Abstract
In this paper, we offer a set of problems for evaluating the power of automated theorem-proving programs and the potential of new ideas. Since the problems published in the proceedings of the first CADE conference proved to be so useful, and since researchers are now far more disposed to implementing and testing their ideas, a new set of problems is in order to complement those that have been widely studied. In general, the new problems provide a far greater challenge for an automated theorem-proving program than those in the first set do. Indeed, to our knowledge, five of the six problems we propose for study have never been proved with a theorem-proving program. For each problem, we give a set of statements that can easily be translated into a standard set of clauses. We also state each problem in its mathematical and logical form. In many cases, we provide a proof of the theorem from which a problem is taken so that one can measure a program's progress in its attempt to solve the problem. Two of the theorems we discuss are of especial interest in that they answer previously open questions concerning the constructibility of two types of combinator. We also include a brief description of a new strategy for restricting the application of paramodulation. All of the problems we propose for study emphasize the role of equality. This paper is tutorial in nature.
This work was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under contract W-31-109-Eng-38.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
Barendregt, H. P., The Lambda Calculus: Its Syntax and Semantics, North-Holland, Amsterdam (1981).
Curry, H. B., and Feys, R., Combinatory Logic I, North-Holland, Amsterdam (1958).
Curry, H. B., Hindley, J. R., and Seldin, J. P., Combinatory Logic II, North-Holland, Amsterdam (1972).
McCharen, J., Overbeek, R., and Wos, L., “Problems and experiments for and with automated theorem proving programs”, IEEE Transactions on Computers C-25, pp. 773–782 (1976).
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, Edinburgh (1969).
Smullyan, R., To Mock a Mockingbird, Alfred A. Knopf, New York (1985).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1988 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wos, L., McCune, W. (1988). Challenge problems focusing on equality and combinatory logic: Evaluating automated theorem-proving programs. In: Lusk, E., Overbeek, R. (eds) 9th International Conference on Automated Deduction. CADE 1988. Lecture Notes in Computer Science, vol 310. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0012870
Download citation
DOI: https://doi.org/10.1007/BFb0012870
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-19343-2
Online ISBN: 978-3-540-39216-3
eBook Packages: Springer Book Archive