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