Existence of Semiregular Topological Space which is not Completely Hausdorff

Theorem
There exists at least one example of a semiregular topological space which is not a completely Hausdorff space.

Proof
Let $T$ be a simplified Arens square.

From Simplified Arens Square is Semiregular, $T$ is a semiregular space.

From Simplified Arens Square is not Completely Hausdorff, $T$ is not a $T_3$ space.

Hence the result.