Consider the following premises. forall x_2: U_1(x_2) -> Q_1(x_2). exists x_2: Q_2(x_2) -> Q(x_2). forall x_2: Q_1(x_2) -> Q_2(x_2). Can we infer forall x_2: ~(U_1(x_2) -> Q(x_2)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.