Non-finite generation conjecture for non-zero CQP monoids

Let $M$ be a CQP monoid, meaning a monoid satisfying the CQP property defined earlier in the paper. The conjecture is:

Non-finite generation conjecture. If $M$ is a non-zero CQP monoid, then $M$ is not finitely generated as a monoid.

This conjecture concerns the generation of CQP monoids, with the universal CP monoid $U$ as a motivating example. The supplied text does not state whether the conjecture has been resolved.