%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWW326+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 : n014.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 3.14s 17.56s
% Output : CNFRefutation 3.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of formulae : 26 ( 7 unt; 0 def)
% Number of atoms : 70 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 75 ( 31 ~; 29 |; 3 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 35 ( 7 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_1,hypothesis,
! [X0,X1] :
( 'c$uNatural$uOevaln'('c$uCom$uOcom$uOWhile'('v$ub','v$uc'),X0,'v$un',X1)
=> ( ! [X2] :
( hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),X2),'v$uG'))
=> 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua','v$un',X2) )
=> ! [X3] :
( 'v$uP'(X3,X0)
=> ( ~ hBOOL(hAPP('v$ub',X1))
& 'v$uP'(X3,X1) ) ) ) ) ).
fof(conj_2,conjecture,
( ! [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$un',X0) )
=> ! [X1,X2] :
( 'v$uP'(X1,X2)
=> ! [X3] :
( 'c$uNatural$uOevaln'('c$uCom$uOcom$uOWhile'('v$ub','v$uc'),X2,'v$un',X3)
=> ( ~ hBOOL(hAPP('v$ub',X3))
& 'v$uP'(X1,X3) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( ! [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$un',X0) )
=> ! [X1,X2] :
( 'v$uP'(X1,X2)
=> ! [X3] :
( 'c$uNatural$uOevaln'('c$uCom$uOcom$uOWhile'('v$ub','v$uc'),X2,'v$un',X3)
=> ( ~ hBOOL(hAPP('v$ub',X3))
& 'v$uP'(X1,X3) ) ) ) ),
inference(negate_conjecture,[status(cth)],[conj_2]) ).
cnf(c132,plain,
( hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK317),'v$uG'))
| 'v$uP'(X2,X1)
| ~ 'v$uP'(X2,X0)
| ~ 'c$uNatural$uOevaln'('c$uCom$uOcom$uOWhile'('v$ub','v$uc'),X0,'v$un',X1) ),
inference(clausification,[status(esa)],[conj_1]) ).
cnf(c133,plain,
( ~ 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua','v$un',sK317)
| 'v$uP'(X2,X1)
| ~ 'v$uP'(X2,X0)
| ~ 'c$uNatural$uOevaln'('c$uCom$uOcom$uOWhile'('v$ub','v$uc'),X0,'v$un',X1) ),
inference(clausification,[status(esa)],[conj_1]) ).
cnf(c134,plain,
( hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK317),'v$uG'))
| ~ hBOOL(hAPP('v$ub',X1))
| ~ 'v$uP'(X2,X0)
| ~ 'c$uNatural$uOevaln'('c$uCom$uOcom$uOWhile'('v$ub','v$uc'),X0,'v$un',X1) ),
inference(clausification,[status(esa)],[conj_1]) ).
cnf(c135,plain,
( ~ 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua','v$un',sK317)
| ~ hBOOL(hAPP('v$ub',X1))
| ~ 'v$uP'(X2,X0)
| ~ 'c$uNatural$uOevaln'('c$uCom$uOcom$uOWhile'('v$ub','v$uc'),X0,'v$un',X1) ),
inference(clausification,[status(esa)],[conj_1]) ).
cnf(c136,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua','v$un',X0)
| ~ hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),X0),'v$uG')) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c137,plain,
'v$uP'(sK319,sK320),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c138,plain,
'c$uNatural$uOevaln'('c$uCom$uOcom$uOWhile'('v$ub','v$uc'),sK320,'v$un',sK321),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c139,plain,
( hBOOL(hAPP('v$ub',sK321))
| ~ 'v$uP'(sK319,sK321) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'v$uP'(X0,sK320)
| 'v$uP'(X0,sK321)
| ~ 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua','v$un',sK317) ),
inference(resolution,[status(thm)],[c133,c138]) ).
cnf(d1,plain,
( ~ 'v$uP'(X0,sK320)
| 'v$uP'(X0,sK321)
| hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK317),'v$uG')) ),
inference(resolution,[status(thm)],[c132,c138]) ).
cnf(d2,plain,
( 'v$uP'(sK319,sK321)
| hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK317),'v$uG')) ),
inference(resolution,[status(thm)],[d1,c137]) ).
cnf(d3,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua','v$un',sK317)
| 'v$uP'(sK319,sK321) ),
inference(resolution,[status(thm)],[d2,c136]) ).
cnf(d4,plain,
( 'v$uP'(X0,sK321)
| ~ 'v$uP'(X0,sK320)
| 'v$uP'(sK319,sK321) ),
inference(resolution,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
( 'v$uP'(sK319,sK321)
| 'v$uP'(sK319,sK321) ),
inference(resolution,[status(thm)],[d4,c137]) ).
cnf(d6,plain,
hBOOL(hAPP('v$ub',sK321)),
inference(resolution,[status(thm)],[d5,c139]) ).
cnf(d7,plain,
( ~ 'v$uP'(X1,X0)
| ~ 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua','v$un',sK317)
| ~ 'c$uNatural$uOevaln'('c$uCom$uOcom$uOWhile'('v$ub','v$uc'),X0,'v$un',sK321) ),
inference(resolution,[status(thm)],[d6,c135]) ).
cnf(d8,plain,
( ~ 'v$uP'(X0,sK320)
| ~ 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua','v$un',sK317) ),
inference(resolution,[status(thm)],[d7,c138]) ).
cnf(d9,plain,
( ~ 'v$uP'(X1,X0)
| ~ 'c$uNatural$uOevaln'('c$uCom$uOcom$uOWhile'('v$ub','v$uc'),X0,'v$un',sK321)
| hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK317),'v$uG')) ),
inference(resolution,[status(thm)],[d6,c134]) ).
cnf(d10,plain,
( ~ 'v$uP'(X0,sK320)
| hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK317),'v$uG')) ),
inference(resolution,[status(thm)],[d9,c138]) ).
cnf(d11,plain,
hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK317),'v$uG')),
inference(resolution,[status(thm)],[d10,c137]) ).
cnf(d12,plain,
'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua','v$un',sK317),
inference(resolution,[status(thm)],[d11,c136]) ).
cnf(d13,plain,
~ 'v$uP'(X0,sK320),
inference(resolution,[status(thm)],[d12,d8]) ).
cnf(d14,plain,
$false,
inference(resolution,[status(thm)],[d13,c137]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW326+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 15:40:17 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.14/17.56 % SZS status Theorem for theBenchmark.p
% 3.14/17.56 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------