Consider the following premises. forall x_6: Q_6(x_6) -> R_6(x_6). forall x_6: S_4(x_6) -> Q_6(x_6). exists x_6: P_5(x_6) <-> R_6(x_6). Can we infer forall x_6: ~(S_4(x_6) -> P_5(x_6)) from them?
That contradicts the premises. Therefore the answer is no.