  More than a dozen young stars host spiral arms in their surrounding
protoplanetary disks. The excitation mechanisms of such arms are under debate.
The two leading hypotheses -- companion-disk interaction and gravitational
instability (GI) -- predict distinct motion for spirals. By imaging the MWC 758
spiral arm system at two epochs spanning ${\sim}5$ yr using the SPHERE
instrument on the Very Large Telescope (VLT), we test the two hypotheses for
the first time. We find that the pattern speeds of the spirals are not
consistent with the GI origin. Our measurements further evince the existence of
a faint "missing planet" driving the disk arms. The average spiral pattern
speed is $0.\!^\circ22\pm0.\!^\circ03$ yr$^{-1}$, pointing to a driver at
$172_{-14}^{+18}$ au around a $1.9$ $M_\odot$ central star if it is on a
circular orbit. In addition, we witness time varying shadowing effects on a
global scale that are likely originated from an inner disk.
