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2018 | OriginalPaper | Chapter

The Higher-Order Prover Leo-III

Authors : Alexander Steen, Christoph Benzmüller

Published in: Automated Reasoning

Publisher: Springer International Publishing

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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.

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previous chapter Formalizing Bachmair and Ganzinger’s Ordered Resolution Prover

next chapter Well-Founded Unions

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

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

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

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.

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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Title: The Higher-Order Prover Leo-III
Authors: Alexander Steen
Christoph Benzmüller
Publisher: Springer International Publishing
Book: Automated Reasoning
Print ISBN: 978-3-319-94204-9

Electronic ISBN: 978-3-319-94205-6

Copyright Year: 2018
DOI: https://doi.org/10.1007/978-3-319-94205-6_8

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