Consider the following premises. p_1 <-> U(c). w -> p_1. forall x_12: U(x_12) -> ~Q_12(x_12). forall x_12: Q_12(x_12). Can we infer ~w from them?
 From forall x_12: U(x_12) -> ~Q_12(x_12), forall x_12: Q_12(x_12) we can infer forall x_12: ~U(x_12). From forall x_12: ~U(x_12) we can infer ~U(c). From p_1 <-> U(c), ~U(c) we can infer ~p_1. Finally, from w -> p_1, ~p_1 we can infer ~w. Therefore, the answer is yes.