Science is inherently atheistic

[Angrboda]

Jor,
It wasn't a pointless swipe. It's an example of an apophatic definition. Atheism (especially hard atheism) is used to describe a large group of people (here especially) that lack belief in God(s).
Supernatural defines beliefs beyond (or without being) what is natural. I could have just as easily said non-naturalistic because in this case they mean the same exact things. From my point of view I prefer super as opposed to non, because in revealing previously held supernatural definitions we add more modern collective knowledge that it is above/outside rather than doesn't exist.

If you truly believe that you can not be descriptive with a apophatic definition please describe what your dog will dig in the backyard to bury a bone in without using the word hole or it's synonym.

We've already stated that with relation to the OP, science isn't exclusively atheistic and rephrased it to science has no religious views and is just another tool like math and would be best described as secular. That it can be used to debunk supernatural claims and that it is only as good as it can test. If you have something to add or comment on that point have at it.

Nobody is claiming that holes exist. It is a description of an absence of something, whose absence can be described by other means. The supernatural is not simply the absence of something, it is something that is claimed to exist. And that requires a positive definition because it is a claim of something existing. If you want to say a hole doesn't exist, I don't have a problem with that. Holes don't exist. If you are saying the supernatural similarly doesn't exist, I don't have a problem with that either, but you do. I don't have the first clue what it means for something to be other than nature, just as I have no idea what color something is if they tell me it is not black. We know what items do not belong to the things that are not belief in a god because the class is well defined. We don't know what things belong to the class of not natural because we don't know what things belong to the class of natural. That is essentially the problem you have. Not nature doesn't point to anything specific. It's just a catchall for anything we can't identify as natural. Which makes all arguments in favor of it essentially arguments from ignorance. So even if there is such a thing as the supernatural, believing that there is is irrational. Are you trying to tell me your beliefs are irrational?

Let me ask you a related question. Are there supernatural causes that are not agents or other intentional subjects? Can dark matter be supernatural?

Addendum, theists often mistake atheism as containing items it doesn't contain. So from observation, theists commonly mistake class boundaries as definite when they aren't, and indefinite when they are. As a practical matter, we can identify beliefs that are not a belief in God, but we can't know what they believe based upon this apophatic definition, even if problematic. It would seem your example proves my point rather than the reverse. We don't know an atheist's positive beliefs that are not a lack of belief in gods, so that class is equally indeterminate if interpreted that way.