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: Aiden, Grace, Ella, Jack, Sofia, and Emma. Aiden told you that Grace is a knight and Emma is a knight. "Jack is a knight if and only if Sofia is a knight," Grace mentioned. In Ella's words: "If Aiden is a knight then Grace is a knight". Jack said that Ella is a knight. Sofia was heard saying, "Aiden is a knave or Sofia is a knight". According to Emma, "Sofia is not 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 Aiden is a knight.  No contradiction is found in their claim that Grace is a knight and Emma is a knight.
 Assume Grace is a knight.  No contradiction is found in their claim that Jack is a knight if and only if Sofia is a knight.
 Assume Jack is a knight.  No contradiction is found in their claim that Ella is a knight.
 Assume Ella is a knight.  No contradiction is found in their claim that If Aiden is a knight then Grace is a knight.
 Assume Sofia is a knight.  No contradiction is found in their claim that Aiden is a knave or Sofia is a knight.
 Assume Emma is a knight.  No contradiction is found in their claim that Sofia is not a knave.
 Therefore, (1) Aiden is a knight
 (2) Grace is a knight
 (3) Ella is a knight
 (4) Jack is a knight
 (5) Sofia is a knight
 (6) 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 6 inhabitants: Aiden, Grace, Ella, Jack, Sofia, and Emma. Aiden told you that Grace is a knight and Emma is a knight. "Jack is a knight if and only if Sofia is a knight," Grace mentioned. In Ella's words: "If Aiden is a knight then Grace is a knight". Jack said that Ella is a knight. Sofia was heard saying, "Aiden is a knave or Sofia is a knight". According to Emma, "Sofia is not 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 Aiden is a knight. No contradiction is found in their claim that Grace is a knight and Emma is a knight.
Assume Grace is a knight. No contradiction is found in their claim that Jack is a knight if and only if Sofia is a knight.
Assume Jack is a knight. No contradiction is found in their claim that Ella is a knight.
Assume Ella is a knight. No contradiction is found in their claim that If Aiden is a knight then Grace is a knight.
Assume Sofia is a knight. No contradiction is found in their claim that Aiden is a knave or Sofia is a knight.
Assume Emma is a knight. No contradiction is found in their claim that Sofia is not a knave.
Therefore, (1) Aiden is a knight
(2) Grace is a knight
(3) Ella is a knight
(4) Jack is a knight
(5) Sofia is a knight
(6) Emma is a knight </think>
<answer> (1) Aiden is a knight
(2) Grace is a knight
(3) Ella is a knight
(4) Jack is a knight
(5) Sofia is a knight
(6) Emma is a knight </answer>
Aiden Grace Ella Jack Sofia Emma
(1) Aiden is a knight
(2) Grace is a knight
(3) Ella is a knight
(4) Jack is a knight
(5) Sofia is a knight
(6) Emma is a knight
(('and', ('telling-truth', 1), ('telling-truth', 5)), ('<=>', ('telling-truth', 3), ('telling-truth', 4)), ('->', ('telling-truth', 0), ('telling-truth', 1)), ('telling-truth', 2), ('or', ('lying', 0), ('telling-truth', 4)), ('not', ('lying', 4)))
rule