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: Oliver, Aurora, Riley, Ethan, Sebastian, and Alexander. In a statement by Oliver: "Riley is a knave and Aurora is a knave". In a statement by Aurora: "Alexander is not a knave". Riley told you that If Aurora is a knave then Oliver is a knight. Ethan asserted: "Sebastian is a knave". Sebastian commented, "If Ethan is a knave then Sebastian is a knight". In Alexander's words: "Sebastian is a knave if and only if Oliver 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 Oliver is a knight.  No contradiction is found in their claim that Riley is a knave and Aurora is a knave.
 Riley cannot be a knight, because this would contradict the claim of Oliver that Riley is a knave and Aurora is a knave.
 Riley cannot be a knave, because this would contradict the false claim of their own that If Aurora is a knave then Oliver is a knight.
 We have exhausted all possibilities for Riley, so let us go back and reconsider Oliver.
 Assume Oliver is a knave.  No contradiction is found in their false claim that Riley is a knave and Aurora is a knave.
 Assume Riley is a knight.  No contradiction is found in their claim that If Aurora is a knave then Oliver is a knight.
 Assume Aurora is a knight.  No contradiction is found in their claim that Alexander is not a knave.
 Assume Alexander is a knight.  No contradiction is found in their claim that Sebastian is a knave if and only if Oliver is a knight.
 Assume Sebastian is a knight.  No contradiction is found in their claim that If Ethan is a knave then Sebastian is a knight.
 Ethan cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave.
 Assume Ethan is a knave.  No contradiction is found in their false claim that Sebastian is a knave.
 Therefore, (1) Oliver is a knave
 (2) Aurora is a knight
 (3) Riley is a knight
 (4) Ethan is a knave
 (5) Sebastian is a knight
 (6) Alexander 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: Oliver, Aurora, Riley, Ethan, Sebastian, and Alexander. In a statement by Oliver: "Riley is a knave and Aurora is a knave". In a statement by Aurora: "Alexander is not a knave". Riley told you that If Aurora is a knave then Oliver is a knight. Ethan asserted: "Sebastian is a knave". Sebastian commented, "If Ethan is a knave then Sebastian is a knight". In Alexander's words: "Sebastian is a knave if and only if Oliver 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 Oliver is a knight. No contradiction is found in their claim that Riley is a knave and Aurora is a knave.
Riley cannot be a knight, because this would contradict the claim of Oliver that Riley is a knave and Aurora is a knave.
Riley cannot be a knave, because this would contradict the false claim of their own that If Aurora is a knave then Oliver is a knight.
We have exhausted all possibilities for Riley, so let us go back and reconsider Oliver.
Assume Oliver is a knave. No contradiction is found in their false claim that Riley is a knave and Aurora is a knave.
Assume Riley is a knight. No contradiction is found in their claim that If Aurora is a knave then Oliver is a knight.
Assume Aurora is a knight. No contradiction is found in their claim that Alexander is not a knave.
Assume Alexander is a knight. No contradiction is found in their claim that Sebastian is a knave if and only if Oliver is a knight.
Assume Sebastian is a knight. No contradiction is found in their claim that If Ethan is a knave then Sebastian is a knight.
Ethan cannot be a knight, because this would contradict the claim of their own that Sebastian is a knave.
Assume Ethan is a knave. No contradiction is found in their false claim that Sebastian is a knave.
Therefore, (1) Oliver is a knave
(2) Aurora is a knight
(3) Riley is a knight
(4) Ethan is a knave
(5) Sebastian is a knight
(6) Alexander is a knight </think>
<answer> (1) Oliver is a knave
(2) Aurora is a knight
(3) Riley is a knight
(4) Ethan is a knave
(5) Sebastian is a knight
(6) Alexander is a knight </answer>
Oliver Aurora Riley Ethan Sebastian Alexander
(1) Oliver is a knave
(2) Aurora is a knight
(3) Riley is a knight
(4) Ethan is a knave
(5) Sebastian is a knight
(6) Alexander is a knight
(('and', ('lying', 2), ('lying', 1)), ('not', ('lying', 5)), ('->', ('lying', 1), ('telling-truth', 0)), ('lying', 4), ('->', ('lying', 3), ('telling-truth', 4)), ('<=>', ('lying', 4), ('telling-truth', 0)))
rule