Abstract. LeoPARD supports the implementation of knowledge representation and reasoning tools for higher-order logic(s). It combines a sophisticated data structure layer (polymorphically typed λ-calculus with nameless spine notation, explicit substitutions, and perfect term sharing) with an ambitious multi-agent blackboard architecture (supporting prover parallelism at the term, clause, and search level). Further features of LeoPARD include a parser for all TPTP dialects, a command line interpreter, and generic means for the integration of external reasoners.

Leo-III is an automated theorem prover for (polymorphic) higher-order logic which supports all common TPTP dialects, including THF, TFF and FOF as well as their rank-1 polymorphic derivatives. It is based on a paramodulation calculus with ordering constraints and, in tradition of its predecessor LEO-II, heavily relies on cooperation with external firstorder theorem provers. Unlike LEO-II, asynchronous cooperation with typed first-order provers and an agent-based internal cooperation scheme is supported. In this paper, we sketch Leo-III's underlying calculus, survey implementation details and give examples of use.

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.

In the Leo-III project, a new agent-based deduction system for classical higher-order logic is developed. Leo-III combines its predecessor's concept of cooperating external specialist systems with a novel agent-based proof procedure. Key goals of the system's development involve parallelism on various levels of the proof search, adaptability for different external specialists, and native support for reasoning in expressive non-classical logics.

While interactive proof assistants for higher-order logic (HOL) commonly admit reasoning within rich type systems, current theorem provers for HOL are mainly based on simply typed lambda-calculi and therefore do not allow such flexibility. In this paper, we present modifications to the higher-order automated theorem prover Leo-III for turning it into a reasoning system for rank-1 polymorphic HOL.To that end, a polymorphic version of HOL and a suitable paramodulation-based calculus are sketched. The implementation is evaluated using a set of polymorphic TPTP THF problems.