


from __future__ import annotations

import random
from collections.abc import Iterable





class    _a				:




	def __init__(   self		:						List[Any]						,   _SCREAMING_SNAKE_CASE		:						List[str]						)->			Tuple:
			lowerCAmelCase__  :     List[str]       	=   {literal: None for literal in literals}




	def __str__(   self		:						List[str]						)->			List[str]:
			return "{" + " , ".join(self.literals						) + "}"




	def __len__(   self		:						Optional[Any]						)->			Optional[int]:
			return len(self.literals						)




	def 				UpperCAmelCase__(   self		:						int						,   _SCREAMING_SNAKE_CASE		:						Dict						)->			Optional[int]:



			for literal in self.literals:
					lowerCAmelCase__  :     Optional[int]       	=   literal[:2]
					if symbol in model:
							lowerCAmelCase__  :     str       	=   model[symbol]
					else:
							continue
					if value is not None:
							# Complement assignment if literal is in complemented form
							if literal.endswith('''\''''						):
									lowerCAmelCase__  :     str       	=   not value
					lowerCAmelCase__  :     Optional[Any]       	=   value




	def 				UpperCAmelCase__(   self		:						str						,   _SCREAMING_SNAKE_CASE		:						Any						)->			Any:



			for literal in self.literals:
					lowerCAmelCase__  :     List[str]       	=   literal.rstrip('''\''''						) if literal.endswith('''\''''						) else literal + '''\''''
					if symbol in self.literals:
							return True

			self.assign(A_						)
			for value in self.literals.values():
					if value in (True, None):
							return value
			return any(self.literals.values()						)





class    _a				:




	def __init__(   self		:						List[str]						,   _SCREAMING_SNAKE_CASE		:						List[Any]						)->			Optional[int]:
			lowerCAmelCase__  :     List[Any]       	=   list(A_						)




	def __str__(   self		:						Optional[int]						)->			Dict:
			return "{" + " , ".join(str(A_						) for clause in self.clauses						) + "}"






def 	lowerCamelCase_       (			):




		"""simple docstring"""






		lowerCAmelCase__  :     Tuple       	=   []
		lowerCAmelCase__  :     Any       	=   random.randint(1      ,  5			)
		lowerCAmelCase__  :     Any       	=   '''A'''
		lowerCAmelCase__  :     Optional[int]       	=   0
		while i < no_of_literals:
				lowerCAmelCase__  :     Tuple       	=   random.randint(1      ,  5			)
				lowerCAmelCase__  :     List[str]       	=   base_var + str(UpperCamelCase__			)
				lowerCAmelCase__  :     Optional[Any]       	=   random.randint(0      ,  1			)
				if var_complement == 1:
						var_name += "'"
				if var_name in literals:
						i -= 1
				else:
						literals.append(UpperCamelCase__			)
				i += 1
		return Clause(UpperCamelCase__			)






def 	lowerCamelCase_       (			):




		"""simple docstring"""






		lowerCAmelCase__  :     List[Any]       	=   set()
		lowerCAmelCase__  :     List[Any]       	=   random.randint(1      ,  10			)
		while len(UpperCamelCase__			) < no_of_clauses:
				clauses.add(generate_clause()			)
		return Formula(UpperCamelCase__			)






def 	lowerCamelCase_       (			_a			):




		"""simple docstring"""






		lowerCAmelCase__  :     int       	=   formula.clauses
		lowerCAmelCase__  :     List[Any]       	=   []
		for clause in formula.clauses:
				for literal in clause.literals:
						lowerCAmelCase__  :     Optional[int]       	=   literal[:2]
						if symbol not in symbols_set:
								symbols_set.append(UpperCamelCase__			)
		return clauses, symbols_set






def 	lowerCamelCase_       (			_a      ,  _a      ,  _a			):




		"""simple docstring"""






		lowerCAmelCase__  :     Union[str, Any]       	=   []
		lowerCAmelCase__  :     Any       	=   {}
		lowerCAmelCase__  :     Any       	=   []

		for clause in clauses:
				if clause.evaluate(UpperCamelCase__			):
						continue
				for literal in clause.literals:
						literals.append(UpperCamelCase__			)

		for s in symbols:
				lowerCAmelCase__  :     Union[str, Any]       	=   s + '''\''''
				if (s in literals and sym not in literals) or (
				    s not in literals and sym in literals
				):
						pure_symbols.append(UpperCamelCase__			)
		for p in pure_symbols:
				lowerCAmelCase__  :     Dict       	=   None
		for s in pure_symbols:
				lowerCAmelCase__  :     Dict       	=   s + '''\''''
				if s in literals:
						lowerCAmelCase__  :     Optional[int]       	=   True
				elif sym in literals:
						lowerCAmelCase__  :     Union[str, Any]       	=   False
		return pure_symbols, assignment






def 	lowerCamelCase_       (			_a      ,  _a			):




		"""simple docstring"""






		lowerCAmelCase__  :     Any       	=   []
		for clause in clauses:
				if len(UpperCamelCase__			) == 1:
						unit_symbols.append(list(clause.literals.keys()			)[0]			)
				else:
						lowerCAmelCase__	,      lowerCAmelCase__  :     Optional[Any]       	=   0, 0
						for literal, value in clause.literals.items():
								if value is False:
										f_count += 1
								elif value is None:
										lowerCAmelCase__  :     str       	=   literal
										n_count += 1
						if f_count == len(UpperCamelCase__			) - 1 and n_count == 1:
								unit_symbols.append(UpperCamelCase__			)
		lowerCAmelCase__  :     List[Any]       	=   {}
		for i in unit_symbols:
				lowerCAmelCase__  :     str       	=   i[:2]
				lowerCAmelCase__  :     str       	=   len(UpperCamelCase__			) == 2
		lowerCAmelCase__  :     str       	=   [i[:2] for i in unit_symbols]

		return unit_symbols, assignment






def 	lowerCamelCase_       (			_a      ,  _a      ,  _a			):




		"""simple docstring"""






		lowerCAmelCase__  :     List[str]       	=   True
		for clause in clauses:
				lowerCAmelCase__  :     Any       	=   clause.evaluate(UpperCamelCase__			)
				if clause_check is False:
						return False, None
				elif clause_check is None:
						lowerCAmelCase__  :     Optional[Any]       	=   False
						continue

		if check_clause_all_true:
				return True, model

		try:
				lowerCAmelCase__	,      lowerCAmelCase__  :     Dict       	=   find_pure_symbols(UpperCamelCase__      ,  UpperCamelCase__      ,  UpperCamelCase__			)
		except RecursionError:
				print('''raises a RecursionError and is'''			)
				return None, {}
		lowerCAmelCase__  :     Optional[int]       	=   None
		if len(UpperCamelCase__			) > 0:
				lowerCAmelCase__	,      lowerCAmelCase__  :     int       	=   pure_symbols[0], assignment[pure_symbols[0]]

		if p:
				lowerCAmelCase__  :     int       	=   model
				lowerCAmelCase__  :     List[str]       	=   value
				lowerCAmelCase__  :     Dict       	=   list(UpperCamelCase__			)
				if p in tmp_symbols:
						tmp_symbols.remove(UpperCamelCase__			)
				return dpll_algorithm(UpperCamelCase__      ,  UpperCamelCase__      ,  UpperCamelCase__			)

		lowerCAmelCase__	,      lowerCAmelCase__  :     List[Any]       	=   find_unit_clauses(UpperCamelCase__      ,  UpperCamelCase__			)
		lowerCAmelCase__  :     int       	=   None
		if len(UpperCamelCase__			) > 0:
				lowerCAmelCase__	,      lowerCAmelCase__  :     List[Any]       	=   unit_symbols[0], assignment[unit_symbols[0]]
		if p:
				lowerCAmelCase__  :     Tuple       	=   model
				lowerCAmelCase__  :     Dict       	=   value
				lowerCAmelCase__  :     Optional[Any]       	=   list(UpperCamelCase__			)
				if p in tmp_symbols:
						tmp_symbols.remove(UpperCamelCase__			)
				return dpll_algorithm(UpperCamelCase__      ,  UpperCamelCase__      ,  UpperCamelCase__			)
		lowerCAmelCase__  :     int       	=   symbols[0]
		lowerCAmelCase__  :     Dict       	=   symbols[1:]
		lowerCAmelCase__	,      lowerCAmelCase__  :     int       	=   model, model
		lowerCAmelCase__	,      lowerCAmelCase__  :     Tuple       	=   True, False

		return dpll_algorithm(UpperCamelCase__      ,  UpperCamelCase__      ,  UpperCamelCase__			) or dpll_algorithm(UpperCamelCase__      ,  UpperCamelCase__      ,  UpperCamelCase__			)


if __name__ == "__main__":
		import doctest

		doctest.testmod()

		lowerCamelCase		=						generate_formula()
		print(f'''The formula {formula} is''', end=''' ''')

		lowerCamelCase		=						generate_parameters(formula)
		lowerCamelCase		=						dpll_algorithm(clauses, symbols, {})

		if solution:
				print(f'''satisfiable with the assignment {model}.''')
		else:
				print('''not satisfiable.''')









"""simple docstring"""






from transformers import ProcessorMixin




class    __snake_case(					__A       ):
    _A       = '''AutoFeatureExtractor'''
    _A       = '''AutoTokenizer'''
