Existence of Normal Space which is not Completely Normal

Theorem
There exists at least one example of a topological space which is a normal space, but is not also a completely normal space.

Proof
Let $T$ be a Tychonoff plank.

From Tychonoff Plank is Normal, $T$ is a normal space.

From Tychonoff Plank is not Completely Normal, $T$ is not a completely normal space.

Hence the result.