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 5 inhabitants: Grace, Sebastian, Charlotte, Noah, and Aurora. Grace noted, "Noah is not a knight". Sebastian expressed that If Noah is a knave then Grace is a knight. Charlotte said, "Aurora is a knight and Aurora is a knave." "Aurora is a knight if and only if Noah is a knight," Noah declared. As Aurora put it, "Noah is a knave or Sebastian 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 Grace is a knight.  No contradiction is found in their claim that Noah is not a knight.
 Noah cannot be a knight, because this would contradict the claim of Grace that Noah is not a knight.
 Assume Noah is a knave.  No contradiction is found in their false claim that Aurora is a knight if and only if Noah is a knight.
 Assume Aurora is a knight.  No contradiction is found in their claim that Noah is a knave or Sebastian is a knave.
 Assume Sebastian is a knight.  No contradiction is found in their claim that If Noah is a knave then Grace is a knight.
 Charlotte cannot be a knight, because this would contradict the claim of their own that Aurora is a knight and Aurora is a knave.
 Assume Charlotte is a knave.  No contradiction is found in their false claim that Aurora is a knight and Aurora is a knave.
 Therefore, (1) Grace is a knight
 (2) Sebastian is a knight
 (3) Charlotte is a knave
 (4) Noah is a knave
 (5) Aurora 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 5 inhabitants: Grace, Sebastian, Charlotte, Noah, and Aurora. Grace noted, "Noah is not a knight". Sebastian expressed that If Noah is a knave then Grace is a knight. Charlotte said, "Aurora is a knight and Aurora is a knave." "Aurora is a knight if and only if Noah is a knight," Noah declared. As Aurora put it, "Noah is a knave or Sebastian 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 Grace is a knight. No contradiction is found in their claim that Noah is not a knight.
Noah cannot be a knight, because this would contradict the claim of Grace that Noah is not a knight.
Assume Noah is a knave. No contradiction is found in their false claim that Aurora is a knight if and only if Noah is a knight.
Assume Aurora is a knight. No contradiction is found in their claim that Noah is a knave or Sebastian is a knave.
Assume Sebastian is a knight. No contradiction is found in their claim that If Noah is a knave then Grace is a knight.
Charlotte cannot be a knight, because this would contradict the claim of their own that Aurora is a knight and Aurora is a knave.
Assume Charlotte is a knave. No contradiction is found in their false claim that Aurora is a knight and Aurora is a knave.
Therefore, (1) Grace is a knight
(2) Sebastian is a knight
(3) Charlotte is a knave
(4) Noah is a knave
(5) Aurora is a knight </think>
<answer> (1) Grace is a knight
(2) Sebastian is a knight
(3) Charlotte is a knave
(4) Noah is a knave
(5) Aurora is a knight </answer>
Grace Sebastian Charlotte Noah Aurora
(1) Grace is a knight
(2) Sebastian is a knight
(3) Charlotte is a knave
(4) Noah is a knave
(5) Aurora is a knight
(('not', ('telling-truth', 3)), ('->', ('lying', 3), ('telling-truth', 0)), ('and', ('telling-truth', 4), ('lying', 4)), ('<=>', ('telling-truth', 4), ('telling-truth', 3)), ('or', ('lying', 3), ('lying', 1)))
rule