Solving satisfiability of ground term algebras using DPLL and unification

datatypes can be viewed as sorted ground term algebras. Unification can be used to solve conjunctions of equations. We give a new algorithm to extend this to the full quantifier free fragment, i.e. including formulas with disjunction and negation. The algorithm is based on unification (to deal with equality) and DPLL (to deal with propositional logic). In this paper we present our algorithm as an instance of a generalized DPLL algorithm. We prove soundness and completeness of the class of generalized DPLL algorithms, in particular for the algorithm for ground term algebras.