Does washing a dog's bowl in the dishwasher transfer impurity to the rest of the dishes and cups, and does washing it once remove the impurity?

We have previously favored the impurity of the entire dog. Therefore, its bowl must be purified with seven washings, one of them with earth or soap. It is necessary to isolate the dog's bowl and purify it with the seven washings, including earth or soap; a single washing is not sufficient. The answer to the question of transferring the impurity of a bowl in a dishwasher depends on how the dishes are placed and how water is poured over them.