%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWW339+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 : n026.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 09:11:43 AM UTC 2026
% Result : Theorem 61.05s 14.81s
% Output : CNFRefutation 61.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 10 unt; 0 def)
% Number of atoms : 50 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 37 ( 12 ~; 13 |; 0 &)
% ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 36 ( 3 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_subsetD,axiom,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'(X3,'tc$uHOL$uObool')),X2),X1))
=> ( hBOOL(hAPP(hAPP('c$umember'(X3),X0),X2))
=> hBOOL(hAPP(hAPP('c$umember'(X3),X0),X1)) ) ) ).
fof(fact_mem__def,axiom,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP('c$umember'(X2),X1),X0))
<=> hBOOL(hAPP(X0,X1)) ) ).
fof(conj_1,hypothesis,
! [X0] :
( ! [X1] :
( hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),X1),'v$uG'))
=> 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,X1) )
=> ! [X1] :
( hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),X1),'v$uts$uH'))
=> 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,X1) ) ) ).
fof(conj_2,hypothesis,
hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua'),'tc$uHOL$uObool')),'v$uts'),'v$uts$uH')) ).
fof(conj_3,conjecture,
! [X0] :
( ! [X1] :
( hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),X1),'v$uG'))
=> 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,X1) )
=> ! [X1] :
( hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),X1),'v$uts'))
=> 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,X1) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ! [X1] :
( hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),X1),'v$uG'))
=> 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,X1) )
=> ! [X1] :
( hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),X1),'v$uts'))
=> 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,X1) ) ),
inference(negate_conjecture,[status(cth)],[conj_3]) ).
cnf(c13,plain,
( ~ hBOOL(hAPP(hAPP('c$umember'(X0),X3),X1))
| hBOOL(hAPP(hAPP('c$umember'(X0),X3),X2))
| ~ hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'(X0,'tc$uHOL$uObool')),X1),X2)) ),
inference(clausification,[status(esa)],[fact_subsetD]) ).
cnf(c19,plain,
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(hAPP(hAPP('c$umember'(X0),X1),X2)) ),
inference(clausification,[status(esa)],[fact_mem__def]) ).
cnf(c20,plain,
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(hAPP('c$umember'(X0),X1),X2)) ),
inference(clausification,[status(esa)],[fact_mem__def]) ).
cnf(c30,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,X1)
| ~ hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),X1),'v$uts$uH'))
| hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK75(X0)),'v$uG')) ),
inference(clausification,[status(esa)],[conj_1]) ).
cnf(c31,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,X1)
| ~ hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),X1),'v$uts$uH'))
| ~ 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,sK75(X0)) ),
inference(clausification,[status(esa)],[conj_1]) ).
cnf(c32,plain,
hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua'),'tc$uHOL$uObool')),'v$uts'),'v$uts$uH')),
inference(clausification,[status(esa)],[conj_2]) ).
cnf(c33,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK77,X0)
| ~ hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),X0),'v$uG')) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c34,plain,
hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK79),'v$uts')),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c35,plain,
~ 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK77,sK79),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
hBOOL(hAPP('v$uts',sK79)),
inference(resolution,[status(thm)],[c19,c34]) ).
cnf(d1,plain,
hBOOL(hAPP(hAPP('c$umember'(X0),sK79),'v$uts')),
inference(resolution,[status(thm)],[c20,d0]) ).
cnf(d2,plain,
( ~ hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),X0),'v$uts'))
| hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),X0),'v$uts$uH')) ),
inference(resolution,[status(thm)],[c32,c13]) ).
cnf(d3,plain,
hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK79),'v$uts$uH')),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
( ~ 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,sK75(X0))
| 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,sK79) ),
inference(resolution,[status(thm)],[d3,c31]) ).
cnf(d5,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,sK79)
| hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK75(X0)),'v$uG')) ),
inference(resolution,[status(thm)],[d3,c30]) ).
cnf(d6,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK77,sK75(X0))
| 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,sK79) ),
inference(resolution,[status(thm)],[d5,c33]) ).
cnf(d7,plain,
'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK77,sK75(sK77)),
inference(resolution,[status(thm)],[d6,c35]) ).
cnf(d8,plain,
'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK77,sK79),
inference(resolution,[status(thm)],[d7,d4]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[c35,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW339+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
% 0.11/0.39 % Computer : n026.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sat Sep 26 15:44:43 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 61.05/14.81 % SZS status Theorem for theBenchmark.p
% 61.05/14.81 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------