Consider the following premises. forall z: Q(z) <-> S_4(z). exists z: W_3(z) -> S_4(z). forall z: ~Q(z). forall z: S(z) <-> W_3(z). Can we infer exists z: ~S(z) from them?
 From forall z: Q(z) <-> S_4(z), forall z: ~Q(z) we can infer forall z: ~S_4(z). From exists z: W_3(z) -> S_4(z), forall z: ~S_4(z) we can infer exists z: ~W_3(z). Finally, from forall z: S(z) <-> W_3(z), exists z: ~W_3(z) we can infer exists z: ~S(z). Therefore, the answer is yes.