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