Minimizing the number of clauses by renaming

  • Thierry Boy de la Tour
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 449)


The problem of translating a formula into a “good” clause form is known to be a very important one in resolution automated theorem proving. Some theorems have such a huge clause form that it is practically impossible to prove them by resolution. Several methods exist to reduce clause forms, some applied before and some after translation. They are generally based on (local or non-local) simplifications. A method consisting in the creation and use of definitions, which we call renaming, has been developed in [5], [4] and [7]. Applying it in an exhaustive way was shown to yield a translation into clause form polynomial in size (see [7]). In this paper we investigate non exhaustive renamings in the purpose of minimizing the number of clauses. We obtain a translation which is shown to be polynomial in size, and optimal in number of clauses when the theorem contains no equivalence. An example shows that this translation is not necessarily optimal in presence of equivalence. Experiments with “challenge” examples show the practical efficiency of this translation.


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  1. [1]
    Thierry Boy de la Tour. A Locally Optimal Transformation Into Clause Form using Partial Formula Renaming. RR 765-I-IMAG — 90 LIFIA, institut IMAG, BP 68, 38402 Saint Martin d'Hères cedex, January 1989.Google Scholar
  2. [2]
    Thierry Boy de la Tour, Ricardo Caferra, and Gilles Chaminade. Some tools for an inference laboratory (atinf). In E. Lusk and R. Overbeek, editors, Proceedings of the 9th International Conference on Automated Deduction, pages 744–745, Springer Lecture Notes in Computer Science 310, 1988.Google Scholar
  3. [3]
    Thierry Boy de la Tour and Gilles Chaminade. Renommage et forme clausale. In Actes des 3e Journées nationales PRC-GDR Intelligence artificielle, pages 183–192, éditions Hermès, March 1990.Google Scholar
  4. [4]
    Elmar Eder. An implementation of a theorem prover based on the connection method. In W. Bibel and B. Petkoff, editors, AIMSA'84, Artificial Intelligence—Methodology Systems Application, pages 121–128, North-Holland, September 1984.Google Scholar
  5. [5]
    L. Henshen, E. Lusk, R. Overbeek, B.T. Smith, R. Veroff, S. Winker, and L. Wos. Challenge problem 1. SIGART newsletter, (72):30–31, July 1980.Google Scholar
  6. [6]
    J.F. Pelletier. Seventy-five problems for testing automatic theorem provers. Journal of Automated Reasoning, 2:191–216, 1986.Google Scholar
  7. [7]
    David A. Plaisted and Steven Greenbaum. A structure-preserving clause form translation. Journal of Symbolic Computation, 2:293–304, 1986.Google Scholar
  8. [8]
    Larry Wos. Automated Reasoning: 33 Basic Research Problems. Prentice-Hall, 1988.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Thierry Boy de la Tour
    • 1
  1. 1.Laboratoire d'Informatique Fondamentale et d'Intelligence ArtificielleIMAG - CNRSGrenoble cedexFrance

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