When an INTP (Introverted, Intuitive, Thinking, Perceiving) is mad, there are several signs and behaviors that can indicate their anger. However, it's important to note that each individual is unique, and these signs may vary from person to person. Here is a detailed description of how you can identify if an INTP is mad:

1. Withdrawal and Isolation: INTPs are known for their introverted nature, and when they are upset, they tend to withdraw and isolate themselves. They may retreat to their own space, avoiding social interactions and preferring solitude. They might also become unresponsive or distant when approached.

2. Intense Focus: When an INTP is angry, they often become highly focused on the source of their anger. They may spend a lot of time analyzing the situation, trying to understand the reasons behind their anger, and seeking logical solutions to resolve the issue.

3. Critical and Argumentative: INTPs have a strong inclination towards logical thinking and analysis. When they are mad, they may express their anger through critical and argumentative behavior. They might engage in debates, pointing out flaws in others' arguments or actions, and challenging their viewpoints.

4. Emotional Restraint: INTPs are not naturally inclined to express their emotions openly. When they are mad, they may try to suppress their emotions and maintain a calm exterior. They might appear composed and detached, even though they are experiencing intense anger internally.

5. Intellectualizing Emotions: INTPs have a tendency to intellectualize their emotions, including anger. They may try to understand the underlying causes of their anger, dissecting it into logical components. They might analyze the situation from different perspectives, seeking rational explanations for their emotional state.

6. Sarcasm and Wit: INTPs often use sarcasm and wit as a defense mechanism, especially when they are upset. When mad, they may employ these tools to express their anger indirectly, using humor and clever remarks to convey their dissatisfaction.

7. Need for Space and Time: INTPs require time and space to process their emotions. When they are mad, they may need some alone time to reflect and regain their emotional balance. They might prefer to distance themselves from the source of their anger until they feel ready to address the issue.

8. Difficulty Expressing Feelings: INTPs struggle with expressing their emotions, including anger. They may find it challenging to articulate their feelings directly, often resorting to indirect methods or relying on others to initiate conversations about their anger.

9. Revisiting Past Arguments: INTPs have a tendency to revisit past arguments or conflicts when they are mad. They may bring up past grievances or unresolved issues as a way to express their anger and frustration.

10. Seeking Logical Solutions: INTPs are problem-solvers by nature. When they are mad, they may channel their anger into finding logical solutions to the issue at hand. They might propose practical ways to resolve conflicts or suggest improvements to prevent similar situations in the future.

It's important to remember that these signs are generalizations and may not apply to every INTP. Additionally, individuals may display different behaviors depending on the severity of their anger and their personal coping mechanisms.