Consider the following premises. forall x_4: R(x_4) <-> U(x_4). forall x_4: ~T(x_4). forall x_4: T(x_4) <-> S(x_4). forall x_4: S(x_4) <-> U(x_4). Can we infer exists x_4: R(x_4) from them? If possible, name the inference rules being used at each step.
 From forall x_4: T(x_4) <-> S(x_4), forall x_4: ~T(x_4) we can infer forall x_4: ~S(x_4) via universal biconditional elimination. From forall x_4: S(x_4) <-> U(x_4), forall x_4: ~S(x_4) we can infer forall x_4: ~U(x_4) via universal biconditional elimination. Finally, from forall x_4: R(x_4) <-> U(x_4), forall x_4: ~U(x_4) we can infer forall x_4: ~R(x_4) via universal biconditional elimination, which contradicts exists x_4: R(x_4). Therefore, the answer is no.