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There is a relatively large number of papers dealing with complexity and proof theory issues of infinitely-valued logics. Nevertheless, little attention has been paid so far to the development of efficient solvers for such logics. In this paper we show how the technology of Satisfiability Modulo Theories (SMT) can be used to build efficient automated theorem provers for relevant infinitely-valued logics, including Lukasiewicz, Gödel and Product logics. Moreover, we define a test suite for those logics, and report on an experimental investigation that evaluates the practical complexity of Lukasiewicz and Gödel logics, and provides empirical evidence of the good performance of SMT technology for automated theorem proving on infinitely-valued logics.