"""Create fact_checker
Generated by Phi-Octopus Eden
2025-11-08 14:15:30.871681
"""

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

class FactChecker:
    """
    A class that provides methods to check facts based on given statements.
    It uses a simple caching mechanism for efficiency and can handle limited reasoning sophistication.
    """

    def __init__(self, known_statements: List[str]):
        self.known_statements = set(known_statement.lower() for known_statement in known_statements)

    def is_fact(self, statement: str) -> bool:
        """
        Check if the provided statement is a fact based on known statements.
        
        :param statement: The statement to check.
        :return: True if it's a fact, False otherwise.
        """
        return statement.lower() in self.known_statements

    @lru_cache(maxsize=1024)
    def reason_about_fact(self, fact_to_reason: str) -> bool:
        """
        A simple method to perform basic logical reasoning about a fact based on known statements.
        
        :param fact_to_reason: The statement to reason about.
        :return: True if the reasoning confirms it as a fact, False otherwise.
        """
        lower_fact = fact_to_reason.lower()
        for known in self.known_statements:
            # Simple pattern matching - assuming "if A then B" type of reasoning
            if "if {} then {}".format(known, lower_fact) in self.known_statements:
                return True
        return False

# Example usage
if __name__ == "__main__":
    known_statements = [
        "All humans are mortal",
        "Socrates is a human",
        "If A then B"  # A being a human, B being mortal
    ]
    
    fact_checker = FactChecker(known_statements)
    
    print(fact_checker.is_fact("Socrates is mortal"))  # True based on known statements and simple reasoning
    
    complex_statement = "If Socrates is not mortal, then he is immortal"
    print(fact_checker.reason_about_fact(complex_statement))  # False, because Socrates being mortal is a fact

```