%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWV905-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/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 09:04:54 AM UTC 2026
% Result : Unsatisfiable 9.10s 8.81s
% Output : CNFRefutation 9.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 18
% Syntax : Number of clauses : 58 ( 33 unt; 2 nHn; 32 RR)
% Number of literals : 92 ( 30 equ; 39 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 3 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 7 con; 0-4 aty)
% Number of variables : 80 ( 20 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_map__add__None_1,axiom,
( hAPP(X0,X4) = 'c$uOption$uOoption$uONone'(X3)
| hAPP('c$uMap$uOmap$u$uadd'(X0,X1,X2,X3),X4) != 'c$uOption$uOoption$uONone'(X3) ) ).
cnf(cls_sup__ge2_0,axiom,
( 'c$ulessequals'(X1,'c$uLattices$uOupper$u$usemilattice$u$uclass$uOsup'(X2,X1,X0),X0)
| ~ 'class$uLattices$uOupper$u$usemilattice'(X0) ) ).
cnf(cls_le__iff__inf_0,axiom,
( ~ 'c$ulessequals'(X1,X2,X0)
| hAPP(hAPP('c$uLattices$uOlower$u$usemilattice$u$uclass$uOinf'(X0),X1),X2) = X1
| ~ 'class$uLattices$uOlower$u$usemilattice'(X0) ) ).
cnf(cls_sup__idem_0,axiom,
( 'c$uLattices$uOupper$u$usemilattice$u$uclass$uOsup'(X1,X1,X0) = X1
| ~ 'class$uLattices$uOupper$u$usemilattice'(X0) ) ).
cnf(cls_Collect__def_0,axiom,
'c$uCollect'(X0,X1) = X0 ).
cnf(cls_empty__fold1SetE_0,axiom,
~ hBOOL(hAPP('c$uFinite$u$uSet$uOfold1Set'(X0,'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X1,'tc$ubool')),X1),X2)) ).
cnf(cls_inf__idem_0,axiom,
( hAPP(hAPP('c$uLattices$uOlower$u$usemilattice$u$uclass$uOinf'(X0),X1),X1) = X1
| ~ 'class$uLattices$uOlower$u$usemilattice'(X0) ) ).
cnf(cls_singleton__conv2_0,axiom,
'c$uCollect'('c$ufequal'(X0,X1),X1) = 'c$uSet$uOinsert'(X0,'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X1,'tc$ubool')),X1) ).
cnf(cls_map__add__dom__app__simps_I1_J_0,axiom,
( ~ hBOOL('c$uin'(X4,'c$uMap$uOdom'(X1,X2,X3),X2))
| hAPP('c$uMap$uOmap$u$uadd'(X0,X1,X2,X3),X4) = hAPP(X1,X4) ) ).
cnf(cls_WT_OBody_0,axiom,
( hAPP('c$uCom$uObody',X0) = 'c$uOption$uOoption$uONone'('tc$uCom$uOcom')
| 'c$uCom$uOWT'('c$uCom$uOcom$uOBODY'(X0)) ) ).
cnf(cls_MGF_0,axiom,
( ~ 'c$uHoare$u$uMirabelle$uOstate$u$unot$u$usingleton'
| ~ 'c$uCom$uOWT$u$ubodies'
| ~ 'c$uCom$uOWT'(X0)
| 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate'),'tc$ubool')),'c$uSet$uOinsert'('c$uHoare$u$uMirabelle$uOMGT'(X0),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate'),'tc$ubool')),'tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate')),'tc$uCom$uOstate') ) ).
cnf(cls_mem__def_0,axiom,
( ~ hBOOL('c$uin'(X1,X0,X2))
| hBOOL(hAPP(X0,X1)) ) ).
cnf(cls_conjecture_0,negated_conjecture,
'c$uHoare$u$uMirabelle$uOstate$u$unot$u$usingleton' ).
cnf(cls_conjecture_1,negated_conjecture,
'c$uCom$uOWT$u$ubodies' ).
cnf(cls_conjecture_3,negated_conjecture,
hBOOL('c$uin'('v$ux','c$uMap$uOdom'('c$uCom$uObody','tc$uCom$uOpname','tc$uCom$uOcom'),'tc$uCom$uOpname')) ).
cnf(cls_conjecture_4,negated_conjecture,
~ 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate'),'tc$ubool')),'c$uSet$uOinsert'('c$uHoare$u$uMirabelle$uOMGT'('c$uCom$uOcom$uOBODY'('v$ux')),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate'),'tc$ubool')),'tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate')),'tc$uCom$uOstate') ).
cnf(clsarity_nat__Lattices_Oupper__semilattice,axiom,
'class$uLattices$uOupper$u$usemilattice'('tc$unat') ).
cnf(clsarity_nat__Lattices_Olower__semilattice,axiom,
'class$uLattices$uOlower$u$usemilattice'('tc$unat') ).
cnf(c2,plain,
( hAPP(X0,X4) = 'c$uOption$uOoption$uONone'(X3)
| hAPP('c$uMap$uOmap$u$uadd'(X0,X1,X2,X3),X4) != 'c$uOption$uOoption$uONone'(X3) ),
inference(clausification,[status(esa)],[cls_map__add__None_1]) ).
cnf(c55,plain,
( 'c$ulessequals'(X1,'c$uLattices$uOupper$u$usemilattice$u$uclass$uOsup'(X2,X1,X0),X0)
| ~ 'class$uLattices$uOupper$u$usemilattice'(X0) ),
inference(clausification,[status(esa)],[cls_sup__ge2_0]) ).
cnf(c64,plain,
( ~ 'c$ulessequals'(X1,X2,X0)
| hAPP(hAPP('c$uLattices$uOlower$u$usemilattice$u$uclass$uOinf'(X0),X1),X2) = X1
| ~ 'class$uLattices$uOlower$u$usemilattice'(X0) ),
inference(clausification,[status(esa)],[cls_le__iff__inf_0]) ).
cnf(c81,plain,
( 'c$uLattices$uOupper$u$usemilattice$u$uclass$uOsup'(X1,X1,X0) = X1
| ~ 'class$uLattices$uOupper$u$usemilattice'(X0) ),
inference(clausification,[status(esa)],[cls_sup__idem_0]) ).
cnf(c105,plain,
'c$uCollect'(X0,X1) = X0,
inference(clausification,[status(esa)],[cls_Collect__def_0]) ).
cnf(c195,plain,
~ hBOOL(hAPP('c$uFinite$u$uSet$uOfold1Set'(X0,'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X1,'tc$ubool')),X1),X2)),
inference(clausification,[status(esa)],[cls_empty__fold1SetE_0]) ).
cnf(c299,plain,
( hAPP(hAPP('c$uLattices$uOlower$u$usemilattice$u$uclass$uOinf'(X0),X1),X1) = X1
| ~ 'class$uLattices$uOlower$u$usemilattice'(X0) ),
inference(clausification,[status(esa)],[cls_inf__idem_0]) ).
cnf(c355,plain,
'c$uCollect'('c$ufequal'(X0,X1),X1) = 'c$uSet$uOinsert'(X0,'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X1,'tc$ubool')),X1),
inference(clausification,[status(esa)],[cls_singleton__conv2_0]) ).
cnf(c384,plain,
( ~ hBOOL('c$uin'(X4,'c$uMap$uOdom'(X1,X2,X3),X2))
| hAPP('c$uMap$uOmap$u$uadd'(X0,X1,X2,X3),X4) = hAPP(X1,X4) ),
inference(clausification,[status(esa)],[cls_map__add__dom__app__simps_I1_J_0]) ).
cnf(c397,plain,
( hAPP('c$uCom$uObody',X0) = 'c$uOption$uOoption$uONone'('tc$uCom$uOcom')
| 'c$uCom$uOWT'('c$uCom$uOcom$uOBODY'(X0)) ),
inference(clausification,[status(esa)],[cls_WT_OBody_0]) ).
cnf(c414,plain,
( ~ 'c$uHoare$u$uMirabelle$uOstate$u$unot$u$usingleton'
| ~ 'c$uCom$uOWT$u$ubodies'
| ~ 'c$uCom$uOWT'(X0)
| 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate'),'tc$ubool')),'c$uSet$uOinsert'('c$uHoare$u$uMirabelle$uOMGT'(X0),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate'),'tc$ubool')),'tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate')),'tc$uCom$uOstate') ),
inference(clausification,[status(esa)],[cls_MGF_0]) ).
cnf(c434,plain,
( ~ hBOOL('c$uin'(X1,X0,X2))
| hBOOL(hAPP(X0,X1)) ),
inference(clausification,[status(esa)],[cls_mem__def_0]) ).
cnf(c444,plain,
'c$uHoare$u$uMirabelle$uOstate$u$unot$u$usingleton',
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c445,plain,
'c$uCom$uOWT$u$ubodies',
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c447,plain,
hBOOL('c$uin'('v$ux','c$uMap$uOdom'('c$uCom$uObody','tc$uCom$uOpname','tc$uCom$uOcom'),'tc$uCom$uOpname')),
inference(clausification,[status(esa)],[cls_conjecture_3]) ).
cnf(c448,plain,
~ 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate'),'tc$ubool')),'c$uSet$uOinsert'('c$uHoare$u$uMirabelle$uOMGT'('c$uCom$uOcom$uOBODY'('v$ux')),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate'),'tc$ubool')),'tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate')),'tc$uCom$uOstate'),
inference(clausification,[status(esa)],[cls_conjecture_4]) ).
cnf(c461,plain,
'class$uLattices$uOupper$u$usemilattice'('tc$unat'),
inference(clausification,[status(esa)],[clsarity_nat__Lattices_Oupper__semilattice]) ).
cnf(c462,plain,
'class$uLattices$uOlower$u$usemilattice'('tc$unat'),
inference(clausification,[status(esa)],[clsarity_nat__Lattices_Olower__semilattice]) ).
cnf(d0,plain,
'c$ufequal'(X0,X1) = 'c$uSet$uOinsert'(X0,'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X1,'tc$ubool')),X1),
inference(demodulation,[status(thm)],[c355,c105]) ).
cnf(d1,plain,
( ~ 'c$uHoare$u$uMirabelle$uOstate$u$unot$u$usingleton'
| ~ 'c$uCom$uOWT$u$ubodies'
| ~ 'c$uCom$uOWT'(X0)
| 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate'),'tc$ubool')),'c$ufequal'('c$uHoare$u$uMirabelle$uOMGT'(X0),'tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate')),'tc$uCom$uOstate') ),
inference(demodulation,[status(thm)],[c414,d0]) ).
cnf(d2,plain,
( ~ 'c$uCom$uOWT$u$ubodies'
| ~ 'c$uCom$uOWT'(X0)
| 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate'),'tc$ubool')),'c$ufequal'('c$uHoare$u$uMirabelle$uOMGT'(X0),'tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate')),'tc$uCom$uOstate') ),
inference(resolution,[status(thm)],[c444,d1]) ).
cnf(d3,plain,
( ~ 'c$uCom$uOWT'(X0)
| 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate'),'tc$ubool')),'c$ufequal'('c$uHoare$u$uMirabelle$uOMGT'(X0),'tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate')),'tc$uCom$uOstate') ),
inference(resolution,[status(thm)],[c445,d2]) ).
cnf(d4,plain,
~ 'c$uHoare$u$uMirabelle$uOhoare$u$uderivs'('c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate'),'tc$ubool')),'c$ufequal'('c$uHoare$u$uMirabelle$uOMGT'('c$uCom$uOcom$uOBODY'('v$ux')),'tc$uHoare$u$uMirabelle$uOtriple'('tc$uCom$uOstate')),'tc$uCom$uOstate'),
inference(demodulation,[status(thm)],[c448,d0]) ).
cnf(d5,plain,
~ 'c$uCom$uOWT'('c$uCom$uOcom$uOBODY'('v$ux')),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
hAPP('c$uCom$uObody','v$ux') = 'c$uOption$uOoption$uONone'('tc$uCom$uOcom'),
inference(resolution,[status(thm)],[d5,c397]) ).
cnf(d7,plain,
hAPP('c$uMap$uOmap$u$uadd'(X0,'c$uCom$uObody','tc$uCom$uOpname','tc$uCom$uOcom'),'v$ux') = hAPP('c$uCom$uObody','v$ux'),
inference(resolution,[status(thm)],[c384,c447]) ).
cnf(d8,plain,
hAPP('c$uMap$uOmap$u$uadd'(X0,'c$uCom$uObody','tc$uCom$uOpname','tc$uCom$uOcom'),'v$ux') = 'c$uOption$uOoption$uONone'('tc$uCom$uOcom'),
inference(demodulation,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
( hAPP(X0,'v$ux') = 'c$uOption$uOoption$uONone'('tc$uCom$uOcom')
| 'c$uOption$uOoption$uONone'('tc$uCom$uOcom') != 'c$uOption$uOoption$uONone'('tc$uCom$uOcom') ),
inference(superposition,[status(thm)],[d8,c2]) ).
cnf(d10,plain,
hAPP(hAPP('c$uLattices$uOlower$u$usemilattice$u$uclass$uOinf'('tc$unat'),X0),X0) = X0,
inference(resolution,[status(thm)],[c299,c462]) ).
cnf(d11,plain,
'c$uLattices$uOupper$u$usemilattice$u$uclass$uOsup'(X0,X0,'tc$unat') = X0,
inference(resolution,[status(thm)],[c81,c461]) ).
cnf(d12,plain,
( ~ 'class$uLattices$uOupper$u$usemilattice'('tc$unat')
| 'c$ulessequals'(X0,X0,'tc$unat') ),
inference(superposition,[status(thm)],[d11,c55]) ).
cnf(d13,plain,
'c$ulessequals'(X0,X0,'tc$unat'),
inference(resolution,[status(thm)],[c461,d12]) ).
cnf(d14,plain,
( ~ 'class$uLattices$uOlower$u$usemilattice'('tc$unat')
| hAPP(hAPP('c$uLattices$uOlower$u$usemilattice$u$uclass$uOinf'('tc$unat'),X0),X0) = X0 ),
inference(resolution,[status(thm)],[d13,c64]) ).
cnf(d15,plain,
( ~ 'class$uLattices$uOlower$u$usemilattice'('tc$unat')
| X0 = X0 ),
inference(demodulation,[status(thm)],[d14,d10]) ).
cnf(d16,plain,
X0 = X0,
inference(resolution,[status(thm)],[c462,d15]) ).
cnf(d17,plain,
hAPP(X0,'v$ux') = 'c$uOption$uOoption$uONone'('tc$uCom$uOcom'),
inference(resolution,[status(thm)],[d16,d9]) ).
cnf(d18,plain,
~ hBOOL('c$uOption$uOoption$uONone'('tc$uCom$uOcom')),
inference(superposition,[status(thm)],[d17,c195]) ).
cnf(d19,plain,
hBOOL(hAPP('c$uMap$uOdom'('c$uCom$uObody','tc$uCom$uOpname','tc$uCom$uOcom'),'v$ux')),
inference(resolution,[status(thm)],[c434,c447]) ).
cnf(d20,plain,
hBOOL('c$uOption$uOoption$uONone'('tc$uCom$uOcom')),
inference(demodulation,[status(thm)],[d19,d17]) ).
cnf(d21,plain,
$false,
inference(resolution,[status(thm)],[d20,d18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV905-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n005.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 15:08:31 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.10/8.81 % SZS status Unsatisfiable for theBenchmark.p
% 9.10/8.81 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------