Morris's conjecture on regular generators of non-FC families

Let $[n]=\{1,\ldots,n\}$ and let $U(\mathcal{S})$ denote the union of the sets in $\mathcal{S}$. A minimal generator of a union-closed family $\mathcal{F}$ is a family whose generated union-closed family is $\mathcal{F}$ and which is minimal with this property. A union-closed family is Non-FC if it does not satisfy Frankl's conjecture. A generator $\mathcal{S}$ is regular when, for every nonempty $A\in\mathcal{S}$ and every $i\in[n]$, replacing $A$ by $A\cup\{i\}$ still generates a Non-FC union-closed family. Morris's conjecture. If $U(\mathcal{S})=[n]$ for $n\geq 3$, and $\mathcal{S}$ is a minimal generator for a Non-FC union-closed family $\mathcal{F}$, then $\mathcal{S}$ is regular. The paper states that it constructs a counterexample to this conjecture, so the claim is refuted.