%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP123-3.004 : 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 : n002.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 12:37:56 PM UTC 2026
% Result : Satisfiable 1.53s 0.62s
% Output : Saturation 1.53s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_52ERROR: Could not build tree for root c_0_68ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(c_0_48,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
c_0_44,
[final] ).
cnf(c_0_49,axiom,
product(X1,X1,X1),
product_idempotence,
[final] ).
cnf(c_0_51,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
c_0_45,
[final] ).
cnf(c_0_53,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_46,
[final] ).
cnf(c_0_54,axiom,
group_element(e_4),
element_4,
[final] ).
cnf(c_0_55,plain,
~ equalish(e_3,e_4),
c_0_47,
[final] ).
cnf(c_0_56,plain,
( ~ product(X1,X2,X2)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]),
[final] ).
cnf(c_0_57,plain,
~ equalish(e_4,e_3),
c_0_50,
[final] ).
cnf(c_0_58,plain,
( ~ product(X2,X1,X2)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_49]),
[final] ).
cnf(c_0_59,negated_conjecture,
( ~ product(X6,X5,X4)
| ~ product(X6,X2,X1)
| ~ product(X4,X5,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X5) ),
c_0_52,
[final] ).
cnf(c_0_60,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_53,c_0_54]),
[final] ).
cnf(c_0_61,axiom,
group_element(e_3),
element_3,
[final] ).
cnf(c_0_62,plain,
~ product(e_3,e_4,e_4),
inference(spm,[status(thm)],[c_0_55,c_0_56]),
[final] ).
cnf(c_0_63,plain,
~ product(e_3,e_4,e_3),
inference(spm,[status(thm)],[c_0_57,c_0_58]),
[final] ).
cnf(c_0_64,negated_conjecture,
( ~ product(X3,X1,X4)
| ~ product(X2,X2,X4)
| ~ product(X2,X1,X3)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_59,c_0_49]),
[final] ).
cnf(c_0_65,plain,
( product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]),c_0_63]),
[final] ).
cnf(c_0_68,negated_conjecture,
( ~ product(e_2,e_4,X1)
| ~ product(e_3,e_3,X1)
| product(e_3,e_4,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_57]),
[final] ).
cnf(c_0_69,plain,
~ equalish(e_2,e_4),
c_0_66,
[final] ).
cnf(c_0_70,plain,
~ equalish(e_4,e_2),
c_0_67,
[final] ).
cnf(c_0_74,axiom,
group_element(e_2),
element_2,
[final] ).
cnf(c_0_75,plain,
~ product(e_2,e_4,e_4),
inference(spm,[status(thm)],[c_0_69,c_0_56]),
[final] ).
cnf(c_0_76,plain,
~ product(e_2,e_4,e_2),
inference(spm,[status(thm)],[c_0_70,c_0_58]),
[final] ).
cnf(c_0_77,axiom,
group_element(e_1),
element_1,
[final] ).
cnf(c_0_78,plain,
~ equalish(e_1,e_4),
c_0_71,
[final] ).
cnf(c_0_79,plain,
~ equalish(e_4,e_1),
c_0_72,
[final] ).
cnf(c_0_84,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_53,c_0_77]),
[final] ).
cnf(c_0_85,plain,
~ product(e_4,e_1,e_4),
inference(spm,[status(thm)],[c_0_78,c_0_58]),
[final] ).
cnf(c_0_86,plain,
~ product(e_4,e_1,e_1),
inference(spm,[status(thm)],[c_0_79,c_0_56]),
[final] ).
cnf(c_0_87,plain,
~ equalish(e_1,e_2),
c_0_80,
[final] ).
cnf(c_0_88,plain,
~ equalish(e_2,e_1),
c_0_81,
[final] ).
cnf(c_0_90,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_53,c_0_61]),
[final] ).
cnf(c_0_91,plain,
~ product(e_4,e_3,e_4),
inference(spm,[status(thm)],[c_0_55,c_0_58]),
[final] ).
cnf(c_0_92,plain,
~ product(e_4,e_3,e_3),
inference(spm,[status(thm)],[c_0_57,c_0_56]),
[final] ).
cnf(c_0_95,plain,
~ product(e_2,e_1,e_2),
inference(spm,[status(thm)],[c_0_87,c_0_58]),
[final] ).
cnf(c_0_96,plain,
~ product(e_2,e_1,e_1),
inference(spm,[status(thm)],[c_0_88,c_0_56]),
[final] ).
cnf(c_0_105,plain,
( ~ greater(X2,X1)
| ~ product(X1,e_1,X2)
| ~ cycle(X1,e_0) ),
c_0_94,
[final] ).
cnf(c_0_107,axiom,
greater(e_4,e_2),
e_4_greater_e_2,
[final] ).
cnf(c_0_108,plain,
( ~ group_element(X1)
| cycle(X1,e_3)
| cycle(X1,e_2)
| cycle(X1,e_1)
| cycle(X1,e_0) ),
c_0_97,
[final] ).
cnf(c_0_110,plain,
~ product(e_1,e_4,e_4),
inference(spm,[status(thm)],[c_0_78,c_0_56]),
[final] ).
cnf(c_0_111,plain,
~ product(e_1,e_4,e_1),
inference(spm,[status(thm)],[c_0_79,c_0_58]),
[final] ).
cnf(c_0_112,plain,
~ equalish(e_2,e_3),
c_0_99,
[final] ).
cnf(c_0_113,plain,
~ equalish(e_3,e_2),
c_0_100,
[final] ).
cnf(c_0_116,plain,
~ equalish(e_1,e_3),
c_0_103,
[final] ).
cnf(c_0_118,plain,
( ~ next(X1,X4)
| ~ greater(X2,e_0)
| ~ product(X1,e_1,X3)
| ~ cycle(X1,X2)
| equalish(X3,X4) ),
c_0_104,
[final] ).
cnf(c_0_123,plain,
~ product(e_2,e_3,e_3),
inference(spm,[status(thm)],[c_0_112,c_0_56]),
[final] ).
cnf(c_0_124,plain,
~ product(e_2,e_3,e_2),
inference(spm,[status(thm)],[c_0_113,c_0_58]),
[final] ).
cnf(c_0_126,plain,
~ equalish(e_3,e_1),
c_0_117,
[final] ).
cnf(c_0_130,axiom,
greater(e_3,e_0),
e_3_greater_e_0,
[final] ).
cnf(c_0_134,plain,
~ product(e_3,e_1,e_3),
inference(spm,[status(thm)],[c_0_116,c_0_58]),
[final] ).
cnf(c_0_135,plain,
~ product(e_3,e_1,e_1),
inference(spm,[status(thm)],[c_0_126,c_0_56]),
[final] ).
cnf(c_0_138,axiom,
next(e_2,e_3),
e_2_then_e_3,
[final] ).
cnf(c_0_145,axiom,
greater(e_2,e_0),
e_2_greater_e_0,
[final] ).
cnf(c_0_150,plain,
~ product(e_1,e_3,e_3),
inference(spm,[status(thm)],[c_0_116,c_0_56]),
[final] ).
cnf(c_0_151,plain,
~ product(e_1,e_3,e_1),
inference(spm,[status(thm)],[c_0_126,c_0_58]),
[final] ).
cnf(c_0_159,axiom,
greater(e_1,e_0),
e_1_greater_e_0,
[final] ).
cnf(c_0_164,axiom,
greater(e_4,e_3),
e_4_greater_e_3,
[final] ).
cnf(c_0_167,plain,
product(e_2,e_1,e_3),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_138]),c_0_57]),
[final] ).
cnf(c_0_172,negated_conjecture,
product(e_1,e_3,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_166,c_0_167])]),
[final] ).
cnf(c_0_173,plain,
( ~ next(X4,X5)
| ~ greater(X2,e_0)
| ~ next(X1,X3)
| ~ cycle(X3,X4)
| ~ cycle(X1,X2)
| equalish(X2,X5) ),
c_0_168,
[final] ).
cnf(c_0_175,negated_conjecture,
~ product(e_3,e_1,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_171,c_0_172])]),
[final] ).
cnf(c_0_176,plain,
( ~ next(X2,X3)
| ~ next(X4,X1)
| ~ cycle(X3,X4)
| ~ cycle(X2,e_3)
| equalish(e_3,X1) ),
inference(spm,[status(thm)],[c_0_173,c_0_130]),
[final] ).
cnf(c_0_179,axiom,
next(e_3,e_4),
e_3_then_e_4,
[final] ).
cnf(c_0_180,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_53,c_0_74]),
[final] ).
cnf(c_0_181,plain,
~ product(e_4,e_2,e_4),
inference(spm,[status(thm)],[c_0_69,c_0_58]),
[final] ).
cnf(c_0_182,plain,
~ product(e_4,e_2,e_2),
inference(spm,[status(thm)],[c_0_70,c_0_56]),
[final] ).
cnf(c_0_184,axiom,
cycle(e_4,e_0),
cycle3,
[final] ).
cnf(c_0_187,axiom,
next(e_0,e_1),
e_0_then_e_1,
[final] ).
cnf(c_0_188,plain,
~ product(e_3,e_2,e_3),
inference(spm,[status(thm)],[c_0_112,c_0_58]),
[final] ).
cnf(c_0_189,plain,
~ product(e_3,e_2,e_2),
inference(spm,[status(thm)],[c_0_113,c_0_56]),
[final] ).
cnf(c_0_191,axiom,
greater(e_3,e_2),
e_3_greater_e_2,
[final] ).
cnf(c_0_192,plain,
( ~ next(X2,X3)
| ~ next(X4,X1)
| ~ cycle(X3,X4)
| ~ cycle(X2,e_2)
| equalish(e_2,X1) ),
inference(spm,[status(thm)],[c_0_173,c_0_145]),
[final] ).
cnf(c_0_197,plain,
~ cycle(e_2,e_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_167]),c_0_191])]),
[final] ).
cnf(c_0_210,plain,
~ product(e_1,e_2,e_2),
inference(spm,[status(thm)],[c_0_87,c_0_56]),
[final] ).
cnf(c_0_211,plain,
~ product(e_1,e_2,e_1),
inference(spm,[status(thm)],[c_0_88,c_0_58]),
[final] ).
cnf(c_0_224,plain,
cycle(e_3,e_1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_187]),c_0_88]),
[final] ).
cnf(c_0_232,plain,
( ~ product(e_3,X1,e_2)
| equalish(X1,e_4)
| product(e_3,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_51,c_0_65]),
[final] ).
cnf(c_0_235,axiom,
next(e_1,e_2),
e_1_then_e_2,
[final] ).
cnf(c_0_236,plain,
( ~ greater(X2,X5)
| ~ greater(X3,X1)
| ~ next(X3,X4)
| ~ cycle(X4,X5)
| ~ cycle(X3,e_0)
| ~ cycle(X1,X2) ),
c_0_225,
[final] ).
cnf(c_0_237,negated_conjecture,
( ~ product(e_1,e_4,X1)
| ~ product(e_2,e_2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_226,c_0_172])]),
[final] ).
cnf(c_0_246,plain,
( cycle(e_2,e_2)
| cycle(e_2,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_234,c_0_235]),c_0_113]),
[final] ).
cnf(c_0_247,plain,
( ~ next(e_4,X1)
| ~ greater(X4,X2)
| ~ greater(e_4,X3)
| ~ cycle(X3,X4)
| ~ cycle(X1,X2) ),
inference(spm,[status(thm)],[c_0_236,c_0_184]),
[final] ).
cnf(c_0_248,negated_conjecture,
~ product(e_1,e_4,e_2),
inference(spm,[status(thm)],[c_0_237,c_0_49]),
[final] ).
cnf(c_0_251,negated_conjecture,
( ~ product(X6,X5,X4)
| ~ product(X6,X2,X1)
| ~ product(X4,X5,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
c_0_240,
[final] ).
cnf(c_0_256,plain,
( ~ next(X2,X3)
| ~ next(X4,X1)
| ~ cycle(X3,X4)
| ~ cycle(X2,e_1)
| equalish(e_1,X1) ),
inference(spm,[status(thm)],[c_0_173,c_0_159]),
[final] ).
cnf(c_0_257,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
c_0_245,
[final] ).
cnf(c_0_258,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_192,c_0_246]),
[final] ).
cnf(c_0_259,plain,
( ~ next(e_4,X2)
| ~ greater(X1,X3)
| ~ cycle(X2,X3)
| ~ cycle(e_2,X1) ),
inference(spm,[status(thm)],[c_0_247,c_0_107]),
[final] ).
cnf(c_0_262,plain,
( ~ next(e_4,X2)
| ~ greater(X1,X3)
| ~ cycle(X2,X3)
| ~ cycle(e_3,X1) ),
inference(spm,[status(thm)],[c_0_247,c_0_164]),
[final] ).
cnf(c_0_263,plain,
product(e_3,e_1,e_4),
inference(sr,[status(thm)],[c_0_142,c_0_175]),
[final] ).
cnf(c_0_264,plain,
product(e_1,e_4,e_3),
inference(sr,[status(thm)],[c_0_122,c_0_248]),
[final] ).
cnf(c_0_265,negated_conjecture,
~ product(e_4,e_2,e_1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_249,c_0_172])]),
[final] ).
cnf(c_0_266,negated_conjecture,
~ product(e_2,e_3,e_1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_161,c_0_167])]),
[final] ).
cnf(c_0_267,negated_conjecture,
~ product(e_1,e_2,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_250,c_0_167])]),
[final] ).
cnf(c_0_281,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_108,c_0_77]),
[final] ).
cnf(c_0_282,axiom,
greater(e_4,e_1),
e_4_greater_e_1,
[final] ).
cnf(c_0_283,plain,
( ~ next(X3,X1)
| ~ next(e_3,X2)
| ~ cycle(X2,X3)
| equalish(e_1,X1) ),
inference(spm,[status(thm)],[c_0_256,c_0_224]),
[final] ).
cnf(c_0_286,plain,
( ~ next(X2,X1)
| ~ cycle(e_3,X2)
| cycle(e_2,e_1)
| equalish(e_2,X1) ),
inference(spm,[status(thm)],[c_0_258,c_0_138]),
[final] ).
cnf(c_0_287,plain,
( ~ next(e_4,X1)
| ~ greater(e_2,X2)
| ~ cycle(X1,X2)
| cycle(e_2,e_1) ),
inference(spm,[status(thm)],[c_0_259,c_0_246]),
[final] ).
cnf(c_0_288,axiom,
greater(e_2,e_1),
e_2_greater_e_1,
[final] ).
cnf(c_0_289,negated_conjecture,
( ~ next(e_2,X1)
| ~ greater(X2,e_0)
| ~ cycle(e_2,X2)
| equalish(e_3,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_260,c_0_172])]),
[final] ).
cnf(c_0_290,plain,
( ~ cycle(X1,X3)
| ~ cycle(X1,X2)
| equalish(X2,X3) ),
c_0_261,
[final] ).
cnf(c_0_291,plain,
( ~ next(e_4,X1)
| ~ greater(e_1,X2)
| ~ cycle(X1,X2) ),
inference(spm,[status(thm)],[c_0_262,c_0_224]),
[final] ).
cnf(c_0_293,negated_conjecture,
( ~ product(X3,X1,X2)
| ~ product(e_1,X1,X3)
| ~ product(e_3,e_4,X2)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_59,c_0_264]),
[final] ).
cnf(c_0_294,negated_conjecture,
( ~ product(X1,X3,X2)
| ~ product(e_1,X3,X1)
| ~ product(e_3,e_4,X2)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_251,c_0_264]),
[final] ).
cnf(c_0_296,plain,
product(e_4,e_1,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_167]),c_0_69]),
[final] ).
cnf(c_0_297,plain,
product(e_4,e_2,e_3),
inference(sr,[status(thm)],[c_0_185,c_0_265]),
[final] ).
cnf(c_0_299,plain,
product(e_2,e_3,e_4),
inference(sr,[status(thm)],[c_0_132,c_0_266]),
[final] ).
cnf(c_0_300,plain,
product(e_1,e_2,e_4),
inference(sr,[status(thm)],[c_0_221,c_0_267]),
[final] ).
cnf(c_0_301,negated_conjecture,
( ~ product(X1,X3,X2)
| ~ product(e_2,X3,X1)
| ~ product(e_3,e_1,X2)
| equalish(X1,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_268,c_0_172])]),
[final] ).
cnf(c_0_302,negated_conjecture,
( ~ product(X3,X1,X2)
| ~ product(e_2,X1,X3)
| ~ product(e_3,e_1,X2)
| equalish(X1,e_1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_269,c_0_172])]),
[final] ).
cnf(c_0_303,negated_conjecture,
( ~ product(X1,X3,X2)
| ~ product(e_2,X3,X1)
| ~ product(e_1,e_4,X2)
| equalish(X1,e_1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_270,c_0_172])]),
[final] ).
cnf(c_0_304,negated_conjecture,
( ~ product(X3,X1,X2)
| ~ product(e_2,X1,X3)
| ~ product(e_1,e_4,X2)
| equalish(X1,e_4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_271,c_0_172])]),
[final] ).
cnf(c_0_305,negated_conjecture,
( ~ product(X1,X3,X2)
| ~ product(e_4,X3,X1)
| ~ product(e_2,e_1,X2)
| equalish(X1,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_272,c_0_172])]),
[final] ).
cnf(c_0_306,negated_conjecture,
( ~ product(X3,X1,X2)
| ~ product(e_4,X1,X3)
| ~ product(e_1,e_3,X2)
| equalish(X1,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_273,c_0_172])]),
[final] ).
cnf(c_0_307,negated_conjecture,
( ~ product(X3,X1,X2)
| ~ product(e_4,X1,X3)
| ~ product(e_2,e_1,X2)
| equalish(X1,e_1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_274,c_0_172])]),
[final] ).
cnf(c_0_308,negated_conjecture,
( ~ product(X1,X3,X2)
| ~ product(e_4,X3,X1)
| ~ product(e_1,e_3,X2)
| equalish(X1,e_1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_275,c_0_172])]),
[final] ).
cnf(c_0_309,negated_conjecture,
( ~ product(X1,X3,X2)
| ~ product(e_3,X3,X1)
| ~ product(e_1,e_2,X2)
| equalish(X1,e_1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_276,c_0_172])]),
[final] ).
cnf(c_0_310,negated_conjecture,
( ~ product(X3,X1,X2)
| ~ product(e_3,X1,X3)
| ~ product(e_1,e_2,X2)
| equalish(X1,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_277,c_0_172])]),
[final] ).
cnf(c_0_316,negated_conjecture,
product(e_4,e_3,e_1),
inference(sr,[status(thm)],[c_0_278,c_0_267]),
[final] ).
cnf(c_0_319,negated_conjecture,
product(e_3,e_2,e_1),
inference(sr,[status(thm)],[c_0_230,c_0_267]),
[final] ).
cnf(c_0_321,negated_conjecture,
( ~ next(e_4,X1)
| ~ greater(X2,e_0)
| ~ cycle(e_4,X2)
| equalish(e_2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_279,c_0_172])]),
[final] ).
cnf(c_0_334,negated_conjecture,
( ~ product(X3,X1,X2)
| ~ product(e_3,X1,X3)
| ~ product(e_2,e_4,X2)
| equalish(X1,e_4)
| product(e_3,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_59,c_0_65]),
[final] ).
cnf(c_0_337,negated_conjecture,
( ~ product(X1,X3,X2)
| ~ product(e_3,X3,X1)
| ~ product(e_2,e_4,X2)
| equalish(X1,e_2)
| product(e_3,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_251,c_0_65]),
[final] ).
cnf(c_0_338,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_236,c_0_281]),
[final] ).
cnf(c_0_339,plain,
( ~ next(e_1,X1)
| ~ greater(X2,e_0)
| ~ cycle(e_1,X2)
| equalish(e_1,X1) ),
inference(spm,[status(thm)],[c_0_118,c_0_49]),
[final] ).
cnf(c_0_340,plain,
( ~ next(e_4,X2)
| ~ greater(X1,X3)
| ~ cycle(X2,X3)
| ~ cycle(e_1,X1) ),
inference(spm,[status(thm)],[c_0_247,c_0_282]),
[final] ).
cnf(c_0_341,plain,
( ~ greater(e_1,e_1)
| ~ cycle(e_1,e_0) ),
inference(spm,[status(thm)],[c_0_105,c_0_49]),
[final] ).
cnf(c_0_342,axiom,
greater(e_4,e_0),
e_4_greater_e_0,
[final] ).
cnf(c_0_343,plain,
( ~ next(X2,X1)
| ~ cycle(e_4,X2)
| equalish(e_1,X1) ),
inference(spm,[status(thm)],[c_0_283,c_0_179]),
[final] ).
cnf(c_0_348,plain,
( ~ product(X2,X2,X1)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_257,c_0_49]),
[final] ).
cnf(c_0_350,plain,
( ~ next(e_1,X1)
| cycle(e_2,e_1)
| equalish(e_2,X1) ),
inference(spm,[status(thm)],[c_0_286,c_0_224]),
[final] ).
cnf(c_0_351,plain,
( ~ next(e_4,X1)
| ~ cycle(X1,e_1)
| cycle(e_2,e_1) ),
inference(spm,[status(thm)],[c_0_287,c_0_288]),
[final] ).
cnf(c_0_352,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_289,c_0_246]),c_0_145])]),
[final] ).
cnf(c_0_353,plain,
( ~ cycle(e_2,X1)
| cycle(e_2,e_1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_290,c_0_246]),
[final] ).
cnf(c_0_354,plain,
( ~ next(e_4,X1)
| ~ cycle(X1,e_0) ),
inference(spm,[status(thm)],[c_0_291,c_0_159]),
[final] ).
cnf(c_0_355,plain,
( ~ next(e_3,X1)
| equalish(e_4,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_292,c_0_224]),c_0_159])]),
[final] ).
cnf(c_0_356,plain,
( ~ cycle(e_3,X1)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_290,c_0_224]),
[final] ).
cnf(c_0_357,negated_conjecture,
( ~ product(X2,X1,e_2)
| ~ product(e_1,X1,X2)
| equalish(X1,e_4)
| product(e_3,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_293,c_0_65]),
[final] ).
cnf(c_0_358,negated_conjecture,
( ~ product(X1,X2,e_2)
| ~ product(e_1,X2,X1)
| equalish(X1,e_3)
| product(e_3,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_294,c_0_65]),
[final] ).
cnf(c_0_359,negated_conjecture,
( ~ product(X3,X1,X2)
| ~ product(e_3,X1,X3)
| ~ product(e_4,e_1,X2)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_59,c_0_263]),
[final] ).
cnf(c_0_360,negated_conjecture,
( ~ product(X1,X3,X2)
| ~ product(e_3,X3,X1)
| ~ product(e_4,e_1,X2)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_251,c_0_263]),
[final] ).
cnf(c_0_361,negated_conjecture,
( ~ product(X2,X1,e_2)
| ~ product(e_3,X1,X2)
| equalish(X1,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_295,c_0_296]),c_0_175]),
[final] ).
cnf(c_0_362,negated_conjecture,
( ~ product(X3,X1,X2)
| ~ product(e_4,X1,X3)
| ~ product(e_3,e_2,X2)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_59,c_0_297]),
[final] ).
cnf(c_0_363,negated_conjecture,
( ~ product(X1,X3,X2)
| ~ product(e_4,X3,X1)
| ~ product(e_3,e_2,X2)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_251,c_0_297]),
[final] ).
cnf(c_0_364,negated_conjecture,
( ~ product(X1,X2,e_2)
| ~ product(e_3,X2,X1)
| equalish(X1,e_4) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_298,c_0_296]),c_0_175]),
[final] ).
cnf(c_0_365,negated_conjecture,
( ~ product(X3,X1,X2)
| ~ product(e_2,X1,X3)
| ~ product(e_4,e_3,X2)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_59,c_0_299]),
[final] ).
cnf(c_0_366,negated_conjecture,
( ~ product(X1,X3,X2)
| ~ product(e_2,X3,X1)
| ~ product(e_4,e_3,X2)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_251,c_0_299]),
[final] ).
cnf(c_0_367,negated_conjecture,
( ~ product(X3,X1,X2)
| ~ product(e_1,X1,X3)
| ~ product(e_4,e_2,X2)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_59,c_0_300]),
[final] ).
cnf(c_0_368,negated_conjecture,
( ~ product(X1,X3,X2)
| ~ product(e_1,X3,X1)
| ~ product(e_4,e_2,X2)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_251,c_0_300]),
[final] ).
cnf(c_0_369,negated_conjecture,
( ~ product(X3,X1,X2)
| ~ product(e_1,X1,X3)
| ~ product(e_2,e_3,X2)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_59,c_0_172]),
[final] ).
cnf(c_0_370,negated_conjecture,
( ~ product(X1,X3,X2)
| ~ product(e_1,X3,X1)
| ~ product(e_2,e_3,X2)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_251,c_0_172]),
[final] ).
cnf(c_0_371,negated_conjecture,
( ~ product(X1,X2,e_4)
| ~ product(e_2,X2,X1)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_301,c_0_263]),
[final] ).
cnf(c_0_372,negated_conjecture,
( ~ product(X2,X1,e_4)
| ~ product(e_2,X1,X2)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_302,c_0_263]),
[final] ).
cnf(c_0_373,negated_conjecture,
( ~ product(X1,X2,e_3)
| ~ product(e_2,X2,X1)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_303,c_0_264]),
[final] ).
cnf(c_0_374,negated_conjecture,
( ~ product(X2,X1,e_3)
| ~ product(e_2,X1,X2)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_304,c_0_264]),
[final] ).
cnf(c_0_375,negated_conjecture,
( ~ product(X1,X2,e_3)
| ~ product(e_4,X2,X1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_305,c_0_167]),
[final] ).
cnf(c_0_376,negated_conjecture,
( ~ product(X2,X1,e_2)
| ~ product(e_4,X1,X2)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_306,c_0_172]),
[final] ).
cnf(c_0_377,negated_conjecture,
( ~ product(X2,X1,e_3)
| ~ product(e_4,X1,X2)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_307,c_0_167]),
[final] ).
cnf(c_0_378,negated_conjecture,
( ~ product(X1,X2,e_2)
| ~ product(e_4,X2,X1)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_308,c_0_172]),
[final] ).
cnf(c_0_379,negated_conjecture,
( ~ product(X1,X2,e_4)
| ~ product(e_3,X2,X1)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_309,c_0_300]),
[final] ).
cnf(c_0_380,negated_conjecture,
( ~ product(X2,X1,e_4)
| ~ product(e_3,X1,X2)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_310,c_0_300]),
[final] ).
cnf(c_0_381,negated_conjecture,
( ~ product(X2,X1,e_3)
| ~ product(e_1,X1,X2)
| equalish(X1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_311,c_0_297]),c_0_267]),
[final] ).
cnf(c_0_382,negated_conjecture,
( ~ product(X1,X2,e_3)
| ~ product(e_1,X2,X1)
| equalish(X1,e_4) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_312,c_0_297]),c_0_267]),
[final] ).
cnf(c_0_383,negated_conjecture,
( ~ product(X2,X1,e_4)
| ~ product(e_1,X1,X2)
| equalish(X1,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_313,c_0_299]),c_0_267]),
[final] ).
cnf(c_0_384,negated_conjecture,
( ~ product(X1,X2,e_4)
| ~ product(e_1,X2,X1)
| equalish(X1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_314,c_0_299]),c_0_267]),
[final] ).
cnf(c_0_385,negated_conjecture,
( ~ product(X2,X1,e_1)
| ~ product(e_2,X1,X2)
| equalish(X1,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_315,c_0_316]),c_0_266]),
[final] ).
cnf(c_0_386,negated_conjecture,
( ~ product(X1,X2,e_1)
| ~ product(e_2,X2,X1)
| equalish(X1,e_4) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_317,c_0_316]),c_0_266]),
[final] ).
cnf(c_0_387,negated_conjecture,
( ~ product(X2,X1,e_1)
| ~ product(e_4,X1,X2)
| equalish(X1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_318,c_0_319]),c_0_265]),
[final] ).
cnf(c_0_388,negated_conjecture,
( ~ product(X1,X2,e_1)
| ~ product(e_4,X2,X1)
| equalish(X1,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_320,c_0_319]),c_0_265]),
[final] ).
cnf(c_0_389,negated_conjecture,
( ~ next(e_4,X1)
| ~ greater(e_0,e_0)
| equalish(e_2,X1) ),
inference(spm,[status(thm)],[c_0_321,c_0_184]),
[final] ).
cnf(c_0_390,plain,
( ~ product(X1,e_4,e_3)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_48,c_0_264]),
[final] ).
cnf(c_0_391,plain,
( ~ product(e_1,e_4,X1)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_257,c_0_264]),
[final] ).
cnf(c_0_392,plain,
( ~ product(X1,e_1,e_4)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_48,c_0_263]),
[final] ).
cnf(c_0_393,plain,
( ~ product(e_3,X1,e_4)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_51,c_0_263]),
[final] ).
cnf(c_0_394,plain,
( ~ product(e_4,X1,e_3)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_51,c_0_297]),
[final] ).
cnf(c_0_395,plain,
( ~ product(e_4,e_2,X1)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_257,c_0_297]),
[final] ).
cnf(c_0_396,plain,
( ~ product(X1,e_3,e_4)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_48,c_0_299]),
[final] ).
cnf(c_0_397,plain,
( ~ product(e_2,X1,e_4)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_51,c_0_299]),
[final] ).
cnf(c_0_398,plain,
( ~ product(e_1,X1,e_3)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_51,c_0_264]),
[final] ).
cnf(c_0_399,plain,
( ~ product(e_3,e_1,X1)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_257,c_0_263]),
[final] ).
cnf(c_0_400,plain,
( ~ product(X1,e_2,e_4)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_48,c_0_300]),
[final] ).
cnf(c_0_401,plain,
( ~ product(e_1,X1,e_4)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_51,c_0_300]),
[final] ).
cnf(c_0_402,plain,
( ~ product(X1,e_2,e_3)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_48,c_0_297]),
[final] ).
cnf(c_0_403,plain,
( ~ product(e_2,e_3,X1)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_257,c_0_299]),
[final] ).
cnf(c_0_404,negated_conjecture,
( ~ product(X1,e_3,e_2)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_48,c_0_172]),
[final] ).
cnf(c_0_405,negated_conjecture,
( ~ product(e_1,e_3,X1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_257,c_0_172]),
[final] ).
cnf(c_0_406,negated_conjecture,
( ~ product(e_3,X1,e_1)
| equalish(X1,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_322,c_0_172])]),
[final] ).
cnf(c_0_407,negated_conjecture,
( ~ product(e_2,e_4,X1)
| equalish(X1,e_1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_323,c_0_172])]),
[final] ).
cnf(c_0_408,negated_conjecture,
( ~ product(X1,e_4,e_1)
| equalish(X1,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_324,c_0_172])]),
[final] ).
cnf(c_0_409,negated_conjecture,
( ~ product(e_4,e_1,X1)
| equalish(X1,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_325,c_0_172])]),
[final] ).
cnf(c_0_410,plain,
( ~ product(X1,e_1,e_3)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_48,c_0_167]),
[final] ).
cnf(c_0_411,plain,
( ~ product(e_2,X1,e_3)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_51,c_0_167]),
[final] ).
cnf(c_0_412,negated_conjecture,
( ~ product(e_4,e_3,X1)
| equalish(X1,e_1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_326,c_0_172])]),
[final] ).
cnf(c_0_413,negated_conjecture,
( ~ product(e_3,e_4,X1)
| ~ product(e_1,e_1,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_264]),c_0_79]),
[final] ).
cnf(c_0_414,negated_conjecture,
( ~ product(e_4,e_1,X1)
| ~ product(e_3,e_3,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_263]),c_0_116]),
[final] ).
cnf(c_0_415,plain,
( ~ product(e_1,e_2,X1)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_257,c_0_300]),
[final] ).
cnf(c_0_416,negated_conjecture,
( ~ product(e_4,X1,e_2)
| equalish(X1,e_1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_327,c_0_172])]),
[final] ).
cnf(c_0_417,negated_conjecture,
( ~ product(e_3,e_2,X1)
| ~ product(e_4,e_4,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_297]),c_0_69]),
[final] ).
cnf(c_0_418,negated_conjecture,
( ~ product(e_4,e_3,X1)
| ~ product(e_2,e_2,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_299]),c_0_113]),
[final] ).
cnf(c_0_419,negated_conjecture,
( ~ product(e_4,e_2,X1)
| ~ product(e_1,e_1,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_300]),c_0_88]),
[final] ).
cnf(c_0_420,negated_conjecture,
( ~ product(e_1,X1,e_2)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_51,c_0_172]),
[final] ).
cnf(c_0_421,negated_conjecture,
( ~ product(e_2,X1,e_1)
| equalish(X1,e_4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_328,c_0_172])]),
[final] ).
cnf(c_0_422,negated_conjecture,
( ~ product(X1,e_1,e_2)
| equalish(X1,e_4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_165,c_0_172])]),
[final] ).
cnf(c_0_423,negated_conjecture,
( ~ product(e_4,X1,e_1)
| equalish(X1,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_329,c_0_172])]),
[final] ).
cnf(c_0_424,negated_conjecture,
( ~ product(e_2,e_3,X1)
| ~ product(e_1,e_1,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_172]),c_0_126]),
[final] ).
cnf(c_0_425,negated_conjecture,
( ~ product(X1,e_3,e_1)
| equalish(X1,e_4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_330,c_0_172])]),
[final] ).
cnf(c_0_426,negated_conjecture,
( ~ product(e_3,e_2,X1)
| equalish(X1,e_1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_331,c_0_172])]),
[final] ).
cnf(c_0_427,plain,
( ~ product(e_2,e_1,X1)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_257,c_0_167]),
[final] ).
cnf(c_0_428,negated_conjecture,
( ~ product(e_2,e_1,X1)
| ~ product(e_4,e_4,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_332,c_0_172])]),
[final] ).
cnf(c_0_429,negated_conjecture,
( ~ product(e_1,e_3,X1)
| ~ product(e_4,e_4,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_285,c_0_172])]),
[final] ).
cnf(c_0_430,negated_conjecture,
( ~ product(X1,e_2,e_1)
| equalish(X1,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_238,c_0_172])]),
[final] ).
cnf(c_0_431,negated_conjecture,
( ~ product(e_1,e_2,X1)
| ~ product(e_3,e_3,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_333,c_0_172])]),
[final] ).
cnf(c_0_432,negated_conjecture,
( ~ product(e_3,e_1,X1)
| ~ product(e_2,e_2,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_167]),c_0_87]),
[final] ).
cnf(c_0_433,negated_conjecture,
( ~ product(X2,X1,e_1)
| ~ product(e_3,X1,X2)
| equalish(X1,e_4)
| product(e_3,e_4,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_334,c_0_335]),c_0_336]),
[final] ).
cnf(c_0_434,negated_conjecture,
( ~ product(X1,X2,e_1)
| ~ product(e_3,X2,X1)
| equalish(X1,e_2)
| product(e_3,e_4,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_337,c_0_335]),c_0_336]),
[final] ).
cnf(c_0_435,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_338,c_0_159]),
[final] ).
cnf(c_0_436,plain,
( ~ product(X1,e_4,e_2)
| equalish(X1,e_3)
| product(e_3,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_48,c_0_65]),
[final] ).
cnf(c_0_437,plain,
( ~ product(e_3,e_4,X1)
| equalish(X1,e_2)
| product(e_3,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_257,c_0_65]),
[final] ).
cnf(c_0_438,plain,
( ~ 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_339,c_0_281]),
[final] ).
cnf(c_0_439,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_290,c_0_281]),
[final] ).
cnf(c_0_440,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_340,c_0_281]),
[final] ).
cnf(c_0_441,plain,
( ~ 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_341,c_0_281]),
[final] ).
cnf(c_0_442,negated_conjecture,
( ~ product(X1,X3,X4)
| ~ product(X2,X2,X4)
| ~ product(X2,X3,X1)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_251,c_0_49]),
[final] ).
cnf(c_0_443,plain,
( ~ next(X2,X3)
| ~ next(X4,X1)
| ~ cycle(X3,X4)
| ~ cycle(X2,e_4)
| equalish(e_4,X1) ),
inference(spm,[status(thm)],[c_0_173,c_0_342]),
[final] ).
cnf(c_0_444,plain,
( ~ next(e_4,X2)
| ~ greater(X1,X3)
| ~ cycle(X2,X3)
| ~ cycle(e_0,X1) ),
inference(spm,[status(thm)],[c_0_247,c_0_342]),
[final] ).
cnf(c_0_445,plain,
( ~ cycle(e_4,X1)
| equalish(X1,e_0) ),
inference(spm,[status(thm)],[c_0_290,c_0_184]),
[final] ).
cnf(c_0_446,plain,
~ cycle(e_4,e_1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_343,c_0_235]),c_0_87]),
[final] ).
cnf(c_0_447,plain,
~ cycle(e_4,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_343,c_0_138]),c_0_116]),
[final] ).
cnf(c_0_448,plain,
~ cycle(e_4,e_3),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_343,c_0_179]),c_0_78]),
[final] ).
cnf(c_0_449,plain,
~ cycle(e_3,e_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_263]),c_0_164])]),
[final] ).
cnf(c_0_450,negated_conjecture,
~ product(e_2,e_4,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_200,c_0_319])]),
[final] ).
cnf(c_0_451,negated_conjecture,
~ product(e_2,e_1,e_4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_344,c_0_172])]),
[final] ).
cnf(c_0_452,negated_conjecture,
~ product(e_1,e_3,e_4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_345,c_0_172])]),
[final] ).
cnf(c_0_453,negated_conjecture,
~ product(e_3,e_2,e_4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_346,c_0_172])]),
[final] ).
cnf(c_0_454,negated_conjecture,
~ greater(e_2,e_4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_347,c_0_172])]),
[final] ).
cnf(c_0_455,plain,
~ product(e_2,e_2,e_1),
inference(spm,[status(thm)],[c_0_87,c_0_348]),
[final] ).
cnf(c_0_456,plain,
~ product(e_3,e_3,e_1),
inference(spm,[status(thm)],[c_0_116,c_0_348]),
[final] ).
cnf(c_0_457,plain,
~ product(e_4,e_4,e_1),
inference(spm,[status(thm)],[c_0_78,c_0_348]),
[final] ).
cnf(c_0_458,plain,
~ product(e_1,e_1,e_2),
inference(spm,[status(thm)],[c_0_88,c_0_348]),
[final] ).
cnf(c_0_459,plain,
~ product(e_3,e_3,e_2),
inference(spm,[status(thm)],[c_0_112,c_0_348]),
[final] ).
cnf(c_0_460,plain,
~ product(e_4,e_4,e_2),
inference(spm,[status(thm)],[c_0_69,c_0_348]),
[final] ).
cnf(c_0_461,plain,
~ product(e_1,e_1,e_3),
inference(spm,[status(thm)],[c_0_126,c_0_348]),
[final] ).
cnf(c_0_462,plain,
~ product(e_2,e_2,e_3),
inference(spm,[status(thm)],[c_0_113,c_0_348]),
[final] ).
cnf(c_0_463,plain,
~ product(e_4,e_4,e_3),
inference(spm,[status(thm)],[c_0_55,c_0_348]),
[final] ).
cnf(c_0_464,plain,
~ product(e_1,e_1,e_4),
inference(spm,[status(thm)],[c_0_79,c_0_348]),
[final] ).
cnf(c_0_465,plain,
~ product(e_2,e_2,e_4),
inference(spm,[status(thm)],[c_0_70,c_0_348]),
[final] ).
cnf(c_0_466,plain,
~ product(e_3,e_3,e_4),
inference(spm,[status(thm)],[c_0_57,c_0_348]),
[final] ).
cnf(c_0_467,plain,
product(e_2,e_4,e_1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_205,c_0_167]),c_0_78]),
[final] ).
cnf(c_0_468,negated_conjecture,
equalish(X1,X1),
inference(spm,[status(thm)],[c_0_349,c_0_49]),
[final] ).
cnf(c_0_469,axiom,
greater(e_3,e_1),
e_3_greater_e_1,
[final] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP123-3.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:01:17 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 1.53/0.62 % Version: 3.5.1
% 1.53/0.62 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.53/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.53/0.62 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.53/0.62 % Starting new_bool_3 with 300s (1) cores
% 1.53/0.62 % Starting new_bool_1 with 300s (1) cores
% 1.53/0.62 % Starting sh5l with 300s (1) cores
% 1.53/0.62 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1576113 completed with status 1
% 1.53/0.62 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 1.53/0.62 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.53/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.53/0.62 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.53/0.62 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.53/0.62 % No SInE strategy applied
% 1.53/0.62 % Search class: FGHNF-FFMM00-SFFFFFNN
% 1.53/0.62 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.53/0.62 % Starting SubtermCWHack with 136s (1) cores
% 1.53/0.62 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.53/0.62 % Starting H----_011_C07_F1_PI_AE_OS_R8_SP_S1U with 136s (1) cores
% 1.53/0.62 % Starting G----_425_C05_02_F1_SE_CS_SP_PS_RG_S04AI with 136s (1) cores
% 1.53/0.62 % Starting G-E--_208_B07--C_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.53/0.62 % G-E--_208_B07--C_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 1576124 completed with status 1
% 1.53/0.62 % Result found by G-E--_208_B07--C_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 1.53/0.62 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.53/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.53/0.62 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.53/0.62 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.53/0.62 % No SInE strategy applied
% 1.53/0.62 % Search class: FGHNF-FFMM00-SFFFFFNN
% 1.53/0.62 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.53/0.62 % Starting SubtermCWHack with 136s (1) cores
% 1.53/0.62 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.53/0.62 % Starting H----_011_C07_F1_PI_AE_OS_R8_SP_S1U with 136s (1) cores
% 1.53/0.62 % Starting G----_425_C05_02_F1_SE_CS_SP_PS_RG_S04AI with 136s (1) cores
% 1.53/0.62 % Starting G-E--_208_B07--C_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.53/0.62 % Preprocessing time : 0.001 s
% 1.53/0.62 % Presaturation interreduction done
% 1.53/0.62
% 1.53/0.62 % No proof found!
% 1.53/0.62 % SZS status Satisfiable
% 1.53/0.62 % SZS output start Saturation
% See solution above
% 1.53/0.62 % Parsed axioms : 44
% 1.53/0.62 % Removed by relevancy pruning/SinE : 0
% 1.53/0.62 % Initial clauses : 44
% 1.53/0.62 % Removed in clause preprocessing : 0
% 1.53/0.62 % Initial clauses in saturation : 44
% 1.53/0.62 % Processed clauses : 2583
% 1.53/0.62 % ...of these trivial : 20
% 1.53/0.62 % ...subsumed : 1585
% 1.53/0.62 % ...remaining for further processing : 978
% 1.53/0.62 % Other redundant clauses eliminated : 0
% 1.53/0.62 % Clauses deleted for lack of memory : 0
% 1.53/0.62 % Backward-subsumed : 366
% 1.53/0.62 % Backward-rewritten : 293
% 1.53/0.62 % Generated clauses : 3955
% 1.53/0.62 % ...of the previous two non-redundant : 2893
% 1.53/0.62 % ...aggressively subsumed : 0
% 1.53/0.62 % Contextual simplify-reflections : 15
% 1.53/0.62 % Paramodulations : 3930
% 1.53/0.62 % Factorizations : 0
% 1.53/0.62 % NegExts : 0
% 1.53/0.62 % Equation resolutions : 0
% 1.53/0.62 % Disequality decompositions : 0
% 1.53/0.62 % Total rewrite steps : 1530
% 1.53/0.62 % ...of those cached : 1501
% 1.53/0.62 % Propositional unsat checks : 0
% 1.53/0.62 % Propositional check models : 0
% 1.53/0.62 % Propositional check unsatisfiable : 0
% 1.53/0.62 % Propositional clauses : 0
% 1.53/0.62 % Propositional clauses after purity: 0
% 1.53/0.62 % Propositional unsat core size : 0
% 1.53/0.62 % Propositional preprocessing time : 0.000
% 1.53/0.62 % Propositional encoding time : 0.000
% 1.53/0.62 % Propositional solver time : 0.000
% 1.53/0.62 % Success case prop preproc time : 0.000
% 1.53/0.62 % Success case prop encoding time : 0.000
% 1.53/0.62 % Success case prop solver time : 0.000
% 1.53/0.62 % Current number of processed clauses : 250
% 1.53/0.62 % Positive orientable unit clauses : 33
% 1.53/0.62 % Positive unorientable unit clauses: 0
% 1.53/0.62 % Negative unit clauses : 63
% 1.53/0.62 % Non-unit-clauses : 154
% 1.53/0.62 % Current number of unprocessed clauses: 0
% 1.53/0.62 % ...number of literals in the above : 0
% 1.53/0.62 % Current number of archived formulas : 0
% 1.53/0.62 % Current number of archived clauses : 728
% 1.53/0.62 % Clause-clause subsumption calls (NU) : 257605
% 1.53/0.62 % Rec. Clause-clause subsumption calls : 80054
% 1.53/0.62 % Non-unit clause-clause subsumptions : 1200
% 1.53/0.62 % Unit Clause-clause subsumption calls : 5786
% 1.53/0.62 % Rewrite failures with RHS unbound : 0
% 1.53/0.62 % BW rewrite match attempts : 86
% 1.53/0.62 % BW rewrite match successes : 13
% 1.53/0.62 % Condensation attempts : 0
% 1.53/0.62 % Condensation successes : 0
% 1.53/0.62 % Termbank termtop insertions : 61367
% 1.53/0.62 % Search garbage collected termcells : 107
% 1.53/0.62
% 1.53/0.62 % -------------------------------------------------
% 1.53/0.62 % User time : 0.194 s
% 1.53/0.62 % System time : 0.006 s
% 1.53/0.62 % Total time : 0.200 s
% 1.53/0.62 % Maximum resident set size: 3660 pages
% 1.53/0.62
% 1.53/0.62 % -------------------------------------------------
% 1.53/0.62 % User time : 0.912 s
% 1.53/0.62 % System time : 0.029 s
% 1.53/0.62 % Total time : 0.941 s
% 1.53/0.62 % Maximum resident set size: 4864 pages
% 1.53/0.62 % E exiting
%------------------------------------------------------------------------------