miniCTX: Neural Theorem Proving with (Long-)Contexts

Real-world formal theorem proving often depends on a wealth of context, including definitions, lemmas, comments, file structure, and other information. We introduce $\texttt{miniCTX}$, which tests a model's ability to prove formal mathematical theorems that depend on new context that is not seen during training. $\texttt{miniCTX}$ contains theorems sourced from real Lean projects and textbooks, each associated with a context that can span tens of thousands of tokens. Models are tasked with proving a theorem given access to code from the theorem's repository, which contains context that is needed for the proof. As a baseline for $\texttt{miniCTX}$, we tested fine-tuning and prompting methods that condition theorem proving on preceding context. Both approaches substantially outperform traditional methods that rely solely on state information. We found that this ability to use context is not captured by previous benchmarks such as $\texttt{miniF2F}$. Alongside $\texttt{miniCTX}$, we offer $\texttt{ntp-toolkit}$ for automatically extracting and annotating theorem proving data, making it easy to add new projects into $\texttt{miniCTX}$ to ensure that contexts are not seen during training. $\texttt{miniCTX}$ offers a challenging and realistic evaluation of neural theorem provers.