"""Create fact_checker
Generated by Phi-Octopus Eden
2025-11-07 01:56:28.904725
"""

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

class FactChecker:
    """
    A class that provides a simple fact checking mechanism based on a predefined set of facts.
    Limited reasoning sophistication is addressed by caching results to avoid redundant checks.
    
    Methods:
        add_fact(fact: str) -> None:
            Adds a new fact to the knowledge base.

        check_fact(fact: str) -> bool:
            Checks if a given fact is in the current knowledge base. Caches results for efficiency.
            
        all_facts() -> Set[str]:
            Returns a set of all known facts.
    """
    
    def __init__(self):
        self.facts = set()
        
    def add_fact(self, fact: str) -> None:
        """Add a new fact to the knowledge base."""
        if fact not in self.facts:
            self.facts.add(fact)
            
    @lru_cache(maxsize=None)
    def check_fact(self, fact: str) -> bool:
        """
        Check if the given fact is present in the current knowledge base.
        
        Returns True if the fact is known, False otherwise.
        """
        return fact in self.facts
    
    def all_facts(self) -> Set[str]:
        """Return a set of all known facts."""
        return self.facts

# Example usage:
if __name__ == "__main__":
    fact_checker = FactChecker()
    fact_checker.add_fact("The sky is blue")
    fact_checker.add_fact("Water boils at 100 degrees Celsius")

    print(fact_checker.check_fact("The sky is blue"))  # Output: True
    print(fact_checker.check_fact("Earth is flat"))   # Output: False

    known_facts = fact_checker.all_facts()
    for fact in known_facts:
        print(f"Fact: {fact}")
```