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: Aurora, Grace, Owen, Oliver, Alexander, Daniel, and Emma. Aurora said, "If Oliver is a knight then Daniel is a knave." "Aurora is a knave," Grace mentioned. "Alexander is not a knight," Owen declared. Oliver told you that Alexander is a knight and Daniel is a knight. Alexander told you that Emma is a knight if and only if Aurora is a knight. Daniel asserted: "Grace is a knave if and only if Alexander is a knave". Emma told you that Oliver is a knight or Oliver 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 Aurora is a knight.  No contradiction is found in their claim that If Oliver is a knight then Daniel is a knave.
 Assume Oliver is a knight.  No contradiction is found in their claim that Alexander is a knight and Daniel is a knight.
 Assume Alexander is a knight.  No contradiction is found in their claim that Emma is a knight if and only if Aurora is a knight.
 Assume Emma is a knight.  No contradiction is found in their claim that Oliver is a knight or Oliver is a knave.
 Daniel cannot be a knight, because this would contradict the claim of Aurora that If Oliver is a knight then Daniel is a knave.
 Daniel cannot be a knave, because this would contradict the claim of Oliver that Alexander is a knight and Daniel is a knight.
 We have exhausted all possibilities for Daniel, so let us go back and reconsider Emma.
 Emma cannot be a knave, because this would contradict the claim of Alexander that Emma is a knight if and only if Aurora is a knight.
 We have exhausted all possibilities for Emma, so let us go back and reconsider Alexander.
 Alexander cannot be a knave, because this would contradict the claim of Oliver that Alexander is a knight and Daniel is a knight.
 We have exhausted all possibilities for Alexander, so let us go back and reconsider Oliver.
 Assume Oliver is a knave.  No contradiction is found in their false claim that Alexander is a knight and Daniel is a knight.
 Assume Alexander is a knight.  No contradiction is found in their claim that Emma is a knight if and only if Aurora is a knight.
 Assume Emma is a knight.  No contradiction is found in their claim that Oliver is a knight or Oliver is a knave.
 Daniel cannot be a knight, because this would contradict the false claim of Oliver that Alexander is a knight and Daniel is a knight.
 Assume Daniel is a knave.  No contradiction is found in their false claim that Grace is a knave if and only if Alexander is a knave.
 Grace cannot be a knight, because this would contradict the claim of their own that Aurora is a knave.
 Assume Grace is a knave.  No contradiction is found in their false claim that Aurora is a knave.
 Owen cannot be a knight, because this would contradict the claim of their own that Alexander is not a knight.
 Assume Owen is a knave.  No contradiction is found in their false claim that Alexander is not a knight.
 Therefore, (1) Aurora is a knight
 (2) Grace is a knave
 (3) Owen is a knave
 (4) Oliver is a knave
 (5) Alexander is a knight
 (6) Daniel is a knave
 (7) Emma 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 7 inhabitants: Aurora, Grace, Owen, Oliver, Alexander, Daniel, and Emma. Aurora said, "If Oliver is a knight then Daniel is a knave." "Aurora is a knave," Grace mentioned. "Alexander is not a knight," Owen declared. Oliver told you that Alexander is a knight and Daniel is a knight. Alexander told you that Emma is a knight if and only if Aurora is a knight. Daniel asserted: "Grace is a knave if and only if Alexander is a knave". Emma told you that Oliver is a knight or Oliver 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 Aurora is a knight. No contradiction is found in their claim that If Oliver is a knight then Daniel is a knave.
Assume Oliver is a knight. No contradiction is found in their claim that Alexander is a knight and Daniel is a knight.
Assume Alexander is a knight. No contradiction is found in their claim that Emma is a knight if and only if Aurora is a knight.
Assume Emma is a knight. No contradiction is found in their claim that Oliver is a knight or Oliver is a knave.
Daniel cannot be a knight, because this would contradict the claim of Aurora that If Oliver is a knight then Daniel is a knave.
Daniel cannot be a knave, because this would contradict the claim of Oliver that Alexander is a knight and Daniel is a knight.
We have exhausted all possibilities for Daniel, so let us go back and reconsider Emma.
Emma cannot be a knave, because this would contradict the claim of Alexander that Emma is a knight if and only if Aurora is a knight.
We have exhausted all possibilities for Emma, so let us go back and reconsider Alexander.
Alexander cannot be a knave, because this would contradict the claim of Oliver that Alexander is a knight and Daniel is a knight.
We have exhausted all possibilities for Alexander, so let us go back and reconsider Oliver.
Assume Oliver is a knave. No contradiction is found in their false claim that Alexander is a knight and Daniel is a knight.
Assume Alexander is a knight. No contradiction is found in their claim that Emma is a knight if and only if Aurora is a knight.
Assume Emma is a knight. No contradiction is found in their claim that Oliver is a knight or Oliver is a knave.
Daniel cannot be a knight, because this would contradict the false claim of Oliver that Alexander is a knight and Daniel is a knight.
Assume Daniel is a knave. No contradiction is found in their false claim that Grace is a knave if and only if Alexander is a knave.
Grace cannot be a knight, because this would contradict the claim of their own that Aurora is a knave.
Assume Grace is a knave. No contradiction is found in their false claim that Aurora is a knave.
Owen cannot be a knight, because this would contradict the claim of their own that Alexander is not a knight.
Assume Owen is a knave. No contradiction is found in their false claim that Alexander is not a knight.
Therefore, (1) Aurora is a knight
(2) Grace is a knave
(3) Owen is a knave
(4) Oliver is a knave
(5) Alexander is a knight
(6) Daniel is a knave
(7) Emma is a knight </think>
<answer> (1) Aurora is a knight
(2) Grace is a knave
(3) Owen is a knave
(4) Oliver is a knave
(5) Alexander is a knight
(6) Daniel is a knave
(7) Emma is a knight </answer>
Aurora Grace Owen Oliver Alexander Daniel Emma
(1) Aurora is a knight
(2) Grace is a knave
(3) Owen is a knave
(4) Oliver is a knave
(5) Alexander is a knight
(6) Daniel is a knave
(7) Emma is a knight
(('->', ('telling-truth', 3), ('lying', 5)), ('lying', 0), ('not', ('telling-truth', 4)), ('and', ('telling-truth', 4), ('telling-truth', 5)), ('<=>', ('telling-truth', 6), ('telling-truth', 0)), ('<=>', ('lying', 1), ('lying', 4)), ('or', ('telling-truth', 3), ('lying', 3)))
rule