Consider the following premises. forall x_3: Q_3(x_3) -> T(x_3). forall x_3: U(x_3) -> T(x_3). forall x_3: U(x_3). exists x_3: R(x_3) -> Q_3(x_3). Can we infer forall x_3: ~T(x_3) from them? If possible, name the inference rules being used at each step.
 From exists x_3: R(x_3) -> Q_3(x_3), forall x_3: Q_3(x_3) -> T(x_3) we can infer exists x_3: R(x_3) -> T(x_3) via existential transitivity. From forall x_3: U(x_3) we can infer forall x_3: U(x_3) or R(x_3) via universal addition. Finally, from forall x_3: U(x_3) -> T(x_3), exists x_3: R(x_3) -> T(x_3), forall x_3: U(x_3) or R(x_3) we can infer exists x_3: T(x_3) via existential disjunction elimination, which contradicts forall x_3: ~T(x_3). Therefore, the answer is no.