%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWW385+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 : n013.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 09:11:47 AM UTC 2026
% Result : Theorem 130.46s 23.40s
% Output : CNFRefutation 130.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 33 ( 15 unt; 0 def)
% Number of atoms : 60 ( 10 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 51 ( 24 ~; 16 |; 0 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 9 con; 0-3 aty)
% Number of variables : 58 ( 5 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_MGF,axiom,
! [X0] :
( 'c$uHoare$u$uMirabelle$uOstate$u$unot$u$usingleton'
=> ( 'c$uCom$uOWT$u$ubodies'
=> ( hBOOL(hAPP('c$uCom$uOWT',X0))
=> 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('tc$uCom$uOstate','c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate'),'tc$uHOL$uObool')),hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate')),hAPP('c$uHoare$u$uMirabelle$uOMGT',X0)),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate'),'tc$uHOL$uObool')))) ) ) ) ).
fof(fact_WT_OBody,axiom,
! [X0] :
( hAPP('c$uCom$uObody',X0) != 'c$uOption$uOoption$uONone'('tc$uCom$uOcom')
=> hBOOL(hAPP('c$uCom$uOWT',hAPP('c$uCom$uOcom$uOBODY',X0))) ) ).
fof(fact_dom__minus,axiom,
! [X0,X1,X2,X3,X4] :
( hAPP(X4,X3) = 'c$uOption$uOoption$uONone'(X2)
=> hAPP(hAPP('c$uGroups$uOminus$u$uclass$uOminus'('tc$ufun'(X1,'tc$uHOL$uObool')),'c$uMap$uOdom'(X1,X2,X4)),hAPP(hAPP('c$uSet$uOinsert'(X1),X3),X0)) = hAPP(hAPP('c$uGroups$uOminus$u$uclass$uOminus'('tc$ufun'(X1,'tc$uHOL$uObool')),'c$uMap$uOdom'(X1,X2,X4)),X0) ) ).
fof(fact_emptyE,axiom,
! [X0,X1] : ~ hBOOL(hAPP(hAPP('c$umember'(X1),X0),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X1,'tc$uHOL$uObool')))) ).
fof(fact_DiffE,axiom,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP('c$umember'(X3),X2),hAPP(hAPP('c$uGroups$uOminus$u$uclass$uOminus'('tc$ufun'(X3,'tc$uHOL$uObool')),X1),X0)))
=> ~ ( hBOOL(hAPP(hAPP('c$umember'(X3),X2),X1))
=> hBOOL(hAPP(hAPP('c$umember'(X3),X2),X0)) ) ) ).
fof(fact_DiffI,axiom,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP('c$umember'(X3),X2),X1))
=> ( ~ hBOOL(hAPP(hAPP('c$umember'(X3),X2),X0))
=> hBOOL(hAPP(hAPP('c$umember'(X3),X2),hAPP(hAPP('c$uGroups$uOminus$u$uclass$uOminus'('tc$ufun'(X3,'tc$uHOL$uObool')),X1),X0))) ) ) ).
fof(fact_insertI1,axiom,
! [X0,X1,X2] : hBOOL(hAPP(hAPP('c$umember'(X2),X1),hAPP(hAPP('c$uSet$uOinsert'(X2),X1),X0))) ).
fof(conj_0,hypothesis,
'c$uHoare$u$uMirabelle$uOstate$u$unot$u$usingleton' ).
fof(conj_1,hypothesis,
'c$uCom$uOWT$u$ubodies' ).
fof(conj_3,conjecture,
! [X0] :
( hBOOL(hAPP(hAPP('c$umember'('tc$uCom$uOpname'),X0),'c$uMap$uOdom'('tc$uCom$uOpname','tc$uCom$uOcom','c$uCom$uObody')))
=> 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('tc$uCom$uOstate','c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate'),'tc$uHOL$uObool')),hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate')),hAPP('c$uHoare$u$uMirabelle$uOMGT',hAPP('c$uCom$uOcom$uOBODY',X0))),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate'),'tc$uHOL$uObool')))) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( hBOOL(hAPP(hAPP('c$umember'('tc$uCom$uOpname'),X0),'c$uMap$uOdom'('tc$uCom$uOpname','tc$uCom$uOcom','c$uCom$uObody')))
=> 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('tc$uCom$uOstate','c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate'),'tc$uHOL$uObool')),hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate')),hAPP('c$uHoare$u$uMirabelle$uOMGT',hAPP('c$uCom$uOcom$uOBODY',X0))),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate'),'tc$uHOL$uObool')))) ),
inference(negate_conjecture,[status(cth)],[conj_3]) ).
cnf(c3,plain,
( 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('tc$uCom$uOstate','c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate'),'tc$uHOL$uObool')),hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate')),hAPP('c$uHoare$u$uMirabelle$uOMGT',X0)),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate'),'tc$uHOL$uObool'))))
| ~ hBOOL(hAPP('c$uCom$uOWT',X0))
| ~ 'c$uCom$uOWT$u$ubodies'
| ~ 'c$uHoare$u$uMirabelle$uOstate$u$unot$u$usingleton' ),
inference(clausification,[status(esa)],[fact_MGF]) ).
cnf(c46,plain,
( hBOOL(hAPP('c$uCom$uOWT',hAPP('c$uCom$uOcom$uOBODY',X0)))
| hAPP('c$uCom$uObody',X0) = 'c$uOption$uOoption$uONone'('tc$uCom$uOcom') ),
inference(clausification,[status(esa)],[fact_WT_OBody]) ).
cnf(c102,plain,
( hAPP(hAPP('c$uGroups$uOminus$u$uclass$uOminus'('tc$ufun'(X3,'tc$uHOL$uObool')),'c$uMap$uOdom'(X3,X2,X0)),hAPP(hAPP('c$uSet$uOinsert'(X3),X1),X4)) = hAPP(hAPP('c$uGroups$uOminus$u$uclass$uOminus'('tc$ufun'(X3,'tc$uHOL$uObool')),'c$uMap$uOdom'(X3,X2,X0)),X4)
| hAPP(X0,X1) != 'c$uOption$uOoption$uONone'(X2) ),
inference(clausification,[status(esa)],[fact_dom__minus]) ).
cnf(c112,plain,
~ hBOOL(hAPP(hAPP('c$umember'(X0),X1),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X0,'tc$uHOL$uObool')))),
inference(clausification,[status(esa)],[fact_emptyE]) ).
cnf(c122,plain,
( ~ hBOOL(hAPP(hAPP('c$umember'(X0),X1),X3))
| ~ hBOOL(hAPP(hAPP('c$umember'(X0),X1),hAPP(hAPP('c$uGroups$uOminus$u$uclass$uOminus'('tc$ufun'(X0,'tc$uHOL$uObool')),X2),X3))) ),
inference(clausification,[status(esa)],[fact_DiffE]) ).
cnf(c123,plain,
( hBOOL(hAPP(hAPP('c$umember'(X0),X1),hAPP(hAPP('c$uGroups$uOminus$u$uclass$uOminus'('tc$ufun'(X0,'tc$uHOL$uObool')),X2),X3)))
| hBOOL(hAPP(hAPP('c$umember'(X0),X1),X3))
| ~ hBOOL(hAPP(hAPP('c$umember'(X0),X1),X2)) ),
inference(clausification,[status(esa)],[fact_DiffI]) ).
cnf(c264,plain,
hBOOL(hAPP(hAPP('c$umember'(X0),X1),hAPP(hAPP('c$uSet$uOinsert'(X0),X1),X2))),
inference(clausification,[status(esa)],[fact_insertI1]) ).
cnf(c4637,plain,
'c$uHoare$u$uMirabelle$uOstate$u$unot$u$usingleton',
inference(clausification,[status(esa)],[conj_0]) ).
cnf(c4638,plain,
'c$uCom$uOWT$u$ubodies',
inference(clausification,[status(esa)],[conj_1]) ).
cnf(c4639,plain,
hBOOL(hAPP(hAPP('c$umember'('tc$uCom$uOpname'),sK10690),'c$uMap$uOdom'('tc$uCom$uOpname','tc$uCom$uOcom','c$uCom$uObody'))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c4640,plain,
~ 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('tc$uCom$uOstate','c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate'),'tc$uHOL$uObool')),hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate')),hAPP('c$uHoare$u$uMirabelle$uOMGT',hAPP('c$uCom$uOcom$uOBODY',sK10690))),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate'),'tc$uHOL$uObool')))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'c$uCom$uOWT$u$ubodies'
| ~ hBOOL(hAPP('c$uCom$uOWT',X0))
| 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('tc$uCom$uOstate','c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate'),'tc$uHOL$uObool')),hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate')),hAPP('c$uHoare$u$uMirabelle$uOMGT',X0)),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate'),'tc$uHOL$uObool')))) ),
inference(resolution,[status(thm)],[c4637,c3]) ).
cnf(d1,plain,
( ~ hBOOL(hAPP('c$uCom$uOWT',X0))
| 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('tc$uCom$uOstate','c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate'),'tc$uHOL$uObool')),hAPP(hAPP('c$uSet$uOinsert'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate')),hAPP('c$uHoare$u$uMirabelle$uOMGT',X0)),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate'),'tc$uHOL$uObool')))) ),
inference(resolution,[status(thm)],[c4638,d0]) ).
cnf(d2,plain,
~ hBOOL(hAPP('c$uCom$uOWT',hAPP('c$uCom$uOcom$uOBODY',sK10690))),
inference(resolution,[status(thm)],[c4640,d1]) ).
cnf(d3,plain,
hAPP('c$uCom$uObody',sK10690) = 'c$uOption$uOoption$uONone'('tc$uCom$uOcom'),
inference(resolution,[status(thm)],[c46,d2]) ).
cnf(d4,plain,
( hAPP(hAPP('c$uGroups$uOminus$u$uclass$uOminus'('tc$ufun'(X1,'tc$uHOL$uObool')),'c$uMap$uOdom'(X1,X0,'c$uCom$uObody')),hAPP(hAPP('c$uSet$uOinsert'(X1),sK10690),X2)) = hAPP(hAPP('c$uGroups$uOminus$u$uclass$uOminus'('tc$ufun'(X1,'tc$uHOL$uObool')),'c$uMap$uOdom'(X1,X0,'c$uCom$uObody')),X2)
| 'c$uOption$uOoption$uONone'('tc$uCom$uOcom') != 'c$uOption$uOoption$uONone'(X0) ),
inference(superposition,[status(thm)],[d3,c102]) ).
cnf(d5,plain,
hAPP(hAPP('c$uGroups$uOminus$u$uclass$uOminus'('tc$ufun'(X0,'tc$uHOL$uObool')),'c$uMap$uOdom'(X0,'tc$uCom$uOcom','c$uCom$uObody')),hAPP(hAPP('c$uSet$uOinsert'(X0),sK10690),X1)) = hAPP(hAPP('c$uGroups$uOminus$u$uclass$uOminus'('tc$ufun'(X0,'tc$uHOL$uObool')),'c$uMap$uOdom'(X0,'tc$uCom$uOcom','c$uCom$uObody')),X1),
inference(equality_resolution,[status(thm)],[d4]) ).
cnf(d6,plain,
( ~ hBOOL(hAPP(hAPP('c$umember'(X0),X2),hAPP(hAPP('c$uSet$uOinsert'(X0),sK10690),X1)))
| ~ hBOOL(hAPP(hAPP('c$umember'(X0),X2),hAPP(hAPP('c$uGroups$uOminus$u$uclass$uOminus'('tc$ufun'(X0,'tc$uHOL$uObool')),'c$uMap$uOdom'(X0,'tc$uCom$uOcom','c$uCom$uObody')),X1))) ),
inference(superposition,[status(thm)],[d5,c122]) ).
cnf(d7,plain,
( ~ hBOOL(hAPP(hAPP('c$umember'(X0),X1),'c$uMap$uOdom'(X0,'tc$uCom$uOcom','c$uCom$uObody')))
| hBOOL(hAPP(hAPP('c$umember'(X0),X1),X2))
| ~ hBOOL(hAPP(hAPP('c$umember'(X0),X1),hAPP(hAPP('c$uSet$uOinsert'(X0),sK10690),X2))) ),
inference(resolution,[status(thm)],[d6,c123]) ).
cnf(d8,plain,
( ~ hBOOL(hAPP(hAPP('c$umember'(X0),sK10690),'c$uMap$uOdom'(X0,'tc$uCom$uOcom','c$uCom$uObody')))
| hBOOL(hAPP(hAPP('c$umember'(X0),sK10690),X1)) ),
inference(resolution,[status(thm)],[c264,d7]) ).
cnf(d9,plain,
hBOOL(hAPP(hAPP('c$umember'('tc$uCom$uOpname'),sK10690),X0)),
inference(resolution,[status(thm)],[d8,c4639]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[d9,c112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW385+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
% 0.06/0.46 % Computer : n013.cluster.edu
% 0.06/0.46 % Model : x86_64 x86_64
% 0.06/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.46 % Memory : 8046.5625MB
% 0.06/0.46 % OS : Linux 6.8.0-71-generic
% 0.06/0.46 % CPULimit : 300
% 0.06/0.46 % WCLimit : 300
% 0.06/0.46 % DateTime : Sat Sep 26 15:47:06 UTC 2026
% 0.06/0.47 % CPUTime :
% 0.06/0.47 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 130.46/23.40 % SZS status Theorem for theBenchmark.p
% 130.46/23.40 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------