Computing Tiny Clause Normal Forms

  • Noran Azmy
  • Christoph Weidenbach
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7898)

Abstract

Automated reasoning systems which build on resolution or superposition typically operate on formulas in clause normal form (CNF). It is well-known that standard CNF translation of a first-order formula may result in an exponential number of clauses. In order to prevent this effect, renaming techniques have been introduced that replace subformulas by atoms over fresh predicates and introduce definitions accordingly. This paper presents generalized renaming. Given a formula and a set of subformulas to be renamed, it is suggested to use one atom to replace all instances of a generalization of a given subformula. A generalized renaming algorithm and an implementation as part of the SPASS theorem prover are described. The new renaming algorithm is faster than the previous one implemented in SPASS. Experiments on the TPTP show that generalized renaming significantly reduces the number of clauses and the average time taken to solve the problems afterward.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Noran Azmy
    • 1
  • Christoph Weidenbach
    • 1
  1. 1.Max Planck Institute for InformaticsGermany

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