Pilsniak's distinguishing index conjecture for 2-connected graphs

Let $G$ be a $2$-connected graph, and let $D'(G)$ denote its distinguishing index and $\Delta(G)$ its maximum degree.

Pilsniak's conjecture.

$$D'(G)\leq 1+\lceil \sqrt{\Delta(G)}\rceil.$$

This conjecture proposes a sharper upper bound for the distinguishing index of 2-connected graphs in terms of their maximum degree. The supplied source does not state whether the conjecture has been resolved.