gpt4

---

I'm doing Prolog experiments.


The grid is 1-indexed.


Top-Left Bottom-Right (TLBR) is used for object bounding boxes, like tY_lX_bY_rX where t=top l=left b=bottom r=right.


The width of the object bounding box has a 'w' prefix, like 'w5' is width=5.
The height of the object bounding box has a 'h' prefix, like 'h3' is height=3.

The number of solid pixels in the object has a 'm' prefix, like 'm12' is mass=12.

The `id` prefixed text has no integer value and should not be considered.
Consider both euclidian distance and manhatten distance between objects, since it may impact the `id` assigned to the object.


```prolog
% Example 1 input grid_width12_height12
object(input1_idP33ffe7_t9_l5_b12_r5_w1_h4_m4_shapeRectangle_scalex1_scaley4, transform(all)).
object(input1_idP33ffe7_t6_l9_b6_r12_w4_h1_m4_shapeRectangle_scalex4_scaley1, transform(all)).
object(input1_idP33ffe7_t6_l1_b6_r2_w2_h1_m2_shapeRectangle_scalex2_scaley1, transform(all)).
object(input1_idP33ffe7_t4_l4_b7_r7_w4_h4_m7_shapePlus_scaleUnknown, transform(all)).
object(input1_idP33ffe7_t1_l5_b2_r5_w1_h2_m2_shapeRectangle_scalex1_scaley2, transform(all)).
object(input1_idPfe7a8k_t3_l3_b8_r8_w6_h6_m20_shapeBox_scaleUnknown, transform(all)).

% Example 1 output grid_width12_height12
object(output1_idP33ffe7_t9_l8_b12_r8_w1_h4_m4_shapeRectangle_scalex1_scaley4, transform(all)).
object(output1_idP33ffe7_t3_l9_b3_r12_w4_h1_m4_shapeRectangle_scalex4_scaley1, transform(all)).
object(output1_idP33ffe7_t3_l1_b3_r2_w2_h1_m2_shapeRectangle_scalex2_scaley1, transform(all)).
object(output1_idP33ffe7_t1_l8_b2_r8_w1_h2_m2_shapeRectangle_scalex1_scaley2, transform(all)).
object(output1_idPfe7a8k_t3_l3_b8_r8_w6_h6_m20_shapeBox_scaleUnknown, transform(all)).

% Example 2 input grid_width12_height12
object(input2_idPz7ea0g_t11_l6_b12_r6_w1_h2_m2_shapeRectangle_scalex1_scaley2, transform(all)).
object(input2_idPz7ea0g_t7_l10_b7_r12_w3_h1_m3_shapeRectangle_scalex3_scaley1, transform(all)).
object(input2_idPz7ea0g_t7_l1_b7_r2_w2_h1_m2_shapeRectangle_scalex2_scaley1, transform(all)).
object(input2_idPz7ea0g_t5_l4_b9_r8_w5_h5_m9_shapePlus_scaleUnknown, transform(all)).
object(input2_idPz7ea0g_t1_l6_b3_r6_w1_h3_m3_shapeRectangle_scalex1_scaley3, transform(all)).
object(input2_idP3d53ef_t4_l3_b10_r9_w7_h7_m24_shapeBox_scaleUnknown, transform(all)).

% Example 2 output grid_width12_height12
object(output2_idPz7ea0g_t11_l9_b12_r9_w1_h2_m2_shapeRectangle_scalex1_scaley2, transform(all)).
object(output2_idPz7ea0g_t4_l10_b4_r12_w3_h1_m3_shapeRectangle_scalex3_scaley1, transform(all)).
object(output2_idPz7ea0g_t4_l1_b4_r2_w2_h1_m2_shapeRectangle_scalex2_scaley1, transform(all)).
object(output2_idPz7ea0g_t1_l9_b3_r9_w1_h3_m3_shapeRectangle_scalex1_scaley3, transform(all)).
object(output2_idP3d53ef_t4_l3_b10_r9_w7_h7_m24_shapeBox_scaleUnknown, transform(all)).

% Example 3 input grid_width12_height12
object(input3_idP989a7f_t9_l7_b12_r7_w1_h4_m4_shapeRectangle_scalex1_scaley4, transform(all)).
object(input3_idP989a7f_t6_l10_b6_r12_w3_h1_m3_shapeRectangle_scalex3_scaley1, transform(all)).
object(input3_idP989a7f_t6_l1_b6_r4_w4_h1_m4_shapeRectangle_scalex4_scaley1, transform(all)).
object(input3_idP989a7f_t5_l6_b7_r8_w3_h3_m5_shapePlus_scalex1_scaley1, transform(all)).
object(input3_idP989a7f_t1_l7_b3_r7_w1_h3_m3_shapeRectangle_scalex1_scaley3, transform(all)).
object(input3_idP33ffe7_t4_l5_b8_r9_w5_h5_m16_shapeBox_scaleUnknown, transform(all)).

% Example 3 output grid_width12_height12
object(output3_idP989a7f_t9_l9_b12_r9_w1_h4_m4_shapeRectangle_scalex1_scaley4, transform(all)).
object(output3_idP989a7f_t4_l10_b4_r12_w3_h1_m3_shapeRectangle_scalex3_scaley1, transform(all)).
object(output3_idP989a7f_t4_l1_b4_r4_w4_h1_m4_shapeRectangle_scalex4_scaley1, transform(all)).
object(output3_idP989a7f_t1_l9_b3_r9_w1_h3_m3_shapeRectangle_scalex1_scaley3, transform(all)).
object(output3_idP33ffe7_t4_l5_b8_r9_w5_h5_m16_shapeBox_scaleUnknown, transform(all)).
```
There number of output objects can be different than the input objects. Also consider the rules with clockwise rotation.
A shape can occlude another shape, so shapeL may appear as shapeRectangle. Sometimes it's the occluded object that gets transformed.
Transformations: sort, gravity towards, rotate, flipx, flipy, move, merge objects, split objects, extract object, fit object inside another object, layout 2..5 objects in a direction while keeping the objects aligned and evenly spaced (remember to update tlbr coordinates). The transformation can be anything, it just have to be simple.


Think step by step, what are the transformations across all the examples, that goes from the input to the output. Explain your reasoning for inserting new objects.
With the following example, I want you to predict what the output should be


```prolog
% Example 4 input grid_width12_height12
object(input4_idP847fa3_t3_l3_b10_r10_w8_h8_m28_shapeBox_scaleUnknown, transform(all)).
object(input4_idP48kmo7_t11_l7_b12_r7_w1_h2_m2_shapeRectangle_scalex1_scaley2, transform(all)).
object(input4_idP48kmo7_t6_l11_b6_r12_w2_h1_m2_shapeRectangle_scalex2_scaley1, transform(all)).
object(input4_idP48kmo7_t6_l1_b6_r2_w2_h1_m2_shapeRectangle_scalex2_scaley1, transform(all)).
object(input4_idP48kmo7_t4_l4_b9_r9_w6_h6_m11_shapePlus_scaleUnknown, transform(all)).
object(input4_idP48kmo7_t1_l7_b2_r7_w1_h2_m2_shapeRectangle_scalex1_scaley2, transform(all)).

% Example 4 output grid_width12_height12
PREDICT the text that starts with object(output4_
```
Repeat the previous example prolog code, with PREDICT replaced with your predictions.

---

Let's analyze the transformations applied to each object from the input to the output for the first three examples.

**Example 1:**
1. The idP33ffe7 object at t9_l5_b12_r5 moves 3 positions to the right.
2. The idP33ffe7 object at t6_l9_b6_r12 moves 3 positions upwards.
3. The idP33ffe7 object at t6_l1_b6_r2 stays at the same position.
4. The idP33ffe7 object at t4_l4_b7_r7 disappears.
5. The idP33ffe7 object at t1_l5_b2_r5 moves 3 positions to the right.
6. The idPfe7a8k object at t3_l3_b8_r8 stays at the same position.

**Example 2:**
1. The idPz7ea0g object at t11_l6_b12_r6 moves 3 positions to the right.
2. The idPz7ea0g object at t7_l10_b7_r12 moves 3 positions upwards.
3. The idPz7ea0g object at t7_l1_b7_r2 stays at the same position.
4. The idPz7ea0g object at t5_l4_b9_r8 disappears.
5. The idPz7ea0g object at t1_l6_b3_r6 moves 3 positions to the right.
6. The idP3d53ef object at t4_l3_b10_r9 stays at the same position.

**Example 3:**
1. The idP989a7f object at t9_l7_b12_r7 moves 2 positions to the right.
2. The idP989a7f object at t6_l10_b6_r12 moves 2 positions upwards.
3. The idP989a7f object at t6_l1_b6_r4 stays at the same position.
4. The idP989a7f object at t5_l6_b7_r8 disappears.
5. The idP989a7f object at t1_l7_b3_r7 moves 2 positions to the right.
6. The idP33ffe7 object at t4_l5_b8_r9 stays at the same position.

For objects with the same id, if the shape is not 'Box', the objects move to the right for top/bottom objects and upwards for left/right objects. The distance moved corresponds to the width or height of the object. If the shape is 'Plus', it disappears.

So for the 4th example, we apply the same rules:

```prolog
% Example 4 output grid_width12_height12
object(output4_idP847fa3_t3_l3_b10_r10_w8_h8_m28_shapeBox_scaleUnknown, transform(all)).
object(output4_idP48kmo7_t11_l10_b12_r10_w1_h2_m2_shapeRectangle_scalex1_scaley2, transform(all)).
object(output4_idP48kmo7_t4_l11_b4_r12_w2_h1_m2_shapeRectangle_scalex2_scaley1, transform(all)).
object(output4_idP48kmo7_t4_l1_b4_r2_w2_h1_m2_shapeRectangle_scalex2_scaley1, transform(all)).
object(output4_idP48kmo7_t1_l10_b2_r10_w1_h2_m2_shapeRectangle_scalex1_scaley2, transform(all)).
```
The idP48kmo7 object at t4_l4_b9_r9 has been omitted in the output, in accordance with the previous observations. All other idP48kmo7 objects have been moved as per the patterns identified earlier. The 'Box' shape object idP847fa3 remains unmodified.

