Consider the following premises. forall x_7: U_3(x_7) or U_4(x_7). forall x_7: T(x_7) or ~U_3(x_7). exists x_7: U_4(x_7) <-> T(x_7). Can we infer exists x_7: T(x_7) from them? If possible, name the inference rules being used at each step.
 From forall x_7: T(x_7) or ~U_3(x_7) we can infer forall x_7: U_3(x_7) -> T(x_7) via universal rewriting. From exists x_7: U_4(x_7) <-> T(x_7) we can infer exists x_7: U_4(x_7) -> T(x_7) via existential biconditional elimination. Finally, from forall x_7: U_3(x_7) -> T(x_7), exists x_7: U_4(x_7) -> T(x_7), forall x_7: U_3(x_7) or U_4(x_7) we can infer exists x_7: T(x_7) via existential disjunction elimination. Therefore, the answer is yes.