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/******************************************************************************
* Top contributors (to current version):
* Aina Niemetz, Kshitij Bansal, Andrew Reynolds
*
* 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 reasoning about sets via the C++ API.
*/
#include <cvc5/cvc5.h>
#include <iostream>
using namespace std;
using namespace cvc5;
int main()
{
TermManager tm;
Solver slv(tm);
// Optionally, set the logic. We need at least UF for equality predicate,
// integers (LIA) and sets (FS).
slv.setLogic("QF_UFLIAFS");
// Produce models
slv.setOption("produce-models", "true");
Sort integer = tm.getIntegerSort();
Sort set = tm.mkSetSort(integer);
// Verify union distributions over intersection
// (A union B) intersection C = (A intersection C) union (B intersection C)
{
Term A = tm.mkConst(set, "A");
Term B = tm.mkConst(set, "B");
Term C = tm.mkConst(set, "C");
Term unionAB = tm.mkTerm(Kind::SET_UNION, {A, B});
Term lhs = tm.mkTerm(Kind::SET_INTER, {unionAB, C});
Term intersectionAC = tm.mkTerm(Kind::SET_INTER, {A, C});
Term intersectionBC = tm.mkTerm(Kind::SET_INTER, {B, C});
Term rhs = tm.mkTerm(Kind::SET_UNION, {intersectionAC, intersectionBC});
Term theorem = tm.mkTerm(Kind::EQUAL, {lhs, rhs});
cout << "cvc5 reports: " << theorem << " is "
<< slv.checkSatAssuming(theorem.notTerm()) << "." << endl;
}
// Verify emptset is a subset of any set
{
Term A = tm.mkConst(set, "A");
Term emptyset = tm.mkEmptySet(set);
Term theorem = tm.mkTerm(Kind::SET_SUBSET, {emptyset, A});
cout << "cvc5 reports: " << theorem << " is "
<< slv.checkSatAssuming(theorem.notTerm()) << "." << endl;
}
// Find me an element in {1, 2} intersection {2, 3}, if there is one.
{
Term one = tm.mkInteger(1);
Term two = tm.mkInteger(2);
Term three = tm.mkInteger(3);
Term singleton_one = tm.mkTerm(Kind::SET_SINGLETON, {one});
Term singleton_two = tm.mkTerm(Kind::SET_SINGLETON, {two});
Term singleton_three = tm.mkTerm(Kind::SET_SINGLETON, {three});
Term one_two = tm.mkTerm(Kind::SET_UNION, {singleton_one, singleton_two});
Term two_three =
tm.mkTerm(Kind::SET_UNION, {singleton_two, singleton_three});
Term intersection = tm.mkTerm(Kind::SET_INTER, {one_two, two_three});
Term x = tm.mkConst(integer, "x");
Term e = tm.mkTerm(Kind::SET_MEMBER, {x, intersection});
Result result = slv.checkSatAssuming(e);
cout << "cvc5 reports: " << e << " is " << result << "." << endl;
if (result.isSat())
{
cout << "For instance, " << slv.getValue(x) << " is a member." << endl;
}
}
}
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