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: Abigail, Matthew, Liam, Jackson, David, Chloe, and Jacob. Abigail was heard saying, "Chloe is a knave". According to Matthew, "Jackson is not a knave". In a statement by Liam: "Jackson is a knave or Jacob is a knave". "Liam is a knight if and only if Chloe is a knight," Jackson declared. David said that Jackson is not a knave. Chloe asserted: "Jackson is a knight". Jacob was heard saying, "If Jacob is a knight then David 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 Abigail is a knight.  No contradiction is found in their claim that Chloe is a knave.
 Chloe cannot be a knight, because this would contradict the claim of Abigail that Chloe is a knave.
 Assume Chloe is a knave.  No contradiction is found in their false claim that Jackson is a knight.
 Jackson cannot be a knight, because this would contradict the false claim of Chloe that Jackson is a knight.
 Assume Jackson is a knave.  No contradiction is found in their false claim that Liam is a knight if and only if Chloe is a knight.
 Assume Liam is a knight.  No contradiction is found in their claim that Jackson is a knave or Jacob is a knave.
 Assume Jacob is a knight.  No contradiction is found in their claim that If Jacob is a knight then David is a knave.
 David cannot be a knight, because this would contradict the claim of their own that Jackson is not a knave.
 Assume David is a knave.  No contradiction is found in their false claim that Jackson is not a knave.
 Matthew cannot be a knight, because this would contradict the claim of their own that Jackson is not a knave.
 Assume Matthew is a knave.  No contradiction is found in their false claim that Jackson is not a knave.
 Therefore, (1) Abigail is a knight
 (2) Matthew is a knave
 (3) Liam is a knight
 (4) Jackson is a knave
 (5) David is a knave
 (6) Chloe is a knave
 (7) Jacob 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: Abigail, Matthew, Liam, Jackson, David, Chloe, and Jacob. Abigail was heard saying, "Chloe is a knave". According to Matthew, "Jackson is not a knave". In a statement by Liam: "Jackson is a knave or Jacob is a knave". "Liam is a knight if and only if Chloe is a knight," Jackson declared. David said that Jackson is not a knave. Chloe asserted: "Jackson is a knight". Jacob was heard saying, "If Jacob is a knight then David 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 Abigail is a knight. No contradiction is found in their claim that Chloe is a knave.
Chloe cannot be a knight, because this would contradict the claim of Abigail that Chloe is a knave.
Assume Chloe is a knave. No contradiction is found in their false claim that Jackson is a knight.
Jackson cannot be a knight, because this would contradict the false claim of Chloe that Jackson is a knight.
Assume Jackson is a knave. No contradiction is found in their false claim that Liam is a knight if and only if Chloe is a knight.
Assume Liam is a knight. No contradiction is found in their claim that Jackson is a knave or Jacob is a knave.
Assume Jacob is a knight. No contradiction is found in their claim that If Jacob is a knight then David is a knave.
David cannot be a knight, because this would contradict the claim of their own that Jackson is not a knave.
Assume David is a knave. No contradiction is found in their false claim that Jackson is not a knave.
Matthew cannot be a knight, because this would contradict the claim of their own that Jackson is not a knave.
Assume Matthew is a knave. No contradiction is found in their false claim that Jackson is not a knave.
Therefore, (1) Abigail is a knight
(2) Matthew is a knave
(3) Liam is a knight
(4) Jackson is a knave
(5) David is a knave
(6) Chloe is a knave
(7) Jacob is a knight </think>
<answer> (1) Abigail is a knight
(2) Matthew is a knave
(3) Liam is a knight
(4) Jackson is a knave
(5) David is a knave
(6) Chloe is a knave
(7) Jacob is a knight </answer>
Abigail Matthew Liam Jackson David Chloe Jacob
(1) Abigail is a knight
(2) Matthew is a knave
(3) Liam is a knight
(4) Jackson is a knave
(5) David is a knave
(6) Chloe is a knave
(7) Jacob is a knight
(('lying', 5), ('not', ('lying', 3)), ('or', ('lying', 3), ('lying', 6)), ('<=>', ('telling-truth', 2), ('telling-truth', 5)), ('not', ('lying', 3)), ('telling-truth', 3), ('->', ('telling-truth', 6), ('lying', 4)))
rule