%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SYO657-1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 09:46:52 AM UTC 2026
% Result : Unsatisfiable 17.52s 2.84s
% Output : CNFRefutation 17.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 16
% Syntax : Number of clauses : 82 ( 7 unt; 65 nHn; 65 RR)
% Number of literals : 454 ( 0 equ; 221 neg)
% Maximal clause size : 11 ( 5 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 : 99 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_10,axiom,
( '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(X1))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(suc(X0))) ) ).
cnf(clause_45,axiom,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'LE\''(f(suc(suc(X0))),s(s('\'0\''))) ) ).
cnf(clause_17,axiom,
'\'LE\''(f(X0),s(s('\'0\''))) ).
cnf(clause_23,axiom,
( iLEQ(suc(X0),suc(X0))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X0)) ) ).
cnf(clause_9,axiom,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(X0))
| ~ '\'LE\''(f(X0),s(s('\'0\''))) ) ).
cnf(clause_34,axiom,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| ~ '\'LE\''(f(X0),s('\'0\'')) ) ).
cnf(clause_41,axiom,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(suc(X0)))) ) ).
cnf(clause_26,axiom,
( iLEQ(suc(X0),suc(X0))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0)) ) ).
cnf(clause_43,axiom,
( ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X1))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''('\'0\'',f(suc(X0))) ) ).
cnf(clause_40,axiom,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s('\'0\'')) ) ).
cnf(clause_51,axiom,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'LE\''(f(suc(suc(X0))),s('\'0\'')) ) ).
cnf(clause_24,axiom,
~ '\'LE\''(f(z),'\'0\'') ).
cnf(clause_32,axiom,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s(s('\'0\''))) ) ).
cnf(clause_52,axiom,
( '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ iLEQ(suc(X0),suc(X1)) ) ).
cnf(clause_5,axiom,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0)))) ) ).
cnf(clause_33,axiom,
( ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X1))))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ iLEQ(suc(X0),suc(X1)) ) ).
cnf(c0,plain,
( ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(X1))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_10]) ).
cnf(c1,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'LE\''(f(suc(suc(X0))),s(s('\'0\''))) ),
inference(clausification,[status(esa)],[clause_45]) ).
cnf(c2,plain,
'\'LE\''(f(X0),s(s('\'0\''))),
inference(clausification,[status(esa)],[clause_17]) ).
cnf(c3,plain,
( iLEQ(suc(X0),suc(X0))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X0)) ),
inference(clausification,[status(esa)],[clause_23]) ).
cnf(c6,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(X0))
| ~ '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(clausification,[status(esa)],[clause_9]) ).
cnf(c7,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| ~ '\'LE\''(f(X0),s('\'0\'')) ),
inference(clausification,[status(esa)],[clause_34]) ).
cnf(c8,plain,
( ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(suc(X0)))) ),
inference(clausification,[status(esa)],[clause_41]) ).
cnf(c10,plain,
( iLEQ(suc(X0),suc(X0))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(clausification,[status(esa)],[clause_26]) ).
cnf(c11,plain,
( ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''('\'0\'',f(X1))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(clausification,[status(esa)],[clause_43]) ).
cnf(c12,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s('\'0\'')) ),
inference(clausification,[status(esa)],[clause_40]) ).
cnf(c13,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'LE\''(f(suc(suc(X0))),s('\'0\'')) ),
inference(clausification,[status(esa)],[clause_51]) ).
cnf(c14,plain,
~ '\'LE\''(f(z),'\'0\''),
inference(clausification,[status(esa)],[clause_24]) ).
cnf(c15,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s(s('\'0\''))) ),
inference(clausification,[status(esa)],[clause_32]) ).
cnf(c16,plain,
( '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(X1))
| '\'E\''(f(X1),f(suc(X1)))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(clausification,[status(esa)],[clause_52]) ).
cnf(c17,plain,
( ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_5]) ).
cnf(c19,plain,
( ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X1))))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_33]) ).
cnf(d0,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[c2,c6]) ).
cnf(d1,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[d0,c7]) ).
cnf(d2,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[c2,c15]) ).
cnf(d3,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s('\'0\''),f(X0))
| '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d2,c3]) ).
cnf(d4,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[c2,c1]) ).
cnf(d5,plain,
( '\'LE\''(f(X0),s('\'0\''))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[c17,d4]) ).
cnf(d6,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
( '\'LE\''(f(X0),s('\'0\''))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s('\'0\''),f(X0))
| '\'LE\''(f(X0),s('\'0\''))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[d6,d3]) ).
cnf(d8,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),s('\'0\''))
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[status(thm)],[d7,d1]) ).
cnf(d9,plain,
( '\'LE\''(f(X1),s('\'0\''))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[c16,d2]) ).
cnf(d10,plain,
( '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d9,d2]) ).
cnf(d11,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(X0))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
( '\'LE\''(f(X1),s('\'0\''))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[c19,d4]) ).
cnf(d13,plain,
( '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d12,d4]) ).
cnf(d14,plain,
( '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d13,d2]) ).
cnf(d15,plain,
( '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d14,d2]) ).
cnf(d16,plain,
( '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X1),'\'0\'')
| ~ '\'E\''(s('\'0\''),f(X1))
| '\'E\''('\'0\'',f(X1))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d15,d11]) ).
cnf(d17,plain,
( '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X1),'\'0\'')
| ~ '\'E\''(s('\'0\''),f(X1))
| '\'E\''('\'0\'',f(X1))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0))
| '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d16,d11]) ).
cnf(d18,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'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)],[d17,d8]) ).
cnf(d19,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)],[d18,d1]) ).
cnf(d20,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d19,c7]) ).
cnf(d21,plain,
'\'E\''('\'0\'',f(z)),
inference(resolution,[status(thm)],[d20,c14]) ).
cnf(d22,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0)))
| '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[d0,c12]) ).
cnf(d23,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)],[d7,d22]) ).
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(suc(X0)),s('\'0\''))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| '\'E\''(f(suc(X0)),f(suc(suc(X0))))
| '\'E\''(f(suc(X0)),f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d10,d23]) ).
cnf(d25,plain,
( '\'LE\''(f(suc(X1)),s('\'0\''))
| '\'LE\''(f(X1),'\'0\'')
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| '\'E\''('\'0\'',f(suc(X1)))
| '\'LE\''(f(suc(X1)),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X0),suc(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d15,d24]) ).
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(suc(X0)),s('\'0\''))
| '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(f(suc(X0)),f(suc(suc(X0))))
| '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d25,d23]) ).
cnf(d27,plain,
( '\'LE\''(f(suc(X0)),s('\'0\''))
| '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| '\'E\''('\'0\'',f(suc(X0)))
| '\'LE\''(f(suc(X0)),s('\'0\''))
| '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d26,d24]) ).
cnf(d28,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)],[d27,d22]) ).
cnf(d29,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0)))
| '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d28,c12]) ).
cnf(d30,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[c10,c8]) ).
cnf(d31,plain,
( '\'E\''(s('\'0\''),f(suc(suc(X0))))
| '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[c13,d0]) ).
cnf(d32,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(suc(X0))))
| '\'LE\''(f(suc(suc(X0))),s('\'0\''))
| iLEQ(suc(suc(suc(X0))),suc(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d7,d31]) ).
cnf(d33,plain,
( '\'LE\''(f(suc(suc(X0))),s('\'0\''))
| '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(suc(X0))))
| '\'LE\''(f(suc(suc(X0))),s('\'0\''))
| '\'LE\''(f(suc(suc(X0))),s('\'0\''))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| '\'E\''(f(suc(suc(X0))),f(suc(suc(suc(X0)))))
| '\'E\''(f(suc(suc(X0))),f(suc(suc(suc(X0))))) ),
inference(resolution,[status(thm)],[d10,d32]) ).
cnf(d34,plain,
( '\'LE\''(f(suc(suc(X1))),s('\'0\''))
| '\'LE\''(f(X1),'\'0\'')
| ~ '\'E\''(s('\'0\''),f(suc(suc(X1))))
| '\'E\''('\'0\'',f(suc(suc(X1))))
| '\'LE\''(f(suc(suc(X1))),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X0),suc(suc(suc(X1))))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X1))))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[d15,d33]) ).
cnf(d35,plain,
( '\'LE\''(f(suc(suc(X0))),s('\'0\''))
| '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(suc(X0))))
| '\'LE\''(f(suc(suc(X0))),s('\'0\''))
| '\'LE\''(f(suc(suc(X0))),s('\'0\''))
| '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'E\''(f(suc(suc(X0))),f(suc(suc(suc(X0)))))
| '\'E\''('\'0\'',f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d34,d32]) ).
cnf(d36,plain,
( '\'LE\''(f(suc(suc(X0))),s('\'0\''))
| '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| '\'E\''('\'0\'',f(suc(suc(X0))))
| '\'LE\''(f(suc(suc(X0))),s('\'0\''))
| '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| '\'E\''('\'0\'',f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d35,d33]) ).
cnf(d37,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(suc(X0))))
| '\'LE\''(f(suc(suc(X0))),s('\'0\''))
| '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d36,d31]) ).
cnf(d38,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(suc(X0))))
| '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[d37,c13]) ).
cnf(d39,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d38,d30]) ).
cnf(d40,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d39,d29]) ).
cnf(d41,plain,
( '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d40,c0]) ).
cnf(d42,plain,
( ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(X1))
| '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d41,c11]) ).
cnf(d43,plain,
( '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X1),'\'0\'')
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d42,d41]) ).
cnf(d44,plain,
( '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d43,d38]) ).
cnf(d45,plain,
( '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d44,d38]) ).
cnf(d46,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)],[d45,d40]) ).
cnf(d47,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d46,d29]) ).
cnf(d48,plain,
'\'LE\''(f(z),'\'0\''),
inference(resolution,[status(thm)],[d47,d21]) ).
cnf(d49,plain,
$false,
inference(resolution,[status(thm)],[c14,d48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO657-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 19:46:27 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.52/2.84 % SZS status Unsatisfiable for theBenchmark.p
% 17.52/2.84 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------