Consider the following premises. ~P(a_17). forall x_17: P(x_17) -> S_17(x_17). w <-> P(a_17). S_17(a_17) -> w. Can we infer ~w from them?
 From forall x_17: P(x_17) -> S_17(x_17) we can infer P(a_17) -> S_17(a_17). From w <-> P(a_17) we can infer w -> P(a_17). From P(a_17) -> S_17(a_17), S_17(a_17) -> w we can infer P(a_17) -> w. From w -> P(a_17), P(a_17) -> w we can infer w <-> P(a_17). Finally, from w <-> P(a_17), ~P(a_17) we can infer ~w. Therefore, the answer is yes.