What happens if there is a tie in the senate and there is no vice president?

Under the Senate's rules, a bill has to receive a majority (meaning more than half) of the votes to pass. Therefore, if there is a tie and there is no Vice President to break the tie, the bill fails because is has not received a majority.

A previous answer asserted that the President Pro Tempore would break the tie--however, the President Pro Tem is a Senator and therefore would presumably have already voted.