Integrating Simplex with Tableaux

TL;DR: An extension of a tableau-based calculus to deal with linear arithmetic is proposed, consisting of a smooth integration of arithmetic deductive rules to the basic tableau rules, so that there is a natural interleaving between arithmetic and regular analytic rules.

Abstract: We propose an extension of a tableau-based calculus to deal with linear arithmetic. This extension consists of a smooth integration of arithmetic deductive rules to the basic tableau rules, so that there is a natural interleaving between arithmetic and regular analytic rules. The arithmetic rules rely on the general simplex algorithm to compute solutions for systems over rationals, as well as on the branch and bound method to deal with integer systems. We also describe our implementation in the framework of Zenon, an automated theorem prover that is able to deal with first order logic with equality. This implementation has been provided with a backend verifier that relies on the Coq proof assistant, and which can verify the validity of the generated arithmetic proofs. Finally, we present some experimental results over the arithmetic category of the TPTP library, and problems of program verification coming from the benchmark provided by the BWare project.