%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWW313+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 : n005.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 09:11:40 AM UTC 2026
% Result : Theorem 12.80s 12.01s
% Output : CNFRefutation 12.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 10 unt; 0 def)
% Number of atoms : 22 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 13 ( 6 ~; 4 |; 0 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_asm,axiom,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'(X2),'tc$uHOL$uObool')),X1),X0))
=> 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'(X2,X0,X1) ) ).
fof(fact_weaken,axiom,
! [X0,X1,X2,X3] :
( 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'(X3,X2,X1)
=> ( hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'(X3),'tc$uHOL$uObool')),X0),X1))
=> 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'(X3,X2,X0) ) ) ).
fof(conj_0,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$uG')) ).
fof(conj_1,hypothesis,
hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua'),'tc$uHOL$uObool')),'v$uG'),'v$uGa')) ).
fof(conj_2,conjecture,
'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('t$ua','v$uGa','v$uts') ).
fof(negated_conjecture,negated_conjecture,
~ 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('t$ua','v$uGa','v$uts'),
inference(negate_conjecture,[status(cth)],[conj_2]) ).
cnf(c0,plain,
( 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'(X0,X2,X1)
| ~ hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'(X0),'tc$uHOL$uObool')),X1),X2)) ),
inference(clausification,[status(esa)],[fact_asm]) ).
cnf(c1,plain,
( ~ hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'(X0),'tc$uHOL$uObool')),X3),X2))
| 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'(X0,X1,X3)
| ~ 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'(X0,X1,X2) ),
inference(clausification,[status(esa)],[fact_weaken]) ).
cnf(c6,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$uG')),
inference(clausification,[status(esa)],[conj_0]) ).
cnf(c7,plain,
hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua'),'tc$uHOL$uObool')),'v$uG'),'v$uGa')),
inference(clausification,[status(esa)],[conj_1]) ).
cnf(c8,plain,
~ 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('t$ua','v$uGa','v$uts'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('t$ua','v$uGa','v$uG'),
inference(resolution,[status(thm)],[c7,c0]) ).
cnf(d1,plain,
( 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('t$ua',X0,'v$uts')
| ~ 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('t$ua',X0,'v$uG') ),
inference(resolution,[status(thm)],[c6,c1]) ).
cnf(d2,plain,
'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('t$ua','v$uGa','v$uts'),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
$false,
inference(resolution,[status(thm)],[c8,d2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW313+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
% 0.07/0.34 % Computer : n005.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 26 15:38:32 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.80/12.01 % SZS status Theorem for theBenchmark.p
% 12.80/12.01 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------