Optimizing proof search in model elimination

  • John Harrison
Session 5A
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1104)


Many implementations of model elimination perform proof search by iteratively increasing a bound on the total size of the proof. We propose an optimized version of this search mode using a simple divide-and-conquer refinement. Optimized and unoptimized modes are compared, together with depth-bounded and best-first search, over the entire TPTP problem library. The optimized size-bounded mode seems to be the overall winner, but for each strategy there are problems on which it performs best. Some attempt is made to analyze why. We emphasize that our optimization, and other implementation techniques like caching, are rather general: they are not dependent on the details of model elimination, or even that the search is concerned with theorem proving. As such, we believe that this study is a useful complement to research on extending the model elimination calculus.


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  1. 1.
    O. L. Astrachan and M. E. Stickel. Caching and lemmaizing in model elimination theorem provers. In D. Kapur, editor, 11th International Conference on Automated Deduction, volume 607 of Lecture Notes in Computer Science, pages 224–238, 1992. Springer-Verlag.Google Scholar
  2. 2.
    P. Baumgartner and U. Furbach. Model elimination without contrapositives and its application to PTTP. Research report 12-93, Institute for Computer Science, University of Koblenz, 1993.Google Scholar
  3. 3.
    B. Beckert and J. Posegga. leanT A P: Lean, tableau-based deduction. Journal of Automated Reasoning, 15:339–358, 1995.CrossRefGoogle Scholar
  4. 4.
    M. J. C. Gordon and T. F. Melham. Introduction to HOL: a theorem proving environment for higher order logic. Cambridge University Press, 1993.Google Scholar
  5. 5.
    R. E. Korf. Depth-first iterative-deepening: An optimal admissible tree search. Artificial Intelligence, 27:97–109, 1985.MathSciNetGoogle Scholar
  6. 6.
    R. Letz, J. Schumann, S. Bayerl, and W. Bibel. SETHEO: A high-performance theorem proven. Journal of Automated Reasoning, 8:183–212, 1992.MathSciNetGoogle Scholar
  7. 7.
    R. Letz, K. Mayr, and C. Goller. Controlled integrations of the cut rule into connection tableau calculi. Technical Report AR-94-01, TU München, 1994.Google Scholar
  8. 8.
    V. Lifschitz. Mechanical Theorem Proving in the USSR: the Leningrad School. Monograph Series on Soviet Union. Delphic Associates, 1986. See also ‘What is the inverse method?’ in the Journal of Automated Reasoning, vol. 5, pp. 1–23, 1989.Google Scholar
  9. 9.
    D. W. Loveland. Mechanical theorem-proving by model elimination. Journal of the ACM, 15:236–251, 1968.CrossRefGoogle Scholar
  10. 10.
    D. Michie. “Memo” functions and machine learning. Nature, 218:19–22, 1968.Google Scholar
  11. 11.
    L. C. Paulson. Isabelle: a generic theorem prover, volume 828 of Lecture Notes in Computer Science. Springer-Verlag, 1994. With contributions by Tobias Nipkow.Google Scholar
  12. 12.
    D. A. Plaisted. A sequent-style model elimination strategy and a positive refinement. Journal of Automated Reasoning, 6:389–402, 1990.CrossRefGoogle Scholar
  13. 13.
    P. Rudnicki. Obvious inferences. Journal of Automated Reasoning, 3:383–393, 1987.CrossRefGoogle Scholar
  14. 14.
    M. E. Stickel. A Prolog Technology Theorem Prover: Implementation by an extended Prolog compiler. Journal of Automated Reasoning, 4:353–380, 1988.CrossRefGoogle Scholar
  15. 15.
    C. B. Suttner and G. Sutcliffe. The TPTP problem library. Technical Report AR-95-03, TU München, 1995.Google Scholar
  16. 16.
    M. Tarver. An examination of the Prolog Technology Theorem-Prover. In M. E. Stickel, editor, 10th International Conference on Automated Deduction, volume 449 of Lecture Notes in Computer Science, pages 322–335, 1990. Springer-Verlag.Google Scholar
  17. 17.
    P. Weis and X. Leroy. Le langage Caml. InterEditions, 1993. See also the CAML Web page: http://pauillac.inria.fr/caml/.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • John Harrison
    • 1
  1. 1.Department of Computer ScienceÅbo Akademi UniversityTurkuFinland

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