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Proofs by induction are important in many computer science and arti cial intelligence applications, in particular, in program veri cation and speci cation systems. We present a new method to prove (and disprove) automatically inductive properties. Given a set of axioms, a well-suited induction scheme is constructed automatically. We call such an induction scheme a test set. Then, for proving a property, we just instantiate it with terms from the test set and apply pure algebraic simpli cationdoi:10.1093/logcom/5.5.631 fatcat:4z7dvzo74zflfduyzs5grwceka