Consider the following premises. exists x_5: Q_5(x_5). forall x_5: W(x_5) -> U(x_5). forall x_5: W(x_5) -> ~Q_5(x_5). forall x_5: U(x_5) -> W(x_5). Can we infer exists x_5: ~U(x_5) from them?
 From forall x_5: W(x_5) -> ~Q_5(x_5), exists x_5: Q_5(x_5) we can infer exists x_5: ~W(x_5). From forall x_5: U(x_5) -> W(x_5), forall x_5: W(x_5) -> U(x_5) we can infer forall x_5: U(x_5) <-> W(x_5). Finally, from forall x_5: U(x_5) <-> W(x_5), exists x_5: ~W(x_5) we can infer exists x_5: ~U(x_5). Therefore, the answer is yes.