"""Create fact_checker
Generated by Phi-Octopus Eden
2025-11-07 17:21:16.262737
"""

```python
from typing import List, Dict


class FactChecker:
    """
    A simple fact-checking system that verifies if a given statement is true based on predefined facts.
    """

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

    def add_fact(self, statement: str, value: bool) -> None:
        """
        Add or update a factual statement.

        :param statement: The fact to be added or updated
        :param value: True if the statement is true, False otherwise
        """
        self.facts[statement] = value

    def check_fact(self, statement: str) -> bool:
        """
        Check if a given statement is in the system's knowledge base and return its truth value.

        :param statement: The fact to be checked
        :return: True if the statement is true, False otherwise. Returns None if the statement is not found.
        """
        return self.facts.get(statement)

    def verify_statement(self, statement: str) -> bool:
        """
        Verify a statement based on available facts and limited reasoning.

        This method checks for direct truth values first, then tries to infer from existing facts.
        Limited reasoning means it can only handle simple logical inferences.

        :param statement: The statement to be verified
        :return: True if the statement is deemed true, False otherwise. Returns None if no inference can be made.
        """
        # Direct lookup for truth value
        result = self.check_fact(statement)
        if result is not None:
            return result

        # Simple logical inferences (AND, OR) based on existing facts
        for fact in self.facts.keys():
            inferred_statement = statement.replace("A", fact).replace("B", "not A")
            if all(fact in inferred_statement and self.check_fact(fact) is not None for fact in ("A", "B")):
                return True  # If both parts of the OR are true, infer the OR statement

        return False  # Default to False if no direct or simple logical inference can be made


# Example usage
if __name__ == "__main__":
    checker = FactChecker()
    checker.add_fact("The sky is blue", True)
    checker.add_fact("Penguins live in Antarctica", True)

    print(checker.verify_statement("The sky is blue OR penguins live in Antarctica"))  # Expected: True
    print(checker.verify_statement("Penguins live in Australia"))  # Expected: None (no fact found)
    print(checker.verify_statement("Penguins don't live in Antarctica"))  # Expected: False
```

This code defines a `FactChecker` class that can add and check facts, with limited reasoning capabilities to infer simple logical statements based on existing facts.