TSTP Solution File: GRP128-3.005 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP128-3.005 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 22:26:10 EDT 2022
% Result : Unsatisfiable 0.56s 0.59s
% Output : Proof 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP128-3.005 : TPTP v8.1.0. Released v1.2.0.
% 0.12/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.35 % Computer : n021.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Wed Aug 31 14:58:27 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.15/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.36 Usage: tptp [options] [-file:]file
% 0.15/0.36 -h, -? prints this message.
% 0.15/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.36 -m, -model generate model.
% 0.15/0.36 -p, -proof generate proof.
% 0.15/0.36 -c, -core generate unsat core of named formulas.
% 0.15/0.36 -st, -statistics display statistics.
% 0.15/0.36 -t:timeout set timeout (in second).
% 0.15/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.36 -<param>:<value> configuration parameter and value.
% 0.15/0.36 -o:<output-file> file to place output in.
% 0.56/0.59 % SZS status Unsatisfiable
% 0.56/0.59 % SZS output start Proof
% 0.56/0.59 tff(product_type, type, (
% 0.56/0.59 product: ( $i * $i * $i ) > $o)).
% 0.56/0.59 tff(e_5_type, type, (
% 0.56/0.59 e_5: $i)).
% 0.56/0.59 tff(e_2_type, type, (
% 0.56/0.59 e_2: $i)).
% 0.56/0.59 tff(e_4_type, type, (
% 0.56/0.59 e_4: $i)).
% 0.56/0.59 tff(e_1_type, type, (
% 0.56/0.59 e_1: $i)).
% 0.56/0.59 tff(cycle_type, type, (
% 0.56/0.59 cycle: ( $i * $i ) > $o)).
% 0.56/0.59 tff(e_0_type, type, (
% 0.56/0.59 e_0: $i)).
% 0.56/0.59 tff(next_type, type, (
% 0.56/0.59 next: ( $i * $i ) > $o)).
% 0.56/0.59 tff(greater_type, type, (
% 0.56/0.59 greater: ( $i * $i ) > $o)).
% 0.56/0.59 tff(e_3_type, type, (
% 0.56/0.59 e_3: $i)).
% 0.56/0.59 tff(equalish_type, type, (
% 0.56/0.59 equalish: ( $i * $i ) > $o)).
% 0.56/0.59 tff(group_element_type, type, (
% 0.56/0.59 group_element: $i > $o)).
% 0.56/0.59 tff(1,assumption,(~product(e_4, e_5, e_2)), introduced(assumption)).
% 0.56/0.59 tff(2,assumption,(cycle(e_4, e_0)), introduced(assumption)).
% 0.56/0.59 tff(3,plain,
% 0.56/0.59 (^[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))))),
% 0.56/0.59 inference(bind,[status(th)],[])).
% 0.56/0.59 tff(4,plain,
% 0.56/0.59 (![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)))),
% 0.56/0.59 inference(quant_intro,[status(thm)],[3])).
% 0.56/0.59 tff(5,plain,
% 0.56/0.59 (![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)))),
% 0.56/0.59 inference(rewrite,[status(thm)],[])).
% 0.56/0.59 tff(6,plain,
% 0.56/0.59 (^[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)))))),
% 0.56/0.59 inference(bind,[status(th)],[])).
% 0.56/0.59 tff(7,plain,
% 0.56/0.59 (![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)))),
% 0.56/0.60 inference(quant_intro,[status(thm)],[6])).
% 0.56/0.60 tff(8,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')).
% 0.56/0.60 tff(9,plain,
% 0.56/0.60 (![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)))),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.56/0.60 tff(10,plain,
% 0.56/0.60 (![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)))),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.56/0.60 tff(11,plain,(
% 0.56/0.60 ![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)))),
% 0.56/0.60 inference(skolemize,[status(sab)],[10])).
% 0.56/0.60 tff(12,plain,
% 0.56/0.60 (![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)))),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.56/0.60 tff(13,plain,
% 0.56/0.60 (cycle(e_5, e_0) <=> cycle(e_5, e_0)),
% 0.56/0.60 inference(rewrite,[status(thm)],[])).
% 0.56/0.60 tff(14,axiom,(cycle(e_5, e_0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cycle3')).
% 0.56/0.60 tff(15,plain,
% 0.56/0.60 (cycle(e_5, e_0)),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.56/0.60 tff(16,plain,
% 0.56/0.60 (greater(e_4, e_1) <=> greater(e_4, e_1)),
% 0.56/0.60 inference(rewrite,[status(thm)],[])).
% 0.56/0.60 tff(17,axiom,(greater(e_4, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_greater_e_1')).
% 0.56/0.60 tff(18,plain,
% 0.56/0.60 (greater(e_4, e_1)),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.56/0.60 tff(19,plain,
% 0.56/0.60 (greater(e_4, e_0) <=> greater(e_4, e_0)),
% 0.56/0.60 inference(rewrite,[status(thm)],[])).
% 0.56/0.60 tff(20,axiom,(greater(e_4, e_0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_greater_e_0')).
% 0.56/0.60 tff(21,plain,
% 0.56/0.60 (greater(e_4, e_0)),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.56/0.60 tff(22,plain,
% 0.56/0.60 (next(e_4, e_5) <=> next(e_4, e_5)),
% 0.56/0.60 inference(rewrite,[status(thm)],[])).
% 0.56/0.60 tff(23,axiom,(next(e_4, e_5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_then_e_5')).
% 0.56/0.60 tff(24,plain,
% 0.56/0.60 (next(e_4, e_5)),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.56/0.60 tff(25,plain,
% 0.56/0.60 (((~![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_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_4)))) <=> ((~![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_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_4)))),
% 0.56/0.60 inference(rewrite,[status(thm)],[])).
% 0.56/0.60 tff(26,plain,
% 0.56/0.60 (((~greater(e_4, e_0)) | (~greater(e_4, e_1)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_1, e_4))) <=> ((~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_4)))),
% 0.56/0.60 inference(rewrite,[status(thm)],[])).
% 0.56/0.60 tff(27,plain,
% 0.56/0.60 (((~![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_4, e_0)) | (~greater(e_4, e_1)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_1, e_4)))) <=> ((~![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_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_4))))),
% 0.56/0.60 inference(monotonicity,[status(thm)],[26])).
% 0.56/0.60 tff(28,plain,
% 0.56/0.60 (((~![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_4, e_0)) | (~greater(e_4, e_1)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_1, e_4)))) <=> ((~![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_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_4)))),
% 0.56/0.60 inference(transitivity,[status(thm)],[27, 25])).
% 0.56/0.60 tff(29,plain,
% 0.56/0.60 ((~![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_4, e_0)) | (~greater(e_4, e_1)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_1, e_4)))),
% 0.56/0.60 inference(quant_inst,[status(thm)],[])).
% 0.56/0.60 tff(30,plain,
% 0.56/0.60 ((~![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_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_4))),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.56/0.60 tff(31,plain,
% 0.56/0.60 ((~cycle(e_4, e_0)) | (~cycle(e_1, e_4))),
% 0.56/0.60 inference(unit_resolution,[status(thm)],[30, 24, 21, 18, 15, 12])).
% 0.56/0.60 tff(32,plain,
% 0.56/0.60 (~cycle(e_1, e_4)),
% 0.56/0.60 inference(unit_resolution,[status(thm)],[31, 2])).
% 0.56/0.60 tff(33,plain,
% 0.56/0.60 (greater(e_3, e_0) <=> greater(e_3, e_0)),
% 0.56/0.60 inference(rewrite,[status(thm)],[])).
% 0.56/0.60 tff(34,axiom,(greater(e_3, e_0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_greater_e_0')).
% 0.56/0.60 tff(35,plain,
% 0.56/0.60 (greater(e_3, e_0)),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.56/0.60 tff(36,plain,
% 0.56/0.60 (((~![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_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_1)) | (~cycle(e_1, 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_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_3)))),
% 0.56/0.60 inference(rewrite,[status(thm)],[])).
% 0.56/0.60 tff(37,plain,
% 0.56/0.60 (((~greater(e_3, e_0)) | (~greater(e_4, e_1)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_1, e_3))) <=> ((~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_3)))),
% 0.56/0.60 inference(rewrite,[status(thm)],[])).
% 0.56/0.60 tff(38,plain,
% 0.56/0.60 (((~![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_4, e_1)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_1, 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_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_3))))),
% 0.56/0.60 inference(monotonicity,[status(thm)],[37])).
% 0.56/0.60 tff(39,plain,
% 0.56/0.60 (((~![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_4, e_1)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_1, 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_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_3)))),
% 0.56/0.60 inference(transitivity,[status(thm)],[38, 36])).
% 0.56/0.60 tff(40,plain,
% 0.56/0.60 ((~![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_4, e_1)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_1, e_3)))),
% 0.56/0.60 inference(quant_inst,[status(thm)],[])).
% 0.56/0.60 tff(41,plain,
% 0.56/0.60 ((~![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_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_3))),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.56/0.60 tff(42,plain,
% 0.56/0.60 ((~cycle(e_4, e_0)) | (~cycle(e_1, e_3))),
% 0.56/0.60 inference(unit_resolution,[status(thm)],[41, 24, 35, 18, 15, 12])).
% 0.56/0.60 tff(43,plain,
% 0.56/0.60 (~cycle(e_1, e_3)),
% 0.56/0.60 inference(unit_resolution,[status(thm)],[42, 2])).
% 0.56/0.60 tff(44,assumption,(product(e_1, e_1, e_4)), introduced(assumption)).
% 0.56/0.60 tff(45,plain,
% 0.56/0.60 (^[Y: $i, X: $i] : refl(((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0))) <=> ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0))))),
% 0.56/0.60 inference(bind,[status(th)],[])).
% 0.56/0.60 tff(46,plain,
% 0.56/0.60 (![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0))) <=> ![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))),
% 0.56/0.60 inference(quant_intro,[status(thm)],[45])).
% 0.56/0.60 tff(47,plain,
% 0.56/0.60 (![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0))) <=> ![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))),
% 0.56/0.60 inference(rewrite,[status(thm)],[])).
% 0.56/0.60 tff(48,plain,
% 0.56/0.60 (^[Y: $i, X: $i] : rewrite((((~cycle(X, e_0)) | (~product(X, e_1, Y))) | (~greater(Y, X))) <=> ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0))))),
% 0.56/0.60 inference(bind,[status(th)],[])).
% 0.56/0.60 tff(49,plain,
% 0.56/0.60 (![Y: $i, X: $i] : (((~cycle(X, e_0)) | (~product(X, e_1, Y))) | (~greater(Y, X))) <=> ![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))),
% 0.56/0.60 inference(quant_intro,[status(thm)],[48])).
% 0.56/0.60 tff(50,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')).
% 0.56/0.60 tff(51,plain,
% 0.56/0.60 (![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.56/0.60 tff(52,plain,
% 0.56/0.60 (![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.56/0.60 tff(53,plain,(
% 0.56/0.60 ![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))),
% 0.56/0.60 inference(skolemize,[status(sab)],[52])).
% 0.56/0.60 tff(54,plain,
% 0.56/0.60 (![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.56/0.60 tff(55,plain,
% 0.56/0.60 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~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] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_4, e_1)) | (~product(e_1, e_1, e_4)))),
% 0.56/0.60 inference(rewrite,[status(thm)],[])).
% 0.56/0.60 tff(56,plain,
% 0.56/0.60 (((~product(e_1, e_1, e_4)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_0))) <=> ((~cycle(e_1, e_0)) | (~greater(e_4, e_1)) | (~product(e_1, e_1, e_4)))),
% 0.56/0.60 inference(rewrite,[status(thm)],[])).
% 0.56/0.60 tff(57,plain,
% 0.56/0.60 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_1, e_1, e_4)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_1, e_0)) | (~greater(e_4, e_1)) | (~product(e_1, e_1, e_4))))),
% 0.56/0.60 inference(monotonicity,[status(thm)],[56])).
% 0.56/0.60 tff(58,plain,
% 0.56/0.60 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_1, e_1, e_4)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_4, e_1)) | (~product(e_1, e_1, e_4)))),
% 0.56/0.60 inference(transitivity,[status(thm)],[57, 55])).
% 0.56/0.60 tff(59,plain,
% 0.56/0.60 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_1, e_1, e_4)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_0)))),
% 0.56/0.60 inference(quant_inst,[status(thm)],[])).
% 0.56/0.60 tff(60,plain,
% 0.56/0.60 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_4, e_1)) | (~product(e_1, e_1, e_4))),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.56/0.60 tff(61,plain,
% 0.56/0.60 ((~cycle(e_1, e_0)) | (~product(e_1, e_1, e_4))),
% 0.56/0.60 inference(unit_resolution,[status(thm)],[60, 18, 54])).
% 0.56/0.60 tff(62,plain,
% 0.56/0.60 (~cycle(e_1, e_0)),
% 0.56/0.60 inference(unit_resolution,[status(thm)],[61, 44])).
% 0.56/0.60 tff(63,assumption,(~cycle(e_1, e_3)), introduced(assumption)).
% 0.56/0.60 tff(64,assumption,(~cycle(e_1, e_4)), introduced(assumption)).
% 0.56/0.60 tff(65,assumption,(cycle(e_1, e_1)), introduced(assumption)).
% 0.56/0.60 tff(66,plain,
% 0.56/0.60 ((~equalish(e_4, e_2)) <=> (~equalish(e_4, e_2))),
% 0.56/0.60 inference(rewrite,[status(thm)],[])).
% 0.56/0.60 tff(67,axiom,(~equalish(e_4, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_is_not_e_2')).
% 0.56/0.60 tff(68,plain,
% 0.56/0.60 (~equalish(e_4, e_2)),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.56/0.60 tff(69,plain,
% 0.56/0.60 (^[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))))),
% 0.56/0.60 inference(bind,[status(th)],[])).
% 0.56/0.60 tff(70,plain,
% 0.56/0.60 (![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)))),
% 0.56/0.60 inference(quant_intro,[status(thm)],[69])).
% 0.56/0.60 tff(71,plain,
% 0.56/0.60 (![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)))),
% 0.56/0.60 inference(rewrite,[status(thm)],[])).
% 0.56/0.60 tff(72,plain,
% 0.56/0.60 (^[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)))))),
% 0.56/0.60 inference(bind,[status(th)],[])).
% 0.56/0.60 tff(73,plain,
% 0.56/0.60 (![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)))),
% 0.56/0.60 inference(quant_intro,[status(thm)],[72])).
% 0.56/0.60 tff(74,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')).
% 0.56/0.60 tff(75,plain,
% 0.56/0.60 (![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)))),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.56/0.60 tff(76,plain,
% 0.56/0.60 (![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)))),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.56/0.60 tff(77,plain,(
% 0.56/0.60 ![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)))),
% 0.56/0.60 inference(skolemize,[status(sab)],[76])).
% 0.56/0.60 tff(78,plain,
% 0.56/0.60 (![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)))),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.56/0.60 tff(79,plain,
% 0.56/0.60 (greater(e_1, e_0) <=> greater(e_1, e_0)),
% 0.56/0.60 inference(rewrite,[status(thm)],[])).
% 0.56/0.60 tff(80,axiom,(greater(e_1, e_0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_greater_e_0')).
% 0.56/0.60 tff(81,plain,
% 0.56/0.60 (greater(e_1, e_0)),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.56/0.60 tff(82,plain,
% 0.56/0.60 (next(e_1, e_2) <=> next(e_1, e_2)),
% 0.56/0.60 inference(rewrite,[status(thm)],[])).
% 0.56/0.60 tff(83,axiom,(next(e_1, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_then_e_2')).
% 0.56/0.60 tff(84,plain,
% 0.56/0.60 (next(e_1, e_2)),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.56/0.60 tff(85,plain,
% 0.56/0.60 (((~![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)))),
% 0.56/0.60 inference(rewrite,[status(thm)],[])).
% 0.56/0.60 tff(86,plain,
% 0.56/0.60 (((~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)))),
% 0.56/0.60 inference(rewrite,[status(thm)],[])).
% 0.56/0.60 tff(87,plain,
% 0.56/0.60 (((~![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))))),
% 0.56/0.60 inference(monotonicity,[status(thm)],[86])).
% 0.56/0.60 tff(88,plain,
% 0.56/0.60 (((~![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)))),
% 0.56/0.60 inference(transitivity,[status(thm)],[87, 85])).
% 0.56/0.60 tff(89,plain,
% 0.56/0.60 ((~![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)))),
% 0.56/0.60 inference(quant_inst,[status(thm)],[])).
% 0.56/0.60 tff(90,plain,
% 0.56/0.60 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_4))),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.56/0.61 tff(91,plain,
% 0.56/0.61 ($false),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[90, 84, 81, 78, 68, 65, 44])).
% 0.56/0.61 tff(92,plain,((~cycle(e_1, e_1)) | (~product(e_1, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.61 tff(93,plain,
% 0.56/0.61 (~cycle(e_1, e_1)),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[92, 44])).
% 0.56/0.61 tff(94,plain,
% 0.56/0.61 (group_element(e_1) <=> group_element(e_1)),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(95,axiom,(group_element(e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_1')).
% 0.56/0.61 tff(96,plain,
% 0.56/0.61 (group_element(e_1)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.56/0.61 tff(97,plain,
% 0.56/0.61 (^[X: $i] : refl((cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) <=> (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))))),
% 0.56/0.61 inference(bind,[status(th)],[])).
% 0.56/0.61 tff(98,plain,
% 0.56/0.61 (![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) <=> ![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.56/0.61 inference(quant_intro,[status(thm)],[97])).
% 0.56/0.61 tff(99,plain,
% 0.56/0.61 (![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) <=> ![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(100,plain,
% 0.56/0.61 (^[X: $i] : trans(monotonicity(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))))), (((((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) | cycle(X, e_3)) | cycle(X, e_4)) <=> ((cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) | cycle(X, e_4)))), rewrite(((cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X))) | cycle(X, e_4)) <=> (cycle(X, e_4) | 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_4)) <=> (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))))),
% 0.56/0.61 inference(bind,[status(th)],[])).
% 0.56/0.61 tff(101,plain,
% 0.56/0.61 (![X: $i] : ((((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) | cycle(X, e_3)) | cycle(X, e_4)) <=> ![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.56/0.61 inference(quant_intro,[status(thm)],[100])).
% 0.56/0.61 tff(102,axiom,(![X: $i] : ((((((~group_element(X)) | cycle(X, e_0)) | cycle(X, e_1)) | cycle(X, e_2)) | cycle(X, e_3)) | cycle(X, e_4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cycle2')).
% 0.56/0.61 tff(103,plain,
% 0.56/0.61 (![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.56/0.61 tff(104,plain,
% 0.56/0.61 (![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.56/0.61 tff(105,plain,(
% 0.56/0.61 ![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.56/0.61 inference(skolemize,[status(sab)],[104])).
% 0.56/0.61 tff(106,plain,
% 0.56/0.61 (![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.56/0.61 tff(107,plain,
% 0.56/0.61 (((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_1, e_4) | 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_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_1, e_4) | cycle(e_1, e_3) | cycle(e_1, e_2) | cycle(e_1, e_1) | cycle(e_1, e_0) | (~group_element(e_1)))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(108,plain,
% 0.56/0.61 ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_1, e_4) | cycle(e_1, e_3) | cycle(e_1, e_2) | cycle(e_1, e_1) | cycle(e_1, e_0) | (~group_element(e_1)))),
% 0.56/0.61 inference(quant_inst,[status(thm)],[])).
% 0.56/0.61 tff(109,plain,
% 0.56/0.61 ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_1, e_4) | cycle(e_1, e_3) | cycle(e_1, e_2) | cycle(e_1, e_1) | cycle(e_1, e_0) | (~group_element(e_1))),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.56/0.61 tff(110,plain,
% 0.56/0.61 (cycle(e_1, e_4) | cycle(e_1, e_3) | cycle(e_1, e_2) | cycle(e_1, e_1) | cycle(e_1, e_0)),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[109, 106, 96])).
% 0.56/0.61 tff(111,plain,
% 0.56/0.61 (cycle(e_1, e_2)),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[110, 93, 64, 63, 62])).
% 0.56/0.61 tff(112,plain,
% 0.56/0.61 (greater(e_2, e_0) <=> greater(e_2, e_0)),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(113,axiom,(greater(e_2, e_0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_greater_e_0')).
% 0.56/0.61 tff(114,plain,
% 0.56/0.61 (greater(e_2, e_0)),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.56/0.61 tff(115,plain,
% 0.56/0.61 (((~![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)))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(116,plain,
% 0.56/0.61 (((~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)))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(117,plain,
% 0.56/0.61 (((~![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))))),
% 0.56/0.61 inference(monotonicity,[status(thm)],[116])).
% 0.56/0.61 tff(118,plain,
% 0.56/0.61 (((~![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)))),
% 0.56/0.61 inference(transitivity,[status(thm)],[117, 115])).
% 0.56/0.61 tff(119,plain,
% 0.56/0.61 ((~![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)))),
% 0.56/0.61 inference(quant_inst,[status(thm)],[])).
% 0.56/0.61 tff(120,plain,
% 0.56/0.61 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~product(e_1, e_1, e_4))),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.56/0.61 tff(121,plain,
% 0.56/0.61 ($false),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[120, 84, 114, 78, 68, 111, 44])).
% 0.56/0.61 tff(122,plain,((~product(e_1, e_1, e_4)) | cycle(e_1, e_4) | cycle(e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.61 tff(123,plain,
% 0.56/0.61 (~product(e_1, e_1, e_4)),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[122, 43, 32])).
% 0.56/0.61 tff(124,assumption,(~cycle(e_1, e_0)), introduced(assumption)).
% 0.56/0.61 tff(125,plain,
% 0.56/0.61 (((~![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_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_1, e_1)) | (~greater(e_4, 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_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_1, e_1)) | (~greater(e_4, e_1)))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(126,plain,
% 0.56/0.61 (((~greater(e_1, e_0)) | (~greater(e_4, e_1)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_1, e_1))) <=> ((~cycle(e_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_1, e_1)) | (~greater(e_4, e_1)))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(127,plain,
% 0.56/0.61 (((~![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_4, e_1)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, 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_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_1, e_1)) | (~greater(e_4, e_1))))),
% 0.56/0.61 inference(monotonicity,[status(thm)],[126])).
% 0.56/0.61 tff(128,plain,
% 0.56/0.61 (((~![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_4, e_1)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, 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_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_1, e_1)) | (~greater(e_4, e_1)))),
% 0.56/0.61 inference(transitivity,[status(thm)],[127, 125])).
% 0.56/0.61 tff(129,plain,
% 0.56/0.61 ((~![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_4, e_1)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_1, e_1)))),
% 0.56/0.61 inference(quant_inst,[status(thm)],[])).
% 0.56/0.61 tff(130,plain,
% 0.56/0.61 ((~![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_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_1, e_1)) | (~greater(e_4, e_1))),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.56/0.61 tff(131,plain,
% 0.56/0.61 ((~cycle(e_4, e_0)) | (~cycle(e_1, e_1))),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[130, 24, 81, 18, 15, 12])).
% 0.56/0.61 tff(132,plain,
% 0.56/0.61 (~cycle(e_1, e_1)),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[131, 2])).
% 0.56/0.61 tff(133,plain,
% 0.56/0.61 (((~![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_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, 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_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_2)))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(134,plain,
% 0.56/0.61 (((~greater(e_2, e_0)) | (~greater(e_4, e_1)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_1, e_2))) <=> ((~cycle(e_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_2)))),
% 0.56/0.61 inference(rewrite,[status(thm)],[])).
% 0.56/0.61 tff(135,plain,
% 0.56/0.61 (((~![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_4, e_1)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, 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_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_2))))),
% 0.56/0.61 inference(monotonicity,[status(thm)],[134])).
% 0.56/0.61 tff(136,plain,
% 0.56/0.61 (((~![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_4, e_1)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, 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_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_2)))),
% 0.56/0.61 inference(transitivity,[status(thm)],[135, 133])).
% 0.56/0.61 tff(137,plain,
% 0.56/0.61 ((~![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_4, e_1)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_1, e_2)))),
% 0.56/0.61 inference(quant_inst,[status(thm)],[])).
% 0.56/0.61 tff(138,plain,
% 0.56/0.61 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_2))),
% 0.56/0.61 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.56/0.61 tff(139,plain,
% 0.56/0.61 ((~cycle(e_4, e_0)) | (~cycle(e_1, e_2))),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[138, 24, 114, 18, 15, 12])).
% 0.56/0.61 tff(140,plain,
% 0.56/0.61 (~cycle(e_1, e_2)),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[139, 2])).
% 0.56/0.61 tff(141,plain,
% 0.56/0.61 ($false),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[110, 140, 132, 64, 63, 124])).
% 0.56/0.61 tff(142,plain,((~cycle(e_4, e_0)) | cycle(e_1, e_4) | cycle(e_1, e_3) | cycle(e_1, e_0)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.61 tff(143,plain,
% 0.56/0.62 (cycle(e_1, e_0)),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[142, 2, 43, 32])).
% 0.56/0.62 tff(144,assumption,(~product(e_1, e_1, e_1)), introduced(assumption)).
% 0.56/0.62 tff(145,assumption,(cycle(e_1, e_0)), introduced(assumption)).
% 0.56/0.62 tff(146,plain,
% 0.56/0.62 (greater(e_5, e_1) <=> greater(e_5, e_1)),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(147,axiom,(greater(e_5, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_5_greater_e_1')).
% 0.56/0.62 tff(148,plain,
% 0.56/0.62 (greater(e_5, e_1)),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.56/0.62 tff(149,plain,
% 0.56/0.62 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_1, e_0)) | (~greater(e_5, e_1)) | (~product(e_1, e_1, e_5)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_5, e_1)) | (~product(e_1, e_1, e_5)))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(150,plain,
% 0.56/0.62 (((~product(e_1, e_1, e_5)) | (~greater(e_5, e_1)) | (~cycle(e_1, e_0))) <=> ((~cycle(e_1, e_0)) | (~greater(e_5, e_1)) | (~product(e_1, e_1, e_5)))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(151,plain,
% 0.56/0.62 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_1, e_1, e_5)) | (~greater(e_5, e_1)) | (~cycle(e_1, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_1, e_0)) | (~greater(e_5, e_1)) | (~product(e_1, e_1, e_5))))),
% 0.56/0.62 inference(monotonicity,[status(thm)],[150])).
% 0.56/0.62 tff(152,plain,
% 0.56/0.62 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_1, e_1, e_5)) | (~greater(e_5, e_1)) | (~cycle(e_1, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_5, e_1)) | (~product(e_1, e_1, e_5)))),
% 0.56/0.62 inference(transitivity,[status(thm)],[151, 149])).
% 0.56/0.62 tff(153,plain,
% 0.56/0.62 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_1, e_1, e_5)) | (~greater(e_5, e_1)) | (~cycle(e_1, e_0)))),
% 0.56/0.62 inference(quant_inst,[status(thm)],[])).
% 0.56/0.62 tff(154,plain,
% 0.56/0.62 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_5, e_1)) | (~product(e_1, e_1, e_5))),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.56/0.62 tff(155,plain,
% 0.56/0.62 ((~cycle(e_1, e_0)) | (~product(e_1, e_1, e_5))),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[154, 148, 54])).
% 0.56/0.62 tff(156,plain,
% 0.56/0.62 (~product(e_1, e_1, e_5)),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[155, 145])).
% 0.56/0.62 tff(157,plain,
% 0.56/0.62 (greater(e_2, e_1) <=> greater(e_2, e_1)),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(158,axiom,(greater(e_2, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_greater_e_1')).
% 0.56/0.62 tff(159,plain,
% 0.56/0.62 (greater(e_2, e_1)),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.56/0.62 tff(160,plain,
% 0.56/0.62 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~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] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_2, e_1)) | (~product(e_1, e_1, e_2)))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(161,plain,
% 0.56/0.62 (((~product(e_1, e_1, e_2)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_0))) <=> ((~cycle(e_1, e_0)) | (~greater(e_2, e_1)) | (~product(e_1, e_1, e_2)))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(162,plain,
% 0.56/0.62 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_1, e_1, e_2)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_1, e_0)) | (~greater(e_2, e_1)) | (~product(e_1, e_1, e_2))))),
% 0.56/0.62 inference(monotonicity,[status(thm)],[161])).
% 0.56/0.62 tff(163,plain,
% 0.56/0.62 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_1, e_1, e_2)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_2, e_1)) | (~product(e_1, e_1, e_2)))),
% 0.56/0.62 inference(transitivity,[status(thm)],[162, 160])).
% 0.56/0.62 tff(164,plain,
% 0.56/0.62 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_1, e_1, e_2)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_0)))),
% 0.56/0.62 inference(quant_inst,[status(thm)],[])).
% 0.56/0.62 tff(165,plain,
% 0.56/0.62 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_2, e_1)) | (~product(e_1, e_1, e_2))),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.56/0.62 tff(166,plain,
% 0.56/0.62 ((~cycle(e_1, e_0)) | (~product(e_1, e_1, e_2))),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[165, 159, 54])).
% 0.56/0.62 tff(167,plain,
% 0.56/0.62 (~product(e_1, e_1, e_2)),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[166, 145])).
% 0.56/0.62 tff(168,plain,
% 0.56/0.62 (greater(e_3, e_1) <=> greater(e_3, e_1)),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(169,axiom,(greater(e_3, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_greater_e_1')).
% 0.56/0.62 tff(170,plain,
% 0.56/0.62 (greater(e_3, e_1)),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.56/0.62 tff(171,plain,
% 0.56/0.62 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~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] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_3, e_1)) | (~product(e_1, e_1, e_3)))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(172,plain,
% 0.56/0.62 (((~product(e_1, e_1, e_3)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_0))) <=> ((~cycle(e_1, e_0)) | (~greater(e_3, e_1)) | (~product(e_1, e_1, e_3)))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(173,plain,
% 0.56/0.62 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_1, e_1, e_3)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_1, e_0)) | (~greater(e_3, e_1)) | (~product(e_1, e_1, e_3))))),
% 0.56/0.62 inference(monotonicity,[status(thm)],[172])).
% 0.56/0.62 tff(174,plain,
% 0.56/0.62 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_1, e_1, e_3)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_3, e_1)) | (~product(e_1, e_1, e_3)))),
% 0.56/0.62 inference(transitivity,[status(thm)],[173, 171])).
% 0.56/0.62 tff(175,plain,
% 0.56/0.62 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_1, e_1, e_3)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_0)))),
% 0.56/0.62 inference(quant_inst,[status(thm)],[])).
% 0.56/0.62 tff(176,plain,
% 0.56/0.62 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_1, e_0)) | (~greater(e_3, e_1)) | (~product(e_1, e_1, e_3))),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.56/0.62 tff(177,plain,
% 0.56/0.62 ((~cycle(e_1, e_0)) | (~product(e_1, e_1, e_3))),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[176, 170, 54])).
% 0.56/0.62 tff(178,plain,
% 0.56/0.62 (~product(e_1, e_1, e_3)),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[177, 145])).
% 0.56/0.62 tff(179,assumption,(~product(e_1, e_1, e_4)), introduced(assumption)).
% 0.56/0.62 tff(180,plain,
% 0.56/0.62 (^[Y: $i, X: $i] : refl(((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) <=> ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))))),
% 0.56/0.62 inference(bind,[status(th)],[])).
% 0.56/0.62 tff(181,plain,
% 0.56/0.62 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) <=> ![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.56/0.62 inference(quant_intro,[status(thm)],[180])).
% 0.56/0.62 tff(182,plain,
% 0.56/0.62 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y))) <=> ![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(183,plain,
% 0.56/0.62 (^[Y: $i, X: $i] : trans(monotonicity(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))))), ((((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) | product(X, Y, e_5)) <=> (((~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(X, Y, e_5)))), rewrite((((~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(X, Y, e_5)) <=> ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))), ((((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) | product(X, Y, e_5)) <=> ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))))),
% 0.56/0.62 inference(bind,[status(th)],[])).
% 0.56/0.62 tff(184,plain,
% 0.56/0.62 (![Y: $i, X: $i] : (((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) | product(X, Y, e_5)) <=> ![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.56/0.62 inference(quant_intro,[status(thm)],[183])).
% 0.56/0.62 tff(185,axiom,(![Y: $i, X: $i] : (((((((~group_element(X)) | (~group_element(Y))) | product(X, Y, e_1)) | product(X, Y, e_2)) | product(X, Y, e_3)) | product(X, Y, e_4)) | product(X, Y, e_5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','product_total_function1')).
% 0.56/0.62 tff(186,plain,
% 0.56/0.62 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.56/0.62 tff(187,plain,
% 0.56/0.62 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[186, 182])).
% 0.56/0.62 tff(188,plain,(
% 0.56/0.62 ![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.56/0.62 inference(skolemize,[status(sab)],[187])).
% 0.56/0.62 tff(189,plain,
% 0.56/0.62 (![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[188, 181])).
% 0.56/0.62 tff(190,plain,
% 0.56/0.62 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(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_5) | product(e_1, e_1, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(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_5) | product(e_1, e_1, e_1))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(191,plain,
% 0.56/0.62 (((~group_element(e_1)) | product(e_1, e_1, e_5) | product(e_1, e_1, e_4) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1))) <=> ((~group_element(e_1)) | product(e_1, e_1, e_2) | product(e_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_5) | product(e_1, e_1, e_1))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(192,plain,
% 0.56/0.62 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_1, e_5) | product(e_1, e_1, e_4) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(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_5) | product(e_1, e_1, e_1)))),
% 0.56/0.62 inference(monotonicity,[status(thm)],[191])).
% 0.56/0.62 tff(193,plain,
% 0.56/0.62 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_1, e_5) | product(e_1, e_1, e_4) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(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_5) | product(e_1, e_1, e_1))),
% 0.56/0.62 inference(transitivity,[status(thm)],[192, 190])).
% 0.56/0.62 tff(194,plain,
% 0.56/0.62 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_1, e_5) | product(e_1, e_1, e_4) | product(e_1, e_1, e_3) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | (~group_element(e_1)))),
% 0.56/0.62 inference(quant_inst,[status(thm)],[])).
% 0.56/0.62 tff(195,plain,
% 0.56/0.62 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | product(e_1, e_1, e_2) | product(e_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_5) | product(e_1, e_1, e_1)),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.56/0.62 tff(196,plain,
% 0.56/0.62 (product(e_1, e_1, e_2) | product(e_1, e_1, e_3) | product(e_1, e_1, e_5) | product(e_1, e_1, e_1)),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[195, 96, 189, 179])).
% 0.56/0.62 tff(197,plain,
% 0.56/0.62 ($false),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[196, 178, 167, 156, 144])).
% 0.56/0.62 tff(198,plain,((~cycle(e_1, e_0)) | product(e_1, e_1, e_1) | product(e_1, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.62 tff(199,plain,
% 0.56/0.62 (product(e_1, e_1, e_1)),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[198, 143, 123])).
% 0.56/0.62 tff(200,assumption,(product(e_4, e_1, e_1)), introduced(assumption)).
% 0.56/0.62 tff(201,assumption,(product(e_1, e_1, e_1)), introduced(assumption)).
% 0.56/0.62 tff(202,plain,
% 0.56/0.62 (^[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))))),
% 0.56/0.62 inference(bind,[status(th)],[])).
% 0.56/0.62 tff(203,plain,
% 0.56/0.62 (![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)))),
% 0.56/0.62 inference(quant_intro,[status(thm)],[202])).
% 0.56/0.62 tff(204,plain,
% 0.56/0.62 (![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)))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(205,plain,
% 0.56/0.62 (^[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)))))),
% 0.56/0.62 inference(bind,[status(th)],[])).
% 0.56/0.62 tff(206,plain,
% 0.56/0.62 (![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)))),
% 0.56/0.62 inference(quant_intro,[status(thm)],[205])).
% 0.56/0.62 tff(207,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')).
% 0.56/0.62 tff(208,plain,
% 0.56/0.62 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.56/0.62 tff(209,plain,
% 0.56/0.62 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[208, 204])).
% 0.56/0.62 tff(210,plain,(
% 0.56/0.62 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.56/0.62 inference(skolemize,[status(sab)],[209])).
% 0.56/0.62 tff(211,plain,
% 0.56/0.62 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[210, 203])).
% 0.56/0.62 tff(212,plain,
% 0.56/0.62 ((~equalish(e_4, e_1)) <=> (~equalish(e_4, e_1))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(213,axiom,(~equalish(e_4, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_is_not_e_1')).
% 0.56/0.62 tff(214,plain,
% 0.56/0.62 (~equalish(e_4, e_1)),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.56/0.63 tff(215,plain,
% 0.56/0.63 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1)))),
% 0.56/0.63 inference(rewrite,[status(thm)],[])).
% 0.56/0.63 tff(216,plain,
% 0.56/0.63 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1)))),
% 0.56/0.63 inference(quant_inst,[status(thm)],[])).
% 0.56/0.63 tff(217,plain,
% 0.56/0.63 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_4, e_1, e_1))),
% 0.56/0.63 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.56/0.63 tff(218,plain,
% 0.56/0.63 ($false),
% 0.56/0.63 inference(unit_resolution,[status(thm)],[217, 214, 211, 201, 200])).
% 0.56/0.63 tff(219,plain,((~product(e_4, e_1, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.63 tff(220,plain,
% 0.56/0.63 (~product(e_4, e_1, e_1)),
% 0.56/0.63 inference(unit_resolution,[status(thm)],[219, 199])).
% 0.56/0.63 tff(221,plain,
% 0.56/0.63 (greater(e_5, e_4) <=> greater(e_5, e_4)),
% 0.56/0.63 inference(rewrite,[status(thm)],[])).
% 0.56/0.63 tff(222,axiom,(greater(e_5, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_5_greater_e_4')).
% 0.56/0.63 tff(223,plain,
% 0.56/0.63 (greater(e_5, e_4)),
% 0.56/0.63 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.56/0.63 tff(224,plain,
% 0.56/0.63 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_4, e_0)) | (~greater(e_5, e_4)) | (~product(e_4, e_1, e_5)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_4, e_0)) | (~greater(e_5, e_4)) | (~product(e_4, e_1, e_5)))),
% 0.56/0.63 inference(rewrite,[status(thm)],[])).
% 0.56/0.63 tff(225,plain,
% 0.56/0.63 (((~product(e_4, e_1, e_5)) | (~greater(e_5, e_4)) | (~cycle(e_4, e_0))) <=> ((~cycle(e_4, e_0)) | (~greater(e_5, e_4)) | (~product(e_4, e_1, e_5)))),
% 0.56/0.63 inference(rewrite,[status(thm)],[])).
% 0.56/0.63 tff(226,plain,
% 0.56/0.63 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_4, e_1, e_5)) | (~greater(e_5, e_4)) | (~cycle(e_4, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_4, e_0)) | (~greater(e_5, e_4)) | (~product(e_4, e_1, e_5))))),
% 0.56/0.63 inference(monotonicity,[status(thm)],[225])).
% 0.56/0.63 tff(227,plain,
% 0.56/0.63 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_4, e_1, e_5)) | (~greater(e_5, e_4)) | (~cycle(e_4, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_4, e_0)) | (~greater(e_5, e_4)) | (~product(e_4, e_1, e_5)))),
% 0.56/0.63 inference(transitivity,[status(thm)],[226, 224])).
% 0.56/0.63 tff(228,plain,
% 0.56/0.63 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_4, e_1, e_5)) | (~greater(e_5, e_4)) | (~cycle(e_4, e_0)))),
% 0.56/0.63 inference(quant_inst,[status(thm)],[])).
% 0.56/0.63 tff(229,plain,
% 0.56/0.63 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_4, e_0)) | (~greater(e_5, e_4)) | (~product(e_4, e_1, e_5))),
% 0.56/0.63 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.56/0.63 tff(230,plain,
% 0.56/0.63 ((~cycle(e_4, e_0)) | (~product(e_4, e_1, e_5))),
% 0.56/0.63 inference(unit_resolution,[status(thm)],[229, 223, 54])).
% 0.56/0.63 tff(231,plain,
% 0.56/0.63 (~product(e_4, e_1, e_5)),
% 0.56/0.63 inference(unit_resolution,[status(thm)],[230, 2])).
% 0.56/0.63 tff(232,plain,
% 0.56/0.63 (greater(e_4, e_3) <=> greater(e_4, e_3)),
% 0.56/0.63 inference(rewrite,[status(thm)],[])).
% 0.56/0.63 tff(233,axiom,(greater(e_4, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_greater_e_3')).
% 0.56/0.63 tff(234,plain,
% 0.56/0.63 (greater(e_4, e_3)),
% 0.56/0.63 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.56/0.63 tff(235,plain,
% 0.56/0.63 (((~![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_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_3)) | (~cycle(e_3, 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_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_3)) | (~cycle(e_3, e_2)))),
% 0.56/0.63 inference(rewrite,[status(thm)],[])).
% 0.56/0.63 tff(236,plain,
% 0.56/0.63 (((~greater(e_2, e_0)) | (~greater(e_4, e_3)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_2))) <=> ((~cycle(e_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_3)) | (~cycle(e_3, e_2)))),
% 0.56/0.63 inference(rewrite,[status(thm)],[])).
% 0.56/0.63 tff(237,plain,
% 0.56/0.63 (((~![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_4, e_3)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_3, 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_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_3)) | (~cycle(e_3, e_2))))),
% 0.56/0.63 inference(monotonicity,[status(thm)],[236])).
% 0.56/0.63 tff(238,plain,
% 0.56/0.63 (((~![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_4, e_3)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_3, 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_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_3)) | (~cycle(e_3, e_2)))),
% 0.56/0.63 inference(transitivity,[status(thm)],[237, 235])).
% 0.56/0.63 tff(239,plain,
% 0.56/0.63 ((~![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_4, e_3)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_2)))),
% 0.56/0.63 inference(quant_inst,[status(thm)],[])).
% 0.56/0.63 tff(240,plain,
% 0.56/0.63 ((~![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_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_3)) | (~cycle(e_3, e_2))),
% 0.56/0.63 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.56/0.63 tff(241,plain,
% 0.56/0.63 ((~cycle(e_4, e_0)) | (~cycle(e_3, e_2))),
% 0.56/0.63 inference(unit_resolution,[status(thm)],[240, 24, 114, 234, 15, 12])).
% 0.56/0.63 tff(242,plain,
% 0.56/0.63 (~cycle(e_3, e_2)),
% 0.56/0.63 inference(unit_resolution,[status(thm)],[241, 2])).
% 0.56/0.63 tff(243,assumption,(cycle(e_3, e_3)), introduced(assumption)).
% 0.56/0.63 tff(244,plain,
% 0.56/0.63 (((~![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_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_3)) | (~cycle(e_3, 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_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_3)) | (~cycle(e_3, e_3)))),
% 0.56/0.63 inference(rewrite,[status(thm)],[])).
% 0.56/0.63 tff(245,plain,
% 0.56/0.63 (((~greater(e_3, e_0)) | (~greater(e_4, e_3)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_3))) <=> ((~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_3)) | (~cycle(e_3, e_3)))),
% 0.56/0.63 inference(rewrite,[status(thm)],[])).
% 0.61/0.63 tff(246,plain,
% 0.61/0.63 (((~![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_4, e_3)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_3, 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_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_3)) | (~cycle(e_3, e_3))))),
% 0.61/0.63 inference(monotonicity,[status(thm)],[245])).
% 0.61/0.63 tff(247,plain,
% 0.61/0.63 (((~![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_4, e_3)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_3, 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_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_3)) | (~cycle(e_3, e_3)))),
% 0.61/0.63 inference(transitivity,[status(thm)],[246, 244])).
% 0.61/0.63 tff(248,plain,
% 0.61/0.63 ((~![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_4, e_3)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_3)))),
% 0.61/0.63 inference(quant_inst,[status(thm)],[])).
% 0.61/0.63 tff(249,plain,
% 0.61/0.63 ((~![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_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_3)) | (~cycle(e_3, e_3))),
% 0.61/0.63 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.61/0.63 tff(250,plain,
% 0.61/0.63 ((~cycle(e_4, e_0)) | (~cycle(e_3, e_3))),
% 0.61/0.63 inference(unit_resolution,[status(thm)],[249, 24, 35, 234, 15, 12])).
% 0.61/0.63 tff(251,plain,
% 0.61/0.63 (~cycle(e_4, e_0)),
% 0.61/0.63 inference(unit_resolution,[status(thm)],[250, 243])).
% 0.61/0.63 tff(252,assumption,(cycle(e_4, e_1)), introduced(assumption)).
% 0.61/0.63 tff(253,plain,
% 0.61/0.63 ((~equalish(e_3, e_2)) <=> (~equalish(e_3, e_2))),
% 0.61/0.63 inference(rewrite,[status(thm)],[])).
% 0.61/0.63 tff(254,axiom,(~equalish(e_3, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_2')).
% 0.61/0.63 tff(255,plain,
% 0.61/0.63 (~equalish(e_3, e_2)),
% 0.61/0.63 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.61/0.63 tff(256,plain,
% 0.61/0.63 (^[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))))),
% 0.61/0.63 inference(bind,[status(th)],[])).
% 0.61/0.63 tff(257,plain,
% 0.61/0.63 (![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)))),
% 0.61/0.63 inference(quant_intro,[status(thm)],[256])).
% 0.61/0.63 tff(258,plain,
% 0.61/0.63 (![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)))),
% 0.61/0.63 inference(rewrite,[status(thm)],[])).
% 0.61/0.63 tff(259,plain,
% 0.61/0.63 (^[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)))))),
% 0.61/0.63 inference(bind,[status(th)],[])).
% 0.61/0.63 tff(260,plain,
% 0.61/0.63 (![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)))),
% 0.61/0.63 inference(quant_intro,[status(thm)],[259])).
% 0.61/0.63 tff(261,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')).
% 0.61/0.63 tff(262,plain,
% 0.61/0.63 (![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)))),
% 0.61/0.63 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.61/0.63 tff(263,plain,
% 0.61/0.63 (![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)))),
% 0.61/0.63 inference(modus_ponens,[status(thm)],[262, 258])).
% 0.61/0.63 tff(264,plain,(
% 0.61/0.63 ![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)))),
% 0.61/0.63 inference(skolemize,[status(sab)],[263])).
% 0.61/0.63 tff(265,plain,
% 0.61/0.63 (![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)))),
% 0.61/0.63 inference(modus_ponens,[status(thm)],[264, 257])).
% 0.61/0.63 tff(266,plain,
% 0.61/0.63 (next(e_3, e_4) <=> next(e_3, e_4)),
% 0.61/0.63 inference(rewrite,[status(thm)],[])).
% 0.61/0.63 tff(267,axiom,(next(e_3, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_then_e_4')).
% 0.61/0.63 tff(268,plain,
% 0.61/0.63 (next(e_3, e_4)),
% 0.61/0.63 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.61/0.63 tff(269,plain,
% 0.61/0.63 (((~![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)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~cycle(e_4, 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)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~cycle(e_4, e_1)))),
% 0.61/0.63 inference(rewrite,[status(thm)],[])).
% 0.61/0.63 tff(270,plain,
% 0.61/0.63 (((~cycle(e_3, e_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1))) <=> (equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~cycle(e_4, e_1)))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(271,plain,
% 0.61/0.64 (((~![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_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, 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)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~cycle(e_4, e_1))))),
% 0.61/0.64 inference(monotonicity,[status(thm)],[270])).
% 0.61/0.64 tff(272,plain,
% 0.61/0.64 (((~![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_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, 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)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~cycle(e_4, e_1)))),
% 0.61/0.64 inference(transitivity,[status(thm)],[271, 269])).
% 0.61/0.64 tff(273,plain,
% 0.61/0.64 ((~![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_3)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)))),
% 0.61/0.64 inference(quant_inst,[status(thm)],[])).
% 0.61/0.64 tff(274,plain,
% 0.61/0.64 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~cycle(e_4, e_1))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.61/0.64 tff(275,plain,
% 0.61/0.64 ($false),
% 0.61/0.64 inference(unit_resolution,[status(thm)],[274, 84, 268, 35, 265, 255, 243, 252])).
% 0.61/0.64 tff(276,plain,((~cycle(e_3, e_3)) | (~cycle(e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.61/0.64 tff(277,plain,
% 0.61/0.64 (~cycle(e_4, e_1)),
% 0.61/0.64 inference(unit_resolution,[status(thm)],[276, 243])).
% 0.61/0.64 tff(278,assumption,(cycle(e_4, e_3)), introduced(assumption)).
% 0.61/0.64 tff(279,plain,
% 0.61/0.64 ((~equalish(e_3, e_1)) <=> (~equalish(e_3, e_1))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(280,axiom,(~equalish(e_3, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_1')).
% 0.61/0.64 tff(281,plain,
% 0.61/0.64 (~equalish(e_3, e_1)),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.61/0.64 tff(282,plain,
% 0.61/0.64 (next(e_0, e_1) <=> next(e_0, e_1)),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(283,axiom,(next(e_0, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_0_then_e_1')).
% 0.61/0.64 tff(284,plain,
% 0.61/0.64 (next(e_0, e_1)),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[283, 282])).
% 0.61/0.64 tff(285,plain,
% 0.61/0.64 (((~![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_1) | (~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_3)) | (~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_3, e_1) | (~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_3)) | (~next(e_0, e_1)))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(286,plain,
% 0.61/0.64 (((~cycle(e_4, e_3)) | equalish(e_3, e_1) | (~next(e_0, e_1)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0))) <=> (equalish(e_3, e_1) | (~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_3)) | (~next(e_0, e_1)))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(287,plain,
% 0.61/0.64 (((~![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_4, e_3)) | equalish(e_3, e_1) | (~next(e_0, e_1)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, 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_3, e_1) | (~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_3)) | (~next(e_0, e_1))))),
% 0.61/0.64 inference(monotonicity,[status(thm)],[286])).
% 0.61/0.64 tff(288,plain,
% 0.61/0.64 (((~![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_4, e_3)) | equalish(e_3, e_1) | (~next(e_0, e_1)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, 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_3, e_1) | (~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_3)) | (~next(e_0, e_1)))),
% 0.61/0.64 inference(transitivity,[status(thm)],[287, 285])).
% 0.61/0.64 tff(289,plain,
% 0.61/0.64 ((~![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_4, e_3)) | equalish(e_3, e_1) | (~next(e_0, e_1)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)))),
% 0.61/0.64 inference(quant_inst,[status(thm)],[])).
% 0.61/0.64 tff(290,plain,
% 0.61/0.64 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_1) | (~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_3)) | (~next(e_0, e_1))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.61/0.64 tff(291,plain,
% 0.61/0.64 ($false),
% 0.61/0.64 inference(unit_resolution,[status(thm)],[290, 284, 24, 35, 15, 265, 281, 278])).
% 0.61/0.64 tff(292,plain,(~cycle(e_4, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.61/0.64 tff(293,assumption,(cycle(e_4, e_2)), introduced(assumption)).
% 0.61/0.64 tff(294,plain,
% 0.61/0.64 ((~equalish(e_2, e_1)) <=> (~equalish(e_2, e_1))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(295,axiom,(~equalish(e_2, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_1')).
% 0.61/0.64 tff(296,plain,
% 0.61/0.64 (~equalish(e_2, e_1)),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.61/0.64 tff(297,plain,
% 0.61/0.64 (((~![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_5, e_0)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, 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_5, e_0)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_2)) | (~next(e_0, e_1)))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(298,plain,
% 0.61/0.64 (((~cycle(e_4, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0))) <=> (equalish(e_2, e_1) | (~cycle(e_5, e_0)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_2)) | (~next(e_0, e_1)))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(299,plain,
% 0.61/0.64 (((~![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_4, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, 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_5, e_0)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_2)) | (~next(e_0, e_1))))),
% 0.62/0.64 inference(monotonicity,[status(thm)],[298])).
% 0.62/0.64 tff(300,plain,
% 0.62/0.64 (((~![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_4, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, 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_5, e_0)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_2)) | (~next(e_0, e_1)))),
% 0.62/0.64 inference(transitivity,[status(thm)],[299, 297])).
% 0.62/0.64 tff(301,plain,
% 0.62/0.64 ((~![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_4, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)))),
% 0.62/0.64 inference(quant_inst,[status(thm)],[])).
% 0.62/0.64 tff(302,plain,
% 0.62/0.64 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_1) | (~cycle(e_5, e_0)) | (~greater(e_2, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_2)) | (~next(e_0, e_1))),
% 0.62/0.64 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.62/0.64 tff(303,plain,
% 0.62/0.64 ($false),
% 0.62/0.64 inference(unit_resolution,[status(thm)],[302, 284, 24, 114, 15, 265, 296, 293])).
% 0.62/0.64 tff(304,plain,(~cycle(e_4, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.64 tff(305,assumption,(cycle(e_4, e_4)), introduced(assumption)).
% 0.62/0.64 tff(306,plain,
% 0.62/0.64 (((~![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_4, e_1) | (~cycle(e_5, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_4)) | (~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_4, e_1) | (~cycle(e_5, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_4)) | (~next(e_0, e_1)))),
% 0.62/0.64 inference(rewrite,[status(thm)],[])).
% 0.62/0.64 tff(307,plain,
% 0.62/0.64 (((~cycle(e_4, e_4)) | equalish(e_4, e_1) | (~next(e_0, e_1)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0))) <=> (equalish(e_4, e_1) | (~cycle(e_5, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_4)) | (~next(e_0, e_1)))),
% 0.62/0.64 inference(rewrite,[status(thm)],[])).
% 0.62/0.64 tff(308,plain,
% 0.62/0.64 (((~![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_4, e_4)) | equalish(e_4, e_1) | (~next(e_0, e_1)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, 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_4, e_1) | (~cycle(e_5, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_4)) | (~next(e_0, e_1))))),
% 0.62/0.64 inference(monotonicity,[status(thm)],[307])).
% 0.62/0.64 tff(309,plain,
% 0.62/0.64 (((~![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_4, e_4)) | equalish(e_4, e_1) | (~next(e_0, e_1)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, 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_4, e_1) | (~cycle(e_5, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_4)) | (~next(e_0, e_1)))),
% 0.62/0.64 inference(transitivity,[status(thm)],[308, 306])).
% 0.62/0.64 tff(310,plain,
% 0.62/0.64 ((~![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_4, e_4)) | equalish(e_4, e_1) | (~next(e_0, e_1)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)))),
% 0.62/0.64 inference(quant_inst,[status(thm)],[])).
% 0.62/0.64 tff(311,plain,
% 0.62/0.64 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_4, e_1) | (~cycle(e_5, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_4)) | (~next(e_0, e_1))),
% 0.62/0.64 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.62/0.64 tff(312,plain,
% 0.62/0.64 ($false),
% 0.62/0.64 inference(unit_resolution,[status(thm)],[311, 284, 24, 21, 15, 265, 214, 305])).
% 0.62/0.64 tff(313,plain,(~cycle(e_4, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.64 tff(314,plain,
% 0.62/0.64 (group_element(e_4) <=> group_element(e_4)),
% 0.62/0.64 inference(rewrite,[status(thm)],[])).
% 0.62/0.64 tff(315,axiom,(group_element(e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_4')).
% 0.62/0.64 tff(316,plain,
% 0.62/0.64 (group_element(e_4)),
% 0.62/0.64 inference(modus_ponens,[status(thm)],[315, 314])).
% 0.62/0.64 tff(317,plain,
% 0.62/0.64 (((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_4, e_4) | cycle(e_4, e_3) | cycle(e_4, e_2) | cycle(e_4, e_1) | cycle(e_4, e_0) | (~group_element(e_4)))) <=> ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_4, e_4) | cycle(e_4, e_3) | cycle(e_4, e_2) | cycle(e_4, e_1) | cycle(e_4, e_0) | (~group_element(e_4)))),
% 0.62/0.64 inference(rewrite,[status(thm)],[])).
% 0.62/0.64 tff(318,plain,
% 0.62/0.64 ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_4, e_4) | cycle(e_4, e_3) | cycle(e_4, e_2) | cycle(e_4, e_1) | cycle(e_4, e_0) | (~group_element(e_4)))),
% 0.62/0.64 inference(quant_inst,[status(thm)],[])).
% 0.62/0.64 tff(319,plain,
% 0.62/0.64 ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_4, e_4) | cycle(e_4, e_3) | cycle(e_4, e_2) | cycle(e_4, e_1) | cycle(e_4, e_0) | (~group_element(e_4))),
% 0.62/0.64 inference(modus_ponens,[status(thm)],[318, 317])).
% 0.62/0.64 tff(320,plain,
% 0.62/0.64 (cycle(e_4, e_4) | cycle(e_4, e_3) | cycle(e_4, e_2) | cycle(e_4, e_1) | cycle(e_4, e_0)),
% 0.62/0.64 inference(unit_resolution,[status(thm)],[319, 106, 316])).
% 0.62/0.64 tff(321,plain,
% 0.62/0.64 (cycle(e_4, e_1) | cycle(e_4, e_0)),
% 0.62/0.64 inference(unit_resolution,[status(thm)],[320, 313, 304, 292])).
% 0.62/0.64 tff(322,plain,
% 0.62/0.64 ($false),
% 0.62/0.64 inference(unit_resolution,[status(thm)],[321, 277, 251])).
% 0.62/0.64 tff(323,plain,(~cycle(e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.64 tff(324,plain,
% 0.62/0.64 (greater(e_4, e_2) <=> greater(e_4, e_2)),
% 0.62/0.64 inference(rewrite,[status(thm)],[])).
% 0.62/0.64 tff(325,axiom,(greater(e_4, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_greater_e_2')).
% 0.62/0.64 tff(326,plain,
% 0.62/0.64 (greater(e_4, e_2)),
% 0.62/0.64 inference(modus_ponens,[status(thm)],[325, 324])).
% 0.62/0.64 tff(327,plain,
% 0.62/0.64 (((~![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_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_4)))) <=> ((~![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_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_4)))),
% 0.62/0.64 inference(rewrite,[status(thm)],[])).
% 0.62/0.64 tff(328,plain,
% 0.62/0.64 (((~greater(e_4, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_4))) <=> ((~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_4)))),
% 0.62/0.64 inference(rewrite,[status(thm)],[])).
% 0.62/0.64 tff(329,plain,
% 0.62/0.64 (((~![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_4, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_4)))) <=> ((~![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_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_4))))),
% 0.62/0.65 inference(monotonicity,[status(thm)],[328])).
% 0.62/0.65 tff(330,plain,
% 0.62/0.65 (((~![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_4, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_4)))) <=> ((~![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_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_4)))),
% 0.62/0.65 inference(transitivity,[status(thm)],[329, 327])).
% 0.62/0.65 tff(331,plain,
% 0.62/0.65 ((~![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_4, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_4)))),
% 0.62/0.65 inference(quant_inst,[status(thm)],[])).
% 0.62/0.65 tff(332,plain,
% 0.62/0.65 ((~![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_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_4))),
% 0.62/0.65 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.62/0.65 tff(333,plain,
% 0.62/0.65 ((~cycle(e_4, e_0)) | (~cycle(e_2, e_4))),
% 0.62/0.65 inference(unit_resolution,[status(thm)],[332, 24, 21, 326, 15, 12])).
% 0.62/0.65 tff(334,plain,
% 0.62/0.65 (~cycle(e_2, e_4)),
% 0.62/0.65 inference(unit_resolution,[status(thm)],[333, 2])).
% 0.62/0.65 tff(335,plain,
% 0.62/0.65 (((~![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_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, 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_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_3)))),
% 0.62/0.65 inference(rewrite,[status(thm)],[])).
% 0.62/0.65 tff(336,plain,
% 0.62/0.65 (((~greater(e_3, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_3))) <=> ((~cycle(e_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_3)))),
% 0.62/0.65 inference(rewrite,[status(thm)],[])).
% 0.62/0.65 tff(337,plain,
% 0.62/0.65 (((~![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_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, 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_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_3))))),
% 0.62/0.65 inference(monotonicity,[status(thm)],[336])).
% 0.62/0.65 tff(338,plain,
% 0.62/0.65 (((~![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_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, 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_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_3)))),
% 0.62/0.65 inference(transitivity,[status(thm)],[337, 335])).
% 0.62/0.65 tff(339,plain,
% 0.62/0.65 ((~![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_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_3)))),
% 0.62/0.65 inference(quant_inst,[status(thm)],[])).
% 0.62/0.65 tff(340,plain,
% 0.62/0.65 ((~![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_5, e_0)) | (~greater(e_3, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_3))),
% 0.62/0.65 inference(modus_ponens,[status(thm)],[339, 338])).
% 0.62/0.65 tff(341,plain,
% 0.62/0.65 ((~cycle(e_4, e_0)) | (~cycle(e_2, e_3))),
% 0.62/0.65 inference(unit_resolution,[status(thm)],[340, 24, 35, 326, 15, 12])).
% 0.62/0.65 tff(342,plain,
% 0.62/0.65 (~cycle(e_2, e_3)),
% 0.62/0.65 inference(unit_resolution,[status(thm)],[341, 2])).
% 0.62/0.65 tff(343,plain,
% 0.62/0.65 (((~![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_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, 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_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_2)))),
% 0.62/0.65 inference(rewrite,[status(thm)],[])).
% 0.62/0.65 tff(344,plain,
% 0.62/0.65 (((~greater(e_2, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_2))) <=> ((~cycle(e_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_2)))),
% 0.62/0.65 inference(rewrite,[status(thm)],[])).
% 0.62/0.65 tff(345,plain,
% 0.62/0.65 (((~![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_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, 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_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_2))))),
% 0.62/0.65 inference(monotonicity,[status(thm)],[344])).
% 0.62/0.65 tff(346,plain,
% 0.62/0.65 (((~![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_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, 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_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_2)))),
% 0.62/0.65 inference(transitivity,[status(thm)],[345, 343])).
% 0.62/0.65 tff(347,plain,
% 0.62/0.65 ((~![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_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_2)))),
% 0.62/0.65 inference(quant_inst,[status(thm)],[])).
% 0.62/0.65 tff(348,plain,
% 0.62/0.65 ((~![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_5, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_2))),
% 0.62/0.65 inference(modus_ponens,[status(thm)],[347, 346])).
% 0.62/0.65 tff(349,plain,
% 0.62/0.65 ((~cycle(e_4, e_0)) | (~cycle(e_2, e_2))),
% 0.62/0.65 inference(unit_resolution,[status(thm)],[348, 24, 114, 326, 15, 12])).
% 0.62/0.65 tff(350,plain,
% 0.62/0.65 (~cycle(e_2, e_2)),
% 0.62/0.65 inference(unit_resolution,[status(thm)],[349, 2])).
% 0.62/0.65 tff(351,plain,
% 0.62/0.65 (((~![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_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_1)) | (~greater(e_4, 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_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_1)) | (~greater(e_4, e_2)))),
% 0.62/0.65 inference(rewrite,[status(thm)],[])).
% 0.62/0.65 tff(352,plain,
% 0.62/0.65 (((~greater(e_1, e_0)) | (~greater(e_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_1))) <=> ((~cycle(e_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_1)) | (~greater(e_4, e_2)))),
% 0.62/0.65 inference(rewrite,[status(thm)],[])).
% 0.62/0.65 tff(353,plain,
% 0.62/0.65 (((~![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_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, 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_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_1)) | (~greater(e_4, e_2))))),
% 0.62/0.65 inference(monotonicity,[status(thm)],[352])).
% 0.62/0.65 tff(354,plain,
% 0.62/0.65 (((~![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_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, 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_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_1)) | (~greater(e_4, e_2)))),
% 0.62/0.65 inference(transitivity,[status(thm)],[353, 351])).
% 0.62/0.65 tff(355,plain,
% 0.62/0.65 ((~![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_4, e_2)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_2, e_1)))),
% 0.62/0.65 inference(quant_inst,[status(thm)],[])).
% 0.62/0.65 tff(356,plain,
% 0.62/0.65 ((~![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_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~cycle(e_2, e_1)) | (~greater(e_4, e_2))),
% 0.62/0.65 inference(modus_ponens,[status(thm)],[355, 354])).
% 0.62/0.65 tff(357,plain,
% 0.62/0.65 ((~cycle(e_4, e_0)) | (~cycle(e_2, e_1))),
% 0.62/0.65 inference(unit_resolution,[status(thm)],[356, 24, 81, 326, 15, 12])).
% 0.62/0.65 tff(358,plain,
% 0.62/0.65 (~cycle(e_2, e_1)),
% 0.62/0.65 inference(unit_resolution,[status(thm)],[357, 2])).
% 0.62/0.65 tff(359,plain,
% 0.62/0.65 (group_element(e_2) <=> group_element(e_2)),
% 0.62/0.65 inference(rewrite,[status(thm)],[])).
% 0.62/0.65 tff(360,axiom,(group_element(e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_2')).
% 0.62/0.65 tff(361,plain,
% 0.62/0.65 (group_element(e_2)),
% 0.62/0.65 inference(modus_ponens,[status(thm)],[360, 359])).
% 0.62/0.65 tff(362,plain,
% 0.62/0.65 (((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_2, e_4) | 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_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_2, e_4) | cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0) | (~group_element(e_2)))),
% 0.62/0.65 inference(rewrite,[status(thm)],[])).
% 0.62/0.65 tff(363,plain,
% 0.62/0.65 ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_2, e_4) | cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0) | (~group_element(e_2)))),
% 0.62/0.65 inference(quant_inst,[status(thm)],[])).
% 0.62/0.65 tff(364,plain,
% 0.62/0.65 ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_2, e_4) | cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0) | (~group_element(e_2))),
% 0.62/0.65 inference(modus_ponens,[status(thm)],[363, 362])).
% 0.62/0.65 tff(365,plain,
% 0.62/0.65 (cycle(e_2, e_4) | cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_1) | cycle(e_2, e_0)),
% 0.62/0.65 inference(unit_resolution,[status(thm)],[364, 106, 361])).
% 0.62/0.65 tff(366,plain,
% 0.62/0.65 (cycle(e_2, e_0)),
% 0.62/0.65 inference(unit_resolution,[status(thm)],[365, 358, 350, 342, 334])).
% 0.62/0.65 tff(367,plain,
% 0.62/0.65 (~product(e_1, e_1, e_5)),
% 0.62/0.65 inference(unit_resolution,[status(thm)],[155, 143])).
% 0.62/0.65 tff(368,plain,
% 0.62/0.65 (~product(e_1, e_1, e_3)),
% 0.62/0.65 inference(unit_resolution,[status(thm)],[177, 143])).
% 0.62/0.65 tff(369,plain,
% 0.62/0.65 (~product(e_1, e_1, e_2)),
% 0.62/0.65 inference(unit_resolution,[status(thm)],[166, 143])).
% 0.62/0.65 tff(370,plain,
% 0.62/0.65 (product(e_1, e_1, e_1)),
% 0.62/0.65 inference(unit_resolution,[status(thm)],[195, 96, 189, 369, 368, 123, 367])).
% 0.62/0.65 tff(371,assumption,(product(e_2, e_1, e_1)), introduced(assumption)).
% 0.62/0.65 tff(372,plain,
% 0.62/0.65 (((~![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)))),
% 0.62/0.65 inference(rewrite,[status(thm)],[])).
% 0.62/0.65 tff(373,plain,
% 0.62/0.65 ((~![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)))),
% 0.62/0.65 inference(quant_inst,[status(thm)],[])).
% 0.62/0.65 tff(374,plain,
% 0.62/0.65 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_2, e_1, e_1))),
% 0.62/0.65 inference(modus_ponens,[status(thm)],[373, 372])).
% 0.62/0.65 tff(375,plain,
% 0.62/0.65 ($false),
% 0.62/0.65 inference(unit_resolution,[status(thm)],[374, 296, 211, 201, 371])).
% 0.62/0.65 tff(376,plain,((~product(e_2, e_1, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.62/0.65 tff(377,plain,
% 0.62/0.65 (~product(e_2, e_1, e_1)),
% 0.62/0.65 inference(unit_resolution,[status(thm)],[376, 370])).
% 0.62/0.65 tff(378,assumption,(~product(e_2, e_1, e_2)), introduced(assumption)).
% 0.62/0.65 tff(379,assumption,(~product(e_2, e_1, e_1)), introduced(assumption)).
% 0.62/0.65 tff(380,assumption,(cycle(e_2, e_0)), introduced(assumption)).
% 0.62/0.65 tff(381,plain,
% 0.62/0.65 (greater(e_5, e_2) <=> greater(e_5, e_2)),
% 0.62/0.65 inference(rewrite,[status(thm)],[])).
% 0.62/0.65 tff(382,axiom,(greater(e_5, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_5_greater_e_2')).
% 0.62/0.65 tff(383,plain,
% 0.62/0.65 (greater(e_5, e_2)),
% 0.62/0.65 inference(modus_ponens,[status(thm)],[382, 381])).
% 0.62/0.65 tff(384,plain,
% 0.62/0.65 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_2, e_0)) | (~greater(e_5, e_2)) | (~product(e_2, e_1, e_5)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_5, e_2)) | (~product(e_2, e_1, e_5)))),
% 0.62/0.65 inference(rewrite,[status(thm)],[])).
% 0.62/0.65 tff(385,plain,
% 0.62/0.65 (((~product(e_2, e_1, e_5)) | (~greater(e_5, e_2)) | (~cycle(e_2, e_0))) <=> ((~cycle(e_2, e_0)) | (~greater(e_5, e_2)) | (~product(e_2, e_1, e_5)))),
% 0.62/0.65 inference(rewrite,[status(thm)],[])).
% 0.62/0.65 tff(386,plain,
% 0.62/0.65 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_5)) | (~greater(e_5, e_2)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_2, e_0)) | (~greater(e_5, e_2)) | (~product(e_2, e_1, e_5))))),
% 0.62/0.66 inference(monotonicity,[status(thm)],[385])).
% 0.62/0.66 tff(387,plain,
% 0.62/0.66 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_5)) | (~greater(e_5, e_2)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_5, e_2)) | (~product(e_2, e_1, e_5)))),
% 0.62/0.66 inference(transitivity,[status(thm)],[386, 384])).
% 0.62/0.66 tff(388,plain,
% 0.62/0.66 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_5)) | (~greater(e_5, e_2)) | (~cycle(e_2, e_0)))),
% 0.62/0.66 inference(quant_inst,[status(thm)],[])).
% 0.62/0.66 tff(389,plain,
% 0.62/0.66 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_5, e_2)) | (~product(e_2, e_1, e_5))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[388, 387])).
% 0.62/0.66 tff(390,plain,
% 0.62/0.66 ((~cycle(e_2, e_0)) | (~product(e_2, e_1, e_5))),
% 0.62/0.66 inference(unit_resolution,[status(thm)],[389, 383, 54])).
% 0.62/0.66 tff(391,plain,
% 0.62/0.66 (~product(e_2, e_1, e_5)),
% 0.62/0.66 inference(unit_resolution,[status(thm)],[390, 380])).
% 0.62/0.66 tff(392,plain,
% 0.62/0.66 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~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] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(393,plain,
% 0.62/0.66 (((~product(e_2, e_1, e_4)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_0))) <=> ((~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(394,plain,
% 0.62/0.66 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_4)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4))))),
% 0.62/0.66 inference(monotonicity,[status(thm)],[393])).
% 0.62/0.66 tff(395,plain,
% 0.62/0.66 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_4)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4)))),
% 0.62/0.66 inference(transitivity,[status(thm)],[394, 392])).
% 0.62/0.66 tff(396,plain,
% 0.62/0.66 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_4)) | (~greater(e_4, e_2)) | (~cycle(e_2, e_0)))),
% 0.62/0.66 inference(quant_inst,[status(thm)],[])).
% 0.62/0.66 tff(397,plain,
% 0.62/0.66 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_4, e_2)) | (~product(e_2, e_1, e_4))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[396, 395])).
% 0.62/0.66 tff(398,plain,
% 0.62/0.66 ((~cycle(e_2, e_0)) | (~product(e_2, e_1, e_4))),
% 0.62/0.66 inference(unit_resolution,[status(thm)],[397, 326, 54])).
% 0.62/0.66 tff(399,plain,
% 0.62/0.66 (~product(e_2, e_1, e_4)),
% 0.62/0.66 inference(unit_resolution,[status(thm)],[398, 380])).
% 0.62/0.66 tff(400,plain,
% 0.62/0.66 (greater(e_3, e_2) <=> greater(e_3, e_2)),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(401,axiom,(greater(e_3, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_greater_e_2')).
% 0.62/0.66 tff(402,plain,
% 0.62/0.66 (greater(e_3, e_2)),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[401, 400])).
% 0.62/0.66 tff(403,plain,
% 0.62/0.66 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~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] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(404,plain,
% 0.62/0.66 (((~product(e_2, e_1, e_3)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_0))) <=> ((~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(405,plain,
% 0.62/0.66 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_3)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3))))),
% 0.62/0.66 inference(monotonicity,[status(thm)],[404])).
% 0.62/0.66 tff(406,plain,
% 0.62/0.66 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_3)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.62/0.66 inference(transitivity,[status(thm)],[405, 403])).
% 0.62/0.66 tff(407,plain,
% 0.62/0.66 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_2, e_1, e_3)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_0)))),
% 0.62/0.66 inference(quant_inst,[status(thm)],[])).
% 0.62/0.66 tff(408,plain,
% 0.62/0.66 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_2, e_0)) | (~greater(e_3, e_2)) | (~product(e_2, e_1, e_3))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[407, 406])).
% 0.62/0.66 tff(409,plain,
% 0.62/0.66 ((~cycle(e_2, e_0)) | (~product(e_2, e_1, e_3))),
% 0.62/0.66 inference(unit_resolution,[status(thm)],[408, 402, 54])).
% 0.62/0.66 tff(410,plain,
% 0.62/0.66 (~product(e_2, e_1, e_3)),
% 0.62/0.66 inference(unit_resolution,[status(thm)],[409, 380])).
% 0.62/0.66 tff(411,plain,
% 0.62/0.66 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(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_5) | 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_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(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_5) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(412,plain,
% 0.62/0.66 (((~group_element(e_2)) | product(e_2, e_1, e_5) | product(e_2, e_1, e_4) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1))) <=> ((~group_element(e_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_5) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(413,plain,
% 0.62/0.66 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_2, e_1, e_5) | product(e_2, e_1, e_4) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(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_5) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1)))),
% 0.62/0.66 inference(monotonicity,[status(thm)],[412])).
% 0.62/0.66 tff(414,plain,
% 0.62/0.66 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_2, e_1, e_5) | product(e_2, e_1, e_4) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(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_5) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1))),
% 0.62/0.66 inference(transitivity,[status(thm)],[413, 411])).
% 0.62/0.66 tff(415,plain,
% 0.62/0.66 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_2, e_1, e_5) | product(e_2, e_1, e_4) | product(e_2, e_1, e_3) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1) | (~group_element(e_1)))),
% 0.62/0.66 inference(quant_inst,[status(thm)],[])).
% 0.62/0.66 tff(416,plain,
% 0.62/0.66 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_5) | product(e_2, e_1, e_2) | product(e_2, e_1, e_1)),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[415, 414])).
% 0.62/0.66 tff(417,plain,
% 0.62/0.66 ($false),
% 0.62/0.66 inference(unit_resolution,[status(thm)],[416, 96, 361, 189, 410, 399, 391, 379, 378])).
% 0.62/0.66 tff(418,plain,((~cycle(e_2, e_0)) | product(e_2, e_1, e_1) | product(e_2, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.66 tff(419,plain,
% 0.62/0.66 (product(e_2, e_1, e_2)),
% 0.62/0.66 inference(unit_resolution,[status(thm)],[418, 377, 366])).
% 0.62/0.66 tff(420,assumption,(~cycle(e_3, e_3)), introduced(assumption)).
% 0.62/0.66 tff(421,plain,
% 0.62/0.66 (((~![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_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_3)) | (~cycle(e_3, e_4)))) <=> ((~![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_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_3)) | (~cycle(e_3, e_4)))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(422,plain,
% 0.62/0.66 (((~greater(e_4, e_0)) | (~greater(e_4, e_3)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_4))) <=> ((~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_3)) | (~cycle(e_3, e_4)))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(423,plain,
% 0.62/0.66 (((~![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_4, e_0)) | (~greater(e_4, e_3)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_4)))) <=> ((~![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_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_3)) | (~cycle(e_3, e_4))))),
% 0.62/0.66 inference(monotonicity,[status(thm)],[422])).
% 0.62/0.66 tff(424,plain,
% 0.62/0.66 (((~![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_4, e_0)) | (~greater(e_4, e_3)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_4)))) <=> ((~![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_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_3)) | (~cycle(e_3, e_4)))),
% 0.62/0.66 inference(transitivity,[status(thm)],[423, 421])).
% 0.62/0.66 tff(425,plain,
% 0.62/0.66 ((~![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_4, e_0)) | (~greater(e_4, e_3)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_4)))),
% 0.62/0.66 inference(quant_inst,[status(thm)],[])).
% 0.62/0.66 tff(426,plain,
% 0.62/0.66 ((~![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_5, e_0)) | (~cycle(e_4, e_0)) | (~greater(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_3)) | (~cycle(e_3, e_4))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[425, 424])).
% 0.62/0.66 tff(427,plain,
% 0.62/0.66 ((~cycle(e_4, e_0)) | (~cycle(e_3, e_4))),
% 0.62/0.66 inference(unit_resolution,[status(thm)],[426, 24, 21, 234, 15, 12])).
% 0.62/0.66 tff(428,plain,
% 0.62/0.66 (~cycle(e_3, e_4)),
% 0.62/0.66 inference(unit_resolution,[status(thm)],[427, 2])).
% 0.62/0.66 tff(429,assumption,(~cycle(e_3, e_2)), introduced(assumption)).
% 0.62/0.66 tff(430,plain,
% 0.62/0.66 (((~![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_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_3)) | (~cycle(e_3, 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_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_3)) | (~cycle(e_3, e_1)))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(431,plain,
% 0.62/0.66 (((~greater(e_1, e_0)) | (~greater(e_4, e_3)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_1))) <=> ((~cycle(e_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_3)) | (~cycle(e_3, e_1)))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(432,plain,
% 0.62/0.66 (((~![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_4, e_3)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_3, 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_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_3)) | (~cycle(e_3, e_1))))),
% 0.62/0.66 inference(monotonicity,[status(thm)],[431])).
% 0.62/0.66 tff(433,plain,
% 0.62/0.66 (((~![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_4, e_3)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_3, 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_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_3)) | (~cycle(e_3, e_1)))),
% 0.62/0.66 inference(transitivity,[status(thm)],[432, 430])).
% 0.62/0.66 tff(434,plain,
% 0.62/0.66 ((~![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_4, e_3)) | (~next(e_4, e_5)) | (~cycle(e_5, e_0)) | (~cycle(e_4, e_0)) | (~cycle(e_3, e_1)))),
% 0.62/0.66 inference(quant_inst,[status(thm)],[])).
% 0.62/0.66 tff(435,plain,
% 0.62/0.66 ((~![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_5, e_0)) | (~greater(e_1, e_0)) | (~cycle(e_4, e_0)) | (~next(e_4, e_5)) | (~greater(e_4, e_3)) | (~cycle(e_3, e_1))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[434, 433])).
% 0.62/0.66 tff(436,plain,
% 0.62/0.66 ((~cycle(e_4, e_0)) | (~cycle(e_3, e_1))),
% 0.62/0.66 inference(unit_resolution,[status(thm)],[435, 24, 81, 234, 15, 12])).
% 0.62/0.66 tff(437,plain,
% 0.62/0.66 (~cycle(e_3, e_1)),
% 0.62/0.66 inference(unit_resolution,[status(thm)],[436, 2])).
% 0.62/0.66 tff(438,plain,
% 0.62/0.66 (group_element(e_3) <=> group_element(e_3)),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(439,axiom,(group_element(e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_3')).
% 0.62/0.67 tff(440,plain,
% 0.62/0.67 (group_element(e_3)),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[439, 438])).
% 0.62/0.67 tff(441,plain,
% 0.62/0.67 (((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_3, e_4) | 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_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_3, e_4) | cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0) | (~group_element(e_3)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(442,plain,
% 0.62/0.67 ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | (cycle(e_3, e_4) | cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0) | (~group_element(e_3)))),
% 0.62/0.67 inference(quant_inst,[status(thm)],[])).
% 0.62/0.67 tff(443,plain,
% 0.62/0.67 ((~![X: $i] : (cycle(X, e_4) | cycle(X, e_3) | cycle(X, e_2) | cycle(X, e_1) | cycle(X, e_0) | (~group_element(X)))) | cycle(e_3, e_4) | cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0) | (~group_element(e_3))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[442, 441])).
% 0.62/0.67 tff(444,plain,
% 0.62/0.67 (cycle(e_3, e_4) | cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_1) | cycle(e_3, e_0)),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[443, 106, 440])).
% 0.62/0.67 tff(445,plain,
% 0.62/0.67 (cycle(e_3, e_0)),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[444, 437, 429, 428, 420])).
% 0.62/0.67 tff(446,assumption,(~product(e_3, e_1, e_3)), introduced(assumption)).
% 0.62/0.67 tff(447,assumption,(product(e_3, e_1, e_1)), introduced(assumption)).
% 0.62/0.67 tff(448,plain,
% 0.62/0.67 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(449,plain,
% 0.62/0.67 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1)))),
% 0.62/0.67 inference(quant_inst,[status(thm)],[])).
% 0.62/0.67 tff(450,plain,
% 0.62/0.67 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_3, e_1, e_1))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[449, 448])).
% 0.62/0.67 tff(451,plain,
% 0.62/0.67 ($false),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[450, 281, 211, 201, 447])).
% 0.62/0.67 tff(452,plain,((~product(e_3, e_1, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.62/0.67 tff(453,plain,
% 0.62/0.67 (~product(e_3, e_1, e_1)),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[452, 370])).
% 0.62/0.67 tff(454,assumption,(~product(e_3, e_1, e_1)), introduced(assumption)).
% 0.62/0.67 tff(455,assumption,(~product(e_3, e_1, e_2)), introduced(assumption)).
% 0.62/0.67 tff(456,assumption,(cycle(e_3, e_0)), introduced(assumption)).
% 0.62/0.67 tff(457,plain,
% 0.62/0.67 (greater(e_5, e_3) <=> greater(e_5, e_3)),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(458,axiom,(greater(e_5, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_5_greater_e_3')).
% 0.62/0.67 tff(459,plain,
% 0.62/0.67 (greater(e_5, e_3)),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[458, 457])).
% 0.62/0.67 tff(460,plain,
% 0.62/0.67 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_3, e_0)) | (~greater(e_5, e_3)) | (~product(e_3, e_1, e_5)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_3, e_0)) | (~greater(e_5, e_3)) | (~product(e_3, e_1, e_5)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(461,plain,
% 0.62/0.67 (((~product(e_3, e_1, e_5)) | (~greater(e_5, e_3)) | (~cycle(e_3, e_0))) <=> ((~cycle(e_3, e_0)) | (~greater(e_5, e_3)) | (~product(e_3, e_1, e_5)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(462,plain,
% 0.62/0.67 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_3, e_1, e_5)) | (~greater(e_5, e_3)) | (~cycle(e_3, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_3, e_0)) | (~greater(e_5, e_3)) | (~product(e_3, e_1, e_5))))),
% 0.62/0.67 inference(monotonicity,[status(thm)],[461])).
% 0.62/0.67 tff(463,plain,
% 0.62/0.67 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_3, e_1, e_5)) | (~greater(e_5, e_3)) | (~cycle(e_3, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_3, e_0)) | (~greater(e_5, e_3)) | (~product(e_3, e_1, e_5)))),
% 0.62/0.67 inference(transitivity,[status(thm)],[462, 460])).
% 0.62/0.67 tff(464,plain,
% 0.62/0.67 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_3, e_1, e_5)) | (~greater(e_5, e_3)) | (~cycle(e_3, e_0)))),
% 0.62/0.67 inference(quant_inst,[status(thm)],[])).
% 0.62/0.67 tff(465,plain,
% 0.62/0.67 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_3, e_0)) | (~greater(e_5, e_3)) | (~product(e_3, e_1, e_5))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[464, 463])).
% 0.62/0.67 tff(466,plain,
% 0.62/0.67 ((~cycle(e_3, e_0)) | (~product(e_3, e_1, e_5))),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[465, 459, 54])).
% 0.62/0.67 tff(467,plain,
% 0.62/0.67 (~product(e_3, e_1, e_5)),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[466, 456])).
% 0.62/0.67 tff(468,plain,
% 0.62/0.67 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_3, e_0)) | (~greater(e_4, e_3)) | (~product(e_3, e_1, e_4)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_3, e_0)) | (~greater(e_4, e_3)) | (~product(e_3, e_1, e_4)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(469,plain,
% 0.62/0.67 (((~product(e_3, e_1, e_4)) | (~greater(e_4, e_3)) | (~cycle(e_3, e_0))) <=> ((~cycle(e_3, e_0)) | (~greater(e_4, e_3)) | (~product(e_3, e_1, e_4)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(470,plain,
% 0.62/0.67 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_3, e_1, e_4)) | (~greater(e_4, e_3)) | (~cycle(e_3, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~cycle(e_3, e_0)) | (~greater(e_4, e_3)) | (~product(e_3, e_1, e_4))))),
% 0.62/0.67 inference(monotonicity,[status(thm)],[469])).
% 0.62/0.67 tff(471,plain,
% 0.62/0.67 (((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_3, e_1, e_4)) | (~greater(e_4, e_3)) | (~cycle(e_3, e_0)))) <=> ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_3, e_0)) | (~greater(e_4, e_3)) | (~product(e_3, e_1, e_4)))),
% 0.62/0.67 inference(transitivity,[status(thm)],[470, 468])).
% 0.62/0.67 tff(472,plain,
% 0.62/0.67 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | ((~product(e_3, e_1, e_4)) | (~greater(e_4, e_3)) | (~cycle(e_3, e_0)))),
% 0.62/0.67 inference(quant_inst,[status(thm)],[])).
% 0.62/0.67 tff(473,plain,
% 0.62/0.67 ((~![Y: $i, X: $i] : ((~product(X, e_1, Y)) | (~greater(Y, X)) | (~cycle(X, e_0)))) | (~cycle(e_3, e_0)) | (~greater(e_4, e_3)) | (~product(e_3, e_1, e_4))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[472, 471])).
% 0.62/0.67 tff(474,plain,
% 0.62/0.67 ((~cycle(e_3, e_0)) | (~product(e_3, e_1, e_4))),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[473, 234, 54])).
% 0.62/0.67 tff(475,plain,
% 0.62/0.67 (~product(e_3, e_1, e_4)),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[474, 456])).
% 0.62/0.67 tff(476,plain,
% 0.62/0.67 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_5) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | product(e_3, e_1, e_3))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_5) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | product(e_3, e_1, e_3))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(477,plain,
% 0.62/0.67 (((~group_element(e_3)) | product(e_3, e_1, e_5) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1))) <=> ((~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_5) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | product(e_3, e_1, e_3))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(478,plain,
% 0.62/0.67 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_1, e_5) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_5) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | product(e_3, e_1, e_3)))),
% 0.62/0.67 inference(monotonicity,[status(thm)],[477])).
% 0.62/0.67 tff(479,plain,
% 0.62/0.67 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_1, e_5) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_5) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | product(e_3, e_1, e_3))),
% 0.62/0.67 inference(transitivity,[status(thm)],[478, 476])).
% 0.62/0.67 tff(480,plain,
% 0.62/0.67 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_1, e_5) | product(e_3, e_1, e_4) | product(e_3, e_1, e_3) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | (~group_element(e_1)))),
% 0.62/0.67 inference(quant_inst,[status(thm)],[])).
% 0.62/0.67 tff(481,plain,
% 0.62/0.67 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_3)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_5) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | product(e_3, e_1, e_3)),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[480, 479])).
% 0.62/0.67 tff(482,plain,
% 0.62/0.67 ($false),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[481, 96, 440, 189, 475, 467, 455, 454, 446])).
% 0.62/0.67 tff(483,plain,((~cycle(e_3, e_0)) | product(e_3, e_1, e_2) | product(e_3, e_1, e_1) | product(e_3, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.67 tff(484,plain,
% 0.62/0.67 (product(e_3, e_1, e_2)),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[483, 453, 446, 445])).
% 0.62/0.67 tff(485,assumption,(product(e_3, e_1, e_2)), introduced(assumption)).
% 0.62/0.67 tff(486,assumption,(product(e_2, e_1, e_2)), introduced(assumption)).
% 0.62/0.67 tff(487,plain,
% 0.62/0.67 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(488,plain,
% 0.62/0.67 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.62/0.67 inference(quant_inst,[status(thm)],[])).
% 0.62/0.67 tff(489,plain,
% 0.62/0.67 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_3, e_1, e_2))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[488, 487])).
% 0.62/0.67 tff(490,plain,
% 0.62/0.67 ($false),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[489, 255, 211, 486, 485])).
% 0.62/0.67 tff(491,plain,((~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.62/0.67 tff(492,plain,
% 0.62/0.67 ($false),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[491, 484, 419])).
% 0.62/0.67 tff(493,plain,((~cycle(e_4, e_0)) | product(e_3, e_1, e_3) | cycle(e_3, e_2) | cycle(e_3, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.67 tff(494,plain,
% 0.62/0.67 (product(e_3, e_1, e_3)),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[493, 2, 323, 242])).
% 0.62/0.67 tff(495,assumption,(product(e_3, e_1, e_3)), introduced(assumption)).
% 0.62/0.67 tff(496,assumption,(product(e_4, e_1, e_3)), introduced(assumption)).
% 0.62/0.67 tff(497,plain,
% 0.62/0.67 ((~equalish(e_4, e_3)) <=> (~equalish(e_4, e_3))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(498,axiom,(~equalish(e_4, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_4_is_not_e_3')).
% 0.62/0.67 tff(499,plain,
% 0.62/0.67 (~equalish(e_4, e_3)),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[498, 497])).
% 0.62/0.67 tff(500,plain,
% 0.62/0.67 (((~![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_3)) | (~product(e_4, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_4, e_1, e_3)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(501,plain,
% 0.62/0.67 ((~![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_3)) | (~product(e_4, e_1, e_3)))),
% 0.62/0.67 inference(quant_inst,[status(thm)],[])).
% 0.62/0.67 tff(502,plain,
% 0.62/0.67 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_4, e_1, e_3))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[501, 500])).
% 0.62/0.67 tff(503,plain,
% 0.62/0.67 ($false),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[502, 499, 211, 496, 495])).
% 0.62/0.67 tff(504,plain,((~product(e_4, e_1, e_3)) | (~product(e_3, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.62/0.67 tff(505,plain,
% 0.62/0.67 (~product(e_4, e_1, e_3)),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[504, 494])).
% 0.62/0.67 tff(506,assumption,(product(e_4, e_1, e_4)), introduced(assumption)).
% 0.62/0.67 tff(507,plain,
% 0.62/0.67 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : refl((product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1))) <=> (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1))))),
% 0.62/0.67 inference(bind,[status(th)],[])).
% 0.62/0.67 tff(508,plain,
% 0.62/0.67 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.62/0.67 inference(quant_intro,[status(thm)],[507])).
% 0.62/0.67 tff(509,plain,
% 0.62/0.67 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1))) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(510,plain,
% 0.62/0.67 (^[Y: $i, Z1: $i, X: $i, Z2: $i] : rewrite((((~product(X, Y, Z1)) | (~product(Z1, Y, Z2))) | product(X, Z1, Z2)) <=> (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1))))),
% 0.62/0.67 inference(bind,[status(th)],[])).
% 0.62/0.67 tff(511,plain,
% 0.62/0.67 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Z1, Y, Z2))) | product(X, Z1, Z2)) <=> ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.62/0.67 inference(quant_intro,[status(thm)],[510])).
% 0.62/0.67 tff(512,axiom,(![Y: $i, Z1: $i, X: $i, Z2: $i] : (((~product(X, Y, Z1)) | (~product(Z1, Y, Z2))) | product(X, Z1, Z2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','qg3')).
% 0.62/0.67 tff(513,plain,
% 0.62/0.67 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[512, 511])).
% 0.62/0.67 tff(514,plain,
% 0.62/0.67 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[513, 509])).
% 0.62/0.67 tff(515,plain,(
% 0.62/0.67 ![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.62/0.67 inference(skolemize,[status(sab)],[514])).
% 0.62/0.67 tff(516,plain,
% 0.62/0.67 (![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[515, 508])).
% 0.62/0.67 tff(517,plain,
% 0.62/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_4, e_4) | (~product(e_4, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_4, e_4) | (~product(e_4, e_1, e_4)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(518,plain,
% 0.62/0.67 ((product(e_4, e_4, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_1, e_4))) <=> (product(e_4, e_4, e_4) | (~product(e_4, e_1, e_4)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(519,plain,
% 0.62/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_4, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_4, e_4) | (~product(e_4, e_1, e_4))))),
% 0.62/0.67 inference(monotonicity,[status(thm)],[518])).
% 0.62/0.67 tff(520,plain,
% 0.62/0.67 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_4, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_4, e_4) | (~product(e_4, e_1, e_4)))),
% 0.62/0.67 inference(transitivity,[status(thm)],[519, 517])).
% 0.62/0.67 tff(521,plain,
% 0.62/0.67 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_4, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_1, e_4)))),
% 0.62/0.67 inference(quant_inst,[status(thm)],[])).
% 0.62/0.67 tff(522,plain,
% 0.62/0.67 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_4, e_4) | (~product(e_4, e_1, e_4))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[521, 520])).
% 0.62/0.67 tff(523,plain,
% 0.62/0.67 (product(e_4, e_4, e_4) | (~product(e_4, e_1, e_4))),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[522, 516])).
% 0.62/0.67 tff(524,plain,
% 0.62/0.67 (product(e_4, e_4, e_4)),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[523, 506])).
% 0.62/0.67 tff(525,plain,
% 0.62/0.67 (^[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))))),
% 0.62/0.67 inference(bind,[status(th)],[])).
% 0.62/0.67 tff(526,plain,
% 0.62/0.67 (![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)))),
% 0.62/0.67 inference(quant_intro,[status(thm)],[525])).
% 0.62/0.67 tff(527,plain,
% 0.62/0.67 (![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)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(528,plain,
% 0.62/0.67 (^[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)))))),
% 0.62/0.68 inference(bind,[status(th)],[])).
% 0.62/0.68 tff(529,plain,
% 0.62/0.68 (![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)))),
% 0.62/0.68 inference(quant_intro,[status(thm)],[528])).
% 0.62/0.68 tff(530,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')).
% 0.62/0.68 tff(531,plain,
% 0.62/0.68 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[530, 529])).
% 0.62/0.68 tff(532,plain,
% 0.62/0.68 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[531, 527])).
% 0.62/0.68 tff(533,plain,(
% 0.62/0.68 ![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.62/0.68 inference(skolemize,[status(sab)],[532])).
% 0.62/0.68 tff(534,plain,
% 0.62/0.68 (![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[533, 526])).
% 0.62/0.68 tff(535,plain,
% 0.62/0.68 ((~equalish(e_1, e_4)) <=> (~equalish(e_1, e_4))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(536,axiom,(~equalish(e_1, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_4')).
% 0.62/0.68 tff(537,plain,
% 0.62/0.68 (~equalish(e_1, e_4)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[536, 535])).
% 0.62/0.68 tff(538,plain,
% 0.62/0.68 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(539,plain,
% 0.62/0.68 ((equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4))) <=> (equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(540,plain,
% 0.62/0.68 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4))))),
% 0.62/0.68 inference(monotonicity,[status(thm)],[539])).
% 0.62/0.68 tff(541,plain,
% 0.62/0.68 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4)))),
% 0.62/0.68 inference(transitivity,[status(thm)],[540, 538])).
% 0.62/0.68 tff(542,plain,
% 0.62/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_1, e_4) | (~product(e_4, e_4, e_4)) | (~product(e_4, e_1, e_4)))),
% 0.62/0.68 inference(quant_inst,[status(thm)],[])).
% 0.62/0.68 tff(543,plain,
% 0.62/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_1, e_4) | (~product(e_4, e_1, e_4)) | (~product(e_4, e_4, e_4))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[542, 541])).
% 0.62/0.68 tff(544,plain,
% 0.62/0.68 ($false),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[543, 537, 534, 524, 506])).
% 0.62/0.68 tff(545,plain,(~product(e_4, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.68 tff(546,plain,
% 0.62/0.68 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(547,plain,
% 0.62/0.68 (((~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1))) <=> ((~group_element(e_1)) | (~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(548,plain,
% 0.62/0.68 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1)))),
% 0.62/0.68 inference(monotonicity,[status(thm)],[547])).
% 0.62/0.68 tff(549,plain,
% 0.62/0.68 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1))),
% 0.62/0.68 inference(transitivity,[status(thm)],[548, 546])).
% 0.62/0.68 tff(550,plain,
% 0.62/0.68 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1) | (~group_element(e_1)))),
% 0.62/0.68 inference(quant_inst,[status(thm)],[])).
% 0.62/0.68 tff(551,plain,
% 0.62/0.68 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_4)) | product(e_4, e_1, e_5) | product(e_4, e_1, e_4) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[550, 549])).
% 0.62/0.68 tff(552,plain,
% 0.62/0.68 (product(e_4, e_1, e_5) | product(e_4, e_1, e_3) | product(e_4, e_1, e_2) | product(e_4, e_1, e_1)),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[551, 96, 316, 189, 545])).
% 0.62/0.68 tff(553,plain,
% 0.62/0.68 (product(e_4, e_1, e_2)),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[552, 505, 231, 220])).
% 0.62/0.68 tff(554,plain,
% 0.62/0.68 (cycle(e_2, e_0)),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[365, 342, 358, 350, 334])).
% 0.62/0.68 tff(555,plain,
% 0.62/0.68 (~product(e_2, e_1, e_1)),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[376, 199])).
% 0.62/0.68 tff(556,plain,
% 0.62/0.68 (product(e_2, e_1, e_2)),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[418, 555, 554])).
% 0.62/0.68 tff(557,assumption,(product(e_4, e_1, e_2)), introduced(assumption)).
% 0.62/0.68 tff(558,plain,
% 0.62/0.68 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_2, e_1, e_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_2) | (~product(e_2, e_1, e_2)) | (~product(e_4, e_1, e_2)))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(559,plain,
% 0.62/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_4, e_1, e_2)))),
% 0.62/0.68 inference(quant_inst,[status(thm)],[])).
% 0.62/0.68 tff(560,plain,
% 0.62/0.68 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_4, e_1, e_2))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[559, 558])).
% 0.62/0.68 tff(561,plain,
% 0.62/0.68 ($false),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[560, 68, 211, 557, 486])).
% 0.62/0.68 tff(562,plain,((~product(e_4, e_1, e_2)) | (~product(e_2, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.62/0.68 tff(563,plain,
% 0.62/0.68 ($false),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[562, 556, 553])).
% 0.62/0.68 tff(564,plain,(~cycle(e_4, e_0)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.68 tff(565,plain,
% 0.62/0.68 (cycle(e_4, e_1)),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[321, 564])).
% 0.62/0.68 tff(566,plain,
% 0.62/0.68 ((~equalish(e_1, e_5)) <=> (~equalish(e_1, e_5))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(567,axiom,(~equalish(e_1, e_5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_5')).
% 0.62/0.68 tff(568,plain,
% 0.62/0.68 (~equalish(e_1, e_5)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[567, 566])).
% 0.62/0.68 tff(569,plain,
% 0.62/0.68 (((~![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_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, 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_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_1)))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(570,plain,
% 0.62/0.68 (((~greater(e_1, e_0)) | (~cycle(e_4, e_1)) | equalish(e_1, e_5) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_1))) <=> (equalish(e_1, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_1)))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(571,plain,
% 0.62/0.68 (((~![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_4, e_1)) | equalish(e_1, e_5) | (~next(e_4, e_5)) | (~product(e_4, 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_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_1))))),
% 0.62/0.68 inference(monotonicity,[status(thm)],[570])).
% 0.62/0.68 tff(572,plain,
% 0.62/0.68 (((~![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_4, e_1)) | equalish(e_1, e_5) | (~next(e_4, e_5)) | (~product(e_4, 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_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_1)))),
% 0.62/0.68 inference(transitivity,[status(thm)],[571, 569])).
% 0.62/0.68 tff(573,plain,
% 0.62/0.68 ((~![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_4, e_1)) | equalish(e_1, e_5) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_1)))),
% 0.62/0.68 inference(quant_inst,[status(thm)],[])).
% 0.62/0.68 tff(574,plain,
% 0.62/0.68 ((~![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_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_1))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[573, 572])).
% 0.62/0.68 tff(575,plain,
% 0.62/0.68 (~product(e_4, e_1, e_1)),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[574, 24, 81, 78, 568, 565])).
% 0.62/0.68 tff(576,plain,
% 0.62/0.68 ((~equalish(e_2, e_5)) <=> (~equalish(e_2, e_5))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(577,axiom,(~equalish(e_2, e_5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_5')).
% 0.62/0.68 tff(578,plain,
% 0.62/0.68 (~equalish(e_2, e_5)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[577, 576])).
% 0.62/0.68 tff(579,plain,
% 0.62/0.68 (((~![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_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, 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_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_2)))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(580,plain,
% 0.62/0.68 (((~greater(e_1, e_0)) | (~cycle(e_4, e_1)) | equalish(e_2, e_5) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_2))) <=> (equalish(e_2, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_2)))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(581,plain,
% 0.62/0.68 (((~![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_4, e_1)) | equalish(e_2, e_5) | (~next(e_4, e_5)) | (~product(e_4, 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_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_2))))),
% 0.62/0.68 inference(monotonicity,[status(thm)],[580])).
% 0.62/0.68 tff(582,plain,
% 0.62/0.68 (((~![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_4, e_1)) | equalish(e_2, e_5) | (~next(e_4, e_5)) | (~product(e_4, 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_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_2)))),
% 0.62/0.68 inference(transitivity,[status(thm)],[581, 579])).
% 0.62/0.68 tff(583,plain,
% 0.62/0.68 ((~![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_4, e_1)) | equalish(e_2, e_5) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_2)))),
% 0.62/0.68 inference(quant_inst,[status(thm)],[])).
% 0.62/0.68 tff(584,plain,
% 0.62/0.68 ((~![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_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_2))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[583, 582])).
% 0.62/0.68 tff(585,plain,
% 0.62/0.68 (~product(e_4, e_1, e_2)),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[584, 24, 81, 78, 578, 565])).
% 0.62/0.68 tff(586,plain,
% 0.62/0.68 ((~equalish(e_3, e_5)) <=> (~equalish(e_3, e_5))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(587,axiom,(~equalish(e_3, e_5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_5')).
% 0.62/0.68 tff(588,plain,
% 0.62/0.68 (~equalish(e_3, e_5)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[587, 586])).
% 0.62/0.68 tff(589,plain,
% 0.62/0.68 (((~![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_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, 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_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_3)))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(590,plain,
% 0.62/0.69 (((~greater(e_1, e_0)) | (~cycle(e_4, e_1)) | equalish(e_3, e_5) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_3))) <=> (equalish(e_3, e_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_3)))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(591,plain,
% 0.62/0.69 (((~![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_4, e_1)) | equalish(e_3, e_5) | (~next(e_4, e_5)) | (~product(e_4, 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_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_3))))),
% 0.62/0.69 inference(monotonicity,[status(thm)],[590])).
% 0.62/0.69 tff(592,plain,
% 0.62/0.69 (((~![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_4, e_1)) | equalish(e_3, e_5) | (~next(e_4, e_5)) | (~product(e_4, 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_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_3)))),
% 0.62/0.69 inference(transitivity,[status(thm)],[591, 589])).
% 0.62/0.69 tff(593,plain,
% 0.62/0.69 ((~![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_4, e_1)) | equalish(e_3, e_5) | (~next(e_4, e_5)) | (~product(e_4, e_1, e_3)))),
% 0.62/0.69 inference(quant_inst,[status(thm)],[])).
% 0.62/0.69 tff(594,plain,
% 0.62/0.69 ((~![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_5) | (~greater(e_1, e_0)) | (~next(e_4, e_5)) | (~cycle(e_4, e_1)) | (~product(e_4, e_1, e_3))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[593, 592])).
% 0.62/0.69 tff(595,plain,
% 0.62/0.69 (~product(e_4, e_1, e_3)),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[594, 24, 81, 78, 588, 565])).
% 0.62/0.69 tff(596,plain,
% 0.62/0.69 (product(e_4, e_1, e_5)),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[552, 595, 585, 575])).
% 0.62/0.69 tff(597,assumption,(product(e_2, e_1, e_3)), introduced(assumption)).
% 0.62/0.69 tff(598,plain,
% 0.62/0.69 ((~equalish(e_2, e_3)) <=> (~equalish(e_2, e_3))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(599,axiom,(~equalish(e_2, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_3')).
% 0.62/0.69 tff(600,plain,
% 0.62/0.69 (~equalish(e_2, e_3)),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[599, 598])).
% 0.62/0.69 tff(601,plain,
% 0.62/0.69 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(602,plain,
% 0.62/0.69 ((equalish(e_2, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3))) <=> (equalish(e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(603,plain,
% 0.62/0.69 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_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_3) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3))))),
% 0.62/0.69 inference(monotonicity,[status(thm)],[602])).
% 0.62/0.69 tff(604,plain,
% 0.62/0.69 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_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_3) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.62/0.69 inference(transitivity,[status(thm)],[603, 601])).
% 0.62/0.69 tff(605,plain,
% 0.62/0.69 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_2, e_3) | (~product(e_3, e_1, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.62/0.69 inference(quant_inst,[status(thm)],[])).
% 0.62/0.69 tff(606,plain,
% 0.62/0.69 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[605, 604])).
% 0.62/0.69 tff(607,plain,
% 0.62/0.69 ($false),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[606, 600, 211, 597, 495])).
% 0.62/0.69 tff(608,plain,((~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.62/0.69 tff(609,plain,
% 0.62/0.69 (~product(e_2, e_1, e_3)),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[608, 495])).
% 0.62/0.69 tff(610,assumption,(cycle(e_3, e_2)), introduced(assumption)).
% 0.62/0.69 tff(611,plain,
% 0.62/0.69 ((~equalish(e_3, e_4)) <=> (~equalish(e_3, e_4))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(612,axiom,(~equalish(e_3, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_3_is_not_e_4')).
% 0.62/0.69 tff(613,plain,
% 0.62/0.69 (~equalish(e_3, e_4)),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[612, 611])).
% 0.62/0.69 tff(614,plain,
% 0.62/0.69 (((~![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_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~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_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_3)))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(615,plain,
% 0.62/0.69 (((~greater(e_2, e_0)) | (~cycle(e_3, e_2)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_3))) <=> (equalish(e_3, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_3)))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(616,plain,
% 0.62/0.69 (((~![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_3, e_2)) | 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_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_3))))),
% 0.62/0.69 inference(monotonicity,[status(thm)],[615])).
% 0.62/0.69 tff(617,plain,
% 0.62/0.69 (((~![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_3, e_2)) | 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_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_3)))),
% 0.62/0.69 inference(transitivity,[status(thm)],[616, 614])).
% 0.62/0.69 tff(618,plain,
% 0.62/0.69 ((~![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_3, e_2)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_3)))),
% 0.62/0.69 inference(quant_inst,[status(thm)],[])).
% 0.62/0.69 tff(619,plain,
% 0.62/0.69 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_3, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_3))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[618, 617])).
% 0.62/0.69 tff(620,plain,
% 0.62/0.69 ($false),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[619, 268, 114, 78, 613, 610, 495])).
% 0.62/0.69 tff(621,plain,((~cycle(e_3, e_2)) | (~product(e_3, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.62/0.69 tff(622,plain,
% 0.62/0.69 (~cycle(e_3, e_2)),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[621, 495])).
% 0.62/0.69 tff(623,assumption,(cycle(e_3, e_4)), introduced(assumption)).
% 0.62/0.69 tff(624,plain,
% 0.62/0.69 (((~![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_4, e_2) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | (~cycle(e_4, 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_4, e_2) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | (~cycle(e_4, e_1)))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(625,plain,
% 0.62/0.69 (((~cycle(e_3, e_4)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1))) <=> (equalish(e_4, e_2) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | (~cycle(e_4, e_1)))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(626,plain,
% 0.62/0.69 (((~![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_4)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, 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_4, e_2) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | (~cycle(e_4, e_1))))),
% 0.62/0.69 inference(monotonicity,[status(thm)],[625])).
% 0.62/0.69 tff(627,plain,
% 0.62/0.69 (((~![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_4)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, 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_4, e_2) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | (~cycle(e_4, e_1)))),
% 0.62/0.69 inference(transitivity,[status(thm)],[626, 624])).
% 0.62/0.69 tff(628,plain,
% 0.62/0.69 ((~![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_4)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)))),
% 0.62/0.69 inference(quant_inst,[status(thm)],[])).
% 0.62/0.69 tff(629,plain,
% 0.62/0.69 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | (~cycle(e_4, e_1))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[628, 627])).
% 0.62/0.69 tff(630,plain,
% 0.62/0.69 ($false),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[629, 84, 268, 21, 265, 68, 623, 252])).
% 0.62/0.69 tff(631,plain,((~cycle(e_3, e_4)) | (~cycle(e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.62/0.69 tff(632,plain,
% 0.62/0.69 (~cycle(e_3, e_4)),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[631, 565])).
% 0.62/0.69 tff(633,assumption,(cycle(e_3, e_1)), introduced(assumption)).
% 0.62/0.69 tff(634,plain,
% 0.62/0.69 (~cycle(e_4, e_0)),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[436, 633])).
% 0.62/0.69 tff(635,plain,
% 0.62/0.69 ((~equalish(e_1, e_2)) <=> (~equalish(e_1, e_2))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(636,axiom,(~equalish(e_1, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_2')).
% 0.62/0.69 tff(637,plain,
% 0.62/0.69 (~equalish(e_1, e_2)),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[636, 635])).
% 0.62/0.69 tff(638,plain,
% 0.62/0.69 (((~![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_3, e_4)) | (~cycle(e_3, e_1)) | (~cycle(e_4, 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_3, e_4)) | (~cycle(e_3, e_1)) | (~cycle(e_4, e_1)))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(639,plain,
% 0.62/0.69 (((~cycle(e_3, e_1)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1))) <=> (equalish(e_1, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~cycle(e_4, e_1)))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(640,plain,
% 0.62/0.69 (((~![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_1)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, 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_3, e_4)) | (~cycle(e_3, e_1)) | (~cycle(e_4, e_1))))),
% 0.62/0.69 inference(monotonicity,[status(thm)],[639])).
% 0.62/0.69 tff(641,plain,
% 0.62/0.69 (((~![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_1)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, 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_3, e_4)) | (~cycle(e_3, e_1)) | (~cycle(e_4, e_1)))),
% 0.62/0.69 inference(transitivity,[status(thm)],[640, 638])).
% 0.62/0.69 tff(642,plain,
% 0.62/0.69 ((~![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_1)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_1, e_0)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)))),
% 0.62/0.69 inference(quant_inst,[status(thm)],[])).
% 0.62/0.69 tff(643,plain,
% 0.62/0.69 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_1, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~cycle(e_3, e_1)) | (~cycle(e_4, e_1))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[642, 641])).
% 0.62/0.69 tff(644,plain,
% 0.62/0.69 ($false),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[643, 84, 268, 81, 265, 637, 633, 252])).
% 0.62/0.69 tff(645,plain,((~cycle(e_3, e_1)) | (~cycle(e_4, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.62/0.69 tff(646,plain,
% 0.62/0.69 (~cycle(e_4, e_1)),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[645, 633])).
% 0.62/0.69 tff(647,plain,
% 0.62/0.69 ($false),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[321, 646, 634])).
% 0.62/0.69 tff(648,plain,(~cycle(e_3, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.69 tff(649,plain,
% 0.62/0.69 (cycle(e_3, e_2) | cycle(e_3, e_0)),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[444, 648, 632, 323])).
% 0.62/0.69 tff(650,plain,
% 0.62/0.69 (cycle(e_3, e_0)),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[649, 622])).
% 0.62/0.69 tff(651,plain,
% 0.62/0.69 (((~![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)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3)) | (~cycle(e_4, 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)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3)) | (~cycle(e_4, e_1)))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(652,plain,
% 0.62/0.70 (((~greater(e_3, e_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_3))) <=> ((~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3)) | (~cycle(e_4, e_1)))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(653,plain,
% 0.62/0.70 (((~![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_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3)) | (~cycle(e_4, e_1))))),
% 0.62/0.70 inference(monotonicity,[status(thm)],[652])).
% 0.62/0.70 tff(654,plain,
% 0.62/0.70 (((~![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_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3)) | (~cycle(e_4, e_1)))),
% 0.62/0.70 inference(transitivity,[status(thm)],[653, 651])).
% 0.62/0.70 tff(655,plain,
% 0.62/0.70 ((~![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_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_3)))),
% 0.62/0.70 inference(quant_inst,[status(thm)],[])).
% 0.62/0.70 tff(656,plain,
% 0.62/0.70 ((~![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)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_3)) | (~cycle(e_4, e_1))),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[655, 654])).
% 0.62/0.70 tff(657,plain,
% 0.62/0.70 ((~cycle(e_3, e_0)) | (~cycle(e_2, e_3)) | (~cycle(e_4, e_1))),
% 0.62/0.70 inference(unit_resolution,[status(thm)],[656, 268, 170, 402, 12])).
% 0.62/0.70 tff(658,plain,
% 0.62/0.70 ((~cycle(e_3, e_0)) | (~cycle(e_2, e_3))),
% 0.62/0.70 inference(unit_resolution,[status(thm)],[657, 565])).
% 0.62/0.70 tff(659,plain,
% 0.62/0.70 (~cycle(e_2, e_3)),
% 0.62/0.70 inference(unit_resolution,[status(thm)],[658, 650])).
% 0.62/0.70 tff(660,plain,
% 0.62/0.70 (((~![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)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_3)) | (~cycle(e_4, 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)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_3)) | (~cycle(e_4, e_1)))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(661,plain,
% 0.62/0.70 (((~greater(e_3, e_1)) | (~greater(e_3, e_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_1, e_3))) <=> ((~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_3)) | (~cycle(e_4, e_1)))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(662,plain,
% 0.62/0.70 (((~![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_1)) | (~greater(e_3, e_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_1, 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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_3)) | (~cycle(e_4, e_1))))),
% 0.62/0.70 inference(monotonicity,[status(thm)],[661])).
% 0.62/0.70 tff(663,plain,
% 0.62/0.70 (((~![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_1)) | (~greater(e_3, e_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_1, 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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_3)) | (~cycle(e_4, e_1)))),
% 0.62/0.70 inference(transitivity,[status(thm)],[662, 660])).
% 0.62/0.70 tff(664,plain,
% 0.62/0.70 ((~![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_1)) | (~greater(e_3, e_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_1, e_3)))),
% 0.62/0.70 inference(quant_inst,[status(thm)],[])).
% 0.62/0.70 tff(665,plain,
% 0.62/0.70 ((~![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)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_3)) | (~cycle(e_4, e_1))),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[664, 663])).
% 0.62/0.70 tff(666,plain,
% 0.62/0.70 ((~cycle(e_3, e_0)) | (~cycle(e_1, e_3)) | (~cycle(e_4, e_1))),
% 0.62/0.70 inference(unit_resolution,[status(thm)],[665, 268, 170, 12])).
% 0.62/0.70 tff(667,plain,
% 0.62/0.70 ((~cycle(e_3, e_0)) | (~cycle(e_1, e_3))),
% 0.62/0.70 inference(unit_resolution,[status(thm)],[666, 565])).
% 0.62/0.70 tff(668,plain,
% 0.62/0.70 (~cycle(e_1, e_3)),
% 0.62/0.70 inference(unit_resolution,[status(thm)],[667, 456])).
% 0.62/0.70 tff(669,plain,
% 0.62/0.70 (((~![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)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_4)) | (~cycle(e_4, 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)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_4)) | (~cycle(e_4, e_1)))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(670,plain,
% 0.62/0.70 (((~greater(e_4, e_1)) | (~greater(e_3, e_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_1, e_4))) <=> ((~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_4)) | (~cycle(e_4, e_1)))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(671,plain,
% 0.62/0.70 (((~![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_4, e_1)) | (~greater(e_3, e_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_1, e_4)))) <=> ((~![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)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_4)) | (~cycle(e_4, e_1))))),
% 0.62/0.70 inference(monotonicity,[status(thm)],[670])).
% 0.62/0.70 tff(672,plain,
% 0.62/0.70 (((~![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_4, e_1)) | (~greater(e_3, e_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_1, e_4)))) <=> ((~![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)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_4)) | (~cycle(e_4, e_1)))),
% 0.62/0.70 inference(transitivity,[status(thm)],[671, 669])).
% 0.62/0.70 tff(673,plain,
% 0.62/0.70 ((~![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_4, e_1)) | (~greater(e_3, e_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_1, e_4)))),
% 0.62/0.70 inference(quant_inst,[status(thm)],[])).
% 0.62/0.70 tff(674,plain,
% 0.62/0.70 ((~![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)) | (~next(e_3, e_4)) | (~greater(e_3, e_1)) | (~greater(e_4, e_1)) | (~cycle(e_1, e_4)) | (~cycle(e_4, e_1))),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[673, 672])).
% 0.62/0.70 tff(675,plain,
% 0.62/0.70 ((~cycle(e_3, e_0)) | (~cycle(e_1, e_4)) | (~cycle(e_4, e_1))),
% 0.62/0.70 inference(unit_resolution,[status(thm)],[674, 268, 170, 18, 12])).
% 0.62/0.70 tff(676,plain,
% 0.62/0.70 ((~cycle(e_3, e_0)) | (~cycle(e_1, e_4))),
% 0.62/0.70 inference(unit_resolution,[status(thm)],[675, 565])).
% 0.62/0.70 tff(677,plain,
% 0.62/0.70 (~cycle(e_1, e_4)),
% 0.62/0.70 inference(unit_resolution,[status(thm)],[676, 456])).
% 0.62/0.70 tff(678,plain,
% 0.62/0.70 (~product(e_1, e_1, e_4)),
% 0.62/0.70 inference(unit_resolution,[status(thm)],[122, 677, 668])).
% 0.62/0.70 tff(679,plain,
% 0.62/0.70 (((~![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)) | (~next(e_3, e_4)) | (~greater(e_2, e_1)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_2)) | (~cycle(e_4, 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)) | (~next(e_3, e_4)) | (~greater(e_2, e_1)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_2)) | (~cycle(e_4, e_1)))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(680,plain,
% 0.62/0.70 (((~greater(e_2, e_1)) | (~greater(e_3, e_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_1, e_2))) <=> ((~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_2, e_1)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_2)) | (~cycle(e_4, e_1)))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(681,plain,
% 0.62/0.70 (((~![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_1)) | (~greater(e_3, e_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, 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)) | (~next(e_3, e_4)) | (~greater(e_2, e_1)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_2)) | (~cycle(e_4, e_1))))),
% 0.62/0.70 inference(monotonicity,[status(thm)],[680])).
% 0.62/0.70 tff(682,plain,
% 0.62/0.70 (((~![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_1)) | (~greater(e_3, e_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, 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)) | (~next(e_3, e_4)) | (~greater(e_2, e_1)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_2)) | (~cycle(e_4, e_1)))),
% 0.62/0.70 inference(transitivity,[status(thm)],[681, 679])).
% 0.62/0.70 tff(683,plain,
% 0.62/0.70 ((~![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_1)) | (~greater(e_3, e_1)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_1, e_2)))),
% 0.62/0.70 inference(quant_inst,[status(thm)],[])).
% 0.62/0.70 tff(684,plain,
% 0.62/0.70 ((~![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)) | (~next(e_3, e_4)) | (~greater(e_2, e_1)) | (~greater(e_3, e_1)) | (~cycle(e_1, e_2)) | (~cycle(e_4, e_1))),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[683, 682])).
% 0.62/0.70 tff(685,plain,
% 0.62/0.70 ((~cycle(e_3, e_0)) | (~cycle(e_1, e_2)) | (~cycle(e_4, e_1))),
% 0.62/0.70 inference(unit_resolution,[status(thm)],[684, 268, 159, 170, 12])).
% 0.62/0.70 tff(686,plain,
% 0.62/0.70 ((~cycle(e_3, e_0)) | (~cycle(e_1, e_2))),
% 0.62/0.70 inference(unit_resolution,[status(thm)],[685, 565])).
% 0.62/0.70 tff(687,plain,
% 0.62/0.70 (~cycle(e_1, e_2)),
% 0.62/0.70 inference(unit_resolution,[status(thm)],[686, 456])).
% 0.62/0.70 tff(688,plain,
% 0.62/0.70 (((~![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)) | (~next(e_3, e_4)) | (~greater(e_2, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2)) | (~cycle(e_4, 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)) | (~next(e_3, e_4)) | (~greater(e_2, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2)) | (~cycle(e_4, e_1)))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(689,plain,
% 0.62/0.70 (((~greater(e_2, e_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_2))) <=> ((~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_2, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2)) | (~cycle(e_4, e_1)))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(690,plain,
% 0.62/0.70 (((~![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_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_2, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2)) | (~cycle(e_4, e_1))))),
% 0.62/0.70 inference(monotonicity,[status(thm)],[689])).
% 0.62/0.70 tff(691,plain,
% 0.62/0.70 (((~![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_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~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_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_2, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2)) | (~cycle(e_4, e_1)))),
% 0.62/0.70 inference(transitivity,[status(thm)],[690, 688])).
% 0.62/0.70 tff(692,plain,
% 0.62/0.70 ((~![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_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_2)))),
% 0.62/0.70 inference(quant_inst,[status(thm)],[])).
% 0.62/0.70 tff(693,plain,
% 0.62/0.70 ((~![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)) | (~next(e_3, e_4)) | (~greater(e_2, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_2)) | (~cycle(e_4, e_1))),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[692, 691])).
% 0.62/0.70 tff(694,plain,
% 0.62/0.70 ((~cycle(e_3, e_0)) | (~cycle(e_2, e_2)) | (~cycle(e_4, e_1))),
% 0.62/0.70 inference(unit_resolution,[status(thm)],[693, 268, 159, 402, 12])).
% 0.62/0.70 tff(695,plain,
% 0.62/0.70 ((~cycle(e_3, e_0)) | (~cycle(e_2, e_2))),
% 0.62/0.70 inference(unit_resolution,[status(thm)],[694, 565])).
% 0.62/0.70 tff(696,plain,
% 0.62/0.70 (~cycle(e_2, e_2)),
% 0.62/0.70 inference(unit_resolution,[status(thm)],[695, 456])).
% 0.62/0.70 tff(697,assumption,(~cycle(e_2, e_3)), introduced(assumption)).
% 0.68/0.71 tff(698,plain,
% 0.68/0.71 (((~![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)) | (~next(e_3, e_4)) | (~greater(e_4, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_4)) | (~cycle(e_4, 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)) | (~next(e_3, e_4)) | (~greater(e_4, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_4)) | (~cycle(e_4, e_1)))),
% 0.68/0.71 inference(rewrite,[status(thm)],[])).
% 0.68/0.71 tff(699,plain,
% 0.68/0.71 (((~greater(e_4, e_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_4))) <=> ((~cycle(e_3, e_0)) | (~next(e_3, e_4)) | (~greater(e_4, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_4)) | (~cycle(e_4, e_1)))),
% 0.68/0.71 inference(rewrite,[status(thm)],[])).
% 0.68/0.71 tff(700,plain,
% 0.68/0.71 (((~![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_4, e_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_4)))) <=> ((~![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)) | (~next(e_3, e_4)) | (~greater(e_4, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_4)) | (~cycle(e_4, e_1))))),
% 0.68/0.71 inference(monotonicity,[status(thm)],[699])).
% 0.68/0.71 tff(701,plain,
% 0.68/0.71 (((~![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_4, e_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_4)))) <=> ((~![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)) | (~next(e_3, e_4)) | (~greater(e_4, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_4)) | (~cycle(e_4, e_1)))),
% 0.68/0.71 inference(transitivity,[status(thm)],[700, 698])).
% 0.68/0.71 tff(702,plain,
% 0.68/0.71 ((~![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_4, e_1)) | (~greater(e_3, e_2)) | (~next(e_3, e_4)) | (~cycle(e_4, e_1)) | (~cycle(e_3, e_0)) | (~cycle(e_2, e_4)))),
% 0.68/0.71 inference(quant_inst,[status(thm)],[])).
% 0.68/0.71 tff(703,plain,
% 0.68/0.71 ((~![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)) | (~next(e_3, e_4)) | (~greater(e_4, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_2, e_4)) | (~cycle(e_4, e_1))),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[702, 701])).
% 0.68/0.71 tff(704,plain,
% 0.68/0.71 ((~cycle(e_3, e_0)) | (~cycle(e_2, e_4)) | (~cycle(e_4, e_1))),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[703, 268, 18, 402, 12])).
% 0.68/0.71 tff(705,plain,
% 0.68/0.71 ((~cycle(e_3, e_0)) | (~cycle(e_2, e_4))),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[704, 565])).
% 0.68/0.71 tff(706,plain,
% 0.68/0.71 (~cycle(e_2, e_4)),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[705, 456])).
% 0.68/0.71 tff(707,assumption,(~cycle(e_2, e_4)), introduced(assumption)).
% 0.68/0.71 tff(708,assumption,(~cycle(e_2, e_2)), introduced(assumption)).
% 0.68/0.71 tff(709,plain,
% 0.68/0.71 (next(e_2, e_3) <=> next(e_2, e_3)),
% 0.68/0.71 inference(rewrite,[status(thm)],[])).
% 0.68/0.71 tff(710,axiom,(next(e_2, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_then_e_3')).
% 0.68/0.71 tff(711,plain,
% 0.68/0.71 (next(e_2, e_3)),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[710, 709])).
% 0.68/0.71 tff(712,plain,
% 0.68/0.71 (((~![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)) | (~cycle(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)) | (~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)))) | (~greater(e_1, e_0)) | (~cycle(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_1)))),
% 0.68/0.71 inference(rewrite,[status(thm)],[])).
% 0.68/0.71 tff(713,plain,
% 0.68/0.71 (((~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))) <=> ((~greater(e_1, e_0)) | (~cycle(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_1)))),
% 0.68/0.71 inference(rewrite,[status(thm)],[])).
% 0.68/0.71 tff(714,plain,
% 0.68/0.71 (((~![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)))) | ((~greater(e_1, e_0)) | (~cycle(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_1))))),
% 0.68/0.71 inference(monotonicity,[status(thm)],[713])).
% 0.68/0.71 tff(715,plain,
% 0.68/0.71 (((~![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)))) | (~greater(e_1, e_0)) | (~cycle(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_1)))),
% 0.68/0.71 inference(transitivity,[status(thm)],[714, 712])).
% 0.68/0.71 tff(716,plain,
% 0.68/0.71 ((~![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)))),
% 0.68/0.71 inference(quant_inst,[status(thm)],[])).
% 0.68/0.71 tff(717,plain,
% 0.68/0.71 ((~![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)) | (~cycle(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_0)) | (~greater(e_2, e_1)) | (~cycle(e_1, e_1))),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[716, 715])).
% 0.68/0.71 tff(718,plain,
% 0.68/0.71 ((~cycle(e_2, e_0)) | (~cycle(e_3, e_0)) | (~cycle(e_1, e_1))),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[717, 711, 81, 159, 12])).
% 0.68/0.71 tff(719,plain,
% 0.68/0.71 (~cycle(e_2, e_0)),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[718, 65, 456])).
% 0.68/0.71 tff(720,assumption,(cycle(e_2, e_1)), introduced(assumption)).
% 0.68/0.71 tff(721,plain,
% 0.68/0.71 (((~![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)) | (~cycle(e_1, e_1)) | (~cycle(e_2, 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)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_1)))),
% 0.68/0.71 inference(rewrite,[status(thm)],[])).
% 0.68/0.71 tff(722,plain,
% 0.68/0.71 (((~cycle(e_1, e_1)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_1))) <=> (equalish(e_1, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_1)))),
% 0.68/0.71 inference(rewrite,[status(thm)],[])).
% 0.68/0.71 tff(723,plain,
% 0.68/0.71 (((~![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_1, e_1)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, 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)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_1))))),
% 0.68/0.71 inference(monotonicity,[status(thm)],[722])).
% 0.68/0.71 tff(724,plain,
% 0.68/0.71 (((~![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_1, e_1)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, 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)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_1)))),
% 0.68/0.71 inference(transitivity,[status(thm)],[723, 721])).
% 0.68/0.71 tff(725,plain,
% 0.68/0.71 ((~![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_1, e_1)) | equalish(e_1, e_2) | (~next(e_1, e_2)) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_1)))),
% 0.68/0.71 inference(quant_inst,[status(thm)],[])).
% 0.68/0.71 tff(726,plain,
% 0.68/0.71 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_1, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_1))),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[725, 724])).
% 0.68/0.71 tff(727,plain,
% 0.68/0.71 ($false),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[726, 84, 81, 265, 637, 65, 720])).
% 0.68/0.71 tff(728,plain,((~cycle(e_1, e_1)) | (~cycle(e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.68/0.71 tff(729,plain,
% 0.68/0.71 (~cycle(e_2, e_1)),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[728, 65])).
% 0.68/0.71 tff(730,plain,
% 0.68/0.71 ($false),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[365, 729, 719, 708, 697, 707])).
% 0.68/0.71 tff(731,plain,((~cycle(e_1, e_1)) | cycle(e_2, e_2) | cycle(e_2, e_3) | cycle(e_2, e_4) | (~cycle(e_3, e_0))), inference(lemma,lemma(discharge,[]))).
% 0.68/0.71 tff(732,plain,
% 0.68/0.71 (~cycle(e_1, e_1)),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[731, 706, 697, 696, 456])).
% 0.68/0.71 tff(733,plain,
% 0.68/0.71 (cycle(e_1, e_0)),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[110, 732, 687, 677, 668])).
% 0.68/0.71 tff(734,assumption,(~product(e_2, e_1, e_3)), introduced(assumption)).
% 0.68/0.71 tff(735,assumption,(~product(e_2, e_2, e_2)), introduced(assumption)).
% 0.68/0.71 tff(736,plain,
% 0.68/0.71 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2)))),
% 0.68/0.71 inference(rewrite,[status(thm)],[])).
% 0.68/0.71 tff(737,plain,
% 0.68/0.71 ((product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_1, e_2))) <=> (product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2)))),
% 0.68/0.71 inference(rewrite,[status(thm)],[])).
% 0.68/0.71 tff(738,plain,
% 0.68/0.71 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2))))),
% 0.68/0.71 inference(monotonicity,[status(thm)],[737])).
% 0.68/0.71 tff(739,plain,
% 0.68/0.71 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2)))),
% 0.68/0.71 inference(transitivity,[status(thm)],[738, 736])).
% 0.68/0.71 tff(740,plain,
% 0.68/0.71 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_1, e_2)))),
% 0.68/0.71 inference(quant_inst,[status(thm)],[])).
% 0.68/0.71 tff(741,plain,
% 0.68/0.71 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2))),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[740, 739])).
% 0.68/0.71 tff(742,plain,
% 0.68/0.71 ($false),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[741, 516, 486, 735])).
% 0.68/0.71 tff(743,plain,(product(e_2, e_2, e_2) | (~product(e_2, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.68/0.71 tff(744,plain,
% 0.68/0.71 (product(e_2, e_2, e_2)),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[743, 486])).
% 0.68/0.71 tff(745,plain,
% 0.68/0.71 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.68/0.71 inference(rewrite,[status(thm)],[])).
% 0.68/0.71 tff(746,plain,
% 0.68/0.71 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.68/0.71 inference(quant_inst,[status(thm)],[])).
% 0.68/0.71 tff(747,plain,
% 0.68/0.71 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_2)) | (~product(e_2, e_2, e_2))),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[746, 745])).
% 0.68/0.71 tff(748,plain,
% 0.68/0.71 ($false),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[747, 296, 534, 486, 744])).
% 0.68/0.71 tff(749,plain,(~product(e_2, e_1, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.71 tff(750,plain,
% 0.68/0.71 (~cycle(e_2, e_0)),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[418, 378, 379])).
% 0.68/0.71 tff(751,plain,
% 0.68/0.71 (cycle(e_2, e_1)),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[365, 750, 697, 708, 707])).
% 0.68/0.71 tff(752,plain,
% 0.68/0.71 (((~![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)))),
% 0.68/0.71 inference(rewrite,[status(thm)],[])).
% 0.68/0.71 tff(753,plain,
% 0.68/0.71 (((~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)))),
% 0.68/0.71 inference(rewrite,[status(thm)],[])).
% 0.68/0.71 tff(754,plain,
% 0.68/0.71 (((~![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))))),
% 0.68/0.71 inference(monotonicity,[status(thm)],[753])).
% 0.68/0.71 tff(755,plain,
% 0.68/0.71 (((~![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)))),
% 0.68/0.71 inference(transitivity,[status(thm)],[754, 752])).
% 0.68/0.72 tff(756,plain,
% 0.68/0.72 ((~![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)))),
% 0.68/0.72 inference(quant_inst,[status(thm)],[])).
% 0.68/0.72 tff(757,plain,
% 0.68/0.72 ((~![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))),
% 0.68/0.72 inference(modus_ponens,[status(thm)],[756, 755])).
% 0.68/0.72 tff(758,plain,
% 0.68/0.72 (~product(e_2, e_1, e_4)),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[757, 711, 81, 78, 499, 751])).
% 0.68/0.72 tff(759,plain,
% 0.68/0.72 ((~equalish(e_5, e_3)) <=> (~equalish(e_5, e_3))),
% 0.68/0.72 inference(rewrite,[status(thm)],[])).
% 0.68/0.72 tff(760,axiom,(~equalish(e_5, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_5_is_not_e_3')).
% 0.68/0.72 tff(761,plain,
% 0.68/0.72 (~equalish(e_5, e_3)),
% 0.68/0.72 inference(modus_ponens,[status(thm)],[760, 759])).
% 0.68/0.72 tff(762,plain,
% 0.68/0.72 (((~![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_5, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_5)))) <=> ((~![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_5, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_5)))),
% 0.68/0.72 inference(rewrite,[status(thm)],[])).
% 0.68/0.72 tff(763,plain,
% 0.68/0.72 (((~greater(e_1, e_0)) | (~cycle(e_2, e_1)) | equalish(e_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5))) <=> (equalish(e_5, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_5)))),
% 0.68/0.72 inference(rewrite,[status(thm)],[])).
% 0.68/0.72 tff(764,plain,
% 0.68/0.72 (((~![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_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))) <=> ((~![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_5, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_5))))),
% 0.68/0.72 inference(monotonicity,[status(thm)],[763])).
% 0.68/0.72 tff(765,plain,
% 0.68/0.72 (((~![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_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))) <=> ((~![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_5, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_5)))),
% 0.68/0.72 inference(transitivity,[status(thm)],[764, 762])).
% 0.68/0.72 tff(766,plain,
% 0.68/0.72 ((~![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_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))),
% 0.68/0.72 inference(quant_inst,[status(thm)],[])).
% 0.68/0.72 tff(767,plain,
% 0.68/0.72 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_5, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~product(e_2, e_1, e_5))),
% 0.68/0.72 inference(modus_ponens,[status(thm)],[766, 765])).
% 0.68/0.72 tff(768,plain,
% 0.68/0.72 (~product(e_2, e_1, e_5)),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[767, 711, 81, 78, 761, 751])).
% 0.68/0.72 tff(769,plain,
% 0.68/0.72 (product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_5) | product(e_2, e_1, e_2)),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[416, 96, 361, 189, 379])).
% 0.68/0.72 tff(770,plain,
% 0.68/0.72 ($false),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[769, 768, 758, 734, 378])).
% 0.68/0.72 tff(771,plain,(product(e_2, e_1, e_2) | product(e_2, e_1, e_3) | product(e_2, e_1, e_1) | cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.72 tff(772,plain,
% 0.68/0.72 (product(e_2, e_1, e_3) | product(e_2, e_1, e_1) | cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_4)),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[771, 749])).
% 0.68/0.72 tff(773,plain,
% 0.68/0.72 (product(e_2, e_1, e_1)),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[772, 706, 697, 696, 734])).
% 0.68/0.72 tff(774,plain,
% 0.68/0.72 (~product(e_1, e_1, e_1)),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[376, 773])).
% 0.68/0.72 tff(775,plain,
% 0.68/0.72 ($false),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[198, 774, 733, 678])).
% 0.68/0.72 tff(776,plain,((~cycle(e_3, e_0)) | cycle(e_2, e_3) | product(e_2, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.72 tff(777,plain,
% 0.68/0.72 ($false),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[776, 659, 650, 609])).
% 0.68/0.72 tff(778,plain,(~product(e_3, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.72 tff(779,assumption,(cycle(e_2, e_3)), introduced(assumption)).
% 0.68/0.72 tff(780,assumption,(cycle(e_1, e_3)), introduced(assumption)).
% 0.68/0.72 tff(781,plain,
% 0.68/0.72 (((~![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_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_3)) | (~cycle(e_2, 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_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_3)) | (~cycle(e_2, e_3)))),
% 0.68/0.72 inference(rewrite,[status(thm)],[])).
% 0.68/0.72 tff(782,plain,
% 0.68/0.72 (((~cycle(e_1, e_3)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~greater(e_3, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_3))) <=> (equalish(e_3, e_4) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_3)) | (~cycle(e_2, e_3)))),
% 0.68/0.72 inference(rewrite,[status(thm)],[])).
% 0.68/0.72 tff(783,plain,
% 0.68/0.72 (((~![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_1, e_3)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~greater(e_3, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, 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_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_3)) | (~cycle(e_2, e_3))))),
% 0.68/0.72 inference(monotonicity,[status(thm)],[782])).
% 0.68/0.72 tff(784,plain,
% 0.68/0.72 (((~![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_1, e_3)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~greater(e_3, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, 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_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_3)) | (~cycle(e_2, e_3)))),
% 0.68/0.72 inference(transitivity,[status(thm)],[783, 781])).
% 0.68/0.72 tff(785,plain,
% 0.68/0.72 ((~![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_1, e_3)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~greater(e_3, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_3)))),
% 0.68/0.72 inference(quant_inst,[status(thm)],[])).
% 0.68/0.72 tff(786,plain,
% 0.68/0.72 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_3, e_4) | (~next(e_1, e_2)) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_3)) | (~cycle(e_2, e_3))),
% 0.68/0.72 inference(modus_ponens,[status(thm)],[785, 784])).
% 0.68/0.72 tff(787,plain,
% 0.68/0.72 ($false),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[786, 84, 268, 35, 265, 613, 780, 779])).
% 0.68/0.72 tff(788,plain,((~cycle(e_1, e_3)) | (~cycle(e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.68/0.72 tff(789,plain,
% 0.68/0.72 (~cycle(e_1, e_3)),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[788, 779])).
% 0.68/0.72 tff(790,plain,
% 0.68/0.72 (((~![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_1, e_2)) | (~next(e_3, e_4)) | (~cycle(e_1, e_1)) | (~cycle(e_2, 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_1, e_2)) | (~next(e_3, e_4)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_3)))),
% 0.68/0.72 inference(rewrite,[status(thm)],[])).
% 0.68/0.72 tff(791,plain,
% 0.68/0.72 (((~cycle(e_1, e_1)) | equalish(e_1, e_4) | (~next(e_3, e_4)) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_3))) <=> (equalish(e_1, e_4) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_3)))),
% 0.68/0.72 inference(rewrite,[status(thm)],[])).
% 0.68/0.72 tff(792,plain,
% 0.68/0.72 (((~![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_1, e_1)) | equalish(e_1, e_4) | (~next(e_3, e_4)) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, 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_1, e_2)) | (~next(e_3, e_4)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_3))))),
% 0.68/0.72 inference(monotonicity,[status(thm)],[791])).
% 0.68/0.72 tff(793,plain,
% 0.68/0.72 (((~![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_1, e_1)) | equalish(e_1, e_4) | (~next(e_3, e_4)) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, 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_1, e_2)) | (~next(e_3, e_4)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_3)))),
% 0.68/0.72 inference(transitivity,[status(thm)],[792, 790])).
% 0.68/0.72 tff(794,plain,
% 0.68/0.72 ((~![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_1, e_1)) | equalish(e_1, e_4) | (~next(e_3, e_4)) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_3)))),
% 0.68/0.72 inference(quant_inst,[status(thm)],[])).
% 0.68/0.72 tff(795,plain,
% 0.68/0.72 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_1, e_4) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_3, e_4)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_3))),
% 0.68/0.72 inference(modus_ponens,[status(thm)],[794, 793])).
% 0.68/0.72 tff(796,plain,
% 0.68/0.72 ($false),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[795, 84, 268, 81, 265, 537, 65, 779])).
% 0.68/0.72 tff(797,plain,((~cycle(e_1, e_1)) | (~cycle(e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.68/0.72 tff(798,plain,
% 0.68/0.72 (~cycle(e_1, e_1)),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[797, 779])).
% 0.68/0.72 tff(799,assumption,(cycle(e_1, e_2)), introduced(assumption)).
% 0.68/0.72 tff(800,plain,
% 0.68/0.72 ((~equalish(e_2, e_4)) <=> (~equalish(e_2, e_4))),
% 0.68/0.72 inference(rewrite,[status(thm)],[])).
% 0.68/0.72 tff(801,axiom,(~equalish(e_2, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_2_is_not_e_4')).
% 0.68/0.72 tff(802,plain,
% 0.68/0.72 (~equalish(e_2, e_4)),
% 0.68/0.72 inference(modus_ponens,[status(thm)],[801, 800])).
% 0.68/0.72 tff(803,plain,
% 0.68/0.72 (((~![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) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_2)) | (~cycle(e_2, 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) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_2)) | (~cycle(e_2, e_3)))),
% 0.68/0.72 inference(rewrite,[status(thm)],[])).
% 0.68/0.72 tff(804,plain,
% 0.68/0.72 (((~cycle(e_1, e_2)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~greater(e_2, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_3))) <=> (equalish(e_2, e_4) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_2)) | (~cycle(e_2, e_3)))),
% 0.68/0.72 inference(rewrite,[status(thm)],[])).
% 0.68/0.72 tff(805,plain,
% 0.68/0.72 (((~![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_1, e_2)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~greater(e_2, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, 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) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_2)) | (~cycle(e_2, e_3))))),
% 0.68/0.72 inference(monotonicity,[status(thm)],[804])).
% 0.68/0.72 tff(806,plain,
% 0.68/0.72 (((~![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_1, e_2)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~greater(e_2, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, 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) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_2)) | (~cycle(e_2, e_3)))),
% 0.68/0.72 inference(transitivity,[status(thm)],[805, 803])).
% 0.68/0.72 tff(807,plain,
% 0.68/0.72 ((~![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_1, e_2)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~greater(e_2, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_3)))),
% 0.68/0.72 inference(quant_inst,[status(thm)],[])).
% 0.68/0.72 tff(808,plain,
% 0.68/0.72 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_4) | (~next(e_1, e_2)) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_1, e_2)) | (~cycle(e_2, e_3))),
% 0.68/0.72 inference(modus_ponens,[status(thm)],[807, 806])).
% 0.68/0.72 tff(809,plain,
% 0.68/0.72 ($false),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[808, 84, 268, 114, 265, 802, 799, 779])).
% 0.68/0.72 tff(810,plain,((~cycle(e_1, e_2)) | (~cycle(e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.68/0.72 tff(811,plain,
% 0.68/0.72 (~cycle(e_1, e_2)),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[810, 779])).
% 0.68/0.72 tff(812,plain,
% 0.68/0.72 ((~equalish(e_1, e_3)) <=> (~equalish(e_1, e_3))),
% 0.68/0.72 inference(rewrite,[status(thm)],[])).
% 0.68/0.72 tff(813,axiom,(~equalish(e_1, e_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_1_is_not_e_3')).
% 0.68/0.72 tff(814,plain,
% 0.68/0.72 (~equalish(e_1, e_3)),
% 0.68/0.72 inference(modus_ponens,[status(thm)],[813, 812])).
% 0.68/0.72 tff(815,plain,
% 0.68/0.72 (((~![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) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(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) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_1)))),
% 0.68/0.72 inference(rewrite,[status(thm)],[])).
% 0.68/0.72 tff(816,plain,
% 0.68/0.72 (((~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | equalish(e_1, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_1))) <=> (equalish(e_1, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_1)))),
% 0.68/0.73 inference(rewrite,[status(thm)],[])).
% 0.68/0.73 tff(817,plain,
% 0.68/0.73 (((~![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_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) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_1))))),
% 0.68/0.73 inference(monotonicity,[status(thm)],[816])).
% 0.68/0.73 tff(818,plain,
% 0.68/0.73 (((~![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_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) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_1)))),
% 0.68/0.73 inference(transitivity,[status(thm)],[817, 815])).
% 0.68/0.73 tff(819,plain,
% 0.68/0.73 ((~![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_1, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_1)))),
% 0.68/0.73 inference(quant_inst,[status(thm)],[])).
% 0.68/0.73 tff(820,plain,
% 0.68/0.73 ((~![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) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_1))),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[819, 818])).
% 0.68/0.73 tff(821,plain,
% 0.68/0.73 (~product(e_2, e_1, e_1)),
% 0.68/0.73 inference(unit_resolution,[status(thm)],[820, 711, 35, 78, 814, 779])).
% 0.68/0.73 tff(822,plain,
% 0.68/0.73 (((~![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_5, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_5)))) <=> ((~![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_5, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_5)))),
% 0.68/0.73 inference(rewrite,[status(thm)],[])).
% 0.68/0.73 tff(823,plain,
% 0.68/0.73 (((~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | equalish(e_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5))) <=> (equalish(e_5, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_5)))),
% 0.68/0.73 inference(rewrite,[status(thm)],[])).
% 0.68/0.73 tff(824,plain,
% 0.68/0.73 (((~![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_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))) <=> ((~![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_5, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_5))))),
% 0.68/0.73 inference(monotonicity,[status(thm)],[823])).
% 0.68/0.73 tff(825,plain,
% 0.68/0.73 (((~![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_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))) <=> ((~![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_5, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_5)))),
% 0.68/0.73 inference(transitivity,[status(thm)],[824, 822])).
% 0.68/0.73 tff(826,plain,
% 0.68/0.73 ((~![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_5, e_3) | (~next(e_2, e_3)) | (~product(e_2, e_1, e_5)))),
% 0.68/0.73 inference(quant_inst,[status(thm)],[])).
% 0.68/0.73 tff(827,plain,
% 0.68/0.73 ((~![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_5, e_3) | (~next(e_2, e_3)) | (~greater(e_3, e_0)) | (~cycle(e_2, e_3)) | (~product(e_2, e_1, e_5))),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[826, 825])).
% 0.68/0.73 tff(828,plain,
% 0.68/0.73 (~product(e_2, e_1, e_5)),
% 0.68/0.73 inference(unit_resolution,[status(thm)],[827, 711, 35, 78, 761, 779])).
% 0.68/0.73 tff(829,plain,
% 0.68/0.73 (((~![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)))),
% 0.68/0.73 inference(rewrite,[status(thm)],[])).
% 0.68/0.73 tff(830,plain,
% 0.68/0.73 (((~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)))),
% 0.68/0.73 inference(rewrite,[status(thm)],[])).
% 0.68/0.73 tff(831,plain,
% 0.68/0.73 (((~![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))))),
% 0.68/0.73 inference(monotonicity,[status(thm)],[830])).
% 0.68/0.73 tff(832,plain,
% 0.68/0.73 (((~![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)))),
% 0.68/0.73 inference(transitivity,[status(thm)],[831, 829])).
% 0.68/0.73 tff(833,plain,
% 0.68/0.73 ((~![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)))),
% 0.68/0.73 inference(quant_inst,[status(thm)],[])).
% 0.68/0.73 tff(834,plain,
% 0.68/0.73 ((~![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))),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[833, 832])).
% 0.68/0.73 tff(835,plain,
% 0.68/0.73 (~product(e_2, e_1, e_4)),
% 0.68/0.73 inference(unit_resolution,[status(thm)],[834, 711, 35, 78, 499, 779])).
% 0.68/0.73 tff(836,plain,
% 0.68/0.73 (product(e_2, e_1, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_5) | product(e_2, e_1, e_1)),
% 0.68/0.73 inference(unit_resolution,[status(thm)],[416, 96, 361, 189, 749])).
% 0.68/0.73 tff(837,plain,
% 0.68/0.73 (product(e_2, e_1, e_3)),
% 0.68/0.73 inference(unit_resolution,[status(thm)],[836, 835, 828, 821])).
% 0.68/0.73 tff(838,assumption,(product(e_5, e_1, e_3)), introduced(assumption)).
% 0.68/0.73 tff(839,plain,
% 0.68/0.73 ((~equalish(e_5, e_2)) <=> (~equalish(e_5, e_2))),
% 0.68/0.73 inference(rewrite,[status(thm)],[])).
% 0.68/0.73 tff(840,axiom,(~equalish(e_5, e_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_5_is_not_e_2')).
% 0.68/0.73 tff(841,plain,
% 0.68/0.73 (~equalish(e_5, e_2)),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[840, 839])).
% 0.68/0.73 tff(842,plain,
% 0.68/0.73 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_5, 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_5, e_2) | (~product(e_5, e_1, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.68/0.73 inference(rewrite,[status(thm)],[])).
% 0.68/0.73 tff(843,plain,
% 0.68/0.73 ((equalish(e_5, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_5, e_1, e_3))) <=> (equalish(e_5, e_2) | (~product(e_5, e_1, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.68/0.73 inference(rewrite,[status(thm)],[])).
% 0.68/0.73 tff(844,plain,
% 0.68/0.73 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_5, 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_5, e_2) | (~product(e_5, e_1, e_3)) | (~product(e_2, e_1, e_3))))),
% 0.68/0.73 inference(monotonicity,[status(thm)],[843])).
% 0.68/0.73 tff(845,plain,
% 0.68/0.73 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_5, 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_5, e_2) | (~product(e_5, e_1, e_3)) | (~product(e_2, e_1, e_3)))),
% 0.68/0.73 inference(transitivity,[status(thm)],[844, 842])).
% 0.68/0.73 tff(846,plain,
% 0.68/0.73 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_2) | (~product(e_2, e_1, e_3)) | (~product(e_5, e_1, e_3)))),
% 0.68/0.73 inference(quant_inst,[status(thm)],[])).
% 0.68/0.73 tff(847,plain,
% 0.68/0.73 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_2) | (~product(e_5, e_1, e_3)) | (~product(e_2, e_1, e_3))),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[846, 845])).
% 0.68/0.73 tff(848,plain,
% 0.68/0.73 ($false),
% 0.68/0.73 inference(unit_resolution,[status(thm)],[847, 841, 211, 838, 597])).
% 0.68/0.73 tff(849,plain,((~product(e_5, e_1, e_3)) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.68/0.73 tff(850,plain,
% 0.68/0.73 (~product(e_5, e_1, e_3)),
% 0.68/0.73 inference(unit_resolution,[status(thm)],[849, 837])).
% 0.68/0.73 tff(851,plain,
% 0.68/0.73 (~cycle(e_3, e_0)),
% 0.68/0.73 inference(unit_resolution,[status(thm)],[658, 779])).
% 0.68/0.73 tff(852,assumption,(~cycle(e_3, e_0)), introduced(assumption)).
% 0.68/0.73 tff(853,plain,
% 0.68/0.73 (~cycle(e_4, e_0)),
% 0.68/0.73 inference(unit_resolution,[status(thm)],[493, 420, 429, 446])).
% 0.68/0.73 tff(854,plain,
% 0.68/0.73 (cycle(e_4, e_1)),
% 0.68/0.73 inference(unit_resolution,[status(thm)],[321, 853])).
% 0.68/0.73 tff(855,plain,
% 0.68/0.73 (~cycle(e_3, e_1)),
% 0.68/0.73 inference(unit_resolution,[status(thm)],[645, 854])).
% 0.68/0.73 tff(856,plain,
% 0.68/0.73 (~cycle(e_3, e_4)),
% 0.68/0.73 inference(unit_resolution,[status(thm)],[631, 854])).
% 0.68/0.73 tff(857,plain,
% 0.68/0.73 ($false),
% 0.68/0.73 inference(unit_resolution,[status(thm)],[444, 856, 855, 429, 852, 420])).
% 0.68/0.73 tff(858,plain,(cycle(e_3, e_3) | cycle(e_3, e_2) | cycle(e_3, e_0) | product(e_3, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.73 tff(859,plain,
% 0.68/0.73 (cycle(e_3, e_2) | cycle(e_3, e_0) | product(e_3, e_1, e_3)),
% 0.68/0.73 inference(unit_resolution,[status(thm)],[858, 323])).
% 0.68/0.73 tff(860,plain,
% 0.68/0.73 (cycle(e_3, e_2)),
% 0.68/0.73 inference(unit_resolution,[status(thm)],[859, 851, 446])).
% 0.68/0.73 tff(861,plain,
% 0.68/0.73 (((~![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_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~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_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_1)))),
% 0.68/0.73 inference(rewrite,[status(thm)],[])).
% 0.68/0.73 tff(862,plain,
% 0.68/0.73 (((~greater(e_2, e_0)) | (~cycle(e_3, e_2)) | equalish(e_1, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_1))) <=> (equalish(e_1, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_1)))),
% 0.68/0.73 inference(rewrite,[status(thm)],[])).
% 0.68/0.73 tff(863,plain,
% 0.68/0.73 (((~![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_3, e_2)) | 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_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_1))))),
% 0.68/0.73 inference(monotonicity,[status(thm)],[862])).
% 0.68/0.73 tff(864,plain,
% 0.68/0.73 (((~![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_3, e_2)) | 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_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_1)))),
% 0.68/0.73 inference(transitivity,[status(thm)],[863, 861])).
% 0.68/0.73 tff(865,plain,
% 0.68/0.73 ((~![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_3, e_2)) | equalish(e_1, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_1)))),
% 0.68/0.73 inference(quant_inst,[status(thm)],[])).
% 0.68/0.73 tff(866,plain,
% 0.68/0.73 ((~![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_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_1))),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[865, 864])).
% 0.68/0.73 tff(867,plain,
% 0.68/0.73 (~product(e_3, e_1, e_1)),
% 0.68/0.73 inference(unit_resolution,[status(thm)],[866, 268, 114, 78, 537, 860])).
% 0.68/0.73 tff(868,plain,
% 0.68/0.73 ((~equalish(e_5, e_4)) <=> (~equalish(e_5, e_4))),
% 0.68/0.73 inference(rewrite,[status(thm)],[])).
% 0.68/0.73 tff(869,axiom,(~equalish(e_5, e_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_5_is_not_e_4')).
% 0.68/0.73 tff(870,plain,
% 0.68/0.73 (~equalish(e_5, e_4)),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[869, 868])).
% 0.68/0.73 tff(871,plain,
% 0.68/0.73 (((~![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_5, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_5)))) <=> ((~![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_5, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_5)))),
% 0.68/0.73 inference(rewrite,[status(thm)],[])).
% 0.68/0.73 tff(872,plain,
% 0.68/0.73 (((~greater(e_2, e_0)) | (~cycle(e_3, e_2)) | equalish(e_5, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5))) <=> (equalish(e_5, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_5)))),
% 0.68/0.73 inference(rewrite,[status(thm)],[])).
% 0.68/0.73 tff(873,plain,
% 0.68/0.73 (((~![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_3, e_2)) | equalish(e_5, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5)))) <=> ((~![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_5, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_5))))),
% 0.68/0.73 inference(monotonicity,[status(thm)],[872])).
% 0.68/0.73 tff(874,plain,
% 0.68/0.73 (((~![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_3, e_2)) | equalish(e_5, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5)))) <=> ((~![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_5, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_5)))),
% 0.68/0.74 inference(transitivity,[status(thm)],[873, 871])).
% 0.68/0.74 tff(875,plain,
% 0.68/0.74 ((~![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_3, e_2)) | equalish(e_5, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_5)))),
% 0.68/0.74 inference(quant_inst,[status(thm)],[])).
% 0.68/0.74 tff(876,plain,
% 0.68/0.74 ((~![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_5, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_5))),
% 0.68/0.74 inference(modus_ponens,[status(thm)],[875, 874])).
% 0.68/0.74 tff(877,plain,
% 0.68/0.74 (~product(e_3, e_1, e_5)),
% 0.68/0.74 inference(unit_resolution,[status(thm)],[876, 268, 114, 78, 870, 860])).
% 0.68/0.74 tff(878,assumption,(~cycle(e_3, e_1)), introduced(assumption)).
% 0.68/0.74 tff(879,assumption,(~product(e_3, e_1, e_5)), introduced(assumption)).
% 0.68/0.74 tff(880,assumption,(~product(e_3, e_1, e_4)), introduced(assumption)).
% 0.68/0.74 tff(881,plain,
% 0.68/0.74 (~product(e_3, e_1, e_3)),
% 0.68/0.74 inference(unit_resolution,[status(thm)],[619, 268, 114, 78, 613, 610])).
% 0.68/0.74 tff(882,plain,
% 0.68/0.74 (((~![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_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~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_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.68/0.74 inference(rewrite,[status(thm)],[])).
% 0.68/0.74 tff(883,plain,
% 0.68/0.74 (((~greater(e_2, e_0)) | (~cycle(e_3, e_2)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2))) <=> (equalish(e_2, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.68/0.74 inference(rewrite,[status(thm)],[])).
% 0.68/0.74 tff(884,plain,
% 0.68/0.74 (((~![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_3, e_2)) | 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_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_2))))),
% 0.68/0.74 inference(monotonicity,[status(thm)],[883])).
% 0.68/0.74 tff(885,plain,
% 0.68/0.74 (((~![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_3, e_2)) | 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_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_2)))),
% 0.68/0.74 inference(transitivity,[status(thm)],[884, 882])).
% 0.68/0.74 tff(886,plain,
% 0.68/0.74 ((~![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_3, e_2)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2)))),
% 0.68/0.74 inference(quant_inst,[status(thm)],[])).
% 0.68/0.74 tff(887,plain,
% 0.68/0.74 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_4) | (~greater(e_2, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_2)) | (~product(e_3, e_1, e_2))),
% 0.68/0.74 inference(modus_ponens,[status(thm)],[886, 885])).
% 0.68/0.74 tff(888,plain,
% 0.68/0.74 (~product(e_3, e_1, e_2)),
% 0.68/0.74 inference(unit_resolution,[status(thm)],[887, 268, 114, 78, 802, 610])).
% 0.68/0.74 tff(889,plain,
% 0.68/0.74 ($false),
% 0.68/0.74 inference(unit_resolution,[status(thm)],[481, 96, 440, 189, 880, 879, 888, 454, 881])).
% 0.68/0.74 tff(890,plain,((~cycle(e_3, e_2)) | product(e_3, e_1, e_4) | product(e_3, e_1, e_5) | product(e_3, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.74 tff(891,plain,
% 0.68/0.74 (~cycle(e_3, e_2)),
% 0.68/0.74 inference(unit_resolution,[status(thm)],[890, 880, 879, 454])).
% 0.68/0.74 tff(892,plain,
% 0.68/0.74 (((~![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) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(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) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | (~product(e_3, e_1, e_3)))),
% 0.68/0.74 inference(rewrite,[status(thm)],[])).
% 0.68/0.74 tff(893,plain,
% 0.68/0.74 (((~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_3))) <=> (equalish(e_3, e_4) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | (~product(e_3, e_1, e_3)))),
% 0.68/0.74 inference(rewrite,[status(thm)],[])).
% 0.68/0.74 tff(894,plain,
% 0.68/0.74 (((~![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_4, e_0)) | (~cycle(e_3, e_4)) | 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) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | (~product(e_3, e_1, e_3))))),
% 0.68/0.74 inference(monotonicity,[status(thm)],[893])).
% 0.68/0.74 tff(895,plain,
% 0.68/0.74 (((~![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_4, e_0)) | (~cycle(e_3, e_4)) | 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) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | (~product(e_3, e_1, e_3)))),
% 0.68/0.74 inference(transitivity,[status(thm)],[894, 892])).
% 0.68/0.74 tff(896,plain,
% 0.68/0.74 ((~![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_4, e_0)) | (~cycle(e_3, e_4)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_3)))),
% 0.68/0.74 inference(quant_inst,[status(thm)],[])).
% 0.68/0.74 tff(897,plain,
% 0.68/0.74 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | (~product(e_3, e_1, e_3))),
% 0.68/0.74 inference(modus_ponens,[status(thm)],[896, 895])).
% 0.68/0.74 tff(898,plain,
% 0.68/0.74 ($false),
% 0.68/0.74 inference(unit_resolution,[status(thm)],[897, 268, 21, 78, 613, 623, 495])).
% 0.68/0.74 tff(899,plain,((~cycle(e_3, e_4)) | (~product(e_3, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.68/0.74 tff(900,plain,
% 0.68/0.74 (~cycle(e_3, e_4)),
% 0.68/0.74 inference(unit_resolution,[status(thm)],[899, 495])).
% 0.68/0.74 tff(901,plain,
% 0.68/0.74 (cycle(e_3, e_3)),
% 0.68/0.74 inference(unit_resolution,[status(thm)],[444, 900, 852, 878, 429])).
% 0.68/0.74 tff(902,plain,
% 0.68/0.74 (((~![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_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~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_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.68/0.74 inference(rewrite,[status(thm)],[])).
% 0.68/0.74 tff(903,plain,
% 0.68/0.74 (((~greater(e_3, e_0)) | (~cycle(e_3, e_3)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_3))) <=> (equalish(e_3, e_4) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.68/0.74 inference(rewrite,[status(thm)],[])).
% 0.68/0.74 tff(904,plain,
% 0.68/0.74 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_3, e_0)) | (~cycle(e_3, e_3)) | equalish(e_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_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~product(e_3, e_1, e_3))))),
% 0.68/0.74 inference(monotonicity,[status(thm)],[903])).
% 0.68/0.74 tff(905,plain,
% 0.68/0.74 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_3, e_0)) | (~cycle(e_3, e_3)) | equalish(e_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_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~product(e_3, e_1, e_3)))),
% 0.68/0.74 inference(transitivity,[status(thm)],[904, 902])).
% 0.68/0.74 tff(906,plain,
% 0.68/0.74 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_3, e_0)) | (~cycle(e_3, e_3)) | equalish(e_3, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_3)))),
% 0.68/0.74 inference(quant_inst,[status(thm)],[])).
% 0.68/0.74 tff(907,plain,
% 0.68/0.74 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_3, e_4) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~product(e_3, e_1, e_3))),
% 0.68/0.74 inference(modus_ponens,[status(thm)],[906, 905])).
% 0.68/0.74 tff(908,plain,
% 0.68/0.74 ($false),
% 0.68/0.74 inference(unit_resolution,[status(thm)],[907, 268, 35, 78, 613, 901, 495])).
% 0.68/0.74 tff(909,plain,((~product(e_3, e_1, e_3)) | cycle(e_3, e_0) | cycle(e_3, e_1) | cycle(e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.74 tff(910,plain,
% 0.68/0.74 (~product(e_3, e_1, e_3)),
% 0.68/0.74 inference(unit_resolution,[status(thm)],[909, 891, 878, 852])).
% 0.68/0.74 tff(911,plain,
% 0.68/0.74 (product(e_3, e_1, e_2) | product(e_3, e_1, e_3)),
% 0.68/0.74 inference(unit_resolution,[status(thm)],[481, 96, 440, 189, 880, 879, 454])).
% 0.68/0.74 tff(912,plain,
% 0.68/0.74 (product(e_3, e_1, e_2)),
% 0.68/0.74 inference(unit_resolution,[status(thm)],[911, 910])).
% 0.68/0.74 tff(913,plain,
% 0.68/0.74 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_2, e_4) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~product(e_3, e_1, e_2)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_4) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.68/0.74 inference(rewrite,[status(thm)],[])).
% 0.68/0.74 tff(914,plain,
% 0.68/0.74 (((~greater(e_3, e_0)) | (~cycle(e_3, e_3)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2))) <=> (equalish(e_2, e_4) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.68/0.74 inference(rewrite,[status(thm)],[])).
% 0.68/0.74 tff(915,plain,
% 0.68/0.74 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_3, e_0)) | (~cycle(e_3, e_3)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | (equalish(e_2, e_4) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~product(e_3, e_1, e_2))))),
% 0.68/0.75 inference(monotonicity,[status(thm)],[914])).
% 0.68/0.75 tff(916,plain,
% 0.68/0.75 (((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_3, e_0)) | (~cycle(e_3, e_3)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2)))) <=> ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_4) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~product(e_3, e_1, e_2)))),
% 0.68/0.75 inference(transitivity,[status(thm)],[915, 913])).
% 0.68/0.75 tff(917,plain,
% 0.68/0.75 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | ((~greater(e_3, e_0)) | (~cycle(e_3, e_3)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2)))),
% 0.68/0.75 inference(quant_inst,[status(thm)],[])).
% 0.68/0.75 tff(918,plain,
% 0.68/0.75 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_4) | (~greater(e_3, e_0)) | (~next(e_3, e_4)) | (~cycle(e_3, e_3)) | (~product(e_3, e_1, e_2))),
% 0.68/0.75 inference(modus_ponens,[status(thm)],[917, 916])).
% 0.68/0.75 tff(919,plain,
% 0.68/0.75 ($false),
% 0.68/0.75 inference(unit_resolution,[status(thm)],[918, 268, 35, 78, 802, 243, 485])).
% 0.68/0.75 tff(920,plain,((~cycle(e_3, e_3)) | (~product(e_3, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.68/0.75 tff(921,plain,
% 0.68/0.75 (~cycle(e_3, e_3)),
% 0.68/0.75 inference(unit_resolution,[status(thm)],[920, 912])).
% 0.68/0.75 tff(922,plain,
% 0.68/0.75 (cycle(e_3, e_4)),
% 0.68/0.75 inference(unit_resolution,[status(thm)],[444, 921, 852, 878, 891])).
% 0.68/0.75 tff(923,plain,
% 0.68/0.75 (((~![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) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(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) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | (~product(e_3, e_1, e_2)))),
% 0.68/0.75 inference(rewrite,[status(thm)],[])).
% 0.68/0.75 tff(924,plain,
% 0.68/0.75 (((~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2))) <=> (equalish(e_2, e_4) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | (~product(e_3, e_1, e_2)))),
% 0.68/0.75 inference(rewrite,[status(thm)],[])).
% 0.68/0.75 tff(925,plain,
% 0.68/0.75 (((~![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_4, e_0)) | (~cycle(e_3, e_4)) | 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) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | (~product(e_3, e_1, e_2))))),
% 0.68/0.75 inference(monotonicity,[status(thm)],[924])).
% 0.68/0.75 tff(926,plain,
% 0.68/0.75 (((~![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_4, e_0)) | (~cycle(e_3, e_4)) | 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) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | (~product(e_3, e_1, e_2)))),
% 0.68/0.75 inference(transitivity,[status(thm)],[925, 923])).
% 0.68/0.75 tff(927,plain,
% 0.68/0.75 ((~![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_4, e_0)) | (~cycle(e_3, e_4)) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~product(e_3, e_1, e_2)))),
% 0.68/0.75 inference(quant_inst,[status(thm)],[])).
% 0.68/0.75 tff(928,plain,
% 0.68/0.75 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_2, e_4) | (~next(e_3, e_4)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_4)) | (~product(e_3, e_1, e_2))),
% 0.68/0.75 inference(modus_ponens,[status(thm)],[927, 926])).
% 0.68/0.75 tff(929,plain,
% 0.68/0.75 ($false),
% 0.68/0.75 inference(unit_resolution,[status(thm)],[928, 268, 21, 78, 802, 922, 912])).
% 0.68/0.75 tff(930,plain,(product(e_3, e_1, e_4) | cycle(e_3, e_0) | cycle(e_3, e_1) | product(e_3, e_1, e_5) | product(e_3, e_1, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.75 tff(931,plain,
% 0.68/0.75 (product(e_3, e_1, e_4) | cycle(e_3, e_0) | product(e_3, e_1, e_5) | product(e_3, e_1, e_1)),
% 0.68/0.75 inference(unit_resolution,[status(thm)],[930, 648])).
% 0.68/0.75 tff(932,plain,
% 0.68/0.75 (product(e_3, e_1, e_4)),
% 0.68/0.75 inference(unit_resolution,[status(thm)],[931, 877, 851, 867])).
% 0.68/0.75 tff(933,assumption,(product(e_3, e_1, e_4)), introduced(assumption)).
% 0.68/0.75 tff(934,assumption,(product(e_5, e_1, e_4)), introduced(assumption)).
% 0.68/0.75 tff(935,plain,
% 0.68/0.75 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_5, 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_5, e_3) | (~product(e_5, e_1, e_4)) | (~product(e_3, e_1, e_4)))),
% 0.68/0.75 inference(rewrite,[status(thm)],[])).
% 0.68/0.75 tff(936,plain,
% 0.68/0.75 ((equalish(e_5, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_5, e_1, e_4))) <=> (equalish(e_5, e_3) | (~product(e_5, e_1, e_4)) | (~product(e_3, e_1, e_4)))),
% 0.68/0.75 inference(rewrite,[status(thm)],[])).
% 0.68/0.75 tff(937,plain,
% 0.68/0.75 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_5, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_5, e_1, e_4)) | (~product(e_3, e_1, e_4))))),
% 0.68/0.75 inference(monotonicity,[status(thm)],[936])).
% 0.68/0.75 tff(938,plain,
% 0.68/0.75 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_5, e_1, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_3) | (~product(e_5, e_1, e_4)) | (~product(e_3, e_1, e_4)))),
% 0.68/0.75 inference(transitivity,[status(thm)],[937, 935])).
% 0.68/0.75 tff(939,plain,
% 0.68/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_1, e_4)) | (~product(e_5, e_1, e_4)))),
% 0.68/0.75 inference(quant_inst,[status(thm)],[])).
% 0.68/0.75 tff(940,plain,
% 0.68/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_3) | (~product(e_5, e_1, e_4)) | (~product(e_3, e_1, e_4))),
% 0.68/0.75 inference(modus_ponens,[status(thm)],[939, 938])).
% 0.68/0.75 tff(941,plain,
% 0.68/0.75 ($false),
% 0.68/0.75 inference(unit_resolution,[status(thm)],[940, 761, 211, 934, 933])).
% 0.68/0.75 tff(942,plain,((~product(e_5, e_1, e_4)) | (~product(e_3, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.68/0.75 tff(943,plain,
% 0.68/0.75 (~product(e_5, e_1, e_4)),
% 0.68/0.75 inference(unit_resolution,[status(thm)],[942, 932])).
% 0.68/0.75 tff(944,assumption,(~cycle(e_1, e_1)), introduced(assumption)).
% 0.68/0.75 tff(945,assumption,(~cycle(e_1, e_2)), introduced(assumption)).
% 0.68/0.75 tff(946,assumption,(~product(e_5, e_1, e_4)), introduced(assumption)).
% 0.68/0.75 tff(947,assumption,(~product(e_5, e_1, e_3)), introduced(assumption)).
% 0.68/0.75 tff(948,assumption,(~product(e_5, e_1, e_2)), introduced(assumption)).
% 0.68/0.75 tff(949,assumption,(product(e_4, e_1, e_5)), introduced(assumption)).
% 0.68/0.75 tff(950,assumption,(product(e_5, e_1, e_5)), introduced(assumption)).
% 0.68/0.75 tff(951,plain,
% 0.68/0.75 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_4) | (~product(e_5, e_1, e_5)) | (~product(e_4, e_1, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_4) | (~product(e_5, e_1, e_5)) | (~product(e_4, e_1, e_5)))),
% 0.68/0.75 inference(rewrite,[status(thm)],[])).
% 0.68/0.75 tff(952,plain,
% 0.68/0.75 ((equalish(e_5, e_4) | (~product(e_4, e_1, e_5)) | (~product(e_5, e_1, e_5))) <=> (equalish(e_5, e_4) | (~product(e_5, e_1, e_5)) | (~product(e_4, e_1, e_5)))),
% 0.68/0.75 inference(rewrite,[status(thm)],[])).
% 0.68/0.75 tff(953,plain,
% 0.68/0.75 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_4) | (~product(e_4, e_1, e_5)) | (~product(e_5, e_1, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_4) | (~product(e_5, e_1, e_5)) | (~product(e_4, e_1, e_5))))),
% 0.68/0.75 inference(monotonicity,[status(thm)],[952])).
% 0.68/0.75 tff(954,plain,
% 0.68/0.75 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_4) | (~product(e_4, e_1, e_5)) | (~product(e_5, e_1, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_4) | (~product(e_5, e_1, e_5)) | (~product(e_4, e_1, e_5)))),
% 0.68/0.75 inference(transitivity,[status(thm)],[953, 951])).
% 0.68/0.75 tff(955,plain,
% 0.68/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_4) | (~product(e_4, e_1, e_5)) | (~product(e_5, e_1, e_5)))),
% 0.68/0.75 inference(quant_inst,[status(thm)],[])).
% 0.68/0.75 tff(956,plain,
% 0.68/0.75 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_4) | (~product(e_5, e_1, e_5)) | (~product(e_4, e_1, e_5))),
% 0.68/0.75 inference(modus_ponens,[status(thm)],[955, 954])).
% 0.68/0.75 tff(957,plain,
% 0.68/0.75 ($false),
% 0.68/0.75 inference(unit_resolution,[status(thm)],[956, 870, 211, 950, 949])).
% 0.68/0.75 tff(958,plain,((~product(e_5, e_1, e_5)) | (~product(e_4, e_1, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.68/0.75 tff(959,plain,
% 0.68/0.75 (~product(e_5, e_1, e_5)),
% 0.68/0.75 inference(unit_resolution,[status(thm)],[958, 596])).
% 0.68/0.75 tff(960,plain,
% 0.68/0.75 (group_element(e_5) <=> group_element(e_5)),
% 0.68/0.75 inference(rewrite,[status(thm)],[])).
% 0.68/0.75 tff(961,axiom,(group_element(e_5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','element_5')).
% 0.68/0.75 tff(962,plain,
% 0.68/0.75 (group_element(e_5)),
% 0.68/0.75 inference(modus_ponens,[status(thm)],[961, 960])).
% 0.68/0.75 tff(963,plain,
% 0.68/0.75 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (product(e_5, e_1, e_1) | product(e_5, e_1, e_2) | product(e_5, e_1, e_3) | product(e_5, e_1, e_4) | product(e_5, e_1, e_5) | (~group_element(e_1)) | (~group_element(e_5)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | product(e_5, e_1, e_1) | product(e_5, e_1, e_2) | product(e_5, e_1, e_3) | product(e_5, e_1, e_4) | product(e_5, e_1, e_5) | (~group_element(e_1)) | (~group_element(e_5)))),
% 0.68/0.75 inference(rewrite,[status(thm)],[])).
% 0.68/0.75 tff(964,plain,
% 0.68/0.75 (((~group_element(e_5)) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | (~group_element(e_1))) <=> (product(e_5, e_1, e_1) | product(e_5, e_1, e_2) | product(e_5, e_1, e_3) | product(e_5, e_1, e_4) | product(e_5, e_1, e_5) | (~group_element(e_1)) | (~group_element(e_5)))),
% 0.68/0.75 inference(rewrite,[status(thm)],[])).
% 0.68/0.75 tff(965,plain,
% 0.68/0.75 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_5)) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (product(e_5, e_1, e_1) | product(e_5, e_1, e_2) | product(e_5, e_1, e_3) | product(e_5, e_1, e_4) | product(e_5, e_1, e_5) | (~group_element(e_1)) | (~group_element(e_5))))),
% 0.68/0.75 inference(monotonicity,[status(thm)],[964])).
% 0.68/0.75 tff(966,plain,
% 0.68/0.75 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_5)) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | (~group_element(e_1)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | product(e_5, e_1, e_1) | product(e_5, e_1, e_2) | product(e_5, e_1, e_3) | product(e_5, e_1, e_4) | product(e_5, e_1, e_5) | (~group_element(e_1)) | (~group_element(e_5)))),
% 0.68/0.75 inference(transitivity,[status(thm)],[965, 963])).
% 0.68/0.75 tff(967,plain,
% 0.68/0.75 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_5)) | product(e_5, e_1, e_5) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3) | product(e_5, e_1, e_2) | product(e_5, e_1, e_1) | (~group_element(e_1)))),
% 0.68/0.75 inference(quant_inst,[status(thm)],[])).
% 0.68/0.75 tff(968,plain,
% 0.68/0.75 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | product(e_5, e_1, e_1) | product(e_5, e_1, e_2) | product(e_5, e_1, e_3) | product(e_5, e_1, e_4) | product(e_5, e_1, e_5) | (~group_element(e_1)) | (~group_element(e_5))),
% 0.68/0.75 inference(modus_ponens,[status(thm)],[967, 966])).
% 0.68/0.75 tff(969,plain,
% 0.68/0.75 (product(e_5, e_1, e_1) | product(e_5, e_1, e_2) | product(e_5, e_1, e_3) | product(e_5, e_1, e_4)),
% 0.68/0.75 inference(unit_resolution,[status(thm)],[968, 96, 962, 189, 959])).
% 0.68/0.75 tff(970,plain,
% 0.68/0.75 (product(e_5, e_1, e_1)),
% 0.68/0.75 inference(unit_resolution,[status(thm)],[969, 948, 947, 946])).
% 0.68/0.75 tff(971,assumption,(product(e_5, e_1, e_1)), introduced(assumption)).
% 0.68/0.75 tff(972,plain,
% 0.68/0.75 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_5, e_1, e_1)) | product(e_5, e_1, e_4) | (~product(e_1, e_1, e_4)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_5, e_1, e_1)) | product(e_5, e_1, e_4) | (~product(e_1, e_1, e_4)))),
% 0.68/0.75 inference(rewrite,[status(thm)],[])).
% 0.68/0.75 tff(973,plain,
% 0.68/0.75 ((product(e_5, e_1, e_4) | (~product(e_1, e_1, e_4)) | (~product(e_5, e_1, e_1))) <=> ((~product(e_5, e_1, e_1)) | product(e_5, e_1, e_4) | (~product(e_1, e_1, e_4)))),
% 0.68/0.75 inference(rewrite,[status(thm)],[])).
% 0.68/0.75 tff(974,plain,
% 0.68/0.75 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_1, e_4) | (~product(e_1, e_1, e_4)) | (~product(e_5, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_5, e_1, e_1)) | product(e_5, e_1, e_4) | (~product(e_1, e_1, e_4))))),
% 0.68/0.75 inference(monotonicity,[status(thm)],[973])).
% 0.68/0.75 tff(975,plain,
% 0.68/0.75 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_1, e_4) | (~product(e_1, e_1, e_4)) | (~product(e_5, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_5, e_1, e_1)) | product(e_5, e_1, e_4) | (~product(e_1, e_1, e_4)))),
% 0.68/0.75 inference(transitivity,[status(thm)],[974, 972])).
% 0.68/0.75 tff(976,plain,
% 0.68/0.75 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_1, e_4) | (~product(e_1, e_1, e_4)) | (~product(e_5, e_1, e_1)))),
% 0.68/0.75 inference(quant_inst,[status(thm)],[])).
% 0.68/0.75 tff(977,plain,
% 0.68/0.75 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_5, e_1, e_1)) | product(e_5, e_1, e_4) | (~product(e_1, e_1, e_4))),
% 0.68/0.76 inference(modus_ponens,[status(thm)],[976, 975])).
% 0.68/0.76 tff(978,plain,
% 0.68/0.76 ($false),
% 0.68/0.76 inference(unit_resolution,[status(thm)],[977, 516, 971, 946, 44])).
% 0.68/0.76 tff(979,plain,((~product(e_1, e_1, e_4)) | (~product(e_5, e_1, e_1)) | product(e_5, e_1, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.76 tff(980,plain,
% 0.68/0.76 (~product(e_1, e_1, e_4)),
% 0.68/0.76 inference(unit_resolution,[status(thm)],[979, 970, 946])).
% 0.68/0.76 tff(981,plain,
% 0.68/0.76 (~cycle(e_1, e_0)),
% 0.68/0.76 inference(unit_resolution,[status(thm)],[198, 179, 144])).
% 0.68/0.76 tff(982,plain,
% 0.68/0.76 (cycle(e_1, e_4)),
% 0.68/0.76 inference(unit_resolution,[status(thm)],[110, 981, 945, 944, 63])).
% 0.68/0.76 tff(983,plain,
% 0.68/0.76 (((~![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_4, e_0)) | (~cycle(e_1, e_4)) | (~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_4, e_0)) | (~cycle(e_1, e_4)) | (~product(e_1, e_1, e_3)))),
% 0.68/0.76 inference(rewrite,[status(thm)],[])).
% 0.68/0.76 tff(984,plain,
% 0.68/0.76 (((~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | 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_4, e_0)) | (~cycle(e_1, e_4)) | (~product(e_1, e_1, e_3)))),
% 0.68/0.76 inference(rewrite,[status(thm)],[])).
% 0.68/0.76 tff(985,plain,
% 0.68/0.76 (((~![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_4, e_0)) | (~cycle(e_1, e_4)) | 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_4, e_0)) | (~cycle(e_1, e_4)) | (~product(e_1, e_1, e_3))))),
% 0.68/0.76 inference(monotonicity,[status(thm)],[984])).
% 0.68/0.76 tff(986,plain,
% 0.68/0.76 (((~![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_4, e_0)) | (~cycle(e_1, e_4)) | 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_4, e_0)) | (~cycle(e_1, e_4)) | (~product(e_1, e_1, e_3)))),
% 0.68/0.76 inference(transitivity,[status(thm)],[985, 983])).
% 0.68/0.76 tff(987,plain,
% 0.68/0.76 ((~![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_4, e_0)) | (~cycle(e_1, e_4)) | equalish(e_3, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_3)))),
% 0.68/0.76 inference(quant_inst,[status(thm)],[])).
% 0.68/0.76 tff(988,plain,
% 0.68/0.76 ((~![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_4, e_0)) | (~cycle(e_1, e_4)) | (~product(e_1, e_1, e_3))),
% 0.68/0.76 inference(modus_ponens,[status(thm)],[987, 986])).
% 0.68/0.76 tff(989,plain,
% 0.68/0.76 (~product(e_1, e_1, e_3)),
% 0.68/0.76 inference(unit_resolution,[status(thm)],[988, 84, 21, 78, 255, 982])).
% 0.68/0.76 tff(990,plain,
% 0.68/0.76 (((~![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_5, e_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | (~product(e_1, e_1, e_5)))) <=> ((~![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_5, e_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | (~product(e_1, e_1, e_5)))),
% 0.68/0.76 inference(rewrite,[status(thm)],[])).
% 0.68/0.76 tff(991,plain,
% 0.68/0.76 (((~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | equalish(e_5, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_5))) <=> (equalish(e_5, e_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | (~product(e_1, e_1, e_5)))),
% 0.68/0.76 inference(rewrite,[status(thm)],[])).
% 0.68/0.76 tff(992,plain,
% 0.68/0.76 (((~![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_4, e_0)) | (~cycle(e_1, e_4)) | equalish(e_5, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_5)))) <=> ((~![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_5, e_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | (~product(e_1, e_1, e_5))))),
% 0.68/0.76 inference(monotonicity,[status(thm)],[991])).
% 0.68/0.76 tff(993,plain,
% 0.68/0.76 (((~![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_4, e_0)) | (~cycle(e_1, e_4)) | equalish(e_5, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_5)))) <=> ((~![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_5, e_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | (~product(e_1, e_1, e_5)))),
% 0.68/0.76 inference(transitivity,[status(thm)],[992, 990])).
% 0.68/0.76 tff(994,plain,
% 0.68/0.76 ((~![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_4, e_0)) | (~cycle(e_1, e_4)) | equalish(e_5, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_5)))),
% 0.68/0.76 inference(quant_inst,[status(thm)],[])).
% 0.68/0.76 tff(995,plain,
% 0.68/0.76 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_5, e_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | (~product(e_1, e_1, e_5))),
% 0.68/0.76 inference(modus_ponens,[status(thm)],[994, 993])).
% 0.68/0.76 tff(996,plain,
% 0.68/0.76 (~product(e_1, e_1, e_5)),
% 0.68/0.76 inference(unit_resolution,[status(thm)],[995, 84, 21, 78, 841, 982])).
% 0.68/0.76 tff(997,assumption,(~product(e_1, e_1, e_2)), introduced(assumption)).
% 0.68/0.76 tff(998,plain,
% 0.68/0.76 (product(e_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_5)),
% 0.68/0.76 inference(unit_resolution,[status(thm)],[195, 96, 189, 997, 144])).
% 0.68/0.76 tff(999,plain,
% 0.68/0.76 ($false),
% 0.68/0.76 inference(unit_resolution,[status(thm)],[998, 996, 989, 179])).
% 0.68/0.76 tff(1000,plain,(product(e_1, e_1, e_4) | product(e_1, e_1, e_2) | product(e_1, e_1, e_1) | cycle(e_1, e_2) | cycle(e_1, e_1) | cycle(e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.76 tff(1001,plain,
% 0.68/0.76 (product(e_1, e_1, e_2)),
% 0.68/0.76 inference(unit_resolution,[status(thm)],[1000, 980, 144, 945, 944, 63])).
% 0.68/0.76 tff(1002,plain,
% 0.68/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_5, e_1, e_1)) | product(e_5, e_1, e_2) | (~product(e_1, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_5, e_1, e_1)) | product(e_5, e_1, e_2) | (~product(e_1, e_1, e_2)))),
% 0.68/0.76 inference(rewrite,[status(thm)],[])).
% 0.68/0.76 tff(1003,plain,
% 0.68/0.76 ((product(e_5, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_5, e_1, e_1))) <=> ((~product(e_5, e_1, e_1)) | product(e_5, e_1, e_2) | (~product(e_1, e_1, e_2)))),
% 0.68/0.76 inference(rewrite,[status(thm)],[])).
% 0.68/0.76 tff(1004,plain,
% 0.68/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_5, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_5, e_1, e_1)) | product(e_5, e_1, e_2) | (~product(e_1, e_1, e_2))))),
% 0.68/0.76 inference(monotonicity,[status(thm)],[1003])).
% 0.68/0.76 tff(1005,plain,
% 0.68/0.76 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_5, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_5, e_1, e_1)) | product(e_5, e_1, e_2) | (~product(e_1, e_1, e_2)))),
% 0.68/0.76 inference(transitivity,[status(thm)],[1004, 1002])).
% 0.68/0.76 tff(1006,plain,
% 0.68/0.76 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_5, e_1, e_1)))),
% 0.68/0.76 inference(quant_inst,[status(thm)],[])).
% 0.68/0.76 tff(1007,plain,
% 0.68/0.76 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_5, e_1, e_1)) | product(e_5, e_1, e_2) | (~product(e_1, e_1, e_2))),
% 0.68/0.76 inference(modus_ponens,[status(thm)],[1006, 1005])).
% 0.68/0.76 tff(1008,plain,
% 0.68/0.76 ($false),
% 0.68/0.76 inference(unit_resolution,[status(thm)],[1007, 516, 970, 948, 1001])).
% 0.68/0.76 tff(1009,plain,(product(e_5, e_1, e_2) | product(e_1, e_1, e_1) | cycle(e_1, e_2) | cycle(e_1, e_1) | cycle(e_1, e_3) | product(e_5, e_1, e_4) | product(e_5, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.76 tff(1010,plain,
% 0.68/0.76 (product(e_5, e_1, e_2)),
% 0.68/0.76 inference(unit_resolution,[status(thm)],[1009, 811, 144, 798, 789, 943, 850])).
% 0.68/0.76 tff(1011,assumption,(product(e_1, e_1, e_2)), introduced(assumption)).
% 0.68/0.76 tff(1012,assumption,(product(e_5, e_1, e_2)), introduced(assumption)).
% 0.68/0.76 tff(1013,plain,
% 0.68/0.76 ((~equalish(e_5, e_1)) <=> (~equalish(e_5, e_1))),
% 0.68/0.76 inference(rewrite,[status(thm)],[])).
% 0.68/0.76 tff(1014,axiom,(~equalish(e_5, e_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e_5_is_not_e_1')).
% 0.68/0.76 tff(1015,plain,
% 0.68/0.76 (~equalish(e_5, e_1)),
% 0.68/0.76 inference(modus_ponens,[status(thm)],[1014, 1013])).
% 0.68/0.76 tff(1016,plain,
% 0.68/0.76 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_5, e_1, e_2)) | (~product(e_1, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_1) | (~product(e_5, e_1, e_2)) | (~product(e_1, e_1, e_2)))),
% 0.68/0.76 inference(rewrite,[status(thm)],[])).
% 0.68/0.76 tff(1017,plain,
% 0.68/0.76 ((equalish(e_5, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_5, e_1, e_2))) <=> (equalish(e_5, e_1) | (~product(e_5, e_1, e_2)) | (~product(e_1, e_1, e_2)))),
% 0.68/0.76 inference(rewrite,[status(thm)],[])).
% 0.68/0.76 tff(1018,plain,
% 0.68/0.76 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_5, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_5, e_1, e_2)) | (~product(e_1, e_1, e_2))))),
% 0.68/0.76 inference(monotonicity,[status(thm)],[1017])).
% 0.68/0.76 tff(1019,plain,
% 0.68/0.76 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_5, e_1, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_1) | (~product(e_5, e_1, e_2)) | (~product(e_1, e_1, e_2)))),
% 0.68/0.76 inference(transitivity,[status(thm)],[1018, 1016])).
% 0.68/0.76 tff(1020,plain,
% 0.68/0.76 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_1, e_1, e_2)) | (~product(e_5, e_1, e_2)))),
% 0.68/0.76 inference(quant_inst,[status(thm)],[])).
% 0.68/0.76 tff(1021,plain,
% 0.68/0.76 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_1) | (~product(e_5, e_1, e_2)) | (~product(e_1, e_1, e_2))),
% 0.68/0.76 inference(modus_ponens,[status(thm)],[1020, 1019])).
% 0.68/0.76 tff(1022,plain,
% 0.68/0.76 ($false),
% 0.68/0.76 inference(unit_resolution,[status(thm)],[1021, 1015, 211, 1012, 1011])).
% 0.68/0.76 tff(1023,plain,((~product(e_5, e_1, e_2)) | (~product(e_1, e_1, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.68/0.76 tff(1024,plain,
% 0.68/0.76 (~product(e_1, e_1, e_2)),
% 0.68/0.76 inference(unit_resolution,[status(thm)],[1023, 1010])).
% 0.68/0.76 tff(1025,plain,
% 0.74/0.76 (product(e_1, e_1, e_4)),
% 0.74/0.76 inference(unit_resolution,[status(thm)],[1000, 1024, 144, 811, 798, 789])).
% 0.74/0.76 tff(1026,plain,
% 0.74/0.76 (cycle(e_1, e_4)),
% 0.74/0.76 inference(unit_resolution,[status(thm)],[122, 1025, 789])).
% 0.74/0.76 tff(1027,plain,
% 0.74/0.76 (((~![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_4, e_0)) | (~cycle(e_1, e_4)) | (~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_4, e_0)) | (~cycle(e_1, e_4)) | (~product(e_1, e_1, e_4)))),
% 0.74/0.76 inference(rewrite,[status(thm)],[])).
% 0.74/0.76 tff(1028,plain,
% 0.74/0.76 (((~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | 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_4, e_0)) | (~cycle(e_1, e_4)) | (~product(e_1, e_1, e_4)))),
% 0.74/0.76 inference(rewrite,[status(thm)],[])).
% 0.74/0.76 tff(1029,plain,
% 0.74/0.76 (((~![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_4, e_0)) | (~cycle(e_1, e_4)) | 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_4, e_0)) | (~cycle(e_1, e_4)) | (~product(e_1, e_1, e_4))))),
% 0.74/0.76 inference(monotonicity,[status(thm)],[1028])).
% 0.74/0.76 tff(1030,plain,
% 0.74/0.76 (((~![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_4, e_0)) | (~cycle(e_1, e_4)) | 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_4, e_0)) | (~cycle(e_1, e_4)) | (~product(e_1, e_1, e_4)))),
% 0.74/0.76 inference(transitivity,[status(thm)],[1029, 1027])).
% 0.74/0.76 tff(1031,plain,
% 0.74/0.76 ((~![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_4, e_0)) | (~cycle(e_1, e_4)) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_4)))),
% 0.74/0.76 inference(quant_inst,[status(thm)],[])).
% 0.74/0.76 tff(1032,plain,
% 0.74/0.76 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_4, e_2) | (~next(e_1, e_2)) | (~greater(e_4, e_0)) | (~cycle(e_1, e_4)) | (~product(e_1, e_1, e_4))),
% 0.74/0.76 inference(modus_ponens,[status(thm)],[1031, 1030])).
% 0.74/0.76 tff(1033,plain,
% 0.74/0.76 ($false),
% 0.74/0.76 inference(unit_resolution,[status(thm)],[1032, 84, 21, 78, 68, 1026, 1025])).
% 0.74/0.76 tff(1034,plain,((~cycle(e_2, e_3)) | product(e_1, e_1, e_1) | product(e_3, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.76 tff(1035,plain,
% 0.74/0.76 (~cycle(e_2, e_3)),
% 0.74/0.76 inference(unit_resolution,[status(thm)],[1034, 144, 446])).
% 0.74/0.76 tff(1036,plain,
% 0.74/0.76 (~cycle(e_3, e_0)),
% 0.74/0.76 inference(unit_resolution,[status(thm)],[667, 780])).
% 0.74/0.76 tff(1037,plain,
% 0.74/0.76 (cycle(e_3, e_2)),
% 0.74/0.76 inference(unit_resolution,[status(thm)],[859, 1036, 446])).
% 0.74/0.76 tff(1038,assumption,(cycle(e_2, e_2)), introduced(assumption)).
% 0.74/0.76 tff(1039,plain,
% 0.74/0.76 (((~![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_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~cycle(e_3, e_2)))) <=> ((~![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_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~cycle(e_3, e_2)))),
% 0.74/0.76 inference(rewrite,[status(thm)],[])).
% 0.74/0.76 tff(1040,plain,
% 0.74/0.76 (((~cycle(e_2, e_2)) | equalish(e_2, e_3) | (~next(e_2, e_3)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2))) <=> (equalish(e_2, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~cycle(e_3, e_2)))),
% 0.74/0.77 inference(rewrite,[status(thm)],[])).
% 0.74/0.77 tff(1041,plain,
% 0.74/0.77 (((~![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_3) | (~next(e_2, e_3)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2)))) <=> ((~![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_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~cycle(e_3, e_2))))),
% 0.74/0.77 inference(monotonicity,[status(thm)],[1040])).
% 0.74/0.77 tff(1042,plain,
% 0.74/0.77 (((~![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_3) | (~next(e_2, e_3)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2)))) <=> ((~![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_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~cycle(e_3, e_2)))),
% 0.74/0.77 inference(transitivity,[status(thm)],[1041, 1039])).
% 0.74/0.77 tff(1043,plain,
% 0.74/0.77 ((~![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_3) | (~next(e_2, e_3)) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2)))),
% 0.74/0.77 inference(quant_inst,[status(thm)],[])).
% 0.74/0.77 tff(1044,plain,
% 0.74/0.77 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_3) | (~greater(e_2, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_2)) | (~cycle(e_3, e_2))),
% 0.74/0.77 inference(modus_ponens,[status(thm)],[1043, 1042])).
% 0.74/0.77 tff(1045,plain,
% 0.74/0.77 ($false),
% 0.74/0.77 inference(unit_resolution,[status(thm)],[1044, 711, 114, 265, 600, 1038, 610])).
% 0.74/0.77 tff(1046,plain,((~cycle(e_2, e_2)) | (~cycle(e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.77 tff(1047,plain,
% 0.74/0.77 (~cycle(e_2, e_2)),
% 0.74/0.77 inference(unit_resolution,[status(thm)],[1046, 610])).
% 0.74/0.77 tff(1048,assumption,(~cycle(e_2, e_0)), introduced(assumption)).
% 0.74/0.77 tff(1049,assumption,(cycle(e_2, e_4)), introduced(assumption)).
% 0.74/0.77 tff(1050,plain,
% 0.74/0.77 (((~![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_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_2)) | (~cycle(e_2, e_4)))) <=> ((~![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_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_2)) | (~cycle(e_2, e_4)))),
% 0.74/0.77 inference(rewrite,[status(thm)],[])).
% 0.74/0.77 tff(1051,plain,
% 0.74/0.77 (((~cycle(e_2, e_4)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2))) <=> (equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_2)) | (~cycle(e_2, e_4)))),
% 0.74/0.77 inference(rewrite,[status(thm)],[])).
% 0.74/0.77 tff(1052,plain,
% 0.74/0.77 (((~![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_4)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2)))) <=> ((~![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_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_2)) | (~cycle(e_2, e_4))))),
% 0.74/0.77 inference(monotonicity,[status(thm)],[1051])).
% 0.74/0.77 tff(1053,plain,
% 0.74/0.77 (((~![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_4)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2)))) <=> ((~![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_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_2)) | (~cycle(e_2, e_4)))),
% 0.74/0.77 inference(transitivity,[status(thm)],[1052, 1050])).
% 0.74/0.77 tff(1054,plain,
% 0.74/0.77 ((~![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_4)) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2)))),
% 0.74/0.77 inference(quant_inst,[status(thm)],[])).
% 0.74/0.77 tff(1055,plain,
% 0.74/0.77 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_4, e_3) | (~next(e_2, e_3)) | (~greater(e_4, e_0)) | (~cycle(e_3, e_2)) | (~cycle(e_2, e_4))),
% 0.74/0.77 inference(modus_ponens,[status(thm)],[1054, 1053])).
% 0.74/0.77 tff(1056,plain,
% 0.74/0.77 ($false),
% 0.74/0.77 inference(unit_resolution,[status(thm)],[1055, 711, 21, 265, 499, 1049, 610])).
% 0.74/0.77 tff(1057,plain,((~cycle(e_2, e_4)) | (~cycle(e_3, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.77 tff(1058,plain,
% 0.74/0.77 (~cycle(e_2, e_4)),
% 0.74/0.77 inference(unit_resolution,[status(thm)],[1057, 610])).
% 0.74/0.77 tff(1059,plain,
% 0.74/0.77 (cycle(e_2, e_1)),
% 0.74/0.77 inference(unit_resolution,[status(thm)],[365, 1058, 1048, 697, 1047])).
% 0.74/0.77 tff(1060,plain,
% 0.74/0.77 (((~![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_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_2)))) <=> ((~![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_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_2)))),
% 0.74/0.77 inference(rewrite,[status(thm)],[])).
% 0.74/0.77 tff(1061,plain,
% 0.74/0.77 (((~cycle(e_2, e_1)) | equalish(e_1, e_3) | (~next(e_2, e_3)) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2))) <=> (equalish(e_1, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_2)))),
% 0.74/0.77 inference(rewrite,[status(thm)],[])).
% 0.74/0.77 tff(1062,plain,
% 0.74/0.77 (((~![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_3) | (~next(e_2, e_3)) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2)))) <=> ((~![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_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_2))))),
% 0.74/0.77 inference(monotonicity,[status(thm)],[1061])).
% 0.74/0.77 tff(1063,plain,
% 0.74/0.77 (((~![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_3) | (~next(e_2, e_3)) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2)))) <=> ((~![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_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_2)))),
% 0.74/0.77 inference(transitivity,[status(thm)],[1062, 1060])).
% 0.74/0.77 tff(1064,plain,
% 0.74/0.77 ((~![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_3) | (~next(e_2, e_3)) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2)))),
% 0.74/0.77 inference(quant_inst,[status(thm)],[])).
% 0.74/0.77 tff(1065,plain,
% 0.74/0.77 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_1, e_3) | (~greater(e_1, e_0)) | (~next(e_2, e_3)) | (~cycle(e_2, e_1)) | (~cycle(e_3, e_2))),
% 0.74/0.77 inference(modus_ponens,[status(thm)],[1064, 1063])).
% 0.74/0.77 tff(1066,plain,
% 0.74/0.77 ($false),
% 0.74/0.77 inference(unit_resolution,[status(thm)],[1065, 711, 81, 265, 814, 1059, 610])).
% 0.74/0.77 tff(1067,plain,((~cycle(e_3, e_2)) | cycle(e_2, e_0) | cycle(e_2, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.77 tff(1068,plain,
% 0.74/0.77 (cycle(e_2, e_0)),
% 0.74/0.77 inference(unit_resolution,[status(thm)],[1067, 1037, 697])).
% 0.74/0.77 tff(1069,plain,
% 0.74/0.77 (((~![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_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_3, e_2)) | (~cycle(e_1, 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_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_3, e_2)) | (~cycle(e_1, e_3)))),
% 0.74/0.77 inference(rewrite,[status(thm)],[])).
% 0.74/0.77 tff(1070,plain,
% 0.74/0.77 (((~greater(e_3, e_2)) | (~greater(e_2, e_1)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2)) | (~cycle(e_2, e_0)) | (~cycle(e_1, e_3))) <=> ((~cycle(e_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_3, e_2)) | (~cycle(e_1, e_3)))),
% 0.74/0.77 inference(rewrite,[status(thm)],[])).
% 0.74/0.77 tff(1071,plain,
% 0.74/0.77 (((~![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_2)) | (~greater(e_2, e_1)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2)) | (~cycle(e_2, e_0)) | (~cycle(e_1, 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_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_3, e_2)) | (~cycle(e_1, e_3))))),
% 0.74/0.77 inference(monotonicity,[status(thm)],[1070])).
% 0.74/0.77 tff(1072,plain,
% 0.74/0.77 (((~![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_2)) | (~greater(e_2, e_1)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2)) | (~cycle(e_2, e_0)) | (~cycle(e_1, 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_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_3, e_2)) | (~cycle(e_1, e_3)))),
% 0.74/0.77 inference(transitivity,[status(thm)],[1071, 1069])).
% 0.74/0.77 tff(1073,plain,
% 0.74/0.77 ((~![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_2)) | (~greater(e_2, e_1)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2)) | (~cycle(e_2, e_0)) | (~cycle(e_1, e_3)))),
% 0.74/0.77 inference(quant_inst,[status(thm)],[])).
% 0.74/0.77 tff(1074,plain,
% 0.74/0.77 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~greater(e_3, e_2)) | (~cycle(e_3, e_2)) | (~cycle(e_1, e_3))),
% 0.74/0.77 inference(modus_ponens,[status(thm)],[1073, 1072])).
% 0.74/0.77 tff(1075,plain,
% 0.74/0.77 ((~cycle(e_2, e_0)) | (~cycle(e_3, e_2)) | (~cycle(e_1, e_3))),
% 0.74/0.77 inference(unit_resolution,[status(thm)],[1074, 711, 159, 402, 12])).
% 0.74/0.77 tff(1076,plain,
% 0.74/0.77 ($false),
% 0.74/0.77 inference(unit_resolution,[status(thm)],[1075, 1068, 1037, 780])).
% 0.74/0.77 tff(1077,plain,((~cycle(e_1, e_3)) | cycle(e_2, e_3) | product(e_3, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.77 tff(1078,plain,
% 0.74/0.77 (~cycle(e_1, e_3)),
% 0.74/0.77 inference(unit_resolution,[status(thm)],[1077, 1035, 446])).
% 0.74/0.77 tff(1079,assumption,(cycle(e_1, e_4)), introduced(assumption)).
% 0.74/0.77 tff(1080,plain,
% 0.74/0.77 (~cycle(e_3, e_0)),
% 0.74/0.77 inference(unit_resolution,[status(thm)],[676, 1079])).
% 0.74/0.77 tff(1081,plain,
% 0.74/0.77 (cycle(e_3, e_2)),
% 0.74/0.77 inference(unit_resolution,[status(thm)],[859, 1080, 446])).
% 0.74/0.77 tff(1082,plain,
% 0.74/0.77 (cycle(e_2, e_0)),
% 0.74/0.77 inference(unit_resolution,[status(thm)],[1067, 1081, 697])).
% 0.74/0.77 tff(1083,plain,
% 0.74/0.77 (((~![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_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~greater(e_4, e_2)) | (~cycle(e_3, e_2)) | (~cycle(e_1, e_4)))) <=> ((~![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_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~greater(e_4, e_2)) | (~cycle(e_3, e_2)) | (~cycle(e_1, e_4)))),
% 0.74/0.77 inference(rewrite,[status(thm)],[])).
% 0.74/0.77 tff(1084,plain,
% 0.74/0.77 (((~greater(e_4, e_2)) | (~greater(e_2, e_1)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2)) | (~cycle(e_2, e_0)) | (~cycle(e_1, e_4))) <=> ((~cycle(e_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~greater(e_4, e_2)) | (~cycle(e_3, e_2)) | (~cycle(e_1, e_4)))),
% 0.74/0.77 inference(rewrite,[status(thm)],[])).
% 0.74/0.77 tff(1085,plain,
% 0.74/0.77 (((~![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_4, e_2)) | (~greater(e_2, e_1)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2)) | (~cycle(e_2, e_0)) | (~cycle(e_1, e_4)))) <=> ((~![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_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~greater(e_4, e_2)) | (~cycle(e_3, e_2)) | (~cycle(e_1, e_4))))),
% 0.74/0.77 inference(monotonicity,[status(thm)],[1084])).
% 0.74/0.77 tff(1086,plain,
% 0.74/0.77 (((~![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_4, e_2)) | (~greater(e_2, e_1)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2)) | (~cycle(e_2, e_0)) | (~cycle(e_1, e_4)))) <=> ((~![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_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~greater(e_4, e_2)) | (~cycle(e_3, e_2)) | (~cycle(e_1, e_4)))),
% 0.74/0.77 inference(transitivity,[status(thm)],[1085, 1083])).
% 0.74/0.77 tff(1087,plain,
% 0.74/0.77 ((~![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_4, e_2)) | (~greater(e_2, e_1)) | (~next(e_2, e_3)) | (~cycle(e_3, e_2)) | (~cycle(e_2, e_0)) | (~cycle(e_1, e_4)))),
% 0.74/0.77 inference(quant_inst,[status(thm)],[])).
% 0.74/0.77 tff(1088,plain,
% 0.74/0.77 ((~![W: $i, Y: $i, Z1: $i, X: $i, Z2: $i] : ((~greater(Z1, Z2)) | (~greater(Y, X)) | (~next(Y, W)) | (~cycle(W, Z2)) | (~cycle(Y, e_0)) | (~cycle(X, Z1)))) | (~cycle(e_2, e_0)) | (~next(e_2, e_3)) | (~greater(e_2, e_1)) | (~greater(e_4, e_2)) | (~cycle(e_3, e_2)) | (~cycle(e_1, e_4))),
% 0.74/0.77 inference(modus_ponens,[status(thm)],[1087, 1086])).
% 0.74/0.77 tff(1089,plain,
% 0.74/0.77 ((~cycle(e_2, e_0)) | (~cycle(e_3, e_2)) | (~cycle(e_1, e_4))),
% 0.74/0.77 inference(unit_resolution,[status(thm)],[1088, 711, 159, 326, 12])).
% 0.74/0.77 tff(1090,plain,
% 0.74/0.77 ($false),
% 0.74/0.77 inference(unit_resolution,[status(thm)],[1089, 1082, 1081, 1079])).
% 0.74/0.77 tff(1091,plain,((~cycle(e_1, e_4)) | cycle(e_2, e_3) | product(e_3, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.77 tff(1092,plain,
% 0.74/0.77 (~cycle(e_1, e_4)),
% 0.74/0.77 inference(unit_resolution,[status(thm)],[1091, 1035, 446])).
% 0.74/0.77 tff(1093,plain,
% 0.74/0.77 (~cycle(e_3, e_0)),
% 0.74/0.77 inference(unit_resolution,[status(thm)],[686, 799])).
% 0.74/0.78 tff(1094,plain,
% 0.74/0.78 (cycle(e_3, e_2)),
% 0.74/0.78 inference(unit_resolution,[status(thm)],[859, 1093, 446])).
% 0.74/0.78 tff(1095,plain,
% 0.74/0.78 (cycle(e_2, e_0)),
% 0.74/0.78 inference(unit_resolution,[status(thm)],[1067, 1094, 697])).
% 0.74/0.78 tff(1096,plain,
% 0.74/0.78 (((~![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) | (~next(e_1, e_2)) | (~cycle(e_2, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_1, 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) | (~next(e_1, e_2)) | (~cycle(e_2, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~next(e_0, e_1)))),
% 0.74/0.78 inference(rewrite,[status(thm)],[])).
% 0.74/0.78 tff(1097,plain,
% 0.74/0.78 (((~cycle(e_1, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_0))) <=> (equalish(e_2, e_1) | (~next(e_1, e_2)) | (~cycle(e_2, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~next(e_0, e_1)))),
% 0.74/0.78 inference(rewrite,[status(thm)],[])).
% 0.74/0.78 tff(1098,plain,
% 0.74/0.78 (((~![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_1, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, 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) | (~next(e_1, e_2)) | (~cycle(e_2, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~next(e_0, e_1))))),
% 0.74/0.78 inference(monotonicity,[status(thm)],[1097])).
% 0.74/0.78 tff(1099,plain,
% 0.74/0.78 (((~![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_1, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, 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) | (~next(e_1, e_2)) | (~cycle(e_2, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~next(e_0, e_1)))),
% 0.74/0.78 inference(transitivity,[status(thm)],[1098, 1096])).
% 0.74/0.78 tff(1100,plain,
% 0.74/0.78 ((~![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_1, e_2)) | equalish(e_2, e_1) | (~next(e_0, e_1)) | (~greater(e_2, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_0)))),
% 0.74/0.78 inference(quant_inst,[status(thm)],[])).
% 0.74/0.78 tff(1101,plain,
% 0.74/0.78 ((~![W: $i, Z: $i, Y: $i, Z1: $i, X: $i] : ((~cycle(X, Y)) | equalish(Y, Z1) | (~next(Z, Z1)) | (~greater(Y, e_0)) | (~next(X, W)) | (~cycle(W, Z)))) | equalish(e_2, e_1) | (~next(e_1, e_2)) | (~cycle(e_2, e_0)) | (~greater(e_2, e_0)) | (~cycle(e_1, e_2)) | (~next(e_0, e_1))),
% 0.74/0.78 inference(modus_ponens,[status(thm)],[1100, 1099])).
% 0.74/0.78 tff(1102,plain,
% 0.74/0.78 ($false),
% 0.74/0.78 inference(unit_resolution,[status(thm)],[1101, 284, 84, 114, 265, 296, 799, 1095])).
% 0.74/0.78 tff(1103,plain,((~cycle(e_1, e_2)) | cycle(e_2, e_3) | product(e_3, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.78 tff(1104,plain,
% 0.74/0.78 (~cycle(e_1, e_2)),
% 0.74/0.78 inference(unit_resolution,[status(thm)],[1103, 1035, 446])).
% 0.74/0.78 tff(1105,plain,
% 0.74/0.78 (~product(e_1, e_1, e_4)),
% 0.74/0.78 inference(unit_resolution,[status(thm)],[122, 1092, 1078])).
% 0.74/0.78 tff(1106,plain,
% 0.74/0.78 (~cycle(e_1, e_0)),
% 0.74/0.78 inference(unit_resolution,[status(thm)],[198, 1105, 144])).
% 0.74/0.78 tff(1107,plain,
% 0.74/0.78 (cycle(e_1, e_1)),
% 0.74/0.78 inference(unit_resolution,[status(thm)],[110, 1106, 1104, 1092, 1078])).
% 0.74/0.78 tff(1108,plain,
% 0.74/0.78 (((~![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_5) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_4, e_5)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_4)))) <=> ((~![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_5) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_4, e_5)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_4)))),
% 0.74/0.78 inference(rewrite,[status(thm)],[])).
% 0.74/0.78 tff(1109,plain,
% 0.74/0.78 (((~cycle(e_1, e_1)) | equalish(e_1, e_5) | (~next(e_4, e_5)) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_4))) <=> (equalish(e_1, e_5) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_4, e_5)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_4)))),
% 0.74/0.78 inference(rewrite,[status(thm)],[])).
% 0.74/0.78 tff(1110,plain,
% 0.74/0.78 (((~![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_1, e_1)) | equalish(e_1, e_5) | (~next(e_4, e_5)) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_4)))) <=> ((~![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_5) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_4, e_5)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_4))))),
% 0.74/0.78 inference(monotonicity,[status(thm)],[1109])).
% 0.74/0.78 tff(1111,plain,
% 0.74/0.78 (((~![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_1, e_1)) | equalish(e_1, e_5) | (~next(e_4, e_5)) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_4)))) <=> ((~![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_5) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_4, e_5)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_4)))),
% 0.74/0.78 inference(transitivity,[status(thm)],[1110, 1108])).
% 0.74/0.78 tff(1112,plain,
% 0.74/0.78 ((~![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_1, e_1)) | equalish(e_1, e_5) | (~next(e_4, e_5)) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_4)))),
% 0.74/0.78 inference(quant_inst,[status(thm)],[])).
% 0.74/0.78 tff(1113,plain,
% 0.74/0.78 ((~![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_5) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_4, e_5)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_4))),
% 0.74/0.78 inference(modus_ponens,[status(thm)],[1112, 1111])).
% 0.74/0.78 tff(1114,plain,
% 0.74/0.78 (~cycle(e_2, e_4)),
% 0.74/0.78 inference(unit_resolution,[status(thm)],[1113, 84, 24, 81, 265, 568, 1107])).
% 0.74/0.78 tff(1115,plain,
% 0.74/0.78 (~cycle(e_2, e_1)),
% 0.74/0.78 inference(unit_resolution,[status(thm)],[728, 1107])).
% 0.74/0.78 tff(1116,plain,
% 0.74/0.78 (((~![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_3) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_2)))) <=> ((~![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_3) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_2)))),
% 0.74/0.78 inference(rewrite,[status(thm)],[])).
% 0.74/0.78 tff(1117,plain,
% 0.74/0.78 (((~cycle(e_1, e_1)) | equalish(e_1, e_3) | (~next(e_2, e_3)) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_2))) <=> (equalish(e_1, e_3) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_2)))),
% 0.74/0.78 inference(rewrite,[status(thm)],[])).
% 0.74/0.78 tff(1118,plain,
% 0.74/0.78 (((~![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_1, e_1)) | equalish(e_1, e_3) | (~next(e_2, e_3)) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_2)))) <=> ((~![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_3) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_2))))),
% 0.74/0.78 inference(monotonicity,[status(thm)],[1117])).
% 0.74/0.78 tff(1119,plain,
% 0.74/0.78 (((~![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_1, e_1)) | equalish(e_1, e_3) | (~next(e_2, e_3)) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_2)))) <=> ((~![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_3) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_2)))),
% 0.74/0.78 inference(transitivity,[status(thm)],[1118, 1116])).
% 0.74/0.78 tff(1120,plain,
% 0.74/0.78 ((~![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_1, e_1)) | equalish(e_1, e_3) | (~next(e_2, e_3)) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_2, e_2)))),
% 0.74/0.78 inference(quant_inst,[status(thm)],[])).
% 0.74/0.78 tff(1121,plain,
% 0.74/0.78 ((~![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_3) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~next(e_2, e_3)) | (~cycle(e_1, e_1)) | (~cycle(e_2, e_2))),
% 0.74/0.78 inference(modus_ponens,[status(thm)],[1120, 1119])).
% 0.74/0.78 tff(1122,plain,
% 0.74/0.78 (~cycle(e_2, e_2)),
% 0.74/0.78 inference(unit_resolution,[status(thm)],[1121, 84, 711, 81, 265, 814, 1107])).
% 0.74/0.78 tff(1123,plain,
% 0.74/0.78 (cycle(e_1, e_1)),
% 0.74/0.78 inference(unit_resolution,[status(thm)],[1000, 997, 144, 945, 179, 63])).
% 0.74/0.78 tff(1124,plain,
% 0.74/0.78 (((~![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)))),
% 0.74/0.78 inference(rewrite,[status(thm)],[])).
% 0.74/0.78 tff(1125,plain,
% 0.74/0.78 (((~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)))),
% 0.74/0.78 inference(rewrite,[status(thm)],[])).
% 0.74/0.78 tff(1126,plain,
% 0.74/0.78 (((~![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))))),
% 0.74/0.78 inference(monotonicity,[status(thm)],[1125])).
% 0.74/0.78 tff(1127,plain,
% 0.74/0.78 (((~![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)))),
% 0.74/0.78 inference(transitivity,[status(thm)],[1126, 1124])).
% 0.74/0.78 tff(1128,plain,
% 0.74/0.78 ((~![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)))),
% 0.74/0.78 inference(quant_inst,[status(thm)],[])).
% 0.74/0.78 tff(1129,plain,
% 0.74/0.78 ((~![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))),
% 0.74/0.78 inference(modus_ponens,[status(thm)],[1128, 1127])).
% 0.74/0.78 tff(1130,plain,
% 0.74/0.78 (~product(e_1, e_1, e_3)),
% 0.74/0.78 inference(unit_resolution,[status(thm)],[1129, 84, 81, 78, 255, 1123])).
% 0.74/0.78 tff(1131,plain,
% 0.74/0.78 (((~![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_5, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_5)))) <=> ((~![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_5, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_5)))),
% 0.74/0.78 inference(rewrite,[status(thm)],[])).
% 0.74/0.78 tff(1132,plain,
% 0.74/0.78 (((~greater(e_1, e_0)) | (~cycle(e_1, e_1)) | equalish(e_5, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_5))) <=> (equalish(e_5, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_5)))),
% 0.74/0.78 inference(rewrite,[status(thm)],[])).
% 0.74/0.78 tff(1133,plain,
% 0.74/0.78 (((~![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_5, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_5)))) <=> ((~![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_5, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_5))))),
% 0.74/0.78 inference(monotonicity,[status(thm)],[1132])).
% 0.74/0.78 tff(1134,plain,
% 0.74/0.78 (((~![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_5, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_5)))) <=> ((~![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_5, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_5)))),
% 0.74/0.78 inference(transitivity,[status(thm)],[1133, 1131])).
% 0.74/0.78 tff(1135,plain,
% 0.74/0.78 ((~![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_5, e_2) | (~next(e_1, e_2)) | (~product(e_1, e_1, e_5)))),
% 0.74/0.78 inference(quant_inst,[status(thm)],[])).
% 0.74/0.78 tff(1136,plain,
% 0.74/0.78 ((~![Z: $i, Y: $i, X: $i, X1: $i] : ((~greater(Y, e_0)) | (~cycle(X, Y)) | equalish(Z, X1) | (~next(X, X1)) | (~product(X, e_1, Z)))) | equalish(e_5, e_2) | (~greater(e_1, e_0)) | (~next(e_1, e_2)) | (~cycle(e_1, e_1)) | (~product(e_1, e_1, e_5))),
% 0.74/0.78 inference(modus_ponens,[status(thm)],[1135, 1134])).
% 0.74/0.78 tff(1137,plain,
% 0.74/0.78 (~product(e_1, e_1, e_5)),
% 0.74/0.78 inference(unit_resolution,[status(thm)],[1136, 84, 81, 78, 841, 1123])).
% 0.74/0.78 tff(1138,plain,
% 0.74/0.78 (product(e_1, e_1, e_2) | product(e_1, e_1, e_3) | product(e_1, e_1, e_4) | product(e_1, e_1, e_5)),
% 0.74/0.78 inference(unit_resolution,[status(thm)],[195, 96, 189, 144])).
% 0.74/0.78 tff(1139,plain,
% 0.74/0.78 ($false),
% 0.74/0.78 inference(unit_resolution,[status(thm)],[1138, 1137, 1130, 179, 997])).
% 0.74/0.78 tff(1140,plain,(product(e_1, e_1, e_2) | product(e_1, e_1, e_4) | product(e_1, e_1, e_1) | cycle(e_1, e_2) | cycle(e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.78 tff(1141,plain,
% 0.74/0.78 (product(e_1, e_1, e_2)),
% 0.74/0.78 inference(unit_resolution,[status(thm)],[1140, 1105, 144, 1104, 1078])).
% 0.74/0.78 tff(1142,plain,
% 0.74/0.78 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_2)) | product(e_2, e_1, e_2) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_2) | (~product(e_2, e_1, e_1)))),
% 0.74/0.79 inference(rewrite,[status(thm)],[])).
% 0.74/0.79 tff(1143,plain,
% 0.74/0.79 ((product(e_2, e_1, 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_2) | (~product(e_2, e_1, e_1)))),
% 0.74/0.79 inference(rewrite,[status(thm)],[])).
% 0.74/0.79 tff(1144,plain,
% 0.74/0.79 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_1, e_1, e_2)) | product(e_2, e_1, e_2) | (~product(e_2, e_1, e_1))))),
% 0.74/0.79 inference(monotonicity,[status(thm)],[1143])).
% 0.74/0.79 tff(1145,plain,
% 0.74/0.79 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_2) | (~product(e_2, e_1, e_1)))),
% 0.74/0.79 inference(transitivity,[status(thm)],[1144, 1142])).
% 0.74/0.79 tff(1146,plain,
% 0.74/0.79 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_1, e_1, e_2)) | (~product(e_2, e_1, e_1)))),
% 0.74/0.79 inference(quant_inst,[status(thm)],[])).
% 0.74/0.79 tff(1147,plain,
% 0.74/0.79 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_1, e_1, e_2)) | product(e_2, e_1, e_2) | (~product(e_2, e_1, e_1))),
% 0.74/0.79 inference(modus_ponens,[status(thm)],[1146, 1145])).
% 0.74/0.79 tff(1148,plain,
% 0.74/0.79 (~product(e_2, e_1, e_1)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1147, 516, 1141, 749])).
% 0.74/0.79 tff(1149,plain,
% 0.74/0.79 ((~cycle(e_2, e_0)) | product(e_2, e_1, e_1)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[418, 749])).
% 0.74/0.79 tff(1150,plain,
% 0.74/0.79 (~cycle(e_2, e_0)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1149, 1148])).
% 0.74/0.79 tff(1151,plain,
% 0.74/0.79 ($false),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[365, 1150, 1122, 1035, 1115, 1114])).
% 0.74/0.79 tff(1152,plain,(product(e_1, e_1, e_1) | product(e_3, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.79 tff(1153,plain,
% 0.74/0.79 (product(e_1, e_1, e_1)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1152, 778])).
% 0.74/0.79 tff(1154,plain,
% 0.74/0.79 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_5, 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_5, e_1) | (~product(e_5, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.74/0.79 inference(rewrite,[status(thm)],[])).
% 0.74/0.79 tff(1155,plain,
% 0.74/0.79 ((equalish(e_5, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_5, e_1, e_1))) <=> (equalish(e_5, e_1) | (~product(e_5, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.74/0.79 inference(rewrite,[status(thm)],[])).
% 0.74/0.79 tff(1156,plain,
% 0.74/0.79 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_5, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_5, e_1, e_1)) | (~product(e_1, e_1, e_1))))),
% 0.74/0.79 inference(monotonicity,[status(thm)],[1155])).
% 0.74/0.79 tff(1157,plain,
% 0.74/0.79 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_5, e_1, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_1) | (~product(e_5, e_1, e_1)) | (~product(e_1, e_1, e_1)))),
% 0.74/0.79 inference(transitivity,[status(thm)],[1156, 1154])).
% 0.74/0.79 tff(1158,plain,
% 0.74/0.79 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_5, e_1, e_1)))),
% 0.74/0.79 inference(quant_inst,[status(thm)],[])).
% 0.74/0.79 tff(1159,plain,
% 0.74/0.79 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_1) | (~product(e_5, e_1, e_1)) | (~product(e_1, e_1, e_1))),
% 0.74/0.79 inference(modus_ponens,[status(thm)],[1158, 1157])).
% 0.74/0.79 tff(1160,plain,
% 0.74/0.79 ($false),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1159, 1015, 211, 971, 201])).
% 0.74/0.79 tff(1161,plain,((~product(e_5, e_1, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.79 tff(1162,plain,
% 0.74/0.79 (~product(e_5, e_1, e_1)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1161, 1153])).
% 0.74/0.79 tff(1163,plain,
% 0.74/0.79 (product(e_1, e_1, e_1)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1152, 446])).
% 0.74/0.79 tff(1164,plain,
% 0.74/0.79 (~product(e_2, e_1, e_1)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[376, 1163])).
% 0.74/0.79 tff(1165,plain,
% 0.74/0.79 (~cycle(e_2, e_0)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1149, 1164])).
% 0.74/0.79 tff(1166,plain,
% 0.74/0.79 (~cycle(e_3, e_2)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1067, 697, 1165])).
% 0.74/0.79 tff(1167,plain,
% 0.74/0.79 (cycle(e_3, e_0)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[649, 1166])).
% 0.74/0.79 tff(1168,plain,
% 0.74/0.79 (~cycle(e_2, e_4)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[705, 1167])).
% 0.74/0.79 tff(1169,plain,
% 0.74/0.79 (~cycle(e_2, e_2)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[695, 1167])).
% 0.74/0.79 tff(1170,plain,
% 0.74/0.79 (~product(e_3, e_1, e_1)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[452, 1163])).
% 0.74/0.79 tff(1171,plain,
% 0.74/0.79 (product(e_3, e_1, e_2)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[483, 1167, 446, 1170])).
% 0.74/0.79 tff(1172,plain,
% 0.74/0.79 (~product(e_2, e_1, e_2)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[491, 485])).
% 0.74/0.79 tff(1173,plain,
% 0.74/0.79 (~cycle(e_2, e_0)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[418, 1172, 379])).
% 0.74/0.79 tff(1174,plain,
% 0.74/0.79 (cycle(e_2, e_1)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[365, 1173, 697, 708, 707])).
% 0.74/0.79 tff(1175,plain,
% 0.74/0.79 (~product(e_2, e_1, e_4)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[757, 711, 81, 78, 499, 1174])).
% 0.74/0.79 tff(1176,plain,
% 0.74/0.79 (~product(e_2, e_1, e_5)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[767, 711, 81, 78, 761, 1174])).
% 0.74/0.79 tff(1177,assumption,(product(e_2, e_3, e_2)), introduced(assumption)).
% 0.74/0.79 tff(1178,plain,
% 0.74/0.79 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2)))),
% 0.74/0.79 inference(rewrite,[status(thm)],[])).
% 0.74/0.79 tff(1179,plain,
% 0.74/0.79 ((product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_3, e_2))) <=> (product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2)))),
% 0.74/0.79 inference(rewrite,[status(thm)],[])).
% 0.74/0.79 tff(1180,plain,
% 0.74/0.79 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2))))),
% 0.74/0.79 inference(monotonicity,[status(thm)],[1179])).
% 0.74/0.79 tff(1181,plain,
% 0.74/0.79 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_3, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2)))),
% 0.74/0.79 inference(transitivity,[status(thm)],[1180, 1178])).
% 0.74/0.79 tff(1182,plain,
% 0.74/0.79 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_3, e_2)))),
% 0.74/0.79 inference(quant_inst,[status(thm)],[])).
% 0.74/0.79 tff(1183,plain,
% 0.74/0.79 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2))),
% 0.74/0.79 inference(modus_ponens,[status(thm)],[1182, 1181])).
% 0.74/0.79 tff(1184,plain,
% 0.74/0.79 (product(e_2, e_2, e_2) | (~product(e_2, e_3, e_2))),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1183, 516])).
% 0.74/0.79 tff(1185,plain,
% 0.74/0.79 (product(e_2, e_2, e_2)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1184, 1177])).
% 0.74/0.79 tff(1186,plain,
% 0.74/0.79 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.74/0.79 inference(rewrite,[status(thm)],[])).
% 0.74/0.79 tff(1187,plain,
% 0.74/0.79 ((equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_3, e_2))) <=> (equalish(e_3, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.74/0.79 inference(rewrite,[status(thm)],[])).
% 0.74/0.79 tff(1188,plain,
% 0.74/0.79 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_2, e_2))))),
% 0.74/0.79 inference(monotonicity,[status(thm)],[1187])).
% 0.74/0.79 tff(1189,plain,
% 0.74/0.79 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_3, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.74/0.79 inference(transitivity,[status(thm)],[1188, 1186])).
% 0.74/0.79 tff(1190,plain,
% 0.74/0.79 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_3, e_2)))),
% 0.74/0.79 inference(quant_inst,[status(thm)],[])).
% 0.74/0.79 tff(1191,plain,
% 0.74/0.79 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_2, e_3, e_2)) | (~product(e_2, e_2, e_2))),
% 0.74/0.79 inference(modus_ponens,[status(thm)],[1190, 1189])).
% 0.74/0.79 tff(1192,plain,
% 0.74/0.79 ($false),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1191, 255, 534, 1185, 1177])).
% 0.74/0.79 tff(1193,plain,(~product(e_2, e_3, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.79 tff(1194,plain,
% 0.74/0.79 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_2, e_3, e_2) | (~product(e_3, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_2, e_3, e_2) | (~product(e_3, e_1, e_2)))),
% 0.74/0.79 inference(rewrite,[status(thm)],[])).
% 0.74/0.79 tff(1195,plain,
% 0.74/0.79 ((product(e_2, e_3, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_3))) <=> ((~product(e_2, e_1, e_3)) | product(e_2, e_3, e_2) | (~product(e_3, e_1, e_2)))),
% 0.74/0.79 inference(rewrite,[status(thm)],[])).
% 0.74/0.79 tff(1196,plain,
% 0.74/0.79 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | product(e_2, e_3, e_2) | (~product(e_3, e_1, e_2))))),
% 0.74/0.79 inference(monotonicity,[status(thm)],[1195])).
% 0.74/0.79 tff(1197,plain,
% 0.74/0.79 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_2, e_3, e_2) | (~product(e_3, e_1, e_2)))),
% 0.74/0.79 inference(transitivity,[status(thm)],[1196, 1194])).
% 0.74/0.79 tff(1198,plain,
% 0.74/0.79 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_2) | (~product(e_3, e_1, e_2)) | (~product(e_2, e_1, e_3)))),
% 0.74/0.79 inference(quant_inst,[status(thm)],[])).
% 0.74/0.79 tff(1199,plain,
% 0.74/0.79 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | product(e_2, e_3, e_2) | (~product(e_3, e_1, e_2))),
% 0.74/0.79 inference(modus_ponens,[status(thm)],[1198, 1197])).
% 0.74/0.79 tff(1200,plain,
% 0.74/0.79 ((~product(e_2, e_1, e_3)) | product(e_2, e_3, e_2) | (~product(e_3, e_1, e_2))),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1199, 516])).
% 0.74/0.79 tff(1201,plain,
% 0.74/0.79 (~product(e_2, e_1, e_3)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1200, 485, 1193])).
% 0.74/0.79 tff(1202,plain,
% 0.74/0.79 (product(e_2, e_1, e_4) | product(e_2, e_1, e_5)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[416, 96, 361, 189, 1201, 379, 1172])).
% 0.74/0.79 tff(1203,plain,
% 0.74/0.79 ($false),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1202, 1176, 1175])).
% 0.74/0.79 tff(1204,plain,((~product(e_3, e_1, e_2)) | product(e_2, e_1, e_1) | cycle(e_2, e_3) | cycle(e_2, e_2) | cycle(e_2, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.79 tff(1205,plain,
% 0.74/0.79 ($false),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1204, 1171, 1169, 697, 1164, 1168])).
% 0.74/0.79 tff(1206,plain,(cycle(e_2, e_3) | product(e_3, e_1, e_3)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.79 tff(1207,plain,
% 0.74/0.79 (cycle(e_2, e_3)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1206, 778])).
% 0.74/0.79 tff(1208,plain,
% 0.74/0.79 (~product(e_2, e_1, e_4)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[834, 711, 35, 78, 499, 1207])).
% 0.74/0.79 tff(1209,plain,
% 0.74/0.79 (~product(e_2, e_1, e_1)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[376, 1153])).
% 0.74/0.79 tff(1210,plain,
% 0.74/0.79 (~product(e_2, e_1, e_5)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[827, 711, 35, 78, 761, 1207])).
% 0.74/0.79 tff(1211,plain,
% 0.74/0.79 (product(e_2, e_1, e_3)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[836, 1210, 1209, 1208])).
% 0.74/0.79 tff(1212,plain,
% 0.74/0.79 (~product(e_5, e_1, e_3)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[849, 1211])).
% 0.74/0.79 tff(1213,plain,
% 0.74/0.79 (~product(e_3, e_1, e_1)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[452, 1153])).
% 0.74/0.79 tff(1214,plain,
% 0.74/0.79 (~cycle(e_3, e_0)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[658, 1207])).
% 0.74/0.79 tff(1215,plain,
% 0.74/0.79 (cycle(e_3, e_2)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[649, 1214])).
% 0.74/0.79 tff(1216,plain,
% 0.74/0.79 (~product(e_3, e_1, e_5)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[876, 268, 114, 78, 870, 1215])).
% 0.74/0.79 tff(1217,plain,
% 0.74/0.79 (product(e_3, e_1, e_4)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[931, 1216, 1214, 1213])).
% 0.74/0.79 tff(1218,plain,
% 0.74/0.79 (~product(e_5, e_1, e_4)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[942, 1217])).
% 0.74/0.79 tff(1219,plain,
% 0.74/0.79 (product(e_5, e_1, e_2)),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[969, 1218, 1212, 1162])).
% 0.74/0.79 tff(1220,plain,
% 0.74/0.79 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_5, e_1, e_2)) | (~product(e_4, e_1, e_5)) | product(e_4, e_5, e_2))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_5, e_1, e_2)) | (~product(e_4, e_1, e_5)) | product(e_4, e_5, e_2))),
% 0.74/0.79 inference(rewrite,[status(thm)],[])).
% 0.74/0.79 tff(1221,plain,
% 0.74/0.79 ((product(e_4, e_5, e_2) | (~product(e_5, e_1, e_2)) | (~product(e_4, e_1, e_5))) <=> ((~product(e_5, e_1, e_2)) | (~product(e_4, e_1, e_5)) | product(e_4, e_5, e_2))),
% 0.74/0.79 inference(rewrite,[status(thm)],[])).
% 0.74/0.79 tff(1222,plain,
% 0.74/0.79 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_5, e_2) | (~product(e_5, e_1, e_2)) | (~product(e_4, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_5, e_1, e_2)) | (~product(e_4, e_1, e_5)) | product(e_4, e_5, e_2)))),
% 0.74/0.80 inference(monotonicity,[status(thm)],[1221])).
% 0.74/0.80 tff(1223,plain,
% 0.74/0.80 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_5, e_2) | (~product(e_5, e_1, e_2)) | (~product(e_4, e_1, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_5, e_1, e_2)) | (~product(e_4, e_1, e_5)) | product(e_4, e_5, e_2))),
% 0.74/0.80 inference(transitivity,[status(thm)],[1222, 1220])).
% 0.74/0.80 tff(1224,plain,
% 0.74/0.80 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_5, e_2) | (~product(e_5, e_1, e_2)) | (~product(e_4, e_1, e_5)))),
% 0.74/0.80 inference(quant_inst,[status(thm)],[])).
% 0.74/0.80 tff(1225,plain,
% 0.74/0.80 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_5, e_1, e_2)) | (~product(e_4, e_1, e_5)) | product(e_4, e_5, e_2)),
% 0.74/0.80 inference(modus_ponens,[status(thm)],[1224, 1223])).
% 0.74/0.80 tff(1226,plain,
% 0.74/0.80 ($false),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1225, 516, 1219, 596, 1])).
% 0.74/0.80 tff(1227,plain,(product(e_4, e_5, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.80 tff(1228,assumption,(~product(e_4, e_2, e_5)), introduced(assumption)).
% 0.74/0.80 tff(1229,assumption,(product(e_4, e_2, e_1)), introduced(assumption)).
% 0.74/0.80 tff(1230,assumption,(product(e_1, e_2, e_4)), introduced(assumption)).
% 0.74/0.80 tff(1231,plain,
% 0.74/0.80 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_4, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_4, e_2, e_1)))),
% 0.74/0.80 inference(rewrite,[status(thm)],[])).
% 0.74/0.80 tff(1232,plain,
% 0.74/0.80 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_1, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_4, e_2, e_1)))),
% 0.74/0.80 inference(quant_inst,[status(thm)],[])).
% 0.74/0.80 tff(1233,plain,
% 0.74/0.80 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_1, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_4, e_2, e_1))),
% 0.74/0.80 inference(modus_ponens,[status(thm)],[1232, 1231])).
% 0.74/0.80 tff(1234,plain,
% 0.74/0.80 ($false),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1233, 516, 545, 1229, 1230])).
% 0.74/0.80 tff(1235,plain,((~product(e_1, e_2, e_4)) | (~product(e_4, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.80 tff(1236,plain,
% 0.74/0.80 (~product(e_1, e_2, e_4)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1235, 1229])).
% 0.74/0.80 tff(1237,assumption,(~product(e_5, e_2, e_3)), introduced(assumption)).
% 0.74/0.80 tff(1238,plain,
% 0.74/0.80 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_5, e_1, e_2)) | (~product(e_2, e_1, e_3)) | product(e_5, e_2, e_3))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_5, e_1, e_2)) | (~product(e_2, e_1, e_3)) | product(e_5, e_2, e_3))),
% 0.74/0.80 inference(rewrite,[status(thm)],[])).
% 0.74/0.80 tff(1239,plain,
% 0.74/0.80 ((product(e_5, e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_5, e_1, e_2))) <=> ((~product(e_5, e_1, e_2)) | (~product(e_2, e_1, e_3)) | product(e_5, e_2, e_3))),
% 0.74/0.80 inference(rewrite,[status(thm)],[])).
% 0.74/0.80 tff(1240,plain,
% 0.74/0.80 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_5, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_5, e_1, e_2)) | (~product(e_2, e_1, e_3)) | product(e_5, e_2, e_3)))),
% 0.74/0.80 inference(monotonicity,[status(thm)],[1239])).
% 0.74/0.80 tff(1241,plain,
% 0.74/0.80 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_5, e_1, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_5, e_1, e_2)) | (~product(e_2, e_1, e_3)) | product(e_5, e_2, e_3))),
% 0.74/0.80 inference(transitivity,[status(thm)],[1240, 1238])).
% 0.74/0.80 tff(1242,plain,
% 0.74/0.80 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_5, e_2, e_3) | (~product(e_2, e_1, e_3)) | (~product(e_5, e_1, e_2)))),
% 0.74/0.80 inference(quant_inst,[status(thm)],[])).
% 0.74/0.80 tff(1243,plain,
% 0.74/0.80 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_5, e_1, e_2)) | (~product(e_2, e_1, e_3)) | product(e_5, e_2, e_3)),
% 0.74/0.80 inference(modus_ponens,[status(thm)],[1242, 1241])).
% 0.74/0.80 tff(1244,plain,
% 0.74/0.80 ($false),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1243, 516, 1012, 597, 1237])).
% 0.74/0.80 tff(1245,plain,(product(e_5, e_2, e_3) | (~product(e_5, e_1, e_2)) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.80 tff(1246,plain,
% 0.74/0.80 (product(e_5, e_2, e_3)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1245, 1219, 1211])).
% 0.74/0.80 tff(1247,assumption,(product(e_1, e_2, e_3)), introduced(assumption)).
% 0.74/0.80 tff(1248,assumption,(product(e_5, e_2, e_3)), introduced(assumption)).
% 0.74/0.80 tff(1249,plain,
% 0.74/0.80 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_5) | (~product(e_5, e_2, e_3)) | (~product(e_1, 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_1, e_5) | (~product(e_5, e_2, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.74/0.80 inference(rewrite,[status(thm)],[])).
% 0.74/0.80 tff(1250,plain,
% 0.74/0.80 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_1, e_5) | (~product(e_5, e_2, e_3)) | (~product(e_1, e_2, e_3)))),
% 0.74/0.80 inference(quant_inst,[status(thm)],[])).
% 0.74/0.80 tff(1251,plain,
% 0.74/0.80 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_1, e_5) | (~product(e_5, e_2, e_3)) | (~product(e_1, e_2, e_3))),
% 0.74/0.80 inference(modus_ponens,[status(thm)],[1250, 1249])).
% 0.74/0.80 tff(1252,plain,
% 0.74/0.80 ($false),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1251, 568, 211, 1248, 1247])).
% 0.74/0.80 tff(1253,plain,((~product(e_1, e_2, e_3)) | (~product(e_5, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.80 tff(1254,plain,
% 0.74/0.80 (~product(e_1, e_2, e_3)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1253, 1246])).
% 0.74/0.80 tff(1255,plain,
% 0.74/0.80 (cycle(e_2, e_3)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1206, 446])).
% 0.74/0.80 tff(1256,plain,
% 0.74/0.80 (~product(e_2, e_1, e_4)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[834, 711, 35, 78, 499, 1255])).
% 0.74/0.80 tff(1257,plain,
% 0.74/0.80 (~product(e_2, e_1, e_5)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[827, 711, 35, 78, 761, 1255])).
% 0.74/0.80 tff(1258,plain,
% 0.74/0.80 (product(e_2, e_1, e_3)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[836, 1257, 1164, 1256])).
% 0.74/0.80 tff(1259,assumption,(product(e_2, e_5, e_3)), introduced(assumption)).
% 0.74/0.80 tff(1260,plain,
% 0.74/0.80 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_5, e_3)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_5, e_3)))),
% 0.74/0.80 inference(rewrite,[status(thm)],[])).
% 0.74/0.80 tff(1261,plain,
% 0.74/0.80 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_5, e_3)))),
% 0.74/0.80 inference(quant_inst,[status(thm)],[])).
% 0.74/0.80 tff(1262,plain,
% 0.74/0.80 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_5, e_3))),
% 0.74/0.80 inference(modus_ponens,[status(thm)],[1261, 1260])).
% 0.74/0.80 tff(1263,plain,
% 0.74/0.80 ($false),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1262, 1015, 534, 597, 1259])).
% 0.74/0.80 tff(1264,plain,((~product(e_2, e_5, e_3)) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.80 tff(1265,plain,
% 0.74/0.80 (~product(e_2, e_5, e_3)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1264, 1258])).
% 0.74/0.80 tff(1266,plain,
% 0.74/0.80 (~cycle(e_3, e_0)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[658, 1255])).
% 0.74/0.80 tff(1267,plain,
% 0.74/0.80 (cycle(e_3, e_2)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[859, 1266, 446])).
% 0.74/0.80 tff(1268,plain,
% 0.74/0.80 (~product(e_3, e_1, e_5)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[876, 268, 114, 78, 870, 1267])).
% 0.74/0.80 tff(1269,plain,
% 0.74/0.80 (product(e_3, e_1, e_4)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[931, 1268, 1266, 1170])).
% 0.74/0.80 tff(1270,assumption,(~product(e_2, e_3, e_4)), introduced(assumption)).
% 0.74/0.80 tff(1271,plain,
% 0.74/0.80 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_4)) | product(e_2, e_3, e_4))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_4)) | product(e_2, e_3, e_4))),
% 0.74/0.80 inference(rewrite,[status(thm)],[])).
% 0.74/0.80 tff(1272,plain,
% 0.74/0.80 ((product(e_2, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_2, e_1, e_3))) <=> ((~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_4)) | product(e_2, e_3, e_4))),
% 0.74/0.80 inference(rewrite,[status(thm)],[])).
% 0.74/0.80 tff(1273,plain,
% 0.74/0.80 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_4)) | product(e_2, e_3, e_4)))),
% 0.74/0.80 inference(monotonicity,[status(thm)],[1272])).
% 0.74/0.80 tff(1274,plain,
% 0.74/0.80 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_2, e_1, e_3)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_4)) | product(e_2, e_3, e_4))),
% 0.74/0.80 inference(transitivity,[status(thm)],[1273, 1271])).
% 0.74/0.80 tff(1275,plain,
% 0.74/0.80 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_3, e_4) | (~product(e_3, e_1, e_4)) | (~product(e_2, e_1, e_3)))),
% 0.74/0.80 inference(quant_inst,[status(thm)],[])).
% 0.74/0.80 tff(1276,plain,
% 0.74/0.80 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_4)) | product(e_2, e_3, e_4)),
% 0.74/0.80 inference(modus_ponens,[status(thm)],[1275, 1274])).
% 0.74/0.80 tff(1277,plain,
% 0.74/0.80 ($false),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1276, 516, 597, 933, 1270])).
% 0.74/0.80 tff(1278,plain,(product(e_2, e_3, e_4) | (~product(e_2, e_1, e_3)) | (~product(e_3, e_1, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.80 tff(1279,plain,
% 0.74/0.80 (product(e_2, e_3, e_4)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1278, 1258, 1269])).
% 0.74/0.80 tff(1280,assumption,(product(e_2, e_3, e_4)), introduced(assumption)).
% 0.74/0.80 tff(1281,assumption,(product(e_2, e_2, e_4)), introduced(assumption)).
% 0.74/0.80 tff(1282,plain,
% 0.74/0.80 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_2, e_2, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_2, e_2, e_4)))),
% 0.74/0.80 inference(rewrite,[status(thm)],[])).
% 0.74/0.80 tff(1283,plain,
% 0.74/0.80 ((equalish(e_3, e_2) | (~product(e_2, e_2, e_4)) | (~product(e_2, e_3, e_4))) <=> (equalish(e_3, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_2, e_2, e_4)))),
% 0.74/0.80 inference(rewrite,[status(thm)],[])).
% 0.74/0.80 tff(1284,plain,
% 0.74/0.80 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_4)) | (~product(e_2, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_2, e_2, e_4))))),
% 0.74/0.80 inference(monotonicity,[status(thm)],[1283])).
% 0.74/0.80 tff(1285,plain,
% 0.74/0.80 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_4)) | (~product(e_2, e_3, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_2, e_2, e_4)))),
% 0.74/0.80 inference(transitivity,[status(thm)],[1284, 1282])).
% 0.74/0.80 tff(1286,plain,
% 0.74/0.80 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_4)) | (~product(e_2, e_3, e_4)))),
% 0.74/0.80 inference(quant_inst,[status(thm)],[])).
% 0.74/0.80 tff(1287,plain,
% 0.74/0.80 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_3, e_2) | (~product(e_2, e_3, e_4)) | (~product(e_2, e_2, e_4))),
% 0.74/0.80 inference(modus_ponens,[status(thm)],[1286, 1285])).
% 0.74/0.80 tff(1288,plain,
% 0.74/0.80 ($false),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1287, 255, 534, 1281, 1280])).
% 0.74/0.80 tff(1289,plain,((~product(e_2, e_3, e_4)) | (~product(e_2, e_2, e_4))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.80 tff(1290,plain,
% 0.74/0.80 (~product(e_2, e_2, e_4)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1289, 1279])).
% 0.74/0.80 tff(1291,assumption,(product(e_2, e_2, e_3)), introduced(assumption)).
% 0.74/0.80 tff(1292,plain,
% 0.74/0.80 (((~![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)))),
% 0.74/0.80 inference(rewrite,[status(thm)],[])).
% 0.74/0.80 tff(1293,plain,
% 0.74/0.80 ((~![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)))),
% 0.74/0.80 inference(quant_inst,[status(thm)],[])).
% 0.74/0.80 tff(1294,plain,
% 0.74/0.80 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_2, e_1, e_3)) | (~product(e_2, e_2, e_3))),
% 0.74/0.80 inference(modus_ponens,[status(thm)],[1293, 1292])).
% 0.74/0.80 tff(1295,plain,
% 0.74/0.80 ($false),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1294, 296, 534, 597, 1291])).
% 0.74/0.80 tff(1296,plain,((~product(e_2, e_2, e_3)) | (~product(e_2, e_1, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.80 tff(1297,plain,
% 0.74/0.80 (~product(e_2, e_2, e_3)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1296, 1258])).
% 0.74/0.80 tff(1298,plain,
% 0.74/0.80 (~product(e_5, e_1, e_1)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1161, 1163])).
% 0.74/0.80 tff(1299,plain,
% 0.74/0.80 (~product(e_5, e_1, e_3)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[849, 1258])).
% 0.74/0.80 tff(1300,plain,
% 0.74/0.80 (~product(e_5, e_1, e_4)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[942, 1269])).
% 0.74/0.80 tff(1301,plain,
% 0.74/0.80 (product(e_5, e_1, e_2)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[969, 1300, 1299, 1298])).
% 0.74/0.80 tff(1302,plain,
% 0.74/0.80 (product(e_5, e_2, e_3)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1245, 1301, 1258])).
% 0.74/0.80 tff(1303,plain,
% 0.74/0.80 (~product(e_1, e_2, e_3)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1253, 1302])).
% 0.74/0.80 tff(1304,assumption,(product(e_1, e_2, e_1)), introduced(assumption)).
% 0.74/0.80 tff(1305,plain,
% 0.74/0.80 (((~![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_1, e_1, e_1)) | (~product(e_1, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.74/0.80 inference(rewrite,[status(thm)],[])).
% 0.74/0.80 tff(1306,plain,
% 0.74/0.80 ((~![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_1, e_1, e_1)) | (~product(e_1, e_2, e_1)))),
% 0.74/0.80 inference(quant_inst,[status(thm)],[])).
% 0.74/0.80 tff(1307,plain,
% 0.74/0.80 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_1, e_1, e_1)) | (~product(e_1, e_2, e_1))),
% 0.74/0.80 inference(modus_ponens,[status(thm)],[1306, 1305])).
% 0.74/0.80 tff(1308,plain,
% 0.74/0.80 ($false),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1307, 296, 534, 201, 1304])).
% 0.74/0.80 tff(1309,plain,((~product(e_1, e_2, e_1)) | (~product(e_1, e_1, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.80 tff(1310,plain,
% 0.74/0.80 (~product(e_1, e_2, e_1)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1309, 1163])).
% 0.74/0.80 tff(1311,assumption,(~product(e_2, e_1, e_5)), introduced(assumption)).
% 0.74/0.80 tff(1312,assumption,(product(e_2, e_2, e_1)), introduced(assumption)).
% 0.74/0.80 tff(1313,assumption,(product(e_1, e_2, e_5)), introduced(assumption)).
% 0.74/0.80 tff(1314,plain,
% 0.74/0.80 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_5) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_5)))),
% 0.74/0.80 inference(rewrite,[status(thm)],[])).
% 0.74/0.80 tff(1315,plain,
% 0.74/0.80 ((product(e_2, e_1, e_5) | (~product(e_1, e_2, e_5)) | (~product(e_2, e_2, e_1))) <=> (product(e_2, e_1, e_5) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_5)))),
% 0.74/0.80 inference(rewrite,[status(thm)],[])).
% 0.74/0.80 tff(1316,plain,
% 0.74/0.80 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_1, e_2, e_5)) | (~product(e_2, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_5))))),
% 0.74/0.80 inference(monotonicity,[status(thm)],[1315])).
% 0.74/0.80 tff(1317,plain,
% 0.74/0.80 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_1, e_2, e_5)) | (~product(e_2, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_5) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_5)))),
% 0.74/0.80 inference(transitivity,[status(thm)],[1316, 1314])).
% 0.74/0.80 tff(1318,plain,
% 0.74/0.80 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_5) | (~product(e_1, e_2, e_5)) | (~product(e_2, e_2, e_1)))),
% 0.74/0.80 inference(quant_inst,[status(thm)],[])).
% 0.74/0.80 tff(1319,plain,
% 0.74/0.80 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_5) | (~product(e_2, e_2, e_1)) | (~product(e_1, e_2, e_5))),
% 0.74/0.80 inference(modus_ponens,[status(thm)],[1318, 1317])).
% 0.74/0.80 tff(1320,plain,
% 0.74/0.80 ($false),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1319, 516, 1311, 1312, 1313])).
% 0.74/0.80 tff(1321,plain,((~product(e_1, e_2, e_5)) | product(e_2, e_1, e_5) | (~product(e_2, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.80 tff(1322,plain,
% 0.74/0.80 (~product(e_1, e_2, e_5)),
% 0.74/0.80 inference(unit_resolution,[status(thm)],[1321, 1312, 1311])).
% 0.74/0.80 tff(1323,assumption,(~product(e_1, e_2, e_3)), introduced(assumption)).
% 0.74/0.80 tff(1324,assumption,(~product(e_1, e_2, e_1)), introduced(assumption)).
% 0.74/0.80 tff(1325,assumption,(~product(e_2, e_1, e_4)), introduced(assumption)).
% 0.74/0.80 tff(1326,plain,
% 0.74/0.80 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_2, e_1)))),
% 0.74/0.81 inference(rewrite,[status(thm)],[])).
% 0.74/0.81 tff(1327,plain,
% 0.74/0.81 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_2, e_1)))),
% 0.74/0.81 inference(quant_inst,[status(thm)],[])).
% 0.74/0.81 tff(1328,plain,
% 0.74/0.81 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_4) | (~product(e_1, e_2, e_4)) | (~product(e_2, e_2, e_1))),
% 0.74/0.81 inference(modus_ponens,[status(thm)],[1327, 1326])).
% 0.74/0.81 tff(1329,plain,
% 0.74/0.81 ($false),
% 0.74/0.81 inference(unit_resolution,[status(thm)],[1328, 516, 1325, 1312, 1230])).
% 0.74/0.81 tff(1330,plain,((~product(e_1, e_2, e_4)) | product(e_2, e_1, e_4) | (~product(e_2, e_2, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.81 tff(1331,plain,
% 0.74/0.81 (~product(e_1, e_2, e_4)),
% 0.74/0.81 inference(unit_resolution,[status(thm)],[1330, 1312, 1325])).
% 0.74/0.81 tff(1332,plain,
% 0.74/0.81 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_3) | product(e_1, e_2, e_4) | product(e_1, e_2, e_2) | product(e_1, e_2, e_5))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_3) | product(e_1, e_2, e_4) | product(e_1, e_2, e_2) | product(e_1, e_2, e_5))),
% 0.74/0.81 inference(rewrite,[status(thm)],[])).
% 0.74/0.81 tff(1333,plain,
% 0.74/0.81 (((~group_element(e_1)) | product(e_1, e_2, e_5) | 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_3) | product(e_1, e_2, e_4) | product(e_1, e_2, e_2) | product(e_1, e_2, e_5))),
% 0.74/0.81 inference(rewrite,[status(thm)],[])).
% 0.74/0.81 tff(1334,plain,
% 0.74/0.81 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_2, e_5) | 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_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_3) | product(e_1, e_2, e_4) | product(e_1, e_2, e_2) | product(e_1, e_2, e_5)))),
% 0.74/0.81 inference(monotonicity,[status(thm)],[1333])).
% 0.74/0.81 tff(1335,plain,
% 0.74/0.81 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_2, e_5) | 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_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_3) | product(e_1, e_2, e_4) | product(e_1, e_2, e_2) | product(e_1, e_2, e_5))),
% 0.74/0.81 inference(transitivity,[status(thm)],[1334, 1332])).
% 0.74/0.81 tff(1336,plain,
% 0.74/0.81 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_1)) | product(e_1, e_2, e_5) | 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)))),
% 0.74/0.81 inference(quant_inst,[status(thm)],[])).
% 0.74/0.81 tff(1337,plain,
% 0.74/0.81 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_1)) | (~group_element(e_2)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_3) | product(e_1, e_2, e_4) | product(e_1, e_2, e_2) | product(e_1, e_2, e_5)),
% 0.74/0.81 inference(modus_ponens,[status(thm)],[1336, 1335])).
% 0.74/0.81 tff(1338,plain,
% 0.74/0.81 (product(e_1, e_2, e_1) | product(e_1, e_2, e_3) | product(e_1, e_2, e_4) | product(e_1, e_2, e_2) | product(e_1, e_2, e_5)),
% 0.74/0.81 inference(unit_resolution,[status(thm)],[1337, 96, 361, 189])).
% 0.74/0.81 tff(1339,plain,
% 0.74/0.81 (product(e_1, e_2, e_2)),
% 0.74/0.81 inference(unit_resolution,[status(thm)],[1338, 1331, 1324, 1323, 1322])).
% 0.74/0.81 tff(1340,plain,
% 0.74/0.81 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_1)))),
% 0.74/0.81 inference(rewrite,[status(thm)],[])).
% 0.74/0.81 tff(1341,plain,
% 0.74/0.81 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_1)))),
% 0.74/0.81 inference(quant_inst,[status(thm)],[])).
% 0.74/0.81 tff(1342,plain,
% 0.74/0.81 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_2, e_1, e_2) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_1))),
% 0.74/0.81 inference(modus_ponens,[status(thm)],[1341, 1340])).
% 0.74/0.81 tff(1343,plain,
% 0.74/0.81 ($false),
% 0.74/0.81 inference(unit_resolution,[status(thm)],[1342, 516, 749, 1312, 1339])).
% 0.74/0.81 tff(1344,plain,((~product(e_2, e_2, e_1)) | product(e_1, e_2, e_1) | product(e_1, e_2, e_3) | product(e_2, e_1, e_4) | product(e_2, e_1, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.81 tff(1345,plain,
% 0.74/0.81 (~product(e_2, e_2, e_1)),
% 0.74/0.81 inference(unit_resolution,[status(thm)],[1344, 1310, 1303, 1256, 1257])).
% 0.74/0.81 tff(1346,plain,
% 0.74/0.81 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_5) | product(e_2, e_2, e_4) | product(e_2, e_2, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_5) | product(e_2, e_2, e_4) | product(e_2, e_2, e_1))),
% 0.74/0.81 inference(rewrite,[status(thm)],[])).
% 0.74/0.81 tff(1347,plain,
% 0.74/0.81 (((~group_element(e_2)) | product(e_2, e_2, e_5) | product(e_2, e_2, e_4) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2))) <=> ((~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_5) | product(e_2, e_2, e_4) | product(e_2, e_2, e_1))),
% 0.74/0.81 inference(rewrite,[status(thm)],[])).
% 0.74/0.81 tff(1348,plain,
% 0.74/0.81 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_2, e_2, e_5) | product(e_2, e_2, e_4) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_5) | product(e_2, e_2, e_4) | product(e_2, e_2, e_1)))),
% 0.74/0.81 inference(monotonicity,[status(thm)],[1347])).
% 0.74/0.81 tff(1349,plain,
% 0.74/0.81 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_2, e_2, e_5) | product(e_2, e_2, e_4) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_5) | product(e_2, e_2, e_4) | product(e_2, e_2, e_1))),
% 0.74/0.81 inference(transitivity,[status(thm)],[1348, 1346])).
% 0.74/0.81 tff(1350,plain,
% 0.74/0.81 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_2, e_2, e_5) | product(e_2, e_2, e_4) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_1) | (~group_element(e_2)))),
% 0.74/0.81 inference(quant_inst,[status(thm)],[])).
% 0.74/0.81 tff(1351,plain,
% 0.74/0.81 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_2)) | product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_5) | product(e_2, e_2, e_4) | product(e_2, e_2, e_1)),
% 0.74/0.81 inference(modus_ponens,[status(thm)],[1350, 1349])).
% 0.74/0.81 tff(1352,plain,
% 0.74/0.81 (product(e_2, e_2, e_3) | product(e_2, e_2, e_2) | product(e_2, e_2, e_5) | product(e_2, e_2, e_4) | product(e_2, e_2, e_1)),
% 0.74/0.81 inference(unit_resolution,[status(thm)],[1351, 361, 189])).
% 0.74/0.81 tff(1353,plain,
% 0.74/0.81 (product(e_2, e_2, e_5)),
% 0.74/0.81 inference(unit_resolution,[status(thm)],[1352, 1345, 1297, 1290, 735])).
% 0.74/0.81 tff(1354,plain,
% 0.74/0.81 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_5, e_2, e_3)) | product(e_2, e_5, e_3) | (~product(e_2, e_2, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_5, e_2, e_3)) | product(e_2, e_5, e_3) | (~product(e_2, e_2, e_5)))),
% 0.74/0.81 inference(rewrite,[status(thm)],[])).
% 0.74/0.81 tff(1355,plain,
% 0.74/0.81 ((product(e_2, e_5, e_3) | (~product(e_5, e_2, e_3)) | (~product(e_2, e_2, e_5))) <=> ((~product(e_5, e_2, e_3)) | product(e_2, e_5, e_3) | (~product(e_2, e_2, e_5)))),
% 0.74/0.81 inference(rewrite,[status(thm)],[])).
% 0.74/0.81 tff(1356,plain,
% 0.74/0.81 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_5, e_3) | (~product(e_5, e_2, e_3)) | (~product(e_2, e_2, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | ((~product(e_5, e_2, e_3)) | product(e_2, e_5, e_3) | (~product(e_2, e_2, e_5))))),
% 0.74/0.81 inference(monotonicity,[status(thm)],[1355])).
% 0.74/0.81 tff(1357,plain,
% 0.74/0.81 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_5, e_3) | (~product(e_5, e_2, e_3)) | (~product(e_2, e_2, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_5, e_2, e_3)) | product(e_2, e_5, e_3) | (~product(e_2, e_2, e_5)))),
% 0.74/0.81 inference(transitivity,[status(thm)],[1356, 1354])).
% 0.74/0.81 tff(1358,plain,
% 0.74/0.81 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_2, e_5, e_3) | (~product(e_5, e_2, e_3)) | (~product(e_2, e_2, e_5)))),
% 0.74/0.81 inference(quant_inst,[status(thm)],[])).
% 0.74/0.81 tff(1359,plain,
% 0.74/0.81 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (~product(e_5, e_2, e_3)) | product(e_2, e_5, e_3) | (~product(e_2, e_2, e_5))),
% 0.74/0.81 inference(modus_ponens,[status(thm)],[1358, 1357])).
% 0.74/0.81 tff(1360,plain,
% 0.74/0.81 ($false),
% 0.74/0.81 inference(unit_resolution,[status(thm)],[1359, 516, 1302, 1353, 1265])).
% 0.74/0.81 tff(1361,plain,(product(e_3, e_1, e_3) | product(e_2, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.81 tff(1362,plain,
% 0.74/0.81 (product(e_2, e_2, e_2)),
% 0.74/0.81 inference(unit_resolution,[status(thm)],[1361, 778])).
% 0.74/0.81 tff(1363,assumption,(product(e_1, e_2, e_2)), introduced(assumption)).
% 0.74/0.81 tff(1364,assumption,(product(e_2, e_2, e_2)), introduced(assumption)).
% 0.74/0.81 tff(1365,plain,
% 0.74/0.81 (((~![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)))),
% 0.74/0.81 inference(rewrite,[status(thm)],[])).
% 0.74/0.81 tff(1366,plain,
% 0.74/0.81 ((~![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)))),
% 0.74/0.81 inference(quant_inst,[status(thm)],[])).
% 0.74/0.81 tff(1367,plain,
% 0.74/0.81 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_2, e_1) | (~product(e_1, e_2, e_2)) | (~product(e_2, e_2, e_2))),
% 0.74/0.81 inference(modus_ponens,[status(thm)],[1366, 1365])).
% 0.74/0.81 tff(1368,plain,
% 0.74/0.81 ($false),
% 0.74/0.81 inference(unit_resolution,[status(thm)],[1367, 296, 211, 1364, 1363])).
% 0.74/0.81 tff(1369,plain,((~product(e_2, e_2, e_2)) | (~product(e_1, e_2, e_2))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.81 tff(1370,plain,
% 0.74/0.81 (~product(e_1, e_2, e_2)),
% 0.74/0.81 inference(unit_resolution,[status(thm)],[1369, 1362])).
% 0.74/0.81 tff(1371,plain,
% 0.74/0.81 (~product(e_1, e_2, e_1)),
% 0.74/0.81 inference(unit_resolution,[status(thm)],[1309, 1153])).
% 0.74/0.81 tff(1372,plain,
% 0.74/0.81 (product(e_1, e_2, e_4) | product(e_1, e_2, e_5)),
% 0.74/0.81 inference(unit_resolution,[status(thm)],[1338, 1371, 1370, 1254])).
% 0.74/0.81 tff(1373,plain,
% 0.74/0.81 (product(e_1, e_2, e_5)),
% 0.74/0.81 inference(unit_resolution,[status(thm)],[1372, 1236])).
% 0.74/0.81 tff(1374,assumption,(product(e_3, e_2, e_5)), introduced(assumption)).
% 0.74/0.81 tff(1375,plain,
% 0.74/0.81 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_2, e_5)) | (~product(e_3, e_2, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_2, e_5)) | (~product(e_3, e_2, e_5)))),
% 0.74/0.81 inference(rewrite,[status(thm)],[])).
% 0.74/0.81 tff(1376,plain,
% 0.74/0.81 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_1) | (~product(e_1, e_2, e_5)) | (~product(e_3, e_2, e_5)))),
% 0.74/0.81 inference(quant_inst,[status(thm)],[])).
% 0.74/0.81 tff(1377,plain,
% 0.74/0.81 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_1) | (~product(e_1, e_2, e_5)) | (~product(e_3, e_2, e_5))),
% 0.74/0.81 inference(modus_ponens,[status(thm)],[1376, 1375])).
% 0.74/0.81 tff(1378,plain,
% 0.74/0.81 ($false),
% 0.74/0.81 inference(unit_resolution,[status(thm)],[1377, 281, 211, 1313, 1374])).
% 0.74/0.81 tff(1379,plain,((~product(e_3, e_2, e_5)) | (~product(e_1, e_2, e_5))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.81 tff(1380,plain,
% 0.74/0.81 (~product(e_3, e_2, e_5)),
% 0.74/0.81 inference(unit_resolution,[status(thm)],[1379, 1373])).
% 0.74/0.81 tff(1381,assumption,(product(e_3, e_2, e_2)), introduced(assumption)).
% 0.74/0.81 tff(1382,plain,
% 0.74/0.81 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.74/0.81 inference(rewrite,[status(thm)],[])).
% 0.74/0.81 tff(1383,plain,
% 0.74/0.81 ((equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2))) <=> (equalish(e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.74/0.81 inference(rewrite,[status(thm)],[])).
% 0.74/0.81 tff(1384,plain,
% 0.74/0.81 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2))))),
% 0.74/0.82 inference(monotonicity,[status(thm)],[1383])).
% 0.74/0.82 tff(1385,plain,
% 0.74/0.82 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.74/0.82 inference(transitivity,[status(thm)],[1384, 1382])).
% 0.74/0.82 tff(1386,plain,
% 0.74/0.82 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_3, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_3, e_2, e_2)))),
% 0.74/0.82 inference(quant_inst,[status(thm)],[])).
% 0.74/0.82 tff(1387,plain,
% 0.74/0.82 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_3, e_2) | (~product(e_3, e_2, e_2)) | (~product(e_2, e_2, e_2))),
% 0.74/0.82 inference(modus_ponens,[status(thm)],[1386, 1385])).
% 0.74/0.82 tff(1388,plain,
% 0.74/0.82 ($false),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1387, 255, 211, 1362, 1381])).
% 0.74/0.82 tff(1389,plain,(~product(e_3, e_2, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.82 tff(1390,assumption,(product(e_3, e_2, e_4)), introduced(assumption)).
% 0.74/0.82 tff(1391,plain,
% 0.74/0.82 (((~![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)))),
% 0.74/0.82 inference(rewrite,[status(thm)],[])).
% 0.74/0.82 tff(1392,plain,
% 0.74/0.82 ((~![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)))),
% 0.74/0.82 inference(quant_inst,[status(thm)],[])).
% 0.74/0.82 tff(1393,plain,
% 0.74/0.82 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_3, e_1, e_4)) | (~product(e_3, e_2, e_4))),
% 0.74/0.82 inference(modus_ponens,[status(thm)],[1392, 1391])).
% 0.74/0.82 tff(1394,plain,
% 0.74/0.82 ($false),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1393, 296, 534, 1217, 1390])).
% 0.74/0.82 tff(1395,plain,(~product(e_3, e_2, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.82 tff(1396,assumption,(product(e_3, e_2, e_3)), introduced(assumption)).
% 0.74/0.82 tff(1397,plain,
% 0.74/0.82 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_5, e_2, e_3)) | (~product(e_3, 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_5, e_3) | (~product(e_5, e_2, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.74/0.82 inference(rewrite,[status(thm)],[])).
% 0.74/0.82 tff(1398,plain,
% 0.74/0.82 ((equalish(e_5, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_5, e_2, e_3))) <=> (equalish(e_5, e_3) | (~product(e_5, e_2, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.74/0.82 inference(rewrite,[status(thm)],[])).
% 0.74/0.82 tff(1399,plain,
% 0.74/0.82 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_5, 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_5, e_3) | (~product(e_5, e_2, e_3)) | (~product(e_3, e_2, e_3))))),
% 0.74/0.82 inference(monotonicity,[status(thm)],[1398])).
% 0.74/0.82 tff(1400,plain,
% 0.74/0.82 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_5, 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_5, e_3) | (~product(e_5, e_2, e_3)) | (~product(e_3, e_2, e_3)))),
% 0.74/0.82 inference(transitivity,[status(thm)],[1399, 1397])).
% 0.74/0.82 tff(1401,plain,
% 0.74/0.82 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_5, e_3) | (~product(e_3, e_2, e_3)) | (~product(e_5, e_2, e_3)))),
% 0.74/0.82 inference(quant_inst,[status(thm)],[])).
% 0.74/0.82 tff(1402,plain,
% 0.74/0.82 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_5, e_3) | (~product(e_5, e_2, e_3)) | (~product(e_3, e_2, e_3))),
% 0.74/0.82 inference(modus_ponens,[status(thm)],[1401, 1400])).
% 0.74/0.82 tff(1403,plain,
% 0.74/0.82 ($false),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1402, 761, 211, 1248, 1396])).
% 0.74/0.82 tff(1404,plain,((~product(e_5, e_2, e_3)) | (~product(e_3, e_2, e_3))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.82 tff(1405,plain,
% 0.74/0.82 (~product(e_3, e_2, e_3)),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1404, 1246])).
% 0.74/0.82 tff(1406,plain,
% 0.74/0.82 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | (~group_element(e_3)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1) | product(e_3, e_2, e_5) | product(e_3, e_2, e_4) | product(e_3, e_2, e_2))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_2)) | (~group_element(e_3)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1) | product(e_3, e_2, e_5) | product(e_3, e_2, e_4) | product(e_3, e_2, e_2))),
% 0.74/0.82 inference(rewrite,[status(thm)],[])).
% 0.74/0.82 tff(1407,plain,
% 0.74/0.82 (((~group_element(e_3)) | product(e_3, e_2, e_5) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2))) <=> ((~group_element(e_2)) | (~group_element(e_3)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1) | product(e_3, e_2, e_5) | product(e_3, e_2, e_4) | product(e_3, e_2, e_2))),
% 0.74/0.82 inference(rewrite,[status(thm)],[])).
% 0.74/0.82 tff(1408,plain,
% 0.74/0.82 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_2, e_5) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | (~group_element(e_3)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1) | product(e_3, e_2, e_5) | product(e_3, e_2, e_4) | product(e_3, e_2, e_2)))),
% 0.74/0.82 inference(monotonicity,[status(thm)],[1407])).
% 0.74/0.82 tff(1409,plain,
% 0.74/0.82 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_2, e_5) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_2)) | (~group_element(e_3)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1) | product(e_3, e_2, e_5) | product(e_3, e_2, e_4) | product(e_3, e_2, e_2))),
% 0.74/0.82 inference(transitivity,[status(thm)],[1408, 1406])).
% 0.74/0.82 tff(1410,plain,
% 0.74/0.82 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_3)) | product(e_3, e_2, e_5) | product(e_3, e_2, e_4) | product(e_3, e_2, e_3) | product(e_3, e_2, e_2) | product(e_3, e_2, e_1) | (~group_element(e_2)))),
% 0.74/0.82 inference(quant_inst,[status(thm)],[])).
% 0.74/0.82 tff(1411,plain,
% 0.74/0.82 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_2)) | (~group_element(e_3)) | product(e_3, e_2, e_3) | product(e_3, e_2, e_1) | product(e_3, e_2, e_5) | product(e_3, e_2, e_4) | product(e_3, e_2, e_2)),
% 0.74/0.82 inference(modus_ponens,[status(thm)],[1410, 1409])).
% 0.74/0.82 tff(1412,plain,
% 0.74/0.82 (product(e_3, e_2, e_1) | product(e_3, e_2, e_5) | product(e_3, e_2, e_2)),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1411, 361, 440, 189, 1405, 1395])).
% 0.74/0.82 tff(1413,plain,
% 0.74/0.82 (product(e_3, e_2, e_1) | product(e_3, e_2, e_5)),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1412, 1389])).
% 0.74/0.82 tff(1414,plain,
% 0.74/0.82 (product(e_3, e_2, e_1)),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1413, 1380])).
% 0.74/0.82 tff(1415,plain,
% 0.74/0.82 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_4, e_2, e_1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_4, e_2, e_1)))),
% 0.74/0.82 inference(rewrite,[status(thm)],[])).
% 0.74/0.82 tff(1416,plain,
% 0.74/0.82 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | (equalish(e_4, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_4, e_2, e_1)))),
% 0.74/0.82 inference(quant_inst,[status(thm)],[])).
% 0.74/0.82 tff(1417,plain,
% 0.74/0.82 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(Z, Y, X)) | (~product(W, Y, X)))) | equalish(e_4, e_3) | (~product(e_3, e_2, e_1)) | (~product(e_4, e_2, e_1))),
% 0.74/0.82 inference(modus_ponens,[status(thm)],[1416, 1415])).
% 0.74/0.82 tff(1418,plain,
% 0.74/0.82 ($false),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1417, 499, 211, 1229, 1414])).
% 0.74/0.82 tff(1419,plain,(~product(e_4, e_2, e_1)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.82 tff(1420,assumption,(~product(e_4, e_2, e_1)), introduced(assumption)).
% 0.74/0.82 tff(1421,assumption,(product(e_2, e_5, e_1)), introduced(assumption)).
% 0.74/0.82 tff(1422,plain,
% 0.74/0.82 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_2, e_1) | (~product(e_4, e_5, e_2)) | (~product(e_2, e_5, e_1)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_2, e_1) | (~product(e_4, e_5, e_2)) | (~product(e_2, e_5, e_1)))),
% 0.74/0.82 inference(rewrite,[status(thm)],[])).
% 0.74/0.82 tff(1423,plain,
% 0.74/0.82 ((product(e_4, e_2, e_1) | (~product(e_2, e_5, e_1)) | (~product(e_4, e_5, e_2))) <=> (product(e_4, e_2, e_1) | (~product(e_4, e_5, e_2)) | (~product(e_2, e_5, e_1)))),
% 0.74/0.82 inference(rewrite,[status(thm)],[])).
% 0.74/0.82 tff(1424,plain,
% 0.74/0.82 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_2, e_1) | (~product(e_2, e_5, e_1)) | (~product(e_4, e_5, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_2, e_1) | (~product(e_4, e_5, e_2)) | (~product(e_2, e_5, e_1))))),
% 0.74/0.82 inference(monotonicity,[status(thm)],[1423])).
% 0.74/0.82 tff(1425,plain,
% 0.74/0.82 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_2, e_1) | (~product(e_2, e_5, e_1)) | (~product(e_4, e_5, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_2, e_1) | (~product(e_4, e_5, e_2)) | (~product(e_2, e_5, e_1)))),
% 0.74/0.82 inference(transitivity,[status(thm)],[1424, 1422])).
% 0.74/0.82 tff(1426,plain,
% 0.74/0.82 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_2, e_1) | (~product(e_2, e_5, e_1)) | (~product(e_4, e_5, e_2)))),
% 0.74/0.82 inference(quant_inst,[status(thm)],[])).
% 0.74/0.82 tff(1427,plain,
% 0.74/0.82 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_2, e_1) | (~product(e_4, e_5, e_2)) | (~product(e_2, e_5, e_1))),
% 0.74/0.82 inference(modus_ponens,[status(thm)],[1426, 1425])).
% 0.74/0.82 tff(1428,plain,
% 0.74/0.82 ($false),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1427, 516, 1421, 1420, 1227])).
% 0.74/0.82 tff(1429,plain,(product(e_4, e_2, e_1) | (~product(e_2, e_5, e_1))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.82 tff(1430,plain,
% 0.74/0.82 (~product(e_2, e_5, e_1)),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1429, 1419])).
% 0.74/0.82 tff(1431,assumption,(product(e_2, e_5, e_2)), introduced(assumption)).
% 0.74/0.82 tff(1432,plain,
% 0.74/0.82 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_2, e_5, e_2)) | (~product(e_2, e_2, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_2) | (~product(e_2, e_5, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.74/0.82 inference(rewrite,[status(thm)],[])).
% 0.74/0.82 tff(1433,plain,
% 0.74/0.82 ((equalish(e_5, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_5, e_2))) <=> (equalish(e_5, e_2) | (~product(e_2, e_5, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.74/0.82 inference(rewrite,[status(thm)],[])).
% 0.74/0.82 tff(1434,plain,
% 0.74/0.82 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_5, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_2, e_5, e_2)) | (~product(e_2, e_2, e_2))))),
% 0.74/0.82 inference(monotonicity,[status(thm)],[1433])).
% 0.74/0.82 tff(1435,plain,
% 0.74/0.82 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_5, e_2)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_2) | (~product(e_2, e_5, e_2)) | (~product(e_2, e_2, e_2)))),
% 0.74/0.82 inference(transitivity,[status(thm)],[1434, 1432])).
% 0.74/0.82 tff(1436,plain,
% 0.74/0.82 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_2) | (~product(e_2, e_2, e_2)) | (~product(e_2, e_5, e_2)))),
% 0.74/0.82 inference(quant_inst,[status(thm)],[])).
% 0.74/0.82 tff(1437,plain,
% 0.74/0.82 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_2) | (~product(e_2, e_5, e_2)) | (~product(e_2, e_2, e_2))),
% 0.74/0.82 inference(modus_ponens,[status(thm)],[1436, 1435])).
% 0.74/0.82 tff(1438,plain,
% 0.74/0.82 ($false),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1437, 841, 534, 1362, 1431])).
% 0.74/0.82 tff(1439,plain,(~product(e_2, e_5, e_2)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.82 tff(1440,plain,
% 0.74/0.82 (product(e_2, e_3, e_4)),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1278, 1211, 1217])).
% 0.74/0.82 tff(1441,assumption,(product(e_2, e_5, e_4)), introduced(assumption)).
% 0.74/0.82 tff(1442,plain,
% 0.74/0.82 (((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_3) | (~product(e_2, e_3, e_4)) | (~product(e_2, e_5, e_4)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_3) | (~product(e_2, e_3, e_4)) | (~product(e_2, e_5, e_4)))),
% 0.74/0.82 inference(rewrite,[status(thm)],[])).
% 0.74/0.82 tff(1443,plain,
% 0.74/0.82 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | (equalish(e_5, e_3) | (~product(e_2, e_3, e_4)) | (~product(e_2, e_5, e_4)))),
% 0.74/0.82 inference(quant_inst,[status(thm)],[])).
% 0.74/0.82 tff(1444,plain,
% 0.74/0.82 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_5, e_3) | (~product(e_2, e_3, e_4)) | (~product(e_2, e_5, e_4))),
% 0.74/0.82 inference(modus_ponens,[status(thm)],[1443, 1442])).
% 0.74/0.82 tff(1445,plain,
% 0.74/0.82 ($false),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1444, 761, 534, 1441, 1440])).
% 0.74/0.82 tff(1446,plain,(~product(e_2, e_5, e_4)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.82 tff(1447,plain,
% 0.74/0.82 (~product(e_2, e_5, e_3)),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1264, 1211])).
% 0.74/0.83 tff(1448,plain,
% 0.74/0.83 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | (~group_element(e_5)) | product(e_2, e_5, e_3) | product(e_2, e_5, e_5) | product(e_2, e_5, e_2) | product(e_2, e_5, e_4) | product(e_2, e_5, e_1))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_2)) | (~group_element(e_5)) | product(e_2, e_5, e_3) | product(e_2, e_5, e_5) | product(e_2, e_5, e_2) | product(e_2, e_5, e_4) | product(e_2, e_5, e_1))),
% 0.74/0.83 inference(rewrite,[status(thm)],[])).
% 0.74/0.83 tff(1449,plain,
% 0.74/0.83 (((~group_element(e_2)) | product(e_2, e_5, e_5) | product(e_2, e_5, e_4) | product(e_2, e_5, e_3) | product(e_2, e_5, e_2) | product(e_2, e_5, e_1) | (~group_element(e_5))) <=> ((~group_element(e_2)) | (~group_element(e_5)) | product(e_2, e_5, e_3) | product(e_2, e_5, e_5) | product(e_2, e_5, e_2) | product(e_2, e_5, e_4) | product(e_2, e_5, e_1))),
% 0.74/0.83 inference(rewrite,[status(thm)],[])).
% 0.74/0.83 tff(1450,plain,
% 0.74/0.83 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_2, e_5, e_5) | product(e_2, e_5, e_4) | product(e_2, e_5, e_3) | product(e_2, e_5, e_2) | product(e_2, e_5, e_1) | (~group_element(e_5)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | (~group_element(e_5)) | product(e_2, e_5, e_3) | product(e_2, e_5, e_5) | product(e_2, e_5, e_2) | product(e_2, e_5, e_4) | product(e_2, e_5, e_1)))),
% 0.74/0.83 inference(monotonicity,[status(thm)],[1449])).
% 0.74/0.83 tff(1451,plain,
% 0.74/0.83 (((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_2, e_5, e_5) | product(e_2, e_5, e_4) | product(e_2, e_5, e_3) | product(e_2, e_5, e_2) | product(e_2, e_5, e_1) | (~group_element(e_5)))) <=> ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_2)) | (~group_element(e_5)) | product(e_2, e_5, e_3) | product(e_2, e_5, e_5) | product(e_2, e_5, e_2) | product(e_2, e_5, e_4) | product(e_2, e_5, e_1))),
% 0.74/0.83 inference(transitivity,[status(thm)],[1450, 1448])).
% 0.74/0.83 tff(1452,plain,
% 0.74/0.83 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | ((~group_element(e_2)) | product(e_2, e_5, e_5) | product(e_2, e_5, e_4) | product(e_2, e_5, e_3) | product(e_2, e_5, e_2) | product(e_2, e_5, e_1) | (~group_element(e_5)))),
% 0.74/0.83 inference(quant_inst,[status(thm)],[])).
% 0.74/0.83 tff(1453,plain,
% 0.74/0.83 ((~![Y: $i, X: $i] : ((~group_element(X)) | product(X, Y, e_5) | product(X, Y, e_4) | product(X, Y, e_3) | product(X, Y, e_2) | product(X, Y, e_1) | (~group_element(Y)))) | (~group_element(e_2)) | (~group_element(e_5)) | product(e_2, e_5, e_3) | product(e_2, e_5, e_5) | product(e_2, e_5, e_2) | product(e_2, e_5, e_4) | product(e_2, e_5, e_1)),
% 0.74/0.83 inference(modus_ponens,[status(thm)],[1452, 1451])).
% 0.74/0.83 tff(1454,plain,
% 0.74/0.83 (product(e_2, e_5, e_3) | product(e_2, e_5, e_5) | product(e_2, e_5, e_2) | product(e_2, e_5, e_4) | product(e_2, e_5, e_1)),
% 0.74/0.83 inference(unit_resolution,[status(thm)],[1453, 361, 962, 189])).
% 0.74/0.83 tff(1455,plain,
% 0.74/0.83 (product(e_2, e_5, e_5) | product(e_2, e_5, e_2) | product(e_2, e_5, e_4) | product(e_2, e_5, e_1)),
% 0.74/0.83 inference(unit_resolution,[status(thm)],[1454, 1447])).
% 0.74/0.83 tff(1456,plain,
% 0.74/0.83 (product(e_2, e_5, e_5) | product(e_2, e_5, e_2) | product(e_2, e_5, e_1)),
% 0.74/0.83 inference(unit_resolution,[status(thm)],[1455, 1446])).
% 0.74/0.83 tff(1457,plain,
% 0.74/0.83 (product(e_2, e_5, e_5) | product(e_2, e_5, e_1)),
% 0.74/0.83 inference(unit_resolution,[status(thm)],[1456, 1439])).
% 0.74/0.83 tff(1458,plain,
% 0.74/0.83 (product(e_2, e_5, e_5)),
% 0.74/0.83 inference(unit_resolution,[status(thm)],[1457, 1430])).
% 0.74/0.83 tff(1459,plain,
% 0.74/0.83 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_2, e_5) | (~product(e_4, e_5, e_2)) | (~product(e_2, e_5, e_5)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_2, e_5) | (~product(e_4, e_5, e_2)) | (~product(e_2, e_5, e_5)))),
% 0.74/0.83 inference(rewrite,[status(thm)],[])).
% 0.74/0.83 tff(1460,plain,
% 0.74/0.83 ((product(e_4, e_2, e_5) | (~product(e_2, e_5, e_5)) | (~product(e_4, e_5, e_2))) <=> (product(e_4, e_2, e_5) | (~product(e_4, e_5, e_2)) | (~product(e_2, e_5, e_5)))),
% 0.74/0.83 inference(rewrite,[status(thm)],[])).
% 0.74/0.83 tff(1461,plain,
% 0.74/0.83 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_2, e_5) | (~product(e_2, e_5, e_5)) | (~product(e_4, e_5, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_2, e_5) | (~product(e_4, e_5, e_2)) | (~product(e_2, e_5, e_5))))),
% 0.74/0.83 inference(monotonicity,[status(thm)],[1460])).
% 0.74/0.83 tff(1462,plain,
% 0.74/0.83 (((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_2, e_5) | (~product(e_2, e_5, e_5)) | (~product(e_4, e_5, e_2)))) <=> ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_2, e_5) | (~product(e_4, e_5, e_2)) | (~product(e_2, e_5, e_5)))),
% 0.74/0.83 inference(transitivity,[status(thm)],[1461, 1459])).
% 0.74/0.83 tff(1463,plain,
% 0.74/0.83 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | (product(e_4, e_2, e_5) | (~product(e_2, e_5, e_5)) | (~product(e_4, e_5, e_2)))),
% 0.74/0.83 inference(quant_inst,[status(thm)],[])).
% 0.74/0.83 tff(1464,plain,
% 0.74/0.83 ((~![Y: $i, Z1: $i, X: $i, Z2: $i] : (product(X, Z1, Z2) | (~product(Z1, Y, Z2)) | (~product(X, Y, Z1)))) | product(e_4, e_2, e_5) | (~product(e_4, e_5, e_2)) | (~product(e_2, e_5, e_5))),
% 0.74/0.83 inference(modus_ponens,[status(thm)],[1463, 1462])).
% 0.74/0.83 tff(1465,plain,
% 0.74/0.83 ($false),
% 0.74/0.83 inference(unit_resolution,[status(thm)],[1464, 516, 1458, 1228, 1227])).
% 0.74/0.83 tff(1466,plain,(product(e_4, e_2, e_5)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.83 tff(1467,plain,
% 0.74/0.83 (((~![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_4, e_1, e_5)) | (~product(e_4, e_2, e_5)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_4, e_1, e_5)) | (~product(e_4, e_2, e_5)))),
% 0.74/0.83 inference(rewrite,[status(thm)],[])).
% 0.74/0.83 tff(1468,plain,
% 0.74/0.83 ((~![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_4, e_1, e_5)) | (~product(e_4, e_2, e_5)))),
% 0.74/0.83 inference(quant_inst,[status(thm)],[])).
% 0.74/0.83 tff(1469,plain,
% 0.74/0.83 ((~![W: $i, Z: $i, Y: $i, X: $i] : (equalish(W, Z) | (~product(X, Z, Y)) | (~product(X, W, Y)))) | equalish(e_2, e_1) | (~product(e_4, e_1, e_5)) | (~product(e_4, e_2, e_5))),
% 0.74/0.83 inference(modus_ponens,[status(thm)],[1468, 1467])).
% 0.74/0.83 tff(1470,plain,
% 0.74/0.83 ($false),
% 0.74/0.83 inference(unit_resolution,[status(thm)],[1469, 296, 534, 596, 1466])).
% 0.74/0.83 % SZS output end Proof
%------------------------------------------------------------------------------