TSTP Solution File: GRP123-3.003 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP123-3.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 22:25:55 EDT 2022
% Result : Unsatisfiable 0.21s 0.45s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP123-3.003 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n027.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 31 15:06:02 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.45 % SZS status Unsatisfiable
% 0.21/0.45 % SZS output start Proof
% 0.21/0.45 tff(product_type, type, (
% 0.21/0.45 product: ( $i * $i * $i ) > $o)).
% 0.21/0.45 tff(e_1_type, type, (
% 0.21/0.45 e_1: $i)).
% 0.21/0.45 tff(e_3_type, type, (
% 0.21/0.45 e_3: $i)).
% 0.21/0.45 tff(equalish_type, type, (
% 0.21/0.45 equalish: ( $i * $i ) > $o)).
% 0.21/0.45 tff(e_2_type, type, (
% 0.21/0.45 e_2: $i)).
% 0.21/0.45 tff(cycle_type, type, (
% 0.21/0.45 cycle: ( $i * $i ) > $o)).
% 0.21/0.45 tff(e_0_type, type, (
% 0.21/0.45 e_0: $i)).
% 0.21/0.45 tff(greater_type, type, (
% 0.21/0.45 greater: ( $i * $i ) > $o)).
% 0.21/0.45 tff(group_element_type, type, (
% 0.21/0.45 group_element: $i > $o)).
% 0.21/0.45 tff(next_type, type, (
% 0.21/0.45 next: ( $i * $i ) > $o)).
% 0.21/0.45 tff(1,assumption,(product(e_1, e_1, e_1)), introduced(assumption)).
% 0.21/0.45 tff(2,plain,
% 0.21/0.45 (^[X: $i] : refl(product(X, X, X) <=> product(X, X, X))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(3,plain,
% 0.21/0.45 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.21/0.45 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.45 tff(4,plain,
% 0.21/0.45 (![X: $i] : product(X, X, X) <=> ![X: $i] : product(X, X, X)),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(5,axiom,(![X: $i] : product(X, X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_idempotence')).
% 0.21/0.45 tff(6,plain,
% 0.21/0.45 (![X: $i] : product(X, X, X)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.21/0.45 tff(7,plain,(
% 0.21/0.45 ![X: $i] : product(X, X, X)),
% 0.21/0.45 inference(skolemize,[status(sab)],[6])).
% 0.21/0.45 tff(8,plain,
% 0.21/0.45 (![X: $i] : product(X, X, X)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.21/0.45 tff(9,plain,
% 0.21/0.45 ((~![X: $i] : product(X, X, X)) | product(e_3, e_3, e_3)),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(10,plain,
% 0.21/0.45 (product(e_3, e_3, e_3)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.21/0.45 tff(11,assumption,(product(e_3, e_1, e_3)), introduced(assumption)).
% 0.21/0.45 tff(12,plain,
% 0.21/0.45 (^[Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : refl(((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2)) <=> ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2)))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(13,plain,
% 0.21/0.45 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2)) <=> ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[12])).
% 0.21/0.45 tff(14,plain,
% 0.21/0.45 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2)) <=> ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(15,plain,
% 0.21/0.45 (^[Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, Y1, X1))) <=> ((~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))), (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, Y1, X1))) | (~product(Z2, Y2, X2))) <=> (((~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | (~product(Z2, Y2, X2))))), rewrite((((~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | (~product(Z2, Y2, X2))) <=> ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)))), (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, Y1, X1))) | (~product(Z2, Y2, X2))) <=> ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))))), ((((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, Y1, X1))) | (~product(Z2, Y2, X2))) | equalish(Y1, Y2)) <=> (((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | equalish(Y1, Y2)))), rewrite((((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1))) | equalish(Y1, Y2)) <=> ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))), ((((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, Y1, X1))) | (~product(Z2, Y2, X2))) | equalish(Y1, Y2)) <=> ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(16,plain,
% 0.21/0.46 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, Y1, X1))) | (~product(Z2, Y2, X2))) | equalish(Y1, Y2)) <=> ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[15])).
% 0.21/0.46 tff(17,axiom,(![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : (((((~product(X1, Y1, Z1)) | (~product(X2, Y2, Z1))) | (~product(Z2, Y1, X1))) | (~product(Z2, Y2, X2))) | equalish(Y1, Y2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qg1_2')).
% 0.21/0.46 tff(18,plain,
% 0.21/0.46 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.21/0.46 tff(19,plain,
% 0.21/0.46 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.21/0.46 tff(20,plain,(
% 0.21/0.46 ![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.21/0.46 inference(skolemize,[status(sab)],[19])).
% 0.21/0.46 tff(21,plain,
% 0.21/0.46 (![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.21/0.46 tff(22,plain,
% 0.21/0.46 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(23,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.21/0.46 tff(24,plain,
% 0.21/0.46 (~equalish(e_3, e_1)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.21/0.46 tff(25,plain,
% 0.21/0.46 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_3, e_1) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_3)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_3, e_1) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(26,plain,
% 0.21/0.46 (((~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_3)) | equalish(e_3, e_1)) <=> (equalish(e_3, e_1) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(27,plain,
% 0.21/0.46 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_3)) | equalish(e_3, e_1))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_3, e_1) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_3))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[26])).
% 0.21/0.46 tff(28,plain,
% 0.21/0.46 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_3)) | equalish(e_3, e_1))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_3, e_1) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_3)))),
% 0.21/0.46 inference(transitivity,[status(thm)],[27, 25])).
% 0.21/0.46 tff(29,plain,
% 0.21/0.46 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_3)) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_3)) | equalish(e_3, e_1))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(30,plain,
% 0.21/0.46 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_3, e_1) | (~product(e_3, e_1, e_3)) | (~product(e_3, e_3, e_3))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.21/0.46 tff(31,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[30, 24, 21, 11, 10])).
% 0.21/0.46 tff(32,plain,(~product(e_3, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(33,plain,
% 0.21/0.46 ((~![X: $i] : product(X, X, X)) | product(e_2, e_2, e_2)),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(34,plain,
% 0.21/0.46 (product(e_2, e_2, e_2)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[33, 8])).
% 0.21/0.46 tff(35,assumption,(cycle(e_2, e_0)), introduced(assumption)).
% 0.21/0.46 tff(36,plain,
% 0.21/0.46 (^[Y: $i, X: $i] : refl(((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0))) <=> ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(37,plain,
% 0.21/0.46 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0))) <=> ![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[36])).
% 0.21/0.46 tff(38,plain,
% 0.21/0.46 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0))) <=> ![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(39,plain,
% 0.21/0.46 (^[Y: $i, X: $i] : rewrite((((~cycle(X, e_0)) | (~product(X, e_1, Y))) | (~greater(Y, X))) <=> ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(40,plain,
% 0.21/0.46 (![Y: $i, X: $i] : (((~cycle(X, e_0)) | (~product(X, e_1, Y))) | (~greater(Y, X))) <=> ![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[39])).
% 0.21/0.46 tff(41,axiom,(![Y: $i, X: $i] : (((~cycle(X, e_0)) | (~product(X, e_1, Y))) | (~greater(Y, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cycle6')).
% 0.21/0.46 tff(42,plain,
% 0.21/0.46 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.21/0.46 tff(43,plain,
% 0.21/0.46 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.21/0.46 tff(44,plain,(
% 0.21/0.46 ![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[43])).
% 0.21/0.46 tff(45,plain,
% 0.21/0.46 (![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.21/0.46 tff(46,plain,
% 0.21/0.46 (greater(e_3, e_2) <=> greater(e_3, e_2)),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(47,axiom,(greater(e_3, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_greater_e_2')).
% 0.21/0.46 tff(48,plain,
% 0.21/0.46 (greater(e_3, e_2)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.21/0.46 tff(49,plain,
% 0.21/0.46 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(50,plain,
% 0.21/0.46 (((~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)) | (~cycle(e_2, e_0))) <=> ((~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(51,plain,
% 0.21/0.46 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[50])).
% 0.21/0.46 tff(52,plain,
% 0.21/0.46 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.21/0.46 inference(transitivity,[status(thm)],[51, 49])).
% 0.21/0.46 tff(53,plain,
% 0.21/0.46 ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)) | (~cycle(e_2, e_0)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(54,plain,
% 0.21/0.46 ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.21/0.46 tff(55,plain,
% 0.21/0.46 ((~cycle(e_2, e_0)) | (~product(e_2, e_1, e_3))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[54, 48, 45])).
% 0.21/0.46 tff(56,plain,
% 0.21/0.46 (~product(e_2, e_1, e_3)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[55, 35])).
% 0.21/0.46 tff(57,assumption,(product(e_2, e_1, e_2)), introduced(assumption)).
% 0.21/0.46 tff(58,plain,
% 0.21/0.46 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(59,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.21/0.46 tff(60,plain,
% 0.21/0.46 (~equalish(e_2, e_1)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.21/0.46 tff(61,plain,
% 0.21/0.46 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(62,plain,
% 0.21/0.46 (((~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)) | equalish(e_2, e_1)) <=> (equalish(e_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(63,plain,
% 0.21/0.46 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)) | equalish(e_2, e_1))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[62])).
% 0.21/0.46 tff(64,plain,
% 0.21/0.46 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)) | equalish(e_2, e_1))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[63, 61])).
% 0.21/0.47 tff(65,plain,
% 0.21/0.47 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)) | equalish(e_2, e_1))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(66,plain,
% 0.21/0.47 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.21/0.47 tff(67,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[66, 60, 21, 34, 57])).
% 0.21/0.47 tff(68,plain,(~product(e_2, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(69,plain,
% 0.21/0.47 (^[Y: $i, X: $i] : refl(((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) <=> ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(70,plain,
% 0.21/0.47 (![Y: $i, X: $i] : ((~group_element(X)) | 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_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[69])).
% 0.21/0.47 tff(71,plain,
% 0.21/0.47 (![Y: $i, X: $i] : ((~group_element(X)) | 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_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(72,plain,
% 0.21/0.47 (^[Y: $i, X: $i] : 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)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(73,plain,
% 0.21/0.47 (![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)) <=> ![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[72])).
% 0.21/0.47 tff(74,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))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_total_function1')).
% 0.21/0.47 tff(75,plain,
% 0.21/0.47 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.21/0.47 tff(76,plain,
% 0.21/0.47 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.21/0.47 tff(77,plain,(
% 0.21/0.47 ![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[76])).
% 0.21/0.47 tff(78,plain,
% 0.21/0.47 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.21/0.47 tff(79,plain,
% 0.21/0.47 (group_element(e_2) <=> group_element(e_2)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(80,axiom,(group_element(e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_2')).
% 0.21/0.47 tff(81,plain,
% 0.21/0.47 (group_element(e_2)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.21/0.47 tff(82,plain,
% 0.21/0.47 (group_element(e_1) <=> group_element(e_1)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(83,axiom,(group_element(e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_1')).
% 0.21/0.47 tff(84,plain,
% 0.21/0.47 (group_element(e_1)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.21/0.47 tff(85,plain,
% 0.21/0.47 (((~![Y: $i, X: $i] : ((~group_element(X)) | 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_1) | product(e_2, e_1, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | 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_1) | product(e_2, e_1, e_2))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(86,plain,
% 0.21/0.47 (((~group_element(e_2)) | 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_1) | product(e_2, e_1, e_2))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(87,plain,
% 0.21/0.47 (((~![Y: $i, X: $i] : ((~group_element(X)) | 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_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_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_1) | product(e_2, e_1, e_2)))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[86])).
% 0.21/0.47 tff(88,plain,
% 0.21/0.47 (((~![Y: $i, X: $i] : ((~group_element(X)) | 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_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_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_1) | product(e_2, e_1, e_2))),
% 0.21/0.47 inference(transitivity,[status(thm)],[87, 85])).
% 0.21/0.47 tff(89,plain,
% 0.21/0.47 ((~![Y: $i, X: $i] : ((~group_element(X)) | 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_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(90,plain,
% 0.21/0.47 ((~![Y: $i, X: $i] : ((~group_element(X)) | 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_1) | product(e_2, e_1, e_2)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.21/0.47 tff(91,plain,
% 0.21/0.47 (product(e_2, e_1, e_3) | product(e_2, e_1, e_1)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[90, 84, 81, 78, 68])).
% 0.21/0.47 tff(92,plain,
% 0.21/0.47 (product(e_2, e_1, e_1)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[91, 56])).
% 0.21/0.47 tff(93,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.21/0.47 tff(94,plain,
% 0.21/0.47 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(95,plain,
% 0.21/0.47 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[94])).
% 0.21/0.47 tff(96,plain,
% 0.21/0.47 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(97,plain,
% 0.21/0.47 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite(((~product(W, Y, X)) | (~product(Z, Y, X))) <=> ((~product(Z, Y, X)) | (~product(W, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> (((~product(Z, Y, X)) | (~product(W, Y, X))) | equalish(W, Z)))), rewrite((((~product(Z, Y, X)) | (~product(W, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))), ((((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(98,plain,
% 0.21/0.47 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[97])).
% 0.21/0.47 tff(99,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(W, Y, X)) | (~product(Z, Y, X))) | equalish(W, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_left_cancellation')).
% 0.21/0.47 tff(100,plain,
% 0.21/0.47 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.21/0.47 tff(101,plain,
% 0.21/0.47 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.21/0.47 tff(102,plain,(
% 0.21/0.47 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[101])).
% 0.21/0.47 tff(103,plain,
% 0.21/0.47 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.21/0.47 tff(104,plain,
% 0.21/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(105,plain,
% 0.21/0.47 ((equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1))) <=> (equalish(e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(106,plain,
% 0.21/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[105])).
% 0.21/0.47 tff(107,plain,
% 0.21/0.47 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[106, 104])).
% 0.21/0.48 tff(108,plain,
% 0.21/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(109,plain,
% 0.21/0.48 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.21/0.48 tff(110,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[109, 60, 103, 93, 1])).
% 0.21/0.48 tff(111,plain,((~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(112,plain,
% 0.21/0.48 (~product(e_1, e_1, e_1)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[111, 92])).
% 0.21/0.48 tff(113,plain,
% 0.21/0.48 (^[W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : refl(((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) <=> ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(114,plain,
% 0.21/0.48 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) <=> ![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[113])).
% 0.21/0.48 tff(115,plain,
% 0.21/0.48 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) <=> ![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(116,plain,
% 0.21/0.48 (^[W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) <=> ((~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))), (((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) <=> (((~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~next(Y, W))))), rewrite((((~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~next(Y, W))) <=> ((~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))), (((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) <=> ((~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))))), ((((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) | (~greater(Y, X))) <=> (((~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~greater(Y, X))))), rewrite((((~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~greater(Y, X))) <=> ((~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))), ((((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) | (~greater(Y, X))) <=> ((~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))))), (((((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) | (~greater(Y, X))) | (~greater(Z1, Z2))) <=> (((~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~greater(Z1, Z2))))), rewrite((((~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1))) | (~greater(Z1, Z2))) <=> ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))), (((((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) | (~greater(Y, X))) | (~greater(Z1, Z2))) <=> ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(117,plain,
% 0.21/0.48 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((((((~cycle(X, Z1)) | (~cycle(Y, e_0))) | (~cycle(W, Z2))) | (~next(Y, W))) | (~greater(Y, X))) | (~greater(Z1, Z2))) <=> ![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[116])).
% 0.21/0.48 tff(118,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/sandbox2/benchmark/theBenchmark.p','cycle5')).
% 0.21/0.48 tff(119,plain,
% 0.21/0.48 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.21/0.48 tff(120,plain,
% 0.21/0.48 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.21/0.48 tff(121,plain,(
% 0.21/0.48 ![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.21/0.48 inference(skolemize,[status(sab)],[120])).
% 0.21/0.48 tff(122,plain,
% 0.21/0.48 (![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[121, 114])).
% 0.21/0.48 tff(123,plain,
% 0.21/0.48 (cycle(e_3, e_0) <=> cycle(e_3, e_0)),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(124,axiom,(cycle(e_3, e_0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cycle3')).
% 0.21/0.48 tff(125,plain,
% 0.21/0.48 (cycle(e_3, e_0)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.21/0.48 tff(126,plain,
% 0.21/0.48 (greater(e_2, e_1) <=> greater(e_2, e_1)),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(127,axiom,(greater(e_2, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_greater_e_1')).
% 0.21/0.48 tff(128,plain,
% 0.21/0.48 (greater(e_2, e_1)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.21/0.48 tff(129,plain,
% 0.21/0.48 (greater(e_1, e_0) <=> greater(e_1, e_0)),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(130,axiom,(greater(e_1, e_0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_greater_e_0')).
% 0.21/0.48 tff(131,plain,
% 0.21/0.48 (greater(e_1, e_0)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.21/0.48 tff(132,plain,
% 0.21/0.48 (next(e_2, e_3) <=> next(e_2, e_3)),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(133,axiom,(next(e_2, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_then_e_3')).
% 0.21/0.48 tff(134,plain,
% 0.21/0.48 (next(e_2, e_3)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.21/0.48 tff(135,plain,
% 0.21/0.48 (((~![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_3, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~cycle(e_1, 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_3, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_1)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(136,plain,
% 0.21/0.48 (((~greater(e_1, e_0)) | (~greater(e_2, e_1)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_0)) | (~cycle(e_1, e_1))) <=> ((~cycle(e_3, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_1)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(137,plain,
% 0.21/0.48 (((~![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_2, e_1)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_0)) | (~cycle(e_1, 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_3, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_1))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[136])).
% 0.21/0.48 tff(138,plain,
% 0.21/0.48 (((~![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_2, e_1)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_0)) | (~cycle(e_1, 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_3, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_1)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[137, 135])).
% 0.21/0.48 tff(139,plain,
% 0.21/0.48 ((~![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_2, e_1)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_0)) | (~cycle(e_1, e_1)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(140,plain,
% 0.21/0.48 ((~![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_3, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_1))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.21/0.48 tff(141,plain,
% 0.21/0.48 ((~cycle(e_2, e_0)) | (~cycle(e_1, e_1))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[140, 134, 131, 128, 125, 122])).
% 0.21/0.48 tff(142,plain,
% 0.21/0.48 (~cycle(e_1, e_1)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[141, 35])).
% 0.21/0.48 tff(143,plain,
% 0.21/0.48 (greater(e_2, e_0) <=> greater(e_2, e_0)),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(144,axiom,(greater(e_2, e_0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_2_greater_e_0')).
% 0.21/0.48 tff(145,plain,
% 0.21/0.48 (greater(e_2, e_0)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.21/0.48 tff(146,plain,
% 0.21/0.48 (((~![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_3, e_0)) | (~cycle(e_2, e_0)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~cycle(e_1, 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_3, e_0)) | (~cycle(e_2, e_0)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_2)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(147,plain,
% 0.21/0.48 (((~greater(e_2, e_0)) | (~greater(e_2, e_1)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_0)) | (~cycle(e_1, e_2))) <=> ((~cycle(e_3, e_0)) | (~cycle(e_2, e_0)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_2)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(148,plain,
% 0.21/0.48 (((~![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_2, e_1)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_0)) | (~cycle(e_1, 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_3, e_0)) | (~cycle(e_2, e_0)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_2))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[147])).
% 0.21/0.48 tff(149,plain,
% 0.21/0.48 (((~![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_2, e_1)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_0)) | (~cycle(e_1, 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_3, e_0)) | (~cycle(e_2, e_0)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_2)))),
% 0.21/0.49 inference(transitivity,[status(thm)],[148, 146])).
% 0.21/0.49 tff(150,plain,
% 0.21/0.49 ((~![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_2, e_1)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_0)) | (~cycle(e_1, e_2)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(151,plain,
% 0.21/0.49 ((~![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_3, e_0)) | (~cycle(e_2, e_0)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_2))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.21/0.49 tff(152,plain,
% 0.21/0.49 ((~cycle(e_2, e_0)) | (~cycle(e_1, e_2))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[151, 134, 145, 128, 125, 122])).
% 0.21/0.49 tff(153,plain,
% 0.21/0.49 (~cycle(e_1, e_2)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[152, 35])).
% 0.21/0.49 tff(154,plain,
% 0.21/0.49 (^[X: $i] : refl((cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) <=> (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(155,plain,
% 0.21/0.49 (![X: $i] : (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) <=> ![X: $i] : (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[154])).
% 0.21/0.49 tff(156,plain,
% 0.21/0.49 (![X: $i] : (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) <=> ![X: $i] : (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(157,plain,
% 0.21/0.49 (^[X: $i] : 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)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(158,plain,
% 0.21/0.49 (![X: $i] : ((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) <=> ![X: $i] : (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[157])).
% 0.21/0.49 tff(159,axiom,(![X: $i] : ((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cycle2')).
% 0.21/0.49 tff(160,plain,
% 0.21/0.49 (![X: $i] : (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.21/0.49 tff(161,plain,
% 0.21/0.49 (![X: $i] : (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[160, 156])).
% 0.21/0.49 tff(162,plain,(
% 0.21/0.49 ![X: $i] : (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[161])).
% 0.21/0.49 tff(163,plain,
% 0.21/0.49 (![X: $i] : (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[162, 155])).
% 0.21/0.49 tff(164,plain,
% 0.21/0.49 (((~![X: $i] : (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_1, e_2) | cycle(e_1, e_1) | cycle(e_1, e_0) | (~group_element(e_1)))) <=> ((~![X: $i] : (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_1, e_2) | cycle(e_1, e_1) | cycle(e_1, e_0) | (~group_element(e_1)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(165,plain,
% 0.21/0.49 ((~![X: $i] : (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_1, e_2) | cycle(e_1, e_1) | cycle(e_1, e_0) | (~group_element(e_1)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(166,plain,
% 0.21/0.49 ((~![X: $i] : (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_1, e_2) | cycle(e_1, e_1) | cycle(e_1, e_0) | (~group_element(e_1))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.21/0.49 tff(167,plain,
% 0.21/0.49 (cycle(e_1, e_2) | cycle(e_1, e_1) | cycle(e_1, e_0)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[166, 163, 84])).
% 0.21/0.49 tff(168,plain,
% 0.21/0.49 (cycle(e_1, e_0)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[167, 153, 142])).
% 0.21/0.49 tff(169,plain,
% 0.21/0.49 (greater(e_3, e_1) <=> greater(e_3, e_1)),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(170,axiom,(greater(e_3, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_3_greater_e_1')).
% 0.21/0.49 tff(171,plain,
% 0.21/0.49 (greater(e_3, e_1)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.21/0.49 tff(172,plain,
% 0.21/0.49 (((~![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)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(173,plain,
% 0.21/0.49 (((~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)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(174,plain,
% 0.21/0.49 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_3, e_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))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[173])).
% 0.21/0.49 tff(175,plain,
% 0.21/0.49 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_3, e_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)))),
% 0.21/0.49 inference(transitivity,[status(thm)],[174, 172])).
% 0.21/0.49 tff(176,plain,
% 0.21/0.49 ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_3, e_1)) | (~product(e_1, e_1, e_3)) | (~cycle(e_1, e_0)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(177,plain,
% 0.21/0.49 ((~![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))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.21/0.49 tff(178,plain,
% 0.21/0.49 ((~cycle(e_1, e_0)) | (~product(e_1, e_1, e_3))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[177, 171, 45])).
% 0.21/0.49 tff(179,plain,
% 0.21/0.49 (~product(e_1, e_1, e_3)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[178, 168])).
% 0.21/0.49 tff(180,plain,
% 0.21/0.49 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~cycle(e_1, e_0)) | (~greater(e_2, e_1)) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_2, e_1)) | (~product(e_1, e_1, e_2)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(181,plain,
% 0.21/0.49 (((~greater(e_2, e_1)) | (~product(e_1, e_1, e_2)) | (~cycle(e_1, e_0))) <=> ((~cycle(e_1, e_0)) | (~greater(e_2, e_1)) | (~product(e_1, e_1, e_2)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(182,plain,
% 0.21/0.49 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_2, e_1)) | (~product(e_1, e_1, e_2)) | (~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_2, e_1)) | (~product(e_1, e_1, e_2))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[181])).
% 0.21/0.49 tff(183,plain,
% 0.21/0.49 (((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_2, e_1)) | (~product(e_1, e_1, e_2)) | (~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_2, e_1)) | (~product(e_1, e_1, e_2)))),
% 0.21/0.49 inference(transitivity,[status(thm)],[182, 180])).
% 0.21/0.49 tff(184,plain,
% 0.21/0.49 ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | ((~greater(e_2, e_1)) | (~product(e_1, e_1, e_2)) | (~cycle(e_1, e_0)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(185,plain,
% 0.21/0.49 ((~![Y: $i, X: $i] : ((~greater(Y, X)) | (~product(X, e_1, Y)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_2, e_1)) | (~product(e_1, e_1, e_2))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.21/0.49 tff(186,plain,
% 0.21/0.49 ((~cycle(e_1, e_0)) | (~product(e_1, e_1, e_2))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[185, 128, 45])).
% 0.21/0.49 tff(187,plain,
% 0.21/0.49 (~product(e_1, e_1, e_2)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[186, 168])).
% 0.21/0.49 tff(188,plain,
% 0.21/0.49 (((~![Y: $i, X: $i] : ((~group_element(X)) | 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_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | 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_1))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(189,plain,
% 0.21/0.49 (((~group_element(e_1)) | 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_1))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(190,plain,
% 0.21/0.49 (((~![Y: $i, X: $i] : ((~group_element(X)) | 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_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_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_1)))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[189])).
% 0.21/0.49 tff(191,plain,
% 0.21/0.49 (((~![Y: $i, X: $i] : ((~group_element(X)) | 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_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_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_1))),
% 0.21/0.49 inference(transitivity,[status(thm)],[190, 188])).
% 0.21/0.49 tff(192,plain,
% 0.21/0.49 ((~![Y: $i, X: $i] : ((~group_element(X)) | 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_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(193,plain,
% 0.21/0.49 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | product(e_1, e_1, e_2) | product(e_1, e_1, e_3) | product(e_1, e_1, e_1)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.21/0.49 tff(194,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[193, 84, 78, 187, 179, 112])).
% 0.21/0.49 tff(195,plain,(~cycle(e_2, e_0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(196,assumption,(cycle(e_2, e_2)), introduced(assumption)).
% 0.21/0.49 tff(197,plain,
% 0.21/0.49 (^[W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : refl(((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) <=> ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(198,plain,
% 0.21/0.49 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) <=> ![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[197])).
% 0.21/0.49 tff(199,plain,
% 0.21/0.49 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) <=> ![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(200,plain,
% 0.21/0.49 (^[W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) <=> ((~cycle(X, Y)) | (~next(X, W)) | (~cycle(W, Z)))), (((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) <=> (((~cycle(X, Y)) | (~next(X, W)) | (~cycle(W, Z))) | (~greater(Y, e_0))))), rewrite((((~cycle(X, Y)) | (~next(X, W)) | (~cycle(W, Z))) | (~greater(Y, e_0))) <=> ((~cycle(X, Y)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))), (((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) <=> ((~cycle(X, Y)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))))), ((((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) | (~next(Z, Z1))) <=> (((~cycle(X, Y)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) | (~next(Z, Z1))))), rewrite((((~cycle(X, Y)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) | (~next(Z, Z1))) <=> ((~cycle(X, Y)) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))), ((((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) | (~next(Z, Z1))) <=> ((~cycle(X, Y)) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))))), (((((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) | (~next(Z, Z1))) | equalish(Y, Z1)) <=> (((~cycle(X, Y)) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) | equalish(Y, Z1)))), rewrite((((~cycle(X, Y)) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z))) | equalish(Y, Z1)) <=> ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))), (((((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) | (~next(Z, Z1))) | equalish(Y, Z1)) <=> ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(201,plain,
% 0.21/0.49 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((((((~cycle(X, Y)) | (~cycle(W, Z))) | (~next(X, W))) | (~greater(Y, e_0))) | (~next(Z, Z1))) | equalish(Y, Z1)) <=> ![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[200])).
% 0.21/0.49 tff(202,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/sandbox2/benchmark/theBenchmark.p','cycle4')).
% 0.21/0.49 tff(203,plain,
% 0.21/0.49 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.21/0.49 tff(204,plain,
% 0.21/0.49 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[203, 199])).
% 0.21/0.49 tff(205,plain,(
% 0.21/0.49 ![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[204])).
% 0.21/0.49 tff(206,plain,
% 0.21/0.49 (![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[205, 198])).
% 0.21/0.49 tff(207,plain,
% 0.21/0.49 (next(e_0, e_1) <=> next(e_0, e_1)),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(208,axiom,(next(e_0, e_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_0_then_e_1')).
% 0.21/0.49 tff(209,plain,
% 0.21/0.49 (next(e_0, e_1)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.21/0.49 tff(210,plain,
% 0.21/0.49 (((~![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_3, e_0)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, 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_3, e_0)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~next(e_0, e_1)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(211,plain,
% 0.21/0.49 (((~cycle(e_2, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0))) <=> (equalish(e_2, e_1) | (~cycle(e_3, e_0)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~next(e_0, e_1)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(212,plain,
% 0.21/0.49 (((~![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_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, 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_3, e_0)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~next(e_0, e_1))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[211])).
% 0.21/0.49 tff(213,plain,
% 0.21/0.49 (((~![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_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, 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_3, e_0)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~next(e_0, e_1)))),
% 0.21/0.49 inference(transitivity,[status(thm)],[212, 210])).
% 0.21/0.49 tff(214,plain,
% 0.21/0.49 ((~![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_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(215,plain,
% 0.21/0.49 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_1) | (~cycle(e_3, e_0)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~next(e_0, e_1))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.21/0.49 tff(216,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[215, 209, 134, 145, 125, 206, 60, 196])).
% 0.21/0.49 tff(217,plain,(~cycle(e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(218,plain,
% 0.21/0.49 (((~![X: $i] : (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0) | (~group_element(e_2)))) <=> ((~![X: $i] : (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0) | (~group_element(e_2)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(219,plain,
% 0.21/0.50 ((~![X: $i] : (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0) | (~group_element(e_2)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(220,plain,
% 0.21/0.50 ((~![X: $i] : (cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0) | (~group_element(e_2))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.21/0.50 tff(221,plain,
% 0.21/0.50 (cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[220, 163, 81])).
% 0.21/0.50 tff(222,plain,
% 0.21/0.50 (cycle(e_2, e_1) | cycle(e_2, e_0)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[221, 217])).
% 0.21/0.50 tff(223,plain,
% 0.21/0.50 (cycle(e_2, e_1)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[222, 195])).
% 0.21/0.50 tff(224,plain,
% 0.21/0.50 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(225,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.21/0.50 tff(226,plain,
% 0.21/0.50 (~equalish(e_1, e_3)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.21/0.50 tff(227,plain,
% 0.21/0.50 (^[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))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(228,plain,
% 0.21/0.50 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z))) <=> ![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[227])).
% 0.21/0.50 tff(229,plain,
% 0.21/0.50 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z))) <=> ![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(230,plain,
% 0.21/0.50 (^[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)))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(231,plain,
% 0.21/0.50 (![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)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[230])).
% 0.21/0.50 tff(232,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/sandbox2/benchmark/theBenchmark.p','cycle7')).
% 0.21/0.50 tff(233,plain,
% 0.21/0.50 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.21/0.50 tff(234,plain,
% 0.21/0.50 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[233, 229])).
% 0.21/0.50 tff(235,plain,(
% 0.21/0.50 ![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.21/0.50 inference(skolemize,[status(sab)],[234])).
% 0.21/0.50 tff(236,plain,
% 0.21/0.50 (![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[235, 228])).
% 0.21/0.50 tff(237,plain,
% 0.21/0.50 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_1, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~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_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(238,plain,
% 0.21/0.50 (((~greater(e_1, e_0)) | (~cycle(e_2, e_1)) | equalish(e_1, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_1))) <=> (equalish(e_1, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(239,plain,
% 0.21/0.50 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_2, e_1)) | equalish(e_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_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_1))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[238])).
% 0.21/0.50 tff(240,plain,
% 0.21/0.50 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_2, e_1)) | equalish(e_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_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_1)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[239, 237])).
% 0.21/0.50 tff(241,plain,
% 0.21/0.50 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_1, e_0)) | (~cycle(e_2, e_1)) | equalish(e_1, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_1)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(242,plain,
% 0.21/0.50 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_1, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_1))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.21/0.50 tff(243,plain,
% 0.21/0.50 (~product(e_2, e_1, e_1)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[242, 134, 131, 236, 226, 223])).
% 0.21/0.50 tff(244,plain,
% 0.21/0.50 (product(e_2, e_1, e_3)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[91, 243])).
% 0.21/0.50 tff(245,plain,
% 0.21/0.50 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(246,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.21/0.50 tff(247,plain,
% 0.21/0.50 (~equalish(e_1, e_2)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.21/0.50 tff(248,plain,
% 0.21/0.50 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_1, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_2)))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_2)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(249,plain,
% 0.21/0.50 (((~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_1, e_2)) | equalish(e_1, e_2)) <=> (equalish(e_1, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_2)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(250,plain,
% 0.21/0.50 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_1, e_2)) | equalish(e_1, e_2))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | (equalish(e_1, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_2))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[249])).
% 0.21/0.50 tff(251,plain,
% 0.21/0.50 (((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_1, e_2)) | equalish(e_1, e_2))) <=> ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_2)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[250, 248])).
% 0.21/0.50 tff(252,plain,
% 0.21/0.50 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | ((~product(e_2, e_2, e_2)) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_1, e_2)) | equalish(e_1, e_2))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(253,plain,
% 0.21/0.50 ((~![Y2: $i, Y1: $i, Z1: $i, X2: $i, Z2: $i, X1: $i] : ((~product(Z2, Y2, X2)) | (~product(Z2, Y1, X1)) | (~product(X2, Y2, Z1)) | (~product(X1, Y1, Z1)) | equalish(Y1, Y2))) | equalish(e_1, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_2))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.21/0.50 tff(254,plain,
% 0.21/0.50 (~product(e_3, e_1, e_2)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[253, 247, 21, 244, 34])).
% 0.21/0.50 tff(255,plain,
% 0.21/0.50 (group_element(e_3) <=> group_element(e_3)),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(256,axiom,(group_element(e_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','element_3')).
% 0.21/0.50 tff(257,plain,
% 0.21/0.50 (group_element(e_3)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.21/0.50 tff(258,plain,
% 0.21/0.50 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (product(e_3, e_1, e_1) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3) | (~group_element(e_1)) | (~group_element(e_3)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | product(e_3, e_1, e_1) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3) | (~group_element(e_1)) | (~group_element(e_3)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(259,plain,
% 0.21/0.50 (((~group_element(e_3)) | 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))) <=> (product(e_3, e_1, e_1) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3) | (~group_element(e_1)) | (~group_element(e_3)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(260,plain,
% 0.21/0.51 (((~![Y: $i, X: $i] : ((~group_element(X)) | 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_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_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (product(e_3, e_1, e_1) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3) | (~group_element(e_1)) | (~group_element(e_3))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[259])).
% 0.21/0.51 tff(261,plain,
% 0.21/0.51 (((~![Y: $i, X: $i] : ((~group_element(X)) | 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_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_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | product(e_3, e_1, e_1) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3) | (~group_element(e_1)) | (~group_element(e_3)))),
% 0.21/0.51 inference(transitivity,[status(thm)],[260, 258])).
% 0.21/0.51 tff(262,plain,
% 0.21/0.51 ((~![Y: $i, X: $i] : ((~group_element(X)) | 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_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(263,plain,
% 0.21/0.51 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | product(e_3, e_1, e_1) | product(e_3, e_1, e_2) | product(e_3, e_1, e_3) | (~group_element(e_1)) | (~group_element(e_3))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.21/0.51 tff(264,plain,
% 0.21/0.51 (product(e_3, e_1, e_1) | product(e_3, e_1, e_3)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[263, 84, 257, 78, 254])).
% 0.21/0.51 tff(265,plain,
% 0.21/0.51 (product(e_3, e_1, e_1)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[264, 32])).
% 0.21/0.51 tff(266,plain,
% 0.21/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(267,plain,
% 0.21/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_3) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(268,plain,
% 0.21/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_3) | (~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.21/0.51 tff(269,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[268, 226, 103, 265, 1])).
% 0.21/0.51 tff(270,plain,(~product(e_1, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.51 tff(271,plain,
% 0.21/0.51 ((~![X: $i] : product(X, X, X)) | product(e_1, e_1, e_1)),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(272,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[271, 8, 270])).
% 0.21/0.51 % SZS output end Proof
%------------------------------------------------------------------------------