% More examples for *math* handlers
  
example( [X0,X1,X2,X3,X4]) :-
       +87*X0  +52*X1  +27*X2  -54*X3  +56*X4 =<  -93,
       +33*X0  -10*X1  +61*X2  -28*X3  -29*X4 =<   63,
       -68*X0   +8*X1  +35*X2  +68*X3  +35*X4 =<  -85,
       +90*X0  +60*X1  -76*X2  -53*X3  +24*X4 =<  -68,
       -95*X0  -10*X1  +64*X2  +76*X3  -24*X4 =<   33,
       +43*X0  -22*X1  +67*X2  -68*X3  -92*X4 =<  -97,
       +39*X0   +7*X1  +62*X2  +54*X3  -26*X4 =<  -27,
       +48*X0  -13*X1   +7*X2  -61*X3  -59*X4 =<   -2,
       +49*X0  -23*X1  -31*X2  -76*X3  +27*X4 =<    3,
       -50*X0  +58*X1   -1*X2  +57*X3  +20*X4 =<    6,
       -13*X0  -63*X1  +81*X2   -3*X3  +70*X4 =<   64,
       +20*X0  +67*X1  -23*X2  -41*X3  -66*X4 =<   52,
       -81*X0  -44*X1  +19*X2  -22*X3  -73*X4 =<  -17,
       -43*X0   -9*X1  +14*X2  +27*X3  +40*X4 =<   39,
       +16*X0  +83*X1  +89*X2  +25*X3  +55*X4 =<   36,
        +2*X0  +40*X1  +65*X2  +59*X3  -32*X4 =<   13,
       -65*X0  -11*X1  +10*X2  -13*X3  +91*X4 =<   49,
       +93*X0  -73*X1  +91*X2   -1*X3  +23*X4 =<  -87.



top2 :- example( [X0,X1,X2,X3,X4]).

%     X3=<-5/4-35/68*X2-2/17*X1+X0-35/68*X4,
%     X3>=68/53-76/53*X2+60/53*X1+90/53*X0+24/53*X4,
%     X3=<-1/2-31/27*X2-7/54*X1-13/18*X0+13/27*X4,
%     X3>=17/22+19/22*X2-2*X1-81/22*X0-73/22*X4,
%     X3=<33/76-16/19*X2+5/38*X1+5/4*X0+6/19*X4,
%     X3>=87+91*X2-73*X1+93*X0+23*X4,
%     X3>=-3/76-31/76*X2-23/76*X1+49/76*X0+27/76*X4,
%     X3=<13/9-14/27*X2+1/3*X1+43/27*X0-40/27*X4,
%     X3=<2/19+1/57*X2-58/57*X1+50/57*X0-20/57*X4 

top3 :- example( [X0,_,_,_,X4]).

%     X0>=477804/40409+6973307/969816*X4,
%     X0>=7357764/4517605-5006476/13552815*X4,
%     X0>=58416/36205-4659804/12418315*X4,
%     X0>=3139326/1972045-745308/1972045*X4,
%     X0>=67158/43105-16394/43105*X4,
%     X0>=1327097/6210451-2619277/6210451*X4,
%     X0=<-688135/1217232-2174029/811488*X4 

% Detection of Implied Equalities
                       
top4 :- A=<B, 
	B=<C, 
	C=<D, 
	A>=D.

%     B =:= A,
%     C =:= A,
%     D =:= A  

top5 :-   
              X11 + X12 + X13 + X14 + X15 =:= 1000,
              X21 + X22 + X23 + X24 + X25 =:= 1000,
            
              4*X11 + 5*X21 - Y21 - Z21 =< 0,
             -4*X12 - 5*X22 + Y22 + Z22 =:= 0,
             -4*X13 - 5*X23 + Y24 - Y25 + Z24 - Z25 =:= 0,
             -4*X14 - 5*X24 + Y21 - Y22 - Y23 + Y25
                            + Z21 - Z22 - Z23 + Z25 =:= 0,
             -4*X15 - 5*X25 + Y23 - Y24 + Z23 - Z24 =:= 0,
            
              7*X11 + 9*X21 >= 0,
              7*X12 + 9*X22 =< 3000,
              7*X13 + 9*X23 =< 200,
              7*X14 + 9*X24 =< 10000,
              7*X15 + 9*X25 =< 7000,
            
              Z21 =< 5000,
              Z22 =< 250,
              Z23 =< 600,
              Z24 =< 7000,
              Z25 =< 4000,
            
              X11 >= 0, X12 >= 0, X13 >= 0, X14 >= 0, X15 >= 0,
              X21 >= 0, X22 >= 0, X23 >= 0, X24 >= 0, X25 >= 0,
            
              Y21 >= 0, Y22 >= 0, Y23 >= 0, Y24 >= 0, Y25 >= 0,
            
              Z21 >= 0, Z22 >= 0, Z23 >= 0, Z24 >= 0, Z25 >= 0,
            
              M =:= 99999,
              - Min =:= 99999 * X11 + 99999 * X21 + 4 * Y21 + 7 * Y22 + 
			3 * Y23 +  8*Y24 + 5*Y25.

%       M =:= 99999,
%       Min =:= 23450,
%       X11 =:= 0,
%       X12 =:= 0,
%       X13 =:= 0,
%       X14 =:= 1000,
%       X15 =:= 0,
%       X21 =:= 0,
%       X22 =:= 50,
%       X23 =:= 1850/3-X25,
%       X24 =:= 1000/3,
%       Y21 =:= 4000,
%       Y22 =:= 0,
%       Y23 =:= 7450/3,
%       Y24 =:= 0,
%       Y25 =:= 0,
%       Z21 =:= 5000,
%       Z22 =:= 250,
%       Z23 =:= 600,
%       Z24 =:= 9250/3-5*X25,
%       Z25 =:= 0,
%       X25 >= 5350/9,
%       X25 =< 1850/3