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: Joseph, Emily, Ava, Jack, Abigail, Benjamin, and Matthew. Joseph commented, "Matthew is a knight if and only if Abigail is a knight". "Abigail is a knave and Ava is a knight" - Emily. Ava expressed that Jack is a knight and Emily is a knight. Jack asserted: "Abigail is a knight and Matthew is a knight". "Matthew is a knight" - Abigail. Benjamin told you that Abigail is a knave or Benjamin is a knight. Matthew noted, "Jack is a knight if and only if Benjamin 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 Joseph is a knight.  No contradiction is found in their claim that Matthew is a knight if and only if Abigail is a knight.
 Assume Matthew is a knight.  No contradiction is found in their claim that Jack is a knight if and only if Benjamin is a knave.
 Assume Jack is a knight.  No contradiction is found in their claim that Abigail is a knight and Matthew is a knight.
 Assume Abigail is a knight.  No contradiction is found in their claim that Matthew is a knight.
 Benjamin cannot be a knight, because this would contradict the claim of Matthew that Jack is a knight if and only if Benjamin is a knave.
 Assume Benjamin is a knave.  No contradiction is found in their false claim that Abigail is a knave or Benjamin is a knight.
 Emily cannot be a knight, because this would contradict the claim of their own that Abigail is a knave and Ava is a knight.
 Assume Emily is a knave.  No contradiction is found in their false claim that Abigail is a knave and Ava is a knight.
 Ava cannot be a knight, because this would contradict the claim of their own that Jack is a knight and Emily is a knight.
 Assume Ava is a knave.  No contradiction is found in their false claim that Jack is a knight and Emily is a knight.
 Therefore, (1) Joseph is a knight
 (2) Emily is a knave
 (3) Ava is a knave
 (4) Jack is a knight
 (5) Abigail is a knight
 (6) Benjamin is a knave
 (7) Matthew 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: Joseph, Emily, Ava, Jack, Abigail, Benjamin, and Matthew. Joseph commented, "Matthew is a knight if and only if Abigail is a knight". "Abigail is a knave and Ava is a knight" - Emily. Ava expressed that Jack is a knight and Emily is a knight. Jack asserted: "Abigail is a knight and Matthew is a knight". "Matthew is a knight" - Abigail. Benjamin told you that Abigail is a knave or Benjamin is a knight. Matthew noted, "Jack is a knight if and only if Benjamin 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 Joseph is a knight. No contradiction is found in their claim that Matthew is a knight if and only if Abigail is a knight.
Assume Matthew is a knight. No contradiction is found in their claim that Jack is a knight if and only if Benjamin is a knave.
Assume Jack is a knight. No contradiction is found in their claim that Abigail is a knight and Matthew is a knight.
Assume Abigail is a knight. No contradiction is found in their claim that Matthew is a knight.
Benjamin cannot be a knight, because this would contradict the claim of Matthew that Jack is a knight if and only if Benjamin is a knave.
Assume Benjamin is a knave. No contradiction is found in their false claim that Abigail is a knave or Benjamin is a knight.
Emily cannot be a knight, because this would contradict the claim of their own that Abigail is a knave and Ava is a knight.
Assume Emily is a knave. No contradiction is found in their false claim that Abigail is a knave and Ava is a knight.
Ava cannot be a knight, because this would contradict the claim of their own that Jack is a knight and Emily is a knight.
Assume Ava is a knave. No contradiction is found in their false claim that Jack is a knight and Emily is a knight.
Therefore, (1) Joseph is a knight
(2) Emily is a knave
(3) Ava is a knave
(4) Jack is a knight
(5) Abigail is a knight
(6) Benjamin is a knave
(7) Matthew is a knight </think>
<answer> (1) Joseph is a knight
(2) Emily is a knave
(3) Ava is a knave
(4) Jack is a knight
(5) Abigail is a knight
(6) Benjamin is a knave
(7) Matthew is a knight </answer>
Joseph Emily Ava Jack Abigail Benjamin Matthew
(1) Joseph is a knight
(2) Emily is a knave
(3) Ava is a knave
(4) Jack is a knight
(5) Abigail is a knight
(6) Benjamin is a knave
(7) Matthew is a knight
(('<=>', ('telling-truth', 6), ('telling-truth', 4)), ('and', ('lying', 4), ('telling-truth', 2)), ('and', ('telling-truth', 3), ('telling-truth', 1)), ('and', ('telling-truth', 4), ('telling-truth', 6)), ('telling-truth', 6), ('or', ('lying', 4), ('telling-truth', 5)), ('<=>', ('telling-truth', 3), ('lying', 5)))
rule