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

Maximiliano Cristiá, Ricardo D. Katz, Gianfranco Rossi

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.