  In this chapter we present a case study, drawn from our research work, on the
application of a fully automated theorem prover together with an automatic
counter-example generator in the investigation of a class of algebraic
structures. We will see that these tools, when combined with human insight and
traditional algebraic methods, help us to explore the problem space quickly and
effectively. The counter-example generator rapidly rules out many false
conjectures, while the theorem prover is often much more efficient than a human
being at verifying algebraic identities. The specific tools in our case study
are Prover9 and Mace4; the algebraic structures are generalisations of Heyting
algebras known as hoops. We will see how this approach helped us to discover
new theorems and to find new or improved proofs of known results. We also make
some suggestions for how one might deploy these tools to supplement a more
conventional approach to teaching algebra.
