IneqAgent：用符号计算与 MCTS 在 Lean4 中自动证明不等式
IneqAgent: Agentic Inequality Proving in Lean with Symbolic Computation
用 LLM 加符号计算在 Lean4 里自动证不等式，186 题解出 175 题，还顺手推进了两个猜想，数学形式化爱好者别错过。
IneqAgent 是一个把 LLM 推理与符号计算结合的智能体框架，用于在 Lean4 中做不等式形式化证明。它在 lemma 层面用蒙特卡洛树搜索协调引理构造、目标改写和符号后端选择，后端包括 sum-of-squares、Bernstein 和逐次差代换，用于生成精确证书。在四个基准共 186 道题上，搭载 DeepSeek-V4-Flash 的 IneqAgent 解出 175 题，成功率 94.09%，为评测方法中最高。该框架还给出了 Dittert 猜想在四维和五维的 Lean 验证强化版本，并证明了蕴含四维 Merris 猜想的 Holens--Djokovic (4,4) 不等式。
IneqAgent: Agentic Inequality Proving in Lean with Symbolic Computation
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.
