Consider the following premises. exists y: U_4(y) -> T_3(y). forall y: T_3(y) -> U_4(y). forall y: T_3(y). Can we infer forall y: ~U_4(y) from them? If possible, name the inference rules being used at each step.
 From exists y: U_4(y) -> T_3(y), forall y: T_3(y) -> U_4(y) we can infer exists y: U_4(y) <-> T_3(y) via existential biconditional introduction. From exists y: U_4(y) <-> T_3(y) we can infer exists y: T_3(y) -> U_4(y) via existential biconditional elimination. Finally, from exists y: T_3(y) -> U_4(y), forall y: T_3(y) we can infer exists y: U_4(y) via existential modus ponens, which contradicts forall y: ~U_4(y). Therefore, the answer is no.