Consider the following premises. exists x_7: W(x_7) <-> Q(x_7). forall x_7: P(x_7) -> W(x_7). forall x_7: P_7(x_7) or Q(x_7). forall x_7: ~P_7(x_7) or P(x_7). Can we infer exists x_7: W(x_7) from them? If possible, name the inference rules being used at each step.
 From forall x_7: P_7(x_7) or Q(x_7), forall x_7: ~P_7(x_7) or P(x_7) we can infer forall x_7: Q(x_7) or P(x_7) via universal resolution. From exists x_7: W(x_7) <-> Q(x_7) we can infer exists x_7: Q(x_7) -> W(x_7) via existential biconditional elimination. Finally, from exists x_7: Q(x_7) -> W(x_7), forall x_7: P(x_7) -> W(x_7), forall x_7: Q(x_7) or P(x_7) we can infer exists x_7: W(x_7) via existential disjunction elimination. Therefore, the answer is yes.