code: 
  '''simple docstring'''
  
  from __future__ import annotations
  
  import random
  from collections.abc import Iterable
  
  
  class   a_  :
  
  
  
  
         def __init__(     self   ,   snake_case_  ):
           _lowerCAmelCase       :  dict[str, bool | None]   				=					{literal: None for literal in literals}
  
  
  
  
         def __str__(     self  ):
           return "{" + " , ".join(self.literals  ) + "}"
  
  
  
  
         def __len__(     self  ):
           return len(self.literals  )
  
  
  
  
         def 							__UpperCamelCase       (     self   ,   snake_case_  ):
           for literal in self.literals:
             _lowerCAmelCase       :  Tuple   				=					literal[:2]
             if symbol in model:
               _lowerCAmelCase       :  List[str]   				=					model[symbol]
             else:
               continue
             if value is not None:
               # Complement assignment if literal is in complemented form
               if literal.endswith("""\'"""  ):
                 _lowerCAmelCase       :  List[str]   				=					not value
             _lowerCAmelCase       :  Dict   				=					value
  
  
  
  
  
  
  
         def 							__UpperCamelCase       (     self   ,   snake_case_  ):
           for literal in self.literals:
             _lowerCAmelCase       :  Any   				=					literal.rstrip("""\'"""  ) if literal.endswith("""\'"""  ) else literal + '\''
             if symbol in self.literals:
               return True
  
           self.assign(SCREAMING_SNAKE_CASE_  )
           for value in self.literals.values():
             if value in (True, None):
               return value
           return any(self.literals.values()  )
  
  
  
  class   a_  :
  
  
  
  
         def __init__(     self   ,   snake_case_  ):
           _lowerCAmelCase       :  Union[str, Any]   				=					list(SCREAMING_SNAKE_CASE_  )
  
  
  
  
  
  
  
         def __str__(     self  ):
           return "{" + " , ".join(str(SCREAMING_SNAKE_CASE_  ) for clause in self.clauses  ) + "}"
  
  
  
  def 	_UpperCAmelCase				(  )    ->						Clause:
    _lowerCAmelCase       :  List[Any]   				=					[]
    _lowerCAmelCase       :  Dict   				=					random.randint(1  ,      5		)
    _lowerCAmelCase       :  Any   				=					'A'
    _lowerCAmelCase       :  List[str]   				=					0
    while i < no_of_literals:
      _lowerCAmelCase       :  str   				=					random.randint(1  ,      5		)
      _lowerCAmelCase       :  int   				=					base_var + str(snake_case__		)
      _lowerCAmelCase       :  str   				=					random.randint(0  ,      1		)
      if var_complement == 1:
        var_name += "'"
      if var_name in literals:
        i -= 1
      else:
        literals.append(snake_case__		)
      i += 1
    return Clause(snake_case__		)
  
  
  def 	_UpperCAmelCase				(  )    ->						Formula:
    _lowerCAmelCase       :  set[Clause]   				=					set()
    _lowerCAmelCase       :  List[str]   				=					random.randint(1  ,      10		)
    while len(snake_case__		) < no_of_clauses:
      clauses.add(generate_clause()		)
    return Formula(snake_case__		)
  
  
  def 	_UpperCAmelCase				(  _lowerCamelCase						:       Formula		)    ->						tuple[list[Clause], list[str]]:
    _lowerCAmelCase       :  List[Any]   				=					formula.clauses
    _lowerCAmelCase       :  List[Any]   				=					[]
    for clause in formula.clauses:
      for literal in clause.literals:
        _lowerCAmelCase       :  str   				=					literal[:2]
        if symbol not in symbols_set:
          symbols_set.append(snake_case__		)
    return clauses, symbols_set
  
  
  def 	_UpperCAmelCase				(  _lowerCamelCase						:       list[Clause]  ,      _lowerCamelCase						:       list[str]  ,      _lowerCamelCase						:       dict[str, bool | None]		)    ->						tuple[list[str], dict[str, bool | None]]:
    _lowerCAmelCase       :  Any   				=					[]
    _lowerCAmelCase       :  dict[str, bool | None]   				=					{}
    _lowerCAmelCase       :  str   				=					[]
  
    for clause in clauses:
      if clause.evaluate(snake_case__		):
        continue
      for literal in clause.literals:
        literals.append(snake_case__		)
  
    for s in symbols:
      _lowerCAmelCase       :  str   				=					s + '\''
      if (s in literals and sym not in literals) or (
          s not in literals and sym in literals
      ):
        pure_symbols.append(snake_case__		)
    for p in pure_symbols:
      _lowerCAmelCase       :  List[str]   				=					None
    for s in pure_symbols:
      _lowerCAmelCase       :  Optional[int]   				=					s + '\''
      if s in literals:
        _lowerCAmelCase       :  List[str]   				=					True
      elif sym in literals:
        _lowerCAmelCase       :  Union[str, Any]   				=					False
    return pure_symbols, assignment
  
  
  def 	_UpperCAmelCase				(  _lowerCamelCase						:       list[Clause]  ,      _lowerCamelCase						:       dict[str, bool | None]		)    ->						tuple[list[str], dict[str, bool | None]]:
    _lowerCAmelCase       :  Any   				=					[]
    for clause in clauses:
      if len(snake_case__		) == 1:
        unit_symbols.append(list(clause.literals.keys()		)[0]		)
      else:
        _lowerCAmelCase       :  Optional[int]   				=					0, 0
        for literal, value in clause.literals.items():
          if value is False:
            f_count += 1
          elif value is None:
            _lowerCAmelCase       :  int   				=					literal
            n_count += 1
        if f_count == len(snake_case__		) - 1 and n_count == 1:
          unit_symbols.append(snake_case__		)
    _lowerCAmelCase       :  dict[str, bool | None]   				=					{}
    for i in unit_symbols:
      _lowerCAmelCase       :  List[str]   				=					i[:2]
      _lowerCAmelCase       :  Optional[Any]   				=					len(snake_case__		) == 2
    _lowerCAmelCase       :  Tuple   				=					[i[:2] for i in unit_symbols]
  
    return unit_symbols, assignment
  
  
  def 	_UpperCAmelCase				(  _lowerCamelCase						:       list[Clause]  ,      _lowerCamelCase						:       list[str]  ,      _lowerCamelCase						:       dict[str, bool | None]		)    ->						tuple[bool | None, dict[str, bool | None] | None]:
    _lowerCAmelCase       :  Optional[Any]   				=					True
    for clause in clauses:
      _lowerCAmelCase       :  Tuple   				=					clause.evaluate(snake_case__		)
      if clause_check is False:
        return False, None
      elif clause_check is None:
        _lowerCAmelCase       :  Any   				=					False
        continue
  
    if check_clause_all_true:
      return True, model
  
    try:
      _lowerCAmelCase       :  Dict   				=					find_pure_symbols(snake_case__  ,      snake_case__  ,      snake_case__		)
    except RecursionError:
      print("""raises a RecursionError and is"""		)
      return None, {}
    _lowerCAmelCase       :  Tuple   				=					None
    if len(snake_case__		) > 0:
      _lowerCAmelCase       :  Any   				=					pure_symbols[0], assignment[pure_symbols[0]]
  
    if p:
      _lowerCAmelCase       :  int   				=					model
      _lowerCAmelCase       :  List[str]   				=					value
      _lowerCAmelCase       :  Tuple   				=					list(snake_case__		)
      if p in tmp_symbols:
        tmp_symbols.remove(snake_case__		)
      return dpll_algorithm(snake_case__  ,      snake_case__  ,      snake_case__		)
  
    _lowerCAmelCase       :  int   				=					find_unit_clauses(snake_case__  ,      snake_case__		)
    _lowerCAmelCase       :  List[Any]   				=					None
    if len(snake_case__		) > 0:
      _lowerCAmelCase       :  int   				=					unit_symbols[0], assignment[unit_symbols[0]]
    if p:
      _lowerCAmelCase       :  Optional[int]   				=					model
      _lowerCAmelCase       :  str   				=					value
      _lowerCAmelCase       :  Union[str, Any]   				=					list(snake_case__		)
      if p in tmp_symbols:
        tmp_symbols.remove(snake_case__		)
      return dpll_algorithm(snake_case__  ,      snake_case__  ,      snake_case__		)
    _lowerCAmelCase       :  List[Any]   				=					symbols[0]
    _lowerCAmelCase       :  Optional[Any]   				=					symbols[1:]
    _lowerCAmelCase       :  int   				=					model, model
    _lowerCAmelCase       :  Optional[int]   				=					True, False
  
    return dpll_algorithm(snake_case__  ,      snake_case__  ,      snake_case__		) or dpll_algorithm(snake_case__  ,      snake_case__  ,      snake_case__		)
  
  
  if __name__ == "__main__":
       import doctest
  
       doctest.testmod()
  
       UpperCamelCase_     			=       generate_formula()
       print(F'The formula {formula} is', end=""" """)
  
       UpperCamelCase_			,					UpperCamelCase_     			=       generate_parameters(formula)
       UpperCamelCase_			,					UpperCamelCase_     			=       dpll_algorithm(clauses, symbols, {})
  
       if solution:
            print(F'satisfiable with the assignment {model}.')
       else:
            print("""not satisfiable.""")
  
  
  
  
  
  
style_context: 
  '''simple docstring'''
  
  def 	_UpperCAmelCase				(  _lowerCamelCase						:       int  ,      _lowerCamelCase						:       int  ,      _lowerCamelCase						:       int		)    ->						float:
    if common_ratio == 1:
      # Formula for sum if common ratio is 1
      return num_of_terms * first_term
  
    # Formula for finding sum of n terms of a GeometricProgression
    return (first_term / (1 - common_ratio)) * (1 - common_ratio**num_of_terms)
  
  
  