The Bousfield class decomposition conjecture for D

Let $D=aH\mathbf{F}_p\vee H\mathbf{F}_p$, where $a$ denotes the acyclic complement operation, and let $K(n)$, $A(n)$, and $H\mathbf{F}_p$ have their usual meanings.

The decomposition conjecture for D. One has

$$\langle D\rangle=\bigvee_{n\geq 0}\langle K(n)\rangle\vee\bigvee_{n\geq 2}\langle A(n)\rangle\vee\langle H\mathbf{F}_p\rangle.$$

The statement is presented as a desired description of the sublattice generated by $D$; the source gives no resolution.