Consider the following premises. ~P_12(a_11). u_1. forall x_12: Q_12(x_12) -> P_12(x_12). forall x_12: P_12(x_12) -> Q_12(x_12). Can we infer Q_12(a_11) 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). Finally, from P_12(a_11) <-> Q_12(a_11), ~P_12(a_11) we can infer ~Q_12(a_11), which contradicts Q_12(a_11). Therefore, the answer is no.