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Martin Jonáš
DTEDI
Commits
a6c04467
Commit
a6c04467
authored
Sep 05, 2016
by
Martin Jonas
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Polshing
parent
e1cf28a7
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Chapters/Chapter02.tex
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a6c04467
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@@ -760,13 +760,13 @@ its model $M$ and another call to the \QFBV solver is made to
determine whether
$
M
$
is also a~model of
$
\forall
x
_
1
, x
_
2
,
\dots
, x
_
n
\,
(
\psi
)
$
. This is achieved by asking
the solver whether the formula
$
\neg
\widehat
{
\psi
}$
is satisfiable,
where
$
\widehat
{
\psi
}$
is the formula
$
\psi
$
after
substitut
ing
v
al
ues
of
all variables except for
$
x
_
1
\ldots
x
_
n
$
and uninterpreted
functions replace
d by their values in
$
M
$
. If
$
\neg
\widehat
{
\psi
}$
is
not
satisfiable, then the structure
$
M
$
is indeed a model of the
formula
$
\forall
x
_
1
, x
_
2
,
\dots
, x
_
n
\,
(
\psi
)
$
, therefore the entire
formula
is satisfiable and
$
M
$
is its model. If
$
\neg
\widehat
{
\psi
}$
is
satisfiable, we get values
$
v
_
1
,
\dots
, v
_
n
$
such that
where
$
\widehat
{
\psi
}$
is the formula
$
\psi
$
after
replac
ing al
l
uninterpreted functions and
all variables except for
$
x
_
1
\ldots
x
_
n
$
an
d by their values in
$
M
$
. If
$
\neg
\widehat
{
\psi
}$
is
not
satisfiable, then the structure
$
M
$
is indeed a model of the
formula
$
\forall
x
_
1
, x
_
2
,
\dots
, x
_
n
\,
(
\psi
)
$
, therefore the entire
formula
is satisfiable and
$
M
$
is its model. If
$
\neg
\widehat
{
\psi
}$
is
satisfiable, we get values
$
v
_
1
,
\dots
, v
_
n
$
such that
$
\neg\widehat
{
\psi
}
[
v
_
1
,
\dots
, v
_
n
]
$
holds. To rule out
$
M
$
as a
model of the input formula, the instance
$
\psi
[
v
_
1
,
\dots
, v
_
n
]
$
of
the quantified formula is added to the quantifier-free part, i.e.~the
...
...
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