Sure! Here's a test case generator for the given problem statement:

```python
import random

def generate_test_case():
    # Generate a random value for N
    N = random.randint(1, 18)
    
    # Generate 2^N random integers for the hardness values
    A = [random.randint(1, 10**9) for _ in range(2**N)]
    
    return N, A

def print_test_case(N, A):
    print(N)
    for hardness in A:
        print(hardness)

# Example of generating and printing a test case
if __name__ == "__main__":
    N, A = generate_test_case()
    print_test_case(N, A)
```

This script generates a test case for the problem statement involving a knockout tournament of stones with given hardness values. The function `generate_test_case` creates a random value for `N` between 1 and 18, and then generates `2^N` random integers for the hardness values, each between 1 and `10^9`. The function `print_test_case` is used to print the generated test case in the required format.

You can run the script to generate and print a test case. This will help you to test your solution by providing various random inputs.