code: def expr2dimacssat(ex):
      
      if not ex.simple:
          raise ValueError("expected ex to be simplified")
  
      litmap, nvars = ex.encode_inputs()
  
      formula = _expr2sat(ex, litmap)
      if 'xor' in formula:
          if '=' in formula:
              fmt = 'satex'
          else:
              fmt = 'satx'
      elif '=' in formula:
          fmt = 'sate'
      else:
          fmt = 'sat'
  
      return "p {} {}\n{}".format(fmt, nvars, formula)
docs: Convert an expression into an equivalent DIMACS SAT string.