Your answer is quite right and complete, Venay.Singh84. This deserves to be 'The best answer'.
With 5 statements that can be true or false there are 32 possibilities. Most combinations are contradictory, but 4 are acceptable and without contradiction. It are the four that you mentioned. Unfortunately for the riddle this means that any thirteen characters, whether in the clues or not, will do. In fact it means that there is no problem. The man trapped in the room does not have to figure out a password because any thirteen characters are good.