Rayleigh conjecture for spanning-forest generating functions

Let $G=(V,E)$ be a graph, and let $F_G(\mathbf{w})$ denote its spanning-forest generating function (SFGF), where $\mathbf{w}$ is the vector of edge weights. A multivariate polynomial is Rayleigh when it satisfies the Rayleigh inequalities for all nonnegative edge weights.

Spanning-forest Rayleigh conjecture. For any graph $G=(V,E)$, the SFGF $F_G(\mathbf{w})$ is Rayleigh.

A positive answer would imply that the spanning-forest distribution on a graph is negatively correlated, connecting the claim to conjectures of Kahn and of Grimmett and Winkler. The source does not specify whether this conjecture has been resolved.