$\mathbf {The \ Problem \ is}:$ Give an example of an Urysohn space which is not semi-regular .
$\mathbf {My \ approach}:$ Actually, it is an exercise problem from Willard's book( exc: $14F$) . I tried some examples inspired from Sierpinski space, and slotted plane .
I think the slotted plane will work because if $N$ is a nhood of $z \in \mathbb R^2$ , then $N=\{z\} \cup A$ where $A$ is an usual open disc of $z$ with finitely many st lines through $z$ removed. Then $cl(N) = A \cup \{\text{finitely many lines that were removed}\} \cup Fr(A)$ hence $int(cl(N)) \neq N$ ; thus slotted plane isn't semi-regular .
But it's Urysohn, as real plane is Urysohn and removal of finitely many st lines doesn't affect anything.
I am still in some confusion , a small hint is warmly appreciated .