Does Seedborn Muse untap Time Vault
Yes.

Time Vault only prevents itself from being untapped during its controller's untap step. It doesn't hinder attempts to untap it at any other time.

There's a ruling about this on Seedborn Muse:


  Other effects can prevent a permanent from untapping during an untap step. You do need to look carefully, however, as many effects say that the permanent does not untap during its controller’s untap step, and this card’s ability occurs during other players’ untap steps. If a card does say this, then Seedborn Muse can untap it. But some other abilities are not written this way and can still prevent a card from untapping.