# When Does Structured Knowledge Help Neural Theorem Proving?

arXiv: https://arxiv.org/abs/2609.34460 · HTML: https://mlsanity.com/paper/2609.34460/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 52 of its 71 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 30 of 52)

- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversation](https://mlsanity.com/paper/2308.08155/) (2023)
- [MetaGPT: Meta Programming for A Multi-Agent Collaborative Framework](https://mlsanity.com/paper/2308.00352/) (2023)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [When Not to Trust Language Models: Investigating Effectiveness of Parametric and Non-Parametric Memories](https://mlsanity.com/paper/2212.10511/) (2022)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [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)
- [Autoformalization with Large Language Models](https://mlsanity.com/paper/2205.12615/) (2022)
- [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)
- [Large Language Models for Generative Information Extraction: A Survey](https://mlsanity.com/paper/2312.17617/) (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)
- [Goedel-Prover-V2: Scaling Formal Theorem Proving with Scaffolded Data Synthesis and Self-Correction](https://mlsanity.com/paper/2508.03613/) (2025)
- [Goedel-Prover: A Frontier Model for Open-Source Automated Theorem Proving](https://mlsanity.com/paper/2502.07640/) (2025)
- [Revisiting Relation Extraction in the era of Large Language Models](https://mlsanity.com/paper/2305.05003/) (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)
- [DeepMath - Deep Sequence Models for Premise Selection](https://mlsanity.com/paper/1606.04442/) (2016)
- [NaturalProofs: Mathematical Theorem Proving in Natural Language](https://mlsanity.com/paper/2104.01112/) (2021)
- [STP: Self-play LLM Theorem Provers with Iterative Conjecturing and Proving](https://mlsanity.com/paper/2502.00212/) (2025)
- [Mathematical exploration and discovery at scale](https://mlsanity.com/paper/2511.02864/) (2025)
- [Hilbert: Recursively Building Formal Proofs with Informal Reasoning](https://mlsanity.com/paper/2509.22819/) (2025)
- [Lean Copilot: Large Language Models as Copilots for Theorem Proving in Lean](https://mlsanity.com/paper/2404.12534/) (2024)

## Abstract (arXiv)

Does structured mathematical knowledge help LLMs prove theorems in Lean 4? If so, for which models, and does the answer vary by problem? Formal libraries such as Mathlib encode 285,000+ verified theorems with syntactic dependencies, but the semantic layer mathematicians rely on for discovery (analogies, generalizations, cross-domain bridges) remains implicit. We introduce MathAgent, which builds this layer as a knowledge graph, MathKG, and uses it to augment LLM theorem provers. MathKG connects 364 Mathlib theorems and definitions by 9,434 typed semantic edges inferred via LLM-based relation extraction anchored to verified Mathlib declarations. We run a controlled ablation across four augmentation modes (no context, knowledge-graph context, Mathlib retrieval, both) and five models: Qwen3-8B/32B, their Lean-specialized derivatives Goedel-Prover-V2-8B/32B, and Claude Sonnet 4.6, on miniF2F, plus PutnamBench and MathOlympiadBench for Sonnet. Three findings emerge. (i) Specialization dominates augmentation: Lean fine-tuning adds 33-38 percentage points of solve rate in every mode, and a specialized 8B model beats a 4× larger general one by 29-35 points, while no augmentation mode improves solve rate by more than 3 points. (ii) Augmentation is capability-conditioned: knowledge-graph context helps small models but hurts large ones, with the specialized model gaining more relative to its general base at every scale. (iii) Yet the augmentation modes solve different problems: an oracle selecting the best mode per problem solves 6% to 58% more than the unaugmented prover, a complementarity effect that strengthens on harder problems (32% more on PutnamBench). These results motivate adaptive strategies that select augmentation by model capability and problem. Code, data, and artifacts are available at https://github.com/sarehnabi/mathagent