Consider the following premises. forall y_4: Q(y_4) -> S_2(y_4). exists y_4: ~S(y_4) or P_1(y_4). forall y_4: S_2(y_4) -> Q(y_4). forall y_4: ~Q(y_4). forall y_4: S(y_4) or S_2(y_4). Can we infer exists y_4: ~S(y_4) or P_1(y_4) from them?
That is one of the premises. Therefore, the answer is yes.