code: def satisfiable(
      expr,
      algorithm=None,
      all_models=False,
      minimal=False,
      use_lra_theory=False,
  ):
      """
      Check satisfiability of a propositional sentence.
      Returns a model when it succeeds.
      Returns {true: true} for trivially true expressions.
  
      On setting all_models to True, if given expr is satisfiable then
      returns a generator of models. However, if expr is unsatisfiable
      then returns a generator containing the single element False.
  
      Examples
      ========
  
      >>> from sympy.abc import A, B
      >>> from sympy.logic.inference import satisfiable
      >>> satisfiable(A & ~B)
      {A: True, B: False}
      >>> satisfiable(A & ~A)
      False
      >>> satisfiable(True)
      {True: True}
      >>> next(satisfiable(A & ~A, all_models=True))
      False
      >>> models = satisfiable((A >> B) & B, all_models=True)
      >>> next(models)
      {A: False, B: True}
      >>> next(models)
      {A: True, B: True}
      >>> def use_models(models):
      ...     for model in models:
      ...         if model:
      ...             # Do something with the model.
      ...             print(model)
      ...         else:
      ...             # Given expr is unsatisfiable.
      ...             print("UNSAT")
      >>> use_models(satisfiable(A >> ~A, all_models=True))
      {A: False}
      >>> use_models(satisfiable(A ^ A, all_models=True))
      UNSAT
  
      """
      if use_lra_theory:
          if algorithm is not None and algorithm != "dpll2":
              raise ValueError(
                  f"Currently only dpll2 can handle using lra theory. {algorithm} is not handled."
              )
          algorithm = "dpll2"
  
      if algorithm is None or algorithm == "pycosat":
          pycosat = import_module("pycosat")
          if pycosat is not None:
              algorithm = "pycosat"
          else:
              if algorithm == "pycosat":
                  raise ImportError("pycosat module is not present")
              # Silently fall back to dpll2 if pycosat
              # is not installed
              algorithm = "dpll2"
  
      if algorithm == "minisat22":
          pysat = import_module("pysat")
          if pysat is None:
              algorithm = "dpll2"
  
      if algorithm == "z3":
          z3 = import_module("z3")
          if z3 is None:
              algorithm = "dpll2"
  
      if algorithm == "dpll":
          from sympy.logic.algorithms.dpll import dpll_satisfiable
  
          return dpll_satisfiable(expr)
      elif algorithm == "dpll2":
          from sympy.logic.algorithms.dpll2 import dpll_satisfiable
  
          return dpll_satisfiable(
              expr, all_models, use_lra_theory=use_lra_theory
          )
      elif algorithm == "pycosat":
          from sympy.logic.algorithms.pycosat_wrapper import (
              pycosat_satisfiable,
          )
  
          return pycosat_satisfiable(expr, all_models)
      elif algorithm == "minisat22":
          from sympy.logic.algorithms.minisat22_wrapper import (
              minisat22_satisfiable,
          )
  
          return minisat22_satisfiable(expr, all_models, minimal)
      elif algorithm == "z3":
          from sympy.logic.algorithms.z3_wrapper import z3_satisfiable
  
          return z3_satisfiable(expr, all_models)
  
      raise NotImplementedError
  
imports: from sympy.logic.boolalg import And, Not, conjuncts, to_cnf, BooleanFunction
  from sympy.core.sorting import ordered
  from sympy.core.sympify import sympify
  from sympy.external.importtools import import_module
label_desc: Use image node_id 2 for calling a global function with example usage: satisfiable(expr, algorithm, all_models, minimal, use_lra_theory) and returns: dpll_satisfiable, dpll_satisfiable, pycosat_satisfiable, minisat22_satisfiable, z3_satisfiable