%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP127-2.005 : 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 : n001.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 12:38:04 PM UTC 2026
% Result : Satisfiable 1.06s 0.68s
% Output : Saturation 1.06s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_46ERROR: Could not build tree for root c_0_55ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(c_0_49,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_46,
[final] ).
cnf(c_0_50,axiom,
group_element(e_1),
element_1,
[final] ).
cnf(c_0_51,plain,
~ equalish(e_1,e_5),
c_0_47,
[final] ).
cnf(c_0_52,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
c_0_48,
[final] ).
cnf(c_0_55,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_49,c_0_50]),
[final] ).
cnf(c_0_56,axiom,
group_element(e_5),
element_5,
[final] ).
cnf(c_0_57,plain,
( ~ product(e_1,X1,X2)
| ~ product(e_5,X1,X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]),
[final] ).
cnf(c_0_58,axiom,
product(X1,X1,X1),
product_idempotence,
[final] ).
cnf(c_0_59,plain,
( ~ greater(X2,X3)
| ~ next(X1,X3)
| ~ product(X1,e_1,X2) ),
c_0_53,
[final] ).
cnf(c_0_60,axiom,
greater(e_5,e_4),
e_5_greater_e_4,
[final] ).
cnf(c_0_63,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
c_0_54,
[final] ).
cnf(c_0_65,plain,
~ product(e_5,e_1,e_1),
inference(spm,[status(thm)],[c_0_57,c_0_58]),
[final] ).
cnf(c_0_66,axiom,
group_element(e_3),
element_3,
[final] ).
cnf(c_0_67,plain,
( ~ next(X1,e_4)
| ~ product(X1,e_1,e_5) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]),
[final] ).
cnf(c_0_68,axiom,
next(e_3,e_4),
e_3_then_e_4,
[final] ).
cnf(c_0_69,plain,
~ equalish(e_1,e_3),
c_0_61,
[final] ).
cnf(c_0_70,axiom,
greater(e_5,e_3),
e_5_greater_e_3,
[final] ).
cnf(c_0_71,plain,
~ equalish(e_3,e_5),
c_0_62,
[final] ).
cnf(c_0_72,plain,
( ~ product(X1,e_1,X2)
| ~ product(X1,e_5,X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_63]),
[final] ).
cnf(c_0_75,plain,
~ product(e_3,e_1,e_5),
inference(spm,[status(thm)],[c_0_67,c_0_68]),
[final] ).
cnf(c_0_76,plain,
( ~ product(e_1,X1,X2)
| ~ product(e_3,X1,X2) ),
inference(spm,[status(thm)],[c_0_69,c_0_52]),
[final] ).
cnf(c_0_77,axiom,
group_element(e_2),
element_2,
[final] ).
cnf(c_0_78,plain,
( ~ next(X1,e_3)
| ~ product(X1,e_1,e_5) ),
inference(spm,[status(thm)],[c_0_59,c_0_70]),
[final] ).
cnf(c_0_79,axiom,
next(e_2,e_3),
e_2_then_e_3,
[final] ).
cnf(c_0_80,axiom,
greater(e_4,e_3),
e_4_greater_e_3,
[final] ).
cnf(c_0_83,plain,
( ~ product(e_3,X1,X2)
| ~ product(e_5,X1,X2) ),
inference(spm,[status(thm)],[c_0_71,c_0_52]),
[final] ).
cnf(c_0_86,plain,
~ product(e_3,e_1,e_1),
inference(spm,[status(thm)],[c_0_76,c_0_58]),
[final] ).
cnf(c_0_89,plain,
~ product(e_2,e_1,e_5),
inference(spm,[status(thm)],[c_0_78,c_0_79]),
[final] ).
cnf(c_0_90,plain,
( ~ next(X1,e_3)
| ~ product(X1,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_59,c_0_80]),
[final] ).
cnf(c_0_91,plain,
~ equalish(e_2,e_1),
c_0_81,
[final] ).
cnf(c_0_93,plain,
~ equalish(e_2,e_5),
c_0_82,
[final] ).
cnf(c_0_96,plain,
~ equalish(e_2,e_3),
c_0_87,
[final] ).
cnf(c_0_98,plain,
~ product(e_2,e_1,e_4),
inference(spm,[status(thm)],[c_0_90,c_0_79]),
[final] ).
cnf(c_0_99,plain,
( ~ product(e_2,X1,X2)
| ~ product(e_1,X1,X2) ),
inference(spm,[status(thm)],[c_0_91,c_0_52]),
[final] ).
cnf(c_0_100,plain,
~ equalish(e_1,e_4),
c_0_92,
[final] ).
cnf(c_0_102,plain,
( ~ product(e_2,X1,X2)
| ~ product(e_5,X1,X2) ),
inference(spm,[status(thm)],[c_0_93,c_0_52]),
[final] ).
cnf(c_0_104,plain,
( ~ product(e_2,X1,X2)
| ~ product(e_3,X1,X2) ),
inference(spm,[status(thm)],[c_0_96,c_0_52]),
[final] ).
cnf(c_0_106,plain,
~ product(e_2,e_1,e_1),
inference(spm,[status(thm)],[c_0_99,c_0_58]),
[final] ).
cnf(c_0_109,axiom,
group_element(e_4),
element_4,
[final] ).
cnf(c_0_110,plain,
( ~ product(e_1,X1,X2)
| ~ product(e_4,X1,X2) ),
inference(spm,[status(thm)],[c_0_100,c_0_52]),
[final] ).
cnf(c_0_111,plain,
~ equalish(e_4,e_5),
c_0_101,
[final] ).
cnf(c_0_114,plain,
~ equalish(e_3,e_4),
c_0_107,
[final] ).
cnf(c_0_115,plain,
~ equalish(e_2,e_4),
c_0_108,
[final] ).
cnf(c_0_117,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_49,c_0_109]),
[final] ).
cnf(c_0_119,plain,
~ product(e_4,e_1,e_1),
inference(spm,[status(thm)],[c_0_110,c_0_58]),
[final] ).
cnf(c_0_120,plain,
( ~ product(e_4,X1,X2)
| ~ product(e_5,X1,X2) ),
inference(spm,[status(thm)],[c_0_111,c_0_52]),
[final] ).
cnf(c_0_122,plain,
( ~ product(e_3,X1,X2)
| ~ product(e_4,X1,X2) ),
inference(spm,[status(thm)],[c_0_114,c_0_52]),
[final] ).
cnf(c_0_123,plain,
( ~ product(e_2,X1,X2)
| ~ product(e_4,X1,X2) ),
inference(spm,[status(thm)],[c_0_115,c_0_52]),
[final] ).
cnf(c_0_124,negated_conjecture,
( ~ product(X3,X1,X4)
| ~ product(X1,X2,X3)
| product(X4,X1,X2) ),
c_0_116,
[final] ).
cnf(c_0_127,plain,
~ product(e_4,e_1,e_2),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_122]),c_0_123]),
[final] ).
cnf(c_0_128,plain,
( ~ product(X1,e_4,X2)
| ~ product(X1,e_5,X2) ),
inference(spm,[status(thm)],[c_0_111,c_0_63]),
[final] ).
cnf(c_0_129,plain,
( ~ product(X1,e_1,X2)
| ~ product(X1,e_4,X2) ),
inference(spm,[status(thm)],[c_0_100,c_0_63]),
[final] ).
cnf(c_0_132,plain,
~ product(e_5,e_4,e_5),
inference(spm,[status(thm)],[c_0_128,c_0_58]),
[final] ).
cnf(c_0_133,plain,
~ product(e_1,e_4,e_1),
inference(spm,[status(thm)],[c_0_129,c_0_58]),
[final] ).
cnf(c_0_140,axiom,
greater(e_4,e_2),
e_4_greater_e_2,
[final] ).
cnf(c_0_142,negated_conjecture,
( ~ product(X1,X2,X1)
| product(X1,X1,X2) ),
inference(spm,[status(thm)],[c_0_124,c_0_58]),
[final] ).
cnf(c_0_144,plain,
( ~ next(X1,e_2)
| ~ product(X1,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_59,c_0_140]),
[final] ).
cnf(c_0_145,axiom,
next(e_1,e_2),
e_1_then_e_2,
[final] ).
cnf(c_0_149,plain,
~ product(e_1,e_1,e_4),
inference(spm,[status(thm)],[c_0_144,c_0_145]),
[final] ).
cnf(c_0_164,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_49,c_0_77]),
[final] ).
cnf(c_0_165,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
c_0_158,
[final] ).
cnf(c_0_170,plain,
( ~ product(X1,X2,e_2)
| ~ product(X1,X2,e_1) ),
inference(spm,[status(thm)],[c_0_91,c_0_165]),
[final] ).
cnf(c_0_175,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_49,c_0_56]),
[final] ).
cnf(c_0_176,axiom,
greater(e_5,e_2),
e_5_greater_e_2,
[final] ).
cnf(c_0_177,plain,
( ~ product(X1,e_2,X2)
| ~ product(X1,e_1,X2) ),
inference(spm,[status(thm)],[c_0_91,c_0_63]),
[final] ).
cnf(c_0_180,plain,
~ product(e_1,e_1,e_2),
inference(spm,[status(thm)],[c_0_170,c_0_58]),
[final] ).
cnf(c_0_185,plain,
( ~ next(X1,e_2)
| ~ product(X1,e_1,e_5) ),
inference(spm,[status(thm)],[c_0_59,c_0_176]),
[final] ).
cnf(c_0_187,plain,
~ product(e_2,e_5,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_178]),c_0_58])]),
[final] ).
cnf(c_0_191,plain,
~ product(e_2,e_4,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_181]),c_0_58])]),
[final] ).
cnf(c_0_192,plain,
~ product(e_2,e_4,e_4),
inference(spm,[status(thm)],[c_0_123,c_0_58]),
[final] ).
cnf(c_0_196,plain,
~ product(e_1,e_1,e_5),
inference(spm,[status(thm)],[c_0_185,c_0_145]),
[final] ).
cnf(c_0_198,plain,
~ product(e_2,e_5,e_5),
inference(spm,[status(thm)],[c_0_102,c_0_58]),
[final] ).
cnf(c_0_201,negated_conjecture,
~ product(e_2,e_4,e_2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_193]),c_0_194]),
[final] ).
cnf(c_0_202,plain,
( ~ product(X1,e_2,X2)
| ~ product(X1,e_4,X2) ),
inference(spm,[status(thm)],[c_0_115,c_0_63]),
[final] ).
cnf(c_0_208,plain,
~ product(e_4,e_2,e_4),
inference(spm,[status(thm)],[c_0_202,c_0_58]),
[final] ).
cnf(c_0_221,plain,
( ~ product(X1,e_2,X2)
| ~ product(X1,e_5,X2) ),
inference(spm,[status(thm)],[c_0_93,c_0_63]),
[final] ).
cnf(c_0_224,negated_conjecture,
product(e_2,e_4,e_5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_222]),c_0_58])]),
[final] ).
cnf(c_0_227,plain,
~ product(e_3,e_4,e_4),
inference(spm,[status(thm)],[c_0_122,c_0_58]),
[final] ).
cnf(c_0_232,negated_conjecture,
~ product(e_3,e_4,e_2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_228]),c_0_229]),
[final] ).
cnf(c_0_236,negated_conjecture,
~ product(e_3,e_4,e_3),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_233]),c_0_234]),
[final] ).
cnf(c_0_240,plain,
~ product(e_4,e_5,e_5),
inference(spm,[status(thm)],[c_0_120,c_0_58]),
[final] ).
cnf(c_0_241,plain,
~ product(e_2,e_4,e_1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_238]),c_0_224])]),
[final] ).
cnf(c_0_243,negated_conjecture,
product(e_3,e_4,e_1),
inference(sr,[status(thm)],[c_0_161,c_0_241]),
[final] ).
cnf(c_0_245,plain,
( ~ product(X1,X2,e_4)
| ~ product(X1,X2,e_5) ),
inference(spm,[status(thm)],[c_0_111,c_0_165]),
[final] ).
cnf(c_0_247,negated_conjecture,
( ~ product(e_4,X1,e_3)
| product(e_1,e_4,X1) ),
inference(spm,[status(thm)],[c_0_124,c_0_243]),
[final] ).
cnf(c_0_249,negated_conjecture,
( ~ product(e_4,X1,e_2)
| product(e_5,e_4,X1) ),
inference(spm,[status(thm)],[c_0_124,c_0_224]),
[final] ).
cnf(c_0_250,plain,
~ product(e_5,e_5,e_4),
inference(spm,[status(thm)],[c_0_245,c_0_58]),
[final] ).
cnf(c_0_252,negated_conjecture,
~ product(e_4,e_1,e_3),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_247]),c_0_149]),
[final] ).
cnf(c_0_254,negated_conjecture,
~ product(e_4,e_5,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_249]),c_0_250]),
[final] ).
cnf(c_0_262,plain,
~ product(e_3,e_5,e_5),
inference(spm,[status(thm)],[c_0_83,c_0_58]),
[final] ).
cnf(c_0_263,plain,
( ~ product(X1,X2,e_2)
| ~ product(X1,X2,e_4) ),
inference(spm,[status(thm)],[c_0_115,c_0_165]),
[final] ).
cnf(c_0_267,negated_conjecture,
~ product(e_3,e_1,e_2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_263,c_0_264]),c_0_104]),
[final] ).
cnf(c_0_268,plain,
( ~ product(X1,e_3,X2)
| ~ product(X1,e_4,X2) ),
inference(spm,[status(thm)],[c_0_114,c_0_63]),
[final] ).
cnf(c_0_273,plain,
( ~ product(X1,e_1,X2)
| ~ product(X1,e_3,X2) ),
inference(spm,[status(thm)],[c_0_69,c_0_63]),
[final] ).
cnf(c_0_277,plain,
~ product(e_3,e_3,e_1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_272]),c_0_224])]),
[final] ).
cnf(c_0_278,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_49,c_0_66]),
[final] ).
cnf(c_0_282,negated_conjecture,
~ product(e_3,e_5,e_4),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_276]),c_0_277]),
[final] ).
cnf(c_0_284,plain,
~ product(e_2,e_3,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_279]),c_0_58])]),
[final] ).
cnf(c_0_285,plain,
( ~ product(X1,e_3,X2)
| ~ product(X1,e_5,X2) ),
inference(spm,[status(thm)],[c_0_71,c_0_63]),
[final] ).
cnf(c_0_289,negated_conjecture,
~ product(e_2,e_3,e_5),
inference(spm,[status(thm)],[c_0_268,c_0_224]),
[final] ).
cnf(c_0_291,negated_conjecture,
~ product(e_2,e_2,e_5),
inference(spm,[status(thm)],[c_0_202,c_0_224]),
[final] ).
cnf(c_0_293,negated_conjecture,
product(e_3,e_5,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_285,c_0_287]),c_0_58])]),
[final] ).
cnf(c_0_295,plain,
~ product(e_1,e_5,e_1),
inference(spm,[status(thm)],[c_0_72,c_0_58]),
[final] ).
cnf(c_0_297,negated_conjecture,
~ product(e_2,e_3,e_4),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_290]),c_0_291]),
[final] ).
cnf(c_0_298,negated_conjecture,
~ product(e_5,e_4,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_292,c_0_293])]),
[final] ).
cnf(c_0_301,plain,
( ~ product(X1,X2,e_1)
| ~ product(X1,X2,e_5) ),
inference(spm,[status(thm)],[c_0_51,c_0_165]),
[final] ).
cnf(c_0_303,plain,
( ~ product(X1,e_2,X2)
| ~ product(X1,e_3,X2) ),
inference(spm,[status(thm)],[c_0_96,c_0_63]),
[final] ).
cnf(c_0_306,plain,
( ~ product(X1,X2,e_1)
| ~ product(X1,X2,e_3) ),
inference(spm,[status(thm)],[c_0_69,c_0_165]),
[final] ).
cnf(c_0_308,negated_conjecture,
product(e_5,e_4,e_3),
inference(sr,[status(thm)],[c_0_172,c_0_298]),
[final] ).
cnf(c_0_310,negated_conjecture,
~ product(e_3,e_4,e_5),
inference(spm,[status(thm)],[c_0_301,c_0_243]),
[final] ).
cnf(c_0_311,plain,
( ~ product(X1,X2,e_3)
| ~ product(X1,X2,e_5) ),
inference(spm,[status(thm)],[c_0_71,c_0_165]),
[final] ).
cnf(c_0_312,plain,
( ~ product(X1,X2,e_2)
| ~ product(X1,X2,e_5) ),
inference(spm,[status(thm)],[c_0_93,c_0_165]),
[final] ).
cnf(c_0_315,negated_conjecture,
~ product(e_2,e_2,e_3),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_305]),c_0_306]),
[final] ).
cnf(c_0_317,plain,
~ product(e_3,e_2,e_3),
inference(spm,[status(thm)],[c_0_303,c_0_58]),
[final] ).
cnf(c_0_321,negated_conjecture,
( ~ product(e_4,X1,e_3)
| ~ product(e_5,e_4,X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_247]),
[final] ).
cnf(c_0_324,axiom,
greater(e_3,e_2),
e_3_greater_e_2,
[final] ).
cnf(c_0_326,negated_conjecture,
~ product(e_2,e_2,e_1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_314]),c_0_315]),
[final] ).
cnf(c_0_328,plain,
~ product(e_3,e_2,e_1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_318]),c_0_224])]),
[final] ).
cnf(c_0_331,plain,
~ product(e_4,e_3,e_4),
inference(spm,[status(thm)],[c_0_268,c_0_58]),
[final] ).
cnf(c_0_335,negated_conjecture,
~ product(e_4,e_5,e_3),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_322,c_0_230]),c_0_323]),
[final] ).
cnf(c_0_338,plain,
( ~ next(X1,e_2)
| ~ product(X1,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_59,c_0_324]),
[final] ).
cnf(c_0_339,negated_conjecture,
product(e_2,e_5,e_4),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_325]),c_0_326]),
[final] ).
cnf(c_0_341,negated_conjecture,
~ product(e_3,e_2,e_4),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_329]),c_0_277]),
[final] ).
cnf(c_0_343,negated_conjecture,
~ product(e_2,e_1,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_332]),c_0_277]),
[final] ).
cnf(c_0_345,negated_conjecture,
~ product(e_4,e_4,e_5),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_336]),c_0_301]),
[final] ).
cnf(c_0_348,plain,
~ product(e_1,e_1,e_3),
inference(spm,[status(thm)],[c_0_338,c_0_145]),
[final] ).
cnf(c_0_351,negated_conjecture,
~ product(e_3,e_2,e_2),
inference(spm,[status(thm)],[c_0_221,c_0_293]),
[final] ).
cnf(c_0_354,plain,
~ product(e_1,e_2,e_1),
inference(spm,[status(thm)],[c_0_177,c_0_58]),
[final] ).
cnf(c_0_357,negated_conjecture,
product(e_3,e_1,e_4),
inference(sr,[status(thm)],[c_0_264,c_0_343]),
[final] ).
cnf(c_0_358,negated_conjecture,
~ product(e_4,e_3,e_3),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_344]),c_0_345]),
[final] ).
cnf(c_0_359,plain,
~ product(e_4,e_3,e_5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_346]),c_0_58])]),
[final] ).
cnf(c_0_360,plain,
~ product(e_1,e_3,e_1),
inference(spm,[status(thm)],[c_0_273,c_0_58]),
[final] ).
cnf(c_0_363,negated_conjecture,
product(e_1,e_4,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_286,c_0_293])]),
[final] ).
cnf(c_0_366,plain,
product(e_3,e_2,e_5),
inference(sr,[status(thm)],[c_0_350,c_0_351]),
[final] ).
cnf(c_0_367,negated_conjecture,
~ product(e_1,e_2,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_352,c_0_293])]),
[final] ).
cnf(c_0_369,negated_conjecture,
( ~ product(e_5,X1,e_2)
| product(e_4,e_5,X1) ),
inference(spm,[status(thm)],[c_0_124,c_0_339]),
[final] ).
cnf(c_0_376,negated_conjecture,
product(e_4,e_3,e_2),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_356,c_0_357]),c_0_358]),c_0_359]),c_0_360]),
[final] ).
cnf(c_0_378,negated_conjecture,
~ product(e_1,e_3,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_362]),c_0_363])]),
[final] ).
cnf(c_0_379,negated_conjecture,
~ product(e_1,e_3,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_364,c_0_293])]),
[final] ).
cnf(c_0_381,negated_conjecture,
~ product(e_1,e_2,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_368]),c_0_363])]),
[final] ).
cnf(c_0_385,negated_conjecture,
~ product(e_4,e_2,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_373,c_0_293])]),
[final] ).
cnf(c_0_386,plain,
~ product(e_4,e_2,e_5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_374]),c_0_58])]),
[final] ).
cnf(c_0_387,negated_conjecture,
( ~ product(e_1,X1,e_3)
| product(e_4,e_1,X1) ),
inference(spm,[status(thm)],[c_0_124,c_0_357]),
[final] ).
cnf(c_0_389,negated_conjecture,
~ product(e_2,e_3,e_2),
inference(spm,[status(thm)],[c_0_123,c_0_376]),
[final] ).
cnf(c_0_391,negated_conjecture,
product(e_1,e_2,e_4),
inference(sr,[status(thm)],[c_0_380,c_0_381]),
[final] ).
cnf(c_0_392,negated_conjecture,
( ~ product(e_3,X1,e_4)
| product(e_2,e_3,X1) ),
inference(spm,[status(thm)],[c_0_124,c_0_376]),
[final] ).
cnf(c_0_393,negated_conjecture,
product(e_4,e_5,e_1),
inference(sr,[status(thm)],[c_0_382,c_0_343]),
[final] ).
cnf(c_0_397,negated_conjecture,
product(e_1,e_3,e_5),
inference(sr,[status(thm)],[c_0_388,c_0_389]),
[final] ).
cnf(c_0_398,negated_conjecture,
product(e_5,e_3,e_4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_303,c_0_390]),c_0_391])]),
[final] ).
cnf(c_0_399,negated_conjecture,
product(e_2,e_3,e_1),
inference(spm,[status(thm)],[c_0_392,c_0_357]),
[final] ).
cnf(c_0_400,plain,
( ~ product(X1,X2,e_2)
| ~ product(X1,X2,e_3) ),
inference(spm,[status(thm)],[c_0_96,c_0_165]),
[final] ).
cnf(c_0_401,negated_conjecture,
( ~ product(e_5,X1,e_4)
| product(e_1,e_5,X1) ),
inference(spm,[status(thm)],[c_0_124,c_0_393]),
[final] ).
cnf(c_0_402,negated_conjecture,
product(e_5,e_2,e_1),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_394,c_0_341]),c_0_343]),c_0_351]),
[final] ).
cnf(c_0_403,negated_conjecture,
product(e_4,e_2,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_395]),c_0_366])]),
[final] ).
cnf(c_0_404,negated_conjecture,
product(e_4,e_1,e_5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_396]),c_0_363])]),
[final] ).
cnf(c_0_405,negated_conjecture,
( ~ product(e_3,X1,e_1)
| product(e_5,e_3,X1) ),
inference(spm,[status(thm)],[c_0_124,c_0_397]),
[final] ).
cnf(c_0_406,negated_conjecture,
( ~ product(e_3,X1,e_5)
| product(e_4,e_3,X1) ),
inference(spm,[status(thm)],[c_0_124,c_0_398]),
[final] ).
cnf(c_0_407,negated_conjecture,
( ~ product(e_3,X1,e_2)
| product(e_1,e_3,X1) ),
inference(spm,[status(thm)],[c_0_124,c_0_399]),
[final] ).
cnf(c_0_408,negated_conjecture,
~ product(e_1,e_5,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_400,c_0_401]),c_0_398])]),
[final] ).
cnf(c_0_409,negated_conjecture,
( ~ product(e_2,X1,e_5)
| product(e_1,e_2,X1) ),
inference(spm,[status(thm)],[c_0_124,c_0_402]),
[final] ).
cnf(c_0_410,negated_conjecture,
( ~ product(e_2,X1,e_1)
| product(e_4,e_2,X1) ),
inference(spm,[status(thm)],[c_0_124,c_0_391]),
[final] ).
cnf(c_0_411,negated_conjecture,
( ~ product(e_2,X1,e_4)
| product(e_3,e_2,X1) ),
inference(spm,[status(thm)],[c_0_124,c_0_403]),
[final] ).
cnf(c_0_412,negated_conjecture,
( ~ product(e_2,X1,e_3)
| product(e_5,e_2,X1) ),
inference(spm,[status(thm)],[c_0_124,c_0_366]),
[final] ).
cnf(c_0_414,negated_conjecture,
( ~ product(e_1,X1,e_4)
| product(e_5,e_1,X1) ),
inference(spm,[status(thm)],[c_0_124,c_0_404]),
[final] ).
cnf(c_0_418,negated_conjecture,
( ~ product(e_3,X1,e_1)
| ~ product(e_5,e_2,X1) ),
inference(spm,[status(thm)],[c_0_303,c_0_405]),
[final] ).
cnf(c_0_419,negated_conjecture,
( ~ product(e_3,X1,e_5)
| ~ product(e_4,e_2,X1) ),
inference(spm,[status(thm)],[c_0_303,c_0_406]),
[final] ).
cnf(c_0_420,negated_conjecture,
( ~ product(e_3,X1,e_2)
| ~ product(e_1,e_2,X1) ),
inference(spm,[status(thm)],[c_0_303,c_0_407]),
[final] ).
cnf(c_0_421,negated_conjecture,
( ~ product(e_5,X1,e_4)
| ~ product(e_1,e_4,X1) ),
inference(spm,[status(thm)],[c_0_128,c_0_401]),
[final] ).
cnf(c_0_422,negated_conjecture,
( ~ product(e_5,X1,e_4)
| ~ product(e_1,e_3,X1) ),
inference(spm,[status(thm)],[c_0_285,c_0_401]),
[final] ).
cnf(c_0_423,negated_conjecture,
( ~ product(e_5,X1,e_4)
| ~ product(e_1,e_2,X1) ),
inference(spm,[status(thm)],[c_0_221,c_0_401]),
[final] ).
cnf(c_0_424,negated_conjecture,
( ~ product(e_4,X1,e_2)
| ~ product(e_5,e_3,X1) ),
inference(spm,[status(thm)],[c_0_268,c_0_249]),
[final] ).
cnf(c_0_425,negated_conjecture,
( ~ product(e_4,X1,e_3)
| ~ product(e_1,e_2,X1) ),
inference(spm,[status(thm)],[c_0_202,c_0_247]),
[final] ).
cnf(c_0_426,negated_conjecture,
( ~ product(e_4,X1,e_3)
| ~ product(e_1,e_3,X1) ),
inference(spm,[status(thm)],[c_0_268,c_0_247]),
[final] ).
cnf(c_0_427,negated_conjecture,
product(e_1,e_5,e_3),
inference(sr,[status(thm)],[c_0_349,c_0_408]),
[final] ).
cnf(c_0_428,negated_conjecture,
( ~ product(e_4,X1,e_2)
| ~ product(e_5,e_2,X1) ),
inference(spm,[status(thm)],[c_0_202,c_0_249]),
[final] ).
cnf(c_0_429,negated_conjecture,
( ~ product(e_3,X1,e_1)
| ~ product(e_3,X2,e_5)
| product(X1,e_3,X2) ),
inference(spm,[status(thm)],[c_0_124,c_0_405]),
[final] ).
cnf(c_0_430,negated_conjecture,
( ~ product(e_2,X1,e_5)
| ~ product(e_2,X2,e_1)
| product(X1,e_2,X2) ),
inference(spm,[status(thm)],[c_0_124,c_0_409]),
[final] ).
cnf(c_0_431,negated_conjecture,
( ~ product(e_3,X1,e_5)
| ~ product(e_3,X2,e_4)
| product(X1,e_3,X2) ),
inference(spm,[status(thm)],[c_0_124,c_0_406]),
[final] ).
cnf(c_0_432,negated_conjecture,
( ~ product(e_3,X1,e_2)
| ~ product(e_3,X2,e_1)
| product(X1,e_3,X2) ),
inference(spm,[status(thm)],[c_0_124,c_0_407]),
[final] ).
cnf(c_0_433,negated_conjecture,
( ~ product(e_2,X1,e_1)
| ~ product(e_2,X2,e_4)
| product(X1,e_2,X2) ),
inference(spm,[status(thm)],[c_0_124,c_0_410]),
[final] ).
cnf(c_0_434,negated_conjecture,
( ~ product(e_5,X1,e_4)
| ~ product(e_5,X2,e_1)
| product(X1,e_5,X2) ),
inference(spm,[status(thm)],[c_0_124,c_0_401]),
[final] ).
cnf(c_0_435,negated_conjecture,
( ~ product(e_2,X1,e_4)
| ~ product(e_2,X2,e_3)
| product(X1,e_2,X2) ),
inference(spm,[status(thm)],[c_0_124,c_0_411]),
[final] ).
cnf(c_0_436,plain,
product(e_2,e_1,e_3),
inference(sr,[status(thm)],[c_0_113,c_0_343]),
[final] ).
cnf(c_0_437,negated_conjecture,
( ~ product(e_2,X1,e_3)
| ~ product(e_2,X2,e_5)
| product(X1,e_2,X2) ),
inference(spm,[status(thm)],[c_0_124,c_0_412]),
[final] ).
cnf(c_0_438,negated_conjecture,
( ~ product(e_4,X1,e_2)
| ~ product(e_4,X2,e_5)
| product(X1,e_4,X2) ),
inference(spm,[status(thm)],[c_0_124,c_0_249]),
[final] ).
cnf(c_0_439,negated_conjecture,
( ~ product(e_4,X1,e_3)
| ~ product(e_4,X2,e_1)
| product(X1,e_4,X2) ),
inference(spm,[status(thm)],[c_0_124,c_0_247]),
[final] ).
cnf(c_0_440,plain,
product(e_5,e_1,e_2),
inference(sr,[status(thm)],[c_0_370,c_0_343]),
[final] ).
cnf(c_0_442,axiom,
greater(e_2,e_1),
e_2_greater_e_1,
[final] ).
cnf(c_0_443,axiom,
greater(e_3,e_1),
e_3_greater_e_1,
[final] ).
cnf(c_0_444,axiom,
greater(e_4,e_1),
e_4_greater_e_1,
[final] ).
cnf(c_0_445,axiom,
greater(e_5,e_1),
e_5_greater_e_1,
[final] ).
cnf(c_0_448,plain,
( ~ product(X1,X2,e_1)
| ~ product(X1,X2,e_4) ),
inference(spm,[status(thm)],[c_0_100,c_0_165]),
[final] ).
cnf(c_0_449,plain,
( ~ product(X1,X2,e_3)
| ~ product(X1,X2,e_4) ),
inference(spm,[status(thm)],[c_0_114,c_0_165]),
[final] ).
cnf(c_0_472,negated_conjecture,
( ~ product(e_2,X1,e_3)
| ~ product(e_3,X1,e_1) ),
inference(spm,[status(thm)],[c_0_418,c_0_412]),
[final] ).
cnf(c_0_473,negated_conjecture,
( ~ product(e_2,X1,e_1)
| ~ product(e_3,X1,e_5) ),
inference(spm,[status(thm)],[c_0_419,c_0_410]),
[final] ).
cnf(c_0_474,negated_conjecture,
( ~ product(e_2,X1,e_5)
| ~ product(e_3,X1,e_2) ),
inference(spm,[status(thm)],[c_0_420,c_0_409]),
[final] ).
cnf(c_0_475,negated_conjecture,
( ~ product(e_4,X1,e_3)
| ~ product(e_5,X1,e_4) ),
inference(spm,[status(thm)],[c_0_421,c_0_247]),
[final] ).
cnf(c_0_476,negated_conjecture,
( ~ product(e_3,X1,e_2)
| ~ product(e_5,X1,e_4) ),
inference(spm,[status(thm)],[c_0_422,c_0_407]),
[final] ).
cnf(c_0_477,negated_conjecture,
( ~ product(e_2,X1,e_5)
| ~ product(e_5,X1,e_4) ),
inference(spm,[status(thm)],[c_0_423,c_0_409]),
[final] ).
cnf(c_0_478,negated_conjecture,
( ~ product(e_3,X1,e_1)
| ~ product(e_4,X1,e_2) ),
inference(spm,[status(thm)],[c_0_424,c_0_405]),
[final] ).
cnf(c_0_479,negated_conjecture,
( ~ product(e_3,X1,e_1)
| ~ product(e_4,e_3,X1) ),
inference(spm,[status(thm)],[c_0_120,c_0_405]),
[final] ).
cnf(c_0_480,negated_conjecture,
( ~ product(e_3,X1,e_1)
| ~ product(e_3,e_3,X1) ),
inference(spm,[status(thm)],[c_0_83,c_0_405]),
[final] ).
cnf(c_0_481,negated_conjecture,
( ~ product(e_3,X1,e_1)
| ~ product(e_2,e_3,X1) ),
inference(spm,[status(thm)],[c_0_102,c_0_405]),
[final] ).
cnf(c_0_482,negated_conjecture,
( ~ product(e_2,X1,e_5)
| ~ product(e_4,X1,e_3) ),
inference(spm,[status(thm)],[c_0_425,c_0_409]),
[final] ).
cnf(c_0_483,negated_conjecture,
( ~ product(e_2,X1,e_5)
| ~ product(e_3,e_2,X1) ),
inference(spm,[status(thm)],[c_0_76,c_0_409]),
[final] ).
cnf(c_0_484,negated_conjecture,
( ~ product(e_2,X1,e_5)
| ~ product(e_4,e_2,X1) ),
inference(spm,[status(thm)],[c_0_110,c_0_409]),
[final] ).
cnf(c_0_485,negated_conjecture,
( ~ product(e_2,X1,e_5)
| ~ product(e_5,e_2,X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_409]),
[final] ).
cnf(c_0_486,negated_conjecture,
( ~ product(e_2,X1,e_5)
| ~ product(e_2,e_2,X1) ),
inference(spm,[status(thm)],[c_0_99,c_0_409]),
[final] ).
cnf(c_0_487,negated_conjecture,
( ~ product(e_3,X1,e_5)
| ~ product(e_3,e_3,X1) ),
inference(spm,[status(thm)],[c_0_122,c_0_406]),
[final] ).
cnf(c_0_488,negated_conjecture,
( ~ product(e_3,X1,e_5)
| ~ product(e_2,e_3,X1) ),
inference(spm,[status(thm)],[c_0_123,c_0_406]),
[final] ).
cnf(c_0_489,negated_conjecture,
( ~ product(e_3,X1,e_2)
| ~ product(e_4,X1,e_3) ),
inference(spm,[status(thm)],[c_0_426,c_0_407]),
[final] ).
cnf(c_0_490,negated_conjecture,
( ~ product(e_3,X1,e_2)
| ~ product(e_3,e_3,X1) ),
inference(spm,[status(thm)],[c_0_76,c_0_407]),
[final] ).
cnf(c_0_491,negated_conjecture,
( ~ product(e_3,X1,e_2)
| ~ product(e_4,e_3,X1) ),
inference(spm,[status(thm)],[c_0_110,c_0_407]),
[final] ).
cnf(c_0_492,negated_conjecture,
( ~ product(e_3,X1,e_2)
| ~ product(e_5,e_3,X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_407]),
[final] ).
cnf(c_0_493,negated_conjecture,
( ~ product(e_3,X1,e_2)
| ~ product(e_2,e_3,X1) ),
inference(spm,[status(thm)],[c_0_99,c_0_407]),
[final] ).
cnf(c_0_494,negated_conjecture,
( ~ product(e_2,X1,e_1)
| ~ product(e_3,e_2,X1) ),
inference(spm,[status(thm)],[c_0_122,c_0_410]),
[final] ).
cnf(c_0_495,negated_conjecture,
( ~ product(e_2,X1,e_1)
| ~ product(e_2,e_2,X1) ),
inference(spm,[status(thm)],[c_0_123,c_0_410]),
[final] ).
cnf(c_0_496,negated_conjecture,
( ~ product(e_5,X1,e_4)
| ~ product(e_3,e_5,X1) ),
inference(spm,[status(thm)],[c_0_76,c_0_401]),
[final] ).
cnf(c_0_497,negated_conjecture,
( ~ product(e_5,X1,e_4)
| ~ product(e_4,e_5,X1) ),
inference(spm,[status(thm)],[c_0_110,c_0_401]),
[final] ).
cnf(c_0_498,negated_conjecture,
( ~ product(e_5,X1,e_4)
| ~ product(e_5,e_5,X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_401]),
[final] ).
cnf(c_0_499,negated_conjecture,
( ~ product(e_5,X1,e_4)
| ~ product(e_2,e_5,X1) ),
inference(spm,[status(thm)],[c_0_99,c_0_401]),
[final] ).
cnf(c_0_500,negated_conjecture,
( ~ product(e_5,X1,e_1)
| product(e_3,e_5,X1) ),
inference(spm,[status(thm)],[c_0_124,c_0_427]),
[final] ).
cnf(c_0_501,negated_conjecture,
( ~ product(e_2,X1,e_4)
| ~ product(e_2,e_2,X1) ),
inference(spm,[status(thm)],[c_0_104,c_0_411]),
[final] ).
cnf(c_0_502,negated_conjecture,
( ~ product(e_2,X1,e_3)
| ~ product(e_4,X1,e_2) ),
inference(spm,[status(thm)],[c_0_428,c_0_412]),
[final] ).
cnf(c_0_503,negated_conjecture,
( ~ product(e_2,X1,e_3)
| ~ product(e_4,e_2,X1) ),
inference(spm,[status(thm)],[c_0_120,c_0_412]),
[final] ).
cnf(c_0_504,negated_conjecture,
( ~ product(e_2,X1,e_3)
| ~ product(e_3,e_2,X1) ),
inference(spm,[status(thm)],[c_0_83,c_0_412]),
[final] ).
cnf(c_0_505,negated_conjecture,
( ~ product(e_2,X1,e_3)
| ~ product(e_2,e_2,X1) ),
inference(spm,[status(thm)],[c_0_102,c_0_412]),
[final] ).
cnf(c_0_506,negated_conjecture,
( ~ product(e_3,X1,e_1)
| product(X1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_429,c_0_366]),
[final] ).
cnf(c_0_507,negated_conjecture,
( ~ product(e_2,X1,e_5)
| product(X1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_430,c_0_399]),
[final] ).
cnf(c_0_508,negated_conjecture,
( ~ product(e_3,X1,e_5)
| product(X1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_431,c_0_357]),
[final] ).
cnf(c_0_509,negated_conjecture,
( ~ product(e_3,X1,e_2)
| product(X1,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_432,c_0_243]),
[final] ).
cnf(c_0_510,negated_conjecture,
( ~ product(e_2,X1,e_1)
| product(X1,e_2,e_5) ),
inference(spm,[status(thm)],[c_0_433,c_0_339]),
[final] ).
cnf(c_0_511,negated_conjecture,
( ~ product(e_5,X1,e_4)
| product(X1,e_5,e_2) ),
inference(spm,[status(thm)],[c_0_434,c_0_402]),
[final] ).
cnf(c_0_512,negated_conjecture,
( ~ product(e_2,X1,e_4)
| product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_435,c_0_436]),
[final] ).
cnf(c_0_513,negated_conjecture,
( ~ product(e_2,X1,e_3)
| product(X1,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_437,c_0_224]),
[final] ).
cnf(c_0_514,negated_conjecture,
( ~ product(e_4,X1,e_2)
| product(X1,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_438,c_0_404]),
[final] ).
cnf(c_0_515,negated_conjecture,
( ~ product(e_4,X1,e_3)
| product(X1,e_4,e_5) ),
inference(spm,[status(thm)],[c_0_439,c_0_393]),
[final] ).
cnf(c_0_516,negated_conjecture,
( ~ product(e_1,X1,e_5)
| product(e_2,e_1,X1) ),
inference(spm,[status(thm)],[c_0_124,c_0_440]),
[final] ).
cnf(c_0_517,negated_conjecture,
( ~ product(e_1,X1,e_2)
| product(e_3,e_1,X1) ),
inference(spm,[status(thm)],[c_0_124,c_0_436]),
[final] ).
cnf(c_0_518,negated_conjecture,
( ~ product(e_4,X1,e_5)
| product(e_3,e_4,X1) ),
inference(spm,[status(thm)],[c_0_124,c_0_308]),
[final] ).
cnf(c_0_519,negated_conjecture,
( ~ product(e_5,X1,e_3)
| product(e_2,e_5,X1) ),
inference(spm,[status(thm)],[c_0_124,c_0_293]),
[final] ).
cnf(c_0_520,negated_conjecture,
( ~ product(e_4,X1,e_1)
| product(e_2,e_4,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_441,c_0_293])]),
[final] ).
cnf(c_0_521,negated_conjecture,
( ~ product(e_4,X1,e_3)
| ~ product(e_3,e_4,X1) ),
inference(spm,[status(thm)],[c_0_76,c_0_247]),
[final] ).
cnf(c_0_522,negated_conjecture,
( ~ product(e_4,X1,e_3)
| ~ product(e_4,e_4,X1) ),
inference(spm,[status(thm)],[c_0_110,c_0_247]),
[final] ).
cnf(c_0_523,negated_conjecture,
( ~ product(e_4,X1,e_3)
| ~ product(e_2,e_4,X1) ),
inference(spm,[status(thm)],[c_0_99,c_0_247]),
[final] ).
cnf(c_0_524,negated_conjecture,
( ~ product(e_4,X1,e_2)
| ~ product(e_4,e_4,X1) ),
inference(spm,[status(thm)],[c_0_120,c_0_249]),
[final] ).
cnf(c_0_525,negated_conjecture,
( ~ product(e_4,X1,e_2)
| ~ product(e_3,e_4,X1) ),
inference(spm,[status(thm)],[c_0_83,c_0_249]),
[final] ).
cnf(c_0_526,negated_conjecture,
( ~ product(e_4,X1,e_2)
| ~ product(e_2,e_4,X1) ),
inference(spm,[status(thm)],[c_0_102,c_0_249]),
[final] ).
cnf(c_0_527,plain,
( ~ next(X1,e_1)
| ~ product(X1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_59,c_0_442]),
[final] ).
cnf(c_0_528,plain,
( ~ next(X1,e_1)
| ~ product(X1,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_59,c_0_443]),
[final] ).
cnf(c_0_529,plain,
( ~ next(X1,e_1)
| ~ product(X1,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_59,c_0_444]),
[final] ).
cnf(c_0_530,plain,
( ~ next(X1,e_1)
| ~ product(X1,e_1,e_5) ),
inference(spm,[status(thm)],[c_0_59,c_0_445]),
[final] ).
cnf(c_0_531,negated_conjecture,
~ product(e_1,e_2,e_5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_303,c_0_446]),c_0_391])]),
[final] ).
cnf(c_0_532,negated_conjecture,
~ product(e_5,e_4,e_4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_312,c_0_447]),c_0_440])]),
[final] ).
cnf(c_0_533,negated_conjecture,
~ product(e_3,e_3,e_5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_400,c_0_406]),c_0_376])]),
[final] ).
cnf(c_0_534,negated_conjecture,
~ product(e_1,e_3,e_4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_245,c_0_407]),c_0_293])]),
[final] ).
cnf(c_0_535,negated_conjecture,
~ product(e_4,e_1,e_4),
inference(spm,[status(thm)],[c_0_245,c_0_404]),
[final] ).
cnf(c_0_536,negated_conjecture,
~ product(e_5,e_1,e_4),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_401]),c_0_196]),
[final] ).
cnf(c_0_537,negated_conjecture,
~ product(e_4,e_5,e_4),
inference(spm,[status(thm)],[c_0_448,c_0_393]),
[final] ).
cnf(c_0_538,plain,
~ product(e_5,e_3,e_2),
inference(spm,[status(thm)],[c_0_273,c_0_440]),
[final] ).
cnf(c_0_539,plain,
~ product(e_5,e_2,e_2),
inference(spm,[status(thm)],[c_0_177,c_0_440]),
[final] ).
cnf(c_0_540,negated_conjecture,
~ product(e_3,e_1,e_3),
inference(spm,[status(thm)],[c_0_449,c_0_357]),
[final] ).
cnf(c_0_541,negated_conjecture,
~ product(e_3,e_5,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_450]),c_0_363])]),
[final] ).
cnf(c_0_542,negated_conjecture,
~ product(e_1,e_4,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_451]),c_0_363])]),
[final] ).
cnf(c_0_543,negated_conjecture,
~ product(e_5,e_2,e_4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_452]),c_0_403])]),
[final] ).
cnf(c_0_544,negated_conjecture,
~ product(e_3,e_5,e_1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_453]),c_0_345]),
[final] ).
cnf(c_0_545,negated_conjecture,
~ product(e_2,e_5,e_1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_454]),c_0_345]),
[final] ).
cnf(c_0_546,negated_conjecture,
~ product(e_4,e_4,e_1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_455]),c_0_345]),
[final] ).
cnf(c_0_547,negated_conjecture,
~ product(e_4,e_3,e_1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_456]),c_0_345]),
[final] ).
cnf(c_0_548,negated_conjecture,
~ product(e_4,e_2,e_1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_457]),c_0_345]),
[final] ).
cnf(c_0_549,negated_conjecture,
~ product(e_2,e_5,e_2),
inference(spm,[status(thm)],[c_0_104,c_0_293]),
[final] ).
cnf(c_0_550,negated_conjecture,
~ product(e_5,e_3,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_458,c_0_293])]),
[final] ).
cnf(c_0_551,negated_conjecture,
~ product(e_5,e_2,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_459,c_0_293])]),
[final] ).
cnf(c_0_552,negated_conjecture,
~ product(e_3,e_3,e_4),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_460]),c_0_277]),
[final] ).
cnf(c_0_553,negated_conjecture,
~ product(e_2,e_2,e_4),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_461]),c_0_291]),
[final] ).
cnf(c_0_554,plain,
~ product(e_5,e_3,e_5),
inference(spm,[status(thm)],[c_0_285,c_0_58]),
[final] ).
cnf(c_0_555,plain,
~ product(e_5,e_5,e_3),
inference(spm,[status(thm)],[c_0_311,c_0_58]),
[final] ).
cnf(c_0_556,plain,
~ product(e_4,e_4,e_3),
inference(spm,[status(thm)],[c_0_449,c_0_58]),
[final] ).
cnf(c_0_557,plain,
~ product(e_5,e_2,e_5),
inference(spm,[status(thm)],[c_0_221,c_0_58]),
[final] ).
cnf(c_0_558,plain,
~ product(e_5,e_5,e_2),
inference(spm,[status(thm)],[c_0_312,c_0_58]),
[final] ).
cnf(c_0_559,plain,
~ product(e_4,e_4,e_2),
inference(spm,[status(thm)],[c_0_263,c_0_58]),
[final] ).
cnf(c_0_560,plain,
~ product(e_3,e_3,e_2),
inference(spm,[status(thm)],[c_0_400,c_0_58]),
[final] ).
cnf(c_0_561,plain,
~ equalish(e_5,e_4),
c_0_462,
[final] ).
cnf(c_0_562,plain,
~ equalish(e_5,e_3),
c_0_463,
[final] ).
cnf(c_0_563,plain,
~ equalish(e_5,e_2),
c_0_464,
[final] ).
cnf(c_0_564,plain,
~ equalish(e_5,e_1),
c_0_465,
[final] ).
cnf(c_0_565,plain,
~ equalish(e_4,e_3),
c_0_466,
[final] ).
cnf(c_0_566,plain,
~ equalish(e_4,e_2),
c_0_467,
[final] ).
cnf(c_0_567,plain,
~ equalish(e_4,e_1),
c_0_468,
[final] ).
cnf(c_0_568,plain,
~ equalish(e_3,e_2),
c_0_469,
[final] ).
cnf(c_0_569,plain,
~ equalish(e_3,e_1),
c_0_470,
[final] ).
cnf(c_0_570,plain,
~ equalish(e_1,e_2),
c_0_471,
[final] ).
cnf(c_0_571,axiom,
next(e_4,e_5),
e_4_then_e_5,
[final] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP127-2.005 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.44 % Computer : n001.cluster.edu
% 0.20/0.44 % Model : x86_64 x86_64
% 0.20/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.44 % Memory : 8046.5625MB
% 0.20/0.44 % OS : Linux 6.8.0-71-generic
% 0.20/0.44 % CPULimit : 300
% 0.20/0.44 % WCLimit : 300
% 0.20/0.44 % DateTime : Sun Sep 20 20:05:42 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.45 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.28/0.52 Running first-order theorem proving
% 0.28/0.52 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
% 1.06/0.68 % Version: 3.5.1
% 1.06/0.68 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.06/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.06/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.06/0.68 % Starting new_bool_3 with 300s (1) cores
% 1.06/0.68 % Starting new_bool_1 with 300s (1) cores
% 1.06/0.68 % Starting sh5l with 300s (1) cores
% 1.06/0.68 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1276797 completed with status 1
% 1.06/0.68 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 1.06/0.68 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.06/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.06/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.06/0.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.06/0.68 % No SInE strategy applied
% 1.06/0.68 % Search class: FGHNF-FFSM00-SFFFFFNN
% 1.06/0.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.06/0.68 % Starting SubtermCWHack with 136s (1) cores
% 1.06/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.06/0.68 % Starting G----_404_C05_02_F1_SE_CS_SP_PS_RG_S04AI with 136s (1) cores
% 1.06/0.68 % Starting new_bool_3 with 136s (1) cores
% 1.06/0.68 % Starting new_bool_1 with 136s (1) cores
% 1.06/0.68 % G----_404_C05_02_F1_SE_CS_SP_PS_RG_S04AI with pid 1276806 completed with status 1
% 1.06/0.68 % Result found by G----_404_C05_02_F1_SE_CS_SP_PS_RG_S04AI
% 1.06/0.68 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.06/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.06/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.06/0.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.06/0.68 % No SInE strategy applied
% 1.06/0.68 % Search class: FGHNF-FFSM00-SFFFFFNN
% 1.06/0.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.06/0.68 % Starting SubtermCWHack with 136s (1) cores
% 1.06/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.06/0.68 % Starting G----_404_C05_02_F1_SE_CS_SP_PS_RG_S04AI with 136s (1) cores
% 1.06/0.68 % Preprocessing time : 0.001 s
% 1.06/0.68 % Presaturation interreduction done
% 1.06/0.68
% 1.06/0.68 % No proof found!
% 1.06/0.68 % SZS status Satisfiable
% 1.06/0.68 % SZS output start Saturation
% See solution above
% 1.06/0.68 % Parsed axioms : 46
% 1.06/0.68 % Removed by relevancy pruning/SinE : 0
% 1.06/0.68 % Initial clauses : 46
% 1.06/0.68 % Removed in clause preprocessing : 0
% 1.06/0.68 % Initial clauses in saturation : 46
% 1.06/0.68 % Processed clauses : 1827
% 1.06/0.68 % ...of these trivial : 28
% 1.06/0.68 % ...subsumed : 749
% 1.06/0.68 % ...remaining for further processing : 1050
% 1.06/0.68 % Other redundant clauses eliminated : 0
% 1.06/0.68 % Clauses deleted for lack of memory : 0
% 1.06/0.68 % Backward-subsumed : 566
% 1.06/0.68 % Backward-rewritten : 53
% 1.06/0.68 % Generated clauses : 3558
% 1.06/0.68 % ...of the previous two non-redundant : 3226
% 1.06/0.68 % ...aggressively subsumed : 0
% 1.06/0.68 % Contextual simplify-reflections : 49
% 1.06/0.68 % Paramodulations : 3466
% 1.06/0.68 % Factorizations : 0
% 1.06/0.68 % NegExts : 0
% 1.06/0.68 % Equation resolutions : 0
% 1.06/0.68 % Disequality decompositions : 0
% 1.06/0.68 % Total rewrite steps : 304
% 1.06/0.68 % ...of those cached : 278
% 1.06/0.68 % Propositional unsat checks : 0
% 1.06/0.68 % Propositional check models : 0
% 1.06/0.68 % Propositional check unsatisfiable : 0
% 1.06/0.68 % Propositional clauses : 0
% 1.06/0.68 % Propositional clauses after purity: 0
% 1.06/0.68 % Propositional unsat core size : 0
% 1.06/0.68 % Propositional preprocessing time : 0.000
% 1.06/0.68 % Propositional encoding time : 0.000
% 1.06/0.68 % Propositional solver time : 0.000
% 1.06/0.68 % Success case prop preproc time : 0.000
% 1.06/0.68 % Success case prop encoding time : 0.000
% 1.06/0.68 % Success case prop solver time : 0.000
% 1.06/0.68 % Current number of processed clauses : 293
% 1.06/0.68 % Positive orientable unit clauses : 40
% 1.06/0.68 % Positive unorientable unit clauses: 0
% 1.06/0.68 % Negative unit clauses : 111
% 1.06/0.68 % Non-unit-clauses : 142
% 1.06/0.68 % Current number of unprocessed clauses: 0
% 1.06/0.68 % ...number of literals in the above : 0
% 1.06/0.68 % Current number of archived formulas : 0
% 1.06/0.68 % Current number of archived clauses : 757
% 1.06/0.68 % Clause-clause subsumption calls (NU) : 47552
% 1.06/0.68 % Rec. Clause-clause subsumption calls : 27067
% 1.06/0.68 % Non-unit clause-clause subsumptions : 511
% 1.06/0.68 % Unit Clause-clause subsumption calls : 1742
% 1.06/0.68 % Rewrite failures with RHS unbound : 0
% 1.06/0.68 % BW rewrite match attempts : 107
% 1.06/0.68 % BW rewrite match successes : 17
% 1.06/0.68 % Condensation attempts : 0
% 1.06/0.68 % Condensation successes : 0
% 1.06/0.68 % Termbank termtop insertions : 38266
% 1.06/0.68 % Search garbage collected termcells : 72
% 1.06/0.68
% 1.06/0.68 % -------------------------------------------------
% 1.06/0.68 % User time : 0.126 s
% 1.06/0.68 % System time : 0.006 s
% 1.06/0.68 % Total time : 0.132 s
% 1.06/0.68 % Maximum resident set size: 3600 pages
% 1.06/0.68
% 1.06/0.68 % -------------------------------------------------
% 1.06/0.68 % User time : 0.642 s
% 1.06/0.68 % System time : 0.029 s
% 1.06/0.68 % Total time : 0.671 s
% 1.06/0.68 % Maximum resident set size: 4864 pages
% 1.06/0.68 % E exiting
%------------------------------------------------------------------------------