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: Penelope, Amelia, Oliver, Lily, Aiden, Henry, and Sofia. In Penelope's words: "Henry is a knave". "Aiden is a knave" - Amelia. Oliver remarked, "If Aiden is a knight then Sofia is a knave". "Henry is a knave and Lily is a knight," Lily declared. According to Aiden, "Lily is a knight if and only if Amelia is a knave". Henry said, "Aiden is a knight." Sofia commented, "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 Penelope 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 Penelope that Henry is a knave.
 Assume Henry is a knave.  No contradiction is found in their false claim that Aiden is a knight.
 Aiden cannot be a knight, because this would contradict the false claim of Henry that Aiden is a knight.
 Assume Aiden is a knave.  No contradiction is found in their false claim that Lily is a knight if and only if Amelia is a knave.
 Assume Lily is a knight.  No contradiction is found in their claim that Henry is a knave and Lily is a knight.
 Assume Amelia is a knight.  No contradiction is found in their claim that Aiden is a knave.
 Assume Oliver is a knight.  No contradiction is found in their claim that If Aiden is a knight then Sofia is a knave.
 Sofia cannot be a knight, because this would contradict the claim of their own that Lily is not a knight.
 Assume Sofia is a knave.  No contradiction is found in their false claim that Lily is not a knight.
 Therefore, (1) Penelope is a knight
 (2) Amelia is a knight
 (3) Oliver is a knight
 (4) Lily is a knight
 (5) Aiden is a knave
 (6) Henry is a knave
 (7) 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 7 inhabitants: Penelope, Amelia, Oliver, Lily, Aiden, Henry, and Sofia. In Penelope's words: "Henry is a knave". "Aiden is a knave" - Amelia. Oliver remarked, "If Aiden is a knight then Sofia is a knave". "Henry is a knave and Lily is a knight," Lily declared. According to Aiden, "Lily is a knight if and only if Amelia is a knave". Henry said, "Aiden is a knight." Sofia commented, "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 Penelope 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 Penelope that Henry is a knave.
Assume Henry is a knave. No contradiction is found in their false claim that Aiden is a knight.
Aiden cannot be a knight, because this would contradict the false claim of Henry that Aiden is a knight.
Assume Aiden is a knave. No contradiction is found in their false claim that Lily is a knight if and only if Amelia is a knave.
Assume Lily is a knight. No contradiction is found in their claim that Henry is a knave and Lily is a knight.
Assume Amelia is a knight. No contradiction is found in their claim that Aiden is a knave.
Assume Oliver is a knight. No contradiction is found in their claim that If Aiden is a knight then Sofia is a knave.
Sofia cannot be a knight, because this would contradict the claim of their own that Lily is not a knight.
Assume Sofia is a knave. No contradiction is found in their false claim that Lily is not a knight.
Therefore, (1) Penelope is a knight
(2) Amelia is a knight
(3) Oliver is a knight
(4) Lily is a knight
(5) Aiden is a knave
(6) Henry is a knave
(7) Sofia is a knave </think>
<answer> (1) Penelope is a knight
(2) Amelia is a knight
(3) Oliver is a knight
(4) Lily is a knight
(5) Aiden is a knave
(6) Henry is a knave
(7) Sofia is a knave </answer>
Penelope Amelia Oliver Lily Aiden Henry Sofia
(1) Penelope is a knight
(2) Amelia is a knight
(3) Oliver is a knight
(4) Lily is a knight
(5) Aiden is a knave
(6) Henry is a knave
(7) Sofia is a knave
(('lying', 5), ('lying', 4), ('->', ('telling-truth', 4), ('lying', 6)), ('and', ('lying', 5), ('telling-truth', 3)), ('<=>', ('telling-truth', 3), ('lying', 1)), ('telling-truth', 4), ('not', ('telling-truth', 3)))
rule