A Minimal Agent for Automated Theorem Proving
| Authors | Borja Requena Pozo et al. |
| Year | 2026 |
| Field | AI / Agents |
| arXiv | 2602.24273 |
| Download | |
| Categories | cs.AI |
Abstract
We propose a minimal agentic baseline that enables systematic comparison across different AI-based theorem prover architectures. This design implements the core features shared among state-of-the-art systems: iterative proof refinement, library search and context management. We evaluate our baseline using qualitatively different benchmarks and compare various popular models and design choices, and demonstrate competitive performance compared to state-of-the-art approaches, while using a significantly simpler architecture. Our results demonstrate consistent advantages of an iterative approach over multiple single-shot generations, especially in terms of sample efficiency and cost effectiveness. The implementation is released open-source as a candidate reference for future research and as an accessible prover for the community.
Engineering Breakdown
Plain English
This paper introduces a minimal, reference-quality agent architecture for automated theorem proving that serves as a standardized baseline for comparing different AI-powered proof systems. The authors implement core features found in state-of-the-art theorem provers—iterative proof refinement, library search, and context management—but in a significantly simpler form that achieves competitive performance. Key finding: iterative approaches substantially outperform single-shot generation across multiple benchmarks, with better sample efficiency and lower costs. The work is released as open-source to enable consistent evaluation and comparison across future research.
Core Technical Contribution
The core novelty is defining and implementing a minimal yet complete agent baseline that strips away complexity while retaining essential capabilities for theorem proving. Rather than building a novel algorithm, the authors systematically identify which architectural components (iterative refinement loops, search over learned representations, token-level context management) are actually necessary and sufficient for competitive performance. This is valuable because prior theorem provers often obscured which design choices drove improvements versus added unnecessary complexity. The minimal design enables cleaner ablation studies and makes it easier for researchers to understand what matters when comparing models and approaches.
How It Works
The agent operates as an iterative loop: given a theorem statement, the system generates candidate proof steps, then refines them based on feedback from a theorem verifier or constraint checker. Input consists of the formal problem statement plus access to a library of prior lemmas and proofs (retrieved via learned search). At each iteration, the agent maintains a context window tracking the current proof state, intermediate goals, and relevant library items. The core loop repeats until a complete proof is found or iteration limits are reached. The system uses standard language models as the generation backbone but wraps them in this agentic scaffolding—the innovation is the simplicity of the wrapper, not the underlying model. Output is a valid formal proof that can be machine-verified.
Production Impact
For teams building formal verification systems or automated reasoning tools, this work provides a reproducible baseline that reduces engineering effort—you get a known-good reference implementation rather than reverse-engineering capabilities from multiple papers. The emphasis on iterative refinement over single-shot approaches directly translates to better cost-effectiveness in production: fewer expensive model calls per solved problem, and predictable scaling behavior as you add more iterations. The open-source release means you can adopt this as a foundation and customize library search, context management, or the underlying model without reimplementing core logic. Trade-offs include latency (iterative solving takes multiple model calls, so wall-clock time increases even if total tokens decrease) and the need for a working theorem verifier in your formal framework (the agent cannot work standalone).
Limitations and When Not to Use This
The approach assumes access to a reliable, fast theorem verifier—it cannot work with informal or partially formal problem statements. Sample efficiency improvements assume the underlying language model is reasonably capable; for weak models, iteration may just amplify errors rather than refine solutions. The minimal design, while elegant for research, may not capture domain-specific optimizations that production systems need (specialized proof search heuristics, tactic-specific context selection). The paper does not address generalization to theorem domains far from the training distribution, nor does it fully explore what happens when the library is incomplete or misleading. Follow-up work should investigate how library quality and size affect performance, and whether the architecture scales to larger, more complex mathematical domains.
Research Context
This builds on a line of work in neural theorem proving (prior work by Polu, Sutskever, and others) but shifts focus from novel architectures toward systematic benchmarking and baseline establishment. The paper contributes to the broader agent research agenda by showing that simple, transparent agent loops can outperform end-to-end models—relevant beyond theorem proving to code generation, planning, and reasoning tasks. It directly enables the research community to compare apples-to-apples: by releasing a reference implementation, papers can now report 'improvement over minimal baseline' rather than claiming incomparable results on different codebases. The emphasis on sample efficiency and cost-effectiveness aligns with recent trends in the field toward practical, deployable systems rather than benchmark-chasing.
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