Prime ideals of the Witt enveloping algebra contain primitive ideals

Let $W$ be the Witt algebra and let $\operatorname{U}(W)$ be its universal enveloping algebra. The Witt prime-to-primitive containment conjecture. Every proper prime ideal of $\operatorname{U}(W)$ contains a proper primitive ideal. This is an enveloping-algebra analogue of a Poisson result, and the supplied text does not state whether it has been resolved.