%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SYO666-1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:47:13 AM UTC 2026
% Result : Unsatisfiable 13.67s 2.17s
% Output : CNFRefutation 13.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 10
% Syntax : Number of clauses : 58 ( 7 unt; 41 nHn; 45 RR)
% Number of literals : 476 ( 0 equ; 285 neg)
% Maximal clause size : 19 ( 8 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 : 133 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_102,axiom,
( ~ '\'E\''('\'0\'',f(X5))
| ~ '\'E\''('\'0\'',f(X3))
| ~ '\'E\''('\'0\'',f(suc(X5)))
| ~ iLEQ(suc(X2),suc(X4))
| ~ '\'E\''('\'0\'',f(X4))
| ~ '\'E\''('\'0\'',f(suc(X3)))
| ~ iLEQ(suc(X4),suc(X5))
| ~ '\'E\''('\'0\'',f(X0))
| ~ iLEQ(suc(X5),suc(X0))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(suc(X4)))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X3))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ iLEQ(suc(X0),suc(X1)) ) ).
cnf(clause_12,axiom,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0)) ) ).
cnf(clause_98,axiom,
~ '\'LE\''(f(z),'\'0\'') ).
cnf(clause_123,axiom,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s('\'0\'')) ) ).
cnf(clause_42,axiom,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| ~ '\'LE\''(f(X0),s('\'0\'')) ) ).
cnf(clause_83,axiom,
'\'LE\''(f(X0),s(s('\'0\''))) ).
cnf(clause_70,axiom,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X0)) ) ).
cnf(clause_29,axiom,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s(s('\'0\''))) ) ).
cnf(clause_185,axiom,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(X0))
| ~ '\'LE\''(f(X0),s(s('\'0\''))) ) ).
cnf(clause_179,axiom,
( ~ '\'E\''(s('\'0\''),f(suc(X5)))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X4))
| ~ iLEQ(suc(X3),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(X5))
| ~ '\'E\''(s('\'0\''),f(suc(X4)))
| ~ iLEQ(suc(X2),suc(X5))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X4))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ iLEQ(suc(X4),suc(X1))
| ~ '\'E\''(s('\'0\''),f(suc(X3)))
| ~ '\'E\''(s('\'0\''),f(X3))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(s('\'0\''),f(X0)) ) ).
cnf(c0,plain,
( ~ '\'E\''('\'0\'',f(suc(X4)))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(suc(X5)))
| ~ iLEQ(suc(X3),suc(X0))
| ~ iLEQ(suc(X2),suc(X5))
| ~ iLEQ(suc(X1),suc(X4))
| ~ iLEQ(suc(X5),suc(X3))
| ~ '\'E\''('\'0\'',f(X5))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X4))
| ~ '\'E\''('\'0\'',f(X3))
| ~ '\'E\''('\'0\'',f(suc(X3)))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_102]) ).
cnf(c1,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(clausification,[status(esa)],[clause_12]) ).
cnf(c2,plain,
~ '\'LE\''(f(z),'\'0\''),
inference(clausification,[status(esa)],[clause_98]) ).
cnf(c3,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s('\'0\'')) ),
inference(clausification,[status(esa)],[clause_123]) ).
cnf(c4,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| ~ '\'LE\''(f(X0),s('\'0\'')) ),
inference(clausification,[status(esa)],[clause_42]) ).
cnf(c5,plain,
'\'LE\''(f(X0),s(s('\'0\''))),
inference(clausification,[status(esa)],[clause_83]) ).
cnf(c6,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X0)) ),
inference(clausification,[status(esa)],[clause_70]) ).
cnf(c7,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s(s('\'0\''))) ),
inference(clausification,[status(esa)],[clause_29]) ).
cnf(c8,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(X0))
| ~ '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(clausification,[status(esa)],[clause_185]) ).
cnf(c9,plain,
( ~ iLEQ(suc(X5),suc(X3))
| ~ iLEQ(suc(X4),suc(X2))
| ~ '\'E\''(s('\'0\''),f(X3))
| ~ iLEQ(suc(X1),suc(X5))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X5)))
| ~ '\'E\''(s('\'0\''),f(X4))
| ~ '\'E\''(s('\'0\''),f(X5))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ iLEQ(suc(X2),suc(X1))
| ~ '\'E\''(s('\'0\''),f(suc(X3)))
| ~ '\'E\''(s('\'0\''),f(suc(X4)))
| ~ iLEQ(suc(X3),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0)) ),
inference(clausification,[status(esa)],[clause_179]) ).
cnf(d0,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[c5,c8]) ).
cnf(d1,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[d0,c4]) ).
cnf(d2,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[c5,c7]) ).
cnf(d3,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s('\'0\''),f(X0))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d2,c6]) ).
cnf(d4,plain,
( '\'LE\''(f(X0),s('\'0\''))
| iLEQ(suc(X0),suc(X0))
| '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d1,d3]) ).
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,c4]) ).
cnf(d6,plain,
( '\'LE\''(f(X5),s('\'0\''))
| ~ iLEQ(suc(X5),suc(X2))
| ~ iLEQ(suc(X4),suc(X1))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X1),suc(X5))
| ~ iLEQ(suc(X0),suc(X3))
| ~ '\'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))
| ~ '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[c9,d2]) ).
cnf(d7,plain,
( '\'LE\''(f(X5),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X5),suc(X2))
| ~ iLEQ(suc(X4),suc(X0))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X4))
| ~ iLEQ(suc(X0),suc(X3))
| ~ '\'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(X5))
| ~ '\'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(X5),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X5),suc(X2))
| ~ iLEQ(suc(X4),suc(X1))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X1),suc(X5))
| ~ iLEQ(suc(X0),suc(X3))
| ~ '\'E\''(s('\'0\''),f(suc(X3)))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'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))
| ~ '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[d7,d2]) ).
cnf(d9,plain,
( '\'LE\''(f(X4),s('\'0\''))
| '\'LE\''(f(X5),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X5),suc(X2))
| ~ iLEQ(suc(X4),suc(X0))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X4))
| ~ iLEQ(suc(X0),suc(X3))
| ~ '\'E\''(s('\'0\''),f(suc(X3)))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'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))
| ~ '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[d8,d2]) ).
cnf(d10,plain,
( '\'LE\''(f(X3),s('\'0\''))
| '\'LE\''(f(X5),s('\'0\''))
| '\'LE\''(f(X4),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X5),suc(X2))
| ~ iLEQ(suc(X4),suc(X1))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X1),suc(X5))
| ~ iLEQ(suc(X0),suc(X3))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'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))
| ~ '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[d9,d2]) ).
cnf(d11,plain,
( '\'LE\''(f(X3),s('\'0\''))
| '\'LE\''(f(X5),s('\'0\''))
| '\'LE\''(f(X4),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X5),suc(X2))
| ~ iLEQ(suc(X4),suc(X0))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X4))
| ~ iLEQ(suc(X0),suc(X3))
| ~ '\'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))
| ~ '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[d10,d2]) ).
cnf(d12,plain,
( '\'LE\''(f(X2),'\'0\'')
| '\'E\''('\'0\'',f(X2))
| '\'LE\''(f(X2),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(X1))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X3))
| ~ '\'E\''(s('\'0\''),f(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)],[d11,d5]) ).
cnf(d13,plain,
( '\'LE\''(f(X2),'\'0\'')
| '\'E\''('\'0\'',f(X2))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X3),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| ~ iLEQ(suc(X3),suc(X0))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X3))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X3))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d12,d5]) ).
cnf(d14,plain,
( '\'LE\''(f(X2),'\'0\'')
| '\'E\''('\'0\'',f(X2))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X2),s('\'0\''))
| ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X2),suc(X1))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(X2))
| '\'E\''('\'0\'',f(X1))
| '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d13,d5]) ).
cnf(d15,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0))
| '\'E\''('\'0\'',f(X0))
| '\'E\''('\'0\'',f(X1))
| '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d14,d5]) ).
cnf(d16,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(X0))
| '\'E\''('\'0\'',f(X0))
| '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d15,d5]) ).
cnf(d17,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d16,d1]) ).
cnf(d18,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d17,c4]) ).
cnf(d19,plain,
'\'E\''('\'0\'',f(z)),
inference(resolution,[status(thm)],[d18,c2]) ).
cnf(d20,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0)))
| '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[d0,c3]) ).
cnf(d21,plain,
( '\'LE\''(f(suc(X0)),s('\'0\''))
| iLEQ(suc(suc(X0)),suc(suc(X0)))
| '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d20,d3]) ).
cnf(d22,plain,
( '\'LE\''(f(suc(X2)),s('\'0\''))
| '\'LE\''(f(X2),'\'0\'')
| '\'E\''('\'0\'',f(suc(X2)))
| '\'LE\''(f(suc(X2)),s('\'0\''))
| '\'LE\''(f(X4),s('\'0\''))
| '\'LE\''(f(X3),s('\'0\''))
| '\'LE\''(f(suc(X2)),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X4),suc(X1))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X1),suc(suc(X2)))
| ~ iLEQ(suc(X0),suc(X3))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(X4))
| ~ '\'E\''(s('\'0\''),f(X3))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[d11,d21]) ).
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(X3),s('\'0\''))
| '\'LE\''(f(suc(X0)),s('\'0\''))
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X3))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d22,d21]) ).
cnf(d24,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\''))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| ~ iLEQ(suc(X2),suc(suc(X0)))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d23,d21]) ).
cnf(d25,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(X1),s('\'0\''))
| '\'LE\''(f(suc(X0)),s('\'0\''))
| ~ iLEQ(suc(X1),suc(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d24,d21]) ).
cnf(d26,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\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d25,d21]) ).
cnf(d27,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)],[d26,d20]) ).
cnf(d28,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0)))
| '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d27,c3]) ).
cnf(d29,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d28,c1]) ).
cnf(d30,plain,
( ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X4),suc(X0))
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X1),suc(X3))
| ~ '\'E\''('\'0\'',f(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))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(X4))
| ~ '\'E\''('\'0\'',f(X3))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d29,c0]) ).
cnf(d31,plain,
( '\'LE\''(f(X3),'\'0\'')
| ~ '\'E\''('\'0\'',f(X3))
| '\'LE\''(f(X3),'\'0\'')
| ~ iLEQ(suc(X3),suc(X1))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X3))
| ~ '\'E\''('\'0\'',f(suc(X3)))
| ~ '\'E\''('\'0\'',f(suc(X3)))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X3))
| ~ '\'E\''('\'0\'',f(X3))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d30,d29]) ).
cnf(d32,plain,
( '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d31,d29]) ).
cnf(d33,plain,
( '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d32,d29]) ).
cnf(d34,plain,
( '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d33,d29]) ).
cnf(d35,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d34,d28]) ).
cnf(d36,plain,
'\'LE\''(f(z),'\'0\''),
inference(resolution,[status(thm)],[d35,d19]) ).
cnf(d37,plain,
$false,
inference(resolution,[status(thm)],[c2,d36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO666-1 : 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 : n006.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 19:43:55 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.67/2.17 % SZS status Unsatisfiable for theBenchmark.p
% 13.67/2.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------