<s>
In	O
computer	O
science	O
,	O
DPLL(T )	O
is	O
a	O
framework	O
for	O
determining	O
the	O
satisfiability	O
of	O
SMT	B-Application
problems	O
.	O
</s>
<s>
The	O
algorithm	O
extends	O
the	O
original	O
SAT-solving	O
DPLL	B-Application
algorithm	I-Application
with	O
the	O
ability	O
to	O
reason	O
about	O
an	O
arbitrary	O
theory	O
T	O
.	O
At	O
a	O
high	O
level	O
,	O
the	O
algorithm	O
works	O
by	O
transforming	O
an	O
SMT	B-Application
problem	O
into	O
a	O
SAT	B-Algorithm
formula	O
where	O
atoms	O
are	O
replaced	O
with	O
Boolean	O
variables	O
.	O
</s>
<s>
The	O
algorithm	O
repeatedly	O
finds	O
a	O
satisfying	O
valuation	O
for	O
the	O
SAT	B-Algorithm
problem	I-Algorithm
,	O
consults	O
a	O
theory	B-Application
solver	I-Application
to	O
check	O
consistency	O
under	O
the	O
domain-specific	O
theory	O
,	O
and	O
then	O
(	O
if	O
a	O
contradiction	O
is	O
found	O
)	O
refines	O
the	O
SAT	B-Algorithm
formula	O
with	O
this	O
information	O
.	O
</s>
<s>
Many	O
modern	O
SMT	B-Application
solvers	I-Application
,	O
such	O
as	O
Microsoft	O
's	O
Z3	B-Language
Theorem	I-Language
Prover	I-Language
,	O
use	O
DPLL(T )	O
to	O
power	O
their	O
core	O
solving	O
capabilities	O
.	O
</s>
