The synergy between deep learning models and traditional automation tools plays a pivotal role in developing robust neural theorem provers (NTPs). However, for proof synthesis with LLMs, previous work applies automation tools either only when the model explicitly calls the method, or only at a single granularity level, failing to fully exploit the power of built-in tactics and off-the-shelf automated theorem provers. In this work, we propose ProofAug, a novel theorem proving method that enjoys superior sample efficiency through equipping proof-generation LLMs with automation methods in different granularities via fine-grained structure analysis of model-generated proof proposals. Furthermore, ProofAug serves as a versatile plug-and-play module that seamlessly integrates with any tree-search algorithm, enabling our construction of an efficient recursive proving (ERP) module to further enhance performance. The superiority of our method is validated on the miniF2F-test benchmark using the open-source deepseek-math-7b-base model and the Isabelle proof assistant. Notably, by additionally employing a mixed prompting strategy, we achieve a cumulative pass rate of 66.0% after curation of the dataset (61.9% for the original version), setting a new SOTA across all proof languages with a total sample budget of only 2100. Our code is available at https://github.com/haoxiongliu/ProofAug.

Recently, a growing number of researchers have applied machine learning to assist users of interactive theorem provers. However, the expressive nature of underlying logics and esoteric structures of proof documents impede machine learning practitioners, who often do not have much expertise in formal logic, let alone Isabelle/HOL, from achieving a large scale success in this field. In this data description, we present a simple dataset that contains data on over 400k proof method applications along with over 100 extracted features for each in a format that can be processed easily without any knowledge about formal logic. Our simple data format allows machine learning practitioners to try machine learning tools to predict proof methods in Isabelle/HOL without requiring domain expertise in logic.

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 intensive. Recently, researchers have extracted heuristics of interactive proof development from existing large proof corpora using supervised learning. However, such existing proof corpora present only one way of proving conjectures, while there are often multiple equivalently effective ways to prove one conjecture. In this abstract, we identify challenges in discovering heuristics for automatic proof search and propose our novel approach to improve heuristics of automatic proof search in Isabelle/HOL using evolutionary computation.

Deciding which sub-tool to use for a given proof state requires expertise specific to each ITP. To mitigate this problem, we present PaMpeR, a Proof Method Recommendation system for Isabelle/HOL. Given a proof state, PaMpeR recommends proof methods to discharge the proof goal and provides qualitative explanations as to why it suggests these methods. PaMpeR generates these recommendations based on existing hand-written proof corpora, thus transferring experienced users' expertise to new users. Our evaluation shows that PaMpeR correctly predicts experienced users' proof methods invocation especially when it comes to special purpose proof methods.

A general game player is a system that understands the rules of unknown games and learns to play these games well without human intervention. A major challenge for research in General Game Playing is to endow a player with the ability to extract and prove game-specific knowledge from the mere game rules. We define a formal language to express temporally extended — yet local — properties of games. We also develop a provably correct proof theory for this language using the paradigm of Answer Set Programming, and we report on experiments with a practical implementation of this proof system in combination with a successful general game player.