Non-Trivial Discrete Space is not Arc-Connected

Corollary to Non-Trivial Discrete Space is not Connected
Let $T = \left({S, \tau}\right)$ be a non-trivial discrete topological space.

$T$ is not arc-connected.

Proof
$T$ is arc-connected.

From:
 * Arc-Connected Space is Path-Connected
 * Path-Connected Space is Connected

we have that $T$ is connected.

But this directly contradicts Non-Trivial Discrete Space is not Connected.

The result follows from Proof by Contradiction.