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Large language models (LLMs) have shown increasing competence in solving mathematical reasoning problems. However, many open-source LLMs still struggle with errors in calculation and semantic understanding during intermediate reasoning…
Formal reasoning and automated theorem proving constitute a challenging subfield of machine learning, in which machines are tasked with proving mathematical theorems using formal languages like Lean. A formal verification system can check…
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…
The demand for synthetic data in mathematical reasoning has increased due to its potential to enhance the mathematical capabilities of large language models (LLMs). However, ensuring the validity of intermediate reasoning steps remains a…
Formal methods is pivotal for verifying the reliability of critical systems through rigorous mathematical proofs. However, its adoption is hindered by labor-intensive manual proofs and the expertise required to use theorem provers. Recent…
Humans generally acquire new skills without compromising the old; however, the opposite holds for Large Language Models (LLMs), e.g., from LLaMA to CodeLLaMA. To this end, we propose a new post-pretraining method for LLMs with an expansion…
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…
Formal verification via theorem proving enables the expressive specification and rigorous proof of software correctness, but it is difficult to scale due to the significant manual effort and expertise required. While Large Language Models…
We are interested in understanding how well Transformer language models (TLMs) can perform reasoning tasks when trained on knowledge encoded in the form of natural language. We investigate their systematic generalization abilities on a…
This paper investigates the logical reasoning capabilities of large language models (LLMs). For a precisely defined yet tractable formulation, we choose the conceptually simple but technically complex task of constructing proofs in Boolean…
In recent months, large language models (LLMs) have made significant progress in mathematical proof generation, but further advancement is hindered by the lack of a large-scale, high-quality dataset of human-evaluated proofs. While…
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…
Mathematical reasoning demands two critical, complementary skills: constructing rigorous proofs for true statements and discovering counterexamples that disprove false ones. However, current AI efforts in mathematics focus almost…
Traditional language model-based theorem proving assumes that by training on a sufficient amount of formal proof data, a model will learn to prove theorems. Our key observation is that a wealth of informal information that is not present in…
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…
Large language models~(LLMs) present an intriguing avenue of exploration in the domain of formal theorem proving. Nonetheless, the full utilization of these models, particularly in terms of demonstration formatting and organization, remains…
In the field of large language model (LLM)-based proof generation, despite extensive training on large datasets such as ArXiv, LLMs still exhibit only modest performance on proving tasks of moderate difficulty. We believe that this is…
Mechanical reasoning is a key area of research that lies at the crossroads of mathematical logic and artificial intelligence. The main aim to develop mechanical reasoning systems (also known as theorem provers) was to enable mathematicians…
Formal theorem proving with TLA+ provides rigorous guarantees for system specifications, but constructing proofs requires substantial expertise and effort. While large language models have shown promise in automating proofs for tactic-based…
Large language models (LLMs) can prove mathematical theorems formally by generating proof steps (\textit{a.k.a.} tactics) within a proof system. However, the space of possible tactics is vast and complex, while the available training data…