Consider the following premises. p_11 <-> q. forall x_7: P(x_7) <-> S_7(x_7). p_11 <-> S_7(a_7). ~q. Can we infer P(a_7) from them?
 From p_11 <-> q, ~q we can infer ~p_11. From forall x_7: P(x_7) <-> S_7(x_7) we can infer P(a_7) <-> S_7(a_7). From p_11 <-> S_7(a_7), ~p_11 we can infer ~S_7(a_7). Finally, from P(a_7) <-> S_7(a_7), ~S_7(a_7) we can infer ~P(a_7), which contradicts P(a_7). Therefore, the answer is no.