The Higher-Order Prover Leo-II

@article{Benzmller2015TheHP,
  title={The Higher-Order Prover Leo-II},
  author={Christoph Benzm{\"u}ller and Nikolai Sultana and Lawrence Charles Paulson and Frank Theiss},
  journal={Journal of Automated Reasoning},
  year={2015},
  volume={55},
  pages={389 - 404}
}
Leo-II is an automated theorem prover for classical higher-order logic. The prover has pioneered cooperative higher-order–first-order proof automation, it has influenced the development of the TPTP THF infrastructure for higher-order logic, and it has been applied in a wide array of problems. Leo-II may also be called in proof assistants as an external aid tool to save user effort. For this it is crucial that Leo-II returns proof information in a standardised syntax, so that these proofs can… 
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References

SHOWING 1-10 OF 101 REFERENCES
Understanding LEO-II's proofs
TLDR
Leo-II’s proof objects are discussed, with a focus on using Leo-II proofs within other systems and on generating joint higherorder{rst-order proof objects in TPTP format.
System Description: LEO - A Higher-Order Theorem Prover
TLDR
Leo uses a higher-order Logic based upon Church's simply typed λ-calculus, so that the comprehension axioms are implicitly handled by αβη-equality, and extensionality principles are build in into Leo’s unification, and hence do not have to be axiomatized in order to achieve Henkin completeness.
Automated Reasoning in Higher-Order Logic using the TPTP THF Infrastructure
TLDR
Key developments have been the specification of the THF language, the addition of higher-order problems to theTPTP, the development of the TPTP THF infrastructure, several ATP systems for higher- order logic, and the use of higher -order ATP in a range of domains.
Automating Access Control Logics in Simple Type Theory with LEO-II (Techreport)
TLDR
This paper describes a sound and complete embedding of different access control logics in simple type theory and shows that the off the shelf theorem prover LEO-II can be applied to automate reasoning in prominent access controlLogics.
MleanCoP: A Connection Prover for First-Order Modal Logic
TLDR
MleanCoP is a fully automated theorem prover for first-order modal logic that supports heterogeneous multimodal logics and outputs a compact prefixed connection proof.
TFF1: The TPTP Typed First-Order Form with Rank-1 Polymorphism
TLDR
The TFF1 format is introduced, an extension of TFF0 with rank-1 polymorphism, designed to be easy to process by existing reasoning tools that support ML-style polymorphism.
Analytic Tableaux for Higher-Order Logic with Choice
TLDR
A cut-free ground tableau calculus for Church’s simple type theory with choice for higher-order automated theorem provers is presented and completeness of the tableAU calculus relative to Henkin models is proved.
LEO-II Version 1.5
TLDR
Recent improvements made to Leo-II, the theorem-provers used to prove theorems in classical higherorder logic, are described.
TPS: A theorem-proving system for classical type theory
TLDR
TPS has been designed to be a general research tool for manipulating wffs of first- and higher-order logic, and searching for proofs of such wFFs interactively or automatically, or in a combination of these modes.
Extensional Higher-Order Paramodulation and RUE-Resolution
TLDR
Two approaches to primitive equality treatment in higher-order (HO) automated theorem proving are presented: a calculus EP adapting traditional first-orders paramodulation, and a calculus ERUE adapting FO RUE-Resolution to classical type theory, i.e., HO logic based on Church's simply typed λ-calculus.
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