%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWW328+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 : n009.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 09:11:42 AM UTC 2026
% Result : Theorem 39.36s 13.65s
% Output : CNFRefutation 39.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 52 ( 14 unt; 0 def)
% Number of atoms : 151 ( 19 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 170 ( 71 ~; 77 |; 6 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 17 ( 17 usr; 12 con; 0-2 aty)
% Number of variables : 50 ( 11 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_0,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) )
=> ! [X2,X3] :
( ( hBOOL(hAPP('v$ub',X3))
& 'v$uP'(X2,X3) )
=> ! [X4] :
( 'c$uNatural$uOevaln'('v$uc',X3,X0,X4)
=> 'v$uP'(X2,X4) ) ) ) ).
fof(conj_1,hypothesis,
hBOOL(hAPP('v$uba','v$us0')) ).
fof(conj_2,hypothesis,
'c$uNatural$uOevaln'('v$uca','v$us0','v$una','v$us1') ).
fof(conj_5,hypothesis,
( 'c$uCom$uOcom$uOWhile'('v$uba','v$uca') = 'c$uCom$uOcom$uOWhile'('v$ub','v$uc')
=> ( ! [X0] :
( hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),X0),'v$uG'))
=> 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua','v$una',X0) )
=> ! [X1] :
( 'v$uP'(X1,'v$us1')
=> ( ~ hBOOL(hAPP('v$ub','v$us2'))
& 'v$uP'(X1,'v$us2') ) ) ) ) ).
fof(conj_6,conjecture,
( ( 'v$uca' = 'v$uc'
& 'v$uba' = 'v$ub' )
=> ( ! [X0] :
( hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),X0),'v$uG'))
=> 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua','v$una',X0) )
=> ! [X1] :
( 'v$uP'(X1,'v$us0')
=> ( ~ hBOOL(hAPP('v$ub','v$us2'))
& 'v$uP'(X1,'v$us2') ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( ( 'v$uca' = 'v$uc'
& 'v$uba' = 'v$ub' )
=> ( ! [X0] :
( hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),X0),'v$uG'))
=> 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua','v$una',X0) )
=> ! [X1] :
( 'v$uP'(X1,'v$us0')
=> ( ~ hBOOL(hAPP('v$ub','v$us2'))
& 'v$uP'(X1,'v$us2') ) ) ) ),
inference(negate_conjecture,[status(cth)],[conj_6]) ).
cnf(c43,plain,
( ~ hBOOL(hAPP('v$ub',X2))
| ~ 'v$uP'(X0,X2)
| hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK127(X3)),'v$uG'))
| ~ 'c$uNatural$uOevaln'('v$uc',X2,X3,X1)
| 'v$uP'(X0,X1) ),
inference(clausification,[status(esa)],[conj_0]) ).
cnf(c44,plain,
( ~ hBOOL(hAPP('v$ub',X2))
| ~ 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X3,sK127(X3))
| ~ 'v$uP'(X0,X2)
| ~ 'c$uNatural$uOevaln'('v$uc',X2,X3,X1)
| 'v$uP'(X0,X1) ),
inference(clausification,[status(esa)],[conj_0]) ).
cnf(c45,plain,
hBOOL(hAPP('v$uba','v$us0')),
inference(clausification,[status(esa)],[conj_1]) ).
cnf(c46,plain,
'c$uNatural$uOevaln'('v$uca','v$us0','v$una','v$us1'),
inference(clausification,[status(esa)],[conj_2]) ).
cnf(c52,plain,
( hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK134),'v$uG'))
| 'v$uP'(X0,'v$us2')
| ~ 'v$uP'(X0,'v$us1')
| 'c$uCom$uOcom$uOWhile'('v$uba','v$uca') != 'c$uCom$uOcom$uOWhile'('v$ub','v$uc') ),
inference(clausification,[status(esa)],[conj_5]) ).
cnf(c53,plain,
( ~ 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua','v$una',sK134)
| 'v$uP'(X0,'v$us2')
| ~ 'v$uP'(X0,'v$us1')
| 'c$uCom$uOcom$uOWhile'('v$uba','v$uca') != 'c$uCom$uOcom$uOWhile'('v$ub','v$uc') ),
inference(clausification,[status(esa)],[conj_5]) ).
cnf(c54,plain,
( hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK134),'v$uG'))
| ~ hBOOL(hAPP('v$ub','v$us2'))
| ~ 'v$uP'(X0,'v$us1')
| 'c$uCom$uOcom$uOWhile'('v$uba','v$uca') != 'c$uCom$uOcom$uOWhile'('v$ub','v$uc') ),
inference(clausification,[status(esa)],[conj_5]) ).
cnf(c55,plain,
( ~ 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua','v$una',sK134)
| ~ hBOOL(hAPP('v$ub','v$us2'))
| ~ 'v$uP'(X0,'v$us1')
| 'c$uCom$uOcom$uOWhile'('v$uba','v$uca') != 'c$uCom$uOcom$uOWhile'('v$ub','v$uc') ),
inference(clausification,[status(esa)],[conj_5]) ).
cnf(c56,plain,
'v$uca' = 'v$uc',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c57,plain,
'v$uba' = 'v$ub',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c58,plain,
'v$uP'(sK135,'v$us0'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c59,plain,
( hBOOL(hAPP('v$ub','v$us2'))
| ~ 'v$uP'(sK135,'v$us2') ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c60,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua','v$una',X0)
| ~ hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),X0),'v$uG')) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'c$uNatural$uOevaln'('v$uc','v$us0','v$una','v$us1'),
inference(demodulation,[status(thm)],[c46,c56]) ).
cnf(d1,plain,
hBOOL(hAPP('v$ub','v$us0')),
inference(demodulation,[status(thm)],[c45,c57]) ).
cnf(d2,plain,
( ~ 'v$uP'(X2,'v$us0')
| 'v$uP'(X2,X1)
| ~ 'c$uNatural$uOevaln'('v$uc','v$us0',X0,X1)
| ~ 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,sK127(X0)) ),
inference(resolution,[status(thm)],[c44,d1]) ).
cnf(d3,plain,
( ~ 'v$uP'(X2,'v$us0')
| 'v$uP'(X2,X1)
| ~ 'c$uNatural$uOevaln'('v$uc','v$us0',X0,X1)
| hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK127(X0)),'v$uG')) ),
inference(resolution,[status(thm)],[c43,d1]) ).
cnf(d4,plain,
( ~ 'v$uP'(X0,'v$us0')
| 'v$uP'(X0,'v$us1')
| hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK127('v$una')),'v$uG')) ),
inference(resolution,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
( 'v$uP'(sK135,'v$us1')
| hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK127('v$una')),'v$uG')) ),
inference(resolution,[status(thm)],[d4,c58]) ).
cnf(d6,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua','v$una',sK127('v$una'))
| 'v$uP'(sK135,'v$us1') ),
inference(resolution,[status(thm)],[d5,c60]) ).
cnf(d7,plain,
( ~ 'v$uP'(X1,'v$us0')
| 'v$uP'(X1,X0)
| ~ 'c$uNatural$uOevaln'('v$uc','v$us0','v$una',X0)
| 'v$uP'(sK135,'v$us1') ),
inference(resolution,[status(thm)],[d6,d2]) ).
cnf(d8,plain,
( 'v$uP'(sK135,'v$us1')
| ~ 'v$uP'(X0,'v$us0')
| 'v$uP'(X0,'v$us1') ),
inference(resolution,[status(thm)],[d7,d0]) ).
cnf(d9,plain,
( 'v$uP'(sK135,'v$us1')
| 'v$uP'(sK135,'v$us1') ),
inference(resolution,[status(thm)],[d8,c58]) ).
cnf(d10,plain,
( ~ 'v$uP'(X0,'v$us1')
| ~ 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua','v$una',sK134)
| ~ hBOOL(hAPP('v$ub','v$us2'))
| 'c$uCom$uOcom$uOWhile'('v$ub','v$uca') != 'c$uCom$uOcom$uOWhile'('v$ub','v$uc') ),
inference(demodulation,[status(thm)],[c55,c57]) ).
cnf(d11,plain,
( ~ 'v$uP'(X0,'v$us1')
| ~ 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua','v$una',sK134)
| ~ hBOOL(hAPP('v$ub','v$us2'))
| 'c$uCom$uOcom$uOWhile'('v$ub','v$uc') != 'c$uCom$uOcom$uOWhile'('v$ub','v$uc') ),
inference(demodulation,[status(thm)],[d10,c56]) ).
cnf(d12,plain,
( ~ 'v$uP'(X0,'v$us1')
| ~ 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua','v$una',sK134)
| ~ hBOOL(hAPP('v$ub','v$us2')) ),
inference(equality_resolution,[status(thm)],[d11]) ).
cnf(d13,plain,
( 'v$uP'(X0,'v$us2')
| ~ 'v$uP'(X0,'v$us1')
| ~ 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua','v$una',sK134)
| 'c$uCom$uOcom$uOWhile'('v$ub','v$uca') != 'c$uCom$uOcom$uOWhile'('v$ub','v$uc') ),
inference(demodulation,[status(thm)],[c53,c57]) ).
cnf(d14,plain,
( 'v$uP'(X0,'v$us2')
| ~ 'v$uP'(X0,'v$us1')
| ~ 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua','v$una',sK134)
| 'c$uCom$uOcom$uOWhile'('v$ub','v$uc') != 'c$uCom$uOcom$uOWhile'('v$ub','v$uc') ),
inference(demodulation,[status(thm)],[d13,c56]) ).
cnf(d15,plain,
( 'v$uP'(X0,'v$us2')
| ~ 'v$uP'(X0,'v$us1')
| ~ 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua','v$una',sK134) ),
inference(equality_resolution,[status(thm)],[d14]) ).
cnf(d16,plain,
( 'v$uP'(X0,'v$us2')
| ~ 'v$uP'(X0,'v$us1')
| hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK134),'v$uG'))
| 'c$uCom$uOcom$uOWhile'('v$ub','v$uca') != 'c$uCom$uOcom$uOWhile'('v$ub','v$uc') ),
inference(demodulation,[status(thm)],[c52,c57]) ).
cnf(d17,plain,
( 'v$uP'(X0,'v$us2')
| ~ 'v$uP'(X0,'v$us1')
| hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK134),'v$uG'))
| 'c$uCom$uOcom$uOWhile'('v$ub','v$uc') != 'c$uCom$uOcom$uOWhile'('v$ub','v$uc') ),
inference(demodulation,[status(thm)],[d16,c56]) ).
cnf(d18,plain,
( 'v$uP'(X0,'v$us2')
| ~ 'v$uP'(X0,'v$us1')
| hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK134),'v$uG')) ),
inference(equality_resolution,[status(thm)],[d17]) ).
cnf(d19,plain,
( 'v$uP'(sK135,'v$us2')
| hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK134),'v$uG')) ),
inference(resolution,[status(thm)],[d9,d18]) ).
cnf(d20,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua','v$una',sK134)
| 'v$uP'(sK135,'v$us2') ),
inference(resolution,[status(thm)],[d19,c60]) ).
cnf(d21,plain,
( 'v$uP'(X0,'v$us2')
| ~ 'v$uP'(X0,'v$us1')
| 'v$uP'(sK135,'v$us2') ),
inference(resolution,[status(thm)],[d20,d15]) ).
cnf(d22,plain,
( 'v$uP'(sK135,'v$us2')
| 'v$uP'(sK135,'v$us2') ),
inference(resolution,[status(thm)],[d21,d9]) ).
cnf(d23,plain,
hBOOL(hAPP('v$ub','v$us2')),
inference(resolution,[status(thm)],[d22,c59]) ).
cnf(d24,plain,
( ~ 'v$uP'(X0,'v$us1')
| ~ 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua','v$una',sK134) ),
inference(resolution,[status(thm)],[d23,d12]) ).
cnf(d25,plain,
( ~ 'v$uP'(X0,'v$us1')
| ~ hBOOL(hAPP('v$ub','v$us2'))
| hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK134),'v$uG'))
| 'c$uCom$uOcom$uOWhile'('v$ub','v$uca') != 'c$uCom$uOcom$uOWhile'('v$ub','v$uc') ),
inference(demodulation,[status(thm)],[c54,c57]) ).
cnf(d26,plain,
( ~ 'v$uP'(X0,'v$us1')
| ~ hBOOL(hAPP('v$ub','v$us2'))
| hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK134),'v$uG'))
| 'c$uCom$uOcom$uOWhile'('v$ub','v$uc') != 'c$uCom$uOcom$uOWhile'('v$ub','v$uc') ),
inference(demodulation,[status(thm)],[d25,c56]) ).
cnf(d27,plain,
( ~ 'v$uP'(X0,'v$us1')
| ~ hBOOL(hAPP('v$ub','v$us2'))
| hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK134),'v$uG')) ),
inference(equality_resolution,[status(thm)],[d26]) ).
cnf(d28,plain,
( ~ 'v$uP'(X0,'v$us1')
| hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK134),'v$uG')) ),
inference(resolution,[status(thm)],[d23,d27]) ).
cnf(d29,plain,
hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK134),'v$uG')),
inference(resolution,[status(thm)],[d28,d9]) ).
cnf(d30,plain,
'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua','v$una',sK134),
inference(resolution,[status(thm)],[d29,c60]) ).
cnf(d31,plain,
~ 'v$uP'(X0,'v$us1'),
inference(resolution,[status(thm)],[d30,d24]) ).
cnf(d32,plain,
$false,
inference(resolution,[status(thm)],[d31,d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW328+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
% 0.09/0.57 % Computer : n009.cluster.edu
% 0.09/0.57 % Model : x86_64 x86_64
% 0.09/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.57 % Memory : 8046.5625MB
% 0.09/0.57 % OS : Linux 6.8.0-71-generic
% 0.09/0.57 % CPULimit : 300
% 0.09/0.57 % WCLimit : 300
% 0.09/0.57 % DateTime : Sat Sep 26 15:40:15 UTC 2026
% 0.09/0.57 % CPUTime :
% 0.09/0.57 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 39.36/13.65 % SZS status Theorem for theBenchmark.p
% 39.36/13.65 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------