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: Penelope, Elizabeth, Mia, Emily, and Ava. Penelope remarked, "Mia is a knave if and only if Emily is a knight". Elizabeth expressed that If Emily is a knight then Elizabeth is a knight. Mia stated, "Mia is a knight if and only if Ava is a knight". Emily stated, "Mia is a knave and Ava is a knave". Ava noted, "Mia 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 Penelope is a knight.  No contradiction is found in their claim that Mia is a knave if and only if Emily is a knight.
 Assume Mia is a knight.  No contradiction is found in their claim that Mia is a knight if and only if Ava is a knight.
 Assume Ava is a knight.  No contradiction is found in their claim that Mia is not a knave.
 Emily cannot be a knight, because this would contradict the claim of Penelope that Mia is a knave if and only if Emily is a knight.
 Assume Emily is a knave.  No contradiction is found in their false claim that Mia is a knave and Ava is a knave.
 Assume Elizabeth is a knight.  No contradiction is found in their claim that If Emily is a knight then Elizabeth is a knight.
 Therefore, (1) Penelope is a knight
 (2) Elizabeth is a knight
 (3) Mia is a knight
 (4) Emily is a knave
 (5) Ava 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: Penelope, Elizabeth, Mia, Emily, and Ava. Penelope remarked, "Mia is a knave if and only if Emily is a knight". Elizabeth expressed that If Emily is a knight then Elizabeth is a knight. Mia stated, "Mia is a knight if and only if Ava is a knight". Emily stated, "Mia is a knave and Ava is a knave". Ava noted, "Mia 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 Penelope is a knight. No contradiction is found in their claim that Mia is a knave if and only if Emily is a knight.
Assume Mia is a knight. No contradiction is found in their claim that Mia is a knight if and only if Ava is a knight.
Assume Ava is a knight. No contradiction is found in their claim that Mia is not a knave.
Emily cannot be a knight, because this would contradict the claim of Penelope that Mia is a knave if and only if Emily is a knight.
Assume Emily is a knave. No contradiction is found in their false claim that Mia is a knave and Ava is a knave.
Assume Elizabeth is a knight. No contradiction is found in their claim that If Emily is a knight then Elizabeth is a knight.
Therefore, (1) Penelope is a knight
(2) Elizabeth is a knight
(3) Mia is a knight
(4) Emily is a knave
(5) Ava is a knight </think>
<answer> (1) Penelope is a knight
(2) Elizabeth is a knight
(3) Mia is a knight
(4) Emily is a knave
(5) Ava is a knight </answer>
Penelope Elizabeth Mia Emily Ava
(1) Penelope is a knight
(2) Elizabeth is a knight
(3) Mia is a knight
(4) Emily is a knave
(5) Ava is a knight
(('<=>', ('lying', 2), ('telling-truth', 3)), ('->', ('telling-truth', 3), ('telling-truth', 1)), ('<=>', ('telling-truth', 2), ('telling-truth', 4)), ('and', ('lying', 2), ('lying', 4)), ('not', ('lying', 2)))
rule