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/******************************************************************************
* Top contributors (to current version):
* Aina Niemetz, Tim King, Haniel Barbosa
*
* This file is part of the cvc5 project.
*
* Copyright (c) 2009-2025 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.
*/
#include <iostream>
#include <cvc5/cvc5.h>
using namespace std;
using namespace cvc5;
int main()
{
TermManager tm;
Solver slv(tm);
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 = tm.getRealSort();
Sort integer = tm.getIntegerSort();
// Variables
Term x = tm.mkConst(integer, "x");
Term y = tm.mkConst(real, "y");
// Constants
Term three = tm.mkInteger(3);
Term neg2 = tm.mkInteger(-2);
Term two_thirds = tm.mkReal(2, 3);
// Terms
Term three_y = tm.mkTerm(Kind::MULT, {three, y});
Term diff = tm.mkTerm(Kind::SUB, {y, x});
// Formulas
Term x_geq_3y = tm.mkTerm(Kind::GEQ, {x, three_y});
Term x_leq_y = tm.mkTerm(Kind::LEQ, {x, y});
Term neg2_lt_x = tm.mkTerm(Kind::LT, {neg2, x});
Term assertions = tm.mkTerm(Kind::AND, {x_geq_3y, x_leq_y, neg2_lt_x});
cout << "Given the assertions " << assertions << endl;
slv.assertFormula(assertions);
slv.push();
Term diff_leq_two_thirds = tm.mkTerm(Kind::LEQ, {diff, two_thirds});
cout << "Prove that " << diff_leq_two_thirds << " with cvc5." << endl;
cout << "cvc5 should report UNSAT." << endl;
cout << "Result from cvc5 is: "
<< slv.checkSatAssuming(diff_leq_two_thirds.notTerm()) << endl;
slv.pop();
cout << endl;
slv.push();
Term diff_is_two_thirds = tm.mkTerm(Kind::EQUAL, {diff, two_thirds});
slv.assertFormula(diff_is_two_thirds);
cout << "Show that the assertions are consistent with " << endl;
cout << diff_is_two_thirds << " with cvc5." << endl;
cout << "cvc5 should report SAT." << endl;
cout << "Result from cvc5 is: " << slv.checkSat() << endl;
slv.pop();
cout << "Thus the maximum value of (y - x) is 2/3."<< endl;
return 0;
}
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