(177,plain,
% 0.20/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product2(X, Y, Z)) | (~product2(X, Y, W)))) | equalish(e_3, e_2) | (~product2(e_2, e_2, e_2)) | (~product2(e_2, e_2, e_3))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.20/0.43 tff(178,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[177, 174, 171, 161, 9])).
% 0.20/0.43 % SZS output end Proof
% 0.20/0.44 % E exiting
%------------------------------------------------------------------------------