Consider the following premises. forall x_15: T(x_15) <-> U(x_15). exists x_15: W(x_15) <-> Q_15(x_15). forall x_15: T(x_15) -> W(x_15). forall x_15: ~Q_15(x_15). Can we infer exists x_15: ~U(x_15) from them? If possible, name the inference rules being used at each step.
 From exists x_15: W(x_15) <-> Q_15(x_15), forall x_15: ~Q_15(x_15) we can infer exists x_15: ~W(x_15) via existential biconditional elimination. From forall x_15: T(x_15) -> W(x_15), exists x_15: ~W(x_15) we can infer exists x_15: ~T(x_15) via existential modus tollens. Finally, from forall x_15: T(x_15) <-> U(x_15), exists x_15: ~T(x_15) we can infer exists x_15: ~U(x_15) via existential biconditional elimination. Therefore, the answer is yes.