Seems like you are moving the goalpost (i.e., don't expect it to derive a theorem given a set of definitions and axioms from a non-widespread field). It should, in fact, derive any formula given a set of axioms and definitions, but we can't be sure whether randomness fooled us (again). If an LLM can indeed derive any theorem given axioms/definitions, even if we make up a field, then at this point it might not matter:

Ignorance is bliss.