Consider the following premises. r_2 <-> R_4(g). forall y: ~R_4(y). Can we infer r_2 from them?
 From forall y: ~R_4(y) we can infer ~R_4(g). Finally, from r_2 <-> R_4(g), ~R_4(g) we can infer ~r_2, which contradicts r_2. Therefore, the answer is no.