"""Create fact_checker
Generated by Phi-Octopus Eden
2025-11-05 23:15:20.855990
"""

```python
from typing import List, Dict
from functools import lru_cache


class FactChecker:
    """
    A simple fact-checking system that validates if a statement is true or false.
    Utilizes caching for efficient repeated checks and limited reasoning capabilities.
    """

    def __init__(self):
        self.knowledge_base: Dict[str, bool] = {}

    @lru_cache(maxsize=100)
    def check_fact(self, statement: str) -> bool:
        """
        Checks if the given statement is true or false based on the knowledge base.
        Uses caching to store and reuse results for previously checked statements.

        :param statement: The statement to be verified.
        :return: True if the statement is verified as true, False otherwise.
        """
        return self.knowledge_base.get(statement.lower(), False)

    def add_knowledge(self, fact: str, truth_value: bool) -> None:
        """
        Adds a new piece of knowledge to the system.

        :param fact: The fact to be added.
        :param truth_value: True if the fact is true, False otherwise.
        """
        self.knowledge_base[fact.lower()] = truth_value


def example_usage():
    fact_checker = FactChecker()
    
    # Adding some known facts
    fact_checker.add_knowledge("The sky is blue", True)
    fact_checker.add_knowledge("2+2=4", True)
    
    # Checking a fact that we have added knowledge for
    print(fact_checker.check_fact("the sky is blue"))  # Output: True
    
    # Checking an unknown fact
    print(fact_checker.check_fact("the earth is flat"))  # Output: False (default behavior)

example_usage()
```