The fork and its role in unification of closure algebras

We consider the two-pronged fork frame $F$ and the variety $\mathbf{E}\mathbf{q}(B_F)$ generated by its dual closure algebra $B_F$. We describe the finite projective algebras in $\mathbf{E}\mathbf{q}(B_F)$ and give a purely semantic proof that unification in $\mathbf{E}\mathbf{q}(B_F)$ is finitary and not unitary.