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#! /usr/bin/python
#####################
## SimpleVC.py
## Top contributors (to current version):
## Morgan Deters, Aina Niemetz, Andres Noetzli
## This file is part of the CVC4 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.
##
##! \file SimpleVC.py
### \verbatim
### Original author: mdeters
### Major contributors: none
### Minor contributors (to current version): none
### This file is part of the CVC4 prototype.
### Copyright (c) 2009, 2010, 2011 The Analysis of Computer Systems Group (ACSys)
### Courant Institute of Mathematical Sciences
### New York University
### See the file COPYING in the top-level source directory for licensing
### information.\endverbatim
###
### \brief A simple demonstration of the Python interface
###
### A simple demonstration of the Python interface. Compare to the
### C++ interface in simple_vc_cxx.cpp; they are quite similar.
###
### To run from a build directory, use something like:
###
### PYTHONPATH=src/bindings/python python ../examples/SimpleVC.py
####
import CVC4
from CVC4 import ExprManager, SmtEngine, Rational, Expr
import sys
def main():
em = ExprManager()
smt = SmtEngine(em)
# Prove that for integers x and y:
# x > 0 AND y > 0 => 2x + y >= 3
integer = em.integerType()
x = em.mkVar("x", integer)
y = em.mkVar("y", integer)
zero = em.mkConst(Rational(0))
x_positive = em.mkExpr(CVC4.GT, x, zero)
y_positive = em.mkExpr(CVC4.GT, y, zero)
two = em.mkConst(Rational(2))
twox = em.mkExpr(CVC4.MULT, two, x)
twox_plus_y = em.mkExpr(CVC4.PLUS, twox, y)
three = em.mkConst(Rational(3))
twox_plus_y_geq_3 = em.mkExpr(CVC4.GEQ, twox_plus_y, three)
formula = Expr(em.mkExpr(CVC4.AND, x_positive, y_positive)).impExpr(Expr(twox_plus_y_geq_3))
print("Checking entailment of formula " + formula.toString() + " with CVC4.")
print("CVC4 should report ENTAILED .")
print("Result from CVC4 is: " + smt.checkEntailed(formula).toString())
return 0
if __name__ == '__main__':
sys.exit(main())
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