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/******************************************************************************
* Top contributors (to current version):
* Aina Niemetz, Tim King, Mudathir Mohamed
*
* This file is part of the cvc5 project.
*
* Copyright (c) 2009-2021 by the authors listed in the file AUTHORS
* in the top-level source directory and their institutional affiliations.
* All rights reserved. See the file COPYING in the top-level source
* directory for licensing information.
* ****************************************************************************
*
* A simple demonstration of the linear arithmetic solving capabilities and
* the push pop of cvc5. This also gives an example option.
*/
import io.github.cvc5.api.*;
public class LinearArith
{
public static void main(String args[]) throws CVC5ApiException
{
try (Solver slv = new Solver())
{
slv.setLogic("QF_LIRA"); // Set the logic
// Prove that if given x (Integer) and y (Real) then
// the maximum value of y - x is 2/3
// Sorts
Sort real = slv.getRealSort();
Sort integer = slv.getIntegerSort();
// Variables
Term x = slv.mkConst(integer, "x");
Term y = slv.mkConst(real, "y");
// Constants
Term three = slv.mkInteger(3);
Term neg2 = slv.mkInteger(-2);
Term two_thirds = slv.mkReal(2, 3);
// Terms
Term three_y = slv.mkTerm(Kind.MULT, three, y);
Term diff = slv.mkTerm(Kind.MINUS, y, x);
// Formulas
Term x_geq_3y = slv.mkTerm(Kind.GEQ, x, three_y);
Term x_leq_y = slv.mkTerm(Kind.LEQ, x, y);
Term neg2_lt_x = slv.mkTerm(Kind.LT, neg2, x);
Term assertions = slv.mkTerm(Kind.AND, x_geq_3y, x_leq_y, neg2_lt_x);
System.out.println("Given the assertions " + assertions);
slv.assertFormula(assertions);
slv.push();
Term diff_leq_two_thirds = slv.mkTerm(Kind.LEQ, diff, two_thirds);
System.out.println("Prove that " + diff_leq_two_thirds + " with cvc5.");
System.out.println("cvc5 should report ENTAILED.");
System.out.println("Result from cvc5 is: " + slv.checkEntailed(diff_leq_two_thirds));
slv.pop();
System.out.println();
slv.push();
Term diff_is_two_thirds = slv.mkTerm(Kind.EQUAL, diff, two_thirds);
slv.assertFormula(diff_is_two_thirds);
System.out.println("Show that the assertions are consistent with ");
System.out.println(diff_is_two_thirds + " with cvc5.");
System.out.println("cvc5 should report SAT.");
System.out.println("Result from cvc5 is: " + slv.checkSat());
slv.pop();
System.out.println("Thus the maximum value of (y - x) is 2/3.");
}
}
}
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