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, William, Jacob, Harper, Grace, and Sebastian. "Jacob is a knight or Grace is a knight," Aiden declared. William told you that Grace is a knight or Jacob is a knave. "If Sebastian is a knave then Harper is a knight," Jacob claimed. Harper remarked, "Aiden is a knave if and only if William is a knight". Grace noted, "Jacob is a knight". Sebastian asserted: "Sebastian 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 Aiden is a knight.  No contradiction is found in their claim that Jacob is a knight or Grace is a knight.
 Assume Jacob is a knight.  No contradiction is found in their claim that If Sebastian is a knave then Harper is a knight.
 Assume Sebastian is a knight.  No contradiction is found in their claim that Sebastian is a knight.
 Assume Harper is a knight.  No contradiction is found in their claim that Aiden is a knave if and only if William is a knight.
 William cannot be a knight, because this would contradict the claim of Harper that Aiden is a knave if and only if William is a knight.
 Assume William is a knave.  No contradiction is found in their false claim that Grace is a knight or Jacob is a knave.
 Grace cannot be a knight, because this would contradict the false claim of William that Grace is a knight or Jacob is a knave.
 Grace cannot be a knave, because this would contradict the false claim of their own that Jacob is a knight.
 We have exhausted all possibilities for Grace and William, so let us go back and reconsider Harper.
 Assume Harper is a knave.  No contradiction is found in their false claim that Aiden is a knave if and only if William is a knight.
 Assume William is a knight.  No contradiction is found in their claim that Grace is a knight or Jacob is a knave.
 Assume Grace is a knight.  No contradiction is found in their claim that Jacob is a knight.
 Therefore, (1) Aiden is a knight
 (2) William is a knight
 (3) Jacob is a knight
 (4) Harper is a knave
 (5) Grace is a knight
 (6) Sebastian 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, William, Jacob, Harper, Grace, and Sebastian. "Jacob is a knight or Grace is a knight," Aiden declared. William told you that Grace is a knight or Jacob is a knave. "If Sebastian is a knave then Harper is a knight," Jacob claimed. Harper remarked, "Aiden is a knave if and only if William is a knight". Grace noted, "Jacob is a knight". Sebastian asserted: "Sebastian 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 Aiden is a knight. No contradiction is found in their claim that Jacob is a knight or Grace is a knight.
Assume Jacob is a knight. No contradiction is found in their claim that If Sebastian is a knave then Harper is a knight.
Assume Sebastian is a knight. No contradiction is found in their claim that Sebastian is a knight.
Assume Harper is a knight. No contradiction is found in their claim that Aiden is a knave if and only if William is a knight.
William cannot be a knight, because this would contradict the claim of Harper that Aiden is a knave if and only if William is a knight.
Assume William is a knave. No contradiction is found in their false claim that Grace is a knight or Jacob is a knave.
Grace cannot be a knight, because this would contradict the false claim of William that Grace is a knight or Jacob is a knave.
Grace cannot be a knave, because this would contradict the false claim of their own that Jacob is a knight.
We have exhausted all possibilities for Grace and William, so let us go back and reconsider Harper.
Assume Harper is a knave. No contradiction is found in their false claim that Aiden is a knave if and only if William is a knight.
Assume William is a knight. No contradiction is found in their claim that Grace is a knight or Jacob is a knave.
Assume Grace is a knight. No contradiction is found in their claim that Jacob is a knight.
Therefore, (1) Aiden is a knight
(2) William is a knight
(3) Jacob is a knight
(4) Harper is a knave
(5) Grace is a knight
(6) Sebastian is a knight </think>
<answer> (1) Aiden is a knight
(2) William is a knight
(3) Jacob is a knight
(4) Harper is a knave
(5) Grace is a knight
(6) Sebastian is a knight </answer>
Aiden William Jacob Harper Grace Sebastian
(1) Aiden is a knight
(2) William is a knight
(3) Jacob is a knight
(4) Harper is a knave
(5) Grace is a knight
(6) Sebastian is a knight
(('or', ('telling-truth', 2), ('telling-truth', 4)), ('or', ('telling-truth', 4), ('lying', 2)), ('->', ('lying', 5), ('telling-truth', 3)), ('<=>', ('lying', 0), ('telling-truth', 1)), ('telling-truth', 2), ('telling-truth', 5))
rule