They claim that they perceive a mode of being superior to your existence on this earth. The mystics of spirit call it “another dimension,” which consists of denying dimensions. The mystics of muscle call it “the future,” which consists of denying the present. To exist is to possess identity. What identity are they able to give to their superior realm? They keep telling you what it isnot, but never tell you what it is. All their identifications consist of negating: God is that which no human mind can know, they say—and proceed to demand that you consider it knowledge—God is non-man, heaven is non-earth, soul is non-body, virtue is non-profit, A is non-A, perception is non-sensory, knowledge is non-reason. Their definitions are not acts of defining, but of wiping out. Galt's Speech - Ayn Rand

What is meant by “the supernatural”? Supposedly, a realm that transcends nature. What is nature? Nature is existence—the sum of that which is. It is usually called “nature” when we think of it as a system of interconnected, interacting entities governed by law. So “nature” really means the universe of entities acting and interacting in accordance with their identities. What, then, is “super-nature”? Something beyond the universe, beyond entities, beyond identity. It would have to be: a form of existence beyond existence—a kind of entity beyond anything man knows about entities—a something which contradicts everything man knows about the identity of that which is. In short, a contradiction of every metaphysical essential. Leonard Peikoff

There is no way to prove a “super-existence” by inference from existence; supernaturalism can be accepted only on faith. Leonard Peikoff,