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Yes, it's possible to use a customized theory with an SMT solver. SMT solvers are designed to support multiple theories, and users can define their customized theories using the solver’s language of choice. The customized theory can be implemented by providing axioms, definitions, and inference rules, which extend the existing theory supported by the solver. Once this is done, the user can use the customized theory with the solver to check the satisfiability of logical formulas. However, implementing customized theories can be challenging and requires expertise in both the underlying theory and the SMT solver's implementation.