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