Consider the following premises. forall x_8: P_8(x_8). forall z: P_8(z) <-> S(z). Can we infer ~S(g) from them?
 From forall x_8: P_8(x_8) we can infer P_8(g). From forall z: P_8(z) <-> S(z) we can infer P_8(g) <-> S(g). From P_8(g) <-> S(g) we can infer P_8(g) -> S(g). Finally, from P_8(g) -> S(g), P_8(g) we can infer S(g), which contradicts ~S(g). Therefore, the answer is no.