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: Emma, Evelyn, Olivia, Aria, and Victoria. Emma expressed that Emma is a knight and Aria is a knave. In a statement by Evelyn: "Victoria is a knave if and only if Aria is a knave". In Olivia's words: "If Emma is a knight then Victoria is a knight". As Aria put it, "Victoria is a knave or Olivia is a knave". In Victoria's words: "Emma is a knave if and only if Olivia is 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 Emma is a knight.  No contradiction is found in their claim that Emma is a knight and Aria is a knave.
 Aria cannot be a knight, because this would contradict the claim of Emma that Emma is a knight and Aria is a knave.
 Assume Aria is a knave.  No contradiction is found in their false claim that Victoria is a knave or Olivia is a knave.
 Assume Victoria is a knight.  No contradiction is found in their claim that Emma is a knave if and only if Olivia is a knight.
 Olivia cannot be a knight, because this would contradict the claim of Victoria that Emma is a knave if and only if Olivia is a knight.
 Olivia cannot be a knave, because this would contradict the false claim of their own that If Emma is a knight then Victoria is a knight.
 We have exhausted all possibilities for Olivia, so let us go back and reconsider Victoria.
 Victoria cannot be a knave, because this would contradict the false claim of Aria that Victoria is a knave or Olivia is a knave.
 We have exhausted all possibilities for Victoria and Aria, so let us go back and reconsider Emma.
 Assume Emma is a knave.  No contradiction is found in their false claim that Emma is a knight and Aria is a knave.
 Assume Aria is a knight.  No contradiction is found in their claim that Victoria is a knave or Olivia is a knave.
 Assume Victoria is a knight.  No contradiction is found in their claim that Emma is a knave if and only if Olivia is a knight.
 Olivia cannot be a knight, because this would contradict the claim of Aria that Victoria is a knave or Olivia is a knave.
 Olivia cannot be a knave, because this would contradict the false claim of their own that If Emma is a knight then Victoria is a knight.
 We have exhausted all possibilities for Olivia, so let us go back and reconsider Victoria.
 Assume Victoria is a knave.  No contradiction is found in their false claim that Emma is a knave if and only if Olivia is a knight.
 Olivia cannot be a knight, because this would contradict the false claim of Victoria that Emma is a knave if and only if Olivia is a knight.
 Olivia cannot be a knave, because this would contradict the false claim of their own that If Emma is a knight then Victoria is a knight.
 We have exhausted all possibilities for Olivia and Victoria, so let us go back and reconsider Aria.
 Assume Aria is a knave.  No contradiction is found in their false claim that Victoria is a knave or Olivia is a knave.
 Assume Victoria is a knight.  No contradiction is found in their claim that Emma is a knave if and only if Olivia is a knight.
 Assume Olivia is a knight.  No contradiction is found in their claim that If Emma is a knight then Victoria is a knight.
 Evelyn cannot be a knight, because this would contradict the claim of their own that Victoria is a knave if and only if Aria is a knave.
 Assume Evelyn is a knave.  No contradiction is found in their false claim that Victoria is a knave if and only if Aria is a knave.
 Therefore, (1) Emma is a knave
 (2) Evelyn is a knave
 (3) Olivia is a knight
 (4) Aria is a knave
 (5) Victoria 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: Emma, Evelyn, Olivia, Aria, and Victoria. Emma expressed that Emma is a knight and Aria is a knave. In a statement by Evelyn: "Victoria is a knave if and only if Aria is a knave". In Olivia's words: "If Emma is a knight then Victoria is a knight". As Aria put it, "Victoria is a knave or Olivia is a knave". In Victoria's words: "Emma is a knave if and only if Olivia is 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 Emma is a knight. No contradiction is found in their claim that Emma is a knight and Aria is a knave.
Aria cannot be a knight, because this would contradict the claim of Emma that Emma is a knight and Aria is a knave.
Assume Aria is a knave. No contradiction is found in their false claim that Victoria is a knave or Olivia is a knave.
Assume Victoria is a knight. No contradiction is found in their claim that Emma is a knave if and only if Olivia is a knight.
Olivia cannot be a knight, because this would contradict the claim of Victoria that Emma is a knave if and only if Olivia is a knight.
Olivia cannot be a knave, because this would contradict the false claim of their own that If Emma is a knight then Victoria is a knight.
We have exhausted all possibilities for Olivia, so let us go back and reconsider Victoria.
Victoria cannot be a knave, because this would contradict the false claim of Aria that Victoria is a knave or Olivia is a knave.
We have exhausted all possibilities for Victoria and Aria, so let us go back and reconsider Emma.
Assume Emma is a knave. No contradiction is found in their false claim that Emma is a knight and Aria is a knave.
Assume Aria is a knight. No contradiction is found in their claim that Victoria is a knave or Olivia is a knave.
Assume Victoria is a knight. No contradiction is found in their claim that Emma is a knave if and only if Olivia is a knight.
Olivia cannot be a knight, because this would contradict the claim of Aria that Victoria is a knave or Olivia is a knave.
Olivia cannot be a knave, because this would contradict the false claim of their own that If Emma is a knight then Victoria is a knight.
We have exhausted all possibilities for Olivia, so let us go back and reconsider Victoria.
Assume Victoria is a knave. No contradiction is found in their false claim that Emma is a knave if and only if Olivia is a knight.
Olivia cannot be a knight, because this would contradict the false claim of Victoria that Emma is a knave if and only if Olivia is a knight.
Olivia cannot be a knave, because this would contradict the false claim of their own that If Emma is a knight then Victoria is a knight.
We have exhausted all possibilities for Olivia and Victoria, so let us go back and reconsider Aria.
Assume Aria is a knave. No contradiction is found in their false claim that Victoria is a knave or Olivia is a knave.
Assume Victoria is a knight. No contradiction is found in their claim that Emma is a knave if and only if Olivia is a knight.
Assume Olivia is a knight. No contradiction is found in their claim that If Emma is a knight then Victoria is a knight.
Evelyn cannot be a knight, because this would contradict the claim of their own that Victoria is a knave if and only if Aria is a knave.
Assume Evelyn is a knave. No contradiction is found in their false claim that Victoria is a knave if and only if Aria is a knave.
Therefore, (1) Emma is a knave
(2) Evelyn is a knave
(3) Olivia is a knight
(4) Aria is a knave
(5) Victoria is a knight </think>
<answer> (1) Emma is a knave
(2) Evelyn is a knave
(3) Olivia is a knight
(4) Aria is a knave
(5) Victoria is a knight </answer>
Emma Evelyn Olivia Aria Victoria
(1) Emma is a knave
(2) Evelyn is a knave
(3) Olivia is a knight
(4) Aria is a knave
(5) Victoria is a knight
(('and', ('telling-truth', 0), ('lying', 3)), ('<=>', ('lying', 4), ('lying', 3)), ('->', ('telling-truth', 0), ('telling-truth', 4)), ('or', ('lying', 4), ('lying', 2)), ('<=>', ('lying', 0), ('telling-truth', 2)))
rule