code: 
  
  
  from __future__ import annotations
  
  import random
  from collections.abc import Iterable
  
  class 						snake_case			:
  			'''simple docstring'''
  
  			def __init__(	self     :     str							,							lowerCAmelCase_     :     list[str]					)					->					None:
  
  
  
  
  								"""simple docstring"""
  
  
  
  
  
  
  								SCREAMING_SNAKE_CASE_	      =       {literal: None for literal in literals}
  
  			def __str__(	self     :     Dict					)					->					str:
  
  
  
  
  								"""simple docstring"""
  
  
  
  
  
  
  								return "{" + " , ".join(self.literals					) + "}"
  
  			def __len__(	self     :     List[str]					)					->					int:
  
  
  
  
  								"""simple docstring"""
  
  
  
  
  
  
  								return len(self.literals					)
  
  			def _lowercase (	self     :     Optional[Any]							,							lowerCAmelCase_     :     dict[str, bool | None]					)					->					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 _lowercase (	self     :     Optional[Any]							,							lowerCAmelCase_     :     dict[str, bool | None]					)					->					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(lowerCAmelCase_					)
  								for value in self.literals.values():
  													if value in (True, None):
  																		return value
  								return any(self.literals.values()					)
  
  class 						snake_case			:
  			'''simple docstring'''
  
  			def __init__(	self     :     Any							,							lowerCAmelCase_     :     Iterable[Clause]					)					->					None:
  
  
  
  
  								"""simple docstring"""
  
  
  
  
  
  
  								SCREAMING_SNAKE_CASE_	      =       list(lowerCAmelCase_					)
  
  
  
  
  			def __str__(	self     :     Union[str, Any]					)					->					str:
  
  
  
  
  								"""simple docstring"""
  
  
  
  
  
  
  								return "{" + " , ".join(str(lowerCAmelCase_					) for clause in self.clauses					) + "}"
  
  
  
  
  
  
  
  def 							UpperCAmelCase				(     )->		Clause:
  
  
  
  
  
  
  
  					'''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(UpperCAmelCase      )
  										SCREAMING_SNAKE_CASE_	      =       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 							UpperCAmelCase				(     )->		Formula:
  
  
  
  
  
  
  
  					'''simple docstring'''
  
  
  
  					SCREAMING_SNAKE_CASE_	      =       set()
  					SCREAMING_SNAKE_CASE_	      =       random.randint(1				,10      )
  					while len(UpperCAmelCase      ) < no_of_clauses:
  										clauses.add(generate_clause()      )
  					return Formula(UpperCAmelCase      )
  
  
  
  
  
  
  
  def 							UpperCAmelCase				(     UpperCAmelCase      )->		tuple[list[Clause], list[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(UpperCAmelCase      )
  					return clauses, symbols_set
  
  
  
  
  
  
  
  def 							UpperCAmelCase				(     UpperCAmelCase				,UpperCAmelCase				,UpperCAmelCase      )->		tuple[list[str], dict[str, bool | None]]:
  
  
  
  
  
  
  
  					'''simple docstring'''
  
  
  
  					SCREAMING_SNAKE_CASE_	      =       []
  					SCREAMING_SNAKE_CASE_	      =       {}
  					SCREAMING_SNAKE_CASE_	      =       []
  
  					for clause in clauses:
  										if clause.evaluate(UpperCAmelCase      ):
  															continue
  										for literal in clause.literals:
  															literals.append(UpperCAmelCase      )
  
  					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(UpperCAmelCase      )
  					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 							UpperCAmelCase				(     UpperCAmelCase				,UpperCAmelCase      )->		tuple[list[str], dict[str, bool | None]]:
  
  
  
  
  
  
  
  					'''simple docstring'''
  
  
  
  					SCREAMING_SNAKE_CASE_	      =       []
  					for clause in clauses:
  										if len(UpperCAmelCase      ) == 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(UpperCAmelCase      ) - 1 and n_count == 1:
  																				unit_symbols.append(UpperCAmelCase      )
  					SCREAMING_SNAKE_CASE_	      =       {}
  					for i in unit_symbols:
  										SCREAMING_SNAKE_CASE_	      =       i[:2]
  										SCREAMING_SNAKE_CASE_	      =       len(UpperCAmelCase      ) == 2
  					SCREAMING_SNAKE_CASE_	      =       [i[:2] for i in unit_symbols]
  
  					return unit_symbols, assignment
  
  
  
  
  
  
  
  def 							UpperCAmelCase				(     UpperCAmelCase				,UpperCAmelCase				,UpperCAmelCase      )->		tuple[bool | None, dict[str, bool | None] | None]:
  
  
  
  
  
  
  
  					'''simple docstring'''
  
  
  
  					SCREAMING_SNAKE_CASE_	      =       True
  					for clause in clauses:
  										SCREAMING_SNAKE_CASE_	      =       clause.evaluate(UpperCAmelCase      )
  										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(UpperCAmelCase				,UpperCAmelCase				,UpperCAmelCase      )
  					except RecursionError:
  										print('''raises a RecursionError and is'''      )
  										return None, {}
  					SCREAMING_SNAKE_CASE_	      =       None
  					if len(UpperCAmelCase      ) > 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(UpperCAmelCase      )
  										if p in tmp_symbols:
  															tmp_symbols.remove(UpperCAmelCase      )
  										return dpll_algorithm(UpperCAmelCase				,UpperCAmelCase				,UpperCAmelCase      )
  
  					SCREAMING_SNAKE_CASE_      ,SCREAMING_SNAKE_CASE_	      =       find_unit_clauses(UpperCAmelCase				,UpperCAmelCase      )
  					SCREAMING_SNAKE_CASE_	      =       None
  					if len(UpperCAmelCase      ) > 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(UpperCAmelCase      )
  										if p in tmp_symbols:
  															tmp_symbols.remove(UpperCAmelCase      )
  										return dpll_algorithm(UpperCAmelCase				,UpperCAmelCase				,UpperCAmelCase      )
  					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(UpperCAmelCase				,UpperCAmelCase				,UpperCAmelCase      ) or dpll_algorithm(UpperCAmelCase				,UpperCAmelCase				,UpperCAmelCase      )
  
  
  if __name__ == "__main__":
  		import doctest
  
  		doctest.testmod()
  
  		A_														=      generate_formula()
  		print(F'The formula {formula} is', end=" ")
  
  		A_							,A_														=      generate_parameters(formula)
  		A_							,A_														=      dpll_algorithm(clauses, symbols, {})
  
  		if solution:
  				print(F'satisfiable with the assignment {model}.')
  		else:
  				print("not satisfiable.")
  
  
  
style_context: 
  
  
  def 							UpperCAmelCase				(     UpperCAmelCase      )->		bool:
  
  
  
  
  
  
  
  					'''simple docstring'''
  
  
  
  					if not isinstance(UpperCAmelCase				,UpperCAmelCase      ):
  										SCREAMING_SNAKE_CASE_	      =       f'''Input value of [number={number}] must be an integer'''
  										raise TypeError(UpperCAmelCase      )
  					if number < 0 or number % 2 == 1:
  										return False
  					SCREAMING_SNAKE_CASE_	      =       int(number**0.5      )
  					return number == number_sqrt * (number_sqrt + 1)
  
  
  if __name__ == "__main__":
  		import doctest
  
  		doctest.testmod()
  
  
  