Abstract
This paper reports the results of an experiment in using the Boyer-Moore Theorem Prover in seeking computer-checked proofs in Group Theory. Starting from the axioms for groups and elementary list and number theory, the theorem prover was led to the proofs of two basic theorems in Elementary Group Theory by a sequence of lemmas suggested by the author. The computer proofs illustrate the effective use of the Boyer-Moore Theorem Prover in Group Theory.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
R. S. Boyer and J S. Moore, A Computational Logic, Academic Press, New York, 1979.
R. S. Boyer and J S. Moore, A Computational Logic Handbook, Perspectives in Computing Vol. 23, Academic Press, New York, 1988.
R. S. Boyer, E. Lusk, W. McCune, R. Overbeek, M. Stickel and L. Wos, ‘Set theory in first-order logic: clauses for Gödel's axioms’, J. Automated Reasoning 2 (1986) 287–327.
C. Chang and R. Lee, Symbolic Logic and Mechanical Theorem Proving, Academic Press, New York, 1973.
Thomas W. Hungerford, Algebra, Springer-Verlag, New York, 1980.
Matt Kaufmann, ‘DEFN-SK: An Extension of the Boyer-Moore Theorem Prover to Handle First-Order Quantifiers’, Tech. Report 43, Computational Logic, Inc., 1989.
David M. Russinoff, ‘A mechanical proof of Wilson's theorem’, J. Automated Reasoning 1 (1985) 121–139.
N. Shankar, ‘Towards mechanical metamathematics’, J. Automated Reasoning 1(4) (1985) 407–434.
L. Wos, Automated Reasoning: 33 Basic Research Problems, Prentice-Hall, Englewood Cliffs, New Jersey, 1987.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Yu, Y. Computer proofs in Group Theory. J Autom Reasoning 6, 251–286 (1990). https://doi.org/10.1007/BF00244488
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00244488