"There are not $n$ $S$-neighbours $y_1, \dots, y_n$ of $x$ with $C$ in $\mathcal{L}(y_i)$ and $y_i \not = y_j$ for $1 \leq i < j \leq n$."
If there are $n-1$ such $S$-neighbours, is that entailed by this sentence? Or this sentence only entails that there's no such $S$-neighbors?