How is a thick mattress made of sponge and springs, which has been contaminated with urine or vomit, purified without damaging it, and is wiping it with a cloth dampened with water and soap sufficient?

The method for purifying an impure object is by washing it with pure water until the water that separates from it becomes pure and unchanged by the impurity. However, if the impurity has permeated the interior of the impure object, such as grain that has absorbed impurity, or impure dough, or impure meat, or a vessel that has absorbed impurity, or a knife that has been wetted with impure water, then it cannot be purified by washing, because the washing does not eradicate the particles of impurity. If you wish to pray on this carpet, the trace of impurity must be removed from its surface by wiping it with a cloth moistened with water and soap or similar substances. But if it is dry and whatever comes into contact with it is also dry, then it is permissible to use it for other purposes, such as sitting on it.