Consider the following premises. forall y_4: S_3(y_4). forall y_4: ~S_3(y_4). exists y_4: Q_3(y_4) -> ~Q(y_4). Can we infer exists y_4: ~Q_3(y_4) from them?
 From forall y_4: S_3(y_4) we can infer forall y_4: S_3(y_4) or Q(y_4). From forall y_4: S_3(y_4) or Q(y_4), forall y_4: ~S_3(y_4) we can infer forall y_4: Q(y_4). Finally, from exists y_4: Q_3(y_4) -> ~Q(y_4), forall y_4: Q(y_4) we can infer exists y_4: ~Q_3(y_4). Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.