%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP128-2.006 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:07:09 AM UTC 2025
% Result : Unsatisfiable 0.41s 0.61s
% Output : Proof 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP128-2.006 : TPTP v9.0.0. Released v1.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n011.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 15:43:41 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.41/0.61 % SZS status Unsatisfiable
% 0.41/0.61 % SZS output start Proof
% 0.41/0.61 tff(product_type, type, (
% 0.41/0.61 product: ( $i * $i * $i ) > $o)).
% 0.41/0.61 tff(e_2_type, type, (
% 0.41/0.61 e_2: $i)).
% 0.41/0.61 tff(e_1_type, type, (
% 0.41/0.61 e_1: $i)).
% 0.41/0.61 tff(e_6_type, type, (
% 0.41/0.61 e_6: $i)).
% 0.41/0.61 tff(e_5_type, type, (
% 0.41/0.61 e_5: $i)).
% 0.41/0.61 tff(e_3_type, type, (
% 0.41/0.61 e_3: $i)).
% 0.41/0.61 tff(e_4_type, type, (
% 0.41/0.61 e_4: $i)).
% 0.41/0.61 tff(equalish_type, type, (
% 0.41/0.61 equalish: ( $i * $i ) > $o)).
% 0.41/0.61 tff(next_type, type, (
% 0.41/0.61 next: ( $i * $i ) > $o)).
% 0.41/0.61 tff(greater_type, type, (
% 0.41/0.61 greater: ( $i * $i ) > $o)).
% 0.41/0.61 tff(group_element_type, type, (
% 0.41/0.61 group_element: $i > $o)).
% 0.41/0.61 tff(1,assumption,(product(e_6, e_1, e_2)), introduced(assumption)).
% 0.41/0.61 tff(2,assumption,(product(e_4, e_1, e_2)), introduced(assumption)).
% 0.41/0.61 tff(3,plain,
% 0.41/0.61 (^[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))))),
% 0.41/0.61 inference(bind,[status(th)],[])).
% 0.41/0.61 tff(4,plain,
% 0.41/0.61 (![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)))),
% 0.41/0.61 inference(quant_intro,[status(thm)],[3])).
% 0.41/0.61 tff(5,plain,
% 0.41/0.61 (![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)))),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(6,plain,
% 0.41/0.61 (^[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)))))),
% 0.41/0.61 inference(bind,[status(th)],[])).
% 0.41/0.61 tff(7,plain,
% 0.41/0.61 (![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)))),
% 0.41/0.61 inference(quant_intro,[status(thm)],[6])).
% 0.41/0.61 tff(8,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_left_cancellation')).
% 0.41/0.61 tff(9,plain,
% 0.41/0.61 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.41/0.61 tff(10,plain,
% 0.41/0.61 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.41/0.61 tff(11,plain,(
% 0.41/0.61 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.41/0.61 inference(skolemize,[status(sab)],[10])).
% 0.41/0.61 tff(12,plain,
% 0.41/0.61 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.41/0.61 tff(13,plain,
% 0.41/0.61 ((~equalish(e_6, e_4)) <=> (~equalish(e_6, e_4))),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(14,axiom,(~equalish(e_6, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_6_is_not_e_4')).
% 0.41/0.61 tff(15,plain,
% 0.41/0.61 (~equalish(e_6, e_4)),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.41/0.61 tff(16,plain,
% 0.41/0.61 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_4) | (~product(e_4, e_1, e_2)) | (~product(e_6, 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_6, e_4) | (~product(e_4, e_1, e_2)) | (~product(e_6, e_1, e_2)))),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(17,plain,
% 0.41/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_4) | (~product(e_4, e_1, e_2)) | (~product(e_6, e_1, e_2)))),
% 0.41/0.61 inference(quant_inst,[status(thm)],[])).
% 0.41/0.61 tff(18,plain,
% 0.41/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_4) | (~product(e_4, e_1, e_2)) | (~product(e_6, e_1, e_2))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.41/0.61 tff(19,plain,
% 0.41/0.61 ($false),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[18, 15, 12, 2, 1])).
% 0.41/0.61 tff(20,plain,((~product(e_6, e_1, e_2)) | (~product(e_4, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.41/0.61 tff(21,plain,
% 0.41/0.61 (~product(e_4, e_1, e_2)),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[20, 1])).
% 0.41/0.61 tff(22,assumption,(~product(e_4, e_1, e_5)), introduced(assumption)).
% 0.41/0.61 tff(23,assumption,(~product(e_4, e_1, e_2)), introduced(assumption)).
% 0.41/0.61 tff(24,assumption,(product(e_4, e_1, e_1)), introduced(assumption)).
% 0.41/0.61 tff(25,assumption,(product(e_1, e_1, e_1)), introduced(assumption)).
% 0.41/0.61 tff(26,plain,
% 0.41/0.61 ((~equalish(e_4, e_1)) <=> (~equalish(e_4, e_1))),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(27,axiom,(~equalish(e_4, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_is_not_e_1')).
% 0.41/0.61 tff(28,plain,
% 0.41/0.61 (~equalish(e_4, e_1)),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.41/0.61 tff(29,plain,
% 0.41/0.61 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1)))),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(30,plain,
% 0.41/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1)))),
% 0.41/0.61 inference(quant_inst,[status(thm)],[])).
% 0.41/0.61 tff(31,plain,
% 0.41/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.41/0.61 tff(32,plain,
% 0.41/0.61 ($false),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[31, 28, 12, 25, 24])).
% 0.41/0.61 tff(33,plain,((~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.41/0.61 tff(34,plain,
% 0.41/0.61 (~product(e_1, e_1, e_1)),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[33, 24])).
% 0.41/0.61 tff(35,plain,
% 0.41/0.61 (^[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))))),
% 0.41/0.61 inference(bind,[status(th)],[])).
% 0.41/0.61 tff(36,plain,
% 0.41/0.61 (![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)))),
% 0.41/0.61 inference(quant_intro,[status(thm)],[35])).
% 0.41/0.61 tff(37,plain,
% 0.41/0.61 (![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)))),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(38,plain,
% 0.41/0.61 (^[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)))))),
% 0.41/0.61 inference(bind,[status(th)],[])).
% 0.41/0.61 tff(39,plain,
% 0.41/0.61 (![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)))),
% 0.41/0.61 inference(quant_intro,[status(thm)],[38])).
% 0.41/0.61 tff(40,axiom,(![Y: $i, X: $i, X1: $i] : (((~product(X, e_1, Y)) | (~next(X, X1))) | (~greater(Y, X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','no_redundancy')).
% 0.41/0.61 tff(41,plain,
% 0.41/0.61 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.41/0.61 tff(42,plain,
% 0.41/0.61 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.41/0.61 tff(43,plain,(
% 0.41/0.61 ![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.41/0.61 inference(skolemize,[status(sab)],[42])).
% 0.41/0.61 tff(44,plain,
% 0.41/0.61 (![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.41/0.61 tff(45,plain,
% 0.41/0.61 (greater(e_6, e_2) <=> greater(e_6, e_2)),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(46,axiom,(greater(e_6, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_6_greater_e_2')).
% 0.41/0.61 tff(47,plain,
% 0.41/0.61 (greater(e_6, e_2)),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.41/0.61 tff(48,plain,
% 0.41/0.61 (next(e_1, e_2) <=> next(e_1, e_2)),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(49,axiom,(next(e_1, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_then_e_2')).
% 0.41/0.61 tff(50,plain,
% 0.41/0.61 (next(e_1, e_2)),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.41/0.61 tff(51,plain,
% 0.41/0.61 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_6, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_6)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_6, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_6)))),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(52,plain,
% 0.41/0.61 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_6, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_6)))),
% 0.41/0.61 inference(quant_inst,[status(thm)],[])).
% 0.41/0.61 tff(53,plain,
% 0.41/0.61 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_6, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_6))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.41/0.61 tff(54,plain,
% 0.41/0.61 (~product(e_1, e_1, e_6)),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[53, 50, 47, 44])).
% 0.41/0.61 tff(55,plain,
% 0.41/0.61 (greater(e_5, e_2) <=> greater(e_5, e_2)),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(56,axiom,(greater(e_5, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_5_greater_e_2')).
% 0.41/0.61 tff(57,plain,
% 0.41/0.61 (greater(e_5, e_2)),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.41/0.61 tff(58,plain,
% 0.41/0.61 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_5, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_5)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_5, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_5)))),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(59,plain,
% 0.41/0.61 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_5, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_5)))),
% 0.41/0.61 inference(quant_inst,[status(thm)],[])).
% 0.41/0.61 tff(60,plain,
% 0.41/0.61 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_5, e_2)) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_5))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.41/0.61 tff(61,plain,
% 0.41/0.61 (~product(e_1, e_1, e_5)),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[60, 50, 57, 44])).
% 0.41/0.61 tff(62,plain,
% 0.41/0.61 (greater(e_4, e_2) <=> greater(e_4, e_2)),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(63,axiom,(greater(e_4, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_greater_e_2')).
% 0.41/0.61 tff(64,plain,
% 0.41/0.61 (greater(e_4, e_2)),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.41/0.61 tff(65,plain,
% 0.41/0.61 (((~![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)))),
% 0.41/0.62 inference(rewrite,[status(thm)],[])).
% 0.41/0.62 tff(66,plain,
% 0.41/0.62 ((~![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)))),
% 0.41/0.62 inference(quant_inst,[status(thm)],[])).
% 0.41/0.62 tff(67,plain,
% 0.41/0.62 ((~![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))),
% 0.41/0.62 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.41/0.62 tff(68,plain,
% 0.41/0.62 (~product(e_1, e_1, e_4)),
% 0.41/0.62 inference(unit_resolution,[status(thm)],[67, 50, 64, 44])).
% 0.41/0.62 tff(69,plain,
% 0.41/0.62 (greater(e_3, e_2) <=> greater(e_3, e_2)),
% 0.41/0.62 inference(rewrite,[status(thm)],[])).
% 0.41/0.62 tff(70,axiom,(greater(e_3, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_greater_e_2')).
% 0.41/0.62 tff(71,plain,
% 0.41/0.62 (greater(e_3, e_2)),
% 0.41/0.62 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.41/0.62 tff(72,plain,
% 0.41/0.62 (((~![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)))),
% 0.41/0.62 inference(rewrite,[status(thm)],[])).
% 0.41/0.62 tff(73,plain,
% 0.41/0.62 ((~![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)))),
% 0.41/0.62 inference(quant_inst,[status(thm)],[])).
% 0.41/0.62 tff(74,plain,
% 0.41/0.62 ((~![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))),
% 0.41/0.62 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.41/0.62 tff(75,plain,
% 0.41/0.62 (~product(e_1, e_1, e_3)),
% 0.41/0.62 inference(unit_resolution,[status(thm)],[74, 50, 71, 44])).
% 0.41/0.62 tff(76,plain,
% 0.41/0.62 (^[Y: $i, X: $i] : refl((product(X, Y, e_6) | product(X, Y, e_5) | 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_6) | product(X, Y, e_5) | 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))))),
% 0.41/0.62 inference(bind,[status(th)],[])).
% 0.41/0.62 tff(77,plain,
% 0.41/0.62 (![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6) | product(X, Y, e_5) | 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)))),
% 0.41/0.62 inference(quant_intro,[status(thm)],[76])).
% 0.41/0.62 tff(78,plain,
% 0.41/0.62 (![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6) | product(X, Y, e_5) | 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)))),
% 0.41/0.62 inference(rewrite,[status(thm)],[])).
% 0.41/0.62 tff(79,plain,
% 0.41/0.62 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(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))))), ((((((((~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_5)) <=> ((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_5)))), rewrite(((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_5)) <=> (product(X, Y, e_5) | 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_5)) <=> (product(X, Y, e_5) | 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_5)) | product(X, Y, e_6)) <=> ((product(X, Y, e_5) | 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_6)))), rewrite(((product(X, Y, e_5) | 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_6)) <=> (product(X, Y, e_6) | product(X, Y, e_5) | 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_5)) | product(X, Y, e_6)) <=> (product(X, Y, e_6) | product(X, Y, e_5) | 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)))))),
% 0.41/0.62 inference(bind,[status(th)],[])).
% 0.41/0.62 tff(80,plain,
% 0.41/0.62 (![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)) | product(X, Y, e_5)) | product(X, Y, e_6)) <=> ![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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)))),
% 0.41/0.62 inference(quant_intro,[status(thm)],[79])).
% 0.41/0.62 tff(81,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)) | product(X, Y, e_5)) | product(X, Y, e_6))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_total_function1')).
% 0.41/0.62 tff(82,plain,
% 0.41/0.62 (![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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)))),
% 0.41/0.62 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.41/0.62 tff(83,plain,
% 0.41/0.62 (![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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)))),
% 0.41/0.62 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.41/0.62 tff(84,plain,(
% 0.41/0.62 ![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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)))),
% 0.41/0.62 inference(skolemize,[status(sab)],[83])).
% 0.41/0.62 tff(85,plain,
% 0.41/0.62 (![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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)))),
% 0.41/0.62 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.41/0.62 tff(86,plain,
% 0.41/0.62 (group_element(e_1) <=> group_element(e_1)),
% 0.41/0.62 inference(rewrite,[status(thm)],[])).
% 0.41/0.62 tff(87,axiom,(group_element(e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_1')).
% 0.41/0.62 tff(88,plain,
% 0.41/0.62 (group_element(e_1)),
% 0.41/0.62 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.41/0.62 tff(89,plain,
% 0.41/0.62 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5) | product(e_1, e_1, e_6) | 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_6) | product(X, Y, e_5) | 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_5) | product(e_1, e_1, e_6) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))),
% 0.41/0.62 inference(rewrite,[status(thm)],[])).
% 0.41/0.62 tff(90,plain,
% 0.41/0.62 ((product(e_1, e_1, e_6) | product(e_1, e_1, e_5) | 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_5) | product(e_1, e_1, e_6) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))),
% 0.41/0.62 inference(rewrite,[status(thm)],[])).
% 0.41/0.62 tff(91,plain,
% 0.41/0.62 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6) | product(e_1, e_1, e_5) | 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_6) | product(X, Y, e_5) | 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_5) | product(e_1, e_1, e_6) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1))))),
% 0.41/0.62 inference(monotonicity,[status(thm)],[90])).
% 0.41/0.62 tff(92,plain,
% 0.41/0.62 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6) | product(e_1, e_1, e_5) | 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_6) | product(X, Y, e_5) | 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_5) | product(e_1, e_1, e_6) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))),
% 0.41/0.62 inference(transitivity,[status(thm)],[91, 89])).
% 0.41/0.62 tff(93,plain,
% 0.41/0.62 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6) | product(e_1, e_1, e_5) | 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)))),
% 0.41/0.62 inference(quant_inst,[status(thm)],[])).
% 0.41/0.62 tff(94,plain,
% 0.41/0.62 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5) | product(e_1, e_1, e_6) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1))),
% 0.41/0.62 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.41/0.62 tff(95,plain,
% 0.41/0.62 (product(e_1, e_1, e_2) | product(e_1, e_1, e_1)),
% 0.41/0.62 inference(unit_resolution,[status(thm)],[94, 88, 85, 75, 68, 61, 54])).
% 0.41/0.62 tff(96,plain,
% 0.41/0.62 (product(e_1, e_1, e_2)),
% 0.41/0.62 inference(unit_resolution,[status(thm)],[95, 34])).
% 0.41/0.62 tff(97,plain,
% 0.41/0.62 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl((product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1))) <=> (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1))))),
% 0.41/0.62 inference(bind,[status(th)],[])).
% 0.41/0.62 tff(98,plain,
% 0.41/0.62 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.41/0.62 inference(quant_intro,[status(thm)],[97])).
% 0.41/0.62 tff(99,plain,
% 0.41/0.62 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.41/0.62 inference(rewrite,[status(thm)],[])).
% 0.41/0.62 tff(100,plain,
% 0.41/0.62 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : rewrite((((~product(X, Y, Z1)) | (~product(Z1, Y, Z2))) | product(X, Z1, Z2)) <=> (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1))))),
% 0.41/0.62 inference(bind,[status(th)],[])).
% 0.41/0.62 tff(101,plain,
% 0.41/0.62 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Z1, Y, Z2))) | product(X, Z1, Z2)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.41/0.62 inference(quant_intro,[status(thm)],[100])).
% 0.41/0.62 tff(102,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Z1, Y, Z2))) | product(X, Z1, Z2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qg3')).
% 0.41/0.62 tff(103,plain,
% 0.41/0.62 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.41/0.62 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.41/0.62 tff(104,plain,
% 0.41/0.62 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.41/0.62 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.41/0.62 tff(105,plain,(
% 0.41/0.62 ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.41/0.62 inference(skolemize,[status(sab)],[104])).
% 0.41/0.62 tff(106,plain,
% 0.41/0.62 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.41/0.62 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.41/0.62 tff(107,plain,
% 0.41/0.62 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, 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(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_4, e_1, e_1)))),
% 0.41/0.62 inference(rewrite,[status(thm)],[])).
% 0.41/0.62 tff(108,plain,
% 0.41/0.62 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_4, e_1, e_1)))),
% 0.41/0.62 inference(quant_inst,[status(thm)],[])).
% 0.41/0.62 tff(109,plain,
% 0.41/0.62 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_4, e_1, e_1))),
% 0.41/0.62 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.41/0.62 tff(110,plain,
% 0.41/0.62 ($false),
% 0.41/0.62 inference(unit_resolution,[status(thm)],[109, 106, 96, 23, 24])).
% 0.41/0.62 tff(111,plain,((~product(e_4, e_1, e_1)) | product(e_4, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.41/0.62 tff(112,plain,
% 0.41/0.62 (~product(e_4, e_1, e_1)),
% 0.41/0.62 inference(unit_resolution,[status(thm)],[111, 23])).
% 0.41/0.62 tff(113,assumption,(product(e_2, e_1, e_2)), introduced(assumption)).
% 0.41/0.62 tff(114,plain,
% 0.41/0.62 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_2)) | product(e_2, e_2, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_2)) | product(e_2, e_2, e_2))),
% 0.41/0.62 inference(rewrite,[status(thm)],[])).
% 0.41/0.62 tff(115,plain,
% 0.41/0.62 ((product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_1, e_2))) <=> ((~product(e_2, e_1, e_2)) | product(e_2, e_2, e_2))),
% 0.41/0.62 inference(rewrite,[status(thm)],[])).
% 0.41/0.62 tff(116,plain,
% 0.41/0.62 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_2)) | product(e_2, e_2, e_2)))),
% 0.41/0.62 inference(monotonicity,[status(thm)],[115])).
% 0.41/0.62 tff(117,plain,
% 0.41/0.62 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_2)) | product(e_2, e_2, e_2))),
% 0.41/0.62 inference(transitivity,[status(thm)],[116, 114])).
% 0.41/0.62 tff(118,plain,
% 0.41/0.62 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.41/0.62 inference(quant_inst,[status(thm)],[])).
% 0.41/0.62 tff(119,plain,
% 0.41/0.62 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_2)) | product(e_2, e_2, e_2)),
% 0.41/0.62 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.41/0.62 tff(120,plain,
% 0.41/0.62 ((~product(e_2, e_1, e_2)) | product(e_2, e_2, e_2)),
% 0.41/0.62 inference(unit_resolution,[status(thm)],[119, 106])).
% 0.41/0.62 tff(121,plain,
% 0.41/0.62 (product(e_2, e_2, e_2)),
% 0.41/0.62 inference(unit_resolution,[status(thm)],[120, 113])).
% 0.41/0.62 tff(122,plain,
% 0.41/0.62 (^[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))))),
% 0.41/0.62 inference(bind,[status(th)],[])).
% 0.41/0.62 tff(123,plain,
% 0.41/0.62 (![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)))),
% 0.41/0.62 inference(quant_intro,[status(thm)],[122])).
% 0.41/0.62 tff(124,plain,
% 0.41/0.62 (![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)))),
% 0.41/0.62 inference(rewrite,[status(thm)],[])).
% 0.41/0.62 tff(125,plain,
% 0.41/0.62 (^[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)))))),
% 0.41/0.63 inference(bind,[status(th)],[])).
% 0.41/0.63 tff(126,plain,
% 0.41/0.63 (![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)))),
% 0.41/0.63 inference(quant_intro,[status(thm)],[125])).
% 0.41/0.63 tff(127,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_right_cancellation')).
% 0.41/0.63 tff(128,plain,
% 0.41/0.63 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.41/0.63 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.41/0.63 tff(129,plain,
% 0.41/0.63 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.41/0.63 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.41/0.63 tff(130,plain,(
% 0.41/0.63 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.41/0.63 inference(skolemize,[status(sab)],[129])).
% 0.41/0.63 tff(131,plain,
% 0.41/0.63 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.41/0.63 inference(modus_ponens,[status(thm)],[130, 123])).
% 0.41/0.63 tff(132,plain,
% 0.41/0.63 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.41/0.63 inference(rewrite,[status(thm)],[])).
% 0.41/0.63 tff(133,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.41/0.63 tff(134,plain,
% 0.41/0.63 (~equalish(e_1, e_2)),
% 0.41/0.63 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.41/0.63 tff(135,plain,
% 0.41/0.63 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_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_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.41/0.63 inference(rewrite,[status(thm)],[])).
% 0.41/0.63 tff(136,plain,
% 0.41/0.63 ((equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2))) <=> (equalish(e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.41/0.63 inference(rewrite,[status(thm)],[])).
% 0.41/0.63 tff(137,plain,
% 0.41/0.63 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_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_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2))))),
% 0.41/0.63 inference(monotonicity,[status(thm)],[136])).
% 0.41/0.63 tff(138,plain,
% 0.41/0.63 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_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_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.41/0.63 inference(transitivity,[status(thm)],[137, 135])).
% 0.41/0.63 tff(139,plain,
% 0.41/0.63 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.41/0.63 inference(quant_inst,[status(thm)],[])).
% 0.41/0.63 tff(140,plain,
% 0.41/0.63 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2))),
% 0.41/0.63 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.41/0.63 tff(141,plain,
% 0.41/0.63 ($false),
% 0.41/0.63 inference(unit_resolution,[status(thm)],[140, 134, 131, 113, 121])).
% 0.41/0.63 tff(142,plain,(~product(e_2, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.41/0.63 tff(143,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.41/0.63 tff(144,plain,
% 0.41/0.63 (((~![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_2, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.41/0.63 inference(rewrite,[status(thm)],[])).
% 0.41/0.63 tff(145,plain,
% 0.41/0.63 ((~![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)))),
% 0.41/0.63 inference(quant_inst,[status(thm)],[])).
% 0.41/0.63 tff(146,plain,
% 0.41/0.63 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_2) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1))),
% 0.41/0.63 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.41/0.63 tff(147,plain,
% 0.41/0.63 ($false),
% 0.41/0.63 inference(unit_resolution,[status(thm)],[146, 134, 12, 25, 143])).
% 0.41/0.63 tff(148,plain,((~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.41/0.63 tff(149,plain,
% 0.41/0.63 (~product(e_1, e_1, e_1)),
% 0.41/0.63 inference(unit_resolution,[status(thm)],[148, 143])).
% 0.41/0.63 tff(150,plain,
% 0.41/0.63 (product(e_1, e_1, e_2)),
% 0.41/0.63 inference(unit_resolution,[status(thm)],[95, 149])).
% 0.41/0.63 tff(151,plain,
% 0.41/0.63 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1)) | product(e_1, e_2, e_1))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1)) | product(e_1, e_2, e_1))),
% 0.41/0.63 inference(rewrite,[status(thm)],[])).
% 0.41/0.63 tff(152,plain,
% 0.41/0.63 ((product(e_1, e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2))) <=> ((~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1)) | product(e_1, e_2, e_1))),
% 0.41/0.63 inference(rewrite,[status(thm)],[])).
% 0.41/0.63 tff(153,plain,
% 0.41/0.63 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1)) | product(e_1, e_2, e_1)))),
% 0.41/0.63 inference(monotonicity,[status(thm)],[152])).
% 0.41/0.63 tff(154,plain,
% 0.41/0.63 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1)) | product(e_1, e_2, e_1))),
% 0.41/0.63 inference(transitivity,[status(thm)],[153, 151])).
% 0.41/0.63 tff(155,plain,
% 0.41/0.63 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_2)))),
% 0.41/0.63 inference(quant_inst,[status(thm)],[])).
% 0.41/0.63 tff(156,plain,
% 0.41/0.63 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1)) | product(e_1, e_2, e_1)),
% 0.41/0.63 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.41/0.63 tff(157,plain,
% 0.41/0.63 ((~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1)) | product(e_1, e_2, e_1)),
% 0.41/0.63 inference(unit_resolution,[status(thm)],[156, 106])).
% 0.41/0.63 tff(158,plain,
% 0.41/0.63 (product(e_1, e_2, e_1)),
% 0.41/0.63 inference(unit_resolution,[status(thm)],[157, 150, 143])).
% 0.41/0.63 tff(159,plain,
% 0.41/0.63 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1)))),
% 0.41/0.63 inference(rewrite,[status(thm)],[])).
% 0.41/0.63 tff(160,plain,
% 0.41/0.63 ((product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_2, e_1))) <=> (product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1)))),
% 0.41/0.63 inference(rewrite,[status(thm)],[])).
% 0.41/0.63 tff(161,plain,
% 0.41/0.63 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1))))),
% 0.41/0.63 inference(monotonicity,[status(thm)],[160])).
% 0.41/0.63 tff(162,plain,
% 0.41/0.63 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1)))),
% 0.41/0.63 inference(transitivity,[status(thm)],[161, 159])).
% 0.41/0.63 tff(163,plain,
% 0.41/0.63 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.41/0.63 inference(quant_inst,[status(thm)],[])).
% 0.41/0.63 tff(164,plain,
% 0.41/0.63 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_1) | (~product(e_1, e_2, e_1))),
% 0.41/0.63 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.41/0.63 tff(165,plain,
% 0.41/0.63 ($false),
% 0.41/0.63 inference(unit_resolution,[status(thm)],[164, 106, 149, 158])).
% 0.41/0.63 tff(166,plain,(~product(e_2, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.41/0.63 tff(167,plain,
% 0.41/0.63 (greater(e_6, e_3) <=> greater(e_6, e_3)),
% 0.41/0.63 inference(rewrite,[status(thm)],[])).
% 0.41/0.63 tff(168,axiom,(greater(e_6, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_6_greater_e_3')).
% 0.41/0.63 tff(169,plain,
% 0.41/0.63 (greater(e_6, e_3)),
% 0.41/0.63 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.41/0.63 tff(170,plain,
% 0.41/0.63 (next(e_2, e_3) <=> next(e_2, e_3)),
% 0.41/0.63 inference(rewrite,[status(thm)],[])).
% 0.41/0.63 tff(171,axiom,(next(e_2, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_then_e_3')).
% 0.41/0.63 tff(172,plain,
% 0.41/0.63 (next(e_2, e_3)),
% 0.41/0.63 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.41/0.63 tff(173,plain,
% 0.41/0.63 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_6, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_6)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_6, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_6)))),
% 0.41/0.63 inference(rewrite,[status(thm)],[])).
% 0.41/0.63 tff(174,plain,
% 0.41/0.63 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_6, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_6)))),
% 0.41/0.63 inference(quant_inst,[status(thm)],[])).
% 0.41/0.63 tff(175,plain,
% 0.41/0.63 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_6, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_6))),
% 0.41/0.63 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.41/0.63 tff(176,plain,
% 0.41/0.63 (~product(e_2, e_1, e_6)),
% 0.41/0.63 inference(unit_resolution,[status(thm)],[175, 172, 169, 44])).
% 0.41/0.63 tff(177,plain,
% 0.41/0.63 (greater(e_5, e_3) <=> greater(e_5, e_3)),
% 0.41/0.63 inference(rewrite,[status(thm)],[])).
% 0.41/0.63 tff(178,axiom,(greater(e_5, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_5_greater_e_3')).
% 0.41/0.63 tff(179,plain,
% 0.41/0.63 (greater(e_5, e_3)),
% 0.41/0.63 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.41/0.63 tff(180,plain,
% 0.41/0.63 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_5, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_5, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))),
% 0.41/0.63 inference(rewrite,[status(thm)],[])).
% 0.41/0.63 tff(181,plain,
% 0.47/0.63 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_5, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(182,plain,
% 0.47/0.63 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_5, e_3)) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.47/0.63 tff(183,plain,
% 0.47/0.63 (~product(e_2, e_1, e_5)),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[182, 172, 179, 44])).
% 0.47/0.63 tff(184,plain,
% 0.47/0.63 (greater(e_4, e_3) <=> greater(e_4, e_3)),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(185,axiom,(greater(e_4, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_greater_e_3')).
% 0.47/0.63 tff(186,plain,
% 0.47/0.63 (greater(e_4, e_3)),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.47/0.63 tff(187,plain,
% 0.47/0.63 (((~![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)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(188,plain,
% 0.47/0.63 ((~![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)))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(189,plain,
% 0.47/0.63 ((~![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))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.47/0.63 tff(190,plain,
% 0.47/0.63 (~product(e_2, e_1, e_4)),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[189, 172, 186, 44])).
% 0.47/0.63 tff(191,plain,
% 0.47/0.63 (group_element(e_2) <=> group_element(e_2)),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(192,axiom,(group_element(e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_2')).
% 0.47/0.63 tff(193,plain,
% 0.47/0.63 (group_element(e_2)),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.47/0.63 tff(194,plain,
% 0.47/0.63 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5) | product(e_2, e_1, e_6) | (~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_6) | product(X, Y, e_5) | 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_5) | product(e_2, e_1, e_6) | (~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)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(195,plain,
% 0.47/0.63 ((product(e_2, e_1, e_6) | product(e_2, e_1, e_5) | 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) | product(e_2, e_1, e_5) | product(e_2, e_1, e_6) | (~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)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(196,plain,
% 0.47/0.63 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6) | product(e_2, e_1, e_5) | 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_6) | product(X, Y, e_5) | 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_5) | product(e_2, e_1, e_6) | (~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))))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[195])).
% 0.47/0.63 tff(197,plain,
% 0.47/0.63 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6) | product(e_2, e_1, e_5) | 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_6) | product(X, Y, e_5) | 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_5) | product(e_2, e_1, e_6) | (~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)))),
% 0.47/0.63 inference(transitivity,[status(thm)],[196, 194])).
% 0.47/0.63 tff(198,plain,
% 0.47/0.63 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6) | product(e_2, e_1, e_5) | 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)))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(199,plain,
% 0.47/0.63 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5) | product(e_2, e_1, e_6) | (~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))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.47/0.63 tff(200,plain,
% 0.47/0.63 (product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1)),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[199, 88, 193, 85, 190, 183, 176])).
% 0.47/0.63 tff(201,plain,
% 0.47/0.63 (product(e_2, e_1, e_3) | product(e_2, e_1, e_2)),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[200, 166])).
% 0.47/0.63 tff(202,plain,
% 0.47/0.63 (product(e_2, e_1, e_3)),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[201, 142])).
% 0.47/0.63 tff(203,assumption,(product(e_4, e_1, e_3)), introduced(assumption)).
% 0.47/0.63 tff(204,assumption,(product(e_2, e_1, e_3)), introduced(assumption)).
% 0.47/0.63 tff(205,plain,
% 0.47/0.63 ((~equalish(e_4, e_2)) <=> (~equalish(e_4, e_2))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(206,axiom,(~equalish(e_4, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_is_not_e_2')).
% 0.47/0.63 tff(207,plain,
% 0.47/0.63 (~equalish(e_4, e_2)),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.47/0.63 tff(208,plain,
% 0.47/0.63 (((~![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)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(209,plain,
% 0.47/0.64 ((~![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)))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(210,plain,
% 0.47/0.64 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_4, e_1, e_3))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.47/0.64 tff(211,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[210, 207, 12, 204, 203])).
% 0.47/0.64 tff(212,plain,((~product(e_4, e_1, e_3)) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(213,plain,
% 0.47/0.64 (~product(e_4, e_1, e_3)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[212, 202])).
% 0.47/0.64 tff(214,assumption,(product(e_4, e_1, e_4)), introduced(assumption)).
% 0.47/0.64 tff(215,plain,
% 0.47/0.64 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_4, e_1, e_4)) | product(e_4, e_4, e_4))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_1, e_4)) | product(e_4, e_4, e_4))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(216,plain,
% 0.47/0.64 ((product(e_4, e_4, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_1, e_4))) <=> ((~product(e_4, e_1, e_4)) | product(e_4, e_4, e_4))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(217,plain,
% 0.47/0.64 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_4, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_4, e_1, e_4)) | product(e_4, e_4, e_4)))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[216])).
% 0.47/0.64 tff(218,plain,
% 0.47/0.64 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_4, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_1, e_4)) | product(e_4, e_4, e_4))),
% 0.47/0.64 inference(transitivity,[status(thm)],[217, 215])).
% 0.47/0.64 tff(219,plain,
% 0.47/0.64 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_4, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_1, e_4)))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(220,plain,
% 0.47/0.64 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_1, e_4)) | product(e_4, e_4, e_4)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.47/0.64 tff(221,plain,
% 0.47/0.64 ((~product(e_4, e_1, e_4)) | product(e_4, e_4, e_4)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[220, 106])).
% 0.47/0.64 tff(222,plain,
% 0.47/0.64 (product(e_4, e_4, e_4)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[221, 214])).
% 0.47/0.64 tff(223,plain,
% 0.47/0.64 ((~equalish(e_1, e_4)) <=> (~equalish(e_1, e_4))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(224,axiom,(~equalish(e_1, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_4')).
% 0.47/0.64 tff(225,plain,
% 0.47/0.64 (~equalish(e_1, e_4)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.47/0.64 tff(226,plain,
% 0.47/0.64 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(227,plain,
% 0.47/0.64 ((equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4))) <=> (equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(228,plain,
% 0.47/0.64 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[227])).
% 0.47/0.64 tff(229,plain,
% 0.47/0.64 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.47/0.64 inference(transitivity,[status(thm)],[228, 226])).
% 0.47/0.64 tff(230,plain,
% 0.47/0.64 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4)))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(231,plain,
% 0.47/0.64 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.47/0.64 tff(232,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[231, 225, 131, 214, 222])).
% 0.47/0.64 tff(233,plain,(~product(e_4, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(234,plain,
% 0.47/0.64 (greater(e_6, e_5) <=> greater(e_6, e_5)),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(235,axiom,(greater(e_6, e_5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_6_greater_e_5')).
% 0.47/0.64 tff(236,plain,
% 0.47/0.64 (greater(e_6, e_5)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.47/0.64 tff(237,plain,
% 0.47/0.64 (next(e_4, e_5) <=> next(e_4, e_5)),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(238,axiom,(next(e_4, e_5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_then_e_5')).
% 0.47/0.64 tff(239,plain,
% 0.47/0.64 (next(e_4, e_5)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.47/0.64 tff(240,plain,
% 0.47/0.64 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_6, e_5)) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_6)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_6, e_5)) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_6)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(241,plain,
% 0.47/0.64 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_6, e_5)) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_6)))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(242,plain,
% 0.47/0.64 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_6, e_5)) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_6))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.47/0.64 tff(243,plain,
% 0.47/0.64 (~product(e_4, e_1, e_6)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[242, 239, 236, 44])).
% 0.47/0.64 tff(244,plain,
% 0.47/0.64 (group_element(e_4) <=> group_element(e_4)),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(245,axiom,(group_element(e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_4')).
% 0.47/0.64 tff(246,plain,
% 0.47/0.64 (group_element(e_4)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.47/0.64 tff(247,plain,
% 0.47/0.64 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6) | (~group_element(e_1)) | product(e_4, e_1, e_5) | 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_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6) | (~group_element(e_1)) | product(e_4, e_1, e_5) | 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_4)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(248,plain,
% 0.47/0.64 ((product(e_4, e_1, e_6) | product(e_4, e_1, e_5) | 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))) <=> (product(e_4, e_1, e_6) | (~group_element(e_1)) | product(e_4, e_1, e_5) | 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_4)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(249,plain,
% 0.47/0.64 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6) | product(e_4, e_1, e_5) | 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_6) | product(X, Y, e_5) | 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_6) | (~group_element(e_1)) | product(e_4, e_1, e_5) | 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_4))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[248])).
% 0.47/0.64 tff(250,plain,
% 0.47/0.64 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6) | product(e_4, e_1, e_5) | 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_6) | product(X, Y, e_5) | 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_6) | (~group_element(e_1)) | product(e_4, e_1, e_5) | 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_4)))),
% 0.47/0.64 inference(transitivity,[status(thm)],[249, 247])).
% 0.47/0.64 tff(251,plain,
% 0.47/0.64 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6) | product(e_4, e_1, e_5) | 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)))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(252,plain,
% 0.47/0.64 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_4, e_1, e_6) | (~group_element(e_1)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_4))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.47/0.64 tff(253,plain,
% 0.47/0.64 (product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[252, 88, 246, 85, 243])).
% 0.47/0.64 tff(254,plain,
% 0.47/0.64 (product(e_4, e_1, e_5) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[253, 233])).
% 0.47/0.64 tff(255,plain,
% 0.47/0.64 (product(e_4, e_1, e_5) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[254, 213])).
% 0.47/0.64 tff(256,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[255, 112, 23, 22])).
% 0.47/0.64 tff(257,plain,(product(e_4, e_1, e_2) | product(e_4, e_1, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(258,plain,
% 0.47/0.64 (product(e_4, e_1, e_5)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[257, 21])).
% 0.47/0.64 tff(259,assumption,(~product(e_3, e_1, e_4)), introduced(assumption)).
% 0.47/0.64 tff(260,assumption,(product(e_2, e_3, e_2)), introduced(assumption)).
% 0.47/0.64 tff(261,assumption,(product(e_2, e_2, e_2)), introduced(assumption)).
% 0.47/0.64 tff(262,plain,
% 0.47/0.64 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(263,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.47/0.64 tff(264,plain,
% 0.47/0.64 (~equalish(e_2, e_3)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.47/0.64 tff(265,plain,
% 0.47/0.64 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_2, e_2, e_2)) | (~product(e_2, 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_2, e_3) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_3, e_2)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(266,plain,
% 0.47/0.64 ((equalish(e_2, e_3) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_2, e_2))) <=> (equalish(e_2, e_3) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_3, e_2)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(267,plain,
% 0.47/0.64 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_2, e_3, 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_3) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_3, e_2))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[266])).
% 0.47/0.64 tff(268,plain,
% 0.47/0.64 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_2, e_3, 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_3) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_3, e_2)))),
% 0.47/0.64 inference(transitivity,[status(thm)],[267, 265])).
% 0.47/0.64 tff(269,plain,
% 0.47/0.64 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(270,plain,
% 0.47/0.64 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_3, e_2))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.47/0.64 tff(271,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[270, 264, 131, 260, 261])).
% 0.47/0.64 tff(272,plain,((~product(e_2, e_2, e_2)) | (~product(e_2, e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(273,plain,
% 0.47/0.64 (~product(e_2, e_2, e_2)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[272, 260])).
% 0.47/0.64 tff(274,plain,
% 0.47/0.64 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(275,plain,
% 0.47/0.64 ((product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_3, e_2))) <=> (product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(276,plain,
% 0.47/0.64 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[275])).
% 0.47/0.64 tff(277,plain,
% 0.47/0.64 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2)))),
% 0.47/0.64 inference(transitivity,[status(thm)],[276, 274])).
% 0.47/0.64 tff(278,plain,
% 0.47/0.64 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_3, e_2)))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(279,plain,
% 0.47/0.64 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.47/0.64 tff(280,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[279, 106, 260, 273])).
% 0.47/0.65 tff(281,plain,(~product(e_2, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.65 tff(282,assumption,(~product(e_2, e_3, e_2)), introduced(assumption)).
% 0.47/0.65 tff(283,assumption,(product(e_3, e_1, e_2)), introduced(assumption)).
% 0.47/0.65 tff(284,plain,
% 0.47/0.65 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_2, e_3, e_2) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_2, e_3, e_2) | (~product(e_3, e_1, e_2)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(285,plain,
% 0.47/0.65 ((product(e_2, e_3, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_3))) <=> ((~product(e_2, e_1, e_3)) | product(e_2, e_3, e_2) | (~product(e_3, e_1, e_2)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(286,plain,
% 0.47/0.65 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_2, e_3, e_2) | (~product(e_3, e_1, e_2))))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[285])).
% 0.47/0.65 tff(287,plain,
% 0.47/0.65 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_2, e_3, e_2) | (~product(e_3, e_1, e_2)))),
% 0.47/0.65 inference(transitivity,[status(thm)],[286, 284])).
% 0.47/0.65 tff(288,plain,
% 0.47/0.65 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(289,plain,
% 0.47/0.65 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_2, e_3, e_2) | (~product(e_3, e_1, e_2))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[288, 287])).
% 0.47/0.65 tff(290,plain,
% 0.47/0.65 ($false),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[289, 106, 202, 283, 282])).
% 0.47/0.65 tff(291,plain,(product(e_2, e_3, e_2) | (~product(e_3, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.65 tff(292,plain,
% 0.47/0.65 (~product(e_3, e_1, e_2)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[291, 281])).
% 0.47/0.65 tff(293,assumption,(product(e_3, e_1, e_3)), introduced(assumption)).
% 0.47/0.65 tff(294,plain,
% 0.47/0.65 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(295,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.47/0.65 tff(296,plain,
% 0.47/0.65 (~equalish(e_3, e_2)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.47/0.65 tff(297,plain,
% 0.47/0.65 (((~![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_1, e_3)) | (~product(e_2, 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_3, e_2) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(298,plain,
% 0.47/0.65 ((equalish(e_3, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3))) <=> (equalish(e_3, e_2) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(299,plain,
% 0.47/0.65 (((~![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_1, e_3)) | (~product(e_3, 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_3, e_2) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3))))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[298])).
% 0.47/0.65 tff(300,plain,
% 0.47/0.65 (((~![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_1, e_3)) | (~product(e_3, 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_3, e_2) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.47/0.65 inference(transitivity,[status(thm)],[299, 297])).
% 0.47/0.65 tff(301,plain,
% 0.47/0.65 ((~![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_1, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(302,plain,
% 0.47/0.65 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.47/0.65 tff(303,plain,
% 0.47/0.65 ($false),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[302, 296, 12, 204, 293])).
% 0.47/0.65 tff(304,plain,((~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.65 tff(305,plain,
% 0.47/0.65 (~product(e_3, e_1, e_3)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[304, 202])).
% 0.47/0.65 tff(306,plain,
% 0.47/0.65 (greater(e_6, e_4) <=> greater(e_6, e_4)),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(307,axiom,(greater(e_6, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_6_greater_e_4')).
% 0.47/0.65 tff(308,plain,
% 0.47/0.65 (greater(e_6, e_4)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.47/0.65 tff(309,plain,
% 0.47/0.65 (next(e_3, e_4) <=> next(e_3, e_4)),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(310,axiom,(next(e_3, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_then_e_4')).
% 0.47/0.65 tff(311,plain,
% 0.47/0.65 (next(e_3, e_4)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.47/0.65 tff(312,plain,
% 0.47/0.65 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_6, e_4)) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_6)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_6, e_4)) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_6)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(313,plain,
% 0.47/0.65 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_6, e_4)) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_6)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(314,plain,
% 0.47/0.65 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_6, e_4)) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_6))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[313, 312])).
% 0.47/0.65 tff(315,plain,
% 0.47/0.65 (~product(e_3, e_1, e_6)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[314, 311, 308, 44])).
% 0.47/0.65 tff(316,plain,
% 0.47/0.65 (greater(e_5, e_4) <=> greater(e_5, e_4)),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(317,axiom,(greater(e_5, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_5_greater_e_4')).
% 0.47/0.65 tff(318,plain,
% 0.47/0.65 (greater(e_5, e_4)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[317, 316])).
% 0.47/0.65 tff(319,plain,
% 0.47/0.65 (((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_5, e_4)) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5)))) <=> ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_5, e_4)) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(320,plain,
% 0.47/0.65 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | ((~greater(e_5, e_4)) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(321,plain,
% 0.47/0.65 ((~![Y: $i, X: $i, X1: $i] : ((~greater(Y, X1)) | (~next(X, X1)) | (~product(X, e_1, Y)))) | (~greater(e_5, e_4)) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.47/0.65 tff(322,plain,
% 0.47/0.65 (~product(e_3, e_1, e_5)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[321, 311, 318, 44])).
% 0.47/0.65 tff(323,plain,
% 0.47/0.65 (group_element(e_3) <=> group_element(e_3)),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(324,axiom,(group_element(e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_3')).
% 0.47/0.65 tff(325,plain,
% 0.47/0.65 (group_element(e_3)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[324, 323])).
% 0.47/0.65 tff(326,plain,
% 0.47/0.65 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_5) | product(e_3, e_1, e_6) | (~group_element(e_1)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_1, e_5) | product(e_3, e_1, e_6) | (~group_element(e_1)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_3)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(327,plain,
% 0.47/0.65 ((product(e_3, e_1, e_6) | product(e_3, e_1, e_5) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3))) <=> (product(e_3, e_1, e_5) | product(e_3, e_1, e_6) | (~group_element(e_1)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_3)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(328,plain,
% 0.47/0.65 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_6) | product(e_3, e_1, e_5) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_5) | product(e_3, e_1, e_6) | (~group_element(e_1)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_3))))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[327])).
% 0.47/0.65 tff(329,plain,
% 0.47/0.65 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_6) | product(e_3, e_1, e_5) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_1, e_5) | product(e_3, e_1, e_6) | (~group_element(e_1)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_3)))),
% 0.47/0.65 inference(transitivity,[status(thm)],[328, 326])).
% 0.47/0.65 tff(330,plain,
% 0.47/0.65 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_1, e_6) | product(e_3, e_1, e_5) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_3)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(331,plain,
% 0.47/0.65 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_1, e_5) | product(e_3, e_1, e_6) | (~group_element(e_1)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_3))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[330, 329])).
% 0.47/0.65 tff(332,plain,
% 0.47/0.65 (product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[331, 88, 325, 85, 322, 315])).
% 0.47/0.65 tff(333,plain,
% 0.47/0.65 (product(e_3, e_1, e_4) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[332, 305])).
% 0.47/0.65 tff(334,plain,
% 0.47/0.65 (product(e_3, e_1, e_4) | product(e_3, e_1, e_1)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[333, 292])).
% 0.47/0.65 tff(335,plain,
% 0.47/0.65 (product(e_3, e_1, e_1)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[334, 259])).
% 0.47/0.65 tff(336,assumption,(product(e_1, e_1, e_2)), introduced(assumption)).
% 0.47/0.65 tff(337,plain,
% 0.47/0.65 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(338,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.47/0.65 tff(339,plain,
% 0.47/0.65 (~equalish(e_3, e_1)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[338, 337])).
% 0.47/0.65 tff(340,plain,
% 0.47/0.65 (((~![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_1, e_2)) | (~product(e_3, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(341,plain,
% 0.47/0.65 ((~![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_1, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(342,plain,
% 0.47/0.65 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_3, e_1, e_2))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[341, 340])).
% 0.47/0.65 tff(343,plain,
% 0.47/0.65 ($false),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[342, 339, 12, 336, 283])).
% 0.47/0.65 tff(344,plain,((~product(e_3, e_1, e_2)) | (~product(e_1, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.65 tff(345,plain,
% 0.47/0.65 (~product(e_3, e_1, e_2)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[344, 336])).
% 0.47/0.65 tff(346,plain,
% 0.47/0.65 (product(e_3, e_1, e_1)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[333, 345, 259])).
% 0.47/0.65 tff(347,plain,
% 0.47/0.65 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_3, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_3, e_1, e_1)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(348,plain,
% 0.47/0.65 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_3, e_1, e_1)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(349,plain,
% 0.47/0.65 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_3, e_1, e_1))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[348, 347])).
% 0.47/0.65 tff(350,plain,
% 0.47/0.65 ($false),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[349, 106, 336, 345, 346])).
% 0.47/0.65 tff(351,plain,((~product(e_1, e_1, e_2)) | product(e_3, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.65 tff(352,plain,
% 0.47/0.65 (~product(e_1, e_1, e_2)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[351, 259])).
% 0.47/0.65 tff(353,plain,
% 0.47/0.65 (product(e_1, e_1, e_1)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[95, 352])).
% 0.47/0.65 tff(354,assumption,(product(e_3, e_1, e_1)), introduced(assumption)).
% 0.47/0.65 tff(355,plain,
% 0.47/0.65 (((~![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_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_3, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(356,plain,
% 0.49/0.66 ((equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1))) <=> (equalish(e_3, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(357,plain,
% 0.49/0.66 (((~![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_1, e_1)) | (~product(e_3, 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_3, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1))))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[356])).
% 0.49/0.66 tff(358,plain,
% 0.49/0.66 (((~![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_1, e_1)) | (~product(e_3, 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_3, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.49/0.66 inference(transitivity,[status(thm)],[357, 355])).
% 0.49/0.66 tff(359,plain,
% 0.49/0.66 ((~![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_1, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.49/0.66 inference(quant_inst,[status(thm)],[])).
% 0.49/0.66 tff(360,plain,
% 0.49/0.66 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[359, 358])).
% 0.49/0.66 tff(361,plain,
% 0.49/0.66 ($false),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[360, 339, 12, 25, 354])).
% 0.49/0.66 tff(362,plain,((~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.66 tff(363,plain,
% 0.49/0.66 ($false),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[362, 353, 335])).
% 0.49/0.66 tff(364,plain,(product(e_3, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.66 tff(365,plain,
% 0.49/0.66 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_4, e_5) | (~product(e_4, e_1, e_5)) | (~product(e_3, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_4, e_5) | (~product(e_4, e_1, e_5)) | (~product(e_3, e_1, e_4)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(366,plain,
% 0.49/0.66 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_4, e_5) | (~product(e_4, e_1, e_5)) | (~product(e_3, e_1, e_4)))),
% 0.49/0.66 inference(quant_inst,[status(thm)],[])).
% 0.49/0.66 tff(367,plain,
% 0.49/0.66 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_4, e_5) | (~product(e_4, e_1, e_5)) | (~product(e_3, e_1, e_4))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[366, 365])).
% 0.49/0.66 tff(368,plain,
% 0.49/0.66 (product(e_3, e_4, e_5) | (~product(e_4, e_1, e_5)) | (~product(e_3, e_1, e_4))),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[367, 106])).
% 0.49/0.66 tff(369,plain,
% 0.49/0.66 (product(e_3, e_4, e_5) | (~product(e_4, e_1, e_5))),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[368, 364])).
% 0.49/0.66 tff(370,plain,
% 0.49/0.66 (product(e_3, e_4, e_5)),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[369, 258])).
% 0.49/0.66 tff(371,assumption,(product(e_3, e_2, e_5)), introduced(assumption)).
% 0.49/0.66 tff(372,assumption,(product(e_3, e_4, e_5)), introduced(assumption)).
% 0.49/0.66 tff(373,plain,
% 0.49/0.66 ((~equalish(e_2, e_4)) <=> (~equalish(e_2, e_4))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(374,axiom,(~equalish(e_2, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_4')).
% 0.49/0.66 tff(375,plain,
% 0.49/0.66 (~equalish(e_2, e_4)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[374, 373])).
% 0.49/0.66 tff(376,plain,
% 0.49/0.66 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_3, e_4, e_5)) | (~product(e_3, e_2, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_3, e_4, e_5)) | (~product(e_3, e_2, e_5)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(377,plain,
% 0.49/0.66 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_3, e_4, e_5)) | (~product(e_3, e_2, e_5)))),
% 0.49/0.66 inference(quant_inst,[status(thm)],[])).
% 0.49/0.66 tff(378,plain,
% 0.49/0.66 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_3, e_4, e_5)) | (~product(e_3, e_2, e_5))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[377, 376])).
% 0.49/0.66 tff(379,plain,
% 0.49/0.66 ($false),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[378, 375, 131, 372, 371])).
% 0.49/0.66 tff(380,plain,((~product(e_3, e_2, e_5)) | (~product(e_3, e_4, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.66 tff(381,plain,
% 0.49/0.66 (~product(e_3, e_2, e_5)),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[380, 370])).
% 0.49/0.66 tff(382,assumption,(~product(e_5, e_1, e_6)), introduced(assumption)).
% 0.49/0.66 tff(383,assumption,(product(e_5, e_1, e_5)), introduced(assumption)).
% 0.49/0.66 tff(384,assumption,(~product(e_5, e_5, e_5)), introduced(assumption)).
% 0.49/0.66 tff(385,plain,
% 0.49/0.66 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_5, e_5) | (~product(e_5, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_5, e_5) | (~product(e_5, e_1, e_5)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(386,plain,
% 0.49/0.66 ((product(e_5, e_5, e_5) | (~product(e_5, e_1, e_5)) | (~product(e_5, e_1, e_5))) <=> (product(e_5, e_5, e_5) | (~product(e_5, e_1, e_5)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(387,plain,
% 0.49/0.66 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_5, e_5) | (~product(e_5, e_1, e_5)) | (~product(e_5, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_5, e_5) | (~product(e_5, e_1, e_5))))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[386])).
% 0.49/0.66 tff(388,plain,
% 0.49/0.66 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_5, e_5) | (~product(e_5, e_1, e_5)) | (~product(e_5, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_5, e_5) | (~product(e_5, e_1, e_5)))),
% 0.49/0.66 inference(transitivity,[status(thm)],[387, 385])).
% 0.49/0.66 tff(389,plain,
% 0.49/0.66 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_5, e_5) | (~product(e_5, e_1, e_5)) | (~product(e_5, e_1, e_5)))),
% 0.49/0.66 inference(quant_inst,[status(thm)],[])).
% 0.49/0.66 tff(390,plain,
% 0.49/0.66 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_5, e_5) | (~product(e_5, e_1, e_5))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[389, 388])).
% 0.49/0.66 tff(391,plain,
% 0.49/0.66 ($false),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[390, 106, 384, 383])).
% 0.49/0.66 tff(392,plain,(product(e_5, e_5, e_5) | (~product(e_5, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.66 tff(393,plain,
% 0.49/0.66 (product(e_5, e_5, e_5)),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[392, 383])).
% 0.49/0.66 tff(394,plain,
% 0.49/0.66 ((~equalish(e_5, e_1)) <=> (~equalish(e_5, e_1))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(395,axiom,(~equalish(e_5, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_5_is_not_e_1')).
% 0.49/0.66 tff(396,plain,
% 0.49/0.66 (~equalish(e_5, e_1)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[395, 394])).
% 0.49/0.66 tff(397,plain,
% 0.49/0.66 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_1) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_1, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_1) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_1, e_5)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(398,plain,
% 0.49/0.66 ((equalish(e_5, e_1) | (~product(e_5, e_1, e_5)) | (~product(e_5, e_5, e_5))) <=> (equalish(e_5, e_1) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_1, e_5)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(399,plain,
% 0.49/0.66 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_1) | (~product(e_5, e_1, e_5)) | (~product(e_5, e_5, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_1) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_1, e_5))))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[398])).
% 0.49/0.66 tff(400,plain,
% 0.49/0.66 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_1) | (~product(e_5, e_1, e_5)) | (~product(e_5, e_5, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_1) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_1, e_5)))),
% 0.49/0.66 inference(transitivity,[status(thm)],[399, 397])).
% 0.49/0.66 tff(401,plain,
% 0.49/0.66 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_1) | (~product(e_5, e_1, e_5)) | (~product(e_5, e_5, e_5)))),
% 0.49/0.66 inference(quant_inst,[status(thm)],[])).
% 0.49/0.66 tff(402,plain,
% 0.49/0.66 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_1) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_1, e_5))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[401, 400])).
% 0.49/0.66 tff(403,plain,
% 0.49/0.66 ($false),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[402, 396, 131, 393, 383])).
% 0.49/0.66 tff(404,plain,(~product(e_5, e_1, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.66 tff(405,assumption,(product(e_5, e_1, e_2)), introduced(assumption)).
% 0.49/0.66 tff(406,plain,
% 0.49/0.66 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_5, 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_5, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_5, e_1, e_2)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(407,plain,
% 0.49/0.66 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_5, e_1, e_2)))),
% 0.49/0.66 inference(quant_inst,[status(thm)],[])).
% 0.49/0.66 tff(408,plain,
% 0.49/0.66 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_5, e_1, e_2))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[407, 406])).
% 0.49/0.66 tff(409,plain,
% 0.49/0.66 ($false),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[408, 396, 12, 336, 405])).
% 0.49/0.66 tff(410,plain,((~product(e_5, e_1, e_2)) | (~product(e_1, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.66 tff(411,plain,
% 0.49/0.66 (~product(e_5, e_1, e_2)),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[410, 336])).
% 0.49/0.66 tff(412,assumption,(~product(e_5, e_1, e_5)), introduced(assumption)).
% 0.49/0.66 tff(413,assumption,(product(e_5, e_1, e_4)), introduced(assumption)).
% 0.49/0.66 tff(414,plain,
% 0.49/0.66 ((~equalish(e_5, e_3)) <=> (~equalish(e_5, e_3))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(415,axiom,(~equalish(e_5, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_5_is_not_e_3')).
% 0.49/0.66 tff(416,plain,
% 0.49/0.66 (~equalish(e_5, e_3)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[415, 414])).
% 0.49/0.66 tff(417,plain,
% 0.49/0.66 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_5, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_5, e_1, e_4)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(418,plain,
% 0.49/0.66 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_5, e_1, e_4)))),
% 0.49/0.66 inference(quant_inst,[status(thm)],[])).
% 0.49/0.66 tff(419,plain,
% 0.49/0.66 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_5, e_1, e_4))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[418, 417])).
% 0.49/0.66 tff(420,plain,
% 0.49/0.66 ($false),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[419, 416, 12, 364, 413])).
% 0.49/0.66 tff(421,plain,(~product(e_5, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.66 tff(422,assumption,(~product(e_2, e_3, e_4)), introduced(assumption)).
% 0.49/0.66 tff(423,assumption,(product(e_3, e_1, e_4)), introduced(assumption)).
% 0.49/0.66 tff(424,plain,
% 0.49/0.66 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_2, e_3, e_4) | (~product(e_3, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_2, e_3, e_4) | (~product(e_3, e_1, e_4)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(425,plain,
% 0.49/0.66 ((product(e_2, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_2, e_1, e_3))) <=> ((~product(e_2, e_1, e_3)) | product(e_2, e_3, e_4) | (~product(e_3, e_1, e_4)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(426,plain,
% 0.49/0.66 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_2, e_3, e_4) | (~product(e_3, e_1, e_4))))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[425])).
% 0.49/0.66 tff(427,plain,
% 0.49/0.66 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_2, e_3, e_4) | (~product(e_3, e_1, e_4)))),
% 0.49/0.66 inference(transitivity,[status(thm)],[426, 424])).
% 0.49/0.66 tff(428,plain,
% 0.49/0.66 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_2, e_1, e_3)))),
% 0.49/0.66 inference(quant_inst,[status(thm)],[])).
% 0.49/0.66 tff(429,plain,
% 0.49/0.66 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_2, e_3, e_4) | (~product(e_3, e_1, e_4))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[428, 427])).
% 0.49/0.66 tff(430,plain,
% 0.49/0.66 ($false),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[429, 106, 204, 423, 422])).
% 0.49/0.66 tff(431,plain,(product(e_2, e_3, e_4) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.66 tff(432,plain,
% 0.49/0.66 (product(e_2, e_3, e_4) | (~product(e_3, e_1, e_4))),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[431, 202])).
% 0.49/0.66 tff(433,plain,
% 0.49/0.66 (product(e_2, e_3, e_4)),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[432, 364])).
% 0.49/0.66 tff(434,assumption,(product(e_5, e_3, e_4)), introduced(assumption)).
% 0.49/0.66 tff(435,plain,
% 0.49/0.66 ((~equalish(e_5, e_2)) <=> (~equalish(e_5, e_2))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(436,axiom,(~equalish(e_5, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_5_is_not_e_2')).
% 0.49/0.66 tff(437,plain,
% 0.49/0.66 (~equalish(e_5, e_2)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[436, 435])).
% 0.49/0.66 tff(438,plain,
% 0.49/0.66 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_5, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_5, e_3, e_4)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(439,plain,
% 0.49/0.66 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_5, e_3, e_4)))),
% 0.49/0.66 inference(quant_inst,[status(thm)],[])).
% 0.49/0.66 tff(440,plain,
% 0.49/0.66 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_5, e_3, e_4))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[439, 438])).
% 0.49/0.66 tff(441,plain,
% 0.49/0.66 ($false),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[440, 437, 12, 434, 433])).
% 0.49/0.66 tff(442,plain,(~product(e_5, e_3, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.66 tff(443,plain,
% 0.49/0.66 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_5, e_3, e_4) | (~product(e_5, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | product(e_5, e_3, e_4) | (~product(e_5, e_1, e_3)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(444,plain,
% 0.49/0.66 ((product(e_5, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_5, e_1, e_3))) <=> ((~product(e_3, e_1, e_4)) | product(e_5, e_3, e_4) | (~product(e_5, e_1, e_3)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(445,plain,
% 0.49/0.66 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_5, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_5, e_3, e_4) | (~product(e_5, e_1, e_3))))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[444])).
% 0.49/0.66 tff(446,plain,
% 0.49/0.66 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_5, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | product(e_5, e_3, e_4) | (~product(e_5, e_1, e_3)))),
% 0.49/0.66 inference(transitivity,[status(thm)],[445, 443])).
% 0.49/0.66 tff(447,plain,
% 0.49/0.66 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_5, e_1, e_3)))),
% 0.49/0.66 inference(quant_inst,[status(thm)],[])).
% 0.49/0.66 tff(448,plain,
% 0.49/0.66 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | product(e_5, e_3, e_4) | (~product(e_5, e_1, e_3))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[447, 446])).
% 0.49/0.66 tff(449,plain,
% 0.49/0.66 (~product(e_5, e_1, e_3)),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[448, 106, 364, 442])).
% 0.49/0.66 tff(450,plain,
% 0.49/0.66 (group_element(e_5) <=> group_element(e_5)),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(451,axiom,(group_element(e_5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_5')).
% 0.49/0.66 tff(452,plain,
% 0.49/0.66 (group_element(e_5)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[451, 450])).
% 0.49/0.66 tff(453,plain,
% 0.49/0.66 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5)) | product(e_5, e_1, e_6) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_1) | product(e_5, e_1, e_2))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5)) | product(e_5, e_1, e_6) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_1) | product(e_5, e_1, e_2))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(454,plain,
% 0.49/0.67 ((product(e_5, e_1, e_6) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_5))) <=> ((~group_element(e_1)) | (~group_element(e_5)) | product(e_5, e_1, e_6) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_1) | product(e_5, e_1, e_2))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(455,plain,
% 0.49/0.67 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5, e_1, e_6) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_5)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5)) | product(e_5, e_1, e_6) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_1) | product(e_5, e_1, e_2)))),
% 0.49/0.67 inference(monotonicity,[status(thm)],[454])).
% 0.49/0.67 tff(456,plain,
% 0.49/0.67 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5, e_1, e_6) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_5)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5)) | product(e_5, e_1, e_6) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_1) | product(e_5, e_1, e_2))),
% 0.49/0.67 inference(transitivity,[status(thm)],[455, 453])).
% 0.49/0.67 tff(457,plain,
% 0.49/0.67 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5, e_1, e_6) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_5)))),
% 0.49/0.67 inference(quant_inst,[status(thm)],[])).
% 0.49/0.67 tff(458,plain,
% 0.49/0.67 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5)) | product(e_5, e_1, e_6) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_1) | product(e_5, e_1, e_2)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[457, 456])).
% 0.49/0.67 tff(459,plain,
% 0.49/0.67 (product(e_5, e_1, e_6) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4) | product(e_5, e_1, e_1) | product(e_5, e_1, e_2)),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[458, 88, 452, 85, 449])).
% 0.49/0.67 tff(460,plain,
% 0.49/0.67 (product(e_5, e_1, e_6) | product(e_5, e_1, e_5) | product(e_5, e_1, e_1) | product(e_5, e_1, e_2)),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[459, 421])).
% 0.49/0.67 tff(461,plain,
% 0.49/0.67 (product(e_5, e_1, e_1)),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[460, 411, 382, 412])).
% 0.49/0.67 tff(462,plain,
% 0.49/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_2)) | (~product(e_5, e_1, e_1)) | product(e_5, e_1, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_2)) | (~product(e_5, e_1, e_1)) | product(e_5, e_1, e_2))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(463,plain,
% 0.49/0.67 ((product(e_5, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_5, e_1, e_1))) <=> ((~product(e_1, e_1, e_2)) | (~product(e_5, e_1, e_1)) | product(e_5, e_1, e_2))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(464,plain,
% 0.49/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_5, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_2)) | (~product(e_5, e_1, e_1)) | product(e_5, e_1, e_2)))),
% 0.49/0.67 inference(monotonicity,[status(thm)],[463])).
% 0.49/0.67 tff(465,plain,
% 0.49/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_5, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_2)) | (~product(e_5, e_1, e_1)) | product(e_5, e_1, e_2))),
% 0.49/0.67 inference(transitivity,[status(thm)],[464, 462])).
% 0.49/0.67 tff(466,plain,
% 0.49/0.67 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_5, e_1, e_1)))),
% 0.49/0.67 inference(quant_inst,[status(thm)],[])).
% 0.49/0.67 tff(467,plain,
% 0.49/0.67 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_2)) | (~product(e_5, e_1, e_1)) | product(e_5, e_1, e_2)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[466, 465])).
% 0.49/0.67 tff(468,plain,
% 0.49/0.67 ($false),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[467, 106, 336, 461, 411])).
% 0.49/0.67 tff(469,plain,((~product(e_1, e_1, e_2)) | product(e_5, e_1, e_6) | product(e_5, e_1, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.67 tff(470,plain,
% 0.49/0.67 ((~product(e_1, e_1, e_2)) | product(e_5, e_1, e_6)),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[469, 404])).
% 0.49/0.67 tff(471,plain,
% 0.49/0.67 (~product(e_1, e_1, e_2)),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[470, 382])).
% 0.49/0.67 tff(472,plain,
% 0.49/0.67 (product(e_1, e_1, e_1)),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[95, 471])).
% 0.49/0.67 tff(473,assumption,(product(e_5, e_1, e_1)), introduced(assumption)).
% 0.49/0.67 tff(474,plain,
% 0.49/0.67 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_5, 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_5, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_5, e_1, e_1)))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(475,plain,
% 0.49/0.67 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_5, e_1, e_1)))),
% 0.49/0.67 inference(quant_inst,[status(thm)],[])).
% 0.49/0.67 tff(476,plain,
% 0.49/0.67 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_5, e_1, e_1))),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[475, 474])).
% 0.49/0.67 tff(477,plain,
% 0.49/0.67 ($false),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[476, 396, 12, 25, 473])).
% 0.49/0.67 tff(478,plain,((~product(e_5, e_1, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.67 tff(479,plain,
% 0.49/0.67 (~product(e_5, e_1, e_1)),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[478, 472])).
% 0.49/0.67 tff(480,plain,
% 0.49/0.67 (product(e_5, e_1, e_6) | product(e_5, e_1, e_1) | product(e_5, e_1, e_2)),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[460, 404])).
% 0.49/0.67 tff(481,plain,
% 0.49/0.67 (product(e_5, e_1, e_2)),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[480, 479, 382])).
% 0.49/0.67 tff(482,assumption,(product(e_6, e_1, e_1)), introduced(assumption)).
% 0.49/0.67 tff(483,plain,
% 0.49/0.67 ((~equalish(e_6, e_1)) <=> (~equalish(e_6, e_1))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(484,axiom,(~equalish(e_6, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_6_is_not_e_1')).
% 0.49/0.67 tff(485,plain,
% 0.49/0.67 (~equalish(e_6, e_1)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[484, 483])).
% 0.49/0.67 tff(486,plain,
% 0.49/0.67 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_6, 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_6, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_6, e_1, e_1)))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(487,plain,
% 0.49/0.67 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_6, e_1, e_1)))),
% 0.49/0.67 inference(quant_inst,[status(thm)],[])).
% 0.49/0.67 tff(488,plain,
% 0.49/0.67 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_6, e_1, e_1))),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[487, 486])).
% 0.49/0.67 tff(489,plain,
% 0.49/0.67 ($false),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[488, 485, 12, 25, 482])).
% 0.49/0.67 tff(490,plain,((~product(e_6, e_1, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.67 tff(491,plain,
% 0.49/0.67 (~product(e_6, e_1, e_1)),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[490, 472])).
% 0.49/0.67 tff(492,assumption,(product(e_6, e_1, e_6)), introduced(assumption)).
% 0.49/0.67 tff(493,plain,
% 0.49/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_6, e_6) | (~product(e_6, e_1, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_6, e_6, e_6) | (~product(e_6, e_1, e_6)))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(494,plain,
% 0.49/0.67 ((product(e_6, e_6, e_6) | (~product(e_6, e_1, e_6)) | (~product(e_6, e_1, e_6))) <=> (product(e_6, e_6, e_6) | (~product(e_6, e_1, e_6)))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(495,plain,
% 0.49/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_6, e_6) | (~product(e_6, e_1, e_6)) | (~product(e_6, e_1, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_6, e_6) | (~product(e_6, e_1, e_6))))),
% 0.49/0.67 inference(monotonicity,[status(thm)],[494])).
% 0.49/0.67 tff(496,plain,
% 0.49/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_6, e_6) | (~product(e_6, e_1, e_6)) | (~product(e_6, e_1, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_6, e_6, e_6) | (~product(e_6, e_1, e_6)))),
% 0.49/0.67 inference(transitivity,[status(thm)],[495, 493])).
% 0.49/0.67 tff(497,plain,
% 0.49/0.67 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_6, e_6) | (~product(e_6, e_1, e_6)) | (~product(e_6, e_1, e_6)))),
% 0.49/0.67 inference(quant_inst,[status(thm)],[])).
% 0.49/0.67 tff(498,plain,
% 0.49/0.67 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_6, e_6, e_6) | (~product(e_6, e_1, e_6))),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[497, 496])).
% 0.49/0.67 tff(499,plain,
% 0.49/0.67 (product(e_6, e_6, e_6) | (~product(e_6, e_1, e_6))),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[498, 106])).
% 0.49/0.67 tff(500,plain,
% 0.49/0.67 (product(e_6, e_6, e_6)),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[499, 492])).
% 0.49/0.67 tff(501,plain,
% 0.49/0.67 ((~equalish(e_1, e_6)) <=> (~equalish(e_1, e_6))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(502,axiom,(~equalish(e_1, e_6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_6')).
% 0.49/0.67 tff(503,plain,
% 0.49/0.67 (~equalish(e_1, e_6)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[502, 501])).
% 0.49/0.67 tff(504,plain,
% 0.49/0.67 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_6) | (~product(e_6, e_1, e_6)) | (~product(e_6, e_6, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_6) | (~product(e_6, e_1, e_6)) | (~product(e_6, e_6, e_6)))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(505,plain,
% 0.49/0.67 ((equalish(e_1, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_6, e_1, e_6))) <=> (equalish(e_1, e_6) | (~product(e_6, e_1, e_6)) | (~product(e_6, e_6, e_6)))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(506,plain,
% 0.49/0.67 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_6, e_1, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_6) | (~product(e_6, e_1, e_6)) | (~product(e_6, e_6, e_6))))),
% 0.49/0.67 inference(monotonicity,[status(thm)],[505])).
% 0.49/0.67 tff(507,plain,
% 0.49/0.67 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_6, e_1, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_6) | (~product(e_6, e_1, e_6)) | (~product(e_6, e_6, e_6)))),
% 0.49/0.67 inference(transitivity,[status(thm)],[506, 504])).
% 0.49/0.67 tff(508,plain,
% 0.49/0.67 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_6) | (~product(e_6, e_6, e_6)) | (~product(e_6, e_1, e_6)))),
% 0.49/0.67 inference(quant_inst,[status(thm)],[])).
% 0.49/0.67 tff(509,plain,
% 0.49/0.67 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_6) | (~product(e_6, e_1, e_6)) | (~product(e_6, e_6, e_6))),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[508, 507])).
% 0.49/0.67 tff(510,plain,
% 0.49/0.67 ($false),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[509, 503, 131, 492, 500])).
% 0.49/0.67 tff(511,plain,(~product(e_6, e_1, e_6)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.67 tff(512,plain,
% 0.49/0.67 ((~equalish(e_5, e_4)) <=> (~equalish(e_5, e_4))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(513,axiom,(~equalish(e_5, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_5_is_not_e_4')).
% 0.49/0.67 tff(514,plain,
% 0.49/0.67 (~equalish(e_5, e_4)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[513, 512])).
% 0.49/0.67 tff(515,plain,
% 0.49/0.67 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_4) | (~product(e_4, e_1, e_2)) | (~product(e_5, 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_5, e_4) | (~product(e_4, e_1, e_2)) | (~product(e_5, e_1, e_2)))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(516,plain,
% 0.49/0.67 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_4) | (~product(e_4, e_1, e_2)) | (~product(e_5, e_1, e_2)))),
% 0.49/0.67 inference(quant_inst,[status(thm)],[])).
% 0.49/0.67 tff(517,plain,
% 0.49/0.67 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_4) | (~product(e_4, e_1, e_2)) | (~product(e_5, e_1, e_2))),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[516, 515])).
% 0.49/0.67 tff(518,plain,
% 0.49/0.67 ($false),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[517, 514, 12, 2, 405])).
% 0.49/0.67 tff(519,plain,((~product(e_5, e_1, e_2)) | (~product(e_4, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.67 tff(520,plain,
% 0.49/0.67 (~product(e_4, e_1, e_2)),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[519, 481])).
% 0.49/0.67 tff(521,plain,
% 0.49/0.67 (product(e_4, e_1, e_5)),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[257, 520])).
% 0.49/0.67 tff(522,assumption,(product(e_6, e_1, e_5)), introduced(assumption)).
% 0.49/0.67 tff(523,assumption,(product(e_4, e_1, e_5)), introduced(assumption)).
% 0.49/0.67 tff(524,plain,
% 0.49/0.67 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_4) | (~product(e_4, e_1, e_5)) | (~product(e_6, e_1, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_4) | (~product(e_4, e_1, e_5)) | (~product(e_6, e_1, e_5)))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(525,plain,
% 0.49/0.67 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_4) | (~product(e_4, e_1, e_5)) | (~product(e_6, e_1, e_5)))),
% 0.49/0.67 inference(quant_inst,[status(thm)],[])).
% 0.49/0.67 tff(526,plain,
% 0.49/0.67 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_4) | (~product(e_4, e_1, e_5)) | (~product(e_6, e_1, e_5))),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[525, 524])).
% 0.49/0.67 tff(527,plain,
% 0.49/0.67 ($false),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[526, 15, 12, 523, 522])).
% 0.49/0.67 tff(528,plain,((~product(e_6, e_1, e_5)) | (~product(e_4, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.67 tff(529,plain,
% 0.49/0.67 (~product(e_6, e_1, e_5)),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[528, 521])).
% 0.49/0.67 tff(530,assumption,(product(e_6, e_1, e_3)), introduced(assumption)).
% 0.49/0.67 tff(531,plain,
% 0.49/0.67 ((~equalish(e_6, e_2)) <=> (~equalish(e_6, e_2))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(532,axiom,(~equalish(e_6, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_6_is_not_e_2')).
% 0.49/0.67 tff(533,plain,
% 0.49/0.67 (~equalish(e_6, e_2)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[532, 531])).
% 0.49/0.67 tff(534,plain,
% 0.49/0.67 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_6, 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_6, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_6, e_1, e_3)))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(535,plain,
% 0.49/0.67 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_6, e_1, e_3)))),
% 0.49/0.68 inference(quant_inst,[status(thm)],[])).
% 0.49/0.68 tff(536,plain,
% 0.49/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_6, e_1, e_3))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[535, 534])).
% 0.49/0.68 tff(537,plain,
% 0.49/0.68 ($false),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[536, 533, 12, 202, 530])).
% 0.49/0.68 tff(538,plain,(~product(e_6, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.68 tff(539,assumption,(product(e_6, e_1, e_4)), introduced(assumption)).
% 0.49/0.68 tff(540,plain,
% 0.49/0.68 ((~equalish(e_6, e_3)) <=> (~equalish(e_6, e_3))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(541,axiom,(~equalish(e_6, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_6_is_not_e_3')).
% 0.49/0.68 tff(542,plain,
% 0.49/0.68 (~equalish(e_6, e_3)),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[541, 540])).
% 0.49/0.68 tff(543,plain,
% 0.49/0.68 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_3) | (~product(e_6, e_1, e_4)) | (~product(e_3, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_3) | (~product(e_6, e_1, e_4)) | (~product(e_3, e_1, e_4)))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(544,plain,
% 0.49/0.68 ((equalish(e_6, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_6, e_1, e_4))) <=> (equalish(e_6, e_3) | (~product(e_6, e_1, e_4)) | (~product(e_3, e_1, e_4)))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(545,plain,
% 0.49/0.68 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_6, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_3) | (~product(e_6, e_1, e_4)) | (~product(e_3, e_1, e_4))))),
% 0.49/0.68 inference(monotonicity,[status(thm)],[544])).
% 0.49/0.68 tff(546,plain,
% 0.49/0.68 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_6, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_3) | (~product(e_6, e_1, e_4)) | (~product(e_3, e_1, e_4)))),
% 0.49/0.68 inference(transitivity,[status(thm)],[545, 543])).
% 0.49/0.68 tff(547,plain,
% 0.49/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_6, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_6, e_1, e_4)))),
% 0.49/0.68 inference(quant_inst,[status(thm)],[])).
% 0.49/0.68 tff(548,plain,
% 0.49/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_6, e_3) | (~product(e_6, e_1, e_4)) | (~product(e_3, e_1, e_4))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[547, 546])).
% 0.49/0.68 tff(549,plain,
% 0.49/0.68 ($false),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[548, 542, 12, 364, 539])).
% 0.49/0.68 tff(550,plain,(~product(e_6, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.68 tff(551,plain,
% 0.49/0.68 (group_element(e_6) <=> group_element(e_6)),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(552,axiom,(group_element(e_6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_6')).
% 0.49/0.68 tff(553,plain,
% 0.49/0.68 (group_element(e_6)),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[552, 551])).
% 0.49/0.68 tff(554,plain,
% 0.49/0.68 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6)) | product(e_6, e_1, e_3) | product(e_6, e_1, e_4) | product(e_6, e_1, e_1) | product(e_6, e_1, e_2) | product(e_6, e_1, e_5) | product(e_6, e_1, e_6))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6)) | product(e_6, e_1, e_3) | product(e_6, e_1, e_4) | product(e_6, e_1, e_1) | product(e_6, e_1, e_2) | product(e_6, e_1, e_5) | product(e_6, e_1, e_6))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(555,plain,
% 0.49/0.68 ((product(e_6, e_1, e_6) | product(e_6, e_1, e_5) | product(e_6, e_1, e_4) | product(e_6, e_1, e_3) | product(e_6, e_1, e_2) | product(e_6, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_6))) <=> ((~group_element(e_1)) | (~group_element(e_6)) | product(e_6, e_1, e_3) | product(e_6, e_1, e_4) | product(e_6, e_1, e_1) | product(e_6, e_1, e_2) | product(e_6, e_1, e_5) | product(e_6, e_1, e_6))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(556,plain,
% 0.49/0.68 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6, e_1, e_6) | product(e_6, e_1, e_5) | product(e_6, e_1, e_4) | product(e_6, e_1, e_3) | product(e_6, e_1, e_2) | product(e_6, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_6)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6)) | product(e_6, e_1, e_3) | product(e_6, e_1, e_4) | product(e_6, e_1, e_1) | product(e_6, e_1, e_2) | product(e_6, e_1, e_5) | product(e_6, e_1, e_6)))),
% 0.49/0.68 inference(monotonicity,[status(thm)],[555])).
% 0.49/0.68 tff(557,plain,
% 0.49/0.68 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6, e_1, e_6) | product(e_6, e_1, e_5) | product(e_6, e_1, e_4) | product(e_6, e_1, e_3) | product(e_6, e_1, e_2) | product(e_6, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_6)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6)) | product(e_6, e_1, e_3) | product(e_6, e_1, e_4) | product(e_6, e_1, e_1) | product(e_6, e_1, e_2) | product(e_6, e_1, e_5) | product(e_6, e_1, e_6))),
% 0.49/0.68 inference(transitivity,[status(thm)],[556, 554])).
% 0.49/0.68 tff(558,plain,
% 0.49/0.68 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6, e_1, e_6) | product(e_6, e_1, e_5) | product(e_6, e_1, e_4) | product(e_6, e_1, e_3) | product(e_6, e_1, e_2) | product(e_6, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_6)))),
% 0.49/0.68 inference(quant_inst,[status(thm)],[])).
% 0.49/0.68 tff(559,plain,
% 0.49/0.68 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6)) | product(e_6, e_1, e_3) | product(e_6, e_1, e_4) | product(e_6, e_1, e_1) | product(e_6, e_1, e_2) | product(e_6, e_1, e_5) | product(e_6, e_1, e_6)),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[558, 557])).
% 0.49/0.68 tff(560,plain,
% 0.49/0.68 (product(e_6, e_1, e_3) | product(e_6, e_1, e_4) | product(e_6, e_1, e_1) | product(e_6, e_1, e_2) | product(e_6, e_1, e_5) | product(e_6, e_1, e_6)),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[559, 88, 553, 85])).
% 0.49/0.68 tff(561,plain,
% 0.49/0.68 (product(e_6, e_1, e_1) | product(e_6, e_1, e_2) | product(e_6, e_1, e_5) | product(e_6, e_1, e_6)),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[560, 550, 538])).
% 0.49/0.68 tff(562,plain,
% 0.49/0.68 (product(e_6, e_1, e_2)),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[561, 529, 511, 491])).
% 0.49/0.68 tff(563,plain,
% 0.49/0.68 ((~equalish(e_5, e_6)) <=> (~equalish(e_5, e_6))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(564,axiom,(~equalish(e_5, e_6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_5_is_not_e_6')).
% 0.49/0.68 tff(565,plain,
% 0.49/0.68 (~equalish(e_5, e_6)),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[564, 563])).
% 0.49/0.68 tff(566,plain,
% 0.49/0.68 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_6) | (~product(e_6, e_1, e_2)) | (~product(e_5, 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_5, e_6) | (~product(e_6, e_1, e_2)) | (~product(e_5, e_1, e_2)))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(567,plain,
% 0.49/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_6) | (~product(e_6, e_1, e_2)) | (~product(e_5, e_1, e_2)))),
% 0.49/0.68 inference(quant_inst,[status(thm)],[])).
% 0.49/0.68 tff(568,plain,
% 0.49/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_6) | (~product(e_6, e_1, e_2)) | (~product(e_5, e_1, e_2))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[567, 566])).
% 0.49/0.68 tff(569,plain,
% 0.49/0.68 ($false),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[568, 565, 12, 562, 481])).
% 0.49/0.68 tff(570,plain,(product(e_5, e_1, e_6)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.68 tff(571,assumption,(product(e_5, e_1, e_6)), introduced(assumption)).
% 0.49/0.68 tff(572,assumption,(~product(e_5, e_6, e_2)), introduced(assumption)).
% 0.49/0.68 tff(573,plain,
% 0.49/0.68 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_6, e_1, e_2)) | product(e_5, e_6, e_2) | (~product(e_5, e_1, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_6, e_1, e_2)) | product(e_5, e_6, e_2) | (~product(e_5, e_1, e_6)))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(574,plain,
% 0.49/0.68 ((product(e_5, e_6, e_2) | (~product(e_6, e_1, e_2)) | (~product(e_5, e_1, e_6))) <=> ((~product(e_6, e_1, e_2)) | product(e_5, e_6, e_2) | (~product(e_5, e_1, e_6)))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(575,plain,
% 0.49/0.68 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_6, e_2) | (~product(e_6, e_1, e_2)) | (~product(e_5, e_1, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_6, e_1, e_2)) | product(e_5, e_6, e_2) | (~product(e_5, e_1, e_6))))),
% 0.49/0.68 inference(monotonicity,[status(thm)],[574])).
% 0.49/0.68 tff(576,plain,
% 0.49/0.68 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_6, e_2) | (~product(e_6, e_1, e_2)) | (~product(e_5, e_1, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_6, e_1, e_2)) | product(e_5, e_6, e_2) | (~product(e_5, e_1, e_6)))),
% 0.49/0.68 inference(transitivity,[status(thm)],[575, 573])).
% 0.49/0.68 tff(577,plain,
% 0.49/0.68 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_6, e_2) | (~product(e_6, e_1, e_2)) | (~product(e_5, e_1, e_6)))),
% 0.49/0.68 inference(quant_inst,[status(thm)],[])).
% 0.49/0.68 tff(578,plain,
% 0.49/0.68 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_6, e_1, e_2)) | product(e_5, e_6, e_2) | (~product(e_5, e_1, e_6))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[577, 576])).
% 0.49/0.68 tff(579,plain,
% 0.49/0.68 ($false),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[578, 106, 1, 572, 571])).
% 0.49/0.68 tff(580,plain,(product(e_5, e_6, e_2) | (~product(e_6, e_1, e_2)) | (~product(e_5, e_1, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.68 tff(581,plain,
% 0.49/0.68 (product(e_5, e_6, e_2) | (~product(e_6, e_1, e_2))),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[580, 570])).
% 0.49/0.68 tff(582,plain,
% 0.49/0.68 (product(e_5, e_6, e_2)),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[581, 1])).
% 0.49/0.68 tff(583,assumption,(product(e_5, e_6, e_2)), introduced(assumption)).
% 0.49/0.68 tff(584,assumption,(product(e_2, e_5, e_2)), introduced(assumption)).
% 0.49/0.68 tff(585,plain,
% 0.49/0.68 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_5, e_2)) | product(e_2, e_2, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_5, e_2)) | product(e_2, e_2, e_2))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(586,plain,
% 0.49/0.68 ((product(e_2, e_2, e_2) | (~product(e_2, e_5, e_2)) | (~product(e_2, e_5, e_2))) <=> ((~product(e_2, e_5, e_2)) | product(e_2, e_2, e_2))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(587,plain,
% 0.49/0.68 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_5, e_2)) | (~product(e_2, e_5, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_5, e_2)) | product(e_2, e_2, e_2)))),
% 0.49/0.68 inference(monotonicity,[status(thm)],[586])).
% 0.49/0.68 tff(588,plain,
% 0.49/0.68 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_5, e_2)) | (~product(e_2, e_5, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_5, e_2)) | product(e_2, e_2, e_2))),
% 0.49/0.68 inference(transitivity,[status(thm)],[587, 585])).
% 0.49/0.68 tff(589,plain,
% 0.49/0.68 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_5, e_2)) | (~product(e_2, e_5, e_2)))),
% 0.49/0.68 inference(quant_inst,[status(thm)],[])).
% 0.49/0.68 tff(590,plain,
% 0.49/0.68 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_5, e_2)) | product(e_2, e_2, e_2)),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[589, 588])).
% 0.49/0.68 tff(591,plain,
% 0.49/0.68 ((~product(e_2, e_5, e_2)) | product(e_2, e_2, e_2)),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[590, 106])).
% 0.49/0.68 tff(592,plain,
% 0.49/0.68 (product(e_2, e_2, e_2)),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[591, 584])).
% 0.49/0.68 tff(593,plain,
% 0.49/0.68 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_2, e_5, 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_5, e_2) | (~product(e_2, e_5, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(594,plain,
% 0.49/0.68 ((equalish(e_5, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_5, e_2))) <=> (equalish(e_5, e_2) | (~product(e_2, e_5, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(595,plain,
% 0.49/0.68 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_5, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_2, e_5, e_2)) | (~product(e_2, e_2, e_2))))),
% 0.49/0.68 inference(monotonicity,[status(thm)],[594])).
% 0.49/0.68 tff(596,plain,
% 0.49/0.68 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_5, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_2) | (~product(e_2, e_5, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.49/0.68 inference(transitivity,[status(thm)],[595, 593])).
% 0.49/0.68 tff(597,plain,
% 0.49/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_5, e_2)))),
% 0.49/0.68 inference(quant_inst,[status(thm)],[])).
% 0.49/0.68 tff(598,plain,
% 0.49/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_2) | (~product(e_2, e_5, e_2)) | (~product(e_2, e_2, e_2))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[597, 596])).
% 0.49/0.68 tff(599,plain,
% 0.49/0.68 ($false),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[598, 437, 131, 584, 592])).
% 0.49/0.68 tff(600,plain,(~product(e_2, e_5, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.68 tff(601,assumption,(product(e_2, e_6, e_5)), introduced(assumption)).
% 0.49/0.68 tff(602,plain,
% 0.49/0.68 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_5, e_2) | (~product(e_5, e_6, e_2)) | (~product(e_2, e_6, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_5, e_2) | (~product(e_5, e_6, e_2)) | (~product(e_2, e_6, e_5)))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(603,plain,
% 0.49/0.68 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_5, e_2) | (~product(e_5, e_6, e_2)) | (~product(e_2, e_6, e_5)))),
% 0.49/0.68 inference(quant_inst,[status(thm)],[])).
% 0.49/0.68 tff(604,plain,
% 0.49/0.68 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_5, e_2) | (~product(e_5, e_6, e_2)) | (~product(e_2, e_6, e_5))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[603, 602])).
% 0.49/0.68 tff(605,plain,
% 0.49/0.68 ($false),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[604, 106, 601, 600, 583])).
% 0.49/0.68 tff(606,plain,((~product(e_5, e_6, e_2)) | (~product(e_2, e_6, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.68 tff(607,plain,
% 0.49/0.68 (~product(e_2, e_6, e_5)),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[606, 582])).
% 0.49/0.68 tff(608,assumption,(product(e_2, e_6, e_2)), introduced(assumption)).
% 0.49/0.68 tff(609,plain,
% 0.49/0.68 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_6, e_2)) | (~product(e_5, e_6, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_2) | (~product(e_2, e_6, e_2)) | (~product(e_5, e_6, e_2)))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(610,plain,
% 0.49/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_6, e_2)) | (~product(e_5, e_6, e_2)))),
% 0.49/0.69 inference(quant_inst,[status(thm)],[])).
% 0.49/0.69 tff(611,plain,
% 0.49/0.69 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_2) | (~product(e_2, e_6, e_2)) | (~product(e_5, e_6, e_2))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[610, 609])).
% 0.49/0.69 tff(612,plain,
% 0.49/0.69 ($false),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[611, 437, 12, 608, 583])).
% 0.49/0.69 tff(613,plain,((~product(e_5, e_6, e_2)) | (~product(e_2, e_6, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.69 tff(614,plain,
% 0.49/0.69 (~product(e_2, e_6, e_2)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[613, 582])).
% 0.49/0.69 tff(615,assumption,(product(e_2, e_4, e_5)), introduced(assumption)).
% 0.49/0.69 tff(616,plain,
% 0.49/0.69 (((~![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_4, e_5)) | (~product(e_2, e_4, e_5)))) <=> ((~![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_4, e_5)) | (~product(e_2, e_4, e_5)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(617,plain,
% 0.49/0.69 ((~![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_4, e_5)) | (~product(e_2, e_4, e_5)))),
% 0.49/0.69 inference(quant_inst,[status(thm)],[])).
% 0.49/0.69 tff(618,plain,
% 0.49/0.69 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_4, e_5)) | (~product(e_2, e_4, e_5))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[617, 616])).
% 0.49/0.69 tff(619,plain,
% 0.49/0.69 ($false),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[618, 264, 12, 372, 615])).
% 0.49/0.69 tff(620,plain,((~product(e_2, e_4, e_5)) | (~product(e_3, e_4, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.69 tff(621,plain,
% 0.49/0.69 (~product(e_2, e_4, e_5)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[620, 370])).
% 0.49/0.69 tff(622,assumption,(~product(e_2, e_6, e_2)), introduced(assumption)).
% 0.49/0.69 tff(623,assumption,(~product(e_2, e_6, e_5)), introduced(assumption)).
% 0.49/0.69 tff(624,assumption,(product(e_2, e_5, e_6)), introduced(assumption)).
% 0.49/0.69 tff(625,assumption,(product(e_2, e_6, e_6)), introduced(assumption)).
% 0.49/0.69 tff(626,plain,
% 0.49/0.69 ((~equalish(e_6, e_5)) <=> (~equalish(e_6, e_5))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(627,axiom,(~equalish(e_6, e_5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_6_is_not_e_5')).
% 0.49/0.69 tff(628,plain,
% 0.49/0.69 (~equalish(e_6, e_5)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[627, 626])).
% 0.49/0.69 tff(629,plain,
% 0.49/0.69 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_5) | (~product(e_2, e_5, e_6)) | (~product(e_2, e_6, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_5) | (~product(e_2, e_5, e_6)) | (~product(e_2, e_6, e_6)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(630,plain,
% 0.49/0.69 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_5) | (~product(e_2, e_5, e_6)) | (~product(e_2, e_6, e_6)))),
% 0.49/0.69 inference(quant_inst,[status(thm)],[])).
% 0.49/0.69 tff(631,plain,
% 0.49/0.69 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_5) | (~product(e_2, e_5, e_6)) | (~product(e_2, e_6, e_6))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[630, 629])).
% 0.49/0.69 tff(632,plain,
% 0.49/0.69 ($false),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[631, 628, 131, 625, 624])).
% 0.49/0.69 tff(633,plain,((~product(e_2, e_6, e_6)) | (~product(e_2, e_5, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.69 tff(634,plain,
% 0.49/0.69 (~product(e_2, e_6, e_6)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[633, 624])).
% 0.49/0.69 tff(635,assumption,(product(e_2, e_3, e_4)), introduced(assumption)).
% 0.49/0.69 tff(636,assumption,(product(e_2, e_6, e_4)), introduced(assumption)).
% 0.49/0.69 tff(637,plain,
% 0.49/0.69 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_3) | (~product(e_2, e_6, 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_6, e_3) | (~product(e_2, e_6, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(638,plain,
% 0.49/0.69 ((equalish(e_6, e_3) | (~product(e_2, e_3, e_4)) | (~product(e_2, e_6, e_4))) <=> (equalish(e_6, e_3) | (~product(e_2, e_6, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(639,plain,
% 0.49/0.69 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_3) | (~product(e_2, e_3, e_4)) | (~product(e_2, e_6, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_3) | (~product(e_2, e_6, e_4)) | (~product(e_2, e_3, e_4))))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[638])).
% 0.49/0.69 tff(640,plain,
% 0.49/0.69 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_3) | (~product(e_2, e_3, e_4)) | (~product(e_2, e_6, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_3) | (~product(e_2, e_6, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.49/0.69 inference(transitivity,[status(thm)],[639, 637])).
% 0.49/0.69 tff(641,plain,
% 0.49/0.69 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_3) | (~product(e_2, e_3, e_4)) | (~product(e_2, e_6, e_4)))),
% 0.49/0.69 inference(quant_inst,[status(thm)],[])).
% 0.49/0.69 tff(642,plain,
% 0.49/0.69 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_3) | (~product(e_2, e_6, e_4)) | (~product(e_2, e_3, e_4))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[641, 640])).
% 0.49/0.69 tff(643,plain,
% 0.49/0.69 ($false),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[642, 542, 131, 636, 635])).
% 0.49/0.69 tff(644,plain,((~product(e_2, e_6, e_4)) | (~product(e_2, e_3, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.69 tff(645,plain,
% 0.49/0.69 (~product(e_2, e_6, e_4)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[644, 433])).
% 0.49/0.69 tff(646,assumption,(product(e_2, e_6, e_3)), introduced(assumption)).
% 0.49/0.69 tff(647,plain,
% 0.49/0.69 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_6, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_6, e_3)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(648,plain,
% 0.49/0.69 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_6, e_3)))),
% 0.49/0.69 inference(quant_inst,[status(thm)],[])).
% 0.49/0.69 tff(649,plain,
% 0.49/0.69 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_6, e_3))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[648, 647])).
% 0.49/0.69 tff(650,plain,
% 0.49/0.69 ($false),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[649, 485, 131, 202, 646])).
% 0.49/0.69 tff(651,plain,(~product(e_2, e_6, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.69 tff(652,plain,
% 0.49/0.69 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6, e_6) | product(e_2, e_6, e_5) | product(e_2, e_6, e_4) | product(e_2, e_6, e_3) | product(e_2, e_6, e_2) | product(e_2, e_6, e_1) | (~group_element(e_6)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6, e_6) | product(e_2, e_6, e_5) | product(e_2, e_6, e_4) | product(e_2, e_6, e_3) | product(e_2, e_6, e_2) | product(e_2, e_6, e_1) | (~group_element(e_6)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(653,plain,
% 0.49/0.69 ((product(e_2, e_6, e_6) | product(e_2, e_6, e_5) | product(e_2, e_6, e_4) | product(e_2, e_6, e_3) | product(e_2, e_6, e_2) | product(e_2, e_6, e_1) | (~group_element(e_6)) | (~group_element(e_2))) <=> ((~group_element(e_2)) | product(e_2, e_6, e_6) | product(e_2, e_6, e_5) | product(e_2, e_6, e_4) | product(e_2, e_6, e_3) | product(e_2, e_6, e_2) | product(e_2, e_6, e_1) | (~group_element(e_6)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(654,plain,
% 0.49/0.69 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6, e_6) | product(e_2, e_6, e_5) | product(e_2, e_6, e_4) | product(e_2, e_6, e_3) | product(e_2, e_6, e_2) | product(e_2, e_6, e_1) | (~group_element(e_6)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6, e_6) | product(e_2, e_6, e_5) | product(e_2, e_6, e_4) | product(e_2, e_6, e_3) | product(e_2, e_6, e_2) | product(e_2, e_6, e_1) | (~group_element(e_6))))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[653])).
% 0.49/0.69 tff(655,plain,
% 0.49/0.69 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6, e_6) | product(e_2, e_6, e_5) | product(e_2, e_6, e_4) | product(e_2, e_6, e_3) | product(e_2, e_6, e_2) | product(e_2, e_6, e_1) | (~group_element(e_6)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6, e_6) | product(e_2, e_6, e_5) | product(e_2, e_6, e_4) | product(e_2, e_6, e_3) | product(e_2, e_6, e_2) | product(e_2, e_6, e_1) | (~group_element(e_6)))),
% 0.49/0.69 inference(transitivity,[status(thm)],[654, 652])).
% 0.49/0.69 tff(656,plain,
% 0.49/0.69 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6, e_6) | product(e_2, e_6, e_5) | product(e_2, e_6, e_4) | product(e_2, e_6, e_3) | product(e_2, e_6, e_2) | product(e_2, e_6, e_1) | (~group_element(e_6)) | (~group_element(e_2)))),
% 0.49/0.69 inference(quant_inst,[status(thm)],[])).
% 0.49/0.69 tff(657,plain,
% 0.49/0.69 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6, e_6) | product(e_2, e_6, e_5) | product(e_2, e_6, e_4) | product(e_2, e_6, e_3) | product(e_2, e_6, e_2) | product(e_2, e_6, e_1) | (~group_element(e_6))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[656, 655])).
% 0.49/0.69 tff(658,plain,
% 0.49/0.69 (product(e_2, e_6, e_6) | product(e_2, e_6, e_5) | product(e_2, e_6, e_4) | product(e_2, e_6, e_3) | product(e_2, e_6, e_2) | product(e_2, e_6, e_1)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[657, 193, 553, 85])).
% 0.49/0.69 tff(659,plain,
% 0.49/0.69 (product(e_2, e_6, e_6) | product(e_2, e_6, e_5) | product(e_2, e_6, e_4) | product(e_2, e_6, e_2) | product(e_2, e_6, e_1)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[658, 651])).
% 0.49/0.69 tff(660,plain,
% 0.49/0.69 (product(e_2, e_6, e_6) | product(e_2, e_6, e_5) | product(e_2, e_6, e_2) | product(e_2, e_6, e_1)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[659, 645])).
% 0.49/0.69 tff(661,plain,
% 0.49/0.69 (product(e_2, e_6, e_1)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[660, 634, 623, 622])).
% 0.49/0.69 tff(662,assumption,(~product(e_2, e_4, e_5)), introduced(assumption)).
% 0.49/0.69 tff(663,assumption,(product(e_2, e_4, e_6)), introduced(assumption)).
% 0.49/0.69 tff(664,plain,
% 0.49/0.69 ((~equalish(e_4, e_5)) <=> (~equalish(e_4, e_5))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(665,axiom,(~equalish(e_4, e_5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_is_not_e_5')).
% 0.49/0.69 tff(666,plain,
% 0.49/0.69 (~equalish(e_4, e_5)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[665, 664])).
% 0.49/0.69 tff(667,plain,
% 0.49/0.69 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_5) | (~product(e_2, e_5, e_6)) | (~product(e_2, e_4, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_5) | (~product(e_2, e_5, e_6)) | (~product(e_2, e_4, e_6)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(668,plain,
% 0.49/0.69 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_5) | (~product(e_2, e_5, e_6)) | (~product(e_2, e_4, e_6)))),
% 0.49/0.69 inference(quant_inst,[status(thm)],[])).
% 0.49/0.69 tff(669,plain,
% 0.49/0.69 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_5) | (~product(e_2, e_5, e_6)) | (~product(e_2, e_4, e_6))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[668, 667])).
% 0.49/0.69 tff(670,plain,
% 0.49/0.69 ($false),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[669, 666, 131, 624, 663])).
% 0.49/0.69 tff(671,plain,((~product(e_2, e_4, e_6)) | (~product(e_2, e_5, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.69 tff(672,plain,
% 0.49/0.69 (~product(e_2, e_4, e_6)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[671, 624])).
% 0.49/0.69 tff(673,assumption,(product(e_2, e_4, e_4)), introduced(assumption)).
% 0.49/0.69 tff(674,plain,
% 0.49/0.69 ((~equalish(e_4, e_3)) <=> (~equalish(e_4, e_3))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(675,axiom,(~equalish(e_4, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_is_not_e_3')).
% 0.49/0.69 tff(676,plain,
% 0.49/0.69 (~equalish(e_4, e_3)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[675, 674])).
% 0.49/0.69 tff(677,plain,
% 0.49/0.69 (((~![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_2, e_3, e_4)) | (~product(e_2, 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_2, e_3, e_4)) | (~product(e_2, e_4, e_4)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(678,plain,
% 0.49/0.69 ((~![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_2, e_3, e_4)) | (~product(e_2, e_4, e_4)))),
% 0.49/0.69 inference(quant_inst,[status(thm)],[])).
% 0.49/0.69 tff(679,plain,
% 0.49/0.69 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_2, e_3, e_4)) | (~product(e_2, e_4, e_4))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[678, 677])).
% 0.49/0.69 tff(680,plain,
% 0.49/0.69 ($false),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[679, 676, 131, 433, 673])).
% 0.49/0.69 tff(681,plain,(~product(e_2, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.69 tff(682,assumption,(product(e_2, e_4, e_2)), introduced(assumption)).
% 0.49/0.69 tff(683,plain,
% 0.49/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_2) | (~product(e_2, e_4, e_2)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(684,plain,
% 0.49/0.69 ((product(e_2, e_2, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_2, e_4, e_2))) <=> (product(e_2, e_2, e_2) | (~product(e_2, e_4, e_2)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(685,plain,
% 0.49/0.69 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_2, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_4, e_2))))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[684])).
% 0.49/0.70 tff(686,plain,
% 0.49/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_2, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_2) | (~product(e_2, e_4, e_2)))),
% 0.49/0.70 inference(transitivity,[status(thm)],[685, 683])).
% 0.49/0.70 tff(687,plain,
% 0.49/0.70 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_2, e_4, e_2)))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(688,plain,
% 0.49/0.70 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_2) | (~product(e_2, e_4, e_2))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[687, 686])).
% 0.49/0.70 tff(689,plain,
% 0.49/0.70 (product(e_2, e_2, e_2) | (~product(e_2, e_4, e_2))),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[688, 106])).
% 0.49/0.70 tff(690,plain,
% 0.49/0.70 (product(e_2, e_2, e_2)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[689, 682])).
% 0.49/0.70 tff(691,plain,
% 0.49/0.70 (((~![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)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(692,plain,
% 0.49/0.70 ((~![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)))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(693,plain,
% 0.49/0.70 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[692, 691])).
% 0.49/0.70 tff(694,plain,
% 0.49/0.70 ($false),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[693, 207, 131, 690, 682])).
% 0.49/0.70 tff(695,plain,(~product(e_2, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.70 tff(696,assumption,(product(e_2, e_4, e_3)), introduced(assumption)).
% 0.49/0.70 tff(697,plain,
% 0.49/0.70 (((~![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)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(698,plain,
% 0.49/0.70 ((~![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)))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(699,plain,
% 0.49/0.70 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[698, 697])).
% 0.49/0.70 tff(700,plain,
% 0.49/0.70 ($false),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[699, 28, 131, 202, 696])).
% 0.49/0.70 tff(701,plain,(~product(e_2, e_4, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.70 tff(702,plain,
% 0.49/0.70 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5) | product(e_2, e_4, e_4) | product(e_2, e_4, e_6) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5) | product(e_2, e_4, e_4) | product(e_2, e_4, e_6) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(703,plain,
% 0.49/0.70 ((product(e_2, e_4, e_6) | product(e_2, e_4, e_5) | 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_5) | product(e_2, e_4, e_4) | product(e_2, e_4, e_6) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(704,plain,
% 0.49/0.70 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6) | product(e_2, e_4, e_5) | 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_6) | product(X, Y, e_5) | 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_5) | product(e_2, e_4, e_4) | product(e_2, e_4, e_6) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2)))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[703])).
% 0.49/0.70 tff(705,plain,
% 0.49/0.70 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6) | product(e_2, e_4, e_5) | 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_6) | product(X, Y, e_5) | 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_5) | product(e_2, e_4, e_4) | product(e_2, e_4, e_6) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2))),
% 0.49/0.70 inference(transitivity,[status(thm)],[704, 702])).
% 0.49/0.70 tff(706,plain,
% 0.49/0.70 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6) | product(e_2, e_4, e_5) | 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)))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(707,plain,
% 0.49/0.70 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5) | product(e_2, e_4, e_4) | product(e_2, e_4, e_6) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[706, 705])).
% 0.49/0.70 tff(708,plain,
% 0.49/0.70 (product(e_2, e_4, e_5) | product(e_2, e_4, e_4) | product(e_2, e_4, e_6) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[707, 193, 246, 85])).
% 0.49/0.70 tff(709,plain,
% 0.49/0.70 (product(e_2, e_4, e_5) | product(e_2, e_4, e_4) | product(e_2, e_4, e_6) | product(e_2, e_4, e_1) | product(e_2, e_4, e_2)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[708, 701])).
% 0.49/0.70 tff(710,plain,
% 0.49/0.70 (product(e_2, e_4, e_5) | product(e_2, e_4, e_4) | product(e_2, e_4, e_6) | product(e_2, e_4, e_1)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[709, 695])).
% 0.49/0.70 tff(711,plain,
% 0.49/0.70 (product(e_2, e_4, e_5) | product(e_2, e_4, e_6) | product(e_2, e_4, e_1)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[710, 681])).
% 0.49/0.70 tff(712,plain,
% 0.49/0.70 (product(e_2, e_4, e_1)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[711, 672, 662])).
% 0.49/0.70 tff(713,assumption,(product(e_2, e_4, e_1)), introduced(assumption)).
% 0.49/0.70 tff(714,assumption,(product(e_2, e_6, e_1)), introduced(assumption)).
% 0.49/0.70 tff(715,plain,
% 0.49/0.70 ((~equalish(e_4, e_6)) <=> (~equalish(e_4, e_6))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(716,axiom,(~equalish(e_4, e_6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_is_not_e_6')).
% 0.49/0.70 tff(717,plain,
% 0.49/0.70 (~equalish(e_4, e_6)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[716, 715])).
% 0.49/0.70 tff(718,plain,
% 0.49/0.70 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_6) | (~product(e_2, e_4, e_1)) | (~product(e_2, e_6, 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_6) | (~product(e_2, e_4, e_1)) | (~product(e_2, e_6, e_1)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(719,plain,
% 0.49/0.70 ((equalish(e_4, e_6) | (~product(e_2, e_6, e_1)) | (~product(e_2, e_4, e_1))) <=> (equalish(e_4, e_6) | (~product(e_2, e_4, e_1)) | (~product(e_2, e_6, e_1)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(720,plain,
% 0.49/0.70 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_6) | (~product(e_2, e_6, e_1)) | (~product(e_2, 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_6) | (~product(e_2, e_4, e_1)) | (~product(e_2, e_6, e_1))))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[719])).
% 0.49/0.70 tff(721,plain,
% 0.49/0.70 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_6) | (~product(e_2, e_6, e_1)) | (~product(e_2, 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_6) | (~product(e_2, e_4, e_1)) | (~product(e_2, e_6, e_1)))),
% 0.49/0.70 inference(transitivity,[status(thm)],[720, 718])).
% 0.49/0.70 tff(722,plain,
% 0.49/0.70 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_6) | (~product(e_2, e_6, e_1)) | (~product(e_2, e_4, e_1)))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(723,plain,
% 0.49/0.70 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_6) | (~product(e_2, e_4, e_1)) | (~product(e_2, e_6, e_1))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[722, 721])).
% 0.49/0.70 tff(724,plain,
% 0.49/0.70 ($false),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[723, 717, 131, 714, 713])).
% 0.49/0.70 tff(725,plain,((~product(e_2, e_4, e_1)) | (~product(e_2, e_6, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.70 tff(726,plain,
% 0.49/0.70 ($false),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[725, 712, 661])).
% 0.49/0.70 tff(727,plain,((~product(e_2, e_5, e_6)) | product(e_2, e_4, e_5) | product(e_2, e_6, e_5) | product(e_2, e_6, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.70 tff(728,plain,
% 0.49/0.70 (~product(e_2, e_5, e_6)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[727, 621, 614, 607])).
% 0.49/0.70 tff(729,assumption,(~product(e_4, e_5, e_6)), introduced(assumption)).
% 0.49/0.70 tff(730,plain,
% 0.49/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_4, e_1, e_5)) | product(e_4, e_5, e_6) | (~product(e_5, e_1, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_1, e_5)) | product(e_4, e_5, e_6) | (~product(e_5, e_1, e_6)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(731,plain,
% 0.49/0.70 ((product(e_4, e_5, e_6) | (~product(e_5, e_1, e_6)) | (~product(e_4, e_1, e_5))) <=> ((~product(e_4, e_1, e_5)) | product(e_4, e_5, e_6) | (~product(e_5, e_1, e_6)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(732,plain,
% 0.49/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_5, e_6) | (~product(e_5, e_1, e_6)) | (~product(e_4, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_4, e_1, e_5)) | product(e_4, e_5, e_6) | (~product(e_5, e_1, e_6))))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[731])).
% 0.49/0.70 tff(733,plain,
% 0.49/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_5, e_6) | (~product(e_5, e_1, e_6)) | (~product(e_4, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_1, e_5)) | product(e_4, e_5, e_6) | (~product(e_5, e_1, e_6)))),
% 0.49/0.70 inference(transitivity,[status(thm)],[732, 730])).
% 0.49/0.70 tff(734,plain,
% 0.49/0.70 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_5, e_6) | (~product(e_5, e_1, e_6)) | (~product(e_4, e_1, e_5)))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(735,plain,
% 0.49/0.70 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_1, e_5)) | product(e_4, e_5, e_6) | (~product(e_5, e_1, e_6))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[734, 733])).
% 0.49/0.70 tff(736,plain,
% 0.49/0.70 ($false),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[735, 106, 523, 570, 729])).
% 0.49/0.70 tff(737,plain,(product(e_4, e_5, e_6) | (~product(e_4, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.70 tff(738,plain,
% 0.49/0.70 (product(e_4, e_5, e_6)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[737, 258])).
% 0.49/0.70 tff(739,assumption,(product(e_4, e_5, e_6)), introduced(assumption)).
% 0.49/0.70 tff(740,assumption,(product(e_3, e_5, e_6)), introduced(assumption)).
% 0.49/0.70 tff(741,plain,
% 0.49/0.70 ((~equalish(e_3, e_4)) <=> (~equalish(e_3, e_4))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(742,axiom,(~equalish(e_3, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_4')).
% 0.49/0.70 tff(743,plain,
% 0.49/0.70 (~equalish(e_3, e_4)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[742, 741])).
% 0.49/0.70 tff(744,plain,
% 0.49/0.70 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_4, e_5, e_6)) | (~product(e_3, e_5, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_4) | (~product(e_4, e_5, e_6)) | (~product(e_3, e_5, e_6)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(745,plain,
% 0.49/0.70 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_4, e_5, e_6)) | (~product(e_3, e_5, e_6)))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(746,plain,
% 0.49/0.70 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_4) | (~product(e_4, e_5, e_6)) | (~product(e_3, e_5, e_6))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[745, 744])).
% 0.49/0.70 tff(747,plain,
% 0.49/0.70 ($false),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[746, 743, 12, 740, 739])).
% 0.49/0.70 tff(748,plain,((~product(e_3, e_5, e_6)) | (~product(e_4, e_5, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.70 tff(749,plain,
% 0.49/0.70 (~product(e_3, e_5, e_6)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[748, 738])).
% 0.49/0.70 tff(750,assumption,(product(e_5, e_4, e_6)), introduced(assumption)).
% 0.49/0.70 tff(751,assumption,(~product(e_3, e_5, e_6)), introduced(assumption)).
% 0.49/0.70 tff(752,plain,
% 0.49/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_5, e_6) | (~product(e_3, e_4, e_5)) | (~product(e_5, e_4, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_5, e_6) | (~product(e_3, e_4, e_5)) | (~product(e_5, e_4, e_6)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(753,plain,
% 0.49/0.70 ((product(e_3, e_5, e_6) | (~product(e_5, e_4, e_6)) | (~product(e_3, e_4, e_5))) <=> (product(e_3, e_5, e_6) | (~product(e_3, e_4, e_5)) | (~product(e_5, e_4, e_6)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(754,plain,
% 0.49/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_5, e_6) | (~product(e_5, e_4, e_6)) | (~product(e_3, e_4, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_5, e_6) | (~product(e_3, e_4, e_5)) | (~product(e_5, e_4, e_6))))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[753])).
% 0.49/0.70 tff(755,plain,
% 0.49/0.70 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_5, e_6) | (~product(e_5, e_4, e_6)) | (~product(e_3, e_4, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_5, e_6) | (~product(e_3, e_4, e_5)) | (~product(e_5, e_4, e_6)))),
% 0.49/0.70 inference(transitivity,[status(thm)],[754, 752])).
% 0.49/0.70 tff(756,plain,
% 0.49/0.70 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_5, e_6) | (~product(e_5, e_4, e_6)) | (~product(e_3, e_4, e_5)))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(757,plain,
% 0.49/0.70 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_5, e_6) | (~product(e_3, e_4, e_5)) | (~product(e_5, e_4, e_6))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[756, 755])).
% 0.49/0.70 tff(758,plain,
% 0.49/0.70 ($false),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[757, 106, 751, 372, 750])).
% 0.49/0.70 tff(759,plain,((~product(e_5, e_4, e_6)) | product(e_3, e_5, e_6) | (~product(e_3, e_4, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.70 tff(760,plain,
% 0.49/0.70 (~product(e_5, e_4, e_6)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[759, 749, 370])).
% 0.49/0.70 tff(761,assumption,(product(e_5, e_4, e_2)), introduced(assumption)).
% 0.49/0.70 tff(762,plain,
% 0.49/0.70 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_6) | (~product(e_5, e_4, e_2)) | (~product(e_5, e_6, 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_6) | (~product(e_5, e_4, e_2)) | (~product(e_5, e_6, e_2)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(763,plain,
% 0.49/0.71 ((equalish(e_4, e_6) | (~product(e_5, e_6, e_2)) | (~product(e_5, e_4, e_2))) <=> (equalish(e_4, e_6) | (~product(e_5, e_4, e_2)) | (~product(e_5, e_6, e_2)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(764,plain,
% 0.49/0.71 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_6) | (~product(e_5, e_6, e_2)) | (~product(e_5, 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_6) | (~product(e_5, e_4, e_2)) | (~product(e_5, e_6, e_2))))),
% 0.49/0.71 inference(monotonicity,[status(thm)],[763])).
% 0.49/0.71 tff(765,plain,
% 0.49/0.71 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_6) | (~product(e_5, e_6, e_2)) | (~product(e_5, 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_6) | (~product(e_5, e_4, e_2)) | (~product(e_5, e_6, e_2)))),
% 0.49/0.71 inference(transitivity,[status(thm)],[764, 762])).
% 0.49/0.71 tff(766,plain,
% 0.49/0.71 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_6) | (~product(e_5, e_6, e_2)) | (~product(e_5, e_4, e_2)))),
% 0.49/0.71 inference(quant_inst,[status(thm)],[])).
% 0.49/0.71 tff(767,plain,
% 0.49/0.71 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_6) | (~product(e_5, e_4, e_2)) | (~product(e_5, e_6, e_2))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[766, 765])).
% 0.49/0.71 tff(768,plain,
% 0.49/0.71 ($false),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[767, 717, 131, 583, 761])).
% 0.49/0.71 tff(769,plain,((~product(e_5, e_4, e_2)) | (~product(e_5, e_6, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.71 tff(770,plain,
% 0.49/0.71 (~product(e_5, e_4, e_2)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[769, 582])).
% 0.49/0.71 tff(771,assumption,(product(e_5, e_4, e_5)), introduced(assumption)).
% 0.49/0.71 tff(772,plain,
% 0.49/0.71 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_4, e_5)) | (~product(e_5, e_4, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_3) | (~product(e_3, e_4, e_5)) | (~product(e_5, e_4, e_5)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(773,plain,
% 0.49/0.71 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_4, e_5)) | (~product(e_5, e_4, e_5)))),
% 0.49/0.71 inference(quant_inst,[status(thm)],[])).
% 0.49/0.71 tff(774,plain,
% 0.49/0.71 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_3) | (~product(e_3, e_4, e_5)) | (~product(e_5, e_4, e_5))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[773, 772])).
% 0.49/0.71 tff(775,plain,
% 0.49/0.71 ($false),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[774, 416, 12, 372, 771])).
% 0.49/0.71 tff(776,plain,((~product(e_5, e_4, e_5)) | (~product(e_3, e_4, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.71 tff(777,plain,
% 0.49/0.71 (~product(e_5, e_4, e_5)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[776, 370])).
% 0.49/0.71 tff(778,assumption,(product(e_5, e_3, e_5)), introduced(assumption)).
% 0.49/0.71 tff(779,plain,
% 0.49/0.71 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_5, e_3, e_5)) | product(e_5, e_5, e_5))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_5, e_3, e_5)) | product(e_5, e_5, e_5))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(780,plain,
% 0.49/0.71 ((product(e_5, e_5, e_5) | (~product(e_5, e_3, e_5)) | (~product(e_5, e_3, e_5))) <=> ((~product(e_5, e_3, e_5)) | product(e_5, e_5, e_5))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(781,plain,
% 0.49/0.71 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_5, e_5) | (~product(e_5, e_3, e_5)) | (~product(e_5, e_3, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_5, e_3, e_5)) | product(e_5, e_5, e_5)))),
% 0.49/0.71 inference(monotonicity,[status(thm)],[780])).
% 0.49/0.71 tff(782,plain,
% 0.49/0.71 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_5, e_5) | (~product(e_5, e_3, e_5)) | (~product(e_5, e_3, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_5, e_3, e_5)) | product(e_5, e_5, e_5))),
% 0.49/0.71 inference(transitivity,[status(thm)],[781, 779])).
% 0.49/0.71 tff(783,plain,
% 0.49/0.71 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_5, e_5) | (~product(e_5, e_3, e_5)) | (~product(e_5, e_3, e_5)))),
% 0.49/0.71 inference(quant_inst,[status(thm)],[])).
% 0.49/0.71 tff(784,plain,
% 0.49/0.71 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_5, e_3, e_5)) | product(e_5, e_5, e_5)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[783, 782])).
% 0.49/0.71 tff(785,plain,
% 0.49/0.71 ((~product(e_5, e_3, e_5)) | product(e_5, e_5, e_5)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[784, 106])).
% 0.49/0.71 tff(786,plain,
% 0.49/0.71 (product(e_5, e_5, e_5)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[785, 778])).
% 0.49/0.71 tff(787,plain,
% 0.49/0.71 ((~equalish(e_3, e_5)) <=> (~equalish(e_3, e_5))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(788,axiom,(~equalish(e_3, e_5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_5')).
% 0.49/0.71 tff(789,plain,
% 0.49/0.71 (~equalish(e_3, e_5)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[788, 787])).
% 0.49/0.71 tff(790,plain,
% 0.49/0.71 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_5, e_3, e_5)) | (~product(e_5, e_5, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_5) | (~product(e_5, e_3, e_5)) | (~product(e_5, e_5, e_5)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(791,plain,
% 0.49/0.71 ((equalish(e_3, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_3, e_5))) <=> (equalish(e_3, e_5) | (~product(e_5, e_3, e_5)) | (~product(e_5, e_5, e_5)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(792,plain,
% 0.49/0.71 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_3, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_5, e_3, e_5)) | (~product(e_5, e_5, e_5))))),
% 0.49/0.71 inference(monotonicity,[status(thm)],[791])).
% 0.49/0.71 tff(793,plain,
% 0.49/0.71 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_3, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_5) | (~product(e_5, e_3, e_5)) | (~product(e_5, e_5, e_5)))),
% 0.49/0.71 inference(transitivity,[status(thm)],[792, 790])).
% 0.49/0.71 tff(794,plain,
% 0.49/0.71 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_3, e_5)))),
% 0.49/0.71 inference(quant_inst,[status(thm)],[])).
% 0.49/0.71 tff(795,plain,
% 0.49/0.71 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_5) | (~product(e_5, e_3, e_5)) | (~product(e_5, e_5, e_5))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[794, 793])).
% 0.49/0.71 tff(796,plain,
% 0.49/0.71 ($false),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[795, 789, 131, 778, 786])).
% 0.49/0.71 tff(797,plain,(~product(e_5, e_3, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.71 tff(798,plain,
% 0.49/0.71 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_3, e_5) | (~product(e_3, e_4, e_5)) | (~product(e_5, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_3, e_5) | (~product(e_3, e_4, e_5)) | (~product(e_5, e_4, e_3)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(799,plain,
% 0.49/0.71 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_3, e_5) | (~product(e_3, e_4, e_5)) | (~product(e_5, e_4, e_3)))),
% 0.49/0.71 inference(quant_inst,[status(thm)],[])).
% 0.49/0.71 tff(800,plain,
% 0.49/0.71 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_3, e_5) | (~product(e_3, e_4, e_5)) | (~product(e_5, e_4, e_3))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[799, 798])).
% 0.49/0.71 tff(801,plain,
% 0.49/0.71 (~product(e_5, e_4, e_3)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[800, 106, 370, 797])).
% 0.49/0.71 tff(802,assumption,(~product(e_5, e_4, e_2)), introduced(assumption)).
% 0.49/0.71 tff(803,assumption,(~product(e_5, e_4, e_1)), introduced(assumption)).
% 0.49/0.71 tff(804,assumption,(~product(e_5, e_4, e_6)), introduced(assumption)).
% 0.49/0.71 tff(805,assumption,(~product(e_5, e_4, e_5)), introduced(assumption)).
% 0.49/0.71 tff(806,assumption,(~product(e_5, e_4, e_3)), introduced(assumption)).
% 0.49/0.71 tff(807,plain,
% 0.49/0.71 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_4)) | (~group_element(e_5)) | product(e_5, e_4, e_6) | product(e_5, e_4, e_3) | product(e_5, e_4, e_1) | product(e_5, e_4, e_2) | product(e_5, e_4, e_5) | product(e_5, e_4, e_4))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_4)) | (~group_element(e_5)) | product(e_5, e_4, e_6) | product(e_5, e_4, e_3) | product(e_5, e_4, e_1) | product(e_5, e_4, e_2) | product(e_5, e_4, e_5) | product(e_5, e_4, e_4))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(808,plain,
% 0.49/0.71 ((product(e_5, e_4, e_6) | product(e_5, e_4, e_5) | product(e_5, e_4, e_4) | product(e_5, e_4, e_3) | product(e_5, e_4, e_2) | product(e_5, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_5))) <=> ((~group_element(e_4)) | (~group_element(e_5)) | product(e_5, e_4, e_6) | product(e_5, e_4, e_3) | product(e_5, e_4, e_1) | product(e_5, e_4, e_2) | product(e_5, e_4, e_5) | product(e_5, e_4, e_4))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(809,plain,
% 0.49/0.71 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5, e_4, e_6) | product(e_5, e_4, e_5) | product(e_5, e_4, e_4) | product(e_5, e_4, e_3) | product(e_5, e_4, e_2) | product(e_5, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_5)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_4)) | (~group_element(e_5)) | product(e_5, e_4, e_6) | product(e_5, e_4, e_3) | product(e_5, e_4, e_1) | product(e_5, e_4, e_2) | product(e_5, e_4, e_5) | product(e_5, e_4, e_4)))),
% 0.49/0.71 inference(monotonicity,[status(thm)],[808])).
% 0.49/0.71 tff(810,plain,
% 0.49/0.71 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5, e_4, e_6) | product(e_5, e_4, e_5) | product(e_5, e_4, e_4) | product(e_5, e_4, e_3) | product(e_5, e_4, e_2) | product(e_5, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_5)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_4)) | (~group_element(e_5)) | product(e_5, e_4, e_6) | product(e_5, e_4, e_3) | product(e_5, e_4, e_1) | product(e_5, e_4, e_2) | product(e_5, e_4, e_5) | product(e_5, e_4, e_4))),
% 0.49/0.71 inference(transitivity,[status(thm)],[809, 807])).
% 0.49/0.71 tff(811,plain,
% 0.49/0.71 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5, e_4, e_6) | product(e_5, e_4, e_5) | product(e_5, e_4, e_4) | product(e_5, e_4, e_3) | product(e_5, e_4, e_2) | product(e_5, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_5)))),
% 0.49/0.71 inference(quant_inst,[status(thm)],[])).
% 0.49/0.71 tff(812,plain,
% 0.49/0.71 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_4)) | (~group_element(e_5)) | product(e_5, e_4, e_6) | product(e_5, e_4, e_3) | product(e_5, e_4, e_1) | product(e_5, e_4, e_2) | product(e_5, e_4, e_5) | product(e_5, e_4, e_4)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[811, 810])).
% 0.49/0.71 tff(813,plain,
% 0.49/0.71 (product(e_5, e_4, e_6) | product(e_5, e_4, e_1) | product(e_5, e_4, e_2) | product(e_5, e_4, e_5) | product(e_5, e_4, e_4)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[812, 246, 452, 85, 806])).
% 0.49/0.71 tff(814,plain,
% 0.49/0.71 (product(e_5, e_4, e_4)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[813, 805, 804, 803, 802])).
% 0.49/0.71 tff(815,assumption,(product(e_4, e_4, e_2)), introduced(assumption)).
% 0.49/0.71 tff(816,assumption,(product(e_5, e_4, e_4)), introduced(assumption)).
% 0.49/0.71 tff(817,plain,
% 0.49/0.71 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_4, e_2) | (~product(e_5, e_4, e_4)) | (~product(e_4, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_4, e_2) | (~product(e_5, e_4, e_4)) | (~product(e_4, e_4, e_2)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(818,plain,
% 0.49/0.71 ((product(e_5, e_4, e_2) | (~product(e_4, e_4, e_2)) | (~product(e_5, e_4, e_4))) <=> (product(e_5, e_4, e_2) | (~product(e_5, e_4, e_4)) | (~product(e_4, e_4, e_2)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(819,plain,
% 0.49/0.71 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_4, e_2) | (~product(e_4, e_4, e_2)) | (~product(e_5, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_4, e_2) | (~product(e_5, e_4, e_4)) | (~product(e_4, e_4, e_2))))),
% 0.49/0.71 inference(monotonicity,[status(thm)],[818])).
% 0.49/0.71 tff(820,plain,
% 0.49/0.71 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_4, e_2) | (~product(e_4, e_4, e_2)) | (~product(e_5, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_4, e_2) | (~product(e_5, e_4, e_4)) | (~product(e_4, e_4, e_2)))),
% 0.49/0.71 inference(transitivity,[status(thm)],[819, 817])).
% 0.49/0.71 tff(821,plain,
% 0.49/0.71 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_4, e_2) | (~product(e_4, e_4, e_2)) | (~product(e_5, e_4, e_4)))),
% 0.49/0.71 inference(quant_inst,[status(thm)],[])).
% 0.49/0.71 tff(822,plain,
% 0.49/0.71 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_4, e_2) | (~product(e_5, e_4, e_4)) | (~product(e_4, e_4, e_2))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[821, 820])).
% 0.49/0.71 tff(823,plain,
% 0.49/0.71 ($false),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[822, 106, 816, 815, 802])).
% 0.49/0.71 tff(824,plain,((~product(e_4, e_4, e_2)) | (~product(e_5, e_4, e_4)) | product(e_5, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.71 tff(825,plain,
% 0.49/0.71 (~product(e_4, e_4, e_2)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[824, 814, 802])).
% 0.49/0.71 tff(826,assumption,(product(e_4, e_4, e_1)), introduced(assumption)).
% 0.49/0.71 tff(827,plain,
% 0.49/0.71 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_4, e_1) | (~product(e_5, e_4, e_4)) | (~product(e_4, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_4, e_1) | (~product(e_5, e_4, e_4)) | (~product(e_4, e_4, e_1)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(828,plain,
% 0.49/0.71 ((product(e_5, e_4, e_1) | (~product(e_4, e_4, e_1)) | (~product(e_5, e_4, e_4))) <=> (product(e_5, e_4, e_1) | (~product(e_5, e_4, e_4)) | (~product(e_4, e_4, e_1)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(829,plain,
% 0.49/0.71 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_4, e_1) | (~product(e_4, e_4, e_1)) | (~product(e_5, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_4, e_1) | (~product(e_5, e_4, e_4)) | (~product(e_4, e_4, e_1))))),
% 0.49/0.71 inference(monotonicity,[status(thm)],[828])).
% 0.49/0.71 tff(830,plain,
% 0.49/0.71 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_4, e_1) | (~product(e_4, e_4, e_1)) | (~product(e_5, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_4, e_1) | (~product(e_5, e_4, e_4)) | (~product(e_4, e_4, e_1)))),
% 0.49/0.71 inference(transitivity,[status(thm)],[829, 827])).
% 0.49/0.71 tff(831,plain,
% 0.49/0.71 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_4, e_1) | (~product(e_4, e_4, e_1)) | (~product(e_5, e_4, e_4)))),
% 0.49/0.71 inference(quant_inst,[status(thm)],[])).
% 0.49/0.71 tff(832,plain,
% 0.49/0.71 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_4, e_1) | (~product(e_5, e_4, e_4)) | (~product(e_4, e_4, e_1))),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[831, 830])).
% 0.49/0.72 tff(833,plain,
% 0.49/0.72 ($false),
% 0.49/0.72 inference(unit_resolution,[status(thm)],[832, 106, 803, 816, 826])).
% 0.49/0.72 tff(834,plain,((~product(e_4, e_4, e_1)) | product(e_5, e_4, e_1) | (~product(e_5, e_4, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.72 tff(835,plain,
% 0.49/0.72 (~product(e_4, e_4, e_1)),
% 0.49/0.72 inference(unit_resolution,[status(thm)],[834, 814, 803])).
% 0.49/0.72 tff(836,assumption,(product(e_4, e_4, e_3)), introduced(assumption)).
% 0.49/0.72 tff(837,plain,
% 0.49/0.72 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_4, e_3) | (~product(e_5, e_4, e_4)) | (~product(e_4, e_4, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_4, e_3) | (~product(e_5, e_4, e_4)) | (~product(e_4, e_4, e_3)))),
% 0.49/0.72 inference(rewrite,[status(thm)],[])).
% 0.49/0.72 tff(838,plain,
% 0.49/0.72 ((product(e_5, e_4, e_3) | (~product(e_4, e_4, e_3)) | (~product(e_5, e_4, e_4))) <=> (product(e_5, e_4, e_3) | (~product(e_5, e_4, e_4)) | (~product(e_4, e_4, e_3)))),
% 0.49/0.72 inference(rewrite,[status(thm)],[])).
% 0.49/0.72 tff(839,plain,
% 0.49/0.72 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_4, e_3) | (~product(e_4, e_4, e_3)) | (~product(e_5, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_4, e_3) | (~product(e_5, e_4, e_4)) | (~product(e_4, e_4, e_3))))),
% 0.49/0.72 inference(monotonicity,[status(thm)],[838])).
% 0.49/0.72 tff(840,plain,
% 0.49/0.72 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_4, e_3) | (~product(e_4, e_4, e_3)) | (~product(e_5, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_4, e_3) | (~product(e_5, e_4, e_4)) | (~product(e_4, e_4, e_3)))),
% 0.49/0.72 inference(transitivity,[status(thm)],[839, 837])).
% 0.49/0.72 tff(841,plain,
% 0.49/0.72 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_4, e_3) | (~product(e_4, e_4, e_3)) | (~product(e_5, e_4, e_4)))),
% 0.49/0.72 inference(quant_inst,[status(thm)],[])).
% 0.49/0.72 tff(842,plain,
% 0.49/0.72 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_4, e_3) | (~product(e_5, e_4, e_4)) | (~product(e_4, e_4, e_3))),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[841, 840])).
% 0.49/0.72 tff(843,plain,
% 0.49/0.72 ($false),
% 0.49/0.72 inference(unit_resolution,[status(thm)],[842, 106, 816, 836, 806])).
% 0.49/0.72 tff(844,plain,((~product(e_4, e_4, e_3)) | (~product(e_5, e_4, e_4)) | product(e_5, e_4, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.72 tff(845,plain,
% 0.49/0.72 (~product(e_4, e_4, e_3)),
% 0.49/0.72 inference(unit_resolution,[status(thm)],[844, 814, 806])).
% 0.49/0.72 tff(846,assumption,(~product(e_4, e_4, e_1)), introduced(assumption)).
% 0.49/0.72 tff(847,assumption,(~product(e_4, e_4, e_2)), introduced(assumption)).
% 0.49/0.72 tff(848,assumption,(~product(e_4, e_4, e_3)), introduced(assumption)).
% 0.49/0.72 tff(849,assumption,(~product(e_4, e_4, e_4)), introduced(assumption)).
% 0.49/0.72 tff(850,assumption,(product(e_4, e_4, e_5)), introduced(assumption)).
% 0.49/0.72 tff(851,plain,
% 0.49/0.72 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_4, e_5) | (~product(e_5, e_4, e_4)) | (~product(e_4, e_4, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_4, e_5) | (~product(e_5, e_4, e_4)) | (~product(e_4, e_4, e_5)))),
% 0.49/0.72 inference(rewrite,[status(thm)],[])).
% 0.49/0.72 tff(852,plain,
% 0.49/0.72 ((product(e_5, e_4, e_5) | (~product(e_4, e_4, e_5)) | (~product(e_5, e_4, e_4))) <=> (product(e_5, e_4, e_5) | (~product(e_5, e_4, e_4)) | (~product(e_4, e_4, e_5)))),
% 0.49/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(853,plain,
% 0.56/0.72 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_4, e_5) | (~product(e_4, e_4, e_5)) | (~product(e_5, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_4, e_5) | (~product(e_5, e_4, e_4)) | (~product(e_4, e_4, e_5))))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[852])).
% 0.56/0.72 tff(854,plain,
% 0.56/0.72 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_4, e_5) | (~product(e_4, e_4, e_5)) | (~product(e_5, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_4, e_5) | (~product(e_5, e_4, e_4)) | (~product(e_4, e_4, e_5)))),
% 0.56/0.72 inference(transitivity,[status(thm)],[853, 851])).
% 0.56/0.72 tff(855,plain,
% 0.56/0.72 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_4, e_5) | (~product(e_4, e_4, e_5)) | (~product(e_5, e_4, e_4)))),
% 0.56/0.72 inference(quant_inst,[status(thm)],[])).
% 0.56/0.72 tff(856,plain,
% 0.56/0.72 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_4, e_5) | (~product(e_5, e_4, e_4)) | (~product(e_4, e_4, e_5))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[855, 854])).
% 0.56/0.72 tff(857,plain,
% 0.56/0.72 ($false),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[856, 106, 816, 850, 805])).
% 0.56/0.72 tff(858,plain,((~product(e_4, e_4, e_5)) | (~product(e_5, e_4, e_4)) | product(e_5, e_4, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.72 tff(859,plain,
% 0.56/0.72 (~product(e_4, e_4, e_5)),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[858, 816, 805])).
% 0.56/0.72 tff(860,plain,
% 0.56/0.72 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_4)) | product(e_4, e_4, e_4) | product(e_4, e_4, e_6) | product(e_4, e_4, e_5) | product(e_4, e_4, e_3) | product(e_4, e_4, e_2) | product(e_4, e_4, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_4)) | product(e_4, e_4, e_4) | product(e_4, e_4, e_6) | product(e_4, e_4, e_5) | product(e_4, e_4, e_3) | product(e_4, e_4, e_2) | product(e_4, e_4, e_1))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(861,plain,
% 0.56/0.72 ((product(e_4, e_4, e_6) | product(e_4, e_4, e_5) | product(e_4, e_4, e_4) | product(e_4, e_4, e_3) | product(e_4, e_4, e_2) | product(e_4, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_4))) <=> ((~group_element(e_4)) | product(e_4, e_4, e_4) | product(e_4, e_4, e_6) | product(e_4, e_4, e_5) | product(e_4, e_4, e_3) | product(e_4, e_4, e_2) | product(e_4, e_4, e_1))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(862,plain,
% 0.56/0.72 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_4, e_6) | product(e_4, e_4, e_5) | product(e_4, e_4, e_4) | product(e_4, e_4, e_3) | product(e_4, e_4, e_2) | product(e_4, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_4)) | product(e_4, e_4, e_4) | product(e_4, e_4, e_6) | product(e_4, e_4, e_5) | product(e_4, e_4, e_3) | product(e_4, e_4, e_2) | product(e_4, e_4, e_1)))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[861])).
% 0.56/0.72 tff(863,plain,
% 0.56/0.72 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_4, e_6) | product(e_4, e_4, e_5) | product(e_4, e_4, e_4) | product(e_4, e_4, e_3) | product(e_4, e_4, e_2) | product(e_4, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_4)) | product(e_4, e_4, e_4) | product(e_4, e_4, e_6) | product(e_4, e_4, e_5) | product(e_4, e_4, e_3) | product(e_4, e_4, e_2) | product(e_4, e_4, e_1))),
% 0.56/0.72 inference(transitivity,[status(thm)],[862, 860])).
% 0.56/0.72 tff(864,plain,
% 0.56/0.72 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_4, e_6) | product(e_4, e_4, e_5) | product(e_4, e_4, e_4) | product(e_4, e_4, e_3) | product(e_4, e_4, e_2) | product(e_4, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_4)))),
% 0.56/0.72 inference(quant_inst,[status(thm)],[])).
% 0.56/0.72 tff(865,plain,
% 0.56/0.72 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_4)) | product(e_4, e_4, e_4) | product(e_4, e_4, e_6) | product(e_4, e_4, e_5) | product(e_4, e_4, e_3) | product(e_4, e_4, e_2) | product(e_4, e_4, e_1)),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[864, 863])).
% 0.56/0.72 tff(866,plain,
% 0.56/0.72 (product(e_4, e_4, e_4) | product(e_4, e_4, e_6) | product(e_4, e_4, e_5) | product(e_4, e_4, e_3) | product(e_4, e_4, e_2) | product(e_4, e_4, e_1)),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[865, 246, 85])).
% 0.56/0.72 tff(867,plain,
% 0.56/0.72 (product(e_4, e_4, e_6)),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[866, 859, 849, 848, 847, 846])).
% 0.56/0.72 tff(868,plain,
% 0.56/0.72 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_4, e_6) | (~product(e_5, e_4, e_4)) | (~product(e_4, e_4, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_4, e_6) | (~product(e_5, e_4, e_4)) | (~product(e_4, e_4, e_6)))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(869,plain,
% 0.56/0.72 ((product(e_5, e_4, e_6) | (~product(e_4, e_4, e_6)) | (~product(e_5, e_4, e_4))) <=> (product(e_5, e_4, e_6) | (~product(e_5, e_4, e_4)) | (~product(e_4, e_4, e_6)))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(870,plain,
% 0.56/0.72 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_4, e_6) | (~product(e_4, e_4, e_6)) | (~product(e_5, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_4, e_6) | (~product(e_5, e_4, e_4)) | (~product(e_4, e_4, e_6))))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[869])).
% 0.56/0.72 tff(871,plain,
% 0.56/0.72 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_4, e_6) | (~product(e_4, e_4, e_6)) | (~product(e_5, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_4, e_6) | (~product(e_5, e_4, e_4)) | (~product(e_4, e_4, e_6)))),
% 0.56/0.72 inference(transitivity,[status(thm)],[870, 868])).
% 0.56/0.72 tff(872,plain,
% 0.56/0.72 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_4, e_6) | (~product(e_4, e_4, e_6)) | (~product(e_5, e_4, e_4)))),
% 0.56/0.72 inference(quant_inst,[status(thm)],[])).
% 0.56/0.72 tff(873,plain,
% 0.56/0.72 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_4, e_6) | (~product(e_5, e_4, e_4)) | (~product(e_4, e_4, e_6))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[872, 871])).
% 0.56/0.72 tff(874,plain,
% 0.56/0.72 ($false),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[873, 106, 816, 867, 804])).
% 0.56/0.72 tff(875,plain,((~product(e_5, e_4, e_4)) | product(e_5, e_4, e_6) | product(e_4, e_4, e_4) | product(e_4, e_4, e_3) | product(e_4, e_4, e_2) | product(e_4, e_4, e_1) | product(e_5, e_4, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.72 tff(876,plain,
% 0.56/0.72 (product(e_4, e_4, e_4)),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[875, 845, 814, 835, 825, 804, 805])).
% 0.56/0.72 tff(877,plain,
% 0.56/0.72 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_5) | (~product(e_4, e_4, e_4)) | (~product(e_5, 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_4, e_5) | (~product(e_4, e_4, e_4)) | (~product(e_5, e_4, e_4)))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(878,plain,
% 0.56/0.72 ((equalish(e_4, e_5) | (~product(e_5, e_4, e_4)) | (~product(e_4, e_4, e_4))) <=> (equalish(e_4, e_5) | (~product(e_4, e_4, e_4)) | (~product(e_5, e_4, e_4)))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(879,plain,
% 0.56/0.72 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_5) | (~product(e_5, e_4, e_4)) | (~product(e_4, 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_4, e_5) | (~product(e_4, e_4, e_4)) | (~product(e_5, e_4, e_4))))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[878])).
% 0.56/0.72 tff(880,plain,
% 0.56/0.72 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_5) | (~product(e_5, e_4, e_4)) | (~product(e_4, 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_4, e_5) | (~product(e_4, e_4, e_4)) | (~product(e_5, e_4, e_4)))),
% 0.56/0.72 inference(transitivity,[status(thm)],[879, 877])).
% 0.56/0.72 tff(881,plain,
% 0.56/0.72 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_5) | (~product(e_5, e_4, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.56/0.72 inference(quant_inst,[status(thm)],[])).
% 0.56/0.72 tff(882,plain,
% 0.56/0.72 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_5) | (~product(e_4, e_4, e_4)) | (~product(e_5, e_4, e_4))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[881, 880])).
% 0.56/0.72 tff(883,plain,
% 0.56/0.72 ($false),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[882, 666, 12, 876, 814])).
% 0.56/0.72 tff(884,plain,(product(e_5, e_4, e_5) | product(e_5, e_4, e_6) | product(e_5, e_4, e_3) | product(e_5, e_4, e_2) | product(e_5, e_4, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.72 tff(885,plain,
% 0.56/0.72 (product(e_5, e_4, e_1)),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[884, 801, 777, 770, 760])).
% 0.56/0.72 tff(886,assumption,(product(e_5, e_4, e_1)), introduced(assumption)).
% 0.56/0.72 tff(887,plain,
% 0.56/0.72 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_4, e_1)) | (~product(e_5, e_4, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_2) | (~product(e_2, e_4, e_1)) | (~product(e_5, e_4, e_1)))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(888,plain,
% 0.56/0.72 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_4, e_1)) | (~product(e_5, e_4, e_1)))),
% 0.56/0.72 inference(quant_inst,[status(thm)],[])).
% 0.56/0.72 tff(889,plain,
% 0.56/0.72 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_2) | (~product(e_2, e_4, e_1)) | (~product(e_5, e_4, e_1))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[888, 887])).
% 0.56/0.72 tff(890,plain,
% 0.56/0.72 ($false),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[889, 437, 12, 713, 886])).
% 0.56/0.72 tff(891,plain,((~product(e_5, e_4, e_1)) | (~product(e_2, e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.72 tff(892,plain,
% 0.56/0.72 (~product(e_2, e_4, e_1)),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[891, 885])).
% 0.56/0.72 tff(893,plain,
% 0.56/0.72 (product(e_2, e_4, e_6)),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[711, 892, 621])).
% 0.56/0.73 tff(894,plain,
% 0.56/0.73 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_6) | (~product(e_2, e_6, e_6)) | (~product(e_2, e_4, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_6) | (~product(e_2, e_6, e_6)) | (~product(e_2, e_4, e_6)))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(895,plain,
% 0.56/0.73 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_6) | (~product(e_2, e_6, e_6)) | (~product(e_2, e_4, e_6)))),
% 0.56/0.73 inference(quant_inst,[status(thm)],[])).
% 0.56/0.73 tff(896,plain,
% 0.56/0.73 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_6) | (~product(e_2, e_6, e_6)) | (~product(e_2, e_4, e_6))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[895, 894])).
% 0.56/0.73 tff(897,plain,
% 0.56/0.73 ($false),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[896, 717, 131, 625, 663])).
% 0.56/0.73 tff(898,plain,((~product(e_2, e_4, e_6)) | (~product(e_2, e_6, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.73 tff(899,plain,
% 0.56/0.73 (~product(e_2, e_6, e_6)),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[898, 893])).
% 0.56/0.73 tff(900,assumption,(product(e_5, e_6, e_5)), introduced(assumption)).
% 0.56/0.73 tff(901,assumption,(product(e_5, e_5, e_5)), introduced(assumption)).
% 0.56/0.73 tff(902,plain,
% 0.56/0.73 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_6) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_6, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_6) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_6, e_5)))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(903,plain,
% 0.56/0.73 ((equalish(e_5, e_6) | (~product(e_5, e_6, e_5)) | (~product(e_5, e_5, e_5))) <=> (equalish(e_5, e_6) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_6, e_5)))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(904,plain,
% 0.56/0.73 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_6) | (~product(e_5, e_6, e_5)) | (~product(e_5, e_5, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_6) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_6, e_5))))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[903])).
% 0.56/0.73 tff(905,plain,
% 0.56/0.73 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_6) | (~product(e_5, e_6, e_5)) | (~product(e_5, e_5, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_6) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_6, e_5)))),
% 0.56/0.73 inference(transitivity,[status(thm)],[904, 902])).
% 0.56/0.73 tff(906,plain,
% 0.56/0.73 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_6) | (~product(e_5, e_6, e_5)) | (~product(e_5, e_5, e_5)))),
% 0.56/0.73 inference(quant_inst,[status(thm)],[])).
% 0.56/0.73 tff(907,plain,
% 0.56/0.73 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_6) | (~product(e_5, e_5, e_5)) | (~product(e_5, e_6, e_5))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[906, 905])).
% 0.56/0.73 tff(908,plain,
% 0.56/0.73 ($false),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[907, 565, 131, 901, 900])).
% 0.56/0.73 tff(909,plain,((~product(e_5, e_5, e_5)) | (~product(e_5, e_6, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.73 tff(910,plain,
% 0.56/0.73 (~product(e_5, e_5, e_5)),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[909, 900])).
% 0.56/0.73 tff(911,plain,
% 0.56/0.73 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_5, e_5) | (~product(e_5, e_6, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_5, e_5) | (~product(e_5, e_6, e_5)))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(912,plain,
% 0.56/0.73 ((product(e_5, e_5, e_5) | (~product(e_5, e_6, e_5)) | (~product(e_5, e_6, e_5))) <=> (product(e_5, e_5, e_5) | (~product(e_5, e_6, e_5)))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(913,plain,
% 0.56/0.73 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_5, e_5) | (~product(e_5, e_6, e_5)) | (~product(e_5, e_6, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_5, e_5) | (~product(e_5, e_6, e_5))))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[912])).
% 0.56/0.73 tff(914,plain,
% 0.56/0.73 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_5, e_5) | (~product(e_5, e_6, e_5)) | (~product(e_5, e_6, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_5, e_5) | (~product(e_5, e_6, e_5)))),
% 0.56/0.73 inference(transitivity,[status(thm)],[913, 911])).
% 0.56/0.73 tff(915,plain,
% 0.56/0.73 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_5, e_5) | (~product(e_5, e_6, e_5)) | (~product(e_5, e_6, e_5)))),
% 0.56/0.73 inference(quant_inst,[status(thm)],[])).
% 0.56/0.73 tff(916,plain,
% 0.56/0.73 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_5, e_5, e_5) | (~product(e_5, e_6, e_5))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[915, 914])).
% 0.56/0.73 tff(917,plain,
% 0.56/0.73 ($false),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[916, 106, 910, 900])).
% 0.56/0.73 tff(918,plain,(~product(e_5, e_6, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.73 tff(919,assumption,(~product(e_5, e_6, e_5)), introduced(assumption)).
% 0.56/0.73 tff(920,plain,
% 0.56/0.73 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_6, e_1, e_5)) | product(e_5, e_6, e_5) | (~product(e_5, e_1, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_6, e_1, e_5)) | product(e_5, e_6, e_5) | (~product(e_5, e_1, e_6)))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(921,plain,
% 0.56/0.73 ((product(e_5, e_6, e_5) | (~product(e_6, e_1, e_5)) | (~product(e_5, e_1, e_6))) <=> ((~product(e_6, e_1, e_5)) | product(e_5, e_6, e_5) | (~product(e_5, e_1, e_6)))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(922,plain,
% 0.56/0.73 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_6, e_5) | (~product(e_6, e_1, e_5)) | (~product(e_5, e_1, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_6, e_1, e_5)) | product(e_5, e_6, e_5) | (~product(e_5, e_1, e_6))))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[921])).
% 0.56/0.73 tff(923,plain,
% 0.56/0.73 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_6, e_5) | (~product(e_6, e_1, e_5)) | (~product(e_5, e_1, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_6, e_1, e_5)) | product(e_5, e_6, e_5) | (~product(e_5, e_1, e_6)))),
% 0.56/0.73 inference(transitivity,[status(thm)],[922, 920])).
% 0.56/0.73 tff(924,plain,
% 0.56/0.73 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_6, e_5) | (~product(e_6, e_1, e_5)) | (~product(e_5, e_1, e_6)))),
% 0.56/0.73 inference(quant_inst,[status(thm)],[])).
% 0.56/0.73 tff(925,plain,
% 0.56/0.73 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_6, e_1, e_5)) | product(e_5, e_6, e_5) | (~product(e_5, e_1, e_6))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[924, 923])).
% 0.56/0.73 tff(926,plain,
% 0.56/0.73 ($false),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[925, 106, 522, 919, 570])).
% 0.56/0.73 tff(927,plain,(product(e_5, e_6, e_5) | (~product(e_6, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.73 tff(928,plain,
% 0.56/0.73 (~product(e_6, e_1, e_5)),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[927, 918])).
% 0.56/0.73 tff(929,assumption,(~product(e_2, e_6, e_6)), introduced(assumption)).
% 0.56/0.73 tff(930,assumption,(~product(e_3, e_2, e_5)), introduced(assumption)).
% 0.56/0.73 tff(931,assumption,(~product(e_2, e_5, e_6)), introduced(assumption)).
% 0.56/0.73 tff(932,plain,
% 0.56/0.73 (~product(e_3, e_4, e_5)),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[620, 615])).
% 0.56/0.73 tff(933,plain,
% 0.56/0.73 (~product(e_4, e_1, e_5)),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[369, 932])).
% 0.56/0.73 tff(934,plain,
% 0.56/0.73 (product(e_4, e_1, e_2)),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[257, 933])).
% 0.56/0.73 tff(935,plain,
% 0.56/0.73 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_3, e_4, e_2) | (~product(e_4, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | product(e_3, e_4, e_2) | (~product(e_4, e_1, e_2)))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(936,plain,
% 0.56/0.73 ((product(e_3, e_4, e_2) | (~product(e_4, e_1, e_2)) | (~product(e_3, e_1, e_4))) <=> ((~product(e_3, e_1, e_4)) | product(e_3, e_4, e_2) | (~product(e_4, e_1, e_2)))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(937,plain,
% 0.56/0.73 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_4, e_2) | (~product(e_4, e_1, e_2)) | (~product(e_3, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_1, e_4)) | product(e_3, e_4, e_2) | (~product(e_4, e_1, e_2))))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[936])).
% 0.56/0.73 tff(938,plain,
% 0.56/0.73 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_4, e_2) | (~product(e_4, e_1, e_2)) | (~product(e_3, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | product(e_3, e_4, e_2) | (~product(e_4, e_1, e_2)))),
% 0.56/0.73 inference(transitivity,[status(thm)],[937, 935])).
% 0.56/0.73 tff(939,plain,
% 0.56/0.73 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_4, e_2) | (~product(e_4, e_1, e_2)) | (~product(e_3, e_1, e_4)))),
% 0.56/0.73 inference(quant_inst,[status(thm)],[])).
% 0.56/0.73 tff(940,plain,
% 0.56/0.73 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_1, e_4)) | product(e_3, e_4, e_2) | (~product(e_4, e_1, e_2))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[939, 938])).
% 0.56/0.73 tff(941,plain,
% 0.56/0.73 ((~product(e_3, e_1, e_4)) | product(e_3, e_4, e_2) | (~product(e_4, e_1, e_2))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[940, 106])).
% 0.56/0.73 tff(942,plain,
% 0.56/0.73 (product(e_3, e_4, e_2) | (~product(e_4, e_1, e_2))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[941, 364])).
% 0.56/0.73 tff(943,plain,
% 0.56/0.73 (product(e_3, e_4, e_2)),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[942, 934])).
% 0.56/0.73 tff(944,plain,
% 0.56/0.73 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_2, e_5) | (~product(e_3, e_4, e_2)) | (~product(e_2, e_4, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_2, e_5) | (~product(e_3, e_4, e_2)) | (~product(e_2, e_4, e_5)))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(945,plain,
% 0.56/0.73 ((product(e_3, e_2, e_5) | (~product(e_2, e_4, e_5)) | (~product(e_3, e_4, e_2))) <=> (product(e_3, e_2, e_5) | (~product(e_3, e_4, e_2)) | (~product(e_2, e_4, e_5)))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(946,plain,
% 0.56/0.73 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_2, e_5) | (~product(e_2, e_4, e_5)) | (~product(e_3, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_2, e_5) | (~product(e_3, e_4, e_2)) | (~product(e_2, e_4, e_5))))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[945])).
% 0.56/0.73 tff(947,plain,
% 0.56/0.73 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_2, e_5) | (~product(e_2, e_4, e_5)) | (~product(e_3, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_2, e_5) | (~product(e_3, e_4, e_2)) | (~product(e_2, e_4, e_5)))),
% 0.56/0.73 inference(transitivity,[status(thm)],[946, 944])).
% 0.56/0.73 tff(948,plain,
% 0.56/0.73 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_2, e_5) | (~product(e_2, e_4, e_5)) | (~product(e_3, e_4, e_2)))),
% 0.56/0.73 inference(quant_inst,[status(thm)],[])).
% 0.56/0.73 tff(949,plain,
% 0.56/0.73 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_2, e_5) | (~product(e_3, e_4, e_2)) | (~product(e_2, e_4, e_5))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[948, 947])).
% 0.56/0.73 tff(950,plain,
% 0.56/0.73 ($false),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[949, 106, 615, 930, 943])).
% 0.56/0.73 tff(951,plain,(product(e_3, e_2, e_5) | (~product(e_2, e_4, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.73 tff(952,plain,
% 0.56/0.73 (~product(e_2, e_4, e_5)),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[951, 930])).
% 0.56/0.73 tff(953,assumption,(product(e_2, e_2, e_6)), introduced(assumption)).
% 0.56/0.73 tff(954,plain,
% 0.56/0.73 ((~equalish(e_2, e_6)) <=> (~equalish(e_2, e_6))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(955,axiom,(~equalish(e_2, e_6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_6')).
% 0.56/0.73 tff(956,plain,
% 0.56/0.73 (~equalish(e_2, e_6)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[955, 954])).
% 0.56/0.73 tff(957,plain,
% 0.56/0.73 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_6) | (~product(e_2, e_6, e_6)) | (~product(e_2, e_2, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_6) | (~product(e_2, e_6, e_6)) | (~product(e_2, e_2, e_6)))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(958,plain,
% 0.56/0.73 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_6) | (~product(e_2, e_6, e_6)) | (~product(e_2, e_2, e_6)))),
% 0.56/0.73 inference(quant_inst,[status(thm)],[])).
% 0.56/0.73 tff(959,plain,
% 0.56/0.73 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_6) | (~product(e_2, e_6, e_6)) | (~product(e_2, e_2, e_6))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[958, 957])).
% 0.56/0.73 tff(960,plain,
% 0.56/0.73 ($false),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[959, 956, 131, 625, 953])).
% 0.56/0.73 tff(961,plain,((~product(e_2, e_2, e_6)) | (~product(e_2, e_6, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.73 tff(962,plain,
% 0.56/0.73 (~product(e_2, e_6, e_6)),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[961, 953])).
% 0.56/0.73 tff(963,plain,
% 0.56/0.73 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_2, e_5, e_6)) | (~product(e_2, e_2, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_2) | (~product(e_2, e_5, e_6)) | (~product(e_2, e_2, e_6)))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(964,plain,
% 0.56/0.73 ((equalish(e_5, e_2) | (~product(e_2, e_2, e_6)) | (~product(e_2, e_5, e_6))) <=> (equalish(e_5, e_2) | (~product(e_2, e_5, e_6)) | (~product(e_2, e_2, e_6)))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(965,plain,
% 0.56/0.73 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_2, e_2, e_6)) | (~product(e_2, e_5, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_2, e_5, e_6)) | (~product(e_2, e_2, e_6))))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[964])).
% 0.56/0.74 tff(966,plain,
% 0.56/0.74 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_2, e_2, e_6)) | (~product(e_2, e_5, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_2) | (~product(e_2, e_5, e_6)) | (~product(e_2, e_2, e_6)))),
% 0.56/0.74 inference(transitivity,[status(thm)],[965, 963])).
% 0.56/0.74 tff(967,plain,
% 0.56/0.74 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_2, e_2, e_6)) | (~product(e_2, e_5, e_6)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(968,plain,
% 0.56/0.74 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_2) | (~product(e_2, e_5, e_6)) | (~product(e_2, e_2, e_6))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[967, 966])).
% 0.56/0.74 tff(969,plain,
% 0.56/0.74 ($false),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[968, 437, 131, 624, 953])).
% 0.56/0.74 tff(970,plain,((~product(e_2, e_5, e_6)) | (~product(e_2, e_2, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.74 tff(971,plain,
% 0.56/0.74 (~product(e_2, e_5, e_6)),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[970, 953])).
% 0.56/0.74 tff(972,plain,
% 0.56/0.74 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_2, e_2, e_6)) | (~product(e_2, e_4, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_2, e_2, e_6)) | (~product(e_2, e_4, e_6)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(973,plain,
% 0.56/0.74 ((equalish(e_2, e_4) | (~product(e_2, e_4, e_6)) | (~product(e_2, e_2, e_6))) <=> (equalish(e_2, e_4) | (~product(e_2, e_2, e_6)) | (~product(e_2, e_4, e_6)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(974,plain,
% 0.56/0.74 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_2, e_4, e_6)) | (~product(e_2, e_2, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_2, e_2, e_6)) | (~product(e_2, e_4, e_6))))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[973])).
% 0.56/0.74 tff(975,plain,
% 0.56/0.74 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_2, e_4, e_6)) | (~product(e_2, e_2, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_2, e_2, e_6)) | (~product(e_2, e_4, e_6)))),
% 0.56/0.74 inference(transitivity,[status(thm)],[974, 972])).
% 0.56/0.74 tff(976,plain,
% 0.56/0.74 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_2, e_4, e_6)) | (~product(e_2, e_2, e_6)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(977,plain,
% 0.56/0.74 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_2, e_2, e_6)) | (~product(e_2, e_4, e_6))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[976, 975])).
% 0.56/0.74 tff(978,plain,
% 0.56/0.74 ($false),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[977, 375, 131, 953, 663])).
% 0.56/0.74 tff(979,plain,((~product(e_2, e_2, e_6)) | (~product(e_2, e_4, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.74 tff(980,plain,
% 0.56/0.74 (~product(e_2, e_4, e_6)),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[979, 953])).
% 0.56/0.74 tff(981,assumption,(product(e_2, e_5, e_1)), introduced(assumption)).
% 0.56/0.74 tff(982,plain,
% 0.56/0.74 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_5) | (~product(e_2, e_5, e_1)) | (~product(e_2, e_6, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_5) | (~product(e_2, e_5, e_1)) | (~product(e_2, e_6, e_1)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(983,plain,
% 0.56/0.74 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_5) | (~product(e_2, e_5, e_1)) | (~product(e_2, e_6, e_1)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(984,plain,
% 0.56/0.74 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_5) | (~product(e_2, e_5, e_1)) | (~product(e_2, e_6, e_1))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[983, 982])).
% 0.56/0.74 tff(985,plain,
% 0.56/0.74 ($false),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[984, 628, 131, 714, 981])).
% 0.56/0.74 tff(986,plain,((~product(e_2, e_6, e_1)) | (~product(e_2, e_5, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.74 tff(987,plain,
% 0.56/0.74 (~product(e_2, e_5, e_1)),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[986, 714])).
% 0.56/0.74 tff(988,assumption,(product(e_2, e_5, e_4)), introduced(assumption)).
% 0.56/0.74 tff(989,plain,
% 0.56/0.74 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_2, e_5, 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_5) | (~product(e_2, e_5, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(990,plain,
% 0.56/0.74 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_5) | (~product(e_2, e_5, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(991,plain,
% 0.56/0.74 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_5) | (~product(e_2, e_5, e_4)) | (~product(e_2, e_3, e_4))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[990, 989])).
% 0.56/0.74 tff(992,plain,
% 0.56/0.74 ($false),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[991, 789, 131, 988, 635])).
% 0.56/0.74 tff(993,plain,((~product(e_2, e_3, e_4)) | (~product(e_2, e_5, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.74 tff(994,plain,
% 0.56/0.74 (~product(e_2, e_5, e_4)),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[993, 433])).
% 0.56/0.74 tff(995,assumption,(product(e_2, e_5, e_3)), introduced(assumption)).
% 0.56/0.74 tff(996,plain,
% 0.56/0.74 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_5, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_5, e_3)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(997,plain,
% 0.56/0.74 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_5, e_3)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(998,plain,
% 0.56/0.74 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_5, e_3))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[997, 996])).
% 0.56/0.74 tff(999,plain,
% 0.56/0.74 ($false),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[998, 396, 131, 204, 995])).
% 0.56/0.74 tff(1000,plain,((~product(e_2, e_5, e_3)) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.74 tff(1001,plain,
% 0.56/0.74 (~product(e_2, e_5, e_3)),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[1000, 202])).
% 0.56/0.74 tff(1002,plain,
% 0.56/0.74 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5, e_4) | (~group_element(e_5)) | product(e_2, e_5, e_1) | product(e_2, e_5, e_5) | product(e_2, e_5, e_3) | product(e_2, e_5, e_2) | product(e_2, e_5, e_6))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5, e_4) | (~group_element(e_5)) | product(e_2, e_5, e_1) | product(e_2, e_5, e_5) | product(e_2, e_5, e_3) | product(e_2, e_5, e_2) | product(e_2, e_5, e_6))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(1003,plain,
% 0.56/0.74 ((product(e_2, e_5, e_6) | product(e_2, e_5, e_5) | product(e_2, e_5, e_4) | product(e_2, e_5, e_3) | product(e_2, e_5, e_2) | product(e_2, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_2))) <=> ((~group_element(e_2)) | product(e_2, e_5, e_4) | (~group_element(e_5)) | product(e_2, e_5, e_1) | product(e_2, e_5, e_5) | product(e_2, e_5, e_3) | product(e_2, e_5, e_2) | product(e_2, e_5, e_6))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(1004,plain,
% 0.56/0.74 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5, e_6) | product(e_2, e_5, e_5) | product(e_2, e_5, e_4) | product(e_2, e_5, e_3) | product(e_2, e_5, e_2) | product(e_2, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5, e_4) | (~group_element(e_5)) | product(e_2, e_5, e_1) | product(e_2, e_5, e_5) | product(e_2, e_5, e_3) | product(e_2, e_5, e_2) | product(e_2, e_5, e_6)))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[1003])).
% 0.56/0.74 tff(1005,plain,
% 0.56/0.74 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5, e_6) | product(e_2, e_5, e_5) | product(e_2, e_5, e_4) | product(e_2, e_5, e_3) | product(e_2, e_5, e_2) | product(e_2, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5, e_4) | (~group_element(e_5)) | product(e_2, e_5, e_1) | product(e_2, e_5, e_5) | product(e_2, e_5, e_3) | product(e_2, e_5, e_2) | product(e_2, e_5, e_6))),
% 0.56/0.74 inference(transitivity,[status(thm)],[1004, 1002])).
% 0.56/0.74 tff(1006,plain,
% 0.56/0.74 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5, e_6) | product(e_2, e_5, e_5) | product(e_2, e_5, e_4) | product(e_2, e_5, e_3) | product(e_2, e_5, e_2) | product(e_2, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_2)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(1007,plain,
% 0.56/0.74 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5, e_4) | (~group_element(e_5)) | product(e_2, e_5, e_1) | product(e_2, e_5, e_5) | product(e_2, e_5, e_3) | product(e_2, e_5, e_2) | product(e_2, e_5, e_6)),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[1006, 1005])).
% 0.56/0.74 tff(1008,plain,
% 0.56/0.74 (product(e_2, e_5, e_4) | product(e_2, e_5, e_1) | product(e_2, e_5, e_5) | product(e_2, e_5, e_3) | product(e_2, e_5, e_2) | product(e_2, e_5, e_6)),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[1007, 193, 452, 85])).
% 0.56/0.74 tff(1009,plain,
% 0.56/0.74 (product(e_2, e_5, e_4) | product(e_2, e_5, e_1) | product(e_2, e_5, e_5) | product(e_2, e_5, e_3) | product(e_2, e_5, e_6)),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[1008, 600])).
% 0.56/0.74 tff(1010,plain,
% 0.56/0.74 (product(e_2, e_5, e_4) | product(e_2, e_5, e_1) | product(e_2, e_5, e_5) | product(e_2, e_5, e_6)),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[1009, 1001])).
% 0.56/0.74 tff(1011,plain,
% 0.56/0.74 (product(e_2, e_5, e_1) | product(e_2, e_5, e_5) | product(e_2, e_5, e_6)),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[1010, 994])).
% 0.56/0.74 tff(1012,plain,
% 0.56/0.74 (product(e_2, e_5, e_5)),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[1011, 987, 931])).
% 0.56/0.74 tff(1013,assumption,(~product(e_2, e_4, e_6)), introduced(assumption)).
% 0.56/0.74 tff(1014,plain,
% 0.56/0.74 (~product(e_2, e_4, e_1)),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[725, 714])).
% 0.56/0.74 tff(1015,plain,
% 0.56/0.74 (product(e_2, e_4, e_5)),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[711, 1014, 1013])).
% 0.56/0.74 tff(1016,assumption,(product(e_2, e_5, e_5)), introduced(assumption)).
% 0.56/0.74 tff(1017,plain,
% 0.56/0.74 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_5) | (~product(e_2, e_5, e_5)) | (~product(e_2, e_4, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_5) | (~product(e_2, e_5, e_5)) | (~product(e_2, e_4, e_5)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(1018,plain,
% 0.56/0.74 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_5) | (~product(e_2, e_5, e_5)) | (~product(e_2, e_4, e_5)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(1019,plain,
% 0.56/0.74 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_5) | (~product(e_2, e_5, e_5)) | (~product(e_2, e_4, e_5))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[1018, 1017])).
% 0.56/0.74 tff(1020,plain,
% 0.56/0.74 ($false),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[1019, 666, 131, 1016, 615])).
% 0.56/0.74 tff(1021,plain,((~product(e_2, e_4, e_5)) | (~product(e_2, e_5, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.74 tff(1022,plain,
% 0.56/0.74 ($false),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[1021, 1015, 1012])).
% 0.56/0.74 tff(1023,plain,((~product(e_2, e_6, e_1)) | product(e_2, e_4, e_6) | product(e_2, e_5, e_6)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.74 tff(1024,plain,
% 0.56/0.74 (~product(e_2, e_6, e_1)),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[1023, 980, 971])).
% 0.56/0.74 tff(1025,plain,
% 0.56/0.74 (product(e_2, e_6, e_5)),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[660, 1024, 622, 962])).
% 0.56/0.74 tff(1026,plain,
% 0.56/0.74 (product(e_2, e_4, e_1)),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[711, 980, 662])).
% 0.56/0.74 tff(1027,plain,
% 0.56/0.74 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_5) | (~product(e_2, e_5, e_1)) | (~product(e_2, 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_5) | (~product(e_2, e_5, e_1)) | (~product(e_2, e_4, e_1)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(1028,plain,
% 0.56/0.74 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_5) | (~product(e_2, e_5, e_1)) | (~product(e_2, e_4, e_1)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(1029,plain,
% 0.56/0.74 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_5) | (~product(e_2, e_5, e_1)) | (~product(e_2, e_4, e_1))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[1028, 1027])).
% 0.56/0.74 tff(1030,plain,
% 0.56/0.74 ($false),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[1029, 666, 131, 981, 713])).
% 0.56/0.74 tff(1031,plain,((~product(e_2, e_4, e_1)) | (~product(e_2, e_5, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.74 tff(1032,plain,
% 0.56/0.74 (~product(e_2, e_5, e_1)),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[1031, 1026])).
% 0.56/0.74 tff(1033,plain,
% 0.56/0.74 (product(e_2, e_5, e_5)),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[1011, 1032, 971])).
% 0.56/0.74 tff(1034,plain,
% 0.56/0.74 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_5) | (~product(e_2, e_5, e_5)) | (~product(e_2, e_6, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_5) | (~product(e_2, e_5, e_5)) | (~product(e_2, e_6, e_5)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(1035,plain,
% 0.56/0.74 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_5) | (~product(e_2, e_5, e_5)) | (~product(e_2, e_6, e_5)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(1036,plain,
% 0.56/0.74 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_5) | (~product(e_2, e_5, e_5)) | (~product(e_2, e_6, e_5))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[1035, 1034])).
% 0.56/0.74 tff(1037,plain,
% 0.56/0.74 ($false),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[1036, 628, 131, 601, 1016])).
% 0.56/0.74 tff(1038,plain,((~product(e_2, e_6, e_5)) | (~product(e_2, e_5, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.74 tff(1039,plain,
% 0.56/0.74 ($false),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[1038, 1033, 1025])).
% 0.56/0.74 tff(1040,plain,((~product(e_2, e_2, e_6)) | product(e_2, e_6, e_2) | product(e_2, e_4, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.74 tff(1041,plain,
% 0.56/0.74 (~product(e_2, e_2, e_6)),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[1040, 622, 952])).
% 0.56/0.74 tff(1042,assumption,(product(e_2, e_2, e_5)), introduced(assumption)).
% 0.56/0.74 tff(1043,plain,
% 0.56/0.74 ((~equalish(e_2, e_5)) <=> (~equalish(e_2, e_5))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(1044,axiom,(~equalish(e_2, e_5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_5')).
% 0.56/0.74 tff(1045,plain,
% 0.56/0.74 (~equalish(e_2, e_5)),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[1044, 1043])).
% 0.56/0.74 tff(1046,plain,
% 0.56/0.74 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_5) | (~product(e_2, e_5, e_5)) | (~product(e_2, e_2, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_5) | (~product(e_2, e_5, e_5)) | (~product(e_2, e_2, e_5)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(1047,plain,
% 0.56/0.74 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_5) | (~product(e_2, e_5, e_5)) | (~product(e_2, e_2, e_5)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(1048,plain,
% 0.56/0.74 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_5) | (~product(e_2, e_5, e_5)) | (~product(e_2, e_2, e_5))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[1047, 1046])).
% 0.56/0.74 tff(1049,plain,
% 0.56/0.74 ($false),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[1048, 1045, 131, 1016, 1042])).
% 0.56/0.74 tff(1050,plain,((~product(e_2, e_2, e_5)) | (~product(e_2, e_5, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.74 tff(1051,plain,
% 0.56/0.74 (~product(e_2, e_5, e_5)),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[1050, 1042])).
% 0.56/0.74 tff(1052,plain,
% 0.56/0.74 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_2) | (~product(e_2, e_6, e_5)) | (~product(e_2, e_2, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_2) | (~product(e_2, e_6, e_5)) | (~product(e_2, e_2, e_5)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(1053,plain,
% 0.56/0.74 ((equalish(e_6, e_2) | (~product(e_2, e_2, e_5)) | (~product(e_2, e_6, e_5))) <=> (equalish(e_6, e_2) | (~product(e_2, e_6, e_5)) | (~product(e_2, e_2, e_5)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(1054,plain,
% 0.56/0.74 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_2) | (~product(e_2, e_2, e_5)) | (~product(e_2, e_6, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_2) | (~product(e_2, e_6, e_5)) | (~product(e_2, e_2, e_5))))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[1053])).
% 0.56/0.74 tff(1055,plain,
% 0.56/0.74 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_2) | (~product(e_2, e_2, e_5)) | (~product(e_2, e_6, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_2) | (~product(e_2, e_6, e_5)) | (~product(e_2, e_2, e_5)))),
% 0.56/0.74 inference(transitivity,[status(thm)],[1054, 1052])).
% 0.56/0.74 tff(1056,plain,
% 0.56/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_6, e_2) | (~product(e_2, e_2, e_5)) | (~product(e_2, e_6, e_5)))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(1057,plain,
% 0.56/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_6, e_2) | (~product(e_2, e_6, e_5)) | (~product(e_2, e_2, e_5))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[1056, 1055])).
% 0.56/0.75 tff(1058,plain,
% 0.56/0.75 ($false),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[1057, 533, 131, 601, 1042])).
% 0.56/0.75 tff(1059,plain,((~product(e_2, e_6, e_5)) | (~product(e_2, e_2, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.75 tff(1060,plain,
% 0.56/0.75 (~product(e_2, e_6, e_5)),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[1059, 1042])).
% 0.56/0.75 tff(1061,assumption,(~product(e_2, e_5, e_5)), introduced(assumption)).
% 0.56/0.75 tff(1062,plain,
% 0.56/0.75 (~product(e_2, e_5, e_6)),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[727, 622, 623, 662])).
% 0.56/0.75 tff(1063,plain,
% 0.56/0.75 (product(e_2, e_5, e_1)),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[1011, 1062, 1061])).
% 0.56/0.75 tff(1064,plain,
% 0.56/0.75 (~product(e_2, e_6, e_1)),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[986, 1063])).
% 0.56/0.75 tff(1065,plain,
% 0.56/0.75 (product(e_2, e_6, e_6)),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[660, 1064, 623, 622])).
% 0.56/0.75 tff(1066,plain,
% 0.56/0.75 (~product(e_2, e_4, e_1)),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[1031, 1063])).
% 0.56/0.75 tff(1067,plain,
% 0.56/0.75 (product(e_2, e_4, e_6)),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[711, 1066, 662])).
% 0.56/0.75 tff(1068,plain,
% 0.56/0.75 ($false),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[898, 1067, 1065])).
% 0.56/0.75 tff(1069,plain,(product(e_2, e_6, e_2) | product(e_2, e_4, e_5) | product(e_2, e_6, e_5) | product(e_2, e_5, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.75 tff(1070,plain,
% 0.56/0.75 ($false),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[1069, 1060, 1051, 662, 622])).
% 0.56/0.75 tff(1071,plain,((~product(e_2, e_2, e_5)) | product(e_2, e_4, e_5) | product(e_2, e_6, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.75 tff(1072,plain,
% 0.56/0.75 (~product(e_2, e_2, e_5)),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[1071, 622, 952])).
% 0.56/0.75 tff(1073,plain,
% 0.56/0.75 (product(e_2, e_6, e_5)),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[1069, 1061, 952, 622])).
% 0.56/0.75 tff(1074,plain,
% 0.56/0.75 (~product(e_5, e_6, e_2)),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[606, 1073])).
% 0.56/0.75 tff(1075,plain,
% 0.56/0.75 (~product(e_6, e_1, e_2)),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[581, 1074])).
% 0.56/0.75 tff(1076,plain,
% 0.56/0.75 (product(e_6, e_1, e_1) | product(e_6, e_1, e_2) | product(e_6, e_1, e_5)),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[561, 511])).
% 0.56/0.75 tff(1077,plain,
% 0.56/0.75 (product(e_6, e_1, e_1)),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[1076, 1075, 928])).
% 0.56/0.75 tff(1078,plain,
% 0.56/0.75 (~product(e_1, e_1, e_1)),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[490, 1077])).
% 0.56/0.75 tff(1079,plain,
% 0.56/0.75 (product(e_1, e_1, e_2)),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[95, 1078])).
% 0.56/0.75 tff(1080,plain,
% 0.56/0.75 (((~![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)))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(1081,plain,
% 0.56/0.75 ((~![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)))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(1082,plain,
% 0.56/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_4, e_1, e_2))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[1081, 1080])).
% 0.56/0.75 tff(1083,plain,
% 0.56/0.75 ($false),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[1082, 28, 12, 336, 2])).
% 0.56/0.75 tff(1084,plain,((~product(e_4, e_1, e_2)) | (~product(e_1, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.75 tff(1085,plain,
% 0.56/0.75 (~product(e_4, e_1, e_2)),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[1084, 1079])).
% 0.56/0.75 tff(1086,plain,
% 0.56/0.75 (product(e_4, e_1, e_5)),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[257, 1085])).
% 0.56/0.75 tff(1087,plain,
% 0.56/0.75 (product(e_3, e_4, e_5)),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[369, 1086])).
% 0.56/0.75 tff(1088,assumption,(product(e_3, e_5, e_5)), introduced(assumption)).
% 0.56/0.75 tff(1089,plain,
% 0.56/0.75 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_4) | (~product(e_3, e_4, e_5)) | (~product(e_3, e_5, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_4) | (~product(e_3, e_4, e_5)) | (~product(e_3, e_5, e_5)))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(1090,plain,
% 0.56/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_4) | (~product(e_3, e_4, e_5)) | (~product(e_3, e_5, e_5)))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(1091,plain,
% 0.56/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_4) | (~product(e_3, e_4, e_5)) | (~product(e_3, e_5, e_5))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[1090, 1089])).
% 0.56/0.75 tff(1092,plain,
% 0.56/0.75 ($false),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[1091, 514, 131, 1088, 372])).
% 0.56/0.75 tff(1093,plain,((~product(e_3, e_5, e_5)) | (~product(e_3, e_4, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.75 tff(1094,plain,
% 0.56/0.75 (~product(e_3, e_5, e_5)),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[1093, 1087])).
% 0.56/0.75 tff(1095,plain,
% 0.56/0.75 (product(e_2, e_5, e_1)),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[1011, 1061, 931])).
% 0.56/0.75 tff(1096,assumption,(~product(e_3, e_2, e_1)), introduced(assumption)).
% 0.56/0.75 tff(1097,assumption,(~product(e_2, e_5, e_4)), introduced(assumption)).
% 0.56/0.75 tff(1098,assumption,(~product(e_2, e_5, e_3)), introduced(assumption)).
% 0.56/0.75 tff(1099,assumption,(product(e_3, e_5, e_2)), introduced(assumption)).
% 0.56/0.75 tff(1100,plain,
% 0.56/0.75 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_5, e_1)) | product(e_3, e_2, e_1) | (~product(e_3, e_5, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_5, e_1)) | product(e_3, e_2, e_1) | (~product(e_3, e_5, e_2)))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(1101,plain,
% 0.56/0.75 ((product(e_3, e_2, e_1) | (~product(e_2, e_5, e_1)) | (~product(e_3, e_5, e_2))) <=> ((~product(e_2, e_5, e_1)) | product(e_3, e_2, e_1) | (~product(e_3, e_5, e_2)))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(1102,plain,
% 0.56/0.75 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_2, e_1) | (~product(e_2, e_5, e_1)) | (~product(e_3, e_5, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_5, e_1)) | product(e_3, e_2, e_1) | (~product(e_3, e_5, e_2))))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[1101])).
% 0.56/0.75 tff(1103,plain,
% 0.56/0.75 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_2, e_1) | (~product(e_2, e_5, e_1)) | (~product(e_3, e_5, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_5, e_1)) | product(e_3, e_2, e_1) | (~product(e_3, e_5, e_2)))),
% 0.56/0.75 inference(transitivity,[status(thm)],[1102, 1100])).
% 0.56/0.75 tff(1104,plain,
% 0.56/0.75 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_2, e_1) | (~product(e_2, e_5, e_1)) | (~product(e_3, e_5, e_2)))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(1105,plain,
% 0.56/0.75 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_5, e_1)) | product(e_3, e_2, e_1) | (~product(e_3, e_5, e_2))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[1104, 1103])).
% 0.56/0.75 tff(1106,plain,
% 0.56/0.75 ($false),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[1105, 106, 1099, 981, 1096])).
% 0.56/0.75 tff(1107,plain,((~product(e_2, e_5, e_1)) | (~product(e_3, e_5, e_2)) | product(e_3, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.75 tff(1108,plain,
% 0.56/0.75 (~product(e_2, e_5, e_1)),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[1107, 1099, 1096])).
% 0.56/0.75 tff(1109,plain,
% 0.56/0.75 (product(e_2, e_5, e_2)),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[1008, 1108, 1098, 1097, 931, 1061])).
% 0.56/0.75 tff(1110,plain,
% 0.56/0.75 (((~![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_5, e_2)) | (~product(e_3, e_5, 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_5, e_2)) | (~product(e_3, e_5, e_2)))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(1111,plain,
% 0.56/0.75 ((equalish(e_2, e_3) | (~product(e_3, e_5, e_2)) | (~product(e_2, e_5, e_2))) <=> (equalish(e_2, e_3) | (~product(e_2, e_5, e_2)) | (~product(e_3, e_5, e_2)))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(1112,plain,
% 0.56/0.75 (((~![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_5, e_2)) | (~product(e_2, e_5, 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_5, e_2)) | (~product(e_3, e_5, e_2))))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[1111])).
% 0.56/0.75 tff(1113,plain,
% 0.56/0.75 (((~![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_5, e_2)) | (~product(e_2, e_5, 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_5, e_2)) | (~product(e_3, e_5, e_2)))),
% 0.56/0.75 inference(transitivity,[status(thm)],[1112, 1110])).
% 0.56/0.75 tff(1114,plain,
% 0.56/0.75 ((~![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_5, e_2)) | (~product(e_2, e_5, e_2)))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(1115,plain,
% 0.56/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_2, e_5, e_2)) | (~product(e_3, e_5, e_2))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[1114, 1113])).
% 0.56/0.75 tff(1116,plain,
% 0.56/0.75 ($false),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[1115, 264, 12, 1099, 1109])).
% 0.56/0.75 tff(1117,plain,((~product(e_3, e_5, e_2)) | product(e_2, e_5, e_3) | product(e_2, e_5, e_4) | product(e_2, e_5, e_6) | product(e_2, e_5, e_5) | product(e_3, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.75 tff(1118,plain,
% 0.56/0.75 ((~product(e_3, e_5, e_2)) | product(e_2, e_5, e_4) | product(e_2, e_5, e_6) | product(e_2, e_5, e_5) | product(e_3, e_2, e_1)),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[1117, 1001])).
% 0.56/0.75 tff(1119,plain,
% 0.56/0.75 ((~product(e_3, e_5, e_2)) | product(e_2, e_5, e_6) | product(e_2, e_5, e_5) | product(e_3, e_2, e_1)),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[1118, 994])).
% 0.56/0.75 tff(1120,plain,
% 0.56/0.75 (~product(e_3, e_5, e_2)),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[1119, 1061, 1096, 931])).
% 0.56/0.75 tff(1121,assumption,(~product(e_3, e_5, e_5)), introduced(assumption)).
% 0.56/0.75 tff(1122,assumption,(~product(e_2, e_2, e_6)), introduced(assumption)).
% 0.56/0.75 tff(1123,assumption,(~product(e_2, e_2, e_5)), introduced(assumption)).
% 0.56/0.75 tff(1124,assumption,(product(e_2, e_2, e_1)), introduced(assumption)).
% 0.56/0.75 tff(1125,plain,
% 0.56/0.75 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_5) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_5, 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_5) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_5, e_1)))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(1126,plain,
% 0.56/0.75 ((equalish(e_2, e_5) | (~product(e_2, e_5, e_1)) | (~product(e_2, e_2, e_1))) <=> (equalish(e_2, e_5) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_5, e_1)))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(1127,plain,
% 0.56/0.75 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_5) | (~product(e_2, e_5, 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_5) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_5, e_1))))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[1126])).
% 0.56/0.75 tff(1128,plain,
% 0.56/0.75 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_5) | (~product(e_2, e_5, 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_5) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_5, e_1)))),
% 0.56/0.75 inference(transitivity,[status(thm)],[1127, 1125])).
% 0.56/0.75 tff(1129,plain,
% 0.56/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_5) | (~product(e_2, e_5, e_1)) | (~product(e_2, e_2, e_1)))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(1130,plain,
% 0.56/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_5) | (~product(e_2, e_2, e_1)) | (~product(e_2, e_5, e_1))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[1129, 1128])).
% 0.56/0.75 tff(1131,plain,
% 0.56/0.75 ($false),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[1130, 1045, 131, 981, 1124])).
% 0.56/0.75 tff(1132,plain,((~product(e_2, e_2, e_1)) | (~product(e_2, e_5, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.75 tff(1133,plain,
% 0.56/0.75 (~product(e_2, e_2, e_1)),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[1132, 1095])).
% 0.56/0.75 tff(1134,assumption,(product(e_2, e_2, e_4)), introduced(assumption)).
% 0.56/0.75 tff(1135,plain,
% 0.56/0.75 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_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_2, e_3) | (~product(e_2, e_2, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(1136,plain,
% 0.56/0.75 ((equalish(e_2, e_3) | (~product(e_2, e_3, e_4)) | (~product(e_2, e_2, e_4))) <=> (equalish(e_2, e_3) | (~product(e_2, e_2, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(1137,plain,
% 0.56/0.75 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_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_2, e_3) | (~product(e_2, e_2, e_4)) | (~product(e_2, e_3, e_4))))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[1136])).
% 0.56/0.75 tff(1138,plain,
% 0.56/0.75 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_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_2, e_3) | (~product(e_2, e_2, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.56/0.75 inference(transitivity,[status(thm)],[1137, 1135])).
% 0.56/0.75 tff(1139,plain,
% 0.56/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_2, e_3, e_4)) | (~product(e_2, e_2, e_4)))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(1140,plain,
% 0.56/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_2, e_2, e_4)) | (~product(e_2, e_3, e_4))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[1139, 1138])).
% 0.56/0.75 tff(1141,plain,
% 0.56/0.75 ($false),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[1140, 264, 131, 635, 1134])).
% 0.56/0.75 tff(1142,plain,((~product(e_2, e_2, e_4)) | (~product(e_2, e_3, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.76 tff(1143,plain,
% 0.56/0.76 (~product(e_2, e_2, e_4)),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[1142, 433])).
% 0.56/0.76 tff(1144,assumption,(product(e_2, e_2, e_3)), introduced(assumption)).
% 0.56/0.76 tff(1145,plain,
% 0.56/0.76 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(1146,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.56/0.76 tff(1147,plain,
% 0.56/0.76 (~equalish(e_2, e_1)),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[1146, 1145])).
% 0.56/0.76 tff(1148,plain,
% 0.56/0.76 (((~![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)))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(1149,plain,
% 0.56/0.76 ((~![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)))),
% 0.56/0.76 inference(quant_inst,[status(thm)],[])).
% 0.56/0.76 tff(1150,plain,
% 0.56/0.76 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_3))),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[1149, 1148])).
% 0.56/0.76 tff(1151,plain,
% 0.56/0.76 ($false),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[1150, 1147, 131, 202, 1144])).
% 0.56/0.76 tff(1152,plain,(~product(e_2, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.76 tff(1153,plain,
% 0.56/0.76 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_3) | product(e_2, e_2, e_1) | product(e_2, e_2, e_6) | product(e_2, e_2, e_5) | product(e_2, e_2, e_4))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_3) | product(e_2, e_2, e_1) | product(e_2, e_2, e_6) | product(e_2, e_2, e_5) | product(e_2, e_2, e_4))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(1154,plain,
% 0.56/0.76 ((product(e_2, e_2, e_6) | product(e_2, e_2, e_5) | 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_3) | product(e_2, e_2, e_1) | product(e_2, e_2, e_6) | product(e_2, e_2, e_5) | product(e_2, e_2, e_4))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(1155,plain,
% 0.56/0.76 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6) | product(e_2, e_2, e_5) | 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_6) | product(X, Y, e_5) | 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_3) | product(e_2, e_2, e_1) | product(e_2, e_2, e_6) | product(e_2, e_2, e_5) | product(e_2, e_2, e_4)))),
% 0.56/0.76 inference(monotonicity,[status(thm)],[1154])).
% 0.56/0.76 tff(1156,plain,
% 0.56/0.76 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6) | product(e_2, e_2, e_5) | 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_6) | product(X, Y, e_5) | 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_3) | product(e_2, e_2, e_1) | product(e_2, e_2, e_6) | product(e_2, e_2, e_5) | product(e_2, e_2, e_4))),
% 0.56/0.76 inference(transitivity,[status(thm)],[1155, 1153])).
% 0.56/0.76 tff(1157,plain,
% 0.56/0.76 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6) | product(e_2, e_2, e_5) | 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)))),
% 0.56/0.76 inference(quant_inst,[status(thm)],[])).
% 0.56/0.76 tff(1158,plain,
% 0.56/0.76 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_3) | product(e_2, e_2, e_1) | product(e_2, e_2, e_6) | product(e_2, e_2, e_5) | product(e_2, e_2, e_4)),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[1157, 1156])).
% 0.56/0.76 tff(1159,plain,
% 0.56/0.76 (product(e_2, e_2, e_2) | product(e_2, e_2, e_3) | product(e_2, e_2, e_1) | product(e_2, e_2, e_6) | product(e_2, e_2, e_5) | product(e_2, e_2, e_4)),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[1158, 193, 85])).
% 0.56/0.76 tff(1160,plain,
% 0.56/0.76 (product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | product(e_2, e_2, e_6) | product(e_2, e_2, e_5) | product(e_2, e_2, e_4)),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[1159, 1152])).
% 0.56/0.76 tff(1161,plain,
% 0.56/0.76 (product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | product(e_2, e_2, e_6) | product(e_2, e_2, e_5)),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[1160, 1143])).
% 0.56/0.76 tff(1162,plain,
% 0.56/0.76 (product(e_2, e_2, e_2)),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[1161, 1133, 1123, 1122])).
% 0.56/0.76 tff(1163,assumption,(product(e_3, e_2, e_2)), introduced(assumption)).
% 0.56/0.76 tff(1164,plain,
% 0.56/0.76 (((~![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_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_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(1165,plain,
% 0.56/0.76 ((~![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_2)) | (~product(e_3, e_2, e_2)))),
% 0.56/0.76 inference(quant_inst,[status(thm)],[])).
% 0.56/0.76 tff(1166,plain,
% 0.56/0.76 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2))),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[1165, 1164])).
% 0.56/0.76 tff(1167,plain,
% 0.56/0.76 ($false),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[1166, 296, 12, 261, 1163])).
% 0.56/0.76 tff(1168,plain,((~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.76 tff(1169,plain,
% 0.56/0.76 (~product(e_3, e_2, e_2)),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[1168, 1162])).
% 0.56/0.76 tff(1170,assumption,(product(e_3, e_2, e_3)), introduced(assumption)).
% 0.56/0.76 tff(1171,assumption,(product(e_3, e_3, e_3)), introduced(assumption)).
% 0.56/0.76 tff(1172,plain,
% 0.56/0.76 (((~![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_3, e_2, e_3)) | (~product(e_3, 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_3, e_2, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(1173,plain,
% 0.56/0.76 ((~![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_3, e_2, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(1174,plain,
% 0.60/0.76 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_3, e_3))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[1173, 1172])).
% 0.60/0.76 tff(1175,plain,
% 0.60/0.76 ($false),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[1174, 296, 131, 1171, 1170])).
% 0.60/0.76 tff(1176,plain,((~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.76 tff(1177,plain,
% 0.60/0.76 (~product(e_3, e_3, e_3)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[1176, 1170])).
% 0.60/0.76 tff(1178,plain,
% 0.60/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_3) | (~product(e_3, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_3) | (~product(e_3, e_2, e_3)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(1179,plain,
% 0.60/0.76 ((product(e_3, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_2, e_3))) <=> (product(e_3, e_3, e_3) | (~product(e_3, e_2, e_3)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(1180,plain,
% 0.60/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_3) | (~product(e_3, e_2, e_3))))),
% 0.60/0.76 inference(monotonicity,[status(thm)],[1179])).
% 0.60/0.76 tff(1181,plain,
% 0.60/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_3) | (~product(e_3, e_2, e_3)))),
% 0.60/0.76 inference(transitivity,[status(thm)],[1180, 1178])).
% 0.60/0.76 tff(1182,plain,
% 0.60/0.76 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(1183,plain,
% 0.60/0.76 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_3, e_3) | (~product(e_3, e_2, e_3))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[1182, 1181])).
% 0.60/0.76 tff(1184,plain,
% 0.60/0.76 ($false),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[1183, 106, 1177, 1170])).
% 0.60/0.76 tff(1185,plain,(~product(e_3, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.76 tff(1186,assumption,(product(e_3, e_2, e_4)), introduced(assumption)).
% 0.60/0.76 tff(1187,plain,
% 0.60/0.76 (((~![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_3, e_1, e_4)) | (~product(e_3, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_2, e_4)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(1188,plain,
% 0.60/0.76 ((~![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_3, e_1, e_4)) | (~product(e_3, e_2, e_4)))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(1189,plain,
% 0.60/0.76 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_2, e_4))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[1188, 1187])).
% 0.60/0.76 tff(1190,plain,
% 0.60/0.76 ($false),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[1189, 1147, 131, 364, 1186])).
% 0.60/0.76 tff(1191,plain,(~product(e_3, e_2, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.76 tff(1192,plain,
% 0.60/0.76 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_3)) | product(e_3, e_2, e_1) | product(e_3, e_2, e_6) | product(e_3, e_2, e_5) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_3)) | product(e_3, e_2, e_1) | product(e_3, e_2, e_6) | product(e_3, e_2, e_5) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(1193,plain,
% 0.60/0.76 ((product(e_3, e_2, e_6) | product(e_3, e_2, e_5) | 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)) | (~group_element(e_3)) | product(e_3, e_2, e_1) | product(e_3, e_2, e_6) | product(e_3, e_2, e_5) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(1194,plain,
% 0.60/0.76 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6) | product(e_3, e_2, e_5) | 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_6) | product(X, Y, e_5) | 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_3)) | product(e_3, e_2, e_1) | product(e_3, e_2, e_6) | product(e_3, e_2, e_5) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2)))),
% 0.60/0.76 inference(monotonicity,[status(thm)],[1193])).
% 0.60/0.76 tff(1195,plain,
% 0.60/0.76 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6) | product(e_3, e_2, e_5) | 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_6) | product(X, Y, e_5) | 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_3)) | product(e_3, e_2, e_1) | product(e_3, e_2, e_6) | product(e_3, e_2, e_5) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2))),
% 0.60/0.76 inference(transitivity,[status(thm)],[1194, 1192])).
% 0.60/0.76 tff(1196,plain,
% 0.60/0.76 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_6) | product(e_3, e_2, e_5) | 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)))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(1197,plain,
% 0.60/0.76 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_3)) | product(e_3, e_2, e_1) | product(e_3, e_2, e_6) | product(e_3, e_2, e_5) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[1196, 1195])).
% 0.60/0.76 tff(1198,plain,
% 0.60/0.76 (product(e_3, e_2, e_1) | product(e_3, e_2, e_6) | product(e_3, e_2, e_5) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[1197, 193, 325, 85])).
% 0.60/0.76 tff(1199,plain,
% 0.60/0.76 (product(e_3, e_2, e_1) | product(e_3, e_2, e_6) | product(e_3, e_2, e_5) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[1198, 1191])).
% 0.60/0.76 tff(1200,plain,
% 0.60/0.76 (product(e_3, e_2, e_1) | product(e_3, e_2, e_6) | product(e_3, e_2, e_5) | product(e_3, e_2, e_2)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[1199, 1185])).
% 0.60/0.76 tff(1201,plain,
% 0.60/0.76 (product(e_3, e_2, e_6)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[1200, 1169, 930, 1096])).
% 0.60/0.76 tff(1202,assumption,(product(e_3, e_2, e_6)), introduced(assumption)).
% 0.60/0.76 tff(1203,plain,
% 0.60/0.76 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_3, e_5, e_6)) | (~product(e_3, e_2, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_2) | (~product(e_3, e_5, e_6)) | (~product(e_3, e_2, e_6)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(1204,plain,
% 0.60/0.76 ((equalish(e_5, e_2) | (~product(e_3, e_2, e_6)) | (~product(e_3, e_5, e_6))) <=> (equalish(e_5, e_2) | (~product(e_3, e_5, e_6)) | (~product(e_3, e_2, e_6)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(1205,plain,
% 0.60/0.76 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_3, e_2, e_6)) | (~product(e_3, e_5, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_3, e_5, e_6)) | (~product(e_3, e_2, e_6))))),
% 0.60/0.76 inference(monotonicity,[status(thm)],[1204])).
% 0.60/0.76 tff(1206,plain,
% 0.60/0.76 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_3, e_2, e_6)) | (~product(e_3, e_5, e_6)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_2) | (~product(e_3, e_5, e_6)) | (~product(e_3, e_2, e_6)))),
% 0.60/0.76 inference(transitivity,[status(thm)],[1205, 1203])).
% 0.60/0.76 tff(1207,plain,
% 0.60/0.76 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_3, e_2, e_6)) | (~product(e_3, e_5, e_6)))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(1208,plain,
% 0.60/0.76 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_2) | (~product(e_3, e_5, e_6)) | (~product(e_3, e_2, e_6))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[1207, 1206])).
% 0.60/0.76 tff(1209,plain,
% 0.60/0.76 ($false),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[1208, 437, 131, 740, 1202])).
% 0.60/0.76 tff(1210,plain,((~product(e_3, e_5, e_6)) | (~product(e_3, e_2, e_6))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.76 tff(1211,plain,
% 0.60/0.76 (~product(e_3, e_5, e_6)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[1210, 1201])).
% 0.60/0.76 tff(1212,assumption,(product(e_3, e_5, e_4)), introduced(assumption)).
% 0.60/0.76 tff(1213,plain,
% 0.60/0.76 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_5, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_5, e_4)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(1214,plain,
% 0.60/0.76 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_5, e_4)))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(1215,plain,
% 0.60/0.76 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_5, e_4))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[1214, 1213])).
% 0.60/0.76 tff(1216,plain,
% 0.60/0.76 ($false),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[1215, 396, 131, 423, 1212])).
% 0.60/0.76 tff(1217,plain,((~product(e_3, e_5, e_4)) | (~product(e_3, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.77 tff(1218,plain,
% 0.60/0.77 (~product(e_3, e_5, e_4)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1217, 364])).
% 0.60/0.77 tff(1219,assumption,(product(e_3, e_5, e_3)), introduced(assumption)).
% 0.60/0.77 tff(1220,plain,
% 0.60/0.77 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_5, e_3)) | product(e_3, e_3, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_5, e_3)) | product(e_3, e_3, e_3))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1221,plain,
% 0.60/0.77 ((product(e_3, e_3, e_3) | (~product(e_3, e_5, e_3)) | (~product(e_3, e_5, e_3))) <=> ((~product(e_3, e_5, e_3)) | product(e_3, e_3, e_3))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1222,plain,
% 0.60/0.77 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_3) | (~product(e_3, e_5, e_3)) | (~product(e_3, e_5, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_3, e_5, e_3)) | product(e_3, e_3, e_3)))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[1221])).
% 0.60/0.77 tff(1223,plain,
% 0.60/0.77 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_3) | (~product(e_3, e_5, e_3)) | (~product(e_3, e_5, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_5, e_3)) | product(e_3, e_3, e_3))),
% 0.60/0.77 inference(transitivity,[status(thm)],[1222, 1220])).
% 0.60/0.77 tff(1224,plain,
% 0.60/0.77 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_3, e_3) | (~product(e_3, e_5, e_3)) | (~product(e_3, e_5, e_3)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(1225,plain,
% 0.60/0.77 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_3, e_5, e_3)) | product(e_3, e_3, e_3)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1224, 1223])).
% 0.60/0.77 tff(1226,plain,
% 0.60/0.77 ((~product(e_3, e_5, e_3)) | product(e_3, e_3, e_3)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1225, 106])).
% 0.60/0.77 tff(1227,plain,
% 0.60/0.77 (product(e_3, e_3, e_3)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1226, 1219])).
% 0.60/0.77 tff(1228,plain,
% 0.60/0.77 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_3) | (~product(e_3, e_5, e_3)) | (~product(e_3, 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_5, e_3) | (~product(e_3, e_5, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1229,plain,
% 0.60/0.77 ((equalish(e_5, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_5, e_3))) <=> (equalish(e_5, e_3) | (~product(e_3, e_5, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1230,plain,
% 0.60/0.77 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_5, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_3) | (~product(e_3, e_5, e_3)) | (~product(e_3, e_3, e_3))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[1229])).
% 0.60/0.77 tff(1231,plain,
% 0.60/0.77 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_5, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_3) | (~product(e_3, e_5, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.60/0.77 inference(transitivity,[status(thm)],[1230, 1228])).
% 0.60/0.77 tff(1232,plain,
% 0.60/0.77 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_5, e_3)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(1233,plain,
% 0.60/0.77 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_3) | (~product(e_3, e_5, e_3)) | (~product(e_3, e_3, e_3))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1232, 1231])).
% 0.60/0.77 tff(1234,plain,
% 0.60/0.77 ($false),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1233, 416, 131, 1219, 1227])).
% 0.60/0.77 tff(1235,plain,(~product(e_3, e_5, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.77 tff(1236,plain,
% 0.60/0.77 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_3)) | product(e_3, e_5, e_6) | (~group_element(e_5)) | product(e_3, e_5, e_2) | product(e_3, e_5, e_1) | product(e_3, e_5, e_3) | product(e_3, e_5, e_4) | product(e_3, e_5, e_5))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_3)) | product(e_3, e_5, e_6) | (~group_element(e_5)) | product(e_3, e_5, e_2) | product(e_3, e_5, e_1) | product(e_3, e_5, e_3) | product(e_3, e_5, e_4) | product(e_3, e_5, e_5))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1237,plain,
% 0.60/0.77 ((product(e_3, e_5, e_6) | product(e_3, e_5, e_5) | product(e_3, e_5, e_4) | product(e_3, e_5, e_3) | product(e_3, e_5, e_2) | product(e_3, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_3))) <=> ((~group_element(e_3)) | product(e_3, e_5, e_6) | (~group_element(e_5)) | product(e_3, e_5, e_2) | product(e_3, e_5, e_1) | product(e_3, e_5, e_3) | product(e_3, e_5, e_4) | product(e_3, e_5, e_5))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1238,plain,
% 0.60/0.77 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5, e_6) | product(e_3, e_5, e_5) | product(e_3, e_5, e_4) | product(e_3, e_5, e_3) | product(e_3, e_5, e_2) | product(e_3, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_3)) | product(e_3, e_5, e_6) | (~group_element(e_5)) | product(e_3, e_5, e_2) | product(e_3, e_5, e_1) | product(e_3, e_5, e_3) | product(e_3, e_5, e_4) | product(e_3, e_5, e_5)))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[1237])).
% 0.60/0.77 tff(1239,plain,
% 0.60/0.77 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5, e_6) | product(e_3, e_5, e_5) | product(e_3, e_5, e_4) | product(e_3, e_5, e_3) | product(e_3, e_5, e_2) | product(e_3, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_3)) | product(e_3, e_5, e_6) | (~group_element(e_5)) | product(e_3, e_5, e_2) | product(e_3, e_5, e_1) | product(e_3, e_5, e_3) | product(e_3, e_5, e_4) | product(e_3, e_5, e_5))),
% 0.60/0.77 inference(transitivity,[status(thm)],[1238, 1236])).
% 0.60/0.77 tff(1240,plain,
% 0.60/0.77 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5, e_6) | product(e_3, e_5, e_5) | product(e_3, e_5, e_4) | product(e_3, e_5, e_3) | product(e_3, e_5, e_2) | product(e_3, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_3)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(1241,plain,
% 0.60/0.77 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_3)) | product(e_3, e_5, e_6) | (~group_element(e_5)) | product(e_3, e_5, e_2) | product(e_3, e_5, e_1) | product(e_3, e_5, e_3) | product(e_3, e_5, e_4) | product(e_3, e_5, e_5)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1240, 1239])).
% 0.60/0.77 tff(1242,plain,
% 0.60/0.77 (product(e_3, e_5, e_6) | product(e_3, e_5, e_2) | product(e_3, e_5, e_1) | product(e_3, e_5, e_3) | product(e_3, e_5, e_4) | product(e_3, e_5, e_5)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1241, 325, 452, 85])).
% 0.60/0.77 tff(1243,plain,
% 0.60/0.77 (product(e_3, e_5, e_6) | product(e_3, e_5, e_2) | product(e_3, e_5, e_1) | product(e_3, e_5, e_4) | product(e_3, e_5, e_5)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1242, 1235])).
% 0.60/0.77 tff(1244,plain,
% 0.60/0.77 (product(e_3, e_5, e_6) | product(e_3, e_5, e_2) | product(e_3, e_5, e_1) | product(e_3, e_5, e_5)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1243, 1218])).
% 0.60/0.77 tff(1245,plain,
% 0.60/0.77 (product(e_3, e_5, e_1)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1244, 1211, 1121, 1120])).
% 0.60/0.77 tff(1246,plain,
% 0.60/0.77 (((~![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_5, e_1)) | (~product(e_2, e_5, 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_5, e_1)) | (~product(e_2, e_5, e_1)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1247,plain,
% 0.60/0.77 ((~![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_5, e_1)) | (~product(e_2, e_5, e_1)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(1248,plain,
% 0.60/0.77 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_3, e_5, e_1)) | (~product(e_2, e_5, e_1))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1247, 1246])).
% 0.60/0.77 tff(1249,plain,
% 0.60/0.77 ($false),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1248, 264, 12, 1245, 1095])).
% 0.60/0.77 tff(1250,plain,(product(e_2, e_5, e_5) | product(e_3, e_5, e_5) | product(e_3, e_2, e_5) | product(e_3, e_2, e_1) | product(e_2, e_2, e_5) | product(e_2, e_2, e_6) | product(e_2, e_5, e_6)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.77 tff(1251,plain,
% 0.60/0.77 (product(e_3, e_2, e_1)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1250, 1094, 930, 931, 1061, 1072, 1041])).
% 0.60/0.77 tff(1252,plain,
% 0.60/0.77 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_3)) | product(e_1, e_2, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_3)) | product(e_1, e_2, e_3))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1253,plain,
% 0.60/0.77 ((product(e_1, e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_1, e_2))) <=> ((~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_3)) | product(e_1, e_2, e_3))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1254,plain,
% 0.60/0.77 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_3)) | product(e_1, e_2, e_3)))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[1253])).
% 0.60/0.77 tff(1255,plain,
% 0.60/0.77 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_3)) | product(e_1, e_2, e_3))),
% 0.60/0.77 inference(transitivity,[status(thm)],[1254, 1252])).
% 0.60/0.77 tff(1256,plain,
% 0.60/0.77 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_1, e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_1, e_1, e_2)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(1257,plain,
% 0.60/0.77 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_3)) | product(e_1, e_2, e_3)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1256, 1255])).
% 0.60/0.77 tff(1258,plain,
% 0.60/0.77 ((~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_3)) | product(e_1, e_2, e_3)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1257, 106])).
% 0.60/0.77 tff(1259,plain,
% 0.60/0.77 ((~product(e_1, e_1, e_2)) | product(e_1, e_2, e_3)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1258, 202])).
% 0.60/0.77 tff(1260,plain,
% 0.60/0.77 (product(e_1, e_2, e_3)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1259, 1079])).
% 0.60/0.77 tff(1261,plain,
% 0.60/0.77 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_1, e_2, e_3)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1262,plain,
% 0.60/0.77 ((product(e_3, e_1, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_1))) <=> (product(e_3, e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_1, e_2, e_3)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1263,plain,
% 0.60/0.77 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_1, e_2, e_3))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[1262])).
% 0.60/0.77 tff(1264,plain,
% 0.60/0.77 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_1, e_2, e_3)))),
% 0.60/0.77 inference(transitivity,[status(thm)],[1263, 1261])).
% 0.60/0.77 tff(1265,plain,
% 0.60/0.77 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_3, e_2, e_1)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(1266,plain,
% 0.60/0.77 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_1, e_2, e_3))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1265, 1264])).
% 0.60/0.77 tff(1267,plain,
% 0.60/0.77 ($false),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1266, 106, 305, 1260, 1251])).
% 0.60/0.77 tff(1268,plain,(product(e_2, e_5, e_5) | product(e_3, e_2, e_5) | product(e_2, e_5, e_6) | product(e_2, e_6, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.77 tff(1269,plain,
% 0.60/0.77 (product(e_2, e_5, e_5)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1268, 622, 931, 930])).
% 0.60/0.77 tff(1270,plain,
% 0.60/0.77 (~product(e_2, e_6, e_5)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1038, 1269])).
% 0.60/0.77 tff(1271,plain,
% 0.60/0.77 (product(e_2, e_6, e_1)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[660, 1270, 929, 622])).
% 0.60/0.77 tff(1272,assumption,(product(e_5, e_6, e_1)), introduced(assumption)).
% 0.60/0.77 tff(1273,plain,
% 0.60/0.77 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_6, e_1)) | (~product(e_5, e_6, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_2) | (~product(e_2, e_6, e_1)) | (~product(e_5, e_6, e_1)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1274,plain,
% 0.60/0.78 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_6, e_1)) | (~product(e_5, e_6, e_1)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(1275,plain,
% 0.60/0.78 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_2) | (~product(e_2, e_6, e_1)) | (~product(e_5, e_6, e_1))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1274, 1273])).
% 0.60/0.78 tff(1276,plain,
% 0.60/0.78 ($false),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1275, 437, 12, 714, 1272])).
% 0.60/0.78 tff(1277,plain,((~product(e_5, e_6, e_1)) | (~product(e_2, e_6, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.78 tff(1278,plain,
% 0.60/0.78 (~product(e_5, e_6, e_1)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1277, 1271])).
% 0.60/0.78 tff(1279,assumption,(~product(e_5, e_6, e_1)), introduced(assumption)).
% 0.60/0.78 tff(1280,plain,
% 0.60/0.78 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_6, e_1, e_1)) | product(e_5, e_6, e_1) | (~product(e_5, e_1, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_6, e_1, e_1)) | product(e_5, e_6, e_1) | (~product(e_5, e_1, e_6)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1281,plain,
% 0.60/0.78 ((product(e_5, e_6, e_1) | (~product(e_6, e_1, e_1)) | (~product(e_5, e_1, e_6))) <=> ((~product(e_6, e_1, e_1)) | product(e_5, e_6, e_1) | (~product(e_5, e_1, e_6)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1282,plain,
% 0.60/0.78 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_6, e_1) | (~product(e_6, e_1, e_1)) | (~product(e_5, e_1, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_6, e_1, e_1)) | product(e_5, e_6, e_1) | (~product(e_5, e_1, e_6))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[1281])).
% 0.60/0.78 tff(1283,plain,
% 0.60/0.78 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_6, e_1) | (~product(e_6, e_1, e_1)) | (~product(e_5, e_1, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_6, e_1, e_1)) | product(e_5, e_6, e_1) | (~product(e_5, e_1, e_6)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[1282, 1280])).
% 0.60/0.78 tff(1284,plain,
% 0.60/0.78 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_6, e_1) | (~product(e_6, e_1, e_1)) | (~product(e_5, e_1, e_6)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(1285,plain,
% 0.60/0.78 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_6, e_1, e_1)) | product(e_5, e_6, e_1) | (~product(e_5, e_1, e_6))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1284, 1283])).
% 0.60/0.78 tff(1286,plain,
% 0.60/0.78 ($false),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1285, 106, 482, 1279, 570])).
% 0.60/0.78 tff(1287,plain,(product(e_5, e_6, e_1) | (~product(e_6, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.78 tff(1288,plain,
% 0.60/0.78 (~product(e_6, e_1, e_1)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1287, 1278])).
% 0.60/0.78 tff(1289,plain,
% 0.60/0.78 (product(e_6, e_1, e_2)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1076, 1288, 928])).
% 0.60/0.78 tff(1290,plain,
% 0.60/0.78 (~product(e_4, e_1, e_2)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[20, 1289])).
% 0.60/0.78 tff(1291,plain,
% 0.60/0.78 (product(e_4, e_1, e_5)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[257, 1290])).
% 0.60/0.78 tff(1292,plain,
% 0.60/0.78 (product(e_4, e_5, e_6)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[737, 1291])).
% 0.60/0.78 tff(1293,plain,
% 0.60/0.78 (product(e_3, e_4, e_5)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[369, 1291])).
% 0.60/0.78 tff(1294,plain,
% 0.60/0.78 (~product(e_3, e_5, e_6)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[748, 1292])).
% 0.60/0.78 tff(1295,plain,
% 0.60/0.78 (~product(e_5, e_4, e_6)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[759, 1294, 1293])).
% 0.60/0.78 tff(1296,plain,
% 0.60/0.78 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_4, e_5, e_6)) | product(e_5, e_4, e_6) | (~product(e_5, e_5, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_5, e_6)) | product(e_5, e_4, e_6) | (~product(e_5, e_5, e_4)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1297,plain,
% 0.60/0.78 ((product(e_5, e_4, e_6) | (~product(e_4, e_5, e_6)) | (~product(e_5, e_5, e_4))) <=> ((~product(e_4, e_5, e_6)) | product(e_5, e_4, e_6) | (~product(e_5, e_5, e_4)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1298,plain,
% 0.60/0.78 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_4, e_6) | (~product(e_4, e_5, e_6)) | (~product(e_5, e_5, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_4, e_5, e_6)) | product(e_5, e_4, e_6) | (~product(e_5, e_5, e_4))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[1297])).
% 0.60/0.78 tff(1299,plain,
% 0.60/0.78 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_4, e_6) | (~product(e_4, e_5, e_6)) | (~product(e_5, e_5, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_5, e_6)) | product(e_5, e_4, e_6) | (~product(e_5, e_5, e_4)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[1298, 1296])).
% 0.60/0.78 tff(1300,plain,
% 0.60/0.78 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_4, e_6) | (~product(e_4, e_5, e_6)) | (~product(e_5, e_5, e_4)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(1301,plain,
% 0.60/0.78 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_4, e_5, e_6)) | product(e_5, e_4, e_6) | (~product(e_5, e_5, e_4))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1300, 1299])).
% 0.60/0.78 tff(1302,plain,
% 0.60/0.78 (~product(e_5, e_5, e_4)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1301, 106, 1295, 1292])).
% 0.60/0.78 tff(1303,plain,
% 0.60/0.78 (product(e_5, e_6, e_2)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[581, 1289])).
% 0.60/0.78 tff(1304,assumption,(product(e_5, e_5, e_2)), introduced(assumption)).
% 0.60/0.78 tff(1305,plain,
% 0.60/0.78 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_6) | (~product(e_5, e_5, e_2)) | (~product(e_5, e_6, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_6) | (~product(e_5, e_5, e_2)) | (~product(e_5, e_6, e_2)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1306,plain,
% 0.60/0.78 ((equalish(e_5, e_6) | (~product(e_5, e_6, e_2)) | (~product(e_5, e_5, e_2))) <=> (equalish(e_5, e_6) | (~product(e_5, e_5, e_2)) | (~product(e_5, e_6, e_2)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1307,plain,
% 0.60/0.78 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_6) | (~product(e_5, e_6, e_2)) | (~product(e_5, e_5, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_6) | (~product(e_5, e_5, e_2)) | (~product(e_5, e_6, e_2))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[1306])).
% 0.60/0.78 tff(1308,plain,
% 0.60/0.78 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_6) | (~product(e_5, e_6, e_2)) | (~product(e_5, e_5, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_6) | (~product(e_5, e_5, e_2)) | (~product(e_5, e_6, e_2)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[1307, 1305])).
% 0.60/0.78 tff(1309,plain,
% 0.60/0.78 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_6) | (~product(e_5, e_6, e_2)) | (~product(e_5, e_5, e_2)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(1310,plain,
% 0.60/0.78 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_6) | (~product(e_5, e_5, e_2)) | (~product(e_5, e_6, e_2))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1309, 1308])).
% 0.60/0.78 tff(1311,plain,
% 0.60/0.78 ($false),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1310, 565, 131, 583, 1304])).
% 0.60/0.78 tff(1312,plain,((~product(e_5, e_5, e_2)) | (~product(e_5, e_6, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.78 tff(1313,plain,
% 0.60/0.78 (~product(e_5, e_5, e_2)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1312, 1303])).
% 0.60/0.78 tff(1314,assumption,(product(e_5, e_5, e_3)), introduced(assumption)).
% 0.60/0.78 tff(1315,plain,
% 0.60/0.78 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_5, e_3) | (~product(e_5, e_5, e_3)) | (~product(e_2, e_5, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_5, e_3) | (~product(e_5, e_5, e_3)) | (~product(e_2, e_5, e_5)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1316,plain,
% 0.60/0.78 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_5, e_3) | (~product(e_5, e_5, e_3)) | (~product(e_2, e_5, e_5)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(1317,plain,
% 0.60/0.78 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_5, e_3) | (~product(e_5, e_5, e_3)) | (~product(e_2, e_5, e_5))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1316, 1315])).
% 0.60/0.78 tff(1318,plain,
% 0.60/0.78 ($false),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1317, 106, 1016, 1001, 1314])).
% 0.60/0.78 tff(1319,plain,((~product(e_5, e_5, e_3)) | (~product(e_2, e_5, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.78 tff(1320,plain,
% 0.60/0.78 (~product(e_5, e_5, e_3)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1319, 1269])).
% 0.60/0.78 tff(1321,assumption,(product(e_5, e_5, e_6)), introduced(assumption)).
% 0.60/0.78 tff(1322,plain,
% 0.60/0.78 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_5, e_6) | (~product(e_2, e_5, e_5)) | (~product(e_5, e_5, e_6)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_5, e_6) | (~product(e_2, e_5, e_5)) | (~product(e_5, e_5, e_6)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1323,plain,
% 0.60/0.78 ((product(e_2, e_5, e_6) | (~product(e_5, e_5, e_6)) | (~product(e_2, e_5, e_5))) <=> (product(e_2, e_5, e_6) | (~product(e_2, e_5, e_5)) | (~product(e_5, e_5, e_6)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1324,plain,
% 0.60/0.78 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_5, e_6) | (~product(e_5, e_5, e_6)) | (~product(e_2, e_5, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_5, e_6) | (~product(e_2, e_5, e_5)) | (~product(e_5, e_5, e_6))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[1323])).
% 0.60/0.78 tff(1325,plain,
% 0.60/0.78 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_5, e_6) | (~product(e_5, e_5, e_6)) | (~product(e_2, e_5, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_5, e_6) | (~product(e_2, e_5, e_5)) | (~product(e_5, e_5, e_6)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[1324, 1322])).
% 0.60/0.78 tff(1326,plain,
% 0.60/0.78 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_5, e_6) | (~product(e_5, e_5, e_6)) | (~product(e_2, e_5, e_5)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(1327,plain,
% 0.60/0.78 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_5, e_6) | (~product(e_2, e_5, e_5)) | (~product(e_5, e_5, e_6))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1326, 1325])).
% 0.60/0.78 tff(1328,plain,
% 0.60/0.78 ($false),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1327, 106, 1016, 931, 1321])).
% 0.60/0.78 tff(1329,plain,((~product(e_5, e_5, e_6)) | (~product(e_2, e_5, e_5)) | product(e_2, e_5, e_6)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.78 tff(1330,plain,
% 0.60/0.78 (~product(e_5, e_5, e_6)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1329, 1269, 931])).
% 0.60/0.78 tff(1331,plain,
% 0.60/0.78 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5)) | product(e_5, e_5, e_3) | product(e_5, e_5, e_6) | product(e_5, e_5, e_4) | product(e_5, e_5, e_5) | product(e_5, e_5, e_2) | product(e_5, e_5, e_1))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5)) | product(e_5, e_5, e_3) | product(e_5, e_5, e_6) | product(e_5, e_5, e_4) | product(e_5, e_5, e_5) | product(e_5, e_5, e_2) | product(e_5, e_5, e_1))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1332,plain,
% 0.60/0.78 ((product(e_5, e_5, e_6) | product(e_5, e_5, e_5) | product(e_5, e_5, e_4) | product(e_5, e_5, e_3) | product(e_5, e_5, e_2) | product(e_5, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_5))) <=> ((~group_element(e_5)) | product(e_5, e_5, e_3) | product(e_5, e_5, e_6) | product(e_5, e_5, e_4) | product(e_5, e_5, e_5) | product(e_5, e_5, e_2) | product(e_5, e_5, e_1))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1333,plain,
% 0.60/0.78 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5, e_5, e_6) | product(e_5, e_5, e_5) | product(e_5, e_5, e_4) | product(e_5, e_5, e_3) | product(e_5, e_5, e_2) | product(e_5, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_5)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5)) | product(e_5, e_5, e_3) | product(e_5, e_5, e_6) | product(e_5, e_5, e_4) | product(e_5, e_5, e_5) | product(e_5, e_5, e_2) | product(e_5, e_5, e_1)))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[1332])).
% 0.60/0.78 tff(1334,plain,
% 0.60/0.78 (((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5, e_5, e_6) | product(e_5, e_5, e_5) | product(e_5, e_5, e_4) | product(e_5, e_5, e_3) | product(e_5, e_5, e_2) | product(e_5, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_5)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5)) | product(e_5, e_5, e_3) | product(e_5, e_5, e_6) | product(e_5, e_5, e_4) | product(e_5, e_5, e_5) | product(e_5, e_5, e_2) | product(e_5, e_5, e_1))),
% 0.60/0.78 inference(transitivity,[status(thm)],[1333, 1331])).
% 0.60/0.78 tff(1335,plain,
% 0.60/0.78 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5, e_5, e_6) | product(e_5, e_5, e_5) | product(e_5, e_5, e_4) | product(e_5, e_5, e_3) | product(e_5, e_5, e_2) | product(e_5, e_5, e_1) | (~group_element(e_5)) | (~group_element(e_5)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(1336,plain,
% 0.60/0.78 ((~![Y: $i, X: $i] : (product(X, Y, e_6) | product(X, Y, e_5) | 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_5)) | product(e_5, e_5, e_3) | product(e_5, e_5, e_6) | product(e_5, e_5, e_4) | product(e_5, e_5, e_5) | product(e_5, e_5, e_2) | product(e_5, e_5, e_1)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1335, 1334])).
% 0.60/0.79 tff(1337,plain,
% 0.60/0.79 (product(e_5, e_5, e_3) | product(e_5, e_5, e_6) | product(e_5, e_5, e_4) | product(e_5, e_5, e_5) | product(e_5, e_5, e_2) | product(e_5, e_5, e_1)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1336, 452, 85])).
% 0.60/0.79 tff(1338,plain,
% 0.60/0.79 (product(e_5, e_5, e_1)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1337, 1330, 1320, 1313, 1302, 384])).
% 0.60/0.79 tff(1339,assumption,(product(e_5, e_5, e_1)), introduced(assumption)).
% 0.60/0.79 tff(1340,plain,
% 0.60/0.79 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_5) | (~product(e_5, e_5, e_1)) | (~product(e_5, 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_5) | (~product(e_5, e_5, e_1)) | (~product(e_5, e_4, e_1)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1341,plain,
% 0.60/0.79 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_5) | (~product(e_5, e_5, e_1)) | (~product(e_5, e_4, e_1)))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(1342,plain,
% 0.60/0.79 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_5) | (~product(e_5, e_5, e_1)) | (~product(e_5, e_4, e_1))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1341, 1340])).
% 0.60/0.79 tff(1343,plain,
% 0.60/0.79 ($false),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1342, 666, 131, 1339, 886])).
% 0.60/0.79 tff(1344,plain,((~product(e_5, e_4, e_1)) | (~product(e_5, e_5, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.79 tff(1345,plain,
% 0.60/0.79 (~product(e_5, e_4, e_1)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1344, 1338])).
% 0.60/0.79 tff(1346,plain,
% 0.60/0.79 (~product(e_5, e_4, e_2)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[769, 1303])).
% 0.60/0.79 tff(1347,plain,
% 0.60/0.79 (~product(e_5, e_4, e_3)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[800, 106, 1293, 797])).
% 0.60/0.79 tff(1348,plain,
% 0.60/0.79 (product(e_5, e_4, e_5)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[884, 1295, 1347, 1346, 1345])).
% 0.60/0.79 tff(1349,plain,
% 0.60/0.79 ($false),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[774, 416, 12, 1293, 1348])).
% 0.60/0.79 tff(1350,plain,(product(e_2, e_6, e_2) | product(e_5, e_5, e_5) | product(e_2, e_5, e_6) | product(e_2, e_6, e_6) | product(e_3, e_2, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.79 tff(1351,plain,
% 0.60/0.79 (product(e_5, e_5, e_5)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1350, 899, 614, 728, 381])).
% 0.60/0.79 tff(1352,plain,
% 0.60/0.79 (product(e_2, e_5, e_5)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1069, 621, 607, 614])).
% 0.60/0.79 tff(1353,plain,
% 0.60/0.79 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_5, e_5)) | (~product(e_5, e_5, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_2) | (~product(e_2, e_5, e_5)) | (~product(e_5, e_5, e_5)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1354,plain,
% 0.60/0.79 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_5, e_5)) | (~product(e_5, e_5, e_5)))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(1355,plain,
% 0.60/0.79 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_2) | (~product(e_2, e_5, e_5)) | (~product(e_5, e_5, e_5))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1354, 1353])).
% 0.60/0.79 tff(1356,plain,
% 0.60/0.79 ($false),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1355, 437, 12, 1352, 1351])).
% 0.60/0.79 tff(1357,plain,(~product(e_6, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.79 tff(1358,plain,
% 0.60/0.79 (product(e_6, e_1, e_1) | product(e_6, e_1, e_2)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1076, 928])).
% 0.60/0.79 tff(1359,plain,
% 0.60/0.79 (product(e_6, e_1, e_1)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1358, 1357])).
% 0.60/0.79 tff(1360,plain,
% 0.60/0.79 (~product(e_1, e_1, e_1)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[490, 1359])).
% 0.60/0.79 tff(1361,plain,
% 0.60/0.79 (product(e_1, e_1, e_2)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[95, 1360])).
% 0.60/0.79 tff(1362,plain,
% 0.60/0.79 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_2)) | (~product(e_6, e_1, e_1)) | product(e_6, e_1, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_2)) | (~product(e_6, e_1, e_1)) | product(e_6, e_1, e_2))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1363,plain,
% 0.60/0.79 ((product(e_6, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_6, e_1, e_1))) <=> ((~product(e_1, e_1, e_2)) | (~product(e_6, e_1, e_1)) | product(e_6, e_1, e_2))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1364,plain,
% 0.60/0.79 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_6, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_2)) | (~product(e_6, e_1, e_1)) | product(e_6, e_1, e_2)))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[1363])).
% 0.60/0.79 tff(1365,plain,
% 0.60/0.79 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_6, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_2)) | (~product(e_6, e_1, e_1)) | product(e_6, e_1, e_2))),
% 0.60/0.79 inference(transitivity,[status(thm)],[1364, 1362])).
% 0.60/0.79 tff(1366,plain,
% 0.60/0.79 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_6, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_6, e_1, e_1)))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(1367,plain,
% 0.60/0.79 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_2)) | (~product(e_6, e_1, e_1)) | product(e_6, e_1, e_2)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1366, 1365])).
% 0.60/0.79 tff(1368,plain,
% 0.60/0.79 ($false),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1367, 106, 1361, 1359, 1357])).
% 0.60/0.79 % SZS output end Proof
% 0.60/0.79 % E exiting
%------------------------------------------------------------------------------