Consider the following premises. forall y: Q(y) -> Q_1(y). forall y: Q(y) -> T(y). exists y: T(y) -> Q(y). forall y: Q_1(y) -> Q(y). forall y: ~T(y). Can we infer forall y: Q_1(y) from them? If possible, name the inference rules being used at each step.
 From forall y: Q_1(y) -> Q(y), forall y: Q(y) -> Q_1(y) we can infer forall y: Q_1(y) <-> Q(y) via universal biconditional introduction. From exists y: T(y) -> Q(y), forall y: Q(y) -> T(y) we can infer exists y: T(y) <-> Q(y) via existential biconditional introduction. From exists y: T(y) <-> Q(y), forall y: ~T(y) we can infer exists y: ~Q(y) via existential biconditional elimination. Finally, from forall y: Q_1(y) <-> Q(y), exists y: ~Q(y) we can infer exists y: ~Q_1(y) via existential biconditional elimination, which contradicts forall y: Q_1(y). Therefore, the answer is no.