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: Aurora, Avery, Emma, Abigail, Jackson, Joseph, and Oliver. Aurora told you that Jackson is not a knave. "Abigail is a knave and Jackson is a knight," Avery declared. Emma commented, "Abigail is a knave if and only if Avery is a knave". Abigail stated, "Abigail is a knight and Aurora is a knight". Jackson said, "Emma is a knight or Abigail is a knight." "Abigail is not a knight," Joseph claimed. As Oliver put it, "Emma 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 Aurora is a knight.  No contradiction is found in their claim that Jackson is not a knave.
 Assume Jackson is a knight.  No contradiction is found in their claim that Emma is a knight or Abigail is a knight.
 Assume Emma is a knight.  No contradiction is found in their claim that Abigail is a knave if and only if Avery is a knave.
 Assume Abigail is a knight.  No contradiction is found in their claim that Abigail is a knight and Aurora is a knight.
 Avery cannot be a knight, because this would contradict the claim of their own that Abigail is a knave and Jackson is a knight.
 Avery cannot be a knave, because this would contradict the claim of Emma that Abigail is a knave if and only if Avery is a knave.
 We have exhausted all possibilities for Avery, so let us go back and reconsider Abigail.
 Assume Abigail is a knave.  No contradiction is found in their false claim that Abigail is a knight and Aurora is a knight.
 Avery cannot be a knight, because this would contradict the claim of Emma that Abigail is a knave if and only if Avery is a knave.
 Avery cannot be a knave, because this would contradict the false claim of their own that Abigail is a knave and Jackson is a knight.
 We have exhausted all possibilities for Avery and Abigail, so let us go back and reconsider Emma.
 Assume Emma is a knave.  No contradiction is found in their false claim that Abigail is a knave if and only if Avery is a knave.
 Assume Abigail is a knight.  No contradiction is found in their claim that Abigail is a knight and Aurora is a knight.
 Avery cannot be a knight, because this would contradict the claim of their own that Abigail is a knave and Jackson is a knight.
 Assume Avery is a knave.  No contradiction is found in their false claim that Abigail is a knave and Jackson is a knight.
 Joseph cannot be a knight, because this would contradict the claim of their own that Abigail is not a knight.
 Assume Joseph is a knave.  No contradiction is found in their false claim that Abigail is not a knight.
 Assume Oliver is a knight.  No contradiction is found in their claim that Emma is a knave.
 Therefore, (1) Aurora is a knight
 (2) Avery is a knave
 (3) Emma is a knave
 (4) Abigail is a knight
 (5) Jackson is a knight
 (6) Joseph is a knave
 (7) Oliver 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 7 inhabitants: Aurora, Avery, Emma, Abigail, Jackson, Joseph, and Oliver. Aurora told you that Jackson is not a knave. "Abigail is a knave and Jackson is a knight," Avery declared. Emma commented, "Abigail is a knave if and only if Avery is a knave". Abigail stated, "Abigail is a knight and Aurora is a knight". Jackson said, "Emma is a knight or Abigail is a knight." "Abigail is not a knight," Joseph claimed. As Oliver put it, "Emma 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 Aurora is a knight. No contradiction is found in their claim that Jackson is not a knave.
Assume Jackson is a knight. No contradiction is found in their claim that Emma is a knight or Abigail is a knight.
Assume Emma is a knight. No contradiction is found in their claim that Abigail is a knave if and only if Avery is a knave.
Assume Abigail is a knight. No contradiction is found in their claim that Abigail is a knight and Aurora is a knight.
Avery cannot be a knight, because this would contradict the claim of their own that Abigail is a knave and Jackson is a knight.
Avery cannot be a knave, because this would contradict the claim of Emma that Abigail is a knave if and only if Avery is a knave.
We have exhausted all possibilities for Avery, so let us go back and reconsider Abigail.
Assume Abigail is a knave. No contradiction is found in their false claim that Abigail is a knight and Aurora is a knight.
Avery cannot be a knight, because this would contradict the claim of Emma that Abigail is a knave if and only if Avery is a knave.
Avery cannot be a knave, because this would contradict the false claim of their own that Abigail is a knave and Jackson is a knight.
We have exhausted all possibilities for Avery and Abigail, so let us go back and reconsider Emma.
Assume Emma is a knave. No contradiction is found in their false claim that Abigail is a knave if and only if Avery is a knave.
Assume Abigail is a knight. No contradiction is found in their claim that Abigail is a knight and Aurora is a knight.
Avery cannot be a knight, because this would contradict the claim of their own that Abigail is a knave and Jackson is a knight.
Assume Avery is a knave. No contradiction is found in their false claim that Abigail is a knave and Jackson is a knight.
Joseph cannot be a knight, because this would contradict the claim of their own that Abigail is not a knight.
Assume Joseph is a knave. No contradiction is found in their false claim that Abigail is not a knight.
Assume Oliver is a knight. No contradiction is found in their claim that Emma is a knave.
Therefore, (1) Aurora is a knight
(2) Avery is a knave
(3) Emma is a knave
(4) Abigail is a knight
(5) Jackson is a knight
(6) Joseph is a knave
(7) Oliver is a knight </think>
<answer> (1) Aurora is a knight
(2) Avery is a knave
(3) Emma is a knave
(4) Abigail is a knight
(5) Jackson is a knight
(6) Joseph is a knave
(7) Oliver is a knight </answer>
Aurora Avery Emma Abigail Jackson Joseph Oliver
(1) Aurora is a knight
(2) Avery is a knave
(3) Emma is a knave
(4) Abigail is a knight
(5) Jackson is a knight
(6) Joseph is a knave
(7) Oliver is a knight
(('not', ('lying', 4)), ('and', ('lying', 3), ('telling-truth', 4)), ('<=>', ('lying', 3), ('lying', 1)), ('and', ('telling-truth', 3), ('telling-truth', 0)), ('or', ('telling-truth', 2), ('telling-truth', 3)), ('not', ('telling-truth', 3)), ('lying', 2))
rule