%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWV284-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 09:01:53 AM UTC 2026
% Result : Unsatisfiable 10.08s 2.01s
% Output : CNFRefutation 10.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 19 ( 7 unt; 2 nHn; 12 RR)
% Number of literals : 31 ( 0 equ; 16 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 32 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
'c$ulessequals'(X0,'v$ux'(X0),'tc$unat') ).
cnf(cls_conjecture_1,negated_conjecture,
( ~ 'c$ulessequals'('v$uN',X0,'tc$unat')
| ~ 'c$uin'('c$uMessage$uOmsg$uONonce'(X0),'c$uEvent$uOused'('v$ulist'),'tc$uMessage$uOmsg') ) ).
cnf(cls_conjecture_2,negated_conjecture,
( 'c$uin'('c$uMessage$uOmsg$uONonce'('v$ux'(X0)),'c$uMessage$uOparts'('c$uinsert'('v$umsg','c$uemptyset','tc$uMessage$uOmsg')),'tc$uMessage$uOmsg')
| 'c$uin'('c$uMessage$uOmsg$uONonce'('v$ux'(X0)),'c$uEvent$uOused'('v$ulist'),'tc$uMessage$uOmsg') ) ).
cnf(cls_Message_Omsg__Nonce__supply_0,axiom,
( ~ 'c$ulessequals'('v$usko$u$uupX'(X1),X0,'tc$unat')
| ~ 'c$uin'('c$uMessage$uOmsg$uONonce'(X0),'c$uMessage$uOparts'('c$uinsert'(X1,'c$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$ulessequals'(X0,'v$ux'(X0),'tc$unat'),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c1,plain,
( ~ 'c$ulessequals'('v$uN',X0,'tc$unat')
| ~ 'c$uin'('c$uMessage$uOmsg$uONonce'(X0),'c$uEvent$uOused'('v$ulist'),'tc$uMessage$uOmsg') ),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c2,plain,
( 'c$uin'('c$uMessage$uOmsg$uONonce'('v$ux'(X0)),'c$uMessage$uOparts'('c$uinsert'('v$umsg','c$uemptyset','tc$uMessage$uOmsg')),'tc$uMessage$uOmsg')
| 'c$uin'('c$uMessage$uOmsg$uONonce'('v$ux'(X0)),'c$uEvent$uOused'('v$ulist'),'tc$uMessage$uOmsg') ),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c3,plain,
( ~ 'c$ulessequals'('v$usko$u$uupX'(X1),X0,'tc$unat')
| ~ 'c$uin'('c$uMessage$uOmsg$uONonce'(X0),'c$uMessage$uOparts'('c$uinsert'(X1,'c$uemptyset','tc$uMessage$uOmsg')),'tc$uMessage$uOmsg') ),
inference(clausification,[status(esa)],[cls_Message_Omsg__Nonce__supply_0]) ).
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$ulessequals'(X0,'v$ux'('c$uplus'(X0,X1,'tc$unat')),'tc$unat'),
inference(resolution,[status(thm)],[c5,c0]) ).
cnf(d1,plain,
'c$ulessequals'(X0,'v$ux'('c$uplus'('c$uplus'(X1,X0,'tc$unat'),X2,'tc$unat')),'tc$unat'),
inference(resolution,[status(thm)],[d0,c4]) ).
cnf(d2,plain,
'c$ulessequals'(X0,'v$ux'('c$uplus'(X1,X0,'tc$unat')),'tc$unat'),
inference(resolution,[status(thm)],[c4,c0]) ).
cnf(d3,plain,
( 'c$uin'('c$uMessage$uOmsg$uONonce'('v$ux'(X0)),'c$uEvent$uOused'('v$ulist'),'tc$uMessage$uOmsg')
| ~ 'c$ulessequals'('v$usko$u$uupX'('v$umsg'),'v$ux'(X0),'tc$unat') ),
inference(resolution,[status(thm)],[c3,c2]) ).
cnf(d4,plain,
( ~ 'c$ulessequals'('v$uN','v$ux'(X0),'tc$unat')
| ~ 'c$ulessequals'('v$usko$u$uupX'('v$umsg'),'v$ux'(X0),'tc$unat') ),
inference(resolution,[status(thm)],[d3,c1]) ).
cnf(d5,plain,
~ 'c$ulessequals'('v$uN','v$ux'('c$uplus'(X0,'v$usko$u$uupX'('v$umsg'),'tc$unat')),'tc$unat'),
inference(resolution,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[d5,d1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV284-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n004.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 13:27:21 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.08/2.01 % SZS status Unsatisfiable for theBenchmark.p
% 10.08/2.01 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------