  We present an environment, benchmark, and deep learning driven automated
theorem prover for higher-order logic. Higher-order interactive theorem provers
enable the formalization of arbitrary mathematical theories and thereby present
an interesting, open-ended challenge for deep learning. We provide an
open-source framework based on the HOL Light theorem prover that can be used as
a reinforcement learning environment. HOL Light comes with a broad coverage of
basic mathematical theorems on calculus and the formal proof of the Kepler
conjecture, from which we derive a challenging benchmark for automated
reasoning. We also present a deep reinforcement learning driven automated
theorem prover, DeepHOL, with strong initial results on this benchmark.
