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: Lily, Amelia, Henry, David, and Sofia. Lily said that David is a knave. In a statement by Amelia: "Sofia is not a knight". Henry told you that Sofia is a knave. In a statement by David: "Lily is a knave if and only if Henry is a knight". In a statement by Sofia: "Lily is not a knight". 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 Lily is a knight.  No contradiction is found in their claim that David is a knave.
 David cannot be a knight, because this would contradict the claim of Lily that David is a knave.
 Assume David is a knave.  No contradiction is found in their false claim that Lily is a knave if and only if Henry is a knight.
 Assume Henry is a knight.  No contradiction is found in their claim that Sofia is a knave.
 Sofia cannot be a knight, because this would contradict the claim of Henry that Sofia is a knave.
 Assume Sofia is a knave.  No contradiction is found in their false claim that Lily is not a knight.
 Assume Amelia is a knight.  No contradiction is found in their claim that Sofia is not a knight.
 Therefore, (1) Lily is a knight
 (2) Amelia is a knight
 (3) Henry is a knight
 (4) David is a knave
 (5) Sofia 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: Lily, Amelia, Henry, David, and Sofia. Lily said that David is a knave. In a statement by Amelia: "Sofia is not a knight". Henry told you that Sofia is a knave. In a statement by David: "Lily is a knave if and only if Henry is a knight". In a statement by Sofia: "Lily is not a knight". 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 Lily is a knight. No contradiction is found in their claim that David is a knave.
David cannot be a knight, because this would contradict the claim of Lily that David is a knave.
Assume David is a knave. No contradiction is found in their false claim that Lily is a knave if and only if Henry is a knight.
Assume Henry is a knight. No contradiction is found in their claim that Sofia is a knave.
Sofia cannot be a knight, because this would contradict the claim of Henry that Sofia is a knave.
Assume Sofia is a knave. No contradiction is found in their false claim that Lily is not a knight.
Assume Amelia is a knight. No contradiction is found in their claim that Sofia is not a knight.
Therefore, (1) Lily is a knight
(2) Amelia is a knight
(3) Henry is a knight
(4) David is a knave
(5) Sofia is a knave </think>
<answer> (1) Lily is a knight
(2) Amelia is a knight
(3) Henry is a knight
(4) David is a knave
(5) Sofia is a knave </answer>
Lily Amelia Henry David Sofia
(1) Lily is a knight
(2) Amelia is a knight
(3) Henry is a knight
(4) David is a knave
(5) Sofia is a knave
(('lying', 3), ('not', ('telling-truth', 4)), ('lying', 4), ('<=>', ('lying', 0), ('telling-truth', 2)), ('not', ('telling-truth', 0)))
rule