# TaoBench: Do Automated Theorem Prover LLMs Generalize Beyond MathLib?

arXiv: https://arxiv.org/abs/2603.12744 · HTML: https://mlsanity.com/paper/2603.12744/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 27 references that are in the map.
- First posted on arXiv 13 Mar 2026.

## Builds on (most cited first, 14 of 14)

- [DeepSeek-V3.2: Pushing the Frontier of Open Large Language Models](https://mlsanity.com/paper/2512.02556/) (2025)
- [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)
- [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)
- [PutnamBench: Evaluating Neural Theorem-Provers on the Putnam Mathematical Competition](https://mlsanity.com/paper/2407.11214/) (2024)
- [Goedel-Prover: A Frontier Model for Open-Source Automated Theorem Proving](https://mlsanity.com/paper/2502.07640/) (2025)
- [Lean Workbook: A large-scale Lean problem set formalized from natural language math problems](https://mlsanity.com/paper/2406.03847/) (2024)
- [STP: Self-play LLM Theorem Provers with Iterative Conjecturing and Proving](https://mlsanity.com/paper/2502.00212/) (2025)
- [Lean-STaR: Learning to Interleave Thinking and Proving](https://mlsanity.com/paper/2407.10040/) (2024)
- [Herald: A Natural Language Annotated Lean 4 Dataset](https://mlsanity.com/paper/2410.10878/) (2024)
- [FormalMATH: Benchmarking Formal Mathematical Reasoning of Large Language Models](https://mlsanity.com/paper/2505.02735/) (2025)
- [Scaling up Multi-Turn Off-Policy RL and Multi-Agent Tree Search for LLM Step-Provers](https://mlsanity.com/paper/2509.06493/) (2025)
- [FATE: A Formal Benchmark Series for Frontier Algebra of Multiple Difficulty Levels](https://mlsanity.com/paper/2511.02872/) (2025)

## Built on by (most cited first, 6 of 6)

- [Beyond Benchmarks: MathArena as an Evaluation Platform for Mathematics with LLMs](https://mlsanity.com/paper/2605.00674/) (2026)
- [LEAP: Supercharging LLMs for Formal Mathematics with Agentic Frameworks](https://mlsanity.com/paper/2606.03303/) (2026)
- [Not All Proofs Are Equal: Evaluating LLM Proof Quality Beyond Correctness](https://mlsanity.com/paper/2605.10379/) (2026)
- [LAMP: Lean-based Agentic framework with MCP and Proof Repair](https://mlsanity.com/paper/2606.28841/) (2026)
- [AxQM: A Textbook-Scale Benchmark for Formal Proof Synthesis in a Library of Finite-Dimensional Quantum Mechanics](https://mlsanity.com/paper/2609.05157/) (2026)
- [StochBench: A Domain-Specific Benchmark for Stochastic Processes in Lean](https://mlsanity.com/paper/2609.09264/) (2026)

## Abstract (arXiv)

Automated theorem proving (ATP) benchmarks largely consist of problems formalized in MathLib, so current ATP training and evaluation are heavily biased toward MathLib's definitional framework. However, frontier mathematics is often exploratory and prototype-heavy, relying on bespoke constructions that deviate from standard libraries. In this work, we evaluate the robustness of current ATP systems when applied to a novel definitional framework, specifically examining the performance gap between standard library problems and bespoke mathematical constructions. We introduce TaoBench, an undergraduate-level benchmark derived from Terence Tao's Analysis I, which formalizes analysis by constructing core mathematical concepts from scratch, without relying on standard Mathlib definitions, as well as by mixing from-scratch and MathLib constructions. For fair evaluation, we build an agentic pipeline that automatically extracts a compilable, self-contained local environment for each problem. To isolate the effect of definitional frameworks, we additionally translate every problem into a mathematically equivalent Mathlib formulation, yielding paired TaoBench-Mathlib statements for direct comparison. While state-of-the-art ATP models perform capably within the MathLib framework, performance drops by an average of roughly 26% on the definitionally equivalent Tao formulation. This indicates that the main bottleneck is limited generalization across definitional frameworks rather than task difficulty. TaoBench thus highlights a gap between benchmark performance and applicability, and provides a concrete foundation for developing and testing provers better aligned with research mathematics.