Consider the following premises. forall y_1: U(y_1) -> ~Q(y_1). forall y_1: S(y_1) -> U(y_1). forall y_1: Q(y_1). exists y_1: U(y_1) -> S(y_1). Can we infer exists y_1: ~S(y_1) from them?
 From exists y_1: U(y_1) -> S(y_1), forall y_1: S(y_1) -> U(y_1) we can infer exists y_1: U(y_1) <-> S(y_1). From forall y_1: U(y_1) -> ~Q(y_1), forall y_1: Q(y_1) we can infer forall y_1: ~U(y_1). Finally, from exists y_1: U(y_1) <-> S(y_1), forall y_1: ~U(y_1) we can infer exists y_1: ~S(y_1). Therefore, the answer is yes.