Consider the following premises. exists z_4: U_3(z_4) <-> S_4(z_4). forall z_4: S_4(z_4). Can we infer exists z_4: U_3(z_4) or T(z_4) from them? If possible, name the inference rules being used at each step.
 From exists z_4: U_3(z_4) <-> S_4(z_4) we can infer exists z_4: S_4(z_4) -> U_3(z_4) via existential biconditional elimination. From exists z_4: S_4(z_4) -> U_3(z_4), forall z_4: S_4(z_4) we can infer exists z_4: U_3(z_4) via existential modus ponens. Finally, from exists z_4: U_3(z_4) we can infer exists z_4: U_3(z_4) or T(z_4) via existential addition. Therefore, the answer is yes.