%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SYO633-1 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 09:46:49 AM UTC 2026
% Result : Unsatisfiable 10.41s 1.94s
% Output : CNFRefutation 10.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of clauses : 34 ( 10 unt; 0 nHn; 12 RR)
% Number of literals : 102 ( 0 equ; 76 neg)
% Maximal clause size : 6 ( 3 avg)
% Maximal term depth : 9 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 98 ( 95 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_5_03,axiom,
( ~ '\'E\''(f(X5),s(s(s(s(s('\'0\''))))))
| ~ '\'E\''(f(X4),'\'0\'')
| ~ '\'E\''(f(X3),s('\'0\''))
| ~ '\'E\''(f(X2),s(s(s('\'0\''))))
| ~ '\'E\''(f(X1),s(s(s(s('\'0\'')))))
| ~ '\'E\''(f(X0),s(s('\'0\''))) ) ).
cnf(clause_6_04,axiom,
'\'E\''(f(X0),s(s(s(s('\'0\''))))) ).
cnf(clause_8_05,axiom,
'\'E\''(f(X0),s(s(s(s(s('\'0\'')))))) ).
cnf(clause_2_07,axiom,
( '\'E\''(f('\'AP\''(s(s(s(s(s(s('\'0\'')))))),X5)),'\'0\'')
| ~ '\'E\''(f(X4),s(s(s(s(s('\'0\''))))))
| ~ '\'E\''(f(X3),s('\'0\''))
| ~ '\'E\''(f(X2),s(s(s('\'0\''))))
| ~ '\'E\''(f(X1),s(s(s(s('\'0\'')))))
| ~ '\'E\''(f(X0),s(s('\'0\''))) ) ).
cnf(clause_12_09,axiom,
( '\'E\''(f('\'AP\''(s(s(s(s(s(s('\'0\'')))))),X4)),s('\'0\''))
| ~ '\'E\''(f(X3),s(s('\'0\'')))
| ~ '\'E\''(f(X2),s(s(s('\'0\''))))
| ~ '\'E\''(f(X1),s(s(s(s(s('\'0\''))))))
| ~ '\'E\''(f(X0),s(s(s(s('\'0\''))))) ) ).
cnf(clause_1_10,axiom,
( '\'E\''(f(X1),s(s(s('\'0\''))))
| ~ '\'E\''(f(X1),s(s(s(s(s('\'0\''))))))
| ~ '\'E\''(f(X0),s(s(s(s('\'0\''))))) ) ).
cnf(clause_4_12,axiom,
( '\'E\''(f('\'AP\''(s(s(s(s(s(s('\'0\'')))))),X3)),s(s('\'0\'')))
| ~ '\'E\''(f(X2),s(s(s('\'0\''))))
| ~ '\'E\''(f(X1),s(s(s(s(s('\'0\''))))))
| ~ '\'E\''(f(X0),s(s(s(s('\'0\''))))) ) ).
cnf(c2,plain,
( ~ '\'E\''(f(X5),s(s(s('\'0\''))))
| ~ '\'E\''(f(X4),s('\'0\''))
| ~ '\'E\''(f(X3),s(s(s(s('\'0\'')))))
| ~ '\'E\''(f(X2),s(s(s(s(s('\'0\''))))))
| ~ '\'E\''(f(X1),s(s('\'0\'')))
| ~ '\'E\''(f(X0),'\'0\'') ),
inference(clausification,[status(esa)],[clause_5_03]) ).
cnf(c3,plain,
'\'E\''(f(X0),s(s(s(s('\'0\''))))),
inference(clausification,[status(esa)],[clause_6_04]) ).
cnf(c4,plain,
'\'E\''(f(X0),s(s(s(s(s('\'0\'')))))),
inference(clausification,[status(esa)],[clause_8_05]) ).
cnf(c6,plain,
( ~ '\'E\''(f(X5),s(s(s(s(s('\'0\''))))))
| '\'E\''(f('\'AP\''(s(s(s(s(s(s('\'0\'')))))),X4)),'\'0\'')
| ~ '\'E\''(f(X3),s(s('\'0\'')))
| ~ '\'E\''(f(X2),s('\'0\''))
| ~ '\'E\''(f(X1),s(s(s('\'0\''))))
| ~ '\'E\''(f(X0),s(s(s(s('\'0\''))))) ),
inference(clausification,[status(esa)],[clause_2_07]) ).
cnf(c8,plain,
( ~ '\'E\''(f(X4),s(s('\'0\'')))
| ~ '\'E\''(f(X3),s(s(s(s(s('\'0\''))))))
| ~ '\'E\''(f(X2),s(s(s('\'0\''))))
| ~ '\'E\''(f(X1),s(s(s(s('\'0\'')))))
| '\'E\''(f('\'AP\''(s(s(s(s(s(s('\'0\'')))))),X0)),s('\'0\'')) ),
inference(clausification,[status(esa)],[clause_12_09]) ).
cnf(c9,plain,
( '\'E\''(f(X1),s(s(s('\'0\''))))
| ~ '\'E\''(f(X1),s(s(s(s(s('\'0\''))))))
| ~ '\'E\''(f(X0),s(s(s(s('\'0\''))))) ),
inference(clausification,[status(esa)],[clause_1_10]) ).
cnf(c11,plain,
( '\'E\''(f('\'AP\''(s(s(s(s(s(s('\'0\'')))))),X3)),s(s('\'0\'')))
| ~ '\'E\''(f(X2),s(s(s('\'0\''))))
| ~ '\'E\''(f(X1),s(s(s(s(s('\'0\''))))))
| ~ '\'E\''(f(X0),s(s(s(s('\'0\''))))) ),
inference(clausification,[status(esa)],[clause_4_12]) ).
cnf(d0,plain,
( '\'E\''(f('\'AP\''(s(s(s(s(s(s('\'0\'')))))),X2)),s(s('\'0\'')))
| ~ '\'E\''(f(X1),s(s(s(s(s('\'0\''))))))
| ~ '\'E\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[c3,c11]) ).
cnf(d1,plain,
( '\'E\''(f('\'AP\''(s(s(s(s(s(s('\'0\'')))))),X1)),s(s('\'0\'')))
| ~ '\'E\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[c4,d0]) ).
cnf(d2,plain,
( '\'E\''(f(X0),s(s(s('\'0\''))))
| ~ '\'E\''(f(X0),s(s(s(s(s('\'0\'')))))) ),
inference(resolution,[status(thm)],[c3,c9]) ).
cnf(d3,plain,
'\'E\''(f(X0),s(s(s('\'0\'')))),
inference(resolution,[status(thm)],[c4,d2]) ).
cnf(d4,plain,
'\'E\''(f('\'AP\''(s(s(s(s(s(s('\'0\'')))))),X0)),s(s('\'0\''))),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
( '\'E\''(f('\'AP\''(s(s(s(s(s(s('\'0\'')))))),X3)),s('\'0\''))
| ~ '\'E\''(f(X2),s(s(s(s(s('\'0\''))))))
| ~ '\'E\''(f(X1),s(s(s('\'0\''))))
| ~ '\'E\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[c3,c8]) ).
cnf(d6,plain,
( '\'E\''(f('\'AP\''(s(s(s(s(s(s('\'0\'')))))),X2)),s('\'0\''))
| ~ '\'E\''(f(X1),s(s('\'0\'')))
| ~ '\'E\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[c4,d5]) ).
cnf(d7,plain,
( '\'E\''(f('\'AP\''(s(s(s(s(s(s('\'0\'')))))),X1)),s('\'0\''))
| ~ '\'E\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d3,d6]) ).
cnf(d8,plain,
'\'E\''(f('\'AP\''(s(s(s(s(s(s('\'0\'')))))),X0)),s('\'0\'')),
inference(resolution,[status(thm)],[d7,d4]) ).
cnf(d9,plain,
( '\'E\''(f('\'AP\''(s(s(s(s(s(s('\'0\'')))))),X4)),'\'0\'')
| ~ '\'E\''(f(X3),s('\'0\''))
| ~ '\'E\''(f(X2),s(s(s('\'0\''))))
| ~ '\'E\''(f(X1),s(s('\'0\'')))
| ~ '\'E\''(f(X0),s(s(s(s(s('\'0\'')))))) ),
inference(resolution,[status(thm)],[c3,c6]) ).
cnf(d10,plain,
( '\'E\''(f('\'AP\''(s(s(s(s(s(s('\'0\'')))))),X3)),'\'0\'')
| ~ '\'E\''(f(X2),s(s('\'0\'')))
| ~ '\'E\''(f(X1),s(s(s('\'0\''))))
| ~ '\'E\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[c4,d9]) ).
cnf(d11,plain,
( '\'E\''(f('\'AP\''(s(s(s(s(s(s('\'0\'')))))),X2)),'\'0\'')
| ~ '\'E\''(f(X1),s('\'0\''))
| ~ '\'E\''(f(X0),s(s('\'0\''))) ),
inference(resolution,[status(thm)],[d3,d10]) ).
cnf(d12,plain,
( '\'E\''(f('\'AP\''(s(s(s(s(s(s('\'0\'')))))),X1)),'\'0\'')
| ~ '\'E\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d11,d4]) ).
cnf(d13,plain,
( ~ '\'E\''(f(X4),s('\'0\''))
| ~ '\'E\''(f(X3),s(s('\'0\'')))
| ~ '\'E\''(f(X2),s(s(s(s(s('\'0\''))))))
| ~ '\'E\''(f(X1),'\'0\'')
| ~ '\'E\''(f(X0),s(s(s('\'0\'')))) ),
inference(resolution,[status(thm)],[c3,c2]) ).
cnf(d14,plain,
( ~ '\'E\''(f(X3),s(s(s('\'0\''))))
| ~ '\'E\''(f(X2),'\'0\'')
| ~ '\'E\''(f(X1),s(s('\'0\'')))
| ~ '\'E\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[c4,d13]) ).
cnf(d15,plain,
( ~ '\'E\''(f(X2),s('\'0\''))
| ~ '\'E\''(f(X1),s(s('\'0\'')))
| ~ '\'E\''(f(X0),'\'0\'') ),
inference(resolution,[status(thm)],[d3,d14]) ).
cnf(d16,plain,
( ~ '\'E\''(f(X1),'\'0\'')
| ~ '\'E\''(f(X0),s('\'0\'')) ),
inference(resolution,[status(thm)],[d15,d4]) ).
cnf(d17,plain,
~ '\'E\''(f(X0),'\'0\''),
inference(resolution,[status(thm)],[d8,d16]) ).
cnf(d18,plain,
~ '\'E\''(f(X0),s('\'0\'')),
inference(resolution,[status(thm)],[d17,d12]) ).
cnf(d19,plain,
$false,
inference(resolution,[status(thm)],[d18,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO633-1 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.38 % Computer : n015.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sat Sep 26 19:44:14 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.41/1.94 % SZS status Unsatisfiable for theBenchmark.p
% 10.41/1.94 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------