%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SYO656-1 : 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 09:46:51 AM UTC 2026
% Result : Unsatisfiable 148.11s 20.57s
% Output : CNFRefutation 148.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 9
% Syntax : Number of clauses : 50 ( 7 unt; 38 nHn; 45 RR)
% Number of literals : 682 ( 0 equ; 513 neg)
% Maximal clause size : 31 ( 13 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 : 145 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_1185,axiom,
( '\'E\''(f(X5),f(suc(X5)))
| '\'E\''(f(X4),f(suc(X4)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X2),f(suc(X2)))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X3),f(suc(X3)))
| ~ iLEQ(suc(X2),suc(X5))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(suc(X5)))
| ~ '\'E\''('\'0\'',f(X3))
| ~ '\'E\''('\'0\'',f(suc(X3)))
| ~ '\'E\''('\'0\'',f(X1))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X4),suc(X3))
| ~ '\'E\''('\'0\'',f(X5))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(X4))
| ~ '\'E\''('\'0\'',f(suc(X4)))
| ~ iLEQ(suc(X3),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X1)) ) ).
cnf(clause_181,axiom,
( iLEQ(suc(X0),suc(X0))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0)) ) ).
cnf(clause_613,axiom,
~ '\'LE\''(f(z),'\'0\'') ).
cnf(clause_73,axiom,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'LE\''(f(suc(suc(X0))),s('\'0\'')) ) ).
cnf(clause_1201,axiom,
( ~ iLEQ(suc(X3),suc(X0))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(suc(suc(X2))))
| ~ '\'E\''('\'0\'',f(X3))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X4))
| ~ '\'E\''('\'0\'',f(suc(X4)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''(f(X5),f(suc(X5)))
| ~ '\'E\''('\'0\'',f(suc(suc(X3))))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ iLEQ(suc(X2),suc(X3))
| ~ '\'E\''(f(X3),f(suc(X3)))
| ~ iLEQ(suc(X5),suc(X4))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(X5))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''('\'0\'',f(suc(suc(X5))))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X5)))
| ~ '\'E\''('\'0\'',f(suc(suc(X4))))
| ~ '\'E\''(f(X4),f(suc(X4)))
| ~ iLEQ(suc(X4),suc(X1))
| ~ '\'E\''('\'0\'',f(suc(X3)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''('\'0\'',f(suc(suc(X0)))) ) ).
cnf(clause_968,axiom,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s('\'0\'')) ) ).
cnf(clause_1005,axiom,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| ~ '\'LE\''(f(X0),s('\'0\'')) ) ).
cnf(clause_1153,axiom,
'\'LE\''(f(X0),s('\'0\'')) ).
cnf(clause_854,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(c5,plain,
( ~ iLEQ(suc(X4),suc(X3))
| '\'E\''(f(X4),f(suc(X4)))
| ~ '\'E\''('\'0\'',f(suc(X5)))
| ~ '\'E\''('\'0\'',f(suc(X4)))
| ~ '\'E\''('\'0\'',f(X4))
| ~ '\'E\''('\'0\'',f(X1))
| ~ iLEQ(suc(X3),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(X5))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X3))
| '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| '\'E\''(f(X3),f(suc(X3)))
| ~ iLEQ(suc(X0),suc(X5))
| '\'E\''(f(X5),f(suc(X5)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''('\'0\'',f(X2))
| ~ iLEQ(suc(X2),suc(X4))
| ~ '\'E\''('\'0\'',f(suc(X3)))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(clausification,[status(esa)],[clause_1185]) ).
cnf(c9,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_181]) ).
cnf(c12,plain,
~ '\'LE\''(f(z),'\'0\''),
inference(clausification,[status(esa)],[clause_613]) ).
cnf(c14,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'LE\''(f(suc(suc(X0))),s('\'0\'')) ),
inference(clausification,[status(esa)],[clause_73]) ).
cnf(c35,plain,
( ~ '\'E\''(f(X5),f(suc(X5)))
| ~ '\'E\''('\'0\'',f(suc(X3)))
| ~ iLEQ(suc(X4),suc(X2))
| ~ '\'E\''('\'0\'',f(suc(X5)))
| ~ '\'E\''('\'0\'',f(suc(suc(X2))))
| ~ '\'E\''('\'0\'',f(X3))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(suc(X4))))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(suc(X5))))
| ~ iLEQ(suc(X2),suc(X5))
| ~ '\'E\''(f(X3),f(suc(X3)))
| ~ '\'E\''('\'0\'',f(X5))
| ~ iLEQ(suc(X3),suc(X4))
| ~ '\'E\''('\'0\'',f(suc(suc(X3))))
| ~ '\'E\''('\'0\'',f(X4))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(suc(X4)))
| ~ '\'E\''(f(X4),f(suc(X4)))
| ~ iLEQ(suc(X1),suc(X3))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_1201]) ).
cnf(c45,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s('\'0\'')) ),
inference(clausification,[status(esa)],[clause_968]) ).
cnf(c62,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| ~ '\'LE\''(f(X0),s('\'0\'')) ),
inference(clausification,[status(esa)],[clause_1005]) ).
cnf(c64,plain,
'\'LE\''(f(X0),s('\'0\'')),
inference(clausification,[status(esa)],[clause_1153]) ).
cnf(c69,plain,
( ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_854]) ).
cnf(d0,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[c64,c62]) ).
cnf(d1,plain,
'\'E\''('\'0\'',f(z)),
inference(resolution,[status(thm)],[d0,c12]) ).
cnf(d2,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[c64,c45]) ).
cnf(d3,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[c64,c14]) ).
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)],[c69,c9]) ).
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,
( ~ iLEQ(suc(X0),suc(X3))
| ~ iLEQ(suc(X4),suc(X1))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X2))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'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(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)],[d6,c5]) ).
cnf(d8,plain,
( '\'LE\''(f(X1),'\'0\'')
| ~ '\'E\''('\'0\'',f(X1))
| '\'LE\''(f(X1),'\'0\'')
| ~ 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)],[d7,d6]) ).
cnf(d9,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)],[d8,d6]) ).
cnf(d10,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)],[d9,d6]) ).
cnf(d11,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)],[d10,d6]) ).
cnf(d12,plain,
( '\'LE\''(f(X5),'\'0\'')
| ~ '\'E\''('\'0\'',f(suc(X5)))
| ~ '\'E\''('\'0\'',f(X5))
| ~ iLEQ(suc(X5),suc(X3))
| ~ iLEQ(suc(X4),suc(X1))
| ~ iLEQ(suc(X2),suc(X4))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X5))
| ~ '\'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\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(suc(X5))))
| ~ '\'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(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))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[c35,d11]) ).
cnf(d13,plain,
( '\'LE\''(f(X5),'\'0\'')
| ~ '\'E\''('\'0\'',f(suc(X5)))
| ~ '\'E\''('\'0\'',f(X5))
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X5),suc(X0))
| ~ iLEQ(suc(X4),suc(X5))
| ~ iLEQ(suc(X3),suc(X1))
| ~ iLEQ(suc(X1),suc(X4))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'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(X5))))
| ~ '\'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(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))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d12,d11]) ).
cnf(d14,plain,
( '\'LE\''(f(X4),'\'0\'')
| ~ '\'E\''('\'0\'',f(suc(X4)))
| ~ '\'E\''('\'0\'',f(X4))
| '\'LE\''(f(X5),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X5),suc(X3))
| ~ iLEQ(suc(X4),suc(X1))
| ~ iLEQ(suc(X2),suc(X4))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X5))
| ~ '\'E\''(f(X3),f(suc(X3)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(suc(X5))))
| ~ '\'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(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))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d13,d11]) ).
cnf(d15,plain,
( '\'LE\''(f(X4),'\'0\'')
| ~ '\'E\''('\'0\'',f(suc(X4)))
| ~ '\'E\''('\'0\'',f(X4))
| '\'LE\''(f(X5),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X5),suc(X0))
| ~ iLEQ(suc(X4),suc(X5))
| ~ iLEQ(suc(X3),suc(X1))
| ~ iLEQ(suc(X1),suc(X4))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'E\''(f(X3),f(suc(X3)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(suc(X5))))
| ~ '\'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(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))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d14,d11]) ).
cnf(d16,plain,
( '\'LE\''(f(X3),'\'0\'')
| ~ '\'E\''('\'0\'',f(suc(X3)))
| ~ '\'E\''('\'0\'',f(X3))
| '\'LE\''(f(X5),'\'0\'')
| '\'LE\''(f(X4),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X5),suc(X3))
| ~ iLEQ(suc(X4),suc(X1))
| ~ iLEQ(suc(X2),suc(X4))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X5))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(suc(X5))))
| ~ '\'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(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))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d15,d11]) ).
cnf(d17,plain,
( '\'LE\''(f(X3),'\'0\'')
| ~ '\'E\''('\'0\'',f(suc(X3)))
| ~ '\'E\''('\'0\'',f(X3))
| '\'LE\''(f(X5),'\'0\'')
| '\'LE\''(f(X4),'\'0\'')
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X5),suc(X0))
| ~ iLEQ(suc(X4),suc(X5))
| ~ iLEQ(suc(X3),suc(X1))
| ~ iLEQ(suc(X1),suc(X4))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'E\''('\'0\'',f(suc(suc(X5))))
| ~ '\'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(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))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d16,d11]) ).
cnf(d18,plain,
( '\'LE\''(f(X5),'\'0\'')
| '\'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(X3))
| ~ iLEQ(suc(X4),suc(X1))
| ~ iLEQ(suc(X2),suc(X4))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X5))
| ~ '\'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(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))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d17,d3]) ).
cnf(d19,plain,
( '\'LE\''(f(X5),'\'0\'')
| '\'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(X0))
| ~ iLEQ(suc(X4),suc(X5))
| ~ iLEQ(suc(X3),suc(X1))
| ~ iLEQ(suc(X1),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(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))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d18,d3]) ).
cnf(d20,plain,
( '\'LE\''(f(X4),'\'0\'')
| '\'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(X3))
| ~ iLEQ(suc(X4),suc(X1))
| ~ iLEQ(suc(X2),suc(X4))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X5))
| ~ '\'E\''('\'0\'',f(suc(suc(X3))))
| ~ '\'E\''('\'0\'',f(suc(suc(X2))))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'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))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d19,d3]) ).
cnf(d21,plain,
( '\'LE\''(f(X4),'\'0\'')
| '\'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(X0))
| ~ iLEQ(suc(X4),suc(X5))
| ~ iLEQ(suc(X3),suc(X1))
| ~ iLEQ(suc(X1),suc(X4))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'E\''('\'0\'',f(suc(suc(X3))))
| ~ '\'E\''('\'0\'',f(suc(suc(X2))))
| ~ '\'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))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d20,d3]) ).
cnf(d22,plain,
( '\'LE\''(f(X3),'\'0\'')
| '\'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(X3))
| ~ iLEQ(suc(X4),suc(X1))
| ~ iLEQ(suc(X2),suc(X4))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X5))
| ~ '\'E\''('\'0\'',f(suc(suc(X2))))
| ~ '\'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))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d21,d3]) ).
cnf(d23,plain,
( '\'LE\''(f(X3),'\'0\'')
| '\'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(X0))
| ~ iLEQ(suc(X4),suc(X5))
| ~ iLEQ(suc(X3),suc(X1))
| ~ iLEQ(suc(X1),suc(X4))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'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))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d22,d3]) ).
cnf(d24,plain,
( '\'LE\''(f(X3),'\'0\'')
| ~ '\'E\''('\'0\'',f(X3))
| '\'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(X1))
| ~ iLEQ(suc(X2),suc(X4))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X3))
| ~ '\'E\''('\'0\'',f(suc(X3)))
| ~ '\'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(X3))
| ~ '\'E\''('\'0\'',f(X4))
| ~ '\'E\''('\'0\'',f(X3))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d23,d6]) ).
cnf(d25,plain,
( '\'LE\''(f(X1),'\'0\'')
| ~ '\'E\''('\'0\'',f(X1))
| '\'LE\''(f(X1),'\'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(X0))
| ~ iLEQ(suc(X0),suc(X3))
| ~ '\'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)],[d24,d6]) ).
cnf(d26,plain,
( '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),'\'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(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)],[d25,d6]) ).
cnf(d27,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)],[d26,d6]) ).
cnf(d28,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)],[d27,d6]) ).
cnf(d29,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d28,d2]) ).
cnf(d30,plain,
'\'LE\''(f(z),'\'0\''),
inference(resolution,[status(thm)],[d29,d1]) ).
cnf(d31,plain,
$false,
inference(resolution,[status(thm)],[c12,d30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO656-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 19:45:55 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 148.11/20.57 % SZS status Unsatisfiable for theBenchmark.p
% 148.11/20.57 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------