ProofCompass: Enhancing Specialized Provers with LLM Guidance

Language models have become increasingly powerful tools for formal mathematical reasoning. However, most existing approaches rely exclusively on either large general-purpose models or smaller specialized models, each with distinct limitations, while training specialized large models still requires significant computational resources. This paper introduces ProofCompass, a novel hybrid methodology that achieves remarkable computational efficiency by strategically guiding existing specialized prover methods, such as DeepSeek-Prover-v1.5-RL (DSP-v1.5) with a Large Language Model (LLM) without requiring additional model training. The LLM provides natural language proof strategies and analyzes failed attempts to select intermediate lemmas, enabling effective problem decomposition. On the miniF2F benchmark, ProofCompass demonstrates exceptional resource efficiency: it outperforms DSP-v1.5 ($54.9$\% $\rightarrow$ $55.3$\%) while using 25x fewer attempts ($3200 \rightarrow 128$). Our synergistic approach paves the way for simultaneously improving computational efficiency and accuracy in formal theorem proving.