Special Lagrangian torus fibre conjecture for toric Fano surfaces

Let $Y$ be a toric Fano surface, and let $W(u)$ denote the superpotential of a special Lagrangian torus fibre $L_u$; let $W^{HV}$ be the Hori–Vafa superpotential. Special Lagrangian torus fibre conjecture. There exists a special Lagrangian torus fibre $L_u$ Hamiltonian isotopic to a moment torus fibre. In particular,

$$W(u)=W^{HV}.$$

This would identify the special-Lagrangian-fibration superpotential with the Hori–Vafa mirror of a toric Fano surface; the supplied text gives no resolution status.