User blog comment:DontDrinkH20/Some Explanations of Certain Large Cardinals/@comment-35870936-20181017021650/@comment-25601061-20181017235258

Oh. I should've read more in-depth the links that you gave.

Indeed, it is necessary to show in some way that the substitution of the large cardinals that were originally used in the OCF for smaller ones does not affect its behaviour, but it does not necessarily mean that it is impossible - if ZFC cannot prove it, mostly because of the size of the large cardinals that were originally being used, then we just need to use another set theory, like ZFC + [large cardinal axioms].