Consider the following premises. forall x_8: U(x_8) <-> Q_8(x_8). forall x_8: Q(x_8). forall x_8: Q_8(x_8). Can we infer exists x_8: ~(U(x_8) and Q(x_8)) from them? If possible, name the inference rules being used at each step.
 From forall x_8: U(x_8) <-> Q_8(x_8) we can infer forall x_8: Q_8(x_8) -> U(x_8) via universal biconditional elimination. From forall x_8: Q_8(x_8) -> U(x_8), forall x_8: Q_8(x_8) we can infer forall x_8: U(x_8) via universal modus ponens. Finally, from forall x_8: U(x_8), forall x_8: Q(x_8) we can infer forall x_8: U(x_8) and Q(x_8) via universal conjunction, which contradicts exists x_8: ~(U(x_8) and Q(x_8)). Therefore, the answer is no.