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: Aria, Victoria, Elizabeth, Mia, and Evelyn. In a statement by Aria: "Aria is a knight and Elizabeth is a knight". Victoria stated, "Aria is a knight". Elizabeth remarked, "If Aria is a knight then Victoria is a knight". Mia told you that Evelyn is a knight. "If Aria is a knight then Mia is a knave," Evelyn mentioned. 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 Aria is a knight.  No contradiction is found in their claim that Aria is a knight and Elizabeth is a knight.
 Assume Elizabeth is a knight.  No contradiction is found in their claim that If Aria is a knight then Victoria is a knight.
 Assume Victoria is a knight.  No contradiction is found in their claim that Aria is a knight.
 Assume Mia is a knight.  No contradiction is found in their claim that Evelyn is a knight.
 Evelyn cannot be a knight, because this would contradict the claim of their own that If Aria is a knight then Mia is a knave.
 Evelyn cannot be a knave, because this would contradict the claim of Mia that Evelyn is a knight.
 We have exhausted all possibilities for Evelyn, so let us go back and reconsider Mia.
 Assume Mia is a knave.  No contradiction is found in their false claim that Evelyn is a knight.
 Evelyn cannot be a knight, because this would contradict the false claim of Mia that Evelyn is a knight.
 Evelyn cannot be a knave, because this would contradict the false claim of their own that If Aria is a knight then Mia is a knave.
 We have exhausted all possibilities for Evelyn and Mia, so let us go back and reconsider Victoria.
 Victoria cannot be a knave, because this would contradict the false claim of their own that Aria is a knight.
 We have exhausted all possibilities for Victoria, so let us go back and reconsider Elizabeth.
 Elizabeth cannot be a knave, because this would contradict the claim of Aria that Aria is a knight and Elizabeth is a knight.
 We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Aria.
 Assume Aria is a knave.  No contradiction is found in their false claim that Aria is a knight and Elizabeth is a knight.
 Assume Elizabeth is a knight.  No contradiction is found in their claim that If Aria is a knight then Victoria is a knight.
 Victoria cannot be a knight, because this would contradict the claim of their own that Aria is a knight.
 Assume Victoria is a knave.  No contradiction is found in their false claim that Aria is a knight.
 Assume Mia is a knight.  No contradiction is found in their claim that Evelyn is a knight.
 Assume Evelyn is a knight.  No contradiction is found in their claim that If Aria is a knight then Mia is a knave.
 Therefore, (1) Aria is a knave
 (2) Victoria is a knave
 (3) Elizabeth is a knight
 (4) Mia is a knight
 (5) Evelyn 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: Aria, Victoria, Elizabeth, Mia, and Evelyn. In a statement by Aria: "Aria is a knight and Elizabeth is a knight". Victoria stated, "Aria is a knight". Elizabeth remarked, "If Aria is a knight then Victoria is a knight". Mia told you that Evelyn is a knight. "If Aria is a knight then Mia is a knave," Evelyn mentioned. 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 Aria is a knight. No contradiction is found in their claim that Aria is a knight and Elizabeth is a knight.
Assume Elizabeth is a knight. No contradiction is found in their claim that If Aria is a knight then Victoria is a knight.
Assume Victoria is a knight. No contradiction is found in their claim that Aria is a knight.
Assume Mia is a knight. No contradiction is found in their claim that Evelyn is a knight.
Evelyn cannot be a knight, because this would contradict the claim of their own that If Aria is a knight then Mia is a knave.
Evelyn cannot be a knave, because this would contradict the claim of Mia that Evelyn is a knight.
We have exhausted all possibilities for Evelyn, so let us go back and reconsider Mia.
Assume Mia is a knave. No contradiction is found in their false claim that Evelyn is a knight.
Evelyn cannot be a knight, because this would contradict the false claim of Mia that Evelyn is a knight.
Evelyn cannot be a knave, because this would contradict the false claim of their own that If Aria is a knight then Mia is a knave.
We have exhausted all possibilities for Evelyn and Mia, so let us go back and reconsider Victoria.
Victoria cannot be a knave, because this would contradict the false claim of their own that Aria is a knight.
We have exhausted all possibilities for Victoria, so let us go back and reconsider Elizabeth.
Elizabeth cannot be a knave, because this would contradict the claim of Aria that Aria is a knight and Elizabeth is a knight.
We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Aria.
Assume Aria is a knave. No contradiction is found in their false claim that Aria is a knight and Elizabeth is a knight.
Assume Elizabeth is a knight. No contradiction is found in their claim that If Aria is a knight then Victoria is a knight.
Victoria cannot be a knight, because this would contradict the claim of their own that Aria is a knight.
Assume Victoria is a knave. No contradiction is found in their false claim that Aria is a knight.
Assume Mia is a knight. No contradiction is found in their claim that Evelyn is a knight.
Assume Evelyn is a knight. No contradiction is found in their claim that If Aria is a knight then Mia is a knave.
Therefore, (1) Aria is a knave
(2) Victoria is a knave
(3) Elizabeth is a knight
(4) Mia is a knight
(5) Evelyn is a knight </think>
<answer> (1) Aria is a knave
(2) Victoria is a knave
(3) Elizabeth is a knight
(4) Mia is a knight
(5) Evelyn is a knight </answer>
Aria Victoria Elizabeth Mia Evelyn
(1) Aria is a knave
(2) Victoria is a knave
(3) Elizabeth is a knight
(4) Mia is a knight
(5) Evelyn is a knight
(('and', ('telling-truth', 0), ('telling-truth', 2)), ('telling-truth', 0), ('->', ('telling-truth', 0), ('telling-truth', 1)), ('telling-truth', 4), ('->', ('telling-truth', 0), ('lying', 3)))
rule