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: Ella, Sofia, Emma, Jack, Ava, Aiden, and Grace. In Ella's words: "Ava is not a knave". Sofia said that Ava is a knave. Emma was heard saying, "Jack is a knight". According to Jack, "Sofia is a knight and Ella is a knight". Ava said, "If Ella is a knave then Sofia is a knight." Aiden expressed that If Grace is a knave then Sofia is a knight. Grace was heard saying, "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 Ella is a knight.  No contradiction is found in their claim that Ava is not a knave.
 Assume Ava is a knight.  No contradiction is found in their claim that If Ella is a knave then Sofia is a knight.
 Sofia cannot be a knight, because this would contradict the claim of their own that Ava is a knave.
 Assume Sofia is a knave.  No contradiction is found in their false claim that Ava is a knave.
 Assume Emma is a knight.  No contradiction is found in their claim that Jack is a knight.
 Jack cannot be a knight, because this would contradict the claim of their own that Sofia is a knight and Ella is a knight.
 Jack cannot be a knave, because this would contradict the claim of Emma that Jack is a knight.
 We have exhausted all possibilities for Jack, so let us go back and reconsider Emma.
 Assume Emma is a knave.  No contradiction is found in their false claim that Jack is a knight.
 Jack cannot be a knight, because this would contradict the false claim of Emma that Jack is a knight.
 Assume Jack is a knave.  No contradiction is found in their false claim that Sofia is a knight and Ella is a knight.
 Assume Aiden is a knight.  No contradiction is found in their claim that If Grace is a knave then Sofia is a knight.
 Grace cannot be a knight, because this would contradict the claim of their own that Sofia is not a knave.
 Grace cannot be a knave, because this would contradict the claim of Aiden that If Grace is a knave then Sofia is a knight.
 We have exhausted all possibilities for Grace, so let us go back and reconsider Aiden.
 Assume Aiden is a knave.  No contradiction is found in their false claim that If Grace is a knave then Sofia is a knight.
 Grace cannot be a knight, because this would contradict the false claim of Aiden that If Grace is a knave then Sofia is a knight.
 Assume Grace is a knave.  No contradiction is found in their false claim that Sofia is not a knave.
 Therefore, (1) Ella is a knight
 (2) Sofia is a knave
 (3) Emma is a knave
 (4) Jack is a knave
 (5) Ava is a knight
 (6) Aiden is a knave
 (7) Grace 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: Ella, Sofia, Emma, Jack, Ava, Aiden, and Grace. In Ella's words: "Ava is not a knave". Sofia said that Ava is a knave. Emma was heard saying, "Jack is a knight". According to Jack, "Sofia is a knight and Ella is a knight". Ava said, "If Ella is a knave then Sofia is a knight." Aiden expressed that If Grace is a knave then Sofia is a knight. Grace was heard saying, "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 Ella is a knight. No contradiction is found in their claim that Ava is not a knave.
Assume Ava is a knight. No contradiction is found in their claim that If Ella is a knave then Sofia is a knight.
Sofia cannot be a knight, because this would contradict the claim of their own that Ava is a knave.
Assume Sofia is a knave. No contradiction is found in their false claim that Ava is a knave.
Assume Emma is a knight. No contradiction is found in their claim that Jack is a knight.
Jack cannot be a knight, because this would contradict the claim of their own that Sofia is a knight and Ella is a knight.
Jack cannot be a knave, because this would contradict the claim of Emma that Jack is a knight.
We have exhausted all possibilities for Jack, so let us go back and reconsider Emma.
Assume Emma is a knave. No contradiction is found in their false claim that Jack is a knight.
Jack cannot be a knight, because this would contradict the false claim of Emma that Jack is a knight.
Assume Jack is a knave. No contradiction is found in their false claim that Sofia is a knight and Ella is a knight.
Assume Aiden is a knight. No contradiction is found in their claim that If Grace is a knave then Sofia is a knight.
Grace cannot be a knight, because this would contradict the claim of their own that Sofia is not a knave.
Grace cannot be a knave, because this would contradict the claim of Aiden that If Grace is a knave then Sofia is a knight.
We have exhausted all possibilities for Grace, so let us go back and reconsider Aiden.
Assume Aiden is a knave. No contradiction is found in their false claim that If Grace is a knave then Sofia is a knight.
Grace cannot be a knight, because this would contradict the false claim of Aiden that If Grace is a knave then Sofia is a knight.
Assume Grace is a knave. No contradiction is found in their false claim that Sofia is not a knave.
Therefore, (1) Ella is a knight
(2) Sofia is a knave
(3) Emma is a knave
(4) Jack is a knave
(5) Ava is a knight
(6) Aiden is a knave
(7) Grace is a knave </think>
<answer> (1) Ella is a knight
(2) Sofia is a knave
(3) Emma is a knave
(4) Jack is a knave
(5) Ava is a knight
(6) Aiden is a knave
(7) Grace is a knave </answer>
Ella Sofia Emma Jack Ava Aiden Grace
(1) Ella is a knight
(2) Sofia is a knave
(3) Emma is a knave
(4) Jack is a knave
(5) Ava is a knight
(6) Aiden is a knave
(7) Grace is a knave
(('not', ('lying', 4)), ('lying', 4), ('telling-truth', 3), ('and', ('telling-truth', 1), ('telling-truth', 0)), ('->', ('lying', 0), ('telling-truth', 1)), ('->', ('lying', 6), ('telling-truth', 1)), ('not', ('lying', 1)))
rule