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Challenge problems from nonassociative rings for theorem provers

  • Rick L. Stevens
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 310)

Abstract

The Moufang Identities are proving to be a challenging set of problems for automated theorem proving programs. Aside from one program that uses a new technique that has the axioms of nonassociative ring theorem built in, I know of no other program able to prove these identities. In this short paper I include the axioms for nonassociative rings, statements of the five moufang identities, a natural hand proof of one of the left identities and a human guided paramodulation proof of the same identity. I hope that this paper will provide a starting point for others to attack these interesting problems.

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References

  1. [1]
    L. Wos and G. A. Robinson Paramodulation and set of support. in Proceedings of the IRIA Symposium on Automatic Demonstration, Versailles, France, Springer-Verlag Publ. 1968, 276–310.Google Scholar
  2. [2]
    E. Lusk and R. Overbeek. The Automated Reasoning System ITP. Argonne National Laboratory, ANL-84-27, 1984.Google Scholar
  3. [3]
    R. D. Schafer. An Introduction to Nonassociative Algebras. Academic Press, New York, 1966.Google Scholar
  4. [4]
    K. A. Zhevlakov, et. al. Rings that are Nearly Associative. Academic Press, New York, 1982.Google Scholar
  5. [5]
    R. L. Stevens, Some Experiments in Nonassociative Ring Theory with an Automated Theorem Prover, Journal of Automated Reasoning, Vol 3 No. 2, 1987.Google Scholar
  6. [6]
    T. C. Wang, Case Studies of Z-module Reasoning: Proving Benchmark Theorems from Ring Theory, Journal of Automated Reasoning, Vol 3 No. 4, 1987.Google Scholar
  7. [7]
    T. C. Wang and R. L. Stevens, Solving Open Problems in Right Alternative Rings with Z-Module Reasoning, Submitted to Journal of Automated Reasoning.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Rick L. Stevens
    • 1
  1. 1.Argonne National LaboratoryArgonne

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