Any free software to compute boolean expression?
This Python procedure will evaluate a formula in your format (first argument) against a list of single-letter variables (second argument):

def table( x, v , w = "" ):
   if( v == "" ):
      print( "%s : %d " % ( w, eval( x.replace( "v", " or " ).replace( "~", " ! " ).replace( "+", " and " ))))
   else:
      table( x.replace( v[ 0 ], "0" ), v[ 1 : ], w + "0" )
      table( x.replace( v[ 0 ], "1" ), v[ 1 : ], w + "1" )


for example

table( "(A v B ) + ~ C", "ABC" )


produces

000 : 0 
001 : 0 
010 : 1 
011 : 0 
100 : 1 
101 : 0 
110 : 1 
111 : 0 


To get your answer, evaluate

X = "((A v B) + (~A v ~B)) v ((C v D) + (~C v ~D)) v ((E v F) + (~E v ~F)) v ((G v H) + (~G v ~H)) v ((I v J) + (~I v ~J)) v ((K v L) + (~K v ~L)) v ((M v N) + (~M v ~N)) v ((P v Q) + (~P v ~Q))"
table( X, "ABCDEFGHIJKLMNPQ" )