%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SYO671-1 : 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 : n020.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 09:47:24 AM UTC 2026
% Result : Unsatisfiable 50.71s 7.19s
% Output : CNFRefutation 50.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 23
% Syntax : Number of clauses : 140 ( 5 unt; 120 nHn; 117 RR)
% Number of literals : 1007 ( 0 equ; 566 neg)
% Maximal clause size : 14 ( 7 avg)
% Maximal term depth : 4 ( 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 : 275 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_183,axiom,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s(s(s('\'0\'')))) ) ).
cnf(clause_26,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_217,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_20,axiom,
( ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X1))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X2)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X0))))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(s(s('\'0\'')),f(X2))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X2))))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(X0)) ) ).
cnf(clause_16,axiom,
( '\'E\''(f(X2),f(suc(X2)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X1),f(suc(X1)))
| ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0)) ) ).
cnf(clause_326,axiom,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(X0))
| ~ '\'LE\''(f(X0),s(s('\'0\''))) ) ).
cnf(clause_421,axiom,
'\'LE\''(f(X0),s(s(s('\'0\'')))) ).
cnf(clause_219,axiom,
( ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X1))))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X2))))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X0)) ) ).
cnf(clause_311,axiom,
( '\'E\''(f(X2),f(suc(X2)))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X2)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s(s('\'0\'')),f(X2))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(X0)) ) ).
cnf(clause_83,axiom,
( ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(suc(X2))))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''('\'0\'',f(X0)) ) ).
cnf(clause_37,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_86,axiom,
( iLEQ(suc(X0),suc(X0))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0)) ) ).
cnf(clause_60,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_72,axiom,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'LE\''(f(suc(suc(X0))),s('\'0\'')) ) ).
cnf(clause_91,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_261,axiom,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'LE\''(f(X0),s(s(s('\'0\'')))) ) ).
cnf(clause_116,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_340,axiom,
( '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X2),f(suc(X2)))
| '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X0)) ) ).
cnf(clause_353,axiom,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s('\'0\'')) ) ).
cnf(clause_211,axiom,
~ '\'LE\''(f(z),'\'0\'') ).
cnf(clause_138,axiom,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s(s('\'0\''))) ) ).
cnf(clause_307,axiom,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| ~ '\'LE\''(f(X0),s('\'0\'')) ) ).
cnf(clause_18,axiom,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'LE\''(f(suc(suc(X0))),s(s('\'0\''))) ) ).
cnf(c3,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_183]) ).
cnf(c4,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_26]) ).
cnf(c5,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_217]) ).
cnf(c7,plain,
( ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(X2))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X2)))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X1))))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X0))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X2))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(clausification,[status(esa)],[clause_20]) ).
cnf(c8,plain,
( ~ '\'E\''('\'0\'',f(suc(X2)))
| '\'E\''(f(X1),f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''('\'0\'',f(X2))
| '\'E\''(f(X2),f(suc(X2)))
| ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_16]) ).
cnf(c9,plain,
( '\'LE\''(f(X0),s('\'0\''))
| ~ '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s('\'0\''),f(X0)) ),
inference(clausification,[status(esa)],[clause_326]) ).
cnf(c10,plain,
'\'LE\''(f(X0),s(s(s('\'0\'')))),
inference(clausification,[status(esa)],[clause_421]) ).
cnf(c11,plain,
( ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X2))))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X1))))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0)) ),
inference(clausification,[status(esa)],[clause_219]) ).
cnf(c12,plain,
( '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X2)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(X2))
| ~ iLEQ(suc(X2),suc(X1))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_311]) ).
cnf(c13,plain,
( ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(suc(X2))))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X2))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(clausification,[status(esa)],[clause_83]) ).
cnf(c14,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0)))) ),
inference(clausification,[status(esa)],[clause_37]) ).
cnf(c15,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_86]) ).
cnf(c20,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_60]) ).
cnf(c22,plain,
( '\'LE\''(f(X0),'\'0\'')
| ~ '\'LE\''(f(suc(suc(X0))),s('\'0\''))
| '\'E\''('\'0\'',f(suc(suc(X0)))) ),
inference(clausification,[status(esa)],[clause_72]) ).
cnf(c23,plain,
( ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X0))))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_91]) ).
cnf(c26,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_261]) ).
cnf(c27,plain,
( ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_116]) ).
cnf(c28,plain,
( ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ iLEQ(suc(X2),suc(X0))
| '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(X1))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| '\'E\''(f(X2),f(suc(X2)))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(clausification,[status(esa)],[clause_340]) ).
cnf(c29,plain,
( '\'LE\''(f(X0),'\'0\'')
| ~ '\'LE\''(f(suc(X0)),s('\'0\''))
| '\'E\''('\'0\'',f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_353]) ).
cnf(c33,plain,
~ '\'LE\''(f(z),'\'0\''),
inference(clausification,[status(esa)],[clause_211]) ).
cnf(c35,plain,
( '\'LE\''(f(X0),s('\'0\''))
| ~ '\'LE\''(f(suc(X0)),s(s('\'0\'')))
| '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_138]) ).
cnf(c39,plain,
( '\'LE\''(f(X0),'\'0\'')
| ~ '\'LE\''(f(X0),s('\'0\''))
| '\'E\''('\'0\'',f(X0)) ),
inference(clausification,[status(esa)],[clause_307]) ).
cnf(c40,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_18]) ).
cnf(d0,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(suc(X0))) ),
inference(resolution,[status(thm)],[c10,c3]) ).
cnf(d1,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(X0)) ),
inference(resolution,[status(thm)],[c10,c26]) ).
cnf(d2,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)],[d1,c4]) ).
cnf(d3,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)],[d2,d0]) ).
cnf(d4,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[c10,c5]) ).
cnf(d5,plain,
( '\'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))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0))) ),
inference(resolution,[status(thm)],[c23,d1]) ).
cnf(d6,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)],[d5,d0]) ).
cnf(d7,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)],[d6,d4]) ).
cnf(d8,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)],[d7,d3]) ).
cnf(d9,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X2))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X2)))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ '\'E\''(s(s('\'0\'')),f(X0)) ),
inference(resolution,[status(thm)],[c12,d1]) ).
cnf(d10,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X2),suc(X0))
| '\'E\''(f(X0),f(suc(X0)))
| '\'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(X2)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(X0)) ),
inference(resolution,[status(thm)],[d9,d1]) ).
cnf(d11,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),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)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X2)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0))) ),
inference(resolution,[status(thm)],[d10,d1]) ).
cnf(d12,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X2),s(s('\'0\'')))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X2),suc(X0))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0))) ),
inference(resolution,[status(thm)],[d11,d0]) ).
cnf(d13,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X0))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X2),f(suc(X2)))
| '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0))) ),
inference(resolution,[status(thm)],[d12,d0]) ).
cnf(d14,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),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))) ),
inference(resolution,[status(thm)],[d13,d0]) ).
cnf(d15,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),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)))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d14,d8]) ).
cnf(d16,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)],[d15,d8]) ).
cnf(d17,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X1))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X0))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X2))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X2)))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ '\'E\''(s(s('\'0\'')),f(X0)) ),
inference(resolution,[status(thm)],[c7,d1]) ).
cnf(d18,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(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)) ),
inference(resolution,[status(thm)],[d17,d1]) ).
cnf(d19,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X2))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X1))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X0))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X2)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0))) ),
inference(resolution,[status(thm)],[d18,d1]) ).
cnf(d20,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X2),s(s('\'0\'')))
| ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X2),suc(X1))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X1))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X0))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X2))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0))) ),
inference(resolution,[status(thm)],[d19,d0]) ).
cnf(d21,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(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))) ),
inference(resolution,[status(thm)],[d20,d0]) ).
cnf(d22,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),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)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X2))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X1))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d21,d0]) ).
cnf(d23,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X2),s(s('\'0\'')))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X1))))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d22,d4]) ).
cnf(d24,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d23,d4]) ).
cnf(d25,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d24,d4]) ).
cnf(d26,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X2),s(s('\'0\'')))
| ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X2),suc(X1))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d25,d16]) ).
cnf(d27,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d26,d16]) ).
cnf(d28,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d27,d16]) ).
cnf(d29,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d28,d8]) ).
cnf(d30,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d29,d8]) ).
cnf(d31,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[d30,c35]) ).
cnf(d32,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[d30,c9]) ).
cnf(d33,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)],[d32,c20]) ).
cnf(d34,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)],[d33,d31]) ).
cnf(d35,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d30,c40]) ).
cnf(d36,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)],[d32,c14]) ).
cnf(d37,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)],[d36,d31]) ).
cnf(d38,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)],[d37,d35]) ).
cnf(d39,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)],[d38,d34]) ).
cnf(d40,plain,
( ~ 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)))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d32,c28]) ).
cnf(d41,plain,
( '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X0),suc(X1))
| '\'E\''(f(X2),f(suc(X2)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[d40,d32]) ).
cnf(d42,plain,
( '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),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)))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[d41,d32]) ).
cnf(d43,plain,
( '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X2),suc(X0))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[d42,d31]) ).
cnf(d44,plain,
( '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X0))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X2),f(suc(X2)))
| '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[d43,d31]) ).
cnf(d45,plain,
( '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),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))) ),
inference(resolution,[status(thm)],[d44,d31]) ).
cnf(d46,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),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\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d45,d39]) ).
cnf(d47,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)],[d46,d39]) ).
cnf(d48,plain,
( ~ 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)))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X2))))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X1))))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d32,c11]) ).
cnf(d49,plain,
( '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X2))))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X1))))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[d48,d32]) ).
cnf(d50,plain,
( '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X2))))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X1))))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[d49,d32]) ).
cnf(d51,plain,
( '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X2),suc(X1))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X1))))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X2))))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[d50,d31]) ).
cnf(d52,plain,
( '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X2))))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X1))))
| ~ '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[d51,d31]) ).
cnf(d53,plain,
( '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),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)))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X2))))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X1))))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d52,d31]) ).
cnf(d54,plain,
( '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X1))))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d53,d35]) ).
cnf(d55,plain,
( '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d54,d35]) ).
cnf(d56,plain,
( '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d55,d35]) ).
cnf(d57,plain,
( '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X2),suc(X1))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d56,d47]) ).
cnf(d58,plain,
( '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d57,d47]) ).
cnf(d59,plain,
( '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d58,d47]) ).
cnf(d60,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d59,d39]) ).
cnf(d61,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d60,d39]) ).
cnf(d62,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d61,c29]) ).
cnf(d63,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d61,c39]) ).
cnf(d64,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)],[d63,c15]) ).
cnf(d65,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| iLEQ(suc(X0),suc(X0))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d64,d62]) ).
cnf(d66,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d61,c22]) ).
cnf(d67,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)],[d63,c27]) ).
cnf(d68,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)],[d67,d62]) ).
cnf(d69,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d68,d66]) ).
cnf(d70,plain,
( '\'LE\''(f(X0),'\'0\'')
| iLEQ(suc(X0),suc(X0))
| '\'LE\''(f(X0),'\'0\'')
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[status(thm)],[d69,d65]) ).
cnf(d71,plain,
( ~ 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)))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d63,c8]) ).
cnf(d72,plain,
( '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X1),suc(X0))
| '\'E\''(f(X2),f(suc(X2)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d71,d63]) ).
cnf(d73,plain,
( '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X2))
| '\'E\''(f(X2),f(suc(X2)))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d72,d63]) ).
cnf(d74,plain,
( '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X2),suc(X1))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d73,d62]) ).
cnf(d75,plain,
( '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X1),suc(X2))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X2),f(suc(X2)))
| '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d74,d62]) ).
cnf(d76,plain,
( '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'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))) ),
inference(resolution,[status(thm)],[d75,d62]) ).
cnf(d77,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X0),suc(X1))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d76,d70]) ).
cnf(d78,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)],[d77,d70]) ).
cnf(d79,plain,
( ~ 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)))
| ~ '\'E\''('\'0\'',f(suc(suc(X2))))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d63,c13]) ).
cnf(d80,plain,
( '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(suc(X2))))
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d79,d63]) ).
cnf(d81,plain,
( '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'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)))
| ~ '\'E\''('\'0\'',f(suc(suc(X2))))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d80,d63]) ).
cnf(d82,plain,
( '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''('\'0\'',f(suc(suc(X2))))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d81,d62]) ).
cnf(d83,plain,
( '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''('\'0\'',f(suc(suc(X2))))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d82,d62]) ).
cnf(d84,plain,
( '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'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)))
| ~ '\'E\''('\'0\'',f(suc(suc(X2))))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''('\'0\'',f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d83,d62]) ).
cnf(d85,plain,
( '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''('\'0\'',f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d84,d66]) ).
cnf(d86,plain,
( '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d85,d66]) ).
cnf(d87,plain,
( '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'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))) ),
inference(resolution,[status(thm)],[d86,d66]) ).
cnf(d88,plain,
( '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d87,d78]) ).
cnf(d89,plain,
( '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d88,d78]) ).
cnf(d90,plain,
( '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d89,d78]) ).
cnf(d91,plain,
( '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d90,d70]) ).
cnf(d92,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d91,d70]) ).
cnf(d93,plain,
$false,
inference(resolution,[status(thm)],[d92,c33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO671-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.57 % Computer : n020.cluster.edu
% 0.11/0.57 % Model : x86_64 x86_64
% 0.11/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.57 % Memory : 8046.5625MB
% 0.11/0.57 % OS : Linux 6.8.0-71-generic
% 0.11/0.57 % CPULimit : 300
% 0.11/0.57 % WCLimit : 300
% 0.11/0.57 % DateTime : Sat Sep 26 19:46:04 UTC 2026
% 0.11/0.58 % CPUTime :
% 0.11/0.58 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 50.71/7.19 % SZS status Unsatisfiable for theBenchmark.p
% 50.71/7.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------