Consider the following premises. forall x: ~Q(x). exists x: T(x) <-> Q(x). forall x: U_1(x) <-> T(x). Can we infer forall x: U_1(x) from them? If possible, name the inference rules being used at each step.
 From exists x: T(x) <-> Q(x), forall x: ~Q(x) we can infer exists x: ~T(x) via existential biconditional elimination. Finally, from forall x: U_1(x) <-> T(x), exists x: ~T(x) we can infer exists x: ~U_1(x) via existential biconditional elimination, which contradicts forall x: U_1(x). Therefore, the answer is no.