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.

---

First, we need to understand the transformation rules applied across the provided examples:

1. The objects keep their shapes, widths, heights, and masses - these properties don't seem to change.

2. There's a particular pattern with the objects labeled as "Rectangle". They seem to be moved in the grid to align along the edges.

   - For example, objects at the top or bottom align to the bottom edge, and objects on the left or right align to the right edge.

Based on these observations, we can infer a few transformation rules:

- Rectangular objects are moved towards the border of the grid that they are closest to. 
- For objects that are equidistant from two edges, there seems to be a priority of Bottom > Right > Top > Left.
- The Box objects seem to remain in the same position.
- It appears that objects with the shape "Plus" get occluded and don't appear in the output.

Following these rules, we can predict the output for the fourth example:

```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_l9_b12_r9_w1_h2_m2_shapeRectangle_scalex1_scaley2, transform(all)).
object(output4_idP48kmo7_t3_l11_b3_r12_w2_h1_m2_shapeRectangle_scalex2_scaley1, transform(all)).
object(output4_idP48kmo7_t3_l1_b3_r2_w2_h1_m2_shapeRectangle_scalex2_scaley1, transform(all)).
object(output4_idP48kmo7_t1_l9_b2_r9_w1_h2_m2_shapeRectangle_scalex1_scaley2, transform(all)).
```

Reasoning:
- The box (idP847fa3) stays in the same place according to our observations.
- The rectangles (idP48kmo7) move towards the borders they're closest to.
- The "Plus" shape does not appear in the output, hence it's omitted from the predictions.

