Consider the following premises. exists x_14: W_2(x_14) <-> U(x_14). forall x_14: W_4(x_14). forall x_14: U(x_14). Can we infer exists x_14: W_2(x_14) and W_4(x_14) from them? If possible, name the inference rules being used at each step.
 From exists x_14: W_2(x_14) <-> U(x_14) we can infer exists x_14: U(x_14) -> W_2(x_14) via existential biconditional elimination. From exists x_14: U(x_14) -> W_2(x_14), forall x_14: U(x_14) we can infer exists x_14: W_2(x_14) via existential modus ponens. Finally, from exists x_14: W_2(x_14), forall x_14: W_4(x_14) we can infer exists x_14: W_2(x_14) and W_4(x_14) via existential conjunction. Therefore, the answer is yes.