%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SYO655-1 : 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 : n010.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 09:46:51 AM UTC 2026
% Result : Unsatisfiable 26.32s 4.86s
% Output : CNFRefutation 26.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 9
% Syntax : Number of clauses : 46 ( 7 unt; 34 nHn; 41 RR)
% Number of literals : 510 ( 0 equ; 376 neg)
% Maximal clause size : 26 ( 11 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 : 109 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_5,axiom,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s('\'0\'')) ) ).
cnf(clause_269,axiom,
~ '\'LE\''(f(z),'\'0\'') ).
cnf(clause_125,axiom,
( ~ iLEQ(suc(X2),suc(X3))
| ~ '\'E\''(f(X3),f(suc(X3)))
| ~ '\'E\''('\'0\'',f(suc(X4)))
| ~ '\'E\''('\'0\'',f(X4))
| ~ '\'E\''(f(X4),f(suc(X4)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X3))
| ~ '\'E\''('\'0\'',f(X0))
| ~ iLEQ(suc(X1),suc(X4))
| ~ '\'E\''('\'0\'',f(suc(suc(X3))))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(suc(suc(X4))))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''('\'0\'',f(X1))
| ~ iLEQ(suc(X3),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X3)))
| ~ '\'E\''('\'0\'',f(suc(suc(X2))))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(suc(X0)))) ) ).
cnf(clause_209,axiom,
( '\'E\''(f(X3),f(suc(X3)))
| '\'E\''(f(X4),f(suc(X4)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X2),f(suc(X2)))
| '\'E\''(f(X1),f(suc(X1)))
| ~ iLEQ(suc(X2),suc(X3))
| ~ '\'E\''('\'0\'',f(suc(X4)))
| ~ '\'E\''('\'0\'',f(X4))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(X3))
| ~ '\'E\''('\'0\'',f(X1))
| ~ iLEQ(suc(X0),suc(X4))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X0))
| ~ iLEQ(suc(X3),suc(X1))
| ~ '\'E\''('\'0\'',f(suc(X3)))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X0))) ) ).
cnf(clause_379,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_84,axiom,
( iLEQ(suc(X0),suc(X0))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0)) ) ).
cnf(clause_72,axiom,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'LE\''(f(suc(suc(X0))),s('\'0\'')) ) ).
cnf(clause_497,axiom,
'\'LE\''(f(X0),s('\'0\'')) ).
cnf(clause_513,axiom,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| ~ '\'LE\''(f(X0),s('\'0\'')) ) ).
cnf(c8,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s('\'0\'')) ),
inference(clausification,[status(esa)],[clause_5]) ).
cnf(c10,plain,
~ '\'LE\''(f(z),'\'0\''),
inference(clausification,[status(esa)],[clause_269]) ).
cnf(c14,plain,
( ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X4))
| ~ '\'E\''(f(X4),f(suc(X4)))
| ~ '\'E\''(f(X3),f(suc(X3)))
| ~ '\'E\''('\'0\'',f(suc(suc(X3))))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ iLEQ(suc(X3),suc(X2))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(suc(X4)))
| ~ iLEQ(suc(X0),suc(X4))
| ~ iLEQ(suc(X2),suc(X1))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''('\'0\'',f(X1))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X3)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''('\'0\'',f(suc(suc(X4))))
| ~ '\'E\''('\'0\'',f(X3))
| ~ '\'E\''('\'0\'',f(suc(suc(X2))))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(clausification,[status(esa)],[clause_125]) ).
cnf(c15,plain,
( ~ '\'E\''('\'0\'',f(X2))
| ~ iLEQ(suc(X1),suc(X3))
| '\'E\''(f(X2),f(suc(X2)))
| ~ iLEQ(suc(X2),suc(X4))
| ~ '\'E\''('\'0\'',f(X3))
| ~ '\'E\''('\'0\'',f(X4))
| '\'E\''(f(X3),f(suc(X3)))
| ~ iLEQ(suc(X4),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(X0))
| '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X4)))
| '\'E\''(f(X4),f(suc(X4)))
| ~ '\'E\''('\'0\'',f(suc(X3)))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_209]) ).
cnf(c21,plain,
( ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_379]) ).
cnf(c22,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_84]) ).
cnf(c33,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'LE\''(f(suc(suc(X0))),s('\'0\'')) ),
inference(clausification,[status(esa)],[clause_72]) ).
cnf(c34,plain,
'\'LE\''(f(X0),s('\'0\'')),
inference(clausification,[status(esa)],[clause_497]) ).
cnf(c36,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| ~ '\'LE\''(f(X0),s('\'0\'')) ),
inference(clausification,[status(esa)],[clause_513]) ).
cnf(d0,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[c34,c36]) ).
cnf(d1,plain,
'\'E\''('\'0\'',f(z)),
inference(resolution,[status(thm)],[d0,c10]) ).
cnf(d2,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[c34,c8]) ).
cnf(d3,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[c34,c33]) ).
cnf(d4,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[c21,c22]) ).
cnf(d5,plain,
( '\'LE\''(f(X0),'\'0\'')
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
( '\'LE\''(f(X1),'\'0\'')
| ~ '\'E\''('\'0\'',f(X1))
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X0),suc(X3))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X3),f(suc(X3)))
| '\'E\''(f(X2),f(suc(X2)))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X3)))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X3))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[c15,d6]) ).
cnf(d8,plain,
( '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X2),'\'0\'')
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X2),f(suc(X2)))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'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)],[d7,d6]) ).
cnf(d9,plain,
( '\'LE\''(f(X1),'\'0\'')
| ~ '\'E\''('\'0\'',f(X1))
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X1),suc(X0))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(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)],[d8,d6]) ).
cnf(d10,plain,
( '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'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)) ),
inference(resolution,[status(thm)],[d9,d6]) ).
cnf(d11,plain,
( ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X3),suc(X1))
| ~ iLEQ(suc(X2),suc(X4))
| ~ '\'E\''(f(X4),f(suc(X4)))
| ~ '\'E\''(f(X3),f(suc(X3)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''('\'0\'',f(suc(suc(X4))))
| ~ '\'E\''('\'0\'',f(suc(suc(X3))))
| ~ '\'E\''('\'0\'',f(suc(suc(X2))))
| ~ '\'E\''('\'0\'',f(suc(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(suc(X1)))
| ~ '\'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(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d10,c14]) ).
cnf(d12,plain,
( '\'LE\''(f(X3),'\'0\'')
| ~ '\'E\''('\'0\'',f(suc(X3)))
| ~ '\'E\''('\'0\'',f(X3))
| '\'LE\''(f(X4),'\'0\'')
| ~ iLEQ(suc(X4),suc(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X3))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(suc(X4))))
| ~ '\'E\''('\'0\'',f(suc(suc(X3))))
| ~ '\'E\''('\'0\'',f(suc(suc(X2))))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''('\'0\'',f(suc(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)))
| ~ '\'E\''('\'0\'',f(X4))
| ~ '\'E\''('\'0\'',f(X3))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
( '\'LE\''(f(X4),'\'0\'')
| ~ '\'E\''('\'0\'',f(suc(X4)))
| ~ '\'E\''('\'0\'',f(X4))
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X3),suc(X1))
| ~ iLEQ(suc(X2),suc(X4))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'E\''(f(X3),f(suc(X3)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(suc(X4))))
| ~ '\'E\''('\'0\'',f(suc(suc(X3))))
| ~ '\'E\''('\'0\'',f(suc(suc(X2))))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''('\'0\'',f(suc(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)))
| ~ '\'E\''('\'0\'',f(X4))
| ~ '\'E\''('\'0\'',f(X3))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d12,d10]) ).
cnf(d14,plain,
( '\'LE\''(f(X2),'\'0\'')
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(X2))
| '\'LE\''(f(X4),'\'0\'')
| '\'LE\''(f(X3),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X4),suc(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X3))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(suc(X4))))
| ~ '\'E\''('\'0\'',f(suc(suc(X3))))
| ~ '\'E\''('\'0\'',f(suc(suc(X2))))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''('\'0\'',f(suc(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)))
| ~ '\'E\''('\'0\'',f(X4))
| ~ '\'E\''('\'0\'',f(X3))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d13,d10]) ).
cnf(d15,plain,
( '\'LE\''(f(X3),'\'0\'')
| ~ '\'E\''('\'0\'',f(suc(X3)))
| ~ '\'E\''('\'0\'',f(X3))
| '\'LE\''(f(X4),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X3),suc(X1))
| ~ iLEQ(suc(X2),suc(X4))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'E\''('\'0\'',f(suc(suc(X4))))
| ~ '\'E\''('\'0\'',f(suc(suc(X3))))
| ~ '\'E\''('\'0\'',f(suc(suc(X2))))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''('\'0\'',f(suc(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)))
| ~ '\'E\''('\'0\'',f(X4))
| ~ '\'E\''('\'0\'',f(X3))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d14,d10]) ).
cnf(d16,plain,
( '\'LE\''(f(X4),'\'0\'')
| '\'LE\''(f(X4),'\'0\'')
| '\'LE\''(f(X3),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X4),suc(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X3))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''('\'0\'',f(suc(suc(X3))))
| ~ '\'E\''('\'0\'',f(suc(suc(X2))))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''('\'0\'',f(suc(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)))
| ~ '\'E\''('\'0\'',f(X4))
| ~ '\'E\''('\'0\'',f(X3))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d15,d3]) ).
cnf(d17,plain,
( '\'LE\''(f(X4),'\'0\'')
| '\'LE\''(f(X4),'\'0\'')
| '\'LE\''(f(X3),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X3),suc(X1))
| ~ iLEQ(suc(X2),suc(X4))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'E\''('\'0\'',f(suc(suc(X3))))
| ~ '\'E\''('\'0\'',f(suc(suc(X2))))
| ~ '\'E\''('\'0\'',f(suc(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)))
| ~ '\'E\''('\'0\'',f(X4))
| ~ '\'E\''('\'0\'',f(X3))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d16,d3]) ).
cnf(d18,plain,
( '\'LE\''(f(X3),'\'0\'')
| '\'LE\''(f(X4),'\'0\'')
| '\'LE\''(f(X3),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X4),suc(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X3))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''('\'0\'',f(suc(suc(X2))))
| ~ '\'E\''('\'0\'',f(suc(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)))
| ~ '\'E\''('\'0\'',f(X4))
| ~ '\'E\''('\'0\'',f(X3))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d17,d3]) ).
cnf(d19,plain,
( '\'LE\''(f(X3),'\'0\'')
| '\'LE\''(f(X4),'\'0\'')
| '\'LE\''(f(X3),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X3),suc(X1))
| ~ iLEQ(suc(X2),suc(X4))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'E\''('\'0\'',f(suc(suc(X2))))
| ~ '\'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))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d18,d3]) ).
cnf(d20,plain,
( '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X4),'\'0\'')
| '\'LE\''(f(X3),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X4),suc(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X3))
| ~ 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)))
| ~ '\'E\''('\'0\'',f(X4))
| ~ '\'E\''('\'0\'',f(X3))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d19,d3]) ).
cnf(d21,plain,
( '\'LE\''(f(X3),'\'0\'')
| ~ '\'E\''('\'0\'',f(X3))
| '\'LE\''(f(X3),'\'0\'')
| '\'LE\''(f(X3),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X3),suc(X1))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'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)],[d20,d6]) ).
cnf(d22,plain,
( '\'LE\''(f(X1),'\'0\'')
| ~ '\'E\''('\'0\'',f(X1))
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d21,d6]) ).
cnf(d23,plain,
( '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'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)],[d22,d6]) ).
cnf(d24,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)],[d23,d6]) ).
cnf(d25,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d24,d2]) ).
cnf(d26,plain,
'\'LE\''(f(z),'\'0\''),
inference(resolution,[status(thm)],[d25,d1]) ).
cnf(d27,plain,
$false,
inference(resolution,[status(thm)],[c10,d26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO655-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n010.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 19:43:45 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.32/4.86 % SZS status Unsatisfiable for theBenchmark.p
% 26.32/4.86 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------