%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP124-1.004 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:07:04 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP124-1.004 : TPTP v9.0.0. Released v1.2.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n006.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 15:41:35 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.42 % SZS status Unsatisfiable
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 tff(product_type, type, (
% 0.20/0.42 product: ( $i * $i * $i ) > $o)).
% 0.20/0.42 tff(e_4_type, type, (
% 0.20/0.42 e_4: $i)).
% 0.20/0.42 tff(e_2_type, type, (
% 0.20/0.42 e_2: $i)).
% 0.20/0.42 tff(e_1_type, type, (
% 0.20/0.42 e_1: $i)).
% 0.20/0.42 tff(e_3_type, type, (
% 0.20/0.42 e_3: $i)).
% 0.20/0.42 tff(equalish_type, type, (
% 0.20/0.42 equalish: ( $i * $i ) > $o)).
% 0.20/0.42 tff(group_element_type, type, (
% 0.20/0.42 group_element: $i > $o)).
% 0.20/0.42 tff(1,assumption,(product(e_3, e_2, e_1)), introduced(assumption)).
% 0.20/0.42 tff(2,assumption,(product(e_2, e_1, e_2)), introduced(assumption)).
% 0.20/0.42 tff(3,assumption,(~product(e_2, e_2, e_2)), introduced(assumption)).
% 0.20/0.42 tff(4,plain,
% 0.20/0.42 (^[X: $i] : refl(product(X, X, X) <=> product(X, X, X))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(5,plain,
% 0.20/0.42 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.20/0.42 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.42 tff(6,plain,
% 0.20/0.42 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(7,axiom,(![X: $i] : product(X, X, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_idempotence')).
% 0.20/0.42 tff(8,plain,
% 0.20/0.42 (![X: $i] : product(X, X, X)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.20/0.42 tff(9,plain,(
% 0.20/0.42 ![X: $i] : product(X, X, X)),
% 0.20/0.42 inference(skolemize,[status(sab)],[8])).
% 0.20/0.42 tff(10,plain,
% 0.20/0.42 (![X: $i] : product(X, X, X)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.42 tff(11,plain,
% 0.20/0.42 ((~![X: $i] : product(X, X, X)) | product(e_2, e_2, e_2)),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(12,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[11, 10, 3])).
% 0.20/0.42 tff(13,plain,(product(e_2, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(X, W, Y)) | (~product(X, Z, Y))) <=> ((~product(X, Z, Y)) | (~product(X, W, Y)))), ((((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> (((~product(X, Z, Y)) | (~product(X, W, Y))) | equalish(W, Z)))), rewrite((((~product(X, Z, Y)) | (~product(X, W, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))), ((((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, W, Y)) | (~product(X, Z, Y))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.42 tff(19,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')).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.20/0.42 tff(21,plain,
% 0.20/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.20/0.42 tff(22,plain,(
% 0.20/0.42 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[21])).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(25,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 (~equalish(e_1, e_2)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.20/0.42 tff(27,plain,
% 0.20/0.42 (((~![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_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 ((~![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)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[29, 26, 23, 13, 2])).
% 0.20/0.42 tff(31,plain,(~product(e_2, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 ((~![X: $i] : product(X, X, X)) | product(e_3, e_3, e_3)),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 (product(e_3, e_3, e_3)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[32, 10])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 (^[Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : refl(((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2)) <=> ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2)) <=> ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[34])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2)) <=> ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 (^[Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) <=> ((~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))), (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) <=> (((~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | (~product(Z2, X2, Y2))))), rewrite((((~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | (~product(Z2, X2, Y2))) <=> ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))), (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) <=> ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))))), ((((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) | equalish(Y1, Y2)) <=> (((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | equalish(Y1, Y2)))), rewrite((((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | equalish(Y1, Y2)) <=> ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))), ((((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) | equalish(Y1, Y2)) <=> ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(38,plain,
% 0.20/0.43 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) | equalish(Y1, Y2)) <=> ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[37])).
% 0.20/0.43 tff(39,axiom,(![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, X1, Y1))) | (~product(Z2, X2, Y2))) | equalish(Y1, Y2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qg2_2')).
% 0.20/0.43 tff(40,plain,
% 0.20/0.43 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.20/0.43 tff(41,plain,
% 0.20/0.43 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.20/0.43 tff(42,plain,(
% 0.20/0.43 ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.20/0.43 inference(skolemize,[status(sab)],[41])).
% 0.20/0.43 tff(43,plain,
% 0.20/0.43 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.20/0.43 tff(44,plain,
% 0.20/0.43 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(45,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.20/0.43 tff(46,plain,
% 0.20/0.43 (~equalish(e_1, e_3)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.43 tff(47,plain,
% 0.20/0.43 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_1, e_3)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(48,plain,
% 0.20/0.43 (((~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_1, e_3)) | equalish(e_1, e_3)) <=> (equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_1, e_3)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(49,plain,
% 0.20/0.43 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_1, e_3)) | equalish(e_1, e_3))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_1, e_3))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[48])).
% 0.20/0.43 tff(50,plain,
% 0.20/0.43 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_1, e_3)) | equalish(e_1, e_3))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_1, e_3)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[49, 47])).
% 0.20/0.43 tff(51,plain,
% 0.20/0.43 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_1, e_3)) | equalish(e_1, e_3))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(52,plain,
% 0.20/0.43 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_1)) | (~product(e_2, e_1, e_3))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.43 tff(53,plain,
% 0.20/0.43 (~product(e_2, e_1, e_3)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[52, 46, 43, 33, 1])).
% 0.20/0.43 tff(54,assumption,(~product(e_1, e_1, e_1)), introduced(assumption)).
% 0.20/0.43 tff(55,plain,
% 0.20/0.43 ((~![X: $i] : product(X, X, X)) | product(e_1, e_1, e_1)),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(56,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[55, 10, 54])).
% 0.20/0.43 tff(57,plain,(product(e_1, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(58,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.20/0.43 tff(59,plain,
% 0.20/0.43 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(60,plain,
% 0.20/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[59])).
% 0.20/0.43 tff(61,plain,
% 0.20/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(62,plain,
% 0.20/0.43 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(W, Y, X)) | (~product(Z, Y, X))) <=> ((~product(Z, Y, X)) | (~product(W, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> (((~product(Z, Y, X)) | (~product(W, Y, X))) | equalish(W, Z)))), rewrite((((~product(Z, Y, X)) | (~product(W, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(63,plain,
% 0.20/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[62])).
% 0.20/0.43 tff(64,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')).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.43 tff(66,plain,
% 0.20/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.20/0.43 tff(67,plain,(
% 0.20/0.43 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[66])).
% 0.20/0.43 tff(68,plain,
% 0.20/0.43 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.20/0.43 tff(69,plain,
% 0.20/0.43 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(70,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.20/0.43 tff(71,plain,
% 0.20/0.43 (~equalish(e_2, e_1)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.43 tff(72,plain,
% 0.20/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~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_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(73,plain,
% 0.20/0.43 ((equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1))) <=> (equalish(e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(74,plain,
% 0.20/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[73])).
% 0.20/0.43 tff(75,plain,
% 0.20/0.43 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[74, 72])).
% 0.20/0.43 tff(76,plain,
% 0.20/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(77,plain,
% 0.20/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.43 tff(78,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[77, 71, 68, 58, 57])).
% 0.20/0.43 tff(79,plain,(~product(e_2, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(80,plain,
% 0.20/0.43 (^[Y: $i, X: $i] : refl((product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(81,plain,
% 0.20/0.43 (![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[80])).
% 0.20/0.43 tff(82,plain,
% 0.20/0.43 (![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) <=> ![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(83,plain,
% 0.20/0.43 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) <=> (product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> ((product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_2)))), rewrite(((product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_2)) <=> (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> (product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ((product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_3)))), rewrite(((product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_3)) <=> (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> (product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))))), (((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> ((product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_4)))), rewrite(((product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X))) | product(X, Y, e_4)) <=> (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))), (((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(84,plain,
% 0.20/0.43 (![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> ![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[83])).
% 0.20/0.43 tff(85,axiom,(![Y: $i, X: $i] : ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_total_function1')).
% 0.20/0.43 tff(86,plain,
% 0.20/0.43 (![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.43 tff(87,plain,
% 0.20/0.43 (![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.20/0.44 tff(88,plain,(
% 0.20/0.44 ![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[87])).
% 0.20/0.44 tff(89,plain,
% 0.20/0.44 (![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.20/0.44 tff(90,plain,
% 0.20/0.44 (group_element(e_2) <=> group_element(e_2)),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(91,axiom,(group_element(e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_2')).
% 0.20/0.44 tff(92,plain,
% 0.20/0.44 (group_element(e_2)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.20/0.44 tff(93,plain,
% 0.20/0.44 (group_element(e_1) <=> group_element(e_1)),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(94,axiom,(group_element(e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_1')).
% 0.20/0.44 tff(95,plain,
% 0.20/0.44 (group_element(e_1)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.44 tff(96,plain,
% 0.20/0.44 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_4) | (~group_element(e_2)) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_4) | (~group_element(e_2)) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(97,plain,
% 0.20/0.44 ((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))) <=> ((~group_element(e_1)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_4) | (~group_element(e_2)) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(98,plain,
% 0.20/0.44 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_1, e_4) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_1)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_4) | (~group_element(e_2)) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[97])).
% 0.20/0.44 tff(99,plain,
% 0.20/0.44 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_1, e_4) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_4) | (~group_element(e_2)) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3))),
% 0.20/0.44 inference(transitivity,[status(thm)],[98, 96])).
% 0.20/0.44 tff(100,plain,
% 0.20/0.44 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_1, e_4) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_2)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(101,plain,
% 0.20/0.44 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_1)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_4) | (~group_element(e_2)) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.20/0.44 tff(102,plain,
% 0.20/0.44 (product(e_2, e_1, e_4) | product(e_2, e_1, e_2) | product(e_2, e_1, e_3)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[101, 95, 92, 89, 79])).
% 0.20/0.44 tff(103,plain,
% 0.20/0.44 (product(e_2, e_1, e_4)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[102, 53, 31])).
% 0.20/0.44 tff(104,assumption,(product(e_4, e_2, e_1)), introduced(assumption)).
% 0.20/0.44 tff(105,plain,
% 0.20/0.44 ((~![X: $i] : product(X, X, X)) | product(e_4, e_4, e_4)),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(106,plain,
% 0.20/0.44 (product(e_4, e_4, e_4)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[105, 10])).
% 0.20/0.44 tff(107,assumption,(product(e_2, e_1, e_4)), introduced(assumption)).
% 0.20/0.44 tff(108,plain,
% 0.20/0.44 ((~equalish(e_1, e_4)) <=> (~equalish(e_1, e_4))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(109,axiom,(~equalish(e_1, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_4')).
% 0.20/0.44 tff(110,plain,
% 0.20/0.44 (~equalish(e_1, e_4)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.20/0.44 tff(111,plain,
% 0.20/0.44 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_1, e_4) | (~product(e_2, e_1, e_4)) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_1)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_4) | (~product(e_2, e_1, e_4)) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_1)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(112,plain,
% 0.20/0.44 (((~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_1)) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_1, e_4)) | equalish(e_1, e_4)) <=> (equalish(e_1, e_4) | (~product(e_2, e_1, e_4)) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_1)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(113,plain,
% 0.20/0.44 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_1)) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_1, e_4)) | equalish(e_1, e_4))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_1, e_4) | (~product(e_2, e_1, e_4)) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_1))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[112])).
% 0.20/0.44 tff(114,plain,
% 0.20/0.44 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_1)) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_1, e_4)) | equalish(e_1, e_4))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_4) | (~product(e_2, e_1, e_4)) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_1)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[113, 111])).
% 0.20/0.44 tff(115,plain,
% 0.20/0.44 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_1)) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_1, e_4)) | equalish(e_1, e_4))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(116,plain,
% 0.20/0.44 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_4) | (~product(e_2, e_1, e_4)) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_1))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.20/0.44 tff(117,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[116, 110, 43, 107, 106, 104])).
% 0.20/0.44 tff(118,plain,((~product(e_4, e_2, e_1)) | (~product(e_2, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(119,plain,
% 0.20/0.44 (~product(e_4, e_2, e_1)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[118, 103])).
% 0.20/0.44 tff(120,assumption,(product(e_3, e_4, e_2)), introduced(assumption)).
% 0.20/0.44 tff(121,plain,
% 0.20/0.44 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(122,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.20/0.44 tff(123,plain,
% 0.20/0.44 (~equalish(e_2, e_3)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.20/0.44 tff(124,plain,
% 0.20/0.44 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_2, e_3)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_2, e_3)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(125,plain,
% 0.20/0.45 (((~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_2)) | (~product(e_3, e_3, e_3)) | (~product(e_4, e_2, e_3)) | equalish(e_2, e_3)) <=> (equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_2, e_3)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(126,plain,
% 0.20/0.45 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_2)) | (~product(e_3, e_3, e_3)) | (~product(e_4, e_2, e_3)) | equalish(e_2, e_3))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_2, e_3))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[125])).
% 0.20/0.45 tff(127,plain,
% 0.20/0.45 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_2)) | (~product(e_3, e_3, e_3)) | (~product(e_4, e_2, e_3)) | equalish(e_2, e_3))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_2, e_3)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[126, 124])).
% 0.20/0.45 tff(128,plain,
% 0.20/0.45 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_2)) | (~product(e_3, e_3, e_3)) | (~product(e_4, e_2, e_3)) | equalish(e_2, e_3))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(129,plain,
% 0.20/0.45 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_2)) | (~product(e_4, e_2, e_3))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.20/0.45 tff(130,plain,
% 0.20/0.45 (~product(e_4, e_2, e_3)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[129, 123, 43, 120, 33])).
% 0.20/0.45 tff(131,plain,
% 0.20/0.45 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_2, e_1) | (~product(e_2, e_1, e_4)) | (~product(e_3, e_2, e_1)) | (~product(e_4, e_2, e_4)) | (~product(e_3, e_4, e_2)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_4)) | (~product(e_3, e_2, e_1)) | (~product(e_4, e_2, e_4)) | (~product(e_3, e_4, e_2)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(132,plain,
% 0.20/0.45 (((~product(e_3, e_2, e_1)) | (~product(e_3, e_4, e_2)) | (~product(e_2, e_1, e_4)) | (~product(e_4, e_2, e_4)) | equalish(e_2, e_1)) <=> (equalish(e_2, e_1) | (~product(e_2, e_1, e_4)) | (~product(e_3, e_2, e_1)) | (~product(e_4, e_2, e_4)) | (~product(e_3, e_4, e_2)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(133,plain,
% 0.20/0.45 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_2, e_1)) | (~product(e_3, e_4, e_2)) | (~product(e_2, e_1, e_4)) | (~product(e_4, e_2, e_4)) | equalish(e_2, e_1))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_2, e_1) | (~product(e_2, e_1, e_4)) | (~product(e_3, e_2, e_1)) | (~product(e_4, e_2, e_4)) | (~product(e_3, e_4, e_2))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[132])).
% 0.20/0.45 tff(134,plain,
% 0.20/0.45 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_2, e_1)) | (~product(e_3, e_4, e_2)) | (~product(e_2, e_1, e_4)) | (~product(e_4, e_2, e_4)) | equalish(e_2, e_1))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_4)) | (~product(e_3, e_2, e_1)) | (~product(e_4, e_2, e_4)) | (~product(e_3, e_4, e_2)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[133, 131])).
% 0.20/0.45 tff(135,plain,
% 0.20/0.45 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_2, e_1)) | (~product(e_3, e_4, e_2)) | (~product(e_2, e_1, e_4)) | (~product(e_4, e_2, e_4)) | equalish(e_2, e_1))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(136,plain,
% 0.20/0.45 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_4)) | (~product(e_3, e_2, e_1)) | (~product(e_4, e_2, e_4)) | (~product(e_3, e_4, e_2))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.20/0.45 tff(137,plain,
% 0.20/0.45 (~product(e_4, e_2, e_4)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[136, 71, 43, 103, 120, 1])).
% 0.20/0.45 tff(138,assumption,(product(e_4, e_2, e_2)), introduced(assumption)).
% 0.20/0.45 tff(139,plain,
% 0.20/0.45 ((~equalish(e_4, e_2)) <=> (~equalish(e_4, e_2))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(140,axiom,(~equalish(e_4, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_is_not_e_2')).
% 0.20/0.45 tff(141,plain,
% 0.20/0.45 (~equalish(e_4, e_2)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.20/0.45 tff(142,plain,
% 0.20/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_2, e_2)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(143,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_2, e_2)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(144,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_2, e_2))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.20/0.45 tff(145,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[144, 141, 68, 13, 138])).
% 0.20/0.45 tff(146,plain,(~product(e_4, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(147,plain,
% 0.20/0.45 (group_element(e_4) <=> group_element(e_4)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(148,axiom,(group_element(e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_4')).
% 0.20/0.45 tff(149,plain,
% 0.20/0.45 (group_element(e_4)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.20/0.45 tff(150,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_4)) | (~group_element(e_2)) | product(e_4, e_2, e_1) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | (~group_element(e_2)) | product(e_4, e_2, e_1) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(151,plain,
% 0.20/0.45 ((product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_4))) <=> ((~group_element(e_4)) | (~group_element(e_2)) | product(e_4, e_2, e_1) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(152,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_4)) | (~group_element(e_2)) | product(e_4, e_2, e_1) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[151])).
% 0.20/0.45 tff(153,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | (~group_element(e_2)) | product(e_4, e_2, e_1) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2))),
% 0.20/0.45 inference(transitivity,[status(thm)],[152, 150])).
% 0.20/0.45 tff(154,plain,
% 0.20/0.45 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_4)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(155,plain,
% 0.20/0.45 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | (~group_element(e_2)) | product(e_4, e_2, e_1) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.20/0.45 tff(156,plain,
% 0.20/0.45 (product(e_4, e_2, e_1) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[155, 92, 149, 89, 146])).
% 0.20/0.45 tff(157,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[156, 137, 130, 119])).
% 0.20/0.45 tff(158,plain,((~product(e_3, e_4, e_2)) | (~product(e_3, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(159,plain,
% 0.20/0.45 (~product(e_3, e_4, e_2)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[158, 1])).
% 0.20/0.45 tff(160,assumption,(product(e_3, e_4, e_4)), introduced(assumption)).
% 0.20/0.45 tff(161,plain,
% 0.20/0.45 ((~equalish(e_3, e_4)) <=> (~equalish(e_3, e_4))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(162,axiom,(~equalish(e_3, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_4')).
% 0.20/0.45 tff(163,plain,
% 0.20/0.45 (~equalish(e_3, e_4)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.20/0.45 tff(164,plain,
% 0.20/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_3, 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_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_4, e_4)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(165,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_4, e_4)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(166,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_3, e_4, e_4))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.20/0.45 tff(167,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[166, 163, 68, 160, 106])).
% 0.20/0.45 tff(168,plain,(~product(e_3, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(169,assumption,(product(e_3, e_4, e_3)), introduced(assumption)).
% 0.20/0.45 tff(170,plain,
% 0.20/0.45 ((~equalish(e_4, e_3)) <=> (~equalish(e_4, e_3))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(171,axiom,(~equalish(e_4, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_is_not_e_3')).
% 0.20/0.45 tff(172,plain,
% 0.20/0.45 (~equalish(e_4, e_3)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.20/0.45 tff(173,plain,
% 0.20/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(174,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(175,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_3))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.20/0.45 tff(176,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[175, 172, 23, 169, 33])).
% 0.20/0.45 tff(177,plain,(~product(e_3, e_4, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(178,plain,
% 0.20/0.45 (group_element(e_3) <=> group_element(e_3)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(179,axiom,(group_element(e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_3')).
% 0.20/0.45 tff(180,plain,
% 0.20/0.45 (group_element(e_3)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.20/0.45 tff(181,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | (~group_element(e_4)) | product(e_3, e_4, e_1) | product(e_3, e_4, e_2) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_3, e_4, e_1) | product(e_3, e_4, e_2) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(182,plain,
% 0.20/0.45 ((product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_3))) <=> ((~group_element(e_3)) | (~group_element(e_4)) | product(e_3, e_4, e_1) | product(e_3, e_4, e_2) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(183,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_3)) | (~group_element(e_4)) | product(e_3, e_4, e_1) | product(e_3, e_4, e_2) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[182])).
% 0.20/0.46 tff(184,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_3, e_4, e_1) | product(e_3, e_4, e_2) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3))),
% 0.20/0.46 inference(transitivity,[status(thm)],[183, 181])).
% 0.20/0.46 tff(185,plain,
% 0.20/0.46 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_4, e_4) | product(e_3, e_4, e_3) | product(e_3, e_4, e_2) | product(e_3, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_3)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(186,plain,
% 0.20/0.46 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_3)) | (~group_element(e_4)) | product(e_3, e_4, e_1) | product(e_3, e_4, e_2) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.20/0.46 tff(187,plain,
% 0.20/0.46 (product(e_3, e_4, e_1) | product(e_3, e_4, e_2) | product(e_3, e_4, e_4) | product(e_3, e_4, e_3)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[186, 180, 149, 89])).
% 0.20/0.46 tff(188,plain,
% 0.20/0.46 (product(e_3, e_4, e_1) | product(e_3, e_4, e_2) | product(e_3, e_4, e_4)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[187, 177])).
% 0.20/0.46 tff(189,plain,
% 0.20/0.46 (product(e_3, e_4, e_1) | product(e_3, e_4, e_2)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[188, 168])).
% 0.20/0.46 tff(190,plain,
% 0.20/0.46 (product(e_3, e_4, e_1)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[189, 159])).
% 0.20/0.46 tff(191,plain,
% 0.20/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_3, 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_2) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_4, e_1)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(192,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_4, e_1)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(193,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_2) | (~product(e_3, e_2, e_1)) | (~product(e_3, e_4, e_1))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.20/0.46 tff(194,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[193, 141, 23, 190, 1])).
% 0.20/0.46 tff(195,plain,(~product(e_3, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(196,assumption,(product(e_3, e_2, e_2)), introduced(assumption)).
% 0.20/0.46 tff(197,plain,
% 0.20/0.46 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(198,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.20/0.46 tff(199,plain,
% 0.20/0.46 (~equalish(e_3, e_2)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.20/0.46 tff(200,plain,
% 0.20/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_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)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(201,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(202,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.20/0.46 tff(203,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[202, 199, 68, 196, 13])).
% 0.20/0.46 tff(204,plain,(~product(e_3, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(205,assumption,(product(e_3, e_2, e_3)), introduced(assumption)).
% 0.20/0.46 tff(206,plain,
% 0.20/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, 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_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(207,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(208,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_3))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.20/0.46 tff(209,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[208, 123, 23, 33, 205])).
% 0.20/0.46 tff(210,plain,(~product(e_3, e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(211,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_2, e_1) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | (~group_element(e_3)) | product(e_3, e_2, e_4) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_2, e_1) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | (~group_element(e_3)) | product(e_3, e_2, e_4) | (~group_element(e_2)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(212,plain,
% 0.20/0.46 ((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))) <=> (product(e_3, e_2, e_1) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | (~group_element(e_3)) | product(e_3, e_2, e_4) | (~group_element(e_2)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(213,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_2, e_1) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | (~group_element(e_3)) | product(e_3, e_2, e_4) | (~group_element(e_2))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[212])).
% 0.20/0.46 tff(214,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_2, e_1) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | (~group_element(e_3)) | product(e_3, e_2, e_4) | (~group_element(e_2)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[213, 211])).
% 0.20/0.46 tff(215,plain,
% 0.20/0.46 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)) | (~group_element(e_3)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(216,plain,
% 0.20/0.46 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_3, e_2, e_1) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | (~group_element(e_3)) | product(e_3, e_2, e_4) | (~group_element(e_2))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.20/0.46 tff(217,plain,
% 0.20/0.46 (product(e_3, e_2, e_1) | product(e_3, e_2, e_2) | product(e_3, e_2, e_4)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[216, 92, 180, 89, 210])).
% 0.20/0.46 tff(218,plain,
% 0.20/0.46 (product(e_3, e_2, e_1) | product(e_3, e_2, e_4)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[217, 204])).
% 0.20/0.46 tff(219,plain,
% 0.20/0.46 (product(e_3, e_2, e_4)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[218, 195])).
% 0.20/0.46 tff(220,assumption,(product(e_2, e_4, e_3)), introduced(assumption)).
% 0.20/0.46 tff(221,assumption,(product(e_3, e_2, e_4)), introduced(assumption)).
% 0.20/0.46 tff(222,plain,
% 0.20/0.46 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_4, e_3) | (~product(e_3, e_2, e_4)) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_4, e_3)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_3) | (~product(e_3, e_2, e_4)) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_4, e_3)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(223,plain,
% 0.20/0.46 (((~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_4)) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_4, e_3)) | equalish(e_4, e_3)) <=> (equalish(e_4, e_3) | (~product(e_3, e_2, e_4)) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_4, e_3)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(224,plain,
% 0.20/0.46 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_4)) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_4, e_3)) | equalish(e_4, e_3))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_4, e_3) | (~product(e_3, e_2, e_4)) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_4, e_3))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[223])).
% 0.20/0.46 tff(225,plain,
% 0.20/0.46 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_4)) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_4, e_3)) | equalish(e_4, e_3))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_3) | (~product(e_3, e_2, e_4)) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_4, e_3)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[224, 222])).
% 0.20/0.46 tff(226,plain,
% 0.20/0.46 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_2, e_4)) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_4, e_3)) | equalish(e_4, e_3))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(227,plain,
% 0.20/0.46 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_4, e_3) | (~product(e_3, e_2, e_4)) | (~product(e_3, e_3, e_3)) | (~product(e_2, e_4, e_3))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.20/0.46 tff(228,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[227, 172, 43, 33, 221, 220])).
% 0.20/0.46 tff(229,plain,((~product(e_3, e_2, e_4)) | (~product(e_2, e_4, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(230,plain,
% 0.20/0.46 (~product(e_2, e_4, e_3)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[229, 219])).
% 0.20/0.46 tff(231,assumption,(product(e_2, e_4, e_2)), introduced(assumption)).
% 0.20/0.46 tff(232,plain,
% 0.20/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(233,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(234,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_2))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.20/0.46 tff(235,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[234, 141, 23, 13, 231])).
% 0.20/0.46 tff(236,plain,(~product(e_2, e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(237,assumption,(product(e_2, e_4, e_4)), introduced(assumption)).
% 0.20/0.46 tff(238,plain,
% 0.20/0.46 ((~equalish(e_2, e_4)) <=> (~equalish(e_2, e_4))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(239,axiom,(~equalish(e_2, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_4')).
% 0.20/0.46 tff(240,plain,
% 0.20/0.46 (~equalish(e_2, e_4)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.20/0.46 tff(241,plain,
% 0.20/0.46 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_4, e_4)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(242,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_4, e_4)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(243,plain,
% 0.20/0.46 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_4, e_4))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.20/0.46 tff(244,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[243, 240, 68, 106, 237])).
% 0.20/0.46 tff(245,plain,(~product(e_2, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(246,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_4)) | (~group_element(e_2)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | (~group_element(e_2)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(247,plain,
% 0.20/0.46 ((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_4)) | (~group_element(e_2)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(248,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | ((~group_element(e_4)) | (~group_element(e_2)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[247])).
% 0.20/0.47 tff(249,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | (~group_element(e_2)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3))),
% 0.20/0.47 inference(transitivity,[status(thm)],[248, 246])).
% 0.20/0.47 tff(250,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_2, e_4, e_4) | product(e_2, e_4, e_3) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | (~group_element(e_4)) | (~group_element(e_2)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(251,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (~group_element(e_4)) | (~group_element(e_2)) | product(e_2, e_4, e_4) | product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.20/0.47 tff(252,plain,
% 0.20/0.47 (product(e_2, e_4, e_2) | product(e_2, e_4, e_1) | product(e_2, e_4, e_3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[251, 92, 149, 89, 245])).
% 0.20/0.47 tff(253,plain,
% 0.20/0.47 (product(e_2, e_4, e_1) | product(e_2, e_4, e_3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[252, 236])).
% 0.20/0.47 tff(254,plain,
% 0.20/0.47 (product(e_2, e_4, e_1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[253, 230])).
% 0.20/0.47 tff(255,assumption,(product(e_2, e_4, e_1)), introduced(assumption)).
% 0.20/0.47 tff(256,assumption,(product(e_4, e_1, e_2)), introduced(assumption)).
% 0.20/0.47 tff(257,plain,
% 0.20/0.47 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_1, e_2)) | (~product(e_2, e_4, e_1)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_1, e_2)) | (~product(e_2, e_4, e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(258,plain,
% 0.20/0.47 (((~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_1)) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_1, e_2)) | equalish(e_1, e_2)) <=> (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_1, e_2)) | (~product(e_2, e_4, e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(259,plain,
% 0.20/0.47 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_1)) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_1, e_2)) | equalish(e_1, e_2))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_1, e_2)) | (~product(e_2, e_4, e_1))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[258])).
% 0.20/0.47 tff(260,plain,
% 0.20/0.47 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_1)) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_1, e_2)) | equalish(e_1, e_2))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_1, e_2)) | (~product(e_2, e_4, e_1)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[259, 257])).
% 0.20/0.47 tff(261,plain,
% 0.20/0.47 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_2, e_2, e_2)) | (~product(e_2, e_4, e_1)) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_1, e_2)) | equalish(e_1, e_2))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(262,plain,
% 0.20/0.47 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_1, e_2)) | (~product(e_2, e_4, e_1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.20/0.47 tff(263,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[262, 26, 43, 13, 256, 255])).
% 0.20/0.47 tff(264,plain,((~product(e_2, e_4, e_1)) | (~product(e_4, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(265,plain,
% 0.20/0.47 (~product(e_4, e_1, e_2)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[264, 254])).
% 0.20/0.47 tff(266,assumption,(product(e_4, e_1, e_1)), introduced(assumption)).
% 0.20/0.47 tff(267,plain,
% 0.20/0.47 ((~equalish(e_4, e_1)) <=> (~equalish(e_4, e_1))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(268,axiom,(~equalish(e_4, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_is_not_e_1')).
% 0.20/0.47 tff(269,plain,
% 0.20/0.47 (~equalish(e_4, e_1)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.20/0.47 tff(270,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(271,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(272,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.20/0.47 tff(273,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[272, 269, 68, 266, 57])).
% 0.20/0.47 tff(274,plain,(~product(e_4, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(275,assumption,(product(e_4, e_1, e_4)), introduced(assumption)).
% 0.20/0.47 tff(276,plain,
% 0.20/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_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_4, e_4)) | (~product(e_4, e_1, e_4)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(277,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(278,plain,
% 0.20/0.47 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.20/0.47 tff(279,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[278, 110, 23, 275, 106])).
% 0.20/0.47 tff(280,plain,(~product(e_4, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(281,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_1, e_4) | (~group_element(e_4)) | product(e_4, e_1, e_2) | (~group_element(e_1)) | product(e_4, e_1, e_1) | product(e_4, e_1, e_3))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_4, e_1, e_4) | (~group_element(e_4)) | product(e_4, e_1, e_2) | (~group_element(e_1)) | product(e_4, e_1, e_1) | product(e_4, e_1, e_3))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(282,plain,
% 0.20/0.47 ((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_4) | (~group_element(e_4)) | product(e_4, e_1, e_2) | (~group_element(e_1)) | product(e_4, e_1, e_1) | product(e_4, e_1, e_3))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(283,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_1, e_4) | (~group_element(e_4)) | product(e_4, e_1, e_2) | (~group_element(e_1)) | product(e_4, e_1, e_1) | product(e_4, e_1, e_3)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[282])).
% 0.20/0.47 tff(284,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_4, e_1, e_4) | (~group_element(e_4)) | product(e_4, e_1, e_2) | (~group_element(e_1)) | product(e_4, e_1, e_1) | product(e_4, e_1, e_3))),
% 0.20/0.47 inference(transitivity,[status(thm)],[283, 281])).
% 0.20/0.47 tff(285,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | (product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)) | (~group_element(e_4)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(286,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : (product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)) | (~group_element(X)))) | product(e_4, e_1, e_4) | (~group_element(e_4)) | product(e_4, e_1, e_2) | (~group_element(e_1)) | product(e_4, e_1, e_1) | product(e_4, e_1, e_3)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.20/0.47 tff(287,plain,
% 0.20/0.47 (product(e_4, e_1, e_4) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | product(e_4, e_1, e_3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[286, 95, 149, 89])).
% 0.20/0.47 tff(288,plain,
% 0.20/0.47 (product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | product(e_4, e_1, e_3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[287, 280])).
% 0.20/0.47 tff(289,plain,
% 0.20/0.47 (product(e_4, e_1, e_2) | product(e_4, e_1, e_3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[288, 274])).
% 0.20/0.47 tff(290,plain,
% 0.20/0.47 (product(e_4, e_1, e_3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[289, 265])).
% 0.20/0.47 tff(291,assumption,(product(e_3, e_4, e_1)), introduced(assumption)).
% 0.20/0.47 tff(292,assumption,(product(e_4, e_1, e_3)), introduced(assumption)).
% 0.20/0.47 tff(293,plain,
% 0.20/0.47 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_1, e_3) | (~product(e_4, e_1, e_3)) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_1)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_3) | (~product(e_4, e_1, e_3)) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(294,plain,
% 0.20/0.47 (((~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_1)) | (~product(e_3, e_3, e_3)) | (~product(e_4, e_1, e_3)) | equalish(e_1, e_3)) <=> (equalish(e_1, e_3) | (~product(e_4, e_1, e_3)) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(295,plain,
% 0.20/0.47 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_1)) | (~product(e_3, e_3, e_3)) | (~product(e_4, e_1, e_3)) | equalish(e_1, e_3))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_1, e_3) | (~product(e_4, e_1, e_3)) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_1))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[294])).
% 0.20/0.47 tff(296,plain,
% 0.20/0.47 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_1)) | (~product(e_3, e_3, e_3)) | (~product(e_4, e_1, e_3)) | equalish(e_1, e_3))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_3) | (~product(e_4, e_1, e_3)) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_1)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[295, 293])).
% 0.20/0.47 tff(297,plain,
% 0.20/0.47 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_1)) | (~product(e_3, e_3, e_3)) | (~product(e_4, e_1, e_3)) | equalish(e_1, e_3))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(298,plain,
% 0.20/0.47 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_3) | (~product(e_4, e_1, e_3)) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_4, e_1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.20/0.47 tff(299,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[298, 46, 43, 292, 291, 33])).
% 0.20/0.47 tff(300,plain,((~product(e_3, e_4, e_1)) | (~product(e_4, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(301,plain,
% 0.20/0.47 (~product(e_3, e_4, e_1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[300, 290])).
% 0.20/0.47 tff(302,plain,
% 0.20/0.47 (product(e_3, e_4, e_2)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[189, 301])).
% 0.20/0.47 tff(303,plain,
% 0.20/0.47 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_2, e_4) | (~product(e_3, e_2, e_4)) | (~product(e_4, e_2, e_1)) | (~product(e_3, e_4, e_2)) | (~product(e_2, e_4, e_1)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_2, e_4) | (~product(e_3, e_2, e_4)) | (~product(e_4, e_2, e_1)) | (~product(e_3, e_4, e_2)) | (~product(e_2, e_4, e_1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(304,plain,
% 0.20/0.48 (((~product(e_3, e_2, e_4)) | (~product(e_3, e_4, e_2)) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_2, e_1)) | equalish(e_2, e_4)) <=> (equalish(e_2, e_4) | (~product(e_3, e_2, e_4)) | (~product(e_4, e_2, e_1)) | (~product(e_3, e_4, e_2)) | (~product(e_2, e_4, e_1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(305,plain,
% 0.20/0.48 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_2, e_4)) | (~product(e_3, e_4, e_2)) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_2, e_1)) | equalish(e_2, e_4))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_2, e_4) | (~product(e_3, e_2, e_4)) | (~product(e_4, e_2, e_1)) | (~product(e_3, e_4, e_2)) | (~product(e_2, e_4, e_1))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[304])).
% 0.20/0.48 tff(306,plain,
% 0.20/0.48 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_2, e_4)) | (~product(e_3, e_4, e_2)) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_2, e_1)) | equalish(e_2, e_4))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_2, e_4) | (~product(e_3, e_2, e_4)) | (~product(e_4, e_2, e_1)) | (~product(e_3, e_4, e_2)) | (~product(e_2, e_4, e_1)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[305, 303])).
% 0.20/0.48 tff(307,plain,
% 0.20/0.48 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_2, e_4)) | (~product(e_3, e_4, e_2)) | (~product(e_2, e_4, e_1)) | (~product(e_4, e_2, e_1)) | equalish(e_2, e_4))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(308,plain,
% 0.20/0.48 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, X2, Y2)) | (~product(Z2, X1, Y1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_2, e_4) | (~product(e_3, e_2, e_4)) | (~product(e_4, e_2, e_1)) | (~product(e_3, e_4, e_2)) | (~product(e_2, e_4, e_1))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.20/0.48 tff(309,plain,
% 0.20/0.48 (~product(e_4, e_2, e_1)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[308, 240, 43, 302, 219, 254])).
% 0.20/0.48 tff(310,plain,
% 0.20/0.48 (~product(e_4, e_2, e_3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[129, 123, 43, 302, 33])).
% 0.20/0.48 tff(311,plain,
% 0.20/0.48 (product(e_4, e_2, e_4)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[156, 310, 309])).
% 0.20/0.48 tff(312,plain,
% 0.20/0.48 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_3) | (~product(e_3, e_2, e_4)) | (~product(e_4, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_3, e_2, e_4)) | (~product(e_4, e_2, e_4)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(313,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_3) | (~product(e_3, e_2, e_4)) | (~product(e_4, e_2, e_4)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(314,plain,
% 0.20/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_3, e_2, e_4)) | (~product(e_4, e_2, e_4))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[313, 312])).
% 0.20/0.48 tff(315,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[314, 172, 68, 219, 311])).
% 0.20/0.48 % SZS output end Proof
% 0.20/0.48 % E exiting
%------------------------------------------------------------------------------