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 6 inhabitants: Victoria, Sofia, David, Mason, Grace, and Aurora. Victoria expressed that David is a knight. "If Mason is a knave then Aurora is a knight" - Sofia. David said that Mason is a knight if and only if Sofia is a knave. "If Victoria is a knight then Sofia is a knave," Mason declared. Grace asserted: "David is a knave or Mason is a knave". Aurora expressed that Grace 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 Victoria is a knight.  No contradiction is found in their claim that David is a knight.
 Assume David is a knight.  No contradiction is found in their claim that Mason is a knight if and only if Sofia is a knave.
 Assume Mason is a knight.  No contradiction is found in their claim that If Victoria is a knight then Sofia is a knave.
 Sofia cannot be a knight, because this would contradict the claim of David that Mason is a knight if and only if Sofia is a knave.
 Sofia cannot be a knave, because this would contradict the false claim of their own that If Mason is a knave then Aurora is a knight.
 We have exhausted all possibilities for Sofia, so let us go back and reconsider Mason.
 Assume Mason is a knave.  No contradiction is found in their false claim that If Victoria is a knight then Sofia is a knave.
 Assume Sofia is a knight.  No contradiction is found in their claim that If Mason is a knave then Aurora is a knight.
 Assume Aurora is a knight.  No contradiction is found in their claim that Grace is a knave.
 Grace cannot be a knight, because this would contradict the claim of Aurora that Grace is a knave.
 Grace cannot be a knave, because this would contradict the false claim of their own that David is a knave or Mason is a knave.
 We have exhausted all possibilities for Grace, so let us go back and reconsider Aurora.
 Aurora cannot be a knave, because this would contradict the claim of Sofia that If Mason is a knave then Aurora is a knight.
 We have exhausted all possibilities for Aurora, so let us go back and reconsider Sofia.
 Sofia cannot be a knave, because this would contradict the claim of David that Mason is a knight if and only if Sofia is a knave.
 We have exhausted all possibilities for Sofia and Mason, so let us go back and reconsider David.
 David cannot be a knave, because this would contradict the claim of Victoria that David is a knight.
 We have exhausted all possibilities for David, so let us go back and reconsider Victoria.
 Assume Victoria is a knave.  No contradiction is found in their false claim that David is a knight.
 David cannot be a knight, because this would contradict the false claim of Victoria that David is a knight.
 Assume David is a knave.  No contradiction is found in their false claim that Mason is a knight if and only if Sofia is a knave.
 Assume Mason is a knight.  No contradiction is found in their claim that If Victoria is a knight then Sofia is a knave.
 Assume Sofia is a knight.  No contradiction is found in their claim that If Mason is a knave then Aurora is a knight.
 Assume Aurora is a knight.  No contradiction is found in their claim that Grace is a knave.
 Grace cannot be a knight, because this would contradict the claim of Aurora that Grace is a knave.
 Grace cannot be a knave, because this would contradict the false claim of their own that David is a knave or Mason is a knave.
 We have exhausted all possibilities for Grace, so let us go back and reconsider Aurora.
 Assume Aurora is a knave.  No contradiction is found in their false claim that Grace is a knave.
 Assume Grace is a knight.  No contradiction is found in their claim that David is a knave or Mason is a knave.
 Therefore, (1) Victoria is a knave
 (2) Sofia is a knight
 (3) David is a knave
 (4) Mason is a knight
 (5) Grace is a knight
 (6) Aurora 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 6 inhabitants: Victoria, Sofia, David, Mason, Grace, and Aurora. Victoria expressed that David is a knight. "If Mason is a knave then Aurora is a knight" - Sofia. David said that Mason is a knight if and only if Sofia is a knave. "If Victoria is a knight then Sofia is a knave," Mason declared. Grace asserted: "David is a knave or Mason is a knave". Aurora expressed that Grace 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 Victoria is a knight. No contradiction is found in their claim that David is a knight.
Assume David is a knight. No contradiction is found in their claim that Mason is a knight if and only if Sofia is a knave.
Assume Mason is a knight. No contradiction is found in their claim that If Victoria is a knight then Sofia is a knave.
Sofia cannot be a knight, because this would contradict the claim of David that Mason is a knight if and only if Sofia is a knave.
Sofia cannot be a knave, because this would contradict the false claim of their own that If Mason is a knave then Aurora is a knight.
We have exhausted all possibilities for Sofia, so let us go back and reconsider Mason.
Assume Mason is a knave. No contradiction is found in their false claim that If Victoria is a knight then Sofia is a knave.
Assume Sofia is a knight. No contradiction is found in their claim that If Mason is a knave then Aurora is a knight.
Assume Aurora is a knight. No contradiction is found in their claim that Grace is a knave.
Grace cannot be a knight, because this would contradict the claim of Aurora that Grace is a knave.
Grace cannot be a knave, because this would contradict the false claim of their own that David is a knave or Mason is a knave.
We have exhausted all possibilities for Grace, so let us go back and reconsider Aurora.
Aurora cannot be a knave, because this would contradict the claim of Sofia that If Mason is a knave then Aurora is a knight.
We have exhausted all possibilities for Aurora, so let us go back and reconsider Sofia.
Sofia cannot be a knave, because this would contradict the claim of David that Mason is a knight if and only if Sofia is a knave.
We have exhausted all possibilities for Sofia and Mason, so let us go back and reconsider David.
David cannot be a knave, because this would contradict the claim of Victoria that David is a knight.
We have exhausted all possibilities for David, so let us go back and reconsider Victoria.
Assume Victoria is a knave. No contradiction is found in their false claim that David is a knight.
David cannot be a knight, because this would contradict the false claim of Victoria that David is a knight.
Assume David is a knave. No contradiction is found in their false claim that Mason is a knight if and only if Sofia is a knave.
Assume Mason is a knight. No contradiction is found in their claim that If Victoria is a knight then Sofia is a knave.
Assume Sofia is a knight. No contradiction is found in their claim that If Mason is a knave then Aurora is a knight.
Assume Aurora is a knight. No contradiction is found in their claim that Grace is a knave.
Grace cannot be a knight, because this would contradict the claim of Aurora that Grace is a knave.
Grace cannot be a knave, because this would contradict the false claim of their own that David is a knave or Mason is a knave.
We have exhausted all possibilities for Grace, so let us go back and reconsider Aurora.
Assume Aurora is a knave. No contradiction is found in their false claim that Grace is a knave.
Assume Grace is a knight. No contradiction is found in their claim that David is a knave or Mason is a knave.
Therefore, (1) Victoria is a knave
(2) Sofia is a knight
(3) David is a knave
(4) Mason is a knight
(5) Grace is a knight
(6) Aurora is a knave </think>
<answer> (1) Victoria is a knave
(2) Sofia is a knight
(3) David is a knave
(4) Mason is a knight
(5) Grace is a knight
(6) Aurora is a knave </answer>
Victoria Sofia David Mason Grace Aurora
(1) Victoria is a knave
(2) Sofia is a knight
(3) David is a knave
(4) Mason is a knight
(5) Grace is a knight
(6) Aurora is a knave
(('telling-truth', 2), ('->', ('lying', 3), ('telling-truth', 5)), ('<=>', ('telling-truth', 3), ('lying', 1)), ('->', ('telling-truth', 0), ('lying', 1)), ('or', ('lying', 2), ('lying', 3)), ('lying', 4))
rule