"""Create fact_checker
Generated by Phi-Octopus Eden
2025-11-07 11:48:00.686508
"""

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

class FactChecker:
    """
    A simple fact-checking class that verifies the truthfulness of given statements.
    The class uses a caching mechanism to store previously checked facts for efficiency.
    """

    def __init__(self):
        self.cache = {}
    
    @lru_cache(maxsize=100)
    def check_fact(self, statement: str) -> bool:
        """
        Check if the provided statement is true based on predefined rules or knowledge.

        :param statement: A string representing a fact to be checked.
        :return: True if the statement is verified as true, False otherwise.
        """
        # Example rule-based logic for checking facts
        if "is a" in statement:
            return self._check_is_a_statement(statement)
        elif "has been" in statement:
            return self._check_has_been_statement(statement)
        else:
            return False

    def _check_is_a_statement(self, statement: str) -> bool:
        """
        Helper method to check if a 'is a' type statement is true.

        :param statement: The statement to be checked.
        :return: True if the statement is verified as true, False otherwise.
        """
        entities = statement.split("is a ")
        entity1 = entities[0].strip()
        entity2 = entities[1].strip()

        # Example: 'dog is a mammal'
        known_facts = {
            "dog": ["mammal"],
            "cat": ["mammal"]
        }

        return entity2 in known_facts.get(entity1, [])

    def _check_has_been_statement(self, statement: str) -> bool:
        """
        Helper method to check if a 'has been' type statement is true.

        :param statement: The statement to be checked.
        :return: True if the statement is verified as true, False otherwise.
        """
        entities = statement.split(" has been ")
        event1 = entities[0].strip()
        event2 = entities[1].strip()

        # Example: 'rain has been falling'
        known_events = {
            "raining": ["has been falling"]
        }

        return event2 in known_events.get(event1, [])

def example_usage():
    """
    An example of how to use the FactChecker class.
    """
    fact_checker = FactChecker()
    
    # Example statements
    statements: List[str] = [
        "dog is a mammal",
        "cat has been seen at night",
        "rain has been falling for hours"
    ]
    
    for statement in statements:
        print(f"Checking '{statement}': {fact_checker.check_fact(statement)}")

if __name__ == "__main__":
    example_usage()
```

This code defines a `FactChecker` class with basic fact-checking capabilities. It includes caching to speed up repeated checks on the same facts and examples of how to use it. The logic is simplified for demonstration purposes, with only 'is a' and 'has been' types of statements being checked against predefined knowledge bases.