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10th International Conference on Automated Deduction

Volume 449 of the series Lecture Notes in Computer Science pp 485-499

Date:

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

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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 UR-resolution. 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.