Consider the following premises. forall x_12: Q_12(x_12). forall x_12: P_12(x_12). P_12(a_11) -> p_1. Can we infer ~p_1 from them?
 From forall x_12: P_12(x_12), forall x_12: Q_12(x_12) we can infer forall x_12: P_12(x_12) and Q_12(x_12). From forall x_12: P_12(x_12) and Q_12(x_12) we can infer P_12(a_11) and Q_12(a_11). From P_12(a_11) and Q_12(a_11) we can infer P_12(a_11). Finally, from P_12(a_11) -> p_1, P_12(a_11) we can infer p_1, which contradicts ~p_1. Therefore, the answer is no.