An algorithm for computing theory prime implicates in first order logic

An algorithm based on consensus method to compute the set of prime implicates of a quantifier free first order formula X was presented in an earlier work. In this paper the notion of prime implicates is extended to theory prime implicates in the first order case. We provide an algorithm to compute the theory prime implicates of a Knowledge base X with respect to another knowledge base Y where both X and Y are assumed to be unquantified first order formulas. The partial correctness of the algorithm is proved.