%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWW298+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 09:11:39 AM UTC 2026
% Result : Theorem 69.66s 12.42s
% Output : CNFRefutation 69.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 7 unt; 0 def)
% Number of atoms : 25 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 6 ~; 4 |; 0 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 20 ( 3 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_triple__valid__Suc,axiom,
! [X0,X1,X2] :
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'(X2,hAPP('c$uNat$uOSuc',X1),X0)
=> 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'(X2,X1,X0) ) ).
fof(fact_mem__def,axiom,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP('c$umember'(X2),X1),X0))
<=> hBOOL(hAPP(X0,X1)) ) ).
fof(conj_0,hypothesis,
! [X0] :
( hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),X0),'v$uts'))
=> 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',hAPP('c$uNat$uOSuc','v$un'),X0) ) ).
fof(conj_1,conjecture,
! [X0] :
( hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),X0),'v$uts'))
=> 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua','v$un',X0) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),X0),'v$uts'))
=> 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua','v$un',X0) ),
inference(negate_conjecture,[status(cth)],[conj_1]) ).
cnf(c1,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'(X0,X1,X2)
| ~ 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'(X0,hAPP('c$uNat$uOSuc',X1),X2) ),
inference(clausification,[status(esa)],[fact_triple__valid__Suc]) ).
cnf(c7,plain,
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(hAPP(hAPP('c$umember'(X0),X1),X2)) ),
inference(clausification,[status(esa)],[fact_mem__def]) ).
cnf(c8,plain,
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(hAPP('c$umember'(X0),X1),X2)) ),
inference(clausification,[status(esa)],[fact_mem__def]) ).
cnf(c19,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',hAPP('c$uNat$uOSuc','v$un'),X0)
| ~ hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),X0),'v$uts')) ),
inference(clausification,[status(esa)],[conj_0]) ).
cnf(c20,plain,
hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK47),'v$uts')),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c21,plain,
~ 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua','v$un',sK47),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
hBOOL(hAPP('v$uts',sK47)),
inference(resolution,[status(thm)],[c7,c20]) ).
cnf(d1,plain,
hBOOL(hAPP(hAPP('c$umember'(X0),sK47),'v$uts')),
inference(resolution,[status(thm)],[d0,c8]) ).
cnf(d2,plain,
'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',hAPP('c$uNat$uOSuc','v$un'),sK47),
inference(resolution,[status(thm)],[c19,d1]) ).
cnf(d3,plain,
'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua','v$un',sK47),
inference(resolution,[status(thm)],[d2,c1]) ).
cnf(d4,plain,
$false,
inference(resolution,[status(thm)],[c21,d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW298+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.79 % Computer : n002.cluster.edu
% 0.11/0.79 % Model : x86_64 x86_64
% 0.11/0.79 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.79 % Memory : 8046.5625MB
% 0.11/0.79 % OS : Linux 6.8.0-71-generic
% 0.11/0.79 % CPULimit : 300
% 0.11/0.79 % WCLimit : 300
% 0.11/0.79 % DateTime : Sat Sep 26 15:40:08 UTC 2026
% 0.11/0.79 % CPUTime :
% 0.11/0.79 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 69.66/12.42 % SZS status Theorem for theBenchmark.p
% 69.66/12.42 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------