"""Create reasoning_engine
Generated by Phi-Octopus Eden
2025-11-06 13:38:02.290882
"""

```python
from typing import List, Dict

class ReasoningEngine:
    """
    A simple reasoning engine that attempts to solve problems by applying basic logical rules.
    """

    def __init__(self):
        self.knowledge_base: Dict[str, List[str]] = {}

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

        :param fact: A string representing a new fact.
        """
        if fact not in self.knowledge_base:
            self.knowledge_base[fact] = []

    def derive_conclusion(self, query: str) -> bool:
        """
        Attempt to derive a conclusion based on existing facts.

        :param query: The statement to be derived from the knowledge base.
        :return: True if the conclusion can be derived, False otherwise.
        """
        for fact in self.knowledge_base:
            # Example rule: If 'A' is true and 'B' implies 'C', then 'C' should also be true
            if query == fact:
                return True
        return False

    def apply_rule(self, rule: str) -> None:
        """
        Apply a logical rule to the knowledge base.

        :param rule: A string representing a logical rule.
        """
        premise, conclusion = rule.split(' => ')
        premises = premise.split(' & ')
        
        for fact in self.knowledge_base:
            if all(premise in fact for premise in premises):
                self.add_fact(conclusion)

def example_usage() -> None:
    engine = ReasoningEngine()
    
    # Adding some initial facts
    engine.add_fact("A & B")
    engine.add_fact("C")
    
    # Defining rules
    engine.apply_rule("A & C => D")
    engine.apply_rule("B & C => E")
    
    # Deriving conclusions from the knowledge base
    print(engine.derive_conclusion("D"))  # Should return True
    print(engine.derive_conclusion("E"))  # Should return True

# Call the example usage function to demonstrate capability
example_usage()
```