Mining counterexamples for wide-signature algebras with an Isabelle server

Abstract

We propose an approach for searching for counterexamples of statements about algebraic structures with a medium-sized signature using the Isabelle proof assistant in an efficient, parallel manner. We contribute a Python client Isabelle server and other scripts implementing our approach, and provide results of our computational experiments. In particular, our experiments yield counterexamples that resolve a previously open question regarding the interdependencies between distributive-like identities in residuated binars.