> For the complete documentation index, see [llms.txt](https://docs.moduluszk.io/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.moduluszk.io/performance-the-prover-envelope/solving-not-only-checking.md).

# Solving, not only checking

The rows above prove a completed grid the prover already holds, which is the ordinary shape of a zero-knowledge proof. zkFOL's relations also run the other way: the same predicate that validates a 9x9 grid derives one from its seventeen clues, in roughly 160 ms, and the resulting proof still discloses nothing. The comparator guests as benchmarked cannot express this; a solver would be a separate program, written and proved separately, and it is not what those benchmarks run. This is a capability difference rather than a speed one, which is why it sits outside the prove columns. \[S, benchmark record]