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: Emily, Harper, Aiden, David, Abigail, Joseph, and Jack. In a statement by Emily: "Harper is a knave and Jack is a knight". "David is not a knight," Harper mentioned. Aiden said, "Jack is a knave or Emily is a knave." "Emily is a knight or Jack is a knight," David claimed. Abigail stated, "If Jack is a knight then Aiden is a knave". "Jack is a knave if and only if David is a knave," Joseph claimed. Jack asserted: "If Abigail is a knight then Joseph 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 Emily is a knight.  No contradiction is found in their claim that Harper is a knave and Jack is a knight.
 Harper cannot be a knight, because this would contradict the claim of Emily that Harper is a knave and Jack is a knight.
 Assume Harper is a knave.  No contradiction is found in their false claim that David is not a knight.
 Assume David is a knight.  No contradiction is found in their claim that Emily is a knight or Jack is a knight.
 Assume Jack is a knight.  No contradiction is found in their claim that If Abigail is a knight then Joseph is a knave.
 Assume Abigail is a knight.  No contradiction is found in their claim that If Jack is a knight then Aiden is a knave.
 Aiden cannot be a knight, because this would contradict the claim of their own that Jack is a knave or Emily is a knave.
 Assume Aiden is a knave.  No contradiction is found in their false claim that Jack is a knave or Emily is a knave.
 Joseph cannot be a knight, because this would contradict the claim of Jack that If Abigail is a knight then Joseph is a knave.
 Joseph cannot be a knave, because this would contradict the false claim of their own that Jack is a knave if and only if David is a knave.
 We have exhausted all possibilities for Joseph and Aiden, so let us go back and reconsider Abigail.
 Assume Abigail is a knave.  No contradiction is found in their false claim that If Jack is a knight then Aiden is a knave.
 Aiden cannot be a knight, because this would contradict the claim of their own that Jack is a knave or Emily is a knave.
 Aiden cannot be a knave, because this would contradict the false claim of Abigail that If Jack is a knight then Aiden is a knave.
 We have exhausted all possibilities for Aiden and Abigail, so let us go back and reconsider Jack.
 Jack cannot be a knave, because this would contradict the claim of Emily that Harper is a knave and Jack is a knight.
 We have exhausted all possibilities for Jack, so let us go back and reconsider David.
 David cannot be a knave, because this would contradict the false claim of Harper that David is not a knight.
 We have exhausted all possibilities for David and Harper, so let us go back and reconsider Emily.
 Assume Emily is a knave.  No contradiction is found in their false claim that Harper is a knave and Jack is a knight.
 Assume Harper is a knight.  No contradiction is found in their claim that David is not a knight.
 David cannot be a knight, because this would contradict the claim of Harper that David is not a knight.
 Assume David is a knave.  No contradiction is found in their false claim that Emily is a knight or Jack is a knight.
 Jack cannot be a knight, because this would contradict the false claim of David that Emily is a knight or Jack is a knight.
 Assume Jack is a knave.  No contradiction is found in their false claim that If Abigail is a knight then Joseph is a knave.
 Assume Abigail is a knight.  No contradiction is found in their claim that If Jack is a knight then Aiden is a knave.
 Assume Aiden is a knight.  No contradiction is found in their claim that Jack is a knave or Emily is a knave.
 Assume Joseph is a knight.  No contradiction is found in their claim that Jack is a knave if and only if David is a knave.
 Therefore, (1) Emily is a knave
 (2) Harper is a knight
 (3) Aiden is a knight
 (4) David is a knave
 (5) Abigail is a knight
 (6) Joseph is a knight
 (7) Jack 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: Emily, Harper, Aiden, David, Abigail, Joseph, and Jack. In a statement by Emily: "Harper is a knave and Jack is a knight". "David is not a knight," Harper mentioned. Aiden said, "Jack is a knave or Emily is a knave." "Emily is a knight or Jack is a knight," David claimed. Abigail stated, "If Jack is a knight then Aiden is a knave". "Jack is a knave if and only if David is a knave," Joseph claimed. Jack asserted: "If Abigail is a knight then Joseph 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 Emily is a knight. No contradiction is found in their claim that Harper is a knave and Jack is a knight.
Harper cannot be a knight, because this would contradict the claim of Emily that Harper is a knave and Jack is a knight.
Assume Harper is a knave. No contradiction is found in their false claim that David is not a knight.
Assume David is a knight. No contradiction is found in their claim that Emily is a knight or Jack is a knight.
Assume Jack is a knight. No contradiction is found in their claim that If Abigail is a knight then Joseph is a knave.
Assume Abigail is a knight. No contradiction is found in their claim that If Jack is a knight then Aiden is a knave.
Aiden cannot be a knight, because this would contradict the claim of their own that Jack is a knave or Emily is a knave.
Assume Aiden is a knave. No contradiction is found in their false claim that Jack is a knave or Emily is a knave.
Joseph cannot be a knight, because this would contradict the claim of Jack that If Abigail is a knight then Joseph is a knave.
Joseph cannot be a knave, because this would contradict the false claim of their own that Jack is a knave if and only if David is a knave.
We have exhausted all possibilities for Joseph and Aiden, so let us go back and reconsider Abigail.
Assume Abigail is a knave. No contradiction is found in their false claim that If Jack is a knight then Aiden is a knave.
Aiden cannot be a knight, because this would contradict the claim of their own that Jack is a knave or Emily is a knave.
Aiden cannot be a knave, because this would contradict the false claim of Abigail that If Jack is a knight then Aiden is a knave.
We have exhausted all possibilities for Aiden and Abigail, so let us go back and reconsider Jack.
Jack cannot be a knave, because this would contradict the claim of Emily that Harper is a knave and Jack is a knight.
We have exhausted all possibilities for Jack, so let us go back and reconsider David.
David cannot be a knave, because this would contradict the false claim of Harper that David is not a knight.
We have exhausted all possibilities for David and Harper, so let us go back and reconsider Emily.
Assume Emily is a knave. No contradiction is found in their false claim that Harper is a knave and Jack is a knight.
Assume Harper is a knight. No contradiction is found in their claim that David is not a knight.
David cannot be a knight, because this would contradict the claim of Harper that David is not a knight.
Assume David is a knave. No contradiction is found in their false claim that Emily is a knight or Jack is a knight.
Jack cannot be a knight, because this would contradict the false claim of David that Emily is a knight or Jack is a knight.
Assume Jack is a knave. No contradiction is found in their false claim that If Abigail is a knight then Joseph is a knave.
Assume Abigail is a knight. No contradiction is found in their claim that If Jack is a knight then Aiden is a knave.
Assume Aiden is a knight. No contradiction is found in their claim that Jack is a knave or Emily is a knave.
Assume Joseph is a knight. No contradiction is found in their claim that Jack is a knave if and only if David is a knave.
Therefore, (1) Emily is a knave
(2) Harper is a knight
(3) Aiden is a knight
(4) David is a knave
(5) Abigail is a knight
(6) Joseph is a knight
(7) Jack is a knave </think>
<answer> (1) Emily is a knave
(2) Harper is a knight
(3) Aiden is a knight
(4) David is a knave
(5) Abigail is a knight
(6) Joseph is a knight
(7) Jack is a knave </answer>
Emily Harper Aiden David Abigail Joseph Jack
(1) Emily is a knave
(2) Harper is a knight
(3) Aiden is a knight
(4) David is a knave
(5) Abigail is a knight
(6) Joseph is a knight
(7) Jack is a knave
(('and', ('lying', 1), ('telling-truth', 6)), ('not', ('telling-truth', 3)), ('or', ('lying', 6), ('lying', 0)), ('or', ('telling-truth', 0), ('telling-truth', 6)), ('->', ('telling-truth', 6), ('lying', 2)), ('<=>', ('lying', 6), ('lying', 3)), ('->', ('telling-truth', 4), ('lying', 5)))
rule