10th International Conference on Automated Deduction
Volume 449 of the series Lecture Notes in Computer Science pp 485499
Automated reasoning contributes to mathematics and logic
 L. WosAffiliated withMathematics and Computer Science Division, Argonne National Laboratory
 , S. WinkerAffiliated withMathematics and Computer Science Division, Argonne National Laboratory
 , W. McCuneAffiliated withMathematics and Computer Science Division, Argonne National Laboratory
 , R. OverbeekAffiliated withMathematics and Computer Science Division, Argonne National Laboratory
 , E. LuskAffiliated withMathematics and Computer Science Division, Argonne National Laboratory
 , R. StevensAffiliated withMathematics and Computer Science Division, Argonne National Laboratory
 , R. ButlerAffiliated withDivision of Computer and Information Science, University of North Florida
Abstract
In this article, we present some results of our research focusing on the use of our newest automated reasoning program OTTER to prove theorems from Robbins algebra, equivalential calculus, implicational calculus, combinatory logic, and finite semigroups. Included among the results are answers to open questions and new shorter and less complex proofs to known theorems. To obtain these results, we relied upon our usual paradigm, which heavily emphasizes the role of demodulation, subsumption, set of support, weighting, paramodulation, hyperresolution, and URresolution. Our position is that all of these components are essential, even though we can shed little light on the relative importance of each, the coupling of the various components, and the metarules for making the most effective choices. Indeed, without these components, a program will too often offer inadequate control over the redundancy and irrelevancy of deduced information. We include experimental evidence to support our position, examples producing success when the paradigm is employed, and examples producing failure when it is not. In addition to providing evidence that automated reasoning has made contributions to both mathematics and logic, the theorems we discuss also serve nicely as challenge problems for testing the merits of a new idea or a new program and provide interesting examples for comparing different paradigms.
 Title
 Automated reasoning contributes to mathematics and logic
 Book Title
 10th International Conference on Automated Deduction
 Book Subtitle
 Kaiserslautern, FRG, July 24–27, 1990 Proceedings
 Pages
 pp 485499
 Copyright
 1990
 DOI
 10.1007/3540528857_109
 Print ISBN
 9783540528852
 Online ISBN
 9783540471714
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 449
 Series Subtitle
 Lecture Notes in Artificial Intelligence
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
 Additional Links
 Topics
 Industry Sectors
 Editors
 Authors

 L. Wos ^{(1)}
 S. Winker ^{(1)}
 W. McCune ^{(1)}
 R. Overbeek ^{(1)}
 E. Lusk ^{(1)}
 R. Stevens ^{(1)}
 R. Butler ^{(2)}
 Author Affiliations

 1. Mathematics and Computer Science Division, Argonne National Laboratory, 604394844, Argonne, IL
 2. Division of Computer and Information Science, University of North Florida, 32216, Jacksonville, FL
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