%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SYO677-1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 09:47:25 AM UTC 2026
% Result : Unsatisfiable 27.79s 4.03s
% Output : CNFRefutation 27.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 62
% Number of leaves : 30
% Syntax : Number of clauses : 129 ( 5 unt; 104 nHn; 99 RR)
% Number of literals : 553 ( 0 equ; 290 neg)
% Maximal clause size : 9 ( 4 avg)
% Maximal term depth : 5 ( 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 : 142 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_24,axiom,
( ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X0))))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X1))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(X0)) ) ).
cnf(clause_143,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_38,axiom,
( '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(X0)) ) ).
cnf(clause_15,axiom,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(X0))
| ~ '\'LE\''(f(X0),s(s('\'0\''))) ) ).
cnf(clause_13,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_51,axiom,
( '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0))) ) ).
cnf(clause_97,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_2,axiom,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s('\'0\'')) ) ).
cnf(clause_145,axiom,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| ~ '\'LE\''(f(X0),s('\'0\'')) ) ).
cnf(clause_18,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_61,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_0,axiom,
( '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(X0))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X0))) ) ).
cnf(clause_113,axiom,
'\'LE\''(f(X0),s(s(s(s('\'0\''))))) ).
cnf(clause_73,axiom,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'LE\''(f(X0),s(s(s('\'0\'')))) ) ).
cnf(clause_48,axiom,
( ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0))) ) ).
cnf(clause_140,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_150,axiom,
( iLEQ(suc(X0),suc(X0))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0)) ) ).
cnf(clause_31,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_39,axiom,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s(s('\'0\''))) ) ).
cnf(clause_49,axiom,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'LE\''(f(suc(suc(X0))),s(s('\'0\''))) ) ).
cnf(clause_77,axiom,
~ '\'LE\''(f(z),'\'0\'') ).
cnf(clause_57,axiom,
( ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X1))))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'E\''(s('\'0\''),f(suc(X0))) ) ).
cnf(clause_121,axiom,
( ~ '\'E\''(s(s(s('\'0\''))),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X0))))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X1))))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0))) ) ).
cnf(clause_87,axiom,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s(s(s('\'0\'')))) ) ).
cnf(clause_65,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_84,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_112,axiom,
( '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X1),f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0))) ) ).
cnf(clause_27,axiom,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'LE\''(f(suc(suc(X0))),s('\'0\'')) ) ).
cnf(clause_115,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_114,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(c0,plain,
( ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X1))))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X0))))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s(s('\'0\'')),f(X0)) ),
inference(clausification,[status(esa)],[clause_24]) ).
cnf(c2,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_143]) ).
cnf(c5,plain,
( ~ iLEQ(suc(X1),suc(X0))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_38]) ).
cnf(c6,plain,
( '\'LE\''(f(X0),s('\'0\''))
| ~ '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s('\'0\''),f(X0)) ),
inference(clausification,[status(esa)],[clause_15]) ).
cnf(c8,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_13]) ).
cnf(c9,plain,
( ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| '\'E\''(f(X1),f(suc(X1)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_51]) ).
cnf(c11,plain,
( ~ '\'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))))
| iLEQ(suc(X0),suc(X0)) ),
inference(clausification,[status(esa)],[clause_97]) ).
cnf(c12,plain,
( '\'LE\''(f(X0),'\'0\'')
| ~ '\'LE\''(f(suc(X0)),s('\'0\''))
| '\'E\''('\'0\'',f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_2]) ).
cnf(c13,plain,
( '\'LE\''(f(X0),'\'0\'')
| ~ '\'LE\''(f(X0),s('\'0\''))
| '\'E\''('\'0\'',f(X0)) ),
inference(clausification,[status(esa)],[clause_145]) ).
cnf(c14,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_18]) ).
cnf(c15,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_61]) ).
cnf(c16,plain,
( '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''('\'0\'',f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_0]) ).
cnf(c17,plain,
'\'LE\''(f(X0),s(s(s(s('\'0\''))))),
inference(clausification,[status(esa)],[clause_113]) ).
cnf(c18,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_73]) ).
cnf(c19,plain,
( ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(clausification,[status(esa)],[clause_48]) ).
cnf(c21,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)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X0)))) ),
inference(clausification,[status(esa)],[clause_140]) ).
cnf(c22,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_150]) ).
cnf(c23,plain,
( ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'E\''(s('\'0\''),f(X0))
| iLEQ(suc(X0),suc(X0)) ),
inference(clausification,[status(esa)],[clause_31]) ).
cnf(c24,plain,
( '\'LE\''(f(X0),s('\'0\''))
| ~ '\'LE\''(f(suc(X0)),s(s('\'0\'')))
| '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_39]) ).
cnf(c26,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_49]) ).
cnf(c27,plain,
~ '\'LE\''(f(z),'\'0\''),
inference(clausification,[status(esa)],[clause_77]) ).
cnf(c28,plain,
( ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X1))))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_57]) ).
cnf(c29,plain,
( ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X1))))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X1)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X0)))) ),
inference(clausification,[status(esa)],[clause_121]) ).
cnf(c30,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_87]) ).
cnf(c31,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_65]) ).
cnf(c33,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_84]) ).
cnf(c34,plain,
( ~ '\'E\''(s('\'0\''),f(X1))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_112]) ).
cnf(c35,plain,
( '\'LE\''(f(X0),'\'0\'')
| ~ '\'LE\''(f(suc(suc(X0))),s('\'0\''))
| '\'E\''('\'0\'',f(suc(suc(X0)))) ),
inference(clausification,[status(esa)],[clause_27]) ).
cnf(c36,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_115]) ).
cnf(c37,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_114]) ).
cnf(d0,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'E\''(s(s(s('\'0\''))),f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[c17,c2]) ).
cnf(d1,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'E\''(s(s(s('\'0\''))),f(suc(X0))) ),
inference(resolution,[status(thm)],[c17,c8]) ).
cnf(d2,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'E\''(s(s(s('\'0\''))),f(X0)) ),
inference(resolution,[status(thm)],[c17,c15]) ).
cnf(d3,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| '\'E\''(f(X0),f(suc(X0)))
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[status(thm)],[c31,d2]) ).
cnf(d4,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'E\''(f(X0),f(suc(X0)))
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
( ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d4,c9]) ).
cnf(d6,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d6,d1]) ).
cnf(d8,plain,
( ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X0))))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| iLEQ(suc(X0),suc(X0))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[d7,c21]) ).
cnf(d9,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X0))))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[status(thm)],[d8,d2]) ).
cnf(d10,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X0))))
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[status(thm)],[d9,d1]) ).
cnf(d11,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[status(thm)],[d10,d0]) ).
cnf(d12,plain,
( ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X0))))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X0))))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[d11,c29]) ).
cnf(d13,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X0))))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0)) ),
inference(resolution,[status(thm)],[d12,d7]) ).
cnf(d14,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X0))))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0))) ),
inference(resolution,[status(thm)],[d13,d2]) ).
cnf(d15,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d14,d1]) ).
cnf(d16,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[d15,d0]) ).
cnf(d17,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d16,c14]) ).
cnf(d18,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(suc(X0))) ),
inference(resolution,[status(thm)],[d16,c30]) ).
cnf(d19,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(X0)) ),
inference(resolution,[status(thm)],[d16,c18]) ).
cnf(d20,plain,
( ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| '\'E\''(f(X0),f(suc(X0)))
| iLEQ(suc(X0),suc(X0))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d19,c33]) ).
cnf(d21,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(f(X0),f(suc(X0)))
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[status(thm)],[d20,d18]) ).
cnf(d22,plain,
( ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d21,c5]) ).
cnf(d23,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d22,d19]) ).
cnf(d24,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d23,d18]) ).
cnf(d25,plain,
( ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X0))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| iLEQ(suc(X0),suc(X0))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d24,c11]) ).
cnf(d26,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X0))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[status(thm)],[d25,d19]) ).
cnf(d27,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X0))))
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[status(thm)],[d26,d18]) ).
cnf(d28,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[status(thm)],[d27,d17]) ).
cnf(d29,plain,
( ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X0))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X0))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d28,c0]) ).
cnf(d30,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X0))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(X0)) ),
inference(resolution,[status(thm)],[d29,d24]) ).
cnf(d31,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X0))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0))) ),
inference(resolution,[status(thm)],[d30,d19]) ).
cnf(d32,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d31,d18]) ).
cnf(d33,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d32,d17]) ).
cnf(d34,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d33,c26]) ).
cnf(d35,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[d33,c24]) ).
cnf(d36,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[d33,c6]) ).
cnf(d37,plain,
( ~ '\'E\''(s('\'0\''),f(suc(X0)))
| '\'E\''(f(X0),f(suc(X0)))
| iLEQ(suc(X0),suc(X0))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d36,c36]) ).
cnf(d38,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(f(X0),f(suc(X0)))
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[status(thm)],[d37,d35]) ).
cnf(d39,plain,
( ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(X0))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d38,c34]) ).
cnf(d40,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d39,d36]) ).
cnf(d41,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d40,d35]) ).
cnf(d42,plain,
( ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X0))
| iLEQ(suc(X0),suc(X0))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d41,c23]) ).
cnf(d43,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[status(thm)],[d42,d36]) ).
cnf(d44,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[status(thm)],[d43,d35]) ).
cnf(d45,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[status(thm)],[d44,d34]) ).
cnf(d46,plain,
( ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d45,c28]) ).
cnf(d47,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[d46,d41]) ).
cnf(d48,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[d47,d36]) ).
cnf(d49,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d48,d35]) ).
cnf(d50,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d49,d34]) ).
cnf(d51,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d50,c35]) ).
cnf(d52,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d50,c12]) ).
cnf(d53,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d50,c13]) ).
cnf(d54,plain,
( ~ '\'E\''('\'0\'',f(suc(X0)))
| '\'E\''(f(X0),f(suc(X0)))
| iLEQ(suc(X0),suc(X0))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d53,c22]) ).
cnf(d55,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'E\''(f(X0),f(suc(X0)))
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[status(thm)],[d54,d52]) ).
cnf(d56,plain,
( ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(X0))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X0),'\'0\'')
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d55,c16]) ).
cnf(d57,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''('\'0\'',f(suc(X0)))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d56,d53]) ).
cnf(d58,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d57,d52]) ).
cnf(d59,plain,
( ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0))
| iLEQ(suc(X0),suc(X0))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d58,c37]) ).
cnf(d60,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[status(thm)],[d59,d53]) ).
cnf(d61,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[status(thm)],[d60,d52]) ).
cnf(d62,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[status(thm)],[d61,d51]) ).
cnf(d63,plain,
( ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d62,c19]) ).
cnf(d64,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d63,d58]) ).
cnf(d65,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d64,d53]) ).
cnf(d66,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''('\'0\'',f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d65,d52]) ).
cnf(d67,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d66,d51]) ).
cnf(d68,plain,
$false,
inference(resolution,[status(thm)],[d67,c27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO677-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n012.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 19:44:19 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.79/4.03 % SZS status Unsatisfiable for theBenchmark.p
% 27.79/4.03 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------