%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SYO680-1 : 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 : n004.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 09:47:45 AM UTC 2026
% Result : Unsatisfiable 26.53s 18.96s
% Output : CNFRefutation 26.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 18
% Syntax : Number of clauses : 104 ( 7 unt; 77 nHn; 73 RR)
% Number of literals : 565 ( 0 equ; 222 neg)
% Maximal clause size : 12 ( 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 : 160 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_109,axiom,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0)) ) ).
cnf(clause_104,axiom,
'\'LE\''(f(X0),s(s(s(s('\'0\''))))) ).
cnf(clause_91,axiom,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X0)) ) ).
cnf(clause_114,axiom,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s('\'0\'')) ) ).
cnf(clause_5,axiom,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(X0)) ) ).
cnf(clause_20,axiom,
( ~ '\'E\''(s(s('\'0\'')),f(X2))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X2)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0))) ) ).
cnf(clause_71,axiom,
( ~ '\'E\''(s(s(s('\'0\''))),f(suc(X2)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| ~ iLEQ(suc(X0),suc(X1)) ) ).
cnf(clause_6,axiom,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(X0))
| ~ '\'LE\''(f(X0),s(s('\'0\''))) ) ).
cnf(clause_66,axiom,
~ '\'LE\''(f(z),'\'0\'') ).
cnf(clause_84,axiom,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s(s(s('\'0\'')))) ) ).
cnf(clause_144,axiom,
( ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(X0))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''('\'0\'',f(suc(X0))) ) ).
cnf(clause_127,axiom,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'E\''(s(s(s('\'0\''))),f(X0))
| ~ '\'LE\''(f(X0),s(s(s(s('\'0\''))))) ) ).
cnf(clause_51,axiom,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'LE\''(f(X0),s(s(s('\'0\'')))) ) ).
cnf(clause_21,axiom,
( ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ iLEQ(suc(X0),suc(X1)) ) ).
cnf(clause_102,axiom,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s(s(s(s('\'0\''))))) ) ).
cnf(clause_14,axiom,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0)) ) ).
cnf(clause_96,axiom,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| ~ '\'LE\''(f(X0),s('\'0\'')) ) ).
cnf(clause_15,axiom,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s(s('\'0\''))) ) ).
cnf(c0,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(clausification,[status(esa)],[clause_109]) ).
cnf(c1,plain,
'\'LE\''(f(X0),s(s(s(s('\'0\''))))),
inference(clausification,[status(esa)],[clause_104]) ).
cnf(c2,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X0)) ),
inference(clausification,[status(esa)],[clause_91]) ).
cnf(c3,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s('\'0\'')) ),
inference(clausification,[status(esa)],[clause_114]) ).
cnf(c4,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(X0)) ),
inference(clausification,[status(esa)],[clause_5]) ).
cnf(c5,plain,
( ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(X2))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X2)))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s(s('\'0\'')),f(X0)) ),
inference(clausification,[status(esa)],[clause_20]) ).
cnf(c6,plain,
( ~ '\'E\''(s(s(s('\'0\''))),f(suc(X2)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X2))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0))) ),
inference(clausification,[status(esa)],[clause_71]) ).
cnf(c7,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(X0))
| ~ '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(clausification,[status(esa)],[clause_6]) ).
cnf(c8,plain,
~ '\'LE\''(f(z),'\'0\''),
inference(clausification,[status(esa)],[clause_66]) ).
cnf(c9,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s(s(s('\'0\'')))) ),
inference(clausification,[status(esa)],[clause_84]) ).
cnf(c10,plain,
( ~ '\'E\''('\'0\'',f(suc(X0)))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''('\'0\'',f(X2))
| ~ '\'E\''('\'0\'',f(X1))
| ~ '\'E\''('\'0\'',f(suc(X2)))
| ~ '\'E\''('\'0\'',f(suc(X1)))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(clausification,[status(esa)],[clause_144]) ).
cnf(c11,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'E\''(s(s(s('\'0\''))),f(X0))
| ~ '\'LE\''(f(X0),s(s(s(s('\'0\''))))) ),
inference(clausification,[status(esa)],[clause_127]) ).
cnf(c12,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(clausification,[status(esa)],[clause_51]) ).
cnf(c13,plain,
( ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ iLEQ(suc(X2),suc(X0))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(clausification,[status(esa)],[clause_21]) ).
cnf(c14,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s(s(s(s('\'0\''))))) ),
inference(clausification,[status(esa)],[clause_102]) ).
cnf(c15,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0)) ),
inference(clausification,[status(esa)],[clause_14]) ).
cnf(c16,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| ~ '\'LE\''(f(X0),s('\'0\'')) ),
inference(clausification,[status(esa)],[clause_96]) ).
cnf(c17,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'LE\''(f(suc(X0)),s(s('\'0\''))) ),
inference(clausification,[status(esa)],[clause_15]) ).
cnf(d0,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'E\''(s(s(s('\'0\''))),f(X0)) ),
inference(resolution,[status(thm)],[c1,c11]) ).
cnf(d1,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(X0))
| '\'E\''(s(s(s('\'0\''))),f(X0)) ),
inference(resolution,[status(thm)],[d0,c12]) ).
cnf(d2,plain,
( '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'E\''(s(s(s('\'0\''))),f(suc(X0))) ),
inference(resolution,[status(thm)],[c1,c14]) ).
cnf(d3,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[d2,c15]) ).
cnf(d4,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(X0))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(X0))
| '\'LE\''(f(X0),s(s('\'0\'')))
| iLEQ(suc(X0),suc(X0))
| '\'E\''(s(s('\'0\'')),f(X0)) ),
inference(resolution,[status(thm)],[d4,c12]) ).
cnf(d6,plain,
( ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X2)))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X1)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0))
| ~ '\'E\''(s(s(s('\'0\''))),f(X2))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[d2,c6]) ).
cnf(d7,plain,
( '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X2),s(s(s('\'0\''))))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(s(s(s('\'0\''))),f(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X2))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0)) ),
inference(resolution,[status(thm)],[d6,d2]) ).
cnf(d8,plain,
( '\'LE\''(f(X2),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'E\''(s(s(s('\'0\''))),f(X2))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0)) ),
inference(resolution,[status(thm)],[d7,d2]) ).
cnf(d9,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(X2))
| '\'LE\''(f(X2),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0)) ),
inference(resolution,[status(thm)],[d8,d1]) ).
cnf(d10,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(X2))
| '\'LE\''(f(X2),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s('\'0\'')))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| '\'E\''(s(s('\'0\'')),f(X0)) ),
inference(resolution,[status(thm)],[d9,d1]) ).
cnf(d11,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(X2))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X2),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s('\'0\'')))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X2),suc(X1))
| '\'E\''(s(s('\'0\'')),f(X1))
| '\'E\''(s(s('\'0\'')),f(X0)) ),
inference(resolution,[status(thm)],[d10,d1]) ).
cnf(d12,plain,
( '\'LE\''(f(X1),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(X1))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s('\'0\'')))
| ~ iLEQ(suc(X0),suc(X1))
| '\'E\''(s(s('\'0\'')),f(X1))
| '\'E\''(s(s('\'0\'')),f(X1))
| '\'E\''(s(s('\'0\'')),f(X0)) ),
inference(resolution,[status(thm)],[d11,d5]) ).
cnf(d13,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(X0))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(X0))
| '\'E\''(s(s('\'0\'')),f(X0)) ),
inference(resolution,[status(thm)],[d12,d5]) ).
cnf(d14,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(X0))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(X0)) ),
inference(resolution,[status(thm)],[d13,c12]) ).
cnf(d15,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(X0))
| '\'E\''(s(s('\'0\'')),f(X0)) ),
inference(resolution,[status(thm)],[d14,c7]) ).
cnf(d16,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(suc(X0)))
| '\'E\''(s(s(s('\'0\''))),f(suc(X0))) ),
inference(resolution,[status(thm)],[d0,c9]) ).
cnf(d17,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(suc(X0)))
| '\'LE\''(f(suc(X0)),s(s(s('\'0\''))))
| iLEQ(suc(suc(X0)),suc(suc(X0))) ),
inference(resolution,[status(thm)],[d3,d16]) ).
cnf(d18,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(suc(X0)))
| '\'LE\''(f(X0),s(s('\'0\'')))
| iLEQ(suc(suc(X0)),suc(suc(X0)))
| '\'E\''(s(s('\'0\'')),f(suc(X0))) ),
inference(resolution,[status(thm)],[d17,c9]) ).
cnf(d19,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(suc(X2)))
| '\'LE\''(f(suc(X2)),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s(s('\'0\''))))
| ~ iLEQ(suc(suc(X2)),suc(X0))
| ~ iLEQ(suc(X1),suc(suc(X2)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0)) ),
inference(resolution,[status(thm)],[d8,d16]) ).
cnf(d20,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(suc(X2)))
| '\'LE\''(f(suc(X0)),s(s(s('\'0\''))))
| '\'LE\''(f(suc(X2)),s(s(s('\'0\''))))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s('\'0\'')))
| ~ iLEQ(suc(suc(X0)),suc(suc(X2)))
| ~ iLEQ(suc(X1),suc(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| '\'E\''(s(s('\'0\'')),f(suc(X0))) ),
inference(resolution,[status(thm)],[d19,d16]) ).
cnf(d21,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(suc(X0)))
| '\'LE\''(f(suc(X0)),s(s(s('\'0\''))))
| '\'LE\''(f(suc(X0)),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s('\'0\'')))
| ~ iLEQ(suc(X1),suc(suc(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X1))
| '\'E\''(s(s('\'0\'')),f(suc(X0)))
| '\'E\''(s(s('\'0\'')),f(suc(X0))) ),
inference(resolution,[status(thm)],[d20,d18]) ).
cnf(d22,plain,
( '\'LE\''(f(X1),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(suc(X1)))
| '\'LE\''(f(suc(X0)),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(suc(X1)),s(s(s('\'0\''))))
| ~ iLEQ(suc(suc(X1)),suc(suc(X0)))
| '\'E\''(s(s('\'0\'')),f(suc(X0))) ),
inference(resolution,[status(thm)],[d21,d16]) ).
cnf(d23,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(suc(X0)))
| '\'LE\''(f(suc(X0)),s(s(s('\'0\''))))
| '\'LE\''(f(suc(X0)),s(s(s('\'0\''))))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(suc(X0)))
| '\'E\''(s(s('\'0\'')),f(suc(X0))) ),
inference(resolution,[status(thm)],[d22,d18]) ).
cnf(d24,plain,
( '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(suc(X0)))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(suc(X0))) ),
inference(resolution,[status(thm)],[d23,c9]) ).
cnf(d25,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d24,c4]) ).
cnf(d26,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(X0))
| '\'LE\''(f(X0),s(s('\'0\'')))
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[status(thm)],[d25,d15]) ).
cnf(d27,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(X0))
| '\'LE\''(f(X0),s('\'0\''))
| iLEQ(suc(X0),suc(X0))
| '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[d26,c7]) ).
cnf(d28,plain,
( ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X1),suc(X0))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X2)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X1)))
| ~ '\'E\''(s(s('\'0\'')),f(X0))
| ~ '\'E\''(s(s('\'0\'')),f(X2))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d24,c5]) ).
cnf(d29,plain,
( '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X2),s(s('\'0\'')))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(X2))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ '\'E\''(s(s('\'0\'')),f(X0)) ),
inference(resolution,[status(thm)],[d28,d24]) ).
cnf(d30,plain,
( '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'E\''(s(s('\'0\'')),f(X2))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ '\'E\''(s(s('\'0\'')),f(X0)) ),
inference(resolution,[status(thm)],[d29,d24]) ).
cnf(d31,plain,
( '\'LE\''(f(X2),s('\'0\''))
| '\'E\''(s('\'0\''),f(X2))
| '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X2))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ '\'E\''(s(s('\'0\'')),f(X0)) ),
inference(resolution,[status(thm)],[d30,d15]) ).
cnf(d32,plain,
( '\'LE\''(f(X2),s('\'0\''))
| '\'E\''(s('\'0\''),f(X2))
| '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[d31,d15]) ).
cnf(d33,plain,
( '\'LE\''(f(X2),s('\'0\''))
| '\'E\''(s('\'0\''),f(X2))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X2),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X2),suc(X1))
| '\'E\''(s('\'0\''),f(X1))
| '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[d32,d15]) ).
cnf(d34,plain,
( '\'LE\''(f(X1),s('\'0\''))
| '\'E\''(s('\'0\''),f(X1))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X0),suc(X1))
| '\'E\''(s('\'0\''),f(X1))
| '\'E\''(s('\'0\''),f(X1))
| '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[d33,d27]) ).
cnf(d35,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(X0))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),s(s('\'0\'')))
| '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(X0))
| '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[d34,d27]) ).
cnf(d36,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(X0))
| '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[d35,c7]) ).
cnf(d37,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[d36,c16]) ).
cnf(d38,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(X0)))
| '\'E\''(s(s('\'0\'')),f(suc(X0))) ),
inference(resolution,[status(thm)],[d14,c17]) ).
cnf(d39,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(X0)))
| '\'LE\''(f(suc(X0)),s(s('\'0\'')))
| iLEQ(suc(suc(X0)),suc(suc(X0))) ),
inference(resolution,[status(thm)],[d25,d38]) ).
cnf(d40,plain,
( '\'LE\''(f(X2),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(X2)))
| '\'LE\''(f(suc(X2)),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s(s('\'0\'')))
| ~ iLEQ(suc(suc(X2)),suc(X0))
| ~ iLEQ(suc(X1),suc(suc(X2)))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| ~ '\'E\''(s(s('\'0\'')),f(X0)) ),
inference(resolution,[status(thm)],[d30,d38]) ).
cnf(d41,plain,
( '\'LE\''(f(suc(X0)),s(s('\'0\'')))
| '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(X0)))
| '\'LE\''(f(suc(X0)),s(s('\'0\'')))
| '\'LE\''(f(suc(X0)),s(s('\'0\'')))
| '\'LE\''(f(X1),s(s('\'0\'')))
| '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X1),suc(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[d40,d39]) ).
cnf(d42,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(X0)))
| '\'LE\''(f(suc(X0)),s(s('\'0\'')))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X1),s(s('\'0\'')))
| ~ iLEQ(suc(X1),suc(suc(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(X1))
| '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[d41,d38]) ).
cnf(d43,plain,
( '\'LE\''(f(suc(X0)),s(s('\'0\'')))
| '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(X0)))
| '\'LE\''(f(suc(X0)),s(s('\'0\'')))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(suc(X0)),s(s('\'0\'')))
| ~ '\'E\''(s(s('\'0\'')),f(suc(X0)))
| '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[d42,d39]) ).
cnf(d44,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(X0)))
| '\'LE\''(f(suc(X0)),s(s('\'0\'')))
| '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[d43,d38]) ).
cnf(d45,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(X0)))
| '\'LE\''(f(X0),s('\'0\''))
| '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[d44,c17]) ).
cnf(d46,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''(s('\'0\''),f(X0))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d45,c2]) ).
cnf(d47,plain,
( '\'LE\''(f(X0),s('\'0\''))
| iLEQ(suc(X0),suc(X0))
| '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d37,d46]) ).
cnf(d48,plain,
( ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X2),suc(X1))
| ~ '\'E\''(s('\'0\''),f(suc(X2)))
| ~ '\'E\''(s('\'0\''),f(suc(X1)))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| '\'LE\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d45,c13]) ).
cnf(d49,plain,
( '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X2),s('\'0\''))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[d48,d45]) ).
cnf(d50,plain,
( '\'LE\''(f(X2),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(X0),s('\'0\''))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X0),suc(X2))
| ~ '\'E\''(s('\'0\''),f(X2))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[d49,d45]) ).
cnf(d51,plain,
( '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'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))
| '\'LE\''(f(X0),s('\'0\''))
| '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d47,d50]) ).
cnf(d52,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\''))
| ~ '\'E\''(s('\'0\''),f(X0))
| ~ '\'E\''(s('\'0\''),f(X0))
| '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d51,d47]) ).
cnf(d53,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)],[d52,d37]) ).
cnf(d54,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d53,c16]) ).
cnf(d55,plain,
'\'E\''('\'0\'',f(z)),
inference(resolution,[status(thm)],[d54,c8]) ).
cnf(d56,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0)))
| '\'E\''(s('\'0\''),f(suc(X0))) ),
inference(resolution,[status(thm)],[d36,c3]) ).
cnf(d57,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)],[d56,d46]) ).
cnf(d58,plain,
( '\'LE\''(f(suc(X0)),s('\'0\''))
| '\'LE\''(f(X1),s('\'0\''))
| '\'LE\''(f(suc(X0)),s('\'0\''))
| ~ iLEQ(suc(suc(X0)),suc(X1))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| ~ '\'E\''(s('\'0\''),f(X1))
| ~ '\'E\''(s('\'0\''),f(suc(X0)))
| '\'LE\''(f(suc(X0)),s('\'0\''))
| '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d57,d50]) ).
cnf(d59,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)],[d58,d57]) ).
cnf(d60,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)],[d59,d56]) ).
cnf(d61,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0)))
| '\'LE\''(f(X0),'\'0\'')
| '\'E\''('\'0\'',f(suc(X0))) ),
inference(resolution,[status(thm)],[d60,c3]) ).
cnf(d62,plain,
( iLEQ(suc(X0),suc(X0))
| ~ '\'E\''('\'0\'',f(X0))
| '\'LE\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d61,c0]) ).
cnf(d63,plain,
( ~ 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(X0),'\'0\'')
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d62,c10]) ).
cnf(d64,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)],[d63,d62]) ).
cnf(d65,plain,
( '\'LE\''(f(X0),'\'0\'')
| '\'LE\''(f(X0),'\'0\'')
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[d64,d61]) ).
cnf(d66,plain,
'\'LE\''(f(z),'\'0\''),
inference(resolution,[status(thm)],[d65,d55]) ).
cnf(d67,plain,
$false,
inference(resolution,[status(thm)],[c8,d66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYO680-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/15.46 % Computer : n004.cluster.edu
% 0.18/15.46 % Model : x86_64 x86_64
% 0.18/15.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/15.46 % Memory : 8046.5625MB
% 0.18/15.46 % OS : Linux 6.8.0-71-generic
% 0.18/15.46 % CPULimit : 300
% 0.18/15.46 % WCLimit : 300
% 0.18/15.46 % DateTime : Sat Sep 26 19:45:22 UTC 2026
% 0.18/15.46 % CPUTime :
% 0.18/15.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.53/18.96 % SZS status Unsatisfiable for theBenchmark.p
% 26.53/18.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------