%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWV002-1 : 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 : n009.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 09:01:13 AM UTC 2026
% Result : Unsatisfiable 12.74s 2.01s
% Output : CNFRefutation 12.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 24 ( 15 unt; 3 nHn; 22 RR)
% Number of literals : 39 ( 4 equ; 17 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 15 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_5,negated_conjecture,
'less$uthan'(a(j),a(k)) ).
cnf(clause_6,negated_conjecture,
( ~ 'less$uthan'(a(X0),a(k))
| ~ 'less$uthan'(X0,j)
| 'less$uthan'(X0,i) ) ).
cnf(clause_9,negated_conjecture,
~ 'less$uthan'(q,i) ).
cnf(clause_10,negated_conjecture,
~ 'less$uthan'(j,q) ).
cnf(clause_11,negated_conjecture,
'less$uthan'(a(q),a(j)) ).
cnf(transitivity_of_less_than,axiom,
( ~ 'less$uthan'(X2,X1)
| ~ 'less$uthan'(X0,X2)
| 'less$uthan'(X0,X1) ) ).
cnf(all_related,axiom,
( X0 = X1
| 'less$uthan'(X1,X0)
| 'less$uthan'(X0,X1) ) ).
cnf(x_not_less_than_x,axiom,
~ 'less$uthan'(X0,X0) ).
cnf(c4,plain,
'less$uthan'(a(j),a(k)),
inference(clausification,[status(esa)],[clause_5]) ).
cnf(c5,plain,
( ~ 'less$uthan'(a(X0),a(k))
| ~ 'less$uthan'(X0,j)
| 'less$uthan'(X0,i) ),
inference(clausification,[status(esa)],[clause_6]) ).
cnf(c8,plain,
~ 'less$uthan'(q,i),
inference(clausification,[status(esa)],[clause_9]) ).
cnf(c9,plain,
~ 'less$uthan'(j,q),
inference(clausification,[status(esa)],[clause_10]) ).
cnf(c10,plain,
'less$uthan'(a(q),a(j)),
inference(clausification,[status(esa)],[clause_11]) ).
cnf(c17,plain,
( ~ 'less$uthan'(X2,X1)
| ~ 'less$uthan'(X0,X2)
| 'less$uthan'(X0,X1) ),
inference(clausification,[status(esa)],[transitivity_of_less_than]) ).
cnf(c18,plain,
( X0 = X1
| 'less$uthan'(X1,X0)
| 'less$uthan'(X0,X1) ),
inference(clausification,[status(esa)],[all_related]) ).
cnf(c19,plain,
~ 'less$uthan'(X0,X0),
inference(clausification,[status(esa)],[x_not_less_than_x]) ).
cnf(d0,plain,
( 'less$uthan'(q,j)
| j = q ),
inference(resolution,[status(thm)],[c18,c9]) ).
cnf(d1,plain,
( 'less$uthan'(a(q),X0)
| ~ 'less$uthan'(a(j),X0) ),
inference(resolution,[status(thm)],[c17,c10]) ).
cnf(d2,plain,
'less$uthan'(a(q),a(k)),
inference(resolution,[status(thm)],[d1,c4]) ).
cnf(d3,plain,
( 'less$uthan'(q,i)
| ~ 'less$uthan'(q,j) ),
inference(resolution,[status(thm)],[d2,c5]) ).
cnf(d4,plain,
~ 'less$uthan'(q,j),
inference(resolution,[status(thm)],[c8,d3]) ).
cnf(d5,plain,
j = q,
inference(resolution,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
'less$uthan'(a(j),a(j)),
inference(demodulation,[status(thm)],[c10,d5]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[c19,d6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.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 13:04:44 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.74/2.01 % SZS status Unsatisfiable for theBenchmark.p
% 12.74/2.01 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------