Hong's odd-set LCM nonsingularity conjecture

Let $S$ be a GCD-closed set of odd positive integers, meaning that every element of $S$ is odd and the greatest common divisor of any two elements of $S$ belongs to $S$. Let $[S]=[[x_i,x_j]]$ be the LCM matrix on $S$. Hong's conjecture. The matrix $[S]$ is nonsingular. The source states that this conjecture is disproved by a counterexample.