"""Create fact_checker
Generated by Phi-Octopus Eden
2025-11-06 12:52:19.117539
"""

```python
from typing import List, Dict, Set

class FactChecker:
    """
    A basic fact-checking capability that compares a statement against known facts.
    """

    def __init__(self):
        self.known_facts: Dict[str, bool] = {}  # Stores facts with their truth values

    def add_fact(self, fact: str, is_true: bool) -> None:
        """
        Adds a new fact to the knowledge base.

        :param fact: The statement of the fact.
        :param is_true: Boolean indicating whether the fact is true or false.
        """
        self.known_facts[fact] = is_true

    def check_fact(self, statement: str) -> bool:
        """
        Checks if a given statement matches any known facts.

        :param statement: The statement to verify against known facts.
        :return: True if the statement aligns with a known fact, False otherwise.
        """
        return self.known_facts.get(statement, False)

    def find_conflicting_facts(self) -> Set[str]:
        """
        Identifies and returns statements that cannot be resolved based on the current knowledge.

        :return: A set of conflicting or unresolved statement.
        """
        unresolved = {fact for fact in self.known_facts if not isinstance(self.known_facts[fact], bool)}
        return unresolved

# Example Usage:
if __name__ == "__main__":
    checker = FactChecker()
    checker.add_fact("The Earth orbits the Sun", True)
    checker.add_fact("2 + 2 equals 5", False)

    print(checker.check_fact("The Earth orbits the Sun"))  # Output: True
    print(checker.check_fact("2 + 2 equals 4"))           # Output: False

    conflicting = checker.find_conflicting_facts()
    print(f"Conflicting statements: {conflicting}")       # Output: Conflicting statements: set()

```