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Mathematical theorems are human knowledge able to be accumulated in the form of symbolic representation, and proving theorems has been considered intelligent behavior. Based on the BHK interpretation and the Curry-Howard isomorphism, proof…

Neural and Evolutionary Computing · Computer Science 2016-04-18 Li-An Yang , Jui-Pin Liu , Chao-Hong Chen , Ying-ping Chen

The synergy between deep learning models and traditional automation tools, such as built-in tactics of the proof assistant and off-the-shelf automated theorem provers, plays a crucial role in developing robust and efficient neural theorem…

Machine Learning · Computer Science 2025-06-09 Haoxiong Liu , Jiacheng Sun , Zhenguo Li , Andrew C Yao

Agentic theorem provers combine a reasoning model, retrieval, search, and a proof assistant verifier, yet it remains unclear which components actually improve finite-budget proof success and why they help on real mathematical workloads. We…

Machine Learning · Statistics 2026-05-26 Sho Sonoda , Shunta Akiyama , Yuya Uezato

We present Ax-Prover, a multi-agent system for automated theorem proving in Lean that can solve problems across diverse scientific domains and operate either autonomously or collaboratively with human experts. To achieve this, Ax-Prover…

Automated Theorem Proving (ATP) in formal languages is a foundational challenge for AI. While Large Language Models (LLMs) have driven remarkable progress, a significant gap remains between their powerful informal reasoning capabilities and…

Logic in Computer Science · Computer Science 2025-07-10 Zhenwen Liang , Linfeng Song , Yang Li , Tao Yang , Feng Zhang , Haitao Mi , Dong Yu

Aiming at efficient and dense chain-of-thought (CoT) reasoning, latent reasoning methods fine-tune Large Language Models (LLMs) to substitute discrete language tokens with continuous latent tokens. These methods consume fewer tokens…

Artificial Intelligence · Computer Science 2026-01-30 Zhi Zheng , Wee Sun Lee

Saturation-style automated theorem provers (ATPs) based on the given clause procedure are today the strongest general reasoners for classical first-order logic. The clause selection heuristics in such systems are, however, often evaluating…

Logic in Computer Science · Computer Science 2021-07-22 Karel Chvalovský , Jan Jakubův , Miroslav Olšák , Josef Urban

Automatic (i.e., computer-assisted) theorem proving (ATP) can come in many flavors. This document presents early steps in our effort towards defining object-oriented theorem proving (OOTP) as a new style of ATP. Traditional theorem proving…

Programming Languages · Computer Science 2019-02-28 Moez A. AbdelGawad

The geometry automated theorem proving area distinguishes itself by a large number of specific methods and implementations, different approaches (synthetic, algebraic, semi-synthetic) and different goals and applications (from research in…

Artificial Intelligence · Computer Science 2020-03-02 Nuno Baeta , Pedro Quaresma , Zoltán Kovács

LPTP (Logic Program Theorem Prover) is an interactive natural-deduction-based theorem prover for pure Prolog programs with negation as failure, unification with the occurs check, and a restricted but extensible set of built-in predicates.…

Logic in Computer Science · Computer Science 2026-01-08 Fred Mesnard , Thierry Marianne , Étienne Payet

Interactive Theorem Provers (ITPs) are an indispensable tool in the arsenal of formal method experts as a platform for construction and (formal) verification of proofs. The complexity of the proofs in conjunction with the level of expertise…

Logic in Computer Science · Computer Science 2023-04-21 Eric Yeh , Briland Hitaj , Sam Owre , Maena Quemener , Natarajan Shankar

Automated Theorem Proving (ATP) faces challenges due to its complexity and computational demands. Recent work has explored using Large Language Models (LLMs) for ATP action selection, but these methods can be resource-intensive. This study…

Artificial Intelligence · Computer Science 2024-07-23 Mahdi Buali , Robert Hoehndorf

Automated theorem proving (ATP) has become an appealing domain for exploring the reasoning ability of the recent successful generative language models. However, current ATP benchmarks mainly focus on symbolic inference, but rarely involve…

Proof automation is crucial to large-scale formal mathematics and software/hardware verification projects in ITPs. Sophisticated tools called hammers have been developed to provide general-purpose proof automation in ITPs such as Coq and…

Logic in Computer Science · Computer Science 2025-05-27 Yicheng Qian , Joshua Clune , Clark Barrett , Jeremy Avigad

Automated Theorem Proving (ATP) represents a fundamental challenge in Artificial Intelligence (AI), requiring the construction of machine-verifiable proofs in formal languages such as Lean to evaluate AI reasoning capabilities.…

Artificial Intelligence · Computer Science 2026-01-23 Zhengqing Yan , Xinyang Liu , Yi Zhang , Fan Guo , ChengXun Jia , Junchen Wan , Yao Liu , Qi Liu , Jihao Huang , Kang Song

Although most of the automated theorem-proving approaches depend on formal proof systems, informal theorem proving can align better with large language models' (LLMs) strength in natural language processing. In this work, we identify a…

Artificial Intelligence · Computer Science 2026-04-20 Yunhe Li , Hao Shi , Bowen Deng , Wei Wang , Mengzhe Ruan , Hanxu Hou , Zhongxiang Dai , Siyang Gao , Chao Wang , Shuang Qiu , Linqi Song

I propose a system for Automated Theorem Proving in higher order logic using deep learning and eschewing hand-constructed features. Holophrasm exploits the formalism of the Metamath language and explores partial proof trees using a…

Artificial Intelligence · Computer Science 2016-08-11 Daniel Whalen

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…

Software Engineering · Computer Science 2026-04-22 Yican Sun , Chengwei Shi , Hangzhou Lyu , Yingfei Xiong

Recently, it is often said that the data used for the pre-training of large language models (LLMs) have been exhausted. This paper proposes a solution to the problem: Automated generation of massive reasonable empirical theorems by forward…

Artificial Intelligence · Computer Science 2024-12-18 Jingde Cheng

We study from the proof complexity perspective the (informal) proof search problem: Is there an optimal way to search for propositional proofs? We note that for any fixed proof system there exists a time-optimal proof search algorithm.…

Computational Complexity · Computer Science 2022-07-12 Jan Krajicek