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Proof Development with ΩMEGA: √2 Is Irrational

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Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2002)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2514))

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Abstract

Freek Wiedijk proposed the well-known theorem about the irrationality of √2 as a case study and used this theorem for a comparison of fifteen (interactive) theorem proving systems, which were asked to present their solution (see [48]).

This represents an important shift of emphasis in the field of automated deduction away from the somehow artificial problems of the past as represented, for example, in the test set of the TPTP library [45] back to real mathematical challenges.

In this paper we present an overview of the Ωmega system as far as it is relevant for the purpose of this paper and show the development of a proof for this theorem.

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Authors and Affiliations

  1. FR 6.2 Informatik, Universität des Saarlandes, 66041, Saarbrücken, Germany

    J. Siekmann, C. Benzmüller, A. Fiedler, A. Meier & M. Pollet

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  1. J. Siekmann
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  2. C. Benzmüller
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  3. A. Fiedler
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  4. A. Meier
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  5. M. Pollet
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Editors and Affiliations

  1. Abteilung für Theoretische Informatik, Institut für Algebra und Diskrete Mathematik, Wiedner Hauptstr. 8-10, 1040, Wien, Austria

    Matthias Baaz

  2. Department of Computer Science, University of Manchester, Kilburn Building, Oxford Road, Manchester, M13, 9PL, UK

    Andrei Voronkov

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Siekmann, J., Benzmüller, C., Fiedler, A., Meier, A., Pollet, M. (2002). Proof Development with ΩMEGA: √2 Is Irrational. In: Baaz, M., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2002. Lecture Notes in Computer Science(), vol 2514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36078-6_25

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  • DOI: https://doi.org/10.1007/3-540-36078-6_25

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