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: Ava, Abigail, Aiden, Jack, Harper, and Oliver. Ava asserted: "Abigail is a knave or Jack is a knight". "If Harper is a knight then Aiden is a knave," Abigail claimed. Aiden stated, "If Harper is a knight then Ava is a knave". Jack noted, "Harper is a knave if and only if Aiden is a knight". Harper asserted: "Oliver is not a knight". Oliver expressed that Oliver is a knight and Harper 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 Ava is a knight.  No contradiction is found in their claim that Abigail is a knave or Jack is a knight.
 Assume Abigail is a knight.  No contradiction is found in their claim that If Harper is a knight then Aiden is a knave.
 Assume Harper is a knight.  No contradiction is found in their claim that Oliver is not a knight.
 Oliver cannot be a knight, because this would contradict the claim of Harper that Oliver is not a knight.
 Assume Oliver is a knave.  No contradiction is found in their false claim that Oliver is a knight and Harper is a knight.
 Aiden cannot be a knight, because this would contradict the claim of Abigail that If Harper is a knight then Aiden is a knave.
 Assume Aiden is a knave.  No contradiction is found in their false claim that If Harper is a knight then Ava is a knave.
 Assume Jack is a knight.  No contradiction is found in their claim that Harper is a knave if and only if Aiden is a knight.
 Therefore, (1) Ava is a knight
 (2) Abigail is a knight
 (3) Aiden is a knave
 (4) Jack is a knight
 (5) Harper is a knight
 (6) Oliver 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: Ava, Abigail, Aiden, Jack, Harper, and Oliver. Ava asserted: "Abigail is a knave or Jack is a knight". "If Harper is a knight then Aiden is a knave," Abigail claimed. Aiden stated, "If Harper is a knight then Ava is a knave". Jack noted, "Harper is a knave if and only if Aiden is a knight". Harper asserted: "Oliver is not a knight". Oliver expressed that Oliver is a knight and Harper 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 Ava is a knight. No contradiction is found in their claim that Abigail is a knave or Jack is a knight.
Assume Abigail is a knight. No contradiction is found in their claim that If Harper is a knight then Aiden is a knave.
Assume Harper is a knight. No contradiction is found in their claim that Oliver is not a knight.
Oliver cannot be a knight, because this would contradict the claim of Harper that Oliver is not a knight.
Assume Oliver is a knave. No contradiction is found in their false claim that Oliver is a knight and Harper is a knight.
Aiden cannot be a knight, because this would contradict the claim of Abigail that If Harper is a knight then Aiden is a knave.
Assume Aiden is a knave. No contradiction is found in their false claim that If Harper is a knight then Ava is a knave.
Assume Jack is a knight. No contradiction is found in their claim that Harper is a knave if and only if Aiden is a knight.
Therefore, (1) Ava is a knight
(2) Abigail is a knight
(3) Aiden is a knave
(4) Jack is a knight
(5) Harper is a knight
(6) Oliver is a knave </think>
<answer> (1) Ava is a knight
(2) Abigail is a knight
(3) Aiden is a knave
(4) Jack is a knight
(5) Harper is a knight
(6) Oliver is a knave </answer>
Ava Abigail Aiden Jack Harper Oliver
(1) Ava is a knight
(2) Abigail is a knight
(3) Aiden is a knave
(4) Jack is a knight
(5) Harper is a knight
(6) Oliver is a knave
(('or', ('lying', 1), ('telling-truth', 3)), ('->', ('telling-truth', 4), ('lying', 2)), ('->', ('telling-truth', 4), ('lying', 0)), ('<=>', ('lying', 4), ('telling-truth', 2)), ('not', ('telling-truth', 5)), ('and', ('telling-truth', 5), ('telling-truth', 4)))
rule