Consider the following premises. forall x_11: Q_1(x_11) -> ~Q_11(x_11). w -> R(b). forall x_11: Q_11(x_11). forall x_11: R(x_11) <-> Q_1(x_11). Can we infer ~w from them?
 From forall x_11: Q_1(x_11) -> ~Q_11(x_11), forall x_11: Q_11(x_11) we can infer forall x_11: ~Q_1(x_11). From forall x_11: R(x_11) <-> Q_1(x_11), forall x_11: ~Q_1(x_11) we can infer forall x_11: ~R(x_11). From forall x_11: ~R(x_11) we can infer ~R(b). Finally, from w -> R(b), ~R(b) we can infer ~w. Therefore, the answer is yes.