Consider the following premises. forall y_3: Q(y_3) -> U(y_3). exists y_3: U(y_3) -> T_3(y_3). forall y_3: T_3(y_3) -> Q(y_3). forall y_3: ~U(y_3). Can we infer exists y_3: ~Q(y_3) from them? If possible, name the inference rules being used at each step.
 From exists y_3: U(y_3) -> T_3(y_3), forall y_3: T_3(y_3) -> Q(y_3) we can infer exists y_3: U(y_3) -> Q(y_3) via existential transitivity. From forall y_3: Q(y_3) -> U(y_3), exists y_3: U(y_3) -> Q(y_3) we can infer exists y_3: Q(y_3) <-> U(y_3) via existential biconditional introduction. Finally, from exists y_3: Q(y_3) <-> U(y_3), forall y_3: ~U(y_3) we can infer exists y_3: ~Q(y_3) via existential biconditional elimination. Therefore, the answer is yes.