Strict-inclusion conjecture for classes of free arrangements

Let $\mathcal{IF}$, $\mathcal{DF}$, $\mathcal{AF}$, and $\mathcal{SF}$ denote the classes of free arrangements defined in the paper: inductively free, divisionally free, additionally free, and stair-free arrangements, respectively.

Class-inclusion conjecture. The following strict inclusion and non-inclusion relations should hold:

$$\mathcal{IF}\subsetneq\mathcal{AF}.$$ $$\mathcal{DF}\not\supset\mathcal{AF}.$$ $$\mathcal{DF}\cup\mathcal{AF}\subsetneq\mathcal{SF}.$$

These claims would establish that the newly introduced classes enlarge the inductively free class in distinct ways, while the stair-free class is strictly larger than their union. The source gives no evidence of a resolution.