System description: similarity-based lemma generation for model elimination

Abstract

ATP systems based on model elimination (ME) [5] or the connection tableau calculus [4] have become more and more successful. But a problem regarding the use of ME is the fact that ME proof procedures are among the weakest procedures when the length of existing proofs is considered. The use of lemmas offers a solution to this problem. Successful sub-deductions are stored in form of lemmas and the input clauses are augmented with these formulas. But although lemmas can help to decrease the proof length they also increase the branching rate of the search space. An unbounded generation of lemmas without filtering relevant lemmas is not sensible. Actually, filter mechanisms are in use that ignore the proof task at hand (cp. [1,8]). It may be more appropriate to use similarity criteria between the proof goal and a possible lemma (lemma candidate) in order to filter lemmas. Thus, we will present a model for similarity-based lemma use.