%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWV007-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 13.68s 3.48s
% Output : CNFRefutation 13.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 25 ( 13 unt; 5 nHn; 19 RR)
% Number of literals : 46 ( 6 equ; 19 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 23 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_4,negated_conjecture,
~ 'less$uthan'(n,m) ).
cnf(clause_5,negated_conjecture,
'less$uthan'(i,m) ).
cnf(clause_8,negated_conjecture,
'less$uthan'(a(m),a(k)) ).
cnf(clause_11,negated_conjecture,
( ~ 'less$uthan'(a(X0),a(k))
| ~ 'less$uthan'(X0,successor(n))
| 'less$uthan'(X0,i) ) ).
cnf(less_than_successor,axiom,
'less$uthan'(X0,successor(X0)) ).
cnf(transitivity_of_less_than,axiom,
( ~ 'less$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(anti_symmetry_of_less_than,axiom,
( ~ 'less$uthan'(X1,X0)
| ~ 'less$uthan'(X0,X1) ) ).
cnf(c3,plain,
~ 'less$uthan'(n,m),
inference(clausification,[status(esa)],[clause_4]) ).
cnf(c4,plain,
'less$uthan'(i,m),
inference(clausification,[status(esa)],[clause_5]) ).
cnf(c7,plain,
'less$uthan'(a(m),a(k)),
inference(clausification,[status(esa)],[clause_8]) ).
cnf(c10,plain,
( ~ 'less$uthan'(a(X0),a(k))
| ~ 'less$uthan'(X0,successor(n))
| 'less$uthan'(X0,i) ),
inference(clausification,[status(esa)],[clause_11]) ).
cnf(c16,plain,
'less$uthan'(X0,successor(X0)),
inference(clausification,[status(esa)],[less_than_successor]) ).
cnf(c17,plain,
( ~ 'less$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(c20,plain,
( ~ 'less$uthan'(X1,X0)
| ~ 'less$uthan'(X0,X1) ),
inference(clausification,[status(esa)],[anti_symmetry_of_less_than]) ).
cnf(d0,plain,
( ~ 'less$uthan'(m,successor(n))
| 'less$uthan'(m,i) ),
inference(resolution,[status(thm)],[c10,c7]) ).
cnf(d1,plain,
~ 'less$uthan'(m,i),
inference(resolution,[status(thm)],[c20,c4]) ).
cnf(d2,plain,
~ 'less$uthan'(m,successor(n)),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( 'less$uthan'(X0,X2)
| ~ 'less$uthan'(X1,X2)
| 'less$uthan'(X1,X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c18,c17]) ).
cnf(d4,plain,
( 'less$uthan'(X0,successor(X1))
| 'less$uthan'(X1,X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[d3,c16]) ).
cnf(d5,plain,
( 'less$uthan'(n,m)
| m = n ),
inference(resolution,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
m = n,
inference(resolution,[status(thm)],[c3,d5]) ).
cnf(d7,plain,
~ 'less$uthan'(n,successor(n)),
inference(demodulation,[status(thm)],[d2,d6]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[c16,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV007-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n018.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sat Sep 26 13:06:54 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.68/3.48 % SZS status Unsatisfiable for theBenchmark.p
% 13.68/3.48 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------