The propositional skeleton of $\varphi$ is given to a SAT
solver. If a satisfying assignment is found, it is checked by a theory
solver. If the assignment is consistent with the theory, $\varphi$ is $\mathcal{T}$-satisfiable.
Otherwise, a blocking clause is generated and the SAT solver searches for
a new assignment. This is repeated until either a $\mathcal{T}$-consistent assignment
is found, or the SAT solver cannot find any more assignments.

See figure in lecture notes on page 11.