A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Riley, Zoey, Aria, Jacob, and Benjamin. As Riley put it, "If Benjamin is a knave then Aria is a knight". Zoey stated, "Riley is a knave if and only if Benjamin is a knight". In a statement by Aria: "Riley is a knave". Jacob stated, "Benjamin is a knight if and only if Zoey is a knight". As Benjamin put it, "Jacob is a knight or Aria is a knave". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> 
user
Assume Riley is a knight.  No contradiction is found in their claim that If Benjamin is a knave then Aria is a knight.
 Assume Benjamin is a knight.  No contradiction is found in their claim that Jacob is a knight or Aria is a knave.
 Assume Jacob is a knight.  No contradiction is found in their claim that Benjamin is a knight if and only if Zoey is a knight.
 Zoey cannot be a knight, because this would contradict the claim of their own that Riley is a knave if and only if Benjamin is a knight.
 Zoey cannot be a knave, because this would contradict the claim of Jacob that Benjamin is a knight if and only if Zoey is a knight.
 We have exhausted all possibilities for Zoey, so let us go back and reconsider Jacob.
 Assume Jacob is a knave.  No contradiction is found in their false claim that Benjamin is a knight if and only if Zoey is a knight.
 Zoey cannot be a knight, because this would contradict the claim of their own that Riley is a knave if and only if Benjamin is a knight.
 Assume Zoey is a knave.  No contradiction is found in their false claim that Riley is a knave if and only if Benjamin is a knight.
 Aria cannot be a knight, because this would contradict the claim of their own that Riley is a knave.
 Assume Aria is a knave.  No contradiction is found in their false claim that Riley is a knave.
 Therefore, (1) Riley is a knight
 (2) Zoey is a knave
 (3) Aria is a knave
 (4) Jacob is a knave
 (5) Benjamin is a knight
A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Riley, Zoey, Aria, Jacob, and Benjamin. As Riley put it, "If Benjamin is a knave then Aria is a knight". Zoey stated, "Riley is a knave if and only if Benjamin is a knight". In a statement by Aria: "Riley is a knave". Jacob stated, "Benjamin is a knight if and only if Zoey is a knight". As Benjamin put it, "Jacob is a knight or Aria is a knave". So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> 
Assume Riley is a knight. No contradiction is found in their claim that If Benjamin is a knave then Aria is a knight.
Assume Benjamin is a knight. No contradiction is found in their claim that Jacob is a knight or Aria is a knave.
Assume Jacob is a knight. No contradiction is found in their claim that Benjamin is a knight if and only if Zoey is a knight.
Zoey cannot be a knight, because this would contradict the claim of their own that Riley is a knave if and only if Benjamin is a knight.
Zoey cannot be a knave, because this would contradict the claim of Jacob that Benjamin is a knight if and only if Zoey is a knight.
We have exhausted all possibilities for Zoey, so let us go back and reconsider Jacob.
Assume Jacob is a knave. No contradiction is found in their false claim that Benjamin is a knight if and only if Zoey is a knight.
Zoey cannot be a knight, because this would contradict the claim of their own that Riley is a knave if and only if Benjamin is a knight.
Assume Zoey is a knave. No contradiction is found in their false claim that Riley is a knave if and only if Benjamin is a knight.
Aria cannot be a knight, because this would contradict the claim of their own that Riley is a knave.
Assume Aria is a knave. No contradiction is found in their false claim that Riley is a knave.
Therefore, (1) Riley is a knight
(2) Zoey is a knave
(3) Aria is a knave
(4) Jacob is a knave
(5) Benjamin is a knight </think>
<answer> (1) Riley is a knight
(2) Zoey is a knave
(3) Aria is a knave
(4) Jacob is a knave
(5) Benjamin is a knight </answer>
Riley Zoey Aria Jacob Benjamin
(1) Riley is a knight
(2) Zoey is a knave
(3) Aria is a knave
(4) Jacob is a knave
(5) Benjamin is a knight
(('->', ('lying', 4), ('telling-truth', 2)), ('<=>', ('lying', 0), ('telling-truth', 4)), ('lying', 0), ('<=>', ('telling-truth', 4), ('telling-truth', 1)), ('or', ('telling-truth', 3), ('lying', 2)))
rule