Consider the following premises. forall x_9: Q_9(x_9) -> Q_5(x_9). forall x_9: Q_5(x_9) -> T(x_9). forall x_9: P_9(x_9). forall x_9: P_9(x_9) -> T(x_9). Can we infer ~S_3(e) from them?
We cannot infer that from the premises. Therefore the answer is no.