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Abstract

The performance of a theorem prover crucially depends on the speed of the basic retrieval operations, such as finding terms that are unifiable with (instances of, or more general than) some query term. Among the known indexing methods for term retrieval in deduction systems, Path--Indexing exhibits a good performance in general. However, as Path--Indexing is not a perfect filter, the candidates found by this method have still to be subjected to a unification algorithm in order to detect occur--check failures and indirect clashes. As perfect filters, discrimination trees and abstraction trees thus outperform Path--Indexing in some cases. We present an improved version of Path--Indexing that provides both the query trees and the Path--Index with indirect clash an occur--check information. Thus compared to the standard method we dismiss much more terms as possible candidates.