Proving group isomorphism theorems

Extended abstract
  • Hantao Zhang
Applications of Conditional Rewriting and New Formalisms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 656)


We report the first computer proof of the three isomorphism theorems in group theory. The first theorem, the easiest of the three, was considered by Larry Wos as one of challenging problems for theorem provers. The technique we used is conditional completion which consists of one simplification rule called contextual rewriting and one inference rule called clausal superposition. Conditional completion works on conditional equations made from clauses and is a powerful method for clause-based theorem proving with equality.


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  1. [1]
    Boyer, R.S., Moore, J. S.: (1979) A Computational Logic. Academic Press, New York.Google Scholar
  2. [2]
    Ganzinger, H.: (1987) A completion procedure for conditional equations. In Kaplan, S., Jouannaud, J.-P. (eds) Proc. of Conditional Term Rewriting Systems. Lecture Notes in Computer Science, vol. 308. pp. 62–83.Google Scholar
  3. [3]
    Kaplan S.: (1984) Fair conditional term rewriting systems: unification, termination and confluence. Technical Report, LRI, Orsay.Google Scholar
  4. [4]
    Kapur, D., Zhang, H.: (1989) An overview of RRL: Rewrite Rule Laboratory. In: Dershowitz, N. (ed.): Proc. of the third international conference on rewriting techniques and its applications. Lecture Notes in Computer Science 355, Springer. pp. 513–529.Google Scholar
  5. [5]
    Knuth, D., Dendix, P.: (1970) Simple word problems in universal algebras. In: Leech, (ed.) Computational problems in abstract algebra. New York: Pergamon Press, pp. 263–297.Google Scholar
  6. [6]
    Lankford, D.S.: (1979) Some new approaches to the theory and applications of conditional term rewriting systems. Report MTP-6, Dept. of Mathematics, Lousiana Tech University, Ruston, LA.Google Scholar
  7. [7]
    Remy, J.L.: (1982) Etudes des systemes reecriture conditionelles et applications aux types abstraits algébriques. These d'etat, Universite de Nancy I, Nancy, France.Google Scholar
  8. [8]
    Wos, L.R.: (1988) Automated reasoning: 33 basic research problems. New Jersey: Prentice Hall.Google Scholar
  9. [9]
    Yu, Y.: (1990) Computer proofs in group theory. J. of Automated Reasoning 6 251–286.Google Scholar
  10. [10]
    Zhang, H., Kapur, D.: (1988) First-order logic theorem proving using conditional rewrite rules. In: Lusk, E., Overbeek, R., (eds.): Proc. of 9th international conference on automated deduction. Lecture Notes in Computer Science 310, Springer, pp. 1–20Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Hantao Zhang
    • 1
  1. 1.Department of Computer ScienceThe University of IowaIowa City

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