%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SYO685-1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 : Sun Sep 27 09:47:46 AM UTC 2026
% Result : Unsatisfiable 35.61s 5.66s
% Output : CNFRefutation 35.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 37
% Syntax : Number of clauses : 190 ( 5 unt; 160 nHn; 153 RR)
% Number of literals : 965 ( 0 equ; 497 neg)
% Maximal clause size : 9 ( 5 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 : 267 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_143,axiom,
( iLEQ(suc(X0),suc(X0))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(X0)) ) ).
cnf(clause_130,axiom,
( iLEQ(suc(X0),suc(X0))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(X0)))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(X0)) ) ).
cnf(clause_125,axiom,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'LE\''(f(X0),s(s(s('\'0\'')))) ) ).
cnf(clause_61,axiom,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0)))) ) ).
cnf(clause_169,axiom,
( '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0))
| ~ iLEQ(suc(X0),suc(X1)) ) ).
cnf(clause_28,axiom,
( iLEQ(suc(X0),suc(X0))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0)) ) ).
cnf(clause_97,axiom,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(suc(suc(X0))))
| ~ '\'LE\''(f(suc(suc(X0))),s(s(s('\'0\'')))) ) ).
cnf(clause_74,axiom,
( ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X0))))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X1))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0))) ) ).
cnf(clause_190,axiom,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X0)))) ) ).
cnf(clause_79,axiom,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(X0)))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(suc(X0)))) ) ).
cnf(clause_184,axiom,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(X0))
| ~ '\'LE\''(f(X0),s(s('\'0\''))) ) ).
cnf(clause_191,axiom,
( '\'LE\''(f(X0),s(s(s(s('\'0\'')))))
| '\'E\''(s(s(s(s('\'0\'')))),f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s(s(s(s(s('\'0\'')))))) ) ).
cnf(clause_93,axiom,
( '\'LE\''(f(X0),s(s(s(s('\'0\'')))))
| '\'E\''(s(s(s(s('\'0\'')))),f(suc(suc(X0))))
| ~ '\'LE\''(f(suc(suc(X0))),s(s(s(s(s('\'0\'')))))) ) ).
cnf(clause_40,axiom,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X0)))) ) ).
cnf(clause_95,axiom,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'E\''(s(s(s('\'0\''))),f(X0))
| ~ '\'LE\''(f(X0),s(s(s(s('\'0\''))))) ) ).
cnf(clause_86,axiom,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s(s(s('\'0\'')))) ) ).
cnf(clause_96,axiom,
~ '\'LE\''(f(z),'\'0\'') ).
cnf(clause_175,axiom,
( ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X1))))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X1)) ) ).
cnf(clause_49,axiom,
( '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X1)) ) ).
cnf(clause_52,axiom,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'E\''(s(s(s('\'0\''))),f(suc(suc(X0))))
| ~ '\'LE\''(f(suc(suc(X0))),s(s(s(s('\'0\''))))) ) ).
cnf(clause_168,axiom,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s('\'0\'')) ) ).
cnf(clause_30,axiom,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s(s('\'0\''))) ) ).
cnf(clause_87,axiom,
( '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ iLEQ(suc(X0),suc(X1)) ) ).
cnf(clause_105,axiom,
( ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(X1))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''(f(X0),f(suc(X0))) ) ).
cnf(clause_116,axiom,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'LE\''(f(suc(suc(X0))),s(s('\'0\''))) ) ).
cnf(clause_113,axiom,
( '\'LE\''(f(X0),s(s(s(s('\'0\'')))))
| '\'E\''(s(s(s(s('\'0\'')))),f(X0))
| ~ '\'LE\''(f(X0),s(s(s(s(s('\'0\'')))))) ) ).
cnf(clause_44,axiom,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(suc(X0)))) ) ).
cnf(clause_34,axiom,
( '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X1),f(suc(X1)))
| ~ '\'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(X0)))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(X0)) ) ).
cnf(clause_111,axiom,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s(s(s(s('\'0\''))))) ) ).
cnf(clause_19,axiom,
( iLEQ(suc(X0),suc(X0))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0)) ) ).
cnf(clause_115,axiom,
( '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0))) ) ).
cnf(clause_11,axiom,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'LE\''(f(suc(suc(X0))),s('\'0\'')) ) ).
cnf(clause_73,axiom,
( ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X0))))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X1))))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X1)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X1)) ) ).
cnf(clause_204,axiom,
( iLEQ(suc(X0),suc(X0))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X0)) ) ).
cnf(clause_53,axiom,
'\'LE\''(f(X0),s(s(s(s(s('\'0\'')))))) ).
cnf(clause_183,axiom,
( ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'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))))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(X0)))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(suc(X0))))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(X0)) ) ).
cnf(clause_173,axiom,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| ~ '\'LE\''(f(X0),s('\'0\'')) ) ).
cnf(c0,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_143]) ).
cnf(c1,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(X0)))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(X0))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_130]) ).
cnf(c2,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| ~ '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'E\''(s(s('\'0\'')),f(X0)) ),
inference(clausification,[status(esa)],[clause_125]) ).
cnf(c3,plain,
( ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0)))) ),
inference(clausification,[status(esa)],[clause_61]) ).
cnf(c4,plain,
( '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(clausification,[status(esa)],[clause_169]) ).
cnf(c6,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_28]) ).
cnf(c7,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| ~ '\'LE\''(f(suc(suc(X0))),s(s(s('\'0\''))))
| '\'E\''(s(s('\'0\'')),f(suc(suc(X0)))) ),
inference(clausification,[status(esa)],[clause_97]) ).
cnf(c8,plain,
( ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X1))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X0)))) ),
inference(clausification,[status(esa)],[clause_74]) ).
cnf(c9,plain,
( ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X0))))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0)) ),
inference(clausification,[status(esa)],[clause_190]) ).
cnf(c10,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(X0)))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(suc(X0))))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(X0)) ),
inference(clausification,[status(esa)],[clause_79]) ).
cnf(c12,plain,
( '\'LE\''(f(X0),s('\'0\''))
| ~ '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s('\'0\''),f(X0)) ),
inference(clausification,[status(esa)],[clause_184]) ).
cnf(c14,plain,
( '\'LE\''(f(X0),s(s(s(s('\'0\'')))))
| ~ '\'LE\''(f(suc(X0)),s(s(s(s(s('\'0\''))))))
| '\'E\''(s(s(s(s('\'0\'')))),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_191]) ).
cnf(c15,plain,
( '\'LE\''(f(X0),s(s(s(s('\'0\'')))))
| ~ '\'LE\''(f(suc(suc(X0))),s(s(s(s(s('\'0\''))))))
| '\'E\''(s(s(s(s('\'0\'')))),f(suc(suc(X0)))) ),
inference(clausification,[status(esa)],[clause_93]) ).
cnf(c16,plain,
( ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X0))))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| iLEQ(suc(X0),suc(X0)) ),
inference(clausification,[status(esa)],[clause_40]) ).
cnf(c17,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| ~ '\'LE\''(f(X0),s(s(s(s('\'0\'')))))
| '\'E\''(s(s(s('\'0\''))),f(X0)) ),
inference(clausification,[status(esa)],[clause_95]) ).
cnf(c18,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| ~ '\'LE\''(f(suc(X0)),s(s(s('\'0\''))))
| '\'E\''(s(s('\'0\'')),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_86]) ).
cnf(c19,plain,
~ '\'LE\''(f(z),'\'0\''),
inference(clausification,[status(esa)],[clause_96]) ).
cnf(c20,plain,
( ~ '\'E\''(s('\'0\''),f(suc(suc(X1))))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(clausification,[status(esa)],[clause_175]) ).
cnf(c21,plain,
( ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X1)))
| '\'E\''(f(X1),f(suc(X1)))
| ~ iLEQ(suc(X0),suc(X1))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0)) ),
inference(clausification,[status(esa)],[clause_49]) ).
cnf(c22,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| ~ '\'LE\''(f(suc(suc(X0))),s(s(s(s('\'0\'')))))
| '\'E\''(s(s(s('\'0\''))),f(suc(suc(X0)))) ),
inference(clausification,[status(esa)],[clause_52]) ).
cnf(c28,plain,
( '\'LE\''(f(X0),'\'0\'')
| ~ '\'LE\''(f(suc(X0)),s('\'0\''))
| '\'E\''('\'0\'',f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_168]) ).
cnf(c30,plain,
( '\'LE\''(f(X0),s('\'0\''))
| ~ '\'LE\''(f(suc(X0)),s(s('\'0\'')))
| '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_30]) ).
cnf(c31,plain,
( ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s('\'0\''),f(X1))
| '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_87]) ).
cnf(c32,plain,
( ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''('\'0\'',f(X1))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(clausification,[status(esa)],[clause_105]) ).
cnf(c33,plain,
( '\'LE\''(f(X0),s('\'0\''))
| ~ '\'LE\''(f(suc(suc(X0))),s(s('\'0\'')))
| '\'E\''(s('\'0\''),f(suc(suc(X0)))) ),
inference(clausification,[status(esa)],[clause_116]) ).
cnf(c34,plain,
( '\'LE\''(f(X0),s(s(s(s('\'0\'')))))
| ~ '\'LE\''(f(X0),s(s(s(s(s('\'0\''))))))
| '\'E\''(s(s(s(s('\'0\'')))),f(X0)) ),
inference(clausification,[status(esa)],[clause_113]) ).
cnf(c35,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(suc(X0)))) ),
inference(clausification,[status(esa)],[clause_44]) ).
cnf(c36,plain,
( '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(X0)))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(X1))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(X0)) ),
inference(clausification,[status(esa)],[clause_34]) ).
cnf(c37,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| ~ '\'LE\''(f(suc(X0)),s(s(s(s('\'0\'')))))
| '\'E\''(s(s(s('\'0\''))),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_111]) ).
cnf(c38,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_19]) ).
cnf(c39,plain,
( '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_115]) ).
cnf(c40,plain,
( '\'LE\''(f(X0),'\'0\'')
| ~ '\'LE\''(f(suc(suc(X0))),s('\'0\''))
| '\'E\''('\'0\'',f(suc(suc(X0)))) ),
inference(clausification,[status(esa)],[clause_11]) ).
cnf(c42,plain,
( ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X1))))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X0))))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0)) ),
inference(clausification,[status(esa)],[clause_73]) ).
cnf(c43,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X0))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_204]) ).
cnf(c44,plain,
'\'LE\''(f(X0),s(s(s(s(s('\'0\'')))))),
inference(clausification,[status(esa)],[clause_53]) ).
cnf(c45,plain,
( ~ '\'E\''(s(s(s(s('\'0\'')))),f(X0))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(X1)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(X1))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(X0)))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(suc(X1))))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(suc(X0)))) ),
inference(clausification,[status(esa)],[clause_183]) ).
cnf(c46,plain,
( '\'LE\''(f(X0),'\'0\'')
| ~ '\'LE\''(f(X0),s('\'0\''))
| '\'E\''('\'0\'',f(X0)) ),
inference(clausification,[status(esa)],[clause_173]) ).
cnf(d0,plain,
( '\'LE\''(f(X0),s(s(s(s('\'0\'')))))
| '\'E\''(s(s(s(s('\'0\'')))),f(suc(X0))) ),
inference(resolution,[status(thm)],[c44,c14]) ).
cnf(d1,plain,
( '\'LE\''(f(X0),s(s(s(s('\'0\'')))))
| '\'E\''(s(s(s(s('\'0\'')))),f(X0)) ),
inference(resolution,[status(thm)],[c44,c34]) ).
cnf(d2,plain,
( iLEQ(suc(X0),suc(X0))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(X0)))
| '\'LE\''(f(X0),s(s(s(s('\'0\''))))) ),
inference(resolution,[status(thm)],[d1,c1]) ).
cnf(d3,plain,
( '\'LE\''(f(X0),s(s(s(s('\'0\'')))))
| '\'LE\''(f(X0),s(s(s(s('\'0\'')))))
| iLEQ(suc(X0),suc(X0))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( '\'LE\''(f(X0),s(s(s(s('\'0\'')))))
| '\'E\''(s(s(s(s('\'0\'')))),f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[c44,c15]) ).
cnf(d5,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(suc(X0))))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(X0)))
| '\'LE\''(f(X0),s(s(s(s('\'0\''))))) ),
inference(resolution,[status(thm)],[d1,c10]) ).
cnf(d6,plain,
( '\'LE\''(f(X0),s(s(s(s('\'0\'')))))
| '\'LE\''(f(X0),s(s(s(s('\'0\'')))))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
( '\'LE\''(f(X0),s(s(s(s('\'0\'')))))
| '\'LE\''(f(X0),s(s(s(s('\'0\'')))))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d6,d4]) ).
cnf(d8,plain,
( '\'LE\''(f(X0),s(s(s(s('\'0\'')))))
| iLEQ(suc(X0),suc(X0))
| '\'LE\''(f(X0),s(s(s(s('\'0\'')))))
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[status(thm)],[d7,d3]) ).
cnf(d9,plain,
( '\'LE\''(f(X1),s(s(s(s('\'0\'')))))
| ~ iLEQ(suc(X1),suc(X0))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(X0)))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(X1)))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(X0)) ),
inference(resolution,[status(thm)],[c36,d1]) ).
cnf(d10,plain,
( '\'LE\''(f(X1),s(s(s(s('\'0\'')))))
| '\'LE\''(f(X0),s(s(s(s('\'0\'')))))
| ~ iLEQ(suc(X0),suc(X1))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(X1)))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(X0))) ),
inference(resolution,[status(thm)],[d9,d1]) ).
cnf(d11,plain,
( '\'LE\''(f(X1),s(s(s(s('\'0\'')))))
| '\'LE\''(f(X0),s(s(s(s('\'0\'')))))
| '\'LE\''(f(X1),s(s(s(s('\'0\'')))))
| ~ iLEQ(suc(X0),suc(X1))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(X0))) ),
inference(resolution,[status(thm)],[d10,d0]) ).
cnf(d12,plain,
( '\'LE\''(f(X1),s(s(s(s('\'0\'')))))
| '\'LE\''(f(X1),s(s(s(s('\'0\'')))))
| '\'LE\''(f(X0),s(s(s(s('\'0\'')))))
| ~ iLEQ(suc(X1),suc(X0))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d11,d0]) ).
cnf(d13,plain,
( '\'LE\''(f(X0),s(s(s(s('\'0\'')))))
| '\'LE\''(f(X0),s(s(s(s('\'0\'')))))
| '\'LE\''(f(X0),s(s(s(s('\'0\'')))))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d12,d8]) ).
cnf(d14,plain,
( '\'LE\''(f(X1),s(s(s(s('\'0\'')))))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(suc(X0))))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(suc(X1))))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(X0)))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(X1)))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(X0)) ),
inference(resolution,[status(thm)],[c45,d1]) ).
cnf(d15,plain,
( '\'LE\''(f(X1),s(s(s(s('\'0\'')))))
| '\'LE\''(f(X0),s(s(s(s('\'0\'')))))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(suc(X1))))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(suc(X0))))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(X1)))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(X0))) ),
inference(resolution,[status(thm)],[d14,d1]) ).
cnf(d16,plain,
( '\'LE\''(f(X1),s(s(s(s('\'0\'')))))
| '\'LE\''(f(X0),s(s(s(s('\'0\'')))))
| '\'LE\''(f(X1),s(s(s(s('\'0\'')))))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(suc(X0))))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(suc(X1))))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(X0))) ),
inference(resolution,[status(thm)],[d15,d0]) ).
cnf(d17,plain,
( '\'LE\''(f(X1),s(s(s(s('\'0\'')))))
| '\'LE\''(f(X1),s(s(s(s('\'0\'')))))
| '\'LE\''(f(X0),s(s(s(s('\'0\'')))))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(suc(X1))))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d16,d0]) ).
cnf(d18,plain,
( '\'LE\''(f(X1),s(s(s(s('\'0\'')))))
| '\'LE\''(f(X0),s(s(s(s('\'0\'')))))
| '\'LE\''(f(X1),s(s(s(s('\'0\'')))))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d17,d4]) ).
cnf(d19,plain,
( '\'LE\''(f(X1),s(s(s(s('\'0\'')))))
| '\'LE\''(f(X1),s(s(s(s('\'0\'')))))
| '\'LE\''(f(X0),s(s(s(s('\'0\'')))))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d18,d4]) ).
cnf(d20,plain,
( '\'LE\''(f(X1),s(s(s(s('\'0\'')))))
| '\'LE\''(f(X0),s(s(s(s('\'0\'')))))
| '\'LE\''(f(X1),s(s(s(s('\'0\'')))))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d19,d13]) ).
cnf(d21,plain,
( '\'LE\''(f(X1),s(s(s(s('\'0\'')))))
| '\'LE\''(f(X1),s(s(s(s('\'0\'')))))
| '\'LE\''(f(X0),s(s(s(s('\'0\'')))))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d20,d13]) ).
cnf(d22,plain,
( '\'LE\''(f(X0),s(s(s(s('\'0\'')))))
| '\'LE\''(f(X0),s(s(s(s('\'0\'')))))
| '\'LE\''(f(X0),s(s(s(s('\'0\''))))) ),
inference(resolution,[status(thm)],[d21,d8]) ).
cnf(d23,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'E\''(s(s(s('\'0\''))),f(suc(X0))) ),
inference(resolution,[status(thm)],[d22,c37]) ).
cnf(d24,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'E\''(s(s(s('\'0\''))),f(X0)) ),
inference(resolution,[status(thm)],[d22,c17]) ).
cnf(d25,plain,
( iLEQ(suc(X0),suc(X0))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[d24,c6]) ).
cnf(d26,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| iLEQ(suc(X0),suc(X0))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d25,d23]) ).
cnf(d27,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'E\''(s(s(s('\'0\''))),f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d22,c22]) ).
cnf(d28,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X0))))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[d24,c9]) ).
cnf(d29,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d28,d23]) ).
cnf(d30,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d29,d27]) ).
cnf(d31,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| iLEQ(suc(X0),suc(X0))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[status(thm)],[d30,d26]) ).
cnf(d32,plain,
( ~ iLEQ(suc(X0),suc(X1))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[d24,c21]) ).
cnf(d33,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| ~ iLEQ(suc(X1),suc(X0))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0))) ),
inference(resolution,[status(thm)],[d32,d24]) ).
cnf(d34,plain,
( '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| ~ iLEQ(suc(X1),suc(X0))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0))) ),
inference(resolution,[status(thm)],[d33,d23]) ).
cnf(d35,plain,
( '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| ~ iLEQ(suc(X0),suc(X1))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d34,d23]) ).
cnf(d36,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d35,d31]) ).
cnf(d37,plain,
( ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X1))))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X0))))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[d24,c42]) ).
cnf(d38,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X1))))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X0))))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0))) ),
inference(resolution,[status(thm)],[d37,d24]) ).
cnf(d39,plain,
( '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X0))))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X1))))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0))) ),
inference(resolution,[status(thm)],[d38,d23]) ).
cnf(d40,plain,
( '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X1))))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d39,d23]) ).
cnf(d41,plain,
( '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d40,d27]) ).
cnf(d42,plain,
( '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d41,d27]) ).
cnf(d43,plain,
( '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d42,d36]) ).
cnf(d44,plain,
( '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d43,d36]) ).
cnf(d45,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[d44,d31]) ).
cnf(d46,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(suc(X0))) ),
inference(resolution,[status(thm)],[d45,c18]) ).
cnf(d47,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(X0)) ),
inference(resolution,[status(thm)],[d45,c2]) ).
cnf(d48,plain,
( iLEQ(suc(X0),suc(X0))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d47,c0]) ).
cnf(d49,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| iLEQ(suc(X0),suc(X0))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d48,d46]) ).
cnf(d50,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d45,c7]) ).
cnf(d51,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X0))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d47,c16]) ).
cnf(d52,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d51,d46]) ).
cnf(d53,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d52,d50]) ).
cnf(d54,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| iLEQ(suc(X0),suc(X0))
| '\'LE\''(f(X0),s(s('\'0\'')))
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[status(thm)],[d53,d49]) ).
cnf(d55,plain,
( ~ iLEQ(suc(X1),suc(X0))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d47,c39]) ).
cnf(d56,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| ~ iLEQ(suc(X0),suc(X1))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0))) ),
inference(resolution,[status(thm)],[d55,d47]) ).
cnf(d57,plain,
( '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| ~ iLEQ(suc(X0),suc(X1))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0))) ),
inference(resolution,[status(thm)],[d56,d46]) ).
cnf(d58,plain,
( '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| ~ iLEQ(suc(X1),suc(X0))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d57,d46]) ).
cnf(d59,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d58,d54]) ).
cnf(d60,plain,
( ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X1))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X0))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d47,c8]) ).
cnf(d61,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X1))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X0))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0))) ),
inference(resolution,[status(thm)],[d60,d47]) ).
cnf(d62,plain,
( '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X0))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X1))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0))) ),
inference(resolution,[status(thm)],[d61,d46]) ).
cnf(d63,plain,
( '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X1))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d62,d46]) ).
cnf(d64,plain,
( '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d63,d50]) ).
cnf(d65,plain,
( '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d64,d50]) ).
cnf(d66,plain,
( '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d65,d59]) ).
cnf(d67,plain,
( '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d66,d59]) ).
cnf(d68,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d67,d54]) ).
cnf(d69,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[d68,c30]) ).
cnf(d70,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[d68,c12]) ).
cnf(d71,plain,
( iLEQ(suc(X0),suc(X0))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d70,c43]) ).
cnf(d72,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| iLEQ(suc(X0),suc(X0))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d71,d69]) ).
cnf(d73,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d68,c33]) ).
cnf(d74,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d70,c3]) ).
cnf(d75,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d74,d69]) ).
cnf(d76,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d75,d73]) ).
cnf(d77,plain,
( '\'LE\''(f(X0),s('\'0\''))
| iLEQ(suc(X0),suc(X0))
| '\'LE\''(f(X0),s('\'0\''))
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[status(thm)],[d76,d72]) ).
cnf(d78,plain,
( ~ iLEQ(suc(X1),suc(X0))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X1))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d70,c31]) ).
cnf(d79,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| ~ iLEQ(suc(X0),suc(X1))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[d78,d70]) ).
cnf(d80,plain,
( '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| ~ iLEQ(suc(X0),suc(X1))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[d79,d69]) ).
cnf(d81,plain,
( '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X1),suc(X0))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d80,d69]) ).
cnf(d82,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d81,d77]) ).
cnf(d83,plain,
( ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X1))))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X1))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d70,c20]) ).
cnf(d84,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X1))))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[d83,d70]) ).
cnf(d85,plain,
( '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X1))))
| ~ '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[d84,d69]) ).
cnf(d86,plain,
( '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X1))))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d85,d69]) ).
cnf(d87,plain,
( '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d86,d73]) ).
cnf(d88,plain,
( '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d87,d73]) ).
cnf(d89,plain,
( '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d88,d82]) ).
cnf(d90,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d89,d82]) ).
cnf(d91,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d90,d77]) ).
cnf(d92,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d91,c28]) ).
cnf(d93,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d91,c46]) ).
cnf(d94,plain,
( iLEQ(suc(X0),suc(X0))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d93,c38]) ).
cnf(d95,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| iLEQ(suc(X0),suc(X0))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d94,d92]) ).
cnf(d96,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d91,c40]) ).
cnf(d97,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d93,c35]) ).
cnf(d98,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d97,d92]) ).
cnf(d99,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d98,d96]) ).
cnf(d100,plain,
( '\'LE\''(f(X0),'\'0\'')
| iLEQ(suc(X0),suc(X0))
| '\'LE\''(f(X0),'\'0\'')
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[status(thm)],[d99,d95]) ).
cnf(d101,plain,
( ~ iLEQ(suc(X0),suc(X1))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X1))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d93,c4]) ).
cnf(d102,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| ~ iLEQ(suc(X1),suc(X0))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d101,d93]) ).
cnf(d103,plain,
( '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| ~ iLEQ(suc(X1),suc(X0))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d102,d92]) ).
cnf(d104,plain,
( '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X0),suc(X1))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d103,d92]) ).
cnf(d105,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d104,d100]) ).
cnf(d106,plain,
( ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X1))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d93,c32]) ).
cnf(d107,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d106,d93]) ).
cnf(d108,plain,
( '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d107,d92]) ).
cnf(d109,plain,
( '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''('\'0\'',f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d108,d92]) ).
cnf(d110,plain,
( '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d109,d96]) ).
cnf(d111,plain,
( '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d110,d96]) ).
cnf(d112,plain,
( '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d111,d105]) ).
cnf(d113,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d112,d105]) ).
cnf(d114,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d113,d100]) ).
cnf(d115,plain,
$false,
inference(resolution,[status(thm)],[d114,c19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO685-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n013.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 19:45:21 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 35.61/5.66 % SZS status Unsatisfiable for theBenchmark.p
% 35.61/5.66 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------