Formal-series correlation inequality for FKG probability measures

Let $X$ be a finite set, let $\mu$ be an FKG probability measure on $2^X$, and let $p(A)=p_1(A)t+p_2(A)t^2+\cdots$ be a formal series whose coefficients are nonnegative monotone functions on $2^X$. Formal-series FKG conjecture. The following formal series has nonnegative coefficients:

$$1-\prod_{A\in 2^X}(1-p(A))^{\mu(A)}\geq 0.$$

This is a formal-series version of the correlation inequalities considered in the paper. The source presents it as a conjecture from the cited earlier work; its resolution is not established by the supplied text.