Consider the following premises. forall x_12: P_12(x_12) and Q_12(x_12). forall x_12: P_7(x_12) -> ~P_12(x_12). s -> P_7(f). Can we infer forall x_12: P_7(x_12) -> ~P_12(x_12) from them?
That is one of the premises. Therefore, the answer is yes.