Consider the following premises. exists x_11: P(x_11) -> S(x_11). forall x_11: Q_1(x_11) -> S(x_11). forall x_11: P(x_11) -> Q_1(x_11). forall x_11: S(x_11) -> P(x_11). Can we infer exists x_11: S(x_11) <-> P(x_11) from them?
Yes.