<user>
A: E is a liar and B is a truth-teller.
B: D is a truth-teller.
C: If B is a truth-teller, then E is a truth-teller.
D: If A is a truth-teller, then F is a truth-teller.
E: A is a liar.
F: E is a liar and A is a liar.
</user>
<assistant>
REASONING:
Let's assume A is a truth-teller.
If A is a truth-teller, A's statement is true and E is a liar and B is a truth-teller.
If E is a liar, E's statement is false and A is a truth-teller.
This contradicts our assumption, so A must be a liar.
If A is a liar, A's statement is false, so either E is a truth-teller or B is a liar or both.
Let's assume E is a truth-teller.
If E is a truth-teller, E's statement is true and A is liar.
This does not lead to a contradiction.
Let's assume B is a truth-teller.
If B is a truth-teller, B's statement that D is a truth-teller is true.
If D is a truth-teller, D's statement is true, so either A is a liar or A is a truth-teller and F is a truth-teller.
Since we know A is a liar this does not lead to any contradiction.
Let's assume C is a truth-teller.
If C is a truth-teller, then C's statement is true and B is either a liar or B is a truth-teller or E is a truth-teller.
Since we know B is a truth-teller, E must also be a truth-teller, which does not lead to any contradiction.
Let's assume D is a truth-teller.
If D is a truth-teller, then D's statement must be true, so either A is a liar or A is a truth-teller and F is a truth-teller.
We know A is a liar, so this does not lead to any contradictions.
Let's assume F is a truth-teller.
If F is a truth-teller, F's statement is true and E is a liar and A is a liar.
This leads to a contradiction, since we assume E is a truth-teller, so F must be a liar.
If F is a liar, F's statement is false if either E is a truth-teller or A is truth-teller or both, which does not lead to a contradiction.
Therefore we can conclude:

CONCLUSION:
A: liar
B: truth-teller
C: truth-teller
D: truth-teller
E: truth-teller
F: liar
</assistant>
---
<user>
A: F is a truth-teller and E is a liar.
B: F is a liar.
C: B is a liar.
D: A is a truth-teller and F is a truth-teller.
E: If B is a liar, then D is a liar.
F: E is a liar and C is a liar.
</user>
<assistant>
REASONING:
Let's assume A is a truth-teller.
If A is a truth-teller, then A's statement must be true and F is a truth-teller and E is a truth-teller.
If F is a truth-teller, then F's statement must be true and E is a liar and C is a liar.
This leads to a contradiction, so A must be a liar.
If A is a liar, A's statement is false, so either F is a liar or E is a truth-teller or both.
Let's assume F is a liar.
If F is a liar, F's statement is false, and either E is a truth-teller or C is a truth-teller or both.
Let's assume E is a truth-teller.
If E is a truth-teller, E's statement is true and either B is a truth-teller or B is a liar and D is a liar.
Let's assume B is a truth-teller.
If B is a truth-teller, B's statement is true and F is a liar.
This does not lead to any contradiction.
Let's assume C is a truth-teller.
If C is a truth-teller, C's statement is true and B is a liar.
This contradicts our assumption that B is a truth-teller, so C must be a liar.
Let's assume D is a truth-teller.
If D is a truth-teller, D is a truth-teller and A is a truth-teller and F is a truth-teller.
This contradicts the fact that A is liar and the assumption that F is a liar.
Therefore D must be a liar.
Since we have no contradictions we can conclude:

CONCLUSION:
A: liar
B: truth-teller
C: liar
D: liar
E: truth-teller
F: liar
</assistant>
---
<user>
A: C is a liar.
B: D is a liar and C is a truth-teller.
C: E is a liar.
D: If B is a liar, then F is a truth-teller.
E: A is a truth-teller.
F: B is a liar and A is a truth-teller.
</user>
<assistant>
REASONING:
Let's assume A is a truth-teller.
If A is a truth-teller, A's statement is true and C is a liar.
If C is a liar, C's statement is false and E is a truth-teller.
If E is a truth-teller, E's statement is true and A is a truth-teller.
This does not lead to a contradiction.
Let's assume B is a truth-teller.
If B is a truth-teller, B's statement is true and D is truth-teller and C is a truth-teller.
This leads to a contradiction, since we know that C is a liar, therefore B must be a liar.
If B is a liar, B's statement is false and either D is a truth-teller or C is a liar or both.
Let's assume D is a truth-teller.
If D is a truth-teller, D's statement is true and B is either a truth-teller or B is a liar and F is a truth-teller.
Since we know B is a liar, F must be a truth-teller.
If F is a truth-teller, F's statement must be true and B must be a liar and A must be a truth-teller.
This does not contradict the previous assumptions, so we can conclude:

CONCLUSION:
A: truth-teller
B: liar
C: liar
D: truth-teller
E: truth-teller
F: truth-teller
</assistant>
---
<user>
A: B is a liar and C is a truth-teller.
B: A is a truth-teller.
C: D is a liar.
D: A is a liar.
E: If F is a truth-teller, then A is a liar.
F: A is a liar and D is a truth-teller.
</user>
<assistant>
REASONING:
Let's assume A is a truth-teller.
If A is a truth-teller, A's statement is true and B is a liar and C is a truth-teller.
If B is a liar, B's statement is false and A is a liar, which contradicts the assumption that A is a truth-teller.
Therefore, A must be a liar.
If A is a liar, A's statement must be false and either B is a truth-teller or C is a liar or both.
Let's assume B is a truth-teller.
If B is a truth-teller, B's statement must be true and A must be a truth-teller.
Since we know A is a liar, this leads to a contradiction and B must be a liar.
If B is a liar, A's statement can only be false if C is a liar.
If C is a liar, D's statement must be false and D must be truth-teller.
If D is a truth-teller, D's statement is true and A is a liar, which does not lead to a contradiction.
Let's assume E is a truth-teller.
If E is a truth-teller, E's statement is true, so either F is a liar or F is a truth-teller and A is a liar.
Let's assume F is a truth-teller.
If F is a truth-teller, F's statement is true and A is a liar and D is a truth-teller.
This does not lead to a contradiction, so we can conclude:

CONCLUSION:
A: liar
B: liar
C: liar
D: truth-teller
E: truth-teller
F: truth-teller
</assistant>
---
<user>
A: D is a liar and F is a truth-teller.
B: A is a liar and E is a liar.
C: If A is a truth-teller, then B is a liar.
D: C is a liar.
E: If D is a truth-teller, then C is a truth-teller.
F: B is a liar.
</user>
<assistant>
REASONING:
Let's assume A is a truth-teller.
If A is a truth-teller, A's statement is true and D is a liar and F is a truth-teller.
If D is a liar, D's statement is false and C is a truth-teller.
If F is a truth-teller, F's statement is true and B is a liar.
If C is a truth-teller, C's statement is true, so either A is a liar or A is a truth-teller and B is a liar.
If B is a liar, B's statement is false, so either A is a truth-teller or E is a truth-teller or both.
Since we assume A is a truth-teller this does not lead to a contradiction.
Let's assume E is a truth-teller.
If E is a truth-teller, E's statement is true and either D is a liar or D is a truth-teller and C is a truth-teller.
This does not lead to a contradiction, so we can conclude:

CONCLUSION:
A: truth-teller
B: liar
C: truth-teller
D: liar
E: truth-teller
F: truth-teller
</assistant>
---
<user>
A: F is a truth-teller and D is a truth-teller.
B: D is a liar.
C: If F is a liar, then B is a truth-teller.
D: B is a liar.
E: C is a truth-teller.
F: E is a liar and D is a truth-teller.
</user>
<assistant>
REASONING:
Let's assume A is a truth-teller.
If A is a truth-teller, A's statement is true and F is a truth-teller and D is a truth-teller.
If F is a truth-teller, F's statement is true and E is a liar and D is a truth-teller.
If D is a truth-teller, D's statement is true and B is a liar.
If E is a liar, E's statement is true and C is a liar.
If B is a liar, B's statement is true and D is a truth-teller.
If C is a liar, C's statement is false and F is a liar and B is a liar.
This leads to a contradiction, since F must be a truth-teller.
Therefore, A must be a liar.
If A is a liar, A's statement is false and either F is a liar or D is a liar or both.
Let's assume F is a liar.
If F is a liar, F's statement is false and either E is a truth-teller or D is a liar or both.
Let's assume E is a truth-teller.
If E is a truth-teller, E's statement is true and C is a truth-teller.
If C is a truth-teller, C's statement is true and either F is a truth-teller or F is a liar and B is a truth-teller.
Since we assume F is a liar, this means B is a truth-teller.
If B is a truth-teller, B's statement is true and D is a liar.
If D is a liar, D's statement is false and B is a truth-teller.
This does not lead to a contradiction.
Let's assume E is a truth-teller.
If E is a truth-teller, E's statement is true and C is a truth-teller.
This does not lead to a contradiction, therefore we can conclude:

CONCLUSION:
A: liar
B: truth-teller
C: truth-teller
D: liar
E: truth-teller
F: liar
</assistant>
---
<user>
A: E is a truth-teller and F is a truth-teller.
B: F is a truth-teller and A is a truth-teller.
C: B is a truth-teller.
D: If A is a truth-teller, then F is a liar.
E: D is a truth-teller and C is a liar.
F: C is a truth-teller and A is a truth-teller.
</user>
<assistant>
REASONING:
Let's assume A is a truth-teller.
If A is a truth-teller, A's statement is true and E is a truth-teller and F is a truth-teller.
If E is a truth-teller, E's statement is true and D is a truth-teller and C is a liar.
If F is a truth-teller, F's statement is true and C is a truth-teller and A is a truth-teller.
This leads to a contradiction with E's statement, therefore A must be a liar.
If A is a liar, A's statement must be false and either E is a liar or F is a liar or both.
Let's assume E is a liar.
If E is a liar, E's statement is false and either D is a liar or C is a truth-teller or both.
Let's assume D is a liar.
If D is a liar, D's statement is false and A is a truth-teller and F is a truth-teller.
This leads to a contradiction, since we know A is a liar, so D must be a truth-teller.
Since D is a truth-teller, E's statement can only be false if C is a truth-teller.
If C is a truth-teller, C's statement is true and B is a truth-teller.
If B is a truth-teller, B's statement is true and F is a truth-teller and A is a truth-teller.
This leads to a contradiction, since we know A is a liar, so C must be a liar.
This contradicts the assumption, that E is a liar, so E must be a truth-teller.
If C is a liar, C's statement is false and B is a liar.
Since A must be a liar and E is a truth-teller, F must be a liar.
Therefore we can conclude:

CONCLUSION:
A: liar
B: liar
C: liar
D: truth-teller
E: truth-teller
F: liar
</assistant>
---
<user>
A: F is a truth-teller.
B: F is a liar and D is a truth-teller.
C: If F is a liar, then A is a liar.
D: E is a liar and A is a liar.
E: A is a truth-teller.
F: C is a truth-teller.
</user>
<assistant>
REASONING:
Let's assume A is a truth-teller.
If A is a truth-teller, A's statement is true and F is a truth-teller.
If F is a truth-teller, F's statement is true and C is a truth-teller.
If C is a truth-teller, C's statement is true and either F is a truth-teller and A is a liar or F is a truth-teller and A is a truth-teller or F is a liar and A is a liar.
Since we assume A is a truth-teller, F must be a truth-teller.
If F is a truth-teller, F's statement is true and C is a truth-teller.
This does not lead to any contradictions.
Let's assume B is a truth-teller.
If B is a truth-teller, B's statement is true and F is a liar and D is a truth-teller.
This contradicts the assumption that F is a truth-teller, so B must be a liar.
If B is a liar, B's statement is false and either F is a truth-teller or D is a liar or both.
Let's assume E is a truth-teller.
If E is a truth-teller, E's statement is true and A is a truth-teller.
This does not lead to any contradictions.
Let's assume D is a truth-teller.
If D is a truth-teller, D's statement is true and E is a liar and A is a liar.
This contradicts the assumption that E is a liar, so D must be a liar.
Therefore we can conclude:

CONCLUSION:
A: truth-teller
B: liar
C: truth-teller
D: liar
E: truth-teller
F: truth-teller
</assistant>
