Root problem

Universe

squares r2 b2
(triangles) ∧ (¬green) r1 b1
green green green green

CoLa

universe (squares) ∨ (triangles) = {r2, b2, r1, b1, green, green, green}; 
property squares = {r2, b2}; 
property (triangles) ∧ (¬green) = {r1, b1}; 
property green = {green, green, green}; 

Configuration

1
1 2
1 2 3
1 2 3 4

CoLa

permutation (size in [1,4]) of entity universe (perm)

Constraints

2 green

CoLa

Position 2: green; 
Nr. squares in [2, 7]; 

0

Configuration of size 1

Universe

squares r2 b2
(triangles) ∧ (¬green) r1 b1
green green green green

CoLa

universe (squares) ∨ (triangles) = {r2, b2, r1, b1, green, green, green}; 
property squares = {r2, b2}; 
property (triangles) ∧ (¬green) = {r1, b1}; 
property green = {green, green, green}; 

Configuration

1

CoLa

Obj 1:  (squares) ∨ (triangles); 

Constraints

2 green

CoLa

Position 2: green; 
Nr. squares in [2, 7]; 

$$\texttip{ 0 }{ Cannot satisfy Nr. squares in [2, 7] :( }$$

0

Configuration of size 2

Universe

green green green green
(triangles) ∧ (¬green) r1 b1
squares r2 b2

CoLa

universe (squares) ∨ (triangles) = {r2, b2, r1, b1, green, green, green}; 
property green = {green, green, green}; 
property (triangles) ∧ (¬green) = {r1, b1}; 
property squares = {r2, b2}; 

Configuration

1 2

CoLa

Obj 1:  (squares) ∨ (triangles); 
Obj 2:  (squares) ∨ (triangles); 

Constraints

2 green

CoLa

Position 2: green; 
Nr. squares in [2, 7]; 

$$\texttip{ 0 }{ No solution found }$$

2

Configuration of size 3

Universe

(triangles) ∧ (¬green) r1 b1
squares r2 b2
green green green green

CoLa

universe (squares) ∨ (triangles) = {r2, b2, r1, b1, green, green, green}; 
property (triangles) ∧ (¬green) = {r1, b1}; 
property squares = {r2, b2}; 
property green = {green, green, green}; 

Configuration

1 2 3

CoLa

Obj 1:  (squares) ∨ (triangles); 
Obj 2:  (squares) ∨ (triangles); 
Obj 3:  (squares) ∨ (triangles); 

Constraints

2 green

CoLa

Position 2: green; 
Nr. squares in [2, 7]; 

1

Left split: case 1 green are s.t. [Nr. squares = 0, Nr. green = 1, Nr. ¬green = 0]

Universe

squares r2 b2
(triangles) ∧ (¬green) r1 b1
green green green green

CoLa

universe green = {green, green, green}; 
property squares = {r2, b2}; 
property (triangles) ∧ (¬green) = {r1, b1}; 

Configuration

1

CoLa

Obj 1:  green; 

Constraints

CoLa

Nr. squares = 0; 
Nr. green = 1; 
Nr. ¬green = 0; 

$$\frac{\texttip{ \binom{ 0 }{ 0 } }{ Choose 0 of 0 (distinguishable) empty for 1 object(s) } \cdot \texttip{ 1! }{ Permutations of 1 green }}{\texttip{ 1! }{ Extra permutations of (indist.) green }}$$

2

Right split removing 1 green

Universe

squares r2 b2
triangles r1 b1 green green green
5

CoLa

universe (squares) ∨ (triangles) = {r2, b2, r1, b1, green, green}; 
property squares = {r2, b2}; 
property triangles = {r1, b1, green, green, green}; 

Configuration

1 2

CoLa

Obj 1:  (squares) ∨ (triangles); 
Obj 2:  (squares) ∨ (triangles); 

Constraints

CoLa

Nr. squares = 2; 

$$\texttip{ \texttip{ 1 }{ Exchangeable choices } \cdot 2! }{ Nr. orders for all objects }$$

18

Configuration of size 4

Universe

(triangles) ∧ (¬green) r1 b1
squares r2 b2
green green green green

CoLa

universe (squares) ∨ (triangles) = {r2, b2, r1, b1, green, green, green}; 
property (triangles) ∧ (¬green) = {r1, b1}; 
property squares = {r2, b2}; 
property green = {green, green, green}; 

Configuration

1 2 3 4

CoLa

Obj 1:  (squares) ∨ (triangles); 
Obj 2:  (squares) ∨ (triangles); 
Obj 3:  (squares) ∨ (triangles); 
Obj 4:  (squares) ∨ (triangles); 

Constraints

2 green

CoLa

Position 2: green; 
Nr. squares in [2, 7]; 

1

Left split: case 1 green are s.t. [Nr. squares = 0, Nr. green = 1, Nr. ¬green = 0]

Universe

squares r2 b2
(triangles) ∧ (¬green) r1 b1
green green green green

CoLa

universe green = {green, green, green}; 
property squares = {r2, b2}; 
property (triangles) ∧ (¬green) = {r1, b1}; 

Configuration

1

CoLa

Obj 1:  green; 

Constraints

CoLa

Nr. squares = 0; 
Nr. green = 1; 
Nr. ¬green = 0; 

$$\frac{\texttip{ \binom{ 0 }{ 0 } }{ Choose 0 of 0 (distinguishable) empty for 1 object(s) } \cdot \texttip{ 1! }{ Permutations of 1 green }}{\texttip{ 1! }{ Extra permutations of (indist.) green }}$$

18

Right split removing 1 green

Universe

squares r2 b2
triangles r1 b1 green green green
5

CoLa

universe (squares) ∨ (triangles) = {r2, b2, r1, b1, green, green}; 
property squares = {r2, b2}; 
property triangles = {r1, b1, green, green, green}; 

Configuration

1 2 3

CoLa

Obj 1:  (squares) ∨ (triangles); 
Obj 2:  (squares) ∨ (triangles); 
Obj 3:  (squares) ∨ (triangles); 

Constraints

CoLa

Nr. squares in [2, 3]; 

2

Left split: case 2 squares are s.t. [Nr. squares = 2]

Universe

squares r2 b2
triangles r1 b1 green green green
5

CoLa

universe squares = {r2, b2}; 
property triangles = {r1, b1, green, green, green}; 

Configuration

1 2

CoLa

Obj 1:  squares; 
Obj 2:  squares; 

Constraints

CoLa

Nr. squares = 2; 

$$\texttip{ 2! }{ Nr. orders for all objects }$$

3

Right split removing 2 squares

Universe

(squares) ∨ (triangles) r1 b1 green green

CoLa

universe (squares) ∨ (triangles) = {r1, b1, green, green}; 

Configuration

1

CoLa

Obj 1:  (squares) ∨ (triangles); 

$$\frac{\texttip{ \binom{ 2 }{ 0 } }{ Choose 0 of 2 (distinguishable) ??? for 1 object(s) } \cdot \texttip{ 1! }{ Permutations of 1 (squares) ∨ (triangles) }}{\texttip{ 1! }{ Extra permutations of (indist.) ??? }} + \frac{\texttip{ \binom{ 2 }{ 1 } }{ Choose 1 of 2 (distinguishable) ??? for 1 object(s) } \cdot \texttip{ 1! }{ Permutations of 1 (squares) ∨ (triangles) }}{\texttip{ 0! }{ Extra permutations of (indist.) ??? }}$$