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