Hayman's conjecture on generalized Picard exceptional values of $f^n f'$

Let $f$ be a transcendental meromorphic function and let $n$ be a positive integer. A finite constant $a$ is a generalized Picard exceptional value of a meromorphic function $g$ if $g-a$ has finitely many zeros.

Hayman's conjecture. The differential polynomial $f^n f'$ cannot have any non-zero generalized Picard exceptional values.

This conjecture concerns the value distribution of differential polynomials and extends Hayman's earlier theorem for transcendental entire functions with $n\geq 2$. The source presents it as a well-known conjecture; its resolution is not established in the supplied text.