// Finds a minimum cost 2-egde-connected spanning subgraph of the weighted graph on 7
// vertices, whose edges and weights can be seen from the objective function.
// The problem was generated automatically in Python and it uses that out of the 2^7-2 =126 subsetsof the vertices which
// are neither empty nor the whole set, we only need to consider half, since they occour in pairs 
// because the condition is fulfilled on a set X if and only if the same condition is fulfilled on 
// its complement.

var int x[1..7,1..7] in 0..1;
minimize 10*x[1,2]+8*x[1,3]+2*x[1,4]+2*x[1,7]+3*x[2,3]+1*x[2,4]+1*x[2,6]+7*x[3,6]+3*x[3,7]+3*x[4,5]+1*x[5,6]+2*x[5,7]
subject to {
 forall (i,j in 1..7) x[i,j]=x[j,i];
x[1,2]+x[1,3]+x[1,4]+x[1,7]>=2;
x[1,2]+x[1,3]+x[1,4]+x[3,7]+x[5,7]>=2;
x[1,2]+x[1,3]+x[1,4]+x[1,7]+x[2,6]+x[3,6]+x[5,6]>=2;
x[1,2]+x[1,3]+x[1,4]+x[2,6]+x[3,6]+x[3,7]+x[5,6]+x[5,7]>=2;
x[1,2]+x[1,3]+x[1,4]+x[1,7]+x[4,5]+x[5,6]+x[5,7]>=2;
x[1,2]+x[1,3]+x[1,4]+x[3,7]+x[4,5]+x[5,6]>=2;
x[1,2]+x[1,3]+x[1,4]+x[1,7]+x[2,6]+x[3,6]+x[4,5]+x[5,7]>=2;
x[1,2]+x[1,3]+x[1,4]+x[2,6]+x[3,6]+x[3,7]+x[4,5]>=2;
x[1,2]+x[1,3]+x[1,7]+x[2,4]+x[4,5]>=2;
x[1,2]+x[1,3]+x[2,4]+x[3,7]+x[4,5]+x[5,7]>=2;
x[1,2]+x[1,3]+x[1,7]+x[2,4]+x[2,6]+x[3,6]+x[4,5]+x[5,6]>=2;
x[1,2]+x[1,3]+x[2,4]+x[2,6]+x[3,6]+x[3,7]+x[4,5]+x[5,6]+x[5,7]>=2;
x[1,2]+x[1,3]+x[1,7]+x[2,4]+x[5,6]+x[5,7]>=2;
x[1,2]+x[1,3]+x[2,4]+x[3,7]+x[5,6]>=2;
x[1,2]+x[1,3]+x[1,7]+x[2,4]+x[2,6]+x[3,6]+x[5,7]>=2;
x[1,2]+x[1,3]+x[2,4]+x[2,6]+x[3,6]+x[3,7]>=2;
x[1,2]+x[1,4]+x[1,7]+x[2,3]+x[3,6]+x[3,7]>=2;
x[1,2]+x[1,4]+x[2,3]+x[3,6]+x[5,7]>=2;
x[1,2]+x[1,4]+x[1,7]+x[2,3]+x[2,6]+x[3,7]+x[5,6]>=2;
x[1,2]+x[1,4]+x[2,3]+x[2,6]+x[5,6]+x[5,7]>=2;
x[1,2]+x[1,4]+x[1,7]+x[2,3]+x[3,6]+x[3,7]+x[4,5]+x[5,6]+x[5,7]>=2;
x[1,2]+x[1,4]+x[2,3]+x[3,6]+x[4,5]+x[5,6]>=2;
x[1,2]+x[1,4]+x[1,7]+x[2,3]+x[2,6]+x[3,7]+x[4,5]+x[5,7]>=2;
x[1,2]+x[1,4]+x[2,3]+x[2,6]+x[4,5]>=2;
x[1,2]+x[1,7]+x[2,3]+x[2,4]+x[3,6]+x[3,7]+x[4,5]>=2;
x[1,2]+x[2,3]+x[2,4]+x[3,6]+x[4,5]+x[5,7]>=2;
x[1,2]+x[1,7]+x[2,3]+x[2,4]+x[2,6]+x[3,7]+x[4,5]+x[5,6]>=2;
x[1,2]+x[2,3]+x[2,4]+x[2,6]+x[4,5]+x[5,6]+x[5,7]>=2;
x[1,2]+x[1,7]+x[2,3]+x[2,4]+x[3,6]+x[3,7]+x[5,6]+x[5,7]>=2;
x[1,2]+x[2,3]+x[2,4]+x[3,6]+x[5,6]>=2;
x[1,2]+x[1,7]+x[2,3]+x[2,4]+x[2,6]+x[3,7]+x[5,7]>=2;
x[1,2]+x[2,3]+x[2,4]+x[2,6]>=2;
x[1,3]+x[1,4]+x[1,7]+x[2,3]+x[2,4]+x[2,6]>=2;
x[1,3]+x[1,4]+x[2,3]+x[2,4]+x[2,6]+x[3,7]+x[5,7]>=2;
x[1,3]+x[1,4]+x[1,7]+x[2,3]+x[2,4]+x[3,6]+x[5,6]>=2;
x[1,3]+x[1,4]+x[2,3]+x[2,4]+x[3,6]+x[3,7]+x[5,6]+x[5,7]>=2;
x[1,3]+x[1,4]+x[1,7]+x[2,3]+x[2,4]+x[2,6]+x[4,5]+x[5,6]+x[5,7]>=2;
x[1,3]+x[1,4]+x[2,3]+x[2,4]+x[2,6]+x[3,7]+x[4,5]+x[5,6]>=2;
x[1,3]+x[1,4]+x[1,7]+x[2,3]+x[2,4]+x[3,6]+x[4,5]+x[5,7]>=2;
x[1,3]+x[1,4]+x[2,3]+x[2,4]+x[3,6]+x[3,7]+x[4,5]>=2;
x[1,3]+x[1,7]+x[2,3]+x[2,6]+x[4,5]>=2;
x[1,3]+x[2,3]+x[2,6]+x[3,7]+x[4,5]+x[5,7]>=2;
x[1,3]+x[1,7]+x[2,3]+x[3,6]+x[4,5]+x[5,6]>=2;
x[1,3]+x[2,3]+x[3,6]+x[3,7]+x[4,5]+x[5,6]+x[5,7]>=2;
x[1,3]+x[1,7]+x[2,3]+x[2,6]+x[5,6]+x[5,7]>=2;
x[1,3]+x[2,3]+x[2,6]+x[3,7]+x[5,6]>=2;
x[1,3]+x[1,7]+x[2,3]+x[3,6]+x[5,7]>=2;
x[1,3]+x[2,3]+x[3,6]+x[3,7]>=2;
x[1,4]+x[1,7]+x[2,4]+x[2,6]+x[3,6]+x[3,7]>=2;
x[1,4]+x[2,4]+x[2,6]+x[3,6]+x[5,7]>=2;
x[1,4]+x[1,7]+x[2,4]+x[3,7]+x[5,6]>=2;
x[1,4]+x[2,4]+x[5,6]+x[5,7]>=2;
x[1,4]+x[1,7]+x[2,4]+x[2,6]+x[3,6]+x[3,7]+x[4,5]+x[5,6]+x[5,7]>=2;
x[1,4]+x[2,4]+x[2,6]+x[3,6]+x[4,5]+x[5,6]>=2;
x[1,4]+x[1,7]+x[2,4]+x[3,7]+x[4,5]+x[5,7]>=2;
x[1,4]+x[2,4]+x[4,5]>=2;
x[1,7]+x[2,6]+x[3,6]+x[3,7]+x[4,5]>=2;
x[2,6]+x[3,6]+x[4,5]+x[5,7]>=2;
x[1,7]+x[3,7]+x[4,5]+x[5,6]>=2;
x[4,5]+x[5,6]+x[5,7]>=2;
x[1,7]+x[2,6]+x[3,6]+x[3,7]+x[5,6]+x[5,7]>=2;
x[2,6]+x[3,6]+x[5,6]>=2;
x[1,7]+x[3,7]+x[5,7]>=2;
};