Consider the following premises. exists z: W_1(z) -> ~T(z). forall z: P_3(z) <-> Q_4(z). forall z: P_3(z) -> T(z). forall z: W(z). forall z: W(z) -> Q_4(z). Can we infer forall z: W_1(z) from them? If possible, name the inference rules being used at each step.
 From forall z: P_3(z) <-> Q_4(z) we can infer forall z: Q_4(z) -> P_3(z) via universal biconditional elimination. From forall z: W(z) -> Q_4(z), forall z: Q_4(z) -> P_3(z) we can infer forall z: W(z) -> P_3(z) via universal transitivity. From forall z: W(z) -> P_3(z), forall z: P_3(z) -> T(z) we can infer forall z: W(z) -> T(z) via universal transitivity. From forall z: W(z) -> T(z), forall z: W(z) we can infer forall z: T(z) via universal modus ponens. Finally, from exists z: W_1(z) -> ~T(z), forall z: T(z) we can infer exists z: ~W_1(z) via existential modus tollens, which contradicts forall z: W_1(z). Therefore, the answer is no.