Consider the following premises. exists z_4: ~S_1(z_4). forall z_4: R(z_4) -> S_1(z_4). forall z_4: W_1(z_4) <-> R(z_4). Can we infer exists z_4: ~W_1(z_4) from them?
 From forall z_4: R(z_4) -> S_1(z_4), exists z_4: ~S_1(z_4) we can infer exists z_4: ~R(z_4). Finally, from forall z_4: W_1(z_4) <-> R(z_4), exists z_4: ~R(z_4) we can infer exists z_4: ~W_1(z_4). Therefore, the answer is yes.