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 eventually be transformed and verified within proof assistants. Recent progress in this direction is reported for the Isabelle/HOL system.
Sledgehammer is a tool that harnesses external first-order automatic theorem provers (ATPs) to discharge interactive proof obligations arising in Isabelle/HOL. We extended it with LEO-II and Satallax, the two most prominent higher-order ATPs, improving its performance on higher-order problems. To explore their usefulness, these ATPs are measured against first-order ATPs and built-in Isabelle tactics on a variety of benchmarks from Isabelle and the TPTP library. Sledgehammer provides an ideal test bench for individual features of LEO-II and Satallax, revealing areas for improvements.
Leo-II cooperates with other theorem-provers to prove theorems in classical higherorder logic. It returns hybrid proofs, which contain inferences made by Leo-II as well as the backend provers with which it cooperates. This article describes recent improvements made to Leo-II.
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