Classification results in quasigroup and loop theory via a combination of automated reasoning tools

We present some novel partial classification results in quasigroup and loop theory. For quasigroups up to size XXX and loops up to size YYY, we describe a unique property which determines the isomorphism (and in the case of loops, the isotopism) class for any example. These invariant properties were generated using a variety of automated techniques – including machine learning and computer algebra – which we present here. Moreover, each result has been automatically verified, again using a variety of techniques – including automated theorem proving, computer algebra and satisfiability solving – and we describe our bootstrapping approach to the generation and verification of these classification results.