Consider the following premises. exists x_8: P_8(x_8) or ~W(x_8). forall x_8: P_8(x_8) <-> W(x_8). Can we infer exists x_8: W(x_8) <-> P_8(x_8) from them?
 From forall x_8: P_8(x_8) <-> W(x_8) we can infer forall x_8: P_8(x_8) -> W(x_8). From exists x_8: P_8(x_8) or ~W(x_8) we can infer exists x_8: W(x_8) -> P_8(x_8). Finally, from exists x_8: W(x_8) -> P_8(x_8), forall x_8: P_8(x_8) -> W(x_8) we can infer exists x_8: W(x_8) <-> P_8(x_8). Therefore, the answer is yes.