Non-trivially true statements in computability with the predicate K of the current mathematical knowledge, which do not express the current mathematical knowledge and may be falsified

The theorem of Royer and Case states that there exists a limit-computable function β_1:N→N which eventually dominates every computable function δ_1:N→N. We present an alternative proof of this theorem. K denotes both the knowledge predicate satisfied by every currently known theorem and the finite set of all currently known theorems. The set K is time-dependent and publicly available. Any theorem of any mathematician from past or present forever belongs to K. The statement ¬K(P≠NP)∧¬K(P=NP) does not justify the title of the article. We prove: (1) there exists a limit-computable function f:N→N of unknown computability which eventually dominates every function δ:N→N with a single-fold Diophantine representation; (2) for every computable functions g:N→N, there exists a limit-computable function f:N→N of unknown computability such that f eventually dominates every function δ:N→N with a single-fold Diophantine representation and f(n)>g(n) for every n∈N. Both (1) and (2) justify the title of the article.