Consider the following premises. forall z: W(z) -> W_4(z). forall z: W(z) or Q(z). forall z: W_1(z). forall z: W_4(z) or ~Q(z). Can we infer forall z: W_1(z) and W_4(z) from them? If possible, name the inference rules being used at each step.
 From forall z: W_4(z) or ~Q(z) we can infer forall z: Q(z) -> W_4(z) via universal rewriting. From forall z: W(z) -> W_4(z), forall z: Q(z) -> W_4(z), forall z: W(z) or Q(z) we can infer forall z: W_4(z) via universal disjunction elimination. Finally, from forall z: W_1(z), forall z: W_4(z) we can infer forall z: W_1(z) and W_4(z) via universal conjunction. Therefore, the answer is yes.