A Neuro-Symbolic Approach for Reliable Proof Generation with LLMs: A Case Study in Euclidean Geometry

Abstract

Large language models (LLMs) struggle with formal domains that require rigorous logical deduction and symbolic reasoning, such as mathematical proof generation. We propose a neuro-symbolic approach that combines LLMs' generative strengths with structured components to overcome this challenge. As a proof of concept, we focus on SAT-level geometry problems. Our approach is two-fold: (1) We retrieve analogous problems and use their proofs to guide the LLM, and (2) a formal verifier evaluates the generated proofs and provides feedback, helping the model fix incorrect proofs. Our method significantly improves proof accuracy across diverse model families, achieving significant gains across all evaluated models: OpenAI o1, GPT-5, Gemini-Flash-2.5, and Claude Sonnet 4.6. Accuracy increases from 10% to 44% for the base models to 68% to 96% with our approach, with both analogous problem guidance and verifier feedback contributing to these improvements. More broadly, shifting to LLMs that generate provably correct conclusions has the potential to dramatically improve their reliability, accuracy and consistency, unlocking complex tasks and critical real-world applications that require trustworthiness.