Consider the following premises. forall x_12: R_12(x_12) <-> S_12(x_12). q_3 <-> r_3. R_12(a_12) <-> q_3. ~S_12(a_12). Can we infer ~r_3 from them?
 From forall x_12: R_12(x_12) <-> S_12(x_12) we can infer R_12(a_12) <-> S_12(a_12). From R_12(a_12) <-> S_12(a_12), ~S_12(a_12) we can infer ~R_12(a_12). From R_12(a_12) <-> q_3, ~R_12(a_12) we can infer ~q_3. Finally, from q_3 <-> r_3, ~q_3 we can infer ~r_3. Therefore, the answer is yes.