code: def test_infinite_strict_inequalities():
      # Extensive testing of the interaction between strict inequalities
      # and constraints containing infinity is needed because
      # the paper's rule for strict inequalities don't work when
      # infinite numbers are allowed. Using the paper's rules you
      # can end up with situations where oo + delta > oo is considered
      # True when oo + delta should be equal to oo.
      # See https://math.stackexchange.com/questions/4757069/can-this-method-of-converting-strict-inequalities-to-equisatisfiable-nonstrict-i
      bf = (-x - y >= -float("inf")) & (x > 0) & (y >= float("inf"))
      enc = boolean_formula_to_encoded_cnf(bf)
      lra, _ = LRASolver.from_encoded_cnf(enc, testing_mode=True)
      for lit in sorted(enc.encoding.values()):
          if lra.assert_lit(lit) is not None:
              break
      assert len(lra.enc_to_boundary) == 3
      assert lra.check()[0] == True
  
imports: from sympy.core.numbers import Rational, I, oo
  from sympy.core.relational import Eq
  from sympy.core.symbol import symbols
  from sympy.core.singleton import S
  from sympy.matrices.dense import Matrix
  from sympy.matrices.dense import randMatrix
  from sympy.assumptions.ask import Q
  from sympy.logic.boolalg import And
  from sympy.abc import x, y, z
  from sympy.assumptions.cnf import CNF, EncodedCNF
  from sympy.functions.elementary.trigonometric import cos
  from sympy.external import import_module
  from sympy.logic.algorithms.lra_theory import LRASolver, UnhandledInput, LRARational, HANDLE_NEGATION
  from sympy.core.random import random, choice, randint
  from sympy.core.sympify import sympify
  from sympy.ntheory.generate import randprime
  from sympy.core.relational import StrictLessThan, StrictGreaterThan
  import itertools
  from sympy.testing.pytest import raises, XFAIL, skip
label_desc: Use image node_id 13 for calling a global function with example usage: test_infinite_strict_inequalities() without return types