Fast Algorithm to Check if a Set of Sets forms an Anti-chain
This problem is SETH-hard at time $n^2$ (Williams 04). There is is no $n^{2-\epsilon}$ algorithm for any $\epsilon &gt; 0$ if the universe has size $\omega(\log n)$.

For small universe size ($c \log n$ for some $c$), there is an algorithm with time $n^{2-1/O(\log c)}$ (Abboud, Williams, Yu 15)