I say, and with God's success: A woman's prayer is not invalidated by seeing men, and it is known that the female companions used to pray with the Prophet (peace be upon him) in the same mosque, so they certainly saw the men, and no one has said that this invalidates their prayer. However, it is preferable for a woman to cover herself as much as she can so that she does not become a temptation by being seen by men. And God knows best.