Consider the following premises. exists z: S_4(z) -> Q_2(z). forall z: S(z) <-> Q_2(z). forall z: ~S(z). forall z: Q_2(z) -> S_4(z). Can we infer exists z: ~S_4(z) from them?
 From exists z: S_4(z) -> Q_2(z), forall z: Q_2(z) -> S_4(z) we can infer exists z: S_4(z) <-> Q_2(z). From forall z: S(z) <-> Q_2(z), forall z: ~S(z) we can infer forall z: ~Q_2(z). Finally, from exists z: S_4(z) <-> Q_2(z), forall z: ~Q_2(z) we can infer exists z: ~S_4(z). Therefore, the answer is yes.