Consider the following premises. forall x_4: T_2(x_4) -> P_2(x_4). forall x_4: R_3(x_4) -> Q_4(x_4). forall x_4: Q_4(x_4) -> P_2(x_4). exists x_4: ~P_3(x_4) or R_3(x_4). forall x_4: P_3(x_4) or T_2(x_4). Can we infer exists x_4: ~P_3(x_4) or R_3(x_4) from them?
That is one of the premises. Therefore, the answer is yes.