%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP129-2.004 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:07:10 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.45s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP129-2.004 : TPTP v9.0.0. Released v1.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 15:43:33 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.45 % SZS status Unsatisfiable
% 0.20/0.45 % SZS output start Proof
% 0.20/0.45 tff(product_type, type, (
% 0.20/0.45 product: ( $i * $i * $i ) > $o)).
% 0.20/0.45 tff(e_2_type, type, (
% 0.20/0.45 e_2: $i)).
% 0.20/0.45 tff(e_4_type, type, (
% 0.20/0.45 e_4: $i)).
% 0.20/0.45 tff(e_1_type, type, (
% 0.20/0.45 e_1: $i)).
% 0.20/0.45 tff(e_3_type, type, (
% 0.20/0.45 e_3: $i)).
% 0.20/0.45 tff(equalish_type, type, (
% 0.20/0.45 equalish: ( $i * $i ) > $o)).
% 0.20/0.45 tff(next_type, type, (
% 0.20/0.45 next: ( $i * $i ) > $o)).
% 0.20/0.45 tff(greater_type, type, (
% 0.20/0.45 greater: ( $i * $i ) > $o)).
% 0.20/0.45 tff(group_element_type, type, (
% 0.20/0.45 group_element: $i > $o)).
% 0.20/0.45 tff(1,assumption,(product(e_4, e_2, e_4)), introduced(assumption)).
% 0.20/0.45 tff(2,assumption,(~product(e_1, e_4, e_2)), introduced(assumption)).
% 0.20/0.45 tff(3,assumption,(product(e_1, e_3, e_2)), introduced(assumption)).
% 0.20/0.45 tff(4,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.20/0.45 tff(5,assumption,(product(e_1, e_1, e_1)), introduced(assumption)).
% 0.20/0.45 tff(6,plain,
% 0.20/0.45 (^[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))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(7,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.45 tff(8,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(9,plain,
% 0.20/0.45 (^[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)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(10,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[9])).
% 0.20/0.45 tff(11,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')).
% 0.20/0.45 tff(12,plain,
% 0.20/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.20/0.45 tff(13,plain,
% 0.20/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.20/0.45 tff(14,plain,(
% 0.20/0.45 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[13])).
% 0.20/0.45 tff(15,plain,
% 0.20/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.20/0.45 tff(16,plain,
% 0.20/0.45 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(17,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.20/0.45 tff(18,plain,
% 0.20/0.45 (~equalish(e_1, e_2)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.20/0.45 tff(19,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_1, e_2) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(20,plain,
% 0.20/0.45 ((equalish(e_1, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1))) <=> (equalish(e_1, e_2) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(21,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_1, e_2) | (~product(e_2, 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_1, e_2) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[20])).
% 0.20/0.46 tff(22,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_1, e_2) | (~product(e_2, 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_1, e_2) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[21, 19])).
% 0.20/0.46 tff(23,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_1, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(24,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.46 tff(25,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[24, 18, 15, 5, 4])).
% 0.20/0.46 tff(26,plain,((~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(27,plain,
% 0.20/0.46 (~product(e_1, e_1, e_1)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[26, 4])).
% 0.20/0.46 tff(28,plain,
% 0.20/0.46 (^[Y: $i, X: $i, X1: $i] : refl(((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y))) <=> ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(29,plain,
% 0.20/0.46 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y))) <=> ![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.46 tff(30,plain,
% 0.20/0.46 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y))) <=> ![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(31,plain,
% 0.20/0.46 (^[Y: $i, X: $i, X1: $i] : trans(monotonicity(rewrite(((~product(X, e_1, Y)) | (~next(X, X1))) <=> ((~next(X, X1)) | (~product(X, e_1, Y)))), ((((~product(X, e_1, Y)) | (~next(X, X1))) | (~greater(Y, X1))) <=> (((~next(X, X1)) | (~product(X, e_1, Y))) | (~greater(Y, X1))))), rewrite((((~next(X, X1)) | (~product(X, e_1, Y))) | (~greater(Y, X1))) <=> ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))), ((((~product(X, e_1, Y)) | (~next(X, X1))) | (~greater(Y, X1))) <=> ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(32,plain,
% 0.20/0.46 (![Y: $i, X: $i, X1: $i] : (((~product(X, e_1, Y)) | (~next(X, X1))) | (~greater(Y, X1))) <=> ![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.46 tff(33,axiom,(![Y: $i, X: $i, X1: $i] : (((~product(X, e_1, Y)) | (~next(X, X1))) | (~greater(Y, X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','no_redundancy')).
% 0.20/0.46 tff(34,plain,
% 0.20/0.46 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.46 tff(35,plain,
% 0.20/0.46 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.20/0.46 tff(36,plain,(
% 0.20/0.46 ![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[35])).
% 0.20/0.46 tff(37,plain,
% 0.20/0.46 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.20/0.46 tff(38,plain,
% 0.20/0.46 (greater(e_4, e_2) <=> greater(e_4, e_2)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(39,axiom,(greater(e_4, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_greater_e_2')).
% 0.20/0.46 tff(40,plain,
% 0.20/0.46 (greater(e_4, e_2)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.20/0.46 tff(41,plain,
% 0.20/0.46 (next(e_1, e_2) <=> next(e_1, e_2)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(42,axiom,(next(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_then_e_2')).
% 0.20/0.46 tff(43,plain,
% 0.20/0.46 (next(e_1, e_2)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.46 tff(44,plain,
% 0.20/0.46 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_4, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_4)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_4, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_4)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(45,plain,
% 0.20/0.46 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_4, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_4)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(46,plain,
% 0.20/0.46 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_4, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_4))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.46 tff(47,plain,
% 0.20/0.46 (~product(e_1, e_1, e_4)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[46, 43, 40, 37])).
% 0.20/0.46 tff(48,plain,
% 0.20/0.46 (greater(e_3, e_2) <=> greater(e_3, e_2)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(49,axiom,(greater(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_greater_e_2')).
% 0.20/0.46 tff(50,plain,
% 0.20/0.46 (greater(e_3, e_2)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.20/0.46 tff(51,plain,
% 0.20/0.46 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_3, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_3, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(52,plain,
% 0.20/0.46 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_3, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(53,plain,
% 0.20/0.46 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_3, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.46 tff(54,plain,
% 0.20/0.46 (~product(e_1, e_1, e_3)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[53, 43, 50, 37])).
% 0.20/0.46 tff(55,plain,
% 0.20/0.46 (^[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))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(56,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))) <=> ![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[55])).
% 0.20/0.46 tff(57,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))) <=> ![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)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(58,plain,
% 0.20/0.46 (^[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)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(59,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[58])).
% 0.20/0.46 tff(60,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')).
% 0.20/0.46 tff(61,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)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.46 tff(62,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)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.20/0.46 tff(63,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)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[62])).
% 0.20/0.46 tff(64,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)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.20/0.46 tff(65,plain,
% 0.20/0.46 (group_element(e_1) <=> group_element(e_1)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(66,axiom,(group_element(e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_1')).
% 0.20/0.46 tff(67,plain,
% 0.20/0.46 (group_element(e_1)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.20/0.46 tff(68,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_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(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)))) | product(e_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(69,plain,
% 0.20/0.46 ((product(e_1, e_1, e_4) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_1))) <=> (product(e_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(70,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_1, e_1, e_4) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)) | (~group_element(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)))) | (product(e_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[69])).
% 0.20/0.46 tff(71,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_1, e_1, e_4) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)) | (~group_element(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)))) | product(e_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[70, 68])).
% 0.20/0.46 tff(72,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_1, e_1, e_4) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_1)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(73,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_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.20/0.46 tff(74,plain,
% 0.20/0.46 (product(e_1, e_1, e_2) | product(e_1, e_1, e_1)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[73, 67, 64, 54, 47])).
% 0.20/0.46 tff(75,plain,
% 0.20/0.46 (product(e_1, e_1, e_2)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[74, 27])).
% 0.20/0.46 tff(76,assumption,(~product(e_1, e_2, e_2)), introduced(assumption)).
% 0.20/0.46 tff(77,assumption,(product(e_1, e_1, e_2)), introduced(assumption)).
% 0.20/0.46 tff(78,plain,
% 0.20/0.46 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl((product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1))) <=> (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(79,plain,
% 0.20/0.46 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[78])).
% 0.20/0.46 tff(80,plain,
% 0.20/0.46 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(81,plain,
% 0.20/0.47 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : trans(monotonicity(rewrite(((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) <=> ((~product(X, Z1, Z2)) | (~product(Y, X, Z1)))), ((((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) | product(Z1, Y, Z2)) <=> (((~product(X, Z1, Z2)) | (~product(Y, X, Z1))) | product(Z1, Y, Z2)))), rewrite((((~product(X, Z1, Z2)) | (~product(Y, X, Z1))) | product(Z1, Y, Z2)) <=> (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))), ((((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) | product(Z1, Y, Z2)) <=> (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(82,plain,
% 0.20/0.47 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) | product(Z1, Y, Z2)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[81])).
% 0.20/0.47 tff(83,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) | product(Z1, Y, Z2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qg3')).
% 0.20/0.47 tff(84,plain,
% 0.20/0.47 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.20/0.47 tff(85,plain,
% 0.20/0.47 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.20/0.47 tff(86,plain,(
% 0.20/0.47 ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[85])).
% 0.20/0.47 tff(87,plain,
% 0.20/0.47 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.20/0.47 tff(88,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(89,plain,
% 0.20/0.47 ((product(e_1, e_2, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1))) <=> (product(e_1, e_2, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(90,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[89])).
% 0.20/0.47 tff(91,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[90, 88])).
% 0.20/0.47 tff(92,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(93,plain,
% 0.20/0.47 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.47 tff(94,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[93, 87, 77, 4, 76])).
% 0.20/0.47 tff(95,plain,((~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1)) | product(e_1, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(96,plain,
% 0.20/0.47 (product(e_1, e_2, e_2)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[95, 75, 4])).
% 0.20/0.47 tff(97,plain,
% 0.20/0.47 (^[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))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(98,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[97])).
% 0.20/0.47 tff(99,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(100,plain,
% 0.20/0.47 (^[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)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(101,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[100])).
% 0.20/0.47 tff(102,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')).
% 0.20/0.47 tff(103,plain,
% 0.20/0.47 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.20/0.47 tff(104,plain,
% 0.20/0.47 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.20/0.47 tff(105,plain,(
% 0.20/0.47 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[104])).
% 0.20/0.47 tff(106,plain,
% 0.20/0.47 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.20/0.47 tff(107,plain,
% 0.20/0.47 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(108,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.20/0.47 tff(109,plain,
% 0.20/0.47 (~equalish(e_2, e_1)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.20/0.47 tff(110,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_2, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, 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_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(111,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_2, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(112,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_2))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.20/0.47 tff(113,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[112, 109, 106, 75, 96])).
% 0.20/0.47 tff(114,plain,(~product(e_2, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(115,assumption,(~product(e_2, e_1, e_3)), introduced(assumption)).
% 0.20/0.47 tff(116,assumption,(~product(e_3, e_2, e_1)), introduced(assumption)).
% 0.20/0.47 tff(117,assumption,(~product(e_2, e_1, e_1)), introduced(assumption)).
% 0.20/0.47 tff(118,plain,
% 0.20/0.47 (greater(e_4, e_3) <=> greater(e_4, e_3)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(119,axiom,(greater(e_4, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_greater_e_3')).
% 0.20/0.47 tff(120,plain,
% 0.20/0.47 (greater(e_4, e_3)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.20/0.47 tff(121,plain,
% 0.20/0.47 (next(e_2, e_3) <=> next(e_2, e_3)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(122,axiom,(next(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_then_e_3')).
% 0.20/0.47 tff(123,plain,
% 0.20/0.47 (next(e_2, e_3)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.20/0.47 tff(124,plain,
% 0.20/0.47 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_4, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_4, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(125,plain,
% 0.20/0.47 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_4, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(126,plain,
% 0.20/0.47 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_4, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.20/0.47 tff(127,plain,
% 0.20/0.47 (~product(e_2, e_1, e_4)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[126, 123, 120, 37])).
% 0.20/0.47 tff(128,plain,
% 0.20/0.47 (group_element(e_2) <=> group_element(e_2)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(129,axiom,(group_element(e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_2')).
% 0.20/0.47 tff(130,plain,
% 0.20/0.47 (group_element(e_2)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.20/0.47 tff(131,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_2, e_1, e_4) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~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)))) | product(e_2, e_1, e_4) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_2)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(132,plain,
% 0.20/0.47 ((product(e_2, e_1, e_4) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2))) <=> (product(e_2, e_1, e_4) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_2)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(133,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_2, e_1, e_4) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~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)))) | (product(e_2, e_1, e_4) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_2))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[132])).
% 0.20/0.47 tff(134,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_2, e_1, e_4) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~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)))) | product(e_2, e_1, e_4) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_2)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[133, 131])).
% 0.20/0.47 tff(135,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_2, e_1, e_4) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(136,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_2, e_1, e_4) | (~group_element(e_1)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_2))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.20/0.47 tff(137,plain,
% 0.20/0.47 (product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[136, 67, 130, 64, 127])).
% 0.20/0.47 tff(138,plain,
% 0.20/0.47 (product(e_2, e_1, e_2)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[137, 117, 115])).
% 0.20/0.47 tff(139,assumption,(product(e_2, e_1, e_2)), introduced(assumption)).
% 0.20/0.47 tff(140,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_2, 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_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(141,plain,
% 0.20/0.47 ((equalish(e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_1, e_2))) <=> (equalish(e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(142,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_1, 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_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_2))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[141])).
% 0.20/0.47 tff(143,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_1, 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_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[142, 140])).
% 0.20/0.47 tff(144,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_1, e_2)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(145,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_2))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.20/0.47 tff(146,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[145, 18, 15, 77, 139])).
% 0.20/0.47 tff(147,plain,((~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(148,plain,
% 0.20/0.47 (~product(e_1, e_1, e_2)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[147, 138])).
% 0.20/0.47 tff(149,plain,
% 0.20/0.47 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(150,plain,
% 0.20/0.48 ((product(e_1, e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_1))) <=> (product(e_1, e_1, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(151,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_2))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[150])).
% 0.20/0.48 tff(152,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[151, 149])).
% 0.20/0.48 tff(153,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_1)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(154,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_2) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_2))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.20/0.48 tff(155,plain,
% 0.20/0.48 (~product(e_1, e_2, e_1)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[154, 87, 148, 138])).
% 0.20/0.48 tff(156,assumption,(product(e_2, e_2, e_1)), introduced(assumption)).
% 0.20/0.48 tff(157,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(158,plain,
% 0.20/0.48 ((product(e_2, e_1, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_2))) <=> (product(e_2, e_1, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(159,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_1))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[158])).
% 0.20/0.48 tff(160,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_1)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[159, 157])).
% 0.20/0.48 tff(161,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(162,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_1))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.20/0.48 tff(163,plain,
% 0.20/0.48 (~product(e_1, e_2, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[162, 87, 117, 156])).
% 0.20/0.48 tff(164,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(165,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_1)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(166,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_1))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.20/0.48 tff(167,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[166, 87, 139, 156, 163])).
% 0.20/0.48 tff(168,plain,((~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_2)) | product(e_2, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(169,plain,
% 0.20/0.48 (~product(e_2, e_2, e_1)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[168, 138, 117])).
% 0.20/0.48 tff(170,assumption,(product(e_2, e_2, e_2)), introduced(assumption)).
% 0.20/0.48 tff(171,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_2, e_1) | (~product(e_2, e_2, e_2)) | (~product(e_2, 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_2, e_1) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(172,plain,
% 0.20/0.48 ((equalish(e_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2))) <=> (equalish(e_2, e_1) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(173,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_2, e_1) | (~product(e_2, e_1, 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_2, e_1) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[172])).
% 0.20/0.48 tff(174,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_2, e_1) | (~product(e_2, e_1, 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_2, e_1) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[173, 171])).
% 0.20/0.48 tff(175,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_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(176,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.20/0.48 tff(177,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[176, 109, 106, 139, 170])).
% 0.20/0.48 tff(178,plain,((~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(179,plain,
% 0.20/0.48 (~product(e_2, e_2, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[178, 138])).
% 0.20/0.48 tff(180,assumption,(product(e_2, e_2, e_3)), introduced(assumption)).
% 0.20/0.48 tff(181,assumption,(~product(e_1, e_2, e_1)), introduced(assumption)).
% 0.20/0.48 tff(182,assumption,(~product(e_1, e_2, e_3)), introduced(assumption)).
% 0.20/0.48 tff(183,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_3)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(184,plain,
% 0.20/0.48 ((product(e_2, e_1, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_2))) <=> (product(e_2, e_1, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_3)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(185,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_3))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[184])).
% 0.20/0.48 tff(186,plain,
% 0.20/0.48 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_3)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[185, 183])).
% 0.20/0.48 tff(187,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(188,plain,
% 0.20/0.48 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_3) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_3))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.20/0.48 tff(189,plain,
% 0.20/0.48 (~product(e_1, e_2, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[188, 87, 115, 180])).
% 0.20/0.48 tff(190,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_1)) | (~group_element(e_2)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, 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_1)) | (~group_element(e_2)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(191,plain,
% 0.20/0.48 ((product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1))) <=> ((~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(192,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_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(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_2)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[191])).
% 0.20/0.48 tff(193,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_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(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_2)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2))),
% 0.20/0.48 inference(transitivity,[status(thm)],[192, 190])).
% 0.20/0.48 tff(194,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_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_1)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(195,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_1)) | (~group_element(e_2)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.20/0.48 tff(196,plain,
% 0.20/0.48 (product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[195, 67, 130, 64, 181])).
% 0.20/0.48 tff(197,plain,
% 0.20/0.48 (product(e_1, e_2, e_4)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[196, 189, 182])).
% 0.20/0.48 tff(198,assumption,(product(e_1, e_2, e_4)), introduced(assumption)).
% 0.20/0.48 tff(199,assumption,(product(e_3, e_2, e_4)), introduced(assumption)).
% 0.20/0.48 tff(200,plain,
% 0.20/0.48 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(201,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.20/0.48 tff(202,plain,
% 0.20/0.48 (~equalish(e_3, e_1)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.20/0.48 tff(203,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_3, e_2, e_4)) | (~product(e_1, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_3, e_2, e_4)) | (~product(e_1, e_2, e_4)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(204,plain,
% 0.20/0.48 ((equalish(e_3, e_1) | (~product(e_1, e_2, e_4)) | (~product(e_3, e_2, e_4))) <=> (equalish(e_3, e_1) | (~product(e_3, e_2, e_4)) | (~product(e_1, e_2, e_4)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(205,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_2, e_4)) | (~product(e_3, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_3, e_2, e_4)) | (~product(e_1, e_2, e_4))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[204])).
% 0.20/0.48 tff(206,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_2, e_4)) | (~product(e_3, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_3, e_2, e_4)) | (~product(e_1, e_2, e_4)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[205, 203])).
% 0.20/0.48 tff(207,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_2, e_4)) | (~product(e_3, e_2, e_4)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(208,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_3, e_2, e_4)) | (~product(e_1, e_2, e_4))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.20/0.48 tff(209,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[208, 202, 15, 199, 198])).
% 0.20/0.48 tff(210,plain,((~product(e_3, e_2, e_4)) | (~product(e_1, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(211,plain,
% 0.20/0.48 (~product(e_3, e_2, e_4)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[210, 197])).
% 0.20/0.48 tff(212,assumption,(product(e_3, e_2, e_3)), introduced(assumption)).
% 0.20/0.48 tff(213,plain,
% 0.20/0.48 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(214,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.20/0.48 tff(215,plain,
% 0.20/0.48 (~equalish(e_3, e_2)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.20/0.48 tff(216,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_3)) | (~product(e_3, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_2, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(217,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(218,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_2, e_3)) | (~product(e_3, e_2, e_3))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.20/0.48 tff(219,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[218, 215, 15, 212, 180])).
% 0.20/0.48 tff(220,plain,((~product(e_3, e_2, e_3)) | (~product(e_2, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(221,plain,
% 0.20/0.48 (~product(e_3, e_2, e_3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[220, 180])).
% 0.20/0.48 tff(222,plain,
% 0.20/0.48 (group_element(e_3) <=> group_element(e_3)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(223,axiom,(group_element(e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_3')).
% 0.20/0.48 tff(224,plain,
% 0.20/0.48 (group_element(e_3)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.20/0.48 tff(225,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_2)) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, 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_2)) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_3)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(226,plain,
% 0.20/0.49 ((product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3))) <=> ((~group_element(e_2)) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_3)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(227,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_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~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_2)) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_3))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[226])).
% 0.20/0.49 tff(228,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_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~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_2)) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_3)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[227, 225])).
% 0.20/0.49 tff(229,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_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(230,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_2)) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_3))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.20/0.49 tff(231,plain,
% 0.20/0.49 (product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[230, 130, 224, 64])).
% 0.20/0.49 tff(232,plain,
% 0.20/0.49 (product(e_3, e_2, e_2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[231, 221, 116, 211])).
% 0.20/0.49 tff(233,assumption,(~product(e_2, e_3, e_3)), introduced(assumption)).
% 0.20/0.49 tff(234,assumption,(product(e_3, e_2, e_2)), introduced(assumption)).
% 0.20/0.49 tff(235,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_3, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_3, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_3, e_2, e_2)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(236,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_3, e_2, e_2)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(237,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_3, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_3, e_2, e_2))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.20/0.49 tff(238,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[237, 87, 234, 180, 233])).
% 0.20/0.49 tff(239,plain,(product(e_2, e_3, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(240,plain,
% 0.20/0.49 (product(e_2, e_3, e_3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[239, 232, 180])).
% 0.20/0.49 tff(241,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_2, e_3, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_2, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_2, e_3, e_3)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(242,plain,
% 0.20/0.49 ((product(e_3, e_2, e_3) | (~product(e_2, e_3, e_3)) | (~product(e_2, e_2, e_3))) <=> (product(e_3, e_2, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_2, e_3, e_3)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(243,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_3) | (~product(e_2, e_3, e_3)) | (~product(e_2, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_2, e_3, e_3))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[242])).
% 0.20/0.49 tff(244,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_3) | (~product(e_2, e_3, e_3)) | (~product(e_2, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_2, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_2, e_3, e_3)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[243, 241])).
% 0.20/0.49 tff(245,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_3) | (~product(e_2, e_3, e_3)) | (~product(e_2, e_2, e_3)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(246,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_3, e_2, e_3) | (~product(e_2, e_2, e_3)) | (~product(e_2, e_3, e_3))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.20/0.49 tff(247,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[246, 87, 221, 180, 240])).
% 0.20/0.49 tff(248,plain,((~product(e_2, e_2, e_3)) | product(e_3, e_2, e_1) | product(e_1, e_2, e_3) | product(e_1, e_2, e_1) | product(e_2, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(249,plain,
% 0.20/0.49 (product(e_1, e_2, e_3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[248, 180, 116, 181, 115])).
% 0.20/0.49 tff(250,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_2, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_2, e_3)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(251,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_2, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_2, e_3)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(252,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_2, e_3))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.20/0.49 tff(253,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[252, 109, 15, 249, 180])).
% 0.20/0.49 tff(254,plain,((~product(e_2, e_2, e_3)) | product(e_3, e_2, e_1) | product(e_1, e_2, e_1) | product(e_2, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(255,plain,
% 0.20/0.49 (~product(e_2, e_2, e_3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[254, 155, 116, 115])).
% 0.20/0.49 tff(256,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_2)) | product(e_2, e_2, e_2) | product(e_2, e_2, e_4) | product(e_2, e_2, e_1) | product(e_2, e_2, 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)) | product(e_2, e_2, e_2) | product(e_2, e_2, e_4) | product(e_2, e_2, e_1) | product(e_2, e_2, e_3))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(257,plain,
% 0.20/0.49 ((product(e_2, e_2, e_4) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_2))) <=> ((~group_element(e_2)) | product(e_2, e_2, e_2) | product(e_2, e_2, e_4) | product(e_2, e_2, e_1) | product(e_2, e_2, e_3))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(258,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_2, e_2, e_4) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2)) | (~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)) | product(e_2, e_2, e_2) | product(e_2, e_2, e_4) | product(e_2, e_2, e_1) | product(e_2, e_2, e_3)))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[257])).
% 0.20/0.49 tff(259,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_2, e_2, e_4) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2)) | (~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)) | product(e_2, e_2, e_2) | product(e_2, e_2, e_4) | product(e_2, e_2, e_1) | product(e_2, e_2, e_3))),
% 0.20/0.49 inference(transitivity,[status(thm)],[258, 256])).
% 0.20/0.49 tff(260,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_2, e_2, e_4) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_2)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(261,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_2)) | product(e_2, e_2, e_2) | product(e_2, e_2, e_4) | product(e_2, e_2, e_1) | product(e_2, e_2, e_3)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.20/0.49 tff(262,plain,
% 0.20/0.49 (product(e_2, e_2, e_2) | product(e_2, e_2, e_4) | product(e_2, e_2, e_1) | product(e_2, e_2, e_3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[261, 130, 64])).
% 0.20/0.49 tff(263,plain,
% 0.20/0.49 (product(e_2, e_2, e_4)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[262, 255, 179, 169])).
% 0.20/0.49 tff(264,assumption,(product(e_2, e_2, e_4)), introduced(assumption)).
% 0.20/0.49 tff(265,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_1, e_2) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_2, e_4)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(266,plain,
% 0.20/0.49 ((equalish(e_1, e_2) | (~product(e_2, e_2, e_4)) | (~product(e_1, e_2, e_4))) <=> (equalish(e_1, e_2) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_2, e_4)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(267,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_1, e_2) | (~product(e_2, e_2, e_4)) | (~product(e_1, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_2) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_2, e_4))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[266])).
% 0.20/0.49 tff(268,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_1, e_2) | (~product(e_2, e_2, e_4)) | (~product(e_1, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_2, e_4)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[267, 265])).
% 0.20/0.49 tff(269,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_1, e_2) | (~product(e_2, e_2, e_4)) | (~product(e_1, e_2, e_4)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(270,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_2, e_4))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.20/0.49 tff(271,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[270, 18, 15, 264, 198])).
% 0.20/0.49 tff(272,plain,((~product(e_1, e_2, e_4)) | (~product(e_2, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(273,plain,
% 0.20/0.49 (~product(e_1, e_2, e_4)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[272, 263])).
% 0.20/0.49 tff(274,assumption,(~product(e_1, e_2, e_4)), introduced(assumption)).
% 0.20/0.49 tff(275,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_4) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_4)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(276,plain,
% 0.20/0.49 ((product(e_2, e_1, e_4) | (~product(e_2, e_2, e_4)) | (~product(e_1, e_2, e_2))) <=> (product(e_2, e_1, e_4) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_4)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(277,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_2, e_2, e_4)) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_4))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[276])).
% 0.20/0.49 tff(278,plain,
% 0.20/0.49 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_2, e_2, e_4)) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_4) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_4)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[277, 275])).
% 0.20/0.49 tff(279,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_2, e_2, e_4)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(280,plain,
% 0.20/0.49 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_4) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_4))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.20/0.49 tff(281,plain,
% 0.20/0.49 (~product(e_1, e_2, e_2)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[280, 87, 127, 264])).
% 0.20/0.49 tff(282,plain,
% 0.20/0.49 (product(e_1, e_2, e_3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[196, 281, 274])).
% 0.20/0.49 tff(283,assumption,(product(e_1, e_2, e_3)), introduced(assumption)).
% 0.20/0.49 tff(284,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_1) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(285,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_1) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(286,plain,
% 0.20/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_3))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.20/0.49 tff(287,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[286, 202, 15, 212, 283])).
% 0.20/0.49 tff(288,plain,((~product(e_3, e_2, e_3)) | (~product(e_1, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(289,plain,
% 0.20/0.49 (~product(e_3, e_2, e_3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[288, 282])).
% 0.20/0.49 tff(290,assumption,(product(e_2, e_3, e_4)), introduced(assumption)).
% 0.20/0.49 tff(291,plain,
% 0.20/0.49 (((~![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_2, e_3, e_4)) | (~product(e_2, 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_3, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_2, e_2, e_4)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(292,plain,
% 0.20/0.50 ((equalish(e_3, e_2) | (~product(e_2, e_2, e_4)) | (~product(e_2, e_3, e_4))) <=> (equalish(e_3, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_2, e_2, e_4)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(293,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_2) | (~product(e_2, e_2, e_4)) | (~product(e_2, 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_2) | (~product(e_2, e_3, e_4)) | (~product(e_2, e_2, e_4))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[292])).
% 0.20/0.50 tff(294,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_2) | (~product(e_2, e_2, e_4)) | (~product(e_2, 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_2) | (~product(e_2, e_3, e_4)) | (~product(e_2, e_2, e_4)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[293, 291])).
% 0.20/0.50 tff(295,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_2) | (~product(e_2, e_2, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(296,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_2, e_2, e_4))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.20/0.50 tff(297,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[296, 215, 106, 264, 290])).
% 0.20/0.50 tff(298,plain,((~product(e_2, e_3, e_4)) | (~product(e_2, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(299,plain,
% 0.20/0.50 (~product(e_2, e_3, e_4)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[298, 264])).
% 0.20/0.50 tff(300,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_2, e_2)) | product(e_2, e_3, e_4) | (~product(e_2, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_2, e_2)) | product(e_2, e_3, e_4) | (~product(e_2, e_2, e_4)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(301,plain,
% 0.20/0.50 ((product(e_2, e_3, e_4) | (~product(e_2, e_2, e_4)) | (~product(e_3, e_2, e_2))) <=> ((~product(e_3, e_2, e_2)) | product(e_2, e_3, e_4) | (~product(e_2, e_2, e_4)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(302,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_4) | (~product(e_2, e_2, e_4)) | (~product(e_3, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_3, e_2, e_2)) | product(e_2, e_3, e_4) | (~product(e_2, e_2, e_4))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[301])).
% 0.20/0.50 tff(303,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_4) | (~product(e_2, e_2, e_4)) | (~product(e_3, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_2, e_2)) | product(e_2, e_3, e_4) | (~product(e_2, e_2, e_4)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[302, 300])).
% 0.20/0.50 tff(304,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_3, e_4) | (~product(e_2, e_2, e_4)) | (~product(e_3, e_2, e_2)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(305,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_3, e_2, e_2)) | product(e_2, e_3, e_4) | (~product(e_2, e_2, e_4))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.20/0.50 tff(306,plain,
% 0.20/0.50 (~product(e_3, e_2, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[305, 87, 264, 299])).
% 0.20/0.50 tff(307,plain,
% 0.20/0.50 (product(e_3, e_2, e_4)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[231, 306, 116, 289])).
% 0.20/0.50 tff(308,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_3, e_2) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_2, e_4)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(309,plain,
% 0.20/0.50 ((equalish(e_3, e_2) | (~product(e_2, e_2, e_4)) | (~product(e_3, e_2, e_4))) <=> (equalish(e_3, e_2) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_2, e_4)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(310,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_3, e_2) | (~product(e_2, e_2, e_4)) | (~product(e_3, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_2, e_4))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[309])).
% 0.20/0.50 tff(311,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_3, e_2) | (~product(e_2, e_2, e_4)) | (~product(e_3, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_2, e_4)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[310, 308])).
% 0.20/0.50 tff(312,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_3, e_2) | (~product(e_2, e_2, e_4)) | (~product(e_3, e_2, e_4)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(313,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_2, e_4)) | (~product(e_2, e_2, e_4))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.20/0.50 tff(314,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[313, 215, 15, 307, 264])).
% 0.20/0.50 tff(315,plain,((~product(e_2, e_2, e_4)) | product(e_3, e_2, e_1) | product(e_1, e_2, e_4) | product(e_1, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(316,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[315, 273, 263, 116, 155])).
% 0.20/0.50 tff(317,plain,(product(e_2, e_1, e_1) | product(e_3, e_2, e_1) | product(e_2, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(318,plain,
% 0.20/0.50 (product(e_2, e_1, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[317, 116, 115])).
% 0.20/0.50 tff(319,plain,
% 0.20/0.50 (~product(e_1, e_1, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[26, 318])).
% 0.20/0.50 tff(320,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(321,plain,
% 0.20/0.50 ((product(e_1, e_1, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_2, e_1))) <=> (product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, 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(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, 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(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, 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(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_2, 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(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_2, e_1, e_1))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[324, 323])).
% 0.20/0.50 tff(326,plain,
% 0.20/0.50 (~product(e_1, e_2, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[325, 87, 319, 318])).
% 0.20/0.50 tff(327,plain,
% 0.20/0.50 (product(e_1, e_1, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[74, 319])).
% 0.20/0.50 tff(328,plain,
% 0.20/0.50 (product(e_1, e_2, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[95, 327, 318])).
% 0.20/0.50 tff(329,assumption,(product(e_1, e_2, e_2)), introduced(assumption)).
% 0.20/0.50 tff(330,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_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, 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_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(331,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_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(332,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.20/0.50 tff(333,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[332, 18, 15, 170, 329])).
% 0.20/0.50 tff(334,plain,((~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(335,plain,
% 0.20/0.50 (~product(e_2, e_2, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[334, 328])).
% 0.20/0.50 tff(336,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_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_2, 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_2, e_1, e_1)) | (~product(e_2, e_2, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(337,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_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_2, e_1)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(338,plain,
% 0.20/0.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_2, e_2, e_1))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[337, 336])).
% 0.20/0.50 tff(339,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[338, 109, 106, 4, 156])).
% 0.20/0.50 tff(340,plain,((~product(e_2, e_2, e_1)) | (~product(e_2, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(341,plain,
% 0.20/0.50 (~product(e_2, e_2, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[340, 318])).
% 0.20/0.50 tff(342,plain,
% 0.20/0.50 (~product(e_2, e_2, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[254, 326, 116, 115])).
% 0.20/0.50 tff(343,plain,
% 0.20/0.50 (product(e_2, e_2, e_4)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[262, 342, 341, 335])).
% 0.20/0.50 tff(344,plain,
% 0.20/0.50 (~product(e_1, e_2, e_4)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[272, 343])).
% 0.20/0.50 tff(345,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[315, 344, 343, 326, 116])).
% 0.20/0.50 tff(346,plain,(product(e_3, e_2, e_1) | product(e_2, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(347,plain,
% 0.20/0.50 (product(e_3, e_2, e_1)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[346, 115])).
% 0.20/0.50 tff(348,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_2, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(349,plain,
% 0.20/0.50 ((product(e_2, e_1, e_1) | (~product(e_3, e_2, e_1)) | (~product(e_1, e_3, e_2))) <=> (product(e_2, e_1, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_2, e_1)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(350,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_3, e_2, e_1)) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_2, e_1))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[349])).
% 0.20/0.50 tff(351,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_3, e_2, e_1)) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_2, e_1)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[350, 348])).
% 0.20/0.50 tff(352,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_3, e_2, e_1)) | (~product(e_1, e_3, e_2)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(353,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_1) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_2, e_1))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[352, 351])).
% 0.20/0.50 tff(354,plain,
% 0.20/0.50 (~product(e_1, e_3, e_2)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[353, 87, 117, 347])).
% 0.20/0.50 tff(355,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_3, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_3, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(356,plain,
% 0.20/0.50 ((product(e_1, e_3, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_2, e_1))) <=> (product(e_1, e_3, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(357,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_3, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_3, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_1, e_2))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[356])).
% 0.20/0.50 tff(358,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_3, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_3, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[357, 355])).
% 0.20/0.50 tff(359,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_3, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_2, e_1)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(360,plain,
% 0.20/0.50 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_3, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_1, e_2))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[359, 358])).
% 0.20/0.50 tff(361,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[360, 87, 138, 347, 354])).
% 0.20/0.50 tff(362,plain,(product(e_2, e_1, e_1) | product(e_2, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(363,plain,
% 0.20/0.50 (product(e_2, e_1, e_3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[362, 114])).
% 0.20/0.50 tff(364,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_3, e_2, e_2) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_2) | (~product(e_1, e_3, e_2)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(365,plain,
% 0.20/0.50 ((product(e_3, e_2, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_3))) <=> ((~product(e_2, e_1, e_3)) | product(e_3, e_2, e_2) | (~product(e_1, e_3, e_2)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(366,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_3, e_2, e_2) | (~product(e_1, e_3, e_2))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[365])).
% 0.20/0.50 tff(367,plain,
% 0.20/0.50 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_2) | (~product(e_1, e_3, e_2)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[366, 364])).
% 0.20/0.51 tff(368,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(369,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_2) | (~product(e_1, e_3, e_2))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[368, 367])).
% 0.20/0.51 tff(370,plain,
% 0.20/0.51 (product(e_3, e_2, e_2) | (~product(e_1, e_3, e_2))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[369, 87, 363])).
% 0.20/0.51 tff(371,plain,
% 0.20/0.51 (product(e_3, e_2, e_2)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[370, 3])).
% 0.20/0.51 tff(372,plain,
% 0.20/0.51 (((~![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_2, e_1, e_3)) | (~product(e_2, 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_2, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_3)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(373,plain,
% 0.20/0.51 ((~![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_2, e_1, e_3)) | (~product(e_2, e_2, e_3)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(374,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_3))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[373, 372])).
% 0.20/0.51 tff(375,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[374, 109, 106, 363, 180])).
% 0.20/0.51 tff(376,plain,(~product(e_2, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(377,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_1, e_2, e_3) | (~product(e_2, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_1, e_2, e_3) | (~product(e_2, e_2, e_1)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(378,plain,
% 0.20/0.51 ((product(e_1, e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_1))) <=> ((~product(e_2, e_1, e_3)) | product(e_1, e_2, e_3) | (~product(e_2, e_2, e_1)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(379,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_1, e_2, e_3) | (~product(e_2, e_2, e_1))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[378])).
% 0.20/0.51 tff(380,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_1, e_2, e_3) | (~product(e_2, e_2, e_1)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[379, 377])).
% 0.20/0.51 tff(381,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_1)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(382,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_1, e_2, e_3) | (~product(e_2, e_2, e_1))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[381, 380])).
% 0.20/0.51 tff(383,plain,
% 0.20/0.51 (~product(e_2, e_2, e_1)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[382, 87, 363, 182])).
% 0.20/0.51 tff(384,assumption,(~product(e_2, e_2, e_1)), introduced(assumption)).
% 0.20/0.51 tff(385,plain,
% 0.20/0.51 (~product(e_2, e_2, e_2)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[334, 329])).
% 0.20/0.51 tff(386,plain,
% 0.20/0.51 (product(e_2, e_2, e_4)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[262, 385, 376, 384])).
% 0.20/0.51 tff(387,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[280, 87, 127, 386, 329])).
% 0.20/0.51 tff(388,plain,((~product(e_1, e_2, e_2)) | product(e_2, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(389,plain,
% 0.20/0.51 (~product(e_1, e_2, e_2)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[388, 383])).
% 0.20/0.51 tff(390,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_1)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(391,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_1)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(392,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_2, e_1))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[391, 390])).
% 0.20/0.51 tff(393,plain,
% 0.20/0.51 (~product(e_1, e_2, e_1)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[392, 87, 54, 363])).
% 0.20/0.51 tff(394,plain,
% 0.20/0.51 (product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[195, 67, 130, 64, 393])).
% 0.20/0.51 tff(395,plain,
% 0.20/0.51 (product(e_1, e_2, e_4)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[394, 389, 182])).
% 0.20/0.51 tff(396,plain,
% 0.20/0.51 (~product(e_2, e_2, e_4)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[272, 395])).
% 0.20/0.51 tff(397,plain,
% 0.20/0.51 (product(e_2, e_2, e_2) | product(e_2, e_2, e_4) | product(e_2, e_2, e_1)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[262, 376])).
% 0.20/0.51 tff(398,plain,
% 0.20/0.51 (product(e_2, e_2, e_2)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[397, 396, 383])).
% 0.20/0.51 tff(399,assumption,(product(e_4, e_2, e_2)), introduced(assumption)).
% 0.20/0.51 tff(400,plain,
% 0.20/0.51 ((~equalish(e_4, e_2)) <=> (~equalish(e_4, e_2))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(401,axiom,(~equalish(e_4, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_2')).
% 0.20/0.51 tff(402,plain,
% 0.20/0.51 (~equalish(e_4, e_2)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[401, 400])).
% 0.20/0.51 tff(403,plain,
% 0.20/0.51 (((~![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_2, e_2, e_2)) | (~product(e_4, e_2, e_2)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(404,plain,
% 0.20/0.51 ((~![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)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(405,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_2, e_2))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[404, 403])).
% 0.20/0.51 tff(406,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[405, 402, 15, 170, 399])).
% 0.20/0.51 tff(407,plain,((~product(e_4, e_2, e_2)) | (~product(e_2, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(408,plain,
% 0.20/0.51 (~product(e_4, e_2, e_2)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[407, 398])).
% 0.20/0.51 tff(409,plain,
% 0.20/0.51 ((~equalish(e_4, e_1)) <=> (~equalish(e_4, e_1))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(410,axiom,(~equalish(e_4, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_1')).
% 0.20/0.51 tff(411,plain,
% 0.20/0.51 (~equalish(e_4, e_1)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[410, 409])).
% 0.20/0.51 tff(412,plain,
% 0.20/0.51 (((~![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_2, e_4)) | (~product(e_4, e_2, e_4)))) <=> ((~![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_2, e_4)) | (~product(e_4, e_2, e_4)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(413,plain,
% 0.20/0.51 ((~![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_2, e_4)) | (~product(e_4, e_2, e_4)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(414,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_2, e_4)) | (~product(e_4, e_2, e_4))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[413, 412])).
% 0.20/0.51 tff(415,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[414, 411, 15, 198, 1])).
% 0.20/0.51 tff(416,plain,((~product(e_4, e_2, e_4)) | (~product(e_1, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(417,plain,
% 0.20/0.51 (~product(e_4, e_2, e_4)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[416, 395])).
% 0.20/0.51 tff(418,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_4) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_4)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(419,plain,
% 0.20/0.51 ((product(e_2, e_1, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_1, e_2))) <=> (product(e_2, e_1, e_4) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_4)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(420,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_4))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[419])).
% 0.20/0.51 tff(421,plain,
% 0.20/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_4) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_4)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[420, 418])).
% 0.20/0.51 tff(422,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_1, e_2)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(423,plain,
% 0.20/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_4) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_4))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[422, 421])).
% 0.20/0.51 tff(424,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[423, 87, 127, 77, 198])).
% 0.20/0.51 tff(425,plain,((~product(e_1, e_2, e_4)) | (~product(e_1, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(426,plain,
% 0.20/0.51 (~product(e_1, e_1, e_2)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[425, 395])).
% 0.20/0.51 tff(427,plain,
% 0.20/0.51 (product(e_1, e_1, e_1)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[74, 426])).
% 0.20/0.51 tff(428,assumption,(product(e_1, e_4, e_1)), introduced(assumption)).
% 0.20/0.51 tff(429,plain,
% 0.20/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(430,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(431,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_4, e_1))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[430, 429])).
% 0.20/0.51 tff(432,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[431, 411, 106, 5, 428])).
% 0.20/0.51 tff(433,plain,((~product(e_1, e_4, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(434,plain,
% 0.20/0.51 (~product(e_1, e_4, e_1)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[433, 427])).
% 0.20/0.51 tff(435,assumption,(product(e_1, e_4, e_4)), introduced(assumption)).
% 0.20/0.51 tff(436,plain,
% 0.20/0.51 (((~![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_1, e_2, e_4)) | (~product(e_1, 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_4, e_2) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_4, e_4)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(437,plain,
% 0.20/0.51 ((~![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_1, e_2, e_4)) | (~product(e_1, e_4, e_4)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(438,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_2) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_4, e_4))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[437, 436])).
% 0.20/0.51 tff(439,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[438, 402, 106, 435, 198])).
% 0.20/0.51 tff(440,plain,((~product(e_1, e_4, e_4)) | (~product(e_1, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(441,plain,
% 0.20/0.51 (~product(e_1, e_4, e_4)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[440, 395])).
% 0.20/0.51 tff(442,plain,
% 0.20/0.51 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(443,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.20/0.51 tff(444,plain,
% 0.20/0.51 (~equalish(e_2, e_3)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[443, 442])).
% 0.20/0.51 tff(445,plain,
% 0.20/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_2, e_2, e_2)) | (~product(e_3, 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_2, e_3) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(446,plain,
% 0.20/0.51 ((equalish(e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2))) <=> (equalish(e_2, e_3) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(447,plain,
% 0.20/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, 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_2, e_3) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[446])).
% 0.20/0.51 tff(448,plain,
% 0.20/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, 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_2, e_3) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[447, 445])).
% 0.20/0.51 tff(449,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(450,plain,
% 0.20/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[449, 448])).
% 0.20/0.51 tff(451,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[450, 444, 15, 234, 170])).
% 0.20/0.51 tff(452,plain,((~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(453,plain,
% 0.20/0.51 (~product(e_3, e_2, e_2)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[452, 398])).
% 0.20/0.51 tff(454,plain,
% 0.20/0.51 (~product(e_1, e_3, e_2)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[370, 453])).
% 0.20/0.51 tff(455,assumption,(product(e_1, e_3, e_4)), introduced(assumption)).
% 0.20/0.51 tff(456,plain,
% 0.20/0.51 (((~![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_1, e_3, e_4)) | (~product(e_1, 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_3, e_2) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_2, e_4)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(457,plain,
% 0.20/0.51 ((equalish(e_3, e_2) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_3, e_4))) <=> (equalish(e_3, e_2) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_2, e_4)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(458,plain,
% 0.20/0.52 (((~![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_1, e_2, e_4)) | (~product(e_1, 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_2) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_2, e_4))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[457])).
% 0.20/0.52 tff(459,plain,
% 0.20/0.52 (((~![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_1, e_2, e_4)) | (~product(e_1, 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_2) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_2, e_4)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[458, 456])).
% 0.20/0.52 tff(460,plain,
% 0.20/0.52 ((~![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_1, e_2, e_4)) | (~product(e_1, e_3, e_4)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(461,plain,
% 0.20/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_2, e_4))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[460, 459])).
% 0.20/0.52 tff(462,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[461, 215, 106, 455, 198])).
% 0.20/0.52 tff(463,plain,((~product(e_1, e_3, e_4)) | (~product(e_1, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(464,plain,
% 0.20/0.52 (~product(e_1, e_3, e_4)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[463, 395])).
% 0.20/0.52 tff(465,assumption,(product(e_1, e_3, e_1)), introduced(assumption)).
% 0.20/0.52 tff(466,plain,
% 0.20/0.52 (((~![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_1, e_1, e_1)) | (~product(e_1, 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_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(467,plain,
% 0.20/0.52 ((~![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_1, e_1, e_1)) | (~product(e_1, e_3, e_1)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(468,plain,
% 0.20/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_3, e_1))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[467, 466])).
% 0.20/0.52 tff(469,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[468, 202, 106, 5, 465])).
% 0.20/0.52 tff(470,plain,((~product(e_1, e_3, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(471,plain,
% 0.20/0.52 (~product(e_1, e_3, e_1)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[470, 427])).
% 0.20/0.52 tff(472,assumption,(~product(e_1, e_3, e_2)), introduced(assumption)).
% 0.20/0.52 tff(473,assumption,(~product(e_1, e_3, e_4)), introduced(assumption)).
% 0.20/0.52 tff(474,assumption,(~product(e_1, e_3, e_1)), introduced(assumption)).
% 0.20/0.52 tff(475,assumption,(~product(e_1, e_3, e_3)), introduced(assumption)).
% 0.20/0.52 tff(476,plain,
% 0.20/0.52 (((~![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_1, e_3, e_3) | product(e_1, e_3, e_4) | product(e_1, e_3, e_1) | product(e_1, e_3, 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_1)) | (~group_element(e_3)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_4) | product(e_1, e_3, e_1) | product(e_1, e_3, e_2))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(477,plain,
% 0.20/0.52 ((product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_1))) <=> ((~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_4) | product(e_1, e_3, e_1) | product(e_1, e_3, e_2))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(478,plain,
% 0.20/0.52 (((~![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_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)) | (~group_element(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_1, e_3, e_3) | product(e_1, e_3, e_4) | product(e_1, e_3, e_1) | product(e_1, e_3, e_2)))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[477])).
% 0.20/0.52 tff(479,plain,
% 0.20/0.52 (((~![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_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)) | (~group_element(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_1, e_3, e_3) | product(e_1, e_3, e_4) | product(e_1, e_3, e_1) | product(e_1, e_3, e_2))),
% 0.20/0.52 inference(transitivity,[status(thm)],[478, 476])).
% 0.20/0.52 tff(480,plain,
% 0.20/0.52 ((~![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_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)) | (~group_element(e_1)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(481,plain,
% 0.20/0.52 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_3) | product(e_1, e_3, e_4) | product(e_1, e_3, e_1) | product(e_1, e_3, e_2)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[480, 479])).
% 0.20/0.52 tff(482,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[481, 67, 224, 64, 475, 474, 473, 472])).
% 0.20/0.52 tff(483,plain,(product(e_1, e_3, e_2) | product(e_1, e_3, e_3) | product(e_1, e_3, e_1) | product(e_1, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(484,plain,
% 0.20/0.52 (product(e_1, e_3, e_3)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[483, 471, 464, 454])).
% 0.20/0.52 tff(485,assumption,(product(e_1, e_4, e_3)), introduced(assumption)).
% 0.20/0.52 tff(486,assumption,(product(e_1, e_3, e_3)), introduced(assumption)).
% 0.20/0.52 tff(487,plain,
% 0.20/0.52 ((~equalish(e_4, e_3)) <=> (~equalish(e_4, e_3))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(488,axiom,(~equalish(e_4, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_4_is_not_e_3')).
% 0.20/0.52 tff(489,plain,
% 0.20/0.52 (~equalish(e_4, e_3)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[488, 487])).
% 0.20/0.52 tff(490,plain,
% 0.20/0.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_4, e_3)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(491,plain,
% 0.20/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_4, e_3)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(492,plain,
% 0.20/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_4, e_3))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[491, 490])).
% 0.20/0.52 tff(493,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[492, 489, 106, 486, 485])).
% 0.20/0.52 tff(494,plain,((~product(e_1, e_4, e_3)) | (~product(e_1, e_3, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(495,plain,
% 0.20/0.52 (~product(e_1, e_4, e_3)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[494, 484])).
% 0.20/0.52 tff(496,plain,
% 0.20/0.52 (group_element(e_4) <=> group_element(e_4)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(497,axiom,(group_element(e_4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_4')).
% 0.20/0.52 tff(498,plain,
% 0.20/0.52 (group_element(e_4)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[497, 496])).
% 0.20/0.52 tff(499,plain,
% 0.20/0.52 (((~![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_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, 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_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(500,plain,
% 0.20/0.52 ((product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_1))) <=> ((~group_element(e_1)) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(501,plain,
% 0.20/0.52 (((~![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_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4)) | (~group_element(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)) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[500])).
% 0.20/0.52 tff(502,plain,
% 0.20/0.52 (((~![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_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4)) | (~group_element(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)) | product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[501, 499])).
% 0.20/0.52 tff(503,plain,
% 0.20/0.52 ((~![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_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_1)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(504,plain,
% 0.20/0.52 ((~![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_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1) | (~group_element(e_4))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[503, 502])).
% 0.20/0.52 tff(505,plain,
% 0.20/0.52 (product(e_1, e_4, e_4) | product(e_1, e_4, e_3) | product(e_1, e_4, e_2) | product(e_1, e_4, e_1)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[504, 67, 498, 64])).
% 0.20/0.52 tff(506,plain,
% 0.20/0.52 (product(e_1, e_4, e_2)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[505, 495, 441, 434])).
% 0.20/0.52 tff(507,assumption,(product(e_4, e_2, e_1)), introduced(assumption)).
% 0.20/0.52 tff(508,assumption,(product(e_1, e_4, e_2)), introduced(assumption)).
% 0.20/0.52 tff(509,plain,
% 0.20/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_1) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_1)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(510,plain,
% 0.20/0.52 ((product(e_2, e_1, e_1) | (~product(e_4, e_2, e_1)) | (~product(e_1, e_4, e_2))) <=> (product(e_2, e_1, e_1) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_1)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(511,plain,
% 0.20/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_4, e_2, e_1)) | (~product(e_1, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_1))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[510])).
% 0.20/0.52 tff(512,plain,
% 0.20/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_4, e_2, e_1)) | (~product(e_1, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_1) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_1)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[511, 509])).
% 0.20/0.52 tff(513,plain,
% 0.20/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_4, e_2, e_1)) | (~product(e_1, e_4, e_2)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(514,plain,
% 0.20/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_1) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_1))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[513, 512])).
% 0.20/0.52 tff(515,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[514, 87, 114, 508, 507])).
% 0.20/0.52 tff(516,plain,((~product(e_4, e_2, e_1)) | (~product(e_1, e_4, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(517,plain,
% 0.20/0.52 (~product(e_4, e_2, e_1)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[516, 506])).
% 0.20/0.52 tff(518,plain,
% 0.20/0.52 (((~![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_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))) <=> ((~![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_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))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(519,plain,
% 0.20/0.52 ((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)) | (~group_element(e_4)) | 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))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(520,plain,
% 0.20/0.52 (((~![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)) | (~group_element(e_4)) | 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)))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[519])).
% 0.20/0.52 tff(521,plain,
% 0.20/0.52 (((~![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)) | (~group_element(e_4)) | 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))),
% 0.20/0.52 inference(transitivity,[status(thm)],[520, 518])).
% 0.20/0.52 tff(522,plain,
% 0.20/0.52 ((~![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)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(523,plain,
% 0.20/0.52 ((~![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_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)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[522, 521])).
% 0.20/0.52 tff(524,plain,
% 0.20/0.52 (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)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[523, 130, 498, 64])).
% 0.20/0.52 tff(525,plain,
% 0.20/0.52 (product(e_4, e_2, e_3)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[524, 517, 417, 408])).
% 0.20/0.52 tff(526,assumption,(product(e_2, e_4, e_3)), introduced(assumption)).
% 0.20/0.52 tff(527,plain,
% 0.20/0.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(528,plain,
% 0.20/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(529,plain,
% 0.20/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[528, 527])).
% 0.20/0.52 tff(530,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[529, 411, 106, 363, 526])).
% 0.20/0.52 tff(531,plain,(~product(e_2, e_4, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(532,plain,
% 0.20/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_2, e_3)) | product(e_2, e_4, e_3) | (~product(e_4, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_2, e_3)) | product(e_2, e_4, e_3) | (~product(e_4, e_4, e_2)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(533,plain,
% 0.20/0.52 ((product(e_2, e_4, e_3) | (~product(e_4, e_2, e_3)) | (~product(e_4, e_4, e_2))) <=> ((~product(e_4, e_2, e_3)) | product(e_2, e_4, e_3) | (~product(e_4, e_4, e_2)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(534,plain,
% 0.20/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_3) | (~product(e_4, e_2, e_3)) | (~product(e_4, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_2, e_3)) | product(e_2, e_4, e_3) | (~product(e_4, e_4, e_2))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[533])).
% 0.20/0.53 tff(535,plain,
% 0.20/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_3) | (~product(e_4, e_2, e_3)) | (~product(e_4, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_2, e_3)) | product(e_2, e_4, e_3) | (~product(e_4, e_4, e_2)))),
% 0.20/0.53 inference(transitivity,[status(thm)],[534, 532])).
% 0.20/0.53 tff(536,plain,
% 0.20/0.53 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_3) | (~product(e_4, e_2, e_3)) | (~product(e_4, e_4, e_2)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(537,plain,
% 0.20/0.53 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_2, e_3)) | product(e_2, e_4, e_3) | (~product(e_4, e_4, e_2))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[536, 535])).
% 0.20/0.53 tff(538,plain,
% 0.20/0.53 (~product(e_4, e_4, e_2)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[537, 87, 531, 525])).
% 0.20/0.53 tff(539,plain,
% 0.20/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_4, e_2)) | (~product(e_4, e_1, e_4)) | product(e_4, e_4, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_1, e_4)) | product(e_4, e_4, e_2))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(540,plain,
% 0.20/0.53 ((product(e_4, e_4, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_1, e_4))) <=> ((~product(e_1, e_4, e_2)) | (~product(e_4, e_1, e_4)) | product(e_4, e_4, e_2))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(541,plain,
% 0.20/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_4, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_4, e_2)) | (~product(e_4, e_1, e_4)) | product(e_4, e_4, e_2)))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[540])).
% 0.20/0.53 tff(542,plain,
% 0.20/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_4, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_1, e_4)) | product(e_4, e_4, e_2))),
% 0.20/0.53 inference(transitivity,[status(thm)],[541, 539])).
% 0.20/0.53 tff(543,plain,
% 0.20/0.53 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_4, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_1, e_4)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(544,plain,
% 0.20/0.53 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_1, e_4)) | product(e_4, e_4, e_2)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[543, 542])).
% 0.20/0.53 tff(545,plain,
% 0.20/0.53 (~product(e_4, e_1, e_4)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[544, 87, 506, 538])).
% 0.20/0.53 tff(546,plain,
% 0.20/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_2, e_4)) | product(e_4, e_1, e_4) | (~product(e_2, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_4)) | product(e_4, e_1, e_4) | (~product(e_2, e_4, e_4)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(547,plain,
% 0.20/0.53 ((product(e_4, e_1, e_4) | (~product(e_2, e_4, e_4)) | (~product(e_1, e_2, e_4))) <=> ((~product(e_1, e_2, e_4)) | product(e_4, e_1, e_4) | (~product(e_2, e_4, e_4)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(548,plain,
% 0.20/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_2, e_4, e_4)) | (~product(e_1, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_2, e_4)) | product(e_4, e_1, e_4) | (~product(e_2, e_4, e_4))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[547])).
% 0.20/0.53 tff(549,plain,
% 0.20/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_2, e_4, e_4)) | (~product(e_1, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_4)) | product(e_4, e_1, e_4) | (~product(e_2, e_4, e_4)))),
% 0.20/0.53 inference(transitivity,[status(thm)],[548, 546])).
% 0.20/0.53 tff(550,plain,
% 0.20/0.53 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_2, e_4, e_4)) | (~product(e_1, e_2, e_4)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(551,plain,
% 0.20/0.53 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_4)) | product(e_4, e_1, e_4) | (~product(e_2, e_4, e_4))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[550, 549])).
% 0.20/0.53 tff(552,plain,
% 0.20/0.53 ((~product(e_1, e_2, e_4)) | product(e_4, e_1, e_4) | (~product(e_2, e_4, e_4))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[551, 87])).
% 0.20/0.53 tff(553,plain,
% 0.20/0.53 (~product(e_2, e_4, e_4)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[552, 545, 395])).
% 0.20/0.53 tff(554,plain,
% 0.20/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_2, e_3) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_4, e_2)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(555,plain,
% 0.20/0.53 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_4, e_2)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(556,plain,
% 0.20/0.53 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_2, e_3) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_4, e_2))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[555, 554])).
% 0.20/0.53 tff(557,plain,
% 0.20/0.53 (~product(e_2, e_4, e_2)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[556, 87, 376, 525])).
% 0.20/0.53 tff(558,plain,
% 0.20/0.53 (((~![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_1) | product(e_2, e_4, e_3) | product(e_2, e_4, e_4) | product(e_2, e_4, 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_1) | product(e_2, e_4, e_3) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(559,plain,
% 0.20/0.53 ((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_1) | product(e_2, e_4, e_3) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(560,plain,
% 0.20/0.53 (((~![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_1) | product(e_2, e_4, e_3) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2)))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[559])).
% 0.20/0.53 tff(561,plain,
% 0.20/0.53 (((~![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_1) | product(e_2, e_4, e_3) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2))),
% 0.20/0.53 inference(transitivity,[status(thm)],[560, 558])).
% 0.20/0.53 tff(562,plain,
% 0.20/0.53 ((~![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)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(563,plain,
% 0.20/0.53 ((~![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_1) | product(e_2, e_4, e_3) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[562, 561])).
% 0.20/0.53 tff(564,plain,
% 0.20/0.53 (product(e_2, e_4, e_1) | product(e_2, e_4, e_3) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[563, 130, 498, 64])).
% 0.20/0.53 tff(565,plain,
% 0.20/0.53 (product(e_2, e_4, e_1) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[564, 531])).
% 0.20/0.53 tff(566,plain,
% 0.20/0.53 (product(e_2, e_4, e_1)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[565, 553, 557])).
% 0.20/0.53 tff(567,assumption,(product(e_2, e_4, e_1)), introduced(assumption)).
% 0.20/0.53 tff(568,assumption,(~product(e_4, e_1, e_4)), introduced(assumption)).
% 0.20/0.53 tff(569,assumption,(~product(e_4, e_1, e_2)), introduced(assumption)).
% 0.20/0.53 tff(570,assumption,(product(e_4, e_1, e_3)), introduced(assumption)).
% 0.20/0.53 tff(571,plain,
% 0.20/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_3) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_3) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_3)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(572,plain,
% 0.20/0.53 ((product(e_1, e_2, e_3) | (~product(e_4, e_1, e_3)) | (~product(e_2, e_4, e_1))) <=> (product(e_1, e_2, e_3) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_3)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(573,plain,
% 0.20/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_3) | (~product(e_4, e_1, e_3)) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_3) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_3))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[572])).
% 0.20/0.53 tff(574,plain,
% 0.20/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_3) | (~product(e_4, e_1, e_3)) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_3) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_3)))),
% 0.20/0.53 inference(transitivity,[status(thm)],[573, 571])).
% 0.20/0.53 tff(575,plain,
% 0.20/0.53 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_3) | (~product(e_4, e_1, e_3)) | (~product(e_2, e_4, e_1)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(576,plain,
% 0.20/0.53 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_3) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_3))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[575, 574])).
% 0.20/0.53 tff(577,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[576, 87, 182, 570, 567])).
% 0.20/0.53 tff(578,plain,((~product(e_4, e_1, e_3)) | product(e_1, e_2, e_3) | (~product(e_2, e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(579,plain,
% 0.20/0.53 (~product(e_4, e_1, e_3)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[578, 567, 182])).
% 0.20/0.53 tff(580,plain,
% 0.20/0.53 (((~![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_4)) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_1) | product(e_4, e_1, 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_1)) | (~group_element(e_4)) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_1) | product(e_4, e_1, e_2))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(581,plain,
% 0.20/0.53 ((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)) | (~group_element(e_4)) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_1) | product(e_4, e_1, e_2))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(582,plain,
% 0.20/0.53 (((~![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)) | (~group_element(e_4)) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_1) | product(e_4, e_1, e_2)))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[581])).
% 0.20/0.53 tff(583,plain,
% 0.20/0.53 (((~![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)) | (~group_element(e_4)) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_1) | product(e_4, e_1, e_2))),
% 0.20/0.53 inference(transitivity,[status(thm)],[582, 580])).
% 0.20/0.53 tff(584,plain,
% 0.20/0.53 ((~![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)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(585,plain,
% 0.20/0.53 ((~![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_4)) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_1) | product(e_4, e_1, e_2)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[584, 583])).
% 0.20/0.53 tff(586,plain,
% 0.20/0.53 (product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_1) | product(e_4, e_1, e_2)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[585, 67, 498, 64])).
% 0.20/0.54 tff(587,plain,
% 0.20/0.54 (product(e_4, e_1, e_1)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[586, 579, 569, 568])).
% 0.20/0.54 tff(588,plain,
% 0.20/0.54 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_1) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_1)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(589,plain,
% 0.20/0.54 ((product(e_1, e_2, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_2, e_4, e_1))) <=> (product(e_1, e_2, e_1) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_1)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(590,plain,
% 0.20/0.54 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_1))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[589])).
% 0.20/0.54 tff(591,plain,
% 0.20/0.54 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_1) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_1)))),
% 0.20/0.54 inference(transitivity,[status(thm)],[590, 588])).
% 0.20/0.54 tff(592,plain,
% 0.20/0.54 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_4, e_1, e_1)) | (~product(e_2, e_4, e_1)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(593,plain,
% 0.20/0.54 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_1) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_1))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[592, 591])).
% 0.20/0.54 tff(594,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[593, 87, 393, 587, 567])).
% 0.20/0.54 tff(595,plain,((~product(e_2, e_4, e_1)) | product(e_4, e_1, e_2) | product(e_4, e_1, e_4) | product(e_1, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(596,plain,
% 0.20/0.54 (product(e_4, e_1, e_2)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[595, 566, 545, 182])).
% 0.20/0.54 tff(597,plain,
% 0.20/0.54 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_1, e_2)) | (~product(e_1, e_2, e_4)) | product(e_2, e_4, e_4))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_1, e_2)) | (~product(e_1, e_2, e_4)) | product(e_2, e_4, e_4))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(598,plain,
% 0.20/0.54 ((product(e_2, e_4, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_4, e_1, e_2))) <=> ((~product(e_4, e_1, e_2)) | (~product(e_1, e_2, e_4)) | product(e_2, e_4, e_4))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(599,plain,
% 0.20/0.54 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_4, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_1, e_2)) | (~product(e_1, e_2, e_4)) | product(e_2, e_4, e_4)))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[598])).
% 0.20/0.54 tff(600,plain,
% 0.20/0.54 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_4, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_1, e_2)) | (~product(e_1, e_2, e_4)) | product(e_2, e_4, e_4))),
% 0.20/0.54 inference(transitivity,[status(thm)],[599, 597])).
% 0.20/0.54 tff(601,plain,
% 0.20/0.54 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_4, e_1, e_2)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(602,plain,
% 0.20/0.54 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_1, e_2)) | (~product(e_1, e_2, e_4)) | product(e_2, e_4, e_4)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[601, 600])).
% 0.20/0.54 tff(603,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[602, 87, 395, 596, 553])).
% 0.20/0.54 tff(604,plain,(product(e_1, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(605,plain,
% 0.20/0.54 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_3)) | product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(606,plain,
% 0.20/0.54 ((product(e_2, e_2, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2))) <=> ((~product(e_1, e_2, e_3)) | product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(607,plain,
% 0.20/0.54 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_2, e_3)) | product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[606])).
% 0.20/0.54 tff(608,plain,
% 0.20/0.54 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_3)) | product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2)))),
% 0.20/0.54 inference(transitivity,[status(thm)],[607, 605])).
% 0.20/0.54 tff(609,plain,
% 0.20/0.54 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(610,plain,
% 0.20/0.54 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_3)) | product(e_2, e_2, e_3) | (~product(e_2, e_1, e_2))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[609, 608])).
% 0.20/0.54 tff(611,plain,
% 0.20/0.54 (~product(e_2, e_1, e_2)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[610, 87, 604, 376])).
% 0.20/0.54 tff(612,plain,
% 0.20/0.54 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(613,plain,
% 0.20/0.54 ((product(e_2, e_1, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_1, e_3, e_2))) <=> (product(e_2, e_1, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(614,plain,
% 0.20/0.54 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_2, e_2))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[613])).
% 0.20/0.54 tff(615,plain,
% 0.20/0.54 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_1, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.20/0.54 inference(transitivity,[status(thm)],[614, 612])).
% 0.20/0.54 tff(616,plain,
% 0.20/0.54 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(617,plain,
% 0.20/0.54 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_2) | (~product(e_1, e_3, e_2)) | (~product(e_3, e_2, e_2))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[616, 615])).
% 0.20/0.54 tff(618,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[617, 87, 611, 371, 3])).
% 0.20/0.54 tff(619,plain,(~product(e_1, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(620,plain,
% 0.20/0.54 (((~![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_1, e_2, e_3)) | (~product(e_1, e_3, e_3)))) <=> ((~![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_1, e_2, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(621,plain,
% 0.20/0.54 ((~![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_1, e_2, e_3)) | (~product(e_1, e_3, e_3)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(622,plain,
% 0.20/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_3))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[621, 620])).
% 0.20/0.54 tff(623,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[622, 215, 106, 283, 486])).
% 0.20/0.54 tff(624,plain,((~product(e_1, e_3, e_3)) | (~product(e_1, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(625,plain,
% 0.20/0.54 (~product(e_1, e_3, e_3)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[624, 604])).
% 0.20/0.54 tff(626,plain,
% 0.20/0.54 (~product(e_1, e_3, e_1)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[470, 5])).
% 0.20/0.54 tff(627,plain,
% 0.20/0.54 (product(e_1, e_3, e_4)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[483, 626, 625, 619])).
% 0.20/0.54 tff(628,plain,
% 0.20/0.54 (((~![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_1, e_2, e_3)) | (~product(e_1, e_4, e_3)))) <=> ((~![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_1, e_2, e_3)) | (~product(e_1, e_4, e_3)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(629,plain,
% 0.20/0.54 ((~![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_1, e_2, e_3)) | (~product(e_1, e_4, e_3)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(630,plain,
% 0.20/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_2) | (~product(e_1, e_2, e_3)) | (~product(e_1, e_4, e_3))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[629, 628])).
% 0.20/0.54 tff(631,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[630, 402, 106, 283, 485])).
% 0.20/0.54 tff(632,plain,((~product(e_1, e_4, e_3)) | (~product(e_1, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(633,plain,
% 0.20/0.54 (~product(e_1, e_4, e_3)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[632, 604])).
% 0.20/0.54 tff(634,plain,
% 0.20/0.54 (~product(e_1, e_4, e_1)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[433, 5])).
% 0.20/0.54 tff(635,plain,
% 0.20/0.54 (product(e_1, e_4, e_4)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[505, 634, 633, 2])).
% 0.20/0.54 tff(636,plain,
% 0.20/0.54 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_1, 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_4, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_4, e_4)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(637,plain,
% 0.20/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_4, e_4)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(638,plain,
% 0.20/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_1, e_3, e_4)) | (~product(e_1, e_4, e_4))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[637, 636])).
% 0.20/0.54 tff(639,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[638, 489, 106, 455, 435])).
% 0.20/0.54 tff(640,plain,((~product(e_1, e_4, e_4)) | (~product(e_1, e_3, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(641,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[640, 635, 627])).
% 0.20/0.54 tff(642,plain,((~product(e_1, e_1, e_1)) | product(e_1, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(643,plain,
% 0.20/0.54 (~product(e_1, e_1, e_1)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[642, 2])).
% 0.20/0.54 tff(644,plain,
% 0.20/0.54 (product(e_1, e_1, e_2)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[74, 643])).
% 0.20/0.54 tff(645,plain,
% 0.20/0.54 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, 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_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_4, e_2)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(646,plain,
% 0.20/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_4, e_2)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(647,plain,
% 0.20/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_4, e_2))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[646, 645])).
% 0.20/0.54 tff(648,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[647, 411, 106, 77, 508])).
% 0.20/0.54 tff(649,plain,((~product(e_1, e_4, e_2)) | (~product(e_1, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(650,plain,
% 0.20/0.54 (~product(e_1, e_4, e_2)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[649, 77])).
% 0.20/0.54 tff(651,plain,
% 0.20/0.54 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_4, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_4, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_4, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_4, e_1, e_1)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(652,plain,
% 0.20/0.54 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_4, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_4, e_1, e_1)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(653,plain,
% 0.20/0.54 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_4, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_4, e_1, e_1))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[652, 651])).
% 0.20/0.54 tff(654,plain,
% 0.20/0.54 (~product(e_4, e_1, e_1)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[653, 87, 77, 650])).
% 0.20/0.54 tff(655,assumption,(product(e_4, e_1, e_2)), introduced(assumption)).
% 0.20/0.54 tff(656,plain,
% 0.20/0.54 (((~![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_2)) | (~product(e_4, 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_4, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_4, e_1, e_2)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(657,plain,
% 0.20/0.54 ((~![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_2)) | (~product(e_4, e_1, e_2)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(658,plain,
% 0.20/0.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_4, e_1, e_2))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[657, 656])).
% 0.20/0.54 tff(659,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[658, 411, 15, 77, 655])).
% 0.20/0.54 tff(660,plain,((~product(e_4, e_1, e_2)) | (~product(e_1, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(661,plain,
% 0.20/0.54 (~product(e_4, e_1, e_2)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[660, 77])).
% 0.20/0.54 tff(662,plain,
% 0.20/0.54 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_1, e_4, e_1)) | (~product(e_4, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_3) | (~product(e_1, e_4, e_1)) | (~product(e_4, e_1, e_3)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(663,plain,
% 0.20/0.54 ((product(e_1, e_1, e_3) | (~product(e_4, e_1, e_3)) | (~product(e_1, e_4, e_1))) <=> (product(e_1, e_1, e_3) | (~product(e_1, e_4, e_1)) | (~product(e_4, e_1, e_3)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(664,plain,
% 0.20/0.54 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_4, e_1, e_3)) | (~product(e_1, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_1, e_4, e_1)) | (~product(e_4, e_1, e_3))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[663])).
% 0.20/0.55 tff(665,plain,
% 0.20/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_4, e_1, e_3)) | (~product(e_1, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_3) | (~product(e_1, e_4, e_1)) | (~product(e_4, e_1, e_3)))),
% 0.20/0.55 inference(transitivity,[status(thm)],[664, 662])).
% 0.20/0.55 tff(666,plain,
% 0.20/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_3) | (~product(e_4, e_1, e_3)) | (~product(e_1, e_4, e_1)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(667,plain,
% 0.20/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_3) | (~product(e_1, e_4, e_1)) | (~product(e_4, e_1, e_3))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[666, 665])).
% 0.20/0.55 tff(668,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[667, 87, 54, 428, 570])).
% 0.20/0.55 tff(669,plain,((~product(e_4, e_1, e_3)) | (~product(e_1, e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(670,plain,
% 0.20/0.55 (~product(e_4, e_1, e_3)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[669, 428])).
% 0.20/0.55 tff(671,assumption,(~product(e_4, e_1, e_1)), introduced(assumption)).
% 0.20/0.55 tff(672,plain,
% 0.20/0.55 (product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[585, 67, 498, 64, 671])).
% 0.20/0.55 tff(673,plain,
% 0.20/0.55 (product(e_4, e_1, e_4)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[672, 670, 569])).
% 0.20/0.55 tff(674,plain,
% 0.20/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_1, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_1, e_4, e_1)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(675,plain,
% 0.20/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_1, e_4, e_1)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(676,plain,
% 0.20/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_1, e_4, e_1))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[675, 674])).
% 0.20/0.55 tff(677,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[676, 87, 47, 428, 673])).
% 0.20/0.55 tff(678,plain,((~product(e_1, e_4, e_1)) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(679,plain,
% 0.20/0.55 (~product(e_1, e_4, e_1)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[678, 661, 654])).
% 0.20/0.55 tff(680,plain,
% 0.20/0.55 (~product(e_1, e_2, e_4)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[425, 77])).
% 0.20/0.55 tff(681,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[112, 109, 106, 77, 329])).
% 0.20/0.55 tff(682,plain,((~product(e_1, e_2, e_2)) | (~product(e_1, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(683,plain,
% 0.20/0.55 (~product(e_1, e_2, e_2)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[682, 77])).
% 0.20/0.55 tff(684,plain,
% 0.20/0.55 (product(e_1, e_2, e_3)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[394, 683, 680])).
% 0.20/0.55 tff(685,plain,
% 0.20/0.55 (~product(e_1, e_4, e_3)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[632, 684])).
% 0.20/0.55 tff(686,plain,
% 0.20/0.55 (product(e_1, e_4, e_4)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[505, 685, 650, 679])).
% 0.20/0.55 tff(687,plain,
% 0.20/0.55 (~product(e_1, e_3, e_4)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[640, 686])).
% 0.20/0.55 tff(688,plain,
% 0.20/0.55 (~product(e_1, e_3, e_3)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[624, 684])).
% 0.20/0.55 tff(689,plain,
% 0.20/0.55 (product(e_1, e_3, e_2)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[483, 688, 474, 687])).
% 0.20/0.55 tff(690,plain,
% 0.20/0.55 (((~![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_1, e_1, e_2)) | (~product(e_1, 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_1, e_1, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(691,plain,
% 0.20/0.55 ((~![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_1, e_1, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(692,plain,
% 0.20/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_3, e_2))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[691, 690])).
% 0.20/0.55 tff(693,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[692, 202, 106, 77, 689])).
% 0.20/0.55 tff(694,plain,((~product(e_1, e_1, e_2)) | product(e_1, e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(695,plain,
% 0.20/0.55 (product(e_1, e_3, e_1)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[694, 644])).
% 0.20/0.55 tff(696,assumption,(product(e_2, e_1, e_3)), introduced(assumption)).
% 0.20/0.55 tff(697,plain,
% 0.20/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_3, e_2, e_1) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_1) | (~product(e_1, e_3, e_1)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(698,plain,
% 0.20/0.55 ((product(e_3, e_2, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_2, e_1, e_3))) <=> ((~product(e_2, e_1, e_3)) | product(e_3, e_2, e_1) | (~product(e_1, e_3, e_1)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(699,plain,
% 0.20/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_3, e_2, e_1) | (~product(e_1, e_3, e_1))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[698])).
% 0.20/0.55 tff(700,plain,
% 0.20/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_1) | (~product(e_1, e_3, e_1)))),
% 0.20/0.55 inference(transitivity,[status(thm)],[699, 697])).
% 0.20/0.55 tff(701,plain,
% 0.20/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_1) | (~product(e_1, e_3, e_1)) | (~product(e_2, e_1, e_3)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(702,plain,
% 0.20/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_1) | (~product(e_1, e_3, e_1))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[701, 700])).
% 0.20/0.55 tff(703,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[702, 87, 696, 116, 465])).
% 0.20/0.55 tff(704,plain,((~product(e_1, e_3, e_1)) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(705,plain,
% 0.20/0.55 ((~product(e_1, e_3, e_1)) | product(e_3, e_2, e_1)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[704, 363])).
% 0.20/0.55 tff(706,plain,
% 0.20/0.55 (product(e_3, e_2, e_1)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[705, 695])).
% 0.20/0.55 tff(707,assumption,(product(e_3, e_2, e_1)), introduced(assumption)).
% 0.20/0.55 tff(708,plain,
% 0.20/0.55 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_2, e_1)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(709,plain,
% 0.20/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_2, e_1)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(710,plain,
% 0.20/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_2, e_1))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[709, 708])).
% 0.20/0.55 tff(711,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[710, 444, 15, 707, 156])).
% 0.20/0.55 tff(712,plain,((~product(e_2, e_2, e_1)) | (~product(e_3, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(713,plain,
% 0.20/0.55 (~product(e_2, e_2, e_1)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[712, 706])).
% 0.20/0.55 tff(714,plain,
% 0.20/0.55 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_4, e_1)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(715,plain,
% 0.20/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_4, e_1)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(716,plain,
% 0.20/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_1, e_3, e_1)) | (~product(e_1, e_4, e_1))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[715, 714])).
% 0.20/0.55 tff(717,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[716, 489, 106, 465, 428])).
% 0.20/0.55 tff(718,plain,((~product(e_1, e_4, e_1)) | (~product(e_1, e_3, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(719,plain,
% 0.20/0.55 (~product(e_1, e_4, e_1)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[718, 695])).
% 0.20/0.55 tff(720,plain,
% 0.20/0.55 (product(e_1, e_4, e_4)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[505, 719, 633, 2])).
% 0.20/0.55 tff(721,assumption,(product(e_2, e_4, e_4)), introduced(assumption)).
% 0.20/0.55 tff(722,plain,
% 0.20/0.55 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_4, e_4)) | (~product(e_2, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_4, e_4)) | (~product(e_2, e_4, e_4)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(723,plain,
% 0.20/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_4, e_4)) | (~product(e_2, e_4, e_4)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(724,plain,
% 0.20/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_4, e_4)) | (~product(e_2, e_4, e_4))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[723, 722])).
% 0.20/0.55 tff(725,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[724, 109, 15, 435, 721])).
% 0.20/0.55 tff(726,plain,((~product(e_2, e_4, e_4)) | (~product(e_1, e_4, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(727,plain,
% 0.20/0.55 (~product(e_2, e_4, e_4)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[726, 720])).
% 0.20/0.55 tff(728,plain,
% 0.20/0.55 (~product(e_1, e_2, e_4)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[425, 644])).
% 0.20/0.55 tff(729,plain,
% 0.20/0.55 (((~![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_1, e_3)) | (~product(e_4, e_1, 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_2) | (~product(e_2, e_1, e_3)) | (~product(e_4, e_1, e_3)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(730,plain,
% 0.20/0.55 ((~![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_1, e_3)) | (~product(e_4, e_1, e_3)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(731,plain,
% 0.20/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_4, e_1, e_3))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[730, 729])).
% 0.20/0.55 tff(732,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[731, 402, 15, 363, 570])).
% 0.20/0.55 tff(733,plain,(~product(e_4, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(734,plain,
% 0.20/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_2, e_3)) | (~product(e_4, e_1, e_2)) | product(e_2, e_4, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_3)) | (~product(e_4, e_1, e_2)) | product(e_2, e_4, e_3))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(735,plain,
% 0.20/0.55 ((product(e_2, e_4, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_4, e_1, e_2))) <=> ((~product(e_1, e_2, e_3)) | (~product(e_4, e_1, e_2)) | product(e_2, e_4, e_3))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(736,plain,
% 0.20/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_4, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_2, e_3)) | (~product(e_4, e_1, e_2)) | product(e_2, e_4, e_3)))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[735])).
% 0.20/0.55 tff(737,plain,
% 0.20/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_4, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_3)) | (~product(e_4, e_1, e_2)) | product(e_2, e_4, e_3))),
% 0.20/0.55 inference(transitivity,[status(thm)],[736, 734])).
% 0.20/0.55 tff(738,plain,
% 0.20/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_4, e_1, e_2)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(739,plain,
% 0.20/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_2, e_3)) | (~product(e_4, e_1, e_2)) | product(e_2, e_4, e_3)),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[738, 737])).
% 0.20/0.55 tff(740,plain,
% 0.20/0.55 (~product(e_4, e_1, e_2)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[739, 87, 604, 531])).
% 0.20/0.55 tff(741,assumption,(product(e_4, e_1, e_4)), introduced(assumption)).
% 0.20/0.55 tff(742,plain,
% 0.20/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_4) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_4) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_4)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(743,plain,
% 0.20/0.55 ((product(e_1, e_2, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_2, e_4, e_1))) <=> (product(e_1, e_2, e_4) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_4)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(744,plain,
% 0.20/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_4) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_4))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[743])).
% 0.20/0.55 tff(745,plain,
% 0.20/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_4) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_4)))),
% 0.20/0.55 inference(transitivity,[status(thm)],[744, 742])).
% 0.20/0.55 tff(746,plain,
% 0.20/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_2, e_4, e_1)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(747,plain,
% 0.20/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_2, e_4) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_4))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[746, 745])).
% 0.20/0.55 tff(748,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[747, 87, 274, 567, 741])).
% 0.20/0.55 tff(749,plain,((~product(e_4, e_1, e_4)) | product(e_1, e_2, e_4) | (~product(e_2, e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(750,plain,
% 0.20/0.55 (~product(e_4, e_1, e_4)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[749, 567, 274])).
% 0.20/0.55 tff(751,plain,
% 0.20/0.55 (product(e_4, e_1, e_1)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[586, 750, 740, 733])).
% 0.20/0.55 tff(752,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[593, 87, 393, 751, 567])).
% 0.20/0.55 tff(753,plain,((~product(e_2, e_4, e_1)) | product(e_1, e_2, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(754,plain,
% 0.20/0.55 (~product(e_2, e_4, e_1)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[753, 728])).
% 0.20/0.55 tff(755,plain,
% 0.20/0.55 (product(e_2, e_4, e_2)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[565, 754, 727])).
% 0.20/0.56 tff(756,assumption,(product(e_2, e_4, e_2)), introduced(assumption)).
% 0.20/0.56 tff(757,plain,
% 0.20/0.56 (((~![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_2, e_2)) | (~product(e_2, e_4, e_2)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(758,plain,
% 0.20/0.56 ((~![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)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(759,plain,
% 0.20/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[758, 757])).
% 0.20/0.56 tff(760,plain,
% 0.20/0.56 ($false),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[759, 402, 106, 170, 756])).
% 0.20/0.56 tff(761,plain,((~product(e_2, e_4, e_2)) | (~product(e_2, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.56 tff(762,plain,
% 0.20/0.56 (~product(e_2, e_2, e_2)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[761, 755])).
% 0.20/0.56 tff(763,assumption,(~product(e_2, e_4, e_4)), introduced(assumption)).
% 0.20/0.56 tff(764,plain,
% 0.20/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_2, e_4)) | product(e_2, e_4, e_4) | (~product(e_4, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_2, e_4)) | product(e_2, e_4, e_4) | (~product(e_4, e_2, e_2)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(765,plain,
% 0.20/0.56 ((product(e_2, e_4, e_4) | (~product(e_2, e_2, e_4)) | (~product(e_4, e_2, e_2))) <=> ((~product(e_2, e_2, e_4)) | product(e_2, e_4, e_4) | (~product(e_4, e_2, e_2)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(766,plain,
% 0.20/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_4) | (~product(e_2, e_2, e_4)) | (~product(e_4, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_2, e_4)) | product(e_2, e_4, e_4) | (~product(e_4, e_2, e_2))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[765])).
% 0.20/0.56 tff(767,plain,
% 0.20/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_4) | (~product(e_2, e_2, e_4)) | (~product(e_4, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_2, e_4)) | product(e_2, e_4, e_4) | (~product(e_4, e_2, e_2)))),
% 0.20/0.56 inference(transitivity,[status(thm)],[766, 764])).
% 0.20/0.56 tff(768,plain,
% 0.20/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_4) | (~product(e_2, e_2, e_4)) | (~product(e_4, e_2, e_2)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(769,plain,
% 0.20/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_2, e_4)) | product(e_2, e_4, e_4) | (~product(e_4, e_2, e_2))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[768, 767])).
% 0.20/0.56 tff(770,plain,
% 0.20/0.56 (~product(e_4, e_2, e_2)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[769, 87, 264, 763])).
% 0.20/0.56 tff(771,plain,
% 0.20/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_2, e_4)) | product(e_4, e_2, e_2) | (~product(e_2, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_2, e_4)) | product(e_4, e_2, e_2) | (~product(e_2, e_4, e_2)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(772,plain,
% 0.20/0.56 ((product(e_4, e_2, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_2, e_2, e_4))) <=> ((~product(e_2, e_2, e_4)) | product(e_4, e_2, e_2) | (~product(e_2, e_4, e_2)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(773,plain,
% 0.20/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_2, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_2, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_2, e_4)) | product(e_4, e_2, e_2) | (~product(e_2, e_4, e_2))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[772])).
% 0.20/0.56 tff(774,plain,
% 0.20/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_2, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_2, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_2, e_4)) | product(e_4, e_2, e_2) | (~product(e_2, e_4, e_2)))),
% 0.20/0.56 inference(transitivity,[status(thm)],[773, 771])).
% 0.20/0.56 tff(775,plain,
% 0.20/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_2, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_2, e_2, e_4)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(776,plain,
% 0.20/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_2, e_4)) | product(e_4, e_2, e_2) | (~product(e_2, e_4, e_2))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[775, 774])).
% 0.20/0.56 tff(777,plain,
% 0.20/0.56 ($false),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[776, 87, 264, 756, 770])).
% 0.20/0.56 tff(778,plain,((~product(e_2, e_2, e_4)) | (~product(e_2, e_4, e_2)) | product(e_2, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.56 tff(779,plain,
% 0.20/0.56 (~product(e_2, e_2, e_4)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[778, 755, 727])).
% 0.20/0.56 tff(780,plain,
% 0.20/0.56 ($false),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[397, 779, 762, 713])).
% 0.20/0.56 tff(781,plain,(product(e_1, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.56 tff(782,plain,
% 0.20/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_4) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_4)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(783,plain,
% 0.20/0.56 ((product(e_2, e_1, e_4) | (~product(e_4, e_2, e_4)) | (~product(e_1, e_4, e_2))) <=> (product(e_2, e_1, e_4) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_4)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(784,plain,
% 0.20/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_4, e_2, e_4)) | (~product(e_1, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_4))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[783])).
% 0.20/0.56 tff(785,plain,
% 0.20/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_4, e_2, e_4)) | (~product(e_1, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_4) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_4)))),
% 0.20/0.56 inference(transitivity,[status(thm)],[784, 782])).
% 0.20/0.56 tff(786,plain,
% 0.20/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_4, e_2, e_4)) | (~product(e_1, e_4, e_2)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(787,plain,
% 0.20/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_4) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_4))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[786, 785])).
% 0.20/0.56 tff(788,plain,
% 0.20/0.56 ($false),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[787, 87, 127, 781, 1])).
% 0.20/0.56 tff(789,plain,(~product(e_4, e_2, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.56 tff(790,assumption,(product(e_4, e_2, e_3)), introduced(assumption)).
% 0.20/0.56 tff(791,plain,
% 0.20/0.56 (((~![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_2, e_3)) | (~product(e_4, e_2, 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_1) | (~product(e_1, e_2, e_3)) | (~product(e_4, e_2, e_3)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(792,plain,
% 0.20/0.56 ((~![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_2, e_3)) | (~product(e_4, e_2, e_3)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(793,plain,
% 0.20/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_4, e_2, e_3))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[792, 791])).
% 0.20/0.56 tff(794,plain,
% 0.20/0.56 ($false),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[793, 411, 15, 604, 790])).
% 0.20/0.56 tff(795,plain,(~product(e_4, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.56 tff(796,plain,
% 0.20/0.56 (~product(e_4, e_2, e_1)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[516, 781])).
% 0.20/0.56 tff(797,plain,
% 0.20/0.56 (product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[524, 796])).
% 0.20/0.56 tff(798,plain,
% 0.20/0.56 (product(e_4, e_2, e_2)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[797, 795, 789])).
% 0.20/0.56 tff(799,plain,
% 0.20/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_2)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(800,plain,
% 0.20/0.56 ((product(e_2, e_1, e_2) | (~product(e_4, e_2, e_2)) | (~product(e_1, e_4, e_2))) <=> (product(e_2, e_1, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_2)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(801,plain,
% 0.20/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_4, e_2, e_2)) | (~product(e_1, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_2))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[800])).
% 0.20/0.56 tff(802,plain,
% 0.20/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_4, e_2, e_2)) | (~product(e_1, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_2)))),
% 0.20/0.56 inference(transitivity,[status(thm)],[801, 799])).
% 0.20/0.56 tff(803,plain,
% 0.20/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_4, e_2, e_2)) | (~product(e_1, e_4, e_2)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(804,plain,
% 0.20/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_2) | (~product(e_1, e_4, e_2)) | (~product(e_4, e_2, e_2))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[803, 802])).
% 0.20/0.56 tff(805,plain,
% 0.20/0.56 ($false),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[804, 87, 611, 781, 798])).
% 0.20/0.56 % SZS output end Proof
% 0.20/0.56 % E exiting
%------------------------------------------------------------------------------