Consider the following premises. s_2 -> U_2(g_2). P(g_2) -> s_2. forall x_3: U_2(x_3) -> P(x_3). forall x_3: P(x_3) -> U_2(x_3). Can we infer forall x_3: U_2(x_3) -> P(x_3) from them?
That is one of the premises. Therefore, the answer is yes.