Consider the following premises. forall z: P(z) -> ~R(z). exists z: W(z) -> Q_1(z). forall z: R(z). forall z: Q_1(z) -> W(z). forall z: P(z) <-> W(z). Can we infer exists z: ~Q_1(z) from them? If possible, name the inference rules being used at each step.
 From exists z: W(z) -> Q_1(z), forall z: Q_1(z) -> W(z) we can infer exists z: W(z) <-> Q_1(z) via existential biconditional introduction. From forall z: P(z) -> ~R(z), forall z: R(z) we can infer forall z: ~P(z) via universal modus tollens. From forall z: P(z) <-> W(z), forall z: ~P(z) we can infer forall z: ~W(z) via universal biconditional elimination. Finally, from exists z: W(z) <-> Q_1(z), forall z: ~W(z) we can infer exists z: ~Q_1(z) via existential biconditional elimination. Therefore, the answer is yes.