Consider the following premises. exists x_6: ~Q_6(x_6). forall x_6: U_4(x_6) -> Q_6(x_6). forall x_6: U_4(x_6) or ~T(x_6). Can we infer exists x_6: ~T(x_6) from them? If possible, name the inference rules being used at each step.
 From forall x_6: U_4(x_6) -> Q_6(x_6), exists x_6: ~Q_6(x_6) we can infer exists x_6: ~U_4(x_6) via existential modus tollens. From forall x_6: U_4(x_6) or ~T(x_6) we can infer forall x_6: T(x_6) -> U_4(x_6) via universal rewriting. Finally, from forall x_6: T(x_6) -> U_4(x_6), exists x_6: ~U_4(x_6) we can infer exists x_6: ~T(x_6) via existential modus tollens. Therefore, the answer is yes.