Consider the following premises. forall z_2: T(z_2) -> Q_3(z_2). forall z_2: P(z_2) -> Q_3(z_2). forall z_2: ~R(z_2) or P(z_2). exists z_2: Q_3(z_2) -> P(z_2). forall z_2: R(z_2) or T(z_2). Can we infer forall z_2: ~Q_3(z_2) from them? If possible, name the inference rules being used at each step.
 From exists z_2: Q_3(z_2) -> P(z_2), forall z_2: P(z_2) -> Q_3(z_2) we can infer exists z_2: Q_3(z_2) <-> P(z_2) via existential biconditional introduction. From forall z_2: R(z_2) or T(z_2), forall z_2: ~R(z_2) or P(z_2) we can infer forall z_2: T(z_2) or P(z_2) via universal resolution. From exists z_2: Q_3(z_2) <-> P(z_2) we can infer exists z_2: P(z_2) -> Q_3(z_2) via existential biconditional elimination. Finally, from forall z_2: T(z_2) -> Q_3(z_2), exists z_2: P(z_2) -> Q_3(z_2), forall z_2: T(z_2) or P(z_2) we can infer exists z_2: Q_3(z_2) via existential disjunction elimination, which contradicts forall z_2: ~Q_3(z_2). Therefore, the answer is no.