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FreeBlueprint-driven Lean 4 theorem proving via AI
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About prompt
A structured prompt for guiding large language models to act as a Formal Theorem Proving Architect, specializing in solving mathematical theorems using the Lean 4 proof assistant. The prompt implements a blueprint-first methodology: it generates a dependency graph of definitions and lemmas, then proves each lemma in parallel with iterative refinement based on compiler feedback. Based on research achieving 99.2% pass@1 on MiniF2F-test and 75.6% on PutnamBench, this prompt enables automated, agentic theorem proving from natural language theorem statements and optional proof sketches.
Key Features
Blueprint-first decomposition generating a dependency graph of definitions and lemmas
Parallel theorem proving of each lemma in topological order with scope isolation
Iterative refinement using Lean 4 compiler feedback to repair broken proofs
Support for natural-language proof sketches as structural guides
High pass rates on benchmarks: 99.2% MiniF2F-test, 75.6% PutnamBench
Pros & Cons
Pros
- Achieves state-of-the-art results on formal theorem proving benchmarks
- Structured blueprint methodology reduces dead-end exploration
- Parallel proving speeds up overall proof construction
- Explicitly handles compiler errors with refinement loops
Cons
- Requires access to a capable large language model (not a standalone tool)
- Needs Lean 4 environment and compiler setup for full workflow
- Complex prompt with many phases may confuse less capable models
- Dependency graph must remain acyclic, limiting some proof strategies
Best For
Automated formal theorem proving in mathematicsGenerating Lean 4 code for mathematical proofsAssisting researchers in formalization of complex theoremsEducational tool for learning formal proof techniques