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 4 inhabitants: Aurora, David, Ava, and William. Aurora commented, "David is a knight and David is a knave". David said, "Aurora is a knight and Aurora is a knave." "If William is a knave then Aurora is a knave," Ava mentioned. William stated, "Ava is not 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
Aurora cannot be a knight, because this would contradict the claim of their own that David is a knight and David is a knave.
 Assume Aurora is a knave.  No contradiction is found in their false claim that David is a knight and David is a knave.
 David cannot be a knight, because this would contradict the claim of their own that Aurora is a knight and Aurora is a knave.
 Assume David is a knave.  No contradiction is found in their false claim that Aurora is a knight and Aurora is a knave.
 Assume Ava is a knight.  No contradiction is found in their claim that If William is a knave then Aurora is a knave.
 Assume William is a knight.  No contradiction is found in their claim that Ava is not a knave.
 Therefore, (1) Aurora is a knave
 (2) David is a knave
 (3) Ava is a knight
 (4) William 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 4 inhabitants: Aurora, David, Ava, and William. Aurora commented, "David is a knight and David is a knave". David said, "Aurora is a knight and Aurora is a knave." "If William is a knave then Aurora is a knave," Ava mentioned. William stated, "Ava is not 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> 
Aurora cannot be a knight, because this would contradict the claim of their own that David is a knight and David is a knave.
Assume Aurora is a knave. No contradiction is found in their false claim that David is a knight and David is a knave.
David cannot be a knight, because this would contradict the claim of their own that Aurora is a knight and Aurora is a knave.
Assume David is a knave. No contradiction is found in their false claim that Aurora is a knight and Aurora is a knave.
Assume Ava is a knight. No contradiction is found in their claim that If William is a knave then Aurora is a knave.
Assume William is a knight. No contradiction is found in their claim that Ava is not a knave.
Therefore, (1) Aurora is a knave
(2) David is a knave
(3) Ava is a knight
(4) William is a knight </think>
<answer> (1) Aurora is a knave
(2) David is a knave
(3) Ava is a knight
(4) William is a knight </answer>
Aurora David Ava William
(1) Aurora is a knave
(2) David is a knave
(3) Ava is a knight
(4) William is a knight
(('and', ('telling-truth', 1), ('lying', 1)), ('and', ('telling-truth', 0), ('lying', 0)), ('->', ('lying', 3), ('lying', 0)), ('not', ('lying', 2)))
rule