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, Alexander, Liam, Lily, Ava, Logan, and Sophia. In Mason's words: "Alexander is a knave". Alexander stated, "Liam is a knave if and only if Ava is a knight". Liam noted, "Alexander is a knave or Sophia is a knave". According to Lily, "If Sophia is a knave then Mason is a knave". Ava expressed that Liam is a knave. Logan said that Sophia is a knave and Liam is a knave. Sophia commented, "Logan 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 Alexander is a knave.
 Alexander cannot be a knight, because this would contradict the claim of Mason that Alexander is a knave.
 Assume Alexander is a knave.  No contradiction is found in their false claim that Liam is a knave if and only if Ava is a knight.
 Assume Liam is a knight.  No contradiction is found in their claim that Alexander is a knave or Sophia is a knave.
 Assume Sophia is a knight.  No contradiction is found in their claim that Logan is not a knight.
 Logan cannot be a knight, because this would contradict the claim of their own that Sophia is a knave and Liam is a knave.
 Assume Logan is a knave.  No contradiction is found in their false claim that Sophia is a knave and Liam is a knave.
 Ava cannot be a knight, because this would contradict the claim of their own that Liam is a knave.
 Ava cannot be a knave, because this would contradict the false claim of Alexander that Liam is a knave if and only if Ava is a knight.
 We have exhausted all possibilities for Ava and Logan, so let us go back and reconsider Sophia.
 Assume Sophia is a knave.  No contradiction is found in their false claim that Logan is not a knight.
 Logan cannot be a knight, because this would contradict the claim of their own that Sophia is a knave and Liam is a knave.
 Logan cannot be a knave, because this would contradict the false claim of Sophia that Logan is not a knight.
 We have exhausted all possibilities for Logan and Sophia, so let us go back and reconsider Liam.
 Liam cannot be a knave, because this would contradict the false claim of their own that Alexander is a knave or Sophia is a knave.
 We have exhausted all possibilities for Liam and Alexander, so let us go back and reconsider Mason.
 Assume Mason is a knave.  No contradiction is found in their false claim that Alexander is a knave.
 Assume Alexander is a knight.  No contradiction is found in their claim that Liam is a knave if and only if Ava is a knight.
 Assume Liam is a knight.  No contradiction is found in their claim that Alexander is a knave or Sophia is a knave.
 Sophia cannot be a knight, because this would contradict the claim of Liam that Alexander is a knave or Sophia is a knave.
 Assume Sophia is a knave.  No contradiction is found in their false claim that Logan is not a knight.
 Logan cannot be a knight, because this would contradict the claim of their own that Sophia is a knave and Liam is a knave.
 Logan cannot be a knave, because this would contradict the false claim of Sophia that Logan is not a knight.
 We have exhausted all possibilities for Logan and Sophia, so let us go back and reconsider Liam.
 Assume Liam is a knave.  No contradiction is found in their false claim that Alexander is a knave or Sophia is a knave.
 Assume Sophia is a knight.  No contradiction is found in their claim that Logan is not a knight.
 Logan cannot be a knight, because this would contradict the claim of their own that Sophia is a knave and Liam is a knave.
 Assume Logan is a knave.  No contradiction is found in their false claim that Sophia is a knave and Liam is a knave.
 Assume Ava is a knight.  No contradiction is found in their claim that Liam is a knave.
 Assume Lily is a knight.  No contradiction is found in their claim that If Sophia is a knave then Mason is a knave.
 Therefore, (1) Mason is a knave
 (2) Alexander is a knight
 (3) Liam is a knave
 (4) Lily is a knight
 (5) Ava is a knight
 (6) Logan is a knave
 (7) Sophia 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: Mason, Alexander, Liam, Lily, Ava, Logan, and Sophia. In Mason's words: "Alexander is a knave". Alexander stated, "Liam is a knave if and only if Ava is a knight". Liam noted, "Alexander is a knave or Sophia is a knave". According to Lily, "If Sophia is a knave then Mason is a knave". Ava expressed that Liam is a knave. Logan said that Sophia is a knave and Liam is a knave. Sophia commented, "Logan 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 Alexander is a knave.
Alexander cannot be a knight, because this would contradict the claim of Mason that Alexander is a knave.
Assume Alexander is a knave. No contradiction is found in their false claim that Liam is a knave if and only if Ava is a knight.
Assume Liam is a knight. No contradiction is found in their claim that Alexander is a knave or Sophia is a knave.
Assume Sophia is a knight. No contradiction is found in their claim that Logan is not a knight.
Logan cannot be a knight, because this would contradict the claim of their own that Sophia is a knave and Liam is a knave.
Assume Logan is a knave. No contradiction is found in their false claim that Sophia is a knave and Liam is a knave.
Ava cannot be a knight, because this would contradict the claim of their own that Liam is a knave.
Ava cannot be a knave, because this would contradict the false claim of Alexander that Liam is a knave if and only if Ava is a knight.
We have exhausted all possibilities for Ava and Logan, so let us go back and reconsider Sophia.
Assume Sophia is a knave. No contradiction is found in their false claim that Logan is not a knight.
Logan cannot be a knight, because this would contradict the claim of their own that Sophia is a knave and Liam is a knave.
Logan cannot be a knave, because this would contradict the false claim of Sophia that Logan is not a knight.
We have exhausted all possibilities for Logan and Sophia, so let us go back and reconsider Liam.
Liam cannot be a knave, because this would contradict the false claim of their own that Alexander is a knave or Sophia is a knave.
We have exhausted all possibilities for Liam and Alexander, so let us go back and reconsider Mason.
Assume Mason is a knave. No contradiction is found in their false claim that Alexander is a knave.
Assume Alexander is a knight. No contradiction is found in their claim that Liam is a knave if and only if Ava is a knight.
Assume Liam is a knight. No contradiction is found in their claim that Alexander is a knave or Sophia is a knave.
Sophia cannot be a knight, because this would contradict the claim of Liam that Alexander is a knave or Sophia is a knave.
Assume Sophia is a knave. No contradiction is found in their false claim that Logan is not a knight.
Logan cannot be a knight, because this would contradict the claim of their own that Sophia is a knave and Liam is a knave.
Logan cannot be a knave, because this would contradict the false claim of Sophia that Logan is not a knight.
We have exhausted all possibilities for Logan and Sophia, so let us go back and reconsider Liam.
Assume Liam is a knave. No contradiction is found in their false claim that Alexander is a knave or Sophia is a knave.
Assume Sophia is a knight. No contradiction is found in their claim that Logan is not a knight.
Logan cannot be a knight, because this would contradict the claim of their own that Sophia is a knave and Liam is a knave.
Assume Logan is a knave. No contradiction is found in their false claim that Sophia is a knave and Liam is a knave.
Assume Ava is a knight. No contradiction is found in their claim that Liam is a knave.
Assume Lily is a knight. No contradiction is found in their claim that If Sophia is a knave then Mason is a knave.
Therefore, (1) Mason is a knave
(2) Alexander is a knight
(3) Liam is a knave
(4) Lily is a knight
(5) Ava is a knight
(6) Logan is a knave
(7) Sophia is a knight </think>
<answer> (1) Mason is a knave
(2) Alexander is a knight
(3) Liam is a knave
(4) Lily is a knight
(5) Ava is a knight
(6) Logan is a knave
(7) Sophia is a knight </answer>
Mason Alexander Liam Lily Ava Logan Sophia
(1) Mason is a knave
(2) Alexander is a knight
(3) Liam is a knave
(4) Lily is a knight
(5) Ava is a knight
(6) Logan is a knave
(7) Sophia is a knight
(('lying', 1), ('<=>', ('lying', 2), ('telling-truth', 4)), ('or', ('lying', 1), ('lying', 6)), ('->', ('lying', 6), ('lying', 0)), ('lying', 2), ('and', ('lying', 6), ('lying', 2)), ('not', ('telling-truth', 5)))
rule