%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SYO661-1 : 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 : n007.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 30.50s 8.21s
% Output : CNFRefutation 30.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 16
% Syntax : Number of clauses : 76 ( 5 unt; 61 nHn; 65 RR)
% Number of literals : 541 ( 0 equ; 352 neg)
% Maximal clause size : 16 ( 7 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 : 129 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_93,axiom,
~ '\'LE\''(f(z),'\'0\'') ).
cnf(clause_51,axiom,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'LE\''(f(suc(suc(X0))),s('\'0\'')) ) ).
cnf(clause_106,axiom,
( '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X2),f(suc(X2)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(suc(X0))) ) ).
cnf(clause_8,axiom,
( ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X1))))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X2))))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(suc(X0))) ) ).
cnf(clause_72,axiom,
'\'LE\''(f(X0),s(s('\'0\''))) ).
cnf(clause_119,axiom,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s(s('\'0\''))) ) ).
cnf(clause_57,axiom,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s('\'0\'')) ) ).
cnf(clause_0,axiom,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| ~ '\'LE\''(f(X0),s('\'0\'')) ) ).
cnf(clause_85,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_109,axiom,
( iLEQ(suc(X0),suc(X0))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0)) ) ).
cnf(clause_204,axiom,
( ~ '\'E\''(f(X1),f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(suc(X2))))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(suc(X0)))) ) ).
cnf(clause_20,axiom,
( '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X2),f(suc(X2)))
| '\'E\''(f(X0),f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X0))
| ~ iLEQ(suc(X2),suc(X1))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0))) ) ).
cnf(clause_148,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_33,axiom,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'LE\''(f(suc(suc(X0))),s(s('\'0\''))) ) ).
cnf(clause_118,axiom,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(X0))
| ~ '\'LE\''(f(X0),s(s('\'0\''))) ) ).
cnf(clause_25,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(c0,plain,
~ '\'LE\''(f(z),'\'0\''),
inference(clausification,[status(esa)],[clause_93]) ).
cnf(c2,plain,
( '\'LE\''(f(X0),'\'0\'')
| ~ '\'LE\''(f(suc(suc(X0))),s('\'0\''))
| '\'E\''('\'0\'',f(suc(suc(X0)))) ),
inference(clausification,[status(esa)],[clause_51]) ).
cnf(c3,plain,
( ~ '\'E\''(s('\'0\''),f(X2))
| '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ iLEQ(suc(X2),suc(X1))
| ~ '\'E\''(s('\'0\''),f(X1))
| '\'E\''(f(X2),f(suc(X2)))
| '\'E\''(f(X1),f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_106]) ).
cnf(c4,plain,
( ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X1))))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X2))))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X0)) ),
inference(clausification,[status(esa)],[clause_8]) ).
cnf(c5,plain,
'\'LE\''(f(X0),s(s('\'0\''))),
inference(clausification,[status(esa)],[clause_72]) ).
cnf(c6,plain,
( '\'LE\''(f(X0),s('\'0\''))
| ~ '\'LE\''(f(suc(X0)),s(s('\'0\'')))
| '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_119]) ).
cnf(c7,plain,
( '\'LE\''(f(X0),'\'0\'')
| ~ '\'LE\''(f(suc(X0)),s('\'0\''))
| '\'E\''('\'0\'',f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_57]) ).
cnf(c8,plain,
( '\'LE\''(f(X0),'\'0\'')
| ~ '\'LE\''(f(X0),s('\'0\''))
| '\'E\''('\'0\'',f(X0)) ),
inference(clausification,[status(esa)],[clause_0]) ).
cnf(c9,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X0))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_85]) ).
cnf(c14,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_109]) ).
cnf(c17,plain,
( ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(suc(X2))))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X1))
| ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(clausification,[status(esa)],[clause_204]) ).
cnf(c19,plain,
( ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| ~ iLEQ(suc(X2),suc(X0))
| '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(X2))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(clausification,[status(esa)],[clause_20]) ).
cnf(c21,plain,
( ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(suc(X0))))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(clausification,[status(esa)],[clause_148]) ).
cnf(c22,plain,
( '\'LE\''(f(X0),s('\'0\''))
| ~ '\'LE\''(f(suc(suc(X0))),s(s('\'0\'')))
| '\'E\''(s('\'0\''),f(suc(suc(X0)))) ),
inference(clausification,[status(esa)],[clause_33]) ).
cnf(c24,plain,
( '\'LE\''(f(X0),s('\'0\''))
| ~ '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s('\'0\''),f(X0)) ),
inference(clausification,[status(esa)],[clause_118]) ).
cnf(c27,plain,
( ~ '\'E\''(f(X0),f(suc(X0)))
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X0)) ),
inference(clausification,[status(esa)],[clause_25]) ).
cnf(d0,plain,
( '\'E\''(s('\'0\''),f(X0))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[c5,c24]) ).
cnf(d1,plain,
( '\'E\''(s('\'0\''),f(suc(X0)))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[c5,c6]) ).
cnf(d2,plain,
( '\'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)],[c9,d1]) ).
cnf(d3,plain,
( '\'E\''(s('\'0\''),f(suc(suc(X0))))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[c5,c22]) ).
cnf(d4,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)],[c27,d3]) ).
cnf(d5,plain,
( '\'LE\''(f(X0),s('\'0\''))
| 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)],[d4,d1]) ).
cnf(d6,plain,
( 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))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
( '\'LE\''(f(X0),s('\'0\''))
| iLEQ(suc(X0),suc(X0))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d6,d0]) ).
cnf(d8,plain,
( '\'LE\''(f(X2),s('\'0\''))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0))
| '\'E\''(f(X2),f(suc(X2)))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[c3,d1]) ).
cnf(d9,plain,
( '\'LE\''(f(X2),s('\'0\''))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0))
| '\'E\''(f(X2),f(suc(X2)))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d8,d1]) ).
cnf(d10,plain,
( '\'LE\''(f(X2),s('\'0\''))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X0))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X2),f(suc(X2)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d9,d1]) ).
cnf(d11,plain,
( '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X1),f(suc(X1)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d10,d7]) ).
cnf(d12,plain,
( '\'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)))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d11,d7]) ).
cnf(d13,plain,
( '\'LE\''(f(X2),s('\'0\''))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X1))))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X0))))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0))) ),
inference(resolution,[status(thm)],[c4,d3]) ).
cnf(d14,plain,
( '\'LE\''(f(X2),s('\'0\''))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s('\'0\''),f(suc(suc(X1))))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d13,d3]) ).
cnf(d15,plain,
( '\'LE\''(f(X2),s('\'0\''))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d14,d3]) ).
cnf(d16,plain,
( '\'LE\''(f(X2),s('\'0\''))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d15,d1]) ).
cnf(d17,plain,
( '\'LE\''(f(X2),s('\'0\''))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d16,d1]) ).
cnf(d18,plain,
( '\'LE\''(f(X1),s('\'0\''))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d17,d1]) ).
cnf(d19,plain,
( ~ '\'E\''(s('\'0\''),f(X2))
| '\'LE\''(f(X2),s('\'0\''))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d18,d12]) ).
cnf(d20,plain,
( ~ '\'E\''(s('\'0\''),f(X2))
| '\'LE\''(f(X2),s('\'0\''))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d19,d12]) ).
cnf(d21,plain,
( ~ '\'E\''(s('\'0\''),f(X1))
| '\'LE\''(f(X1),s('\'0\''))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0))
| '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d20,d12]) ).
cnf(d22,plain,
( '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(X0))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d21,d7]) ).
cnf(d23,plain,
( '\'LE\''(f(X0),s('\'0\''))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(X0))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d22,d7]) ).
cnf(d24,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d23,d0]) ).
cnf(d25,plain,
( '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d24,c8]) ).
cnf(d26,plain,
( '\'E\''('\'0\'',f(suc(X0)))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d24,c7]) ).
cnf(d27,plain,
( '\'E\''('\'0\'',f(suc(suc(X0))))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d24,c2]) ).
cnf(d28,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d27,c21]) ).
cnf(d29,plain,
( iLEQ(suc(X0),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))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d28,c14]) ).
cnf(d30,plain,
( '\'LE\''(f(X0),'\'0\'')
| iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d29,d26]) ).
cnf(d31,plain,
( ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(X1))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d30,c19]) ).
cnf(d32,plain,
( ~ '\'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))
| '\'E\''(f(X0),f(suc(X0)))
| '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d31,d30]) ).
cnf(d33,plain,
( ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''('\'0\'',f(suc(suc(X2))))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d27,c17]) ).
cnf(d34,plain,
( '\'LE\''(f(X2),'\'0\'')
| ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X2),suc(X1))
| ~ '\'E\''('\'0\'',f(suc(suc(X1))))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''(f(X0),f(suc(X0)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X1),f(suc(X1)))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d33,d27]) ).
cnf(d35,plain,
( '\'LE\''(f(X2),'\'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(X0)))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X2),f(suc(X2)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d34,d27]) ).
cnf(d36,plain,
( ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(X2))
| '\'LE\''(f(X2),'\'0\'')
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| ~ '\'E\''(f(X0),f(suc(X0)))
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d35,d32]) ).
cnf(d37,plain,
( ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(X2))
| '\'LE\''(f(X2),'\'0\'')
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''(f(X1),f(suc(X1)))
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d36,d32]) ).
cnf(d38,plain,
( ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(X1))
| '\'LE\''(f(X1),'\'0\'')
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X2),'\'0\'')
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d37,d32]) ).
cnf(d39,plain,
( ~ '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),'\'0\'')
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X1),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d38,d30]) ).
cnf(d40,plain,
( ~ '\'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))
| '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d39,d30]) ).
cnf(d41,plain,
( '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d40,d26]) ).
cnf(d42,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d41,d25]) ).
cnf(d43,plain,
$false,
inference(resolution,[status(thm)],[d42,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO661-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 19:41:54 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 30.50/8.21 % SZS status Unsatisfiable for theBenchmark.p
% 30.50/8.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------