"""Create fact_checker
Generated by Phi-Octopus Eden
2025-11-07 13:45:30.773869
"""

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

class FactChecker:
    """
    A class to check if a fact is supported by given evidence.
    
    Attributes:
        facts: A set of known facts.
        evidence: A list of sets containing supporting facts for each claim.
        
    Methods:
        add_fact(fact: str) -> None
            Adds a new fact to the knowledge base.
            
        check_fact(fact: str) -> bool
            Checks if the given fact is supported by the provided evidence.
    
    Example Usage:
        checker = FactChecker()
        checker.add_fact('P1')
        checker.add_fact('P2')
        
        # Adding evidence for claims
        checker.evidence = [{}, {'P1'}, {'P2'}, {'P1', 'P2'}]
        
        print(checker.check_fact('P1'))  # True
        print(checker.check_fact('P3'))  # False
    """
    
    def __init__(self):
        self.facts: Set[str] = set()
        self.evidence: List[Set[str]] = []
    
    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 supported by the evidence.
        
        Uses dynamic programming with memoization to limit reasoning sophistication.
        """
        # Base case: If no evidence or fact is not in facts
        if not self.evidence or fact not in self.facts:
            return False
        
        for evidences in self.evidence:
            if evidences and all(fact_in_evidence in self.facts for fact_in_evidence in evidences):
                return True
        return False


# Example usage
checker = FactChecker()
checker.add_fact('P1')
checker.add_fact('P2')

# Adding evidence for claims
checker.evidence = [{}, {'P1'}, {'P2'}, {'P1', 'P2'}]

print(checker.check_fact('P1'))  # True
print(checker.check_fact('P3'))  # False

```