/*********************                                                        */
/*! \file simple_vc_cxx.cpp
 ** \verbatim
 ** Top contributors (to current version):
 **   Morgan Deters, Dejan Jovanovic
 ** This file is part of the CVC4 project.
 ** Copyright (c) 2009-2019 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.\endverbatim
 **
 ** \brief A simple demonstration of the C++ interface
 **
 ** A simple demonstration of the C++ interface.  Compare to the Java
 ** interface in SimpleVC.java; they are virtually line-by-line
 ** identical.
 **/

#include <iostream>

#include <cvc4/cvc4.h>

using namespace std;
using namespace CVC4;

int main() {
  ExprManager em;
  SmtEngine smt(&em);

  // Prove that for integers x and y:
  //   x > 0 AND y > 0  =>  2x + y >= 3

  Type integer = em.integerType();

  Expr x = em.mkVar("x", integer);
  Expr y = em.mkVar("y", integer);
  Expr zero = em.mkConst(Rational(0));

  Expr x_positive = em.mkExpr(kind::GT, x, zero);
  Expr y_positive = em.mkExpr(kind::GT, y, zero);

  Expr two = em.mkConst(Rational(2));
  Expr twox = em.mkExpr(kind::MULT, two, x);
  Expr twox_plus_y = em.mkExpr(kind::PLUS, twox, y);

  Expr three = em.mkConst(Rational(3));
  Expr twox_plus_y_geq_3 = em.mkExpr(kind::GEQ, twox_plus_y, three);

  Expr formula =
    em.mkExpr(kind::AND, x_positive, y_positive).
    impExpr(twox_plus_y_geq_3);

  cout << "Checking entailment of formula " << formula << " with CVC4." << endl;
  cout << "CVC4 should report ENTAILED." << endl;
  cout << "Result from CVC4 is: " << smt.checkEntailed(formula) << endl;

  return 0;
}