Induction = I-axiomatization plus first-order consistency

In the early 1980s, there was a number of papers on what should be called proofs by consistency, They describe how to perform inductive proofs, without using an explicit induction scheme, in the context of equational specifications and ground-convergent rewrite systems. The method was explicitly stated as a first-order consistency proof in the case of pure equational, constructor-based specifications. In this paper, we show how, in general, inductive proofs can be reduced to first-order consistency and hence be performed by a first-order theorem prover. Moreover, we extend previous methods, allowing nonequational specifications (even non-Horn specifications) and designing some specific strategies. Finally, we also show how to drop the ground convergence requirement (which is called Saturatedness for general clauses). (C) 2000 Academic Press.