Extracting higher-order goals from the mizar mathematical library

Abstract

Certain constructs allowed in Mizar articles cannot be represented in first-order logic but can be represented in higher-order logic. We describe a way to obtain higher-order theorem proving problems from Mizar articles that make use of these constructs. In particular, higherorder logic is used to represent schemes, a global choice construct and set level binders. The higher-order automated theorem provers Satallax and LEO-II have been run on collections of these problems and the results are discussed.