Which of these firearms does Utah law specifically prohibit from owning?

Utah gun laws do not specifically prohibit any particular types of firearms. As long as residents follow federal firearms regulations, there are no state-level restrictions on the type of firearms that can be owned in Utah. This includes firearms like sawed-off shotguns, fully automatic machine guns with ATF approval, or handguns with barrel lengths less than 4 inches. Thus, the correct answer is that there are no specific types of firearms prohibited by Utah law.