%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP126-1.004 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:07:07 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP126-1.004 : TPTP v9.0.0. Released v1.2.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Thu Jun 19 15:42:55 EDT 2025
% 0.12/0.35 % CPUTime :
% 0.20/0.43 % SZS status Unsatisfiable
% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 tff(product_type, type, (
% 0.20/0.43 product: ( $i * $i * $i ) > $o)).
% 0.20/0.43 tff(e_3_type, type, (
% 0.20/0.43 e_3: $i)).
% 0.20/0.43 tff(e_4_type, type, (
% 0.20/0.43 e_4: $i)).
% 0.20/0.43 tff(e_2_type, type, (
% 0.20/0.43 e_2: $i)).
% 0.20/0.43 tff(e_1_type, type, (
% 0.20/0.43 e_1: $i)).
% 0.20/0.43 tff(equalish_type, type, (
% 0.20/0.43 equalish: ( $i * $i ) > $o)).
% 0.20/0.43 tff(group_element_type, type, (
% 0.20/0.43 group_element: $i > $o)).
% 0.20/0.43 tff(1,assumption,(~product(e_4, e_1, e_3)), introduced(assumption)).
% 0.20/0.43 tff(2,plain,
% 0.20/0.43 (^[X: $i] : refl(product(X, X, X) <=> product(X, X, X))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(3,plain,
% 0.20/0.43 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.20/0.43 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.43 tff(4,plain,
% 0.20/0.43 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(5,axiom,(![X: $i] : product(X, X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_idempotence')).
% 0.20/0.43 tff(6,plain,
% 0.20/0.43 (![X: $i] : product(X, X, X)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.43 tff(7,plain,(
% 0.20/0.43 ![X: $i] : product(X, X, X)),
% 0.20/0.43 inference(skolemize,[status(sab)],[6])).
% 0.20/0.43 tff(8,plain,
% 0.20/0.43 (![X: $i] : product(X, X, X)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.43 tff(9,plain,
% 0.20/0.43 ((~![X: $i] : product(X, X, X)) | product(e_4, e_4, e_4)),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(10,plain,
% 0.20/0.43 (product(e_4, e_4, e_4)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.20/0.43 tff(11,assumption,(product(e_4, e_1, e_4)), introduced(assumption)).
% 0.20/0.43 tff(12,plain,
% 0.20/0.43 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(13,plain,
% 0.20/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.43 tff(14,plain,
% 0.20/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(15,plain,
% 0.20/0.43 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(X, W, Y)) | (~product(X, Z, Y))) <=> ((~product(X, Z, Y)) | (~product(X, W, Y)))), ((((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> (((~product(X, Z, Y)) | (~product(X, W, Y))) | equalish(W, Z)))), rewrite((((~product(X, Z, Y)) | (~product(X, W, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))), ((((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(16,plain,
% 0.20/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.43 tff(17,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_right_cancellation')).
% 0.20/0.43 tff(18,plain,
% 0.20/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.20/0.43 tff(19,plain,
% 0.20/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.43 tff(20,plain,(
% 0.20/0.43 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[19])).
% 0.20/0.43 tff(21,plain,
% 0.20/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.20/0.43 tff(22,plain,
% 0.20/0.43 ((~equalish(e_1, e_4)) <=> (~equalish(e_1, e_4))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(23,axiom,(~equalish(e_1, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_4')).
% 0.20/0.43 tff(24,plain,
% 0.20/0.43 (~equalish(e_1, e_4)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.43 tff(25,plain,
% 0.20/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(26,plain,
% 0.20/0.43 ((equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4))) <=> (equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(27,plain,
% 0.20/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[26])).
% 0.20/0.43 tff(28,plain,
% 0.20/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[27, 25])).
% 0.20/0.43 tff(29,plain,
% 0.20/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(30,plain,
% 0.20/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.43 tff(31,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[30, 24, 21, 11, 10])).
% 0.20/0.43 tff(32,plain,(~product(e_4, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(33,plain,
% 0.20/0.43 ((~![X: $i] : product(X, X, X)) | product(e_1, e_1, e_1)),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(34,plain,
% 0.20/0.43 (product(e_1, e_1, e_1)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[33, 8])).
% 0.20/0.43 tff(35,assumption,(product(e_4, e_1, e_1)), introduced(assumption)).
% 0.20/0.43 tff(36,plain,
% 0.20/0.43 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(37,plain,
% 0.20/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[36])).
% 0.20/0.43 tff(38,plain,
% 0.20/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(39,plain,
% 0.20/0.43 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(W, Y, X)) | (~product(Z, Y, X))) <=> ((~product(Z, Y, X)) | (~product(W, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> (((~product(Z, Y, X)) | (~product(W, Y, X))) | equalish(W, Z)))), rewrite((((~product(Z, Y, X)) | (~product(W, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(40,plain,
% 0.20/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[39])).
% 0.20/0.43 tff(41,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_left_cancellation')).
% 0.20/0.43 tff(42,plain,
% 0.20/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.43 tff(43,plain,
% 0.20/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.20/0.43 tff(44,plain,(
% 0.20/0.43 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[43])).
% 0.20/0.43 tff(45,plain,
% 0.20/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.20/0.43 tff(46,plain,
% 0.20/0.43 ((~equalish(e_4, e_1)) <=> (~equalish(e_4, e_1))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(47,axiom,(~equalish(e_4, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_1')).
% 0.20/0.43 tff(48,plain,
% 0.20/0.43 (~equalish(e_4, e_1)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.43 tff(49,plain,
% 0.20/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(50,plain,
% 0.20/0.43 ((equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1))) <=> (equalish(e_4, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(51,plain,
% 0.20/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[50])).
% 0.20/0.43 tff(52,plain,
% 0.20/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[51, 49])).
% 0.20/0.43 tff(53,plain,
% 0.20/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(54,plain,
% 0.20/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.43 tff(55,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[54, 48, 45, 35, 34])).
% 0.20/0.43 tff(56,plain,(~product(e_4, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(57,plain,
% 0.20/0.43 (^[Y: $i, X: $i] : refl((product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(58,plain,
% 0.20/0.43 (![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[57])).
% 0.20/0.44 tff(59,plain,
% 0.20/0.44 (![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(60,plain,
% 0.20/0.44 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) <=> (product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> ((product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_2)))), rewrite(((product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_2)) <=> (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ((product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_3)))), rewrite(((product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_3)) <=> (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))), (((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> ((product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_4)))), rewrite(((product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_4)) <=> (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(61,plain,
% 0.20/0.44 (![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> ![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[60])).
% 0.20/0.44 tff(62,axiom,(![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_total_function1')).
% 0.20/0.44 tff(63,plain,
% 0.20/0.44 (![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.44 tff(64,plain,
% 0.20/0.44 (![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.20/0.44 tff(65,plain,(
% 0.20/0.44 ![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[64])).
% 0.20/0.44 tff(66,plain,
% 0.20/0.44 (![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.20/0.44 tff(67,plain,
% 0.20/0.44 (group_element(e_4) <=> group_element(e_4)),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(68,axiom,(group_element(e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_4')).
% 0.20/0.44 tff(69,plain,
% 0.20/0.44 (group_element(e_4)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.44 tff(70,plain,
% 0.20/0.44 (group_element(e_1) <=> group_element(e_1)),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(71,axiom,(group_element(e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_1')).
% 0.20/0.44 tff(72,plain,
% 0.20/0.44 (group_element(e_1)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.44 tff(73,plain,
% 0.20/0.44 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | product(e_4, e_1, e_2) | (~group_element(e_4)) | product(e_4, e_1, e_1) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | product(e_4, e_1, e_2) | (~group_element(e_4)) | product(e_4, e_1, e_1) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(74,plain,
% 0.20/0.44 ((product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_4))) <=> ((~group_element(e_1)) | product(e_4, e_1, e_2) | (~group_element(e_4)) | product(e_4, e_1, e_1) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(75,plain,
% 0.20/0.44 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | product(e_4, e_1, e_2) | (~group_element(e_4)) | product(e_4, e_1, e_1) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[74])).
% 0.20/0.44 tff(76,plain,
% 0.20/0.44 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | product(e_4, e_1, e_2) | (~group_element(e_4)) | product(e_4, e_1, e_1) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3))),
% 0.20/0.44 inference(transitivity,[status(thm)],[75, 73])).
% 0.20/0.44 tff(77,plain,
% 0.20/0.44 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_4)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(78,plain,
% 0.20/0.44 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | product(e_4, e_1, e_2) | (~group_element(e_4)) | product(e_4, e_1, e_1) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.20/0.44 tff(79,plain,
% 0.20/0.44 (product(e_4, e_1, e_2) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[78, 72, 69, 66, 56])).
% 0.20/0.44 tff(80,plain,
% 0.20/0.44 (product(e_4, e_1, e_2) | product(e_4, e_1, e_3)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[79, 32])).
% 0.20/0.44 tff(81,plain,
% 0.20/0.44 (product(e_4, e_1, e_2)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[80, 1])).
% 0.20/0.44 tff(82,assumption,(~product(e_4, e_2, e_3)), introduced(assumption)).
% 0.20/0.44 tff(83,assumption,(product(e_4, e_2, e_4)), introduced(assumption)).
% 0.20/0.44 tff(84,plain,
% 0.20/0.44 ((~equalish(e_2, e_4)) <=> (~equalish(e_2, e_4))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(85,axiom,(~equalish(e_2, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_4')).
% 0.20/0.44 tff(86,plain,
% 0.20/0.44 (~equalish(e_2, e_4)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.44 tff(87,plain,
% 0.20/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_4, e_2, e_4)) | (~product(e_4, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_4, e_2, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(88,plain,
% 0.20/0.44 ((equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4))) <=> (equalish(e_2, e_4) | (~product(e_4, e_2, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(89,plain,
% 0.20/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_4, e_2, e_4)) | (~product(e_4, e_4, e_4))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[88])).
% 0.20/0.44 tff(90,plain,
% 0.20/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_4, e_2, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[89, 87])).
% 0.20/0.44 tff(91,plain,
% 0.20/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(92,plain,
% 0.20/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_4, e_2, e_4)) | (~product(e_4, e_4, e_4))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.20/0.44 tff(93,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[92, 86, 21, 83, 10])).
% 0.20/0.44 tff(94,plain,(~product(e_4, e_2, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(95,assumption,(~product(e_4, e_1, e_4)), introduced(assumption)).
% 0.20/0.44 tff(96,assumption,(~product(e_4, e_2, e_4)), introduced(assumption)).
% 0.20/0.44 tff(97,assumption,(product(e_4, e_3, e_2)), introduced(assumption)).
% 0.20/0.44 tff(98,assumption,(product(e_4, e_2, e_2)), introduced(assumption)).
% 0.20/0.44 tff(99,plain,
% 0.20/0.44 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(100,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.20/0.44 tff(101,plain,
% 0.20/0.44 (~equalish(e_2, e_3)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.20/0.44 tff(102,plain,
% 0.20/0.44 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_2, e_2)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(103,plain,
% 0.20/0.44 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_2, e_2)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(104,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_2, e_2))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.20/0.45 tff(105,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[104, 101, 21, 97, 98])).
% 0.20/0.45 tff(106,plain,((~product(e_4, e_2, e_2)) | (~product(e_4, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(107,plain,
% 0.20/0.45 (~product(e_4, e_2, e_2)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[106, 97])).
% 0.20/0.45 tff(108,plain,
% 0.20/0.45 (group_element(e_2) <=> group_element(e_2)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(109,axiom,(group_element(e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_2')).
% 0.20/0.45 tff(110,plain,
% 0.20/0.45 (group_element(e_2)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.20/0.45 tff(111,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | product(e_4, e_2, e_3) | (~group_element(e_4)) | product(e_4, e_2, e_4))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | product(e_4, e_2, e_3) | (~group_element(e_4)) | product(e_4, e_2, e_4))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(112,plain,
% 0.20/0.45 ((product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_4))) <=> ((~group_element(e_2)) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | product(e_4, e_2, e_3) | (~group_element(e_4)) | product(e_4, e_2, e_4))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(113,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | product(e_4, e_2, e_3) | (~group_element(e_4)) | product(e_4, e_2, e_4)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[112])).
% 0.20/0.45 tff(114,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | product(e_4, e_2, e_3) | (~group_element(e_4)) | product(e_4, e_2, e_4))),
% 0.20/0.45 inference(transitivity,[status(thm)],[113, 111])).
% 0.20/0.45 tff(115,plain,
% 0.20/0.45 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_4)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(116,plain,
% 0.20/0.45 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | product(e_4, e_2, e_3) | (~group_element(e_4)) | product(e_4, e_2, e_4)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.20/0.45 tff(117,plain,
% 0.20/0.45 (product(e_4, e_2, e_1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[116, 110, 69, 66, 107, 82, 96])).
% 0.20/0.45 tff(118,plain,
% 0.20/0.45 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(119,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.20/0.45 tff(120,plain,
% 0.20/0.45 (~equalish(e_2, e_1)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.20/0.45 tff(121,plain,
% 0.20/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_4, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_4, e_2, e_1)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(122,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_4, e_2, e_1)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(123,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_4, e_2, e_1))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.20/0.45 tff(124,plain,
% 0.20/0.45 ((~product(e_4, e_1, e_1)) | (~product(e_4, e_2, e_1))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[123, 120, 21])).
% 0.20/0.45 tff(125,plain,
% 0.20/0.45 (~product(e_4, e_1, e_1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[124, 117])).
% 0.20/0.45 tff(126,plain,
% 0.20/0.45 (product(e_4, e_1, e_2)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[78, 72, 69, 66, 125, 1, 95])).
% 0.20/0.45 tff(127,plain,
% 0.20/0.45 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(128,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.20/0.45 tff(129,plain,
% 0.20/0.45 (~equalish(e_1, e_3)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.20/0.45 tff(130,plain,
% 0.20/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_1, e_2)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(131,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_3) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_1, e_2)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(132,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_3) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_1, e_2))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.20/0.45 tff(133,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[132, 129, 21, 97, 126])).
% 0.20/0.45 tff(134,plain,((~product(e_4, e_3, e_2)) | product(e_4, e_1, e_3) | product(e_4, e_1, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(135,plain,
% 0.20/0.45 ((~product(e_4, e_3, e_2)) | product(e_4, e_1, e_3) | product(e_4, e_1, e_4) | product(e_4, e_2, e_3)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[134, 94])).
% 0.20/0.45 tff(136,plain,
% 0.20/0.45 ((~product(e_4, e_3, e_2)) | product(e_4, e_1, e_3) | product(e_4, e_2, e_3)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[135, 32])).
% 0.20/0.45 tff(137,plain,
% 0.20/0.45 (~product(e_4, e_3, e_2)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[136, 82, 1])).
% 0.20/0.45 tff(138,plain,
% 0.20/0.45 ((~![X: $i] : product(X, X, X)) | product(e_2, e_2, e_2)),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(139,plain,
% 0.20/0.45 (product(e_2, e_2, e_2)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[138, 8])).
% 0.20/0.45 tff(140,plain,
% 0.20/0.45 ((~equalish(e_4, e_2)) <=> (~equalish(e_4, e_2))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(141,axiom,(~equalish(e_4, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_2')).
% 0.20/0.45 tff(142,plain,
% 0.20/0.45 (~equalish(e_4, e_2)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.20/0.45 tff(143,plain,
% 0.20/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_4, e_2, e_2)) | (~product(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_4, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(144,plain,
% 0.20/0.45 ((equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_2, e_2))) <=> (equalish(e_4, e_2) | (~product(e_4, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(145,plain,
% 0.20/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_4, e_2, e_2)) | (~product(e_2, e_2, e_2))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[144])).
% 0.20/0.45 tff(146,plain,
% 0.20/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_4, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[145, 143])).
% 0.20/0.45 tff(147,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_2, e_2)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(148,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_4, e_2, e_2)) | (~product(e_2, e_2, e_2))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.20/0.45 tff(149,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[148, 142, 45, 98, 139])).
% 0.20/0.45 tff(150,plain,(~product(e_4, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(151,assumption,(~product(e_4, e_2, e_1)), introduced(assumption)).
% 0.20/0.45 tff(152,assumption,(~product(e_4, e_2, e_2)), introduced(assumption)).
% 0.20/0.45 tff(153,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[116, 110, 69, 66, 152, 151, 82, 96])).
% 0.20/0.45 tff(154,plain,(product(e_4, e_2, e_1) | product(e_4, e_2, e_2) | product(e_4, e_2, e_3) | product(e_4, e_2, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(155,plain,
% 0.20/0.45 (product(e_4, e_2, e_1) | product(e_4, e_2, e_2) | product(e_4, e_2, e_3)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[154, 94])).
% 0.20/0.45 tff(156,plain,
% 0.20/0.45 (product(e_4, e_2, e_1) | product(e_4, e_2, e_3)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[155, 150])).
% 0.20/0.45 tff(157,plain,
% 0.20/0.45 (product(e_4, e_2, e_1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[156, 82])).
% 0.20/0.45 tff(158,assumption,(product(e_4, e_2, e_1)), introduced(assumption)).
% 0.20/0.45 tff(159,assumption,(product(e_4, e_3, e_1)), introduced(assumption)).
% 0.20/0.45 tff(160,plain,
% 0.20/0.45 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(161,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.20/0.45 tff(162,plain,
% 0.20/0.45 (~equalish(e_3, e_2)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.20/0.45 tff(163,plain,
% 0.20/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_4, e_3, e_1)) | (~product(e_4, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_4, e_3, e_1)) | (~product(e_4, e_2, e_1)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(164,plain,
% 0.20/0.45 ((equalish(e_3, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_4, e_3, e_1))) <=> (equalish(e_3, e_2) | (~product(e_4, e_3, e_1)) | (~product(e_4, e_2, e_1)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(165,plain,
% 0.20/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_4, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_4, e_3, e_1)) | (~product(e_4, e_2, e_1))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[164])).
% 0.20/0.46 tff(166,plain,
% 0.20/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_4, e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_4, e_3, e_1)) | (~product(e_4, e_2, e_1)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[165, 163])).
% 0.20/0.46 tff(167,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_4, e_3, e_1)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(168,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_4, e_3, e_1)) | (~product(e_4, e_2, e_1))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.20/0.46 tff(169,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[168, 162, 21, 159, 158])).
% 0.20/0.46 tff(170,plain,((~product(e_4, e_3, e_1)) | (~product(e_4, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(171,plain,
% 0.20/0.46 (~product(e_4, e_3, e_1)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[170, 157])).
% 0.20/0.46 tff(172,assumption,(product(e_4, e_3, e_4)), introduced(assumption)).
% 0.20/0.46 tff(173,plain,
% 0.20/0.46 ((~equalish(e_3, e_4)) <=> (~equalish(e_3, e_4))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(174,axiom,(~equalish(e_3, e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_4')).
% 0.20/0.46 tff(175,plain,
% 0.20/0.46 (~equalish(e_3, e_4)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.20/0.46 tff(176,plain,
% 0.20/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_4) | (~product(e_4, e_3, e_4)) | (~product(e_4, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_4, e_3, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(177,plain,
% 0.20/0.46 ((equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_3, e_4))) <=> (equalish(e_3, e_4) | (~product(e_4, e_3, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(178,plain,
% 0.20/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_4) | (~product(e_4, e_3, e_4)) | (~product(e_4, e_4, e_4))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[177])).
% 0.20/0.46 tff(179,plain,
% 0.20/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_4, e_3, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[178, 176])).
% 0.20/0.46 tff(180,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_3, e_4)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(181,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_4) | (~product(e_4, e_3, e_4)) | (~product(e_4, e_4, e_4))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.20/0.46 tff(182,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[181, 175, 21, 172, 10])).
% 0.20/0.46 tff(183,plain,(~product(e_4, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(184,assumption,(product(e_4, e_3, e_3)), introduced(assumption)).
% 0.20/0.46 tff(185,plain,
% 0.20/0.46 ((~![X: $i] : product(X, X, X)) | product(e_3, e_3, e_3)),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(186,plain,
% 0.20/0.46 (product(e_3, e_3, e_3)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[185, 8])).
% 0.20/0.46 tff(187,plain,
% 0.20/0.46 ((~equalish(e_4, e_3)) <=> (~equalish(e_4, e_3))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(188,axiom,(~equalish(e_4, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_3')).
% 0.20/0.46 tff(189,plain,
% 0.20/0.46 (~equalish(e_4, e_3)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.20/0.46 tff(190,plain,
% 0.20/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_4, e_3, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_4, e_3, e_3)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(191,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_4, e_3, e_3)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(192,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_4, e_3, e_3))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.20/0.46 tff(193,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[192, 189, 45, 186, 184])).
% 0.20/0.46 tff(194,plain,(~product(e_4, e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(195,plain,
% 0.20/0.46 (group_element(e_3) <=> group_element(e_3)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(196,axiom,(group_element(e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_3')).
% 0.20/0.46 tff(197,plain,
% 0.20/0.46 (group_element(e_3)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.20/0.46 tff(198,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_3, e_2) | product(e_4, e_3, e_1) | (~group_element(e_4)) | (~group_element(e_3)) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1) | (~group_element(e_4)) | (~group_element(e_3)) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(199,plain,
% 0.20/0.46 ((product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_4))) <=> (product(e_4, e_3, e_2) | product(e_4, e_3, e_1) | (~group_element(e_4)) | (~group_element(e_3)) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(200,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_3, e_2) | product(e_4, e_3, e_1) | (~group_element(e_4)) | (~group_element(e_3)) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[199])).
% 0.20/0.46 tff(201,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1) | (~group_element(e_4)) | (~group_element(e_3)) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3))),
% 0.20/0.47 inference(transitivity,[status(thm)],[200, 198])).
% 0.20/0.47 tff(202,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_3, e_4) | product(e_4, e_3, e_3) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_4)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(203,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_4, e_3, e_2) | product(e_4, e_3, e_1) | (~group_element(e_4)) | (~group_element(e_3)) | product(e_4, e_3, e_4) | product(e_4, e_3, e_3)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.20/0.47 tff(204,plain,
% 0.20/0.47 (product(e_4, e_3, e_2) | product(e_4, e_3, e_1) | product(e_4, e_3, e_4)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[203, 197, 69, 66, 194])).
% 0.20/0.47 tff(205,plain,
% 0.20/0.47 (product(e_4, e_3, e_2) | product(e_4, e_3, e_1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[204, 183])).
% 0.20/0.47 tff(206,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[205, 171, 137])).
% 0.20/0.47 tff(207,plain,(product(e_4, e_2, e_3) | product(e_4, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(208,plain,
% 0.20/0.47 (product(e_4, e_2, e_3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[207, 1])).
% 0.20/0.47 tff(209,plain,
% 0.20/0.47 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl(((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))) <=> ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(210,plain,
% 0.20/0.47 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[209])).
% 0.20/0.47 tff(211,plain,
% 0.20/0.47 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(212,plain,
% 0.20/0.47 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : rewrite((((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, Y)) <=> ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(213,plain,
% 0.20/0.47 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, Y)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[212])).
% 0.20/0.47 tff(214,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qg4')).
% 0.20/0.47 tff(215,plain,
% 0.20/0.47 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.20/0.47 tff(216,plain,
% 0.20/0.47 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[215, 211])).
% 0.20/0.47 tff(217,plain,(
% 0.20/0.47 ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[216])).
% 0.20/0.47 tff(218,plain,
% 0.20/0.47 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[217, 210])).
% 0.20/0.47 tff(219,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_4)) | product(e_4, e_3, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_4)) | product(e_4, e_3, e_3))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(220,plain,
% 0.20/0.47 (((~product(e_3, e_3, e_3)) | product(e_4, e_3, e_3) | (~product(e_3, e_3, e_4))) <=> ((~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_4)) | product(e_4, e_3, e_3))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(221,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | product(e_4, e_3, e_3) | (~product(e_3, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_4)) | product(e_4, e_3, e_3)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[220])).
% 0.20/0.47 tff(222,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | product(e_4, e_3, e_3) | (~product(e_3, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_4)) | product(e_4, e_3, e_3))),
% 0.20/0.47 inference(transitivity,[status(thm)],[221, 219])).
% 0.20/0.47 tff(223,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_3, e_3)) | product(e_4, e_3, e_3) | (~product(e_3, e_3, e_4)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(224,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_3, e_4)) | product(e_4, e_3, e_3)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.20/0.47 tff(225,plain,
% 0.20/0.47 (~product(e_3, e_3, e_4)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[224, 218, 186, 194])).
% 0.20/0.47 tff(226,assumption,(product(e_4, e_2, e_3)), introduced(assumption)).
% 0.20/0.47 tff(227,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_3)) | product(e_3, e_3, e_4) | (~product(e_2, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_4, e_2, e_3)) | product(e_3, e_3, e_4) | (~product(e_2, e_4, e_3)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(228,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_3)) | product(e_3, e_3, e_4) | (~product(e_2, e_4, e_3)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(229,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_4, e_2, e_3)) | product(e_3, e_3, e_4) | (~product(e_2, e_4, e_3))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.20/0.47 tff(230,plain,
% 0.20/0.47 (~product(e_2, e_4, e_3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[229, 218, 226, 225])).
% 0.20/0.47 tff(231,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_4)) | (~product(e_4, e_2, e_3)) | product(e_4, e_3, e_4))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_2, e_4, e_4)) | (~product(e_4, e_2, e_3)) | product(e_4, e_3, e_4))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(232,plain,
% 0.20/0.47 (((~product(e_4, e_2, e_3)) | product(e_4, e_3, e_4) | (~product(e_2, e_4, e_4))) <=> ((~product(e_2, e_4, e_4)) | (~product(e_4, e_2, e_3)) | product(e_4, e_3, e_4))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(233,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_3)) | product(e_4, e_3, e_4) | (~product(e_2, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_4)) | (~product(e_4, e_2, e_3)) | product(e_4, e_3, e_4)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[232])).
% 0.20/0.47 tff(234,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_3)) | product(e_4, e_3, e_4) | (~product(e_2, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_2, e_4, e_4)) | (~product(e_4, e_2, e_3)) | product(e_4, e_3, e_4))),
% 0.20/0.47 inference(transitivity,[status(thm)],[233, 231])).
% 0.20/0.47 tff(235,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_3)) | product(e_4, e_3, e_4) | (~product(e_2, e_4, e_4)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(236,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_2, e_4, e_4)) | (~product(e_4, e_2, e_3)) | product(e_4, e_3, e_4)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.20/0.47 tff(237,plain,
% 0.20/0.47 (~product(e_2, e_4, e_4)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[236, 218, 226, 183])).
% 0.20/0.47 tff(238,assumption,(product(e_2, e_4, e_2)), introduced(assumption)).
% 0.20/0.47 tff(239,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(240,plain,
% 0.20/0.47 ((equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2))) <=> (equalish(e_4, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(241,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_2, e_2, e_2))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[240])).
% 0.20/0.47 tff(242,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[241, 239])).
% 0.20/0.47 tff(243,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(244,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_2, e_2, e_2))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.20/0.47 tff(245,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[244, 142, 21, 139, 238])).
% 0.20/0.47 tff(246,plain,(~product(e_2, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(247,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | (~group_element(e_4)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | (~group_element(e_4)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(248,plain,
% 0.20/0.48 ((product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_2))) <=> ((~group_element(e_2)) | (~group_element(e_4)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(249,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_2)) | (~group_element(e_4)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[248])).
% 0.20/0.48 tff(250,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | (~group_element(e_4)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3))),
% 0.20/0.48 inference(transitivity,[status(thm)],[249, 247])).
% 0.20/0.48 tff(251,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(252,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_2)) | (~group_element(e_4)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.20/0.48 tff(253,plain,
% 0.20/0.48 (product(e_2, e_4, e_4) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[252, 110, 69, 66, 246])).
% 0.20/0.48 tff(254,plain,
% 0.20/0.48 (product(e_2, e_4, e_1)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[253, 237, 230])).
% 0.20/0.48 tff(255,assumption,(~product(e_3, e_4, e_1)), introduced(assumption)).
% 0.20/0.48 tff(256,assumption,(product(e_4, e_1, e_3)), introduced(assumption)).
% 0.20/0.48 tff(257,plain,
% 0.20/0.48 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(258,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.20/0.48 tff(259,plain,
% 0.20/0.48 (~equalish(e_1, e_2)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.20/0.48 tff(260,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_4, e_1, e_3)) | (~product(e_4, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_4, e_1, e_3)) | (~product(e_4, e_2, e_3)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(261,plain,
% 0.20/0.48 ((equalish(e_1, e_2) | (~product(e_4, e_2, e_3)) | (~product(e_4, e_1, e_3))) <=> (equalish(e_1, e_2) | (~product(e_4, e_1, e_3)) | (~product(e_4, e_2, e_3)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(262,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_4, e_2, e_3)) | (~product(e_4, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_4, e_1, e_3)) | (~product(e_4, e_2, e_3))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[261])).
% 0.20/0.48 tff(263,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_4, e_2, e_3)) | (~product(e_4, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_4, e_1, e_3)) | (~product(e_4, e_2, e_3)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[262, 260])).
% 0.20/0.48 tff(264,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_4, e_2, e_3)) | (~product(e_4, e_1, e_3)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(265,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_4, e_1, e_3)) | (~product(e_4, e_2, e_3))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.20/0.48 tff(266,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[265, 259, 21, 226, 256])).
% 0.20/0.48 tff(267,plain,((~product(e_4, e_1, e_3)) | (~product(e_4, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(268,plain,
% 0.20/0.48 (~product(e_4, e_1, e_3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[267, 226])).
% 0.20/0.48 tff(269,plain,
% 0.20/0.48 (product(e_4, e_1, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[79, 1, 32])).
% 0.20/0.48 tff(270,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_1, e_2)) | product(e_4, e_2, e_4) | (~product(e_1, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_4, e_1, e_2)) | product(e_4, e_2, e_4) | (~product(e_1, e_4, e_4)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(271,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_1, e_2)) | product(e_4, e_2, e_4) | (~product(e_1, e_4, e_4)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(272,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_4, e_1, e_2)) | product(e_4, e_2, e_4) | (~product(e_1, e_4, e_4))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.20/0.48 tff(273,plain,
% 0.20/0.48 (~product(e_1, e_4, e_4)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[272, 218, 269, 94])).
% 0.20/0.48 tff(274,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_4, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_4, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_4, e_1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(275,plain,
% 0.20/0.48 (((~product(e_4, e_4, e_4)) | product(e_1, e_4, e_4) | (~product(e_4, e_4, e_1))) <=> (product(e_1, e_4, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_4, e_1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(276,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_4, e_4)) | product(e_1, e_4, e_4) | (~product(e_4, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_4, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_4, e_1))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[275])).
% 0.20/0.48 tff(277,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_4, e_4)) | product(e_1, e_4, e_4) | (~product(e_4, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_4, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_4, e_1)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[276, 274])).
% 0.20/0.49 tff(278,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_4, e_4)) | product(e_1, e_4, e_4) | (~product(e_4, e_4, e_1)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(279,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_4, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_4, e_1))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.20/0.49 tff(280,plain,
% 0.20/0.49 (~product(e_4, e_4, e_1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[279, 218, 273, 10])).
% 0.20/0.49 tff(281,assumption,(product(e_1, e_3, e_4)), introduced(assumption)).
% 0.20/0.49 tff(282,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_4, e_4, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_4, e_4, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_4)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(283,plain,
% 0.20/0.49 (((~product(e_1, e_3, e_4)) | product(e_4, e_4, e_1) | (~product(e_3, e_1, e_4))) <=> (product(e_4, e_4, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_4)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(284,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_4)) | product(e_4, e_4, e_1) | (~product(e_3, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_4, e_4, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_4))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[283])).
% 0.20/0.49 tff(285,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_4)) | product(e_4, e_4, e_1) | (~product(e_3, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_4, e_4, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_4)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[284, 282])).
% 0.20/0.49 tff(286,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_4)) | product(e_4, e_4, e_1) | (~product(e_3, e_1, e_4)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(287,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_4, e_4, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_4))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.20/0.49 tff(288,plain,
% 0.20/0.49 (~product(e_3, e_1, e_4)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[287, 218, 281, 280])).
% 0.20/0.49 tff(289,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_4, e_1) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_4, e_1) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_4)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(290,plain,
% 0.20/0.49 (((~product(e_1, e_3, e_4)) | product(e_3, e_4, e_1) | (~product(e_3, e_1, e_3))) <=> (product(e_3, e_4, e_1) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_4)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(291,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_4)) | product(e_3, e_4, e_1) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_4, e_1) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_4))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[290])).
% 0.20/0.49 tff(292,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_4)) | product(e_3, e_4, e_1) | (~product(e_3, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_4, e_1) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_4)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[291, 289])).
% 0.20/0.49 tff(293,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_3, e_4)) | product(e_3, e_4, e_1) | (~product(e_3, e_1, e_3)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(294,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_4, e_1) | (~product(e_3, e_1, e_3)) | (~product(e_1, e_3, e_4))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[293, 292])).
% 0.20/0.49 tff(295,plain,
% 0.20/0.49 (~product(e_3, e_1, e_3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[294, 218, 281, 255])).
% 0.20/0.49 tff(296,assumption,(product(e_3, e_1, e_2)), introduced(assumption)).
% 0.20/0.49 tff(297,assumption,(product(e_4, e_1, e_2)), introduced(assumption)).
% 0.20/0.49 tff(298,plain,
% 0.20/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_4, e_1, e_2)) | (~product(e_3, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_4) | (~product(e_4, e_1, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(299,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_4, e_1, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(300,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_4) | (~product(e_4, e_1, e_2)) | (~product(e_3, e_1, e_2))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[299, 298])).
% 0.20/0.49 tff(301,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[300, 175, 45, 297, 296])).
% 0.20/0.49 tff(302,plain,((~product(e_3, e_1, e_2)) | (~product(e_4, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(303,plain,
% 0.20/0.49 (~product(e_3, e_1, e_2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[302, 269])).
% 0.20/0.49 tff(304,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(305,plain,
% 0.20/0.49 ((product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3))) <=> ((~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(306,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1)))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[305])).
% 0.20/0.49 tff(307,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1))),
% 0.20/0.49 inference(transitivity,[status(thm)],[306, 304])).
% 0.20/0.49 tff(308,plain,
% 0.20/0.49 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(309,plain,
% 0.20/0.49 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[308, 307])).
% 0.20/0.49 tff(310,plain,
% 0.20/0.49 (product(e_3, e_1, e_1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[309, 72, 197, 66, 303, 295, 288])).
% 0.20/0.49 tff(311,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_3, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_3, e_1, e_1)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(312,plain,
% 0.20/0.49 (((~product(e_3, e_1, e_1)) | product(e_4, e_1, e_3) | (~product(e_1, e_3, e_4))) <=> (product(e_4, e_1, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_3, e_1, e_1)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(313,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_1)) | product(e_4, e_1, e_3) | (~product(e_1, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_3, e_1, e_1))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[312])).
% 0.20/0.49 tff(314,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_1)) | product(e_4, e_1, e_3) | (~product(e_1, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_3, e_1, e_1)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[313, 311])).
% 0.20/0.49 tff(315,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_1)) | product(e_4, e_1, e_3) | (~product(e_1, e_3, e_4)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(316,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_3, e_1, e_1))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[315, 314])).
% 0.20/0.49 tff(317,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[316, 218, 281, 1, 310])).
% 0.20/0.50 tff(318,plain,((~product(e_1, e_3, e_4)) | product(e_4, e_1, e_3) | product(e_3, e_4, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(319,plain,
% 0.20/0.50 (~product(e_1, e_3, e_4)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[318, 268, 255])).
% 0.20/0.50 tff(320,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_4) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_4) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_4, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(321,plain,
% 0.20/0.50 (((~product(e_4, e_2, e_3)) | product(e_1, e_3, e_4) | (~product(e_2, e_4, e_1))) <=> (product(e_1, e_3, e_4) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_4, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(322,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_3)) | product(e_1, e_3, e_4) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_4) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_4, e_1))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[321])).
% 0.20/0.50 tff(323,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_3)) | product(e_1, e_3, e_4) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_4) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_4, e_1)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[322, 320])).
% 0.20/0.50 tff(324,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_3)) | product(e_1, e_3, e_4) | (~product(e_2, e_4, e_1)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(325,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_4) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_4, e_1))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[324, 323])).
% 0.20/0.50 tff(326,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[325, 218, 319, 226, 254])).
% 0.20/0.50 tff(327,plain,((~product(e_4, e_2, e_3)) | product(e_3, e_4, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(328,plain,
% 0.20/0.50 (product(e_3, e_4, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[327, 208])).
% 0.20/0.50 tff(329,assumption,(product(e_3, e_4, e_1)), introduced(assumption)).
% 0.20/0.50 tff(330,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_1, e_4)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(331,plain,
% 0.20/0.50 (((~product(e_1, e_1, e_1)) | product(e_4, e_1, e_1) | (~product(e_1, e_1, e_4))) <=> (product(e_4, e_1, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_1, e_4)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(332,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_1)) | product(e_4, e_1, e_1) | (~product(e_1, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_1, e_4))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[331])).
% 0.20/0.50 tff(333,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_1)) | product(e_4, e_1, e_1) | (~product(e_1, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_1, e_4)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[332, 330])).
% 0.20/0.50 tff(334,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_1)) | product(e_4, e_1, e_1) | (~product(e_1, e_1, e_4)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(335,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_1, e_4))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[334, 333])).
% 0.20/0.50 tff(336,plain,
% 0.20/0.50 (~product(e_1, e_1, e_4)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[335, 218, 56, 34])).
% 0.20/0.50 tff(337,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_3, e_1)) | product(e_1, e_1, e_4) | (~product(e_3, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_4, e_3, e_1)) | product(e_1, e_1, e_4) | (~product(e_3, e_4, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(338,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_3, e_1)) | product(e_1, e_1, e_4) | (~product(e_3, e_4, e_1)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(339,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_4, e_3, e_1)) | product(e_1, e_1, e_4) | (~product(e_3, e_4, e_1))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[338, 337])).
% 0.20/0.50 tff(340,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[339, 218, 159, 336, 329])).
% 0.20/0.50 tff(341,plain,((~product(e_4, e_3, e_1)) | (~product(e_3, e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(342,plain,
% 0.20/0.50 (~product(e_4, e_3, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[341, 328])).
% 0.20/0.50 tff(343,plain,
% 0.20/0.50 (product(e_4, e_3, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[205, 342])).
% 0.20/0.50 tff(344,plain,
% 0.20/0.50 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(345,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.20/0.50 tff(346,plain,
% 0.20/0.50 (~equalish(e_3, e_1)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.20/0.50 tff(347,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_1, e_2)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(348,plain,
% 0.20/0.50 ((equalish(e_3, e_1) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_3, e_2))) <=> (equalish(e_3, e_1) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_1, e_2)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(349,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_1, e_2))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[348])).
% 0.20/0.50 tff(350,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_1, e_2)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[349, 347])).
% 0.20/0.50 tff(351,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_4, e_1, e_2)) | (~product(e_4, e_3, e_2)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(352,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_4, e_3, e_2)) | (~product(e_4, e_1, e_2))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[351, 350])).
% 0.20/0.50 tff(353,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[352, 346, 21, 343, 81])).
% 0.20/0.50 tff(354,plain,(product(e_4, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(355,plain,
% 0.20/0.50 (~product(e_4, e_2, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[267, 354])).
% 0.20/0.50 tff(356,plain,
% 0.20/0.50 (product(e_4, e_2, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[156, 355])).
% 0.20/0.50 tff(357,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_4)) | (~product(e_4, e_2, e_1)) | product(e_4, e_1, e_4))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_2, e_4, e_4)) | (~product(e_4, e_2, e_1)) | product(e_4, e_1, e_4))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(358,plain,
% 0.20/0.50 (((~product(e_4, e_2, e_1)) | product(e_4, e_1, e_4) | (~product(e_2, e_4, e_4))) <=> ((~product(e_2, e_4, e_4)) | (~product(e_4, e_2, e_1)) | product(e_4, e_1, e_4))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(359,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_1)) | product(e_4, e_1, e_4) | (~product(e_2, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_4)) | (~product(e_4, e_2, e_1)) | product(e_4, e_1, e_4)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[358])).
% 0.20/0.50 tff(360,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_1)) | product(e_4, e_1, e_4) | (~product(e_2, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_2, e_4, e_4)) | (~product(e_4, e_2, e_1)) | product(e_4, e_1, e_4))),
% 0.20/0.50 inference(transitivity,[status(thm)],[359, 357])).
% 0.20/0.50 tff(361,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_1)) | product(e_4, e_1, e_4) | (~product(e_2, e_4, e_4)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(362,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_2, e_4, e_4)) | (~product(e_4, e_2, e_1)) | product(e_4, e_1, e_4)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[361, 360])).
% 0.20/0.50 tff(363,plain,
% 0.20/0.50 ((~product(e_2, e_4, e_4)) | (~product(e_4, e_2, e_1)) | product(e_4, e_1, e_4)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[362, 218])).
% 0.20/0.50 tff(364,plain,
% 0.20/0.50 ((~product(e_2, e_4, e_4)) | (~product(e_4, e_2, e_1))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[363, 32])).
% 0.20/0.50 tff(365,plain,
% 0.20/0.50 (~product(e_2, e_4, e_4)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[364, 356])).
% 0.20/0.50 tff(366,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_4) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_4) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(367,plain,
% 0.20/0.50 (((~product(e_4, e_2, e_1)) | product(e_1, e_1, e_4) | (~product(e_2, e_4, e_1))) <=> (product(e_1, e_1, e_4) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(368,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_1)) | product(e_1, e_1, e_4) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_4) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_1))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[367])).
% 0.20/0.50 tff(369,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_1)) | product(e_1, e_1, e_4) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_4) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_1)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[368, 366])).
% 0.20/0.50 tff(370,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_1)) | product(e_1, e_1, e_4) | (~product(e_2, e_4, e_1)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(371,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_4) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_1))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[370, 369])).
% 0.20/0.50 tff(372,plain,
% 0.20/0.50 (~product(e_2, e_4, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[371, 218, 356, 336])).
% 0.20/0.50 tff(373,plain,
% 0.20/0.50 (product(e_2, e_4, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[253, 372, 365])).
% 0.20/0.50 tff(374,plain,
% 0.20/0.50 (~product(e_4, e_3, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[170, 356])).
% 0.20/0.50 tff(375,plain,
% 0.20/0.50 (product(e_4, e_3, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[205, 374])).
% 0.20/0.50 tff(376,assumption,(product(e_1, e_3, e_2)), introduced(assumption)).
% 0.20/0.50 tff(377,plain,
% 0.20/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_4) | (~product(e_4, e_3, e_2)) | (~product(e_1, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_4) | (~product(e_4, e_3, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(378,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_4) | (~product(e_4, e_3, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(379,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_4) | (~product(e_4, e_3, e_2)) | (~product(e_1, e_3, e_2))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[378, 377])).
% 0.20/0.50 tff(380,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[379, 24, 45, 97, 376])).
% 0.20/0.50 tff(381,plain,((~product(e_1, e_3, e_2)) | (~product(e_4, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(382,plain,
% 0.20/0.50 (~product(e_1, e_3, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[381, 375])).
% 0.20/0.50 tff(383,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_3)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(384,plain,
% 0.20/0.50 (((~product(e_2, e_4, e_3)) | product(e_1, e_3, e_2) | (~product(e_4, e_2, e_1))) <=> (product(e_1, e_3, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_3)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(385,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_3)) | product(e_1, e_3, e_2) | (~product(e_4, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_3, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_3))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[384])).
% 0.20/0.51 tff(386,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_3)) | product(e_1, e_3, e_2) | (~product(e_4, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_3)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[385, 383])).
% 0.20/0.51 tff(387,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_3)) | product(e_1, e_3, e_2) | (~product(e_4, e_2, e_1)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(388,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_3, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_3))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[387, 386])).
% 0.20/0.51 tff(389,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[388, 218, 356, 382, 373])).
% 0.20/0.51 % SZS output end Proof
% 0.20/0.51 % E exiting
%------------------------------------------------------------------------------