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: David, Luke, Aurora, Jacob, and Henry. David commented, "Jacob is not a knave". Luke said that Luke is a knight and David is a knave. Aurora was heard saying, "Jacob is a knight if and only if David is a knight". "Henry is a knave," Jacob mentioned. Henry was heard saying, "Jacob is a knight if and only if Jacob 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 David is a knight.  No contradiction is found in their claim that Jacob is not a knave.
 Assume Jacob is a knight.  No contradiction is found in their claim that Henry is a knave.
 Henry cannot be a knight, because this would contradict the claim of Jacob that Henry is a knave.
 Assume Henry is a knave.  No contradiction is found in their false claim that Jacob is a knight if and only if Jacob is a knave.
 Luke cannot be a knight, because this would contradict the claim of their own that Luke is a knight and David is a knave.
 Assume Luke is a knave.  No contradiction is found in their false claim that Luke is a knight and David is a knave.
 Assume Aurora is a knight.  No contradiction is found in their claim that Jacob is a knight if and only if David is a knight.
 Therefore, (1) David is a knight
 (2) Luke is a knave
 (3) Aurora is a knight
 (4) Jacob is a knight
 (5) Henry 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 5 inhabitants: David, Luke, Aurora, Jacob, and Henry. David commented, "Jacob is not a knave". Luke said that Luke is a knight and David is a knave. Aurora was heard saying, "Jacob is a knight if and only if David is a knight". "Henry is a knave," Jacob mentioned. Henry was heard saying, "Jacob is a knight if and only if Jacob 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 David is a knight. No contradiction is found in their claim that Jacob is not a knave.
Assume Jacob is a knight. No contradiction is found in their claim that Henry is a knave.
Henry cannot be a knight, because this would contradict the claim of Jacob that Henry is a knave.
Assume Henry is a knave. No contradiction is found in their false claim that Jacob is a knight if and only if Jacob is a knave.
Luke cannot be a knight, because this would contradict the claim of their own that Luke is a knight and David is a knave.
Assume Luke is a knave. No contradiction is found in their false claim that Luke is a knight and David is a knave.
Assume Aurora is a knight. No contradiction is found in their claim that Jacob is a knight if and only if David is a knight.
Therefore, (1) David is a knight
(2) Luke is a knave
(3) Aurora is a knight
(4) Jacob is a knight
(5) Henry is a knave </think>
<answer> (1) David is a knight
(2) Luke is a knave
(3) Aurora is a knight
(4) Jacob is a knight
(5) Henry is a knave </answer>
David Luke Aurora Jacob Henry
(1) David is a knight
(2) Luke is a knave
(3) Aurora is a knight
(4) Jacob is a knight
(5) Henry is a knave
(('not', ('lying', 3)), ('and', ('telling-truth', 1), ('lying', 0)), ('<=>', ('telling-truth', 3), ('telling-truth', 0)), ('lying', 4), ('<=>', ('telling-truth', 3), ('lying', 3)))
rule