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International Conference on Logic for Programming Artificial Intelligence and Reasoning

LPAR 2007: Logic for Programming, Artificial Intelligence, and Reasoning pp 546–560Cite as

ATP Cross-Verification of the Mizar MPTP Challenge Problems

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4790))

Abstract

Mizar is a proof assistant used for formalization and mechanical verification of mathematics. The main use of Mizar is in the development of the Mizar Mathematical Library (MML), in which proofs are verified by the Mizar proof checker. The Mizar proof checker has a quite complex implementation, and also lacks the ability to print out detailed atomic proof steps in a format that is easy to verify by an independent proof-checking tool. This can raise concerns about the correctness of the MML. This paper describes how a Mizar-to-ATP translation (the MPTP system), ATP verification tools (the GDV system), and Automated Theorem Proving (ATP) systems, have been used for an independent cross-verification of a part of the MML.

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Authors and Affiliations

  1. Dep’t of Theoretical Computer Science, Charles University in Prague,  

    Josef Urban

  2. Dep’t of Computer Science, University of Miami,  

    Geoff Sutcliffe

Authors
  1. Josef Urban
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  2. Geoff Sutcliffe
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Nachum Dershowitz Andrei Voronkov

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Urban, J., Sutcliffe, G. (2007). ATP Cross-Verification of the Mizar MPTP Challenge Problems. In: Dershowitz, N., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2007. Lecture Notes in Computer Science(), vol 4790. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75560-9_39

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  • DOI: https://doi.org/10.1007/978-3-540-75560-9_39

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-75558-6

  • Online ISBN: 978-3-540-75560-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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