Theorem proving is a fundamental task in mathematics. With the advent of large language models (LLMs) and interactive theorem provers (ITPs) like Lean, there has been growing interest in integrating LLMs and ITPs to automate theorem proving. In this approach, the LLM generates proof steps (tactics), and the ITP checks the applicability of the tactics at the current goal. The two systems work together to complete the proof. In this paper, we introduce DS-Prover, a novel dynamic sampling method for theorem proving. This method dynamically determines the number of tactics to apply to expand the current goal, taking into account the remaining time compared to the total allocated time for proving a theorem. This makes the proof search process more efficient by adjusting the balance between exploration and exploitation as time passes. We also augment the training dataset by decomposing simplification and rewrite tactics with multiple premises into tactics with single premises. This gives the model more examples to learn from and helps it to predict the tactics with premises more accurately. We perform our experiments using the Mathlib dataset of the Lean theorem prover and report the performance on two standard datasets, MiniF2F and ProofNet. Our methods achieve significant performance gains on both datasets. We achieved a state-of-the-art performance (Pass@1) of 14.2% on the ProofNet dataset and a performance of 29.8% on MiniF2F, slightly surpassing the best-reported Pass@1 of 29.6% using Lean.

DS-Prover是一个用于定理证明的创新动态抽样方法，通过根据剩余时间和总分配时间来调整探索和开发之间的平衡，以提高证明搜索过程的效率，并通过拆分简化和重写策略为具有单个前提的策略来扩充训练数据集，从而在MiniF2F和ProofNet两个标准数据集上实现了显著的性能提升。

通过数据增强和动态采样方法提升神经定理证明