Consider the following premises. forall z: ~U(z). exists z: Q_1(z) <-> T_2(z). forall z: T_2(z) <-> U(z). Can we infer forall z: Q_1(z) from them? If possible, name the inference rules being used at each step.
 From forall z: T_2(z) <-> U(z), forall z: ~U(z) we can infer forall z: ~T_2(z) via universal biconditional elimination. Finally, from exists z: Q_1(z) <-> T_2(z), forall z: ~T_2(z) we can infer exists z: ~Q_1(z) via existential biconditional elimination, which contradicts forall z: Q_1(z). Therefore, the answer is no.