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Effective Normalization Techniques for HOL

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Automated Reasoning (IJCAR 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9706))

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Abstract

Normalization procedures are an important component of most automated theorem provers. In this work we present an adaption of advanced first-order normalization techniques for higher-order theorem proving which have been bundled in a stand-alone tool. It can be used in conjunction with any higher-order theorem prover, even though the implemented techniques are primarily targeted on resolution-based provers. We evaluated the normalization procedure on selected problems of the TPTP using multiple HO ATPs. The results show a significant performance increase, in both speed and proving capabilities, for some of the tested problem instances.

This work has been supported by the DFG under grant BE 2501/11-1 (Leo-III).

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Notes

  1. 1.

    With #CNF we denote the number of clauses generated by transforming the given formula into clause normal form.

  2. 2.

    A comprehensive presentation of the different TPTP problem domains and their application domain can be found at http://www.cs.miami.edu/~tptp/cgi-bin/SeeTPTP?Category=Documents&File=OverallSynopsis.

  3. 3.

    The average time results for normalization procedure \(N_3\) are in nearly all cases within a range of \(0.1\,\%\) of the results for \(N_1\). Likewise results apply for \(N_4\) and \(N_2\).

  4. 4.

    The prover LEO-II, for example, is able to detect such (sub-)formulas and to replace them by primitive equalities \(a = b\).

  5. 5.

    The Leonora repository can be found at https://github.com/Ryugoron/Leonora.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Freie Universität Berlin, Berlin, Germany

    Max Wisniewski, Alexander Steen, Kim Kern & Christoph Benzmüller

Authors
  1. Max Wisniewski
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  2. Alexander Steen
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  3. Kim Kern
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  4. Christoph Benzmüller
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Correspondence to Christoph Benzmüller .

Editor information

Editors and Affiliations

  1. Aix-Marseille University, Marseille, France

    Nicola Olivetti

  2. SRI International, Menlo Park, California, USA

    Ashish Tiwari

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Wisniewski, M., Steen, A., Kern, K., Benzmüller, C. (2016). Effective Normalization Techniques for HOL. In: Olivetti, N., Tiwari, A. (eds) Automated Reasoning. IJCAR 2016. Lecture Notes in Computer Science(), vol 9706. Springer, Cham. https://doi.org/10.1007/978-3-319-40229-1_25

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  • DOI: https://doi.org/10.1007/978-3-319-40229-1_25

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