%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWW336+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 174.14s 37.79s
% Output : CNFRefutation 174.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 11 unt; 0 def)
% Number of atoms : 96 ( 3 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 68 ( 16 ~; 38 |; 0 &)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-2 aty)
% Number of variables : 56 ( 7 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_insert__code,axiom,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(hAPP('c$uSet$uOinsert'(X3),X2),X1),X0))
<=> ( hBOOL(hAPP(X1,X0))
| X2 = X0 ) ) ).
fof(fact_mem__def,axiom,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP('c$umember'(X2),X1),X0))
<=> hBOOL(hAPP(X0,X1)) ) ).
fof(fact_insertI1,axiom,
! [X0,X1,X2] : hBOOL(hAPP(hAPP('c$umember'(X2),X1),hAPP(hAPP('c$uSet$uOinsert'(X2),X1),X0))) ).
fof(conj_1,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),hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),'v$ut'),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua'),'tc$uHOL$uObool')))))
=> 'c$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$uts'))
=> 'c$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),hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),'v$ut'),'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),hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),'v$ut'),'v$uts')))
=> 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,X1) ) ),
inference(negate_conjecture,[status(cth)],[conj_4]) ).
cnf(c17,plain,
( X3 = X1
| hBOOL(hAPP(X2,X3))
| ~ hBOOL(hAPP(hAPP(hAPP('c$uSet$uOinsert'(X0),X1),X2),X3)) ),
inference(clausification,[status(esa)],[fact_insert__code]) ).
cnf(c37,plain,
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(hAPP(hAPP('c$umember'(X0),X1),X2)) ),
inference(clausification,[status(esa)],[fact_mem__def]) ).
cnf(c38,plain,
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(hAPP('c$umember'(X0),X1),X2)) ),
inference(clausification,[status(esa)],[fact_mem__def]) ).
cnf(c66,plain,
hBOOL(hAPP(hAPP('c$umember'(X0),X1),hAPP(hAPP('c$uSet$uOinsert'(X0),X1),X2))),
inference(clausification,[status(esa)],[fact_insertI1]) ).
cnf(c128,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,X1)
| ~ hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),X1),hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),'v$ut'),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua'),'tc$uHOL$uObool')))))
| hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK274(X0)),'v$uG')) ),
inference(clausification,[status(esa)],[conj_1]) ).
cnf(c129,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,X1)
| ~ hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),X1),hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),'v$ut'),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua'),'tc$uHOL$uObool')))))
| ~ 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,sK274(X0)) ),
inference(clausification,[status(esa)],[conj_1]) ).
cnf(c131,plain,
( 'c$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$ua')),sK277(X0)),'v$uG')) ),
inference(clausification,[status(esa)],[conj_3]) ).
cnf(c132,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$ua',X0,sK277(X0)) ),
inference(clausification,[status(esa)],[conj_3]) ).
cnf(c133,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK279,X0)
| ~ hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),X0),'v$uG')) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c134,plain,
hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK281),hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),'v$ut'),'v$uts'))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c135,plain,
~ 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK279,sK281),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
hBOOL(hAPP(hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),'v$ut'),'v$uts'),sK281)),
inference(resolution,[status(thm)],[c37,c134]) ).
cnf(d1,plain,
( hBOOL(hAPP('v$uts',sK281))
| sK281 = 'v$ut' ),
inference(resolution,[status(thm)],[d0,c17]) ).
cnf(d2,plain,
( hBOOL(hAPP('v$uts',sK281))
| ~ 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK279,'v$ut') ),
inference(superposition,[status(thm)],[d1,c135]) ).
cnf(d3,plain,
( ~ 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,sK274(X0))
| 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,'v$ut') ),
inference(resolution,[status(thm)],[c129,c66]) ).
cnf(d4,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,'v$ut')
| hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK274(X0)),'v$uG')) ),
inference(resolution,[status(thm)],[c128,c66]) ).
cnf(d5,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK279,sK274(X0))
| 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,'v$ut') ),
inference(resolution,[status(thm)],[d4,c133]) ).
cnf(d6,plain,
( hBOOL(hAPP('v$uts',sK281))
| 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK279,sK274(sK279)) ),
inference(resolution,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
( hBOOL(hAPP(hAPP('c$umember'(X0),sK281),'v$uts'))
| 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK279,sK274(sK279)) ),
inference(resolution,[status(thm)],[d6,c38]) ).
cnf(d8,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,sK281)
| hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK277(X0)),'v$uG'))
| 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK279,sK274(sK279)) ),
inference(resolution,[status(thm)],[d7,c131]) ).
cnf(d9,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK279,sK277(X0))
| 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK279,sK274(sK279))
| 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,sK281) ),
inference(resolution,[status(thm)],[d8,c133]) ).
cnf(d10,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK279,sK277(sK279))
| 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK279,sK274(sK279)) ),
inference(resolution,[status(thm)],[d9,c135]) ).
cnf(d11,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK279,'v$ut')
| 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK279,sK277(sK279)) ),
inference(resolution,[status(thm)],[d10,d3]) ).
cnf(d12,plain,
( hBOOL(hAPP('v$uts',sK281))
| 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK279,sK277(sK279)) ),
inference(resolution,[status(thm)],[d11,d2]) ).
cnf(d13,plain,
( hBOOL(hAPP(hAPP('c$umember'(X0),sK281),'v$uts'))
| 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK279,sK277(sK279)) ),
inference(resolution,[status(thm)],[d12,c38]) ).
cnf(d14,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,sK281)
| hBOOL(hAPP(hAPP('c$umember'('tc$uHoare$u$uMirabelle$uOtriple'('t$ua')),sK277(X0)),'v$uG'))
| 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK279,sK277(sK279)) ),
inference(resolution,[status(thm)],[d13,c131]) ).
cnf(d15,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK279,sK277(X0))
| 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK279,sK277(sK279))
| 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,sK281) ),
inference(resolution,[status(thm)],[d14,c133]) ).
cnf(d16,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK279,sK277(sK279))
| 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK279,sK277(sK279)) ),
inference(resolution,[status(thm)],[d15,c135]) ).
cnf(d17,plain,
( ~ 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,sK277(X0))
| 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,sK281)
| 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK279,sK274(sK279)) ),
inference(resolution,[status(thm)],[d7,c132]) ).
cnf(d18,plain,
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK279,sK274(sK279))
| 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK279,sK281) ),
inference(resolution,[status(thm)],[d16,d17]) ).
cnf(d19,plain,
'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK279,sK274(sK279)),
inference(resolution,[status(thm)],[c135,d18]) ).
cnf(d20,plain,
'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK279,'v$ut'),
inference(resolution,[status(thm)],[d19,d3]) ).
cnf(d21,plain,
hBOOL(hAPP('v$uts',sK281)),
inference(resolution,[status(thm)],[d20,d2]) ).
cnf(d22,plain,
hBOOL(hAPP(hAPP('c$umember'(X0),sK281),'v$uts')),
inference(resolution,[status(thm)],[d21,c38]) ).
cnf(d23,plain,
( ~ 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,sK277(X0))
| 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',X0,sK281) ),
inference(resolution,[status(thm)],[d22,c132]) ).
cnf(d24,plain,
'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua',sK279,sK281),
inference(resolution,[status(thm)],[d23,d16]) ).
cnf(d25,plain,
$false,
inference(resolution,[status(thm)],[c135,d24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW336+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n003.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 15:43:09 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 174.14/37.79 % SZS status Theorem for theBenchmark.p
% 174.14/37.79 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------