Consider the following premises. forall x_16: P_16(x_16) or Q_16(x_16). exists x_16: ~P_16(x_16) or R_16(x_16). forall x_16: R_16(x_16) -> W_4(x_16). forall x_16: Q_16(x_16) <-> W_4(x_16). Can we infer exists x_16: W_4(x_16) or R_4(x_16) from them? If possible, name the inference rules being used at each step.
 From forall x_16: P_16(x_16) or Q_16(x_16), exists x_16: ~P_16(x_16) or R_16(x_16) we can infer exists x_16: Q_16(x_16) or R_16(x_16) via existential resolution. From forall x_16: Q_16(x_16) <-> W_4(x_16) we can infer forall x_16: Q_16(x_16) -> W_4(x_16) via universal biconditional elimination. From forall x_16: Q_16(x_16) -> W_4(x_16), forall x_16: R_16(x_16) -> W_4(x_16), exists x_16: Q_16(x_16) or R_16(x_16) we can infer exists x_16: W_4(x_16) via existential disjunction elimination. Finally, from exists x_16: W_4(x_16) we can infer exists x_16: W_4(x_16) or R_4(x_16) via existential addition. Therefore, the answer is yes.