Consider the following premises. forall x_1: U(x_1) -> W_3(x_1). forall x_1: ~U(x_1). forall x_1: U(x_1) <-> W_3(x_1). Can we infer forall x_1: ~W_3(x_1) from them?
 From forall x_1: U(x_1) <-> W_3(x_1) we can infer forall x_1: W_3(x_1) -> U(x_1). From forall x_1: U(x_1) -> W_3(x_1), forall x_1: W_3(x_1) -> U(x_1) we can infer forall x_1: U(x_1) <-> W_3(x_1). Finally, from forall x_1: U(x_1) <-> W_3(x_1), forall x_1: ~U(x_1) we can infer forall x_1: ~W_3(x_1). Therefore, the answer is yes.