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The propositional skeleton of $\varphi$ is given to a SATsolver. If a satisfying assignment is found, it is checked by a theorysolver. If the assignment is consistent with the theory, $\varphi$ is $\mathcal{T}$-satisfiable.Otherwise, a blocking clause is generated and the SAT solver searches fora new assignment. This is repeated until either a $\mathcal{T}$-consistent assignmentis found, or the SAT solver cannot find any more assignments.
See figure in lecture notes on page 11.
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