ALG195.java

/**
 * 
 */
package kodkod.examples.tptp;

import static kodkod.ast.Formula.*;
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 ALG195+1.p from http://www.cs.miami.edu/~tptp/
 * @author Emina Torlak
 */
public final class ALG195 extends Quasigroups7 {

	/**
	 * Constructs a new instance of ALG195.
	 */
	public ALG195() {}
	
	/**
	 * Parametrization of axioms 12 and 13.
	 * @requires e's are unary, op is ternary
	 */
	Formula ax12and13(Relation[] e, Relation op) {
		return Formula.TRUE;
	}
	
	/**
	 * Parametrization of axioms 14 and 15.
	 * @requires e's are unary, op is ternary
	 */
	Formula ax14and15(Relation[] e, Relation op) {
		final Expression expr0 = e[5].join(op); // op(e5,...)
		final Expression expr1 = e[5].join(expr0); // op(e5,e5)
		final Expression expr2 = expr1.join(expr0); // op(e5,op(e5,e5))
		final Expression expr3 = expr2.join(expr2.join(op)); // op(op(e5,op(e5,e5)),op(e5,op(e5,e5)))
		final Expression expr3a = expr3.join(op); // op(op(op(e5,op(e5,e5)),op(e5,op(e5,e5))),...)
		final Expression expr4 = e[5].join(expr3a); // op(op(op(e5,op(e5,e5)),op(e5,op(e5,e5))),e5)
		// e0 = op(op(op(e5,op(e5,e5)),op(e5,op(e5,e5))),op(e5,op(e5,e5)))
		final Formula f0 = e[0].eq(expr2.join(expr3a));
		// e2 = op(op(e5,op(e5,e5)),op(e5,op(e5,e5)))
		final Formula f2 = e[2].eq(expr3);
		// e3 = op(op(op(e5,op(e5,e5)),op(e5,op(e5,e5))),e5)
		final Formula f3 = e[3].eq(expr4);
		// e4 = op(e5,op(e5,e5))
		final Formula f4 = e[4].eq(expr2);
		// e6 = op(op(op(op(e5,op(e5,e5)),op(e5,op(e5,e5))),e5),op(e5,op(e5,e5)))
		final Formula f6 = e[6].eq(expr2.join(expr4.join(op)));
		return and(f0, f2, f3, f4, f6);
	}
	
	
	
	/**
	 * 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(expr0); // op2(e,op2(e,e))
		final Expression expr3 = expr2.join(expr2.join(op2)); // op2(op2(e,op2(e,e)),op2(e,op2(e,e)))
		final Expression expr3a = expr3.join(op2); // op2(op2(op2(e,op2(e,e)),op2(e,op2(e,e))),...)
		final Expression expr4 = e.join(expr3a); // op2(op2(op2(e,op2(e,e)),op2(e,op2(e,e))),e)
		// h(e10) = op2(op2(op2(e,op2(e,e)),op2(e,op2(e,e))),op2(e,op2(e,e)))
		final Formula f0 = e1[0].join(h).eq(expr2.join(expr3a));
		// h(e11) = op2(e,e)
		final Formula f1 = e1[1].join(h).eq(expr1);
		// h(e12) = op2(op2(e,op2(e,e)),op2(e,op2(e,e)))
		final Formula f2 = e1[2].join(h).eq(expr3);
		// h(e13) = op2(op2(op2(e,op2(e,e)),op2(e,op2(e,e))),e)
		final Formula f3 = e1[3].join(h).eq(expr4);
		// h(e14) = op2(e,op2(e,e))
		final Formula f4 = e1[4].join(h).eq(expr2);
		// h(e16) = op2(op2(op2(op2(e,op2(e,e)),op2(e,op2(e,e))),e),op2(e,op2(e,e)))
		final Formula f6 = e1[6].join(h).eq(expr2.join(expr4.join(op2)));
		
		return and(f0, f1, f2, f3, f4, f6);
	}

	/**
	 * 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, 9-13, second 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();
		
		for(int i = 0; i < 7; i++) {
			op1h.remove(f.tuple("e1"+i, "e1"+i, "e1"+i)); // axiom 12
			op2h.remove(f.tuple("e2"+i, "e2"+i, "e2"+i)); // axiom 13
		}
		
		final TupleSet op1l = f.setOf(f.tuple("e15", "e15", "e11")); // axiom 14, line 2
		final TupleSet op2l = f.setOf(f.tuple("e25", "e25", "e21")); // axiom 15, line 2
		
		op1h.removeAll(f.area(f.tuple("e15", "e15", "e10"), f.tuple("e15", "e15", "e16")));
		op1h.addAll(op1l);
		
		op2h.removeAll(f.area(f.tuple("e25", "e25", "e20"), f.tuple("e25", "e25", "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("e14", "e26"));
		high.addAll(f.area(f.tuple("e16", "e20"), f.tuple("e16", "e26")));
		
		// first line of axioms 16-22
		for(int i = 0; i < 7; i++) {
			Tuple t = f.tuple("e15", "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.ALG195");
		System.exit(1);
	}
	
	/**
	 * Usage: java examples.tptp.ALG195
	 */
	public static void main(String[] args) {
	
		try {
	
			final ALG195 model = new ALG195();
			final Solver solver = new Solver();
			solver.options().setSolver(SATFactory.MiniSat);
			final Formula f = model.checkCO1();
			final Bounds b = model.bounds();
//			System.out.println(model.decls());
//			System.out.println(model.ax2ax7());
//			System.out.println(b);
			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();
		}
	}
}