TSTP Solution File: GRP129-3.004 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP129-3.004 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 22:26:12 EDT 2022
% Result : Unsatisfiable 0.19s 0.50s
% Output : Proof 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GRP129-3.004 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 31 15:24:49 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.50 % SZS status Unsatisfiable
% 0.19/0.50 % SZS output start Proof
% 0.19/0.50 tff(product_type, type, (
% 0.19/0.50 product: ( $i * $i * $i ) > $o)).
% 0.19/0.50 tff(e_1_type, type, (
% 0.19/0.50 e_1: $i)).
% 0.19/0.50 tff(e_2_type, type, (
% 0.19/0.50 e_2: $i)).
% 0.19/0.50 tff(e_4_type, type, (
% 0.19/0.50 e_4: $i)).
% 0.19/0.50 tff(cycle_type, type, (
% 0.19/0.50 cycle: ( $i * $i ) > $o)).
% 0.19/0.50 tff(e_3_type, type, (
% 0.19/0.50 e_3: $i)).
% 0.19/0.50 tff(e_0_type, type, (
% 0.19/0.50 e_0: $i)).
% 0.19/0.50 tff(greater_type, type, (
% 0.19/0.50 greater: ( $i * $i ) > $o)).
% 0.19/0.50 tff(equalish_type, type, (
% 0.19/0.50 equalish: ( $i * $i ) > $o)).
% 0.19/0.50 tff(next_type, type, (
% 0.19/0.50 next: ( $i * $i ) > $o)).
% 0.19/0.50 tff(group_element_type, type, (
% 0.19/0.50 group_element: $i > $o)).
% 0.19/0.50 tff(1,assumption,(product(e_1, e_2, e_2)), introduced(assumption)).
% 0.19/0.50 tff(2,assumption,(product(e_2, e_2, e_4)), introduced(assumption)).
% 0.19/0.50 tff(3,assumption,(product(e_2, e_1, e_4)), introduced(assumption)).
% 0.19/0.50 tff(4,plain,
% 0.19/0.50 (^[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))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(5,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.50 tff(6,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(7,plain,
% 0.19/0.50 (^[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))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(8,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[7])).
% 0.19/0.50 tff(9,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')).
% 0.19/0.50 tff(10,plain,
% 0.19/0.50 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.19/0.50 tff(11,plain,
% 0.19/0.50 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.19/0.50 tff(12,plain,(
% 0.19/0.50 ![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.19/0.50 inference(skolemize,[status(sab)],[11])).
% 0.19/0.50 tff(13,plain,
% 0.19/0.50 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.19/0.50 tff(14,plain,
% 0.19/0.50 (greater(e_4, e_2) <=> greater(e_4, e_2)),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(15,axiom,(greater(e_4, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_greater_e_2')).
% 0.19/0.50 tff(16,plain,
% 0.19/0.50 (greater(e_4, e_2)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.50 tff(17,plain,
% 0.19/0.50 (((~![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)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(18,plain,
% 0.19/0.50 (((~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)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(19,plain,
% 0.19/0.50 (((~![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))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[18])).
% 0.19/0.50 tff(20,plain,
% 0.19/0.50 (((~![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)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[19, 17])).
% 0.19/0.50 tff(21,plain,
% 0.19/0.50 ((~![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)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(22,plain,
% 0.19/0.50 ((~![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))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.50 tff(23,plain,
% 0.19/0.50 ((~cycle(e_2, e_0)) | (~product(e_2, e_1, e_4))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[22, 16, 13])).
% 0.19/0.50 tff(24,plain,
% 0.19/0.50 (~cycle(e_2, e_0)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[23, 3])).
% 0.19/0.50 tff(25,assumption,(cycle(e_2, e_1)), introduced(assumption)).
% 0.19/0.50 tff(26,plain,
% 0.19/0.50 ((~equalish(e_4, e_3)) <=> (~equalish(e_4, e_3))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(27,axiom,(~equalish(e_4, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_is_not_e_3')).
% 0.19/0.50 tff(28,plain,
% 0.19/0.50 (~equalish(e_4, e_3)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.50 tff(29,plain,
% 0.19/0.50 (^[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))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(30,plain,
% 0.19/0.50 (![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))) <=> ![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)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.50 tff(31,plain,
% 0.19/0.50 (![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))) <=> ![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)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(32,plain,
% 0.19/0.50 (^[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)))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(33,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.50 tff(34,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')).
% 0.19/0.50 tff(35,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.50 tff(36,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.19/0.50 tff(37,plain,(
% 0.19/0.50 ![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)))),
% 0.19/0.50 inference(skolemize,[status(sab)],[36])).
% 0.19/0.50 tff(38,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.19/0.50 tff(39,plain,
% 0.19/0.50 (greater(e_1, e_0) <=> greater(e_1, e_0)),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(40,axiom,(greater(e_1, e_0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_greater_e_0')).
% 0.19/0.50 tff(41,plain,
% 0.19/0.50 (greater(e_1, e_0)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.50 tff(42,plain,
% 0.19/0.50 (next(e_2, e_3) <=> next(e_2, e_3)),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(43,axiom,(next(e_2, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_then_e_3')).
% 0.19/0.50 tff(44,plain,
% 0.19/0.50 (next(e_2, e_3)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.19/0.50 tff(45,plain,
% 0.19/0.50 (((~![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)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(46,plain,
% 0.19/0.50 (((~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)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(47,plain,
% 0.19/0.50 (((~![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))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[46])).
% 0.19/0.50 tff(48,plain,
% 0.19/0.50 (((~![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)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[47, 45])).
% 0.19/0.50 tff(49,plain,
% 0.19/0.50 ((~![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)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(50,plain,
% 0.19/0.50 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_4))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.51 tff(51,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[50, 44, 41, 38, 28, 25, 3])).
% 0.19/0.51 tff(52,plain,((~cycle(e_2, e_1)) | (~product(e_2, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.51 tff(53,plain,
% 0.19/0.51 (~cycle(e_2, e_1)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[52, 3])).
% 0.19/0.51 tff(54,assumption,(cycle(e_2, e_2)), introduced(assumption)).
% 0.19/0.51 tff(55,plain,
% 0.19/0.51 (greater(e_2, e_0) <=> greater(e_2, e_0)),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(56,axiom,(greater(e_2, e_0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_greater_e_0')).
% 0.19/0.51 tff(57,plain,
% 0.19/0.51 (greater(e_2, e_0)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.51 tff(58,plain,
% 0.19/0.51 (((~![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)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(59,plain,
% 0.19/0.51 (((~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)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(60,plain,
% 0.19/0.51 (((~![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))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[59])).
% 0.19/0.51 tff(61,plain,
% 0.19/0.51 (((~![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)))),
% 0.19/0.51 inference(transitivity,[status(thm)],[60, 58])).
% 0.19/0.51 tff(62,plain,
% 0.19/0.51 ((~![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)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(63,plain,
% 0.19/0.51 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_4))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.51 tff(64,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[63, 44, 57, 38, 28, 54, 3])).
% 0.19/0.51 tff(65,plain,((~cycle(e_2, e_2)) | (~product(e_2, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.51 tff(66,plain,
% 0.19/0.51 (~cycle(e_2, e_2)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[65, 3])).
% 0.19/0.51 tff(67,plain,
% 0.19/0.51 (group_element(e_2) <=> group_element(e_2)),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(68,axiom,(group_element(e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_2')).
% 0.19/0.51 tff(69,plain,
% 0.19/0.51 (group_element(e_2)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.19/0.51 tff(70,plain,
% 0.19/0.51 (^[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))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(71,plain,
% 0.19/0.51 (![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)))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[70])).
% 0.19/0.51 tff(72,plain,
% 0.19/0.51 (![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)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(73,plain,
% 0.19/0.51 (^[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)))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(74,plain,
% 0.19/0.51 (![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)))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[73])).
% 0.19/0.51 tff(75,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')).
% 0.19/0.51 tff(76,plain,
% 0.19/0.51 (![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.19/0.51 tff(77,plain,
% 0.19/0.51 (![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.19/0.51 tff(78,plain,(
% 0.19/0.51 ![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.19/0.51 inference(skolemize,[status(sab)],[77])).
% 0.19/0.51 tff(79,plain,
% 0.19/0.51 (![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[78, 71])).
% 0.19/0.51 tff(80,plain,
% 0.19/0.51 (((~![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)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(81,plain,
% 0.19/0.51 ((~![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)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(82,plain,
% 0.19/0.51 ((~![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))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.19/0.51 tff(83,plain,
% 0.19/0.51 (cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[82, 79, 69])).
% 0.19/0.51 tff(84,plain,
% 0.19/0.51 (cycle(e_2, e_3)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[83, 66, 53, 24])).
% 0.19/0.51 tff(85,plain,
% 0.19/0.51 (greater(e_3, e_0) <=> greater(e_3, e_0)),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(86,axiom,(greater(e_3, e_0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_greater_e_0')).
% 0.19/0.51 tff(87,plain,
% 0.19/0.51 (greater(e_3, e_0)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.19/0.51 tff(88,plain,
% 0.19/0.51 (((~![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)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(89,plain,
% 0.19/0.51 (((~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)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(90,plain,
% 0.19/0.51 (((~![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))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[89])).
% 0.19/0.51 tff(91,plain,
% 0.19/0.51 (((~![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)))),
% 0.19/0.51 inference(transitivity,[status(thm)],[90, 88])).
% 0.19/0.51 tff(92,plain,
% 0.19/0.51 ((~![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)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(93,plain,
% 0.19/0.51 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_4))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.19/0.51 tff(94,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[93, 44, 87, 38, 28, 84, 3])).
% 0.19/0.51 tff(95,plain,(~product(e_2, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.51 tff(96,plain,
% 0.19/0.51 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl((product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1))) <=> (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(97,plain,
% 0.19/0.51 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[96])).
% 0.19/0.51 tff(98,plain,
% 0.19/0.51 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(99,plain,
% 0.19/0.51 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : trans(monotonicity(rewrite(((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) <=> ((~product(X, Z1, Z2)) | (~product(Y, X, Z1)))), ((((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) | product(Z1, Y, Z2)) <=> (((~product(X, Z1, Z2)) | (~product(Y, X, Z1))) | product(Z1, Y, Z2)))), rewrite((((~product(X, Z1, Z2)) | (~product(Y, X, Z1))) | product(Z1, Y, Z2)) <=> (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))), ((((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) | product(Z1, Y, Z2)) <=> (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(100,plain,
% 0.19/0.51 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) | product(Z1, Y, Z2)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[99])).
% 0.19/0.51 tff(101,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(Y, X, Z1)) | (~product(X, Z1, Z2))) | product(Z1, Y, Z2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qg3')).
% 0.19/0.51 tff(102,plain,
% 0.19/0.51 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.19/0.51 tff(103,plain,
% 0.19/0.51 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.19/0.51 tff(104,plain,(
% 0.19/0.51 ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.19/0.51 inference(skolemize,[status(sab)],[103])).
% 0.19/0.51 tff(105,plain,
% 0.19/0.51 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.19/0.51 tff(106,plain,
% 0.19/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_4) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_4)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(107,plain,
% 0.19/0.51 ((product(e_2, e_1, e_4) | (~product(e_2, e_2, e_4)) | (~product(e_1, e_2, e_2))) <=> (product(e_2, e_1, e_4) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_4)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(108,plain,
% 0.19/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_2, e_2, e_4)) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_4))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[107])).
% 0.19/0.51 tff(109,plain,
% 0.19/0.51 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_2, e_2, e_4)) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_4) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_4)))),
% 0.19/0.51 inference(transitivity,[status(thm)],[108, 106])).
% 0.19/0.51 tff(110,plain,
% 0.19/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_2, e_2, e_4)) | (~product(e_1, e_2, e_2)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(111,plain,
% 0.19/0.51 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_4) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_4))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.19/0.51 tff(112,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[111, 105, 95, 1, 2])).
% 0.19/0.51 tff(113,plain,((~product(e_2, e_2, e_4)) | (~product(e_1, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.51 tff(114,plain,
% 0.19/0.51 (~product(e_2, e_2, e_4)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[113, 1])).
% 0.19/0.51 tff(115,assumption,(product(e_2, e_2, e_2)), introduced(assumption)).
% 0.19/0.51 tff(116,plain,
% 0.19/0.51 (^[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))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(117,plain,
% 0.19/0.51 (![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)))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[116])).
% 0.19/0.51 tff(118,plain,
% 0.19/0.51 (![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)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(119,plain,
% 0.19/0.51 (^[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)))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(120,plain,
% 0.19/0.51 (![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)))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[119])).
% 0.19/0.51 tff(121,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')).
% 0.19/0.51 tff(122,plain,
% 0.19/0.51 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.19/0.51 tff(123,plain,
% 0.19/0.51 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.19/0.51 tff(124,plain,(
% 0.19/0.51 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.51 inference(skolemize,[status(sab)],[123])).
% 0.19/0.51 tff(125,plain,
% 0.19/0.51 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[124, 117])).
% 0.19/0.51 tff(126,plain,
% 0.19/0.51 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(127,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.19/0.51 tff(128,plain,
% 0.19/0.51 (~equalish(e_2, e_1)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.19/0.51 tff(129,plain,
% 0.19/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(130,plain,
% 0.19/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(131,plain,
% 0.19/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.19/0.51 tff(132,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[131, 128, 125, 1, 115])).
% 0.19/0.52 tff(133,plain,((~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.52 tff(134,plain,
% 0.19/0.52 (~product(e_2, e_2, e_2)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[133, 1])).
% 0.19/0.52 tff(135,assumption,(~product(e_1, e_1, e_2)), introduced(assumption)).
% 0.19/0.52 tff(136,assumption,(~product(e_2, e_1, e_3)), introduced(assumption)).
% 0.19/0.52 tff(137,assumption,(product(e_2, e_1, e_2)), introduced(assumption)).
% 0.19/0.52 tff(138,assumption,(product(e_1, e_2, e_3)), introduced(assumption)).
% 0.19/0.52 tff(139,assumption,(product(e_2, e_2, e_3)), introduced(assumption)).
% 0.19/0.52 tff(140,plain,
% 0.19/0.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_2, e_3)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(141,plain,
% 0.19/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_2, e_3)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(142,plain,
% 0.19/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_2, e_3))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.19/0.52 tff(143,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[142, 128, 125, 138, 139])).
% 0.19/0.52 tff(144,plain,((~product(e_2, e_2, e_3)) | (~product(e_1, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.52 tff(145,plain,
% 0.19/0.52 (~product(e_2, e_2, e_3)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[144, 138])).
% 0.19/0.52 tff(146,plain,
% 0.19/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3)) | product(e_2, e_2, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3)) | product(e_2, e_2, e_3))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(147,plain,
% 0.19/0.52 ((product(e_2, e_2, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2))) <=> ((~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3)) | product(e_2, e_2, e_3))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(148,plain,
% 0.19/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3)) | product(e_2, e_2, e_3)))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[147])).
% 0.19/0.52 tff(149,plain,
% 0.19/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3)) | product(e_2, e_2, e_3))),
% 0.19/0.52 inference(transitivity,[status(thm)],[148, 146])).
% 0.19/0.52 tff(150,plain,
% 0.19/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(151,plain,
% 0.19/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_3)) | product(e_2, e_2, e_3)),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.19/0.52 tff(152,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[151, 105, 137, 138, 145])).
% 0.19/0.52 tff(153,plain,((~product(e_1, e_2, e_3)) | (~product(e_2, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.52 tff(154,plain,
% 0.19/0.52 (~product(e_1, e_2, e_3)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[153, 137])).
% 0.19/0.52 tff(155,plain,
% 0.19/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_1)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(156,plain,
% 0.19/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_1)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(157,plain,
% 0.19/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_1, e_2, e_1))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.19/0.52 tff(158,plain,
% 0.19/0.52 (~product(e_1, e_2, e_1)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[157, 105, 135, 137])).
% 0.19/0.52 tff(159,assumption,(product(e_1, e_2, e_4)), introduced(assumption)).
% 0.19/0.52 tff(160,plain,
% 0.19/0.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_2, e_4)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(161,plain,
% 0.19/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_2, e_4)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(162,plain,
% 0.19/0.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_2, e_4))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.19/0.52 tff(163,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[162, 128, 125, 159, 2])).
% 0.19/0.52 tff(164,plain,((~product(e_2, e_2, e_4)) | (~product(e_1, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.52 tff(165,plain,
% 0.19/0.52 (~product(e_2, e_2, e_4)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[164, 159])).
% 0.19/0.52 tff(166,plain,
% 0.19/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_1, e_2)) | product(e_2, e_2, e_4) | (~product(e_1, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_2)) | product(e_2, e_2, e_4) | (~product(e_1, e_2, e_4)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(167,plain,
% 0.19/0.52 ((product(e_2, e_2, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_1, e_2))) <=> ((~product(e_2, e_1, e_2)) | product(e_2, e_2, e_4) | (~product(e_1, e_2, e_4)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(168,plain,
% 0.19/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_1, e_2)) | product(e_2, e_2, e_4) | (~product(e_1, e_2, e_4))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[167])).
% 0.19/0.52 tff(169,plain,
% 0.19/0.52 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_2)) | product(e_2, e_2, e_4) | (~product(e_1, e_2, e_4)))),
% 0.19/0.52 inference(transitivity,[status(thm)],[168, 166])).
% 0.19/0.52 tff(170,plain,
% 0.19/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_1, e_2)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(171,plain,
% 0.19/0.52 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_2)) | product(e_2, e_2, e_4) | (~product(e_1, e_2, e_4))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.19/0.52 tff(172,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[171, 105, 137, 159, 165])).
% 0.19/0.52 tff(173,plain,((~product(e_1, e_2, e_4)) | (~product(e_2, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.52 tff(174,plain,
% 0.19/0.52 (~product(e_1, e_2, e_4)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[173, 137])).
% 0.19/0.52 tff(175,plain,
% 0.19/0.52 (^[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))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(176,plain,
% 0.19/0.52 (![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))) <=> ![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)))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[175])).
% 0.19/0.52 tff(177,plain,
% 0.19/0.52 (![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))) <=> ![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)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(178,plain,
% 0.19/0.52 (^[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)))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(179,plain,
% 0.19/0.52 (![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)))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[178])).
% 0.19/0.52 tff(180,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')).
% 0.19/0.52 tff(181,plain,
% 0.19/0.52 (![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)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.19/0.52 tff(182,plain,
% 0.19/0.52 (![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)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[181, 177])).
% 0.19/0.52 tff(183,plain,(
% 0.19/0.52 ![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)))),
% 0.19/0.52 inference(skolemize,[status(sab)],[182])).
% 0.19/0.52 tff(184,plain,
% 0.19/0.52 (![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)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[183, 176])).
% 0.19/0.52 tff(185,plain,
% 0.19/0.52 (group_element(e_1) <=> group_element(e_1)),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(186,axiom,(group_element(e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_1')).
% 0.19/0.52 tff(187,plain,
% 0.19/0.52 (group_element(e_1)),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.19/0.52 tff(188,plain,
% 0.19/0.52 (((~![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_1)) | (~group_element(e_2)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2))) <=> ((~![Y: $i, X: $i] : ((~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_1, e_2, e_1) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(189,plain,
% 0.19/0.52 (((~group_element(e_1)) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2))) <=> ((~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(190,plain,
% 0.19/0.52 (((~![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_1)) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)))) <=> ((~![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_1, e_2, e_1) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2)))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[189])).
% 0.19/0.52 tff(191,plain,
% 0.19/0.52 (((~![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_1)) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)))) <=> ((~![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_1, e_2, e_1) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2))),
% 0.19/0.53 inference(transitivity,[status(thm)],[190, 188])).
% 0.19/0.53 tff(192,plain,
% 0.19/0.53 ((~![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)) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2) | product(e_1, e_2, e_1) | (~group_element(e_2)))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(193,plain,
% 0.19/0.53 ((~![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_1, e_2, e_1) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3) | product(e_1, e_2, e_2)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.19/0.53 tff(194,plain,
% 0.19/0.53 (product(e_1, e_2, e_3) | product(e_1, e_2, e_2)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[193, 187, 69, 184, 174, 158])).
% 0.19/0.53 tff(195,plain,
% 0.19/0.53 (product(e_1, e_2, e_2)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[194, 154])).
% 0.19/0.53 tff(196,plain,
% 0.19/0.53 (~product(e_2, e_2, e_2)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[133, 195])).
% 0.19/0.53 tff(197,plain,
% 0.19/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_1, e_2)) | product(e_2, e_2, e_2) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_2)) | product(e_2, e_2, e_2) | (~product(e_1, e_2, e_2)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(198,plain,
% 0.19/0.53 ((product(e_2, e_2, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_1, e_2))) <=> ((~product(e_2, e_1, e_2)) | product(e_2, e_2, e_2) | (~product(e_1, e_2, e_2)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(199,plain,
% 0.19/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_1, e_2)) | product(e_2, e_2, e_2) | (~product(e_1, e_2, e_2))))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[198])).
% 0.19/0.53 tff(200,plain,
% 0.19/0.53 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_2)) | product(e_2, e_2, e_2) | (~product(e_1, e_2, e_2)))),
% 0.19/0.53 inference(transitivity,[status(thm)],[199, 197])).
% 0.19/0.53 tff(201,plain,
% 0.19/0.53 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(202,plain,
% 0.19/0.53 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_2)) | product(e_2, e_2, e_2) | (~product(e_1, e_2, e_2))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.19/0.53 tff(203,plain,
% 0.19/0.53 ($false),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[202, 105, 137, 195, 196])).
% 0.19/0.53 tff(204,plain,((~product(e_2, e_1, e_2)) | product(e_1, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.53 tff(205,plain,
% 0.19/0.53 (~product(e_2, e_1, e_2)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[204, 135])).
% 0.19/0.53 tff(206,assumption,(product(e_1, e_1, e_4)), introduced(assumption)).
% 0.19/0.53 tff(207,assumption,(cycle(e_1, e_3)), introduced(assumption)).
% 0.19/0.53 tff(208,plain,
% 0.19/0.53 ((~equalish(e_4, e_2)) <=> (~equalish(e_4, e_2))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(209,axiom,(~equalish(e_4, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_is_not_e_2')).
% 0.45/0.53 tff(210,plain,
% 0.45/0.53 (~equalish(e_4, e_2)),
% 0.45/0.53 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.45/0.53 tff(211,plain,
% 0.45/0.53 (next(e_1, e_2) <=> next(e_1, e_2)),
% 0.45/0.53 inference(rewrite,[status(thm)],[])).
% 0.45/0.53 tff(212,axiom,(next(e_1, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_then_e_2')).
% 0.45/0.53 tff(213,plain,
% 0.45/0.53 (next(e_1, e_2)),
% 0.45/0.53 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.45/0.53 tff(214,plain,
% 0.45/0.53 (((~![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_4, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | (~product(e_1, 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_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | (~product(e_1, e_1, e_4)))),
% 0.45/0.53 inference(rewrite,[status(thm)],[])).
% 0.45/0.53 tff(215,plain,
% 0.45/0.53 (((~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_4))) <=> (equalish(e_4, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | (~product(e_1, e_1, e_4)))),
% 0.45/0.53 inference(rewrite,[status(thm)],[])).
% 0.45/0.53 tff(216,plain,
% 0.45/0.53 (((~![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)))) | ((~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~product(e_1, 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_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | (~product(e_1, e_1, e_4))))),
% 0.45/0.53 inference(monotonicity,[status(thm)],[215])).
% 0.45/0.53 tff(217,plain,
% 0.45/0.53 (((~![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)))) | ((~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~product(e_1, 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_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | (~product(e_1, e_1, e_4)))),
% 0.45/0.53 inference(transitivity,[status(thm)],[216, 214])).
% 0.45/0.53 tff(218,plain,
% 0.45/0.53 ((~![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)))) | ((~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_4)))),
% 0.45/0.53 inference(quant_inst,[status(thm)],[])).
% 0.45/0.53 tff(219,plain,
% 0.45/0.53 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | (~product(e_1, e_1, e_4))),
% 0.45/0.53 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.45/0.53 tff(220,plain,
% 0.45/0.53 ($false),
% 0.45/0.53 inference(unit_resolution,[status(thm)],[219, 213, 87, 38, 210, 207, 206])).
% 0.45/0.53 tff(221,plain,((~cycle(e_1, e_3)) | (~product(e_1, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.45/0.53 tff(222,plain,
% 0.45/0.53 (~cycle(e_1, e_3)),
% 0.45/0.53 inference(unit_resolution,[status(thm)],[221, 206])).
% 0.45/0.53 tff(223,plain,
% 0.45/0.53 (greater(e_4, e_1) <=> greater(e_4, e_1)),
% 0.45/0.53 inference(rewrite,[status(thm)],[])).
% 0.45/0.53 tff(224,axiom,(greater(e_4, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_greater_e_1')).
% 0.45/0.53 tff(225,plain,
% 0.45/0.53 (greater(e_4, e_1)),
% 0.45/0.53 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.45/0.53 tff(226,plain,
% 0.45/0.53 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~cycle(e_1, e_0)) | (~greater(e_4, e_1)) | (~product(e_1, e_1, e_4)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_4, e_1)) | (~product(e_1, e_1, e_4)))),
% 0.45/0.53 inference(rewrite,[status(thm)],[])).
% 0.45/0.53 tff(227,plain,
% 0.45/0.53 (((~greater(e_4, e_1)) | (~product(e_1, e_1, e_4)) | (~cycle(e_1, e_0))) <=> ((~cycle(e_1, e_0)) | (~greater(e_4, e_1)) | (~product(e_1, e_1, e_4)))),
% 0.45/0.53 inference(rewrite,[status(thm)],[])).
% 0.45/0.53 tff(228,plain,
% 0.45/0.53 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_4, e_1)) | (~product(e_1, e_1, e_4)) | (~cycle(e_1, e_0)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~cycle(e_1, e_0)) | (~greater(e_4, e_1)) | (~product(e_1, e_1, e_4))))),
% 0.45/0.53 inference(monotonicity,[status(thm)],[227])).
% 0.45/0.53 tff(229,plain,
% 0.45/0.53 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_4, e_1)) | (~product(e_1, e_1, e_4)) | (~cycle(e_1, e_0)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_4, e_1)) | (~product(e_1, e_1, e_4)))),
% 0.45/0.53 inference(transitivity,[status(thm)],[228, 226])).
% 0.45/0.53 tff(230,plain,
% 0.45/0.53 ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_4, e_1)) | (~product(e_1, e_1, e_4)) | (~cycle(e_1, e_0)))),
% 0.45/0.53 inference(quant_inst,[status(thm)],[])).
% 0.45/0.53 tff(231,plain,
% 0.45/0.53 ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_4, e_1)) | (~product(e_1, e_1, e_4))),
% 0.45/0.53 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.45/0.53 tff(232,plain,
% 0.45/0.53 ((~cycle(e_1, e_0)) | (~product(e_1, e_1, e_4))),
% 0.45/0.53 inference(unit_resolution,[status(thm)],[231, 225, 13])).
% 0.45/0.53 tff(233,plain,
% 0.45/0.53 (~cycle(e_1, e_0)),
% 0.45/0.53 inference(unit_resolution,[status(thm)],[232, 206])).
% 0.45/0.53 tff(234,assumption,(cycle(e_1, e_2)), introduced(assumption)).
% 0.45/0.53 tff(235,plain,
% 0.45/0.53 (((~![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_4, e_2) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~product(e_1, 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_2) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~product(e_1, e_1, e_4)))),
% 0.45/0.53 inference(rewrite,[status(thm)],[])).
% 0.45/0.53 tff(236,plain,
% 0.45/0.53 (((~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_4))) <=> (equalish(e_4, e_2) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~product(e_1, e_1, e_4)))),
% 0.45/0.53 inference(rewrite,[status(thm)],[])).
% 0.45/0.53 tff(237,plain,
% 0.45/0.53 (((~![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)))) | ((~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~product(e_1, 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_2) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~product(e_1, e_1, e_4))))),
% 0.45/0.53 inference(monotonicity,[status(thm)],[236])).
% 0.45/0.53 tff(238,plain,
% 0.45/0.53 (((~![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)))) | ((~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~product(e_1, 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_2) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~product(e_1, e_1, e_4)))),
% 0.45/0.53 inference(transitivity,[status(thm)],[237, 235])).
% 0.45/0.53 tff(239,plain,
% 0.45/0.53 ((~![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)))) | ((~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_4)))),
% 0.45/0.53 inference(quant_inst,[status(thm)],[])).
% 0.45/0.53 tff(240,plain,
% 0.45/0.53 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~product(e_1, e_1, e_4))),
% 0.45/0.53 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.45/0.53 tff(241,plain,
% 0.45/0.53 ($false),
% 0.45/0.53 inference(unit_resolution,[status(thm)],[240, 213, 57, 38, 210, 234, 206])).
% 0.45/0.53 tff(242,plain,((~cycle(e_1, e_2)) | (~product(e_1, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.45/0.53 tff(243,plain,
% 0.45/0.53 (~cycle(e_1, e_2)),
% 0.45/0.53 inference(unit_resolution,[status(thm)],[242, 206])).
% 0.45/0.53 tff(244,plain,
% 0.45/0.53 (((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_1, e_3) | cycle(e_1, e_2) | cycle(e_1, e_1) | cycle(e_1, e_0) | (~group_element(e_1)))) <=> ((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_1, e_3) | cycle(e_1, e_2) | cycle(e_1, e_1) | cycle(e_1, e_0) | (~group_element(e_1)))),
% 0.45/0.53 inference(rewrite,[status(thm)],[])).
% 0.45/0.53 tff(245,plain,
% 0.45/0.53 ((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_1, e_3) | cycle(e_1, e_2) | cycle(e_1, e_1) | cycle(e_1, e_0) | (~group_element(e_1)))),
% 0.45/0.53 inference(quant_inst,[status(thm)],[])).
% 0.45/0.53 tff(246,plain,
% 0.45/0.53 ((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_1, e_3) | cycle(e_1, e_2) | cycle(e_1, e_1) | cycle(e_1, e_0) | (~group_element(e_1))),
% 0.45/0.53 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.45/0.53 tff(247,plain,
% 0.45/0.53 (cycle(e_1, e_3) | cycle(e_1, e_2) | cycle(e_1, e_1) | cycle(e_1, e_0)),
% 0.45/0.53 inference(unit_resolution,[status(thm)],[246, 79, 187])).
% 0.45/0.53 tff(248,plain,
% 0.45/0.53 (cycle(e_1, e_1)),
% 0.45/0.53 inference(unit_resolution,[status(thm)],[247, 243, 233, 222])).
% 0.45/0.53 tff(249,plain,
% 0.45/0.53 (((~![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_4, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, 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_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_4)))),
% 0.45/0.53 inference(rewrite,[status(thm)],[])).
% 0.45/0.53 tff(250,plain,
% 0.45/0.53 (((~greater(e_1, e_0)) | (~cycle(e_1, e_1)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_4))) <=> (equalish(e_4, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_4)))),
% 0.45/0.53 inference(rewrite,[status(thm)],[])).
% 0.45/0.53 tff(251,plain,
% 0.45/0.53 (((~![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)))) | ((~greater(e_1, e_0)) | (~cycle(e_1, e_1)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~product(e_1, 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_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_4))))),
% 0.45/0.53 inference(monotonicity,[status(thm)],[250])).
% 0.45/0.53 tff(252,plain,
% 0.45/0.53 (((~![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)))) | ((~greater(e_1, e_0)) | (~cycle(e_1, e_1)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~product(e_1, 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_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_4)))),
% 0.45/0.53 inference(transitivity,[status(thm)],[251, 249])).
% 0.45/0.53 tff(253,plain,
% 0.45/0.53 ((~![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)))) | ((~greater(e_1, e_0)) | (~cycle(e_1, e_1)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_4)))),
% 0.45/0.54 inference(quant_inst,[status(thm)],[])).
% 0.45/0.54 tff(254,plain,
% 0.45/0.54 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_4))),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[253, 252])).
% 0.45/0.54 tff(255,plain,
% 0.45/0.54 ($false),
% 0.45/0.54 inference(unit_resolution,[status(thm)],[254, 213, 41, 38, 210, 248, 206])).
% 0.45/0.54 tff(256,plain,(~product(e_1, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.45/0.54 tff(257,assumption,(~product(e_1, e_1, e_1)), introduced(assumption)).
% 0.45/0.54 tff(258,assumption,(~product(e_1, e_1, e_4)), introduced(assumption)).
% 0.45/0.54 tff(259,assumption,(product(e_1, e_1, e_3)), introduced(assumption)).
% 0.45/0.54 tff(260,plain,
% 0.45/0.54 (greater(e_3, e_1) <=> greater(e_3, e_1)),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(261,axiom,(greater(e_3, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_greater_e_1')).
% 0.45/0.54 tff(262,plain,
% 0.45/0.54 (greater(e_3, e_1)),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.45/0.54 tff(263,plain,
% 0.45/0.54 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~cycle(e_1, e_0)) | (~greater(e_3, e_1)) | (~product(e_1, e_1, e_3)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_3, e_1)) | (~product(e_1, e_1, e_3)))),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(264,plain,
% 0.45/0.54 (((~greater(e_3, e_1)) | (~product(e_1, e_1, e_3)) | (~cycle(e_1, e_0))) <=> ((~cycle(e_1, e_0)) | (~greater(e_3, e_1)) | (~product(e_1, e_1, e_3)))),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(265,plain,
% 0.45/0.54 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_3, e_1)) | (~product(e_1, e_1, e_3)) | (~cycle(e_1, e_0)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~cycle(e_1, e_0)) | (~greater(e_3, e_1)) | (~product(e_1, e_1, e_3))))),
% 0.45/0.54 inference(monotonicity,[status(thm)],[264])).
% 0.45/0.54 tff(266,plain,
% 0.45/0.54 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_3, e_1)) | (~product(e_1, e_1, e_3)) | (~cycle(e_1, e_0)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_3, e_1)) | (~product(e_1, e_1, e_3)))),
% 0.45/0.54 inference(transitivity,[status(thm)],[265, 263])).
% 0.45/0.54 tff(267,plain,
% 0.45/0.54 ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_3, e_1)) | (~product(e_1, e_1, e_3)) | (~cycle(e_1, e_0)))),
% 0.45/0.54 inference(quant_inst,[status(thm)],[])).
% 0.45/0.54 tff(268,plain,
% 0.45/0.54 ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_3, e_1)) | (~product(e_1, e_1, e_3))),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.45/0.54 tff(269,plain,
% 0.45/0.54 ((~cycle(e_1, e_0)) | (~product(e_1, e_1, e_3))),
% 0.45/0.54 inference(unit_resolution,[status(thm)],[268, 262, 13])).
% 0.45/0.54 tff(270,plain,
% 0.45/0.54 (~cycle(e_1, e_0)),
% 0.45/0.54 inference(unit_resolution,[status(thm)],[269, 259])).
% 0.45/0.54 tff(271,assumption,(~cycle(e_1, e_0)), introduced(assumption)).
% 0.45/0.54 tff(272,assumption,(~cycle(e_1, e_1)), introduced(assumption)).
% 0.45/0.54 tff(273,plain,
% 0.45/0.54 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(274,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.45/0.54 tff(275,plain,
% 0.45/0.54 (~equalish(e_1, e_2)),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.45/0.54 tff(276,plain,
% 0.45/0.54 (((~![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_1, e_2) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~product(e_1, e_1, e_1)))) <=> ((~![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_1, e_2) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~product(e_1, e_1, e_1)))),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(277,plain,
% 0.45/0.54 (((~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_1))) <=> (equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~product(e_1, e_1, e_1)))),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(278,plain,
% 0.45/0.54 (((~![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_2, e_0)) | (~cycle(e_1, e_2)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_1)))) <=> ((~![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_1, e_2) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~product(e_1, e_1, e_1))))),
% 0.45/0.54 inference(monotonicity,[status(thm)],[277])).
% 0.45/0.54 tff(279,plain,
% 0.45/0.54 (((~![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_2, e_0)) | (~cycle(e_1, e_2)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_1)))) <=> ((~![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_1, e_2) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~product(e_1, e_1, e_1)))),
% 0.45/0.54 inference(transitivity,[status(thm)],[278, 276])).
% 0.45/0.54 tff(280,plain,
% 0.45/0.54 ((~![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_2, e_0)) | (~cycle(e_1, e_2)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_1)))),
% 0.45/0.54 inference(quant_inst,[status(thm)],[])).
% 0.45/0.54 tff(281,plain,
% 0.45/0.54 ((~![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_1, e_2) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~product(e_1, e_1, e_1))),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.45/0.54 tff(282,plain,
% 0.45/0.54 (~product(e_1, e_1, e_1)),
% 0.45/0.54 inference(unit_resolution,[status(thm)],[281, 213, 57, 38, 275, 234])).
% 0.45/0.54 tff(283,plain,
% 0.45/0.54 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(284,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.45/0.54 tff(285,plain,
% 0.45/0.54 (~equalish(e_3, e_2)),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[284, 283])).
% 0.45/0.54 tff(286,plain,
% 0.45/0.54 (((~![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_3, e_2) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~product(e_1, e_1, e_3)))) <=> ((~![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_3, e_2) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~product(e_1, e_1, e_3)))),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(287,plain,
% 0.45/0.54 (((~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3))) <=> (equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~product(e_1, e_1, e_3)))),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(288,plain,
% 0.45/0.54 (((~![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_2, e_0)) | (~cycle(e_1, e_2)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))) <=> ((~![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_3, e_2) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~product(e_1, e_1, e_3))))),
% 0.45/0.54 inference(monotonicity,[status(thm)],[287])).
% 0.45/0.54 tff(289,plain,
% 0.45/0.54 (((~![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_2, e_0)) | (~cycle(e_1, e_2)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))) <=> ((~![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_3, e_2) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~product(e_1, e_1, e_3)))),
% 0.45/0.54 inference(transitivity,[status(thm)],[288, 286])).
% 0.45/0.54 tff(290,plain,
% 0.45/0.54 ((~![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_2, e_0)) | (~cycle(e_1, e_2)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))),
% 0.45/0.54 inference(quant_inst,[status(thm)],[])).
% 0.45/0.54 tff(291,plain,
% 0.45/0.54 ((~![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_3, e_2) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~product(e_1, e_1, e_3))),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.45/0.54 tff(292,plain,
% 0.45/0.54 (~product(e_1, e_1, e_3)),
% 0.45/0.54 inference(unit_resolution,[status(thm)],[291, 213, 57, 38, 285, 234])).
% 0.45/0.54 tff(293,plain,
% 0.45/0.54 (((~![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)) | product(e_1, e_1, e_2) | product(e_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, 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)) | product(e_1, e_1, e_2) | product(e_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_1))),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(294,plain,
% 0.45/0.54 (((~group_element(e_1)) | product(e_1, e_1, e_4) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1))) <=> ((~group_element(e_1)) | product(e_1, e_1, e_2) | product(e_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_1))),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(295,plain,
% 0.45/0.54 (((~![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)) | product(e_1, e_1, e_4) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))) <=> ((~![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)) | product(e_1, e_1, e_2) | product(e_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_1)))),
% 0.45/0.54 inference(monotonicity,[status(thm)],[294])).
% 0.45/0.54 tff(296,plain,
% 0.45/0.54 (((~![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)) | product(e_1, e_1, e_4) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))) <=> ((~![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)) | product(e_1, e_1, e_2) | product(e_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_1))),
% 0.45/0.54 inference(transitivity,[status(thm)],[295, 293])).
% 0.45/0.54 tff(297,plain,
% 0.45/0.54 ((~![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)) | product(e_1, e_1, e_4) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))),
% 0.45/0.54 inference(quant_inst,[status(thm)],[])).
% 0.45/0.54 tff(298,plain,
% 0.45/0.54 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | product(e_1, e_1, e_2) | product(e_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_1)),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.45/0.54 tff(299,plain,
% 0.45/0.54 ($false),
% 0.45/0.54 inference(unit_resolution,[status(thm)],[298, 187, 184, 135, 292, 258, 282])).
% 0.45/0.54 tff(300,plain,((~cycle(e_1, e_2)) | product(e_1, e_1, e_2) | product(e_1, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.45/0.54 tff(301,plain,
% 0.45/0.54 (~cycle(e_1, e_2)),
% 0.45/0.54 inference(unit_resolution,[status(thm)],[300, 135, 258])).
% 0.45/0.54 tff(302,plain,
% 0.45/0.54 (cycle(e_1, e_3)),
% 0.45/0.54 inference(unit_resolution,[status(thm)],[247, 301, 272, 271])).
% 0.45/0.54 tff(303,plain,
% 0.45/0.54 (((~![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_1, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | (~product(e_1, e_1, e_1)))) <=> ((~![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_1, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | (~product(e_1, e_1, e_1)))),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(304,plain,
% 0.45/0.54 (((~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_1))) <=> (equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | (~product(e_1, e_1, e_1)))),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(305,plain,
% 0.45/0.54 (((~![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_3, e_0)) | (~cycle(e_1, e_3)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_1)))) <=> ((~![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_1, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | (~product(e_1, e_1, e_1))))),
% 0.45/0.54 inference(monotonicity,[status(thm)],[304])).
% 0.45/0.54 tff(306,plain,
% 0.45/0.54 (((~![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_3, e_0)) | (~cycle(e_1, e_3)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_1)))) <=> ((~![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_1, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | (~product(e_1, e_1, e_1)))),
% 0.45/0.54 inference(transitivity,[status(thm)],[305, 303])).
% 0.45/0.54 tff(307,plain,
% 0.45/0.54 ((~![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_3, e_0)) | (~cycle(e_1, e_3)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_1)))),
% 0.45/0.54 inference(quant_inst,[status(thm)],[])).
% 0.45/0.54 tff(308,plain,
% 0.45/0.54 ((~![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_1, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | (~product(e_1, e_1, e_1))),
% 0.45/0.54 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.45/0.54 tff(309,plain,
% 0.45/0.54 (~product(e_1, e_1, e_1)),
% 0.45/0.54 inference(unit_resolution,[status(thm)],[308, 213, 87, 38, 275, 302])).
% 0.45/0.54 tff(310,plain,
% 0.45/0.54 (((~![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_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | (~product(e_1, e_1, e_3)))) <=> ((~![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_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | (~product(e_1, e_1, e_3)))),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(311,plain,
% 0.45/0.54 (((~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3))) <=> (equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | (~product(e_1, e_1, e_3)))),
% 0.47/0.55 inference(rewrite,[status(thm)],[])).
% 0.47/0.55 tff(312,plain,
% 0.47/0.55 (((~![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_1, e_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))) <=> ((~![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_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | (~product(e_1, e_1, e_3))))),
% 0.47/0.55 inference(monotonicity,[status(thm)],[311])).
% 0.47/0.55 tff(313,plain,
% 0.47/0.55 (((~![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_1, e_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))) <=> ((~![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_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | (~product(e_1, e_1, e_3)))),
% 0.47/0.55 inference(transitivity,[status(thm)],[312, 310])).
% 0.47/0.55 tff(314,plain,
% 0.47/0.55 ((~![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_1, e_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))),
% 0.47/0.55 inference(quant_inst,[status(thm)],[])).
% 0.47/0.55 tff(315,plain,
% 0.47/0.55 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~cycle(e_1, e_3)) | (~product(e_1, e_1, e_3))),
% 0.47/0.55 inference(modus_ponens,[status(thm)],[314, 313])).
% 0.47/0.55 tff(316,plain,
% 0.47/0.55 (~product(e_1, e_1, e_3)),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[315, 213, 87, 38, 285, 302])).
% 0.47/0.55 tff(317,plain,
% 0.47/0.55 ($false),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[298, 187, 184, 135, 316, 258, 309])).
% 0.47/0.55 tff(318,plain,(product(e_1, e_1, e_2) | product(e_1, e_1, e_4) | cycle(e_1, e_1) | cycle(e_1, e_0)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.55 tff(319,plain,
% 0.47/0.55 (cycle(e_1, e_1)),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[318, 270, 135, 258])).
% 0.47/0.55 tff(320,plain,
% 0.47/0.55 (((~![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_3, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_3)))) <=> ((~![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_3, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_3)))),
% 0.47/0.55 inference(rewrite,[status(thm)],[])).
% 0.47/0.55 tff(321,plain,
% 0.47/0.55 (((~greater(e_1, e_0)) | (~cycle(e_1, e_1)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3))) <=> (equalish(e_3, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_3)))),
% 0.47/0.55 inference(rewrite,[status(thm)],[])).
% 0.47/0.55 tff(322,plain,
% 0.47/0.55 (((~![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_1, e_1)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))) <=> ((~![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_3, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_3))))),
% 0.47/0.55 inference(monotonicity,[status(thm)],[321])).
% 0.47/0.55 tff(323,plain,
% 0.47/0.55 (((~![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_1, e_1)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))) <=> ((~![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_3, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_3)))),
% 0.47/0.55 inference(transitivity,[status(thm)],[322, 320])).
% 0.47/0.55 tff(324,plain,
% 0.47/0.55 ((~![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_1, e_1)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))),
% 0.47/0.55 inference(quant_inst,[status(thm)],[])).
% 0.47/0.55 tff(325,plain,
% 0.47/0.55 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_3, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_3))),
% 0.47/0.55 inference(modus_ponens,[status(thm)],[324, 323])).
% 0.47/0.55 tff(326,plain,
% 0.47/0.55 ($false),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[325, 213, 41, 38, 285, 319, 259])).
% 0.47/0.55 tff(327,plain,((~product(e_1, e_1, e_3)) | product(e_1, e_1, e_2) | product(e_1, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.55 tff(328,plain,
% 0.47/0.55 (~product(e_1, e_1, e_3)),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[327, 258, 135])).
% 0.47/0.55 tff(329,plain,
% 0.47/0.55 (product(e_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_1)),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[298, 187, 184, 135])).
% 0.47/0.55 tff(330,plain,
% 0.47/0.55 ($false),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[329, 328, 258, 257])).
% 0.47/0.55 tff(331,plain,(product(e_1, e_1, e_4) | product(e_1, e_1, e_1) | product(e_1, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.55 tff(332,plain,
% 0.47/0.55 (product(e_1, e_1, e_1) | product(e_1, e_1, e_2)),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[331, 256])).
% 0.47/0.55 tff(333,plain,
% 0.47/0.55 (product(e_1, e_1, e_1)),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[332, 135])).
% 0.47/0.55 tff(334,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.47/0.55 tff(335,assumption,(product(e_1, e_1, e_1)), introduced(assumption)).
% 0.47/0.55 tff(336,plain,
% 0.47/0.55 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_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)))),
% 0.47/0.55 inference(rewrite,[status(thm)],[])).
% 0.47/0.55 tff(337,plain,
% 0.47/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.47/0.55 inference(quant_inst,[status(thm)],[])).
% 0.47/0.55 tff(338,plain,
% 0.47/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1))),
% 0.47/0.55 inference(modus_ponens,[status(thm)],[337, 336])).
% 0.47/0.55 tff(339,plain,
% 0.47/0.55 ($false),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[338, 128, 125, 335, 334])).
% 0.47/0.55 tff(340,plain,((~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.55 tff(341,plain,
% 0.47/0.55 (~product(e_2, e_1, e_1)),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[340, 333])).
% 0.47/0.55 tff(342,plain,
% 0.47/0.55 (((~![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))),
% 0.47/0.55 inference(rewrite,[status(thm)],[])).
% 0.47/0.55 tff(343,plain,
% 0.47/0.55 (((~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))),
% 0.47/0.55 inference(rewrite,[status(thm)],[])).
% 0.47/0.55 tff(344,plain,
% 0.47/0.55 (((~![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)))),
% 0.47/0.55 inference(monotonicity,[status(thm)],[343])).
% 0.47/0.55 tff(345,plain,
% 0.47/0.55 (((~![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))),
% 0.47/0.55 inference(transitivity,[status(thm)],[344, 342])).
% 0.47/0.55 tff(346,plain,
% 0.47/0.55 ((~![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)))),
% 0.47/0.55 inference(quant_inst,[status(thm)],[])).
% 0.47/0.55 tff(347,plain,
% 0.47/0.55 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1)),
% 0.47/0.55 inference(modus_ponens,[status(thm)],[346, 345])).
% 0.47/0.55 tff(348,plain,
% 0.47/0.55 (product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1)),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[347, 187, 69, 184, 95])).
% 0.47/0.55 tff(349,plain,
% 0.47/0.55 ($false),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[348, 341, 205, 136])).
% 0.47/0.55 tff(350,plain,(product(e_1, e_1, e_2) | product(e_2, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.55 tff(351,plain,
% 0.47/0.55 (product(e_2, e_1, e_3)),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[350, 135])).
% 0.47/0.55 tff(352,assumption,(product(e_2, e_1, e_3)), introduced(assumption)).
% 0.47/0.55 tff(353,plain,
% 0.47/0.55 (^[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))))),
% 0.47/0.55 inference(bind,[status(th)],[])).
% 0.47/0.55 tff(354,plain,
% 0.47/0.55 (![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)))),
% 0.47/0.55 inference(quant_intro,[status(thm)],[353])).
% 0.47/0.55 tff(355,plain,
% 0.47/0.55 (![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)))),
% 0.47/0.55 inference(rewrite,[status(thm)],[])).
% 0.47/0.55 tff(356,plain,
% 0.47/0.55 (^[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)))))),
% 0.47/0.55 inference(bind,[status(th)],[])).
% 0.47/0.55 tff(357,plain,
% 0.47/0.55 (![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)))),
% 0.47/0.55 inference(quant_intro,[status(thm)],[356])).
% 0.47/0.55 tff(358,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')).
% 0.47/0.55 tff(359,plain,
% 0.47/0.55 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.47/0.55 inference(modus_ponens,[status(thm)],[358, 357])).
% 0.47/0.55 tff(360,plain,
% 0.47/0.55 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.47/0.55 inference(modus_ponens,[status(thm)],[359, 355])).
% 0.47/0.55 tff(361,plain,(
% 0.47/0.55 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.47/0.55 inference(skolemize,[status(sab)],[360])).
% 0.47/0.55 tff(362,plain,
% 0.47/0.55 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.47/0.55 inference(modus_ponens,[status(thm)],[361, 354])).
% 0.47/0.55 tff(363,plain,
% 0.47/0.55 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_3)))),
% 0.47/0.55 inference(rewrite,[status(thm)],[])).
% 0.47/0.55 tff(364,plain,
% 0.47/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_3)))),
% 0.47/0.55 inference(quant_inst,[status(thm)],[])).
% 0.47/0.55 tff(365,plain,
% 0.47/0.55 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_3))),
% 0.47/0.55 inference(modus_ponens,[status(thm)],[364, 363])).
% 0.47/0.55 tff(366,plain,
% 0.47/0.55 ($false),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[365, 128, 362, 352, 139])).
% 0.47/0.55 tff(367,plain,((~product(e_2, e_2, e_3)) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.55 tff(368,plain,
% 0.47/0.55 (~product(e_2, e_2, e_3)),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[367, 351])).
% 0.47/0.55 tff(369,assumption,(product(e_2, e_2, e_1)), introduced(assumption)).
% 0.47/0.55 tff(370,assumption,(~product(e_2, e_1, e_1)), introduced(assumption)).
% 0.47/0.55 tff(371,plain,
% 0.47/0.55 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_2)))),
% 0.47/0.55 inference(rewrite,[status(thm)],[])).
% 0.47/0.55 tff(372,plain,
% 0.47/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_2)))),
% 0.47/0.55 inference(quant_inst,[status(thm)],[])).
% 0.47/0.55 tff(373,plain,
% 0.47/0.55 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_2, e_1, e_1) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_2))),
% 0.47/0.55 inference(modus_ponens,[status(thm)],[372, 371])).
% 0.47/0.55 tff(374,plain,
% 0.47/0.55 ($false),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[373, 105, 1, 370, 369])).
% 0.47/0.55 tff(375,plain,((~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_2)) | product(e_2, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.55 tff(376,plain,
% 0.47/0.55 (~product(e_2, e_2, e_1)),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[375, 341, 1])).
% 0.47/0.55 tff(377,plain,
% 0.47/0.55 (((~![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_2, e_1) | product(e_2, e_2, e_3) | product(e_2, e_2, e_4) | product(e_2, e_2, 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)) | product(e_2, e_2, e_1) | product(e_2, e_2, e_3) | product(e_2, e_2, e_4) | product(e_2, e_2, e_2))),
% 0.47/0.56 inference(rewrite,[status(thm)],[])).
% 0.47/0.56 tff(378,plain,
% 0.47/0.56 (((~group_element(e_2)) | product(e_2, e_2, e_4) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2))) <=> ((~group_element(e_2)) | product(e_2, e_2, e_1) | product(e_2, e_2, e_3) | product(e_2, e_2, e_4) | product(e_2, e_2, e_2))),
% 0.47/0.56 inference(rewrite,[status(thm)],[])).
% 0.47/0.56 tff(379,plain,
% 0.47/0.56 (((~![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_2, e_4) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2)))) <=> ((~![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_2, e_1) | product(e_2, e_2, e_3) | product(e_2, e_2, e_4) | product(e_2, e_2, e_2)))),
% 0.47/0.56 inference(monotonicity,[status(thm)],[378])).
% 0.47/0.56 tff(380,plain,
% 0.47/0.56 (((~![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_2, e_4) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2)))) <=> ((~![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_2, e_1) | product(e_2, e_2, e_3) | product(e_2, e_2, e_4) | product(e_2, e_2, e_2))),
% 0.47/0.56 inference(transitivity,[status(thm)],[379, 377])).
% 0.47/0.56 tff(381,plain,
% 0.47/0.56 ((~![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_2, e_4) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2)))),
% 0.47/0.56 inference(quant_inst,[status(thm)],[])).
% 0.47/0.56 tff(382,plain,
% 0.47/0.56 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_2)) | product(e_2, e_2, e_1) | product(e_2, e_2, e_3) | product(e_2, e_2, e_4) | product(e_2, e_2, e_2)),
% 0.47/0.56 inference(modus_ponens,[status(thm)],[381, 380])).
% 0.47/0.56 tff(383,plain,
% 0.47/0.56 (product(e_2, e_2, e_1) | product(e_2, e_2, e_3) | product(e_2, e_2, e_4) | product(e_2, e_2, e_2)),
% 0.47/0.56 inference(unit_resolution,[status(thm)],[382, 69, 184])).
% 0.47/0.56 tff(384,plain,
% 0.47/0.56 ($false),
% 0.47/0.56 inference(unit_resolution,[status(thm)],[383, 376, 368, 134, 114])).
% 0.47/0.56 tff(385,plain,(product(e_1, e_1, e_2) | (~product(e_1, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.56 tff(386,plain,
% 0.47/0.56 (product(e_1, e_1, e_2)),
% 0.47/0.56 inference(unit_resolution,[status(thm)],[385, 1])).
% 0.47/0.56 tff(387,plain,
% 0.47/0.56 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.47/0.56 inference(rewrite,[status(thm)],[])).
% 0.47/0.56 tff(388,plain,
% 0.47/0.56 ((equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_1, e_2))) <=> (equalish(e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.47/0.56 inference(rewrite,[status(thm)],[])).
% 0.47/0.56 tff(389,plain,
% 0.47/0.56 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_2))))),
% 0.47/0.56 inference(monotonicity,[status(thm)],[388])).
% 0.47/0.56 tff(390,plain,
% 0.47/0.56 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_2)))),
% 0.47/0.56 inference(transitivity,[status(thm)],[389, 387])).
% 0.47/0.56 tff(391,plain,
% 0.47/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_1, e_1, e_2)))),
% 0.47/0.56 inference(quant_inst,[status(thm)],[])).
% 0.47/0.56 tff(392,plain,
% 0.47/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_2, e_2))),
% 0.47/0.56 inference(modus_ponens,[status(thm)],[391, 390])).
% 0.47/0.56 tff(393,plain,
% 0.47/0.56 ($false),
% 0.47/0.56 inference(unit_resolution,[status(thm)],[392, 275, 362, 386, 1])).
% 0.47/0.56 tff(394,plain,(~product(e_1, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.56 tff(395,assumption,(~product(e_1, e_2, e_2)), introduced(assumption)).
% 0.47/0.56 tff(396,plain,
% 0.47/0.56 (product(e_1, e_1, e_2)),
% 0.47/0.56 inference(unit_resolution,[status(thm)],[350, 136])).
% 0.47/0.56 tff(397,assumption,(product(e_1, e_1, e_2)), introduced(assumption)).
% 0.47/0.56 tff(398,plain,
% 0.47/0.56 (((~![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_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.47/0.56 inference(rewrite,[status(thm)],[])).
% 0.47/0.56 tff(399,plain,
% 0.47/0.56 ((~![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_2)) | (~product(e_2, e_1, e_2)))),
% 0.47/0.56 inference(quant_inst,[status(thm)],[])).
% 0.47/0.56 tff(400,plain,
% 0.47/0.56 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_2))),
% 0.47/0.56 inference(modus_ponens,[status(thm)],[399, 398])).
% 0.47/0.56 tff(401,plain,
% 0.47/0.56 ($false),
% 0.47/0.56 inference(unit_resolution,[status(thm)],[400, 128, 125, 397, 137])).
% 0.47/0.56 tff(402,plain,((~product(e_2, e_1, e_2)) | (~product(e_1, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.56 tff(403,plain,
% 0.47/0.56 (~product(e_2, e_1, e_2)),
% 0.47/0.56 inference(unit_resolution,[status(thm)],[402, 396])).
% 0.47/0.56 tff(404,plain,
% 0.47/0.56 (product(e_2, e_1, e_1)),
% 0.47/0.56 inference(unit_resolution,[status(thm)],[348, 403, 136])).
% 0.47/0.56 tff(405,plain,
% 0.47/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1)) | product(e_1, e_2, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1)) | product(e_1, e_2, e_2))),
% 0.47/0.56 inference(rewrite,[status(thm)],[])).
% 0.47/0.56 tff(406,plain,
% 0.47/0.56 ((product(e_1, e_2, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1))) <=> ((~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1)) | product(e_1, e_2, e_2))),
% 0.47/0.56 inference(rewrite,[status(thm)],[])).
% 0.47/0.56 tff(407,plain,
% 0.47/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1)) | product(e_1, e_2, e_2)))),
% 0.47/0.56 inference(monotonicity,[status(thm)],[406])).
% 0.47/0.56 tff(408,plain,
% 0.47/0.56 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1)) | product(e_1, e_2, e_2))),
% 0.47/0.56 inference(transitivity,[status(thm)],[407, 405])).
% 0.47/0.56 tff(409,plain,
% 0.47/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1)))),
% 0.47/0.56 inference(quant_inst,[status(thm)],[])).
% 0.47/0.56 tff(410,plain,
% 0.47/0.56 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1)) | product(e_1, e_2, e_2)),
% 0.47/0.56 inference(modus_ponens,[status(thm)],[409, 408])).
% 0.47/0.56 tff(411,plain,
% 0.47/0.56 ($false),
% 0.47/0.56 inference(unit_resolution,[status(thm)],[410, 105, 396, 395, 404])).
% 0.47/0.56 tff(412,plain,(product(e_2, e_1, e_3) | product(e_1, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.56 tff(413,plain,
% 0.47/0.56 (product(e_2, e_1, e_3)),
% 0.47/0.56 inference(unit_resolution,[status(thm)],[412, 395])).
% 0.47/0.56 tff(414,plain,
% 0.47/0.56 (greater(e_3, e_2) <=> greater(e_3, e_2)),
% 0.47/0.56 inference(rewrite,[status(thm)],[])).
% 0.47/0.56 tff(415,axiom,(greater(e_3, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_greater_e_2')).
% 0.47/0.56 tff(416,plain,
% 0.47/0.56 (greater(e_3, e_2)),
% 0.47/0.56 inference(modus_ponens,[status(thm)],[415, 414])).
% 0.47/0.56 tff(417,plain,
% 0.47/0.56 (((~![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)))),
% 0.47/0.56 inference(rewrite,[status(thm)],[])).
% 0.47/0.56 tff(418,plain,
% 0.47/0.56 (((~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)))),
% 0.47/0.56 inference(rewrite,[status(thm)],[])).
% 0.47/0.56 tff(419,plain,
% 0.47/0.56 (((~![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))))),
% 0.47/0.56 inference(monotonicity,[status(thm)],[418])).
% 0.47/0.56 tff(420,plain,
% 0.47/0.56 (((~![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)))),
% 0.47/0.56 inference(transitivity,[status(thm)],[419, 417])).
% 0.47/0.56 tff(421,plain,
% 0.47/0.56 ((~![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)))),
% 0.47/0.56 inference(quant_inst,[status(thm)],[])).
% 0.47/0.56 tff(422,plain,
% 0.47/0.56 ((~![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))),
% 0.47/0.56 inference(modus_ponens,[status(thm)],[421, 420])).
% 0.47/0.56 tff(423,plain,
% 0.47/0.56 ((~cycle(e_2, e_0)) | (~product(e_2, e_1, e_3))),
% 0.47/0.56 inference(unit_resolution,[status(thm)],[422, 416, 13])).
% 0.47/0.56 tff(424,plain,
% 0.47/0.56 (~cycle(e_2, e_0)),
% 0.47/0.56 inference(unit_resolution,[status(thm)],[423, 413])).
% 0.47/0.56 tff(425,assumption,(~cycle(e_2, e_0)), introduced(assumption)).
% 0.47/0.56 tff(426,assumption,(cycle(e_2, e_3)), introduced(assumption)).
% 0.47/0.56 tff(427,plain,
% 0.47/0.56 (^[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))))),
% 0.47/0.56 inference(bind,[status(th)],[])).
% 0.47/0.56 tff(428,plain,
% 0.47/0.56 (![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)))),
% 0.47/0.56 inference(quant_intro,[status(thm)],[427])).
% 0.47/0.56 tff(429,plain,
% 0.47/0.56 (![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)))),
% 0.47/0.56 inference(rewrite,[status(thm)],[])).
% 0.47/0.56 tff(430,plain,
% 0.47/0.56 (^[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)))))),
% 0.47/0.56 inference(bind,[status(th)],[])).
% 0.47/0.56 tff(431,plain,
% 0.47/0.56 (![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)))),
% 0.47/0.56 inference(quant_intro,[status(thm)],[430])).
% 0.47/0.56 tff(432,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')).
% 0.47/0.56 tff(433,plain,
% 0.47/0.56 (![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)))),
% 0.47/0.56 inference(modus_ponens,[status(thm)],[432, 431])).
% 0.47/0.56 tff(434,plain,
% 0.47/0.56 (![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)))),
% 0.47/0.56 inference(modus_ponens,[status(thm)],[433, 429])).
% 0.47/0.56 tff(435,plain,(
% 0.47/0.56 ![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)))),
% 0.47/0.56 inference(skolemize,[status(sab)],[434])).
% 0.47/0.56 tff(436,plain,
% 0.47/0.56 (![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)))),
% 0.47/0.56 inference(modus_ponens,[status(thm)],[435, 428])).
% 0.47/0.56 tff(437,plain,
% 0.47/0.56 (cycle(e_4, e_0) <=> cycle(e_4, e_0)),
% 0.47/0.56 inference(rewrite,[status(thm)],[])).
% 0.47/0.56 tff(438,axiom,(cycle(e_4, e_0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cycle3')).
% 0.47/0.56 tff(439,plain,
% 0.47/0.56 (cycle(e_4, e_0)),
% 0.47/0.56 inference(modus_ponens,[status(thm)],[438, 437])).
% 0.47/0.56 tff(440,plain,
% 0.47/0.56 (next(e_3, e_4) <=> next(e_3, e_4)),
% 0.47/0.56 inference(rewrite,[status(thm)],[])).
% 0.47/0.56 tff(441,axiom,(next(e_3, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_then_e_4')).
% 0.47/0.56 tff(442,plain,
% 0.47/0.56 (next(e_3, e_4)),
% 0.47/0.56 inference(modus_ponens,[status(thm)],[441, 440])).
% 0.47/0.56 tff(443,plain,
% 0.47/0.56 (((~![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)))),
% 0.47/0.56 inference(rewrite,[status(thm)],[])).
% 0.47/0.56 tff(444,plain,
% 0.47/0.56 (((~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)))),
% 0.47/0.56 inference(rewrite,[status(thm)],[])).
% 0.47/0.56 tff(445,plain,
% 0.47/0.56 (((~![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))))),
% 0.47/0.56 inference(monotonicity,[status(thm)],[444])).
% 0.47/0.56 tff(446,plain,
% 0.47/0.56 (((~![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)))),
% 0.47/0.56 inference(transitivity,[status(thm)],[445, 443])).
% 0.47/0.56 tff(447,plain,
% 0.47/0.56 ((~![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)))),
% 0.47/0.56 inference(quant_inst,[status(thm)],[])).
% 0.47/0.56 tff(448,plain,
% 0.47/0.56 ((~![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))),
% 0.47/0.56 inference(modus_ponens,[status(thm)],[447, 446])).
% 0.47/0.56 tff(449,plain,
% 0.47/0.56 ((~cycle(e_3, e_0)) | (~cycle(e_2, e_3))),
% 0.47/0.56 inference(unit_resolution,[status(thm)],[448, 442, 87, 416, 439, 436])).
% 0.47/0.57 tff(450,plain,
% 0.47/0.57 (~cycle(e_3, e_0)),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[449, 426])).
% 0.47/0.57 tff(451,plain,
% 0.47/0.57 (^[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))))),
% 0.47/0.57 inference(bind,[status(th)],[])).
% 0.47/0.57 tff(452,plain,
% 0.47/0.57 (![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)))),
% 0.47/0.57 inference(quant_intro,[status(thm)],[451])).
% 0.47/0.57 tff(453,plain,
% 0.47/0.57 (![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)))),
% 0.47/0.57 inference(rewrite,[status(thm)],[])).
% 0.47/0.57 tff(454,plain,
% 0.47/0.57 (^[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)))))),
% 0.47/0.57 inference(bind,[status(th)],[])).
% 0.47/0.57 tff(455,plain,
% 0.47/0.57 (![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)))),
% 0.47/0.57 inference(quant_intro,[status(thm)],[454])).
% 0.47/0.57 tff(456,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')).
% 0.47/0.57 tff(457,plain,
% 0.47/0.57 (![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)))),
% 0.47/0.57 inference(modus_ponens,[status(thm)],[456, 455])).
% 0.47/0.57 tff(458,plain,
% 0.47/0.57 (![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)))),
% 0.47/0.57 inference(modus_ponens,[status(thm)],[457, 453])).
% 0.47/0.57 tff(459,plain,(
% 0.47/0.57 ![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)))),
% 0.47/0.57 inference(skolemize,[status(sab)],[458])).
% 0.47/0.57 tff(460,plain,
% 0.47/0.57 (![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)))),
% 0.47/0.57 inference(modus_ponens,[status(thm)],[459, 452])).
% 0.47/0.57 tff(461,plain,
% 0.47/0.57 (((~![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_3, e_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(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_3, e_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_1)))),
% 0.47/0.57 inference(rewrite,[status(thm)],[])).
% 0.47/0.57 tff(462,plain,
% 0.47/0.57 (((~cycle(e_2, e_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_1))) <=> (equalish(e_3, e_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_1)))),
% 0.47/0.57 inference(rewrite,[status(thm)],[])).
% 0.47/0.57 tff(463,plain,
% 0.47/0.57 (((~![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_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, 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_3, e_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_1))))),
% 0.47/0.57 inference(monotonicity,[status(thm)],[462])).
% 0.47/0.57 tff(464,plain,
% 0.47/0.57 (((~![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_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, 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_3, e_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_1)))),
% 0.47/0.57 inference(transitivity,[status(thm)],[463, 461])).
% 0.47/0.57 tff(465,plain,
% 0.47/0.57 ((~![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_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_1)))),
% 0.47/0.57 inference(quant_inst,[status(thm)],[])).
% 0.47/0.57 tff(466,plain,
% 0.47/0.57 ((~![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_3, e_2) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_1))),
% 0.47/0.57 inference(modus_ponens,[status(thm)],[465, 464])).
% 0.47/0.57 tff(467,plain,
% 0.47/0.57 (~cycle(e_3, e_1)),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[466, 213, 44, 87, 460, 285, 426])).
% 0.47/0.57 tff(468,plain,
% 0.47/0.57 ((~equalish(e_3, e_4)) <=> (~equalish(e_3, e_4))),
% 0.47/0.57 inference(rewrite,[status(thm)],[])).
% 0.47/0.57 tff(469,axiom,(~equalish(e_3, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_4')).
% 0.47/0.57 tff(470,plain,
% 0.47/0.57 (~equalish(e_3, e_4)),
% 0.47/0.57 inference(modus_ponens,[status(thm)],[469, 468])).
% 0.47/0.57 tff(471,plain,
% 0.47/0.57 (((~![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_3, e_4) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_3)))) <=> ((~![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_3, e_4) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_3)))),
% 0.47/0.57 inference(rewrite,[status(thm)],[])).
% 0.47/0.57 tff(472,plain,
% 0.47/0.57 (((~cycle(e_2, e_3)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~greater(e_3, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_3))) <=> (equalish(e_3, e_4) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_3)))),
% 0.47/0.57 inference(rewrite,[status(thm)],[])).
% 0.47/0.57 tff(473,plain,
% 0.47/0.57 (((~![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_3)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~greater(e_3, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_3)))) <=> ((~![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_3, e_4) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_3))))),
% 0.47/0.57 inference(monotonicity,[status(thm)],[472])).
% 0.47/0.57 tff(474,plain,
% 0.47/0.57 (((~![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_3)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~greater(e_3, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_3)))) <=> ((~![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_3, e_4) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_3)))),
% 0.47/0.57 inference(transitivity,[status(thm)],[473, 471])).
% 0.47/0.57 tff(475,plain,
% 0.47/0.57 ((~![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_3)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~greater(e_3, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_3)))),
% 0.47/0.57 inference(quant_inst,[status(thm)],[])).
% 0.47/0.57 tff(476,plain,
% 0.47/0.57 ((~![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_3, e_4) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_2, e_3)) | (~cycle(e_3, e_3))),
% 0.47/0.57 inference(modus_ponens,[status(thm)],[475, 474])).
% 0.47/0.57 tff(477,plain,
% 0.47/0.57 (~cycle(e_3, e_3)),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[476, 44, 442, 87, 460, 470, 426])).
% 0.47/0.57 tff(478,assumption,(cycle(e_3, e_2)), introduced(assumption)).
% 0.47/0.57 tff(479,plain,
% 0.47/0.57 (next(e_0, e_1) <=> next(e_0, e_1)),
% 0.47/0.57 inference(rewrite,[status(thm)],[])).
% 0.47/0.57 tff(480,axiom,(next(e_0, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_0_then_e_1')).
% 0.47/0.57 tff(481,plain,
% 0.47/0.57 (next(e_0, e_1)),
% 0.47/0.57 inference(modus_ponens,[status(thm)],[480, 479])).
% 0.47/0.57 tff(482,plain,
% 0.47/0.57 (((~![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)))),
% 0.47/0.57 inference(rewrite,[status(thm)],[])).
% 0.47/0.57 tff(483,plain,
% 0.47/0.57 (((~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)))),
% 0.47/0.57 inference(rewrite,[status(thm)],[])).
% 0.47/0.57 tff(484,plain,
% 0.47/0.57 (((~![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))))),
% 0.47/0.57 inference(monotonicity,[status(thm)],[483])).
% 0.47/0.57 tff(485,plain,
% 0.47/0.57 (((~![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)))),
% 0.47/0.57 inference(transitivity,[status(thm)],[484, 482])).
% 0.47/0.57 tff(486,plain,
% 0.47/0.57 ((~![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)))),
% 0.47/0.57 inference(quant_inst,[status(thm)],[])).
% 0.47/0.57 tff(487,plain,
% 0.47/0.57 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_1) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~next(e_0, e_1))),
% 0.47/0.57 inference(modus_ponens,[status(thm)],[486, 485])).
% 0.47/0.57 tff(488,plain,
% 0.47/0.57 ($false),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[487, 481, 442, 57, 439, 460, 128, 478])).
% 0.47/0.57 tff(489,plain,(~cycle(e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.57 tff(490,plain,
% 0.47/0.57 (group_element(e_3) <=> group_element(e_3)),
% 0.47/0.57 inference(rewrite,[status(thm)],[])).
% 0.47/0.57 tff(491,axiom,(group_element(e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_3')).
% 0.47/0.57 tff(492,plain,
% 0.47/0.57 (group_element(e_3)),
% 0.47/0.57 inference(modus_ponens,[status(thm)],[491, 490])).
% 0.47/0.57 tff(493,plain,
% 0.47/0.57 (((~![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)))),
% 0.47/0.57 inference(rewrite,[status(thm)],[])).
% 0.47/0.57 tff(494,plain,
% 0.47/0.57 ((~![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)))),
% 0.47/0.57 inference(quant_inst,[status(thm)],[])).
% 0.47/0.57 tff(495,plain,
% 0.47/0.57 ((~![X: $i] : (cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0) | (~group_element(e_3))),
% 0.47/0.57 inference(modus_ponens,[status(thm)],[494, 493])).
% 0.47/0.57 tff(496,plain,
% 0.47/0.57 (cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0)),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[495, 79, 492])).
% 0.47/0.57 tff(497,plain,
% 0.47/0.57 (cycle(e_3, e_3) | cycle(e_3, e_1) | cycle(e_3, e_0)),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[496, 489])).
% 0.47/0.57 tff(498,plain,
% 0.47/0.57 ($false),
% 0.47/0.57 inference(unit_resolution,[status(thm)],[497, 477, 467, 450])).
% 0.47/0.57 tff(499,plain,(~cycle(e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.57 tff(500,assumption,(cycle(e_3, e_0)), introduced(assumption)).
% 0.47/0.57 tff(501,plain,
% 0.47/0.58 (((~![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)))),
% 0.47/0.58 inference(rewrite,[status(thm)],[])).
% 0.47/0.58 tff(502,plain,
% 0.47/0.58 (((~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)))),
% 0.47/0.58 inference(rewrite,[status(thm)],[])).
% 0.47/0.58 tff(503,plain,
% 0.47/0.58 (((~![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))))),
% 0.47/0.58 inference(monotonicity,[status(thm)],[502])).
% 0.47/0.58 tff(504,plain,
% 0.47/0.58 (((~![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)))),
% 0.47/0.58 inference(transitivity,[status(thm)],[503, 501])).
% 0.47/0.58 tff(505,plain,
% 0.47/0.58 ((~![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)))),
% 0.47/0.58 inference(quant_inst,[status(thm)],[])).
% 0.47/0.58 tff(506,plain,
% 0.47/0.58 ((~![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))),
% 0.47/0.58 inference(modus_ponens,[status(thm)],[505, 504])).
% 0.47/0.58 tff(507,plain,
% 0.47/0.58 ((~cycle(e_3, e_0)) | (~cycle(e_2, e_1))),
% 0.47/0.58 inference(unit_resolution,[status(thm)],[506, 442, 41, 416, 439, 436])).
% 0.47/0.58 tff(508,plain,
% 0.47/0.58 (~cycle(e_2, e_1)),
% 0.47/0.58 inference(unit_resolution,[status(thm)],[507, 500])).
% 0.47/0.58 tff(509,plain,
% 0.47/0.58 (((~![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)))),
% 0.47/0.58 inference(rewrite,[status(thm)],[])).
% 0.47/0.58 tff(510,plain,
% 0.47/0.58 (((~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)))),
% 0.47/0.58 inference(rewrite,[status(thm)],[])).
% 0.47/0.58 tff(511,plain,
% 0.47/0.58 (((~![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))))),
% 0.47/0.58 inference(monotonicity,[status(thm)],[510])).
% 0.47/0.58 tff(512,plain,
% 0.47/0.58 (((~![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)))),
% 0.47/0.58 inference(transitivity,[status(thm)],[511, 509])).
% 0.47/0.58 tff(513,plain,
% 0.47/0.58 ((~![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)))),
% 0.47/0.58 inference(quant_inst,[status(thm)],[])).
% 0.47/0.58 tff(514,plain,
% 0.47/0.58 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_4, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2))),
% 0.47/0.58 inference(modus_ponens,[status(thm)],[513, 512])).
% 0.47/0.58 tff(515,plain,
% 0.47/0.58 ((~cycle(e_3, e_0)) | (~cycle(e_2, e_2))),
% 0.47/0.58 inference(unit_resolution,[status(thm)],[514, 442, 57, 416, 439, 436])).
% 0.47/0.58 tff(516,plain,
% 0.47/0.58 (~cycle(e_2, e_2)),
% 0.47/0.58 inference(unit_resolution,[status(thm)],[515, 500])).
% 0.47/0.58 tff(517,plain,
% 0.47/0.58 ($false),
% 0.47/0.58 inference(unit_resolution,[status(thm)],[83, 516, 508, 499, 425])).
% 0.47/0.58 tff(518,plain,((~cycle(e_3, e_0)) | cycle(e_2, e_0)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.58 tff(519,plain,
% 0.47/0.58 (~cycle(e_3, e_0)),
% 0.47/0.58 inference(unit_resolution,[status(thm)],[518, 424])).
% 0.47/0.58 tff(520,assumption,(~cycle(e_3, e_0)), introduced(assumption)).
% 0.47/0.58 tff(521,plain,
% 0.47/0.58 (((~![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)))),
% 0.47/0.58 inference(rewrite,[status(thm)],[])).
% 0.47/0.58 tff(522,plain,
% 0.47/0.58 (((~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)))),
% 0.47/0.58 inference(rewrite,[status(thm)],[])).
% 0.47/0.58 tff(523,plain,
% 0.47/0.58 (((~![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))))),
% 0.47/0.58 inference(monotonicity,[status(thm)],[522])).
% 0.47/0.58 tff(524,plain,
% 0.47/0.58 (((~![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)))),
% 0.47/0.58 inference(transitivity,[status(thm)],[523, 521])).
% 0.47/0.58 tff(525,plain,
% 0.47/0.58 ((~![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)))),
% 0.47/0.58 inference(quant_inst,[status(thm)],[])).
% 0.47/0.58 tff(526,plain,
% 0.47/0.58 ((~![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))),
% 0.47/0.58 inference(modus_ponens,[status(thm)],[525, 524])).
% 0.47/0.58 tff(527,plain,
% 0.47/0.58 (~cycle(e_3, e_1)),
% 0.47/0.58 inference(unit_resolution,[status(thm)],[526, 213, 44, 41, 460, 275, 25])).
% 0.47/0.58 tff(528,plain,
% 0.47/0.58 ((~equalish(e_1, e_4)) <=> (~equalish(e_1, e_4))),
% 0.47/0.58 inference(rewrite,[status(thm)],[])).
% 0.47/0.58 tff(529,axiom,(~equalish(e_1, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_4')).
% 0.47/0.58 tff(530,plain,
% 0.47/0.58 (~equalish(e_1, e_4)),
% 0.47/0.58 inference(modus_ponens,[status(thm)],[529, 528])).
% 0.47/0.58 tff(531,plain,
% 0.47/0.58 (((~![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_4) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~next(e_3, e_4)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_3)))) <=> ((~![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_4) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~next(e_3, e_4)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_3)))),
% 0.47/0.58 inference(rewrite,[status(thm)],[])).
% 0.47/0.58 tff(532,plain,
% 0.47/0.58 (((~cycle(e_2, e_1)) | equalish(e_1, e_4) | (~next(e_3, e_4)) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_3))) <=> (equalish(e_1, e_4) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~next(e_3, e_4)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_3)))),
% 0.47/0.58 inference(rewrite,[status(thm)],[])).
% 0.47/0.58 tff(533,plain,
% 0.47/0.58 (((~![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_4) | (~next(e_3, e_4)) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_3)))) <=> ((~![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_4) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~next(e_3, e_4)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_3))))),
% 0.47/0.58 inference(monotonicity,[status(thm)],[532])).
% 0.47/0.58 tff(534,plain,
% 0.47/0.58 (((~![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_4) | (~next(e_3, e_4)) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_3)))) <=> ((~![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_4) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~next(e_3, e_4)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_3)))),
% 0.47/0.58 inference(transitivity,[status(thm)],[533, 531])).
% 0.47/0.58 tff(535,plain,
% 0.47/0.58 ((~![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_4) | (~next(e_3, e_4)) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_3)))),
% 0.47/0.58 inference(quant_inst,[status(thm)],[])).
% 0.47/0.58 tff(536,plain,
% 0.47/0.58 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_1, e_4) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~next(e_3, e_4)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_3))),
% 0.47/0.58 inference(modus_ponens,[status(thm)],[535, 534])).
% 0.47/0.58 tff(537,plain,
% 0.47/0.58 (~cycle(e_3, e_3)),
% 0.47/0.58 inference(unit_resolution,[status(thm)],[536, 44, 442, 41, 460, 530, 25])).
% 0.47/0.58 tff(538,plain,
% 0.47/0.58 ($false),
% 0.47/0.58 inference(unit_resolution,[status(thm)],[497, 537, 527, 520])).
% 0.47/0.58 tff(539,plain,((~cycle(e_2, e_1)) | cycle(e_3, e_0)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.58 tff(540,plain,
% 0.47/0.58 (~cycle(e_2, e_1)),
% 0.47/0.58 inference(unit_resolution,[status(thm)],[539, 519])).
% 0.47/0.58 tff(541,plain,
% 0.47/0.58 (cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0)),
% 0.47/0.58 inference(unit_resolution,[status(thm)],[83, 499])).
% 0.47/0.58 tff(542,plain,
% 0.47/0.58 (cycle(e_2, e_2)),
% 0.47/0.58 inference(unit_resolution,[status(thm)],[541, 540, 424])).
% 0.47/0.58 tff(543,plain,
% 0.47/0.58 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.47/0.58 inference(rewrite,[status(thm)],[])).
% 0.47/0.58 tff(544,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.47/0.58 tff(545,plain,
% 0.47/0.58 (~equalish(e_1, e_3)),
% 0.47/0.58 inference(modus_ponens,[status(thm)],[544, 543])).
% 0.47/0.58 tff(546,plain,
% 0.47/0.58 (((~![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_1, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_1)))) <=> ((~![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_1, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_1)))),
% 0.47/0.58 inference(rewrite,[status(thm)],[])).
% 0.47/0.58 tff(547,plain,
% 0.47/0.58 (((~greater(e_2, e_0)) | (~cycle(e_2, e_2)) | equalish(e_1, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_1))) <=> (equalish(e_1, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_1)))),
% 0.47/0.58 inference(rewrite,[status(thm)],[])).
% 0.47/0.58 tff(548,plain,
% 0.47/0.58 (((~![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_1, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_1)))) <=> ((~![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_1, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_1))))),
% 0.47/0.58 inference(monotonicity,[status(thm)],[547])).
% 0.47/0.58 tff(549,plain,
% 0.47/0.58 (((~![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_1, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_1)))) <=> ((~![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_1, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_1)))),
% 0.47/0.58 inference(transitivity,[status(thm)],[548, 546])).
% 0.47/0.58 tff(550,plain,
% 0.47/0.58 ((~![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_1, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_1)))),
% 0.47/0.58 inference(quant_inst,[status(thm)],[])).
% 0.47/0.58 tff(551,plain,
% 0.47/0.58 ((~![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_1, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~product(e_2, e_1, e_1))),
% 0.47/0.59 inference(modus_ponens,[status(thm)],[550, 549])).
% 0.47/0.59 tff(552,plain,
% 0.47/0.59 (~product(e_2, e_1, e_1)),
% 0.47/0.59 inference(unit_resolution,[status(thm)],[551, 44, 57, 38, 545, 542])).
% 0.47/0.59 tff(553,assumption,(product(e_4, e_1, e_3)), introduced(assumption)).
% 0.47/0.59 tff(554,plain,
% 0.47/0.59 ((~equalish(e_2, e_4)) <=> (~equalish(e_2, e_4))),
% 0.47/0.59 inference(rewrite,[status(thm)],[])).
% 0.47/0.59 tff(555,axiom,(~equalish(e_2, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_4')).
% 0.47/0.59 tff(556,plain,
% 0.47/0.59 (~equalish(e_2, e_4)),
% 0.47/0.59 inference(modus_ponens,[status(thm)],[555, 554])).
% 0.47/0.59 tff(557,plain,
% 0.47/0.59 (((~![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_1, e_3)) | (~product(e_2, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_4) | (~product(e_4, e_1, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.47/0.59 inference(rewrite,[status(thm)],[])).
% 0.47/0.59 tff(558,plain,
% 0.47/0.59 ((~![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_1, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.47/0.59 inference(quant_inst,[status(thm)],[])).
% 0.47/0.59 tff(559,plain,
% 0.47/0.59 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_4) | (~product(e_4, e_1, e_3)) | (~product(e_2, e_1, e_3))),
% 0.47/0.59 inference(modus_ponens,[status(thm)],[558, 557])).
% 0.47/0.59 tff(560,plain,
% 0.47/0.59 ($false),
% 0.47/0.59 inference(unit_resolution,[status(thm)],[559, 556, 125, 553, 352])).
% 0.47/0.59 tff(561,plain,((~product(e_2, e_1, e_3)) | (~product(e_4, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.59 tff(562,plain,
% 0.47/0.59 (~product(e_4, e_1, e_3)),
% 0.47/0.59 inference(unit_resolution,[status(thm)],[561, 413])).
% 0.47/0.59 tff(563,plain,
% 0.47/0.59 (((~![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_4) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~next(e_3, e_4)) | (~cycle(e_2, e_2)) | (~cycle(e_3, e_3)))) <=> ((~![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_4) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~next(e_3, e_4)) | (~cycle(e_2, e_2)) | (~cycle(e_3, e_3)))),
% 0.47/0.59 inference(rewrite,[status(thm)],[])).
% 0.47/0.59 tff(564,plain,
% 0.47/0.59 (((~cycle(e_2, e_2)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_3))) <=> (equalish(e_2, e_4) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~next(e_3, e_4)) | (~cycle(e_2, e_2)) | (~cycle(e_3, e_3)))),
% 0.47/0.59 inference(rewrite,[status(thm)],[])).
% 0.47/0.59 tff(565,plain,
% 0.47/0.59 (((~![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_2)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_3)))) <=> ((~![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_4) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~next(e_3, e_4)) | (~cycle(e_2, e_2)) | (~cycle(e_3, e_3))))),
% 0.47/0.59 inference(monotonicity,[status(thm)],[564])).
% 0.47/0.59 tff(566,plain,
% 0.47/0.59 (((~![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_2)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_3)))) <=> ((~![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_4) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~next(e_3, e_4)) | (~cycle(e_2, e_2)) | (~cycle(e_3, e_3)))),
% 0.47/0.59 inference(transitivity,[status(thm)],[565, 563])).
% 0.47/0.59 tff(567,plain,
% 0.47/0.59 ((~![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_2)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_3)))),
% 0.47/0.59 inference(quant_inst,[status(thm)],[])).
% 0.47/0.59 tff(568,plain,
% 0.47/0.59 ((~![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_4) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~next(e_3, e_4)) | (~cycle(e_2, e_2)) | (~cycle(e_3, e_3))),
% 0.47/0.59 inference(modus_ponens,[status(thm)],[567, 566])).
% 0.47/0.59 tff(569,plain,
% 0.47/0.59 (~cycle(e_3, e_3)),
% 0.47/0.59 inference(unit_resolution,[status(thm)],[568, 44, 442, 57, 460, 556, 542])).
% 0.47/0.59 tff(570,plain,
% 0.47/0.59 (cycle(e_3, e_1)),
% 0.47/0.59 inference(unit_resolution,[status(thm)],[497, 569, 519])).
% 0.47/0.59 tff(571,plain,
% 0.47/0.59 (((~![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_1, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_1)))) <=> ((~![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_1, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.47/0.59 inference(rewrite,[status(thm)],[])).
% 0.47/0.59 tff(572,plain,
% 0.47/0.59 (((~greater(e_1, e_0)) | (~cycle(e_3, e_1)) | equalish(e_1, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_1))) <=> (equalish(e_1, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.47/0.59 inference(rewrite,[status(thm)],[])).
% 0.47/0.59 tff(573,plain,
% 0.47/0.59 (((~![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_1, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_1)))) <=> ((~![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_1, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_1))))),
% 0.47/0.59 inference(monotonicity,[status(thm)],[572])).
% 0.47/0.59 tff(574,plain,
% 0.47/0.59 (((~![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_1, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_1)))) <=> ((~![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_1, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.47/0.59 inference(transitivity,[status(thm)],[573, 571])).
% 0.47/0.59 tff(575,plain,
% 0.47/0.59 ((~![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_1, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_1)))),
% 0.47/0.59 inference(quant_inst,[status(thm)],[])).
% 0.47/0.59 tff(576,plain,
% 0.47/0.59 ((~![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_1, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_1))),
% 0.47/0.59 inference(modus_ponens,[status(thm)],[575, 574])).
% 0.47/0.59 tff(577,plain,
% 0.47/0.59 (~product(e_3, e_1, e_1)),
% 0.47/0.59 inference(unit_resolution,[status(thm)],[576, 442, 41, 38, 530, 570])).
% 0.47/0.59 tff(578,assumption,(product(e_3, e_1, e_2)), introduced(assumption)).
% 0.47/0.59 tff(579,assumption,(cycle(e_3, e_1)), introduced(assumption)).
% 0.47/0.59 tff(580,plain,
% 0.47/0.59 (((~![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)))),
% 0.47/0.59 inference(rewrite,[status(thm)],[])).
% 0.47/0.59 tff(581,plain,
% 0.47/0.59 (((~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)))),
% 0.47/0.59 inference(rewrite,[status(thm)],[])).
% 0.47/0.59 tff(582,plain,
% 0.47/0.59 (((~![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))))),
% 0.47/0.59 inference(monotonicity,[status(thm)],[581])).
% 0.47/0.59 tff(583,plain,
% 0.47/0.59 (((~![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)))),
% 0.47/0.59 inference(transitivity,[status(thm)],[582, 580])).
% 0.47/0.59 tff(584,plain,
% 0.47/0.59 ((~![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)))),
% 0.47/0.59 inference(quant_inst,[status(thm)],[])).
% 0.47/0.59 tff(585,plain,
% 0.47/0.59 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_2))),
% 0.47/0.59 inference(modus_ponens,[status(thm)],[584, 583])).
% 0.47/0.59 tff(586,plain,
% 0.47/0.59 ($false),
% 0.47/0.59 inference(unit_resolution,[status(thm)],[585, 442, 41, 38, 556, 579, 578])).
% 0.47/0.59 tff(587,plain,((~cycle(e_3, e_1)) | (~product(e_3, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.59 tff(588,plain,
% 0.47/0.59 (~product(e_3, e_1, e_2)),
% 0.47/0.59 inference(unit_resolution,[status(thm)],[587, 570])).
% 0.47/0.59 tff(589,plain,
% 0.47/0.59 (((~![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_3, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_3)))) <=> ((~![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_3, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_3)))),
% 0.47/0.59 inference(rewrite,[status(thm)],[])).
% 0.47/0.59 tff(590,plain,
% 0.47/0.59 (((~greater(e_1, e_0)) | (~cycle(e_3, e_1)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_3))) <=> (equalish(e_3, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_3)))),
% 0.47/0.59 inference(rewrite,[status(thm)],[])).
% 0.47/0.59 tff(591,plain,
% 0.47/0.59 (((~![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_3, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_3)))) <=> ((~![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_3, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_3))))),
% 0.47/0.59 inference(monotonicity,[status(thm)],[590])).
% 0.47/0.59 tff(592,plain,
% 0.47/0.59 (((~![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_3, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_3)))) <=> ((~![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_3, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_3)))),
% 0.47/0.59 inference(transitivity,[status(thm)],[591, 589])).
% 0.47/0.59 tff(593,plain,
% 0.47/0.59 ((~![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_3, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_3)))),
% 0.47/0.59 inference(quant_inst,[status(thm)],[])).
% 0.47/0.59 tff(594,plain,
% 0.47/0.59 ((~![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_3, e_4) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~product(e_3, e_1, e_3))),
% 0.47/0.59 inference(modus_ponens,[status(thm)],[593, 592])).
% 0.47/0.59 tff(595,plain,
% 0.47/0.59 (~product(e_3, e_1, e_3)),
% 0.47/0.59 inference(unit_resolution,[status(thm)],[594, 442, 41, 38, 470, 570])).
% 0.47/0.59 tff(596,assumption,(~product(e_3, e_1, e_3)), introduced(assumption)).
% 0.47/0.59 tff(597,assumption,(~product(e_3, e_1, e_1)), introduced(assumption)).
% 0.47/0.59 tff(598,assumption,(~product(e_3, e_1, e_2)), introduced(assumption)).
% 0.47/0.59 tff(599,assumption,(~product(e_3, e_1, e_4)), introduced(assumption)).
% 0.47/0.59 tff(600,plain,
% 0.47/0.59 (((~![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_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1))) <=> ((~![Y: $i, X: $i] : ((~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_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1))),
% 0.47/0.59 inference(rewrite,[status(thm)],[])).
% 0.47/0.59 tff(601,plain,
% 0.47/0.59 (((~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1))) <=> ((~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1))),
% 0.47/0.59 inference(rewrite,[status(thm)],[])).
% 0.47/0.59 tff(602,plain,
% 0.47/0.59 (((~![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_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~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_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1)))),
% 0.47/0.59 inference(monotonicity,[status(thm)],[601])).
% 0.47/0.59 tff(603,plain,
% 0.47/0.59 (((~![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_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~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_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1))),
% 0.47/0.60 inference(transitivity,[status(thm)],[602, 600])).
% 0.47/0.60 tff(604,plain,
% 0.47/0.60 ((~![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_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)))),
% 0.47/0.60 inference(quant_inst,[status(thm)],[])).
% 0.47/0.60 tff(605,plain,
% 0.47/0.60 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1)),
% 0.47/0.60 inference(modus_ponens,[status(thm)],[604, 603])).
% 0.47/0.60 tff(606,plain,
% 0.47/0.60 ($false),
% 0.47/0.60 inference(unit_resolution,[status(thm)],[605, 187, 492, 184, 599, 598, 597, 596])).
% 0.47/0.60 tff(607,plain,(product(e_3, e_1, e_3) | product(e_3, e_1, e_4) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.60 tff(608,plain,
% 0.47/0.60 (product(e_3, e_1, e_4)),
% 0.47/0.60 inference(unit_resolution,[status(thm)],[607, 595, 588, 577])).
% 0.47/0.60 tff(609,assumption,(product(e_3, e_1, e_4)), introduced(assumption)).
% 0.47/0.60 tff(610,assumption,(product(e_4, e_1, e_4)), introduced(assumption)).
% 0.47/0.60 tff(611,plain,
% 0.47/0.60 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_3) | (~product(e_4, e_1, e_4)) | (~product(e_3, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_4, e_1, e_4)) | (~product(e_3, e_1, e_4)))),
% 0.47/0.60 inference(rewrite,[status(thm)],[])).
% 0.47/0.60 tff(612,plain,
% 0.47/0.60 ((equalish(e_4, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_4))) <=> (equalish(e_4, e_3) | (~product(e_4, e_1, e_4)) | (~product(e_3, e_1, e_4)))),
% 0.47/0.60 inference(rewrite,[status(thm)],[])).
% 0.47/0.60 tff(613,plain,
% 0.47/0.60 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_3) | (~product(e_4, e_1, e_4)) | (~product(e_3, e_1, e_4))))),
% 0.47/0.60 inference(monotonicity,[status(thm)],[612])).
% 0.47/0.60 tff(614,plain,
% 0.47/0.60 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_4, e_1, e_4)) | (~product(e_3, e_1, e_4)))),
% 0.47/0.60 inference(transitivity,[status(thm)],[613, 611])).
% 0.47/0.60 tff(615,plain,
% 0.47/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_4, e_1, e_4)))),
% 0.47/0.60 inference(quant_inst,[status(thm)],[])).
% 0.47/0.60 tff(616,plain,
% 0.47/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_4, e_1, e_4)) | (~product(e_3, e_1, e_4))),
% 0.47/0.60 inference(modus_ponens,[status(thm)],[615, 614])).
% 0.47/0.60 tff(617,plain,
% 0.47/0.60 ($false),
% 0.47/0.60 inference(unit_resolution,[status(thm)],[616, 28, 125, 610, 609])).
% 0.47/0.60 tff(618,plain,((~product(e_4, e_1, e_4)) | (~product(e_3, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.60 tff(619,plain,
% 0.47/0.60 (~product(e_4, e_1, e_4)),
% 0.47/0.60 inference(unit_resolution,[status(thm)],[618, 608])).
% 0.47/0.60 tff(620,assumption,(~product(e_4, e_1, e_2)), introduced(assumption)).
% 0.47/0.60 tff(621,plain,
% 0.47/0.60 (group_element(e_4) <=> group_element(e_4)),
% 0.47/0.60 inference(rewrite,[status(thm)],[])).
% 0.47/0.60 tff(622,axiom,(group_element(e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_4')).
% 0.47/0.60 tff(623,plain,
% 0.47/0.60 (group_element(e_4)),
% 0.47/0.60 inference(modus_ponens,[status(thm)],[622, 621])).
% 0.47/0.60 tff(624,plain,
% 0.47/0.60 (((~![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)))) | (product(e_4, e_1, e_1) | product(e_4, e_1, e_2) | product(e_4, e_1, e_3) | product(e_4, e_1, e_4) | (~group_element(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)))) | product(e_4, e_1, e_1) | product(e_4, e_1, e_2) | product(e_4, e_1, e_3) | product(e_4, e_1, e_4) | (~group_element(e_1)) | (~group_element(e_4)))),
% 0.47/0.60 inference(rewrite,[status(thm)],[])).
% 0.47/0.60 tff(625,plain,
% 0.47/0.60 (((~group_element(e_4)) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1))) <=> (product(e_4, e_1, e_1) | product(e_4, e_1, e_2) | product(e_4, e_1, e_3) | product(e_4, e_1, e_4) | (~group_element(e_1)) | (~group_element(e_4)))),
% 0.47/0.60 inference(rewrite,[status(thm)],[])).
% 0.47/0.60 tff(626,plain,
% 0.47/0.60 (((~![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_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)))) <=> ((~![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)))) | (product(e_4, e_1, e_1) | product(e_4, e_1, e_2) | product(e_4, e_1, e_3) | product(e_4, e_1, e_4) | (~group_element(e_1)) | (~group_element(e_4))))),
% 0.47/0.60 inference(monotonicity,[status(thm)],[625])).
% 0.47/0.60 tff(627,plain,
% 0.47/0.60 (((~![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_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)))) <=> ((~![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)))) | product(e_4, e_1, e_1) | product(e_4, e_1, e_2) | product(e_4, e_1, e_3) | product(e_4, e_1, e_4) | (~group_element(e_1)) | (~group_element(e_4)))),
% 0.47/0.60 inference(transitivity,[status(thm)],[626, 624])).
% 0.47/0.60 tff(628,plain,
% 0.47/0.60 ((~![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_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)))),
% 0.47/0.60 inference(quant_inst,[status(thm)],[])).
% 0.47/0.60 tff(629,plain,
% 0.47/0.60 ((~![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)))) | product(e_4, e_1, e_1) | product(e_4, e_1, e_2) | product(e_4, e_1, e_3) | product(e_4, e_1, e_4) | (~group_element(e_1)) | (~group_element(e_4))),
% 0.47/0.60 inference(modus_ponens,[status(thm)],[628, 627])).
% 0.47/0.60 tff(630,plain,
% 0.47/0.60 (product(e_4, e_1, e_1) | product(e_4, e_1, e_3) | product(e_4, e_1, e_4)),
% 0.47/0.60 inference(unit_resolution,[status(thm)],[629, 187, 623, 184, 620])).
% 0.47/0.60 tff(631,plain,
% 0.47/0.60 (product(e_4, e_1, e_1)),
% 0.47/0.60 inference(unit_resolution,[status(thm)],[630, 619, 562])).
% 0.47/0.60 tff(632,assumption,(product(e_4, e_1, e_1)), introduced(assumption)).
% 0.47/0.60 tff(633,plain,
% 0.47/0.60 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_4) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_4) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.47/0.60 inference(rewrite,[status(thm)],[])).
% 0.47/0.60 tff(634,plain,
% 0.47/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_4) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.47/0.60 inference(quant_inst,[status(thm)],[])).
% 0.47/0.60 tff(635,plain,
% 0.47/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_4) | (~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1))),
% 0.47/0.60 inference(modus_ponens,[status(thm)],[634, 633])).
% 0.47/0.60 tff(636,plain,
% 0.47/0.60 ($false),
% 0.47/0.60 inference(unit_resolution,[status(thm)],[635, 530, 125, 632, 335])).
% 0.47/0.60 tff(637,plain,((~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.60 tff(638,plain,
% 0.47/0.60 (~product(e_1, e_1, e_1)),
% 0.47/0.60 inference(unit_resolution,[status(thm)],[637, 631])).
% 0.47/0.60 tff(639,plain,
% 0.47/0.60 (product(e_1, e_1, e_2)),
% 0.47/0.60 inference(unit_resolution,[status(thm)],[332, 638])).
% 0.47/0.60 tff(640,assumption,(product(e_1, e_2, e_1)), introduced(assumption)).
% 0.47/0.60 tff(641,plain,
% 0.47/0.60 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_1, e_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_2, e_1)))),
% 0.47/0.60 inference(rewrite,[status(thm)],[])).
% 0.47/0.60 tff(642,plain,
% 0.47/0.60 ((product(e_2, e_1, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_2))) <=> ((~product(e_1, e_1, e_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_2, e_1)))),
% 0.47/0.60 inference(rewrite,[status(thm)],[])).
% 0.47/0.60 tff(643,plain,
% 0.47/0.60 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_1, e_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_2, e_1))))),
% 0.47/0.60 inference(monotonicity,[status(thm)],[642])).
% 0.47/0.60 tff(644,plain,
% 0.47/0.60 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_2, e_1)))),
% 0.47/0.60 inference(transitivity,[status(thm)],[643, 641])).
% 0.47/0.60 tff(645,plain,
% 0.47/0.60 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_2)))),
% 0.47/0.60 inference(quant_inst,[status(thm)],[])).
% 0.47/0.60 tff(646,plain,
% 0.47/0.60 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_1) | (~product(e_1, e_2, e_1))),
% 0.47/0.60 inference(modus_ponens,[status(thm)],[645, 644])).
% 0.47/0.60 tff(647,plain,
% 0.47/0.60 ($false),
% 0.47/0.60 inference(unit_resolution,[status(thm)],[646, 105, 397, 370, 640])).
% 0.47/0.60 tff(648,plain,((~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.60 tff(649,plain,
% 0.47/0.60 (~product(e_1, e_2, e_1)),
% 0.47/0.60 inference(unit_resolution,[status(thm)],[648, 639, 552])).
% 0.47/0.60 tff(650,assumption,(product(e_3, e_2, e_4)), introduced(assumption)).
% 0.47/0.60 tff(651,plain,
% 0.47/0.60 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_2, e_4)))),
% 0.47/0.60 inference(rewrite,[status(thm)],[])).
% 0.47/0.60 tff(652,plain,
% 0.47/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_2, e_4)))),
% 0.47/0.60 inference(quant_inst,[status(thm)],[])).
% 0.47/0.60 tff(653,plain,
% 0.47/0.60 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_2, e_4))),
% 0.47/0.60 inference(modus_ponens,[status(thm)],[652, 651])).
% 0.47/0.60 tff(654,plain,
% 0.47/0.60 ($false),
% 0.47/0.60 inference(unit_resolution,[status(thm)],[653, 128, 362, 609, 650])).
% 0.47/0.60 tff(655,plain,((~product(e_3, e_2, e_4)) | (~product(e_3, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.60 tff(656,plain,
% 0.47/0.60 (~product(e_3, e_2, e_4)),
% 0.47/0.60 inference(unit_resolution,[status(thm)],[655, 608])).
% 0.47/0.60 tff(657,plain,
% 0.47/0.60 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_3, e_2, e_4) | (~product(e_1, e_3, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_4) | (~product(e_1, e_3, e_4)))),
% 0.47/0.60 inference(rewrite,[status(thm)],[])).
% 0.47/0.60 tff(658,plain,
% 0.47/0.60 ((product(e_3, e_2, e_4) | (~product(e_1, e_3, e_4)) | (~product(e_2, e_1, e_3))) <=> ((~product(e_2, e_1, e_3)) | product(e_3, e_2, e_4) | (~product(e_1, e_3, e_4)))),
% 0.47/0.60 inference(rewrite,[status(thm)],[])).
% 0.47/0.60 tff(659,plain,
% 0.47/0.60 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_4) | (~product(e_1, e_3, e_4)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_3, e_2, e_4) | (~product(e_1, e_3, e_4))))),
% 0.47/0.60 inference(monotonicity,[status(thm)],[658])).
% 0.47/0.60 tff(660,plain,
% 0.47/0.60 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_4) | (~product(e_1, e_3, e_4)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_4) | (~product(e_1, e_3, e_4)))),
% 0.47/0.60 inference(transitivity,[status(thm)],[659, 657])).
% 0.47/0.60 tff(661,plain,
% 0.47/0.60 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_3, e_2, e_4) | (~product(e_1, e_3, e_4)) | (~product(e_2, e_1, e_3)))),
% 0.47/0.60 inference(quant_inst,[status(thm)],[])).
% 0.47/0.60 tff(662,plain,
% 0.47/0.60 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_3, e_2, e_4) | (~product(e_1, e_3, e_4))),
% 0.47/0.60 inference(modus_ponens,[status(thm)],[661, 660])).
% 0.47/0.60 tff(663,plain,
% 0.47/0.60 ((~product(e_2, e_1, e_3)) | product(e_3, e_2, e_4) | (~product(e_1, e_3, e_4))),
% 0.47/0.60 inference(unit_resolution,[status(thm)],[662, 105])).
% 0.47/0.60 tff(664,plain,
% 0.47/0.60 (~product(e_1, e_3, e_4)),
% 0.47/0.60 inference(unit_resolution,[status(thm)],[663, 656, 413])).
% 0.47/0.60 tff(665,plain,
% 0.47/0.60 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_1)))),
% 0.47/0.60 inference(rewrite,[status(thm)],[])).
% 0.47/0.60 tff(666,plain,
% 0.47/0.60 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_1, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_1)))),
% 0.47/0.60 inference(quant_inst,[status(thm)],[])).
% 0.47/0.60 tff(667,plain,
% 0.47/0.60 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_1, e_1, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_1, e_3, e_1))),
% 0.47/0.60 inference(modus_ponens,[status(thm)],[666, 665])).
% 0.47/0.60 tff(668,plain,
% 0.47/0.60 (~product(e_1, e_3, e_1)),
% 0.47/0.60 inference(unit_resolution,[status(thm)],[667, 105, 256, 608])).
% 0.47/0.60 tff(669,assumption,(product(e_1, e_3, e_2)), introduced(assumption)).
% 0.47/0.60 tff(670,plain,
% 0.47/0.60 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.47/0.60 inference(rewrite,[status(thm)],[])).
% 0.47/0.60 tff(671,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.47/0.61 tff(672,plain,
% 0.47/0.61 (~equalish(e_3, e_1)),
% 0.47/0.61 inference(modus_ponens,[status(thm)],[671, 670])).
% 0.47/0.61 tff(673,plain,
% 0.47/0.61 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.47/0.61 inference(rewrite,[status(thm)],[])).
% 0.47/0.61 tff(674,plain,
% 0.47/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_3, e_2)))),
% 0.47/0.61 inference(quant_inst,[status(thm)],[])).
% 0.47/0.61 tff(675,plain,
% 0.47/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_1, e_3, e_2))),
% 0.47/0.61 inference(modus_ponens,[status(thm)],[674, 673])).
% 0.47/0.61 tff(676,plain,
% 0.47/0.61 ($false),
% 0.47/0.61 inference(unit_resolution,[status(thm)],[675, 672, 362, 397, 669])).
% 0.47/0.61 tff(677,plain,((~product(e_1, e_3, e_2)) | (~product(e_1, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.61 tff(678,plain,
% 0.47/0.61 (~product(e_1, e_3, e_2)),
% 0.47/0.61 inference(unit_resolution,[status(thm)],[677, 639])).
% 0.47/0.61 tff(679,plain,
% 0.47/0.61 (((~![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_3)) | product(e_1, e_3, e_1) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, 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_1)) | (~group_element(e_3)) | product(e_1, e_3, e_1) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2))),
% 0.47/0.61 inference(rewrite,[status(thm)],[])).
% 0.47/0.61 tff(680,plain,
% 0.47/0.61 (((~group_element(e_1)) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3))) <=> ((~group_element(e_1)) | (~group_element(e_3)) | product(e_1, e_3, e_1) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2))),
% 0.47/0.61 inference(rewrite,[status(thm)],[])).
% 0.47/0.61 tff(681,plain,
% 0.47/0.61 (((~![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)) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)))) <=> ((~![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_3)) | product(e_1, e_3, e_1) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2)))),
% 0.47/0.61 inference(monotonicity,[status(thm)],[680])).
% 0.47/0.61 tff(682,plain,
% 0.47/0.61 (((~![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)) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)))) <=> ((~![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_3)) | product(e_1, e_3, e_1) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2))),
% 0.47/0.61 inference(transitivity,[status(thm)],[681, 679])).
% 0.47/0.61 tff(683,plain,
% 0.47/0.61 ((~![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)) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2) | product(e_1, e_3, e_1) | (~group_element(e_3)))),
% 0.47/0.61 inference(quant_inst,[status(thm)],[])).
% 0.47/0.61 tff(684,plain,
% 0.47/0.61 ((~![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_3)) | product(e_1, e_3, e_1) | product(e_1, e_3, e_4) | product(e_1, e_3, e_3) | product(e_1, e_3, e_2)),
% 0.47/0.61 inference(modus_ponens,[status(thm)],[683, 682])).
% 0.47/0.61 tff(685,plain,
% 0.47/0.61 (product(e_1, e_3, e_4) | product(e_1, e_3, e_3)),
% 0.47/0.61 inference(unit_resolution,[status(thm)],[684, 187, 492, 184, 678, 668])).
% 0.47/0.61 tff(686,plain,
% 0.47/0.61 (product(e_1, e_3, e_3)),
% 0.47/0.61 inference(unit_resolution,[status(thm)],[685, 664])).
% 0.47/0.61 tff(687,assumption,(product(e_1, e_3, e_3)), introduced(assumption)).
% 0.47/0.61 tff(688,plain,
% 0.47/0.61 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.47/0.61 inference(rewrite,[status(thm)],[])).
% 0.47/0.61 tff(689,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.47/0.61 tff(690,plain,
% 0.47/0.61 (~equalish(e_2, e_3)),
% 0.47/0.61 inference(modus_ponens,[status(thm)],[689, 688])).
% 0.47/0.61 tff(691,plain,
% 0.47/0.61 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_2, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.47/0.61 inference(rewrite,[status(thm)],[])).
% 0.47/0.61 tff(692,plain,
% 0.47/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.47/0.61 inference(quant_inst,[status(thm)],[])).
% 0.47/0.61 tff(693,plain,
% 0.47/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_3) | (~product(e_1, e_3, e_3)) | (~product(e_1, e_2, e_3))),
% 0.47/0.61 inference(modus_ponens,[status(thm)],[692, 691])).
% 0.47/0.61 tff(694,plain,
% 0.47/0.61 ($false),
% 0.47/0.61 inference(unit_resolution,[status(thm)],[693, 690, 362, 138, 687])).
% 0.47/0.61 tff(695,plain,((~product(e_1, e_2, e_3)) | (~product(e_1, e_3, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.61 tff(696,plain,
% 0.47/0.61 (~product(e_1, e_2, e_3)),
% 0.47/0.61 inference(unit_resolution,[status(thm)],[695, 686])).
% 0.47/0.61 tff(697,plain,
% 0.47/0.61 (product(e_1, e_2, e_1) | product(e_1, e_2, e_4) | product(e_1, e_2, e_3)),
% 0.47/0.61 inference(unit_resolution,[status(thm)],[193, 187, 69, 184, 395])).
% 0.47/0.61 tff(698,plain,
% 0.47/0.61 (product(e_1, e_2, e_4)),
% 0.47/0.61 inference(unit_resolution,[status(thm)],[697, 696, 649])).
% 0.47/0.61 tff(699,plain,
% 0.47/0.61 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_1, e_2)) | product(e_2, e_1, e_4) | (~product(e_1, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_4) | (~product(e_1, e_2, e_4)))),
% 0.47/0.61 inference(rewrite,[status(thm)],[])).
% 0.47/0.61 tff(700,plain,
% 0.47/0.61 ((product(e_2, e_1, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_1, e_2))) <=> ((~product(e_1, e_1, e_2)) | product(e_2, e_1, e_4) | (~product(e_1, e_2, e_4)))),
% 0.47/0.61 inference(rewrite,[status(thm)],[])).
% 0.47/0.61 tff(701,plain,
% 0.47/0.61 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_1, e_1, e_2)) | product(e_2, e_1, e_4) | (~product(e_1, e_2, e_4))))),
% 0.47/0.61 inference(monotonicity,[status(thm)],[700])).
% 0.47/0.61 tff(702,plain,
% 0.47/0.61 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_4) | (~product(e_1, e_2, e_4)))),
% 0.47/0.61 inference(transitivity,[status(thm)],[701, 699])).
% 0.47/0.61 tff(703,plain,
% 0.47/0.61 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_1, e_1, e_2)))),
% 0.47/0.61 inference(quant_inst,[status(thm)],[])).
% 0.47/0.61 tff(704,plain,
% 0.47/0.61 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_4) | (~product(e_1, e_2, e_4))),
% 0.47/0.61 inference(modus_ponens,[status(thm)],[703, 702])).
% 0.47/0.61 tff(705,plain,
% 0.47/0.61 ($false),
% 0.47/0.61 inference(unit_resolution,[status(thm)],[704, 105, 639, 95, 698])).
% 0.47/0.61 tff(706,plain,(product(e_1, e_2, e_2) | product(e_4, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.61 tff(707,plain,
% 0.47/0.61 (product(e_4, e_1, e_2)),
% 0.47/0.61 inference(unit_resolution,[status(thm)],[706, 394])).
% 0.47/0.61 tff(708,plain,
% 0.47/0.61 (product(e_2, e_1, e_3)),
% 0.47/0.61 inference(unit_resolution,[status(thm)],[412, 394])).
% 0.47/0.61 tff(709,plain,
% 0.47/0.61 (~cycle(e_2, e_0)),
% 0.47/0.61 inference(unit_resolution,[status(thm)],[423, 708])).
% 0.47/0.61 tff(710,plain,
% 0.47/0.61 (~cycle(e_3, e_0)),
% 0.47/0.61 inference(unit_resolution,[status(thm)],[518, 709])).
% 0.47/0.61 tff(711,plain,
% 0.47/0.61 (~cycle(e_2, e_1)),
% 0.47/0.61 inference(unit_resolution,[status(thm)],[539, 710])).
% 0.47/0.61 tff(712,plain,
% 0.47/0.61 (cycle(e_2, e_2)),
% 0.47/0.61 inference(unit_resolution,[status(thm)],[541, 711, 709])).
% 0.47/0.61 tff(713,plain,
% 0.47/0.61 (~cycle(e_3, e_3)),
% 0.47/0.61 inference(unit_resolution,[status(thm)],[568, 44, 442, 57, 460, 556, 712])).
% 0.47/0.61 tff(714,plain,
% 0.47/0.61 (cycle(e_3, e_1)),
% 0.47/0.61 inference(unit_resolution,[status(thm)],[497, 713, 710])).
% 0.47/0.61 tff(715,plain,
% 0.47/0.61 (~product(e_3, e_1, e_1)),
% 0.47/0.61 inference(unit_resolution,[status(thm)],[576, 442, 41, 38, 530, 714])).
% 0.47/0.61 tff(716,assumption,(product(e_4, e_1, e_2)), introduced(assumption)).
% 0.47/0.61 tff(717,plain,
% 0.47/0.61 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_3) | (~product(e_4, e_1, e_2)) | (~product(e_3, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_4, e_1, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.47/0.61 inference(rewrite,[status(thm)],[])).
% 0.47/0.61 tff(718,plain,
% 0.47/0.61 ((equalish(e_4, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_4, e_1, e_2))) <=> (equalish(e_4, e_3) | (~product(e_4, e_1, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.47/0.61 inference(rewrite,[status(thm)],[])).
% 0.47/0.61 tff(719,plain,
% 0.47/0.61 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_4, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_3) | (~product(e_4, e_1, e_2)) | (~product(e_3, e_1, e_2))))),
% 0.47/0.61 inference(monotonicity,[status(thm)],[718])).
% 0.47/0.61 tff(720,plain,
% 0.47/0.61 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_4, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_4, e_1, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.47/0.61 inference(transitivity,[status(thm)],[719, 717])).
% 0.47/0.61 tff(721,plain,
% 0.47/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_3) | (~product(e_3, e_1, e_2)) | (~product(e_4, e_1, e_2)))),
% 0.47/0.61 inference(quant_inst,[status(thm)],[])).
% 0.47/0.61 tff(722,plain,
% 0.47/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_4, e_1, e_2)) | (~product(e_3, e_1, e_2))),
% 0.47/0.61 inference(modus_ponens,[status(thm)],[721, 720])).
% 0.47/0.61 tff(723,plain,
% 0.47/0.61 ($false),
% 0.47/0.61 inference(unit_resolution,[status(thm)],[722, 28, 125, 716, 578])).
% 0.47/0.61 tff(724,plain,((~product(e_4, e_1, e_2)) | (~product(e_3, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.61 tff(725,plain,
% 0.47/0.61 (~product(e_3, e_1, e_2)),
% 0.47/0.61 inference(unit_resolution,[status(thm)],[724, 707])).
% 0.47/0.61 tff(726,plain,
% 0.47/0.61 (~product(e_3, e_1, e_3)),
% 0.47/0.61 inference(unit_resolution,[status(thm)],[594, 442, 41, 38, 470, 714])).
% 0.47/0.61 tff(727,plain,
% 0.47/0.61 (product(e_3, e_1, e_4)),
% 0.47/0.61 inference(unit_resolution,[status(thm)],[607, 726, 725, 715])).
% 0.47/0.61 tff(728,plain,
% 0.47/0.61 (~product(e_4, e_1, e_4)),
% 0.47/0.61 inference(unit_resolution,[status(thm)],[618, 727])).
% 0.47/0.61 tff(729,assumption,(~product(e_4, e_1, e_4)), introduced(assumption)).
% 0.47/0.61 tff(730,assumption,(product(e_2, e_4, e_4)), introduced(assumption)).
% 0.47/0.61 tff(731,plain,
% 0.47/0.61 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_4, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_4, e_4)))),
% 0.47/0.61 inference(rewrite,[status(thm)],[])).
% 0.47/0.61 tff(732,plain,
% 0.47/0.61 ((product(e_4, e_1, e_4) | (~product(e_2, e_4, e_4)) | (~product(e_1, e_2, e_4))) <=> (product(e_4, e_1, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_4, e_4)))),
% 0.47/0.61 inference(rewrite,[status(thm)],[])).
% 0.47/0.61 tff(733,plain,
% 0.47/0.61 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_2, e_4, e_4)) | (~product(e_1, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_4, e_4))))),
% 0.47/0.61 inference(monotonicity,[status(thm)],[732])).
% 0.47/0.61 tff(734,plain,
% 0.47/0.61 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_2, e_4, e_4)) | (~product(e_1, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_4, e_4)))),
% 0.47/0.61 inference(transitivity,[status(thm)],[733, 731])).
% 0.47/0.61 tff(735,plain,
% 0.47/0.61 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_2, e_4, e_4)) | (~product(e_1, e_2, e_4)))),
% 0.47/0.61 inference(quant_inst,[status(thm)],[])).
% 0.47/0.61 tff(736,plain,
% 0.47/0.61 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | product(e_4, e_1, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_4, e_4))),
% 0.47/0.61 inference(modus_ponens,[status(thm)],[735, 734])).
% 0.47/0.61 tff(737,plain,
% 0.47/0.61 ($false),
% 0.47/0.61 inference(unit_resolution,[status(thm)],[736, 105, 729, 159, 730])).
% 0.47/0.61 tff(738,plain,((~product(e_2, e_4, e_4)) | product(e_4, e_1, e_4) | (~product(e_1, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.61 tff(739,plain,
% 0.47/0.61 (~product(e_2, e_4, e_4)),
% 0.47/0.61 inference(unit_resolution,[status(thm)],[738, 159, 729])).
% 0.47/0.61 tff(740,plain,
% 0.47/0.61 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_1, e_2)) | product(e_2, e_4, e_4) | (~product(e_1, e_2, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_1, e_2)) | product(e_2, e_4, e_4) | (~product(e_1, e_2, e_4)))),
% 0.47/0.61 inference(rewrite,[status(thm)],[])).
% 0.47/0.61 tff(741,plain,
% 0.47/0.61 ((product(e_2, e_4, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_4, e_1, e_2))) <=> ((~product(e_4, e_1, e_2)) | product(e_2, e_4, e_4) | (~product(e_1, e_2, e_4)))),
% 0.47/0.61 inference(rewrite,[status(thm)],[])).
% 0.47/0.61 tff(742,plain,
% 0.47/0.61 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_4, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_1, e_2)) | product(e_2, e_4, e_4) | (~product(e_1, e_2, e_4))))),
% 0.47/0.61 inference(monotonicity,[status(thm)],[741])).
% 0.47/0.61 tff(743,plain,
% 0.47/0.61 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_4, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_1, e_2)) | product(e_2, e_4, e_4) | (~product(e_1, e_2, e_4)))),
% 0.47/0.61 inference(transitivity,[status(thm)],[742, 740])).
% 0.47/0.61 tff(744,plain,
% 0.47/0.61 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_4, e_1, e_2)))),
% 0.47/0.61 inference(quant_inst,[status(thm)],[])).
% 0.47/0.61 tff(745,plain,
% 0.47/0.61 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_1, e_2)) | product(e_2, e_4, e_4) | (~product(e_1, e_2, e_4))),
% 0.47/0.61 inference(modus_ponens,[status(thm)],[744, 743])).
% 0.47/0.61 tff(746,plain,
% 0.47/0.61 ($false),
% 0.47/0.61 inference(unit_resolution,[status(thm)],[745, 105, 716, 159, 739])).
% 0.47/0.61 tff(747,plain,((~product(e_1, e_2, e_4)) | (~product(e_4, e_1, e_2)) | product(e_4, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.61 tff(748,plain,
% 0.47/0.61 (~product(e_1, e_2, e_4)),
% 0.47/0.61 inference(unit_resolution,[status(thm)],[747, 728, 707])).
% 0.47/0.61 tff(749,assumption,(product(e_2, e_4, e_3)), introduced(assumption)).
% 0.47/0.61 tff(750,plain,
% 0.47/0.61 ((~equalish(e_4, e_1)) <=> (~equalish(e_4, e_1))),
% 0.47/0.61 inference(rewrite,[status(thm)],[])).
% 0.47/0.61 tff(751,axiom,(~equalish(e_4, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_is_not_e_1')).
% 0.47/0.61 tff(752,plain,
% 0.47/0.61 (~equalish(e_4, e_1)),
% 0.47/0.61 inference(modus_ponens,[status(thm)],[751, 750])).
% 0.47/0.61 tff(753,plain,
% 0.47/0.61 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3)))),
% 0.47/0.61 inference(rewrite,[status(thm)],[])).
% 0.47/0.61 tff(754,plain,
% 0.47/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_4, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3)))),
% 0.47/0.61 inference(quant_inst,[status(thm)],[])).
% 0.47/0.61 tff(755,plain,
% 0.47/0.61 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_4, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_4, e_3))),
% 0.47/0.61 inference(modus_ponens,[status(thm)],[754, 753])).
% 0.47/0.61 tff(756,plain,
% 0.47/0.61 ($false),
% 0.47/0.61 inference(unit_resolution,[status(thm)],[755, 752, 362, 352, 749])).
% 0.47/0.61 tff(757,plain,((~product(e_2, e_4, e_3)) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.61 tff(758,plain,
% 0.47/0.61 (~product(e_2, e_4, e_3)),
% 0.47/0.61 inference(unit_resolution,[status(thm)],[757, 708])).
% 0.47/0.61 tff(759,assumption,(~product(e_2, e_4, e_3)), introduced(assumption)).
% 0.47/0.61 tff(760,plain,
% 0.47/0.61 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_1, e_2)) | product(e_2, e_4, e_3) | (~product(e_1, e_2, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_1, e_2)) | product(e_2, e_4, e_3) | (~product(e_1, e_2, e_3)))),
% 0.47/0.61 inference(rewrite,[status(thm)],[])).
% 0.47/0.61 tff(761,plain,
% 0.47/0.61 ((product(e_2, e_4, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_4, e_1, e_2))) <=> ((~product(e_4, e_1, e_2)) | product(e_2, e_4, e_3) | (~product(e_1, e_2, e_3)))),
% 0.47/0.61 inference(rewrite,[status(thm)],[])).
% 0.47/0.61 tff(762,plain,
% 0.47/0.61 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_4, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_1, e_2)) | product(e_2, e_4, e_3) | (~product(e_1, e_2, e_3))))),
% 0.47/0.61 inference(monotonicity,[status(thm)],[761])).
% 0.47/0.62 tff(763,plain,
% 0.47/0.62 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_4, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_1, e_2)) | product(e_2, e_4, e_3) | (~product(e_1, e_2, e_3)))),
% 0.47/0.62 inference(transitivity,[status(thm)],[762, 760])).
% 0.47/0.62 tff(764,plain,
% 0.47/0.62 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_3) | (~product(e_1, e_2, e_3)) | (~product(e_4, e_1, e_2)))),
% 0.47/0.62 inference(quant_inst,[status(thm)],[])).
% 0.47/0.62 tff(765,plain,
% 0.47/0.62 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_1, e_2)) | product(e_2, e_4, e_3) | (~product(e_1, e_2, e_3))),
% 0.47/0.62 inference(modus_ponens,[status(thm)],[764, 763])).
% 0.47/0.62 tff(766,plain,
% 0.47/0.62 ($false),
% 0.47/0.62 inference(unit_resolution,[status(thm)],[765, 105, 716, 138, 759])).
% 0.47/0.62 tff(767,plain,((~product(e_1, e_2, e_3)) | (~product(e_4, e_1, e_2)) | product(e_2, e_4, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.62 tff(768,plain,
% 0.47/0.62 (~product(e_1, e_2, e_3)),
% 0.47/0.62 inference(unit_resolution,[status(thm)],[767, 707, 758])).
% 0.47/0.62 tff(769,plain,
% 0.47/0.62 (product(e_1, e_2, e_1) | product(e_1, e_2, e_4)),
% 0.47/0.62 inference(unit_resolution,[status(thm)],[193, 187, 69, 184, 394, 768])).
% 0.47/0.62 tff(770,plain,
% 0.47/0.62 (product(e_1, e_2, e_1)),
% 0.47/0.62 inference(unit_resolution,[status(thm)],[769, 748])).
% 0.47/0.62 tff(771,plain,
% 0.47/0.62 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_1, e_2)) | product(e_1, e_2, e_2) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_1, e_2)) | product(e_1, e_2, e_2) | (~product(e_2, e_4, e_1)))),
% 0.47/0.62 inference(rewrite,[status(thm)],[])).
% 0.47/0.62 tff(772,plain,
% 0.47/0.62 ((product(e_1, e_2, e_2) | (~product(e_4, e_1, e_2)) | (~product(e_2, e_4, e_1))) <=> ((~product(e_4, e_1, e_2)) | product(e_1, e_2, e_2) | (~product(e_2, e_4, e_1)))),
% 0.47/0.62 inference(rewrite,[status(thm)],[])).
% 0.47/0.62 tff(773,plain,
% 0.47/0.62 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_4, e_1, e_2)) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_1, e_2)) | product(e_1, e_2, e_2) | (~product(e_2, e_4, e_1))))),
% 0.47/0.62 inference(monotonicity,[status(thm)],[772])).
% 0.47/0.62 tff(774,plain,
% 0.47/0.62 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_4, e_1, e_2)) | (~product(e_2, e_4, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_1, e_2)) | product(e_1, e_2, e_2) | (~product(e_2, e_4, e_1)))),
% 0.47/0.62 inference(transitivity,[status(thm)],[773, 771])).
% 0.47/0.62 tff(775,plain,
% 0.47/0.62 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_1, e_2, e_2) | (~product(e_4, e_1, e_2)) | (~product(e_2, e_4, e_1)))),
% 0.47/0.62 inference(quant_inst,[status(thm)],[])).
% 0.47/0.62 tff(776,plain,
% 0.47/0.62 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_1, e_2)) | product(e_1, e_2, e_2) | (~product(e_2, e_4, e_1))),
% 0.47/0.62 inference(modus_ponens,[status(thm)],[775, 774])).
% 0.47/0.62 tff(777,plain,
% 0.47/0.62 (~product(e_2, e_4, e_1)),
% 0.47/0.62 inference(unit_resolution,[status(thm)],[776, 105, 707, 394])).
% 0.47/0.62 tff(778,plain,
% 0.47/0.62 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_1, e_2)) | product(e_2, e_4, e_1) | (~product(e_1, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_1, e_2)) | product(e_2, e_4, e_1) | (~product(e_1, e_2, e_1)))),
% 0.47/0.62 inference(rewrite,[status(thm)],[])).
% 0.47/0.62 tff(779,plain,
% 0.47/0.62 ((product(e_2, e_4, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_4, e_1, e_2))) <=> ((~product(e_4, e_1, e_2)) | product(e_2, e_4, e_1) | (~product(e_1, e_2, e_1)))),
% 0.47/0.62 inference(rewrite,[status(thm)],[])).
% 0.47/0.62 tff(780,plain,
% 0.47/0.62 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_4, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | ((~product(e_4, e_1, e_2)) | product(e_2, e_4, e_1) | (~product(e_1, e_2, e_1))))),
% 0.47/0.62 inference(monotonicity,[status(thm)],[779])).
% 0.47/0.62 tff(781,plain,
% 0.47/0.62 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_4, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_1, e_2)) | product(e_2, e_4, e_1) | (~product(e_1, e_2, e_1)))),
% 0.47/0.62 inference(transitivity,[status(thm)],[780, 778])).
% 0.47/0.62 tff(782,plain,
% 0.47/0.62 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (product(e_2, e_4, e_1) | (~product(e_1, e_2, e_1)) | (~product(e_4, e_1, e_2)))),
% 0.47/0.62 inference(quant_inst,[status(thm)],[])).
% 0.47/0.62 tff(783,plain,
% 0.47/0.62 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(Z1, Y, Z2) | (~product(X, Z1, Z2)) | (~product(Y, X, Z1)))) | (~product(e_4, e_1, e_2)) | product(e_2, e_4, e_1) | (~product(e_1, e_2, e_1))),
% 0.47/0.62 inference(modus_ponens,[status(thm)],[782, 781])).
% 0.47/0.62 tff(784,plain,
% 0.47/0.62 ($false),
% 0.47/0.62 inference(unit_resolution,[status(thm)],[783, 105, 707, 777, 770])).
% 0.47/0.62 % SZS output end Proof
%------------------------------------------------------------------------------