Consider the following premises. forall y_4: ~U(y_4). forall y_4: R(y_4) or W_4(y_4). forall y_4: ~R(y_4). exists y_4: U(y_4) or W(y_4). Can we infer exists y_4: W(y_4) and W_4(y_4) from them? If possible, name the inference rules being used at each step.
 From forall y_4: R(y_4) or W_4(y_4), forall y_4: ~R(y_4) we can infer forall y_4: W_4(y_4) via universal disjunctive syllogism. From exists y_4: U(y_4) or W(y_4), forall y_4: ~U(y_4) we can infer exists y_4: W(y_4) via existential disjunctive syllogism. Finally, from exists y_4: W(y_4), forall y_4: W_4(y_4) we can infer exists y_4: W(y_4) and W_4(y_4) via existential conjunction. Therefore, the answer is yes.