Abstract

This report presents a methodology to guide equational reasoning in a goal directed way. Suggested by rippling methods developed in the field of inductive theorem proving we use attributes of terms and heuristics to determine bridge lemmas, i.e. lemmas which have to be used during the proof of the theorem. Once we have found such a bridge lemma we use the techniques of difference unification and rippling to enable its use. Tel. (+49 681) 302 5316, email: cleve@dfki.uni-sb.de y Tel. (+49 681) 302 5317, email: hutter@dfki.uni-sb.de 1 Introduction Automated theorem provers suffer from their inability or inefficiency in solving problems. This effect is especially the case if equality is included. The most promising approach to mechanize equality reasoning stems from Knuth and Bendix [KB70] who restricted the application of equations (by using them as rewrite rules) and formulated their completion calculus which led to an considerable decrease of the search space. The original comple...

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