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 7 inhabitants: Jack, Aurora, Benjamin, Owen, Mason, Jacob, and Luke. Jack said that Aurora is a knight and Jack is a knight. "Luke is a knave and Jack is a knave," Aurora declared. Benjamin asserted: "If Aurora is a knave then Luke is a knave". Owen expressed that Luke is a knight or Benjamin is a knight. Mason asserted: "Aurora is a knight if and only if Owen is a knight". According to Jacob, "If Luke is a knight then Benjamin is a knave". As Luke put it, "Jacob is not a knight". 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 Jack is a knight.  No contradiction is found in their claim that Aurora is a knight and Jack is a knight.
 Aurora cannot be a knight, because this would contradict the claim of their own that Luke is a knave and Jack is a knave.
 Aurora cannot be a knave, because this would contradict the claim of Jack that Aurora is a knight and Jack is a knight.
 We have exhausted all possibilities for Aurora, so let us go back and reconsider Jack.
 Assume Jack is a knave.  No contradiction is found in their false claim that Aurora is a knight and Jack is a knight.
 Assume Aurora is a knight.  No contradiction is found in their claim that Luke is a knave and Jack is a knave.
 Luke cannot be a knight, because this would contradict the claim of Aurora that Luke is a knave and Jack is a knave.
 Assume Luke is a knave.  No contradiction is found in their false claim that Jacob is not a knight.
 Assume Jacob is a knight.  No contradiction is found in their claim that If Luke is a knight then Benjamin is a knave.
 Assume Benjamin is a knight.  No contradiction is found in their claim that If Aurora is a knave then Luke is a knave.
 Assume Owen is a knight.  No contradiction is found in their claim that Luke is a knight or Benjamin is a knight.
 Assume Mason is a knight.  No contradiction is found in their claim that Aurora is a knight if and only if Owen is a knight.
 Therefore, (1) Jack is a knave
 (2) Aurora is a knight
 (3) Benjamin is a knight
 (4) Owen is a knight
 (5) Mason is a knight
 (6) Jacob is a knight
 (7) Luke is a knave
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 7 inhabitants: Jack, Aurora, Benjamin, Owen, Mason, Jacob, and Luke. Jack said that Aurora is a knight and Jack is a knight. "Luke is a knave and Jack is a knave," Aurora declared. Benjamin asserted: "If Aurora is a knave then Luke is a knave". Owen expressed that Luke is a knight or Benjamin is a knight. Mason asserted: "Aurora is a knight if and only if Owen is a knight". According to Jacob, "If Luke is a knight then Benjamin is a knave". As Luke put it, "Jacob is not a knight". 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 Jack is a knight. No contradiction is found in their claim that Aurora is a knight and Jack is a knight.
Aurora cannot be a knight, because this would contradict the claim of their own that Luke is a knave and Jack is a knave.
Aurora cannot be a knave, because this would contradict the claim of Jack that Aurora is a knight and Jack is a knight.
We have exhausted all possibilities for Aurora, so let us go back and reconsider Jack.
Assume Jack is a knave. No contradiction is found in their false claim that Aurora is a knight and Jack is a knight.
Assume Aurora is a knight. No contradiction is found in their claim that Luke is a knave and Jack is a knave.
Luke cannot be a knight, because this would contradict the claim of Aurora that Luke is a knave and Jack is a knave.
Assume Luke is a knave. No contradiction is found in their false claim that Jacob is not a knight.
Assume Jacob is a knight. No contradiction is found in their claim that If Luke is a knight then Benjamin is a knave.
Assume Benjamin is a knight. No contradiction is found in their claim that If Aurora is a knave then Luke is a knave.
Assume Owen is a knight. No contradiction is found in their claim that Luke is a knight or Benjamin is a knight.
Assume Mason is a knight. No contradiction is found in their claim that Aurora is a knight if and only if Owen is a knight.
Therefore, (1) Jack is a knave
(2) Aurora is a knight
(3) Benjamin is a knight
(4) Owen is a knight
(5) Mason is a knight
(6) Jacob is a knight
(7) Luke is a knave </think>
<answer> (1) Jack is a knave
(2) Aurora is a knight
(3) Benjamin is a knight
(4) Owen is a knight
(5) Mason is a knight
(6) Jacob is a knight
(7) Luke is a knave </answer>
Jack Aurora Benjamin Owen Mason Jacob Luke
(1) Jack is a knave
(2) Aurora is a knight
(3) Benjamin is a knight
(4) Owen is a knight
(5) Mason is a knight
(6) Jacob is a knight
(7) Luke is a knave
(('and', ('telling-truth', 1), ('telling-truth', 0)), ('and', ('lying', 6), ('lying', 0)), ('->', ('lying', 1), ('lying', 6)), ('or', ('telling-truth', 6), ('telling-truth', 2)), ('<=>', ('telling-truth', 1), ('telling-truth', 3)), ('->', ('telling-truth', 6), ('lying', 2)), ('not', ('telling-truth', 5)))
rule