%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWV008-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 09:01:14 AM UTC 2026
% Result : Unsatisfiable 12.05s 7.01s
% Output : CNFRefutation 12.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of clauses : 24 ( 14 unt; 7 nHn; 22 RR)
% Number of literals : 43 ( 4 equ; 18 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 11 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_1,negated_conjecture,
~ 'less$uthan'(n,l) ).
cnf(clause_2,negated_conjecture,
'less$uthan'(one,l) ).
cnf(clause_3,negated_conjecture,
'less$uthan'(a(l),a(predecessor(l))) ).
cnf(clause_4,negated_conjecture,
( ~ 'less$uthan'(a(X0),a(predecessor(n)))
| ~ 'less$uthan'(one,n)
| 'less$uthan'(n,X0)
| 'less$uthan'(X0,n) ) ).
cnf(clause_5,negated_conjecture,
( ~ 'less$uthan'(a(X0),a(predecessor(X0)))
| ~ 'less$uthan'(X0,n)
| ~ 'less$uthan'(one,X0) ) ).
cnf(all_related,axiom,
( X0 = X1
| 'less$uthan'(X1,X0)
| 'less$uthan'(X0,X1) ) ).
cnf(x_not_less_than_x,axiom,
~ 'less$uthan'(X0,X0) ).
cnf(c0,plain,
~ 'less$uthan'(n,l),
inference(clausification,[status(esa)],[clause_1]) ).
cnf(c1,plain,
'less$uthan'(one,l),
inference(clausification,[status(esa)],[clause_2]) ).
cnf(c2,plain,
'less$uthan'(a(l),a(predecessor(l))),
inference(clausification,[status(esa)],[clause_3]) ).
cnf(c3,plain,
( ~ 'less$uthan'(a(X0),a(predecessor(n)))
| ~ 'less$uthan'(one,n)
| 'less$uthan'(n,X0)
| 'less$uthan'(X0,n) ),
inference(clausification,[status(esa)],[clause_4]) ).
cnf(c4,plain,
( ~ 'less$uthan'(a(X0),a(predecessor(X0)))
| ~ 'less$uthan'(X0,n)
| ~ 'less$uthan'(one,X0) ),
inference(clausification,[status(esa)],[clause_5]) ).
cnf(c12,plain,
( X0 = X1
| 'less$uthan'(X1,X0)
| 'less$uthan'(X0,X1) ),
inference(clausification,[status(esa)],[all_related]) ).
cnf(c13,plain,
~ 'less$uthan'(X0,X0),
inference(clausification,[status(esa)],[x_not_less_than_x]) ).
cnf(d0,plain,
( 'less$uthan'(l,n)
| n = l ),
inference(resolution,[status(thm)],[c12,c0]) ).
cnf(d1,plain,
( ~ 'less$uthan'(one,l)
| ~ 'less$uthan'(l,n) ),
inference(resolution,[status(thm)],[c4,c2]) ).
cnf(d2,plain,
~ 'less$uthan'(l,n),
inference(resolution,[status(thm)],[c1,d1]) ).
cnf(d3,plain,
n = l,
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
'less$uthan'(a(n),a(predecessor(l))),
inference(demodulation,[status(thm)],[c2,d3]) ).
cnf(d5,plain,
'less$uthan'(a(n),a(predecessor(n))),
inference(demodulation,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
'less$uthan'(one,n),
inference(demodulation,[status(thm)],[c1,d3]) ).
cnf(d7,plain,
( ~ 'less$uthan'(a(X0),a(predecessor(n)))
| 'less$uthan'(n,X0)
| 'less$uthan'(X0,n) ),
inference(resolution,[status(thm)],[d6,c3]) ).
cnf(d8,plain,
( 'less$uthan'(n,n)
| 'less$uthan'(n,n) ),
inference(resolution,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[c13,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV008-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.37 % Computer : n020.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Sat Sep 26 13:05:40 UTC 2026
% 0.11/5.37 % CPUTime :
% 0.11/5.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.05/7.01 % SZS status Unsatisfiable for theBenchmark.p
% 12.05/7.01 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------