Formalize the following proof process based on the given information. Where Each line of formalized proof MUST follow the format specified below.
output_triple = [rule used](input_triple_1, ... , input_triple_n)

Q: Triples:
1. Anne is not big.
2. Anne is cold.
3. Anne is red.
4. Dave is green.
5. Dave is rough.
6. Erin is green.
7. Erin is kind.
8. Erin is rough.
9. Fiona is green.
10. Fiona is not nice.
Rules:
1. If Erin is cold then Erin is rough.
2. If something is rough then it is nice.
3. All green, big things are kind.
4. If Dave is kind then Dave is cold.
5. If something is green and not rough then it is big.
6. All nice, rough things are big.
7. If Dave is cold and Dave is nice then Dave is red.
Based on the above information, is the following statement true or false? Dave is red.
A) True B) False

Proof: To determine if the statement "Dave is red" is true or false, let's evaluate the given information step by step:

From the triples:
1. Dave is green.
2. Dave is rough.

From the rules:
1. If something is rough then it is nice. (Dave is rough, so Dave is nice.)
2. If Dave is cold and Dave is nice then Dave is red. (However, there's no information saying Dave is cold, so we can't use this rule directly.)
3. All nice, rough things are big. (Dave is nice and rough, so Dave is big.)

Now, we need to verify whether Dave being cold can be derived:
1. If Dave is kind then Dave is cold. (To use this, we need to verify if Dave is kind.)
   - All green, big things are kind. (Dave is green and big, so Dave is kind.)
   - Hence, Dave is kind, which according to rule 4, makes Dave cold.

Since now we know:
- Dave is cold.
- Dave is nice.

We can use rule 7:
- If Dave is cold and Dave is nice then Dave is red.

Since both conditions are satisfied, Dave is red.

The statement "Dave is red" is **True (A)**.

Formalized Proof:
"Dave is nice." = [rule2]("Dave is rough.")
"Dave is big." = [rule6]("Dave is nice.", "Dave is rough.")
"Dave is kind." = [rule3]("Dave is green.", "Dave is big.")
"Dave is cold." = [rule4]("Dave is kind.")
"Dave is red." = [rule7]("Dave is cold.", "Dave is nice.")


Q: Triples:
1. Bob is blue.
2. Bob is cold.
3. Bob is quiet.
4. Bob is red.
5. Bob is smart.
6. Bob is young.
7. Fiona is blue.
8. Fiona is red.
9. Fiona is smart.
10. Fiona is young.
11. Gary is young.
12. Harry is red.
Rules:
1. Red, cold people are blue.
2. If someone is quiet then they are furry.
3. If someone is red and smart then they are young.
4. All cold, young people are quiet.
5. If someone is quiet and smart then they are furry.
6. All young, furry people are cold.
7. All quiet, young people are red.
8. All quiet people are red.
9. If someone is young then they are furry.
Based on the above information, is the following statement true or false? Gary is blue.
A) True B) False

Proof: To determine if the statement "Gary is blue" is true or false, let's evaluate the available information:

From the triples:
1. Gary is young.

From the rules:
1. If someone is young then they are furry. (Gary is young, so Gary is furry.)
2. All young, furry people are cold. (Gary is young and furry, so Gary is cold.)
3. All cold, young people are quiet. (Gary is cold and young, so Gary is quiet.)
4. All quiet people are red. (Gary is quiet, so Gary is red.)
5. Red, cold people are blue. (Gary is red and cold, so Gary is blue.)

Thus, based on the provided information and the logical deductions from the rules:
- Gary is blue.

The statement "Gary is blue" is **True (A)**.

Formalized Proof:
"Gary is furry." = [rule9]("Gary is young.")
"Gary is cold." = [rule6]("Gary is young.", "Gary is furry.")
"Gary is quiet." = [rule4]("Gary is cold.", "Gary is young.")
"Gary is red." = [rule8]("Gary is quiet.")
"Gary is blue." = [rule1]("Gary is red.", "Gary is cold.")

Q: Triples:
1. Bob is white.
2. Charlie is blue.
3. Charlie is white.
4. Erin is green.
5. Fiona is quiet.
6. Fiona is red.
7. Fiona is white.
Rules:
1. Quiet things are blue.
2. All smart, big things are green.
3. All white, quiet things are blue.
4. If something is white and red then it is big.
5. Quiet, green things are big.
6. Green, blue things are red.
7. All green things are white.
8. If something is red and big then it is smart.
9. All white things are blue.
Based on the above information, is the following statement true or false? Erin is smart.
A) True B) False

Proof: To determine if the statement "Erin is smart" is true or false, let's analyze the given information:

From the triples:
1. Erin is green.

From the rules:
1. All green things are white. (Erin is green, so Erin is white.)
2. All white things are blue. (Erin is white, so Erin is blue.)
3. Green, blue things are red. (Erin is green and blue, so Erin is red.)
4. If something is white and red then it is big. (Erin is white and red, so Erin is big.)
5. If something is red and big then it is smart. (Erin is red and big, so Erin is smart.)

Following the chain of logical deductions from the rules, Erin fulfills the conditions of being green, white, blue, red, and big, culminating in her being smart based on the rule that if something is red and big then it is smart.

Therefore, the statement "Erin is smart" is **True (A)**.

Formalized Proof:
"Erin is white." = [rule7]("Erin is green.")
"Erin is blue." = [rule9]("Erin is white.")
"Erin is red." = [rule6]("Erin is green.", "Erin is blue.")
"Erin is big." = [rule4]("Erin is white.", "Erin is red.")
"Erin is smart." = [rule8]("Erin is red.", "Erin is big.")

Q: Triples:
1. The bald eagle chases the cow.
2. The bald eagle chases the mouse.   
3. The bald eagle is kind.
4. The cow chases the mouse.
5. The cow is round.
6. The mouse is kind.
7. The mouse is not round.
8. The mouse likes the cow.
9. The tiger does not chase the mouse.
10. The tiger is rough.
11. The tiger likes the mouse.
12. The tiger needs the bald eagle.
Rules:
1. If someone chases the cow then the cow needs the tiger.
2. If the mouse needs the cow then the mouse is not rough.
3. If someone likes the tiger and they like the cow then the cow does not like the tiger.
4. If someone chases the bald eagle then the bald eagle is cold.
5. If someone needs the tiger then they like the bald eagle.
6. If the bald eagle likes the tiger then the tiger needs the mouse.
7. If someone is cold then they chase the tiger.
8. If someone needs the tiger then they chase the bald eagle.
9. If someone chases the tiger then the tiger is round.
Based on the above information, is the following statement true or false? The tiger is round.
A) True B) False

Proof: To determine if the statement "The tiger is round" is true or false, let's examine the information and follow the logical deductions based on the given rules and triples:

From the triples:
- The bald eagle chases the cow.
- The tiger does not chase the mouse.

From the rules:
1. If someone chases the cow then the cow needs the tiger. (The bald eagle chases the cow, so the cow needs the tiger.)
2. If the cow needs the tiger then someone chases the bald eagle (Rule 8). (Since the cow needs the tiger, the tiger needs someone, and if the tiger needs someone, they chase the bald eagle.)
3. If someone chases the bald eagle then the bald eagle is cold (Rule 4). (Someone chases the bald eagle, so the bald eagle is cold.)
4. If someone is cold then they chase the tiger (Rule 7). (The bald eagle is cold, therefore the bald eagle chases the tiger.)
5. If someone chases the tiger then the tiger is round (Rule 9). (The bald eagle chases the tiger, so the tiger is round.)

Using these logical steps derived from the rules and triples, we conclude that the tiger is indeed chased by the bald eagle, and thus according to the rules, the tiger must be round.

Therefore, the statement "The tiger is round" is **True (A)**.

Formalized Proof:
"The cow needs the tiger." = [rule1]("The bald eagle chases the cow.")
"The cow chases the bald eagle." = [rule8]("The cow needs the tiger.")
"The bald eagle is cold." = [rule4]("The cow chases the bald eagle.")
"The bald chases the tiger." = [rule7]("The bald eagle is cold.")
"The tiger is round." = [rule9]("The bald chases the tiger.")

Q: Triples:
1. Anne is nice.
2. Anne is white.
3. Dave is not rough.
4. Gary is nice.
5. Gary is white.
6. Harry is blue.
7. Harry is white.
Rules:
1. If Anne is not white then Anne is blue.
2. If something is white then it is rough.
3. If Anne is blue then Anne is nice.
4. All rough things are furry.
5. Nice things are not green.
6. If Harry is furry then Harry is nice.
7. White, furry things are blue.
8. If something is furry and not green then it is smart.
Based on the above information, is the following statement true or false? Harry is not smart.
A) True B) False

Proof: To determine if the statement "Harry is not smart" is true or false, let's examine the given information and follow logical deductions based on the rules and triples:

From the triples:
- Harry is white.
- Harry is blue.

From the rules:
1. If something is white then it is rough. (Harry is white, so Harry is rough.)
2. All rough things are furry. (Harry is rough, therefore Harry is furry.)
3. White, furry things are blue. (Harry is white and furry, thus confirming Harry is blue.)
4. If something is furry and not green then it is smart. (Harry is furry, and there is no information suggesting Harry is green, so Harry is smart.)

Based on these deductions, Harry meets the conditions set by the rules that make him both furry and smart.

Therefore, the statement "Harry is not smart" is **False (B)**.

Formalized Proof:
"Harry is rough." = [rule2]("Harry is white.")
"Harry is furry." = [rule4]("Harry is rough.")
"Harry is blue." = [rule7]("Harry is white.", "Harry is furry.")
"Harry is smart." = [rule8]("Harry is furry.")

Q: Triples:
1. Bob is cold.
2. Bob is furry.
3. Bob is kind.
4. Bob is nice.
5. Bob is white.
6. Bob is young.
7. Charlie is furry.
8. Charlie is nice.
9. Gary is kind.
10. Gary is nice.
11. Harry is blue.
Rules:
1. If something is white then it is kind.
2. If something is blue and kind then it is young.
3. If something is white then it is nice.
4. If something is kind and white then it is blue.
5. Young things are nice.
6. Blue, kind things are furry.
7. If something is cold then it is white.
8. All cold, furry things are white.
9. Nice things are cold.
Based on the above information, is the following statement true or false? Charlie is not young.
A) True B) False

Proof: To determine if the statement "Charlie is not young" is true or false, we will analyze the provided triples and apply the rules systematically:

From the triples:
- Charlie is furry.
- Charlie is nice.

From the rules:
1. If something is white then it is kind. (Not directly applicable without knowing Charlie's color.)
2. If something is nice then it is cold. (Charlie is nice, so Charlie is cold.)
3. If something is cold then it is white. (Charlie is cold, so Charlie is white.)
4. If something is white then it is nice. (Charlie is white, reinforcing that he is nice.)
5. If something is kind and white then it is blue. (To apply this, we need to confirm if Charlie is kind.)
   - Since Charlie is white and all white things are kind (Rule 1), Charlie is kind.
   - Therefore, being kind and white, Charlie is blue.

Now, applying more rules:
- If something is blue and kind then it is young. (Charlie is blue and kind, so Charlie is young.)

Based on the logical deductions:
- Charlie is young.

Thus, the statement "Charlie is not young" is **False (B)**.

Formalized Proof:
"Charlie is cold." = [rule9]("Charlie is nice.")
"Charlie is white." = [rule7]("Charlie is cold.")
"Charlie is kind." = [rule1]("Charlie is white.")
"Charlie is blue." = [rule4]("Charlie is kind.", "Charlie is white.")
"Charlie is young." = [rule2]("Charlie is blue.", "Charlie is kind.")

Q: Triples:
1. Charlie is round.
2. Charlie is young.
3. Dave is white.
4. Fiona is kind.
5. Fiona is red.
6. Fiona is white.
7. Fiona is young.
8. Harry is kind.
9. Harry is quiet.
10. Harry is round.
Rules:
1. All blue, kind people are quiet.
2. Kind people are blue.
3. All white, red people are round.
4. White people are young.
5. If someone is red then they are white.
6. Quiet people are blue.
7. If someone is young then they are kind.
8. White, blue people are red.
Based on the above information, is the following statement true or false? Dave is not round.
A) True B) False

Proof: To determine if the statement "Dave is not round" is true or false, let's evaluate the information provided by examining each rule and triple step-by-step:

From the triples:
- Dave is white.

From the rules:
1. White people are young. (Dave is white, so Dave is young.)
2. If someone is young then they are kind. (Dave is young, so Dave is kind.)
3. Kind people are blue. (Dave is kind, so Dave is blue.)
4. White, blue people are red. (Dave is white and blue, so Dave is red.)
5. If someone is red then they are white. (Dave is red, confirming again that he is white, although this is redundant as we already knew.)
6. All white, red people are round. (Dave is white and red, so Dave is round.)

Thus, following the provided information and rules, Dave fulfills the conditions to be round based on the rules that apply to him.

Therefore, the statement "Dave is not round" is **False (B)**.

Formalized Proof:
"Dave is young." = [rule4]("Dave is white.")
"Dave is kind." = [rule7]("Dave is young.")
"Dave is blue." = [rule2]("Dave is kind.")
"Dave is red." = [rule8]("Dave is white.", "Dave is blue.")
"Dave is round." = [rule3]("Dave is white.", "Dave is red.")

Q: Triples:
1. Charlie is not blue.
2. Charlie is white.
3. Erin is furry.
4. Gary is not quiet.
5. Gary is rough.
6. Gary is not young.
7. Harry is quiet.
Rules:
1. All white things are green.
2. Quiet things are green.
3. Quiet, rough things are young.
4. Quiet, white things are not blue.
5. If something is blue and white then it is rough.
6. If something is furry then it is rough.
7. If Gary is young then Gary is rough.
8. If Harry is young and Harry is quiet then Harry is not white.
9. Green things are furry.
Based on the above information, is the following statement true or false? Harry is white.
A) True B) False

Proof: To determine if the statement "Harry is white" is true or false, let's carefully analyze the available triples and the rules:

From the triples:
- Harry is quiet.

From the rules:
1. Quiet things are green. (Harry is quiet, so Harry is green.)
2. Green things are furry. (Harry is green, therefore, Harry is furry.)
3. If something is furry then it is rough. (Harry is furry, so Harry is rough.)
4. Quiet, rough things are young. (Harry is quiet and rough, so Harry is young.)
5. If Harry is young and Harry is quiet then Harry is not white. (Harry is young and quiet, so Harry is not white.)

Based on this analysis, since Harry meets the conditions for being young and quiet, the rule that "if Harry is young and Harry is quiet then Harry is not white" directly applies. 

Thus, the statement "Harry is white" is **False (B)**.

Formalized Proof:
"Harry is green." = [rule2]("Harry is quiet.")
"Harry is furry." = [rule9]("Harry is green.")
"Harry is rough." = [rule6]("Harry is furry.")
"Harry is young." = [rule3]("Harry is quiet.", "Harry is rough.")
"Harry is not white." = [rule8]("Harry is young.", "Harry is quiet.")

Q: {{question}}

Proof: 