# 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…

## 69 Citations

The Higher-Order Prover Leo-III

- Computer ScienceIJCAR
- 2018

The automated theorem prover Leo-III for classical higher-order logic with Henkin semantics and choice is presented and natively supports almost every normal higher- order modal logic.

The Higher-Order Prover Leo-III (Extended Version)

- Computer Science
- 2018

The automated theorem prover Leo-III for classical higher-order logic with Henkin semantics and choice is presented and natively supports almost every normal higher- order modal logic.

Extensional Higher-Order Paramodulation in Leo-III

- Computer ScienceJ. Autom. Reason.
- 2021

Leo-III is an automated theorem prover for extensional type theory with Henkin semantics and choice that supports reasoning in polymorphic first-order and higher-order logic, in all normal quantified modal logics, as well as in different deontic logics.

Leo-III Version 1.1 (System description)

- Computer ScienceLPAR
- 2017

This paper sketches Leo-III’s underlying calculus, survey implementation details and give examples of use, and sketches the role of asynchronous cooperation with typed first-order provers and an agent-based internal cooperation scheme.

Going Polymorphic - TH1 Reasoning for Leo-III

- Computer ScienceIWIL@LPAR
- 2017

Modifications to the higher-order automated theorem prover Leo-III are presented for turning it into a reasoning system for rank-1 polymorphic HOL and a suitable paramodulation-based calculus are sketched.

The Higher-Order Prover Leo-III (Extended Abstract)

- Computer Science, MathematicsKI
- 2019

In this extended abstract, the features of Leo-III are surveyed and almost every normal higher-order modal logic is supported.

Set of Support for Higher-Order Reasoning

- Computer SciencePAAR@FLoC
- 2018

Limiting how axioms introduced during translation can improve proof search with higher-order problems is shown and heuristics based on the set-of-support strategy for minimising the effects are introduced.

Extending a brainiac prover to lambda-free higher-order logic

- Computer ScienceTACAS
- 2019

This work proposes to start with the state-of-the-art superposition prover E and gradually enrich it with higher-order features, explaining how to extend the prover’s data structures, algorithms, and heuristics to higher- order logic, a formalism that supports partial application and applied variables.

Invited Talk: On a (Quite) Universal Theorem Proving Approach and Its Application in Metaphysics

- PhilosophyTABLEAUX
- 2015

By employing this approach, the automation of a variety of ambitious logics has recently been pioneered, including variants of first-order and higher-order quantified multimodal logics and conditional logics.

Extracting Higher-Order Goals from the Mizar Mathematical Library

- MathematicsCICM
- 2016

A way to obtain higher-order theorem proving problems from Mizar articles that make use of these constructs, including schemes, a global choice construct and set level binders, is described.

## References

SHOWING 1-10 OF 101 REFERENCES

Understanding LEO-II's proofs

- MathematicsIWIL@LPAR
- 2012

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

- Computer ScienceCADE
- 1998

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

- Computer ScienceJ. Formaliz. Reason.
- 2010

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)

- Computer ScienceSEC
- 2009

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

- Computer ScienceIJCAR
- 2014

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

- Computer ScienceCADE
- 2013

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

- MathematicsJournal of Automated Reasoning
- 2011

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

- MathematicsPxTP@CADE
- 2013

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

- MathematicsJournal of Automated Reasoning
- 2004

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

- Computer ScienceCADE
- 1999

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.