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 6 inhabitants: Luke, Harper, Liam, Lily, Elizabeth, and Aurora. Luke was heard saying, "Aurora is not a knight". "Liam is a knave and Elizabeth is a knight," Harper mentioned. Liam was heard saying, "Elizabeth is a knight". "If Aurora is a knave then Harper is a knight," Lily claimed. Elizabeth said, "Harper is a knave and Luke is a knight." Aurora asserted: "Harper is a knave or Liam is 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 Luke is a knight.  No contradiction is found in their claim that Aurora is not a knight.
 Aurora cannot be a knight, because this would contradict the claim of Luke that Aurora is not a knight.
 Assume Aurora is a knave.  No contradiction is found in their false claim that Harper is a knave or Liam is a knight.
 Assume Harper is a knight.  No contradiction is found in their claim that Liam is a knave and Elizabeth is a knight.
 Liam cannot be a knight, because this would contradict the claim of Harper that Liam is a knave and Elizabeth is a knight.
 Assume Liam is a knave.  No contradiction is found in their false claim that Elizabeth is a knight.
 Elizabeth cannot be a knight, because this would contradict the false claim of Liam that Elizabeth is a knight.
 Elizabeth cannot be a knave, because this would contradict the claim of Harper that Liam is a knave and Elizabeth is a knight.
 We have exhausted all possibilities for Elizabeth and Liam, so let us go back and reconsider Harper.
 Harper cannot be a knave, because this would contradict the false claim of Aurora that Harper is a knave or Liam is a knight.
 We have exhausted all possibilities for Harper and Aurora, so let us go back and reconsider Luke.
 Assume Luke is a knave.  No contradiction is found in their false claim that Aurora is not a knight.
 Assume Aurora is a knight.  No contradiction is found in their claim that Harper is a knave or Liam is a knight.
 Assume Harper is a knight.  No contradiction is found in their claim that Liam is a knave and Elizabeth is a knight.
 Liam cannot be a knight, because this would contradict the claim of Harper that Liam is a knave and Elizabeth is a knight.
 Liam cannot be a knave, because this would contradict the claim of Aurora that Harper is a knave or Liam is a knight.
 We have exhausted all possibilities for Liam, so let us go back and reconsider Harper.
 Assume Harper is a knave.  No contradiction is found in their false claim that Liam is a knave and Elizabeth is a knight.
 Assume Liam is a knight.  No contradiction is found in their claim that Elizabeth is a knight.
 Elizabeth cannot be a knight, because this would contradict the claim of their own that Harper is a knave and Luke is a knight.
 Elizabeth cannot be a knave, because this would contradict the claim of Liam that Elizabeth is a knight.
 We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Liam.
 Assume Liam is a knave.  No contradiction is found in their false claim that Elizabeth is a knight.
 Elizabeth cannot be a knight, because this would contradict the false claim of Harper that Liam is a knave and Elizabeth is a knight.
 Assume Elizabeth is a knave.  No contradiction is found in their false claim that Harper is a knave and Luke is a knight.
 Assume Lily is a knight.  No contradiction is found in their claim that If Aurora is a knave then Harper is a knight.
 Therefore, (1) Luke is a knave
 (2) Harper is a knave
 (3) Liam is a knave
 (4) Lily is a knight
 (5) Elizabeth is a knave
 (6) Aurora 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 6 inhabitants: Luke, Harper, Liam, Lily, Elizabeth, and Aurora. Luke was heard saying, "Aurora is not a knight". "Liam is a knave and Elizabeth is a knight," Harper mentioned. Liam was heard saying, "Elizabeth is a knight". "If Aurora is a knave then Harper is a knight," Lily claimed. Elizabeth said, "Harper is a knave and Luke is a knight." Aurora asserted: "Harper is a knave or Liam is 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 Luke is a knight. No contradiction is found in their claim that Aurora is not a knight.
Aurora cannot be a knight, because this would contradict the claim of Luke that Aurora is not a knight.
Assume Aurora is a knave. No contradiction is found in their false claim that Harper is a knave or Liam is a knight.
Assume Harper is a knight. No contradiction is found in their claim that Liam is a knave and Elizabeth is a knight.
Liam cannot be a knight, because this would contradict the claim of Harper that Liam is a knave and Elizabeth is a knight.
Assume Liam is a knave. No contradiction is found in their false claim that Elizabeth is a knight.
Elizabeth cannot be a knight, because this would contradict the false claim of Liam that Elizabeth is a knight.
Elizabeth cannot be a knave, because this would contradict the claim of Harper that Liam is a knave and Elizabeth is a knight.
We have exhausted all possibilities for Elizabeth and Liam, so let us go back and reconsider Harper.
Harper cannot be a knave, because this would contradict the false claim of Aurora that Harper is a knave or Liam is a knight.
We have exhausted all possibilities for Harper and Aurora, so let us go back and reconsider Luke.
Assume Luke is a knave. No contradiction is found in their false claim that Aurora is not a knight.
Assume Aurora is a knight. No contradiction is found in their claim that Harper is a knave or Liam is a knight.
Assume Harper is a knight. No contradiction is found in their claim that Liam is a knave and Elizabeth is a knight.
Liam cannot be a knight, because this would contradict the claim of Harper that Liam is a knave and Elizabeth is a knight.
Liam cannot be a knave, because this would contradict the claim of Aurora that Harper is a knave or Liam is a knight.
We have exhausted all possibilities for Liam, so let us go back and reconsider Harper.
Assume Harper is a knave. No contradiction is found in their false claim that Liam is a knave and Elizabeth is a knight.
Assume Liam is a knight. No contradiction is found in their claim that Elizabeth is a knight.
Elizabeth cannot be a knight, because this would contradict the claim of their own that Harper is a knave and Luke is a knight.
Elizabeth cannot be a knave, because this would contradict the claim of Liam that Elizabeth is a knight.
We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Liam.
Assume Liam is a knave. No contradiction is found in their false claim that Elizabeth is a knight.
Elizabeth cannot be a knight, because this would contradict the false claim of Harper that Liam is a knave and Elizabeth is a knight.
Assume Elizabeth is a knave. No contradiction is found in their false claim that Harper is a knave and Luke is a knight.
Assume Lily is a knight. No contradiction is found in their claim that If Aurora is a knave then Harper is a knight.
Therefore, (1) Luke is a knave
(2) Harper is a knave
(3) Liam is a knave
(4) Lily is a knight
(5) Elizabeth is a knave
(6) Aurora is a knight </think>
<answer> (1) Luke is a knave
(2) Harper is a knave
(3) Liam is a knave
(4) Lily is a knight
(5) Elizabeth is a knave
(6) Aurora is a knight </answer>
Luke Harper Liam Lily Elizabeth Aurora
(1) Luke is a knave
(2) Harper is a knave
(3) Liam is a knave
(4) Lily is a knight
(5) Elizabeth is a knave
(6) Aurora is a knight
(('not', ('telling-truth', 5)), ('and', ('lying', 2), ('telling-truth', 4)), ('telling-truth', 4), ('->', ('lying', 5), ('telling-truth', 1)), ('and', ('lying', 1), ('telling-truth', 0)), ('or', ('lying', 1), ('telling-truth', 2)))
rule