# NLP written by GAMS Convert at 02/17/22 17:21:46
#
# Equation counts
#     Total        E        G        L        N        X        C        B
#        21        0        0       21        0        0        0        0
#
# Variable counts
#                  x        b        i      s1s      s2s       sc       si
#     Total     cont   binary  integer     sos1     sos2    scont     sint
#        13       13        0        0        0        0        0        0
# FX      0
#
# Nonzero counts
#     Total    const       NL
#        87       27       60
#
# Reformulation has removed 1 variable and 1 equation

from pyomo.environ import *

model = m = ConcreteModel()

m.x1 = Var(within=Reals, bounds=(0.5,1), initialize=0.5)
m.x2 = Var(within=Reals, bounds=(0.5,1), initialize=0.5)
m.x3 = Var(within=Reals, bounds=(0.5,1), initialize=0.5)
m.x4 = Var(within=Reals, bounds=(0,1), initialize=0)
m.x5 = Var(within=Reals, bounds=(0,1), initialize=0)
m.x6 = Var(within=Reals, bounds=(0,1), initialize=0)
m.x7 = Var(within=Reals, bounds=(0,1), initialize=0)
m.x8 = Var(within=Reals, bounds=(0,1), initialize=0)
m.x9 = Var(within=Reals, bounds=(0,1), initialize=0)
m.x10 = Var(within=Reals, bounds=(0,1), initialize=0)
m.x11 = Var(within=Reals, bounds=(0,1), initialize=0)
m.x12 = Var(within=Reals, bounds=(0,1), initialize=0)
m.x13 = Var(within=Reals, bounds=(None,None), initialize=0)

m.obj = Objective(sense=maximize, expr= m.x13)

m.e1 = Constraint(expr= 2 * m.x1 * m.x2 - m.x1 * m.x1 - m.x2 * m.x2 - m.x7 *
    m.x7 + 2 * m.x7 * m.x8 - m.x8 * m.x8 + m.x13 <= 0)
m.e2 = Constraint(expr= 2 * m.x1 * m.x3 - m.x1 * m.x1 - m.x3 * m.x3 - m.x7 *
    m.x7 + 2 * m.x7 * m.x9 - m.x9 * m.x9 + m.x13 <= 0)
m.e3 = Constraint(expr= 2 * m.x1 * m.x4 - m.x1 * m.x1 - m.x4 * m.x4 - m.x7 *
    m.x7 + 2 * m.x7 * m.x10 - m.x10 * m.x10 + m.x13 <= 0)
m.e4 = Constraint(expr= 2 * m.x1 * m.x5 - m.x1 * m.x1 - m.x5 * m.x5 - m.x7 *
    m.x7 + 2 * m.x7 * m.x11 - m.x11 * m.x11 + m.x13 <= 0)
m.e5 = Constraint(expr= 2 * m.x1 * m.x6 - m.x1 * m.x1 - m.x6 * m.x6 - m.x7 *
    m.x7 + 2 * m.x7 * m.x12 - m.x12 * m.x12 + m.x13 <= 0)
m.e6 = Constraint(expr= 2 * m.x2 * m.x3 - m.x2 * m.x2 - m.x3 * m.x3 - m.x8 *
    m.x8 + 2 * m.x8 * m.x9 - m.x9 * m.x9 + m.x13 <= 0)
m.e7 = Constraint(expr= 2 * m.x2 * m.x4 - m.x2 * m.x2 - m.x4 * m.x4 - m.x8 *
    m.x8 + 2 * m.x8 * m.x10 - m.x10 * m.x10 + m.x13 <= 0)
m.e8 = Constraint(expr= 2 * m.x2 * m.x5 - m.x2 * m.x2 - m.x5 * m.x5 - m.x8 *
    m.x8 + 2 * m.x8 * m.x11 - m.x11 * m.x11 + m.x13 <= 0)
m.e9 = Constraint(expr= 2 * m.x2 * m.x6 - m.x2 * m.x2 - m.x6 * m.x6 - m.x8 *
    m.x8 + 2 * m.x8 * m.x12 - m.x12 * m.x12 + m.x13 <= 0)
m.e10 = Constraint(expr= 2 * m.x3 * m.x4 - m.x3 * m.x3 - m.x4 * m.x4 - m.x9 *
    m.x9 + 2 * m.x9 * m.x10 - m.x10 * m.x10 + m.x13 <= 0)
m.e11 = Constraint(expr= 2 * m.x3 * m.x5 - m.x3 * m.x3 - m.x5 * m.x5 - m.x9 *
    m.x9 + 2 * m.x9 * m.x11 - m.x11 * m.x11 + m.x13 <= 0)
m.e12 = Constraint(expr= 2 * m.x3 * m.x6 - m.x3 * m.x3 - m.x6 * m.x6 - m.x9 *
    m.x9 + 2 * m.x9 * m.x12 - m.x12 * m.x12 + m.x13 <= 0)
m.e13 = Constraint(expr= 2 * m.x4 * m.x5 - m.x4 * m.x4 - m.x5 * m.x5 - m.x10 *
    m.x10 + 2 * m.x10 * m.x11 - m.x11 * m.x11 + m.x13 <= 0)
m.e14 = Constraint(expr= 2 * m.x4 * m.x6 - m.x4 * m.x4 - m.x6 * m.x6 - m.x10 *
    m.x10 + 2 * m.x10 * m.x12 - m.x12 * m.x12 + m.x13 <= 0)
m.e15 = Constraint(expr= 2 * m.x5 * m.x6 - m.x5 * m.x5 - m.x6 * m.x6 - m.x11 *
    m.x11 + 2 * m.x11 * m.x12 - m.x12 * m.x12 + m.x13 <= 0)
m.e16 = Constraint(expr= -m.x7 + m.x8 <= 0)
m.e17 = Constraint(expr= -m.x1 + m.x2 <= 0)
m.e18 = Constraint(expr= -m.x2 + m.x3 <= 0)
m.e19 = Constraint(expr= -m.x3 + m.x4 <= 0)
m.e20 = Constraint(expr= -m.x4 + m.x5 <= 0)
m.e21 = Constraint(expr= -m.x5 + m.x6 <= 0)