The Mori cone generation conjecture for the mirror quintic

Let $X_\psi$ be the mirror quintic, and let $M$ denote its Mori cone, namely the cone of numerical equivalence classes of effective curves. For $\mathbf{s},\mathbf{t}\in\{w,v,x,y,z\}$, let $\ell_{\mathbf{t}}$ and $\sigma_{\mathbf{s},\mathbf{t}}$ be the indicated curves on $X_\psi$, and let $\gamma_{\mathbf{m_1},\mathbf{m_2}}$ be the curves constructed above.

Mori cone generation conjecture. The Mori cone $M$ of $X_\psi$ is generated by the classes of the curves $\ell_{\mathbf{t}}$, $\sigma_{\mathbf{s},\mathbf{t}}$, and $\gamma_{\mathbf{m_1},\mathbf{m_2}}$.

This conjecture identifies the proposed generators of the cone of effective curve classes on the mirror quintic. The supplied text does not state whether the claim has been proved or disproved.