Solvable-filtration converse for associated derivatives

Let $K$ be a knot, let $J$ be a derivative associated to an $(n+1)$-solution for $K$, where $n$ is a non-negative integer or half-integer, and let $\Delta_K(t)$ denote the Alexander polynomial of $K$. Solvable-filtration converse. If

$$K\in \mathcal{F}_{n+1}$$

via an $(n+1)$-solution to which $J$ is associated, and $\Delta_K(t)\neq 1$, then

$$J\in \mathcal{F}_n.$$

This conjecture is the solvable-filtration analogue of Kauffman's conjecture. The source states that the same counterexample that disproves Kauffman's conjecture also disproves this formulation.