# **************************************************************************
# File: I4
# Name: Traditionnal interval benchmark
# 
# Reference :
# 
# @article{    VHenMicBen97,
#    author    = "Pascal {Van Hentenryck} and Laurent Michel 
#                 and Fr\'ed\'eric Benhamou",
#    title     = "{\tt Newton} - {C}onstraint {P}rogramming over non-linear 
#                                {C}onstraints",
#    journal   = "Scientific Programming",
#    year      = 1997,
#    note      = "Forthcoming"
# }
# ****************************************************************************
# 
# Solution without splitting:
# Variables: x1,x2,...,x10
# 
# ***************************************************************************



# Domains
var x1  >= -1, <= 1;
var x2  >= -1, <= 1;
var x3  >= -1, <= 1;
var x4  >= -1, <= 1;
var x5  >= -1, <= 1;
var x6  >= -1, <= 1;
var x7  >= -1, <= 1;
var x8  >= -1, <= 1;
var x9  >= -1, <= 1;
var x10 >= -1, <= 1;

subject to
cons1 : x1^2 - 0.25428722 - 0.18324757*(x4*x3*x9)^2  = 0;
cons2 : x2^2 - 0.37842197 - 0.16275449*(x1*x10*x6)^2 = 0;
cons3 : x3^2 - 0.27162577 - 0.16955071*(x1*x2*x10)^2 = 0;
cons4 : x4^2 - 0.19807914 - 0.15585316*(x7*x1*x6)^2  = 0;
cons5 : x5^2 - 0.44166728 - 0.19950920*(x7*x6*x3)^2  = 0;
cons6 : x6^2 - 0.14654113 - 0.18922793*(x8*x5*x10)^2 = 0;
cons7 : x7^2 - 0.42937161 - 0.21180486*(x2*x5*x8)^2  = 0;
cons8 : x8^2 - 0.07056438 - 0.17081208*(x1*x7*x6)^2  = 0;
cons9 : x9^2 - 0.34504906 - 0.19612740*(x10*x6*x8)^2 = 0;
cons10 : x10^2 - 0.42651102 - 0.21466544*(x4*x8*x1)^2 = 0;

solve;
display x1, x10, x2, x3, x4, x5, x6, x7, x8, x9;