Consider the following premises. For all x_8, if x_8 were sad, then x_8 is fast. For all x_8, x_8 is fast if and only if x_8 is sad. For all x_8, if x_8 were fast, then x_8 is sad. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_8 for which if is not true that x_8 is fast if and only if x_8 is sad.
 From the fact that for all x_8, x_8 is fast if and only if x_8 is sad we can infer that for all x_8, if x_8 were fast, then x_8 is sad via universal biconditional elimination. From the fact that for all x_8, if x_8 were fast, then x_8 is sad, and that for all x_8, if x_8 were sad, then x_8 is fast we can infer that for all x_8, x_8 is fast if and only if x_8 is sad via universal biconditional introduction. From the fact that for all x_8, x_8 is fast if and only if x_8 is sad we can infer that for all x_8, if x_8 were sad, then x_8 is fast via universal biconditional elimination. Finally, from the fact that for all x_8, if x_8 were fast, then x_8 is sad, and that for all x_8, if x_8 were sad, then x_8 is fast we can infer that for all x_8, x_8 is fast if and only if x_8 is sad via universal biconditional introduction, which contradicts that There is at least one x_8 for which if is not true that x_8 is fast if and only if x_8 is sad. Therefore, the answer is no.