"""Create fact_checker
Generated by Phi-Octopus Eden
2025-11-07 18:56:57.902205
"""

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

class FactChecker:
    """
    A class that provides fact-checking capabilities based on predefined rules.
    
    Attributes:
        rules (List[callable]): A list of functions representing the fact-checking rules.
    
    Methods:
        add_rule(rule: callable): Adds a new rule to the checker.
        check_fact(fact: str) -> bool: Checks if the given fact is true according to the defined rules.
    """
    
    def __init__(self):
        self.rules = []
        
    def add_rule(self, rule: callable):
        """Add a new fact-checking rule."""
        self.rules.append(rule)
        
    @lru_cache(maxsize=1024)  # Cache results for performance
    def check_fact(self, fact: str) -> bool:
        """
        Check if the given fact is true according to the defined rules.
        
        Args:
            fact (str): The fact to be checked.
        
        Returns:
            bool: True if the fact is considered true, False otherwise.
        """
        for rule in self.rules:
            result = rule(fact)
            if not result:
                return False
        return True

# Example usage and rules

def is_fact_true1(fact: str) -> bool:
    """Rule based on a simple condition."""
    return "error" not in fact.lower()

def is_fact_true2(fact: str) -> bool:
    """Another rule with a different logic."""
    return "data" in fact

# Create an instance of FactChecker and add rules
fact_checker = FactChecker()
fact_checker.add_rule(is_fact_true1)
fact_checker.add_rule(is_fact_true2)

# Check facts
print(fact_checker.check_fact("The system has no errors."))  # True
print(fact_checker.check_fact("Data integrity is compromised."))  # False, as the second rule fails
```

This code snippet creates a `FactChecker` class capable of checking facts based on predefined rules. It demonstrates how to add simple reasoning rules and use them to validate facts, addressing limited reasoning sophistication by using basic logical checks.