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\ This file was automatically generated by Zimpl
\ set A := { "a", "b", "c" };
\ set B := { 1, 2, 3 };
\ set B2:= argmax <b> in B : abs(3-b);
\ set C := { 1 to 4 };
\ set C2:= argmin <c> in C : c;
\ set D := { 7 .. 8 by 2 };
\ set E2:= (B + C) * A;
\ set E := argmax(card(E2)) <i,j> in E2 : i;
\ set F := B inter C;
\ set G := { 1 .. 5 } union D without B;
\ set H := C symdiff { <1>, <2>, <7>, <8> };
\ set J := { <g> in G with g > 3 };
\ set K := { <"a", 1>, <"b", 7>, <"c", 9> };
\ set L[B] := <1> { "a", "b" }, <2> { "c", "d", "e" }, <3> { "f" };
\ set LU := union <b> in B : L[b];
\ set L2[] := <1> { "a", "b" }, <2> { "c", "d", "e" }, <3> { "f" };
\ set L2I := inter <b> in B : (L2[b] + A);
\ set M[<i> in D] := { <3 * i, 7, "d">, <i + 2, 9, "c"> };
\ set N[<i,j> in C * B with i > j] := { i + j, i - j, i * j };
\ set P[] := powerset(C);
\ set Q[] := subsets(C, 3);
\ set R := indexset(P);
\ set S := R;
\ set T := { 1 to 9 } * { 10 to 19 } * { "A", "B" };
\ set T2 := argmin(15) <i,j,k> in T : j - 2 * i;
\ set U := proj(T2, <3,1>);
\ set V := { <a,2> in A*B with a == "a" or a == "b" };
\ set W[<i> in B] := { <c> in C with c <= i };
\ set X := { <i> in { <k> in C with k > 2 } with i mod 2 == 0 };
\ set Y := { -2 .. -2 } + { -4 .. -8 by 2 } + { -16 .. -10 by -2 } + { 7 .. 1 } ;
\ set Y2 := { -2 to -2 } + { -4 to -8 by 2 } + { -16 to -10 by -2 } + { 7 to 1 } ;
\ set Z := C * (A * B);
\ set AA := { <b> in B : 2 * b };
\ set BB := { <a,b> in A*B : <a,b+2> };
\ var a[L2I];
\ var b[B];
\ var c[C];
\ var d[D];
\ var e[E];
\ var f[F];
\ var g[G];
\ var h[H];
\ var j[J];
\ var k[K];
\ var l[LU];
\ var m[M[7]];
\ var n[{ 1 .. 100 }];
\ var p[C];
\ var q[C];
\ var u[U];
\ var v[V];
\ var xabcdefghijklmno[X];
\ var y[Y];
\ var y2[Y2];
\ var z[Z];
\ var aa[AA];
\ var bb[BB];
\ subto a1: sum <i> in L2I : a[i] >= 0;
\ subto b1: sum <i> in B : b[i] >= ord(B2,1,1);
\ subto c1: sum <i> in C : c[i] >= ord(C2,1,1);
\ subto d1: sum <i> in D : d[i] >= 0;
\ subto e1: sum <i1,i2> in E : e[i1,i2] >= 0;
\ subto f1: sum <i> in F : f[i] >= 0;
\ subto g1: sum <i> in G : g[i] >= 0;
\ subto h1: sum <i> in H : h[i] >= 0;
\ subto j1: sum <i> in J : j[i] >= 0;
\ subto k1: sum <i1,i2> in K : k[i1,i2] >= 0;
\ subto l1: forall <i1> in indexset(L) with L[i1] == L2[i1] do sum <i2> in L[i1] : l[i2] >= 0;
\ subto m1: sum <i1,i2,i3> in M[7] : m[i1,i2,i3] >= 0;
\ subto n1: forall <i1,i2> in indexset(N) do sum <i3> in N[i1,i2] : n[i3] >= 0;
\ subto p1: forall <i1> in R do sum <i2> in P[i1] : p[i2] >= 0;
\ subto q1: forall <i1> in indexset(Q) do sum <i2> in Q[i1] : q[i2] >= 0;
\ subto u1: forall <i1,i2> in U do u[i1,i2] >= 0;
\ subto v1: sum <i1,i2> in V : v[i1,i2] >= 0;
\ subto w1: forall <i> in B do sum <w> in W[i]: n[w] >= 0;
\ subto x1: sum <i> in X : xabcdefghijklmno[i] >= 0;
\ subto y1: sum <i> in Y : y[i] >= 0;
\ subto y2: sum <i> in Y2 : y2[i] >= 2;
\ subto z1: sum <i> in {1..card(E)} do e[ord(E,i,1),ord(E,i,2)] >= 5;
\ subto z2: sum <c1,a1,b1> in Z with a1 > "b" do z[c1,a1,b1] <= 8;
\ subto aa1: sum <i> in AA : aa[i] >= 5;
\ subto bb1: sum <i1,i2> in BB : bb[i1,i2] <= 3;
\Problem name: set.zpl
Minimize
Objective:
Subject to
a1_1:
+ a$c + a$b + a$a >= 0
b1_1:
+ b#3 + b#2 + b#1 >= 1
c1_1:
+ c#4 + c#3 + c#2 + c#1 >= 1
d1_1:
+ d#7 >= 0
e1_1:
+ e#4$c + e#4$b + e#4$a + e#3$c + e#3$b + e#3$a
+ e#2$c + e#2$b + e#2$a + e#1$c + e#1$b + e#1$a
>= 0
f1_1:
+ f#3 + f#2 + f#1 >= 0
g1_1:
+ g#7 + g#5 + g#4 >= 0
h1_1:
+ h#8 + h#7 + h#4 + h#3 >= 0
j1_1:
+ j#7 + j#5 + j#4 >= 0
k1_1:
+ k$c#9 + k$b#7 + k$a#1 >= 0
l1_1:
+ l$b + l$a >= 0
l1_2:
+ l$e + l$d + l$c >= 0
l1_3:
+ l$f >= 0
m1_1:
+ m#9#9$c + m#21#7$d >= 0
n1_1:
+ n#2 + n#1 + n#3 >= 0
n1_2:
+ n#3 + n#2 + n#4 >= 0
n1_3:
+ n#6 + n#1 + n#5 >= 0
n1_4:
+ n#4 + n#3 + n#5 >= 0
n1_5:
+ n#8 + n#2 + n#6 >= 0
n1_6:
+ n#12 + n#1 + n#7 >= 0
p1_1:
+ p#1 >= 0
p1_2:
+ p#2 >= 0
p1_3:
+ p#3 >= 0
p1_4:
+ p#4 >= 0
p1_5:
+ p#1 + p#2 >= 0
p1_6:
+ p#1 + p#3 >= 0
p1_7:
+ p#1 + p#4 >= 0
p1_8:
+ p#2 + p#3 >= 0
p1_9:
+ p#2 + p#4 >= 0
p1_10:
+ p#3 + p#4 >= 0
p1_11:
+ p#1 + p#2 + p#3 >= 0
p1_12:
+ p#1 + p#2 + p#4 >= 0
p1_13:
+ p#1 + p#3 + p#4 >= 0
p1_14:
+ p#2 + p#3 + p#4 >= 0
p1_15:
+ p#1 + p#2 + p#3 + p#4 >= 0
q1_1:
+ q#1 + q#2 + q#3 >= 0
q1_2:
+ q#1 + q#2 + q#4 >= 0
q1_3:
+ q#1 + q#3 + q#4 >= 0
q1_4:
+ q#2 + q#3 + q#4 >= 0
u1_1:
+ u$B#7 >= 0
u1_2:
+ u$B#8 >= 0
u1_3:
+ u$B#9 >= 0
u1_4:
+ u$A#8 >= 0
u1_5:
+ u$A#9 >= 0
v1_1:
+ v$b#2 + v$a#2 >= 0
w1_1:
+ n#1 >= 0
w1_2:
+ n#2 + n#1 >= 0
w1_3:
+ n#3 + n#2 + n#1 >= 0
x1_1:
+ xabcdefghijkl@a2 >= 0
y1_1:
+ y#1 + y#2 + y#3 + y#4 + y#5 + y#6
+ y#7 + y#_10@aa + y#_12@a9 + y#_14@a8 + y#_16@a7 + y#_8@a6
+ y#_6@a5 + y#_4@a4 + y#_2@a3 >= 0
y2_1:
+ y2#_2@b2 >= 2
z1_1:
+ e#4$c + e#4$b + e#4$a + e#3$c + e#3$b + e#3$a
+ e#2$c + e#2$b + e#2$a + e#1$c + e#1$b + e#1$a
>= 5
z2_1:
+ z#4$c#3 + z#4$c#2 + z#4$c#1 + z#3$c#3 + z#3$c#2 + z#3$c#1
+ z#2$c#3 + z#2$c#2 + z#2$c#1 + z#1$c#3 + z#1$c#2 + z#1$c#1
<= 8
aa1_1:
+ aa#6 + aa#4 + aa#2 >= 5
bb1_1:
+ bb$c#5 + bb$c#4 + bb$c#3 + bb$b#5 + bb$b#4 + bb$b#3
+ bb$a#5 + bb$a#4 + bb$a#3 <= 3
Bounds
0 <= a$a <= +inf
0 <= a$b <= +inf
0 <= a$c <= +inf
0 <= b#1 <= +inf
0 <= b#2 <= +inf
0 <= b#3 <= +inf
0 <= c#1 <= +inf
0 <= c#2 <= +inf
0 <= c#3 <= +inf
0 <= c#4 <= +inf
0 <= d#7 <= +inf
0 <= e#1$a <= +inf
0 <= e#1$b <= +inf
0 <= e#1$c <= +inf
0 <= e#2$a <= +inf
0 <= e#2$b <= +inf
0 <= e#2$c <= +inf
0 <= e#3$a <= +inf
0 <= e#3$b <= +inf
0 <= e#3$c <= +inf
0 <= e#4$a <= +inf
0 <= e#4$b <= +inf
0 <= e#4$c <= +inf
0 <= f#1 <= +inf
0 <= f#2 <= +inf
0 <= f#3 <= +inf
0 <= g#4 <= +inf
0 <= g#5 <= +inf
0 <= g#7 <= +inf
0 <= h#3 <= +inf
0 <= h#4 <= +inf
0 <= h#7 <= +inf
0 <= h#8 <= +inf
0 <= j#4 <= +inf
0 <= j#5 <= +inf
0 <= j#7 <= +inf
0 <= k$a#1 <= +inf
0 <= k$b#7 <= +inf
0 <= k$c#9 <= +inf
0 <= l$a <= +inf
0 <= l$b <= +inf
0 <= l$c <= +inf
0 <= l$d <= +inf
0 <= l$e <= +inf
0 <= l$f <= +inf
0 <= m#21#7$d <= +inf
0 <= m#9#9$c <= +inf
0 <= n#1 <= +inf
0 <= n#2 <= +inf
0 <= n#3 <= +inf
0 <= n#4 <= +inf
0 <= n#5 <= +inf
0 <= n#6 <= +inf
0 <= n#7 <= +inf
0 <= n#8 <= +inf
0 <= n#12 <= +inf
0 <= p#1 <= +inf
0 <= p#2 <= +inf
0 <= p#3 <= +inf
0 <= p#4 <= +inf
0 <= q#1 <= +inf
0 <= q#2 <= +inf
0 <= q#3 <= +inf
0 <= q#4 <= +inf
0 <= u$B#7 <= +inf
0 <= u$B#8 <= +inf
0 <= u$B#9 <= +inf
0 <= u$A#8 <= +inf
0 <= u$A#9 <= +inf
0 <= v$a#2 <= +inf
0 <= v$b#2 <= +inf
0 <= xabcdefghijkl@a2 <= +inf
0 <= y#_2@a3 <= +inf
0 <= y#_4@a4 <= +inf
0 <= y#_6@a5 <= +inf
0 <= y#_8@a6 <= +inf
0 <= y#_16@a7 <= +inf
0 <= y#_14@a8 <= +inf
0 <= y#_12@a9 <= +inf
0 <= y#_10@aa <= +inf
0 <= y#7 <= +inf
0 <= y#6 <= +inf
0 <= y#5 <= +inf
0 <= y#4 <= +inf
0 <= y#3 <= +inf
0 <= y#2 <= +inf
0 <= y#1 <= +inf
0 <= y2#_2@b2 <= +inf
0 <= z#1$c#1 <= +inf
0 <= z#1$c#2 <= +inf
0 <= z#1$c#3 <= +inf
0 <= z#2$c#1 <= +inf
0 <= z#2$c#2 <= +inf
0 <= z#2$c#3 <= +inf
0 <= z#3$c#1 <= +inf
0 <= z#3$c#2 <= +inf
0 <= z#3$c#3 <= +inf
0 <= z#4$c#1 <= +inf
0 <= z#4$c#2 <= +inf
0 <= z#4$c#3 <= +inf
0 <= aa#2 <= +inf
0 <= aa#4 <= +inf
0 <= aa#6 <= +inf
0 <= bb$a#3 <= +inf
0 <= bb$a#4 <= +inf
0 <= bb$a#5 <= +inf
0 <= bb$b#3 <= +inf
0 <= bb$b#4 <= +inf
0 <= bb$b#5 <= +inf
0 <= bb$c#3 <= +inf
0 <= bb$c#4 <= +inf
0 <= bb$c#5 <= +inf
End
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