# Proof-search in intuitionistic logic based on constraint satisfaction

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## Abstract

We characterize provability in intuitionistic predicate logic in terms of derivation skeletons and constraints and study the problem of instantiations of a skeleton to valid derivations. We prove that for two different notions of a skeleton the problem is respectively polynomial and NP-complete. As an application of our technique, we demonstrate PSPACE-completeness of the prenex fragment of intuitionistic logic. We outline some applications of the proposed technique in automated reasoning.

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© Springer-Verlag Berlin Heidelberg 1996