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/******************************************************************************
* Top contributors (to current version):
* Mudathir Mohamed, Daniel Larraz, Andres Noetzli
*
* 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 with cvc5.
*/
import static io.github.cvc5.Kind.*;
import io.github.cvc5.*;
public class Sets
{
public static void main(String args[]) throws CVC5ApiException
{
TermManager tm = new TermManager();
Solver slv = new Solver(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");
slv.setOption("output-language", "smt2");
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(SET_UNION, A, B);
Term lhs = tm.mkTerm(SET_INTER, unionAB, C);
Term intersectionAC = tm.mkTerm(SET_INTER, A, C);
Term intersectionBC = tm.mkTerm(SET_INTER, B, C);
Term rhs = tm.mkTerm(SET_UNION, intersectionAC, intersectionBC);
Term theorem = tm.mkTerm(EQUAL, lhs, rhs);
System.out.println(
"cvc5 reports: " + theorem + " is " + slv.checkSatAssuming(theorem.notTerm()) + ".");
}
// Verify set.empty is a subset of any set
{
Term A = tm.mkConst(set, "A");
Term emptyset = tm.mkEmptySet(set);
Term theorem = tm.mkTerm(SET_SUBSET, emptyset, A);
System.out.println(
"cvc5 reports: " + theorem + " is " + slv.checkSatAssuming(theorem.notTerm()) + ".");
}
// 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(SET_SINGLETON, one);
Term singleton_two = tm.mkTerm(SET_SINGLETON, two);
Term singleton_three = tm.mkTerm(SET_SINGLETON, three);
Term one_two = tm.mkTerm(SET_UNION, singleton_one, singleton_two);
Term two_three = tm.mkTerm(SET_UNION, singleton_two, singleton_three);
Term intersection = tm.mkTerm(SET_INTER, one_two, two_three);
Term x = tm.mkConst(integer, "x");
Term e = tm.mkTerm(SET_MEMBER, x, intersection);
Result result = slv.checkSatAssuming(e);
System.out.println("cvc5 reports: " + e + " is " + result + ".");
if (result.isSat())
{
System.out.println("For instance, " + slv.getValue(x) + " is a member.");
}
}
}
Context.deletePointers();
}
}
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