Fukaya's Whitehead torsion conjecture for Floer complexes

Let $L_1$ and $L_2$ be exact Lagrangians with Floer homology $HF(L_1,L_2)$ and Floer complex $CF(L_1,L_2)$, whose Whitehead torsion is denoted by $\tau(CF(L_1,L_2))$. Fukaya's conjecture. If

$$HF(L_1,L_2)=0$$

and

$$\tau(CF(L_1,L_2))=0,$$

then there exists an exact symplectic diffeomorphism $\phi$ such that

$$L_1\cap \phi(L_2)=\emptyset.$$

Fukaya proposed this as an invariance and displaceability statement for the Whitehead torsion of Floer complexes under Hamiltonian perturbations; the source provides no resolution.