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 5 inhabitants: Avery, Aria, Amelia, Alexander, and Benjamin. Avery asserted: "Amelia is a knight or Benjamin is a knight". "If Benjamin is a knave then Amelia is a knight," Aria declared. Amelia commented, "Aria is a knight if and only if Benjamin is a knight". Alexander noted, "If Avery is a knave then Aria is a knight". In Benjamin's words: "If Alexander is a knight then Benjamin 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 Avery is a knight.  No contradiction is found in their claim that Amelia is a knight or Benjamin is a knight.
 Assume Amelia is a knight.  No contradiction is found in their claim that Aria is a knight if and only if Benjamin is a knight.
 Assume Aria is a knight.  No contradiction is found in their claim that If Benjamin is a knave then Amelia is a knight.
 Assume Benjamin is a knight.  No contradiction is found in their claim that If Alexander is a knight then Benjamin is a knight.
 Assume Alexander is a knight.  No contradiction is found in their claim that If Avery is a knave then Aria is a knight.
 Therefore, (1) Avery is a knight
 (2) Aria is a knight
 (3) Amelia is a knight
 (4) Alexander is a knight
 (5) Benjamin 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 5 inhabitants: Avery, Aria, Amelia, Alexander, and Benjamin. Avery asserted: "Amelia is a knight or Benjamin is a knight". "If Benjamin is a knave then Amelia is a knight," Aria declared. Amelia commented, "Aria is a knight if and only if Benjamin is a knight". Alexander noted, "If Avery is a knave then Aria is a knight". In Benjamin's words: "If Alexander is a knight then Benjamin 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 Avery is a knight. No contradiction is found in their claim that Amelia is a knight or Benjamin is a knight.
Assume Amelia is a knight. No contradiction is found in their claim that Aria is a knight if and only if Benjamin is a knight.
Assume Aria is a knight. No contradiction is found in their claim that If Benjamin is a knave then Amelia is a knight.
Assume Benjamin is a knight. No contradiction is found in their claim that If Alexander is a knight then Benjamin is a knight.
Assume Alexander is a knight. No contradiction is found in their claim that If Avery is a knave then Aria is a knight.
Therefore, (1) Avery is a knight
(2) Aria is a knight
(3) Amelia is a knight
(4) Alexander is a knight
(5) Benjamin is a knight </think>
<answer> (1) Avery is a knight
(2) Aria is a knight
(3) Amelia is a knight
(4) Alexander is a knight
(5) Benjamin is a knight </answer>
Avery Aria Amelia Alexander Benjamin
(1) Avery is a knight
(2) Aria is a knight
(3) Amelia is a knight
(4) Alexander is a knight
(5) Benjamin is a knight
(('or', ('telling-truth', 2), ('telling-truth', 4)), ('->', ('lying', 4), ('telling-truth', 2)), ('<=>', ('telling-truth', 1), ('telling-truth', 4)), ('->', ('lying', 0), ('telling-truth', 1)), ('->', ('telling-truth', 3), ('telling-truth', 4)))
rule