%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SYO683-1 : 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 : n001.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 29.65s 4.38s
% Output : CNFRefutation 29.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 62
% Number of leaves : 18
% Syntax : Number of clauses : 109 ( 5 unt; 84 nHn; 91 RR)
% Number of literals : 845 ( 0 equ; 514 neg)
% Maximal clause size : 14 ( 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 : 322 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_469,axiom,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0)) ) ).
cnf(clause_398,axiom,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X0)) ) ).
cnf(clause_451,axiom,
'\'LE\''(f(X0),s(s(s(s('\'0\''))))) ).
cnf(clause_29,axiom,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(X0)) ) ).
cnf(clause_560,axiom,
( ~ iLEQ(suc(X4),suc(X0))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X4)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X2)))
| ~ iLEQ(suc(X3),suc(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X3)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X4))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'E\''(s(s(s('\'0\''))),f(X2))
| ~ '\'E\''(s(s(s('\'0\''))),f(X3))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X1)))
| ~ iLEQ(suc(X2),suc(X3))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0))) ) ).
cnf(clause_476,axiom,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s(s(s('\'0\'')))) ) ).
cnf(clause_97,axiom,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'LE\''(f(X0),s(s(s('\'0\'')))) ) ).
cnf(clause_443,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_287,axiom,
~ '\'LE\''(f(z),'\'0\'') ).
cnf(clause_547,axiom,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s('\'0\'')) ) ).
cnf(clause_563,axiom,
( ~ iLEQ(suc(X1),suc(X4))
| ~ '\'E\''(s(s('\'0\'')),f(X2))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| ~ iLEQ(suc(X3),suc(X0))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X3)))
| ~ '\'E\''(s(s('\'0\'')),f(X4))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X2)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X4)))
| ~ '\'E\''(s(s('\'0\'')),f(X3))
| ~ iLEQ(suc(X2),suc(X3))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0))) ) ).
cnf(clause_539,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_59,axiom,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0)) ) ).
cnf(clause_222,axiom,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s(s('\'0\''))) ) ).
cnf(clause_44,axiom,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(X0))
| ~ '\'LE\''(f(X0),s(s('\'0\''))) ) ).
cnf(clause_442,axiom,
( ~ '\'E\''('\'0\'',f(X4))
| ~ iLEQ(suc(X3),suc(X2))
| ~ '\'E\''('\'0\'',f(suc(X4)))
| ~ iLEQ(suc(X4),suc(X0))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X1),suc(X3))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(suc(X3)))
| ~ '\'E\''('\'0\'',f(X3))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0))) ) ).
cnf(clause_89,axiom,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| ~ '\'LE\''(f(X0),s('\'0\'')) ) ).
cnf(clause_151,axiom,
( ~ iLEQ(suc(X2),suc(X4))
| ~ iLEQ(suc(X4),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X4)))
| ~ '\'E\''(s('\'0\''),f(X3))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s('\'0\''),f(X4))
| ~ iLEQ(suc(X3),suc(X2))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X3)))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(suc(X0))) ) ).
cnf(c0,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_469]) ).
cnf(c1,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_398]) ).
cnf(c2,plain,
'\'LE\''(f(X0),s(s(s(s('\'0\''))))),
inference(clausification,[status(esa)],[clause_451]) ).
cnf(c3,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_29]) ).
cnf(c4,plain,
( ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| ~ iLEQ(suc(X4),suc(X3))
| ~ '\'E\''(s(s(s('\'0\''))),f(X2))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X4)))
| ~ iLEQ(suc(X3),suc(X1))
| ~ iLEQ(suc(X0),suc(X4))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X3)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X4))
| ~ '\'E\''(s(s(s('\'0\''))),f(X3))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X2)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0)) ),
inference(clausification,[status(esa)],[clause_560]) ).
cnf(c5,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_476]) ).
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_97]) ).
cnf(c7,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_443]) ).
cnf(c8,plain,
~ '\'LE\''(f(z),'\'0\''),
inference(clausification,[status(esa)],[clause_287]) ).
cnf(c9,plain,
( '\'LE\''(f(X0),'\'0\'')
| ~ '\'LE\''(f(suc(X0)),s('\'0\''))
| '\'E\''('\'0\'',f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_547]) ).
cnf(c10,plain,
( ~ iLEQ(suc(X4),suc(X1))
| ~ '\'E\''(s(s('\'0\'')),f(X4))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X4)))
| ~ iLEQ(suc(X2),suc(X4))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X3)))
| ~ '\'E\''(s(s('\'0\'')),f(X3))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| ~ iLEQ(suc(X0),suc(X3))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X2)))
| ~ iLEQ(suc(X3),suc(X2))
| ~ '\'E\''(s(s('\'0\'')),f(X2))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_563]) ).
cnf(c11,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_539]) ).
cnf(c12,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_59]) ).
cnf(c13,plain,
( '\'LE\''(f(X0),s('\'0\''))
| ~ '\'LE\''(f(suc(X0)),s(s('\'0\'')))
| '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_222]) ).
cnf(c14,plain,
( '\'LE\''(f(X0),s('\'0\''))
| ~ '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s('\'0\''),f(X0)) ),
inference(clausification,[status(esa)],[clause_44]) ).
cnf(c15,plain,
( ~ iLEQ(suc(X3),suc(X1))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(X4))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X0),suc(X4))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X3))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ iLEQ(suc(X4),suc(X3))
| ~ '\'E\''('\'0\'',f(suc(X4)))
| ~ '\'E\''('\'0\'',f(suc(X3)))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_442]) ).
cnf(c16,plain,
( '\'LE\''(f(X0),'\'0\'')
| ~ '\'LE\''(f(X0),s('\'0\''))
| '\'E\''('\'0\'',f(X0)) ),
inference(clausification,[status(esa)],[clause_89]) ).
cnf(c17,plain,
( ~ '\'E\''(s('\'0\''),f(X4))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X4)))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(X3))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X4),suc(X1))
| ~ '\'E\''(s('\'0\''),f(suc(X3)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(X0)) ),
inference(clausification,[status(esa)],[clause_151]) ).
cnf(d0,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'E\''(s(s(s('\'0\''))),f(suc(X0))) ),
inference(resolution,[status(thm)],[c2,c7]) ).
cnf(d1,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'E\''(s(s(s('\'0\''))),f(X0)) ),
inference(resolution,[status(thm)],[c2,c11]) ).
cnf(d2,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[d1,c12]) ).
cnf(d3,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X4))
| ~ iLEQ(suc(X0),suc(X3))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X4)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X3)))
| ~ '\'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(X4))
| ~ '\'E\''(s(s(s('\'0\''))),f(X3))
| ~ '\'E\''(s(s(s('\'0\''))),f(X2))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[d1,c4]) ).
cnf(d5,plain,
( '\'LE\''(f(X3),s(s(s('\'0\''))))
| '\'LE\''(f(X4),s(s(s('\'0\''))))
| ~ iLEQ(suc(X4),suc(X0))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X4)))
| ~ '\'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(suc(X3)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X2))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0)) ),
inference(resolution,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
( '\'LE\''(f(X4),s(s(s('\'0\''))))
| '\'LE\''(f(X3),s(s(s('\'0\''))))
| '\'LE\''(f(X2),s(s(s('\'0\''))))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X4))
| ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X2),suc(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X4)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X3)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X2)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0)) ),
inference(resolution,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
( '\'LE\''(f(X4),s(s(s('\'0\''))))
| '\'LE\''(f(X3),s(s(s('\'0\''))))
| '\'LE\''(f(X2),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X4),suc(X0))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X4)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X3)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X2)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0)) ),
inference(resolution,[status(thm)],[d6,d1]) ).
cnf(d8,plain,
( '\'LE\''(f(X4),s(s(s('\'0\''))))
| '\'LE\''(f(X3),s(s(s('\'0\''))))
| '\'LE\''(f(X2),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X4))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X4)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X3)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X2)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0))) ),
inference(resolution,[status(thm)],[d7,d1]) ).
cnf(d9,plain,
( '\'LE\''(f(X4),s(s(s('\'0\''))))
| '\'LE\''(f(X3),s(s(s('\'0\''))))
| '\'LE\''(f(X2),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X4),s(s(s('\'0\''))))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X4),suc(X0))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X3)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X2)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0))) ),
inference(resolution,[status(thm)],[d8,d0]) ).
cnf(d10,plain,
( '\'LE\''(f(X4),s(s(s('\'0\''))))
| '\'LE\''(f(X2),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X4),s(s(s('\'0\''))))
| '\'LE\''(f(X3),s(s(s('\'0\''))))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X0),suc(X4))
| ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X3),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))) ),
inference(resolution,[status(thm)],[d9,d0]) ).
cnf(d11,plain,
( '\'LE\''(f(X4),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X4),s(s(s('\'0\''))))
| '\'LE\''(f(X3),s(s(s('\'0\''))))
| '\'LE\''(f(X2),s(s(s('\'0\''))))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X4),suc(X0))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X2),suc(X3))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0))) ),
inference(resolution,[status(thm)],[d10,d0]) ).
cnf(d12,plain,
( '\'LE\''(f(X4),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X4),s(s(s('\'0\''))))
| '\'LE\''(f(X3),s(s(s('\'0\''))))
| '\'LE\''(f(X2),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0))) ),
inference(resolution,[status(thm)],[d11,d0]) ).
cnf(d13,plain,
( '\'LE\''(f(X4),s(s(s('\'0\''))))
| '\'LE\''(f(X4),s(s(s('\'0\''))))
| '\'LE\''(f(X3),s(s(s('\'0\''))))
| '\'LE\''(f(X2),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d12,d0]) ).
cnf(d14,plain,
( '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X3),s(s(s('\'0\''))))
| '\'LE\''(f(X2),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d13,d3]) ).
cnf(d15,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X2),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d14,d3]) ).
cnf(d16,plain,
( '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d15,d3]) ).
cnf(d17,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)],[d16,d3]) ).
cnf(d18,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(suc(X0))) ),
inference(resolution,[status(thm)],[d17,c5]) ).
cnf(d19,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(X0)) ),
inference(resolution,[status(thm)],[d17,c6]) ).
cnf(d20,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d19,c3]) ).
cnf(d21,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[status(thm)],[d20,d18]) ).
cnf(d22,plain,
( ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X3),suc(X1))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X4))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X4)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X3)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X2)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(X4))
| ~ '\'E\''(s(s('\'0\'')),f(X3))
| ~ '\'E\''(s(s('\'0\'')),f(X2))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d19,c10]) ).
cnf(d23,plain,
( '\'LE\''(f(X3),s(s('\'0\'')))
| '\'LE\''(f(X4),s(s('\'0\'')))
| ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X3),suc(X0))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X4)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X2)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X3)))
| ~ '\'E\''(s(s('\'0\'')),f(X2))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ '\'E\''(s(s('\'0\'')),f(X0)) ),
inference(resolution,[status(thm)],[d22,d19]) ).
cnf(d24,plain,
( '\'LE\''(f(X4),s(s('\'0\'')))
| '\'LE\''(f(X3),s(s('\'0\'')))
| '\'LE\''(f(X2),s(s('\'0\'')))
| ~ iLEQ(suc(X1),suc(X4))
| ~ iLEQ(suc(X4),suc(X0))
| ~ iLEQ(suc(X3),suc(X1))
| ~ iLEQ(suc(X2),suc(X3))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X4)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X3)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X2)))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ '\'E\''(s(s('\'0\'')),f(X0)) ),
inference(resolution,[status(thm)],[d23,d19]) ).
cnf(d25,plain,
( '\'LE\''(f(X4),s(s('\'0\'')))
| '\'LE\''(f(X3),s(s('\'0\'')))
| '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| ~ iLEQ(suc(X4),suc(X1))
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X2),suc(X4))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X4)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X3)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X2)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(X0)) ),
inference(resolution,[status(thm)],[d24,d19]) ).
cnf(d26,plain,
( '\'LE\''(f(X4),s(s('\'0\'')))
| '\'LE\''(f(X3),s(s('\'0\'')))
| '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X3))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X4)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X3)))
| ~ '\'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)],[d25,d19]) ).
cnf(d27,plain,
( '\'LE\''(f(X4),s(s('\'0\'')))
| '\'LE\''(f(X3),s(s('\'0\'')))
| '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X4),s(s('\'0\'')))
| ~ iLEQ(suc(X3),suc(X0))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X3))
| ~ iLEQ(suc(X0),suc(X4))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X3)))
| ~ '\'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)],[d26,d18]) ).
cnf(d28,plain,
( '\'LE\''(f(X3),s(s('\'0\'')))
| '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X3),s(s('\'0\'')))
| '\'LE\''(f(X4),s(s('\'0\'')))
| ~ iLEQ(suc(X2),suc(X4))
| ~ iLEQ(suc(X1),suc(X3))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X3),suc(X2))
| ~ '\'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)],[d27,d18]) ).
cnf(d29,plain,
( '\'LE\''(f(X3),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X3),s(s('\'0\'')))
| '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X4),s(s('\'0\'')))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X2),suc(X3))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0))) ),
inference(resolution,[status(thm)],[d28,d18]) ).
cnf(d30,plain,
( '\'LE\''(f(X4),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X4),s(s('\'0\'')))
| '\'LE\''(f(X3),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X2),s(s('\'0\'')))
| ~ iLEQ(suc(X0),suc(X3))
| ~ iLEQ(suc(X4),suc(X0))
| ~ iLEQ(suc(X3),suc(X1))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0))) ),
inference(resolution,[status(thm)],[d29,d18]) ).
cnf(d31,plain,
( '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X3),s(s('\'0\'')))
| '\'LE\''(f(X4),s(s('\'0\'')))
| '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d30,d18]) ).
cnf(d32,plain,
( '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X3),s(s('\'0\'')))
| '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d31,d21]) ).
cnf(d33,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d32,d21]) ).
cnf(d34,plain,
( '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d33,d21]) ).
cnf(d35,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d34,d21]) ).
cnf(d36,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[d35,c13]) ).
cnf(d37,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[d35,c14]) ).
cnf(d38,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d37,c1]) ).
cnf(d39,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[status(thm)],[d38,d36]) ).
cnf(d40,plain,
( ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X4))
| ~ '\'E\''(s('\'0\''),f(suc(X4)))
| ~ '\'E\''(s('\'0\''),f(suc(X3)))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X4))
| ~ '\'E\''(s('\'0\''),f(X3))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d37,c17]) ).
cnf(d41,plain,
( '\'LE\''(f(X3),s('\'0\''))
| '\'LE\''(f(X4),s('\'0\''))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X1),suc(X4))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X3),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X4)))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X3)))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[d40,d37]) ).
cnf(d42,plain,
( '\'LE\''(f(X4),s('\'0\''))
| '\'LE\''(f(X3),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X3),suc(X1))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X4)))
| ~ '\'E\''(s('\'0\''),f(suc(X3)))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[d41,d37]) ).
cnf(d43,plain,
( '\'LE\''(f(X4),s('\'0\''))
| '\'LE\''(f(X3),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| ~ iLEQ(suc(X0),suc(X3))
| ~ iLEQ(suc(X4),suc(X0))
| ~ iLEQ(suc(X2),suc(X4))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X4)))
| ~ '\'E\''(s('\'0\''),f(suc(X3)))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[d42,d37]) ).
cnf(d44,plain,
( '\'LE\''(f(X4),s('\'0\''))
| '\'LE\''(f(X3),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X4),suc(X1))
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X0),suc(X4))
| ~ '\'E\''(s('\'0\''),f(suc(X4)))
| ~ '\'E\''(s('\'0\''),f(suc(X3)))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[d43,d37]) ).
cnf(d45,plain,
( '\'LE\''(f(X4),s('\'0\''))
| '\'LE\''(f(X3),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X4),s('\'0\''))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X1),suc(X3))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X4),suc(X2))
| ~ '\'E\''(s('\'0\''),f(suc(X3)))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[d44,d36]) ).
cnf(d46,plain,
( '\'LE\''(f(X4),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X4),s('\'0\''))
| '\'LE\''(f(X3),s('\'0\''))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X4))
| ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X3),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[d45,d36]) ).
cnf(d47,plain,
( '\'LE\''(f(X4),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X4),s('\'0\''))
| '\'LE\''(f(X3),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X4),suc(X0))
| ~ iLEQ(suc(X3),suc(X1))
| ~ iLEQ(suc(X2),suc(X3))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[d46,d36]) ).
cnf(d48,plain,
( '\'LE\''(f(X3),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X3),s('\'0\''))
| '\'LE\''(f(X4),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| ~ iLEQ(suc(X0),suc(X4))
| ~ iLEQ(suc(X4),suc(X2))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[d47,d36]) ).
cnf(d49,plain,
( '\'LE\''(f(X4),s('\'0\''))
| '\'LE\''(f(X4),s('\'0\''))
| '\'LE\''(f(X3),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X4),suc(X0))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d48,d36]) ).
cnf(d50,plain,
( '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X3),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d49,d39]) ).
cnf(d51,plain,
( '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d50,d39]) ).
cnf(d52,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)],[d51,d39]) ).
cnf(d53,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d52,d39]) ).
cnf(d54,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d53,c9]) ).
cnf(d55,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d53,c16]) ).
cnf(d56,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d55,c0]) ).
cnf(d57,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[status(thm)],[d56,d54]) ).
cnf(d58,plain,
( ~ iLEQ(suc(X3),suc(X0))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X4))
| ~ '\'E\''('\'0\'',f(suc(X4)))
| ~ '\'E\''('\'0\'',f(suc(X3)))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X4))
| ~ '\'E\''('\'0\'',f(X3))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d55,c15]) ).
cnf(d59,plain,
( '\'LE\''(f(X3),'\'0\'')
| '\'LE\''(f(X4),'\'0\'')
| ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X4))
| ~ '\'E\''('\'0\'',f(suc(X4)))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X3)))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d58,d55]) ).
cnf(d60,plain,
( '\'LE\''(f(X4),'\'0\'')
| '\'LE\''(f(X3),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X4),suc(X0))
| ~ iLEQ(suc(X2),suc(X3))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X4)))
| ~ '\'E\''('\'0\'',f(suc(X3)))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d59,d55]) ).
cnf(d61,plain,
( '\'LE\''(f(X4),'\'0\'')
| '\'LE\''(f(X3),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| ~ iLEQ(suc(X0),suc(X4))
| ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X4)))
| ~ '\'E\''('\'0\'',f(suc(X3)))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d60,d55]) ).
cnf(d62,plain,
( '\'LE\''(f(X4),'\'0\'')
| '\'LE\''(f(X3),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X4),suc(X0))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''('\'0\'',f(suc(X4)))
| ~ '\'E\''('\'0\'',f(suc(X3)))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d61,d55]) ).
cnf(d63,plain,
( '\'LE\''(f(X4),'\'0\'')
| '\'LE\''(f(X3),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X4),'\'0\'')
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X0),suc(X4))
| ~ iLEQ(suc(X4),suc(X3))
| ~ '\'E\''('\'0\'',f(suc(X3)))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d62,d54]) ).
cnf(d64,plain,
( '\'LE\''(f(X4),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X4),'\'0\'')
| '\'LE\''(f(X3),'\'0\'')
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X4),suc(X0))
| ~ iLEQ(suc(X3),suc(X4))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d63,d54]) ).
cnf(d65,plain,
( '\'LE\''(f(X4),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X4),'\'0\'')
| '\'LE\''(f(X3),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X2),suc(X1))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d64,d54]) ).
cnf(d66,plain,
( '\'LE\''(f(X4),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X4),'\'0\'')
| '\'LE\''(f(X3),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| ~ iLEQ(suc(X4),suc(X0))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d65,d54]) ).
cnf(d67,plain,
( '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X4),'\'0\'')
| '\'LE\''(f(X3),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d66,d54]) ).
cnf(d68,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X3),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d67,d57]) ).
cnf(d69,plain,
( '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d68,d57]) ).
cnf(d70,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d69,d57]) ).
cnf(d71,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d70,d57]) ).
cnf(d72,plain,
$false,
inference(resolution,[status(thm)],[d71,c8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO683-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n001.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 19:51:14 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 29.65/4.38 % SZS status Unsatisfiable for theBenchmark.p
% 29.65/4.38 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------