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#!/usr/bin/env python
###############################################################################
# Top contributors (to current version):
# Makai Mann, Mudathir Mohamed, Aina Niemetz
#
# This file is part of the cvc5 project.
#
# Copyright (c) 2009-2021 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 linear
# arithmetic solver through the Python API. This is a direct translation of
# linear_arith-new.cpp.
##
import pycvc5
from pycvc5 import Kind
if __name__ == "__main__":
slv = pycvc5.Solver()
slv.setLogic("QF_LIRA")
# Prove that if given x (Integer) and y (Real) and some constraints
# then the maximum value of y - x is 2/3
# Sorts
real = slv.getRealSort()
integer = slv.getIntegerSort()
# Variables
x = slv.mkConst(integer, "x")
y = slv.mkConst(real, "y")
# Constants
three = slv.mkInteger(3)
neg2 = slv.mkInteger(-2)
two_thirds = slv.mkReal(2, 3)
# Terms
three_y = slv.mkTerm(Kind.Mult, three, y)
diff = slv.mkTerm(Kind.Minus, y, x)
# Formulas
x_geq_3y = slv.mkTerm(Kind.Geq, x, three_y)
x_leq_y = slv.mkTerm(Kind.Leq, x ,y)
neg2_lt_x = slv.mkTerm(Kind.Lt, neg2, x)
assertions = slv.mkTerm(Kind.And, x_geq_3y, x_leq_y, neg2_lt_x)
print("Given the assertions", assertions)
slv.assertFormula(assertions)
slv.push()
diff_leq_two_thirds = slv.mkTerm(Kind.Leq, diff, two_thirds)
print("Prove that", diff_leq_two_thirds, "with cvc5")
print("cvc5 should report ENTAILED")
print("Result from cvc5 is:",
slv.checkEntailed(diff_leq_two_thirds))
slv.pop()
print()
slv.push()
diff_is_two_thirds = slv.mkTerm(Kind.Equal, diff, two_thirds)
slv.assertFormula(diff_is_two_thirds)
print("Show that the assertions are consistent with\n", diff_is_two_thirds, "with cvc5")
print("cvc5 should report SAT")
print("Result from cvc5 is:", slv.checkSat())
slv.pop()
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