Proof Automation in the Theory of Finite Sets and Finite Set Relation Algebra

Abstract

Abstract $\{log\}$ (‘setlog’) is a satisfiability solver for formulas of the theory of finite sets and finite set relation algebra (FS&RA). As such, it can be used as an automated theorem prover for this theory. $\{log\}$ is able to automatically prove a number of FS&RA theorems, but not all of them. Nevertheless, we have observed that many theorems that $\{log\}$ cannot automatically prove can be divided into a few subgoals automatically dischargeable by $\{log\}$. The purpose of this work is to present a prototype interactive theorem prover (ITP), called $\{log\}$-ITP, providing evidence that a proper integration of $\{log\}$ into world-class ITP’s can deliver a great deal of proof automation concerning FS&RA. An empirical evaluation based on 210 theorems from the TPTP and Coq’s SSReflect libraries shows a noticeable reduction in the size and complexity of the proofs with respect to Coq.