Saturation-based theorem proving: Past successes and future potential

Abstract

Saturation means to compute the closure of a given set of formulas under a given set of inference rules. Resolution, Knuth/Bendix completion, and Superposition are major examples of saturation-based, automated theorem proving methods. More recently, considerable progress has made in this area. New theoretical insight has been gained. In particular the nature of redundancy and of mechanisms for avoiding redundancy is now better understood. This has many applications, both in theory and in practice. New provers based on these ideas are emerging and seem to perform well, outperforming existing automated provers in many respects. The talk surveys some of the theoretical results, describes experience gained from experimentation, and outlines problems and potential for future research.