%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP130-2.005 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 12:38:40 PM UTC 2026
% Result : Satisfiable 3.01s 1.16s
% Output : Saturation 3.01s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_45ERROR: Could not build tree for root c_0_57ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(c_0_47,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_5)
| product(X1,X2,e_4)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
c_0_45,
[final] ).
cnf(c_0_48,axiom,
group_element(e_1),
element_1,
[final] ).
cnf(c_0_49,plain,
( ~ greater(X2,X3)
| ~ next(X1,X3)
| ~ product(X1,e_1,X2) ),
c_0_46,
[final] ).
cnf(c_0_50,axiom,
greater(e_5,e_2),
e_5_greater_e_2,
[final] ).
cnf(c_0_51,axiom,
greater(e_3,e_2),
e_3_greater_e_2,
[final] ).
cnf(c_0_52,axiom,
greater(e_4,e_2),
e_4_greater_e_2,
[final] ).
cnf(c_0_53,axiom,
group_element(e_2),
element_2,
[final] ).
cnf(c_0_57,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)
| product(X1,e_1,e_5) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]),
[final] ).
cnf(c_0_58,plain,
( ~ next(X1,e_2)
| ~ product(X1,e_1,e_5) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]),
[final] ).
cnf(c_0_59,axiom,
next(e_1,e_2),
e_1_then_e_2,
[final] ).
cnf(c_0_60,plain,
( ~ next(X1,e_2)
| ~ product(X1,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_49,c_0_51]),
[final] ).
cnf(c_0_61,plain,
( ~ next(X1,e_2)
| ~ product(X1,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_49,c_0_52]),
[final] ).
cnf(c_0_63,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)
| product(X1,e_2,e_5) ),
inference(spm,[status(thm)],[c_0_47,c_0_53]),
[final] ).
cnf(c_0_64,plain,
~ equalish(e_2,e_1),
c_0_54,
[final] ).
cnf(c_0_65,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
c_0_55,
[final] ).
cnf(c_0_66,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
c_0_56,
[final] ).
cnf(c_0_68,plain,
~ product(e_1,e_1,e_5),
inference(spm,[status(thm)],[c_0_58,c_0_59]),
[final] ).
cnf(c_0_69,plain,
~ product(e_1,e_1,e_3),
inference(spm,[status(thm)],[c_0_60,c_0_59]),
[final] ).
cnf(c_0_70,plain,
~ product(e_1,e_1,e_4),
inference(spm,[status(thm)],[c_0_61,c_0_59]),
[final] ).
cnf(c_0_72,negated_conjecture,
( ~ product(X1,X3,X4)
| ~ product(X1,X2,X3)
| product(X4,X2,X1) ),
c_0_62,
[final] ).
cnf(c_0_74,plain,
( ~ product(X1,X2,e_2)
| ~ product(X1,X2,e_1) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]),
[final] ).
cnf(c_0_75,plain,
( ~ product(X1,e_2,X2)
| ~ product(X1,e_1,X2) ),
inference(spm,[status(thm)],[c_0_64,c_0_66]),
[final] ).
cnf(c_0_76,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_67,c_0_68]),c_0_69]),c_0_70]),
[final] ).
cnf(c_0_77,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
c_0_71,
[final] ).
cnf(c_0_78,axiom,
greater(e_5,e_3),
e_5_greater_e_3,
[final] ).
cnf(c_0_79,axiom,
greater(e_5,e_4),
e_5_greater_e_4,
[final] ).
cnf(c_0_83,plain,
( ~ product(e_2,X1,X2)
| ~ product(e_1,X1,X2) ),
inference(spm,[status(thm)],[c_0_64,c_0_77]),
[final] ).
cnf(c_0_84,plain,
( ~ next(X1,e_3)
| ~ product(X1,e_1,e_5) ),
inference(spm,[status(thm)],[c_0_49,c_0_78]),
[final] ).
cnf(c_0_85,axiom,
next(e_2,e_3),
e_2_then_e_3,
[final] ).
cnf(c_0_86,axiom,
greater(e_4,e_3),
e_4_greater_e_3,
[final] ).
cnf(c_0_87,axiom,
group_element(e_3),
element_3,
[final] ).
cnf(c_0_88,plain,
( ~ next(X1,e_4)
| ~ product(X1,e_1,e_5) ),
inference(spm,[status(thm)],[c_0_49,c_0_79]),
[final] ).
cnf(c_0_89,axiom,
next(e_3,e_4),
e_3_then_e_4,
[final] ).
cnf(c_0_91,plain,
~ equalish(e_2,e_5),
c_0_82,
[final] ).
cnf(c_0_94,plain,
~ product(e_2,e_1,e_5),
inference(spm,[status(thm)],[c_0_84,c_0_85]),
[final] ).
cnf(c_0_95,plain,
( ~ next(X1,e_3)
| ~ product(X1,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_49,c_0_86]),
[final] ).
cnf(c_0_97,plain,
~ product(e_3,e_1,e_5),
inference(spm,[status(thm)],[c_0_88,c_0_89]),
[final] ).
cnf(c_0_99,plain,
( ~ product(e_2,X1,X2)
| ~ product(e_5,X1,X2) ),
inference(spm,[status(thm)],[c_0_91,c_0_77]),
[final] ).
cnf(c_0_102,plain,
~ product(e_2,e_1,e_4),
inference(spm,[status(thm)],[c_0_95,c_0_85]),
[final] ).
cnf(c_0_107,axiom,
group_element(e_4),
element_4,
[final] ).
cnf(c_0_112,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)
| product(X1,e_4,e_5) ),
inference(spm,[status(thm)],[c_0_47,c_0_107]),
[final] ).
cnf(c_0_113,plain,
~ equalish(e_1,e_4),
c_0_108,
[final] ).
cnf(c_0_118,plain,
( ~ product(X1,e_1,X2)
| ~ product(X1,e_4,X2) ),
inference(spm,[status(thm)],[c_0_113,c_0_66]),
[final] ).
cnf(c_0_125,plain,
~ equalish(e_1,e_3),
c_0_120,
[final] ).
cnf(c_0_127,plain,
~ equalish(e_2,e_4),
c_0_121,
[final] ).
cnf(c_0_130,plain,
( ~ product(X1,X2,e_1)
| ~ product(X1,X2,e_3) ),
inference(spm,[status(thm)],[c_0_125,c_0_65]),
[final] ).
cnf(c_0_131,plain,
~ equalish(e_2,e_3),
c_0_126,
[final] ).
cnf(c_0_132,plain,
( ~ product(e_2,X1,X2)
| ~ product(e_4,X1,X2) ),
inference(spm,[status(thm)],[c_0_127,c_0_77]),
[final] ).
cnf(c_0_135,plain,
( ~ product(e_2,X1,X2)
| ~ product(e_3,X1,X2) ),
inference(spm,[status(thm)],[c_0_131,c_0_77]),
[final] ).
cnf(c_0_148,axiom,
group_element(e_5),
element_5,
[final] ).
cnf(c_0_149,plain,
~ equalish(e_1,e_5),
c_0_145,
[final] ).
cnf(c_0_151,plain,
~ equalish(e_4,e_5),
c_0_147,
[final] ).
cnf(c_0_152,plain,
( ~ group_element(X1)
| product(X1,e_5,e_1)
| product(X1,e_5,e_2)
| product(X1,e_5,e_3)
| product(X1,e_5,e_4)
| product(X1,e_5,e_5) ),
inference(spm,[status(thm)],[c_0_47,c_0_148]),
[final] ).
cnf(c_0_153,plain,
( ~ product(X1,e_1,X2)
| ~ product(X1,e_5,X2) ),
inference(spm,[status(thm)],[c_0_149,c_0_66]),
[final] ).
cnf(c_0_158,plain,
( ~ product(X1,e_4,X2)
| ~ product(X1,e_5,X2) ),
inference(spm,[status(thm)],[c_0_151,c_0_66]),
[final] ).
cnf(c_0_165,plain,
~ equalish(e_3,e_4),
c_0_161,
[final] ).
cnf(c_0_168,plain,
( ~ product(X1,X2,e_3)
| ~ product(X1,X2,e_4) ),
inference(spm,[status(thm)],[c_0_165,c_0_65]),
[final] ).
cnf(c_0_176,plain,
( ~ product(X1,e_2,X2)
| ~ product(X1,e_5,X2) ),
inference(spm,[status(thm)],[c_0_91,c_0_66]),
[final] ).
cnf(c_0_180,plain,
~ equalish(e_3,e_5),
c_0_177,
[final] ).
cnf(c_0_182,plain,
( ~ product(X1,X2,e_4)
| ~ product(X1,X2,e_5) ),
inference(spm,[status(thm)],[c_0_151,c_0_65]),
[final] ).
cnf(c_0_183,plain,
( ~ product(X1,X2,e_3)
| ~ product(X1,X2,e_5) ),
inference(spm,[status(thm)],[c_0_180,c_0_65]),
[final] ).
cnf(c_0_187,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)
| product(X1,e_3,e_5) ),
inference(spm,[status(thm)],[c_0_47,c_0_87]),
[final] ).
cnf(c_0_188,plain,
( ~ product(X1,e_1,X2)
| ~ product(X1,e_3,X2) ),
inference(spm,[status(thm)],[c_0_125,c_0_66]),
[final] ).
cnf(c_0_193,plain,
( ~ product(X1,e_3,X2)
| ~ product(X1,e_4,X2) ),
inference(spm,[status(thm)],[c_0_165,c_0_66]),
[final] ).
cnf(c_0_203,negated_conjecture,
~ product(e_2,e_5,e_3),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_160]),c_0_176]),c_0_200]),
[final] ).
cnf(c_0_205,plain,
( ~ product(X1,e_2,X2)
| ~ product(X1,e_3,X2) ),
inference(spm,[status(thm)],[c_0_131,c_0_66]),
[final] ).
cnf(c_0_207,plain,
( ~ product(X1,e_3,X2)
| ~ product(X1,e_5,X2) ),
inference(spm,[status(thm)],[c_0_180,c_0_66]),
[final] ).
cnf(c_0_210,negated_conjecture,
~ product(e_2,e_3,e_3),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_191]),c_0_205]),c_0_206]),
[final] ).
cnf(c_0_217,plain,
( ~ product(e_3,X1,X2)
| ~ product(e_5,X1,X2) ),
inference(spm,[status(thm)],[c_0_180,c_0_77]),
[final] ).
cnf(c_0_224,negated_conjecture,
product(e_2,e_2,e_2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_156]),c_0_219]),
[final] ).
cnf(c_0_226,plain,
( ~ product(X1,X2,e_2)
| ~ product(X1,X2,e_5) ),
inference(spm,[status(thm)],[c_0_91,c_0_65]),
[final] ).
cnf(c_0_228,plain,
( ~ product(X1,X2,e_2)
| ~ product(X1,X2,e_4) ),
inference(spm,[status(thm)],[c_0_127,c_0_65]),
[final] ).
cnf(c_0_231,negated_conjecture,
~ product(e_2,e_3,e_2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_226,c_0_227]),c_0_228]),
[final] ).
cnf(c_0_234,negated_conjecture,
~ product(e_2,e_4,e_2),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_229]),c_0_72]),c_0_193]),c_0_118]),
[final] ).
cnf(c_0_235,plain,
( ~ product(X1,e_2,X2)
| ~ product(X1,e_4,X2) ),
inference(spm,[status(thm)],[c_0_127,c_0_66]),
[final] ).
cnf(c_0_241,negated_conjecture,
~ product(e_2,e_4,e_3),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_140]),c_0_235]),c_0_236]),
[final] ).
cnf(c_0_245,negated_conjecture,
~ product(e_2,e_5,e_2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_226,c_0_230]),c_0_228]),
[final] ).
cnf(c_0_248,negated_conjecture,
~ product(e_2,e_4,e_4),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_238]),c_0_193]),
[final] ).
cnf(c_0_256,negated_conjecture,
~ product(e_2,e_4,e_5),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_249,c_0_250]),c_0_251]),
[final] ).
cnf(c_0_260,plain,
product(e_2,e_4,e_1),
inference(sr,[status(thm)],[c_0_255,c_0_256]),
[final] ).
cnf(c_0_268,negated_conjecture,
( ~ product(e_2,X1,e_4)
| product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_72,c_0_260]),
[final] ).
cnf(c_0_272,negated_conjecture,
( ~ product(e_1,X1,X2)
| ~ product(e_2,X2,e_4)
| product(e_2,X1,e_1) ),
inference(spm,[status(thm)],[c_0_72,c_0_268]),
[final] ).
cnf(c_0_273,negated_conjecture,
~ product(e_2,e_2,e_1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_269,c_0_227]),c_0_270]),
[final] ).
cnf(c_0_297,negated_conjecture,
~ product(e_2,e_2,e_4),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_216]),c_0_228]),
[final] ).
cnf(c_0_298,negated_conjecture,
product(e_2,e_5,e_4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_293]),c_0_224])]),
[final] ).
cnf(c_0_303,negated_conjecture,
~ product(e_2,e_3,e_4),
inference(spm,[status(thm)],[c_0_207,c_0_298]),
[final] ).
cnf(c_0_307,plain,
( ~ product(e_4,X1,X2)
| ~ product(e_5,X1,X2) ),
inference(spm,[status(thm)],[c_0_151,c_0_77]),
[final] ).
cnf(c_0_312,negated_conjecture,
~ product(e_4,e_1,e_2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_307,c_0_308]),c_0_132]),
[final] ).
cnf(c_0_314,plain,
( ~ product(e_1,X1,X2)
| ~ product(e_4,X1,X2) ),
inference(spm,[status(thm)],[c_0_113,c_0_77]),
[final] ).
cnf(c_0_319,negated_conjecture,
~ product(e_1,e_3,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_313,c_0_298])]),
[final] ).
cnf(c_0_323,plain,
( ~ product(e_3,X1,X2)
| ~ product(e_4,X1,X2) ),
inference(spm,[status(thm)],[c_0_165,c_0_77]),
[final] ).
cnf(c_0_325,negated_conjecture,
~ product(e_3,e_1,e_2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_217,c_0_308]),c_0_135]),
[final] ).
cnf(c_0_326,plain,
( ~ product(e_1,X1,X2)
| ~ product(e_3,X1,X2) ),
inference(spm,[status(thm)],[c_0_125,c_0_77]),
[final] ).
cnf(c_0_333,negated_conjecture,
product(e_2,e_3,e_5),
inference(sr,[status(thm)],[c_0_227,c_0_303]),
[final] ).
cnf(c_0_342,negated_conjecture,
( ~ product(e_4,X1,X2)
| ~ product(e_2,X2,e_5)
| product(e_2,X1,e_4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_332,c_0_333])]),
[final] ).
cnf(c_0_345,plain,
( ~ product(X1,X2,e_1)
| ~ product(X1,X2,e_4) ),
inference(spm,[status(thm)],[c_0_113,c_0_65]),
[final] ).
cnf(c_0_346,negated_conjecture,
product(e_4,e_3,e_2),
inference(sr,[status(thm)],[c_0_250,c_0_303]),
[final] ).
cnf(c_0_353,negated_conjecture,
~ product(e_3,e_3,e_4),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_344,c_0_336]),c_0_345]),
[final] ).
cnf(c_0_354,negated_conjecture,
~ product(e_3,e_3,e_2),
inference(spm,[status(thm)],[c_0_323,c_0_346]),
[final] ).
cnf(c_0_359,plain,
( ~ product(X1,X2,e_1)
| ~ product(X1,X2,e_5) ),
inference(spm,[status(thm)],[c_0_149,c_0_65]),
[final] ).
cnf(c_0_362,negated_conjecture,
~ product(e_3,e_3,e_1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_358]),c_0_359]),
[final] ).
cnf(c_0_365,negated_conjecture,
product(e_3,e_5,e_1),
inference(sr,[status(thm)],[c_0_361,c_0_362]),
[final] ).
cnf(c_0_372,negated_conjecture,
( ~ product(e_3,X1,e_5)
| product(e_1,X1,e_3) ),
inference(spm,[status(thm)],[c_0_72,c_0_365]),
[final] ).
cnf(c_0_373,negated_conjecture,
product(e_1,e_2,e_3),
inference(sr,[status(thm)],[c_0_366,c_0_362]),
[final] ).
cnf(c_0_374,plain,
( ~ product(X1,X2,e_2)
| ~ product(X1,X2,e_3) ),
inference(spm,[status(thm)],[c_0_131,c_0_65]),
[final] ).
cnf(c_0_383,negated_conjecture,
~ product(e_3,e_4,e_5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_372]),c_0_373])]),
[final] ).
cnf(c_0_385,negated_conjecture,
~ product(e_3,e_3,e_5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_205,c_0_372]),c_0_373])]),
[final] ).
cnf(c_0_402,negated_conjecture,
product(e_3,e_3,e_3),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_351,c_0_394]),c_0_385]),c_0_353]),c_0_354]),c_0_69]),
[final] ).
cnf(c_0_411,negated_conjecture,
product(e_3,e_4,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_401,c_0_402])]),
[final] ).
cnf(c_0_412,negated_conjecture,
~ product(e_3,e_2,e_4),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_387,c_0_403]),c_0_389]),
[final] ).
cnf(c_0_413,negated_conjecture,
~ product(e_3,e_2,e_3),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_404,c_0_405]),c_0_406]),c_0_75]),
[final] ).
cnf(c_0_415,negated_conjecture,
product(e_1,e_3,e_4),
inference(sr,[status(thm)],[c_0_408,c_0_362]),
[final] ).
cnf(c_0_416,negated_conjecture,
~ product(e_1,e_4,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_409,c_0_298])]),
[final] ).
cnf(c_0_423,negated_conjecture,
product(e_5,e_3,e_1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_420]),c_0_373])]),
[final] ).
cnf(c_0_426,negated_conjecture,
~ product(e_3,e_2,e_2),
inference(spm,[status(thm)],[c_0_235,c_0_411]),
[final] ).
cnf(c_0_428,negated_conjecture,
( ~ product(e_5,X1,e_3)
| product(e_1,X1,e_5) ),
inference(spm,[status(thm)],[c_0_72,c_0_423]),
[final] ).
cnf(c_0_429,negated_conjecture,
( ~ product(e_3,X1,e_4)
| product(e_2,X1,e_3) ),
inference(spm,[status(thm)],[c_0_72,c_0_411]),
[final] ).
cnf(c_0_433,negated_conjecture,
product(e_5,e_4,e_3),
inference(sr,[status(thm)],[c_0_425,c_0_426]),
[final] ).
cnf(c_0_435,negated_conjecture,
~ product(e_5,e_1,e_3),
inference(spm,[status(thm)],[c_0_68,c_0_428]),
[final] ).
cnf(c_0_436,negated_conjecture,
( ~ product(e_2,X1,e_3)
| product(e_5,X1,e_2) ),
inference(spm,[status(thm)],[c_0_72,c_0_333]),
[final] ).
cnf(c_0_444,negated_conjecture,
( ~ product(e_5,X1,e_4)
| product(e_3,X1,e_5) ),
inference(spm,[status(thm)],[c_0_72,c_0_433]),
[final] ).
cnf(c_0_446,plain,
( ~ product(e_1,X1,X2)
| ~ product(e_5,X1,X2) ),
inference(spm,[status(thm)],[c_0_149,c_0_77]),
[final] ).
cnf(c_0_448,negated_conjecture,
product(e_2,e_1,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_437]),c_0_402])]),
[final] ).
cnf(c_0_452,negated_conjecture,
~ product(e_3,e_2,e_1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_361]),c_0_205]),
[final] ).
cnf(c_0_457,negated_conjecture,
product(e_5,e_1,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_444,c_0_445]),c_0_97]),
[final] ).
cnf(c_0_458,negated_conjecture,
~ product(e_5,e_2,e_3),
inference(spm,[status(thm)],[c_0_446,c_0_373]),
[final] ).
cnf(c_0_459,negated_conjecture,
~ product(e_5,e_2,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_447,c_0_448])]),
[final] ).
cnf(c_0_461,negated_conjecture,
~ product(e_4,e_2,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_450,c_0_333])]),
[final] ).
cnf(c_0_462,negated_conjecture,
~ product(e_4,e_2,e_3),
inference(spm,[status(thm)],[c_0_314,c_0_373]),
[final] ).
cnf(c_0_463,negated_conjecture,
~ product(e_4,e_2,e_4),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_451,c_0_430]),c_0_452]),
[final] ).
cnf(c_0_464,negated_conjecture,
~ product(e_4,e_2,e_5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_453,c_0_365])]),
[final] ).
cnf(c_0_468,plain,
product(e_3,e_2,e_5),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_460,c_0_461]),c_0_412]),c_0_413]),c_0_426]),c_0_462]),c_0_463]),c_0_464]),
[final] ).
cnf(c_0_471,negated_conjecture,
product(e_5,e_2,e_4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_217,c_0_467]),c_0_468])]),
[final] ).
cnf(c_0_481,negated_conjecture,
( ~ product(e_5,X1,e_2)
| product(e_4,X1,e_5) ),
inference(spm,[status(thm)],[c_0_72,c_0_471]),
[final] ).
cnf(c_0_482,negated_conjecture,
( ~ product(e_1,X1,X2)
| ~ product(e_5,X2,e_3)
| product(e_5,X1,e_1) ),
inference(spm,[status(thm)],[c_0_72,c_0_428]),
[final] ).
cnf(c_0_483,negated_conjecture,
( ~ product(e_4,X1,e_2)
| product(e_1,X1,e_4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_472,c_0_365])]),
[final] ).
cnf(c_0_488,negated_conjecture,
~ product(e_5,e_5,e_2),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_395,c_0_476]),c_0_303]),c_0_446]),
[final] ).
cnf(c_0_496,negated_conjecture,
product(e_4,e_1,e_5),
inference(spm,[status(thm)],[c_0_481,c_0_457]),
[final] ).
cnf(c_0_498,negated_conjecture,
( ~ product(e_4,X1,e_5)
| product(e_3,X1,e_4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_484,c_0_402])]),
[final] ).
cnf(c_0_499,negated_conjecture,
~ product(e_4,e_4,e_1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_431]),c_0_235]),
[final] ).
cnf(c_0_504,negated_conjecture,
~ product(e_5,e_5,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_489,c_0_428]),c_0_433])]),
[final] ).
cnf(c_0_506,negated_conjecture,
~ product(e_4,e_1,e_1),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_490,c_0_491]),c_0_74]),c_0_492]),c_0_493]),
[final] ).
cnf(c_0_509,negated_conjecture,
~ product(e_4,e_4,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_483]),c_0_415])]),
[final] ).
cnf(c_0_510,negated_conjecture,
( ~ product(e_4,X1,e_1)
| product(e_5,X1,e_4) ),
inference(spm,[status(thm)],[c_0_72,c_0_496]),
[final] ).
cnf(c_0_511,negated_conjecture,
( ~ product(e_4,X1,e_2)
| product(e_5,X1,e_1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_497,c_0_433])]),
[final] ).
cnf(c_0_512,negated_conjecture,
product(e_3,e_1,e_4),
inference(spm,[status(thm)],[c_0_498,c_0_496]),
[final] ).
cnf(c_0_513,negated_conjecture,
( ~ product(e_1,X1,e_3)
| product(e_4,X1,e_1) ),
inference(spm,[status(thm)],[c_0_72,c_0_415]),
[final] ).
cnf(c_0_514,negated_conjecture,
( ~ product(e_1,X1,e_2)
| product(e_3,X1,e_1) ),
inference(spm,[status(thm)],[c_0_72,c_0_373]),
[final] ).
cnf(c_0_515,negated_conjecture,
( ~ product(e_2,X1,e_3)
| product(e_4,X1,e_5) ),
inference(spm,[status(thm)],[c_0_481,c_0_436]),
[final] ).
cnf(c_0_518,plain,
( product(e_5,e_5,e_4)
| product(e_5,e_5,e_5) ),
inference(sr,[status(thm)],[c_0_503,c_0_504]),
[final] ).
cnf(c_0_529,negated_conjecture,
~ product(e_3,e_4,e_4),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_382]),c_0_168]),c_0_228]),
[final] ).
cnf(c_0_530,negated_conjecture,
product(e_4,e_5,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_473,c_0_402])]),
[final] ).
cnf(c_0_531,negated_conjecture,
( ~ product(e_4,X1,e_1)
| ~ product(e_5,X1,e_3) ),
inference(spm,[status(thm)],[c_0_168,c_0_510]),
[final] ).
cnf(c_0_532,negated_conjecture,
( ~ product(e_3,X1,e_2)
| product(e_5,X1,e_3) ),
inference(spm,[status(thm)],[c_0_72,c_0_468]),
[final] ).
cnf(c_0_533,negated_conjecture,
( ~ product(e_4,X1,e_1)
| ~ product(e_5,X1,e_2) ),
inference(spm,[status(thm)],[c_0_228,c_0_510]),
[final] ).
cnf(c_0_534,negated_conjecture,
( ~ product(e_4,X1,e_2)
| ~ product(e_3,X1,e_1) ),
inference(spm,[status(thm)],[c_0_217,c_0_511]),
[final] ).
cnf(c_0_535,negated_conjecture,
( ~ product(e_2,X1,e_5)
| product(e_4,X1,e_2) ),
inference(spm,[status(thm)],[c_0_72,c_0_298]),
[final] ).
cnf(c_0_536,negated_conjecture,
( ~ product(e_5,X1,e_3)
| ~ product(e_4,X1,e_5) ),
inference(spm,[status(thm)],[c_0_314,c_0_428]),
[final] ).
cnf(c_0_537,negated_conjecture,
( ~ product(e_5,X1,e_3)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_226,c_0_428]),
[final] ).
cnf(c_0_538,negated_conjecture,
( ~ product(e_4,X1,e_2)
| ~ product(e_3,X1,e_4) ),
inference(spm,[status(thm)],[c_0_326,c_0_483]),
[final] ).
cnf(c_0_539,negated_conjecture,
( ~ product(e_3,X1,e_1)
| product(e_4,X1,e_3) ),
inference(spm,[status(thm)],[c_0_72,c_0_512]),
[final] ).
cnf(c_0_540,negated_conjecture,
( ~ product(e_3,X1,e_5)
| product(e_4,X1,e_1) ),
inference(spm,[status(thm)],[c_0_513,c_0_372]),
[final] ).
cnf(c_0_541,negated_conjecture,
( ~ product(e_2,X1,e_4)
| product(e_3,X1,e_1) ),
inference(spm,[status(thm)],[c_0_514,c_0_268]),
[final] ).
cnf(c_0_542,negated_conjecture,
( product(e_1,e_4,e_3)
| product(e_1,e_4,e_4)
| product(e_1,e_4,e_5) ),
inference(sr,[status(thm)],[c_0_407,c_0_416]),
[final] ).
cnf(c_0_543,negated_conjecture,
( ~ product(e_5,X1,X2)
| ~ product(e_4,X2,e_2)
| product(e_1,X1,e_5) ),
inference(spm,[status(thm)],[c_0_72,c_0_511]),
[final] ).
cnf(c_0_544,negated_conjecture,
( ~ product(e_2,X1,e_3)
| product(e_3,X1,e_4) ),
inference(spm,[status(thm)],[c_0_498,c_0_515]),
[final] ).
cnf(c_0_545,negated_conjecture,
( ~ product(e_5,X1,X2)
| ~ product(e_2,X2,e_3)
| product(e_2,X1,e_5) ),
inference(spm,[status(thm)],[c_0_72,c_0_436]),
[final] ).
cnf(c_0_546,negated_conjecture,
( ~ product(e_5,X1,e_3)
| product(e_2,X1,e_1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_272,c_0_428]),c_0_298])]),
[final] ).
cnf(c_0_548,negated_conjecture,
( ~ product(e_2,X1,e_1)
| product(e_3,X1,e_2) ),
inference(spm,[status(thm)],[c_0_72,c_0_448]),
[final] ).
cnf(c_0_549,negated_conjecture,
product(e_1,e_5,e_2),
inference(sr,[status(thm)],[c_0_517,c_0_362]),
[final] ).
cnf(c_0_551,axiom,
greater(e_2,e_1),
e_2_greater_e_1,
[final] ).
cnf(c_0_552,axiom,
greater(e_3,e_1),
e_3_greater_e_1,
[final] ).
cnf(c_0_553,axiom,
greater(e_4,e_1),
e_4_greater_e_1,
[final] ).
cnf(c_0_554,axiom,
greater(e_5,e_1),
e_5_greater_e_1,
[final] ).
cnf(c_0_563,negated_conjecture,
~ product(e_3,e_1,e_1),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_522,c_0_491]),c_0_523]),c_0_74]),c_0_524]),
[final] ).
cnf(c_0_586,negated_conjecture,
~ product(e_4,e_4,e_3),
inference(spm,[status(thm)],[c_0_158,c_0_530]),
[final] ).
cnf(c_0_587,negated_conjecture,
( ~ product(e_3,X1,e_2)
| ~ product(e_4,X1,e_1) ),
inference(spm,[status(thm)],[c_0_531,c_0_532]),
[final] ).
cnf(c_0_588,negated_conjecture,
( ~ product(e_2,X1,e_3)
| ~ product(e_4,X1,e_1) ),
inference(spm,[status(thm)],[c_0_533,c_0_436]),
[final] ).
cnf(c_0_589,negated_conjecture,
( ~ product(e_2,X1,e_5)
| ~ product(e_3,X1,e_1) ),
inference(spm,[status(thm)],[c_0_534,c_0_535]),
[final] ).
cnf(c_0_590,negated_conjecture,
( ~ product(e_3,X1,e_2)
| ~ product(e_4,X1,e_5) ),
inference(spm,[status(thm)],[c_0_536,c_0_532]),
[final] ).
cnf(c_0_591,negated_conjecture,
( ~ product(e_2,X1,e_4)
| ~ product(e_5,X1,e_3) ),
inference(spm,[status(thm)],[c_0_537,c_0_268]),
[final] ).
cnf(c_0_592,negated_conjecture,
( ~ product(e_2,X1,e_5)
| ~ product(e_3,X1,e_4) ),
inference(spm,[status(thm)],[c_0_538,c_0_535]),
[final] ).
cnf(c_0_593,negated_conjecture,
( ~ product(e_3,X1,e_1)
| ~ product(e_2,X1,e_3) ),
inference(spm,[status(thm)],[c_0_132,c_0_539]),
[final] ).
cnf(c_0_594,negated_conjecture,
( ~ product(e_4,X1,e_1)
| ~ product(e_3,X1,e_4) ),
inference(spm,[status(thm)],[c_0_217,c_0_510]),
[final] ).
cnf(c_0_595,negated_conjecture,
( ~ product(e_4,X1,e_1)
| ~ product(e_2,X1,e_4) ),
inference(spm,[status(thm)],[c_0_99,c_0_510]),
[final] ).
cnf(c_0_596,negated_conjecture,
( ~ product(e_2,X1,e_3)
| ~ product(e_4,X1,e_4) ),
inference(spm,[status(thm)],[c_0_182,c_0_515]),
[final] ).
cnf(c_0_597,negated_conjecture,
( ~ product(e_4,X1,e_2)
| ~ product(e_2,X1,e_1) ),
inference(spm,[status(thm)],[c_0_99,c_0_511]),
[final] ).
cnf(c_0_598,negated_conjecture,
( ~ product(e_4,X1,e_2)
| ~ product(e_5,X1,e_3) ),
inference(spm,[status(thm)],[c_0_130,c_0_511]),
[final] ).
cnf(c_0_599,negated_conjecture,
( ~ product(e_4,X1,e_2)
| ~ product(e_5,X1,e_5) ),
inference(spm,[status(thm)],[c_0_359,c_0_511]),
[final] ).
cnf(c_0_600,negated_conjecture,
( ~ product(e_3,X1,e_2)
| ~ product(e_4,X1,e_3) ),
inference(spm,[status(thm)],[c_0_307,c_0_532]),
[final] ).
cnf(c_0_601,negated_conjecture,
( ~ product(e_5,X1,e_3)
| ~ product(e_2,X1,e_5) ),
inference(spm,[status(thm)],[c_0_83,c_0_428]),
[final] ).
cnf(c_0_602,negated_conjecture,
( ~ product(e_5,X1,e_3)
| ~ product(e_1,X1,e_4) ),
inference(spm,[status(thm)],[c_0_182,c_0_428]),
[final] ).
cnf(c_0_603,negated_conjecture,
( ~ product(e_3,X1,e_5)
| ~ product(e_2,X1,e_1) ),
inference(spm,[status(thm)],[c_0_132,c_0_540]),
[final] ).
cnf(c_0_604,negated_conjecture,
( ~ product(e_3,X1,e_5)
| ~ product(e_4,X1,e_4) ),
inference(spm,[status(thm)],[c_0_345,c_0_540]),
[final] ).
cnf(c_0_605,negated_conjecture,
( ~ product(e_3,X1,e_5)
| ~ product(e_4,X1,e_2) ),
inference(spm,[status(thm)],[c_0_74,c_0_540]),
[final] ).
cnf(c_0_606,negated_conjecture,
( ~ product(e_2,X1,e_4)
| ~ product(e_3,X1,e_3) ),
inference(spm,[status(thm)],[c_0_130,c_0_541]),
[final] ).
cnf(c_0_607,negated_conjecture,
( ~ product(e_2,X1,e_4)
| ~ product(e_3,X1,e_5) ),
inference(spm,[status(thm)],[c_0_359,c_0_541]),
[final] ).
cnf(c_0_608,negated_conjecture,
( ~ product(e_3,X1,e_5)
| ~ product(e_4,X1,e_3) ),
inference(spm,[status(thm)],[c_0_314,c_0_372]),
[final] ).
cnf(c_0_609,negated_conjecture,
( ~ product(e_3,X1,e_5)
| ~ product(e_5,X1,e_3) ),
inference(spm,[status(thm)],[c_0_446,c_0_372]),
[final] ).
cnf(c_0_610,negated_conjecture,
( ~ product(e_3,X1,e_5)
| ~ product(e_2,X1,e_3) ),
inference(spm,[status(thm)],[c_0_83,c_0_372]),
[final] ).
cnf(c_0_611,negated_conjecture,
( ~ product(e_3,X1,e_5)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_374,c_0_372]),
[final] ).
cnf(c_0_612,negated_conjecture,
( ~ product(e_4,X1,e_2)
| ~ product(e_5,X1,e_4) ),
inference(spm,[status(thm)],[c_0_446,c_0_483]),
[final] ).
cnf(c_0_613,negated_conjecture,
( ~ product(e_4,X1,e_2)
| ~ product(e_1,X1,e_3) ),
inference(spm,[status(thm)],[c_0_168,c_0_483]),
[final] ).
cnf(c_0_614,negated_conjecture,
( ~ product(e_1,X1,e_4)
| product(e_5,X1,e_1)
| product(e_1,e_4,e_4)
| product(e_1,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_72,c_0_542]),
[final] ).
cnf(c_0_615,negated_conjecture,
( ~ product(e_5,X1,X2)
| ~ product(e_2,X2,e_5)
| product(e_1,X1,e_5) ),
inference(spm,[status(thm)],[c_0_543,c_0_535]),
[final] ).
cnf(c_0_616,negated_conjecture,
( ~ product(e_3,X1,X2)
| ~ product(e_2,X2,e_3)
| product(e_4,X1,e_3) ),
inference(spm,[status(thm)],[c_0_72,c_0_544]),
[final] ).
cnf(c_0_617,negated_conjecture,
( ~ product(e_4,X1,X2)
| ~ product(e_3,X2,e_1)
| product(e_3,X1,e_4) ),
inference(spm,[status(thm)],[c_0_72,c_0_539]),
[final] ).
cnf(c_0_618,negated_conjecture,
( ~ product(e_5,X1,X2)
| ~ product(e_4,X2,e_1)
| product(e_4,X1,e_5) ),
inference(spm,[status(thm)],[c_0_72,c_0_510]),
[final] ).
cnf(c_0_619,negated_conjecture,
( ~ product(e_4,X1,X2)
| ~ product(e_2,X2,e_3)
| product(e_5,X1,e_4) ),
inference(spm,[status(thm)],[c_0_72,c_0_515]),
[final] ).
cnf(c_0_620,negated_conjecture,
( ~ product(e_5,X1,X2)
| ~ product(e_3,X2,e_2)
| product(e_3,X1,e_5) ),
inference(spm,[status(thm)],[c_0_72,c_0_532]),
[final] ).
cnf(c_0_621,negated_conjecture,
( ~ product(e_3,X1,e_1)
| product(e_2,X1,e_4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_342,c_0_539]),c_0_333])]),
[final] ).
cnf(c_0_622,negated_conjecture,
( ~ product(e_4,X1,e_1)
| product(e_3,X1,e_5) ),
inference(spm,[status(thm)],[c_0_444,c_0_510]),
[final] ).
cnf(c_0_623,negated_conjecture,
( ~ product(e_5,X1,e_1)
| product(e_2,X1,e_5) ),
inference(spm,[status(thm)],[c_0_72,c_0_457]),
[final] ).
cnf(c_0_624,negated_conjecture,
( ~ product(e_4,X1,e_2)
| product(e_2,X1,e_5) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_545,c_0_511]),c_0_448])]),
[final] ).
cnf(c_0_625,negated_conjecture,
( ~ product(e_3,X1,e_2)
| product(e_2,X1,e_1) ),
inference(spm,[status(thm)],[c_0_546,c_0_532]),
[final] ).
cnf(c_0_626,negated_conjecture,
( ~ product(e_2,X1,e_1)
| product(e_5,X1,e_3)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_547,c_0_548]),
[final] ).
cnf(c_0_627,negated_conjecture,
( ~ product(e_3,X1,X2)
| ~ product(e_2,X2,e_1)
| product(e_2,X1,e_3) ),
inference(spm,[status(thm)],[c_0_72,c_0_548]),
[final] ).
cnf(c_0_628,negated_conjecture,
( ~ product(e_4,X1,X2)
| ~ product(e_3,X2,e_5)
| product(e_1,X1,e_4) ),
inference(spm,[status(thm)],[c_0_72,c_0_540]),
[final] ).
cnf(c_0_629,negated_conjecture,
( ~ product(e_2,X1,e_4)
| product(e_4,X1,e_3)
| product(e_3,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_404,c_0_541]),
[final] ).
cnf(c_0_630,negated_conjecture,
( ~ product(e_3,X1,X2)
| ~ product(e_2,X2,e_4)
| product(e_1,X1,e_3) ),
inference(spm,[status(thm)],[c_0_72,c_0_541]),
[final] ).
cnf(c_0_631,negated_conjecture,
( ~ product(e_1,X1,X2)
| ~ product(e_3,X2,e_5)
| product(e_3,X1,e_1) ),
inference(spm,[status(thm)],[c_0_72,c_0_372]),
[final] ).
cnf(c_0_632,negated_conjecture,
( ~ product(e_1,X1,X2)
| ~ product(e_4,X2,e_2)
| product(e_4,X1,e_1) ),
inference(spm,[status(thm)],[c_0_72,c_0_483]),
[final] ).
cnf(c_0_633,negated_conjecture,
( ~ product(e_1,X1,e_5)
| product(e_2,X1,e_1) ),
inference(spm,[status(thm)],[c_0_72,c_0_549]),
[final] ).
cnf(c_0_634,negated_conjecture,
( ~ product(e_2,X1,e_5)
| product(e_1,X1,e_4)
| product(e_3,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_399,c_0_535]),
[final] ).
cnf(c_0_635,negated_conjecture,
( ~ product(e_2,X1,e_3)
| ~ product(e_4,X1,e_2) ),
inference(spm,[status(thm)],[c_0_307,c_0_436]),
[final] ).
cnf(c_0_636,negated_conjecture,
( ~ product(e_2,X1,e_3)
| ~ product(e_3,X1,e_2) ),
inference(spm,[status(thm)],[c_0_217,c_0_436]),
[final] ).
cnf(c_0_637,negated_conjecture,
( ~ product(e_2,X1,e_5)
| ~ product(e_3,X1,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_550,c_0_333])]),
[final] ).
cnf(c_0_638,negated_conjecture,
( ~ product(e_4,X1,e_3)
| product(e_2,X1,e_4) ),
inference(spm,[status(thm)],[c_0_72,c_0_346]),
[final] ).
cnf(c_0_639,negated_conjecture,
( ~ product(e_2,X1,e_4)
| ~ product(e_3,X1,e_2) ),
inference(spm,[status(thm)],[c_0_326,c_0_268]),
[final] ).
cnf(c_0_640,negated_conjecture,
( ~ product(e_2,X1,e_4)
| ~ product(e_4,X1,e_2) ),
inference(spm,[status(thm)],[c_0_314,c_0_268]),
[final] ).
cnf(c_0_641,negated_conjecture,
( ~ product(e_2,X1,e_4)
| ~ product(e_5,X1,e_2) ),
inference(spm,[status(thm)],[c_0_446,c_0_268]),
[final] ).
cnf(c_0_642,plain,
( ~ next(X1,e_1)
| ~ product(X1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_49,c_0_551]),
[final] ).
cnf(c_0_643,plain,
( ~ next(X1,e_1)
| ~ product(X1,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_49,c_0_552]),
[final] ).
cnf(c_0_644,plain,
( ~ next(X1,e_1)
| ~ product(X1,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_49,c_0_553]),
[final] ).
cnf(c_0_645,plain,
( ~ next(X1,e_1)
| ~ product(X1,e_1,e_5) ),
inference(spm,[status(thm)],[c_0_49,c_0_554]),
[final] ).
cnf(c_0_646,plain,
~ product(e_5,e_4,e_5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_555]),c_0_471])]),
[final] ).
cnf(c_0_647,plain,
~ product(e_5,e_2,e_5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_556]),c_0_471])]),
[final] ).
cnf(c_0_648,negated_conjecture,
~ product(e_1,e_3,e_5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_428]),c_0_433])]),
[final] ).
cnf(c_0_649,negated_conjecture,
~ product(e_1,e_2,e_5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_428]),c_0_433])]),
[final] ).
cnf(c_0_650,negated_conjecture,
~ product(e_4,e_5,e_1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_510]),c_0_471])]),
[final] ).
cnf(c_0_651,negated_conjecture,
~ product(e_3,e_1,e_3),
inference(spm,[status(thm)],[c_0_168,c_0_512]),
[final] ).
cnf(c_0_652,negated_conjecture,
~ product(e_4,e_3,e_5),
inference(spm,[status(thm)],[c_0_188,c_0_496]),
[final] ).
cnf(c_0_653,negated_conjecture,
~ product(e_4,e_4,e_5),
inference(spm,[status(thm)],[c_0_118,c_0_496]),
[final] ).
cnf(c_0_654,negated_conjecture,
~ product(e_4,e_5,e_5),
inference(spm,[status(thm)],[c_0_153,c_0_496]),
[final] ).
cnf(c_0_655,negated_conjecture,
~ product(e_4,e_1,e_4),
inference(spm,[status(thm)],[c_0_182,c_0_496]),
[final] ).
cnf(c_0_656,negated_conjecture,
~ product(e_4,e_1,e_3),
inference(spm,[status(thm)],[c_0_183,c_0_496]),
[final] ).
cnf(c_0_657,negated_conjecture,
~ product(e_3,e_4,e_3),
inference(spm,[status(thm)],[c_0_217,c_0_433]),
[final] ).
cnf(c_0_658,negated_conjecture,
~ product(e_2,e_1,e_2),
inference(spm,[status(thm)],[c_0_374,c_0_448]),
[final] ).
cnf(c_0_659,negated_conjecture,
~ product(e_5,e_4,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_557,c_0_448])]),
[final] ).
cnf(c_0_660,negated_conjecture,
~ product(e_4,e_3,e_3),
inference(spm,[status(thm)],[c_0_207,c_0_530]),
[final] ).
cnf(c_0_661,negated_conjecture,
~ product(e_5,e_2,e_1),
inference(spm,[status(thm)],[c_0_205,c_0_423]),
[final] ).
cnf(c_0_662,negated_conjecture,
~ product(e_5,e_3,e_3),
inference(spm,[status(thm)],[c_0_130,c_0_423]),
[final] ).
cnf(c_0_663,negated_conjecture,
~ product(e_5,e_3,e_5),
inference(spm,[status(thm)],[c_0_359,c_0_423]),
[final] ).
cnf(c_0_664,negated_conjecture,
~ product(e_5,e_3,e_2),
inference(spm,[status(thm)],[c_0_74,c_0_423]),
[final] ).
cnf(c_0_665,negated_conjecture,
~ product(e_1,e_2,e_4),
inference(spm,[status(thm)],[c_0_205,c_0_415]),
[final] ).
cnf(c_0_666,negated_conjecture,
~ product(e_1,e_3,e_3),
inference(spm,[status(thm)],[c_0_168,c_0_415]),
[final] ).
cnf(c_0_667,negated_conjecture,
~ product(e_3,e_5,e_4),
inference(spm,[status(thm)],[c_0_345,c_0_365]),
[final] ).
cnf(c_0_668,negated_conjecture,
~ product(e_5,e_3,e_4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_558,c_0_373])]),
[final] ).
cnf(c_0_669,negated_conjecture,
~ product(e_4,e_3,e_4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_559,c_0_373])]),
[final] ).
cnf(c_0_670,negated_conjecture,
~ product(e_3,e_5,e_5),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_359,c_0_358]),c_0_207]),
[final] ).
cnf(c_0_671,negated_conjecture,
~ product(e_3,e_5,e_3),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_352]),c_0_130]),
[final] ).
cnf(c_0_672,negated_conjecture,
~ product(e_4,e_3,e_1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_431]),c_0_205]),
[final] ).
cnf(c_0_673,negated_conjecture,
~ product(e_2,e_2,e_3),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_404,c_0_521]),c_0_560]),c_0_561]),
[final] ).
cnf(c_0_674,negated_conjecture,
~ product(e_1,e_5,e_1),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_562,c_0_320]),c_0_563]),c_0_314]),
[final] ).
cnf(c_0_675,negated_conjecture,
~ product(e_3,e_5,e_2),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_395,c_0_564]),c_0_303]),c_0_326]),
[final] ).
cnf(c_0_676,negated_conjecture,
~ product(e_4,e_5,e_2),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_395,c_0_565]),c_0_303]),c_0_314]),
[final] ).
cnf(c_0_677,negated_conjecture,
~ product(e_3,e_4,e_1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_361]),c_0_193]),
[final] ).
cnf(c_0_678,negated_conjecture,
~ product(e_2,e_5,e_1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_310]),c_0_135]),
[final] ).
cnf(c_0_679,negated_conjecture,
~ product(e_2,e_5,e_5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_535]),c_0_346])]),
[final] ).
cnf(c_0_680,negated_conjecture,
~ product(e_1,e_4,e_1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_566,c_0_298])]),
[final] ).
cnf(c_0_681,negated_conjecture,
~ product(e_1,e_3,e_1),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_567,c_0_378]),c_0_130]),c_0_74]),
[final] ).
cnf(c_0_682,negated_conjecture,
~ product(e_5,e_1,e_1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_568,c_0_479]),c_0_563]),
[final] ).
cnf(c_0_683,negated_conjecture,
~ product(e_1,e_2,e_2),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_228,c_0_281]),c_0_374]),c_0_569]),
[final] ).
cnf(c_0_684,negated_conjecture,
~ product(e_2,e_1,e_1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_570,c_0_268]),c_0_571]),
[final] ).
cnf(c_0_685,negated_conjecture,
~ product(e_2,e_3,e_1),
inference(spm,[status(thm)],[c_0_256,c_0_572]),
[final] ).
cnf(c_0_686,negated_conjecture,
~ product(e_2,e_2,e_5),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_184]),c_0_573]),
[final] ).
cnf(c_0_687,negated_conjecture,
~ product(e_1,e_2,e_1),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_81]),c_0_574]),c_0_74]),c_0_130]),c_0_345]),
[final] ).
cnf(c_0_688,plain,
~ equalish(e_5,e_4),
c_0_575,
[final] ).
cnf(c_0_689,plain,
~ equalish(e_5,e_3),
c_0_576,
[final] ).
cnf(c_0_690,plain,
~ equalish(e_5,e_2),
c_0_577,
[final] ).
cnf(c_0_691,plain,
~ equalish(e_5,e_1),
c_0_578,
[final] ).
cnf(c_0_692,plain,
~ equalish(e_4,e_3),
c_0_579,
[final] ).
cnf(c_0_693,plain,
~ equalish(e_4,e_2),
c_0_580,
[final] ).
cnf(c_0_694,plain,
~ equalish(e_4,e_1),
c_0_581,
[final] ).
cnf(c_0_695,plain,
~ equalish(e_3,e_2),
c_0_582,
[final] ).
cnf(c_0_696,plain,
~ equalish(e_3,e_1),
c_0_583,
[final] ).
cnf(c_0_697,plain,
~ equalish(e_1,e_2),
c_0_584,
[final] ).
cnf(c_0_698,negated_conjecture,
product(e_4,e_4,e_4),
inference(sr,[status(thm)],[c_0_585,c_0_586]),
[final] ).
cnf(c_0_699,negated_conjecture,
product(e_4,e_2,e_1),
inference(sr,[status(thm)],[c_0_392,c_0_362]),
[final] ).
cnf(c_0_700,axiom,
next(e_4,e_5),
e_4_then_e_5,
[final] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP130-2.005 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.48 % Computer : n005.cluster.edu
% 0.16/0.48 % Model : x86_64 x86_64
% 0.16/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.48 % Memory : 8046.5625MB
% 0.16/0.48 % OS : Linux 6.8.0-71-generic
% 0.16/0.48 % CPULimit : 300
% 0.16/0.48 % WCLimit : 300
% 0.16/0.48 % DateTime : Sun Sep 20 20:01:18 UTC 2026
% 0.16/0.49 % CPUTime :
% 0.16/0.49 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/0.56 Running first-order theorem proving
% 0.22/0.56 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 3.01/1.16 % Version: 3.5.1
% 3.01/1.16 % Preprocessing class: FSMSSMSSSSSNFFN.
% 3.01/1.16 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.01/1.16 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.01/1.16 % Starting new_bool_3 with 300s (1) cores
% 3.01/1.16 % Starting new_bool_1 with 300s (1) cores
% 3.01/1.16 % Starting sh5l with 300s (1) cores
% 3.01/1.16 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1637466 completed with status 1
% 3.01/1.16 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 3.01/1.16 % Preprocessing class: FSMSSMSSSSSNFFN.
% 3.01/1.16 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.01/1.16 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.01/1.16 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.01/1.16 % No SInE strategy applied
% 3.01/1.16 % Search class: FGHNF-FFSM00-SFFFFFNN
% 3.01/1.16 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 3.01/1.16 % Starting SubtermCWHack with 136s (1) cores
% 3.01/1.16 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 3.01/1.16 % Starting G----_404_C05_02_F1_SE_CS_SP_PS_RG_S04AI with 136s (1) cores
% 3.01/1.16 % Starting new_bool_3 with 136s (1) cores
% 3.01/1.16 % Starting new_bool_1 with 136s (1) cores
% 3.01/1.16 % G----_404_C05_02_F1_SE_CS_SP_PS_RG_S04AI with pid 1637474 completed with status 1
% 3.01/1.16 % Result found by G----_404_C05_02_F1_SE_CS_SP_PS_RG_S04AI
% 3.01/1.16 % Preprocessing class: FSMSSMSSSSSNFFN.
% 3.01/1.16 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.01/1.16 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.01/1.16 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.01/1.16 % No SInE strategy applied
% 3.01/1.16 % Search class: FGHNF-FFSM00-SFFFFFNN
% 3.01/1.16 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 3.01/1.16 % Starting SubtermCWHack with 136s (1) cores
% 3.01/1.16 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 3.01/1.16 % Starting G----_404_C05_02_F1_SE_CS_SP_PS_RG_S04AI with 136s (1) cores
% 3.01/1.16 % Preprocessing time : 0.002 s
% 3.01/1.16 % Presaturation interreduction done
% 3.01/1.16
% 3.01/1.16 % No proof found!
% 3.01/1.16 % SZS status Satisfiable
% 3.01/1.16 % SZS output start Saturation
% See solution above
% 3.01/1.16 % Parsed axioms : 45
% 3.01/1.16 % Removed by relevancy pruning/SinE : 0
% 3.01/1.16 % Initial clauses : 45
% 3.01/1.16 % Removed in clause preprocessing : 0
% 3.01/1.16 % Initial clauses in saturation : 45
% 3.01/1.16 % Processed clauses : 3121
% 3.01/1.16 % ...of these trivial : 57
% 3.01/1.16 % ...subsumed : 1354
% 3.01/1.16 % ...remaining for further processing : 1710
% 3.01/1.16 % Other redundant clauses eliminated : 0
% 3.01/1.16 % Clauses deleted for lack of memory : 0
% 3.01/1.16 % Backward-subsumed : 1068
% 3.01/1.16 % Backward-rewritten : 193
% 3.01/1.16 % Generated clauses : 6032
% 3.01/1.16 % ...of the previous two non-redundant : 5476
% 3.01/1.16 % ...aggressively subsumed : 0
% 3.01/1.16 % Contextual simplify-reflections : 367
% 3.01/1.16 % Paramodulations : 5918
% 3.01/1.16 % Factorizations : 0
% 3.01/1.16 % NegExts : 0
% 3.01/1.16 % Equation resolutions : 0
% 3.01/1.16 % Disequality decompositions : 0
% 3.01/1.16 % Total rewrite steps : 440
% 3.01/1.16 % ...of those cached : 418
% 3.01/1.16 % Propositional unsat checks : 0
% 3.01/1.16 % Propositional check models : 0
% 3.01/1.16 % Propositional check unsatisfiable : 0
% 3.01/1.16 % Propositional clauses : 0
% 3.01/1.16 % Propositional clauses after purity: 0
% 3.01/1.16 % Propositional unsat core size : 0
% 3.01/1.16 % Propositional preprocessing time : 0.000
% 3.01/1.16 % Propositional encoding time : 0.000
% 3.01/1.16 % Propositional solver time : 0.000
% 3.01/1.16 % Success case prop preproc time : 0.000
% 3.01/1.16 % Success case prop encoding time : 0.000
% 3.01/1.16 % Success case prop solver time : 0.000
% 3.01/1.16 % Current number of processed clauses : 290
% 3.01/1.16 % Positive orientable unit clauses : 41
% 3.01/1.16 % Positive unorientable unit clauses: 0
% 3.01/1.16 % Negative unit clauses : 107
% 3.01/1.16 % Non-unit-clauses : 142
% 3.01/1.16 % Current number of unprocessed clauses: 0
% 3.01/1.16 % ...number of literals in the above : 0
% 3.01/1.16 % Current number of archived formulas : 0
% 3.01/1.16 % Current number of archived clauses : 1420
% 3.01/1.16 % Clause-clause subsumption calls (NU) : 130247
% 3.01/1.16 % Rec. Clause-clause subsumption calls : 50176
% 3.01/1.16 % Non-unit clause-clause subsumptions : 1560
% 3.01/1.16 % Unit Clause-clause subsumption calls : 3776
% 3.01/1.16 % Rewrite failures with RHS unbound : 0
% 3.01/1.16 % BW rewrite match attempts : 105
% 3.01/1.16 % BW rewrite match successes : 21
% 3.01/1.16 % Condensation attempts : 0
% 3.01/1.16 % Condensation successes : 0
% 3.01/1.16 % Termbank termtop insertions : 72646
% 3.01/1.16 % Search garbage collected termcells : 72
% 3.01/1.16
% 3.01/1.16 % -------------------------------------------------
% 3.01/1.16 % User time : 0.500 s
% 3.01/1.16 % System time : 0.007 s
% 3.01/1.16 % Total time : 0.507 s
% 3.01/1.16 % Maximum resident set size: 3652 pages
% 3.01/1.16
% 3.01/1.16 % -------------------------------------------------
% 3.01/1.16 % User time : 2.398 s
% 3.01/1.16 % System time : 0.049 s
% 3.01/1.16 % Total time : 2.448 s
% 3.01/1.16 % Maximum resident set size: 4864 pages
% 3.01/1.16 % E exiting
%------------------------------------------------------------------------------