Consider the following premises. forall x_12: S_3(x_12) or ~W_2(x_12). forall x_12: P_12(x_12) -> W_2(x_12). exists x_12: P_12(x_12) or ~S_3(x_12). Can we infer forall x_12: ~(W_2(x_12) <-> S_3(x_12)) from them?
 From exists x_12: P_12(x_12) or ~S_3(x_12) we can infer exists x_12: S_3(x_12) -> P_12(x_12). From exists x_12: S_3(x_12) -> P_12(x_12), forall x_12: P_12(x_12) -> W_2(x_12) we can infer exists x_12: S_3(x_12) -> W_2(x_12). From forall x_12: S_3(x_12) or ~W_2(x_12) we can infer forall x_12: W_2(x_12) -> S_3(x_12). Finally, from forall x_12: W_2(x_12) -> S_3(x_12), exists x_12: S_3(x_12) -> W_2(x_12) we can infer exists x_12: W_2(x_12) <-> S_3(x_12), which contradicts forall x_12: ~(W_2(x_12) <-> S_3(x_12)). Therefore, the answer is no.