Consider the following premises. forall x_13: P_13(x_13). exists x_13: P_13(x_13) <-> S_4(x_13). Can we infer forall x_13: ~(S_4(x_13) or Q(x_13)) from them?
 From exists x_13: P_13(x_13) <-> S_4(x_13) we can infer exists x_13: P_13(x_13) -> S_4(x_13). From exists x_13: P_13(x_13) -> S_4(x_13), forall x_13: P_13(x_13) we can infer exists x_13: S_4(x_13). Finally, from exists x_13: S_4(x_13) we can infer exists x_13: S_4(x_13) or Q(x_13), which contradicts forall x_13: ~(S_4(x_13) or Q(x_13)). Therefore, the answer is no.