Consider the following premises. ~S_3(i). forall y: S_1(y) -> S_3(y). forall y: S_1(y) <-> S_3(y). Can we infer S_1(i) from them? If possible, name the inference rules being used at each step.
 From forall y: S_1(y) <-> S_3(y) we can infer forall y: S_3(y) -> S_1(y) via universal biconditional elimination. From forall y: S_3(y) -> S_1(y), forall y: S_1(y) -> S_3(y) we can infer forall y: S_3(y) <-> S_1(y) via universal biconditional introduction. From forall y: S_3(y) <-> S_1(y) we can infer S_3(i) <-> S_1(i) via universal instantiation. Finally, from S_3(i) <-> S_1(i), ~S_3(i) we can infer ~S_1(i) via biconditional elimination, which contradicts S_1(i). Therefore, the answer is no.