Consider the following premises. ~Q_12(a_11). forall x_12: P_12(x_12) -> Q_12(x_12). forall x_12: Q_12(x_12) -> P_12(x_12). Can we infer ~P_12(a_11) or s from them?
 From forall x_12: P_12(x_12) -> Q_12(x_12), forall x_12: Q_12(x_12) -> P_12(x_12) we can infer forall x_12: P_12(x_12) <-> Q_12(x_12). From forall x_12: P_12(x_12) <-> Q_12(x_12) we can infer P_12(a_11) <-> Q_12(a_11). From P_12(a_11) <-> Q_12(a_11), ~Q_12(a_11) we can infer ~P_12(a_11). Finally, from ~P_12(a_11) we can infer ~P_12(a_11) or s. Therefore, the answer is yes.