# Researchers prove AI-generated plans solve all cases in 12 domains

Digest AI · Research · published 2026-09-24T04:00:00Z

Canonical: https://digestai.news/story/researchers-prove-ai-generated-plans-solve-all-cases-in-12-domains

## Summary

A new method lets large language models generate generalized plans in Lean—a formal language—and prove they work for every possible case in a domain. The approach converts PDDL planning problems into Lean code, then uses an LLM to write both the plan and a proof of its correctness. Lean’s kernel verifies the proof, ensuring no edge case is missed.

The team tested it on 13 standard benchmark domains, achieving valid proofs for 12. The method uses **GPT-5.6-Sol** as the LLM. This advances automated planning by shifting from manual verification to automated proof generation, though the work remains theoretical for now.

## Key points

- New method generates plans in Lean and proves they solve every case in a domain
- Uses GPT-5.6-Sol to create both plan and formal proof, verified by Lean’s kernel
- Works for 12 of 13 tested benchmark domains, marking progress in automated completeness proofs

## Why it matters

Proving AI plans work for all cases—without manual checks—could accelerate robotics, logistics, and automation by reducing trial-and-error in real-world systems.

## Sources

1. [Provably Complete Generalized Planning with LLMs](https://arxiv.org/abs/2609.27105) (arXiv cs.AI, 2026-09-24, primary source)

## Cite

Digest AI, "Researchers prove AI-generated plans solve all cases in 12 domains", 24 September 2026, https://digestai.news/story/researchers-prove-ai-generated-plans-solve-all-cases-in-12-domains

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