Related papers: Lean-auto: An Interface between Lean 4 and Automat…
Neural networks have shown substantial promise at automatic theorem-proving in interactive proof assistants (ITPs) like Lean and Coq. However, most neural theorem-proving models are restricted to specific ITPs, leaving out opportunities for…
We present Prover Agent, a novel AI agent for automated theorem proving that integrates large language models (LLMs) with a formal proof assistant, Lean. Prover Agent coordinates an informal reasoning LLM, a formal prover model, and…
In the recent years, we have linked a large corpus of formal mathematics with automated theorem proving (ATP) tools, and started to develop combined AI/ATP systems working in this setting. In this paper we first relate this project to the…
Mechanized theorem proving is becoming the basis of reliable systems programming and rigorous mathematics. Despite decades of progress in proof automation, writing mechanized proofs still requires engineers' expertise and remains labor…
We present LLMSTEP, a tool for integrating a language model into the Lean proof assistant. LLMSTEP is a Lean 4 tactic that sends a user's proof state to a server hosting a language model. The language model generates suggestions, which are…
The demonstrated code-understanding capability of LLMs raises the question of whether they can be used for automated program verification, a task that demands high-level abstract reasoning about program properties that is challenging for…
This paper describes a large set of related theorem proving problems obtained by translating theorems from the HOL4 standard library into multiple logical formalisms. The formalisms are in higher-order logic (with and without type…
Benchmarking automated theorem proving (ATP) systems using standardized problem sets is a well-established method for measuring their performance. However, the availability of such libraries for non-classical logics is very limited. In this…
We describe a very large improvement of existing hammer-style proof automation over large ITP libraries by combining learning and theorem proving. In particular, we have integrated state-of-the-art machine learners into the E automated…
Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In…
Interactive proof assistants are computer programs carefully constructed to check a human-designed proof of a mathematical claim with high confidence in the implementation. However, this only validates truth of a formal claim, which may…
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…
Verifiable formal languages like Lean have profoundly impacted mathematical reasoning, particularly through the use of large language models (LLMs) for automated reasoning. A significant challenge in training LLMs for these formal languages…
Proving mathematical theorems using computer-verifiable formal languages like Lean significantly impacts mathematical reasoning. One approach to formal theorem proving involves generating complete proofs using Large Language Models (LLMs)…
Recent advances in large language models have demonstrated impressive capabilities in mathematical formalization. However, existing benchmarks focus on logical verification of declarative propositions, often neglecting the task of…
Software testing plays a critical role in ensuring that systems behave as intended. However, existing automated testing approaches struggle to match the capabilities of human engineers due to key limitations such as test locality, lack of…
There are several paradigms for integrating interactive and automated theorem provers, combining the convenience of powerful automation with strong soundness guarantees. We introduce a new approach for reconstructing proofs found by SMT…
Mella is a minimalistic dependently typed programming language and interactive theorem prover implemented in Haskell. Its main purpose is to investigate the effective integration of automated theorem provers in a pure and simple setting.…
This paper reports our initial experiments with using external ATP on some corpora built with the ACL2 system. This is intended to provide the first estimate about the usefulness of such external reasoning and AI systems for solving ACL2…
In logical reasoning, it is often the case that only some of a collection of assumptions are needed to reach a conclusion. A strengthening lemma is an assertion that a given conclusion is independent in this sense of a particular…