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