%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SYO664-1 : 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 : n017.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 09:47:03 AM UTC 2026
% Result : Unsatisfiable 12.74s 2.05s
% Output : CNFRefutation 12.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 10
% Syntax : Number of clauses : 54 ( 7 unt; 37 nHn; 41 RR)
% Number of literals : 367 ( 0 equ; 210 neg)
% Maximal clause size : 16 ( 6 avg)
% Maximal term depth : 3 ( 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 : 103 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_37,axiom,
( ~ '\'E\''(s('\'0\''),f(suc(X4)))
| ~ iLEQ(suc(X2),suc(X4))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s('\'0\''),f(X4))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ iLEQ(suc(X4),suc(X0))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ iLEQ(suc(X3),suc(X2))
| ~ '\'E\''(s('\'0\''),f(suc(X3)))
| ~ '\'E\''(s('\'0\''),f(X3))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X0))) ) ).
cnf(clause_70,axiom,
~ '\'LE\''(f(z),'\'0\'') ).
cnf(clause_20,axiom,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(X0))
| ~ '\'LE\''(f(X0),s(s('\'0\''))) ) ).
cnf(clause_66,axiom,
( ~ '\'E\''('\'0\'',f(X3))
| ~ '\'E\''('\'0\'',f(suc(X4)))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(suc(X3)))
| ~ iLEQ(suc(X0),suc(X4))
| ~ '\'E\''('\'0\'',f(X4))
| ~ iLEQ(suc(X3),suc(X0))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ iLEQ(suc(X1),suc(X3))
| ~ iLEQ(suc(X2),suc(X1))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(X0)) ) ).
cnf(clause_58,axiom,
'\'LE\''(f(X0),s(s('\'0\''))) ).
cnf(clause_6,axiom,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0)) ) ).
cnf(clause_117,axiom,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s('\'0\'')) ) ).
cnf(clause_94,axiom,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| ~ '\'LE\''(f(X0),s('\'0\'')) ) ).
cnf(clause_50,axiom,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X0)) ) ).
cnf(clause_83,axiom,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s(s('\'0\''))) ) ).
cnf(c0,plain,
( ~ iLEQ(suc(X4),suc(X3))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X3)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(X3))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X4))
| ~ iLEQ(suc(X1),suc(X4))
| ~ '\'E\''(s('\'0\''),f(suc(X4)))
| ~ iLEQ(suc(X3),suc(X0))
| ~ iLEQ(suc(X2),suc(X1))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_37]) ).
cnf(c1,plain,
~ '\'LE\''(f(z),'\'0\''),
inference(clausification,[status(esa)],[clause_70]) ).
cnf(c2,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(X0))
| ~ '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(clausification,[status(esa)],[clause_20]) ).
cnf(c3,plain,
( ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X4))
| ~ iLEQ(suc(X0),suc(X3))
| ~ '\'E\''('\'0\'',f(X3))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X4)))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(suc(X3)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ iLEQ(suc(X3),suc(X4))
| ~ '\'E\''('\'0\'',f(X0))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''('\'0\'',f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_66]) ).
cnf(c4,plain,
'\'LE\''(f(X0),s(s('\'0\''))),
inference(clausification,[status(esa)],[clause_58]) ).
cnf(c5,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(clausification,[status(esa)],[clause_6]) ).
cnf(c6,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s('\'0\'')) ),
inference(clausification,[status(esa)],[clause_117]) ).
cnf(c7,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| ~ '\'LE\''(f(X0),s('\'0\'')) ),
inference(clausification,[status(esa)],[clause_94]) ).
cnf(c8,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X0)) ),
inference(clausification,[status(esa)],[clause_50]) ).
cnf(c9,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s(s('\'0\''))) ),
inference(clausification,[status(esa)],[clause_83]) ).
cnf(d0,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[c4,c2]) ).
cnf(d1,plain,
( '\'E\''(s('\'0\''),f(X0))
| '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[c7,d0]) ).
cnf(d2,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[c4,c9]) ).
cnf(d3,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s('\'0\''),f(X0))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d2,c8]) ).
cnf(d4,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),s('\'0\''))
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),'\'0\'')
| iLEQ(suc(X0),suc(X0))
| '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d4,c7]) ).
cnf(d6,plain,
( ~ iLEQ(suc(X0),suc(X4))
| ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'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))
| ~ '\'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)],[d2,c0]) ).
cnf(d7,plain,
( '\'LE\''(f(X3),s('\'0\''))
| '\'LE\''(f(X4),s('\'0\''))
| ~ iLEQ(suc(X4),suc(X0))
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X2),suc(X4))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'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))
| ~ '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[d6,d2]) ).
cnf(d8,plain,
( '\'LE\''(f(X4),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X4))
| ~ '\'E\''(s('\'0\''),f(suc(X3)))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(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)],[d7,d2]) ).
cnf(d9,plain,
( '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X4),s('\'0\''))
| '\'LE\''(f(X3),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X4),suc(X0))
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X2),suc(X4))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(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)],[d8,d2]) ).
cnf(d10,plain,
( '\'LE\''(f(X3),s('\'0\''))
| '\'LE\''(f(X4),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X4))
| ~ '\'E\''(s('\'0\''),f(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)],[d9,d2]) ).
cnf(d11,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X3),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(X3))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[d10,d5]) ).
cnf(d12,plain,
( '\'LE\''(f(X2),'\'0\'')
| '\'E\''('\'0\'',f(X2))
| '\'LE\''(f(X2),'\'0\'')
| '\'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\''('\'0\'',f(X2))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[d11,d5]) ).
cnf(d13,plain,
( '\'LE\''(f(X1),'\'0\'')
| '\'E\''('\'0\'',f(X1))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X1),suc(X0))
| '\'E\''('\'0\'',f(X0))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[d12,d5]) ).
cnf(d14,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),s('\'0\''))
| '\'E\''('\'0\'',f(X0))
| '\'E\''('\'0\'',f(X0))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[d13,d5]) ).
cnf(d15,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),s('\'0\''))
| '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d14,d1]) ).
cnf(d16,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d15,c7]) ).
cnf(d17,plain,
'\'E\''('\'0\'',f(z)),
inference(resolution,[status(thm)],[d16,c1]) ).
cnf(d18,plain,
( '\'E\''(s('\'0\''),f(suc(X0)))
| '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[c6,d0]) ).
cnf(d19,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0)))
| '\'LE\''(f(suc(X0)),s('\'0\''))
| iLEQ(suc(suc(X0)),suc(suc(X0))) ),
inference(resolution,[status(thm)],[d3,d18]) ).
cnf(d20,plain,
( '\'LE\''(f(suc(X0)),s('\'0\''))
| '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0)))
| '\'LE\''(f(suc(X0)),s('\'0\''))
| '\'LE\''(f(X3),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(suc(X0)),s('\'0\''))
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X2),suc(suc(X0)))
| ~ iLEQ(suc(suc(X0)),suc(X1))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X3))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[d10,d19]) ).
cnf(d21,plain,
( '\'LE\''(f(suc(X2)),s('\'0\''))
| '\'LE\''(f(X2),'\'0\'')
| '\'E\''('\'0\'',f(suc(X2)))
| '\'LE\''(f(suc(X2)),s('\'0\''))
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(suc(X2)),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X1),suc(suc(X2)))
| ~ iLEQ(suc(X0),suc(X1))
| '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[d20,d19]) ).
cnf(d22,plain,
( '\'LE\''(f(suc(X0)),s('\'0\''))
| '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0)))
| '\'LE\''(f(suc(X0)),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(suc(X0)),s('\'0\''))
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X1),suc(suc(X0)))
| '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[d21,d19]) ).
cnf(d23,plain,
( '\'LE\''(f(suc(X0)),s('\'0\''))
| '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0)))
| '\'LE\''(f(suc(X0)),s('\'0\''))
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(suc(X0)),s('\'0\''))
| '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[d22,d19]) ).
cnf(d24,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0)))
| '\'LE\''(f(suc(X0)),s('\'0\''))
| '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d23,d18]) ).
cnf(d25,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0)))
| '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d24,c6]) ).
cnf(d26,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d25,c5]) ).
cnf(d27,plain,
( ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X3)))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(X3))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d26,c3]) ).
cnf(d28,plain,
( '\'LE\''(f(X2),'\'0\'')
| ~ '\'E\''('\'0\'',f(X2))
| '\'LE\''(f(X2),'\'0\'')
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d27,d26]) ).
cnf(d29,plain,
( '\'LE\''(f(X1),'\'0\'')
| ~ '\'E\''('\'0\'',f(X1))
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d28,d26]) ).
cnf(d30,plain,
( '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d29,d26]) ).
cnf(d31,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d30,d25]) ).
cnf(d32,plain,
'\'LE\''(f(z),'\'0\''),
inference(resolution,[status(thm)],[d31,d17]) ).
cnf(d33,plain,
$false,
inference(resolution,[status(thm)],[c1,d32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO664-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 19:39:35 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.74/2.05 % SZS status Unsatisfiable for theBenchmark.p
% 12.74/2.05 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------