The structure of commutative A-loops Michael Kinyon and Petr Vojtechovsky A-loops, introduced by Bruck and Paige in 1956, are loops for which every inner mapping is an automorphism. In recent work with Premysl Jedlicka, we have learned much about the structure of commutative A-loops. In these talks we will describe this structure. In Part 1, Petr will give the necessary background and discuss the main results and their signficance in understanding commutative A-loops. In Part 2, Michael will focus on how Prover9 was used both to prove and to simplify the proofs of certain results.