code: 
  
  
  
  from __future__ import annotations
  
  import random
  from collections.abc import Iterable
  
  
  
  class        lowerCAmelCase_	:
         def __init__(    self,    SCREAMING_SNAKE_CASE_ )  ->	None:
            UpperCamelCase					:						dict[str, bool | None]					=			{literal: None for literal in literals}
         def __str__(    self )  ->	str:
            return "{" + " , ".join(self.literals ) + "}"
         def __len__(    self )  ->	int:
            return len(self.literals )
         def       snake_case_ (    self,    SCREAMING_SNAKE_CASE_ )  ->	None:
            for literal in self.literals:
               UpperCamelCase					:						Tuple					=			literal[:2]
               if symbol in model:
                  UpperCamelCase					:						List[str]					=			model[symbol]
               else:
                  continue
               if value is not None:
                  # Complement assignment if literal is in complemented form
                  if literal.endswith('\'' ):
                     UpperCamelCase					:						List[str]					=			not value
               UpperCamelCase					:						Dict					=			value
  
  
  
  
  
  
         def       snake_case_ (    self,    SCREAMING_SNAKE_CASE_ )  ->	bool | None:
            for literal in self.literals:
               UpperCamelCase					:						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        lowerCAmelCase_	:
         def __init__(    self,    SCREAMING_SNAKE_CASE_ )  ->	None:
            UpperCamelCase					:						Union[str, Any]					=			list(SCREAMING_SNAKE_CASE_ )
  
  
  
  
  
  
         def __str__(    self )  ->	str:
            return "{" + " , ".join(str(SCREAMING_SNAKE_CASE_ ) for clause in self.clauses ) + "}"
  
  
  
  
  
  
  def 	UpperCamelCase			(     )			->  Clause:
     UpperCamelCase					:						List[Any]					=			[]
     UpperCamelCase					:						Dict					=			random.randint(1 ,  5			)
     UpperCamelCase					:						Any					=			'A'
     UpperCamelCase					:						List[str]					=			0
     while i < no_of_literals:
        UpperCamelCase					:						str					=			random.randint(1 ,  5			)
        UpperCamelCase					:						int					=			base_var + str(snake_case__			)
        UpperCamelCase					:						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:
     UpperCamelCase					:						set[Clause]					=			set()
     UpperCamelCase					:						List[str]					=			random.randint(1 ,  10			)
     while len(snake_case__			) < no_of_clauses:
        clauses.add(generate_clause()			)
     return Formula(snake_case__			)
  
  
  def 	UpperCamelCase			(     snake_case__ :					Formula			)			->  tuple[list[Clause], list[str]]:
     UpperCamelCase					:						List[Any]					=			formula.clauses
     UpperCamelCase					:						List[Any]					=			[]
     for clause in formula.clauses:
        for literal in clause.literals:
           UpperCamelCase					:						str					=			literal[:2]
           if symbol not in symbols_set:
              symbols_set.append(snake_case__			)
     return clauses, symbols_set
  
  
  def 	UpperCamelCase			(     snake_case__ :					list[Clause] ,  snake_case__ :					list[str] ,  snake_case__ :					dict[str, bool | None]			)			->  tuple[list[str], dict[str, bool | None]]:
     UpperCamelCase					:						Any					=			[]
     UpperCamelCase					:						dict[str, bool | None]					=			{}
     UpperCamelCase					:						str					=			[]
  
     for clause in clauses:
        if clause.evaluate(snake_case__			):
           continue
        for literal in clause.literals:
           literals.append(snake_case__			)
  
     for s in symbols:
        UpperCamelCase					:						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:
        UpperCamelCase					:						List[str]					=			None
     for s in pure_symbols:
        UpperCamelCase					:						Optional[int]					=			s + '\''
        if s in literals:
           UpperCamelCase					:						List[str]					=			True
        elif sym in literals:
           UpperCamelCase					:						Union[str, Any]					=			False
     return pure_symbols, assignment
  
  
  def 	UpperCamelCase			(     snake_case__ :					list[Clause] ,  snake_case__ :					dict[str, bool | None]			)			->  tuple[list[str], dict[str, bool | None]]:
     UpperCamelCase					:						Any					=			[]
     for clause in clauses:
        if len(snake_case__			) == 1:
           unit_symbols.append(list(clause.literals.keys()			)[0]			)
        else:
           UpperCamelCase					:						Optional[int]					=			0, 0
           for literal, value in clause.literals.items():
              if value is False:
                 f_count += 1
              elif value is None:
                 UpperCamelCase					:						int					=			literal
                 n_count += 1
           if f_count == len(snake_case__			) - 1 and n_count == 1:
              unit_symbols.append(snake_case__			)
     UpperCamelCase					:						dict[str, bool | None]					=			{}
     for i in unit_symbols:
        UpperCamelCase					:						List[str]					=			i[:2]
        UpperCamelCase					:						Optional[Any]					=			len(snake_case__			) == 2
     UpperCamelCase					:						Tuple					=			[i[:2] for i in unit_symbols]
  
     return unit_symbols, assignment
  
  
  def 	UpperCamelCase			(     snake_case__ :					list[Clause] ,  snake_case__ :					list[str] ,  snake_case__ :					dict[str, bool | None]			)			->  tuple[bool | None, dict[str, bool | None] | None]:
     UpperCamelCase					:						Optional[Any]					=			True
     for clause in clauses:
        UpperCamelCase					:						Tuple					=			clause.evaluate(snake_case__			)
        if clause_check is False:
           return False, None
        elif clause_check is None:
           UpperCamelCase					:						Any					=			False
           continue
  
     if check_clause_all_true:
        return True, model
  
     try:
        UpperCamelCase					:						Dict					=			find_pure_symbols(snake_case__ ,  snake_case__ ,  snake_case__			)
     except RecursionError:
        print('raises a RecursionError and is'			)
        return None, {}
     UpperCamelCase					:						Tuple					=			None
     if len(snake_case__			) > 0:
        UpperCamelCase					:						Any					=			pure_symbols[0], assignment[pure_symbols[0]]
  
     if p:
        UpperCamelCase					:						int					=			model
        UpperCamelCase					:						List[str]					=			value
        UpperCamelCase					:						Tuple					=			list(snake_case__			)
        if p in tmp_symbols:
           tmp_symbols.remove(snake_case__			)
        return dpll_algorithm(snake_case__ ,  snake_case__ ,  snake_case__			)
  
     UpperCamelCase					:						int					=			find_unit_clauses(snake_case__ ,  snake_case__			)
     UpperCamelCase					:						List[Any]					=			None
     if len(snake_case__			) > 0:
        UpperCamelCase					:						int					=			unit_symbols[0], assignment[unit_symbols[0]]
     if p:
        UpperCamelCase					:						Optional[int]					=			model
        UpperCamelCase					:						str					=			value
        UpperCamelCase					:						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__			)
     UpperCamelCase					:						List[Any]					=			symbols[0]
     UpperCamelCase					:						Optional[Any]					=			symbols[1:]
     UpperCamelCase					:						int					=			model, model
     UpperCamelCase					:						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.''')
  
  
  
  
style_context: 
  
  
  
  import unittest
  
  import numpy as np
  
  from transformers.testing_utils import require_torch, require_vision
  from transformers.utils import is_torch_available, is_vision_available
  
  from ...test_image_processing_common import ImageProcessingSavingTestMixin, prepare_image_inputs
  
  
  if is_torch_available():
      import torch
  
  if is_vision_available():
      from PIL import Image
  
      from transformers import ViltImageProcessor
  
  
  
  class        lowerCAmelCase_	(						unittest.TestCase							):
         def __init__(    self,    SCREAMING_SNAKE_CASE_,    SCREAMING_SNAKE_CASE_=7,    SCREAMING_SNAKE_CASE_=3,    SCREAMING_SNAKE_CASE_=18,    SCREAMING_SNAKE_CASE_=30,    SCREAMING_SNAKE_CASE_=400,    SCREAMING_SNAKE_CASE_=True,    SCREAMING_SNAKE_CASE_=None,    SCREAMING_SNAKE_CASE_=2,    SCREAMING_SNAKE_CASE_=True,    SCREAMING_SNAKE_CASE_=[0.5, 0.5, 0.5],    SCREAMING_SNAKE_CASE_=[0.5, 0.5, 0.5],    )  ->	List[Any]:
            UpperCamelCase					:						Optional[int]					=			size if size is not None else {'shortest_edge': 30}
            UpperCamelCase					:						Dict					=			parent
            UpperCamelCase					:						str					=			batch_size
            UpperCamelCase					:						str					=			num_channels
            UpperCamelCase					:						Optional[int]					=			image_size
            UpperCamelCase					:						List[Any]					=			min_resolution
            UpperCamelCase					:						Tuple					=			max_resolution
            UpperCamelCase					:						Tuple					=			do_resize
            UpperCamelCase					:						Any					=			size
            UpperCamelCase					:						int					=			size_divisor
            UpperCamelCase					:						str					=			do_normalize
            UpperCamelCase					:						Optional[int]					=			image_mean
            UpperCamelCase					:						List[str]					=			image_std
         def       snake_case_ (    self )  ->	List[Any]:
            return {
                "image_mean": self.image_mean,
                "image_std": self.image_std,
                "do_normalize": self.do_normalize,
                "do_resize": self.do_resize,
                "size": self.size,
                "size_divisor": self.size_divisor,
            }
  
  
  
  
  
  
         def       snake_case_ (    self,    SCREAMING_SNAKE_CASE_,    SCREAMING_SNAKE_CASE_=False )  ->	Union[str, Any]:
            if not batched:
               UpperCamelCase					:						Optional[Any]					=			self.size['shortest_edge']
               UpperCamelCase					:						int					=			image_inputs[0]
               if isinstance(SCREAMING_SNAKE_CASE_,    Image.Image ):
                  UpperCamelCase			,  UpperCamelCase					:						List[Any]					=			image.size
               else:
                  UpperCamelCase			,  UpperCamelCase					:						List[Any]					=			image.shape[1], image.shape[2]
               UpperCamelCase					:						Any					=			size / min(SCREAMING_SNAKE_CASE_,    SCREAMING_SNAKE_CASE_ )
               if h < w:
                  UpperCamelCase			,  UpperCamelCase					:						Optional[int]					=			size, scale * w
               else:
                  UpperCamelCase			,  UpperCamelCase					:						List[str]					=			scale * h, size
  
               UpperCamelCase					:						int					=			int((1333 / 800) * size )
               if max(SCREAMING_SNAKE_CASE_,    SCREAMING_SNAKE_CASE_ ) > max_size:
                  UpperCamelCase					:						Any					=			max_size / max(SCREAMING_SNAKE_CASE_,    SCREAMING_SNAKE_CASE_ )
                  UpperCamelCase					:						List[Any]					=			newh * scale
                  UpperCamelCase					:						Optional[int]					=			neww * scale
  
               UpperCamelCase			,  UpperCamelCase					:						List[Any]					=			int(newh + 0.5 ), int(neww + 0.5 )
               UpperCamelCase			,  UpperCamelCase					:						int					=			(
                   newh // self.size_divisor * self.size_divisor,
                   neww // self.size_divisor * self.size_divisor,
               )
  
            else:
               UpperCamelCase					:						Dict					=			[]
               for image in image_inputs:
                  UpperCamelCase			,  UpperCamelCase					:						Union[str, Any]					=			self.get_expected_values([image] )
                  expected_values.append((expected_height, expected_width) )
               UpperCamelCase					:						List[str]					=			max(SCREAMING_SNAKE_CASE_,    key=lambda SCREAMING_SNAKE_CASE_ : item[0] )[0]
               UpperCamelCase					:						List[str]					=			max(SCREAMING_SNAKE_CASE_,    key=lambda SCREAMING_SNAKE_CASE_ : item[1] )[1]
  
            return expected_height, expected_width
  
  
  
  
  
  
  @require_torch
  @require_vision
  class        lowerCAmelCase_	(						a__ ,					unittest.TestCase							):
         UpperCAmelCase__       :      List[Any]       =						ViltImageProcessor if is_vision_available() else None
         def       snake_case_ (    self )  ->	Union[str, Any]:
            UpperCamelCase					:						Dict					=			ViltImageProcessingTester(self )
         @property
         def       snake_case_ (    self )  ->	Dict:
            return self.image_processor_tester.prepare_image_processor_dict()
         def       snake_case_ (    self )  ->	Union[str, Any]:
            UpperCamelCase					:						List[str]					=			self.image_processing_class(**self.image_processor_dict )
            self.assertTrue(hasattr(SCREAMING_SNAKE_CASE_,    'image_mean' ) )
            self.assertTrue(hasattr(SCREAMING_SNAKE_CASE_,    'image_std' ) )
            self.assertTrue(hasattr(SCREAMING_SNAKE_CASE_,    'do_normalize' ) )
            self.assertTrue(hasattr(SCREAMING_SNAKE_CASE_,    'do_resize' ) )
            self.assertTrue(hasattr(SCREAMING_SNAKE_CASE_,    'size' ) )
            self.assertTrue(hasattr(SCREAMING_SNAKE_CASE_,    'size_divisor' ) )
         def       snake_case_ (    self )  ->	List[Any]:
            UpperCamelCase					:						Union[str, Any]					=			self.image_processing_class.from_dict(self.image_processor_dict )
            self.assertEqual(image_processor.size,    {'shortest_edge': 30} )
  
            UpperCamelCase					:						Union[str, Any]					=			self.image_processing_class.from_dict(self.image_processor_dict,    size=42 )
            self.assertEqual(image_processor.size,    {'shortest_edge': 42} )
         def       snake_case_ (    self )  ->	Dict:
            pass
         def       snake_case_ (    self )  ->	str:
            # Initialize image_processing
            UpperCamelCase					:						int					=			self.image_processing_class(**self.image_processor_dict )
            # create random PIL images
            UpperCamelCase					:						Any					=			prepare_image_inputs(self.image_processor_tester,    equal_resolution=SCREAMING_SNAKE_CASE_ )
            for image in image_inputs:
               self.assertIsInstance(SCREAMING_SNAKE_CASE_,    Image.Image )
  
            # Test not batched input
            UpperCamelCase					:						int					=			image_processing(image_inputs[0],    return_tensors='pt' ).pixel_values
  
            UpperCamelCase			,  UpperCamelCase					:						Dict					=			self.image_processor_tester.get_expected_values(SCREAMING_SNAKE_CASE_ )
            self.assertEqual(
                encoded_images.shape,    (1, self.image_processor_tester.num_channels, expected_height, expected_width),    )
  
            # Test batched
            UpperCamelCase					:						str					=			image_processing(SCREAMING_SNAKE_CASE_,    return_tensors='pt' ).pixel_values
  
            UpperCamelCase			,  UpperCamelCase					:						Tuple					=			self.image_processor_tester.get_expected_values(SCREAMING_SNAKE_CASE_,    batched=SCREAMING_SNAKE_CASE_ )
            self.assertEqual(
                encoded_images.shape,    (
                    self.image_processor_tester.batch_size,
                    self.image_processor_tester.num_channels,
                    expected_height,
                    expected_width,
                ),    )
         def       snake_case_ (    self )  ->	List[str]:
            # Initialize image_processing
            UpperCamelCase					:						Optional[int]					=			self.image_processing_class(**self.image_processor_dict )
            # create random numpy tensors
            UpperCamelCase					:						Optional[Any]					=			prepare_image_inputs(self.image_processor_tester,    equal_resolution=SCREAMING_SNAKE_CASE_,    numpify=SCREAMING_SNAKE_CASE_ )
            for image in image_inputs:
               self.assertIsInstance(SCREAMING_SNAKE_CASE_,    np.ndarray )
  
            # Test not batched input
            UpperCamelCase					:						Optional[Any]					=			image_processing(image_inputs[0],    return_tensors='pt' ).pixel_values
  
            UpperCamelCase			,  UpperCamelCase					:						str					=			self.image_processor_tester.get_expected_values(SCREAMING_SNAKE_CASE_ )
            self.assertEqual(
                encoded_images.shape,    (1, self.image_processor_tester.num_channels, expected_height, expected_width),    )
  
            # Test batched
            UpperCamelCase					:						Dict					=			image_processing(SCREAMING_SNAKE_CASE_,    return_tensors='pt' ).pixel_values
  
            UpperCamelCase			,  UpperCamelCase					:						Optional[Any]					=			self.image_processor_tester.get_expected_values(SCREAMING_SNAKE_CASE_,    batched=SCREAMING_SNAKE_CASE_ )
            self.assertEqual(
                encoded_images.shape,    (
                    self.image_processor_tester.batch_size,
                    self.image_processor_tester.num_channels,
                    expected_height,
                    expected_width,
                ),    )
  
  
  
  
  
  
         def       snake_case_ (    self )  ->	Optional[Any]:
            # Initialize image_processing
            UpperCamelCase					:						Optional[int]					=			self.image_processing_class(**self.image_processor_dict )
            # create random PyTorch tensors
            UpperCamelCase					:						Dict					=			prepare_image_inputs(self.image_processor_tester,    equal_resolution=SCREAMING_SNAKE_CASE_,    torchify=SCREAMING_SNAKE_CASE_ )
            for image in image_inputs:
               self.assertIsInstance(SCREAMING_SNAKE_CASE_,    torch.Tensor )
  
            # Test not batched input
            UpperCamelCase					:						List[str]					=			image_processing(image_inputs[0],    return_tensors='pt' ).pixel_values
  
            UpperCamelCase			,  UpperCamelCase					:						Union[str, Any]					=			self.image_processor_tester.get_expected_values(SCREAMING_SNAKE_CASE_ )
            self.assertEqual(
                encoded_images.shape,    (1, self.image_processor_tester.num_channels, expected_height, expected_width),    )
  
            # Test batched
            UpperCamelCase					:						List[Any]					=			image_processing(SCREAMING_SNAKE_CASE_,    return_tensors='pt' ).pixel_values
  
            UpperCamelCase			,  UpperCamelCase					:						Dict					=			self.image_processor_tester.get_expected_values(SCREAMING_SNAKE_CASE_,    batched=SCREAMING_SNAKE_CASE_ )
            self.assertEqual(
                encoded_images.shape,    (
                    self.image_processor_tester.batch_size,
                    self.image_processor_tester.num_channels,
                    expected_height,
                    expected_width,
                ),    )
  
  
  
  