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: Aiden, Abigail, Joseph, Jack, Mason, and David. Aiden expressed that Mason is not a knave. Abigail told you that Aiden is not a knight. Joseph said, "Mason is a knight and David is a knight." According to Jack, "Abigail is not a knight". "Joseph is a knave if and only if Jack is a knave," Mason declared. "If David is a knight then Jack is a knight," David mentioned. 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 Aiden is a knight.  No contradiction is found in their claim that Mason is not a knave.
 Assume Mason is a knight.  No contradiction is found in their claim that Joseph is a knave if and only if Jack is a knave.
 Assume Joseph is a knight.  No contradiction is found in their claim that Mason is a knight and David is a knight.
 Assume David is a knight.  No contradiction is found in their claim that If David is a knight then Jack is a knight.
 Assume Jack is a knight.  No contradiction is found in their claim that Abigail is not a knight.
 Abigail cannot be a knight, because this would contradict the claim of their own that Aiden is not a knight.
 Assume Abigail is a knave.  No contradiction is found in their false claim that Aiden is not a knight.
 Therefore, (1) Aiden is a knight
 (2) Abigail is a knave
 (3) Joseph is a knight
 (4) Jack is a knight
 (5) Mason is a knight
 (6) David 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 6 inhabitants: Aiden, Abigail, Joseph, Jack, Mason, and David. Aiden expressed that Mason is not a knave. Abigail told you that Aiden is not a knight. Joseph said, "Mason is a knight and David is a knight." According to Jack, "Abigail is not a knight". "Joseph is a knave if and only if Jack is a knave," Mason declared. "If David is a knight then Jack is a knight," David mentioned. 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 Aiden is a knight. No contradiction is found in their claim that Mason is not a knave.
Assume Mason is a knight. No contradiction is found in their claim that Joseph is a knave if and only if Jack is a knave.
Assume Joseph is a knight. No contradiction is found in their claim that Mason is a knight and David is a knight.
Assume David is a knight. No contradiction is found in their claim that If David is a knight then Jack is a knight.
Assume Jack is a knight. No contradiction is found in their claim that Abigail is not a knight.
Abigail cannot be a knight, because this would contradict the claim of their own that Aiden is not a knight.
Assume Abigail is a knave. No contradiction is found in their false claim that Aiden is not a knight.
Therefore, (1) Aiden is a knight
(2) Abigail is a knave
(3) Joseph is a knight
(4) Jack is a knight
(5) Mason is a knight
(6) David is a knight </think>
<answer> (1) Aiden is a knight
(2) Abigail is a knave
(3) Joseph is a knight
(4) Jack is a knight
(5) Mason is a knight
(6) David is a knight </answer>
Aiden Abigail Joseph Jack Mason David
(1) Aiden is a knight
(2) Abigail is a knave
(3) Joseph is a knight
(4) Jack is a knight
(5) Mason is a knight
(6) David is a knight
(('not', ('lying', 4)), ('not', ('telling-truth', 0)), ('and', ('telling-truth', 4), ('telling-truth', 5)), ('not', ('telling-truth', 1)), ('<=>', ('lying', 2), ('lying', 3)), ('->', ('telling-truth', 5), ('telling-truth', 3)))
rule