Consider the following premises. forall x_9: P_9(x_9) <-> Q_9(x_9). exists x_9: ~Q_9(x_9). forall x_9: P_9(x_9) -> S_2(x_9). forall x_9: S_2(x_9) -> P_9(x_9). Can we infer exists x_9: ~S_2(x_9) from them?
 From forall x_9: P_9(x_9) <-> Q_9(x_9), exists x_9: ~Q_9(x_9) we can infer exists x_9: ~P_9(x_9). From forall x_9: S_2(x_9) -> P_9(x_9), forall x_9: P_9(x_9) -> S_2(x_9) we can infer forall x_9: S_2(x_9) <-> P_9(x_9). Finally, from forall x_9: S_2(x_9) <-> P_9(x_9), exists x_9: ~P_9(x_9) we can infer exists x_9: ~S_2(x_9). Therefore, the answer is yes.