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: Aiden, Benjamin, Amelia, Zoey, Alexander, Avery, and Logan. Aiden stated, "If Logan is a knight then Amelia is a knight". "Alexander is not a knave," Benjamin declared. In Amelia's words: "Benjamin is a knight if and only if Amelia is a knight". In Zoey's words: "Logan is a knight". Alexander asserted: "Zoey is not a knave". Avery expressed that Benjamin is a knave or Alexander is a knave. Logan asserted: "Alexander is a knave or Amelia 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 If Logan is a knight then Amelia is a knight.
 Assume Logan is a knight.  No contradiction is found in their claim that Alexander is a knave or Amelia is a knight.
 Assume Alexander is a knight.  No contradiction is found in their claim that Zoey is not a knave.
 Assume Zoey is a knight.  No contradiction is found in their claim that Logan is a knight.
 Assume Amelia is a knight.  No contradiction is found in their claim that Benjamin is a knight if and only if Amelia is a knight.
 Assume Benjamin is a knight.  No contradiction is found in their claim that Alexander is not a knave.
 Avery cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave or Alexander is a knave.
 Assume Avery is a knave.  No contradiction is found in their false claim that Benjamin is a knave or Alexander is a knave.
 Therefore, (1) Aiden is a knight
 (2) Benjamin is a knight
 (3) Amelia is a knight
 (4) Zoey is a knight
 (5) Alexander is a knight
 (6) Avery is a knave
 (7) Logan 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: Aiden, Benjamin, Amelia, Zoey, Alexander, Avery, and Logan. Aiden stated, "If Logan is a knight then Amelia is a knight". "Alexander is not a knave," Benjamin declared. In Amelia's words: "Benjamin is a knight if and only if Amelia is a knight". In Zoey's words: "Logan is a knight". Alexander asserted: "Zoey is not a knave". Avery expressed that Benjamin is a knave or Alexander is a knave. Logan asserted: "Alexander is a knave or Amelia 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 If Logan is a knight then Amelia is a knight.
Assume Logan is a knight. No contradiction is found in their claim that Alexander is a knave or Amelia is a knight.
Assume Alexander is a knight. No contradiction is found in their claim that Zoey is not a knave.
Assume Zoey is a knight. No contradiction is found in their claim that Logan is a knight.
Assume Amelia is a knight. No contradiction is found in their claim that Benjamin is a knight if and only if Amelia is a knight.
Assume Benjamin is a knight. No contradiction is found in their claim that Alexander is not a knave.
Avery cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave or Alexander is a knave.
Assume Avery is a knave. No contradiction is found in their false claim that Benjamin is a knave or Alexander is a knave.
Therefore, (1) Aiden is a knight
(2) Benjamin is a knight
(3) Amelia is a knight
(4) Zoey is a knight
(5) Alexander is a knight
(6) Avery is a knave
(7) Logan is a knight </think>
<answer> (1) Aiden is a knight
(2) Benjamin is a knight
(3) Amelia is a knight
(4) Zoey is a knight
(5) Alexander is a knight
(6) Avery is a knave
(7) Logan is a knight </answer>
Aiden Benjamin Amelia Zoey Alexander Avery Logan
(1) Aiden is a knight
(2) Benjamin is a knight
(3) Amelia is a knight
(4) Zoey is a knight
(5) Alexander is a knight
(6) Avery is a knave
(7) Logan is a knight
(('->', ('telling-truth', 6), ('telling-truth', 2)), ('not', ('lying', 4)), ('<=>', ('telling-truth', 1), ('telling-truth', 2)), ('telling-truth', 6), ('not', ('lying', 3)), ('or', ('lying', 1), ('lying', 4)), ('or', ('lying', 4), ('telling-truth', 2)))
rule