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 4 inhabitants: Elizabeth, Emma, Zoey, and Sebastian. "Emma is not a knight" - Elizabeth. In Emma's words: "If Zoey is a knave then Sebastian is a knight". "Elizabeth is a knight if and only if Emma is a knight," Zoey claimed. In a statement by Sebastian: "Zoey is a knave or Zoey 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 Elizabeth is a knight.  No contradiction is found in their claim that Emma is not a knight.
 Emma cannot be a knight, because this would contradict the claim of Elizabeth that Emma is not a knight.
 Assume Emma is a knave.  No contradiction is found in their false claim that If Zoey is a knave then Sebastian is a knight.
 Zoey cannot be a knight, because this would contradict the false claim of Emma that If Zoey is a knave then Sebastian is a knight.
 Assume Zoey is a knave.  No contradiction is found in their false claim that Elizabeth is a knight if and only if Emma is a knight.
 Sebastian cannot be a knight, because this would contradict the false claim of Emma that If Zoey is a knave then Sebastian is a knight.
 Sebastian cannot be a knave, because this would contradict the false claim of their own that Zoey is a knave or Zoey is a knight.
 We have exhausted all possibilities for Sebastian, Zoey, and Emma, so let us go back and reconsider Elizabeth.
 Assume Elizabeth is a knave.  No contradiction is found in their false claim that Emma is not a knight.
 Assume Emma is a knight.  No contradiction is found in their claim that If Zoey is a knave then Sebastian is a knight.
 Zoey cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight if and only if Emma is a knight.
 Assume Zoey is a knave.  No contradiction is found in their false claim that Elizabeth is a knight if and only if Emma is a knight.
 Assume Sebastian is a knight.  No contradiction is found in their claim that Zoey is a knave or Zoey is a knight.
 Therefore, (1) Elizabeth is a knave
 (2) Emma is a knight
 (3) Zoey is a knave
 (4) 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 4 inhabitants: Elizabeth, Emma, Zoey, and Sebastian. "Emma is not a knight" - Elizabeth. In Emma's words: "If Zoey is a knave then Sebastian is a knight". "Elizabeth is a knight if and only if Emma is a knight," Zoey claimed. In a statement by Sebastian: "Zoey is a knave or Zoey 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 Elizabeth is a knight. No contradiction is found in their claim that Emma is not a knight.
Emma cannot be a knight, because this would contradict the claim of Elizabeth that Emma is not a knight.
Assume Emma is a knave. No contradiction is found in their false claim that If Zoey is a knave then Sebastian is a knight.
Zoey cannot be a knight, because this would contradict the false claim of Emma that If Zoey is a knave then Sebastian is a knight.
Assume Zoey is a knave. No contradiction is found in their false claim that Elizabeth is a knight if and only if Emma is a knight.
Sebastian cannot be a knight, because this would contradict the false claim of Emma that If Zoey is a knave then Sebastian is a knight.
Sebastian cannot be a knave, because this would contradict the false claim of their own that Zoey is a knave or Zoey is a knight.
We have exhausted all possibilities for Sebastian, Zoey, and Emma, so let us go back and reconsider Elizabeth.
Assume Elizabeth is a knave. No contradiction is found in their false claim that Emma is not a knight.
Assume Emma is a knight. No contradiction is found in their claim that If Zoey is a knave then Sebastian is a knight.
Zoey cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight if and only if Emma is a knight.
Assume Zoey is a knave. No contradiction is found in their false claim that Elizabeth is a knight if and only if Emma is a knight.
Assume Sebastian is a knight. No contradiction is found in their claim that Zoey is a knave or Zoey is a knight.
Therefore, (1) Elizabeth is a knave
(2) Emma is a knight
(3) Zoey is a knave
(4) Sebastian is a knight </think>
<answer> (1) Elizabeth is a knave
(2) Emma is a knight
(3) Zoey is a knave
(4) Sebastian is a knight </answer>
Elizabeth Emma Zoey Sebastian
(1) Elizabeth is a knave
(2) Emma is a knight
(3) Zoey is a knave
(4) Sebastian is a knight
(('not', ('telling-truth', 1)), ('->', ('lying', 2), ('telling-truth', 3)), ('<=>', ('telling-truth', 0), ('telling-truth', 1)), ('or', ('lying', 2), ('telling-truth', 2)))
rule