Sure! For the given problem, we need to create a test case generator that will produce valid test cases according to the problem constraints. Here is the Python function to generate such test cases:

```python
import random

def tcgen():
    # Generate distinct values for a, b, and c
    a = random.randint(1, 5000)
    b = a
    c = a
    while b == a:
        b = random.randint(1, 5000)
    while c == a or c == b:
        c = random.randint(1, 5000)
    
    return a, b, c

# Example usage
for _ in range(5):
    a, b, c = tcgen()
    print(f"{a} {b} {c}")
```

This function generates three distinct integers \( a \), \( b \), and \( c \) within the given constraints. Here's a breakdown of how it works:

1. It first initializes \( a \) with a random integer between 1 and 5000.
2. It then initializes \( b \) and \( c \) to \( a \) to ensure that the initial values are the same.
3. It uses a while loop to ensure that \( b \) and \( c \) are distinct from \( a \) and each other.
4. Finally, it returns the three distinct values \( a \), \( b \), and \( c \).

You can run this function multiple times to generate different test cases. Each time, the function will produce a valid set of inputs according to the problem constraints.