Richards-Sahi conjecture

Let $X$, $Y$, and $Z$ be upward closed subsets of $Q_n$. It is conjectured that

$$2\mu(X\cap Y\cap Z)-\mu(X)\mu(Y\cap Z)-\mu(Y)\mu(X\cap Z)-\mu(Z)\mu(X\cap Y)+\mu(X)\mu(Y)\mu(Z)\ge 0$$

Notation: the poset $Q_n$ is the power set of a set with $n$ elements, ordered by subset relation. A subfamily $F$ of sets is upward closed if whenever $A\in F$ and $A\subset B$, also $B\in F$. Let $\mu$ be the uniform probability measure on $Q_n$.