For each of the following, either construct a formal proof of validity or prove invalidity by means of the STTT. In each case, use the notation in parentheses.

If the butler were present, he would have been seen; and if he had been seen, he would have been questioned. If he had been questioned, he would have replied; and if he had replied, he would have been heard. But the butler was not heard. If the butler was neither seen nor heard, then he must have been on duty; and if he was on duty, he must have been present. Therefore the butler was questioned. ( P, S, Q, R, H, D )