%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWW391+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 09:11:48 AM UTC 2026
% Result : Theorem 16.20s 14.40s
% Output : CNFRefutation 16.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 9 unt; 0 def)
% Number of atoms : 38 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 31 ( 11 ~; 12 |; 2 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 10 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn 8 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_0,hypothesis,
'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('t$ua','v$uG',hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),hAPP(hAPP(hAPP('c$uHoare$u$uMirabelle$uOtriple$uOtriple'('t$ua'),'v$uP'),'v$uc'),'v$uQ')),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua'),'tc$uHOL$uObool')))) ).
fof(conj_1,hypothesis,
'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('t$ua','v$uG',hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),hAPP(hAPP(hAPP('c$uHoare$u$uMirabelle$uOtriple$uOtriple'('t$ua'),'v$uP$uH'),'v$uc'),'v$uQ$uH')),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua'),'tc$uHOL$uObool')))) ).
fof(conj_2,conjecture,
! [X0,X1] :
( ( hBOOL(hAPP(hAPP('v$uP$uH',X0),X1))
| hBOOL(hAPP(hAPP('v$uP',X0),X1)) )
=> ? [X2,X3] :
( ! [X4] :
( ! [X5] :
( hBOOL(hAPP(hAPP(X2,X5),X1))
=> hBOOL(hAPP(hAPP(X3,X5),X4)) )
=> ( hBOOL(hAPP(hAPP('v$uQ$uH',X0),X4))
| hBOOL(hAPP(hAPP('v$uQ',X0),X4)) ) )
& 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('t$ua','v$uG',hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),hAPP(hAPP(hAPP('c$uHoare$u$uMirabelle$uOtriple$uOtriple'('t$ua'),X2),'v$uc'),X3)),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua'),'tc$uHOL$uObool')))) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( ( hBOOL(hAPP(hAPP('v$uP$uH',X0),X1))
| hBOOL(hAPP(hAPP('v$uP',X0),X1)) )
=> ? [X2,X3] :
( ! [X4] :
( ! [X5] :
( hBOOL(hAPP(hAPP(X2,X5),X1))
=> hBOOL(hAPP(hAPP(X3,X5),X4)) )
=> ( hBOOL(hAPP(hAPP('v$uQ$uH',X0),X4))
| hBOOL(hAPP(hAPP('v$uQ',X0),X4)) ) )
& 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('t$ua','v$uG',hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),hAPP(hAPP(hAPP('c$uHoare$u$uMirabelle$uOtriple$uOtriple'('t$ua'),X2),'v$uc'),X3)),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua'),'tc$uHOL$uObool')))) ) ),
inference(negate_conjecture,[status(cth)],[conj_2]) ).
cnf(c143,plain,
'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('t$ua','v$uG',hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),hAPP(hAPP(hAPP('c$uHoare$u$uMirabelle$uOtriple$uOtriple'('t$ua'),'v$uP'),'v$uc'),'v$uQ')),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua'),'tc$uHOL$uObool')))),
inference(clausification,[status(esa)],[conj_0]) ).
cnf(c144,plain,
'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('t$ua','v$uG',hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),hAPP(hAPP(hAPP('c$uHoare$u$uMirabelle$uOtriple$uOtriple'('t$ua'),'v$uP$uH'),'v$uc'),'v$uQ$uH')),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua'),'tc$uHOL$uObool')))),
inference(clausification,[status(esa)],[conj_1]) ).
cnf(c145,plain,
( hBOOL(hAPP(hAPP('v$uP$uH',sK305),sK306))
| hBOOL(hAPP(hAPP('v$uP',sK305),sK306)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c146,plain,
( hBOOL(hAPP(hAPP(X1,X2),sK309(X0,X1)))
| ~ hBOOL(hAPP(hAPP(X0,X2),sK306))
| ~ 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('t$ua','v$uG',hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),hAPP(hAPP(hAPP('c$uHoare$u$uMirabelle$uOtriple$uOtriple'('t$ua'),X0),'v$uc'),X1)),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua'),'tc$uHOL$uObool')))) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c147,plain,
( ~ hBOOL(hAPP(hAPP('v$uQ$uH',sK305),sK309(X0,X1)))
| ~ 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('t$ua','v$uG',hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),hAPP(hAPP(hAPP('c$uHoare$u$uMirabelle$uOtriple$uOtriple'('t$ua'),X0),'v$uc'),X1)),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua'),'tc$uHOL$uObool')))) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c148,plain,
( ~ hBOOL(hAPP(hAPP('v$uQ',sK305),sK309(X0,X1)))
| ~ 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('t$ua','v$uG',hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),hAPP(hAPP(hAPP('c$uHoare$u$uMirabelle$uOtriple$uOtriple'('t$ua'),X0),'v$uc'),X1)),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua'),'tc$uHOL$uObool')))) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ hBOOL(hAPP(hAPP('v$uP$uH',X0),sK306))
| hBOOL(hAPP(hAPP('v$uQ$uH',X0),sK309('v$uP$uH','v$uQ$uH'))) ),
inference(resolution,[status(thm)],[c144,c146]) ).
cnf(d1,plain,
( ~ hBOOL(hAPP(hAPP('v$uP',X0),sK306))
| hBOOL(hAPP(hAPP('v$uQ',X0),sK309('v$uP','v$uQ'))) ),
inference(resolution,[status(thm)],[c143,c146]) ).
cnf(d2,plain,
( hBOOL(hAPP(hAPP('v$uP$uH',sK305),sK306))
| hBOOL(hAPP(hAPP('v$uQ',sK305),sK309('v$uP','v$uQ'))) ),
inference(resolution,[status(thm)],[d1,c145]) ).
cnf(d3,plain,
~ hBOOL(hAPP(hAPP('v$uQ',sK305),sK309('v$uP','v$uQ'))),
inference(resolution,[status(thm)],[c143,c148]) ).
cnf(d4,plain,
hBOOL(hAPP(hAPP('v$uP$uH',sK305),sK306)),
inference(resolution,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
hBOOL(hAPP(hAPP('v$uQ$uH',sK305),sK309('v$uP$uH','v$uQ$uH'))),
inference(resolution,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
~ hBOOL(hAPP(hAPP('v$uQ$uH',sK305),sK309('v$uP$uH','v$uQ$uH'))),
inference(resolution,[status(thm)],[c144,c147]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[d6,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW391+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n005.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 15:48:03 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.20/14.40 % SZS status Theorem for theBenchmark.p
% 16.20/14.40 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------