%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SYO685-1 : TPTP v9.3.1. Released v7.3.0.
% 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 03:52:05 PM UTC 2026
% Result : Unsatisfiable 0.22s 5.61s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 37
% Syntax : Number of clauses : 157 ( 11 unt; 96 nHn; 132 RR)
% Number of literals : 657 ( 0 equ; 429 neg)
% Maximal clause size : 9 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 194 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_34,axiom,
( ~ 'E'(s(s(s(s('0')))),f(X2))
| ~ 'E'(s(s(s(s('0')))),f(suc(X2)))
| ~ 'E'(s(s(s(s('0')))),f(suc(X1)))
| ~ iLEQ(suc(X2),suc(X1))
| ~ 'E'(s(s(s(s('0')))),f(X1))
| 'E'(f(X1),f(suc(X1)))
| 'E'(f(X2),f(suc(X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_34) ).
cnf(clause_130,axiom,
( ~ 'E'(s(s(s(s('0')))),f(suc(X1)))
| ~ 'E'(s(s(s(s('0')))),f(X1))
| iLEQ(suc(X1),suc(X1))
| 'E'(f(X1),f(suc(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_130) ).
cnf(clause_183,axiom,
( ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'(s(s(s(s('0')))),f(X2))
| ~ 'E'(f(X2),f(suc(X2)))
| ~ 'E'(s(s(s(s('0')))),f(suc(X2)))
| ~ 'E'(s(s(s(s('0')))),f(suc(suc(X2))))
| ~ 'E'(s(s(s(s('0')))),f(suc(X1)))
| ~ 'E'(s(s(s(s('0')))),f(suc(suc(X1))))
| ~ iLEQ(suc(X2),suc(X1))
| ~ 'E'(s(s(s(s('0')))),f(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_183) ).
cnf(clause_93,axiom,
( ~ 'LE'(f(suc(suc(X1))),s(s(s(s(s('0'))))))
| 'LE'(f(X1),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(suc(suc(X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_93) ).
cnf(clause_113,axiom,
( ~ 'LE'(f(X1),s(s(s(s(s('0'))))))
| 'LE'(f(X1),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_113) ).
cnf(clause_191,axiom,
( ~ 'LE'(f(suc(X1)),s(s(s(s(s('0'))))))
| 'LE'(f(X1),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(suc(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_191) ).
cnf(clause_53,axiom,
'LE'(f(X1),s(s(s(s(s('0')))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_53) ).
cnf(clause_79,axiom,
( ~ 'E'(s(s(s(s('0')))),f(X1))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'(s(s(s(s('0')))),f(suc(X1)))
| ~ 'E'(s(s(s(s('0')))),f(suc(suc(X1))))
| iLEQ(suc(X1),suc(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_79) ).
cnf(clause_49,axiom,
( ~ 'E'(s(s(s('0'))),f(suc(X2)))
| ~ 'E'(s(s(s('0'))),f(X1))
| ~ 'E'(s(s(s('0'))),f(X2))
| ~ 'E'(s(s(s('0'))),f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X2))
| 'E'(f(X2),f(suc(X2)))
| 'E'(f(X1),f(suc(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_49) ).
cnf(clause_28,axiom,
( ~ 'E'(s(s(s('0'))),f(suc(X1)))
| ~ 'E'(s(s(s('0'))),f(X1))
| iLEQ(suc(X1),suc(X1))
| 'E'(f(X1),f(suc(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_28) ).
cnf(clause_73,axiom,
( ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'(s(s(s('0'))),f(suc(suc(X1))))
| ~ 'E'(s(s(s('0'))),f(suc(suc(X2))))
| ~ 'E'(s(s(s('0'))),f(suc(X2)))
| ~ 'E'(f(X2),f(suc(X2)))
| ~ 'E'(s(s(s('0'))),f(X1))
| ~ 'E'(s(s(s('0'))),f(X2))
| ~ 'E'(s(s(s('0'))),f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_73) ).
cnf(clause_52,axiom,
( ~ 'LE'(f(suc(suc(X1))),s(s(s(s('0')))))
| 'LE'(f(X1),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(suc(suc(X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_52) ).
cnf(clause_95,axiom,
( ~ 'LE'(f(X1),s(s(s(s('0')))))
| 'LE'(f(X1),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_95) ).
cnf(clause_111,axiom,
( ~ 'LE'(f(suc(X1)),s(s(s(s('0')))))
| 'LE'(f(X1),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(suc(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_111) ).
cnf(clause_190,axiom,
( ~ 'E'(s(s(s('0'))),f(X1))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'(s(s(s('0'))),f(suc(X1)))
| ~ 'E'(s(s(s('0'))),f(suc(suc(X1))))
| iLEQ(suc(X1),suc(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_190) ).
cnf(clause_115,axiom,
( ~ 'E'(s(s('0')),f(X2))
| ~ iLEQ(suc(X2),suc(X1))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(suc(X1)))
| 'E'(f(X1),f(suc(X1)))
| 'E'(f(X2),f(suc(X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_115) ).
cnf(clause_143,axiom,
( ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X1))
| iLEQ(suc(X1),suc(X1))
| 'E'(f(X1),f(suc(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_143) ).
cnf(clause_74,axiom,
( ~ 'E'(s(s('0')),f(suc(suc(X1))))
| ~ 'E'(s(s('0')),f(X2))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'(f(X2),f(suc(X2)))
| ~ iLEQ(suc(X2),suc(X1))
| ~ 'E'(s(s('0')),f(suc(suc(X2))))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(suc(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_74) ).
cnf(clause_97,axiom,
( ~ 'LE'(f(suc(suc(X1))),s(s(s('0'))))
| 'LE'(f(X1),s(s('0')))
| 'E'(s(s('0')),f(suc(suc(X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_97) ).
cnf(clause_125,axiom,
( ~ 'LE'(f(X1),s(s(s('0'))))
| 'LE'(f(X1),s(s('0')))
| 'E'(s(s('0')),f(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_125) ).
cnf(clause_86,axiom,
( ~ 'LE'(f(suc(X1)),s(s(s('0'))))
| 'LE'(f(X1),s(s('0')))
| 'E'(s(s('0')),f(suc(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_86) ).
cnf(clause_40,axiom,
( ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(suc(suc(X1))))
| iLEQ(suc(X1),suc(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_40) ).
cnf(clause_87,axiom,
( ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ iLEQ(suc(X1),suc(X2))
| 'E'(f(X2),f(suc(X2)))
| 'E'(f(X1),f(suc(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_87) ).
cnf(clause_204,axiom,
( ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X1))
| iLEQ(suc(X1),suc(X1))
| 'E'(f(X1),f(suc(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_204) ).
cnf(clause_175,axiom,
( ~ 'E'(s('0'),f(X1))
| ~ 'E'(f(X2),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(suc(X1))))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(suc(X2))))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_175) ).
cnf(clause_61,axiom,
( ~ 'E'(s('0'),f(X1))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(suc(X1))))
| iLEQ(suc(X1),suc(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_61) ).
cnf(clause_169,axiom,
( ~ 'E'('0',f(X2))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X1))
| ~ iLEQ(suc(X1),suc(X2))
| 'E'(f(X2),f(suc(X2)))
| 'E'(f(X1),f(suc(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_169) ).
cnf(clause_19,axiom,
( ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X1))
| iLEQ(suc(X1),suc(X1))
| 'E'(f(X1),f(suc(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_19) ).
cnf(clause_116,axiom,
( ~ 'LE'(f(suc(suc(X1))),s(s('0')))
| 'LE'(f(X1),s('0'))
| 'E'(s('0'),f(suc(suc(X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_116) ).
cnf(clause_184,axiom,
( ~ 'LE'(f(X1),s(s('0')))
| 'LE'(f(X1),s('0'))
| 'E'(s('0'),f(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_184) ).
cnf(clause_30,axiom,
( ~ 'LE'(f(suc(X1)),s(s('0')))
| 'LE'(f(X1),s('0'))
| 'E'(s('0'),f(suc(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_30) ).
cnf(clause_105,axiom,
( ~ 'E'(f(X2),f(suc(X2)))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(suc(X2))))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(X2))
| ~ iLEQ(suc(X2),suc(X1))
| ~ 'E'('0',f(suc(suc(X1))))
| ~ 'E'(f(X1),f(suc(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_105) ).
cnf(clause_44,axiom,
( ~ 'E'('0',f(X1))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(suc(X1))))
| iLEQ(suc(X1),suc(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_44) ).
cnf(clause_11,axiom,
( ~ 'LE'(f(suc(suc(X1))),s('0'))
| 'LE'(f(X1),'0')
| 'E'('0',f(suc(suc(X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_11) ).
cnf(clause_173,axiom,
( ~ 'LE'(f(X1),s('0'))
| 'LE'(f(X1),'0')
| 'E'('0',f(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_173) ).
cnf(clause_168,axiom,
( ~ 'LE'(f(suc(X1)),s('0'))
| 'LE'(f(X1),'0')
| 'E'('0',f(suc(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_168) ).
cnf(clause_96,axiom,
~ 'LE'(f(z),'0'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_96) ).
cnf(c_0_37,plain,
( ~ 'E'(s(s(s(s('0')))),f(X2))
| ~ 'E'(s(s(s(s('0')))),f(suc(X2)))
| ~ 'E'(s(s(s(s('0')))),f(suc(X1)))
| ~ iLEQ(suc(X2),suc(X1))
| ~ 'E'(s(s(s(s('0')))),f(X1))
| 'E'(f(X1),f(suc(X1)))
| 'E'(f(X2),f(suc(X2))) ),
inference(fof_simplification,[status(thm)],[clause_34]) ).
cnf(c_0_38,plain,
( ~ 'E'(s(s(s(s('0')))),f(suc(X1)))
| ~ 'E'(s(s(s(s('0')))),f(X1))
| iLEQ(suc(X1),suc(X1))
| 'E'(f(X1),f(suc(X1))) ),
inference(fof_simplification,[status(thm)],[clause_130]) ).
cnf(c_0_39,plain,
( ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'(s(s(s(s('0')))),f(X2))
| ~ 'E'(f(X2),f(suc(X2)))
| ~ 'E'(s(s(s(s('0')))),f(suc(X2)))
| ~ 'E'(s(s(s(s('0')))),f(suc(suc(X2))))
| ~ 'E'(s(s(s(s('0')))),f(suc(X1)))
| ~ 'E'(s(s(s(s('0')))),f(suc(suc(X1))))
| ~ iLEQ(suc(X2),suc(X1))
| ~ 'E'(s(s(s(s('0')))),f(X1)) ),
inference(fof_simplification,[status(thm)],[clause_183]) ).
cnf(c_0_40,plain,
( ~ 'E'(s(s(s(s('0')))),f(X2))
| ~ 'E'(s(s(s(s('0')))),f(suc(X2)))
| ~ 'E'(s(s(s(s('0')))),f(suc(X1)))
| ~ iLEQ(suc(X2),suc(X1))
| ~ 'E'(s(s(s(s('0')))),f(X1))
| 'E'(f(X1),f(suc(X1)))
| 'E'(f(X2),f(suc(X2))) ),
c_0_37 ).
cnf(c_0_41,plain,
( ~ 'E'(s(s(s(s('0')))),f(suc(X1)))
| ~ 'E'(s(s(s(s('0')))),f(X1))
| iLEQ(suc(X1),suc(X1))
| 'E'(f(X1),f(suc(X1))) ),
c_0_38 ).
cnf(c_0_42,plain,
( ~ 'LE'(f(suc(suc(X1))),s(s(s(s(s('0'))))))
| 'LE'(f(X1),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(suc(suc(X1)))) ),
inference(fof_simplification,[status(thm)],[clause_93]) ).
cnf(c_0_43,plain,
( ~ 'LE'(f(X1),s(s(s(s(s('0'))))))
| 'LE'(f(X1),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(X1)) ),
inference(fof_simplification,[status(thm)],[clause_113]) ).
cnf(c_0_44,plain,
( ~ 'LE'(f(suc(X1)),s(s(s(s(s('0'))))))
| 'LE'(f(X1),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(suc(X1))) ),
inference(fof_simplification,[status(thm)],[clause_191]) ).
cnf(c_0_45,plain,
( ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'(s(s(s(s('0')))),f(X2))
| ~ 'E'(f(X2),f(suc(X2)))
| ~ 'E'(s(s(s(s('0')))),f(suc(X2)))
| ~ 'E'(s(s(s(s('0')))),f(suc(suc(X2))))
| ~ 'E'(s(s(s(s('0')))),f(suc(X1)))
| ~ 'E'(s(s(s(s('0')))),f(suc(suc(X1))))
| ~ iLEQ(suc(X2),suc(X1))
| ~ 'E'(s(s(s(s('0')))),f(X1)) ),
c_0_39 ).
cnf(c_0_46,plain,
( ~ 'E'(s(s(s(s('0')))),f(X1))
| ~ 'E'(s(s(s(s('0')))),f(suc(X1)))
| 'E'(f(X1),f(suc(X1))) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_47,plain,
( ~ 'LE'(f(suc(suc(X1))),s(s(s(s(s('0'))))))
| 'LE'(f(X1),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(suc(suc(X1)))) ),
c_0_42 ).
cnf(c_0_48,axiom,
'LE'(f(X1),s(s(s(s(s('0')))))),
clause_53 ).
cnf(c_0_49,plain,
( ~ 'LE'(f(X1),s(s(s(s(s('0'))))))
| 'LE'(f(X1),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(X1)) ),
c_0_43 ).
cnf(c_0_50,plain,
( ~ 'LE'(f(suc(X1)),s(s(s(s(s('0'))))))
| 'LE'(f(X1),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(suc(X1))) ),
c_0_44 ).
cnf(c_0_51,plain,
( ~ 'E'(s(s(s(s('0')))),f(X1))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'(s(s(s(s('0')))),f(suc(X1)))
| ~ 'E'(s(s(s(s('0')))),f(suc(suc(X1))))
| iLEQ(suc(X1),suc(X1)) ),
inference(fof_simplification,[status(thm)],[clause_79]) ).
cnf(c_0_52,plain,
( ~ 'E'(s(s(s(s('0')))),f(X2))
| ~ 'E'(s(s(s(s('0')))),f(X1))
| ~ 'E'(s(s(s(s('0')))),f(suc(X2)))
| ~ 'E'(s(s(s(s('0')))),f(suc(X1)))
| ~ 'E'(s(s(s(s('0')))),f(suc(suc(X2))))
| ~ 'E'(s(s(s(s('0')))),f(suc(suc(X1))))
| ~ iLEQ(suc(X1),suc(X2)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_45,c_0_46]),c_0_46]) ).
cnf(c_0_53,plain,
( 'E'(s(s(s(s('0')))),f(suc(suc(X1))))
| 'LE'(f(X1),s(s(s(s('0'))))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48])]) ).
cnf(c_0_54,plain,
( 'E'(s(s(s(s('0')))),f(X1))
| 'LE'(f(X1),s(s(s(s('0'))))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_48])]) ).
cnf(c_0_55,plain,
( 'E'(s(s(s(s('0')))),f(suc(X1)))
| 'LE'(f(X1),s(s(s(s('0'))))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_48])]) ).
cnf(c_0_56,plain,
( ~ 'E'(s(s(s(s('0')))),f(X1))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'(s(s(s(s('0')))),f(suc(X1)))
| ~ 'E'(s(s(s(s('0')))),f(suc(suc(X1))))
| iLEQ(suc(X1),suc(X1)) ),
c_0_51 ).
cnf(c_0_57,plain,
( ~ 'E'(s(s(s('0'))),f(suc(X2)))
| ~ 'E'(s(s(s('0'))),f(X1))
| ~ 'E'(s(s(s('0'))),f(X2))
| ~ 'E'(s(s(s('0'))),f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X2))
| 'E'(f(X2),f(suc(X2)))
| 'E'(f(X1),f(suc(X1))) ),
inference(fof_simplification,[status(thm)],[clause_49]) ).
cnf(c_0_58,plain,
( ~ 'E'(s(s(s('0'))),f(suc(X1)))
| ~ 'E'(s(s(s('0'))),f(X1))
| iLEQ(suc(X1),suc(X1))
| 'E'(f(X1),f(suc(X1))) ),
inference(fof_simplification,[status(thm)],[clause_28]) ).
cnf(c_0_59,plain,
( ~ 'E'(s(s(s(s('0')))),f(X2))
| ~ 'E'(s(s(s(s('0')))),f(suc(X2)))
| ~ 'E'(s(s(s(s('0')))),f(suc(suc(X2))))
| ~ iLEQ(suc(X1),suc(X2))
| 'LE'(f(X1),s(s(s(s('0'))))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]),c_0_55]) ).
cnf(c_0_60,plain,
( ~ 'E'(s(s(s(s('0')))),f(X1))
| ~ 'E'(s(s(s(s('0')))),f(suc(X1)))
| ~ 'E'(s(s(s(s('0')))),f(suc(suc(X1))))
| iLEQ(suc(X1),suc(X1)) ),
inference(csr,[status(thm)],[c_0_56,c_0_41]) ).
cnf(c_0_61,plain,
( ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'(s(s(s('0'))),f(suc(suc(X1))))
| ~ 'E'(s(s(s('0'))),f(suc(suc(X2))))
| ~ 'E'(s(s(s('0'))),f(suc(X2)))
| ~ 'E'(f(X2),f(suc(X2)))
| ~ 'E'(s(s(s('0'))),f(X1))
| ~ 'E'(s(s(s('0'))),f(X2))
| ~ 'E'(s(s(s('0'))),f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X2)) ),
inference(fof_simplification,[status(thm)],[clause_73]) ).
cnf(c_0_62,plain,
( ~ 'E'(s(s(s('0'))),f(suc(X2)))
| ~ 'E'(s(s(s('0'))),f(X1))
| ~ 'E'(s(s(s('0'))),f(X2))
| ~ 'E'(s(s(s('0'))),f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X2))
| 'E'(f(X2),f(suc(X2)))
| 'E'(f(X1),f(suc(X1))) ),
c_0_57 ).
cnf(c_0_63,plain,
( ~ 'E'(s(s(s('0'))),f(suc(X1)))
| ~ 'E'(s(s(s('0'))),f(X1))
| iLEQ(suc(X1),suc(X1))
| 'E'(f(X1),f(suc(X1))) ),
c_0_58 ).
cnf(c_0_64,plain,
( ~ 'LE'(f(suc(suc(X1))),s(s(s(s('0')))))
| 'LE'(f(X1),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(suc(suc(X1)))) ),
inference(fof_simplification,[status(thm)],[clause_52]) ).
cnf(c_0_65,plain,
( ~ iLEQ(suc(X2),suc(X1))
| 'LE'(f(X2),s(s(s(s('0')))))
| 'LE'(f(X1),s(s(s(s('0'))))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_53]),c_0_54]),c_0_55]) ).
cnf(c_0_66,plain,
( iLEQ(suc(X1),suc(X1))
| 'LE'(f(X1),s(s(s(s('0'))))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_53]),c_0_54]),c_0_55]) ).
cnf(c_0_67,plain,
( ~ 'LE'(f(X1),s(s(s(s('0')))))
| 'LE'(f(X1),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(X1)) ),
inference(fof_simplification,[status(thm)],[clause_95]) ).
cnf(c_0_68,plain,
( ~ 'LE'(f(suc(X1)),s(s(s(s('0')))))
| 'LE'(f(X1),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(suc(X1))) ),
inference(fof_simplification,[status(thm)],[clause_111]) ).
cnf(c_0_69,plain,
( ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'(s(s(s('0'))),f(suc(suc(X1))))
| ~ 'E'(s(s(s('0'))),f(suc(suc(X2))))
| ~ 'E'(s(s(s('0'))),f(suc(X2)))
| ~ 'E'(f(X2),f(suc(X2)))
| ~ 'E'(s(s(s('0'))),f(X1))
| ~ 'E'(s(s(s('0'))),f(X2))
| ~ 'E'(s(s(s('0'))),f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X2)) ),
c_0_61 ).
cnf(c_0_70,plain,
( ~ 'E'(s(s(s('0'))),f(X1))
| ~ 'E'(s(s(s('0'))),f(suc(X1)))
| 'E'(f(X1),f(suc(X1))) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_71,plain,
( ~ 'LE'(f(suc(suc(X1))),s(s(s(s('0')))))
| 'LE'(f(X1),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(suc(suc(X1)))) ),
c_0_64 ).
cnf(c_0_72,plain,
'LE'(f(X1),s(s(s(s('0'))))),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_73,plain,
( ~ 'LE'(f(X1),s(s(s(s('0')))))
| 'LE'(f(X1),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(X1)) ),
c_0_67 ).
cnf(c_0_74,plain,
( ~ 'LE'(f(suc(X1)),s(s(s(s('0')))))
| 'LE'(f(X1),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(suc(X1))) ),
c_0_68 ).
cnf(c_0_75,plain,
( ~ 'E'(s(s(s('0'))),f(X1))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'(s(s(s('0'))),f(suc(X1)))
| ~ 'E'(s(s(s('0'))),f(suc(suc(X1))))
| iLEQ(suc(X1),suc(X1)) ),
inference(fof_simplification,[status(thm)],[clause_190]) ).
cnf(c_0_76,plain,
( ~ 'E'(s(s(s('0'))),f(X1))
| ~ 'E'(s(s(s('0'))),f(X2))
| ~ 'E'(s(s(s('0'))),f(suc(X1)))
| ~ 'E'(s(s(s('0'))),f(suc(X2)))
| ~ 'E'(s(s(s('0'))),f(suc(suc(X1))))
| ~ 'E'(s(s(s('0'))),f(suc(suc(X2))))
| ~ iLEQ(suc(X1),suc(X2)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_69,c_0_70]),c_0_70]) ).
cnf(c_0_77,plain,
( 'E'(s(s(s('0'))),f(suc(suc(X1))))
| 'LE'(f(X1),s(s(s('0')))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_72])]) ).
cnf(c_0_78,plain,
( 'E'(s(s(s('0'))),f(X1))
| 'LE'(f(X1),s(s(s('0')))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_72])]) ).
cnf(c_0_79,plain,
( 'E'(s(s(s('0'))),f(suc(X1)))
| 'LE'(f(X1),s(s(s('0')))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_72])]) ).
cnf(c_0_80,plain,
( ~ 'E'(s(s(s('0'))),f(X1))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'(s(s(s('0'))),f(suc(X1)))
| ~ 'E'(s(s(s('0'))),f(suc(suc(X1))))
| iLEQ(suc(X1),suc(X1)) ),
c_0_75 ).
cnf(c_0_81,plain,
( ~ 'E'(s(s('0')),f(X2))
| ~ iLEQ(suc(X2),suc(X1))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(suc(X1)))
| 'E'(f(X1),f(suc(X1)))
| 'E'(f(X2),f(suc(X2))) ),
inference(fof_simplification,[status(thm)],[clause_115]) ).
cnf(c_0_82,plain,
( ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X1))
| iLEQ(suc(X1),suc(X1))
| 'E'(f(X1),f(suc(X1))) ),
inference(fof_simplification,[status(thm)],[clause_143]) ).
cnf(c_0_83,plain,
( ~ 'E'(s(s(s('0'))),f(X2))
| ~ 'E'(s(s(s('0'))),f(suc(X2)))
| ~ 'E'(s(s(s('0'))),f(suc(suc(X2))))
| ~ iLEQ(suc(X2),suc(X1))
| 'LE'(f(X1),s(s(s('0')))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]),c_0_79]) ).
cnf(c_0_84,plain,
( ~ 'E'(s(s(s('0'))),f(X1))
| ~ 'E'(s(s(s('0'))),f(suc(X1)))
| ~ 'E'(s(s(s('0'))),f(suc(suc(X1))))
| iLEQ(suc(X1),suc(X1)) ),
inference(csr,[status(thm)],[c_0_80,c_0_63]) ).
cnf(c_0_85,plain,
( ~ 'E'(s(s('0')),f(suc(suc(X1))))
| ~ 'E'(s(s('0')),f(X2))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'(f(X2),f(suc(X2)))
| ~ iLEQ(suc(X2),suc(X1))
| ~ 'E'(s(s('0')),f(suc(suc(X2))))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(suc(X1))) ),
inference(fof_simplification,[status(thm)],[clause_74]) ).
cnf(c_0_86,plain,
( ~ 'E'(s(s('0')),f(X2))
| ~ iLEQ(suc(X2),suc(X1))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(suc(X1)))
| 'E'(f(X1),f(suc(X1)))
| 'E'(f(X2),f(suc(X2))) ),
c_0_81 ).
cnf(c_0_87,plain,
( ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X1))
| iLEQ(suc(X1),suc(X1))
| 'E'(f(X1),f(suc(X1))) ),
c_0_82 ).
cnf(c_0_88,plain,
( ~ 'LE'(f(suc(suc(X1))),s(s(s('0'))))
| 'LE'(f(X1),s(s('0')))
| 'E'(s(s('0')),f(suc(suc(X1)))) ),
inference(fof_simplification,[status(thm)],[clause_97]) ).
cnf(c_0_89,plain,
( ~ iLEQ(suc(X1),suc(X2))
| 'LE'(f(X2),s(s(s('0'))))
| 'LE'(f(X1),s(s(s('0')))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_77]),c_0_78]),c_0_79]) ).
cnf(c_0_90,plain,
( iLEQ(suc(X1),suc(X1))
| 'LE'(f(X1),s(s(s('0')))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_77]),c_0_78]),c_0_79]) ).
cnf(c_0_91,plain,
( ~ 'LE'(f(X1),s(s(s('0'))))
| 'LE'(f(X1),s(s('0')))
| 'E'(s(s('0')),f(X1)) ),
inference(fof_simplification,[status(thm)],[clause_125]) ).
cnf(c_0_92,plain,
( ~ 'LE'(f(suc(X1)),s(s(s('0'))))
| 'LE'(f(X1),s(s('0')))
| 'E'(s(s('0')),f(suc(X1))) ),
inference(fof_simplification,[status(thm)],[clause_86]) ).
cnf(c_0_93,plain,
( ~ 'E'(s(s('0')),f(suc(suc(X1))))
| ~ 'E'(s(s('0')),f(X2))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'(f(X2),f(suc(X2)))
| ~ iLEQ(suc(X2),suc(X1))
| ~ 'E'(s(s('0')),f(suc(suc(X2))))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(suc(X1))) ),
c_0_85 ).
cnf(c_0_94,plain,
( ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(suc(X1)))
| 'E'(f(X1),f(suc(X1))) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_95,plain,
( ~ 'LE'(f(suc(suc(X1))),s(s(s('0'))))
| 'LE'(f(X1),s(s('0')))
| 'E'(s(s('0')),f(suc(suc(X1)))) ),
c_0_88 ).
cnf(c_0_96,plain,
'LE'(f(X1),s(s(s('0')))),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_97,plain,
( ~ 'LE'(f(X1),s(s(s('0'))))
| 'LE'(f(X1),s(s('0')))
| 'E'(s(s('0')),f(X1)) ),
c_0_91 ).
cnf(c_0_98,plain,
( ~ 'LE'(f(suc(X1)),s(s(s('0'))))
| 'LE'(f(X1),s(s('0')))
| 'E'(s(s('0')),f(suc(X1))) ),
c_0_92 ).
cnf(c_0_99,plain,
( ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(suc(suc(X1))))
| iLEQ(suc(X1),suc(X1)) ),
inference(fof_simplification,[status(thm)],[clause_40]) ).
cnf(c_0_100,plain,
( ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ iLEQ(suc(X1),suc(X2))
| 'E'(f(X2),f(suc(X2)))
| 'E'(f(X1),f(suc(X1))) ),
inference(fof_simplification,[status(thm)],[clause_87]) ).
cnf(c_0_101,plain,
( ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X1))
| iLEQ(suc(X1),suc(X1))
| 'E'(f(X1),f(suc(X1))) ),
inference(fof_simplification,[status(thm)],[clause_204]) ).
cnf(c_0_102,plain,
( ~ 'E'(s(s('0')),f(X2))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(suc(suc(X2))))
| ~ 'E'(s(s('0')),f(suc(suc(X1))))
| ~ iLEQ(suc(X1),suc(X2)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_93,c_0_94]),c_0_94]) ).
cnf(c_0_103,plain,
( 'E'(s(s('0')),f(suc(suc(X1))))
| 'LE'(f(X1),s(s('0'))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_95,c_0_96])]) ).
cnf(c_0_104,plain,
( 'E'(s(s('0')),f(X1))
| 'LE'(f(X1),s(s('0'))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_96])]) ).
cnf(c_0_105,plain,
( 'E'(s(s('0')),f(suc(X1)))
| 'LE'(f(X1),s(s('0'))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_98,c_0_96])]) ).
cnf(c_0_106,plain,
( ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(suc(suc(X1))))
| iLEQ(suc(X1),suc(X1)) ),
c_0_99 ).
cnf(c_0_107,plain,
( ~ 'E'(s('0'),f(X1))
| ~ 'E'(f(X2),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(suc(X1))))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(suc(X2))))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X2)) ),
inference(fof_simplification,[status(thm)],[clause_175]) ).
cnf(c_0_108,plain,
( ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ iLEQ(suc(X1),suc(X2))
| 'E'(f(X2),f(suc(X2)))
| 'E'(f(X1),f(suc(X1))) ),
c_0_100 ).
cnf(c_0_109,plain,
( ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X1))
| iLEQ(suc(X1),suc(X1))
| 'E'(f(X1),f(suc(X1))) ),
c_0_101 ).
cnf(c_0_110,plain,
( ~ 'E'(s('0'),f(X1))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(suc(X1))))
| iLEQ(suc(X1),suc(X1)) ),
inference(fof_simplification,[status(thm)],[clause_61]) ).
cnf(c_0_111,plain,
( ~ 'E'(s(s('0')),f(X2))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ 'E'(s(s('0')),f(suc(suc(X2))))
| ~ iLEQ(suc(X1),suc(X2))
| 'LE'(f(X1),s(s('0'))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_104]),c_0_105]) ).
cnf(c_0_112,plain,
( ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(suc(suc(X1))))
| iLEQ(suc(X1),suc(X1)) ),
inference(csr,[status(thm)],[c_0_106,c_0_87]) ).
cnf(c_0_113,plain,
( ~ 'E'('0',f(X2))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X1))
| ~ iLEQ(suc(X1),suc(X2))
| 'E'(f(X2),f(suc(X2)))
| 'E'(f(X1),f(suc(X1))) ),
inference(fof_simplification,[status(thm)],[clause_169]) ).
cnf(c_0_114,plain,
( ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X1))
| iLEQ(suc(X1),suc(X1))
| 'E'(f(X1),f(suc(X1))) ),
inference(fof_simplification,[status(thm)],[clause_19]) ).
cnf(c_0_115,plain,
( ~ 'E'(s('0'),f(X1))
| ~ 'E'(f(X2),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(suc(X1))))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(suc(X2))))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X2)) ),
c_0_107 ).
cnf(c_0_116,plain,
( ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X1)))
| 'E'(f(X1),f(suc(X1))) ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_117,plain,
( ~ 'E'(s('0'),f(X1))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(suc(X1))))
| iLEQ(suc(X1),suc(X1)) ),
c_0_110 ).
cnf(c_0_118,plain,
( ~ 'LE'(f(suc(suc(X1))),s(s('0')))
| 'LE'(f(X1),s('0'))
| 'E'(s('0'),f(suc(suc(X1)))) ),
inference(fof_simplification,[status(thm)],[clause_116]) ).
cnf(c_0_119,plain,
( ~ iLEQ(suc(X2),suc(X1))
| 'LE'(f(X2),s(s('0')))
| 'LE'(f(X1),s(s('0'))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_103]),c_0_104]),c_0_105]) ).
cnf(c_0_120,plain,
( iLEQ(suc(X1),suc(X1))
| 'LE'(f(X1),s(s('0'))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_103]),c_0_104]),c_0_105]) ).
cnf(c_0_121,plain,
( ~ 'LE'(f(X1),s(s('0')))
| 'LE'(f(X1),s('0'))
| 'E'(s('0'),f(X1)) ),
inference(fof_simplification,[status(thm)],[clause_184]) ).
cnf(c_0_122,plain,
( ~ 'LE'(f(suc(X1)),s(s('0')))
| 'LE'(f(X1),s('0'))
| 'E'(s('0'),f(suc(X1))) ),
inference(fof_simplification,[status(thm)],[clause_30]) ).
cnf(c_0_123,plain,
( ~ 'E'(f(X2),f(suc(X2)))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(suc(X2))))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(X2))
| ~ iLEQ(suc(X2),suc(X1))
| ~ 'E'('0',f(suc(suc(X1))))
| ~ 'E'(f(X1),f(suc(X1))) ),
inference(fof_simplification,[status(thm)],[clause_105]) ).
cnf(c_0_124,plain,
( ~ 'E'('0',f(X2))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X1))
| ~ iLEQ(suc(X1),suc(X2))
| 'E'(f(X2),f(suc(X2)))
| 'E'(f(X1),f(suc(X1))) ),
c_0_113 ).
cnf(c_0_125,plain,
( ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X1))
| iLEQ(suc(X1),suc(X1))
| 'E'(f(X1),f(suc(X1))) ),
c_0_114 ).
cnf(c_0_126,plain,
( ~ 'E'('0',f(X1))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(suc(X1))))
| iLEQ(suc(X1),suc(X1)) ),
inference(fof_simplification,[status(thm)],[clause_44]) ).
cnf(c_0_127,plain,
( ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(suc(X1))))
| ~ 'E'(s('0'),f(suc(suc(X2))))
| ~ iLEQ(suc(X1),suc(X2)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_115,c_0_116]),c_0_116]) ).
cnf(c_0_128,plain,
( ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(suc(X1))))
| iLEQ(suc(X1),suc(X1)) ),
inference(csr,[status(thm)],[c_0_117,c_0_109]) ).
cnf(c_0_129,plain,
( ~ 'LE'(f(suc(suc(X1))),s(s('0')))
| 'LE'(f(X1),s('0'))
| 'E'(s('0'),f(suc(suc(X1)))) ),
c_0_118 ).
cnf(c_0_130,plain,
'LE'(f(X1),s(s('0'))),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_131,plain,
( ~ 'LE'(f(X1),s(s('0')))
| 'LE'(f(X1),s('0'))
| 'E'(s('0'),f(X1)) ),
c_0_121 ).
cnf(c_0_132,plain,
( ~ 'LE'(f(suc(X1)),s(s('0')))
| 'LE'(f(X1),s('0'))
| 'E'(s('0'),f(suc(X1))) ),
c_0_122 ).
cnf(c_0_133,plain,
( ~ 'E'(f(X2),f(suc(X2)))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(suc(X2))))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(X2))
| ~ iLEQ(suc(X2),suc(X1))
| ~ 'E'('0',f(suc(suc(X1))))
| ~ 'E'(f(X1),f(suc(X1))) ),
c_0_123 ).
cnf(c_0_134,plain,
( ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X1)))
| 'E'(f(X1),f(suc(X1))) ),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_135,plain,
( ~ 'E'('0',f(X1))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(suc(X1))))
| iLEQ(suc(X1),suc(X1)) ),
c_0_126 ).
cnf(c_0_136,plain,
( ~ 'LE'(f(suc(suc(X1))),s('0'))
| 'LE'(f(X1),'0')
| 'E'('0',f(suc(suc(X1)))) ),
inference(fof_simplification,[status(thm)],[clause_11]) ).
cnf(c_0_137,plain,
( ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(suc(X1)))) ),
inference(spm,[status(thm)],[c_0_127,c_0_128]) ).
cnf(c_0_138,plain,
( 'E'(s('0'),f(suc(suc(X1))))
| 'LE'(f(X1),s('0')) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_129,c_0_130])]) ).
cnf(c_0_139,plain,
( 'E'(s('0'),f(X1))
| 'LE'(f(X1),s('0')) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_131,c_0_130])]) ).
cnf(c_0_140,plain,
( 'E'(s('0'),f(suc(X1)))
| 'LE'(f(X1),s('0')) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_132,c_0_130])]) ).
cnf(c_0_141,plain,
( ~ 'LE'(f(X1),s('0'))
| 'LE'(f(X1),'0')
| 'E'('0',f(X1)) ),
inference(fof_simplification,[status(thm)],[clause_173]) ).
cnf(c_0_142,plain,
( ~ 'LE'(f(suc(X1)),s('0'))
| 'LE'(f(X1),'0')
| 'E'('0',f(suc(X1))) ),
inference(fof_simplification,[status(thm)],[clause_168]) ).
cnf(c_0_143,plain,
( ~ 'E'('0',f(X2))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(suc(X2))))
| ~ 'E'('0',f(suc(suc(X1))))
| ~ iLEQ(suc(X1),suc(X2)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_133,c_0_134]),c_0_134]) ).
cnf(c_0_144,plain,
( ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(suc(X1))))
| iLEQ(suc(X1),suc(X1)) ),
inference(csr,[status(thm)],[c_0_135,c_0_125]) ).
cnf(c_0_145,plain,
( ~ 'LE'(f(suc(suc(X1))),s('0'))
| 'LE'(f(X1),'0')
| 'E'('0',f(suc(suc(X1)))) ),
c_0_136 ).
cnf(c_0_146,plain,
'LE'(f(X1),s('0')),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_139]),c_0_140]) ).
cnf(c_0_147,plain,
( ~ 'LE'(f(X1),s('0'))
| 'LE'(f(X1),'0')
| 'E'('0',f(X1)) ),
c_0_141 ).
cnf(c_0_148,plain,
( ~ 'LE'(f(suc(X1)),s('0'))
| 'LE'(f(X1),'0')
| 'E'('0',f(suc(X1))) ),
c_0_142 ).
cnf(c_0_149,plain,
~ 'LE'(f(z),'0'),
inference(fof_simplification,[status(thm)],[clause_96]) ).
cnf(c_0_150,plain,
( ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(suc(X1)))) ),
inference(spm,[status(thm)],[c_0_143,c_0_144]) ).
cnf(c_0_151,plain,
( 'E'('0',f(suc(suc(X1))))
| 'LE'(f(X1),'0') ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_145,c_0_146])]) ).
cnf(c_0_152,plain,
( 'E'('0',f(X1))
| 'LE'(f(X1),'0') ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_147,c_0_146])]) ).
cnf(c_0_153,plain,
( 'E'('0',f(suc(X1)))
| 'LE'(f(X1),'0') ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_148,c_0_146])]) ).
cnf(c_0_154,plain,
~ 'LE'(f(z),'0'),
c_0_149 ).
cnf(c_0_155,plain,
'LE'(f(X1),'0'),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_151]),c_0_152]),c_0_153]) ).
cnf(c_0_156,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_154,c_0_155])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYO685-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/5.44 % Computer : n002.cluster.edu
% 0.17/5.44 % Model : x86_64 x86_64
% 0.17/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.44 % Memory : 8046.5625MB
% 0.17/5.44 % OS : Linux 6.8.0-71-generic
% 0.17/5.44 % CPULimit : 300
% 0.17/5.44 % WCLimit : 300
% 0.17/5.44 % DateTime : Mon Sep 21 12:11:37 UTC 2026
% 0.17/5.45 % CPUTime :
% 0.17/5.45 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/5.50 Running first-order theorem proving
% 0.22/5.50 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
% 0.22/5.61 % Version: 3.5.1
% 0.22/5.61 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.22/5.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/5.61 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.22/5.61 % Starting new_bool_3 with 300s (1) cores
% 0.22/5.61 % Starting new_bool_1 with 300s (1) cores
% 0.22/5.61 % Starting sh5l with 300s (1) cores
% 0.22/5.61 % new_bool_1 with pid 3244095 completed with status 9
% 0.22/5.61 % new_bool_3 with pid 3244094 completed with status 9
% 0.22/5.61 % sh5l with pid 3244098 completed with status 9
% 0.22/5.61 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 3244093 completed with status 0
% 0.22/5.61 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.22/5.61 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.22/5.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/5.61 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.22/5.61 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/5.61 % No SInE strategy applied
% 0.22/5.61 % Search class: FGHNF-FFLF11-MFFFFFNN
% 0.22/5.61 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/5.61 % Starting SubtermCWHack with 136s (1) cores
% 0.22/5.61 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.22/5.61 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.22/5.61 % Starting new_bool_3 with 136s (1) cores
% 0.22/5.61 % Starting new_bool_1 with 136s (1) cores
% 0.22/5.61 % SubtermCWHack with pid 3244108 completed with status 0
% 0.22/5.61 % Result found by SubtermCWHack
% 0.22/5.61 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.22/5.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/5.61 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.22/5.61 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/5.61 % No SInE strategy applied
% 0.22/5.61 % Search class: FGHNF-FFLF11-MFFFFFNN
% 0.22/5.61 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/5.61 % Starting SubtermCWHack with 136s (1) cores
% 0.22/5.61 % Preprocessing time : 0.003 s
% 0.22/5.61
% 0.22/5.61 % Proof found!
% 0.22/5.61 % SZS status Unsatisfiable
% 0.22/5.61 % SZS output start CNFRefutation
% See solution above
% 0.22/5.62 % Parsed axioms : 47
% 0.22/5.62 % Removed by relevancy pruning/SinE : 0
% 0.22/5.62 % Initial clauses : 47
% 0.22/5.62 % Removed in clause preprocessing : 0
% 0.22/5.62 % Initial clauses in saturation : 47
% 0.22/5.62 % Processed clauses : 245
% 0.22/5.62 % ...of these trivial : 0
% 0.22/5.62 % ...subsumed : 53
% 0.22/5.62 % ...remaining for further processing : 192
% 0.22/5.62 % Other redundant clauses eliminated : 0
% 0.22/5.62 % Clauses deleted for lack of memory : 0
% 0.22/5.62 % Backward-subsumed : 103
% 0.22/5.62 % Backward-rewritten : 69
% 0.22/5.62 % Generated clauses : 490
% 0.22/5.62 % ...of the previous two non-redundant : 485
% 0.22/5.62 % ...aggressively subsumed : 0
% 0.22/5.62 % Contextual simplify-reflections : 56
% 0.22/5.62 % Paramodulations : 490
% 0.22/5.62 % Factorizations : 0
% 0.22/5.62 % NegExts : 0
% 0.22/5.62 % Equation resolutions : 0
% 0.22/5.62 % Disequality decompositions : 0
% 0.22/5.62 % Total rewrite steps : 79
% 0.22/5.62 % ...of those cached : 56
% 0.22/5.62 % Propositional unsat checks : 0
% 0.22/5.62 % Propositional check models : 0
% 0.22/5.62 % Propositional check unsatisfiable : 0
% 0.22/5.62 % Propositional clauses : 0
% 0.22/5.62 % Propositional clauses after purity: 0
% 0.22/5.62 % Propositional unsat core size : 0
% 0.22/5.62 % Propositional preprocessing time : 0.000
% 0.22/5.62 % Propositional encoding time : 0.000
% 0.22/5.62 % Propositional solver time : 0.000
% 0.22/5.62 % Success case prop preproc time : 0.000
% 0.22/5.62 % Success case prop encoding time : 0.000
% 0.22/5.62 % Success case prop solver time : 0.000
% 0.22/5.62 % Current number of processed clauses : 20
% 0.22/5.62 % Positive orientable unit clauses : 7
% 0.22/5.62 % Positive unorientable unit clauses: 0
% 0.22/5.62 % Negative unit clauses : 0
% 0.22/5.62 % Non-unit-clauses : 13
% 0.22/5.62 % Current number of unprocessed clauses: 21
% 0.22/5.62 % ...number of literals in the above : 122
% 0.22/5.62 % Current number of archived formulas : 0
% 0.22/5.62 % Current number of archived clauses : 172
% 0.22/5.62 % Clause-clause subsumption calls (NU) : 8605
% 0.22/5.62 % Rec. Clause-clause subsumption calls : 1036
% 0.22/5.62 % Non-unit clause-clause subsumptions : 205
% 0.22/5.62 % Unit Clause-clause subsumption calls : 93
% 0.22/5.62 % Rewrite failures with RHS unbound : 0
% 0.22/5.62 % BW rewrite match attempts : 35
% 0.22/5.62 % BW rewrite match successes : 20
% 0.22/5.62 % Condensation attempts : 0
% 0.22/5.62 % Condensation successes : 0
% 0.22/5.62 % Termbank termtop insertions : 33825
% 0.22/5.62 % Search garbage collected termcells : 253
% 0.22/5.62
% 0.22/5.62 % -------------------------------------------------
% 0.22/5.62 % User time : 0.063 s
% 0.22/5.62 % System time : 0.005 s
% 0.22/5.62 % Total time : 0.068 s
% 0.22/5.62 % Maximum resident set size: 3684 pages
% 0.22/5.62
% 0.22/5.62 % -------------------------------------------------
% 0.22/5.62 % User time : 0.323 s
% 0.22/5.62 % System time : 0.081 s
% 0.22/5.62 % Total time : 0.404 s
% 0.22/5.62 % Maximum resident set size: 4608 pages
% 0.22/5.62 % E exiting
%------------------------------------------------------------------------------