Consider the following premises. q_4 and r_2. forall z: P_2(z) -> R_4(z). forall z: R_4(z) -> P_2(z). ~P_2(a_11). Can we infer ~R_4(a_11) and q_4 from them?
 From q_4 and r_2 we can infer q_4. From forall z: R_4(z) -> P_2(z), forall z: P_2(z) -> R_4(z) we can infer forall z: R_4(z) <-> P_2(z). From forall z: R_4(z) <-> P_2(z) we can infer R_4(a_11) <-> P_2(a_11). From R_4(a_11) <-> P_2(a_11), ~P_2(a_11) we can infer ~R_4(a_11). Finally, from ~R_4(a_11), q_4 we can infer ~R_4(a_11) and q_4. Therefore, the answer is yes.