Consider the following premises. exists x_13: P_13(x_13) <-> S_4(x_13). forall x_13: P_13(x_13). Can we infer exists x_13: S_4(x_13) or Q(x_13) from them? If possible, name the inference rules being used at each step.
 From exists x_13: P_13(x_13) <-> S_4(x_13) we can infer exists x_13: P_13(x_13) -> S_4(x_13) via existential biconditional elimination. From exists x_13: P_13(x_13) -> S_4(x_13), forall x_13: P_13(x_13) we can infer exists x_13: S_4(x_13) via existential modus ponens. Finally, from exists x_13: S_4(x_13) we can infer exists x_13: S_4(x_13) or Q(x_13) via existential addition. Therefore, the answer is yes.