Consider the following premises. forall x_10: P_2(x_10). forall x_10: P_10(x_10) <-> Q_10(x_10). forall x_10: P_2(x_10) -> P_10(x_10). forall x_10: ~Q_10(x_10). Can we infer exists x_10: ~R_4(x_10) from them?
The premises are contradictory and we can infer anything from them. Therefore, the answer is yes.