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A well-defined benchmark is essential for measuring and accelerating researchprogress of machine learning models. In this paper, we present a benchmark forhigh-level mathematical reasoning and study the reasoning capabilities ofneural sequence-to-sequence models. We build a non-synthetic dataset from thelargest repository of proofs written by human experts in a theorem prover. Thedataset has a broad coverage of undergraduate and research-level mathematicaland computer science theorems. In our defined task, a model is required to fillin a missing intermediate proposition given surrounding proofs. This taskprovides a starting point for the long-term goal of having machines generatehuman-readable proofs automatically. Our experiments and analysis reveal thatwhile the task is challenging, neural models can capture non-trivialmathematical reasoning. We further design a hierarchical transformer thatoutperforms the transformer baseline.

IsarStep: a Benchmark for High-level Mathematical Reasoning