%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SYO681-1 : 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 : n006.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 74.09s 18.60s
% Output : CNFRefutation 74.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 58
% Number of leaves : 30
% Syntax : Number of clauses : 166 ( 5 unt; 141 nHn; 141 RR)
% Number of literals : 1209 ( 0 equ; 728 neg)
% Maximal clause size : 16 ( 7 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 : 311 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_658,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_556,axiom,
'\'LE\''(f(X0),s(s(s(s('\'0\''))))) ).
cnf(clause_300,axiom,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'LE\''(f(X0),s(s(s('\'0\'')))) ) ).
cnf(clause_415,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_614,axiom,
( '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''('\'0\'',f(suc(X0))) ) ).
cnf(clause_607,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_486,axiom,
( '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X2)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| ~ iLEQ(suc(X0),suc(X1)) ) ).
cnf(clause_687,axiom,
( '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ iLEQ(suc(X0),suc(X1)) ) ).
cnf(clause_528,axiom,
( ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(s(s('\'0\'')),f(X2))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X2))))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X2)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X1))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X0))))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0))) ) ).
cnf(clause_359,axiom,
~ '\'LE\''(f(z),'\'0\'') ).
cnf(clause_497,axiom,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| ~ '\'LE\''(f(X0),s('\'0\'')) ) ).
cnf(clause_463,axiom,
( '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(s(s('\'0\'')),f(X2))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X2)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0))) ) ).
cnf(clause_95,axiom,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s(s('\'0\''))) ) ).
cnf(clause_125,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_61,axiom,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'LE\''(f(suc(suc(X0))),s('\'0\'')) ) ).
cnf(clause_713,axiom,
( iLEQ(suc(X0),suc(X0))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0)) ) ).
cnf(clause_560,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_103,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_563,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_283,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_457,axiom,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s(s(s('\'0\'')))) ) ).
cnf(clause_663,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_131,axiom,
( ~ '\'E\''(s(s(s('\'0\''))),f(suc(X2)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X1))))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X2))))
| ~ '\'E\''(s(s(s('\'0\''))),f(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X0))))
| ~ iLEQ(suc(X0),suc(X1)) ) ).
cnf(clause_41,axiom,
( ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X2))))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X1))))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ iLEQ(suc(X0),suc(X1)) ) ).
cnf(clause_44,axiom,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(X0))
| ~ '\'LE\''(f(X0),s(s('\'0\''))) ) ).
cnf(clause_550,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_383,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_363,axiom,
( ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(suc(X2))))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''('\'0\'',f(suc(X0))) ) ).
cnf(clause_595,axiom,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s('\'0\'')) ) ).
cnf(clause_508,axiom,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'LE\''(f(suc(suc(X0))),s(s('\'0\''))) ) ).
cnf(c0,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_658]) ).
cnf(c2,plain,
'\'LE\''(f(X0),s(s(s(s('\'0\''))))),
inference(clausification,[status(esa)],[clause_556]) ).
cnf(c6,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_300]) ).
cnf(c7,plain,
( ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X0))))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(X0)) ),
inference(clausification,[status(esa)],[clause_415]) ).
cnf(c8,plain,
( ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''('\'0\'',f(X1))
| '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''('\'0\'',f(X2))
| ~ iLEQ(suc(X1),suc(X0))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_614]) ).
cnf(c9,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_607]) ).
cnf(c13,plain,
( ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(X2))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X2)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X1)))
| '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| ~ iLEQ(suc(X2),suc(X0))
| '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_486]) ).
cnf(c14,plain,
( ~ iLEQ(suc(X1),suc(X2))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X2))
| '\'E\''(f(X2),f(suc(X2)))
| '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(X0)) ),
inference(clausification,[status(esa)],[clause_687]) ).
cnf(c15,plain,
( ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X2)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X2))))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X0))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X1))))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(s(s('\'0\'')),f(X2))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ '\'E\''(s(s('\'0\'')),f(X0)) ),
inference(clausification,[status(esa)],[clause_528]) ).
cnf(c16,plain,
~ '\'LE\''(f(z),'\'0\''),
inference(clausification,[status(esa)],[clause_359]) ).
cnf(c17,plain,
( '\'LE\''(f(X0),'\'0\'')
| ~ '\'LE\''(f(X0),s('\'0\''))
| '\'E\''('\'0\'',f(X0)) ),
inference(clausification,[status(esa)],[clause_497]) ).
cnf(c18,plain,
( '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X2),f(suc(X2)))
| ~ iLEQ(suc(X0),suc(X2))
| '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X2)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ '\'E\''(s(s('\'0\'')),f(X2))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(X0)) ),
inference(clausification,[status(esa)],[clause_463]) ).
cnf(c21,plain,
( '\'LE\''(f(X0),s('\'0\''))
| ~ '\'LE\''(f(suc(X0)),s(s('\'0\'')))
| '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_95]) ).
cnf(c23,plain,
( ~ '\'E\''(s('\'0\''),f(suc(X0)))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'E\''(s('\'0\''),f(X0)) ),
inference(clausification,[status(esa)],[clause_125]) ).
cnf(c24,plain,
( '\'LE\''(f(X0),'\'0\'')
| ~ '\'LE\''(f(suc(suc(X0))),s('\'0\''))
| '\'E\''('\'0\'',f(suc(suc(X0)))) ),
inference(clausification,[status(esa)],[clause_61]) ).
cnf(c25,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_713]) ).
cnf(c26,plain,
( ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(suc(X0)))) ),
inference(clausification,[status(esa)],[clause_560]) ).
cnf(c27,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_103]) ).
cnf(c28,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_563]) ).
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_283]) ).
cnf(c33,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_457]) ).
cnf(c35,plain,
( ~ '\'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))))
| iLEQ(suc(X0),suc(X0)) ),
inference(clausification,[status(esa)],[clause_663]) ).
cnf(c37,plain,
( ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X2))))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X1))))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X0))))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X2))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X2)))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_131]) ).
cnf(c39,plain,
( ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X2))))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X1))))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_41]) ).
cnf(c41,plain,
( '\'LE\''(f(X0),s('\'0\''))
| ~ '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s('\'0\''),f(X0)) ),
inference(clausification,[status(esa)],[clause_44]) ).
cnf(c42,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_550]) ).
cnf(c45,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_383]) ).
cnf(c48,plain,
( ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''('\'0\'',f(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(suc(X2))))
| ~ '\'E\''(f(X0),f(suc(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_363]) ).
cnf(c50,plain,
( '\'LE\''(f(X0),'\'0\'')
| ~ '\'LE\''(f(suc(X0)),s('\'0\''))
| '\'E\''('\'0\'',f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_595]) ).
cnf(c51,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_508]) ).
cnf(d0,plain,
( '\'E\''(s(s(s('\'0\''))),f(X0))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[c2,c0]) ).
cnf(d1,plain,
( '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[c2,c42]) ).
cnf(d2,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[c31,d1]) ).
cnf(d3,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| iLEQ(suc(X0),suc(X0))
| '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( '\'E\''(s(s(s('\'0\''))),f(suc(suc(X0))))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[c2,c27]) ).
cnf(d5,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| 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(resolution,[status(thm)],[c35,d4]) ).
cnf(d6,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[d6,d0]) ).
cnf(d8,plain,
( iLEQ(suc(X0),suc(X0))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| iLEQ(suc(X0),suc(X0))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[d7,d3]) ).
cnf(d9,plain,
( '\'LE\''(f(X2),s(s(s('\'0\''))))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X2))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| '\'E\''(f(X2),f(suc(X2)))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[c13,d1]) ).
cnf(d10,plain,
( '\'LE\''(f(X2),s(s(s('\'0\''))))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X2))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| '\'E\''(f(X2),f(suc(X2)))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[d9,d1]) ).
cnf(d11,plain,
( '\'LE\''(f(X2),s(s(s('\'0\''))))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(X2))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X2),f(suc(X2)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[d10,d1]) ).
cnf(d12,plain,
( '\'LE\''(f(X2),s(s(s('\'0\''))))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| '\'E\''(f(X2),f(suc(X2)))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X2),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[d11,d0]) ).
cnf(d13,plain,
( '\'LE\''(f(X2),s(s(s('\'0\''))))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| '\'E\''(f(X2),f(suc(X2)))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X2),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[d12,d0]) ).
cnf(d14,plain,
( '\'LE\''(f(X1),s(s(s('\'0\''))))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X0),suc(X2))
| '\'E\''(f(X2),f(suc(X2)))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X2),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[d13,d0]) ).
cnf(d15,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| ~ iLEQ(suc(X0),suc(X1))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[d14,d8]) ).
cnf(d16,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[d15,d8]) ).
cnf(d17,plain,
( '\'LE\''(f(X2),s(s(s('\'0\''))))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'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(X2)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X2))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[c37,d4]) ).
cnf(d18,plain,
( '\'LE\''(f(X2),s(s(s('\'0\''))))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(suc(X1))))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X2)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X2))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[d17,d4]) ).
cnf(d19,plain,
( '\'LE\''(f(X2),s(s(s('\'0\''))))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X2),suc(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X2)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(X2))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[d18,d4]) ).
cnf(d20,plain,
( '\'LE\''(f(X2),s(s(s('\'0\''))))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X2))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X2),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[d19,d1]) ).
cnf(d21,plain,
( '\'LE\''(f(X2),s(s(s('\'0\''))))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X2))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X2),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[d20,d1]) ).
cnf(d22,plain,
( '\'LE\''(f(X1),s(s(s('\'0\''))))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(X2))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X2),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[d21,d1]) ).
cnf(d23,plain,
( '\'LE\''(f(X2),s(s(s('\'0\''))))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X2),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[d22,d0]) ).
cnf(d24,plain,
( '\'LE\''(f(X2),s(s(s('\'0\''))))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X2),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[d23,d0]) ).
cnf(d25,plain,
( '\'LE\''(f(X1),s(s(s('\'0\''))))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X2),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[d24,d0]) ).
cnf(d26,plain,
( '\'LE\''(f(X2),s(s(s('\'0\''))))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X2),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[d25,d16]) ).
cnf(d27,plain,
( '\'LE\''(f(X2),s(s(s('\'0\''))))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| '\'LE\''(f(X2),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[d26,d16]) ).
cnf(d28,plain,
( '\'LE\''(f(X1),s(s(s('\'0\''))))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1))
| '\'LE\''(f(X2),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[d27,d16]) ).
cnf(d29,plain,
( '\'LE\''(f(X1),s(s(s('\'0\''))))
| ~ iLEQ(suc(X1),suc(X0))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[d28,d8]) ).
cnf(d30,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)],[d29,d8]) ).
cnf(d31,plain,
( '\'E\''(s(s('\'0\'')),f(X0))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d30,c6]) ).
cnf(d32,plain,
( '\'E\''(s(s('\'0\'')),f(suc(X0)))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d30,c33]) ).
cnf(d33,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d32,c45]) ).
cnf(d34,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| iLEQ(suc(X0),suc(X0))
| '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d33,d31]) ).
cnf(d35,plain,
( '\'E\''(s(s('\'0\'')),f(suc(suc(X0))))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d30,c9]) ).
cnf(d36,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)))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d35,c7]) ).
cnf(d37,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d36,d32]) ).
cnf(d38,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d37,d31]) ).
cnf(d39,plain,
( iLEQ(suc(X0),suc(X0))
| '\'LE\''(f(X0),s(s('\'0\'')))
| iLEQ(suc(X0),suc(X0))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d38,d34]) ).
cnf(d40,plain,
( ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X2),suc(X1))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X2)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'E\''(s(s('\'0\'')),f(X2))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X2),f(suc(X2)))
| '\'E\''(f(X1),f(suc(X1)))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d32,c18]) ).
cnf(d41,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'E\''(s(s('\'0\'')),f(X2))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X2),f(suc(X2)))
| '\'E\''(f(X1),f(suc(X1)))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d40,d32]) ).
cnf(d42,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ '\'E\''(s(s('\'0\'')),f(X2))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X2),f(suc(X2)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d41,d32]) ).
cnf(d43,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| '\'E\''(f(X2),f(suc(X2)))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d42,d31]) ).
cnf(d44,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| '\'E\''(f(X2),f(suc(X2)))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d43,d31]) ).
cnf(d45,plain,
( '\'LE\''(f(X1),s(s('\'0\'')))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X2))
| '\'E\''(f(X2),f(suc(X2)))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d44,d31]) ).
cnf(d46,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| ~ iLEQ(suc(X1),suc(X0))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d45,d39]) ).
cnf(d47,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d46,d39]) ).
cnf(d48,plain,
( ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X2))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X1))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X2)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'E\''(s(s('\'0\'')),f(X2))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d35,c15]) ).
cnf(d49,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X1))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X2)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'E\''(s(s('\'0\'')),f(X2))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d48,d35]) ).
cnf(d50,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X2)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ '\'E\''(s(s('\'0\'')),f(X2))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d49,d35]) ).
cnf(d51,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(X2))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d50,d32]) ).
cnf(d52,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(X2))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d51,d32]) ).
cnf(d53,plain,
( '\'LE\''(f(X1),s(s('\'0\'')))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s(s('\'0\'')),f(X2))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d52,d32]) ).
cnf(d54,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d53,d31]) ).
cnf(d55,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d54,d31]) ).
cnf(d56,plain,
( '\'LE\''(f(X1),s(s('\'0\'')))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d55,d31]) ).
cnf(d57,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d56,d47]) ).
cnf(d58,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(f(X1),f(suc(X1)))
| '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d57,d47]) ).
cnf(d59,plain,
( '\'LE\''(f(X1),s(s('\'0\'')))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X0))
| '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d58,d47]) ).
cnf(d60,plain,
( '\'LE\''(f(X1),s(s('\'0\'')))
| ~ iLEQ(suc(X0),suc(X1))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d59,d39]) ).
cnf(d61,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d60,d39]) ).
cnf(d62,plain,
( '\'E\''(s('\'0\''),f(X0))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d61,c41]) ).
cnf(d63,plain,
( '\'E\''(s('\'0\''),f(suc(X0)))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d61,c21]) ).
cnf(d64,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s('\'0\''),f(X0))
| '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d63,c28]) ).
cnf(d65,plain,
( '\'E\''(s('\'0\''),f(suc(suc(X0))))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d61,c51]) ).
cnf(d66,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d65,c23]) ).
cnf(d67,plain,
( '\'LE\''(f(X0),s('\'0\''))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d66,d63]) ).
cnf(d68,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s('\'0\''),f(X0))
| '\'LE\''(f(X0),s('\'0\''))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s('\'0\''),f(X0))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d67,d64]) ).
cnf(d69,plain,
( '\'LE\''(f(X0),s('\'0\''))
| iLEQ(suc(X0),suc(X0))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d68,d62]) ).
cnf(d70,plain,
( ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X2),f(suc(X2)))
| '\'E\''(f(X1),f(suc(X1)))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d63,c14]) ).
cnf(d71,plain,
( '\'LE\''(f(X2),s('\'0\''))
| ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X2),suc(X1))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X2),f(suc(X2)))
| '\'E\''(f(X1),f(suc(X1)))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d70,d63]) ).
cnf(d72,plain,
( '\'LE\''(f(X2),s('\'0\''))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X0))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X2),f(suc(X2)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d71,d63]) ).
cnf(d73,plain,
( '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d72,d69]) ).
cnf(d74,plain,
( '\'LE\''(f(X0),s('\'0\''))
| ~ '\'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\''))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d73,d69]) ).
cnf(d75,plain,
( ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X2))))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X1))))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d65,c39]) ).
cnf(d76,plain,
( '\'LE\''(f(X2),s('\'0\''))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X1))))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d75,d65]) ).
cnf(d77,plain,
( '\'LE\''(f(X2),s('\'0\''))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d76,d65]) ).
cnf(d78,plain,
( '\'LE\''(f(X2),s('\'0\''))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d77,d63]) ).
cnf(d79,plain,
( '\'LE\''(f(X2),s('\'0\''))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d78,d63]) ).
cnf(d80,plain,
( '\'LE\''(f(X1),s('\'0\''))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d79,d63]) ).
cnf(d81,plain,
( ~ '\'E\''(s('\'0\''),f(X2))
| '\'LE\''(f(X2),s('\'0\''))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d80,d74]) ).
cnf(d82,plain,
( ~ '\'E\''(s('\'0\''),f(X2))
| '\'LE\''(f(X2),s('\'0\''))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d81,d74]) ).
cnf(d83,plain,
( ~ '\'E\''(s('\'0\''),f(X1))
| '\'LE\''(f(X1),s('\'0\''))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d82,d74]) ).
cnf(d84,plain,
( '\'LE\''(f(X1),s('\'0\''))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d83,d69]) ).
cnf(d85,plain,
( '\'LE\''(f(X0),s('\'0\''))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(X0))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d84,d69]) ).
cnf(d86,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d85,d62]) ).
cnf(d87,plain,
( '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d86,c17]) ).
cnf(d88,plain,
( '\'E\''('\'0\'',f(suc(X0)))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d86,c50]) ).
cnf(d89,plain,
( '\'E\''('\'0\'',f(suc(suc(X0))))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d86,c24]) ).
cnf(d90,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d89,c26]) ).
cnf(d91,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d90,c25]) ).
cnf(d92,plain,
( '\'LE\''(f(X0),'\'0\'')
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d91,d88]) ).
cnf(d93,plain,
( ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(X1))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d92,c8]) ).
cnf(d94,plain,
( ~ '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),'\'0\'')
| ~ '\'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)],[d93,d92]) ).
cnf(d95,plain,
( ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X2),suc(X1))
| ~ '\'E\''('\'0\'',f(suc(suc(X2))))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d89,c48]) ).
cnf(d96,plain,
( '\'LE\''(f(X2),'\'0\'')
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d95,d89]) ).
cnf(d97,plain,
( '\'LE\''(f(X2),'\'0\'')
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d96,d89]) ).
cnf(d98,plain,
( ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(X2))
| '\'LE\''(f(X2),'\'0\'')
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d97,d94]) ).
cnf(d99,plain,
( ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(X2))
| '\'LE\''(f(X2),'\'0\'')
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d98,d94]) ).
cnf(d100,plain,
( ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(X1))
| '\'LE\''(f(X1),'\'0\'')
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d99,d94]) ).
cnf(d101,plain,
( ~ '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d100,d92]) ).
cnf(d102,plain,
( ~ '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d101,d92]) ).
cnf(d103,plain,
( '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d102,d88]) ).
cnf(d104,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d103,d87]) ).
cnf(d105,plain,
$false,
inference(resolution,[status(thm)],[d104,c16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO681-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.40 % Computer : n006.cluster.edu
% 0.08/0.40 % Model : x86_64 x86_64
% 0.08/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.40 % Memory : 8046.5625MB
% 0.08/0.40 % OS : Linux 6.8.0-71-generic
% 0.08/0.40 % CPULimit : 300
% 0.08/0.40 % WCLimit : 300
% 0.08/0.40 % DateTime : Sat Sep 26 19:45:14 UTC 2026
% 0.08/0.40 % CPUTime :
% 0.08/0.40 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 74.09/18.60 % SZS status Unsatisfiable for theBenchmark.p
% 74.09/18.60 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------