Consider the following premises. forall x: U(x) <-> T(x). forall x: T(x) -> ~R(x). exists x: R(x). Can we infer forall x: U(x) from them? If possible, name the inference rules being used at each step.
 From forall x: T(x) -> ~R(x), exists x: R(x) we can infer exists x: ~T(x) via existential modus tollens. Finally, from forall x: U(x) <-> T(x), exists x: ~T(x) we can infer exists x: ~U(x) via existential biconditional elimination, which contradicts forall x: U(x). Therefore, the answer is no.