Generalizing DPLL and satisfiability for equalities

We present GDPLL, a generalization of the DPLL procedure. It solves the satisfiability problem for decidable fragments of quantifier-free first-order logic. Sufficient properties are identified for proving soundness, termination and completeness of GDPLL. We show how the original DPLL procedure is an instance. Subsequently the GDPLL instances for equality logic, and the logic of equality over infinite ground term algebras are presented. Based on this, we implemented a decision procedure for abstract datatypes. We provide some benchmarks.