code: 
  
  
  import functools
  from contextlib import contextmanager
  
  import bert_score
  from packaging import version
  
  import datasets
  @contextmanager
  def     UpperCAmelCase__		():
  
  
  
       """simple docstring"""
  
  
  
  
  
  
       def filter_log(UpperCamelCase_       ):
            return False if "This IS expected if you are initializing" in record.msg else True
  
       snake_case					=       datasets.utils.logging.get_logger('''transformers.modeling_utils'''       )
       logger.addFilter(UpperCamelCase_       )
       try:
            yield
       finally:
            logger.removeFilter(UpperCamelCase_       )
  
  
  _SCREAMING_SNAKE_CASE    :				Any       =					"\\n@inproceedings{bert-score,\n  title={BERTScore: Evaluating Text Generation with BERT},\n  author={Tianyi Zhang* and Varsha Kishore* and Felix Wu* and Kilian Q. Weinberger and Yoav Artzi},\n  booktitle={International Conference on Learning Representations},\n  year={2020},\n  url={https://openreview.net/forum?id=SkeHuCVFDr}\n}\n"
  
  _SCREAMING_SNAKE_CASE    :				Optional[int]       =					"\\nBERTScore leverages the pre-trained contextual embeddings from BERT and matches words in candidate and reference\nsentences by cosine similarity.\nIt has been shown to correlate with human judgment on sentence-level and system-level evaluation.\nMoreover, BERTScore computes precision, recall, and F1 measure, which can be useful for evaluating different language\ngeneration tasks.\n\nSee the project's README at https://github.com/Tiiiger/bert_score#readme for more information.\n"
  
  _SCREAMING_SNAKE_CASE    :				int       =					"\nBERTScore Metrics with the hashcode from a source against one or more references.\n\nArgs:\n    predictions (list of str): Prediction/candidate sentences.\n    references (list of str or list of list of str): Reference sentences.\n    lang (str): Language of the sentences; required (e.g. 'en').\n    model_type (str): Bert specification, default using the suggested\n        model for the target language; has to specify at least one of\n        `model_type` or `lang`.\n    num_layers (int): The layer of representation to use,\n        default using the number of layers tuned on WMT16 correlation data.\n    verbose (bool): Turn on intermediate status update.\n    idf (bool or dict): Use idf weighting; can also be a precomputed idf_dict.\n    device (str): On which the contextual embedding model will be allocated on.\n        If this argument is None, the model lives on cuda:0 if cuda is available.\n    nthreads (int): Number of threads.\n    batch_size (int): Bert score processing batch size,\n        at least one of `model_type` or `lang`. `lang` needs to be\n        specified when `rescale_with_baseline` is True.\n    rescale_with_baseline (bool): Rescale bertscore with pre-computed baseline.\n    baseline_path (str): Customized baseline file.\n    use_fast_tokenizer (bool): `use_fast` parameter passed to HF tokenizer. New in version 0.3.10.\n\nReturns:\n    precision: Precision.\n    recall: Recall.\n    f1: F1 score.\n    hashcode: Hashcode of the library.\n\nExamples:\n\n    >>> predictions = [\"hello there\", \"general kenobi\"]\n    >>> references = [\"hello there\", \"general kenobi\"]\n    >>> bertscore = datasets.load_metric(\"bertscore\")\n    >>> results = bertscore.compute(predictions=predictions, references=references, lang=\"en\")\n    >>> print([round(v, 2) for v in results[\"f1\"]])\n    [1.0, 1.0]\n"
  
  @datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION ,      _KWARGS_DESCRIPTION			)
  class 						A__      (					datasets.Metric			):
  
  
  
  
  
  
  
      """simple docstring"""
  
      def 	a_    ( self					):
           return datasets.MetricInfo(
               description=_DESCRIPTION    ,      citation=_CITATION    ,      homepage='''https://github.com/Tiiiger/bert_score'''    ,      inputs_description=_KWARGS_DESCRIPTION    ,      features=datasets.Features(
                   {
                       '''predictions''': datasets.Value('''string'''    ,      id='''sequence'''					),
                       '''references''': datasets.Sequence(datasets.Value('''string'''    ,      id='''sequence'''					)    ,      id='''references'''					),
                   }					)    ,      codebase_urls=['''https://github.com/Tiiiger/bert_score''']    ,      reference_urls=[
                   '''https://github.com/Tiiiger/bert_score''',
                   '''https://arxiv.org/abs/1904.09675''',
               ]    ,      )
      def 	a_    ( self    ,      __snake_case    ,      __snake_case    ,      __snake_case=None    ,      __snake_case=None    ,      __snake_case=None    ,      __snake_case=False    ,      __snake_case=False    ,      __snake_case=None    ,      __snake_case=6_4    ,      __snake_case=4    ,      __snake_case=False    ,      __snake_case=False    ,      __snake_case=None    ,      __snake_case=False    ,      ):
           snake_case					=       bert_score.utils.get_hash
           snake_case					=       bert_score.BERTScorer
  
           if version.parse(bert_score.__version__					) >= version.parse('''0.3.10'''					):
                snake_case					=       functools.partial(__snake_case    ,      use_fast_tokenizer=__snake_case					)
                snake_case					=       functools.partial(__snake_case    ,      use_fast_tokenizer=__snake_case					)
           elif use_fast_tokenizer:
                raise ImportWarning(
                    '''To use a fast tokenizer, the module `bert-score>=0.3.10` is required, and the current version of `bert-score` doesn\'t match this condition.\n'''
                    '''You can install it with `pip install "bert-score>=0.3.10"`.'''					)
  
           if model_type is None:
                assert lang is not None, "either lang or model_type should be specified"
                snake_case					=       bert_score.utils.langamodel[lang.lower()]
  
           if num_layers is None:
                snake_case					=       bert_score.utils.modelalayers[model_type]
  
           snake_case					=       get_hash(
               model=__snake_case    ,      num_layers=__snake_case    ,      idf=__snake_case    ,      rescale_with_baseline=__snake_case    ,      use_custom_baseline=baseline_path is not None    ,      )
  
           with filter_logging_context():
                if not hasattr(self    ,      '''cached_bertscorer'''					) or self.cached_bertscorer.hash != hashcode:
                     snake_case					=       scorer(
                         model_type=__snake_case    ,      num_layers=__snake_case    ,      batch_size=__snake_case    ,      nthreads=__snake_case    ,      all_layers=__snake_case    ,      idf=__snake_case    ,      device=__snake_case    ,      lang=__snake_case    ,      rescale_with_baseline=__snake_case    ,      baseline_path=__snake_case    ,      )
  
           ((snake_case)				,						(snake_case)				,						(snake_case))					=       self.cached_bertscorer.score(
               cands=__snake_case    ,      refs=__snake_case    ,      verbose=__snake_case    ,      batch_size=__snake_case    ,      )
           snake_case					=       {
               '''precision''': P.tolist(),
               '''recall''': R.tolist(),
               '''f1''': F.tolist(),
               '''hashcode''': hashcode,
           }
           return output_dict
      def 	a_    ( self    ,      __snake_case=None    ,      __snake_case=None    ,      **__snake_case					):
           # References can be strings or lists of strings
           # Let's change strings to lists of strings with one element
           if references is not None:
                snake_case					=       [[ref] if isinstance(__snake_case    ,      __snake_case					) else ref for ref in references]
           super().add_batch(predictions=__snake_case    ,      references=__snake_case    ,      **__snake_case					)
  
  
  
  
      def 	a_    ( self    ,      __snake_case=None    ,      __snake_case=None    ,      **__snake_case					):
           # References can be strings or lists of strings
           # Let's change strings to lists of strings with one element
           if isinstance(__snake_case    ,      __snake_case					):
                snake_case					=       [reference]
           super().add(prediction=__snake_case    ,      reference=__snake_case    ,      **__snake_case					)
  
  
  
  
  
style_context: 
  
  
  from __future__ import annotations
  
  import random
  from collections.abc import Iterable
  
  class 						A__      :
  
  
  
  
  
  
  
      """simple docstring"""
  
      def __init__( self    ,      __snake_case					):
           snake_case					=       {literal: None for literal in literals}
      def __str__( self					):
           return "{" + " , ".join(self.literals					) + "}"
      def __len__( self					):
           return len(self.literals					)
      def 	a_    ( self    ,      __snake_case					):
           for literal in self.literals:
                snake_case					=       literal[:2]
                if symbol in model:
                     snake_case					=       model[symbol]
                else:
                     continue
                if value is not None:
                     # Complement assignment if literal is in complemented form
                     if literal.endswith('''\''''					):
                          snake_case					=       not value
                snake_case					=       value
  
  
  
  
      def 	a_    ( self    ,      __snake_case					):
           for literal in self.literals:
                snake_case					=       literal.rstrip('''\''''					) if literal.endswith('''\''''					) else literal + '''\''''
                if symbol in self.literals:
                     return True
  
           self.assign(__snake_case					)
           for value in self.literals.values():
                if value in (True, None):
                     return value
           return any(self.literals.values()					)
  
  
  
  
  
  
  class 						A__      :
  
  
  
  
  
  
  
      """simple docstring"""
  
      def __init__( self    ,      __snake_case					):
           snake_case					=       list(__snake_case					)
  
  
  
  
      def __str__( self					):
           return "{" + " , ".join(str(__snake_case					) for clause in self.clauses					) + "}"
  
  
  
  
  
  
  def     UpperCAmelCase__		():
  
  
  
       """simple docstring"""
  
  
  
  
  
  
       snake_case					=       []
       snake_case					=       random.randint(1							,5       )
       snake_case					=       '''A'''
       snake_case					=       0
       while i < no_of_literals:
            snake_case					=       random.randint(1							,5       )
            snake_case					=       base_var + str(UpperCamelCase_       )
            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__		():
  
  
  
       """simple docstring"""
  
  
  
  
  
  
       snake_case					=       set()
       snake_case					=       random.randint(1							,10       )
       while len(UpperCamelCase_       ) < no_of_clauses:
            clauses.add(generate_clause()       )
       return Formula(UpperCamelCase_       )
  def     UpperCAmelCase__		(UpperCamelCase_       ):
  
  
  
       """simple docstring"""
  
  
  
  
  
  
       snake_case					=       formula.clauses
       snake_case					=       []
       for clause in formula.clauses:
            for literal in clause.literals:
                 snake_case					=       literal[:2]
                 if symbol not in symbols_set:
                      symbols_set.append(UpperCamelCase_       )
       return clauses, symbols_set
  def     UpperCAmelCase__		(UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_       ):
  
  
  
       """simple docstring"""
  
  
  
  
  
  
       snake_case					=       []
       snake_case					=       {}
       snake_case					=       []
  
       for clause in clauses:
            if clause.evaluate(UpperCamelCase_       ):
                 continue
            for literal in clause.literals:
                 literals.append(UpperCamelCase_       )
  
       for s in symbols:
            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:
            snake_case					=       None
       for s in pure_symbols:
            snake_case					=       s + '''\''''
            if s in literals:
                 snake_case					=       True
            elif sym in literals:
                 snake_case					=       False
       return pure_symbols, assignment
  def     UpperCAmelCase__		(UpperCamelCase_							,UpperCamelCase_       ):
  
  
  
       """simple docstring"""
  
  
  
  
  
  
       snake_case					=       []
       for clause in clauses:
            if len(UpperCamelCase_       ) == 1:
                 unit_symbols.append(list(clause.literals.keys()       )[0]       )
            else:
                 snake_case				,						snake_case					=       0, 0
                 for literal, value in clause.literals.items():
                      if value is False:
                           f_count += 1
                      elif value is None:
                           snake_case					=       literal
                           n_count += 1
                 if f_count == len(UpperCamelCase_       ) - 1 and n_count == 1:
                      unit_symbols.append(UpperCamelCase_       )
       snake_case					=       {}
       for i in unit_symbols:
            snake_case					=       i[:2]
            snake_case					=       len(UpperCamelCase_       ) == 2
       snake_case					=       [i[:2] for i in unit_symbols]
  
       return unit_symbols, assignment
  def     UpperCAmelCase__		(UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_       ):
  
  
  
       """simple docstring"""
  
  
  
  
  
  
       snake_case					=       True
       for clause in clauses:
            snake_case					=       clause.evaluate(UpperCamelCase_       )
            if clause_check is False:
                 return False, None
            elif clause_check is None:
                 snake_case					=       False
                 continue
  
       if check_clause_all_true:
            return True, model
  
       try:
            snake_case				,						snake_case					=       find_pure_symbols(UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_       )
       except RecursionError:
            print('''raises a RecursionError and is'''       )
            return None, {}
       snake_case					=       None
       if len(UpperCamelCase_       ) > 0:
            snake_case				,						snake_case					=       pure_symbols[0], assignment[pure_symbols[0]]
  
       if p:
            snake_case					=       model
            snake_case					=       value
            snake_case					=       list(UpperCamelCase_       )
            if p in tmp_symbols:
                 tmp_symbols.remove(UpperCamelCase_       )
            return dpll_algorithm(UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_       )
  
       snake_case				,						snake_case					=       find_unit_clauses(UpperCamelCase_							,UpperCamelCase_       )
       snake_case					=       None
       if len(UpperCamelCase_       ) > 0:
            snake_case				,						snake_case					=       unit_symbols[0], assignment[unit_symbols[0]]
       if p:
            snake_case					=       model
            snake_case					=       value
            snake_case					=       list(UpperCamelCase_       )
            if p in tmp_symbols:
                 tmp_symbols.remove(UpperCamelCase_       )
            return dpll_algorithm(UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_       )
       snake_case					=       symbols[0]
       snake_case					=       symbols[1:]
       snake_case				,						snake_case					=       model, model
       snake_case				,						snake_case					=       True, False
  
       return dpll_algorithm(UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_       ) or dpll_algorithm(UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_       )
  
  
  if __name__ == "__main__":
   import doctest
  
   doctest.testmod()
  
   _SCREAMING_SNAKE_CASE    :				Dict       =					generate_formula()
   print(f'''The formula {formula} is''', end=" ")
  
   _SCREAMING_SNAKE_CASE   ,     _SCREAMING_SNAKE_CASE    :				Any       =					generate_parameters(formula)
   _SCREAMING_SNAKE_CASE   ,     _SCREAMING_SNAKE_CASE    :				Optional[Any]       =					dpll_algorithm(clauses, symbols, {})
  
   if solution:
    print(f'''satisfiable with the assignment {model}.''')
   else:
    print("not satisfiable.")
  
  
  
  
  