Consider the following premises. forall x_7: P_4(x_7) or P_7(x_7). forall x_7: P_7(x_7) <-> S_2(x_7). forall x_7: P_4(x_7) -> S_2(x_7). Can we infer forall x_7: P_7(x_7) <-> S_2(x_7) from them?
That is one of the premises. Therefore, the answer is yes.