Equivalent maximal-ReLU-function minimal-depth conjecture

Let $x_1,\ldots,x_n$ be the coordinate functions on $\mathbb{R}^n$, and let the minimal depth of a CPWL function mean the smallest $m$ for which it is representable by a ReLU neural network in $\Upsilon(m)$.

Hertrich et al.'s equivalent conjecture. The function

$$\max\{x_1,x_2,\ldots,x_n,0\}$$

has minimal depth $\lceil\log_2(n+1)\rceil$.

The paper states this as an equivalent formulation of the general minimum-depth conjecture. It is known in dimensions $n=2,3$, while the general assertion remains open.