Consider the following premises. R_13(a_12) -> P_13(a_12). ~u. forall x_13: P_13(x_13) -> Q_13(x_13). forall x_13: Q_13(x_13) -> R_13(x_13). u <-> P_13(a_12). Can we infer ~R_13(a_12) from them?
 From forall x_13: P_13(x_13) -> Q_13(x_13), forall x_13: Q_13(x_13) -> R_13(x_13) we can infer forall x_13: P_13(x_13) -> R_13(x_13). From forall x_13: P_13(x_13) -> R_13(x_13) we can infer P_13(a_12) -> R_13(a_12). From R_13(a_12) -> P_13(a_12), P_13(a_12) -> R_13(a_12) we can infer R_13(a_12) <-> P_13(a_12). From u <-> P_13(a_12), ~u we can infer ~P_13(a_12). Finally, from R_13(a_12) <-> P_13(a_12), ~P_13(a_12) we can infer ~R_13(a_12). Therefore, the answer is yes.