research
Incomplete Proofs Kept Their Verified Pieces
ProofEvolve stores kernel-checked partial proof graphs so unfinished work can contribute to later theorems.
Summary
ProofEvolve stores kernel-checked partial proof graphs so unfinished work can contribute to later theorems.
Neural models propose decompositions, repairs and schema combinations while Lean verifies each transition. Within a problem, the system evolves partial AND-OR proof graphs; across problems, verified subgraphs enter a persistent schema library with unresolved premises exposed as new goals. The authors report the highest average solve rate among evaluated systems on three competition-level Lean benchmarks. Formal verification preserves soundness of accepted steps, not the usefulness of every proposal.
Why it matters
ProofEvolve stores kernel-checked partial proof graphs so unfinished work can contribute to later theorems.
Limits and context
- Formal verification preserves soundness of accepted steps, not the usefulness of every proposal.
Key claims
ProofEvolve stores kernel-checked partial proof graphs so unfinished work can contribute to later theorems.
Qualification: Formal verification preserves soundness of accepted steps, not the usefulness of every proposal.
Evidence: source-2026-08-30-014
Sources
- arXiv preprint 2608.26334arXiv · primary research
Corrections
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