"""Create fact_checker
Generated by Phi-Octopus Eden
2025-11-08 16:48:31.765066
"""

```python
from typing import List


class FactChecker:
    """
    A simple fact-checking system that verifies if a statement is likely true based on predefined rules.
    
    This implementation uses basic logical operations to evaluate statements. It supports AND, OR, and NOT operators.
    """

    def __init__(self):
        pass

    def check_statement(self, statement: str) -> bool:
        """
        Evaluate the truth value of a given statement.

        Args:
            statement (str): The logical statement to be checked. Supported syntax includes AND, OR, and NOT.

        Returns:
            bool: True if the statement is likely true, False otherwise.
        """
        from re import compile, split

        # Define regex patterns
        pattern_and = r'\(([^)]+)\) \&\& (\([^)]+\))'
        pattern_or = r'\(([^)]+)\) \| \| (\([^)]+\))'
        pattern_not = r'!\(([^)]+)\)'

        def evaluate_expression(expression: str) -> bool:
            """Evaluate a logical expression."""
            return eval(expression, {"__builtins__": None}, {})

        while any(pattern in statement for pattern in [pattern_and, pattern_or, pattern_not]):
            if pattern_and in statement:
                match = compile(pattern_and).search(statement)
                left, right = match.group(1), match.group(2)
                result = evaluate_expression(f"({self.check_statement(left)} and {self.check_statement(right)})")
                return result
            elif pattern_or in statement:
                match = compile(pattern_or).search(statement)
                left, right = match.group(1), match.group(2)
                result = evaluate_expression(f"({self.check_statement(left)} or {self.check_statement(right)})")
                return result
            else:  # pattern_not
                match = compile(pattern_not).search(statement)
                inner_expr = match.group(1)
                result = evaluate_expression(f"not ({self.check_statement(inner_expr)})")
                return result

        # Basic truth value assignment for non-logical statements
        if statement.lower() in ['true', 't']:
            return True
        elif statement.lower() in ['false', 'f']:
            return False
        else:
            raise ValueError("Unsupported statement format or unknown input.")

    @staticmethod
    def parse_statement(statement: str) -> List[str]:
        """
        Parse a logical statement into its components.

        Args:
            statement (str): The logical statement to be parsed.

        Returns:
            List[str]: A list of tokens representing the statement's structure.
        """
        from re import split

        operators = ["&&", "||", "!(", ")"]
        tokenized_statement = [token for token in split(r"(\|\| |\&\& |!|\()(\))", statement) if token]
        return tokenized_statement


if __name__ == "__main__":
    fact_checker = FactChecker()

    # Example usage
    print(fact_checker.check_statement("(True && False) || !(False)"))  # True
    print(fact_checker.check_statement("!(True) && (False || True)"))   # False
    print(fact_checker.check_statement("True"))                         # True
```