Consider the following premises. forall x_13: P_1(x_13) <-> S_13(x_13). q_1. ~P_1(i). Can we infer S_13(i) from them?
 From forall x_13: P_1(x_13) <-> S_13(x_13) we can infer P_1(i) <-> S_13(i). Finally, from P_1(i) <-> S_13(i), ~P_1(i) we can infer ~S_13(i), which contradicts S_13(i). Therefore, the answer is no.