Consider the following premises. w -> r_3. r_3 -> R_12(a_12). R_12(a_12) -> w. forall x_12: ~R_12(x_12). Can we infer ~r_3 from them?
 From forall x_12: ~R_12(x_12) we can infer ~R_12(a_12). From R_12(a_12) -> w, w -> r_3 we can infer R_12(a_12) -> r_3. From r_3 -> R_12(a_12), R_12(a_12) -> r_3 we can infer r_3 <-> R_12(a_12). Finally, from r_3 <-> R_12(a_12), ~R_12(a_12) we can infer ~r_3. Therefore, the answer is yes.