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 7 inhabitants: Emma, Owen, Alexander, Sebastian, Aria, Ava, and William. Emma noted, "Owen is a knight if and only if Sebastian is a knave". As Owen put it, "Ava is a knight and Emma is a knight". Alexander noted, "Ava is a knight and William is a knave". "Owen is a knight" - Sebastian. Aria said that Owen is a knight. "Owen is a knave," Ava claimed. William was heard saying, "Aria is a knight and William 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 Owen is a knight if and only if Sebastian is a knave.
 Assume Owen is a knight.  No contradiction is found in their claim that Ava is a knight and Emma is a knight.
 Ava cannot be a knight, because this would contradict the claim of their own that Owen is a knave.
 Ava cannot be a knave, because this would contradict the claim of Owen that Ava is a knight and Emma is a knight.
 We have exhausted all possibilities for Ava, so let us go back and reconsider Owen.
 Assume Owen is a knave.  No contradiction is found in their false claim that Ava is a knight and Emma is a knight.
 Ava cannot be a knight, because this would contradict the false claim of Owen that Ava is a knight and Emma is a knight.
 Ava cannot be a knave, because this would contradict the false claim of their own that Owen is a knave.
 We have exhausted all possibilities for Ava and Owen, so let us go back and reconsider Emma.
 Assume Emma is a knave.  No contradiction is found in their false claim that Owen is a knight if and only if Sebastian is a knave.
 Owen cannot be a knight, because this would contradict the claim of their own that Ava is a knight and Emma is a knight.
 Assume Owen is a knave.  No contradiction is found in their false claim that Ava is a knight and Emma is a knight.
 Assume Ava is a knight.  No contradiction is found in their claim that Owen is a knave.
 Sebastian cannot be a knight, because this would contradict the false claim of Emma that Owen is a knight if and only if Sebastian is a knave.
 Assume Sebastian is a knave.  No contradiction is found in their false claim that Owen is a knight.
 Assume Alexander is a knight.  No contradiction is found in their claim that Ava is a knight and William is a knave.
 William cannot be a knight, because this would contradict the claim of Alexander that Ava is a knight and William is a knave.
 Assume William is a knave.  No contradiction is found in their false claim that Aria is a knight and William is a knight.
 Aria cannot be a knight, because this would contradict the claim of their own that Owen is a knight.
 Assume Aria is a knave.  No contradiction is found in their false claim that Owen is a knight.
 Therefore, (1) Emma is a knave
 (2) Owen is a knave
 (3) Alexander is a knight
 (4) Sebastian is a knave
 (5) Aria is a knave
 (6) Ava is a knight
 (7) William 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 7 inhabitants: Emma, Owen, Alexander, Sebastian, Aria, Ava, and William. Emma noted, "Owen is a knight if and only if Sebastian is a knave". As Owen put it, "Ava is a knight and Emma is a knight". Alexander noted, "Ava is a knight and William is a knave". "Owen is a knight" - Sebastian. Aria said that Owen is a knight. "Owen is a knave," Ava claimed. William was heard saying, "Aria is a knight and William 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 Owen is a knight if and only if Sebastian is a knave.
Assume Owen is a knight. No contradiction is found in their claim that Ava is a knight and Emma is a knight.
Ava cannot be a knight, because this would contradict the claim of their own that Owen is a knave.
Ava cannot be a knave, because this would contradict the claim of Owen that Ava is a knight and Emma is a knight.
We have exhausted all possibilities for Ava, so let us go back and reconsider Owen.
Assume Owen is a knave. No contradiction is found in their false claim that Ava is a knight and Emma is a knight.
Ava cannot be a knight, because this would contradict the false claim of Owen that Ava is a knight and Emma is a knight.
Ava cannot be a knave, because this would contradict the false claim of their own that Owen is a knave.
We have exhausted all possibilities for Ava and Owen, so let us go back and reconsider Emma.
Assume Emma is a knave. No contradiction is found in their false claim that Owen is a knight if and only if Sebastian is a knave.
Owen cannot be a knight, because this would contradict the claim of their own that Ava is a knight and Emma is a knight.
Assume Owen is a knave. No contradiction is found in their false claim that Ava is a knight and Emma is a knight.
Assume Ava is a knight. No contradiction is found in their claim that Owen is a knave.
Sebastian cannot be a knight, because this would contradict the false claim of Emma that Owen is a knight if and only if Sebastian is a knave.
Assume Sebastian is a knave. No contradiction is found in their false claim that Owen is a knight.
Assume Alexander is a knight. No contradiction is found in their claim that Ava is a knight and William is a knave.
William cannot be a knight, because this would contradict the claim of Alexander that Ava is a knight and William is a knave.
Assume William is a knave. No contradiction is found in their false claim that Aria is a knight and William is a knight.
Aria cannot be a knight, because this would contradict the claim of their own that Owen is a knight.
Assume Aria is a knave. No contradiction is found in their false claim that Owen is a knight.
Therefore, (1) Emma is a knave
(2) Owen is a knave
(3) Alexander is a knight
(4) Sebastian is a knave
(5) Aria is a knave
(6) Ava is a knight
(7) William is a knave </think>
<answer> (1) Emma is a knave
(2) Owen is a knave
(3) Alexander is a knight
(4) Sebastian is a knave
(5) Aria is a knave
(6) Ava is a knight
(7) William is a knave </answer>
Emma Owen Alexander Sebastian Aria Ava William
(1) Emma is a knave
(2) Owen is a knave
(3) Alexander is a knight
(4) Sebastian is a knave
(5) Aria is a knave
(6) Ava is a knight
(7) William is a knave
(('<=>', ('telling-truth', 1), ('lying', 3)), ('and', ('telling-truth', 5), ('telling-truth', 0)), ('and', ('telling-truth', 5), ('lying', 6)), ('telling-truth', 1), ('telling-truth', 1), ('lying', 1), ('and', ('telling-truth', 4), ('telling-truth', 6)))
rule