TSTP Solution File: GRP126-3.004 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP126-3.004 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 22:26:05 EDT 2022
% Result : Unsatisfiable 0.21s 0.48s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP126-3.004 : TPTP v8.1.0. Released v1.2.0.
% 0.13/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.34 % Computer : n011.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Wed Aug 31 14:56:41 EDT 2022
% 0.21/0.35 % CPUTime :
% 0.21/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.21/0.35 Usage: tptp [options] [-file:]file
% 0.21/0.35 -h, -? prints this message.
% 0.21/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.21/0.35 -m, -model generate model.
% 0.21/0.35 -p, -proof generate proof.
% 0.21/0.35 -c, -core generate unsat core of named formulas.
% 0.21/0.35 -st, -statistics display statistics.
% 0.21/0.35 -t:timeout set timeout (in second).
% 0.21/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.21/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.21/0.35 -<param>:<value> configuration parameter and value.
% 0.21/0.35 -o:<output-file> file to place output in.
% 0.21/0.48 % SZS status Unsatisfiable
% 0.21/0.48 % SZS output start Proof
% 0.21/0.48 tff(cycle_type, type, (
% 0.21/0.48 cycle: ( $i * $i ) > $o)).
% 0.21/0.48 tff(e_1_type, type, (
% 0.21/0.48 e_1: $i)).
% 0.21/0.48 tff(e_2_type, type, (
% 0.21/0.48 e_2: $i)).
% 0.21/0.48 tff(e_3_type, type, (
% 0.21/0.48 e_3: $i)).
% 0.21/0.48 tff(product_type, type, (
% 0.21/0.48 product: ( $i * $i * $i ) > $o)).
% 0.21/0.48 tff(e_4_type, type, (
% 0.21/0.48 e_4: $i)).
% 0.21/0.48 tff(equalish_type, type, (
% 0.21/0.48 equalish: ( $i * $i ) > $o)).
% 0.21/0.48 tff(next_type, type, (
% 0.21/0.48 next: ( $i * $i ) > $o)).
% 0.21/0.48 tff(greater_type, type, (
% 0.21/0.48 greater: ( $i * $i ) > $o)).
% 0.21/0.48 tff(e_0_type, type, (
% 0.21/0.48 e_0: $i)).
% 0.21/0.48 tff(group_element_type, type, (
% 0.21/0.48 group_element: $i > $o)).
% 0.21/0.48 tff(1,assumption,(product(e_2, e_1, e_4)), introduced(assumption)).
% 0.21/0.48 tff(2,assumption,(~cycle(e_2, e_1)), introduced(assumption)).
% 0.21/0.48 tff(3,assumption,(cycle(e_2, e_2)), introduced(assumption)).
% 0.21/0.48 tff(4,plain,
% 0.21/0.48 ((~equalish(e_4, e_3)) <=> (~equalish(e_4, e_3))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(5,axiom,(~equalish(e_4, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_is_not_e_3')).
% 0.21/0.48 tff(6,plain,
% 0.21/0.48 (~equalish(e_4, e_3)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.21/0.48 tff(7,plain,
% 0.21/0.48 (^[Z: $i, Y: $i, X: $i, X1: $i] : refl(((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z))) <=> ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(8,plain,
% 0.21/0.48 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z))) <=> ![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[7])).
% 0.21/0.48 tff(9,plain,
% 0.21/0.48 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z))) <=> ![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(10,plain,
% 0.21/0.48 (^[Z: $i, Y: $i, X: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~cycle(X, Y)) | (~product(X, e_1, Z))) | (~greater(Y, e_0))) <=> ((~greater(Y, e_0)) | (~cycle(X, Y)) | (~product(X, e_1, Z)))), (((((~cycle(X, Y)) | (~product(X, e_1, Z))) | (~greater(Y, e_0))) | (~next(X, X1))) <=> (((~greater(Y, e_0)) | (~cycle(X, Y)) | (~product(X, e_1, Z))) | (~next(X, X1))))), rewrite((((~greater(Y, e_0)) | (~cycle(X, Y)) | (~product(X, e_1, Z))) | (~next(X, X1))) <=> ((~greater(Y, e_0)) | (~cycle(X, Y)) | (~next(X, X1)) | (~product(X, e_1, Z)))), (((((~cycle(X, Y)) | (~product(X, e_1, Z))) | (~greater(Y, e_0))) | (~next(X, X1))) <=> ((~greater(Y, e_0)) | (~cycle(X, Y)) | (~next(X, X1)) | (~product(X, e_1, Z))))), ((((((~cycle(X, Y)) | (~product(X, e_1, Z))) | (~greater(Y, e_0))) | (~next(X, X1))) | equalish(Z, X1)) <=> (((~greater(Y, e_0)) | (~cycle(X, Y)) | (~next(X, X1)) | (~product(X, e_1, Z))) | equalish(Z, X1)))), rewrite((((~greater(Y, e_0)) | (~cycle(X, Y)) | (~next(X, X1)) | (~product(X, e_1, Z))) | equalish(Z, X1)) <=> ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))), ((((((~cycle(X, Y)) | (~product(X, e_1, Z))) | (~greater(Y, e_0))) | (~next(X, X1))) | equalish(Z, X1)) <=> ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(11,plain,
% 0.21/0.48 (![Z: $i, Y: $i, X: $i, X1: $i] : (((((~cycle(X, Y)) | (~product(X, e_1, Z))) | (~greater(Y, e_0))) | (~next(X, X1))) | equalish(Z, X1)) <=> ![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.48 tff(12,axiom,(![Z: $i, Y: $i, X: $i, X1: $i] : (((((~cycle(X, Y)) | (~product(X, e_1, Z))) | (~greater(Y, e_0))) | (~next(X, X1))) | equalish(Z, X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cycle7')).
% 0.21/0.48 tff(13,plain,
% 0.21/0.48 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.21/0.48 tff(14,plain,
% 0.21/0.48 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.21/0.48 tff(15,plain,(
% 0.21/0.48 ![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.21/0.48 inference(skolemize,[status(sab)],[14])).
% 0.21/0.48 tff(16,plain,
% 0.21/0.48 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.21/0.48 tff(17,plain,
% 0.21/0.48 (greater(e_2, e_0) <=> greater(e_2, e_0)),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(18,axiom,(greater(e_2, e_0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_greater_e_0')).
% 0.21/0.48 tff(19,plain,
% 0.21/0.48 (greater(e_2, e_0)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.21/0.48 tff(20,plain,
% 0.21/0.48 (next(e_2, e_3) <=> next(e_2, e_3)),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(21,axiom,(next(e_2, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_then_e_3')).
% 0.21/0.48 tff(22,plain,
% 0.21/0.48 (next(e_2, e_3)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.21/0.48 tff(23,plain,
% 0.21/0.48 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_4, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_4)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_4)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(24,plain,
% 0.21/0.48 (((~greater(e_2, e_0)) | (~cycle(e_2, e_2)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4))) <=> (equalish(e_4, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_4)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(25,plain,
% 0.21/0.48 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_2, e_2)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_4, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_4))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[24])).
% 0.21/0.48 tff(26,plain,
% 0.21/0.48 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_2, e_2)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_4)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[25, 23])).
% 0.21/0.48 tff(27,plain,
% 0.21/0.48 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_2, e_0)) | (~cycle(e_2, e_2)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(28,plain,
% 0.21/0.48 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_4))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.21/0.48 tff(29,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[28, 22, 19, 16, 6, 3, 1])).
% 0.21/0.48 tff(30,plain,((~cycle(e_2, e_2)) | (~product(e_2, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(31,plain,
% 0.21/0.49 (~cycle(e_2, e_2)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[30, 1])).
% 0.21/0.49 tff(32,assumption,(cycle(e_2, e_0)), introduced(assumption)).
% 0.21/0.49 tff(33,plain,
% 0.21/0.49 (^[Y: $i, X: $i] : refl(((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0))) <=> ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(34,plain,
% 0.21/0.49 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0))) <=> ![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[33])).
% 0.21/0.49 tff(35,plain,
% 0.21/0.49 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0))) <=> ![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(36,plain,
% 0.21/0.49 (^[Y: $i, X: $i] : rewrite((((~cycle(X, e_0)) | (~product(X, e_1, Y))) | (~greater(Y, X))) <=> ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(37,plain,
% 0.21/0.49 (![Y: $i, X: $i] : (((~cycle(X, e_0)) | (~product(X, e_1, Y))) | (~greater(Y, X))) <=> ![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[36])).
% 0.21/0.49 tff(38,axiom,(![Y: $i, X: $i] : (((~cycle(X, e_0)) | (~product(X, e_1, Y))) | (~greater(Y, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cycle6')).
% 0.21/0.49 tff(39,plain,
% 0.21/0.49 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.21/0.49 tff(40,plain,
% 0.21/0.49 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.21/0.49 tff(41,plain,(
% 0.21/0.49 ![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[40])).
% 0.21/0.49 tff(42,plain,
% 0.21/0.49 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.21/0.49 tff(43,plain,
% 0.21/0.49 (greater(e_3, e_2) <=> greater(e_3, e_2)),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(44,axiom,(greater(e_3, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_greater_e_2')).
% 0.21/0.49 tff(45,plain,
% 0.21/0.49 (greater(e_3, e_2)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.21/0.49 tff(46,plain,
% 0.21/0.49 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(47,plain,
% 0.21/0.49 (((~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)) | (~cycle(e_2, e_0))) <=> ((~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(48,plain,
% 0.21/0.49 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[47])).
% 0.21/0.49 tff(49,plain,
% 0.21/0.49 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.21/0.49 inference(transitivity,[status(thm)],[48, 46])).
% 0.21/0.49 tff(50,plain,
% 0.21/0.49 ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)) | (~cycle(e_2, e_0)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(51,plain,
% 0.21/0.49 ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.21/0.49 tff(52,plain,
% 0.21/0.49 ((~cycle(e_2, e_0)) | (~product(e_2, e_1, e_3))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[51, 45, 42])).
% 0.21/0.49 tff(53,plain,
% 0.21/0.49 (~product(e_2, e_1, e_3)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[52, 32])).
% 0.21/0.49 tff(54,plain,
% 0.21/0.49 (greater(e_4, e_2) <=> greater(e_4, e_2)),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(55,axiom,(greater(e_4, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_greater_e_2')).
% 0.21/0.49 tff(56,plain,
% 0.21/0.49 (greater(e_4, e_2)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.21/0.49 tff(57,plain,
% 0.21/0.49 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(58,plain,
% 0.21/0.49 (((~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)) | (~cycle(e_2, e_0))) <=> ((~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(59,plain,
% 0.21/0.49 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[58])).
% 0.21/0.49 tff(60,plain,
% 0.21/0.49 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)))),
% 0.21/0.49 inference(transitivity,[status(thm)],[59, 57])).
% 0.21/0.49 tff(61,plain,
% 0.21/0.49 ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)) | (~cycle(e_2, e_0)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(62,plain,
% 0.21/0.49 ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.21/0.49 tff(63,plain,
% 0.21/0.49 ((~cycle(e_2, e_0)) | (~product(e_2, e_1, e_4))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[62, 56, 42])).
% 0.21/0.49 tff(64,plain,
% 0.21/0.49 (~product(e_2, e_1, e_4)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[63, 32])).
% 0.21/0.49 tff(65,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.21/0.49 tff(66,assumption,(~product(e_1, e_1, e_1)), introduced(assumption)).
% 0.21/0.49 tff(67,plain,
% 0.21/0.49 (^[X: $i] : refl(product(X, X, X) <=> product(X, X, X))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(68,plain,
% 0.21/0.49 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.21/0.49 inference(quant_intro,[status(thm)],[67])).
% 0.21/0.49 tff(69,plain,
% 0.21/0.49 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(70,axiom,(![X: $i] : product(X, X, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_idempotence')).
% 0.21/0.49 tff(71,plain,
% 0.21/0.49 (![X: $i] : product(X, X, X)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.21/0.49 tff(72,plain,(
% 0.21/0.49 ![X: $i] : product(X, X, X)),
% 0.21/0.49 inference(skolemize,[status(sab)],[71])).
% 0.21/0.49 tff(73,plain,
% 0.21/0.49 (![X: $i] : product(X, X, X)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.21/0.49 tff(74,plain,
% 0.21/0.49 ((~![X: $i] : product(X, X, X)) | product(e_1, e_1, e_1)),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(75,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[74, 73, 66])).
% 0.21/0.49 tff(76,plain,(product(e_1, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(77,plain,
% 0.21/0.49 (^[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))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(78,plain,
% 0.21/0.49 (![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)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[77])).
% 0.21/0.49 tff(79,plain,
% 0.21/0.49 (![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)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(80,plain,
% 0.21/0.49 (^[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)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(81,plain,
% 0.21/0.49 (![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)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[80])).
% 0.21/0.49 tff(82,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')).
% 0.21/0.49 tff(83,plain,
% 0.21/0.49 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.21/0.49 tff(84,plain,
% 0.21/0.49 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.21/0.49 tff(85,plain,(
% 0.21/0.49 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[84])).
% 0.21/0.49 tff(86,plain,
% 0.21/0.49 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.21/0.49 tff(87,plain,
% 0.21/0.49 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(88,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.21/0.49 tff(89,plain,
% 0.21/0.49 (~equalish(e_2, e_1)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.21/0.49 tff(90,plain,
% 0.21/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_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_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(91,plain,
% 0.21/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(92,plain,
% 0.21/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.21/0.49 tff(93,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[92, 89, 86, 76, 65])).
% 0.21/0.49 tff(94,plain,(~product(e_2, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(95,assumption,(~product(e_2, e_2, e_2)), introduced(assumption)).
% 0.21/0.49 tff(96,plain,
% 0.21/0.49 ((~![X: $i] : product(X, X, X)) | product(e_2, e_2, e_2)),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(97,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[96, 73, 95])).
% 0.21/0.49 tff(98,plain,(product(e_2, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(99,assumption,(product(e_2, e_2, e_2)), introduced(assumption)).
% 0.21/0.49 tff(100,assumption,(product(e_2, e_1, e_2)), introduced(assumption)).
% 0.21/0.49 tff(101,plain,
% 0.21/0.49 (^[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))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(102,plain,
% 0.21/0.49 (![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)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[101])).
% 0.21/0.49 tff(103,plain,
% 0.21/0.49 (![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)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(104,plain,
% 0.21/0.49 (^[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)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(105,plain,
% 0.21/0.49 (![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)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[104])).
% 0.21/0.49 tff(106,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')).
% 0.21/0.49 tff(107,plain,
% 0.21/0.49 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.21/0.49 tff(108,plain,
% 0.21/0.49 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.21/0.49 tff(109,plain,(
% 0.21/0.49 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[108])).
% 0.21/0.49 tff(110,plain,
% 0.21/0.49 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.21/0.49 tff(111,plain,
% 0.21/0.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(112,plain,
% 0.21/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(113,plain,
% 0.21/0.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.21/0.49 tff(114,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[113, 89, 110, 100, 99])).
% 0.21/0.49 tff(115,plain,((~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(116,plain,
% 0.21/0.49 (~product(e_2, e_1, e_2)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[115, 98])).
% 0.21/0.49 tff(117,plain,
% 0.21/0.49 (^[Y: $i, X: $i] : refl(((~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)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(118,plain,
% 0.21/0.49 (![Y: $i, X: $i] : ((~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))) <=> ![Y: $i, X: $i] : ((~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)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[117])).
% 0.21/0.49 tff(119,plain,
% 0.21/0.49 (![Y: $i, X: $i] : ((~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))) <=> ![Y: $i, X: $i] : ((~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)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(120,plain,
% 0.21/0.49 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) <=> ((~group_element(X)) | product(X, Y, e_1) | (~group_element(Y)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> (((~group_element(X)) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_2)))), rewrite((((~group_element(X)) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_2)) <=> ((~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))), (((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) <=> ((~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> (((~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_3)))), rewrite((((~group_element(X)) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_3)) <=> ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))), ((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) <=> ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))))), (((((((~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)) <=> (((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_4)))), rewrite((((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) | product(X, Y, e_4)) <=> ((~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)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) <=> ((~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)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(121,plain,
% 0.21/0.49 (![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] : ((~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)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[120])).
% 0.21/0.49 tff(122,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')).
% 0.21/0.49 tff(123,plain,
% 0.21/0.49 (![Y: $i, X: $i] : ((~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)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.21/0.49 tff(124,plain,
% 0.21/0.49 (![Y: $i, X: $i] : ((~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)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.21/0.50 tff(125,plain,(
% 0.21/0.50 ![Y: $i, X: $i] : ((~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)))),
% 0.21/0.50 inference(skolemize,[status(sab)],[124])).
% 0.21/0.50 tff(126,plain,
% 0.21/0.50 (![Y: $i, X: $i] : ((~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)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[125, 118])).
% 0.21/0.50 tff(127,plain,
% 0.21/0.50 (group_element(e_2) <=> group_element(e_2)),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(128,axiom,(group_element(e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_2')).
% 0.21/0.50 tff(129,plain,
% 0.21/0.50 (group_element(e_2)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.21/0.50 tff(130,plain,
% 0.21/0.50 (group_element(e_1) <=> group_element(e_1)),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(131,axiom,(group_element(e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_1')).
% 0.21/0.50 tff(132,plain,
% 0.21/0.50 (group_element(e_1)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.21/0.50 tff(133,plain,
% 0.21/0.50 (((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(134,plain,
% 0.21/0.50 (((~group_element(e_2)) | 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_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(135,plain,
% 0.21/0.50 (((~![Y: $i, X: $i] : ((~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(e_2)) | 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)))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1)))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[134])).
% 0.21/0.50 tff(136,plain,
% 0.21/0.50 (((~![Y: $i, X: $i] : ((~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(e_2)) | 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)))) <=> ((~![Y: $i, X: $i] : ((~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(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1))),
% 0.21/0.50 inference(transitivity,[status(thm)],[135, 133])).
% 0.21/0.50 tff(137,plain,
% 0.21/0.50 ((~![Y: $i, X: $i] : ((~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(e_2)) | 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)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(138,plain,
% 0.21/0.50 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.21/0.50 tff(139,plain,
% 0.21/0.50 (product(e_2, e_1, e_3) | product(e_2, e_1, e_4)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[138, 132, 129, 126, 116, 94])).
% 0.21/0.50 tff(140,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[139, 64, 53])).
% 0.21/0.50 tff(141,plain,(~cycle(e_2, e_0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(142,plain,
% 0.21/0.50 (^[X: $i] : refl((cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) <=> (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(143,plain,
% 0.21/0.50 (![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) <=> ![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[142])).
% 0.21/0.50 tff(144,plain,
% 0.21/0.50 (![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) <=> ![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(145,plain,
% 0.21/0.50 (^[X: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) <=> (cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))), (((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) <=> ((cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) | cycle(X, e_2)))), rewrite(((cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) | cycle(X, e_2)) <=> (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))), (((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) <=> (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))))), ((((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) | cycle(X, e_3)) <=> ((cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) | cycle(X, e_3)))), rewrite(((cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) | cycle(X, e_3)) <=> (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))), ((((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) | cycle(X, e_3)) <=> (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(146,plain,
% 0.21/0.50 (![X: $i] : (((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) | cycle(X, e_3)) <=> ![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[145])).
% 0.21/0.50 tff(147,axiom,(![X: $i] : (((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) | cycle(X, e_3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cycle2')).
% 0.21/0.50 tff(148,plain,
% 0.21/0.50 (![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.21/0.50 tff(149,plain,
% 0.21/0.50 (![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[148, 144])).
% 0.21/0.50 tff(150,plain,(
% 0.21/0.50 ![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.21/0.50 inference(skolemize,[status(sab)],[149])).
% 0.21/0.50 tff(151,plain,
% 0.21/0.50 (![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[150, 143])).
% 0.21/0.50 tff(152,plain,
% 0.21/0.50 (((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0) | (~group_element(e_2)))) <=> ((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0) | (~group_element(e_2)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(153,plain,
% 0.21/0.50 ((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0) | (~group_element(e_2)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(154,plain,
% 0.21/0.50 ((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0) | (~group_element(e_2))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.21/0.50 tff(155,plain,
% 0.21/0.50 (cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[154, 151, 129])).
% 0.21/0.50 tff(156,plain,
% 0.21/0.50 (cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[155, 141])).
% 0.21/0.50 tff(157,plain,
% 0.21/0.50 (cycle(e_2, e_3)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[156, 31, 2])).
% 0.21/0.50 tff(158,plain,
% 0.21/0.50 (greater(e_3, e_0) <=> greater(e_3, e_0)),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(159,axiom,(greater(e_3, e_0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_greater_e_0')).
% 0.21/0.50 tff(160,plain,
% 0.21/0.50 (greater(e_3, e_0)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.21/0.50 tff(161,plain,
% 0.21/0.50 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_4)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(162,plain,
% 0.21/0.50 (((~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4))) <=> (equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(163,plain,
% 0.21/0.50 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_4))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[162])).
% 0.21/0.50 tff(164,plain,
% 0.21/0.50 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[163, 161])).
% 0.21/0.50 tff(165,plain,
% 0.21/0.50 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(166,plain,
% 0.21/0.50 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_4))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.21/0.50 tff(167,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[166, 22, 160, 16, 6, 157, 1])).
% 0.21/0.50 tff(168,plain,((~product(e_2, e_1, e_4)) | cycle(e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(169,plain,
% 0.21/0.50 (cycle(e_2, e_1)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[168, 1])).
% 0.21/0.50 tff(170,plain,
% 0.21/0.50 (greater(e_1, e_0) <=> greater(e_1, e_0)),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(171,axiom,(greater(e_1, e_0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_greater_e_0')).
% 0.21/0.50 tff(172,plain,
% 0.21/0.50 (greater(e_1, e_0)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.21/0.50 tff(173,plain,
% 0.21/0.50 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_4, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_4)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_4)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(174,plain,
% 0.21/0.50 (((~greater(e_1, e_0)) | (~cycle(e_2, e_1)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4))) <=> (equalish(e_4, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_4)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(175,plain,
% 0.21/0.50 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_2, e_1)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_4, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_4))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[174])).
% 0.21/0.50 tff(176,plain,
% 0.21/0.50 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_2, e_1)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_4)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[175, 173])).
% 0.21/0.50 tff(177,plain,
% 0.21/0.50 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_2, e_1)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_4)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(178,plain,
% 0.21/0.50 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_4))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.21/0.50 tff(179,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[178, 22, 172, 16, 6, 169, 1])).
% 0.21/0.50 tff(180,plain,(~product(e_2, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(181,assumption,(~product(e_2, e_4, e_1)), introduced(assumption)).
% 0.21/0.50 tff(182,assumption,(~product(e_2, e_1, e_4)), introduced(assumption)).
% 0.21/0.50 tff(183,plain,
% 0.21/0.50 (product(e_2, e_1, e_3)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[139, 182])).
% 0.21/0.50 tff(184,assumption,(product(e_2, e_4, e_3)), introduced(assumption)).
% 0.21/0.50 tff(185,assumption,(product(e_2, e_1, e_3)), introduced(assumption)).
% 0.21/0.50 tff(186,plain,
% 0.21/0.50 ((~equalish(e_1, e_4)) <=> (~equalish(e_1, e_4))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(187,axiom,(~equalish(e_1, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_4')).
% 0.21/0.50 tff(188,plain,
% 0.21/0.50 (~equalish(e_1, e_4)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.21/0.50 tff(189,plain,
% 0.21/0.50 (((~![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_2, e_1, e_3)) | (~product(e_2, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(190,plain,
% 0.21/0.50 ((equalish(e_1, e_4) | (~product(e_2, e_4, e_3)) | (~product(e_2, e_1, e_3))) <=> (equalish(e_1, e_4) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(191,plain,
% 0.21/0.50 (((~![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_2, e_4, e_3)) | (~product(e_2, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[190])).
% 0.21/0.51 tff(192,plain,
% 0.21/0.51 (((~![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_2, e_4, e_3)) | (~product(e_2, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3)))),
% 0.21/0.51 inference(transitivity,[status(thm)],[191, 189])).
% 0.21/0.51 tff(193,plain,
% 0.21/0.51 ((~![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_2, e_4, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(194,plain,
% 0.21/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.21/0.51 tff(195,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[194, 188, 110, 185, 184])).
% 0.21/0.51 tff(196,plain,((~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.51 tff(197,plain,
% 0.21/0.51 (~product(e_2, e_4, e_3)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[196, 183])).
% 0.21/0.51 tff(198,plain,
% 0.21/0.51 ((~![X: $i] : product(X, X, X)) | product(e_4, e_4, e_4)),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(199,plain,
% 0.21/0.51 (product(e_4, e_4, e_4)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[198, 73])).
% 0.21/0.51 tff(200,assumption,(product(e_2, e_4, e_4)), introduced(assumption)).
% 0.21/0.51 tff(201,plain,
% 0.21/0.51 ((~equalish(e_2, e_4)) <=> (~equalish(e_2, e_4))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(202,axiom,(~equalish(e_2, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_4')).
% 0.21/0.51 tff(203,plain,
% 0.21/0.51 (~equalish(e_2, e_4)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.21/0.51 tff(204,plain,
% 0.21/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_2, e_4, e_4)) | (~product(e_4, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_4) | (~product(e_2, e_4, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(205,plain,
% 0.21/0.51 ((equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_4, e_4))) <=> (equalish(e_2, e_4) | (~product(e_2, e_4, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(206,plain,
% 0.21/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_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_2, e_4, e_4)) | (~product(e_4, e_4, e_4))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[205])).
% 0.21/0.51 tff(207,plain,
% 0.21/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_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_2, e_4, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.21/0.51 inference(transitivity,[status(thm)],[206, 204])).
% 0.21/0.51 tff(208,plain,
% 0.21/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_2, e_4, e_4)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(209,plain,
% 0.21/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_4) | (~product(e_2, e_4, e_4)) | (~product(e_4, e_4, e_4))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.21/0.51 tff(210,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[209, 203, 86, 200, 199])).
% 0.21/0.51 tff(211,plain,(~product(e_2, e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.51 tff(212,plain,
% 0.21/0.51 (group_element(e_4) <=> group_element(e_4)),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(213,axiom,(group_element(e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_4')).
% 0.21/0.51 tff(214,plain,
% 0.21/0.51 (group_element(e_4)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.21/0.51 tff(215,plain,
% 0.21/0.51 (((~![Y: $i, X: $i] : ((~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(e_2)) | product(e_2, e_4, e_2) | product(e_2, e_4, e_3) | product(e_2, e_4, e_1) | product(e_2, e_4, e_4) | (~group_element(e_4)))) <=> ((~![Y: $i, X: $i] : ((~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(e_2)) | product(e_2, e_4, e_2) | product(e_2, e_4, e_3) | product(e_2, e_4, e_1) | product(e_2, e_4, e_4) | (~group_element(e_4)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(216,plain,
% 0.21/0.51 (((~group_element(e_2)) | 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)) | product(e_2, e_4, e_2) | product(e_2, e_4, e_3) | product(e_2, e_4, e_1) | product(e_2, e_4, e_4) | (~group_element(e_4)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(217,plain,
% 0.21/0.51 (((~![Y: $i, X: $i] : ((~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(e_2)) | 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)))) <=> ((~![Y: $i, X: $i] : ((~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(e_2)) | product(e_2, e_4, e_2) | product(e_2, e_4, e_3) | product(e_2, e_4, e_1) | product(e_2, e_4, e_4) | (~group_element(e_4))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[216])).
% 0.21/0.51 tff(218,plain,
% 0.21/0.51 (((~![Y: $i, X: $i] : ((~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(e_2)) | 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)))) <=> ((~![Y: $i, X: $i] : ((~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(e_2)) | product(e_2, e_4, e_2) | product(e_2, e_4, e_3) | product(e_2, e_4, e_1) | product(e_2, e_4, e_4) | (~group_element(e_4)))),
% 0.21/0.51 inference(transitivity,[status(thm)],[217, 215])).
% 0.21/0.51 tff(219,plain,
% 0.21/0.51 ((~![Y: $i, X: $i] : ((~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(e_2)) | 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)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(220,plain,
% 0.21/0.51 ((~![Y: $i, X: $i] : ((~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(e_2)) | product(e_2, e_4, e_2) | product(e_2, e_4, e_3) | product(e_2, e_4, e_1) | product(e_2, e_4, e_4) | (~group_element(e_4))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.21/0.51 tff(221,plain,
% 0.21/0.51 (product(e_2, e_4, e_2) | product(e_2, e_4, e_3) | product(e_2, e_4, e_1) | product(e_2, e_4, e_4)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[220, 129, 214, 126])).
% 0.21/0.51 tff(222,plain,
% 0.21/0.51 (product(e_2, e_4, e_2) | product(e_2, e_4, e_3) | product(e_2, e_4, e_1)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[221, 211])).
% 0.21/0.51 tff(223,plain,
% 0.21/0.51 (product(e_2, e_4, e_2)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[222, 197, 181])).
% 0.21/0.51 tff(224,assumption,(product(e_4, e_2, e_3)), introduced(assumption)).
% 0.21/0.51 tff(225,assumption,(product(e_3, e_2, e_2)), introduced(assumption)).
% 0.21/0.51 tff(226,plain,
% 0.21/0.51 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(227,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.21/0.51 tff(228,plain,
% 0.21/0.51 (~equalish(e_3, e_2)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.21/0.51 tff(229,plain,
% 0.21/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(230,plain,
% 0.21/0.51 ((equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2))) <=> (equalish(e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(231,plain,
% 0.21/0.51 (((~![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_3, e_2, e_2)) | (~product(e_2, e_2, e_2))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[230])).
% 0.21/0.51 tff(232,plain,
% 0.21/0.51 (((~![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_3, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.21/0.51 inference(transitivity,[status(thm)],[231, 229])).
% 0.21/0.51 tff(233,plain,
% 0.21/0.51 ((~![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)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(234,plain,
% 0.21/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.21/0.51 tff(235,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[234, 228, 86, 98, 225])).
% 0.21/0.51 tff(236,plain,(~product(e_3, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.51 tff(237,assumption,(product(e_2, e_4, e_2)), introduced(assumption)).
% 0.21/0.51 tff(238,plain,
% 0.21/0.51 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl(((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))) <=> ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(239,plain,
% 0.21/0.51 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[238])).
% 0.21/0.51 tff(240,plain,
% 0.21/0.51 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(241,plain,
% 0.21/0.51 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : rewrite((((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, Y)) <=> ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(242,plain,
% 0.21/0.51 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, Y)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[241])).
% 0.21/0.51 tff(243,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Y, X, Z2))) | product(Z1, Z2, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qg4')).
% 0.21/0.51 tff(244,plain,
% 0.21/0.51 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.21/0.51 tff(245,plain,
% 0.21/0.51 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[244, 240])).
% 0.21/0.51 tff(246,plain,(
% 0.21/0.51 ![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.21/0.51 inference(skolemize,[status(sab)],[245])).
% 0.21/0.51 tff(247,plain,
% 0.21/0.51 (![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[246, 239])).
% 0.21/0.51 tff(248,plain,
% 0.21/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_2, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_4, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_2, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_4, e_2, e_3)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(249,plain,
% 0.21/0.51 (((~product(e_2, e_4, e_2)) | product(e_3, e_2, e_2) | (~product(e_4, e_2, e_3))) <=> (product(e_3, e_2, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_4, e_2, e_3)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(250,plain,
% 0.21/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_2)) | product(e_3, e_2, e_2) | (~product(e_4, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_2, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_4, e_2, e_3))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[249])).
% 0.21/0.51 tff(251,plain,
% 0.21/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_2)) | product(e_3, e_2, e_2) | (~product(e_4, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_2, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_4, e_2, e_3)))),
% 0.21/0.51 inference(transitivity,[status(thm)],[250, 248])).
% 0.21/0.51 tff(252,plain,
% 0.21/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_2)) | product(e_3, e_2, e_2) | (~product(e_4, e_2, e_3)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(253,plain,
% 0.21/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_2, e_2) | (~product(e_2, e_4, e_2)) | (~product(e_4, e_2, e_3))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.21/0.51 tff(254,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[253, 247, 237, 236, 224])).
% 0.21/0.51 tff(255,plain,((~product(e_2, e_4, e_2)) | (~product(e_4, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.51 tff(256,plain,
% 0.21/0.51 (~product(e_4, e_2, e_3)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[255, 223])).
% 0.21/0.51 tff(257,assumption,(product(e_4, e_2, e_2)), introduced(assumption)).
% 0.21/0.51 tff(258,plain,
% 0.21/0.51 ((~equalish(e_4, e_2)) <=> (~equalish(e_4, e_2))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(259,axiom,(~equalish(e_4, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_is_not_e_2')).
% 0.21/0.51 tff(260,plain,
% 0.21/0.51 (~equalish(e_4, e_2)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.21/0.51 tff(261,plain,
% 0.21/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_2, e_2)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(262,plain,
% 0.21/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_2, e_2)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(263,plain,
% 0.21/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_4, e_2, e_2))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.21/0.51 tff(264,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[263, 260, 86, 98, 257])).
% 0.21/0.51 tff(265,plain,(~product(e_4, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.51 tff(266,assumption,(product(e_4, e_2, e_4)), introduced(assumption)).
% 0.21/0.51 tff(267,plain,
% 0.21/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(268,plain,
% 0.21/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(269,plain,
% 0.21/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_2, e_4))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.21/0.51 tff(270,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[269, 203, 110, 199, 266])).
% 0.21/0.51 tff(271,plain,(~product(e_4, e_2, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.51 tff(272,plain,
% 0.21/0.51 (((~![Y: $i, X: $i] : ((~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(e_2)) | (~group_element(e_4)) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | product(e_4, e_2, e_4))) <=> ((~![Y: $i, X: $i] : ((~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(e_2)) | (~group_element(e_4)) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | product(e_4, e_2, e_4))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(273,plain,
% 0.21/0.51 (((~group_element(e_4)) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | (~group_element(e_2))) <=> ((~group_element(e_2)) | (~group_element(e_4)) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | product(e_4, e_2, e_4))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(274,plain,
% 0.21/0.51 (((~![Y: $i, X: $i] : ((~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(e_4)) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : ((~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(e_2)) | (~group_element(e_4)) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | product(e_4, e_2, e_4)))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[273])).
% 0.21/0.52 tff(275,plain,
% 0.21/0.52 (((~![Y: $i, X: $i] : ((~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(e_4)) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : ((~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(e_2)) | (~group_element(e_4)) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | product(e_4, e_2, e_4))),
% 0.21/0.52 inference(transitivity,[status(thm)],[274, 272])).
% 0.21/0.52 tff(276,plain,
% 0.21/0.52 ((~![Y: $i, X: $i] : ((~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(e_4)) | product(e_4, e_2, e_4) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | (~group_element(e_2)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(277,plain,
% 0.21/0.52 ((~![Y: $i, X: $i] : ((~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(e_2)) | (~group_element(e_4)) | product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1) | product(e_4, e_2, e_4)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[276, 275])).
% 0.21/0.52 tff(278,plain,
% 0.21/0.52 (product(e_4, e_2, e_3) | product(e_4, e_2, e_2) | product(e_4, e_2, e_1)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[277, 129, 214, 126, 271])).
% 0.21/0.52 tff(279,plain,
% 0.21/0.52 (product(e_4, e_2, e_3) | product(e_4, e_2, e_1)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[278, 265])).
% 0.21/0.52 tff(280,plain,
% 0.21/0.52 (product(e_4, e_2, e_1)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[279, 256])).
% 0.21/0.52 tff(281,plain,
% 0.21/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_4) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_2)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(282,plain,
% 0.21/0.52 (((~product(e_4, e_2, e_1)) | product(e_2, e_1, e_4) | (~product(e_2, e_4, e_2))) <=> (product(e_2, e_1, e_4) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_2)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(283,plain,
% 0.21/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_1)) | product(e_2, e_1, e_4) | (~product(e_2, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_2))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[282])).
% 0.21/0.52 tff(284,plain,
% 0.21/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_1)) | product(e_2, e_1, e_4) | (~product(e_2, e_4, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_4) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_2)))),
% 0.21/0.52 inference(transitivity,[status(thm)],[283, 281])).
% 0.21/0.52 tff(285,plain,
% 0.21/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_4, e_2, e_1)) | product(e_2, e_1, e_4) | (~product(e_2, e_4, e_2)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(286,plain,
% 0.21/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_4) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_2))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.21/0.52 tff(287,plain,
% 0.21/0.52 ($false),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[286, 247, 182, 223, 280])).
% 0.21/0.52 tff(288,plain,(product(e_2, e_1, e_4) | product(e_2, e_4, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.52 tff(289,plain,
% 0.21/0.52 (product(e_2, e_4, e_1)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[288, 180])).
% 0.21/0.52 tff(290,assumption,(product(e_2, e_4, e_1)), introduced(assumption)).
% 0.21/0.52 tff(291,plain,
% 0.21/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_1)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(292,plain,
% 0.21/0.52 (((~product(e_1, e_1, e_1)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_2))) <=> ((~product(e_1, e_1, e_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_1)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(293,plain,
% 0.21/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_1)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_1))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[292])).
% 0.21/0.52 tff(294,plain,
% 0.21/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_1)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_1)))),
% 0.21/0.52 inference(transitivity,[status(thm)],[293, 291])).
% 0.21/0.52 tff(295,plain,
% 0.21/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_1)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_2)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(296,plain,
% 0.21/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_1, e_1))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.21/0.52 tff(297,plain,
% 0.21/0.52 (~product(e_1, e_1, e_2)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[296, 247, 76, 94])).
% 0.21/0.52 tff(298,plain,
% 0.21/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_1)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(299,plain,
% 0.21/0.52 (((~product(e_2, e_4, e_1)) | product(e_1, e_1, e_2) | (~product(e_4, e_2, e_1))) <=> (product(e_1, e_1, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_1)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(300,plain,
% 0.21/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_1)) | product(e_1, e_1, e_2) | (~product(e_4, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_1))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[299])).
% 0.21/0.52 tff(301,plain,
% 0.21/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_1)) | product(e_1, e_1, e_2) | (~product(e_4, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_1)))),
% 0.21/0.52 inference(transitivity,[status(thm)],[300, 298])).
% 0.21/0.52 tff(302,plain,
% 0.21/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_1)) | product(e_1, e_1, e_2) | (~product(e_4, e_2, e_1)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(303,plain,
% 0.21/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_1, e_1, e_2) | (~product(e_4, e_2, e_1)) | (~product(e_2, e_4, e_1))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[302, 301])).
% 0.21/0.52 tff(304,plain,
% 0.21/0.52 (~product(e_4, e_2, e_1)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[303, 247, 297, 290])).
% 0.21/0.52 tff(305,assumption,(~product(e_3, e_1, e_2)), introduced(assumption)).
% 0.21/0.52 tff(306,plain,
% 0.21/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_2) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_4, e_1)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(307,plain,
% 0.21/0.52 (((~product(e_2, e_4, e_1)) | product(e_3, e_1, e_2) | (~product(e_4, e_2, e_3))) <=> (product(e_3, e_1, e_2) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_4, e_1)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(308,plain,
% 0.21/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_1)) | product(e_3, e_1, e_2) | (~product(e_4, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_3, e_1, e_2) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_4, e_1))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[307])).
% 0.21/0.52 tff(309,plain,
% 0.21/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_1)) | product(e_3, e_1, e_2) | (~product(e_4, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_2) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_4, e_1)))),
% 0.21/0.52 inference(transitivity,[status(thm)],[308, 306])).
% 0.21/0.52 tff(310,plain,
% 0.21/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_1)) | product(e_3, e_1, e_2) | (~product(e_4, e_2, e_3)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(311,plain,
% 0.21/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_3, e_1, e_2) | (~product(e_4, e_2, e_3)) | (~product(e_2, e_4, e_1))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.21/0.52 tff(312,plain,
% 0.21/0.52 (~product(e_4, e_2, e_3)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[311, 247, 305, 290])).
% 0.21/0.52 tff(313,plain,
% 0.21/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_4, e_2, e_2)) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_2) | (~product(e_4, e_2, e_2)) | (~product(e_2, e_4, e_1)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(314,plain,
% 0.21/0.52 (((~product(e_2, e_4, e_1)) | product(e_2, e_1, e_2) | (~product(e_4, e_2, e_2))) <=> (product(e_2, e_1, e_2) | (~product(e_4, e_2, e_2)) | (~product(e_2, e_4, e_1)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(315,plain,
% 0.21/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_1)) | product(e_2, e_1, e_2) | (~product(e_4, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_4, e_2, e_2)) | (~product(e_2, e_4, e_1))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[314])).
% 0.21/0.52 tff(316,plain,
% 0.21/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_1)) | product(e_2, e_1, e_2) | (~product(e_4, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_2) | (~product(e_4, e_2, e_2)) | (~product(e_2, e_4, e_1)))),
% 0.21/0.52 inference(transitivity,[status(thm)],[315, 313])).
% 0.21/0.52 tff(317,plain,
% 0.21/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | ((~product(e_2, e_4, e_1)) | product(e_2, e_1, e_2) | (~product(e_4, e_2, e_2)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(318,plain,
% 0.21/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : ((~product(Y, X, Z2)) | product(Z1, Z2, Y) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_2) | (~product(e_4, e_2, e_2)) | (~product(e_2, e_4, e_1))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[317, 316])).
% 0.21/0.52 tff(319,plain,
% 0.21/0.52 (~product(e_4, e_2, e_2)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[318, 247, 116, 290])).
% 0.21/0.52 tff(320,plain,
% 0.21/0.52 ($false),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[278, 319, 312, 304])).
% 0.21/0.52 tff(321,plain,((~product(e_2, e_4, e_1)) | product(e_3, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.52 tff(322,plain,
% 0.21/0.52 (product(e_3, e_1, e_2)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[321, 289])).
% 0.21/0.52 tff(323,assumption,(cycle(e_3, e_3)), introduced(assumption)).
% 0.21/0.52 tff(324,plain,
% 0.21/0.52 (next(e_3, e_4) <=> next(e_3, e_4)),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(325,axiom,(next(e_3, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_then_e_4')).
% 0.21/0.52 tff(326,plain,
% 0.21/0.52 (next(e_3, e_4)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[325, 324])).
% 0.21/0.52 tff(327,plain,
% 0.21/0.52 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_2, e_4) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~product(e_3, e_1, e_2)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_4) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(328,plain,
% 0.21/0.52 (((~greater(e_3, e_0)) | (~cycle(e_3, e_3)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2))) <=> (equalish(e_2, e_4) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(329,plain,
% 0.21/0.52 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_3, e_0)) | (~cycle(e_3, e_3)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_2, e_4) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~product(e_3, e_1, e_2))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[328])).
% 0.21/0.52 tff(330,plain,
% 0.21/0.52 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_3, e_0)) | (~cycle(e_3, e_3)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_4) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.21/0.52 inference(transitivity,[status(thm)],[329, 327])).
% 0.21/0.52 tff(331,plain,
% 0.21/0.52 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_3, e_0)) | (~cycle(e_3, e_3)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(332,plain,
% 0.21/0.53 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_4) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~product(e_3, e_1, e_2))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.21/0.53 tff(333,plain,
% 0.21/0.53 ($false),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[332, 326, 160, 16, 203, 323, 322])).
% 0.21/0.53 tff(334,plain,(~cycle(e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.53 tff(335,assumption,(~cycle(e_3, e_3)), introduced(assumption)).
% 0.21/0.53 tff(336,assumption,(cycle(e_2, e_1)), introduced(assumption)).
% 0.21/0.53 tff(337,plain,
% 0.21/0.53 (^[W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : refl(((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) <=> ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(338,plain,
% 0.21/0.53 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) <=> ![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[337])).
% 0.21/0.53 tff(339,plain,
% 0.21/0.53 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) <=> ![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(340,plain,
% 0.21/0.53 (^[W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) <=> ((~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))), (((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) <=> (((~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~next(Y, W))))), rewrite((((~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~next(Y, W))) <=> ((~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))), (((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) <=> ((~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))))), ((((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) | (~greater(Y, X))) <=> (((~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~greater(Y, X))))), rewrite((((~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~greater(Y, X))) <=> ((~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))), ((((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) | (~greater(Y, X))) <=> ((~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))))), (((((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) | (~greater(Y, X))) | (~greater(Z1, Z2))) <=> (((~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~greater(Z1, Z2))))), rewrite((((~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~greater(Z1, Z2))) <=> ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))), (((((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) | (~greater(Y, X))) | (~greater(Z1, Z2))) <=> ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(341,plain,
% 0.21/0.53 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) | (~greater(Y, X))) | (~greater(Z1, Z2))) <=> ![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[340])).
% 0.21/0.53 tff(342,axiom,(![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) | (~greater(Y, X))) | (~greater(Z1, Z2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cycle5')).
% 0.21/0.53 tff(343,plain,
% 0.21/0.53 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[342, 341])).
% 0.21/0.53 tff(344,plain,
% 0.21/0.53 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[343, 339])).
% 0.21/0.53 tff(345,plain,(
% 0.21/0.53 ![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.21/0.53 inference(skolemize,[status(sab)],[344])).
% 0.21/0.53 tff(346,plain,
% 0.21/0.53 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[345, 338])).
% 0.21/0.53 tff(347,plain,
% 0.21/0.53 (cycle(e_4, e_0) <=> cycle(e_4, e_0)),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(348,axiom,(cycle(e_4, e_0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cycle3')).
% 0.21/0.53 tff(349,plain,
% 0.21/0.53 (cycle(e_4, e_0)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[348, 347])).
% 0.21/0.53 tff(350,plain,
% 0.21/0.53 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_4, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_1)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_4, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_1)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(351,plain,
% 0.21/0.53 (((~greater(e_1, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_1))) <=> ((~cycle(e_4, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_1)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(352,plain,
% 0.21/0.53 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_1, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_1)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_4, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_1))))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[351])).
% 0.21/0.53 tff(353,plain,
% 0.21/0.53 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_1, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_1)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_4, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_1)))),
% 0.21/0.53 inference(transitivity,[status(thm)],[352, 350])).
% 0.21/0.53 tff(354,plain,
% 0.21/0.53 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_1, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_1)))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(355,plain,
% 0.21/0.53 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_4, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_1))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[354, 353])).
% 0.21/0.53 tff(356,plain,
% 0.21/0.53 ((~cycle(e_3, e_0)) | (~cycle(e_2, e_1))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[355, 326, 172, 45, 349, 346])).
% 0.21/0.53 tff(357,plain,
% 0.21/0.53 (~cycle(e_3, e_0)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[356, 336])).
% 0.21/0.53 tff(358,assumption,(cycle(e_3, e_2)), introduced(assumption)).
% 0.21/0.53 tff(359,plain,
% 0.21/0.53 (^[W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : refl(((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) <=> ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(360,plain,
% 0.21/0.53 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) <=> ![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[359])).
% 0.21/0.53 tff(361,plain,
% 0.21/0.53 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) <=> ![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(362,plain,
% 0.21/0.53 (^[W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) <=> ((~cycle(X, Y)) | (~next(X, W)) | (~cycle(W, Z)))), (((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) <=> (((~cycle(X, Y)) | (~next(X, W)) | (~cycle(W, Z))) | (~greater(Y, e_0))))), rewrite((((~cycle(X, Y)) | (~next(X, W)) | (~cycle(W, Z))) | (~greater(Y, e_0))) <=> ((~cycle(X, Y)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))), (((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) <=> ((~cycle(X, Y)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))))), ((((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) | (~next(Z, Z1))) <=> (((~cycle(X, Y)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) | (~next(Z, Z1))))), rewrite((((~cycle(X, Y)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) | (~next(Z, Z1))) <=> ((~cycle(X, Y)) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))), ((((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) | (~next(Z, Z1))) <=> ((~cycle(X, Y)) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))))), (((((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) | (~next(Z, Z1))) | equalish(Y, Z1)) <=> (((~cycle(X, Y)) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) | equalish(Y, Z1)))), rewrite((((~cycle(X, Y)) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) | equalish(Y, Z1)) <=> ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))), (((((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) | (~next(Z, Z1))) | equalish(Y, Z1)) <=> ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(363,plain,
% 0.21/0.53 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) | (~next(Z, Z1))) | equalish(Y, Z1)) <=> ![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[362])).
% 0.21/0.53 tff(364,axiom,(![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) | (~next(Z, Z1))) | equalish(Y, Z1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cycle4')).
% 0.21/0.53 tff(365,plain,
% 0.21/0.53 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[364, 363])).
% 0.21/0.53 tff(366,plain,
% 0.21/0.53 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[365, 361])).
% 0.21/0.53 tff(367,plain,(
% 0.21/0.53 ![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.21/0.53 inference(skolemize,[status(sab)],[366])).
% 0.21/0.53 tff(368,plain,
% 0.21/0.53 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[367, 360])).
% 0.21/0.53 tff(369,plain,
% 0.21/0.53 (next(e_0, e_1) <=> next(e_0, e_1)),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(370,axiom,(next(e_0, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_0_then_e_1')).
% 0.21/0.53 tff(371,plain,
% 0.21/0.53 (next(e_0, e_1)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[370, 369])).
% 0.21/0.53 tff(372,plain,
% 0.21/0.53 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_2, e_1) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~next(e_0, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_1) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~next(e_0, e_1)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(373,plain,
% 0.21/0.53 (((~cycle(e_3, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0))) <=> (equalish(e_2, e_1) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~next(e_0, e_1)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(374,plain,
% 0.21/0.53 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_3, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_2, e_1) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~next(e_0, e_1))))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[373])).
% 0.21/0.53 tff(375,plain,
% 0.21/0.53 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_3, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_1) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~next(e_0, e_1)))),
% 0.21/0.53 inference(transitivity,[status(thm)],[374, 372])).
% 0.21/0.53 tff(376,plain,
% 0.21/0.53 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_3, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(377,plain,
% 0.21/0.53 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_1) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~next(e_0, e_1))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[376, 375])).
% 0.21/0.53 tff(378,plain,
% 0.21/0.53 ($false),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[377, 371, 326, 19, 349, 368, 89, 358])).
% 0.21/0.53 tff(379,plain,(~cycle(e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.53 tff(380,plain,
% 0.21/0.53 (group_element(e_3) <=> group_element(e_3)),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(381,axiom,(group_element(e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_3')).
% 0.21/0.53 tff(382,plain,
% 0.21/0.53 (group_element(e_3)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[381, 380])).
% 0.21/0.53 tff(383,plain,
% 0.21/0.53 (((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0) | (~group_element(e_3)))) <=> ((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0) | (~group_element(e_3)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(384,plain,
% 0.21/0.53 ((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0) | (~group_element(e_3)))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(385,plain,
% 0.21/0.53 ((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0) | (~group_element(e_3))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[384, 383])).
% 0.21/0.53 tff(386,plain,
% 0.21/0.53 (cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[385, 151, 382])).
% 0.21/0.53 tff(387,plain,
% 0.21/0.53 (cycle(e_3, e_3) | cycle(e_3, e_1) | cycle(e_3, e_0)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[386, 379])).
% 0.21/0.53 tff(388,plain,
% 0.21/0.53 (cycle(e_3, e_1)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[387, 357, 335])).
% 0.21/0.53 tff(389,plain,
% 0.21/0.53 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(390,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.21/0.53 tff(391,plain,
% 0.21/0.53 (~equalish(e_1, e_2)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[390, 389])).
% 0.21/0.53 tff(392,plain,
% 0.21/0.53 (next(e_1, e_2) <=> next(e_1, e_2)),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(393,axiom,(next(e_1, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_then_e_2')).
% 0.21/0.53 tff(394,plain,
% 0.21/0.53 (next(e_1, e_2)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[393, 392])).
% 0.21/0.53 tff(395,plain,
% 0.21/0.53 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_1, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_1, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_1)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(396,plain,
% 0.21/0.53 (((~cycle(e_2, e_1)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_1))) <=> (equalish(e_1, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_1)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(397,plain,
% 0.21/0.53 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_2, e_1)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | (equalish(e_1, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_1))))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[396])).
% 0.21/0.54 tff(398,plain,
% 0.21/0.54 (((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_2, e_1)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_1, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_1)))),
% 0.21/0.54 inference(transitivity,[status(thm)],[397, 395])).
% 0.21/0.54 tff(399,plain,
% 0.21/0.54 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | ((~cycle(e_2, e_1)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_1)))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(400,plain,
% 0.21/0.54 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_1, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_1))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[399, 398])).
% 0.21/0.54 tff(401,plain,
% 0.21/0.54 ($false),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[400, 394, 22, 172, 368, 391, 336, 388])).
% 0.21/0.54 tff(402,plain,((~cycle(e_2, e_1)) | cycle(e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.54 tff(403,plain,
% 0.21/0.54 (~cycle(e_2, e_1)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[402, 334])).
% 0.21/0.54 tff(404,assumption,(cycle(e_3, e_1)), introduced(assumption)).
% 0.21/0.54 tff(405,plain,
% 0.21/0.54 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_2, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_2)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_2)))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(406,plain,
% 0.21/0.54 (((~greater(e_1, e_0)) | (~cycle(e_3, e_1)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2))) <=> (equalish(e_2, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_2)))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(407,plain,
% 0.21/0.54 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_3, e_1)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_2, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_2))))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[406])).
% 0.21/0.54 tff(408,plain,
% 0.21/0.54 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_3, e_1)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_2)))),
% 0.21/0.54 inference(transitivity,[status(thm)],[407, 405])).
% 0.21/0.54 tff(409,plain,
% 0.21/0.54 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_3, e_1)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2)))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(410,plain,
% 0.21/0.54 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_2))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[409, 408])).
% 0.21/0.54 tff(411,plain,
% 0.21/0.54 ($false),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[410, 326, 172, 16, 203, 404, 322])).
% 0.21/0.54 tff(412,plain,(~cycle(e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.54 tff(413,plain,
% 0.21/0.54 (cycle(e_3, e_0)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[387, 334, 412])).
% 0.21/0.54 tff(414,assumption,(cycle(e_3, e_0)), introduced(assumption)).
% 0.21/0.54 tff(415,plain,
% 0.21/0.54 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2)))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(416,plain,
% 0.21/0.54 (((~greater(e_2, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_2))) <=> ((~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2)))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(417,plain,
% 0.21/0.54 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_2, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_2)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2))))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[416])).
% 0.21/0.54 tff(418,plain,
% 0.21/0.54 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_2, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_2)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2)))),
% 0.21/0.54 inference(transitivity,[status(thm)],[417, 415])).
% 0.21/0.54 tff(419,plain,
% 0.21/0.54 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_2, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_2)))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(420,plain,
% 0.21/0.54 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[419, 418])).
% 0.21/0.54 tff(421,plain,
% 0.21/0.54 ((~cycle(e_3, e_0)) | (~cycle(e_2, e_2))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[420, 326, 19, 45, 349, 346])).
% 0.21/0.54 tff(422,plain,
% 0.21/0.54 (~cycle(e_2, e_2)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[421, 414])).
% 0.21/0.54 tff(423,plain,
% 0.21/0.54 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3)))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(424,plain,
% 0.21/0.54 (((~greater(e_3, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_3))) <=> ((~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3)))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(425,plain,
% 0.21/0.54 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_3, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_3)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3))))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[424])).
% 0.21/0.54 tff(426,plain,
% 0.21/0.54 (((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_3, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_3)))) <=> ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3)))),
% 0.21/0.54 inference(transitivity,[status(thm)],[425, 423])).
% 0.21/0.54 tff(427,plain,
% 0.21/0.54 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | ((~greater(e_3, e_0)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_3)))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(428,plain,
% 0.21/0.54 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_0)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[427, 426])).
% 0.21/0.54 tff(429,plain,
% 0.21/0.54 ((~cycle(e_3, e_0)) | (~cycle(e_2, e_3))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[428, 326, 160, 45, 349, 346])).
% 0.21/0.54 tff(430,plain,
% 0.21/0.54 (~cycle(e_2, e_3)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[429, 414])).
% 0.21/0.54 tff(431,plain,
% 0.21/0.54 ($false),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[155, 430, 422, 141, 2])).
% 0.21/0.54 tff(432,plain,((~cycle(e_3, e_0)) | cycle(e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.54 tff(433,plain,
% 0.21/0.54 ($false),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[432, 413, 403])).
% 0.21/0.54 % SZS output end Proof
%------------------------------------------------------------------------------