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#!/usr/bin/env python
###############################################################################
# Top contributors (to current version):
# Aina Niemetz, Makai Mann, Alex Ozdemir
#
# 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 solving capabilities of the cvc5 sets solver
# through the Python API. This is a direct translation of sets.cpp.
##
import cvc5
from cvc5 import Kind
if __name__ == "__main__":
tm = cvc5.TermManager()
slv = cvc5.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")
integer = tm.getIntegerSort()
set_ = tm.mkSetSort(integer)
# Verify union distributions over intersection
# (A union B) intersection C = (A intersection C) union (B intersection C)
A = tm.mkConst(set_, "A")
B = tm.mkConst(set_, "B")
C = tm.mkConst(set_, "C")
unionAB = tm.mkTerm(Kind.SET_UNION, A, B)
lhs = tm.mkTerm(Kind.SET_INTER, unionAB, C)
intersectionAC = tm.mkTerm(Kind.SET_INTER, A, C)
intersectionBC = tm.mkTerm(Kind.SET_INTER, B, C)
rhs = tm.mkTerm(Kind.SET_UNION, intersectionAC, intersectionBC)
theorem = tm.mkTerm(Kind.EQUAL, lhs, rhs)
print("cvc5 reports: {} is {}".format(
theorem.notTerm(), slv.checkSatAssuming(theorem.notTerm())))
# Verify emptset is a subset of any set
A = tm.mkConst(set_, "A")
emptyset = tm.mkEmptySet(set_)
theorem = tm.mkTerm(Kind.SET_SUBSET, emptyset, A)
print("cvc5 reports: {} is {}".format(
theorem.notTerm(), slv.checkSatAssuming(theorem.notTerm())))
# Find me an element in 1, 2 intersection 2, 3, if there is one.
one = tm.mkInteger(1)
two = tm.mkInteger(2)
three = tm.mkInteger(3)
singleton_one = tm.mkTerm(Kind.SET_SINGLETON, one)
singleton_two = tm.mkTerm(Kind.SET_SINGLETON, two)
singleton_three = tm.mkTerm(Kind.SET_SINGLETON, three)
one_two = tm.mkTerm(Kind.SET_UNION, singleton_one, singleton_two)
two_three = tm.mkTerm(Kind.SET_UNION, singleton_two, singleton_three)
intersection = tm.mkTerm(Kind.SET_INTER, one_two, two_three)
x = tm.mkConst(integer, "x")
e = tm.mkTerm(Kind.SET_MEMBER, x, intersection)
result = slv.checkSatAssuming(e)
print("cvc5 reports: {} is {}".format(e, result))
if result:
print("For instance, {} is a member".format(slv.getValue(x)))
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