I would say all art is derivative, basically a sum of our influences, whether human or machine. And it's complicated, but derivative works can be copyrighted, at least in part, without inherently violating any laws related to the original work, depending on how much has changed/how obvious it is, and depending on each individual judge's subjective opinion.

https://www.legalzoom.com/articles/what-are-derivative-works...

If all art is derivative, then the argument also applies to the LLM output.

If the input has copyright, so does the output.

If the input does not, then neither does the output.

A prompt is not enough to somehow claim artistry, because the weights have a greater influence. You cannot separate the sum of the parts.

The sensible options were that either LLM outputs are derivative of all their training data, or they're new works produced by the machine, which is not a human, and therefore not copyrightable.

Courts have decided they're new works which are not copyrightable.