First-Order Logic Theorem Proving via Counterexample-Guided Abstraction Refinement

Counterexample-guided abstraction refinement is a well-established technique in verification. In this paper we instantiate the idea for firstorder logic theorem proving. Given a clause set N we propose its abstraction into a clause set N ′ belonging to a decidable first-order fragment. The abstraction preserves satisfiability: if N ′ is satisfiable, so is N . A refutation in N ′ can then either be lifted to a refutation in N , or it guides a refinement of N and its abstraction N ′ excluding the previously found refutation that is not liftable.