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: Benjamin, Ava, Matthew, Sebastian, Mason, Jack, and Mia. Benjamin said that Sebastian is not a knight. "Mia is a knave if and only if Benjamin is a knave," Ava declared. As Matthew put it, "Mason is a knave if and only if Sebastian is a knave". In a statement by Sebastian: "Benjamin is a knave if and only if Matthew is a knight". Mason commented, "Benjamin is a knave if and only if Sebastian is a knight". In Jack's words: "Ava is a knave if and only if Mia is a knave". As Mia put it, "Jack is a knight and Matthew 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 Benjamin is a knight.  No contradiction is found in their claim that Sebastian is not a knight.
 Sebastian cannot be a knight, because this would contradict the claim of Benjamin that Sebastian is not a knight.
 Assume Sebastian is a knave.  No contradiction is found in their false claim that Benjamin is a knave if and only if Matthew is a knight.
 Assume Matthew is a knight.  No contradiction is found in their claim that Mason is a knave if and only if Sebastian is a knave.
 Mason cannot be a knight, because this would contradict the claim of Matthew that Mason is a knave if and only if Sebastian is a knave.
 Mason cannot be a knave, because this would contradict the false claim of their own that Benjamin is a knave if and only if Sebastian is a knight.
 We have exhausted all possibilities for Mason, so let us go back and reconsider Matthew.
 Matthew cannot be a knave, because this would contradict the false claim of Sebastian that Benjamin is a knave if and only if Matthew is a knight.
 We have exhausted all possibilities for Matthew and Sebastian, so let us go back and reconsider Benjamin.
 Assume Benjamin is a knave.  No contradiction is found in their false claim that Sebastian is not a knight.
 Assume Sebastian is a knight.  No contradiction is found in their claim that Benjamin is a knave if and only if Matthew is a knight.
 Assume Matthew is a knight.  No contradiction is found in their claim that Mason is a knave if and only if Sebastian is a knave.
 Assume Mason is a knight.  No contradiction is found in their claim that Benjamin is a knave if and only if Sebastian is a knight.
 Assume Ava is a knight.  No contradiction is found in their claim that Mia is a knave if and only if Benjamin is a knave.
 Mia cannot be a knight, because this would contradict the claim of Ava that Mia is a knave if and only if Benjamin is a knave.
 Assume Mia is a knave.  No contradiction is found in their false claim that Jack is a knight and Matthew is a knave.
 Jack cannot be a knight, because this would contradict the claim of their own that Ava is a knave if and only if Mia is a knave.
 Assume Jack is a knave.  No contradiction is found in their false claim that Ava is a knave if and only if Mia is a knave.
 Therefore, (1) Benjamin is a knave
 (2) Ava is a knight
 (3) Matthew is a knight
 (4) Sebastian is a knight
 (5) Mason is a knight
 (6) Jack is a knave
 (7) Mia 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 7 inhabitants: Benjamin, Ava, Matthew, Sebastian, Mason, Jack, and Mia. Benjamin said that Sebastian is not a knight. "Mia is a knave if and only if Benjamin is a knave," Ava declared. As Matthew put it, "Mason is a knave if and only if Sebastian is a knave". In a statement by Sebastian: "Benjamin is a knave if and only if Matthew is a knight". Mason commented, "Benjamin is a knave if and only if Sebastian is a knight". In Jack's words: "Ava is a knave if and only if Mia is a knave". As Mia put it, "Jack is a knight and Matthew 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 Benjamin is a knight. No contradiction is found in their claim that Sebastian is not a knight.
Sebastian cannot be a knight, because this would contradict the claim of Benjamin that Sebastian is not a knight.
Assume Sebastian is a knave. No contradiction is found in their false claim that Benjamin is a knave if and only if Matthew is a knight.
Assume Matthew is a knight. No contradiction is found in their claim that Mason is a knave if and only if Sebastian is a knave.
Mason cannot be a knight, because this would contradict the claim of Matthew that Mason is a knave if and only if Sebastian is a knave.
Mason cannot be a knave, because this would contradict the false claim of their own that Benjamin is a knave if and only if Sebastian is a knight.
We have exhausted all possibilities for Mason, so let us go back and reconsider Matthew.
Matthew cannot be a knave, because this would contradict the false claim of Sebastian that Benjamin is a knave if and only if Matthew is a knight.
We have exhausted all possibilities for Matthew and Sebastian, so let us go back and reconsider Benjamin.
Assume Benjamin is a knave. No contradiction is found in their false claim that Sebastian is not a knight.
Assume Sebastian is a knight. No contradiction is found in their claim that Benjamin is a knave if and only if Matthew is a knight.
Assume Matthew is a knight. No contradiction is found in their claim that Mason is a knave if and only if Sebastian is a knave.
Assume Mason is a knight. No contradiction is found in their claim that Benjamin is a knave if and only if Sebastian is a knight.
Assume Ava is a knight. No contradiction is found in their claim that Mia is a knave if and only if Benjamin is a knave.
Mia cannot be a knight, because this would contradict the claim of Ava that Mia is a knave if and only if Benjamin is a knave.
Assume Mia is a knave. No contradiction is found in their false claim that Jack is a knight and Matthew is a knave.
Jack cannot be a knight, because this would contradict the claim of their own that Ava is a knave if and only if Mia is a knave.
Assume Jack is a knave. No contradiction is found in their false claim that Ava is a knave if and only if Mia is a knave.
Therefore, (1) Benjamin is a knave
(2) Ava is a knight
(3) Matthew is a knight
(4) Sebastian is a knight
(5) Mason is a knight
(6) Jack is a knave
(7) Mia is a knave </think>
<answer> (1) Benjamin is a knave
(2) Ava is a knight
(3) Matthew is a knight
(4) Sebastian is a knight
(5) Mason is a knight
(6) Jack is a knave
(7) Mia is a knave </answer>
Benjamin Ava Matthew Sebastian Mason Jack Mia
(1) Benjamin is a knave
(2) Ava is a knight
(3) Matthew is a knight
(4) Sebastian is a knight
(5) Mason is a knight
(6) Jack is a knave
(7) Mia is a knave
(('not', ('telling-truth', 3)), ('<=>', ('lying', 6), ('lying', 0)), ('<=>', ('lying', 4), ('lying', 3)), ('<=>', ('lying', 0), ('telling-truth', 2)), ('<=>', ('lying', 0), ('telling-truth', 3)), ('<=>', ('lying', 1), ('lying', 6)), ('and', ('telling-truth', 5), ('lying', 2)))
rule