%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWV255-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/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 09:01:47 AM UTC 2026
% Result : Unsatisfiable 13.00s 2.26s
% Output : CNFRefutation 13.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 18 ( 6 unt; 2 nHn; 12 RR)
% Number of literals : 30 ( 0 equ; 16 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 27 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
'c$ulessequals'(X0,'v$uxb'(X0),'tc$unat') ).
cnf(cls_conjecture_1,negated_conjecture,
( ~ 'c$ulessequals'('v$ux',X0,'tc$unat')
| ~ 'c$uin'('c$uMessage$uOmsg$uONonce'(X0),'c$uMessage$uOparts'('c$uinsert'('v$umsg1','c$uemptyset','tc$uMessage$uOmsg')),'tc$uMessage$uOmsg') ) ).
cnf(cls_conjecture_2,negated_conjecture,
( ~ 'c$ulessequals'('v$uxa',X0,'tc$unat')
| ~ 'c$uin'('c$uMessage$uOmsg$uONonce'(X0),'c$uMessage$uOparts'('c$uinsert'('v$umsg2','c$uemptyset','tc$uMessage$uOmsg')),'tc$uMessage$uOmsg') ) ).
cnf(cls_conjecture_3,negated_conjecture,
( 'c$uin'('c$uMessage$uOmsg$uONonce'('v$uxb'(X0)),'c$uMessage$uOparts'('c$uinsert'('v$umsg1','c$uemptyset','tc$uMessage$uOmsg')),'tc$uMessage$uOmsg')
| 'c$uin'('c$uMessage$uOmsg$uONonce'('v$uxb'(X0)),'c$uMessage$uOparts'('c$uinsert'('v$umsg2','c$uemptyset','tc$uMessage$uOmsg')),'tc$uMessage$uOmsg') ) ).
cnf(cls_Nat_Oadd__leE_0,axiom,
( 'c$ulessequals'(X1,X2,'tc$unat')
| ~ 'c$ulessequals'('c$uplus'(X0,X1,'tc$unat'),X2,'tc$unat') ) ).
cnf(cls_Nat_Oadd__leE_1,axiom,
( 'c$ulessequals'(X0,X2,'tc$unat')
| ~ 'c$ulessequals'('c$uplus'(X0,X1,'tc$unat'),X2,'tc$unat') ) ).
cnf(c0,plain,
'c$ulessequals'(X0,'v$uxb'(X0),'tc$unat'),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c1,plain,
( ~ 'c$ulessequals'('v$ux',X0,'tc$unat')
| ~ 'c$uin'('c$uMessage$uOmsg$uONonce'(X0),'c$uMessage$uOparts'('c$uinsert'('v$umsg1','c$uemptyset','tc$uMessage$uOmsg')),'tc$uMessage$uOmsg') ),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c2,plain,
( ~ 'c$ulessequals'('v$uxa',X0,'tc$unat')
| ~ 'c$uin'('c$uMessage$uOmsg$uONonce'(X0),'c$uMessage$uOparts'('c$uinsert'('v$umsg2','c$uemptyset','tc$uMessage$uOmsg')),'tc$uMessage$uOmsg') ),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c3,plain,
( 'c$uin'('c$uMessage$uOmsg$uONonce'('v$uxb'(X0)),'c$uMessage$uOparts'('c$uinsert'('v$umsg1','c$uemptyset','tc$uMessage$uOmsg')),'tc$uMessage$uOmsg')
| 'c$uin'('c$uMessage$uOmsg$uONonce'('v$uxb'(X0)),'c$uMessage$uOparts'('c$uinsert'('v$umsg2','c$uemptyset','tc$uMessage$uOmsg')),'tc$uMessage$uOmsg') ),
inference(clausification,[status(esa)],[cls_conjecture_3]) ).
cnf(c4,plain,
( 'c$ulessequals'(X1,X2,'tc$unat')
| ~ 'c$ulessequals'('c$uplus'(X0,X1,'tc$unat'),X2,'tc$unat') ),
inference(clausification,[status(esa)],[cls_Nat_Oadd__leE_0]) ).
cnf(c5,plain,
( 'c$ulessequals'(X0,X2,'tc$unat')
| ~ 'c$ulessequals'('c$uplus'(X0,X1,'tc$unat'),X2,'tc$unat') ),
inference(clausification,[status(esa)],[cls_Nat_Oadd__leE_1]) ).
cnf(d0,plain,
'c$ulessequals'(X0,'v$uxb'('c$uplus'(X0,X1,'tc$unat')),'tc$unat'),
inference(resolution,[status(thm)],[c5,c0]) ).
cnf(d1,plain,
'c$ulessequals'(X0,'v$uxb'('c$uplus'(X1,X0,'tc$unat')),'tc$unat'),
inference(resolution,[status(thm)],[c4,c0]) ).
cnf(d2,plain,
( ~ 'c$ulessequals'('v$uxa','v$uxb'(X0),'tc$unat')
| 'c$uin'('c$uMessage$uOmsg$uONonce'('v$uxb'(X0)),'c$uMessage$uOparts'('c$uinsert'('v$umsg1','c$uemptyset','tc$uMessage$uOmsg')),'tc$uMessage$uOmsg') ),
inference(resolution,[status(thm)],[c3,c2]) ).
cnf(d3,plain,
( ~ 'c$ulessequals'('v$ux','v$uxb'(X0),'tc$unat')
| ~ 'c$ulessequals'('v$uxa','v$uxb'(X0),'tc$unat') ),
inference(resolution,[status(thm)],[d2,c1]) ).
cnf(d4,plain,
~ 'c$ulessequals'('v$ux','v$uxb'('c$uplus'(X0,'v$uxa','tc$unat')),'tc$unat'),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[d4,d0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV255-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n018.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sat Sep 26 13:25:36 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.00/2.26 % SZS status Unsatisfiable for theBenchmark.p
% 13.00/2.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------