Forum:Can X-Saber Souza destroy obelisk?

Okay so my opponent summoned obelisk the turn before, I synchro summon X-Saber Souza and use its effect for "At the start of the Damage Step, if this card battles an opponent's monster: Destroy that monster (without damage calculation)." Does X-Saber Souza's effect target? and would obelisk be destroyed?