import sympy as sp
from typing import Dict, Any, Optional

class ProofEngine:
    """Attempts to prove or disprove mathematical statements using symbolic computation."""
    def __init__(self):
        pass

    def prove(self, statement: str, variables: Optional[Dict[str, Any]] = None) -> Dict[str, Any]:
        # Try to parse and prove a symbolic statement
        try:
            expr = sp.sympify(statement)
            result = sp.simplify(expr)
            return {"success": True, "result": str(result)}
        except Exception as e:
            return {"success": False, "error": str(e)}

    def find_counterexample(self, statement: str, test_values: Optional[Dict[str, Any]] = None) -> Dict[str, Any]:
        # Try to find a counterexample (very basic, for demo)
        if not test_values:
            test_values = {"x": range(-10, 10)}
        try:
            expr = sp.sympify(statement)
            for x in test_values["x"]:
                if not expr.subs("x", x):
                    return {"counterexample": x}
            return {"counterexample": None}
        except Exception as e:
            return {"error": str(e)}
