Journal of Automated Reasoning

, Volume 1, Issue 2, pp 209–228 | Cite as

Reasoning about equality

  • E. L. Lusk
  • R. A. Overbeek
Problem Corner


This note contains a set of six theorems that can be used to assess the ability of a theorem-proving system to reason about equality. The six theorems are graduated in terms of difficulty: they range from fairly trivial to quite difficult. They do not cover all aspects of equality reasoning, but they have proved useful to us in developing our system.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Knuth D. E. and Bendix, P. B. ‘Simple word problems in universal algebras’, pp. 263–297 in Computational Problems in Abstract Algebra (ed. Leech) Pergamon Press (1970).Google Scholar
  2. 2.
    Lusk, Ewing L. and Overbeek, Ross A. ‘The automated reasoning system ITP’, ANL-84-27, Argonne National Laboratory (April, 1984).Google Scholar
  3. 3.
    Robinson, G. and Wos, L. ‘Paramodulation and theorem proving in first-order theories with equality’, pp. 135–150 in Machine Intelligence 4 (ed. B. Meltzer and D. Michie) Edinburgh University Press (1969).Google Scholar
  4. 4.
    Stickel, Mark E. ‘A case study of theorem proving by the Knuth-Bendix method discovering that x 3=x implies ring commutativity’, in Proceedings of the 7th International Conference on Automated Deduction (ed. R. E. Shostak)Google Scholar
  5. 5.
    Veroff R. ‘Canonicalization and demodulation’, Technical Report ANL-81–6, Argonne National Laboratory, Argonne, Illinois (February 1981).Google Scholar
  6. 6.
    Wos Larry, Overbeek Ross, Lusk Ewing and Boyle Jim, Automated Reasoning: Introduction and Applications, Prentice-Hall, Englewood Cliffs, New Jersey (1984).Google Scholar
  7. 7.
    Wos L. Robinson G. Carson D. and Shalla L. ‘The concept of demodulation in theorem proving’, Journal of the ACM 14, 698–704 (1967).Google Scholar
  8. 8.
    Wos L. and Robinson, G. A. ‘Paramodulation and set of support’, Proceedings of the IRIA Symposium on Automatic Demonstration, Versailles, France, Springer-Verlag pp. 276–310 (1968).Google Scholar

Copyright information

© D. Reidel Publishing Company 1985

Authors and Affiliations

  • E. L. Lusk
    • 1
  • R. A. Overbeek
    • 1
  1. 1.Argonne National LaboratoryArgonneUSA

Personalised recommendations