Consider the following premises. forall x_3: P_3(x_3) <-> Q_2(x_3). forall x_3: S(x_3) <-> Q_2(x_3). forall x_3: ~P_3(x_3). Can we infer forall x_3: ~S(x_3) from them?
 From forall x_3: P_3(x_3) <-> Q_2(x_3), forall x_3: ~P_3(x_3) we can infer forall x_3: ~Q_2(x_3). Finally, from forall x_3: S(x_3) <-> Q_2(x_3), forall x_3: ~Q_2(x_3) we can infer forall x_3: ~S(x_3). Therefore, the answer is yes.