Analogy Makes Proofs Feasible

Many mathematical proofs are hard to generate for humans and even harder for automated theorem provers. Classical techniques of automated theorem proving involve the appli-cation of basic rules, of built-in special procedures, or of tactics. Melis (Melis 1993) introduced a new method for analogical reasoning in automated theorem proving. In this paper we show how the derivational analogy replay method is related and extended to encompass analogy-driven proof plan construction. The method is evaluated by showing the proof plan generation of the Pumping Lemma for context free languages derived by analogy with the proof plan of the Pumping Lemma for regular languages. This is an impressive evaluation test for the analogical reasoning method applied to automated theorem proving, as the automated proof of this Pumping Lemma is beyond the capabilities of any of the current automated theorem provers.