Consider the following premises. forall x_8: P_8(x_8) -> Q_8(x_8). forall x_8: P_8(x_8). forall x_8: P_4(x_8). forall x_8: P_4(x_8) -> Q_4(x_8). Can we infer ~Q_8(a_2) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.