Nonexistence conjecture for four-value sharing by infinite-order meromorphic functions

Let $f$ and $g$ be two distinct non-constant meromorphic functions of infinite order, and let $a_1,a_2,a_3,a_4$ be four distinct values in the extended complex plane. Nonexistence conjecture. There do not exist such $f$ and $g$ that share $a_1,a_2,a_3$ DM and share $a_4$ CM. The finite-order analogue is established in the paper, while this infinite-order case remains open.