Cherlin's almost simple binary primitive group conjecture

Let $G$ be an almost simple primitive permutation group acting on a set $\Omega$, and suppose that its permutation action is binary. Cherlin's almost simple conjecture. Then

$$G=\operatorname{Sym}(\Omega).$$

This statement is presented as sufficient for proving Cherlin's classification conjecture and is reduced from the original conjecture using work of Cherlin and Wiscons. The supplied context does not establish whether this almost simple statement is proved in full, so its status is recorded as open.