Experiments concerning the automated search for elegant proofs

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The research reported in this technical report was spawned by the request to find an elegant proof (of a theorem from Boolean algebra) to replace the known proof consisting of 816 deduced steps. The request was met by finding a proof consisting of 100 deduced steps. The methodology used to obtain the far shorter proof is presented in detail through a sequence of experiments. Although clearly not an algorithm, the methodology is sufficiently general to enable its use for seeking elegant proofs regardless of the domain of study. The methodology relies heavily on the assistance of McCune`s automated reasoning program ... continued below

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31 p.

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Wos, L. July 1, 1997.

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Description

The research reported in this technical report was spawned by the request to find an elegant proof (of a theorem from Boolean algebra) to replace the known proof consisting of 816 deduced steps. The request was met by finding a proof consisting of 100 deduced steps. The methodology used to obtain the far shorter proof is presented in detail through a sequence of experiments. Although clearly not an algorithm, the methodology is sufficiently general to enable its use for seeking elegant proofs regardless of the domain of study. The methodology relies heavily on the assistance of McCune`s automated reasoning program OTTER. Of the aspects of proof elegance, the main focus here is on proof length, with brief attention paid to the type of term present, the number of variables required, and the complexity of deduced steps. The methodology is iterative, relying heavily on the use of three strategies: the resonance strategy, the hot list strategy, and McCune`s ratio strategy. To provide some insight regarding the value of the methodology, the author discusses its successful application to other problems from Boolean algebra and to problems from lattice theory. Research suggestions and challenges are also offered.

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31 p.

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OSTI as DE97008537

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  • Other Information: PBD: Jul 1997

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  • Other: DE97008537
  • Report No.: ANL/MCS/TM--221
  • Grant Number: W-31109-ENG-38
  • DOI: 10.2172/516006 | External Link
  • Office of Scientific & Technical Information Report Number: 516006
  • Archival Resource Key: ark:/67531/metadc691735

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  • July 1, 1997

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  • Aug. 14, 2015, 8:43 a.m.

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  • Dec. 16, 2015, 12:26 p.m.

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Wos, L. Experiments concerning the automated search for elegant proofs, report, July 1, 1997; Illinois. (digital.library.unt.edu/ark:/67531/metadc691735/: accessed October 22, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.