%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWW338+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 : n012.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 13.34s 11.88s
% Output : CNFRefutation 13.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 8 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 48 ( 13 ~; 22 |; 0 &)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 41 ( 3 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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$uH'))
=> 'c$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(conj_3,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$uG$uH'))
=> 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,X1) ) ) ).
fof(conj_4,conjecture,
! [X0] :
( ! [X1] :
( hBOOL(hAPP(hAPP('c$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$ua',X0,X1) ) ),
inference(negate_conjecture,[status(cth)],[conj_4]) ).
cnf(c31,plain,
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(hAPP(hAPP('c$umember'(X0),X1),X2)) ),
inference(clausification,[status(esa)],[fact_mem__def]) ).
cnf(c32,plain,
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(hAPP('c$umember'(X0),X1),X2)) ),
inference(clausification,[status(esa)],[fact_mem__def]) ).
cnf(c45,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,X1)
| ~ hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),X1),'v$uts'))
| hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK117(X0)),'v$uG$uH')) ),
inference(clausification,[status(esa)],[conj_1]) ).
cnf(c46,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,X1)
| ~ hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),X1),'v$uts'))
| ~ 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,sK117(X0)) ),
inference(clausification,[status(esa)],[conj_1]) ).
cnf(c48,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,X1)
| ~ hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),X1),'v$uG$uH'))
| hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK120(X0)),'v$uG')) ),
inference(clausification,[status(esa)],[conj_3]) ).
cnf(c49,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,X1)
| ~ hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),X1),'v$uG$uH'))
| ~ 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,sK120(X0)) ),
inference(clausification,[status(esa)],[conj_3]) ).
cnf(c50,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK122,X0)
| ~ hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),X0),'v$uG')) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c51,plain,
hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK124),'v$uts')),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c52,plain,
~ 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK122,sK124),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
hBOOL(hAPP('v$uts',sK124)),
inference(resolution,[status(thm)],[c31,c51]) ).
cnf(d1,plain,
hBOOL(hAPP(hAPP('c$umember'(X0),sK124),'v$uts')),
inference(resolution,[status(thm)],[c32,d0]) ).
cnf(d2,plain,
( ~ 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,sK117(X0))
| 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,sK124) ),
inference(resolution,[status(thm)],[c46,d1]) ).
cnf(d3,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,sK124)
| hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK117(X0)),'v$uG$uH')) ),
inference(resolution,[status(thm)],[c45,d1]) ).
cnf(d4,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X1,sK124)
| ~ 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,sK120(X0))
| 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,sK117(X1)) ),
inference(resolution,[status(thm)],[c49,d3]) ).
cnf(d5,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X1,sK117(X0))
| hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK120(X1)),'v$uG'))
| 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,sK124) ),
inference(resolution,[status(thm)],[d3,c48]) ).
cnf(d6,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK122,sK120(X0))
| 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X1,sK124)
| 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,sK117(X1)) ),
inference(resolution,[status(thm)],[d5,c50]) ).
cnf(d7,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK122,sK120(X0))
| 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,sK117(sK122)) ),
inference(resolution,[status(thm)],[d6,c52]) ).
cnf(d8,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK122,sK124)
| 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK122,sK120(sK122)) ),
inference(resolution,[status(thm)],[d7,d2]) ).
cnf(d9,plain,
'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK122,sK120(sK122)),
inference(resolution,[status(thm)],[c52,d8]) ).
cnf(d10,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK122,sK117(X0))
| 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,sK124) ),
inference(resolution,[status(thm)],[d9,d4]) ).
cnf(d11,plain,
'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK122,sK117(sK122)),
inference(resolution,[status(thm)],[d10,c52]) ).
cnf(d12,plain,
'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK122,sK124),
inference(resolution,[status(thm)],[d11,d2]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[c52,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWW338+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/5.31 % Computer : n012.cluster.edu
% 0.04/5.31 % Model : x86_64 x86_64
% 0.04/5.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/5.31 % Memory : 8046.5625MB
% 0.04/5.31 % OS : Linux 6.8.0-71-generic
% 0.04/5.31 % CPULimit : 300
% 0.04/5.31 % WCLimit : 300
% 0.04/5.31 % DateTime : Sat Sep 26 15:42:09 UTC 2026
% 0.04/5.31 % CPUTime :
% 0.04/5.31 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.34/11.88 % SZS status Theorem for theBenchmark.p
% 13.34/11.88 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------