%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SYO674-1 : 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 09:47:24 AM UTC 2026
% Result : Unsatisfiable 33.98s 4.93s
% Output : CNFRefutation 33.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 14
% Syntax : Number of clauses : 92 ( 5 unt; 72 nHn; 78 RR)
% Number of literals : 863 ( 0 equ; 539 neg)
% Maximal clause size : 17 ( 9 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 : 329 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_193,axiom,
( ~ iLEQ(suc(X3),suc(X1))
| ~ '\'E\''(s('\'0\''),f(X5))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(suc(X3)))
| ~ iLEQ(suc(X4),suc(X2))
| ~ iLEQ(suc(X5),suc(X4))
| ~ '\'E\''(s('\'0\''),f(X3))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(suc(X4)))
| ~ '\'E\''(s('\'0\''),f(suc(X5)))
| ~ '\'E\''(s('\'0\''),f(X4))
| ~ iLEQ(suc(X2),suc(X3))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0))) ) ).
cnf(clause_298,axiom,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(X0))
| ~ '\'LE\''(f(X0),s(s('\'0\''))) ) ).
cnf(clause_281,axiom,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0)) ) ).
cnf(clause_176,axiom,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| ~ '\'LE\''(f(X0),s('\'0\'')) ) ).
cnf(clause_139,axiom,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'LE\''(f(X0),s(s(s('\'0\'')))) ) ).
cnf(clause_126,axiom,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(X0)) ) ).
cnf(clause_498,axiom,
'\'LE\''(f(X0),s(s(s('\'0\'')))) ).
cnf(clause_204,axiom,
~ '\'LE\''(f(z),'\'0\'') ).
cnf(clause_129,axiom,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s(s(s('\'0\'')))) ) ).
cnf(clause_431,axiom,
( ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X5),suc(X1))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X2)))
| ~ '\'E\''(s(s('\'0\'')),f(X4))
| ~ iLEQ(suc(X4),suc(X5))
| ~ '\'E\''(s(s('\'0\'')),f(X3))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X5)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X3)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X4)))
| ~ iLEQ(suc(X2),suc(X3))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ '\'E\''(s(s('\'0\'')),f(X5))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ iLEQ(suc(X3),suc(X4))
| ~ '\'E\''(s(s('\'0\'')),f(X2))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(X0)) ) ).
cnf(clause_50,axiom,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s('\'0\'')) ) ).
cnf(clause_84,axiom,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s(s('\'0\''))) ) ).
cnf(clause_493,axiom,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X0)) ) ).
cnf(clause_453,axiom,
( ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X4))
| ~ '\'E\''('\'0\'',f(suc(X5)))
| ~ '\'E\''('\'0\'',f(suc(X3)))
| ~ iLEQ(suc(X2),suc(X5))
| ~ '\'E\''('\'0\'',f(suc(X4)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ iLEQ(suc(X1),suc(X3))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(X3))
| ~ '\'E\''('\'0\'',f(X0))
| ~ iLEQ(suc(X4),suc(X2))
| ~ '\'E\''('\'0\'',f(X5))
| ~ iLEQ(suc(X3),suc(X4))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(X1))
| ~ iLEQ(suc(X0),suc(X1)) ) ).
cnf(c0,plain,
( ~ iLEQ(suc(X1),suc(X5))
| ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ iLEQ(suc(X3),suc(X1))
| ~ '\'E\''(s('\'0\''),f(X5))
| ~ '\'E\''(s('\'0\''),f(suc(X3)))
| ~ iLEQ(suc(X4),suc(X3))
| ~ '\'E\''(s('\'0\''),f(X4))
| ~ '\'E\''(s('\'0\''),f(suc(X5)))
| ~ iLEQ(suc(X5),suc(X2))
| ~ '\'E\''(s('\'0\''),f(suc(X4)))
| ~ '\'E\''(s('\'0\''),f(X3))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_193]) ).
cnf(c1,plain,
( '\'LE\''(f(X0),s('\'0\''))
| ~ '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s('\'0\''),f(X0)) ),
inference(clausification,[status(esa)],[clause_298]) ).
cnf(c2,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_281]) ).
cnf(c3,plain,
( '\'LE\''(f(X0),'\'0\'')
| ~ '\'LE\''(f(X0),s('\'0\''))
| '\'E\''('\'0\'',f(X0)) ),
inference(clausification,[status(esa)],[clause_176]) ).
cnf(c4,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_139]) ).
cnf(c5,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_126]) ).
cnf(c6,plain,
'\'LE\''(f(X0),s(s(s('\'0\'')))),
inference(clausification,[status(esa)],[clause_498]) ).
cnf(c7,plain,
~ '\'LE\''(f(z),'\'0\''),
inference(clausification,[status(esa)],[clause_204]) ).
cnf(c8,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_129]) ).
cnf(c9,plain,
( ~ '\'E\''(s(s('\'0\'')),f(suc(X2)))
| ~ iLEQ(suc(X5),suc(X1))
| ~ iLEQ(suc(X1),suc(X4))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X4)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X5)))
| ~ '\'E\''(s(s('\'0\'')),f(X5))
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X0),suc(X5))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X3)))
| ~ '\'E\''(s(s('\'0\'')),f(X4))
| ~ '\'E\''(s(s('\'0\'')),f(X3))
| ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''(s(s('\'0\'')),f(X2))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_431]) ).
cnf(c10,plain,
( '\'LE\''(f(X0),'\'0\'')
| ~ '\'LE\''(f(suc(X0)),s('\'0\''))
| '\'E\''('\'0\'',f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_50]) ).
cnf(c11,plain,
( '\'LE\''(f(X0),s('\'0\''))
| ~ '\'LE\''(f(suc(X0)),s(s('\'0\'')))
| '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_84]) ).
cnf(c12,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_493]) ).
cnf(c13,plain,
( ~ '\'E\''('\'0\'',f(X3))
| ~ '\'E\''('\'0\'',f(suc(X3)))
| ~ '\'E\''('\'0\'',f(X0))
| ~ iLEQ(suc(X5),suc(X4))
| ~ '\'E\''('\'0\'',f(X4))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X4),suc(X0))
| ~ '\'E\''('\'0\'',f(X5))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X5)))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(suc(X4)))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(clausification,[status(esa)],[clause_453]) ).
cnf(d0,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(suc(X0))) ),
inference(resolution,[status(thm)],[c6,c8]) ).
cnf(d1,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(X0)) ),
inference(resolution,[status(thm)],[c6,c4]) ).
cnf(d2,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0))) ),
inference(resolution,[status(thm)],[c5,d1]) ).
cnf(d3,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( '\'LE\''(f(X5),s(s('\'0\'')))
| ~ iLEQ(suc(X4),suc(X2))
| ~ iLEQ(suc(X3),suc(X0))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X3))
| ~ iLEQ(suc(X5),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(suc(X5)))
| ~ '\'E\''(s(s('\'0\'')),f(X4))
| ~ '\'E\''(s(s('\'0\'')),f(X3))
| ~ '\'E\''(s(s('\'0\'')),f(X2))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ '\'E\''(s(s('\'0\'')),f(X0)) ),
inference(resolution,[status(thm)],[c9,d1]) ).
cnf(d5,plain,
( '\'LE\''(f(X5),s(s('\'0\'')))
| '\'LE\''(f(X4),s(s('\'0\'')))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X3))
| ~ iLEQ(suc(X5),suc(X1))
| ~ iLEQ(suc(X4),suc(X5))
| ~ '\'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(suc(X5)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X4)))
| ~ '\'E\''(s(s('\'0\'')),f(X3))
| ~ '\'E\''(s(s('\'0\'')),f(X2))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ '\'E\''(s(s('\'0\'')),f(X0)) ),
inference(resolution,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
( '\'LE\''(f(X5),s(s('\'0\'')))
| '\'LE\''(f(X4),s(s('\'0\'')))
| '\'LE\''(f(X3),s(s('\'0\'')))
| ~ iLEQ(suc(X2),suc(X5))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X3),suc(X1))
| ~ '\'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(X5)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X4)))
| ~ '\'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)],[d5,d1]) ).
cnf(d7,plain,
( '\'LE\''(f(X5),s(s('\'0\'')))
| '\'LE\''(f(X4),s(s('\'0\'')))
| '\'LE\''(f(X3),s(s('\'0\'')))
| '\'LE\''(f(X2),s(s('\'0\'')))
| ~ iLEQ(suc(X1),suc(X5))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X5),suc(X2))
| ~ iLEQ(suc(X4),suc(X0))
| ~ iLEQ(suc(X3),suc(X4))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X5)))
| ~ '\'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)],[d6,d1]) ).
cnf(d8,plain,
( '\'LE\''(f(X5),s(s('\'0\'')))
| '\'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(X0),suc(X5))
| ~ iLEQ(suc(X5),suc(X1))
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X4))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X5)))
| ~ '\'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)],[d7,d1]) ).
cnf(d9,plain,
( '\'LE\''(f(X5),s(s('\'0\'')))
| '\'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(X5),suc(X0))
| ~ iLEQ(suc(X4),suc(X1))
| ~ iLEQ(suc(X3),suc(X5))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X0),suc(X4))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X5)))
| ~ '\'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)],[d8,d1]) ).
cnf(d10,plain,
( '\'LE\''(f(X5),s(s('\'0\'')))
| '\'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(X5),s(s('\'0\'')))
| ~ iLEQ(suc(X4),suc(X0))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X5))
| ~ iLEQ(suc(X0),suc(X3))
| ~ iLEQ(suc(X5),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))) ),
inference(resolution,[status(thm)],[d9,d0]) ).
cnf(d11,plain,
( '\'LE\''(f(X5),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(X5),s(s('\'0\'')))
| '\'LE\''(f(X4),s(s('\'0\'')))
| ~ iLEQ(suc(X3),suc(X0))
| ~ iLEQ(suc(X2),suc(X4))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X5),suc(X3))
| ~ iLEQ(suc(X4),suc(X5))
| ~ '\'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)],[d10,d0]) ).
cnf(d12,plain,
( '\'LE\''(f(X4),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\'')))
| '\'LE\''(f(X5),s(s('\'0\'')))
| '\'LE\''(f(X3),s(s('\'0\'')))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X5))
| ~ iLEQ(suc(X4),suc(X2))
| ~ iLEQ(suc(X5),suc(X3))
| ~ iLEQ(suc(X3),suc(X4))
| ~ '\'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)],[d11,d0]) ).
cnf(d13,plain,
( '\'LE\''(f(X5),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X5),s(s('\'0\'')))
| '\'LE\''(f(X3),s(s('\'0\'')))
| '\'LE\''(f(X4),s(s('\'0\'')))
| '\'LE\''(f(X2),s(s('\'0\'')))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X4),suc(X5))
| ~ iLEQ(suc(X2),suc(X3))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0))) ),
inference(resolution,[status(thm)],[d12,d0]) ).
cnf(d14,plain,
( '\'LE\''(f(X5),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X5),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(X5))
| ~ iLEQ(suc(X5),suc(X4))
| ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X3),suc(X1))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0))) ),
inference(resolution,[status(thm)],[d13,d0]) ).
cnf(d15,plain,
( '\'LE\''(f(X5),s(s('\'0\'')))
| '\'LE\''(f(X5),s(s('\'0\'')))
| '\'LE\''(f(X3),s(s('\'0\'')))
| '\'LE\''(f(X4),s(s('\'0\'')))
| '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| ~ iLEQ(suc(X5),suc(X0))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d14,d0]) ).
cnf(d16,plain,
( '\'LE\''(f(X4),s(s('\'0\'')))
| '\'LE\''(f(X4),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(X4),s(s('\'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)],[d15,d3]) ).
cnf(d17,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X3),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d16,d3]) ).
cnf(d18,plain,
( '\'LE\''(f(X1),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(X2),suc(X0))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d17,d3]) ).
cnf(d19,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)],[d18,d3]) ).
cnf(d20,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d19,d3]) ).
cnf(d21,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[d20,c11]) ).
cnf(d22,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[d20,c1]) ).
cnf(d23,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d22,c12]) ).
cnf(d24,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[status(thm)],[d23,d21]) ).
cnf(d25,plain,
( ~ iLEQ(suc(X5),suc(X3))
| ~ iLEQ(suc(X4),suc(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X4))
| ~ iLEQ(suc(X0),suc(X5))
| ~ '\'E\''(s('\'0\''),f(suc(X5)))
| ~ '\'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(X5))
| ~ '\'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)],[d22,c0]) ).
cnf(d26,plain,
( '\'LE\''(f(X4),s('\'0\''))
| '\'LE\''(f(X5),s('\'0\''))
| ~ iLEQ(suc(X5),suc(X4))
| ~ iLEQ(suc(X3),suc(X0))
| ~ iLEQ(suc(X2),suc(X5))
| ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X4),suc(X1))
| ~ '\'E\''(s('\'0\''),f(suc(X5)))
| ~ '\'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(suc(X4)))
| ~ '\'E\''(s('\'0\''),f(X3))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[d25,d22]) ).
cnf(d27,plain,
( '\'LE\''(f(X5),s('\'0\''))
| '\'LE\''(f(X4),s('\'0\''))
| '\'LE\''(f(X3),s('\'0\''))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X0),suc(X3))
| ~ iLEQ(suc(X5),suc(X2))
| ~ iLEQ(suc(X4),suc(X1))
| ~ iLEQ(suc(X3),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(X5)))
| ~ '\'E\''(s('\'0\''),f(suc(X4)))
| ~ '\'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)],[d26,d22]) ).
cnf(d28,plain,
( '\'LE\''(f(X5),s('\'0\''))
| '\'LE\''(f(X4),s('\'0\''))
| '\'LE\''(f(X3),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| ~ iLEQ(suc(X1),suc(X4))
| ~ iLEQ(suc(X5),suc(X1))
| ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X3),suc(X0))
| ~ iLEQ(suc(X2),suc(X5))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X5)))
| ~ '\'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)],[d27,d22]) ).
cnf(d29,plain,
( '\'LE\''(f(X5),s('\'0\''))
| '\'LE\''(f(X4),s('\'0\''))
| '\'LE\''(f(X3),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| ~ iLEQ(suc(X5),suc(X2))
| ~ iLEQ(suc(X4),suc(X1))
| ~ iLEQ(suc(X3),suc(X0))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X1),suc(X5))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X5)))
| ~ '\'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)],[d28,d22]) ).
cnf(d30,plain,
( '\'LE\''(f(X5),s('\'0\''))
| '\'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(X0))
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X2),suc(X5))
| ~ iLEQ(suc(X1),suc(X4))
| ~ iLEQ(suc(X0),suc(X3))
| ~ '\'E\''(s('\'0\''),f(suc(X5)))
| ~ '\'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)],[d29,d22]) ).
cnf(d31,plain,
( '\'LE\''(f(X5),s('\'0\''))
| '\'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(X5),s('\'0\''))
| ~ iLEQ(suc(X4),suc(X1))
| ~ iLEQ(suc(X3),suc(X0))
| ~ iLEQ(suc(X2),suc(X5))
| ~ iLEQ(suc(X1),suc(X2))
| ~ 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)],[d30,d21]) ).
cnf(d32,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\''))
| '\'LE\''(f(X5),s('\'0\''))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X5))
| ~ iLEQ(suc(X0),suc(X3))
| ~ 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)],[d31,d21]) ).
cnf(d33,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\''))
| '\'LE\''(f(X5),s('\'0\''))
| ~ iLEQ(suc(X2),suc(X4))
| ~ iLEQ(suc(X1),suc(X5))
| ~ iLEQ(suc(X0),suc(X1))
| ~ 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)],[d32,d21]) ).
cnf(d34,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\''))
| '\'LE\''(f(X5),s('\'0\''))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X5))
| ~ iLEQ(suc(X4),suc(X2))
| ~ 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)],[d33,d21]) ).
cnf(d35,plain,
( '\'LE\''(f(X4),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X4),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X3),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X5),s('\'0\''))
| ~ iLEQ(suc(X0),suc(X5))
| ~ iLEQ(suc(X4),suc(X0))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[d34,d21]) ).
cnf(d36,plain,
( '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X4),s('\'0\''))
| '\'LE\''(f(X3),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X5),s('\'0\''))
| ~ iLEQ(suc(X1),suc(X5))
| ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d35,d21]) ).
cnf(d37,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X3),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X4),s('\'0\''))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d36,d24]) ).
cnf(d38,plain,
( '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X3),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d37,d24]) ).
cnf(d39,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d38,d24]) ).
cnf(d40,plain,
( '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d39,d24]) ).
cnf(d41,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d40,d24]) ).
cnf(d42,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d41,c10]) ).
cnf(d43,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d41,c3]) ).
cnf(d44,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d43,c2]) ).
cnf(d45,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[status(thm)],[d44,d42]) ).
cnf(d46,plain,
( ~ iLEQ(suc(X4),suc(X0))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X5))
| ~ '\'E\''('\'0\'',f(suc(X5)))
| ~ '\'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(X5))
| ~ '\'E\''('\'0\'',f(X4))
| ~ '\'E\''('\'0\'',f(X3))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d43,c13]) ).
cnf(d47,plain,
( '\'LE\''(f(X4),'\'0\'')
| '\'LE\''(f(X5),'\'0\'')
| ~ iLEQ(suc(X5),suc(X4))
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X5))
| ~ '\'E\''('\'0\'',f(suc(X5)))
| ~ '\'E\''('\'0\'',f(suc(X3)))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X4)))
| ~ '\'E\''('\'0\'',f(X3))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d46,d43]) ).
cnf(d48,plain,
( '\'LE\''(f(X5),'\'0\'')
| '\'LE\''(f(X4),'\'0\'')
| '\'LE\''(f(X3),'\'0\'')
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X5),suc(X0))
| ~ iLEQ(suc(X3),suc(X4))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X5)))
| ~ '\'E\''('\'0\'',f(suc(X4)))
| ~ '\'E\''('\'0\'',f(suc(X3)))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d47,d43]) ).
cnf(d49,plain,
( '\'LE\''(f(X5),'\'0\'')
| '\'LE\''(f(X4),'\'0\'')
| '\'LE\''(f(X3),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X5))
| ~ iLEQ(suc(X5),suc(X4))
| ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X2),suc(X1))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X5)))
| ~ '\'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)],[d48,d43]) ).
cnf(d50,plain,
( '\'LE\''(f(X5),'\'0\'')
| '\'LE\''(f(X4),'\'0\'')
| '\'LE\''(f(X3),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X5),suc(X0))
| ~ iLEQ(suc(X4),suc(X5))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X5)))
| ~ '\'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)],[d49,d43]) ).
cnf(d51,plain,
( '\'LE\''(f(X5),'\'0\'')
| '\'LE\''(f(X4),'\'0\'')
| '\'LE\''(f(X3),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X5),suc(X4))
| ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X5))
| ~ '\'E\''('\'0\'',f(suc(X5)))
| ~ '\'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)],[d50,d43]) ).
cnf(d52,plain,
( '\'LE\''(f(X5),'\'0\'')
| '\'LE\''(f(X4),'\'0\'')
| '\'LE\''(f(X3),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X5),'\'0\'')
| ~ iLEQ(suc(X4),suc(X5))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X5),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(suc(X0))) ),
inference(resolution,[status(thm)],[d51,d42]) ).
cnf(d53,plain,
( '\'LE\''(f(X5),'\'0\'')
| '\'LE\''(f(X3),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X5),'\'0\'')
| '\'LE\''(f(X4),'\'0\'')
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X0),suc(X5))
| ~ iLEQ(suc(X5),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)],[d52,d42]) ).
cnf(d54,plain,
( '\'LE\''(f(X5),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X5),'\'0\'')
| '\'LE\''(f(X4),'\'0\'')
| '\'LE\''(f(X3),'\'0\'')
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X5),suc(X0))
| ~ iLEQ(suc(X4),suc(X5))
| ~ iLEQ(suc(X3),suc(X4))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d53,d42]) ).
cnf(d55,plain,
( '\'LE\''(f(X5),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X5),'\'0\'')
| '\'LE\''(f(X4),'\'0\'')
| '\'LE\''(f(X3),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X5),suc(X4))
| ~ 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)],[d54,d42]) ).
cnf(d56,plain,
( '\'LE\''(f(X5),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X5),'\'0\'')
| '\'LE\''(f(X4),'\'0\'')
| '\'LE\''(f(X3),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| ~ iLEQ(suc(X5),suc(X0))
| ~ iLEQ(suc(X4),suc(X5))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d55,d42]) ).
cnf(d57,plain,
( '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X5),'\'0\'')
| '\'LE\''(f(X4),'\'0\'')
| '\'LE\''(f(X3),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X5),suc(X4))
| ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d56,d42]) ).
cnf(d58,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X3),'\'0\'')
| '\'LE\''(f(X4),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'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)],[d57,d45]) ).
cnf(d59,plain,
( '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X3),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d58,d45]) ).
cnf(d60,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[d59,d45]) ).
cnf(d61,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)],[d60,d45]) ).
cnf(d62,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d61,d45]) ).
cnf(d63,plain,
$false,
inference(resolution,[status(thm)],[d62,c7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO674-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n001.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 19:50:43 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 33.98/4.93 % SZS status Unsatisfiable for theBenchmark.p
% 33.98/4.93 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------