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: Michael, Lily, Ella, David, Oliver, and Sebastian. Michael expressed that David is a knave. As Lily put it, "Ella is not a knight". According to Ella, "Lily is a knight if and only if Sebastian is a knave". As David put it, "If Ella is a knight then Oliver is a knave". "If Michael is a knave then Lily is a knight" - Oliver. Sebastian was heard saying, "Ella is a knave if and only if Michael 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 Michael is a knight.  No contradiction is found in their claim that David is a knave.
 David cannot be a knight, because this would contradict the claim of Michael that David is a knave.
 Assume David is a knave.  No contradiction is found in their false claim that If Ella is a knight then Oliver is a knave.
 Assume Ella is a knight.  No contradiction is found in their claim that Lily is a knight if and only if Sebastian is a knave.
 Lily cannot be a knight, because this would contradict the claim of their own that Ella is not a knight.
 Assume Lily is a knave.  No contradiction is found in their false claim that Ella is not a knight.
 Sebastian cannot be a knight, because this would contradict the claim of their own that Ella is a knave if and only if Michael is a knight.
 Sebastian cannot be a knave, because this would contradict the claim of Ella that Lily is a knight if and only if Sebastian is a knave.
 We have exhausted all possibilities for Sebastian and Lily, so let us go back and reconsider Ella.
 Ella cannot be a knave, because this would contradict the false claim of David that If Ella is a knight then Oliver is a knave.
 We have exhausted all possibilities for Ella and David, so let us go back and reconsider Michael.
 Assume Michael is a knave.  No contradiction is found in their false claim that David is a knave.
 Assume David is a knight.  No contradiction is found in their claim that If Ella is a knight then Oliver is a knave.
 Assume Ella is a knight.  No contradiction is found in their claim that Lily is a knight if and only if Sebastian is a knave.
 Lily cannot be a knight, because this would contradict the claim of their own that Ella is not a knight.
 Assume Lily is a knave.  No contradiction is found in their false claim that Ella is not a knight.
 Assume Sebastian is a knight.  No contradiction is found in their claim that Ella is a knave if and only if Michael is a knight.
 Oliver cannot be a knight, because this would contradict the claim of David that If Ella is a knight then Oliver is a knave.
 Assume Oliver is a knave.  No contradiction is found in their false claim that If Michael is a knave then Lily is a knight.
 Therefore, (1) Michael is a knave
 (2) Lily is a knave
 (3) Ella is a knight
 (4) David is a knight
 (5) Oliver is a knave
 (6) Sebastian 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: Michael, Lily, Ella, David, Oliver, and Sebastian. Michael expressed that David is a knave. As Lily put it, "Ella is not a knight". According to Ella, "Lily is a knight if and only if Sebastian is a knave". As David put it, "If Ella is a knight then Oliver is a knave". "If Michael is a knave then Lily is a knight" - Oliver. Sebastian was heard saying, "Ella is a knave if and only if Michael 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 Michael is a knight. No contradiction is found in their claim that David is a knave.
David cannot be a knight, because this would contradict the claim of Michael that David is a knave.
Assume David is a knave. No contradiction is found in their false claim that If Ella is a knight then Oliver is a knave.
Assume Ella is a knight. No contradiction is found in their claim that Lily is a knight if and only if Sebastian is a knave.
Lily cannot be a knight, because this would contradict the claim of their own that Ella is not a knight.
Assume Lily is a knave. No contradiction is found in their false claim that Ella is not a knight.
Sebastian cannot be a knight, because this would contradict the claim of their own that Ella is a knave if and only if Michael is a knight.
Sebastian cannot be a knave, because this would contradict the claim of Ella that Lily is a knight if and only if Sebastian is a knave.
We have exhausted all possibilities for Sebastian and Lily, so let us go back and reconsider Ella.
Ella cannot be a knave, because this would contradict the false claim of David that If Ella is a knight then Oliver is a knave.
We have exhausted all possibilities for Ella and David, so let us go back and reconsider Michael.
Assume Michael is a knave. No contradiction is found in their false claim that David is a knave.
Assume David is a knight. No contradiction is found in their claim that If Ella is a knight then Oliver is a knave.
Assume Ella is a knight. No contradiction is found in their claim that Lily is a knight if and only if Sebastian is a knave.
Lily cannot be a knight, because this would contradict the claim of their own that Ella is not a knight.
Assume Lily is a knave. No contradiction is found in their false claim that Ella is not a knight.
Assume Sebastian is a knight. No contradiction is found in their claim that Ella is a knave if and only if Michael is a knight.
Oliver cannot be a knight, because this would contradict the claim of David that If Ella is a knight then Oliver is a knave.
Assume Oliver is a knave. No contradiction is found in their false claim that If Michael is a knave then Lily is a knight.
Therefore, (1) Michael is a knave
(2) Lily is a knave
(3) Ella is a knight
(4) David is a knight
(5) Oliver is a knave
(6) Sebastian is a knight </think>
<answer> (1) Michael is a knave
(2) Lily is a knave
(3) Ella is a knight
(4) David is a knight
(5) Oliver is a knave
(6) Sebastian is a knight </answer>
Michael Lily Ella David Oliver Sebastian
(1) Michael is a knave
(2) Lily is a knave
(3) Ella is a knight
(4) David is a knight
(5) Oliver is a knave
(6) Sebastian is a knight
(('lying', 3), ('not', ('telling-truth', 2)), ('<=>', ('telling-truth', 1), ('lying', 5)), ('->', ('telling-truth', 2), ('lying', 4)), ('->', ('lying', 0), ('telling-truth', 1)), ('<=>', ('lying', 2), ('telling-truth', 0)))
rule