A Minimal Agent for Automated Theorem Proving

A minimal agent for automated theorem proving serves as a baseline to compare different AI theorem prover architectures by focusing on core capabilities such as iterative refinement and library search. This approach allows for standardized evaluation of state-of-the-art agentic systems, highlighting the contributions of individual components like context access, feedback mechanisms, and proof-tree representations. For instance, ablation studies show that removing context search or feedback loops significantly reduces performance, underscoring their importance in effective proof automation . Similarly, iterative error correction—where models refine formalizations based on verifier feedback—has been shown to improve success rates in autoformalization tasks . The use of a minimal agent framework enables researchers to isolate these factors and assess their impact systematically, providing a clearer understanding of how different design choices influence overall performance in formal reasoning tasks . Such standardization is crucial for advancing the field and ensuring meaningful comparisons across systems like HILBERT, AutoRocq, and miniF2F-Dafny

This paper introduces "A Minimal Agent," a streamlined architectural baseline designed specifically for the domain of automated theorem proving (ATP). Addressing the increasing complexity of modern AI provers—which often couple massive language models with intricate search heuristics—the authors propose a stripped-down framework centered on iterative refinement and library search. By focusing on the core mechanics of an agentic loop, the work dissects the proving process into manageable components: retrieving relevant lemmas from a mathematical library and iteratively refining proof states until a valid derivation is found. This approach serves as a controlled environment to study how fundamental agentic behaviors, rather than model scale alone, contribute to solving complex formal proofs.

A key contribution of this research is the establishment of a reproducible standard for evaluating prover architectures. The minimal agent demonstrates that significant performance can be achieved—or at least benchmarked—using a structured search over existing libraries combined with a feedback loop for refinement. This allows researchers to isolate the impact of specific architectural choices, such as the choice of search algorithm or the retrieval mechanism, without the confounding variables present in monolithic systems. The insights provided suggest that the efficacy of an ATP system relies heavily on its ability to effectively navigate the existing mathematical corpus and adaptively refine its strategy based on intermediate verification feedback.

The significance of this work lies in its potential to standardize the assessment of AI systems in formal mathematics. As the field moves toward relying on large-scale models, there is a growing need for minimal baselines to determine whether added complexity yields genuine improvements in reasoning capabilities or merely computational overhead. By providing a clear and modular framework, this material enables the community to make direct comparisons between different prover designs. It ultimately advances the understanding of agentic reasoning in formal contexts, paving the way for more robust and interpretable automated mathematicians.

Summary of "A Minimal Agent for Automated Theorem Proving"

This paper introduces a minimal agentic baseline for automated theorem proving (ATP), designed to serve as a foundational model for comparing and benchmarking AI-driven proof architectures. The agent operates through iterative refinement, where it decomposes problems into subgoals and explores library-based search strategies to construct proofs. By focusing on minimalism, the authors aim to isolate core mechanisms of ATP agents, making it easier to study the impact of architectural choices, such as search heuristics, refinement policies, and proof representation. The work emphasizes reproducibility and modularity, enabling researchers to systematically extend or modify components (e.g., the library of lemmas) to evaluate their contributions.

The key contributions include a lightweight yet effective ATP agent that demonstrates competitive performance on benchmark problems while remaining transparent and easy to adapt. The paper highlights the importance of library search—where the agent leverages a curated set of intermediate results—as a critical component for scaling ATP systems. This approach contrasts with black-box or neural-symbolic methods by prioritizing interpretability and iterative improvement. The work matters because it provides a standardized baseline for future research, particularly in areas like proof assistants, formal verification, and AI-driven math discovery. By offering a minimal yet functional agent, the paper lowers the barrier for experimentation and fosters a more systematic understanding of how different components contribute to ATP success.