%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWW355+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 : 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 09:11:45 AM UTC 2026
% Result : Theorem 136.80s 33.74s
% Output : CNFRefutation 136.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 14 unt; 0 def)
% Number of atoms : 38 ( 5 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 25 ( 11 ~; 11 |; 0 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-2 aty)
% Number of variables : 56 ( 7 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_hoare__derivs_OSkip,axiom,
! [X0,X1,X2] : 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'(X2,X1,hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'(X2)),hAPP(hAPP(hAPP('c$uHoare$u$uMirabelle$uOtriple$uOtriple'(X2),X0),'c$uCom$uOcom$uOSKIP'),X0)),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'(X2),'tc$uHOL$uObool')))) ).
fof(fact_evalc_OSkip,axiom,
! [X0] : hBOOL(hAPP(hAPP('c$uNatural$uOevalc'('c$uCom$uOcom$uOSKIP'),X0),X0)) ).
fof(fact_conseq1,axiom,
! [X0,X1,X2,X3,X4,X5] :
( 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'(X5,X4,hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'(X5)),hAPP(hAPP(hAPP('c$uHoare$u$uMirabelle$uOtriple$uOtriple'(X5),X3),X2),X1)),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'(X5),'tc$uHOL$uObool'))))
=> ( ! [X6,X7] :
( hBOOL(hAPP(hAPP(X0,X6),X7))
=> hBOOL(hAPP(hAPP(X3,X6),X7)) )
=> 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'(X5,X4,hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'(X5)),hAPP(hAPP(hAPP('c$uHoare$u$uMirabelle$uOtriple$uOtriple'(X5),X0),X2),X1)),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'(X5),'tc$uHOL$uObool')))) ) ) ).
fof(fact_singleton__conv2,axiom,
! [X0,X1] : hAPP('c$uSet$uOCollect'(X1),hAPP('c$ufequal',X0)) = hAPP(hAPP('c$uSet$uOinsert'(X1),X0),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X1,'tc$uHOL$uObool'))) ).
fof(help_c__fequal__1,axiom,
! [X0,X1] :
( X1 = X0
| ~ hBOOL(hAPP(hAPP('c$ufequal',X1),X0)) ) ).
fof(conj_2,conjecture,
'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('tc$uCom$uOstate','v$uG',hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate')),hAPP(hAPP(hAPP('c$uHoare$u$uMirabelle$uOtriple$uOtriple'('tc$uCom$uOstate'),'c$ufequal'),'c$uCom$uOcom$uOSKIP'),'c$uNatural$uOevalc'('c$uCom$uOcom$uOSKIP'))),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate'),'tc$uHOL$uObool')))) ).
fof(negated_conjecture,negated_conjecture,
~ 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('tc$uCom$uOstate','v$uG',hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate')),hAPP(hAPP(hAPP('c$uHoare$u$uMirabelle$uOtriple$uOtriple'('tc$uCom$uOstate'),'c$ufequal'),'c$uCom$uOcom$uOSKIP'),'c$uNatural$uOevalc'('c$uCom$uOcom$uOSKIP'))),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate'),'tc$uHOL$uObool')))),
inference(negate_conjecture,[status(cth)],[conj_2]) ).
cnf(c2,plain,
'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'(X0,X1,hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'(X0)),hAPP(hAPP(hAPP('c$uHoare$u$uMirabelle$uOtriple$uOtriple'(X0),X2),'c$uCom$uOcom$uOSKIP'),X2)),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'(X0),'tc$uHOL$uObool')))),
inference(clausification,[status(esa)],[fact_hoare__derivs_OSkip]) ).
cnf(c13,plain,
hBOOL(hAPP(hAPP('c$uNatural$uOevalc'('c$uCom$uOcom$uOSKIP'),X0),X0)),
inference(clausification,[status(esa)],[fact_evalc_OSkip]) ).
cnf(c30,plain,
( hBOOL(hAPP(hAPP(X5,sK69(X5,X2)),sK70(X5,X2)))
| 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'(X0,X1,hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'(X0)),hAPP(hAPP(hAPP('c$uHoare$u$uMirabelle$uOtriple$uOtriple'(X0),X5),X3),X4)),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'(X0),'tc$uHOL$uObool'))))
| ~ 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'(X0,X1,hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'(X0)),hAPP(hAPP(hAPP('c$uHoare$u$uMirabelle$uOtriple$uOtriple'(X0),X2),X3),X4)),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'(X0),'tc$uHOL$uObool')))) ),
inference(clausification,[status(esa)],[fact_conseq1]) ).
cnf(c31,plain,
( ~ hBOOL(hAPP(hAPP(X2,sK69(X5,X2)),sK70(X5,X2)))
| 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'(X0,X1,hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'(X0)),hAPP(hAPP(hAPP('c$uHoare$u$uMirabelle$uOtriple$uOtriple'(X0),X5),X3),X4)),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'(X0),'tc$uHOL$uObool'))))
| ~ 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'(X0,X1,hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'(X0)),hAPP(hAPP(hAPP('c$uHoare$u$uMirabelle$uOtriple$uOtriple'(X0),X2),X3),X4)),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'(X0),'tc$uHOL$uObool')))) ),
inference(clausification,[status(esa)],[fact_conseq1]) ).
cnf(c202,plain,
hAPP(hAPP('c$uSet$uOinsert'(X0),X1),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X0,'tc$uHOL$uObool'))) = hAPP('c$uSet$uOCollect'(X0),hAPP('c$ufequal',X1)),
inference(clausification,[status(esa)],[fact_singleton__conv2]) ).
cnf(c217,plain,
( X1 = X0
| ~ hBOOL(hAPP(hAPP('c$ufequal',X0),X1)) ),
inference(clausification,[status(esa)],[help_c__fequal__1]) ).
cnf(c220,plain,
~ 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('tc$uCom$uOstate','v$uG',hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate')),hAPP(hAPP(hAPP('c$uHoare$u$uMirabelle$uOtriple$uOtriple'('tc$uCom$uOstate'),'c$ufequal'),'c$uCom$uOcom$uOSKIP'),'c$uNatural$uOevalc'('c$uCom$uOcom$uOSKIP'))),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate'),'tc$uHOL$uObool')))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
~ 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('tc$uCom$uOstate','v$uG',hAPP('c$uSet$uOCollect'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate')),hAPP('c$ufequal',hAPP(hAPP(hAPP('c$uHoare$u$uMirabelle$uOtriple$uOtriple'('tc$uCom$uOstate'),'c$ufequal'),'c$uCom$uOcom$uOSKIP'),'c$uNatural$uOevalc'('c$uCom$uOcom$uOSKIP'))))),
inference(demodulation,[status(thm)],[c220,c202]) ).
cnf(d1,plain,
( ~ hBOOL(hAPP(hAPP(X3,sK69(X2,X3)),sK70(X2,X3)))
| 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'(X0,X1,hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'(X0)),hAPP(hAPP(hAPP('c$uHoare$u$uMirabelle$uOtriple$uOtriple'(X0),X2),'c$uCom$uOcom$uOSKIP'),X3)),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'(X0),'tc$uHOL$uObool')))) ),
inference(resolution,[status(thm)],[c31,c2]) ).
cnf(d2,plain,
( ~ hBOOL(hAPP(hAPP(X2,sK69(X1,X2)),sK70(X1,X2)))
| 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'(X0,X3,hAPP('c$uSet$uOCollect'('tc$uHoare$u$uMirabelle$uOtriple'(X0)),hAPP('c$ufequal',hAPP(hAPP(hAPP('c$uHoare$u$uMirabelle$uOtriple$uOtriple'(X0),X1),'c$uCom$uOcom$uOSKIP'),X2)))) ),
inference(demodulation,[status(thm)],[d1,c202]) ).
cnf(d3,plain,
( hBOOL(hAPP(hAPP(X2,sK69(X2,X3)),sK70(X2,X3)))
| 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'(X0,X1,hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'(X0)),hAPP(hAPP(hAPP('c$uHoare$u$uMirabelle$uOtriple$uOtriple'(X0),X2),'c$uCom$uOcom$uOSKIP'),X3)),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'(X0),'tc$uHOL$uObool')))) ),
inference(resolution,[status(thm)],[c30,c2]) ).
cnf(d4,plain,
( hBOOL(hAPP(hAPP(X1,sK69(X1,X2)),sK70(X1,X2)))
| 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'(X0,X3,hAPP('c$uSet$uOCollect'('tc$uHoare$u$uMirabelle$uOtriple'(X0)),hAPP('c$ufequal',hAPP(hAPP(hAPP('c$uHoare$u$uMirabelle$uOtriple$uOtriple'(X0),X1),'c$uCom$uOcom$uOSKIP'),X2)))) ),
inference(demodulation,[status(thm)],[d3,c202]) ).
cnf(d5,plain,
hBOOL(hAPP(hAPP('c$ufequal',sK69('c$ufequal','c$uNatural$uOevalc'('c$uCom$uOcom$uOSKIP'))),sK70('c$ufequal','c$uNatural$uOevalc'('c$uCom$uOcom$uOSKIP')))),
inference(resolution,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
sK70('c$ufequal','c$uNatural$uOevalc'('c$uCom$uOcom$uOSKIP')) = sK69('c$ufequal','c$uNatural$uOevalc'('c$uCom$uOcom$uOSKIP')),
inference(resolution,[status(thm)],[d5,c217]) ).
cnf(d7,plain,
( 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'(X0,X1,hAPP('c$uSet$uOCollect'('tc$uHoare$u$uMirabelle$uOtriple'(X0)),hAPP('c$ufequal',hAPP(hAPP(hAPP('c$uHoare$u$uMirabelle$uOtriple$uOtriple'(X0),'c$ufequal'),'c$uCom$uOcom$uOSKIP'),'c$uNatural$uOevalc'('c$uCom$uOcom$uOSKIP')))))
| ~ hBOOL(hAPP(hAPP('c$uNatural$uOevalc'('c$uCom$uOcom$uOSKIP'),sK69('c$ufequal','c$uNatural$uOevalc'('c$uCom$uOcom$uOSKIP'))),sK69('c$ufequal','c$uNatural$uOevalc'('c$uCom$uOcom$uOSKIP')))) ),
inference(superposition,[status(thm)],[d6,d2]) ).
cnf(d8,plain,
'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'(X0,X1,hAPP('c$uSet$uOCollect'('tc$uHoare$u$uMirabelle$uOtriple'(X0)),hAPP('c$ufequal',hAPP(hAPP(hAPP('c$uHoare$u$uMirabelle$uOtriple$uOtriple'(X0),'c$ufequal'),'c$uCom$uOcom$uOSKIP'),'c$uNatural$uOevalc'('c$uCom$uOcom$uOSKIP'))))),
inference(resolution,[status(thm)],[c13,d7]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[d8,d0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW355+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.39 % Computer : n004.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Sat Sep 26 15:44:14 UTC 2026
% 0.11/5.40 % CPUTime :
% 0.11/5.40 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 136.80/33.74 % SZS status Theorem for theBenchmark.p
% 136.80/33.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------