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: Henry, Ella, Alexander, William, Aurora, Victoria, and Sebastian. Henry said that Ella is a knave. As Ella put it, "If Henry is a knave then William is a knight". "Aurora is a knight if and only if Ella is a knight," Alexander declared. In William's words: "Henry is not a knight". In Aurora's words: "Ella is a knight and Victoria is a knave". Victoria remarked, "Ella is a knight if and only if William is a knight". Sebastian expressed that Victoria 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 Henry is a knight.  No contradiction is found in their claim that Ella is a knave.
 Ella cannot be a knight, because this would contradict the claim of Henry that Ella is a knave.
 Ella cannot be a knave, because this would contradict the false claim of their own that If Henry is a knave then William is a knight.
 We have exhausted all possibilities for Ella, so let us go back and reconsider Henry.
 Assume Henry is a knave.  No contradiction is found in their false claim that Ella is a knave.
 Assume Ella is a knight.  No contradiction is found in their claim that If Henry is a knave then William is a knight.
 Assume William is a knight.  No contradiction is found in their claim that Henry is not a knight.
 Assume Alexander is a knight.  No contradiction is found in their claim that Aurora is a knight if and only if Ella is a knight.
 Assume Aurora is a knight.  No contradiction is found in their claim that Ella is a knight and Victoria is a knave.
 Victoria cannot be a knight, because this would contradict the claim of Aurora that Ella is a knight and Victoria is a knave.
 Victoria cannot be a knave, because this would contradict the false claim of their own that Ella is a knight if and only if William is a knight.
 We have exhausted all possibilities for Victoria, so let us go back and reconsider Aurora.
 Aurora cannot be a knave, because this would contradict the claim of Alexander that Aurora is a knight if and only if Ella is a knight.
 We have exhausted all possibilities for Aurora, so let us go back and reconsider Alexander.
 Assume Alexander is a knave.  No contradiction is found in their false claim that Aurora is a knight if and only if Ella is a knight.
 Aurora cannot be a knight, because this would contradict the false claim of Alexander that Aurora is a knight if and only if Ella is a knight.
 Assume Aurora is a knave.  No contradiction is found in their false claim that Ella is a knight and Victoria is a knave.
 Assume Victoria is a knight.  No contradiction is found in their claim that Ella is a knight if and only if William is a knight.
 Sebastian cannot be a knight, because this would contradict the claim of their own that Victoria is a knave.
 Assume Sebastian is a knave.  No contradiction is found in their false claim that Victoria is a knave.
 Therefore, (1) Henry is a knave
 (2) Ella is a knight
 (3) Alexander is a knave
 (4) William is a knight
 (5) Aurora is a knave
 (6) Victoria is a knight
 (7) Sebastian 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: Henry, Ella, Alexander, William, Aurora, Victoria, and Sebastian. Henry said that Ella is a knave. As Ella put it, "If Henry is a knave then William is a knight". "Aurora is a knight if and only if Ella is a knight," Alexander declared. In William's words: "Henry is not a knight". In Aurora's words: "Ella is a knight and Victoria is a knave". Victoria remarked, "Ella is a knight if and only if William is a knight". Sebastian expressed that Victoria 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 Henry is a knight. No contradiction is found in their claim that Ella is a knave.
Ella cannot be a knight, because this would contradict the claim of Henry that Ella is a knave.
Ella cannot be a knave, because this would contradict the false claim of their own that If Henry is a knave then William is a knight.
We have exhausted all possibilities for Ella, so let us go back and reconsider Henry.
Assume Henry is a knave. No contradiction is found in their false claim that Ella is a knave.
Assume Ella is a knight. No contradiction is found in their claim that If Henry is a knave then William is a knight.
Assume William is a knight. No contradiction is found in their claim that Henry is not a knight.
Assume Alexander is a knight. No contradiction is found in their claim that Aurora is a knight if and only if Ella is a knight.
Assume Aurora is a knight. No contradiction is found in their claim that Ella is a knight and Victoria is a knave.
Victoria cannot be a knight, because this would contradict the claim of Aurora that Ella is a knight and Victoria is a knave.
Victoria cannot be a knave, because this would contradict the false claim of their own that Ella is a knight if and only if William is a knight.
We have exhausted all possibilities for Victoria, so let us go back and reconsider Aurora.
Aurora cannot be a knave, because this would contradict the claim of Alexander that Aurora is a knight if and only if Ella is a knight.
We have exhausted all possibilities for Aurora, so let us go back and reconsider Alexander.
Assume Alexander is a knave. No contradiction is found in their false claim that Aurora is a knight if and only if Ella is a knight.
Aurora cannot be a knight, because this would contradict the false claim of Alexander that Aurora is a knight if and only if Ella is a knight.
Assume Aurora is a knave. No contradiction is found in their false claim that Ella is a knight and Victoria is a knave.
Assume Victoria is a knight. No contradiction is found in their claim that Ella is a knight if and only if William is a knight.
Sebastian cannot be a knight, because this would contradict the claim of their own that Victoria is a knave.
Assume Sebastian is a knave. No contradiction is found in their false claim that Victoria is a knave.
Therefore, (1) Henry is a knave
(2) Ella is a knight
(3) Alexander is a knave
(4) William is a knight
(5) Aurora is a knave
(6) Victoria is a knight
(7) Sebastian is a knave </think>
<answer> (1) Henry is a knave
(2) Ella is a knight
(3) Alexander is a knave
(4) William is a knight
(5) Aurora is a knave
(6) Victoria is a knight
(7) Sebastian is a knave </answer>
Henry Ella Alexander William Aurora Victoria Sebastian
(1) Henry is a knave
(2) Ella is a knight
(3) Alexander is a knave
(4) William is a knight
(5) Aurora is a knave
(6) Victoria is a knight
(7) Sebastian is a knave
(('lying', 1), ('->', ('lying', 0), ('telling-truth', 3)), ('<=>', ('telling-truth', 4), ('telling-truth', 1)), ('not', ('telling-truth', 0)), ('and', ('telling-truth', 1), ('lying', 5)), ('<=>', ('telling-truth', 1), ('telling-truth', 3)), ('lying', 5))
rule