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: Joseph, Noah, Zoey, William, Isabella, Lily, and Oliver. Joseph noted, "If Isabella is a knight then Zoey is a knave". Noah commented, "Isabella is a knight if and only if Oliver is a knave". Zoey said that Isabella is not a knight. According to William, "If Zoey is a knave then Joseph is a knave". Isabella remarked, "Oliver is a knave and Zoey is a knave". Lily asserted: "William is a knight". Oliver was heard saying, "If Zoey is a knight then Isabella 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 Joseph is a knight.  No contradiction is found in their claim that If Isabella is a knight then Zoey is a knave.
 Assume Isabella is a knight.  No contradiction is found in their claim that Oliver is a knave and Zoey is a knave.
 Oliver cannot be a knight, because this would contradict the claim of Isabella that Oliver is a knave and Zoey is a knave.
 Assume Oliver is a knave.  No contradiction is found in their false claim that If Zoey is a knight then Isabella is a knave.
 Zoey cannot be a knight, because this would contradict the claim of Joseph that If Isabella is a knight then Zoey is a knave.
 Zoey cannot be a knave, because this would contradict the false claim of Oliver that If Zoey is a knight then Isabella is a knave.
 We have exhausted all possibilities for Zoey and Oliver, so let us go back and reconsider Isabella.
 Assume Isabella is a knave.  No contradiction is found in their false claim that Oliver is a knave and Zoey is a knave.
 Assume Oliver is a knight.  No contradiction is found in their claim that If Zoey is a knight then Isabella is a knave.
 Assume Zoey is a knight.  No contradiction is found in their claim that Isabella is not a knight.
 Assume Noah is a knight.  No contradiction is found in their claim that Isabella is a knight if and only if Oliver is a knave.
 Assume William is a knight.  No contradiction is found in their claim that If Zoey is a knave then Joseph is a knave.
 Assume Lily is a knight.  No contradiction is found in their claim that William is a knight.
 Therefore, (1) Joseph is a knight
 (2) Noah is a knight
 (3) Zoey is a knight
 (4) William is a knight
 (5) Isabella is a knave
 (6) Lily is a knight
 (7) Oliver 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: Joseph, Noah, Zoey, William, Isabella, Lily, and Oliver. Joseph noted, "If Isabella is a knight then Zoey is a knave". Noah commented, "Isabella is a knight if and only if Oliver is a knave". Zoey said that Isabella is not a knight. According to William, "If Zoey is a knave then Joseph is a knave". Isabella remarked, "Oliver is a knave and Zoey is a knave". Lily asserted: "William is a knight". Oliver was heard saying, "If Zoey is a knight then Isabella 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 Joseph is a knight. No contradiction is found in their claim that If Isabella is a knight then Zoey is a knave.
Assume Isabella is a knight. No contradiction is found in their claim that Oliver is a knave and Zoey is a knave.
Oliver cannot be a knight, because this would contradict the claim of Isabella that Oliver is a knave and Zoey is a knave.
Assume Oliver is a knave. No contradiction is found in their false claim that If Zoey is a knight then Isabella is a knave.
Zoey cannot be a knight, because this would contradict the claim of Joseph that If Isabella is a knight then Zoey is a knave.
Zoey cannot be a knave, because this would contradict the false claim of Oliver that If Zoey is a knight then Isabella is a knave.
We have exhausted all possibilities for Zoey and Oliver, so let us go back and reconsider Isabella.
Assume Isabella is a knave. No contradiction is found in their false claim that Oliver is a knave and Zoey is a knave.
Assume Oliver is a knight. No contradiction is found in their claim that If Zoey is a knight then Isabella is a knave.
Assume Zoey is a knight. No contradiction is found in their claim that Isabella is not a knight.
Assume Noah is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Oliver is a knave.
Assume William is a knight. No contradiction is found in their claim that If Zoey is a knave then Joseph is a knave.
Assume Lily is a knight. No contradiction is found in their claim that William is a knight.
Therefore, (1) Joseph is a knight
(2) Noah is a knight
(3) Zoey is a knight
(4) William is a knight
(5) Isabella is a knave
(6) Lily is a knight
(7) Oliver is a knight </think>
<answer> (1) Joseph is a knight
(2) Noah is a knight
(3) Zoey is a knight
(4) William is a knight
(5) Isabella is a knave
(6) Lily is a knight
(7) Oliver is a knight </answer>
Joseph Noah Zoey William Isabella Lily Oliver
(1) Joseph is a knight
(2) Noah is a knight
(3) Zoey is a knight
(4) William is a knight
(5) Isabella is a knave
(6) Lily is a knight
(7) Oliver is a knight
(('->', ('telling-truth', 4), ('lying', 2)), ('<=>', ('telling-truth', 4), ('lying', 6)), ('not', ('telling-truth', 4)), ('->', ('lying', 2), ('lying', 0)), ('and', ('lying', 6), ('lying', 2)), ('telling-truth', 3), ('->', ('telling-truth', 2), ('lying', 4)))
rule