code: def test_dpll2_satisfiable():
      A, B, C = symbols("A,B,C")
      assert dpll2_satisfiable(A & ~A) is False
      assert dpll2_satisfiable(A & ~B) == {A: True, B: False}
      assert dpll2_satisfiable(A | B) in (
          {A: True},
          {B: True},
          {A: True, B: True},
      )
      assert dpll2_satisfiable((~A | B) & (~B | A)) in (
          {A: True, B: True},
          {A: False, B: False},
      )
      assert dpll2_satisfiable((A | B) & (~B | C)) in (
          {A: True, B: False, C: True},
          {A: True, B: True, C: True},
      )
      assert dpll2_satisfiable(A & B & C) == {A: True, B: True, C: True}
      assert dpll2_satisfiable((A | B) & (A >> B)) in (
          {B: True, A: False},
          {B: True, A: True},
      )
      assert dpll2_satisfiable(Equivalent(A, B) & A) == {
          A: True,
          B: True,
      }
      assert dpll2_satisfiable(Equivalent(A, B) & ~A) == {
          A: False,
          B: False,
      }
  
imports: from sympy.assumptions.ask import Q
  from sympy.core.symbol import symbols
  from sympy.core.relational import Unequality
  from sympy.logic.boolalg import And, Or, Implies, Equivalent, true, false
  from sympy.logic.inference import literal_symbol, pl_true, satisfiable, valid, entails, PropKB
  from sympy.logic.algorithms.dpll import dpll, dpll_satisfiable, find_pure_symbol, find_unit_clause, unit_propagate, find_pure_symbol_int_repr, find_unit_clause_int_repr, unit_propagate_int_repr
  from sympy.logic.algorithms.dpll2 import dpll_satisfiable
  from sympy.logic.algorithms.z3_wrapper import z3_satisfiable
  from sympy.assumptions.cnf import CNF, EncodedCNF
  from sympy.logic.tests.test_lra_theory import make_random_problem
  from sympy.core.random import randint
  from sympy.testing.pytest import raises, skip
  from sympy.external import import_module
label_desc: Use image node_id 10 for calling a global function with example usage: test_dpll2_satisfiable() without return types