Ketchup
Ketchup is already made with enough preservatives to keep the quality and freshness even after you open the bottle, so you don’t need to refrigerate the condiment at all.
Melons
Melons need not be kept in the fridge! If you leave them at room temperature, they will keep their levels of natural antioxidant…well, “level”, as in the same. However, if melons are sliced up, then they should be stored in the fridge but they have to be covered, either with plastic wrap or foil.