Consider the following premises. exists y: U_1(y) -> Q_2(y). forall y: T_1(y) or U_1(y). forall y: T_1(y) -> Q_2(y). forall y: Q_2(y) -> U_1(y). Can we infer forall y: ~Q_2(y) from them? If possible, name the inference rules being used at each step.
 From exists y: U_1(y) -> Q_2(y), forall y: Q_2(y) -> U_1(y) we can infer exists y: U_1(y) <-> Q_2(y) via existential biconditional introduction. From exists y: U_1(y) <-> Q_2(y) we can infer exists y: U_1(y) -> Q_2(y) via existential biconditional elimination. Finally, from forall y: T_1(y) -> Q_2(y), exists y: U_1(y) -> Q_2(y), forall y: T_1(y) or U_1(y) we can infer exists y: Q_2(y) via existential disjunction elimination, which contradicts forall y: ~Q_2(y). Therefore, the answer is no.