code: def test_integer():
      assert satask(Q.integer(1)) is True
      assert satask(Q.integer(S.Half)) is False
  
      assert (
          satask(Q.integer(x + y), Q.integer(x) & Q.integer(y)) is True
      )
      assert satask(Q.integer(x + y), Q.integer(x)) is None
  
      assert (
          satask(Q.integer(x + y), Q.integer(x) & ~Q.integer(y))
          is False
      )
      assert (
          satask(
              Q.integer(x + y + z),
              Q.integer(x) & Q.integer(y) & ~Q.integer(z),
          )
          is False
      )
      assert (
          satask(
              Q.integer(x + y + z),
              Q.integer(x) & ~Q.integer(y) & ~Q.integer(z),
          )
          is None
      )
      assert (
          satask(Q.integer(x + y + z), Q.integer(x) & ~Q.integer(y))
          is None
      )
      assert (
          satask(Q.integer(x + y), Q.integer(x) & Q.irrational(y))
          is False
      )
  
      assert (
          satask(Q.integer(x * y), Q.integer(x) & Q.integer(y)) is True
      )
      assert satask(Q.integer(x * y), Q.integer(x)) is None
  
      assert (
          satask(Q.integer(x * y), Q.integer(x) & ~Q.integer(y)) is None
      )
      assert (
          satask(Q.integer(x * y), Q.integer(x) & ~Q.rational(y))
          is False
      )
      assert (
          satask(
              Q.integer(x * y * z),
              Q.integer(x) & Q.integer(y) & ~Q.rational(z),
          )
          is False
      )
      assert (
          satask(
              Q.integer(x * y * z),
              Q.integer(x) & ~Q.rational(y) & ~Q.rational(z),
          )
          is None
      )
      assert (
          satask(Q.integer(x * y * z), Q.integer(x) & ~Q.rational(y))
          is None
      )
      assert (
          satask(Q.integer(x * y), Q.integer(x) & Q.irrational(y))
          is False
      )
  
imports: from sympy.assumptions.ask import Q
  from sympy.assumptions.assume import assuming
  from sympy.core.numbers import I, pi
  from sympy.core.relational import Eq, Gt
  from sympy.core.singleton import S
  from sympy.core.symbol import symbols
  from sympy.functions.elementary.complexes import Abs
  from sympy.logic.boolalg import Implies
  from sympy.matrices.expressions.matexpr import MatrixSymbol
  from sympy.assumptions.cnf import CNF, Literal
  from sympy.assumptions.satask import satask, extract_predargs, get_relevant_clsfacts
  from sympy.testing.pytest import raises, XFAIL
label_desc: Use image node_id 11 for calling a global function with example usage: test_integer() without return types