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 4 inhabitants: Mason, Victoria, Isabella, and Matthew. Mason expressed that Isabella is a knight if and only if Matthew is a knight. Victoria said that If Isabella is a knave then Matthew is a knight. Isabella stated, "Mason is a knight and Mason is a knave". In Matthew's words: "Isabella 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 Isabella is a knight if and only if Matthew is a knight.
 Isabella cannot be a knight, because this would contradict the claim of their own that Mason is a knight and Mason is a knave.
 Assume Isabella is a knave.  No contradiction is found in their false claim that Mason is a knight and Mason is a knave.
 Matthew cannot be a knight, because this would contradict the claim of Mason that Isabella is a knight if and only if Matthew is a knight.
 Matthew cannot be a knave, because this would contradict the false claim of their own that Isabella is not a knight.
 We have exhausted all possibilities for Matthew and Isabella, so let us go back and reconsider Mason.
 Assume Mason is a knave.  No contradiction is found in their false claim that Isabella is a knight if and only if Matthew is a knight.
 Isabella cannot be a knight, because this would contradict the claim of their own that Mason is a knight and Mason is a knave.
 Assume Isabella is a knave.  No contradiction is found in their false claim that Mason is a knight and Mason is a knave.
 Assume Matthew is a knight.  No contradiction is found in their claim that Isabella is not a knight.
 Assume Victoria is a knight.  No contradiction is found in their claim that If Isabella is a knave then Matthew is a knight.
 Therefore, (1) Mason is a knave
 (2) Victoria is a knight
 (3) Isabella is a knave
 (4) 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 4 inhabitants: Mason, Victoria, Isabella, and Matthew. Mason expressed that Isabella is a knight if and only if Matthew is a knight. Victoria said that If Isabella is a knave then Matthew is a knight. Isabella stated, "Mason is a knight and Mason is a knave". In Matthew's words: "Isabella 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 Isabella is a knight if and only if Matthew is a knight.
Isabella cannot be a knight, because this would contradict the claim of their own that Mason is a knight and Mason is a knave.
Assume Isabella is a knave. No contradiction is found in their false claim that Mason is a knight and Mason is a knave.
Matthew cannot be a knight, because this would contradict the claim of Mason that Isabella is a knight if and only if Matthew is a knight.
Matthew cannot be a knave, because this would contradict the false claim of their own that Isabella is not a knight.
We have exhausted all possibilities for Matthew and Isabella, so let us go back and reconsider Mason.
Assume Mason is a knave. No contradiction is found in their false claim that Isabella is a knight if and only if Matthew is a knight.
Isabella cannot be a knight, because this would contradict the claim of their own that Mason is a knight and Mason is a knave.
Assume Isabella is a knave. No contradiction is found in their false claim that Mason is a knight and Mason is a knave.
Assume Matthew is a knight. No contradiction is found in their claim that Isabella is not a knight.
Assume Victoria is a knight. No contradiction is found in their claim that If Isabella is a knave then Matthew is a knight.
Therefore, (1) Mason is a knave
(2) Victoria is a knight
(3) Isabella is a knave
(4) Matthew is a knight </think>
<answer> (1) Mason is a knave
(2) Victoria is a knight
(3) Isabella is a knave
(4) Matthew is a knight </answer>
Mason Victoria Isabella Matthew
(1) Mason is a knave
(2) Victoria is a knight
(3) Isabella is a knave
(4) Matthew is a knight
(('<=>', ('telling-truth', 2), ('telling-truth', 3)), ('->', ('lying', 2), ('telling-truth', 3)), ('and', ('telling-truth', 0), ('lying', 0)), ('not', ('telling-truth', 2)))
rule