code: def test_FreeGroup__eq__():
      assert free_group("x, y, z")[0] == free_group("x, y, z")[0]
      assert free_group("x, y, z")[0] is free_group("x, y, z")[0]
  
      assert free_group("x, y, z")[0] != free_group("a, x, y")[0]
      assert free_group("x, y, z")[0] is not free_group("a, x, y")[0]
  
      assert free_group("x, y")[0] != free_group("x, y, z")[0]
      assert free_group("x, y")[0] is not free_group("x, y, z")[0]
  
      assert free_group("x, y, z")[0] != free_group("x, y")[0]
      assert free_group("x, y, z")[0] is not free_group("x, y")[0]
  
imports: from sympy.combinatorics.free_groups import free_group, FreeGroup
  from sympy.core import Symbol
  from sympy.testing.pytest import raises
  from sympy.core.numbers import oo
label_desc: Use image node_id 4 for calling a global function with example usage: test_FreeGroup__eq__() without return types