miniF2F-Dafny: LLM-Guided Mathematical Theorem Proving via Auto-Active Verification

LLMs excel at reasoning, but validating their steps remains challenging. Formal verification offers a solution through mechanically checkable proofs. Interactive theorem provers (ITPs) dominate mathematical reasoning but require detailed low-level proof steps, while auto-active verifiers offer automation but focus on software verification. Recent work has begun bridging this divide by evaluating LLMs for software verification in ITPs, but the complementary direction-LLMs for mathematical theorem proving in auto-active verifiers-remains unexplored. We present MINIF2F-DAFNY, the first translation of the widely-used mathematical benchmark miniF2F to an auto-active verifier: Dafny. We find that Dafny's automation alone solves 39-44% of problems with empty proofs, whereas many require substantial proof guidance in ITPs. We evaluate 8 off-the-shelf LLMs on proof generation, with the best model (Claude Opus 4.6) achieving 62.7% cumulative pass@4 on the full test set, improving over the 38.9% empty-proof baseline by 23.8 percentage points. These results show that auto-active verification offers a complementary empirical setting for AI-assisted mathematical reasoning, where LLMs provide high-level guidance while SMT automation handles low-level details. Our benchmark and evaluation infrastructure are publicly available on GitHub. Mantas Bakšys worked on this project during an internship at Amazon Web Services in London, UK.