Challenge problems from nonassociative rings for theorem provers
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.
Unable to display preview. Download preview PDF.
- 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
- E. Lusk and R. Overbeek. The Automated Reasoning System ITP. Argonne National Laboratory, ANL-84-27, 1984.Google Scholar
- R. D. Schafer. An Introduction to Nonassociative Algebras. Academic Press, New York, 1966.Google Scholar
- K. A. Zhevlakov, et. al. Rings that are Nearly Associative. Academic Press, New York, 1982.Google Scholar
- 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
- 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
- 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