content: /**
   * 
   */
  package kodkod.examples.tptp;
  
  import java.util.ArrayList;
  import java.util.List;
  
  import kodkod.ast.Expression;
  import kodkod.ast.Formula;
  import kodkod.ast.Relation;
  import kodkod.engine.Solution;
  import kodkod.engine.Solver;
  import kodkod.engine.satlab.SATFactory;
  import kodkod.instance.Bounds;
  import kodkod.instance.Tuple;
  import kodkod.instance.TupleFactory;
  import kodkod.instance.TupleSet;
  
  /**
   * A KK encoding of ALG197+1.p from http://www.cs.miami.edu/~tptp/
   * @author Emina Torlak
   */
  public final class ALG197 extends Quasigroups7 {
  
  	/**
  	 * Constructs a new instance of ALG197.
  	 */
  	public ALG197() {}
  	
  	
  	/**
  	 * Parametrization of axioms 12 and 13.
  	 * @requires e's are unary, op is ternary
  	 */
  	Formula ax12and13(Relation[] e, Relation op) {
  		final List<Formula> f0 = new ArrayList<Formula>();
  		final List<Formula> f1 = new ArrayList<Formula>();
  		for(int i = 0; i < 7; i++) {
  			Formula f = e[i].join(e[i].join(op)).eq(e[i]);
  			f0.add(f);
  			f1.add(f.not());
  		}
  		return Formula.or(f0).and(Formula.or(f1));
  	}
  	
  	
  	
  	/**
  	 * Parametrization of axioms 14 and 15.
  	 * @requires e's are unary, op is ternary
  	 */
  	Formula ax14and15(Relation[] e, Relation op) {
  		final Expression expr0 = e[6].join(op); // op(e6,...)
  		final Expression expr1 = e[6].join(expr0); // op(e6,e6)
  		final Expression expr2 = expr1.join(expr1.join(op)); // op(op(e6,e6),op(e6,e6))
  		final Expression expr3 = expr2.join(expr0); // op(e6,op(op(e6,e6),op(e6,e6)))
  		// e0 = op(e6,op(e6,e6))
  		final Formula f0 = e[0].eq(expr1.join(expr0));
  		// e1 = op(op(e6,e6),op(e6,e6))
  		final Formula f1 = e[1].eq(expr2);
  		// e2 = op(op(op(e6,e6),op(e6,e6)),op(e6,e6))
  		final Formula f2 = e[2].eq(expr1.join(expr2.join(op)));
  		// e3 = op(e6,op(op(e6,e6),op(e6,e6)))
  		final Formula f3 = e[3].eq(expr3);
  		// e4 = op(e6,op(e6,op(op(e6,e6),op(e6,e6))))
  		final Formula f4 = e[4].eq(expr3.join(expr0));
  		return Formula.and(f0,f1,f2,f3,f4);
  	}
  	
  	/**
  	 * Parametrization of axioms 16-22.
  	 * @requires e is unary, h is binary
  	 */
  	Formula ax16_22(Relation e, Relation h) {
  		final Expression expr0 = e.join(op2); // op2(e,...)
  		final Expression expr1 = e.join(expr0); // op2(e,e)
  		final Expression expr2 = expr1.join(expr1.join(op2)); // op2(op2(e,e),op2(e,e))
  		final Expression expr3 = expr2.join(expr0); // op2(e,op2(op2(e,e),op2(e,e)))
  		//  h(e10) = op2(e,op2(e,e))
  		final Formula f0 = e1[0].join(h).eq(expr1.join(expr0));
  		//  h(e11) = op2(op2(e,e),op2(e,e))
  		final Formula f1 = e1[1].join(h).eq(expr2);
  		//  h(e12) = op2(op2(op2(e,e),op2(e,e)),op2(e,e))
  		final Formula f2 = e1[2].join(h).eq(expr1.join(expr2.join(op2)));
  		//  h(e13) = op2(e,op2(op2(e,e),op2(e,e)))
  		final Formula f3 = e1[3].join(h).eq(expr3);
  		//  h(e14) = op2(e,op2(e,op2(op2(e,e),op2(e,e))))
  		final Formula f4 = e1[4].join(h).eq(expr3.join(expr0));
  		//  h(e15) = op2(e,e)
  		final Formula f5 = e1[5].join(h).eq(expr1);
  		return Formula.and(f0, f1, f2, f3, f4, f5);
  	}
  	/**
  	 * Returns the conjunction of the axioms and the negation of the hypothesis.
  	 * @return axioms() && !co1()
  	 */
  	public final Formula checkCO1() { 
  		return axioms().and(co1().not());
  	}
  	
  	/**
  	 * Returns the bounds the problem (axioms 1, 4, 9-11, last formula of 14-15, and first formula of 16-22).
  	 * @return the bounds for the problem
  	 */
  	public final Bounds bounds() {
  		final Bounds b = super.bounds();
  		final TupleFactory f = b.universe().factory();
  		
  		final TupleSet op1h = b.upperBound(op1).clone();
  		final TupleSet op2h = b.upperBound(op2).clone();
  		
  		final TupleSet op1l = f.setOf(f.tuple("e16", "e16", "e15")); // axiom 14, line 6
  		final TupleSet op2l = f.setOf(f.tuple("e26", "e26", "e25")); // axiom 15, line 6
  		
  		op1h.removeAll(f.area(f.tuple("e16", "e16", "e10"), f.tuple("e16", "e16", "e16")));
  		op1h.addAll(op1l);
  		
  		op2h.removeAll(f.area(f.tuple("e26", "e26", "e20"), f.tuple("e26", "e26", "e26")));
  		op2h.addAll(op2l);
  		
  		b.bound(op1, op1l, op1h);
  		b.bound(op2, op2l, op2h);
  		
  		final TupleSet high = f.area(f.tuple("e10", "e20"), f.tuple("e15", "e26"));
  		
  		// first line of axioms 16-22
  		for(int i = 0; i < 7; i++) {
  			Tuple t = f.tuple("e16", "e2"+i);
  			high.add(t);
  			b.bound(h[i], f.setOf(t), high);
  			high.remove(t);
  		}
  		
  		return b;
  	}
  	
  	private static void usage() {
  		System.out.println("java examples.tptp.ALG197");
  		System.exit(1);
  	}
  	
  	/**
  	 * Usage: java examples.tptp.ALG197
  	 */
  	public static void main(String[] args) {
  	
  		try {
  	
  			final ALG197 model = new ALG197();
  			final Solver solver = new Solver();
  			solver.options().setSolver(SATFactory.DEFAULT);
  			final Formula f = model.checkCO1();
  			final Bounds b = model.bounds();
  			final Solution sol = solver.solve(f, b);
  			if (sol.instance()==null) {
  				System.out.println(sol);
  			} else {
  				System.out.println(sol.stats());
  				model.display(sol.instance());
  			}
  		} catch (NumberFormatException nfe) {
  			usage();
  		}
  	}
  }
  