Consider the following premises. forall y_1: ~T_3(y_1). forall y_1: T_3(y_1) <-> U_1(y_1). exists y_1: U_1(y_1) -> T_3(y_1). Can we infer exists y_1: ~U_1(y_1) from them?
 From forall y_1: T_3(y_1) <-> U_1(y_1) we can infer forall y_1: T_3(y_1) -> U_1(y_1). From forall y_1: T_3(y_1) -> U_1(y_1), exists y_1: U_1(y_1) -> T_3(y_1) we can infer exists y_1: T_3(y_1) <-> U_1(y_1). Finally, from exists y_1: T_3(y_1) <-> U_1(y_1), forall y_1: ~T_3(y_1) we can infer exists y_1: ~U_1(y_1). Therefore, the answer is yes.