Answer
$C_1^{'}$
Work Step by Step
The proper time, $\Delta t_0$ is always measured in the same inertial reference frame as the event. In other words, it's measured by the clock with the same velocity as $S{'}$. $C_1^{'}$ is the only clock in the same reference frame as $S{'}$, so it's reading will be the "proper time."
