Consider the following premises. forall x_3: P_3(x_3) -> S_3(x_3). forall x_3: ~P_3(x_3). forall x_3: P_3(x_3) or ~S_3(x_3). Can we infer exists x_3: S_3(x_3) from them?
 From forall x_3: P_3(x_3) or ~S_3(x_3) we can infer forall x_3: S_3(x_3) -> P_3(x_3). From forall x_3: S_3(x_3) -> P_3(x_3), forall x_3: P_3(x_3) -> S_3(x_3) we can infer forall x_3: S_3(x_3) <-> P_3(x_3). Finally, from forall x_3: S_3(x_3) <-> P_3(x_3), forall x_3: ~P_3(x_3) we can infer forall x_3: ~S_3(x_3), which contradicts exists x_3: S_3(x_3). Therefore, the answer is no.