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Reasoning about equality

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Abstract

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.

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References

  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).

  2. Lusk, Ewing L. and Overbeek, Ross A. ‘The automated reasoning system ITP’, ANL-84-27, Argonne National Laboratory (April, 1984).

  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).

  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)

  5. Veroff R. ‘Canonicalization and demodulation’, Technical Report ANL-81–6, Argonne National Laboratory, Argonne, Illinois (February 1981).

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  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. 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. 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).

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Authors and Affiliations

  1. Argonne National Laboratory, 60439, Argonne, IL, USA

    E. L. Lusk & R. A. Overbeek

Authors
  1. E. L. Lusk
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  2. R. A. Overbeek
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Additional information

This work was supported in part by National Science Foundation grant MCS82-07496 and in part by the Applied Mathematical Sciences Research Program (KC-04-02) of the Office of Energy Research of the U.S. Department of Energy under Contract W-31-109-Eng-38.

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Lusk, E.L., Overbeek, R.A. Reasoning about equality. J Autom Reasoning 1, 209–228 (1985). https://doi.org/10.1007/BF00244996

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  • DOI: https://doi.org/10.1007/BF00244996

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