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: Jacob, Daniel, Aria, Jack, Isabella, Benjamin, and James. "Daniel is a knight," Jacob mentioned. Daniel commented, "James is a knave and James is a knight". In Aria's words: "Daniel is a knight if and only if Jacob is a knave". Jack said, "If Aria is a knight then Jacob is a knight." According to Isabella, "Daniel is a knave". "Jack is a knight if and only if Aria is a knave" - Benjamin. James stated, "If Benjamin is a knight then Jack 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 Jacob is a knight.  No contradiction is found in their claim that Daniel is a knight.
 Daniel cannot be a knight, because this would contradict the claim of their own that James is a knave and James is a knight.
 Daniel cannot be a knave, because this would contradict the claim of Jacob that Daniel is a knight.
 We have exhausted all possibilities for Daniel, so let us go back and reconsider Jacob.
 Assume Jacob is a knave.  No contradiction is found in their false claim that Daniel is a knight.
 Daniel cannot be a knight, because this would contradict the false claim of Jacob that Daniel is a knight.
 Assume Daniel is a knave.  No contradiction is found in their false claim that James is a knave and James is a knight.
 Assume James is a knight.  No contradiction is found in their claim that If Benjamin is a knight then Jack is a knave.
 Assume Benjamin is a knight.  No contradiction is found in their claim that Jack is a knight if and only if Aria is a knave.
 Jack cannot be a knight, because this would contradict the claim of James that If Benjamin is a knight then Jack is a knave.
 Assume Jack is a knave.  No contradiction is found in their false claim that If Aria is a knight then Jacob is a knight.
 Aria cannot be a knight, because this would contradict the claim of their own that Daniel is a knight if and only if Jacob is a knave.
 Aria cannot be a knave, because this would contradict the false claim of Jack that If Aria is a knight then Jacob is a knight.
 We have exhausted all possibilities for Aria and Jack, so let us go back and reconsider Benjamin.
 Assume Benjamin is a knave.  No contradiction is found in their false claim that Jack is a knight if and only if Aria is a knave.
 Assume Jack is a knight.  No contradiction is found in their claim that If Aria is a knight then Jacob is a knight.
 Aria cannot be a knight, because this would contradict the claim of their own that Daniel is a knight if and only if Jacob is a knave.
 Aria cannot be a knave, because this would contradict the false claim of Benjamin that Jack is a knight if and only if Aria is a knave.
 We have exhausted all possibilities for Aria, so let us go back and reconsider Jack.
 Assume Jack is a knave.  No contradiction is found in their false claim that If Aria is a knight then Jacob is a knight.
 Aria cannot be a knight, because this would contradict the claim of their own that Daniel is a knight if and only if Jacob is a knave.
 Aria cannot be a knave, because this would contradict the false claim of Jack that If Aria is a knight then Jacob is a knight.
 We have exhausted all possibilities for Aria, Jack, and Benjamin, so let us go back and reconsider James.
 Assume James is a knave.  No contradiction is found in their false claim that If Benjamin is a knight then Jack is a knave.
 Assume Benjamin is a knight.  No contradiction is found in their claim that Jack is a knight if and only if Aria is a knave.
 Assume Jack is a knight.  No contradiction is found in their claim that If Aria is a knight then Jacob is a knight.
 Aria cannot be a knight, because this would contradict the claim of their own that Daniel is a knight if and only if Jacob is a knave.
 Assume Aria is a knave.  No contradiction is found in their false claim that Daniel is a knight if and only if Jacob is a knave.
 Assume Isabella is a knight.  No contradiction is found in their claim that Daniel is a knave.
 Therefore, (1) Jacob is a knave
 (2) Daniel is a knave
 (3) Aria is a knave
 (4) Jack is a knight
 (5) Isabella is a knight
 (6) Benjamin is a knight
 (7) James is a knave
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: Jacob, Daniel, Aria, Jack, Isabella, Benjamin, and James. "Daniel is a knight," Jacob mentioned. Daniel commented, "James is a knave and James is a knight". In Aria's words: "Daniel is a knight if and only if Jacob is a knave". Jack said, "If Aria is a knight then Jacob is a knight." According to Isabella, "Daniel is a knave". "Jack is a knight if and only if Aria is a knave" - Benjamin. James stated, "If Benjamin is a knight then Jack 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 Jacob is a knight. No contradiction is found in their claim that Daniel is a knight.
Daniel cannot be a knight, because this would contradict the claim of their own that James is a knave and James is a knight.
Daniel cannot be a knave, because this would contradict the claim of Jacob that Daniel is a knight.
We have exhausted all possibilities for Daniel, so let us go back and reconsider Jacob.
Assume Jacob is a knave. No contradiction is found in their false claim that Daniel is a knight.
Daniel cannot be a knight, because this would contradict the false claim of Jacob that Daniel is a knight.
Assume Daniel is a knave. No contradiction is found in their false claim that James is a knave and James is a knight.
Assume James is a knight. No contradiction is found in their claim that If Benjamin is a knight then Jack is a knave.
Assume Benjamin is a knight. No contradiction is found in their claim that Jack is a knight if and only if Aria is a knave.
Jack cannot be a knight, because this would contradict the claim of James that If Benjamin is a knight then Jack is a knave.
Assume Jack is a knave. No contradiction is found in their false claim that If Aria is a knight then Jacob is a knight.
Aria cannot be a knight, because this would contradict the claim of their own that Daniel is a knight if and only if Jacob is a knave.
Aria cannot be a knave, because this would contradict the false claim of Jack that If Aria is a knight then Jacob is a knight.
We have exhausted all possibilities for Aria and Jack, so let us go back and reconsider Benjamin.
Assume Benjamin is a knave. No contradiction is found in their false claim that Jack is a knight if and only if Aria is a knave.
Assume Jack is a knight. No contradiction is found in their claim that If Aria is a knight then Jacob is a knight.
Aria cannot be a knight, because this would contradict the claim of their own that Daniel is a knight if and only if Jacob is a knave.
Aria cannot be a knave, because this would contradict the false claim of Benjamin that Jack is a knight if and only if Aria is a knave.
We have exhausted all possibilities for Aria, so let us go back and reconsider Jack.
Assume Jack is a knave. No contradiction is found in their false claim that If Aria is a knight then Jacob is a knight.
Aria cannot be a knight, because this would contradict the claim of their own that Daniel is a knight if and only if Jacob is a knave.
Aria cannot be a knave, because this would contradict the false claim of Jack that If Aria is a knight then Jacob is a knight.
We have exhausted all possibilities for Aria, Jack, and Benjamin, so let us go back and reconsider James.
Assume James is a knave. No contradiction is found in their false claim that If Benjamin is a knight then Jack is a knave.
Assume Benjamin is a knight. No contradiction is found in their claim that Jack is a knight if and only if Aria is a knave.
Assume Jack is a knight. No contradiction is found in their claim that If Aria is a knight then Jacob is a knight.
Aria cannot be a knight, because this would contradict the claim of their own that Daniel is a knight if and only if Jacob is a knave.
Assume Aria is a knave. No contradiction is found in their false claim that Daniel is a knight if and only if Jacob is a knave.
Assume Isabella is a knight. No contradiction is found in their claim that Daniel is a knave.
Therefore, (1) Jacob is a knave
(2) Daniel is a knave
(3) Aria is a knave
(4) Jack is a knight
(5) Isabella is a knight
(6) Benjamin is a knight
(7) James is a knave </think>
<answer> (1) Jacob is a knave
(2) Daniel is a knave
(3) Aria is a knave
(4) Jack is a knight
(5) Isabella is a knight
(6) Benjamin is a knight
(7) James is a knave </answer>
Jacob Daniel Aria Jack Isabella Benjamin James
(1) Jacob is a knave
(2) Daniel is a knave
(3) Aria is a knave
(4) Jack is a knight
(5) Isabella is a knight
(6) Benjamin is a knight
(7) James is a knave
(('telling-truth', 1), ('and', ('lying', 6), ('telling-truth', 6)), ('<=>', ('telling-truth', 1), ('lying', 0)), ('->', ('telling-truth', 2), ('telling-truth', 0)), ('lying', 1), ('<=>', ('telling-truth', 3), ('lying', 2)), ('->', ('telling-truth', 5), ('lying', 3)))
rule