Exploring Properties of Residue Classes

We report on an experiment in exploring properties of residue classes over the integers with the combined e ort of a multi-strategy proof planner and two computer algebra systems. An exploration module classies a given set and a given operation in terms of the algebraic structure they form. It then calls the proof planner to prove or refute simple properties of the operation. Moreover, we use di erent proof planning strategies to implement various proving techniques: from naive testing of all possible cases to elaborate techniques of equational reasoning and reduction to known cases.