# MINIF2F-DAFNY: LLM-Guided Mathematical Theorem Proving via Auto-Active Verification

arXiv: https://arxiv.org/abs/2512.10187 · HTML: https://mlsanity.com/paper/2512.10187/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 30 of its 56 references that are in the map.
- First posted on arXiv 11 Dec 2025.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 30 of 30)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [LeanDojo: Theorem Proving with Retrieval-Augmented Language Models](https://mlsanity.com/paper/2306.15626/) (2023)
- [MiniF2F: a cross-system benchmark for formal Olympiad-level mathematics](https://mlsanity.com/paper/2109.00110/) (2021)
- [Generative Language Modeling for Automated Theorem Proving](https://mlsanity.com/paper/2009.03393/) (2020)
- [Llemma: An Open Language Model For Mathematics](https://mlsanity.com/paper/2310.10631/) (2023)
- [Draft, Sketch, and Prove: Guiding Formal Theorem Provers with Informal Proofs](https://mlsanity.com/paper/2210.12283/) (2022)
- [DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition](https://mlsanity.com/paper/2504.21801/) (2025)
- [DeepSeek-Prover: Advancing Theorem Proving in LLMs through Large-Scale Synthetic Data](https://mlsanity.com/paper/2405.14333/) (2024)
- [HyperTree Proof Search for Neural Theorem Proving](https://mlsanity.com/paper/2205.11491/) (2022)
- [ProofNet: Autoformalizing and Formally Proving Undergraduate-Level Mathematics](https://mlsanity.com/paper/2302.12433/) (2023)
- [Kimina-Prover Preview: Towards Large Formal Reasoning Models with Reinforcement Learning](https://mlsanity.com/paper/2504.11354/) (2025)
- [PutnamBench: Evaluating Neural Theorem-Provers on the Putnam Mathematical Competition](https://mlsanity.com/paper/2407.11214/) (2024)
- [The Lean mathematical library](https://mlsanity.com/paper/1910.09336/) (2019)
- [LEGO-Prover: Neural Theorem Proving with Growing Libraries](https://mlsanity.com/paper/2310.00656/) (2023)
- [Seed-Prover: Deep and Broad Reasoning for Automated Theorem Proving](https://mlsanity.com/paper/2507.23726/) (2025)
- [An In-Context Learning Agent for Formal Theorem-Proving](https://mlsanity.com/paper/2310.04353/) (2023)
- [Clover: Closed-Loop Verifiable Code Generation](https://mlsanity.com/paper/2310.17807/) (2023)
- [Hilbert: Recursively Building Formal Proofs with Informal Reasoning](https://mlsanity.com/paper/2509.22819/) (2025)
- [Aristotle: IMO-level Automated Theorem Proving](https://mlsanity.com/paper/2510.01346/) (2025)
- [DafnyBench: A Benchmark for Formal Software Verification](https://mlsanity.com/paper/2406.08467/) (2024)
- [FIMO: A Challenge Formal Dataset for Automated Theorem Proving](https://mlsanity.com/paper/2309.04295/) (2023)
- [Verus: Verifying Rust Programs using Linear Ghost Types (extended version)](https://mlsanity.com/paper/2303.05491/) (2023)
- [AutoVerus: Automated Proof Generation for Rust Code](https://mlsanity.com/paper/2409.13082/) (2024)
- [Prover Agent: An Agent-Based Framework for Formal Mathematical Proofs](https://mlsanity.com/paper/2506.19923/) (2025)
- [CLEVER: A Curated Benchmark for Formally Verified Code Generation](https://mlsanity.com/paper/2505.13938/) (2025)
- [A benchmark for vericoding: formally verified program synthesis](https://mlsanity.com/paper/2509.22908/) (2025)
- [From Informal to Formal -- Incorporating and Evaluating LLMs on Natural Language Requirements to Verifiable Formal Proofs](https://mlsanity.com/paper/2501.16207/) (2025)
- [VerifyThisBench: Generating Code, Specifications, and Proofs All at Once](https://mlsanity.com/paper/2505.19271/) (2025)
- [ProofCompass: Enhancing Specialized Provers with LLM Guidance](https://mlsanity.com/paper/2507.14335/) (2025)

## Built on by (most cited first, 2 of 2)

- [SkillForge: Compositional Skill Synthesis with Verification-in-the-Loop for Generating Formally Verified Dafny Programs](https://mlsanity.com/paper/2608.29841/) (2026)
- [Self-Spec Verifiable Code Generation](https://mlsanity.com/paper/2609.39568/) (2026)

## Abstract (arXiv)

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 https://github.com/dafny-lang/miniF2F.