code: ///////////////////////////////////////////////////////////////////////////
  //                   __                _      _   ________               //
  //                  / /   ____  ____ _(_)____/ | / / ____/               //
  //                 / /   / __ \/ __ `/ / ___/  |/ / / __                 //
  //                / /___/ /_/ / /_/ / / /__/ /|  / /_/ /                 //
  //               /_____/\____/\__, /_/\___/_/ |_/\____/                  //
  //                           /____/                                      //
  //                                                                       //
  //               The Next Generation Logic Library                       //
  //                                                                       //
  ///////////////////////////////////////////////////////////////////////////
  //                                                                       //
  //  Copyright 2015-20xx Christoph Zengler                                //
  //                                                                       //
  //  Licensed under the Apache License, Version 2.0 (the "License");      //
  //  you may not use this file except in compliance with the License.     //
  //  You may obtain a copy of the License at                              //
  //                                                                       //
  //  http://www.apache.org/licenses/LICENSE-2.0                           //
  //                                                                       //
  //  Unless required by applicable law or agreed to in writing, software  //
  //  distributed under the License is distributed on an "AS IS" BASIS,    //
  //  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or      //
  //  implied.  See the License for the specific language governing        //
  //  permissions and limitations under the License.                       //
  //                                                                       //
  ///////////////////////////////////////////////////////////////////////////
  
  package org.logicng.transformations.cnf;
  
  import org.logicng.datastructures.ubtrees.UBTree;
  import org.logicng.formulas.FType;
  import org.logicng.formulas.Formula;
  import org.logicng.formulas.FormulaTransformation;
  import org.logicng.formulas.Literal;
  import org.logicng.transformations.Subsumption;
  
  import java.util.ArrayList;
  import java.util.List;
  import java.util.SortedSet;
  
  /**
   * This transformation performs subsumption on a given CNF and returns a new CNF.
   * I.e. performs as many subsumptions as possible.  A subsumption in a CNF means,
   * that e.g. a clause {@code A | B | C} is subsumed by another clause {@code A | B}
   * and can therefore be deleted for an equivalent CNF.
   * @version 2.3.0
   * @since 1.5.0
   */
  public final class CNFSubsumption extends Subsumption implements FormulaTransformation {
  
      private static final CNFSubsumption INSTANCE = new CNFSubsumption();
  
      /**
       * @deprecated In the next version, the standard constructor will be replaced by a private constructor.
       * In order to instantiate an object of this class, use the {@link #get()} method.
       */
      @Deprecated
      public CNFSubsumption() {
          // Intentionally left empty
      }
  
      /**
       * Returns the singleton instance of this function.
       * @return an instance of this function
       */
      public static CNFSubsumption get() {
          return INSTANCE;
      }
  
      @Override
      public Formula apply(final Formula formula, final boolean cache) {
          if (!formula.isCNF()) {
              throw new IllegalArgumentException("CNF subsumption can only be applied to formulas in CNF");
          }
          if (formula.type().precedence() >= FType.LITERAL.precedence() || formula.type() == FType.OR) {
              return formula;
          }
          assert formula.type() == FType.AND;
          final UBTree<Literal> ubTree = generateSubsumedUBTree(formula);
          final List<Formula> clauses = new ArrayList<>();
          for (final SortedSet<Literal> literals : ubTree.allSets()) {
              clauses.add(formula.factory().clause(literals));
          }
          return formula.factory().cnf(clauses);
      }
  }
  