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