%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP128-3.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:42:20 PM UTC 2026
% Result : Satisfiable 1.86s 0.68s
% Output : Saturation 1.86s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_42ERROR: Could not build tree for root c_0_46ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(c_0_43,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_4)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
c_0_42,
[final] ).
cnf(c_0_44,axiom,
group_element(e_1),
element_1,
[final] ).
cnf(c_0_46,plain,
( ~ group_element(X1)
| product(X1,e_1,e_1)
| product(X1,e_1,e_2)
| product(X1,e_1,e_3)
| product(X1,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]),
[final] ).
cnf(c_0_47,axiom,
group_element(e_2),
element_2,
[final] ).
cnf(c_0_50,plain,
( ~ greater(X2,X1)
| ~ product(X1,e_1,X2)
| ~ cycle(X1,e_0) ),
c_0_45,
[final] ).
cnf(c_0_52,axiom,
greater(e_4,e_2),
e_4_greater_e_2,
[final] ).
cnf(c_0_53,plain,
( ~ group_element(X1)
| cycle(X1,e_3)
| cycle(X1,e_2)
| cycle(X1,e_1)
| cycle(X1,e_0) ),
c_0_48,
[final] ).
cnf(c_0_54,plain,
( ~ next(X1,X4)
| ~ greater(X2,e_0)
| ~ product(X1,e_1,X3)
| ~ cycle(X1,X2)
| equalish(X3,X4) ),
c_0_49,
[final] ).
cnf(c_0_58,axiom,
greater(e_4,e_1),
e_4_greater_e_1,
[final] ).
cnf(c_0_61,axiom,
greater(e_3,e_0),
e_3_greater_e_0,
[final] ).
cnf(c_0_64,plain,
( cycle(e_1,e_0)
| cycle(e_1,e_1)
| cycle(e_1,e_2)
| cycle(e_1,e_3) ),
inference(spm,[status(thm)],[c_0_53,c_0_44]),
[final] ).
cnf(c_0_66,axiom,
next(e_2,e_3),
e_2_then_e_3,
[final] ).
cnf(c_0_67,plain,
~ equalish(e_4,e_3),
c_0_62,
[final] ).
cnf(c_0_72,axiom,
greater(e_2,e_0),
e_2_greater_e_0,
[final] ).
cnf(c_0_74,axiom,
next(e_1,e_2),
e_1_then_e_2,
[final] ).
cnf(c_0_75,plain,
~ equalish(e_4,e_2),
c_0_70,
[final] ).
cnf(c_0_79,axiom,
group_element(e_4),
element_4,
[final] ).
cnf(c_0_81,axiom,
greater(e_1,e_0),
e_1_greater_e_0,
[final] ).
cnf(c_0_84,negated_conjecture,
( ~ product(X3,X2,X4)
| ~ product(X1,X2,X3)
| product(X1,X3,X4) ),
c_0_78,
[final] ).
cnf(c_0_89,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
c_0_83,
[final] ).
cnf(c_0_92,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
c_0_86,
[final] ).
cnf(c_0_98,plain,
~ equalish(e_4,e_1),
c_0_91,
[final] ).
cnf(c_0_101,plain,
~ equalish(e_1,e_2),
c_0_95,
[final] ).
cnf(c_0_106,plain,
~ equalish(e_1,e_4),
c_0_103,
[final] ).
cnf(c_0_107,plain,
( ~ group_element(X1)
| product(X1,e_4,e_1)
| product(X1,e_4,e_2)
| product(X1,e_4,e_3)
| product(X1,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_43,c_0_79]),
[final] ).
cnf(c_0_110,plain,
( product(e_4,e_4,e_4)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_107,c_0_79]),
[final] ).
cnf(c_0_111,axiom,
group_element(e_3),
element_3,
[final] ).
cnf(c_0_115,plain,
( ~ product(X1,e_4,e_4)
| equalish(X1,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_92,c_0_110]),
[final] ).
cnf(c_0_117,plain,
~ equalish(e_3,e_4),
c_0_112,
[final] ).
cnf(c_0_124,plain,
~ equalish(e_2,e_4),
c_0_118,
[final] ).
cnf(c_0_131,plain,
~ equalish(e_2,e_1),
c_0_126,
[final] ).
cnf(c_0_150,plain,
( ~ group_element(X1)
| product(X1,e_3,e_1)
| product(X1,e_3,e_2)
| product(X1,e_3,e_3)
| product(X1,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_43,c_0_111]),
[final] ).
cnf(c_0_162,plain,
~ equalish(e_3,e_2),
c_0_154,
[final] ).
cnf(c_0_165,plain,
~ equalish(e_1,e_3),
c_0_157,
[final] ).
cnf(c_0_168,negated_conjecture,
product(e_1,e_1,e_1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_160]),c_0_131]),
[final] ).
cnf(c_0_174,negated_conjecture,
( ~ product(X1,e_1,e_1)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_92,c_0_168]),
[final] ).
cnf(c_0_179,negated_conjecture,
( product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_173]),c_0_67]),
[final] ).
cnf(c_0_184,plain,
~ equalish(e_3,e_1),
c_0_176,
[final] ).
cnf(c_0_187,negated_conjecture,
( ~ product(e_4,X1,e_3)
| equalish(X1,e_3)
| product(e_4,e_3,e_1)
| product(e_4,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_89,c_0_179]),
[final] ).
cnf(c_0_189,plain,
~ equalish(e_2,e_3),
c_0_181,
[final] ).
cnf(c_0_221,negated_conjecture,
( ~ product(e_1,X1,e_1)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_89,c_0_168]),
[final] ).
cnf(c_0_231,plain,
( ~ group_element(X1)
| product(X1,e_2,e_1)
| product(X1,e_2,e_2)
| product(X1,e_2,e_3)
| product(X1,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_43,c_0_47]),
[final] ).
cnf(c_0_241,negated_conjecture,
product(e_1,e_2,e_4),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_237]),c_0_184]),
[final] ).
cnf(c_0_242,negated_conjecture,
( product(e_4,e_2,e_3)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_238,c_0_239]),c_0_75]),
[final] ).
cnf(c_0_244,negated_conjecture,
( ~ product(X1,e_2,e_4)
| product(X1,e_4,e_3)
| product(e_4,e_2,e_1)
| product(e_4,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_84,c_0_242]),
[final] ).
cnf(c_0_251,negated_conjecture,
( ~ product(X1,e_2,e_1)
| product(X1,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_84,c_0_241]),
[final] ).
cnf(c_0_280,negated_conjecture,
product(e_1,e_3,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_279]),c_0_131]),
[final] ).
cnf(c_0_281,negated_conjecture,
( ~ product(X1,e_3,e_1)
| product(X1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_84,c_0_280]),
[final] ).
cnf(c_0_283,negated_conjecture,
( product(e_4,e_1,e_1)
| product(e_4,e_1,e_2) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_225,c_0_280]),c_0_106]),c_0_281]),
[final] ).
cnf(c_0_289,negated_conjecture,
product(e_1,e_4,e_3),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_286]),c_0_98]),
[final] ).
cnf(c_0_297,negated_conjecture,
( ~ product(X1,e_4,e_1)
| product(X1,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_84,c_0_289]),
[final] ).
cnf(c_0_309,negated_conjecture,
product(e_2,e_1,e_3),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_303,c_0_304]),c_0_124]),c_0_297]),
[final] ).
cnf(c_0_312,negated_conjecture,
product(e_2,e_4,e_1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_308,c_0_309]),c_0_189]),
[final] ).
cnf(c_0_314,negated_conjecture,
product(e_3,e_2,e_1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_311,c_0_312]),c_0_189]),
[final] ).
cnf(c_0_317,negated_conjecture,
product(e_3,e_1,e_4),
inference(spm,[status(thm)],[c_0_251,c_0_314]),
[final] ).
cnf(c_0_318,axiom,
greater(e_4,e_3),
e_4_greater_e_3,
[final] ).
cnf(c_0_320,plain,
( ~ next(X4,X5)
| ~ greater(X2,e_0)
| ~ next(X1,X3)
| ~ cycle(X3,X4)
| ~ cycle(X1,X2)
| equalish(X2,X5) ),
c_0_316,
[final] ).
cnf(c_0_322,negated_conjecture,
~ cycle(e_3,e_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_317]),c_0_318])]),
[final] ).
cnf(c_0_325,plain,
( ~ next(X2,X3)
| ~ next(X4,X1)
| ~ cycle(X3,X4)
| ~ cycle(X2,e_3)
| equalish(e_3,X1) ),
inference(spm,[status(thm)],[c_0_320,c_0_61]),
[final] ).
cnf(c_0_331,axiom,
next(e_3,e_4),
e_3_then_e_4,
[final] ).
cnf(c_0_335,negated_conjecture,
( ~ product(X1,e_1,e_4)
| product(X1,e_4,e_2)
| product(e_4,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_84,c_0_283]),
[final] ).
cnf(c_0_337,axiom,
cycle(e_4,e_0),
cycle3,
[final] ).
cnf(c_0_341,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_150,c_0_47]),
[final] ).
cnf(c_0_342,negated_conjecture,
( ~ product(X1,e_3,e_4)
| product(X1,e_4,e_3)
| product(e_4,e_3,e_1)
| product(e_4,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_84,c_0_179]),
[final] ).
cnf(c_0_346,axiom,
next(e_0,e_1),
e_0_then_e_1,
[final] ).
cnf(c_0_353,negated_conjecture,
product(e_3,e_4,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_343]),c_0_98]),
[final] ).
cnf(c_0_354,negated_conjecture,
( ~ product(X1,e_1,e_3)
| product(X1,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_84,c_0_317]),
[final] ).
cnf(c_0_356,axiom,
greater(e_3,e_2),
e_3_greater_e_2,
[final] ).
cnf(c_0_357,plain,
( ~ next(X2,X3)
| ~ next(X4,X1)
| ~ cycle(X3,X4)
| ~ cycle(X2,e_2)
| equalish(e_2,X1) ),
inference(spm,[status(thm)],[c_0_320,c_0_72]),
[final] ).
cnf(c_0_362,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
c_0_350,
[final] ).
cnf(c_0_364,negated_conjecture,
( ~ product(X1,e_4,e_3)
| product(X1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_84,c_0_353]),
[final] ).
cnf(c_0_365,negated_conjecture,
( ~ product(X1,e_3,X2)
| ~ product(X2,e_1,e_3)
| product(X1,X2,e_4) ),
inference(spm,[status(thm)],[c_0_84,c_0_354]),
[final] ).
cnf(c_0_366,negated_conjecture,
( product(e_4,e_3,e_1)
| product(e_4,e_2,e_1)
| product(e_4,e_2,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_355,c_0_280]),c_0_106]),
[final] ).
cnf(c_0_367,negated_conjecture,
~ cycle(e_2,e_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_309]),c_0_356])]),
[final] ).
cnf(c_0_374,negated_conjecture,
( ~ product(X1,e_3,e_2)
| product(X1,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_365,c_0_309]),
[final] ).
cnf(c_0_376,negated_conjecture,
( product(e_4,e_1,e_2)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_281,c_0_366]),
[final] ).
cnf(c_0_380,negated_conjecture,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_370,c_0_299]),c_0_67]),
[final] ).
cnf(c_0_387,plain,
( ~ product(e_4,X1,e_4)
| equalish(X1,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_89,c_0_110]),
[final] ).
cnf(c_0_390,negated_conjecture,
( ~ product(X1,e_2,e_4)
| product(X1,e_4,e_2)
| product(e_4,e_2,e_1)
| product(e_4,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_84,c_0_376]),
[final] ).
cnf(c_0_394,negated_conjecture,
( ~ product(X1,e_2,e_2)
| equalish(X1,e_2)
| product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_92,c_0_380]),
[final] ).
cnf(c_0_395,negated_conjecture,
( ~ product(X1,e_1,e_2)
| product(X1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_84,c_0_309]),
[final] ).
cnf(c_0_404,negated_conjecture,
( ~ product(X1,e_2,e_4)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_92,c_0_241]),
[final] ).
cnf(c_0_406,negated_conjecture,
( ~ product(X1,e_3,e_3)
| equalish(X1,e_4)
| product(e_4,e_3,e_1)
| product(e_4,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_92,c_0_179]),
[final] ).
cnf(c_0_407,negated_conjecture,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_389,c_0_317]),c_0_165]),
[final] ).
cnf(c_0_408,negated_conjecture,
( ~ product(X1,e_1,e_3)
| product(X1,e_4,e_3)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_342,c_0_354]),
[final] ).
cnf(c_0_409,negated_conjecture,
( ~ product(X1,e_2,e_1)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_92,c_0_314]),
[final] ).
cnf(c_0_412,plain,
cycle(e_3,e_1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_392,c_0_346]),c_0_131]),
[final] ).
cnf(c_0_414,negated_conjecture,
( ~ product(e_3,e_2,X1)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_362,c_0_314]),
[final] ).
cnf(c_0_415,negated_conjecture,
( ~ product(e_3,X1,e_4)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_89,c_0_317]),
[final] ).
cnf(c_0_417,negated_conjecture,
( ~ product(X2,X1,e_3)
| ~ product(X2,e_1,e_2)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_89,c_0_395]),
[final] ).
cnf(c_0_420,plain,
( ~ greater(X2,X5)
| ~ greater(X3,X1)
| ~ next(X3,X4)
| ~ cycle(X4,X5)
| ~ cycle(X3,e_0)
| ~ cycle(X1,X2) ),
c_0_399,
[final] ).
cnf(c_0_425,negated_conjecture,
( ~ product(e_4,e_1,e_2)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_395]),c_0_189]),
[final] ).
cnf(c_0_426,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_4,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_404,c_0_405]),c_0_98]),
[final] ).
cnf(c_0_427,negated_conjecture,
( ~ product(X1,e_2,e_3)
| product(X1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_84,c_0_314]),
[final] ).
cnf(c_0_428,negated_conjecture,
( ~ product(X1,e_3,e_2)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_92,c_0_280]),
[final] ).
cnf(c_0_431,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_4,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_409,c_0_410]),c_0_67]),
[final] ).
cnf(c_0_434,negated_conjecture,
~ product(e_3,e_1,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_414,c_0_395]),c_0_184]),
[final] ).
cnf(c_0_435,negated_conjecture,
~ product(e_3,e_1,e_3),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_415,c_0_354]),c_0_184]),
[final] ).
cnf(c_0_436,negated_conjecture,
( product(e_4,e_1,e_2)
| product(e_2,e_2,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_409,c_0_416]),c_0_67]),
[final] ).
cnf(c_0_437,negated_conjecture,
( ~ product(e_4,X1,e_3)
| equalish(X1,e_2)
| product(e_4,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_417,c_0_283]),
[final] ).
cnf(c_0_439,plain,
( ~ next(e_4,X1)
| ~ greater(X4,X2)
| ~ greater(e_4,X3)
| ~ cycle(X3,X4)
| ~ cycle(X1,X2) ),
inference(spm,[status(thm)],[c_0_420,c_0_337]),
[final] ).
cnf(c_0_445,negated_conjecture,
( ~ product(X1,e_3,X2)
| ~ product(X2,e_2,e_3)
| product(X1,X2,e_1) ),
inference(spm,[status(thm)],[c_0_84,c_0_427]),
[final] ).
cnf(c_0_446,negated_conjecture,
( product(e_3,e_3,e_2)
| product(e_3,e_3,e_1)
| product(e_4,e_3,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_428,c_0_429]),c_0_98]),
[final] ).
cnf(c_0_447,negated_conjecture,
( product(e_2,e_4,e_3)
| product(e_4,e_3,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_428,c_0_430]),c_0_98]),
[final] ).
cnf(c_0_449,negated_conjecture,
( ~ product(e_2,X1,e_3)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_89,c_0_309]),
[final] ).
cnf(c_0_450,plain,
( cycle(e_2,e_2)
| cycle(e_2,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_432,c_0_74]),c_0_162]),
[final] ).
cnf(c_0_451,plain,
( ~ next(X2,X3)
| ~ next(X4,X1)
| ~ cycle(X3,X4)
| ~ cycle(X2,e_1)
| equalish(e_1,X1) ),
inference(spm,[status(thm)],[c_0_320,c_0_81]),
[final] ).
cnf(c_0_456,plain,
( ~ next(e_4,X2)
| ~ greater(X1,X3)
| ~ cycle(X2,X3)
| ~ cycle(e_3,X1) ),
inference(spm,[status(thm)],[c_0_439,c_0_318]),
[final] ).
cnf(c_0_462,negated_conjecture,
( ~ product(X2,e_2,e_3)
| ~ product(X1,e_3,e_1)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_92,c_0_427]),
[final] ).
cnf(c_0_463,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_4,e_3,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_428,c_0_444]),c_0_98]),
[final] ).
cnf(c_0_464,negated_conjecture,
( ~ product(X1,e_3,X2)
| ~ product(X2,e_1,e_2)
| product(X1,X2,e_1) ),
inference(spm,[status(thm)],[c_0_445,c_0_395]),
[final] ).
cnf(c_0_465,negated_conjecture,
( ~ product(X2,X1,e_1)
| ~ product(X2,e_2,e_3)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_89,c_0_427]),
[final] ).
cnf(c_0_466,negated_conjecture,
( product(e_4,e_1,e_2)
| product(e_3,e_3,e_1)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_281,c_0_446]),
[final] ).
cnf(c_0_467,negated_conjecture,
( product(e_4,e_1,e_2)
| product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_281,c_0_447]),
[final] ).
cnf(c_0_468,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_4,e_3,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_428,c_0_448]),c_0_98]),
[final] ).
cnf(c_0_469,negated_conjecture,
~ product(e_2,e_1,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_449,c_0_395]),c_0_131]),
[final] ).
cnf(c_0_470,plain,
( ~ next(X3,X1)
| ~ next(e_2,X2)
| ~ cycle(X2,X3)
| cycle(e_2,e_1)
| equalish(e_2,X1) ),
inference(spm,[status(thm)],[c_0_357,c_0_450]),
[final] ).
cnf(c_0_471,plain,
( ~ next(e_4,X2)
| ~ greater(X1,X3)
| ~ cycle(X2,X3)
| ~ cycle(e_2,X1) ),
inference(spm,[status(thm)],[c_0_439,c_0_52]),
[final] ).
cnf(c_0_473,negated_conjecture,
( product(e_2,e_2,e_1)
| product(e_4,e_3,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_428,c_0_453]),c_0_98]),
[final] ).
cnf(c_0_474,negated_conjecture,
( product(e_4,e_3,e_1)
| product(e_4,e_1,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_428,c_0_454]),c_0_98]),
[final] ).
cnf(c_0_475,negated_conjecture,
( ~ product(X2,e_3,X1)
| ~ product(X2,e_2,e_3)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_362,c_0_427]),
[final] ).
cnf(c_0_480,plain,
( ~ next(X3,X1)
| ~ next(e_3,X2)
| ~ cycle(X2,X3)
| equalish(e_1,X1) ),
inference(spm,[status(thm)],[c_0_451,c_0_412]),
[final] ).
cnf(c_0_485,plain,
( ~ cycle(X1,X3)
| ~ cycle(X1,X2)
| equalish(X2,X3) ),
c_0_461,
[final] ).
cnf(c_0_486,negated_conjecture,
( ~ next(e_4,X1)
| ~ greater(X2,e_0)
| ~ cycle(e_4,X2)
| equalish(e_2,X1)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_54,c_0_426]),
[final] ).
cnf(c_0_487,negated_conjecture,
( ~ product(X1,e_2,e_3)
| equalish(e_4,X1)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_462,c_0_463]),
[final] ).
cnf(c_0_488,negated_conjecture,
( ~ product(X1,e_3,e_1)
| equalish(X1,e_4)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_92,c_0_463]),
[final] ).
cnf(c_0_489,negated_conjecture,
( ~ product(X2,e_3,X1)
| ~ product(X2,e_1,e_3)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_362,c_0_354]),
[final] ).
cnf(c_0_490,negated_conjecture,
( ~ product(X1,e_3,e_4)
| product(X1,e_4,e_1)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_464,c_0_426]),
[final] ).
cnf(c_0_491,negated_conjecture,
( ~ product(X1,e_2,X2)
| ~ product(X2,e_1,e_2)
| product(X1,X2,e_3) ),
inference(spm,[status(thm)],[c_0_84,c_0_395]),
[final] ).
cnf(c_0_492,negated_conjecture,
( ~ product(X2,X1,e_1)
| ~ product(X2,e_1,e_2)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_465,c_0_395]),
[final] ).
cnf(c_0_493,negated_conjecture,
( ~ next(e_4,X1)
| ~ greater(X2,e_0)
| ~ cycle(e_4,X2)
| equalish(e_2,X1)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_54,c_0_466]),
[final] ).
cnf(c_0_494,negated_conjecture,
( ~ product(X1,e_3,e_4)
| product(X1,e_4,e_1)
| product(e_3,e_3,e_1)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_84,c_0_446]),
[final] ).
cnf(c_0_495,negated_conjecture,
( ~ product(X1,e_2,e_3)
| equalish(e_4,X1)
| product(e_3,e_3,e_1)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_462,c_0_446]),
[final] ).
cnf(c_0_496,negated_conjecture,
( ~ product(X1,e_3,e_1)
| equalish(X1,e_4)
| product(e_3,e_3,e_1)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_92,c_0_446]),
[final] ).
cnf(c_0_497,negated_conjecture,
( ~ product(X2,e_1,e_3)
| ~ product(X1,e_3,e_4)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_92,c_0_354]),
[final] ).
cnf(c_0_498,negated_conjecture,
( ~ product(X1,e_3,e_4)
| product(X1,e_4,e_1)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_84,c_0_366]),
[final] ).
cnf(c_0_499,negated_conjecture,
( ~ next(e_4,X1)
| ~ greater(X2,e_0)
| ~ cycle(e_4,X2)
| equalish(e_2,X1)
| product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_54,c_0_467]),
[final] ).
cnf(c_0_500,negated_conjecture,
( ~ product(X1,e_3,e_4)
| product(X1,e_4,e_1)
| product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_84,c_0_447]),
[final] ).
cnf(c_0_501,negated_conjecture,
( ~ product(X1,e_2,e_3)
| equalish(e_4,X1)
| product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_462,c_0_447]),
[final] ).
cnf(c_0_502,negated_conjecture,
( ~ product(X1,e_3,e_1)
| equalish(X1,e_4)
| product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_92,c_0_447]),
[final] ).
cnf(c_0_503,negated_conjecture,
( ~ product(X1,e_2,e_3)
| equalish(e_4,X1)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_462,c_0_468]),
[final] ).
cnf(c_0_504,negated_conjecture,
( ~ product(X1,e_3,e_1)
| equalish(X1,e_4)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_92,c_0_468]),
[final] ).
cnf(c_0_505,negated_conjecture,
( ~ next(e_4,X1)
| ~ greater(X2,e_0)
| ~ cycle(e_4,X2)
| equalish(e_2,X1)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_54,c_0_431]),
[final] ).
cnf(c_0_506,negated_conjecture,
( ~ product(X1,e_3,e_4)
| product(X1,e_4,e_1)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_464,c_0_431]),
[final] ).
cnf(c_0_507,negated_conjecture,
( product(e_4,e_1,e_1)
| product(e_4,e_2,e_3)
| product(e_2,e_1,e_1) ),
inference(sr,[status(thm)],[c_0_188,c_0_469]),
[final] ).
cnf(c_0_508,negated_conjecture,
( ~ product(X2,e_1,e_2)
| ~ product(X1,e_2,e_3)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_92,c_0_395]),
[final] ).
cnf(c_0_509,negated_conjecture,
( ~ product(X1,e_2,e_3)
| equalish(X1,e_4)
| product(e_4,e_2,e_1)
| product(e_4,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_92,c_0_242]),
[final] ).
cnf(c_0_510,plain,
( ~ next(X2,X1)
| ~ cycle(e_3,X2)
| cycle(e_2,e_1)
| equalish(e_2,X1) ),
inference(spm,[status(thm)],[c_0_470,c_0_66]),
[final] ).
cnf(c_0_511,plain,
( ~ next(e_4,X1)
| ~ greater(e_2,X2)
| ~ cycle(X1,X2)
| cycle(e_2,e_1) ),
inference(spm,[status(thm)],[c_0_471,c_0_450]),
[final] ).
cnf(c_0_512,axiom,
greater(e_2,e_1),
e_2_greater_e_1,
[final] ).
cnf(c_0_513,negated_conjecture,
( ~ next(e_2,X1)
| ~ greater(X2,e_0)
| ~ cycle(e_2,X2)
| equalish(e_3,X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_309]),
[final] ).
cnf(c_0_514,plain,
( ~ next(e_4,X1)
| ~ greater(e_1,X2)
| ~ cycle(X1,X2) ),
inference(spm,[status(thm)],[c_0_456,c_0_412]),
[final] ).
cnf(c_0_516,negated_conjecture,
( ~ next(e_4,X1)
| ~ greater(X2,e_0)
| ~ cycle(e_4,X2)
| equalish(e_2,X1)
| product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_54,c_0_436]),
[final] ).
cnf(c_0_518,negated_conjecture,
( ~ product(X1,e_2,e_3)
| equalish(e_4,X1)
| product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_462,c_0_473]),
[final] ).
cnf(c_0_519,negated_conjecture,
( ~ product(X1,e_3,e_1)
| equalish(X1,e_4)
| product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_92,c_0_473]),
[final] ).
cnf(c_0_520,negated_conjecture,
( ~ product(X1,e_3,e_4)
| product(X1,e_4,e_1)
| product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_464,c_0_436]),
[final] ).
cnf(c_0_521,negated_conjecture,
( ~ product(X1,e_2,e_3)
| equalish(e_4,X1)
| product(e_4,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_462,c_0_474]),
[final] ).
cnf(c_0_522,negated_conjecture,
( ~ product(X1,e_3,e_1)
| equalish(X1,e_4)
| product(e_4,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_92,c_0_474]),
[final] ).
cnf(c_0_523,negated_conjecture,
( ~ product(X1,e_1,e_3)
| ~ product(X1,e_2,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_475,c_0_354]),c_0_98]),
[final] ).
cnf(c_0_524,negated_conjecture,
( ~ product(X1,e_3,e_4)
| product(X1,e_4,e_1)
| product(e_4,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_464,c_0_283]),
[final] ).
cnf(c_0_525,negated_conjecture,
( ~ product(e_4,e_3,X1)
| equalish(X1,e_3)
| product(e_4,e_3,e_1)
| product(e_4,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_362,c_0_179]),
[final] ).
cnf(c_0_526,negated_conjecture,
( ~ next(e_4,X1)
| ~ greater(X2,e_0)
| ~ cycle(e_4,X2)
| equalish(e_2,X1)
| product(e_4,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_54,c_0_283]),
[final] ).
cnf(c_0_527,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_476,c_0_398]),
[final] ).
cnf(c_0_528,negated_conjecture,
( product(e_2,e_3,e_4)
| product(e_2,e_1,e_1) ),
inference(sr,[status(thm)],[c_0_191,c_0_469]),
[final] ).
cnf(c_0_529,negated_conjecture,
( ~ product(X2,X1,e_4)
| ~ product(X2,e_1,e_3)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_89,c_0_354]),
[final] ).
cnf(c_0_530,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_4,e_2,e_3)
| product(e_4,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_477,c_0_478]),
[final] ).
cnf(c_0_532,negated_conjecture,
( ~ next(e_1,X1)
| ~ greater(X2,e_0)
| ~ cycle(e_1,X2)
| equalish(e_1,X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_168]),
[final] ).
cnf(c_0_533,negated_conjecture,
( ~ greater(e_1,e_1)
| ~ cycle(e_1,e_0) ),
inference(spm,[status(thm)],[c_0_50,c_0_168]),
[final] ).
cnf(c_0_534,plain,
( ~ next(e_1,X1)
| ~ greater(X4,X2)
| ~ greater(e_1,X3)
| ~ cycle(X3,X4)
| ~ cycle(X1,X2)
| cycle(e_1,e_3)
| cycle(e_1,e_2)
| cycle(e_1,e_1) ),
inference(spm,[status(thm)],[c_0_420,c_0_64]),
[final] ).
cnf(c_0_535,plain,
( ~ next(e_4,X2)
| ~ greater(X1,X3)
| ~ cycle(X2,X3)
| ~ cycle(e_1,X1) ),
inference(spm,[status(thm)],[c_0_439,c_0_58]),
[final] ).
cnf(c_0_536,axiom,
greater(e_4,e_0),
e_4_greater_e_0,
[final] ).
cnf(c_0_537,plain,
( ~ next(X2,X1)
| ~ cycle(e_4,X2)
| equalish(e_1,X1) ),
inference(spm,[status(thm)],[c_0_480,c_0_331]),
[final] ).
cnf(c_0_538,negated_conjecture,
( ~ product(e_1,X1,e_4)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_89,c_0_241]),
[final] ).
cnf(c_0_539,negated_conjecture,
( ~ product(e_2,X1,e_1)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_89,c_0_312]),
[final] ).
cnf(c_0_540,negated_conjecture,
( ~ product(e_3,X1,e_1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_89,c_0_314]),
[final] ).
cnf(c_0_541,negated_conjecture,
( ~ product(e_1,X1,e_3)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_89,c_0_289]),
[final] ).
cnf(c_0_547,plain,
( ~ cycle(e_4,X1)
| equalish(X1,e_0) ),
inference(spm,[status(thm)],[c_0_485,c_0_337]),
[final] ).
cnf(c_0_548,negated_conjecture,
( ~ next(e_4,X1)
| ~ greater(e_0,e_0)
| equalish(e_2,X1)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_486,c_0_337]),
[final] ).
cnf(c_0_549,negated_conjecture,
( ~ product(X1,e_1,e_2)
| equalish(e_4,X1)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_487,c_0_395]),
[final] ).
cnf(c_0_550,negated_conjecture,
( ~ product(X1,e_2,e_3)
| equalish(X1,e_4)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_488,c_0_427]),
[final] ).
cnf(c_0_551,negated_conjecture,
( ~ product(e_4,e_3,X1)
| equalish(X1,e_1)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_362,c_0_463]),
[final] ).
cnf(c_0_552,negated_conjecture,
( ~ product(e_4,e_1,e_3)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_489,c_0_463]),c_0_106]),
[final] ).
cnf(c_0_553,negated_conjecture,
( ~ product(X1,e_1,e_3)
| product(X1,e_4,e_1)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_490,c_0_354]),
[final] ).
cnf(c_0_554,negated_conjecture,
( ~ product(X1,e_2,e_4)
| product(X1,e_4,e_3)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_491,c_0_426]),
[final] ).
cnf(c_0_555,negated_conjecture,
( ~ product(X1,e_1,e_4)
| product(X1,e_4,e_2)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_84,c_0_426]),
[final] ).
cnf(c_0_556,negated_conjecture,
( ~ product(e_4,X1,e_1)
| equalish(X1,e_3)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_492,c_0_426]),
[final] ).
cnf(c_0_557,negated_conjecture,
( ~ product(e_4,X1,e_3)
| equalish(X1,e_2)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_417,c_0_426]),
[final] ).
cnf(c_0_558,negated_conjecture,
( ~ product(X1,e_1,e_2)
| equalish(X1,e_4)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_92,c_0_426]),
[final] ).
cnf(c_0_559,negated_conjecture,
( ~ product(e_4,e_1,X1)
| equalish(X1,e_2)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_362,c_0_426]),
[final] ).
cnf(c_0_560,negated_conjecture,
( ~ product(e_4,X1,e_2)
| equalish(X1,e_1)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_89,c_0_426]),
[final] ).
cnf(c_0_561,negated_conjecture,
( ~ next(e_4,X1)
| ~ greater(e_0,e_0)
| equalish(e_2,X1)
| product(e_3,e_3,e_1)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_493,c_0_337]),
[final] ).
cnf(c_0_562,negated_conjecture,
( ~ product(X1,e_1,e_3)
| product(X1,e_4,e_1)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_494,c_0_354]),
[final] ).
cnf(c_0_563,negated_conjecture,
( ~ product(X1,e_2,e_4)
| product(X1,e_4,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_491,c_0_466]),
[final] ).
cnf(c_0_564,negated_conjecture,
( ~ product(X1,e_1,e_4)
| product(X1,e_4,e_2)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_84,c_0_466]),
[final] ).
cnf(c_0_565,negated_conjecture,
( ~ product(X1,e_1,e_2)
| equalish(e_4,X1)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_495,c_0_395]),
[final] ).
cnf(c_0_566,negated_conjecture,
( ~ product(X1,e_2,e_3)
| equalish(X1,e_4)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_496,c_0_427]),
[final] ).
cnf(c_0_567,negated_conjecture,
( ~ product(e_4,X1,e_3)
| equalish(X1,e_2)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_417,c_0_466]),
[final] ).
cnf(c_0_568,negated_conjecture,
( ~ product(X1,e_1,e_2)
| equalish(X1,e_4)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_92,c_0_466]),
[final] ).
cnf(c_0_569,negated_conjecture,
( ~ product(e_4,e_1,X1)
| equalish(X1,e_2)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_362,c_0_466]),
[final] ).
cnf(c_0_570,negated_conjecture,
( ~ product(e_4,X1,e_2)
| equalish(X1,e_1)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_89,c_0_466]),
[final] ).
cnf(c_0_571,negated_conjecture,
( ~ product(e_4,e_3,X1)
| equalish(X1,e_1)
| product(e_3,e_3,e_1)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_362,c_0_446]),
[final] ).
cnf(c_0_572,negated_conjecture,
( ~ product(e_4,X1,e_1)
| equalish(X1,e_3)
| product(e_3,e_3,e_1)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_89,c_0_446]),
[final] ).
cnf(c_0_573,negated_conjecture,
( ~ product(e_4,e_1,e_3)
| product(e_3,e_3,e_1)
| product(e_3,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_489,c_0_446]),c_0_106]),
[final] ).
cnf(c_0_574,negated_conjecture,
( ~ product(X1,e_1,e_3)
| equalish(e_2,X1)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_497,c_0_341]),
[final] ).
cnf(c_0_575,negated_conjecture,
( ~ product(X1,e_1,e_3)
| product(X1,e_4,e_1)
| product(e_4,e_2,e_1)
| product(e_4,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_498,c_0_354]),
[final] ).
cnf(c_0_576,negated_conjecture,
( ~ product(e_4,e_1,e_3)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_387,c_0_354]),c_0_117]),
[final] ).
cnf(c_0_577,negated_conjecture,
( ~ next(e_4,X1)
| ~ greater(e_0,e_0)
| equalish(e_2,X1)
| product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_499,c_0_337]),
[final] ).
cnf(c_0_578,negated_conjecture,
( ~ product(X1,e_1,e_3)
| product(X1,e_4,e_1)
| product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_500,c_0_354]),
[final] ).
cnf(c_0_579,negated_conjecture,
( ~ product(X1,e_2,e_4)
| product(X1,e_4,e_3)
| product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_491,c_0_467]),
[final] ).
cnf(c_0_580,negated_conjecture,
( ~ product(X1,e_1,e_4)
| product(X1,e_4,e_2)
| product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_84,c_0_467]),
[final] ).
cnf(c_0_581,negated_conjecture,
( ~ product(X1,e_1,e_2)
| equalish(e_4,X1)
| product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_501,c_0_395]),
[final] ).
cnf(c_0_582,negated_conjecture,
( ~ product(X1,e_2,e_3)
| equalish(X1,e_4)
| product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_502,c_0_427]),
[final] ).
cnf(c_0_583,negated_conjecture,
( ~ product(e_4,X1,e_3)
| equalish(X1,e_2)
| product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_417,c_0_467]),
[final] ).
cnf(c_0_584,negated_conjecture,
( ~ product(X1,e_1,e_2)
| equalish(X1,e_4)
| product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_92,c_0_467]),
[final] ).
cnf(c_0_585,negated_conjecture,
( ~ product(e_4,e_1,X1)
| equalish(X1,e_2)
| product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_362,c_0_467]),
[final] ).
cnf(c_0_586,negated_conjecture,
( ~ product(e_4,X1,e_2)
| equalish(X1,e_1)
| product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_89,c_0_467]),
[final] ).
cnf(c_0_587,negated_conjecture,
( ~ product(e_4,e_3,X1)
| equalish(X1,e_1)
| product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_362,c_0_447]),
[final] ).
cnf(c_0_588,negated_conjecture,
( ~ product(e_4,X1,e_1)
| equalish(X1,e_3)
| product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_89,c_0_447]),
[final] ).
cnf(c_0_589,negated_conjecture,
( ~ product(e_4,e_1,e_3)
| product(e_2,e_4,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_489,c_0_447]),c_0_106]),
[final] ).
cnf(c_0_590,negated_conjecture,
( ~ product(X1,e_1,e_2)
| equalish(e_4,X1)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_503,c_0_395]),
[final] ).
cnf(c_0_591,negated_conjecture,
( ~ product(X1,e_2,e_3)
| equalish(X1,e_4)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_504,c_0_427]),
[final] ).
cnf(c_0_592,negated_conjecture,
( ~ product(e_4,e_3,X1)
| equalish(X1,e_1)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_362,c_0_468]),
[final] ).
cnf(c_0_593,negated_conjecture,
( ~ product(e_4,e_1,e_3)
| product(e_1,e_4,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_489,c_0_468]),c_0_106]),
[final] ).
cnf(c_0_594,negated_conjecture,
( ~ next(e_4,X1)
| ~ greater(e_0,e_0)
| equalish(e_2,X1)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_505,c_0_337]),
[final] ).
cnf(c_0_595,negated_conjecture,
( ~ product(X1,e_1,e_3)
| product(X1,e_4,e_1)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_506,c_0_354]),
[final] ).
cnf(c_0_596,negated_conjecture,
( ~ product(X1,e_2,e_4)
| product(X1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_491,c_0_431]),
[final] ).
cnf(c_0_597,negated_conjecture,
( ~ product(X1,e_1,e_4)
| product(X1,e_4,e_2)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_84,c_0_431]),
[final] ).
cnf(c_0_598,negated_conjecture,
( ~ product(e_4,X1,e_1)
| equalish(X1,e_3)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_492,c_0_431]),
[final] ).
cnf(c_0_599,negated_conjecture,
( ~ product(e_4,X1,e_3)
| equalish(X1,e_2)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_417,c_0_431]),
[final] ).
cnf(c_0_600,negated_conjecture,
( ~ product(X1,e_1,e_2)
| equalish(X1,e_4)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_92,c_0_431]),
[final] ).
cnf(c_0_601,negated_conjecture,
( ~ product(e_4,e_1,X1)
| equalish(X1,e_2)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_362,c_0_431]),
[final] ).
cnf(c_0_602,negated_conjecture,
( ~ product(e_4,X1,e_2)
| equalish(X1,e_1)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_89,c_0_431]),
[final] ).
cnf(c_0_603,negated_conjecture,
( ~ product(X1,e_3,e_3)
| equalish(X1,e_3)
| product(e_3,e_3,e_1)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_92,c_0_407]),
[final] ).
cnf(c_0_604,negated_conjecture,
( ~ product(e_3,e_3,X1)
| equalish(X1,e_3)
| product(e_3,e_3,e_1)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_362,c_0_407]),
[final] ).
cnf(c_0_605,negated_conjecture,
( ~ product(e_3,X1,e_3)
| equalish(X1,e_3)
| product(e_3,e_3,e_1)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_89,c_0_407]),
[final] ).
cnf(c_0_606,negated_conjecture,
( ~ product(e_4,e_2,X1)
| equalish(X1,e_3)
| product(e_2,e_1,e_1)
| product(e_4,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_362,c_0_507]),
[final] ).
cnf(c_0_607,negated_conjecture,
( ~ product(X1,e_2,e_3)
| equalish(e_4,X1)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_462,c_0_366]),
[final] ).
cnf(c_0_608,negated_conjecture,
( ~ product(X1,e_1,e_2)
| equalish(e_4,X1)
| product(e_4,e_2,e_1)
| product(e_4,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_508,c_0_242]),
[final] ).
cnf(c_0_609,negated_conjecture,
( ~ product(X1,e_1,e_2)
| equalish(X1,e_4)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_509,c_0_395]),
[final] ).
cnf(c_0_610,plain,
( ~ next(e_1,X1)
| cycle(e_2,e_1)
| equalish(e_2,X1) ),
inference(spm,[status(thm)],[c_0_510,c_0_412]),
[final] ).
cnf(c_0_611,plain,
( ~ next(e_4,X1)
| ~ cycle(X1,e_1)
| cycle(e_2,e_1) ),
inference(spm,[status(thm)],[c_0_511,c_0_512]),
[final] ).
cnf(c_0_612,negated_conjecture,
( ~ next(e_2,X1)
| cycle(e_2,e_1)
| equalish(e_3,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_513,c_0_450]),c_0_72])]),
[final] ).
cnf(c_0_613,plain,
( ~ cycle(e_2,X1)
| cycle(e_2,e_1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_485,c_0_450]),
[final] ).
cnf(c_0_614,plain,
( ~ next(e_4,X1)
| ~ cycle(X1,e_0) ),
inference(spm,[status(thm)],[c_0_514,c_0_81]),
[final] ).
cnf(c_0_615,negated_conjecture,
( ~ next(e_3,X1)
| equalish(e_4,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_515,c_0_412]),c_0_81])]),
[final] ).
cnf(c_0_616,plain,
( ~ cycle(e_3,X1)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_485,c_0_412]),
[final] ).
cnf(c_0_617,negated_conjecture,
( ~ product(X1,e_2,e_2)
| equalish(X1,e_4)
| product(e_4,e_2,e_1)
| product(e_4,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_92,c_0_376]),
[final] ).
cnf(c_0_618,negated_conjecture,
( ~ product(e_4,e_2,X1)
| equalish(X1,e_2)
| product(e_4,e_2,e_1)
| product(e_4,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_362,c_0_376]),
[final] ).
cnf(c_0_619,negated_conjecture,
( ~ product(e_4,X1,e_2)
| equalish(X1,e_2)
| product(e_4,e_2,e_1)
| product(e_4,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_89,c_0_376]),
[final] ).
cnf(c_0_620,negated_conjecture,
( ~ product(X1,e_3,e_1)
| equalish(X1,e_4)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_92,c_0_366]),
[final] ).
cnf(c_0_621,negated_conjecture,
( ~ product(e_4,e_3,X1)
| equalish(X1,e_1)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_362,c_0_366]),
[final] ).
cnf(c_0_622,negated_conjecture,
( ~ product(e_4,X1,e_1)
| equalish(X1,e_3)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_89,c_0_366]),
[final] ).
cnf(c_0_623,negated_conjecture,
( ~ next(e_4,X1)
| ~ greater(e_0,e_0)
| equalish(e_2,X1)
| product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_516,c_0_337]),
[final] ).
cnf(c_0_624,plain,
( ~ next(e_0,X1)
| equalish(e_1,X1)
| product(e_3,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_517,c_0_337]),
[final] ).
cnf(c_0_625,negated_conjecture,
( ~ product(X1,e_1,e_2)
| equalish(e_4,X1)
| product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_518,c_0_395]),
[final] ).
cnf(c_0_626,negated_conjecture,
( ~ product(X1,e_2,e_3)
| equalish(X1,e_4)
| product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_519,c_0_427]),
[final] ).
cnf(c_0_627,negated_conjecture,
( ~ product(e_4,e_3,X1)
| equalish(X1,e_1)
| product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_362,c_0_473]),
[final] ).
cnf(c_0_628,negated_conjecture,
( ~ product(e_4,e_1,e_3)
| product(e_2,e_2,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_489,c_0_473]),c_0_106]),
[final] ).
cnf(c_0_629,negated_conjecture,
( ~ product(X1,e_1,e_3)
| product(X1,e_4,e_1)
| product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_520,c_0_354]),
[final] ).
cnf(c_0_630,negated_conjecture,
( ~ product(X1,e_2,e_4)
| product(X1,e_4,e_3)
| product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_491,c_0_436]),
[final] ).
cnf(c_0_631,negated_conjecture,
( ~ product(X1,e_1,e_2)
| equalish(e_4,X1)
| product(e_4,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_521,c_0_395]),
[final] ).
cnf(c_0_632,negated_conjecture,
( ~ product(X1,e_2,e_3)
| equalish(X1,e_4)
| product(e_4,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_522,c_0_427]),
[final] ).
cnf(c_0_633,negated_conjecture,
( ~ product(e_4,e_3,X1)
| equalish(X1,e_1)
| product(e_4,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_362,c_0_474]),
[final] ).
cnf(c_0_634,negated_conjecture,
( ~ product(e_4,e_1,e_3)
| product(e_4,e_1,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_489,c_0_474]),c_0_106]),
[final] ).
cnf(c_0_635,negated_conjecture,
( ~ product(X1,e_1,e_4)
| product(X1,e_4,e_2)
| product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_84,c_0_436]),
[final] ).
cnf(c_0_636,negated_conjecture,
( ~ product(e_4,X1,e_1)
| equalish(X1,e_3)
| product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_492,c_0_436]),
[final] ).
cnf(c_0_637,negated_conjecture,
( ~ product(e_4,X1,e_3)
| equalish(X1,e_2)
| product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_417,c_0_436]),
[final] ).
cnf(c_0_638,negated_conjecture,
( ~ product(X1,e_1,e_2)
| equalish(X1,e_4)
| product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_92,c_0_436]),
[final] ).
cnf(c_0_639,negated_conjecture,
( ~ product(e_4,e_1,X1)
| equalish(X1,e_2)
| product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_362,c_0_436]),
[final] ).
cnf(c_0_640,negated_conjecture,
( ~ product(e_4,X1,e_2)
| equalish(X1,e_1)
| product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_89,c_0_436]),
[final] ).
cnf(c_0_641,negated_conjecture,
( ~ product(e_4,e_1,e_3)
| product(e_4,e_2,e_1)
| product(e_4,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_523,c_0_242]),
[final] ).
cnf(c_0_642,negated_conjecture,
( ~ product(X1,e_1,e_3)
| product(X1,e_4,e_1)
| product(e_4,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_524,c_0_354]),
[final] ).
cnf(c_0_643,negated_conjecture,
( ~ product(e_4,e_1,e_3)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_525,c_0_354]),c_0_67]),
[final] ).
cnf(c_0_644,negated_conjecture,
( ~ product(X1,e_2,e_4)
| product(X1,e_4,e_3)
| product(e_4,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_491,c_0_283]),
[final] ).
cnf(c_0_645,negated_conjecture,
( ~ next(e_4,X1)
| ~ greater(e_0,e_0)
| equalish(e_2,X1)
| product(e_4,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_526,c_0_337]),
[final] ).
cnf(c_0_646,negated_conjecture,
( ~ product(e_4,X1,e_1)
| equalish(X1,e_3)
| product(e_4,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_492,c_0_283]),
[final] ).
cnf(c_0_647,negated_conjecture,
( ~ product(X1,e_1,e_3)
| equalish(e_2,X1)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_497,c_0_527]),
[final] ).
cnf(c_0_648,negated_conjecture,
( ~ product(X1,e_1,e_3)
| equalish(e_2,X1)
| product(e_2,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_497,c_0_528]),
[final] ).
cnf(c_0_649,negated_conjecture,
( ~ product(X1,e_3,e_4)
| equalish(X1,e_2)
| product(e_2,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_92,c_0_528]),
[final] ).
cnf(c_0_650,negated_conjecture,
( ~ product(e_2,e_3,X1)
| equalish(X1,e_4)
| product(e_2,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_362,c_0_528]),
[final] ).
cnf(c_0_651,negated_conjecture,
( ~ product(e_2,e_2,X1)
| equalish(X1,e_2)
| product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_362,c_0_380]),
[final] ).
cnf(c_0_652,negated_conjecture,
( ~ product(e_2,X1,e_2)
| equalish(X1,e_2)
| product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_89,c_0_380]),
[final] ).
cnf(c_0_653,negated_conjecture,
( ~ product(e_2,X1,e_4)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_529,c_0_309]),
[final] ).
cnf(c_0_654,negated_conjecture,
( ~ product(X1,e_1,e_2)
| ~ product(X1,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_523,c_0_395]),
[final] ).
cnf(c_0_655,negated_conjecture,
( ~ product(X2,e_2,X1)
| ~ product(X2,e_1,e_2)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_362,c_0_395]),
[final] ).
cnf(c_0_656,negated_conjecture,
( ~ product(X1,e_4,e_2)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_92,c_0_353]),
[final] ).
cnf(c_0_657,negated_conjecture,
( ~ product(e_3,e_4,X1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_362,c_0_353]),
[final] ).
cnf(c_0_658,negated_conjecture,
( ~ product(e_3,X1,e_2)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_89,c_0_353]),
[final] ).
cnf(c_0_659,negated_conjecture,
( ~ product(X1,e_2,e_3)
| product(X1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_281,c_0_427]),
[final] ).
cnf(c_0_660,negated_conjecture,
( ~ product(X1,e_4,e_2)
| product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_84,c_0_312]),
[final] ).
cnf(c_0_661,negated_conjecture,
( ~ product(X1,e_1,e_4)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_92,c_0_317]),
[final] ).
cnf(c_0_662,negated_conjecture,
( ~ product(e_3,e_1,X1)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_362,c_0_317]),
[final] ).
cnf(c_0_663,negated_conjecture,
( ~ product(X1,e_4,e_1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_92,c_0_312]),
[final] ).
cnf(c_0_664,negated_conjecture,
( ~ product(e_2,e_4,X1)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_362,c_0_312]),
[final] ).
cnf(c_0_665,negated_conjecture,
( ~ product(X1,e_1,e_3)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_92,c_0_309]),
[final] ).
cnf(c_0_666,negated_conjecture,
( ~ product(e_2,e_1,X1)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_362,c_0_309]),
[final] ).
cnf(c_0_667,negated_conjecture,
( ~ product(X1,e_4,e_3)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_92,c_0_289]),
[final] ).
cnf(c_0_668,negated_conjecture,
( ~ product(e_1,e_4,X1)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_362,c_0_289]),
[final] ).
cnf(c_0_669,negated_conjecture,
( ~ product(X1,e_1,e_2)
| equalish(X1,e_4)
| product(e_4,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_92,c_0_283]),
[final] ).
cnf(c_0_670,negated_conjecture,
( ~ product(e_4,e_1,X1)
| equalish(X1,e_2)
| product(e_4,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_362,c_0_283]),
[final] ).
cnf(c_0_671,negated_conjecture,
( ~ product(e_4,X1,e_2)
| equalish(X1,e_1)
| product(e_4,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_89,c_0_283]),
[final] ).
cnf(c_0_672,negated_conjecture,
( ~ product(e_1,e_3,X1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_362,c_0_280]),
[final] ).
cnf(c_0_673,negated_conjecture,
( ~ product(e_1,X1,e_2)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_89,c_0_280]),
[final] ).
cnf(c_0_674,negated_conjecture,
( ~ product(e_4,e_2,X1)
| equalish(X1,e_3)
| product(e_4,e_1,e_1)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_362,c_0_530]),
[final] ).
cnf(c_0_675,negated_conjecture,
( ~ product(X1,e_3,e_4)
| equalish(X1,e_2)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_92,c_0_527]),
[final] ).
cnf(c_0_676,negated_conjecture,
( ~ product(e_2,e_3,X1)
| equalish(X1,e_4)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_362,c_0_527]),
[final] ).
cnf(c_0_677,negated_conjecture,
( ~ product(e_1,e_2,X1)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_362,c_0_241]),
[final] ).
cnf(c_0_678,plain,
( ~ next(e_4,e_1)
| cycle(e_1,e_3)
| cycle(e_1,e_2)
| cycle(e_1,e_1)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_531,c_0_64]),
[final] ).
cnf(c_0_679,plain,
( ~ next(e_4,e_4)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_531,c_0_337]),
[final] ).
cnf(c_0_680,negated_conjecture,
( ~ next(e_1,X1)
| ~ greater(e_0,e_0)
| cycle(e_1,e_3)
| cycle(e_1,e_2)
| cycle(e_1,e_1)
| equalish(e_1,X1) ),
inference(spm,[status(thm)],[c_0_532,c_0_64]),
[final] ).
cnf(c_0_681,negated_conjecture,
( ~ greater(e_1,e_1)
| cycle(e_1,e_3)
| cycle(e_1,e_2)
| cycle(e_1,e_1) ),
inference(spm,[status(thm)],[c_0_533,c_0_64]),
[final] ).
cnf(c_0_682,negated_conjecture,
( ~ product(e_1,e_1,X1)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_362,c_0_168]),
[final] ).
cnf(c_0_683,negated_conjecture,
( ~ product(e_4,e_2,X1)
| equalish(X1,e_3)
| product(e_4,e_2,e_1)
| product(e_4,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_362,c_0_242]),
[final] ).
cnf(c_0_684,negated_conjecture,
( ~ product(e_4,X1,e_3)
| equalish(X1,e_2)
| product(e_4,e_2,e_1)
| product(e_4,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_89,c_0_242]),
[final] ).
cnf(c_0_685,plain,
( ~ product(X1,e_3,e_4)
| equalish(X1,e_2)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_92,c_0_341]),
[final] ).
cnf(c_0_686,plain,
( ~ product(e_2,e_3,X1)
| equalish(X1,e_4)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_362,c_0_341]),
[final] ).
cnf(c_0_687,plain,
( ~ product(e_4,e_4,X1)
| equalish(X1,e_4)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_362,c_0_110]),
[final] ).
cnf(c_0_688,plain,
( ~ next(e_1,X2)
| ~ greater(X1,X3)
| ~ cycle(X2,X3)
| ~ cycle(e_0,X1)
| cycle(e_1,e_1)
| cycle(e_1,e_2)
| cycle(e_1,e_3) ),
inference(spm,[status(thm)],[c_0_534,c_0_81]),
[final] ).
cnf(c_0_689,plain,
( ~ cycle(e_1,X1)
| cycle(e_1,e_3)
| cycle(e_1,e_2)
| cycle(e_1,e_1)
| equalish(X1,e_0) ),
inference(spm,[status(thm)],[c_0_485,c_0_64]),
[final] ).
cnf(c_0_690,plain,
( ~ next(e_4,X1)
| ~ greater(e_0,X2)
| ~ cycle(X1,X2)
| cycle(e_1,e_3)
| cycle(e_1,e_2)
| cycle(e_1,e_1) ),
inference(spm,[status(thm)],[c_0_535,c_0_64]),
[final] ).
cnf(c_0_691,plain,
( ~ next(X2,X3)
| ~ next(X4,X1)
| ~ cycle(X3,X4)
| ~ cycle(X2,e_4)
| equalish(e_4,X1) ),
inference(spm,[status(thm)],[c_0_320,c_0_536]),
[final] ).
cnf(c_0_692,plain,
( ~ next(e_4,X2)
| ~ greater(X1,X3)
| ~ cycle(X2,X3)
| ~ cycle(e_0,X1) ),
inference(spm,[status(thm)],[c_0_439,c_0_536]),
[final] ).
cnf(c_0_693,plain,
~ cycle(e_4,e_1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_537,c_0_74]),c_0_101]),
[final] ).
cnf(c_0_694,plain,
~ cycle(e_4,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_537,c_0_66]),c_0_165]),
[final] ).
cnf(c_0_695,plain,
~ cycle(e_4,e_3),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_537,c_0_331]),c_0_106]),
[final] ).
cnf(c_0_696,negated_conjecture,
~ product(e_1,e_1,e_3),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_538,c_0_354]),c_0_162]),
[final] ).
cnf(c_0_697,negated_conjecture,
~ product(e_1,e_2,e_3),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_427]),c_0_184]),
[final] ).
cnf(c_0_698,negated_conjecture,
~ product(e_2,e_2,e_3),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_539,c_0_427]),c_0_117]),
[final] ).
cnf(c_0_699,negated_conjecture,
~ product(e_3,e_2,e_3),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_540,c_0_427]),c_0_162]),
[final] ).
cnf(c_0_700,negated_conjecture,
~ product(e_1,e_1,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_541,c_0_395]),c_0_124]),
[final] ).
cnf(c_0_701,negated_conjecture,
~ greater(e_2,e_4),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_542]),c_0_98]),
[final] ).
cnf(c_0_702,plain,
equalish(e_1,e_1),
inference(spm,[status(thm)],[c_0_543,c_0_481]),
[final] ).
cnf(c_0_703,plain,
equalish(e_2,e_2),
inference(spm,[status(thm)],[c_0_544,c_0_482]),
[final] ).
cnf(c_0_704,plain,
equalish(e_3,e_3),
inference(spm,[status(thm)],[c_0_545,c_0_483]),
[final] ).
cnf(c_0_705,plain,
equalish(e_4,e_4),
inference(spm,[status(thm)],[c_0_546,c_0_484]),
[final] ).
cnf(c_0_706,plain,
equalish(e_0,e_0),
inference(spm,[status(thm)],[c_0_547,c_0_337]),
[final] ).
cnf(c_0_707,axiom,
greater(e_3,e_1),
e_3_greater_e_1,
[final] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP128-3.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 % Computer : n014.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sun Sep 20 20:00:21 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.86/0.68 % Version: 3.5.1
% 1.86/0.68 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.86/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.86/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.86/0.68 % Starting new_bool_3 with 300s (1) cores
% 1.86/0.68 % Starting new_bool_1 with 300s (1) cores
% 1.86/0.68 % Starting sh5l with 300s (1) cores
% 1.86/0.68 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2222283 completed with status 1
% 1.86/0.68 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 1.86/0.68 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.86/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.86/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.86/0.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.86/0.68 % No SInE strategy applied
% 1.86/0.68 % Search class: FGHNF-FFMM00-SFFFFFNN
% 1.86/0.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.86/0.68 % Starting SubtermCWHack with 136s (1) cores
% 1.86/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.86/0.68 % Starting H----_011_C07_F1_PI_AE_OS_R8_SP_S1U with 136s (1) cores
% 1.86/0.68 % Starting G----_425_C05_02_F1_SE_CS_SP_PS_RG_S04AI with 136s (1) cores
% 1.86/0.68 % Starting G-E--_208_B07--C_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.86/0.68 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2222288 completed with status 1
% 1.86/0.68 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 1.86/0.68 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.86/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.86/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.86/0.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.86/0.68 % No SInE strategy applied
% 1.86/0.68 % Search class: FGHNF-FFMM00-SFFFFFNN
% 1.86/0.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.86/0.68 % Starting SubtermCWHack with 136s (1) cores
% 1.86/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.86/0.68 % Preprocessing time : 0.001 s
% 1.86/0.68 % Presaturation interreduction done
% 1.86/0.68
% 1.86/0.68 % No proof found!
% 1.86/0.68 % SZS status Satisfiable
% 1.86/0.68 % SZS output start Saturation
% See solution above
% 1.86/0.68 % Parsed axioms : 42
% 1.86/0.68 % Removed by relevancy pruning/SinE : 0
% 1.86/0.68 % Initial clauses : 42
% 1.86/0.68 % Removed in clause preprocessing : 0
% 1.86/0.68 % Initial clauses in saturation : 42
% 1.86/0.68 % Processed clauses : 2247
% 1.86/0.68 % ...of these trivial : 4
% 1.86/0.68 % ...subsumed : 717
% 1.86/0.68 % ...remaining for further processing : 1526
% 1.86/0.68 % Other redundant clauses eliminated : 0
% 1.86/0.68 % Clauses deleted for lack of memory : 0
% 1.86/0.68 % Backward-subsumed : 999
% 1.86/0.68 % Backward-rewritten : 133
% 1.86/0.68 % Generated clauses : 10260
% 1.86/0.68 % ...of the previous two non-redundant : 6385
% 1.86/0.68 % ...aggressively subsumed : 0
% 1.86/0.68 % Contextual simplify-reflections : 19
% 1.86/0.68 % Paramodulations : 10245
% 1.86/0.68 % Factorizations : 0
% 1.86/0.68 % NegExts : 0
% 1.86/0.68 % Equation resolutions : 0
% 1.86/0.68 % Disequality decompositions : 0
% 1.86/0.68 % Total rewrite steps : 4055
% 1.86/0.68 % ...of those cached : 4030
% 1.86/0.68 % Propositional unsat checks : 0
% 1.86/0.68 % Propositional check models : 0
% 1.86/0.68 % Propositional check unsatisfiable : 0
% 1.86/0.68 % Propositional clauses : 0
% 1.86/0.68 % Propositional clauses after purity: 0
% 1.86/0.68 % Propositional unsat core size : 0
% 1.86/0.68 % Propositional preprocessing time : 0.000
% 1.86/0.68 % Propositional encoding time : 0.000
% 1.86/0.68 % Propositional solver time : 0.000
% 1.86/0.68 % Success case prop preproc time : 0.000
% 1.86/0.68 % Success case prop encoding time : 0.000
% 1.86/0.68 % Success case prop solver time : 0.000
% 1.86/0.68 % Current number of processed clauses : 337
% 1.86/0.68 % Positive orientable unit clauses : 34
% 1.86/0.68 % Positive unorientable unit clauses: 0
% 1.86/0.68 % Negative unit clauses : 26
% 1.86/0.68 % Non-unit-clauses : 277
% 1.86/0.68 % Current number of unprocessed clauses: 0
% 1.86/0.68 % ...number of literals in the above : 0
% 1.86/0.68 % Current number of archived formulas : 0
% 1.86/0.68 % Current number of archived clauses : 1189
% 1.86/0.68 % Clause-clause subsumption calls (NU) : 132472
% 1.86/0.68 % Rec. Clause-clause subsumption calls : 32848
% 1.86/0.68 % Non-unit clause-clause subsumptions : 1676
% 1.86/0.68 % Unit Clause-clause subsumption calls : 3096
% 1.86/0.68 % Rewrite failures with RHS unbound : 0
% 1.86/0.68 % BW rewrite match attempts : 38
% 1.86/0.68 % BW rewrite match successes : 14
% 1.86/0.68 % Condensation attempts : 0
% 1.86/0.68 % Condensation successes : 0
% 1.86/0.68 % Termbank termtop insertions : 204762
% 1.86/0.68 % Search garbage collected termcells : 98
% 1.86/0.68
% 1.86/0.68 % -------------------------------------------------
% 1.86/0.68 % User time : 0.224 s
% 1.86/0.68 % System time : 0.008 s
% 1.86/0.68 % Total time : 0.232 s
% 1.86/0.68 % Maximum resident set size: 3656 pages
% 1.86/0.68
% 1.86/0.68 % -------------------------------------------------
% 1.86/0.68 % User time : 1.078 s
% 1.86/0.68 % System time : 0.028 s
% 1.86/0.68 % Total time : 1.106 s
% 1.86/0.68 % Maximum resident set size: 4864 pages
% 1.86/0.68 % E exiting
%------------------------------------------------------------------------------