A Clausal Normal Form Translation for FOOL

Abstract

Automated theorem provers for first-order logic usually operate on sets of first-order clauses. It is well-known that the translation of a formula in full first-order logic to a clausal normal form (CNF) can crucially affect performance of a theorem prover. In our recent work we introduced a modification of first-order logic extended by the first class boolean sort and syntactical constructs that mirror features of programming languages. We called this logic FOOL. Formulas in FOOL can be translated to ordinary first-order formulas and checked by first-order theorem provers. While this translation is straightforward, it does not result in a CNF that can be efficiently handled by state-of-the-art theorem provers which use superposition calculus. In this paper we present a new CNF translation algorithm for FOOL that is friendly and efficient for superposition-based first-order provers. We implemented the algorithm in the Vampire theorem prover and evaluated it on a large number of problems coming from formalisation of mathematics and program analysis. Our experimental results show an increase of performance of the prover with our CNF translation compared to the naive translation.