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: Emily, Avery, Matthew, Jack, Chloe, and Sofia. "Sofia is a knave and Matthew is a knight" - Emily. In Avery's words: "Jack is a knight". Matthew asserted: "If Emily is a knight then Matthew is a knight". Jack asserted: "Matthew is a knight". Chloe expressed that Avery is a knight and Jack is a knave. Sofia noted, "Matthew is a knave or Jack is a knave". 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 Emily is a knight.  No contradiction is found in their claim that Sofia is a knave and Matthew is a knight.
 Sofia cannot be a knight, because this would contradict the claim of Emily that Sofia is a knave and Matthew is a knight.
 Assume Sofia is a knave.  No contradiction is found in their false claim that Matthew is a knave or Jack is a knave.
 Assume Matthew is a knight.  No contradiction is found in their claim that If Emily is a knight then Matthew is a knight.
 Assume Jack is a knight.  No contradiction is found in their claim that Matthew is a knight.
 Assume Avery is a knight.  No contradiction is found in their claim that Jack is a knight.
 Chloe cannot be a knight, because this would contradict the claim of their own that Avery is a knight and Jack is a knave.
 Assume Chloe is a knave.  No contradiction is found in their false claim that Avery is a knight and Jack is a knave.
 Therefore, (1) Emily is a knight
 (2) Avery is a knight
 (3) Matthew is a knight
 (4) Jack is a knight
 (5) Chloe is a knave
 (6) Sofia 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 6 inhabitants: Emily, Avery, Matthew, Jack, Chloe, and Sofia. "Sofia is a knave and Matthew is a knight" - Emily. In Avery's words: "Jack is a knight". Matthew asserted: "If Emily is a knight then Matthew is a knight". Jack asserted: "Matthew is a knight". Chloe expressed that Avery is a knight and Jack is a knave. Sofia noted, "Matthew is a knave or Jack is a knave". 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 Emily is a knight. No contradiction is found in their claim that Sofia is a knave and Matthew is a knight.
Sofia cannot be a knight, because this would contradict the claim of Emily that Sofia is a knave and Matthew is a knight.
Assume Sofia is a knave. No contradiction is found in their false claim that Matthew is a knave or Jack is a knave.
Assume Matthew is a knight. No contradiction is found in their claim that If Emily is a knight then Matthew is a knight.
Assume Jack is a knight. No contradiction is found in their claim that Matthew is a knight.
Assume Avery is a knight. No contradiction is found in their claim that Jack is a knight.
Chloe cannot be a knight, because this would contradict the claim of their own that Avery is a knight and Jack is a knave.
Assume Chloe is a knave. No contradiction is found in their false claim that Avery is a knight and Jack is a knave.
Therefore, (1) Emily is a knight
(2) Avery is a knight
(3) Matthew is a knight
(4) Jack is a knight
(5) Chloe is a knave
(6) Sofia is a knave </think>
<answer> (1) Emily is a knight
(2) Avery is a knight
(3) Matthew is a knight
(4) Jack is a knight
(5) Chloe is a knave
(6) Sofia is a knave </answer>
Emily Avery Matthew Jack Chloe Sofia
(1) Emily is a knight
(2) Avery is a knight
(3) Matthew is a knight
(4) Jack is a knight
(5) Chloe is a knave
(6) Sofia is a knave
(('and', ('lying', 5), ('telling-truth', 2)), ('telling-truth', 3), ('->', ('telling-truth', 0), ('telling-truth', 2)), ('telling-truth', 2), ('and', ('telling-truth', 1), ('lying', 3)), ('or', ('lying', 2), ('lying', 3)))
rule