code: def check_if_satisfiable_with_z3(constraints):
      from sympy.external.importtools import import_module
      from sympy.printing.smtlib import smtlib_code
      from sympy.logic.boolalg import And
  
      boolean_formula = And(*constraints)
      z3 = import_module("z3")
      if z3:
          smtlib_string = smtlib_code(boolean_formula)
          s = z3.Solver()
          s.from_string(smtlib_string)
          res = str(s.check())
          if res == "sat":
              return True
          elif res == "unsat":
              return False
          else:
              raise ValueError(
                  f"z3 was not able to check the satisfiability of {boolean_formula}"
              )
  
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 2 for calling a global function with example usage: check_if_satisfiable_with_z3(constraints) and returns: True, False