। । ॥ ५५७ ॥
In plain words
"Consciousness performs the sacrifice and carries out actions"—thus the Veda explicitly teaches its agency. Therefore, the opponent concludes that the self is simply the intellect itself.
Close to the Sanskrit
"Consciousness performs the sacrifice and also performs actions"—thus the agentship of this [intellect] is established directly by the Veda. Therefore, the identity of the self with the intellect is ascertained by the opponent.