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Learning-Assisted Automated Reasoning with Flyspeck

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  • Published: 01 June 2014
  • Volume 53, pages 173–213, (2014)
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Learning-Assisted Automated Reasoning with Flyspeck
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  • Cezary Kaliszyk1 &
  • Josef Urban2 

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An Erratum to this article was published on 18 October 2014

Abstract

The considerable mathematical knowledge encoded by the Flyspeck project is combined with external automated theorem provers (ATPs) and machine-learning premise selection methods trained on the Flyspeck proofs, producing an AI system capable of proving a wide range of mathematical conjectures automatically. The performance of this architecture is evaluated in a bootstrapping scenario emulating the development of Flyspeck from axioms to the last theorem, each time using only the previous theorems and proofs. It is shown that 39 % of the 14185 theorems could be proved in a push-button mode (without any high-level advice and user interaction) in 30 seconds of real time on a fourteen-CPU workstation. The necessary work involves: (i) an implementation of sound translations of the HOL Light logic to ATP formalisms: untyped first-order, polymorphic typed first-order, and typed higher-order, (ii) export of the dependency information from HOL Light and ATP proofs for the machine learners, and (iii) choice of suitable representations and methods for learning from previous proofs, and their integration as advisors with HOL Light. This work is described and discussed here, and an initial analysis of the body of proofs that were found fully automatically is provided.

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Authors and Affiliations

  1. University of Innsbruck, Innsbruck, Austria

    Cezary Kaliszyk

  2. Radboud University, Nijmegen, Netherlands

    Josef Urban

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Kaliszyk, C., Urban, J. Learning-Assisted Automated Reasoning with Flyspeck. J Autom Reasoning 53, 173–213 (2014). https://doi.org/10.1007/s10817-014-9303-3

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  • Received: 31 January 2013

  • Accepted: 24 February 2014

  • Published: 01 June 2014

  • Issue Date: August 2014

  • DOI: https://doi.org/10.1007/s10817-014-9303-3

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Keywords

  • Automated reasoning
  • Interactive theorem proving
  • HOL light
  • Flyspeck
  • Artificial intelligence
  • Machine learning
  • Formal mathematics
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