






from __future__ import annotations

import random
from collections.abc import Iterable



class  __UpperCAmelCase						:







			def __init__(      self:    List[str] ,      UpperCAmelCase_:    list[str]	):







									'''simple docstring'''




									_SCREAMING_SNAKE_CASE       =    {literal: None for literal in literals}







			def __str__(      self:    int	):







									'''simple docstring'''




									return "{" + " , ".join(self.literals	) + "}"







			def __len__(      self:    int	):







									'''simple docstring'''




									return len(self.literals	)







			def 				UpperCamelCase (      self:    Any ,      UpperCAmelCase_:    dict[str, bool | None]	):







									'''simple docstring'''




									for literal in self.literals:
															_SCREAMING_SNAKE_CASE       =    literal[:2]
															if symbol in model:
																					_SCREAMING_SNAKE_CASE       =    model[symbol]
															else:
																					continue
															if value is not None:
																					# Complement assignment if literal is in complemented form
																					if literal.endswith("""'"""	):
																											_SCREAMING_SNAKE_CASE       =    not value
															_SCREAMING_SNAKE_CASE       =    value







			def 				UpperCamelCase (      self:    Optional[int] ,      UpperCAmelCase_:    dict[str, bool | None]	):







									'''simple docstring'''




									for literal in self.literals:
															_SCREAMING_SNAKE_CASE       =    literal.rstrip("""'"""	) if literal.endswith("""'"""	) else literal + """'"""
															if symbol in self.literals:
																					return True

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



class  __UpperCAmelCase						:







			def __init__(      self:    Any ,      UpperCAmelCase_:    Iterable[Clause]	):







									'''simple docstring'''




									_SCREAMING_SNAKE_CASE       =    list(lowercase__	)







			def __str__(      self:    Tuple	):







									'''simple docstring'''




									return "{" + " , ".join(str(lowercase__	) for clause in self.clauses	) + "}"

def 			__lowerCamelCase     (						)				->    Optional[Any]:






						"""simple docstring"""





						_SCREAMING_SNAKE_CASE       =    []
						_SCREAMING_SNAKE_CASE       =    random.randint(1			,5						)
						_SCREAMING_SNAKE_CASE       =    """A"""
						_SCREAMING_SNAKE_CASE       =    0
						while i < no_of_literals:
												_SCREAMING_SNAKE_CASE       =    random.randint(1			,5						)
												_SCREAMING_SNAKE_CASE       =    base_var + str(snake_case__						)
												_SCREAMING_SNAKE_CASE       =    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 			__lowerCamelCase     (						)				->    Dict:






						"""simple docstring"""





						_SCREAMING_SNAKE_CASE       =    set()
						_SCREAMING_SNAKE_CASE       =    random.randint(1			,10						)
						while len(snake_case__						) < no_of_clauses:
												clauses.add(generate_clause()						)
						return Formula(snake_case__						)

def 			__lowerCamelCase     (						snake_case__						)				->    str:






						"""simple docstring"""





						_SCREAMING_SNAKE_CASE       =    formula.clauses
						_SCREAMING_SNAKE_CASE       =    []
						for clause in formula.clauses:
												for literal in clause.literals:
																		_SCREAMING_SNAKE_CASE       =    literal[:2]
																		if symbol not in symbols_set:
																								symbols_set.append(snake_case__						)
						return clauses, symbols_set

def 			__lowerCamelCase     (						snake_case__			,snake_case__			,snake_case__						)				->    Optional[Any]:






						"""simple docstring"""





						_SCREAMING_SNAKE_CASE       =    []
						_SCREAMING_SNAKE_CASE       =    {}
						_SCREAMING_SNAKE_CASE       =    []

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

						for s in symbols:
												_SCREAMING_SNAKE_CASE       =    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:
												_SCREAMING_SNAKE_CASE       =    None
						for s in pure_symbols:
												_SCREAMING_SNAKE_CASE       =    s + """'"""
												if s in literals:
																		_SCREAMING_SNAKE_CASE       =    True
												elif sym in literals:
																		_SCREAMING_SNAKE_CASE       =    False
						return pure_symbols, assignment

def 			__lowerCamelCase     (						snake_case__			,snake_case__						)				->    Tuple:






						"""simple docstring"""





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

						return unit_symbols, assignment

def 			__lowerCamelCase     (						snake_case__			,snake_case__			,snake_case__						)				->    Any:






						"""simple docstring"""





						_SCREAMING_SNAKE_CASE       =    True
						for clause in clauses:
												_SCREAMING_SNAKE_CASE       =    clause.evaluate(snake_case__						)
												if clause_check is False:
																		return False, None
												elif clause_check is None:
																		_SCREAMING_SNAKE_CASE       =    False
																		continue

						if check_clause_all_true:
												return True, model

						try:
												_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE       =    find_pure_symbols(snake_case__			,snake_case__			,snake_case__						)
						except RecursionError:
												print("""raises a RecursionError and is"""						)
												return None, {}
						_SCREAMING_SNAKE_CASE       =    None
						if len(snake_case__						) > 0:
												_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE       =    pure_symbols[0], assignment[pure_symbols[0]]

						if p:
												_SCREAMING_SNAKE_CASE       =    model
												_SCREAMING_SNAKE_CASE       =    value
												_SCREAMING_SNAKE_CASE       =    list(snake_case__						)
												if p in tmp_symbols:
																		tmp_symbols.remove(snake_case__						)
												return dpll_algorithm(snake_case__			,snake_case__			,snake_case__						)

						_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE       =    find_unit_clauses(snake_case__			,snake_case__						)
						_SCREAMING_SNAKE_CASE       =    None
						if len(snake_case__						) > 0:
												_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE       =    unit_symbols[0], assignment[unit_symbols[0]]
						if p:
												_SCREAMING_SNAKE_CASE       =    model
												_SCREAMING_SNAKE_CASE       =    value
												_SCREAMING_SNAKE_CASE       =    list(snake_case__						)
												if p in tmp_symbols:
																		tmp_symbols.remove(snake_case__						)
												return dpll_algorithm(snake_case__			,snake_case__			,snake_case__						)
						_SCREAMING_SNAKE_CASE       =    symbols[0]
						_SCREAMING_SNAKE_CASE       =    symbols[1:]
						_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE       =    model, model
						_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE       =    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												=      generate_parameters(formula)
		UpperCamelCase												=      dpll_algorithm(clauses, symbols, {})

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









'''simple docstring'''







def     _UpperCamelCase				(  snake_case__ = 1_000				):
      __A		 =   []
      __A		 =   []
      __A		 =   3
      __A		 =   5
      __A		 =   1
      while True:
            __A		 =   z * temp
            if result < n:
                  zmulti.append(snake_case__				)
                  temp += 1
            else:
                  __A		 =   1
                  break
      while True:
            __A		 =   x * temp
            if result < n:
                  xmulti.append(snake_case__				)
                  temp += 1
            else:
                  break
      __A		 =   list(set(xmulti + zmulti				)				)
      return sum(snake_case__				)


if __name__ == "__main__":
       print(F"""{solution() = }""")


