To generate test cases for the competitive programming problem described, we need to take into account the constraints and format of the input. Here’s a Python function that generates random test cases:

```python
import random
import string

def generate_random_problem_name():
    # Generate a random problem name with length between 1 and 10
    length = random.randint(1, 10)
    return ''.join(random.choice(string.ascii_uppercase) for _ in range(length))

def tcgen():
    N = random.randint(1, 10**4)
    K = random.randint(1, 26)
    P = [generate_random_problem_name() for _ in range(N)]
    
    # Format the output to match the required input format
    return N, K, P

# Function to print the generated test case in the required format
def print_test_case():
    N, K, P = tcgen()
    print(N, K)
    for problem in P:
        print(problem)

# Example usage:
print_test_case()
```

### Explanation:
1. **generate_random_problem_name:** This function generates a random problem name of length between 1 and 10 using uppercase English letters.
2. **tcgen:** This function generates the test case:
   - `N` is an integer between 1 and 10,000.
   - `K` is an integer between 1 and 26.
   - `P` is a list of `N` problem names generated by the `generate_random_problem_name` function.
3. **print_test_case:** This function prints the generated test case in the required format.

### Usage:
To generate and print a test case, simply call the `print_test_case()` function. This will produce the test case in the format expected by the problem statement. You can run the function multiple times to generate different test cases for extensive testing.

This setup ensures that the generated test cases adhere to the constraints and format specified in the problem statement, making it suitable for testing the solution effectively.