Consider the following premises. forall z_4: Q(z_4) <-> Q_4(z_4). exists z_4: Q_1(z_4) -> Q(z_4). forall z_4: T(z_4) or Q_1(z_4). forall z_4: T(z_4) -> Q(z_4). Can we infer forall z_4: ~Q_4(z_4) from them? If possible, name the inference rules being used at each step.
 From forall z_4: T(z_4) -> Q(z_4), exists z_4: Q_1(z_4) -> Q(z_4), forall z_4: T(z_4) or Q_1(z_4) we can infer exists z_4: Q(z_4) via existential disjunction elimination. From forall z_4: Q(z_4) <-> Q_4(z_4) we can infer forall z_4: Q(z_4) -> Q_4(z_4) via universal biconditional elimination. Finally, from forall z_4: Q(z_4) -> Q_4(z_4), exists z_4: Q(z_4) we can infer exists z_4: Q_4(z_4) via existential modus ponens, which contradicts forall z_4: ~Q_4(z_4). Therefore, the answer is no.