Li et al.'s neighbor product distinguishing total coloring conjecture

Let $G$ be a graph with at least two vertices. The neighbor product distinguishing total chromatic number $\chi”_{\prod}(G)$ is the smallest number of colors in a neighbor product distinguishing total coloring of $G$, where the product at a vertex is the product of its color and the colors of its incident edges. Li et al.'s conjecture.

$$\chi”_{\prod}(G)\leq\Delta(G)+3.$$

This conjecture proposes a uniform upper bound in terms of the maximum degree for neighbor product distinguishing total colorings; the source gives no resolution status.