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The Higher-Order Prover Leo-III

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Automated Reasoning (IJCAR 2018)

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Abstract

The automated theorem prover Leo-III for classical higher-order logic with Henkin semantics and choice is presented. Leo-III is based on extensional higher-order paramodulation and accepts every common TPTP dialect (FOF, TFF, THF), including their recent extensions to rank-1 polymorphism (TF1, TH1). In addition, the prover natively supports almost every normal higher-order modal logic. Leo-III cooperates with first-order reasoning tools using translations to many-sorted first-order logic and produces verifiable proof certificates. The prover is evaluated on heterogeneous benchmark sets.

The work was supported by the German National Research Foundation (DFG) under grant BE 2501/11-1. For an extended version of this paper see arXiv:1802.02732.

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Notes

  1. 1.

    Leo-III is freely available (BSD license) at http://github.com/leoprover/Leo-III.

  2. 2.

    Cf.  http://www.cs.miami.edu/~tptp/TPTP/Proposals/LogicSpecification.html.

  3. 3.

    Cf. [13, §2.2]; we refer to the literature [8] for more details on HOML.

  4. 4.

    Remark on CAX: In this special case of THM (theorem) the given axioms are inconsistent, so that anything follows, including the given conjecture. Unlike most other provers, Leo-III checks for this special situation.

  5. 5.

    This information is extracted from the TPTP problem rating information that is attached to each problem. The unsolved problems are NLP004⌃7, SET013⌃7, SEU558⌃1, SEU683⌃1, SEV143⌃5, SYO037⌃1, SYO062⌃4.004, SYO065⌃4.001, SYO066⌃4.004, MSC007⌃1.003.004, SEU938⌃5 and SEV106⌃5.

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Authors and Affiliations

  1. Institute of Computer Science, Freie Universität Berlin, Berlin, Germany

    Alexander Steen & Christoph Benzmüller

  2. Computer Science and Communications, University of Luxembourg, Esch-sur-Alzette, Luxembourg

    Christoph Benzmüller

Authors
  1. Alexander Steen
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  2. Christoph Benzmüller
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Correspondence to Alexander Steen .

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Editors and Affiliations

  1. Université de Lorraine, Vandoeuvre-lès-Nancy, France

    Didier Galmiche

  2. Baden-Wuerttemberg Cooperative State University, Stuttgart, Germany

    Stephan Schulz

  3. University of Trento, Trento, Italy

    Roberto Sebastiani

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Steen, A., Benzmüller, C. (2018). The Higher-Order Prover Leo-III. In: Galmiche, D., Schulz, S., Sebastiani, R. (eds) Automated Reasoning. IJCAR 2018. Lecture Notes in Computer Science(), vol 10900. Springer, Cham. https://doi.org/10.1007/978-3-319-94205-6_8

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  • DOI: https://doi.org/10.1007/978-3-319-94205-6_8

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