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: Harper, Benjamin, Olivia, Daniel, Henry, Jackson, and Sebastian. According to Harper, "Sebastian is a knave if and only if Henry is a knight". Benjamin asserted: "Henry is a knight if and only if Olivia is a knight". Olivia commented, "Benjamin is a knave and Daniel is a knave". Daniel stated, "Jackson is a knave". Henry told you that Olivia is not a knight. Jackson said that Harper is a knight and Benjamin is a knight. Sebastian told you that Daniel is a knight and Jackson 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 Harper is a knight.  No contradiction is found in their claim that Sebastian is a knave if and only if Henry is a knight.
 Assume Sebastian is a knight.  No contradiction is found in their claim that Daniel is a knight and Jackson is a knight.
 Assume Daniel is a knight.  No contradiction is found in their claim that Jackson is a knave.
 Jackson cannot be a knight, because this would contradict the claim of Daniel that Jackson is a knave.
 Jackson cannot be a knave, because this would contradict the claim of Sebastian that Daniel is a knight and Jackson is a knight.
 We have exhausted all possibilities for Jackson, so let us go back and reconsider Daniel.
 Daniel cannot be a knave, because this would contradict the claim of Sebastian that Daniel is a knight and Jackson is a knight.
 We have exhausted all possibilities for Daniel, so let us go back and reconsider Sebastian.
 Assume Sebastian is a knave.  No contradiction is found in their false claim that Daniel is a knight and Jackson is a knight.
 Assume Daniel is a knight.  No contradiction is found in their claim that Jackson is a knave.
 Jackson cannot be a knight, because this would contradict the claim of Daniel that Jackson is a knave.
 Assume Jackson is a knave.  No contradiction is found in their false claim that Harper is a knight and Benjamin is a knight.
 Benjamin cannot be a knight, because this would contradict the false claim of Jackson that Harper is a knight and Benjamin is a knight.
 Assume Benjamin is a knave.  No contradiction is found in their false claim that Henry is a knight if and only if Olivia is a knight.
 Assume Henry is a knight.  No contradiction is found in their claim that Olivia is not a knight.
 Olivia cannot be a knight, because this would contradict the false claim of Benjamin that Henry is a knight if and only if Olivia is a knight.
 Assume Olivia is a knave.  No contradiction is found in their false claim that Benjamin is a knave and Daniel is a knave.
 Therefore, (1) Harper is a knight
 (2) Benjamin is a knave
 (3) Olivia is a knave
 (4) Daniel is a knight
 (5) Henry is a knight
 (6) Jackson is a knave
 (7) Sebastian 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: Harper, Benjamin, Olivia, Daniel, Henry, Jackson, and Sebastian. According to Harper, "Sebastian is a knave if and only if Henry is a knight". Benjamin asserted: "Henry is a knight if and only if Olivia is a knight". Olivia commented, "Benjamin is a knave and Daniel is a knave". Daniel stated, "Jackson is a knave". Henry told you that Olivia is not a knight. Jackson said that Harper is a knight and Benjamin is a knight. Sebastian told you that Daniel is a knight and Jackson 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 Harper is a knight. No contradiction is found in their claim that Sebastian is a knave if and only if Henry is a knight.
Assume Sebastian is a knight. No contradiction is found in their claim that Daniel is a knight and Jackson is a knight.
Assume Daniel is a knight. No contradiction is found in their claim that Jackson is a knave.
Jackson cannot be a knight, because this would contradict the claim of Daniel that Jackson is a knave.
Jackson cannot be a knave, because this would contradict the claim of Sebastian that Daniel is a knight and Jackson is a knight.
We have exhausted all possibilities for Jackson, so let us go back and reconsider Daniel.
Daniel cannot be a knave, because this would contradict the claim of Sebastian that Daniel is a knight and Jackson is a knight.
We have exhausted all possibilities for Daniel, so let us go back and reconsider Sebastian.
Assume Sebastian is a knave. No contradiction is found in their false claim that Daniel is a knight and Jackson is a knight.
Assume Daniel is a knight. No contradiction is found in their claim that Jackson is a knave.
Jackson cannot be a knight, because this would contradict the claim of Daniel that Jackson is a knave.
Assume Jackson is a knave. No contradiction is found in their false claim that Harper is a knight and Benjamin is a knight.
Benjamin cannot be a knight, because this would contradict the false claim of Jackson that Harper is a knight and Benjamin is a knight.
Assume Benjamin is a knave. No contradiction is found in their false claim that Henry is a knight if and only if Olivia is a knight.
Assume Henry is a knight. No contradiction is found in their claim that Olivia is not a knight.
Olivia cannot be a knight, because this would contradict the false claim of Benjamin that Henry is a knight if and only if Olivia is a knight.
Assume Olivia is a knave. No contradiction is found in their false claim that Benjamin is a knave and Daniel is a knave.
Therefore, (1) Harper is a knight
(2) Benjamin is a knave
(3) Olivia is a knave
(4) Daniel is a knight
(5) Henry is a knight
(6) Jackson is a knave
(7) Sebastian is a knave </think>
<answer> (1) Harper is a knight
(2) Benjamin is a knave
(3) Olivia is a knave
(4) Daniel is a knight
(5) Henry is a knight
(6) Jackson is a knave
(7) Sebastian is a knave </answer>
Harper Benjamin Olivia Daniel Henry Jackson Sebastian
(1) Harper is a knight
(2) Benjamin is a knave
(3) Olivia is a knave
(4) Daniel is a knight
(5) Henry is a knight
(6) Jackson is a knave
(7) Sebastian is a knave
(('<=>', ('lying', 6), ('telling-truth', 4)), ('<=>', ('telling-truth', 4), ('telling-truth', 2)), ('and', ('lying', 1), ('lying', 3)), ('lying', 5), ('not', ('telling-truth', 2)), ('and', ('telling-truth', 0), ('telling-truth', 1)), ('and', ('telling-truth', 3), ('telling-truth', 5)))
rule