code: ///////////////////////////////////////////////////////////////////////////
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  //                  / /   ____  ____ _(_)____/ | / / ____/               //
  //                 / /   / __ \/ __ `/ / ___/  |/ / / __                 //
  //                / /___/ /_/ / /_/ / / /__/ /|  / /_/ /                 //
  //               /_____/\____/\__, /_/\___/_/ |_/\____/                  //
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  //                                                                       //
  //               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.qe;
  
  import org.logicng.datastructures.Assignment;
  import org.logicng.formulas.Formula;
  import org.logicng.formulas.FormulaFactory;
  import org.logicng.formulas.FormulaTransformation;
  import org.logicng.formulas.Variable;
  
  import java.util.Arrays;
  import java.util.Collection;
  
  /**
   * This transformation eliminates a number of existentially quantified variables by replacing them with the Shannon
   * expansion.  If {@code x} is eliminated from a formula {@code f}, the resulting formula is
   * {@code f[true/x] | f[false/x]}.
   * <p>
   * This transformation cannot be cached since it is dependent on the set of literals to eliminate.
   * @version 1.0
   * @since 1.0
   */
  public final class ExistentialQuantifierElimination implements FormulaTransformation {
  
      private final Variable[] elimination;
  
      /**
       * Constructs a new existential quantifier elimination for the given variables.
       * @param variables the variables
       */
      public ExistentialQuantifierElimination(final Variable... variables) {
          this.elimination = Arrays.copyOf(variables, variables.length);
      }
  
      /**
       * Constructs a new existential quantifier elimination for a given collection of variables.
       * @param variables the collection of variables
       */
      public ExistentialQuantifierElimination(final Collection<Variable> variables) {
          this.elimination = variables.toArray(new Variable[0]);
      }
  
      @Override
      public Formula apply(final Formula formula, final boolean cache) {
          Formula result = formula;
          final FormulaFactory f = formula.factory();
          for (final Variable var : this.elimination) {
              result = f.or(result.restrict(new Assignment(var)), result.restrict(new Assignment(var.negate())));
          }
          return result;
      }
  }
  