Consider the following premises. forall z: Q_2(z) <-> R(z). exists z: W_3(z) <-> R(z). forall z: ~Q_2(z). Can we infer forall z: W_3(z) from them? If possible, name the inference rules being used at each step.
 From forall z: Q_2(z) <-> R(z), forall z: ~Q_2(z) we can infer forall z: ~R(z) via universal biconditional elimination. Finally, from exists z: W_3(z) <-> R(z), forall z: ~R(z) we can infer exists z: ~W_3(z) via existential biconditional elimination, which contradicts forall z: W_3(z). Therefore, the answer is no.