Existence of Completely Hausdorff Space which is not Regular

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

Proof
Let $T$ be a half-disc space.

From Half-Disc Space is Completely Hausdorff, $T$ is a completely Hausdorff space.

From Half-Disc Space is not Regular, $T$ is not a regular space.

Hence the result.