Related papers: LeanDojo: Theorem Proving with Retrieval-Augmented…

Despite the success of large language models (LLMs), the task of theorem proving still remains one of the hardest reasoning tasks that is far from being fully solved. Prior methods using language models have demonstrated promising results,…

Mathematical reasoning remains a significant challenge for Large Language Models (LLMs) due to hallucinations. When combined with formal proof assistants like Lean, these hallucinations can be eliminated through rigorous verification,…

Large Language Models (LLMs) have demonstrated significant potential in generating mathematical proofs. However, a persistent challenge is that LLMs occasionally make mistakes, while even a minor mistake can invalidate an entire proof.…

This paper considers the development of an AI-based provably-correct mathematical proof tutor. While Large Language Models (LLMs) allow seamless communication in natural language, they are error prone. Theorem provers such as Lean allow for…

This paper considers the development of an AI-based provably-correct mathematical proof tutor. While Large Language Models (LLMs) allow seamless communication in natural language, they are error prone. Theorem provers such as Lean allow for…

Large language models (LLMs) have been used to generate formal proofs of mathematical theorems in proofs assistants such as Lean. However, we often want to optimize a formal proof with respect to various criteria, depending on its…

Neural theorem proving combines large language models (LLMs) with proof assistants such as Lean, where the correctness of formal proofs can be rigorously verified, leaving no room for hallucination. With existing neural theorem provers…

Large language models (LLMs) often struggle with complex logical reasoning due to logical inconsistencies and the inherent difficulty of such reasoning. We use Lean, a theorem proving framework, to address these challenges. By formalizing…

LLMs have demonstrated strong mathematical reasoning abilities by leveraging reinforcement learning with long chain-of-thought, yet they continue to struggle with theorem proving due to the lack of clear supervision signals when solely…

Automated theorem proving is fundamental to formal methods, and the recent trend is to integrate large language models (LLMs) and proof assistants to form effective proof agents. While existing proof agents show promising performance, they…

Theorem proving serves as a major testbed for evaluating complex reasoning abilities in large language models (LLMs). However, traditional automated theorem proving (ATP) approaches rely heavily on formal proof systems that poorly align…

Large Language Models (LLMs) have emerged as powerful tools in mathematical theorem proving, particularly when utilizing formal languages such as LEAN. A prevalent proof method involves the LLM prover iteratively constructing the proof…

Large Language Models (LLMs) demonstrate impressive mathematical reasoning abilities, but their solutions frequently contain errors that cannot be automatically checked. Formal theorem proving systems such as Lean 4 offer automated…

Premise selection is a key bottleneck for scaling theorem proving in large formal libraries. Yet existing language-based methods often treat premises in isolation, ignoring the web of dependencies that connects them. We present a…

Proof assistants like Lean have revolutionized mathematical proof verification, ensuring high accuracy and reliability. Although large language models (LLMs) show promise in mathematical reasoning, their advancement in formal theorem…

The combination of verifiable languages and LLMs has significantly influenced both the mathematical and computer science communities because it provides a rigorous foundation for theorem proving. Recent advancements in the field provide…

Proving theorems in Lean 4 often requires identifying a scattered set of library lemmas whose joint use enables a concise proof -- a task we call global premise retrieval. Existing tools address adjacent problems: semantic search engines…

Nowadays, formal theorem provers have made monumental progress on high-school and competition-level mathematics, but few of them generalize to more advanced mathematics. In this paper, we present REAL-Prover, a new open-source stepwise…

Large Language Models (LLMs) have demonstrated significant promise in formal theorem proving. In this study, we investigate the ability of LLMs to discover novel theorems and produce verified proofs. We propose a pipeline called…

We introduce LeanConjecturer, a pipeline for automatically generating university-level mathematical conjectures in Lean 4 using Large Language Models (LLMs). Our hybrid approach combines rule-based context extraction with LLM-based theorem…