Existence of Hausdorff Space which is not Completely Hausdorff

Theorem
There exists at least one example of a topological space which is a $T_2$ (Hausdorff) space, but is not also a completely Hausdorff space.

Proof
Let $T$ be an irrational slope topological space.

From Irrational Slope Space is $T_2$, $T$ is a $T_2$ (Hausdorff) space.

From Irrational Slope Space is not Completely Hausdorff, $T$ is not a completely Hausdorff space.