Consider the following premises. Q_10(a_5) <-> w. forall x_10: ~P_10(x_10). forall x_10: P_10(x_10) -> Q_10(x_10). forall x_10: Q_10(x_10) -> P_10(x_10). Can we infer ~w from them?
 From forall x_10: P_10(x_10) -> Q_10(x_10), forall x_10: Q_10(x_10) -> P_10(x_10) we can infer forall x_10: P_10(x_10) <-> Q_10(x_10). From forall x_10: P_10(x_10) <-> Q_10(x_10), forall x_10: ~P_10(x_10) we can infer forall x_10: ~Q_10(x_10). From forall x_10: ~Q_10(x_10) we can infer ~Q_10(a_5). Finally, from Q_10(a_5) <-> w, ~Q_10(a_5) we can infer ~w. Therefore, the answer is yes.