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: Mason, Riley, Grace, Jacob, Aiden, Mia, and Benjamin. As Mason put it, "Jacob is a knave and Grace is a knight". Riley said, "Jacob is a knight." Grace stated, "Aiden is not a knave". "If Benjamin is a knight then Riley is a knave" - Jacob. Aiden was heard saying, "Mason is a knave if and only if Benjamin is a knight". In a statement by Mia: "Mason is a knave". According to Benjamin, "Mia is not 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 Mason is a knight.  No contradiction is found in their claim that Jacob is a knave and Grace is a knight.
 Jacob cannot be a knight, because this would contradict the claim of Mason that Jacob is a knave and Grace is a knight.
 Assume Jacob is a knave.  No contradiction is found in their false claim that If Benjamin is a knight then Riley is a knave.
 Assume Benjamin is a knight.  No contradiction is found in their claim that Mia is not a knight.
 Mia cannot be a knight, because this would contradict the claim of their own that Mason is a knave.
 Assume Mia is a knave.  No contradiction is found in their false claim that Mason is a knave.
 Riley cannot be a knight, because this would contradict the claim of their own that Jacob is a knight.
 Riley cannot be a knave, because this would contradict the false claim of Jacob that If Benjamin is a knight then Riley is a knave.
 We have exhausted all possibilities for Riley and Mia, so let us go back and reconsider Benjamin.
 Benjamin cannot be a knave, because this would contradict the false claim of Jacob that If Benjamin is a knight then Riley is a knave.
 We have exhausted all possibilities for Benjamin and Jacob, so let us go back and reconsider Mason.
 Assume Mason is a knave.  No contradiction is found in their false claim that Jacob is a knave and Grace is a knight.
 Assume Jacob is a knight.  No contradiction is found in their claim that If Benjamin is a knight then Riley is a knave.
 Assume Benjamin is a knight.  No contradiction is found in their claim that Mia is not a knight.
 Mia cannot be a knight, because this would contradict the claim of Benjamin that Mia is not a knight.
 Mia cannot be a knave, because this would contradict the false claim of their own that Mason is a knave.
 We have exhausted all possibilities for Mia, so let us go back and reconsider Benjamin.
 Assume Benjamin is a knave.  No contradiction is found in their false claim that Mia is not a knight.
 Assume Mia is a knight.  No contradiction is found in their claim that Mason is a knave.
 Assume Riley is a knight.  No contradiction is found in their claim that Jacob is a knight.
 Assume Grace is a knight.  No contradiction is found in their claim that Aiden is not a knave.
 Aiden cannot be a knight, because this would contradict the claim of their own that Mason is a knave if and only if Benjamin is a knight.
 Aiden cannot be a knave, because this would contradict the claim of Grace that Aiden is not a knave.
 We have exhausted all possibilities for Aiden, so let us go back and reconsider Grace.
 Assume Grace is a knave.  No contradiction is found in their false claim that Aiden is not a knave.
 Aiden cannot be a knight, because this would contradict the false claim of Grace that Aiden is not a knave.
 Assume Aiden is a knave.  No contradiction is found in their false claim that Mason is a knave if and only if Benjamin is a knight.
 Therefore, (1) Mason is a knave
 (2) Riley is a knight
 (3) Grace is a knave
 (4) Jacob is a knight
 (5) Aiden is a knave
 (6) Mia is a knight
 (7) Benjamin 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: Mason, Riley, Grace, Jacob, Aiden, Mia, and Benjamin. As Mason put it, "Jacob is a knave and Grace is a knight". Riley said, "Jacob is a knight." Grace stated, "Aiden is not a knave". "If Benjamin is a knight then Riley is a knave" - Jacob. Aiden was heard saying, "Mason is a knave if and only if Benjamin is a knight". In a statement by Mia: "Mason is a knave". According to Benjamin, "Mia is not 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 Mason is a knight. No contradiction is found in their claim that Jacob is a knave and Grace is a knight.
Jacob cannot be a knight, because this would contradict the claim of Mason that Jacob is a knave and Grace is a knight.
Assume Jacob is a knave. No contradiction is found in their false claim that If Benjamin is a knight then Riley is a knave.
Assume Benjamin is a knight. No contradiction is found in their claim that Mia is not a knight.
Mia cannot be a knight, because this would contradict the claim of their own that Mason is a knave.
Assume Mia is a knave. No contradiction is found in their false claim that Mason is a knave.
Riley cannot be a knight, because this would contradict the claim of their own that Jacob is a knight.
Riley cannot be a knave, because this would contradict the false claim of Jacob that If Benjamin is a knight then Riley is a knave.
We have exhausted all possibilities for Riley and Mia, so let us go back and reconsider Benjamin.
Benjamin cannot be a knave, because this would contradict the false claim of Jacob that If Benjamin is a knight then Riley is a knave.
We have exhausted all possibilities for Benjamin and Jacob, so let us go back and reconsider Mason.
Assume Mason is a knave. No contradiction is found in their false claim that Jacob is a knave and Grace is a knight.
Assume Jacob is a knight. No contradiction is found in their claim that If Benjamin is a knight then Riley is a knave.
Assume Benjamin is a knight. No contradiction is found in their claim that Mia is not a knight.
Mia cannot be a knight, because this would contradict the claim of Benjamin that Mia is not a knight.
Mia cannot be a knave, because this would contradict the false claim of their own that Mason is a knave.
We have exhausted all possibilities for Mia, so let us go back and reconsider Benjamin.
Assume Benjamin is a knave. No contradiction is found in their false claim that Mia is not a knight.
Assume Mia is a knight. No contradiction is found in their claim that Mason is a knave.
Assume Riley is a knight. No contradiction is found in their claim that Jacob is a knight.
Assume Grace is a knight. No contradiction is found in their claim that Aiden is not a knave.
Aiden cannot be a knight, because this would contradict the claim of their own that Mason is a knave if and only if Benjamin is a knight.
Aiden cannot be a knave, because this would contradict the claim of Grace that Aiden is not a knave.
We have exhausted all possibilities for Aiden, so let us go back and reconsider Grace.
Assume Grace is a knave. No contradiction is found in their false claim that Aiden is not a knave.
Aiden cannot be a knight, because this would contradict the false claim of Grace that Aiden is not a knave.
Assume Aiden is a knave. No contradiction is found in their false claim that Mason is a knave if and only if Benjamin is a knight.
Therefore, (1) Mason is a knave
(2) Riley is a knight
(3) Grace is a knave
(4) Jacob is a knight
(5) Aiden is a knave
(6) Mia is a knight
(7) Benjamin is a knave </think>
<answer> (1) Mason is a knave
(2) Riley is a knight
(3) Grace is a knave
(4) Jacob is a knight
(5) Aiden is a knave
(6) Mia is a knight
(7) Benjamin is a knave </answer>
Mason Riley Grace Jacob Aiden Mia Benjamin
(1) Mason is a knave
(2) Riley is a knight
(3) Grace is a knave
(4) Jacob is a knight
(5) Aiden is a knave
(6) Mia is a knight
(7) Benjamin is a knave
(('and', ('lying', 3), ('telling-truth', 2)), ('telling-truth', 3), ('not', ('lying', 4)), ('->', ('telling-truth', 6), ('lying', 1)), ('<=>', ('lying', 0), ('telling-truth', 6)), ('lying', 0), ('not', ('telling-truth', 5)))
rule