Consider the following premises. forall x_1: W(x_1) -> U_1(x_1). forall x_1: U(x_1) -> U_1(x_1). forall x_1: U_1(x_1) -> U(x_1). exists x_1: ~U(x_1). forall x_1: U_1(x_1) -> W(x_1). Can we infer exists x_1: ~W(x_1) from them?
 From forall x_1: U(x_1) -> U_1(x_1), forall x_1: U_1(x_1) -> U(x_1) we can infer forall x_1: U(x_1) <-> U_1(x_1). From forall x_1: W(x_1) -> U_1(x_1), forall x_1: U_1(x_1) -> W(x_1) we can infer forall x_1: W(x_1) <-> U_1(x_1). From forall x_1: U(x_1) <-> U_1(x_1), exists x_1: ~U(x_1) we can infer exists x_1: ~U_1(x_1). Finally, from forall x_1: W(x_1) <-> U_1(x_1), exists x_1: ~U_1(x_1) we can infer exists x_1: ~W(x_1). Therefore, the answer is yes.