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.dnf;
  
  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 DNF and returns a new DNF.
   * I.e. performs as many subsumptions as possible.  A subsumption in a DNF means,
   * that e.g. a minterm {@code A & B & C} is subsumed by another minterm {@code A & B}
   * and can therefore be deleted for an equivalent DNF.
   * @version 2.3.0
   * @since 1.5.0
   */
  public final class DNFSubsumption extends Subsumption implements FormulaTransformation {
      private static final DNFSubsumption INSTANCE = new DNFSubsumption();
  
      /**
       * @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 DNFSubsumption() {
          // Intentionally left empty
      }
  
      /**
       * Returns the singleton instance of this function.
       * @return an instance of this function
       */
      public static DNFSubsumption get() {
          return INSTANCE;
      }
  
      @Override
      public Formula apply(final Formula formula, final boolean cache) {
          if (!formula.isDNF()) {
              throw new IllegalArgumentException("DNF subsumption can only be applied to formulas in DNF");
          }
          if (formula.type().precedence() >= FType.LITERAL.precedence() || formula.type() == FType.AND) {
              return formula;
          }
          assert formula.type() == FType.OR;
          final UBTree<Literal> ubTree = generateSubsumedUBTree(formula);
          final List<Formula> minterms = new ArrayList<>();
          for (final SortedSet<Literal> literals : ubTree.allSets()) {
              minterms.add(formula.factory().and(literals));
          }
          return formula.factory().or(minterms);
      }
  }
  