Positive correlation for arbitrary three-fluid crossing events

Let $M_n$ be the finite honeycomb-lattice region. For $k=1,2,3$, choose sets $A_k,B_k\subset M_n$, and let $U_k$ be the event that fluid $k$ percolates between $A_k$ and $B_k$. General three-fluid correlation conjecture. For all such choices,

$$P(U_1\cap U_2\cap U_3)\geq P(U_1)P(U_2)P(U_3).$$

This statement generalizes the conjectures for opposite-side and center-to-boundary percolation. Its scope is broader because the endpoint sets are arbitrary, and no proof or resolution is supplied in the paper.