IneqAgent: Agentic Inequality Proving in Lean with Symbolic Computation
Quick Answer
This paper shows that IneqAgent combines LLM reasoning with symbolic computation to achieve a 94.09% success rate in inequality proving using Lean4, solving 175 out of 186 problems.
Quick Take
It outperforms Direct Agent in low inference cost scenarios and has verified strengthenings of Dittert's conjecture and the Holens-Djokovic inequality.
Key Points
- IneqAgent utilizes lemma-level Monte Carlo Tree Search for efficient proof construction.
- Achieved the highest success rate among evaluated methods on four benchmarks.
- Lower mean inference costs compared to Direct Agent for successful runs.
- Verified strengthenings of Dittert's conjecture in dimensions four and five.
- Certified the Holens-Djokovic (4,4) inequality, impacting Merris's conjecture.
DeepSignal Analysis
What happened
IneqAgent is a new framework that combines large language model (LLM) reasoning with symbolic computation for proving inequalities in Lean4. It achieved a 94.09% success rate by solving 175 out of 186 problems, outperforming the Direct Agent in scenarios with low inference costs.
Key evidence
- IneqAgent solved 175 out of 186 inequality problems, resulting in a 94.09% success rate.
- The framework integrates lemma-level Monte Carlo Tree Search for lemma construction and goal reformulation.
- IneqAgent verified strengthenings of Dittert's conjecture in dimensions four and five, and certified the Holens-Djokovic inequality.
Why it matters
The development of IneqAgent signifies a notable advancement in formal mathematical reasoning, particularly in the domain of inequality proving. Its high success rate and efficiency in low inference cost scenarios could enhance the capabilities of automated theorem proving, potentially leading to broader applications in mathematical research and education.
What to watch
Future developments may include improvements in the efficiency of LLM inference costs and the exploration of additional mathematical conjectures. Observing how IneqAgent compares with other frameworks in diverse mathematical contexts will be crucial for assessing its overall impact.
Paper Resources
📖 Reader Mode
~2 min readAbstract:Formal inequality proving requires mathematical reasoning and exact computation, often connected through intermediate lemmas and goal reformulations. We introduce IneqAgent, an agentic framework combining LLM reasoning with symbolic computation for inequality proving in Lean4. Lemma-level Monte Carlo Tree Search coordinates lemma construction, goal reformulation, and symbolic backend selection. Complementary sum-of-squares, Bernstein, and successive difference-substitution backends produce exact certificates for local Lean proof generation. The agent integrates these proofs with LLM-generated steps and uses Lean feedback to construct complete proofs checked against the original theorem statements. On four benchmarks, IneqAgent with DeepSeek-V4-Flash solves 175 of 186 problems (94.09%), achieving the highest overall success rate among the evaluated methods. Across four backbones, it achieves higher success rates at low LLM inference cost thresholds than Direct Agent using the same backbone, with lower mean inference costs over each method's successful runs. We also obtain Lean-verified strengthenings of Dittert's conjecture in dimensions four and five, and certify the Holens--Djokovic $(4,4)$ inequality, implying Merris's conjecture in dimension four.
| Subjects: | Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2610.20681 [cs.AI] |
| (or arXiv:2610.20681v1 [cs.AI] for this version) | |
| https://doi.org/10.48550/arXiv.2610.20681 arXiv-issued DOI via DataCite |
Submission history
From: Gaolei He [view email]
[v1]
Wed, 14 Oct 2026 16:29:11 UTC (203 KB)
— Originally published at arxiv.org
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