Ordered Paramodulation and Resolution as Decision Procedure

In recent years interesting decidability results for syntactically specified classes of clause sets have been achieved by employing resolution as a decision procedure. We extend this line of research by considering also clauses with equality literals. We use a special version of ordered paramodulation and resolution to decide a class of clause sets that corresponds to an extension of the Ackermann class with equality (i.e., prenex formulas with prefixes of type ∃*∀∃*). By encoding Turing machines we also show that slight modifications of the defining conditions for this class lead to undecidability.