Consider the following premises. forall z: R(z) -> W(z). exists z: ~R_3(z). forall z: W(z) -> R(z). forall z: W(z) <-> R_3(z). Can we infer forall z: R(z) from them? If possible, name the inference rules being used at each step.
 From forall z: W(z) -> R(z), forall z: R(z) -> W(z) we can infer forall z: W(z) <-> R(z) via universal biconditional introduction. From forall z: W(z) <-> R_3(z), exists z: ~R_3(z) we can infer exists z: ~W(z) via existential biconditional elimination. Finally, from forall z: W(z) <-> R(z), exists z: ~W(z) we can infer exists z: ~R(z) via existential biconditional elimination, which contradicts forall z: R(z). Therefore, the answer is no.