
'''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.""")







'''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)


