The standard-form negativity conjecture for blow-ups of the plane

Let $D$ be a line bundle in standard form on ${\rm Bl}_{s}(\mathbb{P}^{2})$, meaning that

$$D=dH-\sum_{i=1}^{s}m_{i}E_{i},\qquad m_{1}\geq\cdots\geq m_{s}\geq0,\qquad d\geq m_{1}+m_{2}+m_{3}.$$

Standard-form negativity conjecture. If $s\geq1$ and $D^{2}<0$, then $D$ is not effective. This is presented as a consequence expected from the SHGH conjecture and concerns the effective cone of blow-ups of the projective plane. Its resolution status is not specified in the supplied text.