An AI system can now prove, not just claim, that its plans actually work every time.
Researchers built a pipeline that uses an LLM, GPT-5.6-Sol, to generate "generalized plans" - programs meant to solve every instance of a planning problem, like packing boxes or routing blocks. The twist: the system also converts the planning domain's rules from PDDL into Lean, a formal proof language, and has the same LLM write a mathematical proof that the plan works for every valid instance. Lean's own kernel checks the proof, so there's no room for a persuasive-but-wrong argument to slip through. Across 13 standard benchmark domains, the approach produced a plan with a verified completeness proof for 12 of them.
This matters because prior LLM-based planning work could only claim success by running a pile of test cases and hoping nothing broke outside that sample. That's the same weak spot that undermines trust in a lot of AI-generated code: it looks right until it isn't. Swapping "passed our tests" for "proven correct by a theorem checker" is a real jump in what these systems can promise, especially for domains like logistics or robotics where an edge-case failure isn't just annoying, it's expensive.
One domain still resisted proof, a reminder that formal verification of AI-written plans is progress, not a solved problem, and Lean expertise remains a niche skill standing between this result and anyone actually using it.