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 6 inhabitants: Riley, Charlotte, Aurora, Mia, William, and Elizabeth. "If Aurora is a knight then Elizabeth is a knight" - Riley. In Charlotte's words: "Elizabeth is a knave or Mia is a knave". In Aurora's words: "William is a knight". "Elizabeth is a knave and Mia is a knight" - Mia. William asserted: "Charlotte is a knave". In a statement by Elizabeth: "If Mia is a knave then Riley is 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 Riley is a knight.  No contradiction is found in their claim that If Aurora is a knight then Elizabeth is a knight.
 Assume Aurora is a knight.  No contradiction is found in their claim that William is a knight.
 Assume William is a knight.  No contradiction is found in their claim that Charlotte is a knave.
 Charlotte cannot be a knight, because this would contradict the claim of William that Charlotte is a knave.
 Assume Charlotte is a knave.  No contradiction is found in their false claim that Elizabeth is a knave or Mia is a knave.
 Assume Elizabeth is a knight.  No contradiction is found in their claim that If Mia is a knave then Riley is a knave.
 Mia cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave and Mia is a knight.
 Mia cannot be a knave, because this would contradict the false claim of Charlotte that Elizabeth is a knave or Mia is a knave.
 We have exhausted all possibilities for Mia, so let us go back and reconsider Elizabeth.
 Elizabeth cannot be a knave, because this would contradict the claim of Riley that If Aurora is a knight then Elizabeth is a knight.
 We have exhausted all possibilities for Elizabeth and Charlotte, so let us go back and reconsider William.
 William cannot be a knave, because this would contradict the claim of Aurora that William is a knight.
 We have exhausted all possibilities for William, so let us go back and reconsider Aurora.
 Assume Aurora is a knave.  No contradiction is found in their false claim that William is a knight.
 William cannot be a knight, because this would contradict the false claim of Aurora that William is a knight.
 Assume William is a knave.  No contradiction is found in their false claim that Charlotte is a knave.
 Assume Charlotte is a knight.  No contradiction is found in their claim that Elizabeth is a knave or Mia is a knave.
 Assume Elizabeth is a knight.  No contradiction is found in their claim that If Mia is a knave then Riley is a knave.
 Mia cannot be a knight, because this would contradict the claim of Charlotte that Elizabeth is a knave or Mia is a knave.
 Mia cannot be a knave, because this would contradict the claim of Elizabeth that If Mia is a knave then Riley is a knave.
 We have exhausted all possibilities for Mia, so let us go back and reconsider Elizabeth.
 Assume Elizabeth is a knave.  No contradiction is found in their false claim that If Mia is a knave then Riley is a knave.
 Mia cannot be a knight, because this would contradict the false claim of Elizabeth that If Mia is a knave then Riley is a knave.
 Assume Mia is a knave.  No contradiction is found in their false claim that Elizabeth is a knave and Mia is a knight.
 Therefore, (1) Riley is a knight
 (2) Charlotte is a knight
 (3) Aurora is a knave
 (4) Mia is a knave
 (5) William is a knave
 (6) Elizabeth 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 6 inhabitants: Riley, Charlotte, Aurora, Mia, William, and Elizabeth. "If Aurora is a knight then Elizabeth is a knight" - Riley. In Charlotte's words: "Elizabeth is a knave or Mia is a knave". In Aurora's words: "William is a knight". "Elizabeth is a knave and Mia is a knight" - Mia. William asserted: "Charlotte is a knave". In a statement by Elizabeth: "If Mia is a knave then Riley is 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 Riley is a knight. No contradiction is found in their claim that If Aurora is a knight then Elizabeth is a knight.
Assume Aurora is a knight. No contradiction is found in their claim that William is a knight.
Assume William is a knight. No contradiction is found in their claim that Charlotte is a knave.
Charlotte cannot be a knight, because this would contradict the claim of William that Charlotte is a knave.
Assume Charlotte is a knave. No contradiction is found in their false claim that Elizabeth is a knave or Mia is a knave.
Assume Elizabeth is a knight. No contradiction is found in their claim that If Mia is a knave then Riley is a knave.
Mia cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knave and Mia is a knight.
Mia cannot be a knave, because this would contradict the false claim of Charlotte that Elizabeth is a knave or Mia is a knave.
We have exhausted all possibilities for Mia, so let us go back and reconsider Elizabeth.
Elizabeth cannot be a knave, because this would contradict the claim of Riley that If Aurora is a knight then Elizabeth is a knight.
We have exhausted all possibilities for Elizabeth and Charlotte, so let us go back and reconsider William.
William cannot be a knave, because this would contradict the claim of Aurora that William is a knight.
We have exhausted all possibilities for William, so let us go back and reconsider Aurora.
Assume Aurora is a knave. No contradiction is found in their false claim that William is a knight.
William cannot be a knight, because this would contradict the false claim of Aurora that William is a knight.
Assume William is a knave. No contradiction is found in their false claim that Charlotte is a knave.
Assume Charlotte is a knight. No contradiction is found in their claim that Elizabeth is a knave or Mia is a knave.
Assume Elizabeth is a knight. No contradiction is found in their claim that If Mia is a knave then Riley is a knave.
Mia cannot be a knight, because this would contradict the claim of Charlotte that Elizabeth is a knave or Mia is a knave.
Mia cannot be a knave, because this would contradict the claim of Elizabeth that If Mia is a knave then Riley is a knave.
We have exhausted all possibilities for Mia, so let us go back and reconsider Elizabeth.
Assume Elizabeth is a knave. No contradiction is found in their false claim that If Mia is a knave then Riley is a knave.
Mia cannot be a knight, because this would contradict the false claim of Elizabeth that If Mia is a knave then Riley is a knave.
Assume Mia is a knave. No contradiction is found in their false claim that Elizabeth is a knave and Mia is a knight.
Therefore, (1) Riley is a knight
(2) Charlotte is a knight
(3) Aurora is a knave
(4) Mia is a knave
(5) William is a knave
(6) Elizabeth is a knave </think>
<answer> (1) Riley is a knight
(2) Charlotte is a knight
(3) Aurora is a knave
(4) Mia is a knave
(5) William is a knave
(6) Elizabeth is a knave </answer>
Riley Charlotte Aurora Mia William Elizabeth
(1) Riley is a knight
(2) Charlotte is a knight
(3) Aurora is a knave
(4) Mia is a knave
(5) William is a knave
(6) Elizabeth is a knave
(('->', ('telling-truth', 2), ('telling-truth', 5)), ('or', ('lying', 5), ('lying', 3)), ('telling-truth', 4), ('and', ('lying', 5), ('telling-truth', 3)), ('lying', 1), ('->', ('lying', 3), ('lying', 0)))
rule